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http://math.stackexchange.com/questions/294887/how-to-expand-a-fraction-in-powers-of-z-or-dfrac1z-and-which-to-do-in
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# How to expand a fraction in powers of $z$ or $\dfrac{1}{z}$, and which to do, in determining Laurent series
I have a function $f(z)=\dfrac{12}{z(2-z)(1+z)}$, I'm trying to find the Laurent series for each of the three annuli. The singularities are at $z = 0$, $z = 2$, and $z = -1$, so I'm looking for three Laurent series valid on $(0,1)$, $(1,2)$, and $(2,\infty)$ respectively. I can by partial fractions rewrite $f(z)$ as $\dfrac{4}{z}\bigg(\dfrac{1}{1+z} + \dfrac{1}{2-z} \bigg)$.
In the book that gives this example problem, I read that for $(0,1)$ I need to expand both of those fractions In powers of $z$; for $(1,2)$ I am to expand the second fraction in powers of $\dfrac{1}{z}$, and for $(2,\infty)$ I am to expand both fractions in powers of $\dfrac{1}{z}$.
What I do not understand and would like to know, is what it means to expand any term in powers of $z$ or $\dfrac{1}{z}$, and how to tell in general which expansion to choose when calculating Laurent series. Thanks if anyone can help with my question.
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Take the function $f(z)=\frac{1}{1-z}$. Then for $|z|<1$ you have $f(z)=\sum^\infty_{n=0}z^n$. For $|z|>1$ you can do something similar: notice that $\left|\frac{1}{z}\right| = \frac{1}{|z|}<1$, so: $f(z) = \frac{1}{1-z} = -\frac{1}{z}\frac{1}{1-\frac{1}{z}} = -\frac{1}{z}\sum^\infty_{n=0}\frac{1}{z^n}$. You can generalize easily this method to functions of the type $\frac{a}{b-cz}$, as in your case.
For other types of functions you often use known series expansions (for example $e^z=\sum^\infty_{n=0}\frac{z^n}{n!}$) or other methods.
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https://depositonce.tu-berlin.de/items/08097b01-3e14-4663-b866-3c31aa34949c
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# Clustered chimera states in systems of type-I excitability
## FG Nichtlineare Dynamik und Kontrolle
The chimera state is a fascinating phenomenon of coexisting synchronized and desynchronized behaviour that was discovered in networks of nonlocally coupled identical phase oscillators over ten years ago. Since then, chimeras have been found in numerous theoretical and experimental studies and more recently in models of neuronal dynamics as well. In this work, we consider a generic model for a saddle-node bifurcation on a limit cycle representative of neural excitability type I. We obtain chimera states with multiple coherent regions (clustered chimeras/multi-chimeras) depending on the distance from the excitability threshold, the range of nonlocal coupling and the coupling strength. A detailed stability diagram for these chimera states and other interesting coexisting patterns (like traveling waves) is presented.
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http://aas.org/archives/BAAS/v25n4/aas183/abs/S1609.html
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A Study of the Rosette Shock Front
Session 16 -- Molecular Clouds
Display presentation, Wednesday, January 12, 9:30-6:45, Salons I/II Room (Crystal Gateway)
## [16.09] A Study of the Rosette Shock Front
T.A. Kuchar (Phillips Lab./GPOB)
\font\rma=cmr8 An unresolved compression front ($<1'$, seen in all four bands of high resolution IRAS data) surrounding the Rosette Nebula was mapped in the $^{13}$CO J=1$\rightarrow$0 transition. This compression front results from the thermal expansion of the H\thinspace{\rma II} region into the parent molecular cloud. High spectral (0.68 km s$^{-1}$) and spatial (48$''$) resolution molecular data were obtained using the Five College Radio Astronomy Observatory (FCRAO) QUARRY receivers. Approximately 6500, low noise ($\Delta$T$_{\rm rms}$ = 0.1 -- 0.2 K) spectra were observed over a 1.5 square degree area. The intensity maps show several relatively dense clumps surrounding only a portion of the optical nebula along with more tenuous emission. With a few exceptions, most of these dense clumps have associated IRAS point sources. The kinematics and density structure of these clumps are presented.
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https://aimacode.github.io/aima-exercises/bayes-nets-exercises/ex_9/
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Exercise 14.9
Consider the network for car diagnosis shown in Figure car-starts-figure.
1. Extend the network with the Boolean variables ${IcyWeather}$ and ${StarterMotor}$.
2. Give reasonable conditional probability tables for all the nodes.
3. How many independent values are contained in the joint probability distribution for eight Boolean nodes, assuming that no conditional independence relations are known to hold among them?
4. How many independent probability values do your network tables contain?
5. The conditional distribution for ${Starts}$ could be described as a noisy-AND distribution. Define this family in general and relate it to the noisy-OR distribution.
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https://www.physicsforums.com/threads/difference-between-hourly-wage-and-real-gdp-per-hour-worked.605490/
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# Difference between hourly wage and real GDP per hour worked?
1. May 12, 2012
### theBEAST
In 2008 the real GDP per hour worked was $45.70? I don't think this means that the average person was making$45.70...
Here is that graph that contains this data:
http://dl.dropbox.com/u/64325990/ECON%20102/Capture.PNG [Broken]
Could someone please explain the difference?
Last edited by a moderator: May 6, 2017
2. May 12, 2012
### DrClapeyron
I did some similar work on this not too long ago using US nominal GDP.
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http://math.stackexchange.com/questions/254110/continuous-functions-proof/254133
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# Continuous functions proof
Let $f$ and $g$ be continuous functions on R with the absolute value metric, and let $S$ $\subset$ R be countable. Show that if $f(x)=g(x)$ for all $x\in S^c$ (complement of $S$), then $f(x)=g(x)$ for all $x\in$ R.
Now since $f$ and $g$ are continuous on R, then they are obviously continuous on $S$ and $S^c$, considering R is the union of both. For $f(x)=g(x)$ to be true for all $x$ in R, then it should be sufficient to show that it holds in $S$, because it is given that it is true for $S^c$. I know I have to use the fact that $S$ is countable, but I can't think of how and why. Any hints?
Thank you.
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Hint: If $f(x)\ne g(x)$, then there is an open interval $O$ containing $x$ so that $f(z)\ne g(z)$ for all $z\in O$. – David Mitra Dec 9 '12 at 0:01
@DavidMitra So if $S^c$ is dense in R and I assume, by contradiction, that $f(x)$ is not equal to $g(x)$ for all $x$ in R. I would construct the open interval you have stated above. But since $S^c$ is dense, there exists an $x$ in $S^c$ in the open interval. And by hypothesis $f(x)=g(x)$ for all x in $S^c$, I will then arrive at a contradiction. IS this correct? – Alti Dec 10 '12 at 2:23
Yes, that's correct. You could argue a bit more simply (no need to talk about denseness; though it's ok to do so): $S$ is countable while the open interval is not. It follows that the open interval contains a point of $S^c$. – David Mitra Dec 10 '12 at 2:55
That was much simpler, thank you! – Alti Dec 10 '12 at 4:07
For $x\in S$, every $\epsilon$-neighbourhood is uncountable, hence contains points of $S^c$. Thus we can find a sequence $x_n\to x$ with all $x_n\in S^c$. As $f(x_n)-g(x_n)=0$ for all $x_n$ and $f-g$ is continuous, we also have $f(x)-g(x)=0$.
Actually, we don't need that $S$ is countable, but that $S^c$ is dense (which follows from $S$ countable). But if $S$ is uncountable, the claim need not follow (as $S^c$ need not be dense in $\mathbb R$).
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I just to make sure, is $S^c$ dense because uncountable sets are dense? – Alti Dec 9 '12 at 1:27
@Alti No $\mathbb R_{>0}$ is uncountable but not dense (e.g. there is no point near $-1$) – Hagen von Eitzen Dec 9 '12 at 9:54
Then why is $S^c$ dense? – Alti Dec 9 '12 at 20:27
@Alti because $S$ is countable. – Hagen von Eitzen Dec 9 '12 at 20:46
@Alti For $\epsilon>0$, the $\epsilon$ neighbourhood of $x\in\mathbb R$ is uncountable, hence cannot be a subset of countable $S$, hence intersects $S^c$. – Hagen von Eitzen Dec 10 '12 at 15:55
Since $S$ is countable, $S^c$ is dense. This means $\overline {S^c} = \mathbb R$. Now proof: if two continuous functions coincide on a dense set, they are equal: For that, we can use, that every metric space is also Hausdorff and given that, we know, that the diagonal $\Delta = \{ (x,x) \in \mathbb R \times \mathbb R \, \mid \, x \in \mathbb R \}$ is closed in $\mathbb R\times \mathbb R$. Consider the function $h\colon \mathbb R \to \mathbb R \times \mathbb R, \: h(x) = \bigl(f(x), g(x)\bigr)$. $h$ is continuous, because $f$ and $g$ are. Thus $h^{-1}(\Delta) = \{ x \in \mathbb R \, \mid \, f(x) = g(x) \}$ is closed. Because of $S^c \subset h^{-1}(\Delta)$ we get $\overline {S^c} = \mathbb R \subset h^{-1}(\Delta)$.
I like this proof because it holds for all Hausdorff spaces. I think i've read it in Munkres Topology book.
Hope this helps, Maikel
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What you want is the following:
DEFINITION A set $D\subseteq \Bbb R$ is dense over $\Bbb R$ if for every $x\in \Bbb R$ there exists a sequence $\{x_n\}\subset D$ such that $x_n\to x$.
DEFINITION Given a function $f:X\to Y$, the restriction of $f$ to $D\subset X$ is the function $f\mid _D:D\to Y$ such that $f\mid_D(x)=f(x)$ for each $x\in D$.
THEOREM Let $f$ and $g$ be continuous over $\Bbb R$. Let $D$ be dense over $\Bbb R$. If $f\mid_D=g\mid_D$, then $f=g$. That is, if $g$ and $f$ agree on every point of $D$, then they agree on every point of $\Bbb R$.
PROOF Let $x\in \Bbb R\setminus D$. Then there exists a sequence $\{x_n\}\subset D$ such that $x_n\to x$. And for this sequence $\lim\; f(x_n)=f(x)=g(x)=\lim\; g(x_n)$, so the claim follows. Note that since $\{x_n\}\subset D$, $x_n\neq x$ for each $n$.
The proof is rather simple if you have already characterized continuity in terms of sequences, that is
PROPOSITION Let $f:[a,b]\to \Bbb R$ be continuous. Then $f$ is continuous if, and only if, for each sequence $\{x_n\}\subset [a,b]$ such that $x_n\to x$ (with $x\neq x_n$ for each $n$) we have that $f(x_n)\to f(x)$.
PROOF Suppose $f$ is continuous, and $x_n\to x$. Then for each $\epsilon>0$ we get a $\delta >0$ such that for each $y$, whenever $|x-y|<\delta$, $|f(x)-f(y)|<\epsilon$. Since $x_n\to x$, we can obtain an $N$ such that if $n>N$, then $|x-x_n|<\delta$, so that for $n>N$; $|f(x)-f(x_n)|<\epsilon$, and one direction follows. Can you prove the other direction?
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http://mathematica.stackexchange.com/questions/46655/plotting-the-solutions-of-a-system-of-differential-equations-on-a-simplex
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# Plotting the solutions of a system of differential equations on a simplex
I want to solve and plot the solutions of the following system on the triangle simplex:
x'[t] == x[t]*(2*x[t] - 2)
y'[t] == y[t]*(2*x[t])
z'[t] == z[t]*(2*x[t])
It is assumed that x[t] + y[t] + z[t] == 1 for all times t.
I am looking for output similar to this:
I;m also interested in plotting the frequency changes of x[t],y[t] and z[t] over time. That is, given an initial value, I want to find how the frequencies vary over time?
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related – Kuba Apr 23 '14 at 13:11
Take a look at StreamPlot. – Silvia Apr 23 '14 at 13:42
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http://www.aanda.org/articles/aa/abs/2002/42/aa2213/aa2213.html
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Free access
Issue A&A Volume 394, Number 3, November II 2002 883 - 899 Galactic structure and dynamics http://dx.doi.org/10.1051/0004-6361:20021175
A&A 394, 883-899 (2002)
DOI: 10.1051/0004-6361:20021175
## Old stellar Galactic disc in near-plane regions according to 2MASS: Scales, cut-off, flare and warp
M. López-Corredoira1, 2, A. Cabrera-Lavers2, F. Garzón2, 3 and P. L. Hammersley2
1 Astronomisches Institut der Universität Basel, Venusstrasse 7, 4102 Binningen, Switzerland
2 Instituto de Astrofísica de Canarias, 38200 La Laguna, Tenerife, Spain
3 Departamento de Astrofísica, Universidad de La Laguna, Tenerife, Spain
(Received 21 December 2001 / Accepted 7 August 2002)
Abstract
We have pursued two different methods to analyze the old stellar population near the Galactic plane, using data from the 2MASS survey. The first method is based on the isolation of the red clump giant population in the color-magnitude diagrams and the inversion of its star counts to obtain directly the density distribution along the line of sight. The second method fits the parameters of a disc model to the star counts in 820 regions. Results from both independent methods are consistent with each other. The qualitative conclusions are that the disc is well fitted by an exponential distribution in both the galactocentric distance and height. There is not an abrupt cut-off in the stellar disc (at least within R<15 kpc). There is a strong flare (i.e. an increase of scale-height towards the outer Galaxy) which begins well inside the solar circle, and hence there is a decrease of the scale-height towards the inner Galaxy. Another notable feature is the existence of a warp in the old stellar population whose amplitude is coincident with the amplitude of the gas warp. It is shown for low latitude stars (mean height: pc) in the outer disc (galactocentric radius R> 6 kpc) that: the scale-height in the solar circle is , the scale-length of the surface density is and the scale-length of the space density in the plane (i.e. including the effect of the flare) is . The variation of the scale-height due to the flare follows roughly a law (for kpc; kpc). The warp moves the mean position of the disc to a height pc (for kpc; kpc).
Key words: Galaxy: general -- Galaxy: stellar content -- Galaxy: structure -- infrared: stars
Offprint request: M. López-Corredoira, [email protected]
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https://cs50.readthedocs.io/lab/
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# CS50 Lab¶
CS50 is a programming environment at lab.cs50.io for scaffolded learning that enables
• teachers to create step-by-step programming lessons (labs), providing incremental feedback at each step, and
• students to progress from an empty file (or starter code) to working code, with hints and feedback along the way.
To create a lab as a teacher, all you need is a GitHub account and a (public or private) repository. To log into and work on a lab as a student, all you need is the former. Neither use case requires familiarity with git itself though if or once comfortable with git, you can create labs even more quickly via a command line!
CS50 Lab is essentially an extension of CS50 Sandbox that allows teachers to embed interactive instructions alongside a sandbox. As such, CS50 Lab is, also, essentially a lightweight version of CS50 IDE with problems’ specifications embedded in students’ actual programming environments.
URLs of labs are of the form https://lab.cs50.io/:owner/:repo/:branch/:path, where
• :owner is the lab’s owner, a GitHub user or organization, on github.com,
• :repo is that owner’s repository in which the lab’s source can be found,
• :branch is the branch on which the lab’s source can be found in that repository, and
• :path is the path to the lab’s source on that branch.
The source for a lab like https://lab.cs50.io/cs50/labs/python/loops/ can thus be found in https://github.com/cs50/labs/tree/python/loops/, wherein
• cs50 is the lab’s owner (hey, that’s us),
• labs is the lab’s repository,
• python is the lab’s branch,
• loops is the lab’s path, and heretofore unmentioned,
• tree is just a GitHub-specific trick, sandwiched between :repo and :branch, via which you can browse that branch and path.
## Creation¶
To create a lab:
2. Create a repository, if you don’t have one (that you’d like to use) already.
3. Create a file in that repository called .cs50.yml, optionally inside of one or more directories, using GitHub’s website. Or create (and push) the same using git itself. Configure .cs50.yml per below.
4. Optionally create another file in the same directory as .cs50.yml called README.md, configured per below. While technically optional, without this file your lab won’t have instructions!
5. Optionally create in or upload to that directory (or any descendent thereof) any files you’d like to install in a student’s environment (and automatically open in the text editor’s tabs).
You can then (assuming no mistakes!) visit https://lab.cs50.io/:owner/:repo/:branch/:path, where each of those placeholders is as above, to see your lab!
## Configuration¶
### .cs50.yml¶
To define a lab, it suffices to create a file called .cs50.yml in the root (or subdirectory) of a branch in a repository that contains, minimally, a top-level lab50 key, the value of which is true:
lab50: true
#### window¶
It turns out the above is an abbreviation of (and equivalent to)
lab50:
window:
- editor
- terminal
wherein
• editor signifies that the lab should have an embedded text editor,
• readme signifies that the lab has instructions (written in README.md), and
• terminal signifies that the lab should have an embedded terminal window.
A value of terminal (implicit or explicit) is required.
Also available as values for window are
• browser, which signifies that the lab should have an embedded browser, and
• x, which signifies that the lab should have an embedded X window,
but those two values are mutually exclusive.
It’s worth noting that a lab without readme is functionally similar to CS50 Sandbox. Whereas sandboxes are intended to be temporary, labs are persistent: if a student logs into a lab and makes changes, those changes will persist indefinitely (unless the student resets the lab).
#### files¶
To install files in students’ environments (e.g., foo.c and foo.h), add a key below lab50 called files (as a sibling of window, if explicitly present):
lab50:
files:
- !include foo.c
- !include foo.h
That !include is a (confusing) feature of YAML; it indeed means “include,” not “don’t include,” as a programmer might otherwise assume.
If those files exist (in the same directory as .cs50.yml), they will be copied into students’ environments and opened automatically (if recognized as text files). If those files don’t exist, they will be created as empty (and opened).
Files (e.g., bar.c and bar.h) can also be in subdirectories (of whatever directory .cs50.yml is in):
lab50:
files:
- !include foo/bar.c
- !include foo/bar.h
Alternatively, you can specify subdirectories:
lab50:
files:
- !include foo/
Globbing is also supported, but asterisks have special meaning in YAML, so take care to quote any strings that have wildcards:
lab50:
files:
- !include "foo/*.c"
- !include "foo/*.h"
You can also exclude files, as with:
lab50:
files:
- !exclude "*"
- !include "foo.*"
The value of files is an ordered list, top to bottom, so the above means that all files are excluded by default but foo.* is then included, thereby overriding their exclusion.
#### cmd¶
To specify a command to be run in the sandbox’s terminal window (e.g., python), add a key below lab50 called cmd:
lab50:
cmd: python
The (implicit) default is:
lab50:
cmd: bash
### README.md¶
A lab’s instructions should be written in README.md (which must be in the same directory as .cs50.yml), using GitHub-flavored Markdown. Via CS50-specific “tags” can you add interactive features to those instructions. If present, each should appear on a line of its own but might very work in other contexts too (e.g., in ordered or unordered lists).
Your Markdown can also contain, if need, raw HTML, but not these tags.
Your Markdown can also contain emoji.
#### spoiler¶
To provide students with a spoiler, code or information they should only by clicking a Spoiler button, you can use these tags:
{% spoiler %}
The Answer to the Great Question...
Of Life, the Universe and Everything...
Is...
Forty-two.
{% endspoiler %}
You can override the button’s label with a quoted string. Accordingly, via
{% spoiler "Hint" %}
You're really not going to like it.
{% endspoiler %}
could you provide students with a hint. And via
{% spoiler "Solution" %}
Forty-two.
{% endspoiler %}
could you provide students with a solution.
#### video¶
To embed a YouTube video (responsively) in a lab’s instructions, you can use this tag, wherein the URL can be any URL of a video on YouTube:
{% video https://www.youtube.com/watch?v=oHg5SJYRHA0 %}
## Acknowledgements¶
Special thanks to CS50’s friends at Google and Pluralsight for their support of this app!
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https://socratic.org/questions/59534b437c014929820876c1
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Chemistry
Topics
# How does zinc metal react with hydrochloric acid?
Jun 28, 2017
Zinc metal is oxidized, and hydrogen ion is reduced.........
#### Explanation:
$Z n \left(s\right) + 2 H C l \left(a q\right) \rightarrow Z n C {l}_{2} \left(a q\right) + {H}_{2} \left(g\right) \uparrow$
When we write $H C l \left(a q\right)$ or $Z n C {l}_{2} \left(a q\right)$ we mean the aquated ions in solution, i.e. probably ${H}_{3} {O}^{+}$ and ${\left[Z n {\left(O {H}_{2}\right)}_{6}\right]}^{2 +}$. When we write $Z {n}^{2 +}$ this is a convenient shorthand for the aquated complex.
##### Impact of this question
174 views around the world
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https://www.arxiv-vanity.com/papers/1312.3095/
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arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org.
# On the role of Schwinger’s SU(2) generators for Simple Harmonic Oscillator in 2D Moyal plane
Kaushlendra Kumar1 Shivraj Prajapat2
Biswajit Chakraborty3
11School of Biochemical Engineering,Indian Institute of Technology(BHU), Varanasi 221005, India
22Indian Institute of Science Education and Research(IISER), Pashan Road, Pune 411008, India ,Email:
33S.N.Bose National Centre For Basic Sciences, Salt Lake, Kolkata 700098, India, Email:
###### Abstract
The Hilbert-Schmidt operator formulation of non-commutative quantum mechanics in 2D Moyal plane is shown to allow one to construct Schwinger’s SU(2) generators. Using this the SU(2) symmetry aspect of both commutative and non-commutative harmonic oscillator are studied and compared. Particularly, in the non-commutative case we demonstrate the existence of a critical point in the parameter space of mass() and angular frequency() where there is a manifest SU(2) symmetry for a unphysical harmonic oscillator Hamiltonian built out of commuting (unphysical yet covariantly transforming under SU(2)) position like observable. The existence of this critical point is shown to be a novel aspect in non-commutative harmonic oscillator, which is exploited to obtain the spectrum and the observable mass () and angular frequency () parameters of the physical oscillator-which is generically different from the bare parameters occurring in the Hamiltonian. Finally, we show that a Zeeman term in the Hamiltonian of non-commutative physical harmonic oscillator, is solely responsible for both SU(2) and time reversal symmetry breaking.
## I Introduction
It has been realized some time back that the localization of an event in space-time with arbitrary accuracy is not possible [1]. This idea was also corroborated by considering certain low energy implication in string theory [2]. Ever since then there have been an upsurge of literature involving formulation of quantum mechanics and quantum field theory in these kind of spaces where space-time coordinates are upgraded to the level of operators satisfying non-vanishing commutator algebra. The simplest of such quantized space-time is of Moyal type and the corresponding commutator algebra is given by the following Generally, quantum mechanics and quantum field theory in such space-time are investigated by demoting operator valued coordinate to c-numbers, at the price of replacing point-wise multiplication of fields by star multiplication [3]. However the star operation is not unique and can give rise to inequivalent physical consequences [4, 5]. It is therefore desirable to start with the formulation of quantum mechanics itself at completely operatorial level, so that one can formulate second quantization and eventually construct quantum field theory at a completely operatorial level. Indeed, such an attempt was made in [6],albeit in a nonrelativistic framework using the so called Hilbert-Schmidt operator which was initiated in [7, 8] , with the operator valued space coordinates were taken to correspond to the Moyal-plane satisfying
[^xi,^xj]=iθij=iθϵij (i,j=1,2) (1)
and time was taken to be c-number variable. Clearly, the representation of this coordinate algebra (1) is furnished by a Hilbert space isomorphic to the quantum Hilbert space of 1-d harmonic oscillator and we refer to this space as classical Hilbert space(), which is nothing but boson Fock space
Hc=span{∣n⟩=1√n!(^b†)n|0⟩}∞n=0 (2)
where
^b=1√2θ(^x1+i^x2) (3)
is the lowering operating annihilating the ground state and . This classical Hilbert space is supposed to replace 2-d plane in the commutative quantum mechanics. The corresponding quantum Hilbert space is then identified with the space of Hilbert-Schmidt operators, which are essentially trace-class bounded set of operators acting on . Denoting the elements of quantum Hilbert space by we can write
Hq={|ψ),Trc(ψ†ψ)<∞}. (4)
where subscript ’c’ refers to the trace over classical Hilbert space. This norm is related to the inner product in this , which is defined as
(ϕ|ψ)=Trc(ϕ†ψ) (5)
for . Using this operator formulation, the authors in [8] have obtained the exact spectrum of non-commutative harmonic oscillator. 444The earlier works involving harmonic oscillators on a noncommutative plane employed star product [9] and also Seiberg-Witten map [10][11] in presence of background electromagnetic field. (see also [12][13] for noncommutative Landau problem)It is however not clear how the different basis states in (2) responds to canonical (symplectic) transformation Sp(4,R). A related issue is the nature of ground state for the non-commutative harmonic oscillator and its relation to the vacuum state . Particularly, since the Hamiltonian of the harmonic oscillator has two independent parameter, viz mass and angular frequency having the dimension of length-inverse, it is expected that there will be some favoured value of these parameters where will also correspond to the ground state of non-commutative harmonic oscillator. Furthermore, since a 2D isotropic oscillator Hamiltonian in the commutative plane can have a manifest SO(4) symmetry(after appropriate scaling of phase -space variables), it will be interesting to study the presence/absence of such a symmetry for the corresponding non-commutative harmonic oscillator. Further, since the Euclidean Lorentz group SO(4) splits in to we can focus our attention to one of the SU(2) group itself, where each generator generates simultaneous SO(2) rotations in a pair of two orthogonal planes. Given that the non-commutative coordinates in higher dimension, say, in three dimension fail to transform covariantly under SO(3) rotation [14], in contrast to the commuting position like operator ( being the left/right actions, defined more precisely in the next section), it becomes imperative to check the same in this 2D case also under the SU(2) generators constructed a la Schwinger by using the fact that can be basically identified with ( indicates dual space), although both and transform covariantly under SO(2) rotation in Moyal plane. Furthermore the spectrum of the non-commutative harmonic oscillator as was obtained in [8] is written in terms of “bare” parameters and occurring in the Hamiltonian and the corresponding observables parameters were not identified. In this paper we try to identify the observable parameters and try to compare with the corresponding commuting harmonic oscillator in regard to the preservation of Schwinger’s SU(2) symmetry and also the time reversal symmetry.
The plan of the paper is as follows. In the next section (II) we briefly review how the representations of position and momentum operators acting on (4) and satisfying non-commutative Heisenberg algebra can be obtained. In section III we construct Schwinger’s SU(2) generators for both commutative and non-commutative plane in 2D and identify the commutative “position-like” coordinates transforming covariantly under SU(2). We then consider the commutative harmonic oscillator and write its Hamiltonian in a manifestly SU(2) invariant form and obtain its spectrum in section IV. In the following section V, we consider the non-commutative oscillator and investigate the role of SU(2) symmetry in obtaining the spectrum. We then discuss the time-reversal symmetry in section VI. Finally we conclude in section VII.
## Ii Representation of Non-commutative Heisenberg algebra in 2-D
Having introduced classical and quantum Hilbert spaces (2,4) in the previous section, we now discuss briefly following [7, 8], about the representation of non-commutative Heisenberg algebra.
If and are the representations of the operators and the conjugate momentum respectively acting on , then a unitary representation is obtained by the following action:
^Xiψ=^xiψ, ^Piψ=1θϵij[^xj,ψ]=1θϵij(^XLj−^XRj)ψ, (6)
where and refer to left and right action respectively i.e. and . Note that, we have taken the action of to be left action by default and the momentum operator is taken to act adjointly. This ensures that and satisfy non-commutative Heisenberg algebra:
[^XLi,^XLj]≡[^Xi,^Xj]=iθϵij ; [^Xi,^Pj]=iδij ; [^Pi,^Pj]=0 (7)
It can be checked easily that the right action satisfies
[^XRi,^XRj]=−iθϵij ; [^XLi,^XRj]=0 (8)
The corresponding right actions of annihilation operator is introduced in an analogous manner:
Hq∋|m⟩⟨n|=1√n!|m⟩⟨0|^Bn≡(^BR)n(1√n!|m⟩⟨0|) (9)
so that for any , one defines and and similarly for , where is the representation of (3) acting on and is given by . Note that we are using and to denote Hermitian conjugation over and respectively.
## Iii Angular momentum
We are now going to study angular momentum using Schwinger’s representation. First we will discuss angular momentum operators in commutative 2D case with the help of two decoupled simple harmonic oscillators. Then we will move to non-commutative case where we will see how the roles of angular momentum operators gets interchanged with the operators in commutative case.
### iii.1 Schwinger’s representation of Angular momentum
Schwinger introduced a method to express a general angular momentum in quantum mechanics in terms of the creation () and annihilation () operators of a pair of independent harmonic oscillators satisfying:
[^aα,^aβ]=0=[^a†α,^a†β] and [^aα,^a†β]=δαβ ∀α,β=1,2 (10)
With the help of these operators the number operator and angular momentum operator is defined as follows:
^N=^a†α^aα (11)
^→J=12^a†α{→σ}αβ^aβ ; [^Ji,^Jj]=iϵijk^Jk, (12)
with being our usual Pauli matrices.
### iii.2 Role of Angular momentum operators in commutative 2-D plane
In the commutative case let us choose our basis for a pair of decoupled harmonic oscillators which can be regarded as . We define the creation operators , as and respectively, and their Hermitian conjugates as annihilation operators. Now using Schwinger’s prescription (12) we obtain the three angular momentum operators as
^J1=12(^a†2^a1+^a†1^a2), ^J2=i2(^a†2^a1−^a†1^a2) and ^J3=12(^a†1^a1−^a†2^a2) (13)
such that they satisfy the algebra
[^Ji,^Jj]=iϵijk^Jk (14)
in which and the Casimir operators satisfy following eigen-value equations:
^J3(∣∣m⟩⊗∣∣n⟩) = j3(∣∣m⟩⊗∣∣n⟩), where j3=12(m−n) (15) ^→J2(∣∣m⟩⊗∣∣n⟩) = j(j+1)(∣∣m⟩⊗∣∣n⟩), % where j=12(m+n) (16)
Let us consider the Hamiltonian of two independent harmonic oscillators with same mass and frequency as follows:
^H=12μω2(^X21+^X22)+12μ(^P21+^P22)=ω2⎛⎜⎝^→P2μω+μω^→X2⎞⎟⎠ (17)
This can be identified with the 2D harmonic oscillator on a commutative plane. We can then write the 4D phase space variables in terms of the respective ladder operators as:
^Xα = 1√2μω(^aα+^a†α) (18) ^Pα = i√μω2(^a†α−^aα) ∀ α=1,2 (19)
Now we perform following canonical transformation which would preserve the commutation relation :
^Pα→^pα=^Pα√μω and ^Xα→^xα=√μω^Xα
With this our Hamiltonian becomes , which clearly enjoys SO(4) symmetry in the 4D phase space.
To understand the action of the Schwinger’s angular momentum operators (13) let us calculate the following commutation relations:
[^J3,^xα]=i2(δα2^p2−δα1^p1) and [^J3,^pα]=i2(δα1^x1−δα2^x2) (20)
[^J1,^xα]=−i2(δα1^p2+δα2^p1) and [^J1,^pα]=i2(δα1^x2+δα2^x1) (21)
[^J2,^xα]=i2ϵαβ^xβ and [^J2,^pα]=i2ϵαβ^pα; with α,β=1,2. (22)
From the above relations we can conclude that generates simultaneous SO(2) rotation in and planes. Like-wise in case of the rotation occurs in and planes, where as for the rotation occurs in and planes.
This is however a part of the symmetry only, as the symmetry generated by this ’s corresponds to one of the ’s in the decomposition of so(4) Lie algebra as . To get the other , one has to just flip the sign of one of the momenta components, say of .
### iii.3 Schwinger’s Angular momentum operators in non-commutative 2-D plane
As we have discussed in section-1, the quantum Hilbert space(4) comprises of Hilbert-Schmidt operators, and therefore any generic Hilbert-Schmidt operator can be written as:
∣∣Ψ)=∑m,nCmn|m⟩⟨n|∈Hq
The can be identified with , where is the dual of . Since, there is a one-to-one map between the basis and , the Hilbert spaces, = and (4) are isomorphic. In order to obtain the angular momentum operators acting on i.e the counterpart of the expressions in (13), let us replace with and (and not ) with and their respective Hermitian conjugates. Here the operators and are the operators on quantum Hilbert space such that and (9). Hence we get:
^J1=12(^BR^BL+^BL‡^BR‡), ^J2=i2(^BR^BL−^BL‡^BR‡) and ^J3=12(^BL‡^BL−^BR^BR‡) (23)
Clearly they satisfy the su(2) algebra
[^Ji,^Jj]=iϵijk^Jk, (24)
in which satisfies the eigen-value equation:
^J3|m⟩⟨n|=j3|m⟩⟨n|, where j3=12(m−n) (25)
and the corresponding Casimir operator
^J2=14(^BL‡^BL+^BR^BR‡)(^BL‡^BL+^BR^BR‡+2), (26)
satisfying following eigen-value equation:
^J2|m⟩⟨n|=j(j+1)|m⟩⟨n|, where j=12(m+n) (27)
These pair of eigen-values are exactly identical to the ones in (15) and (16). This suggests that both the basis states and can be labeled alternatively as where and . This is illustrated in following diagram(figure 1). We see from the diagram that all the discrete points with integer-valued coordinates with in the first quadrant represent a basis element of the Hilbert space of states . Hence we find that the Hilbert space gets split up into states of constant value lying on the straight line running parallel to axis e.g. line, line and so on, and takes values within the interval
We can then construct the usual ladder operators , connecting all states belonging to fixed subspace of dimension and the extremal points are annihilated by . This is just what happens in usual quantum mechanics.
We can now express the position and momentum operators in terms of and . By making use of equation (6), the definition [5] and its Hermitian conjugate, and the adjoint action of momenta(6) we get:
^XL1=√θ2(^BL+^B‡L) (28)
^XL2=i√θ2(^B‡L−^BL) (29)
^P1=i√2θ(^BL‡−^BL−^BR‡+^BR) (30)
^P2=1√2θ(^BR‡+^BR−^BL‡−^BL) (31)
Further, the commuting coordinates [5] introduced as
^Xci=12(^XLi+^XRi)=^Xi+θ2ϵij^Pj (32)
satisfying , can be expressed like-wise as:
^Xc1=12√θ2(^BR+^BL+^BL‡+^BR‡) (33)
^Xc2=i2√θ2(^BL‡−^BL+^BR‡−^BR) (34)
To see the similarity of the action of Schwinger’s angular momentum operators with their commutative counterpart(20-22), we first perform following canonical transformation, to construct dimensionless phase space variables:
^Xci→^xci=^Xci√θ and ^Pi→^pi=√θ^Pi ∀ i=1,2 (35)
Then we calculate following commutation relations:
[^xci,^J1]=i2(δi1^p′1−δi2^p′2) and [^p′i,^J1]=i2(δi2^x2−δi1^x1) (36)
[^xci,^J2]=−i2(δi1^p′2+δi2^p′1) and [^p′i,^J2]=i2(δi1^x2+δi2^x1) (37)
[^xci,^J3]=i2ϵij^xj %and [^p′i,^J3]=i2ϵij^p′j (38)
Here we have introduced . So we see that the angular momentum operators are responsible for inducing simultaneous SO(2) rotations in two orthogonal planes of our 4-D phase space. In fact for the rotation occurs in and planes. In case of the rotation occurs in and planes, where as for the rotation occurs in and planes. Here we can also appreciate that roles of commutative and non-commutative angular momentum operators are exchanged in following manner (where superscript C refers to commutative case(20-22) and NC for non-commutative(36-38) case):
^JNC1↔^JC3, ^JNC2↔^JC1 and ^JNC3↔^JC2 (39)
Again like the commutative case this is also a part of rotation in space, as ’s corresponds to only one of the ’s of . In either case, this is just reminiscent of the splitting of the SL(2,C) algebra by taking suitable combinations of spatial rotations with Lorentz boost in dimensional Minkowski space-time, and SL(2,C) happens to be just the double cover of the Lorentz group SO(3,1),whose Euclidean version is the spin group Spin(4), which is the double cover of SO(4). Now we can obtain the rotation matrix for finite rotation generated by in the phase space by using above commutation relations (36-38) which is implemented by the following unitary transformation
Ξ⟶Ξ′ = e−i→λ.→JΞei→λ.→J=R(→λ)Ξ
where the 4-component column matrix comprises of phase space variables and is given by:
Ξ=(^x1c,^x2c,^p12,^p22)T (41)
The matrix representations of the corresponding generators in the 4-dimensional representation are given by . This yields
^J1=i2⎛⎜ ⎜ ⎜⎝0010000−1−10000100⎞⎟ ⎟ ⎟⎠;^J2=i2⎛⎜ ⎜ ⎜⎝000−100−1001001000⎞⎟ ⎟ ⎟⎠;^J3=i2⎛⎜ ⎜ ⎜⎝0100−1000000100−10⎞⎟ ⎟ ⎟⎠ (42)
The corresponding Casimir operator is then given by:
^→J2=^J21+^J22+^J23=12(12+1)I (43)
indicating that this corresponds to spin representation of , which looks odd from a naive consideration, where it appears to be representation as the dimensionality is 2j+1=4. This is however easily explained by fact that the are making simultaneous rotation in two different orthogonal planes through representation. However, the various basis states in fig.1 will transform according to the th representation of Schwinger’s SU(2) generators.
Finally, we would like to point out the important role played by the commuting but unphysical position-like operators (32). It is only , rather than the physical non-commuting position operators , that transform covariantly under SU(2). It is only under SO(2) rotation, generated by , that both and transform covariantly. As has been shown in [14], that in 3D Moyal space also, it is only that transform covariantly under SO(3) rotation, although does not correspond to any physical observable [5]. Further, as we shall see later that this is also true for Bogoliubov transformation, where it undergoes simple scaling transformation and plays a very important role in our analysis, despite being an unphysical observable [5].
## Iv Simple Harmonic Oscillator in commutative plane
In commutative () case the Hamiltonian is given by(17):
^HI=12μω2^→X2+12μ^→P2 (44)
Using the form of position and momentum operators in terms of ladder operators (18-19), we get following result:
^→X2 = 12μω(^a1^a1+^a†1^a†1+^a2^a2+^a†2^a†2)+1μω(^a†1^a1+^a†2^a2+1) (45) ^→P2 = −μω2(^a1^a1+^a†1^a†1+^a2^a2+^a†2^a†2)+μω(^a†1^a1+^a†2^a2+1), (46)
so that our Hamiltonian (44) becomes:
^HI=ω(a†1a1+a†2a2+1), (47)
which is clearly SU(2) invariant as it commutes with angular momentum operators (13). Using our most general state , we get following spectrum:
^HI|m⟩⊗|n⟩=ω(2j+1)|m⟩⊗|n⟩, where j=12(m+n), (48)
which was expected as our state corresponds to pair of simple harmonic oscillator (one ket for each SHO), and the energy of any SHO, say is . SU(2) invariance of the Hamiltonian is also evident from above as spectrum is given by and is independent of and (2j+1) being the dimensionality of j-th subspace.
## V Simple Harmonic oscillator in non-commutative plane
Here we shall first analyze the unphysical Hamiltonian of simple harmonic oscillator involving the commuting coordinates [5], which is shown to yield the same spectrum as in the commutative case(48). This will then pave the way to analyze the physical oscillator involving non-commuting operators.
### v.1 Unphysical SHO involving (^Xci)
Let us first construct following quadratic form:
^H1=(1θ(^→Xc)2+θ4^→P2), (49)
which can be regarded formally as a Hamiltonian of a harmonic oscillator with particular choices of mass and angular frequency parameters. But since it involves (32), which is just a mathematically constructed commuting observable and is devoid of any physical interpretation [5], this oscillator is really unphysical in nature. Now using canonical transformation (35) above Hamiltonian becomes:
^H1=((^xc1)2+(^xc2)2+(^p12)2+(^p22)2)=ΞTΞ using (???), (50)
which is manifestly invariant under one of the SU(2) symmetry group in the decomposition of SO(4) i.e analogous to commuting case.555Actually, it is invariant under the entire SO(4) group itself; the other SU(2) symmetry is realized by flipping the sign of one of the momenta component say of , as was observed earlier. In our present analysis, we shall not make use of this second SU(2). We shall therefore continue to refer to the first SU(2) symmetry only. This is evident from commutation relations (36-38) and unitary transformation (LABEL:b7).
Then (using 30-34), one gets
(^→Xc)2=(^Xc1)2+(^Xc2)2=θ2(^BL‡^BL+^BR^BR‡+1+^BL^BR‡+^BL‡^BR) (51)
^→P2=(^P1)2+(^P2)2=2θ(^BL‡^BL+^BR^BR‡+1−^BL^BR‡−^BL‡^BR), (52)
so that our Hamiltonian (50) becomes:
^H1=12(2θ(^→Xc)2+θ2^→P2)=(^BL‡^BL+^BR^BR‡+1) (53)
Hence for a general basis state we get following spectrum:
^H1|j,j3)=^H1|m⟩⟨n|=(m+n+1)|m⟩⟨n|=(2j+1)|j,j3), using (???) (54)
and the spectrum can be read-off easily, yielding just .
We then consider following Hamiltonian, which is a slight variant for the non-physical planar harmonic oscillator(49), by introducing mass and angular frequency :
^H2=12μ^→P2+12μω2(^→Xc)2 (55)
Naively we expect that this Hamiltonian to be equivalent to (44), however this is not the case because there is a major difference in the construction of actually commuting (44) and mathematically constructed commuting coordinates. The annihilation operators and occurring in(18) act on the left and right slots separately, annihilating the vacuum . In this case we can define creation and annihilation operators in an analogous manner to(18 and 19) as:
^C†i=1√2μω(μω^Xci−i^Pi), ^Ci=1√2μω(μω^Xci+i^Pi) ∀ i=1,2, (56)
which, however involves and acting simultaneously in the left and right slots. One can see that the relevant ground state here i.e. is annihilated by only under a special choice of parameters and , which we call as a
μ0=ω02=1√θ (57)
Also we notice that at this critical point (55) reduces to (49), up to an overall constant: and furthermore, the ladder operators and (56) reduce to the following linear combination of operators and :
^C1=1√2(^BL+^B‡R); ^C2=−i√2(^BL−^B‡R) (58)
It is therefore interesting to see how our Hamiltonian(55) behaves under above condition(57). We find that:
^H2=ω0(1θ(^→Xc)2+θ4^→P2)=ω0(^BL‡^BL+^B
|
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https://scholar.princeton.edu/haidi_chen/bio
|
# Bio
I am a physical and biological oceanographor. I am very interested in contributing to a better mechanistic understanding of physical dynamics in the ocean, e.g. large scale circulation and meso and submesoscale dynamics, and how they influence biological carbon pumping at different spatial and temporal scales, and how these interactions further feedback to current climate.
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https://www.graduate.technion.ac.il/Theses/Abstracts.asp?Id=26433
|
M.Sc Thesis
M.Sc Student Cohen Gil On the Degree of Symmetric Functions on the Boolean Cube Department of Computer Science Professor Amir Shpilka
Abstract
Given a function f from {0,1,?,n} to some subset C of the real numbers, it is a well known fact that there exists a unique interpolation polynomial for f of degree at most n. A natural question is the following: for a restricted set C, how low can the degree of an interpolation polynomial for a non-constant function from {0,1,?,n} to C be? A first result for a question of that nature that appeared in the literature (in the paper “Polynomials with Two Values by Joachim von zur Gathen and James R. Roche) handled the case C={0,1}. In this thesis we study two natural generalizations. The first concerns the restriction C = {0,1,?,c} for some natural c that may depend on n. The second generalization deals with sets C which are finite subsets of the rational numbers, which does not depend on n. In both cases we give new lower bounds. We also simplify and generalize the known results for the case C={0,1}.
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http://mathoverflow.net/revisions/45136/list
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"One can just work head-long into it: [a,b]=a−1b−1ab. $[a,b]=a^{-1}b^{-1}ab$. If there is no cancellation, you cannot have this equal to x−1y−1xyz−1w−1zw; $x^{-1}y^{-1}xyz^{-1}w^{-1}zw$; so either the last letter of a $a$ matches with the first of b, $b$, the first of a $a$ with the first of b $b$ (cancellation in b−1a), $b^{-1}a$), etc. Checking leads to impossibility. – Arturo Magidin"
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https://kundoc.com/pdf-sensitivity-analysis-for-heat-exchanger-networks-.html
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# Sensitivity analysis for heat exchanger networks
## Sensitivity analysis for heat exchanger networks
Chemical Engineering Science, Vol. 46, No. 2, pp. 451458, Printed in Great Britain. SENSITIVITY 1991. ANALYSIS FOR HEAT EXCHANGER NETWORKS+ R. RA...
Chemical Engineering Science, Vol. 46, No. 2, pp. 451458,
Printed in Great Britain.
SENSITIVITY
1991.
ANALYSIS FOR HEAT EXCHANGER NETWORKS+
R. RATNAM Chemical
Engineering
cam-2509/91 1E3.w l 0.00 0 1990 Pergamon Press plc
Division,
and V. S. PATWARDHAN\$ National
Chemical
1990; acceptedfor
Laboratory,
publication
Pune 411008,
India
11 June 1990)
Abstract-The sensitivity of a heat exchanger network (HEN) refers to the deviations in network temperature as a result of changes in operating parameters such as source temperatures, UA values and Row rates. Generating such information by varying one parameter at a time and solving the HEN all over again is straightforward but time consuming. In this study a new approach is developed which is based on the inherently linear nature of HENS. This approach eliminates the need for repeated matrix inversIons and leads to an efficient computational procedure for generating the entire sensitivity information. Illustrative examples are also presented which demonstrate the computational efficiency and indicate that the procedures developed can be applied even when the deviations in operating parameters are large and simultaneous.
INTRODUCTION
The design often been
of heat exchanger networks (HENS) has dominated by two important considera-
tions, namely the utility requirement and the capital cost, mainly because both can be quantified in terms of money. In contrast, the flexibility and the operability of HENS have received attention only rather recently (for example see Saboo and Morari, 1983; Saboo et al., 1985; Marselle et al., 1982; Calandranis and Stephanopoulos, 1986; Halemane and Grossmann, 1983; Swaney and Grossmann, 1985a, b). Kotjabasakis and Linnhoff (1986) have described a procedure for considering flexibility right at the design stage which establishes a trade off between flexibility and the total cost of an HEN. Their procedure makes extensive use of what they termed as sensitivity tables. The sensitivity of an HEN can be characterized by the deviations in network temperatures (global output as well as intermediate temperatures) resulting from given changes in operating conditions such as source temperatures, UA values and stream flow rates. Such information is obviously important in designing HENS which are expected to deal with planned process changes
as well as random
fluctuations,
size, the amount of information to be generated would increase very rapidly indeed. In this paper we address the problem of generating such information in a computationally efficient manner by taking advantage of the linearity that is inherent in HENS. An obvious, brute force method for generating sensitivity information is to perturb one parameter at a time, solve the resulting network as a fresh problem and compare the resulting temperatures with the base case values. This involves repetitive application of the same solution procedure, which becomes time consuming in view of the large number of cases that need to be considered. In this paper, the HEN problem is formulated as a linear problem. It is then shown that once the base case solution is obtained, the effect of variation in any parameter (or any arbitrary combination of parameters) can be calculated with only a minor additional computational effort by making use of the base case results already available. The procedure is illustrated with examples and the results are compared with those reported in the literature. It is also shown that the present procedure is applicable even for large deviations in operational parameters.
and also
in designing control schemes. It is worthwhile looking at the size of the problem that one has to tackle for generating complete information regarding the sensitivity of an HEN. In the illustrative example considered later, there are four process streams, 11 unknown stream temperatures and seven heat exchangers. Thus one has to look at the deviations in 11 temperatures for given changes in each of the 15 operating parameters (four source temperatures, four heat capacity flowrates and seven UA values). In a practical problem which could be of a much larger
‘NCL Communication No. 4852. ‘To whom correspondence should be addressed. 451
THEORY
Consider the counterflow heat exchanger Fig. 1. The heat balance equations
and the design
shown
in
4 =
F,CTl
-
r2)
(1)
4
Fr(r,
-
T3)
(2)
=
equation 4 = (UAW,,
(3)
can be algebraically manipulated to relate the output temperature to the input temperatures as -T2+~1T1+(l-a,)T,=0
(4)
-T4+(l-cx2)T,+a,z-,=0
(5)
452
R.
RATNAM and CP
T.2
Fi
T3 F,
Fig. 1. Schematic
diagram of a countercurrent changer.
heat ex-
where a1 =(P-R)exp(P)/[Pexp(P)-Rexp(R)] 0~~= (R - P) exp (R)/[R
exp
(6)
(R)- P exp (P)]
(7)
P = (UA)/F,
(8)
R = ( UA)/Fi.
(9)
It is easily shown
that a, and txZ are related
P(1 - a,) = R(1 - az).
as (10)
Equations (4)-(g) have been presented earlier (Kern, 1950; Kotjabasakis and Linnhoff, 1986) though in slightly different forms. It may be noted that the sum of the coefficients in eqs(4) and (5) are zero. The parameters P and R (and also the flow ratio Q = FJF, = R/P) are positive. Moreover, both a, and a2 are positive and lie in the range 0 < a, (and G(~)< 1. a, and a2 also have the following physical meaning: 011= (r,
~ Gl/(T,
- TJ)
(11)
a2 = tT4 - T,)l(T,
- T1).
(12)
The utility of these D: values and their relationship with design parameters of heat exchangers of various geometries has been considered in detail elsewhere (Ratnam and Patwardhan, 1990). Let us now consider the solution procedure for a network of heat exchangers. If equations such as eqs (4) and (5) are written for each heat exchanger in the network of m heat exchangers, we get 2m equations. If there are N global streams then the number of intermediate streams is (2m - N), whose temperatures are unknown. These, together with the N unknown global output temperatures, give a total of 2m unknowns. Thus we have a system of 2m linear equations with 2m unknown temperatures, giving a well formulated problem. Each equation involves three temperatures, at least one of which is unknown. We may also have equations where all three temperatures are unknown. We now transfer all the terms involving known source temperatures to the right hand side to get a system of equations that can be represented as AT=B
(13)
where A is a 2m x 2m matrix and T and B are 2mdimensional column vectors. For a given network with known stream properties (source temperatures and heat capacity flow rates) and known UA values, eq. (13) can be solved to give T =A-‘B,
(14)
V. S.
PATWARDHAN
whereby all the temperatures become known. In some cases it may be possible to permute matrix A by row/column operations to a block form which will reduce the computational effort involved in matrix inversion. Consider the case of a network involving stream splits. As far as temperatures are concerned, a splitter does not introduce any new unknown temperatures as all the outlet temperatures in a splitter are equal to the inlet temperature. In the case of a mixer, the outlet temperature is an unknown parameter. However, we get one more equation as the outlet temperature of the mixer can be related to the inlet temperatures and heat capacity flow rates by a heat balance equation. Moreover, this gives an equation that is linear in temperatures. Therefore, the form of eq. (13) remains unchanged even when the network has splitters and/or mixers. The following analysis, which uses eq. (13) as the starting point, is thus applicable in case of splitters and mixers as well, though they are not specifically considered here. SENSITIVITY ANALYSIS
Here we are concerned with the effect of changes in one of the known parameters (source temperatures, heat capacity flow rates and UA values) on the network performance. It may be stressed here that changes in some of the parameters may arise due to fluctuations in the whole plant, or due to causes such as fouling, while some others, such as changes in utility flow rates, can be introduced deliberately. The sensitivity analysis of a network can be a very useful guide in deciding whether the effects of some uncontrollable changes can be nullified by the appropriate manipulation of the controllable factors. The most obvious, brute force method to conduct a sensitivity analysis is to change one parameter at a time, calculate the new A matrix and B vector, and use eq. (14) to calculate the new T vector. Such a procedure involves one matrix inversion for every new value of each parameter, and is computationally lengthy for a complete sensitivity analysis of even medium-sized problems. Such a procedure has been used by Kotjabasakis and Linnhoff (1986), who were mainly interested in illustrating the use of sensitivity analysis in network design. It may be noted that they did not use matrix inversion as such. The example used by them could be solved by a sequential procedure. The entire procedure was used repeatedly by them for calculating the effect of change in each parameter. Here we present a different approach for conducting sensitivity analysis in a computationally efficient manner by avoiding the need for repeated matrix inversions. This is particularly valuable in using sensitivity analysis for network design even for large problems, and where interactive software tools are being used. Let the base case solution be calculated as Tb=A;lh where the subscript
(15)
b refers to the base case. A change
Sensitivity analysis for heat exchanger networks in any of the F or UA values changes both A and B while a change in T, values changes only the B vector
(since all the T, terms were transferred to the right hand side). In general, the new problem may be specified as (Ab + AA)(T, + 4) = b
+ AB
(16)
where AA and AB are the changes in A and B resulting from changes in T,, F and WA values, and 4 (a 2m x 1 vector) represents the deviations in different network temperatures (both global outputs and intermediate streams) that we are interested in. For a given situation, the easiest way of calculating AA and AB is to calculate A,,, and B,,, and subtract from them A, and B, respectively. Since A is a sparse matrix and B is a vector, this does not involve much computation. Expanding eq. (16). subtracting the base case equation *bTb
=
B,
07)
and neglecting the second order term (AA) 4 (which is justified for small deviations; the case of large deviations is considered later), we get A,# + AAT, = AB, which can be rewritten
(18)
as
4 = A; ‘[AB - (AA)T,].
(19)
It is important to note that the inverse appearing in this equation is the base case inverse which is already known. To determine the effect of any parameter change, we just have to calculate corresponding AB and AA, and use eq. (19X which now involves only a matrix multiplication but no additional matrix inversion. It is also worthwhile examining at this point the extent of computation involved. If any of the T, changes, AA = 0 and only two elements of AB are non-zero, which correspond to the equations for the heat exchanger which has the changed T, as an input stream. If any of the UA values change, then at most two rows of AA and at most two elements of AB are non-zero, which correspond to the equations for that particular heat exchanger. If any of the F values change, and if m’ is the number of heat exchangers traversed by that stream, then 2m’ rows of AA and 2m’ elements of AB are non-zero. It is also important to note that any row of AA has at the most three nonzero elements, as is obvious from eqs (4) and (5). These three groups of parameters and their effect on the whole network is considered in detail in the following analysis. Variation in source temperature For this case, AA vanishes and eq. (18) gives I=
A;‘AB.
coefficients
453
of Tsi in these elements.
Then,
AB,=pikATsi AB,=&AT,, and the other elements then gives
of AB are zero. Equation
@j = (DjkP:k +Di,Bii)ATsi
(21) (20)
(22)
where D represents A; 1 (for convenience). The linearity between the deviation in any network temperature and the variation in any Tsi is obvious. It is also easy to show that if several T, values vary simultaneously, their corresponding #j values can be calculated independently and can simply be added up. Variation in UA values When any one or several of the UA values change, both AA and AB are non-zero. An examination of the starting equations, i.e. eqs (4) and (5), indicates that each equation involves only one parameter 01,apart from temperatures. Each of the 2m values depends upon just one UA value, and two flow rates. Consider the case where a particular u, say CL,,,changes. ar appears only in the kth row of A as well as B. It has been mentioned earlier that each equation involves one output and two input temperatures for some heat exchanger. Let TO be the output temperature appearing in the kth equation. Let us define @= -
T; + T;
(23)
where T’, is the base case input temperature corresponding to the output temperature T,, and T; is the other base case input temperature. Since the form of the kth equation is given by eq. (4), it is possible to write [AB-(AA)T&=&Aa,.
(24)
This equation is valid even when several a values vary simultaneously, since only one a value appears in each equation. Combining this with eq. (19) we get
which can be rewritten
as 4 = SAa
(26)
S, = Dij.
(27)
where
The matrix S can be calculated using the base case calculations and source temperatures for a given network. In order to calculate the effect of variation in any or several of the UA values, all that remains to be done is to calculate the new values, evaluate the Aa vector and use eq. (26) to get 4. It may be noted here that S is calculated only once. This leads to a tremendous saving of computation time.
(20)
Let us consider the variation of the source temperature TSi. Let k and I be the element numbers of B which involve TSi. Let pa and Be be the corresponding
Variation in only one UA value When only a single UA value, say (UA),, is varied, a further simplification takes place. Let the kth and Ith
454
R.RATNAM
and V.S. PATWARDHAN
equations refer to the ith heat exchanger. Then, all elements of Au except the kth and Ith elements are zero. Moreover, since CL* and a, are related by eq. (lo), we get Aa, = QiAa,
(28)
where Qi is an appropriately defined flow ratio which is constant. Equation (26) then gives
41 = (Q,Sj,
+ Sjl)Aai-
Variation in F values When any or several of the F values change, both AA and AB are non-zero, in general. As mentioned earlier, each of the 2m a values depends upon two flow rates. A change in any F value changes several a values simultaneously, depending on the heat exchangers traversed by that particular stream. Equations (24)-(27) are applicable in this case as well. Even when only one flow rate changes, at least two a values change. In this case, no linearity such as that given by eq. (28) exists. Therefore, the bj values vary in a complex non-linear manner as flow rates are changed, as shown later in the iilustrative examples. The case of large deviations Equation (18) was obtained from eq. (16) by ignoring the second order terms, which is justified when the deviations are small. If this assumption is removed, then eq. (16) gives b = D(AB - (AA)Cr, + I))
f\$(‘) = 0,
4 t+ l) = 7 D,,\$,g)(Aa)y).
(30)
in 4. It was found that by successive substitu-
r = 0
4(‘+ ‘) = D(AB - (AA)(Tb + &‘))),
r > 0.
(31)
(Am),. does not vary from iteration to iteration. Thus, only +y) needs to be calculated in each iteration to evaluate 4 (‘* L ‘) . This was done by using an index table prepared by the preprocessor (described later) to keep track of the stream numbers corresponding to each of the 2m heat exchanger equations.
ILLUSTRATIVEEXAMPLE
Using the concepts developed in the earlier sections, a generalized software was developed for determining the sensitivity of any heat exchanger network with or without loops and recycles. It has a preprocessor at the front end to facilitate data input. Network topology can be input simply by specifying stream numbers for each heat exchanger in a particular order. The preprocessor computes the A matrix and the B vector, which reflect the network topology. In order to illustrate the results we use the example described by Kotjabasakis and Linnhoff (1986) with the stream data given in Table 1 and the network shown in Fig. 2. The UA values for individual heat exchangers were not specified explicitly by them, and were calculated from their Fig. 2, which gives heat loads for all heat exchangers along with the network temperatures at the base case. Table 2 shows the base case results. Global input temperatures are not listed in this table. The column headed “K and L no.” gives the stream numbers used by Kotjabasakis and Linnhoff (1986), which facilitates comparison with their results. Incidentally, there is a small discrepancy between their Table 1 and their Fig. 2 regarding the target temperature of stream no. 4. It has been taken as 240°C as per their Fig. 2, since the temperature of 280°C mentioned in their Table 1 is clearly unattainable using stream at 254°C as specified in their Table 2.
Table 1. Stream data for example Stream “0.
I
7 13 16 4 10 19
(32)
(29)
Thus, all deviations in network temperatures are proportional to A\cr,values. It may be mentioned here that as UA varies between 0 and cc, the corresponding a varies from 0 to 1. Therefore, Aa is not proportional to AUA except in close vicinity of the base case. Consequently, ( also varies non-linearly with [IA for large changes in WA. This is quite evident from the sensitivity tables presented by Kotjabasakis and Linnhoff (1986).
which is an implicit equation this can be iteratively solved tion, using
Just two or three iterations were found to give good accuracy even for those parameter changes which were very large from a practical point of view. This is further illustrated later with numerical examples. It is worthwhile examining the computational effort involved in evaluating r#P+l) from eq. (31). Using eq. (24), eq. (31) can be rewritten as
Temperature s0”rl.x target WI
300.0
Remarks
(“Cl
80.0 40.0
200.0 40.0 140.0
240.0
20.0 20.0 254.0
40.0 40.0 254.0
180.0
30.0 45.0
Hot Hot Cold
60.0
Cold Cooling water Cooling water Condensing steam
40.0 120.0 70.0
Sensitivity
analysis
for heat exchanger
networks
HEHEAT
Fig. 2. Example
Table 2. Base
Stream no. 2 3 5 6 8 9 11 12 14 15 17 18 20 21
case intermediate temperatures K and L no.+ 1 2 3 4 5 6 7 8 9 10 11
network
and
target
Temperature (“C) 213.3 160.0 80.0 40.0 160.0 71.1 40.0 40.0 140.0 180.0 170.0 213.3 254.0 240.0
+The K and L stream number refers to the corresponding stream number for this example in Kotjabasakis and Linnhoff (1986).
Variation in source temperature The sensitivity of different network temperatures towards different source temperatures is given by the terms in parentheses in eq. (22). The results of this calculation are shown in Table 3. The numbers represent the deviation in network temperature for a 1°C variation in source temperatures. This table matches with the results of Kotjabasakis and Linnhoff (1986), except for the sensitivity of T, L. If we consider a 1°C variation in T,, T,, becomes 213.3 + 0.333 = 213.633”C. With this as the input temperature to the heater, the output temperature T,, from the heater can be easily calculated and turns out to be 24O.llPC. This shows that the sensitivity shown in our Table 2 is the correct sensitivity. For the same reason discrepancies in deviations of this particular temperature have been ignored in subsequent sections.
455
DUTY
(KW)
numbering.
Variation in UA values Consider a variation in the (UA), value. The variations in network temperature calculated from eq. (26) are shown in Table 4 and are seen to match exactly with the results of Kotjabasakis and LinnhofT (1986, their Table 5b). Figure 3 shows some of these in a graphical form. It is seen that 4 values vary with (UA), value in a monotonic but strongly non-linear manner. Equation(29), however, indicates that #j is directly proportional to Alcc,. Figure 4 shows #j values as a function of Au,. Though linearity between tij and Au, is expected in the vicinity of the base case, the linearity that is seen even for large changes in (Lr.4), is somewhat surprising. This certainly does n’ot follow from eq. (19), which assumes deviations to be small, in some sense. The reason lies in the network structure. The example network in Fig. 2 is acyclic. For such networks, the change in the UA of any exchanger and the resulting changes in the output temperatures of that heat exchanger affects other (downstream) temperatures in an exactly linear manner even for large changes. For cyclic networks, however, the change in the UA value of a heat exchanger could influence the inlet temperatures of the same exchanger (due to information feedback inherent in cyclic networks), in which case, 4 values may not remain linear to Aa for large values of Aa. This would necessitate the use of eqs (30)-(32) developed for large deviations. Variation in F values In this case, eq. (26) has to be applied by actually calculating Aa for the new flow rate values. The results obtained by varying the heat capacity flow rate of source stream 4 are shown in Table 5 and are seen to match the results of Kotjabasakis and Linnhoff (1986). Simultaneous variation of several parameters As an illustration, consider the case used by Kotjabasakis and Linnhoff, where r, is 270°C (in-
R.
456
and V. S.
RATNAM
PATWARDHAN
Table 3. Sensitivity of network temperatures (in “C) for 1°C change in source temperature Source stream number Stream no.
7
1
0.3334 0.2929 0.1255 0.0418 0.3333 0.0864 0.0338 0.0338 0.2778 0.308 1 0.5000 0.3333 O.OOW 0.1147
0.3333 0.0909 0.0389 0.0130 0.0000 O.oooO 0.0000 O.OOCKl [email protected] 0.1818 O.CWOO 0.3333 0.0000 0.1147
2 3 5 6 8 9 11 12 14 15 17 18 20 21
16
13 0.0000 0.1212 0.0519 0.0173 0.0000 0.7408 0.2898 0.2899 0.1666 0.0757 0.0000 O.Mx)o O.QOCQ 0.0000
0.3333 0.4950 0.2122 0.0707 0.6667 0.1728 0.0676 0.0676 0.5556 0.4344 0.5000 0.3333 0.0000 0.1147
Table 4. Sensitivity of network temperatures (in “C) for change in UA of heat exchanger no. 2 Percentage
change
in
UA
Stream “0.
2 3 5 6 ; 11 12 14 15 17 18 ::
-
80%
- 12.42 11.68 5.00
1.67 24.8 5 6.44 2.52 2.52 20.71 2.63 - 18.64 ~ 12.42 0.00 - 4.27
-201 -100
-
40%
-
- 4.27 4.02 1.72 0.57 8.55 2.22 0.87 0.87 7.12 0.9 1 - 6.41 ~ 4.27 0.00 - 1.47
20%
0%
- 1.85 1.73 0.74 0.25 3.69 0.96 0.37 0.37 3.08 0.39 - 2.77 1.85 0.00 - 0.64
I
/
0
100 CHANGE
IN
MA),
200%
300%
400%
5.00 - 4.70 - 2.01 - 0.67 - 10.00 - 2.59 - 1.01 - 1.01 - x.33 - 1.06 7.50 5.00 0.00 1.72
7.14 - 6.71 - 2.88 - 0.96 - 14.29 - 3.70 - 1.45 - 1.45 - 11.91 - 1.51 10.71 7.14 0.00 2.46
8.26 ~ 7.76 - 3.33 - 1.11 - 16.52 - 4.28 - 1.68 - 1.68 - 13.77 - 1.75 12.39 8.26 0.00 2.84
I
I
200
300
1%)
Fig. 3. Effect of (UA), on several 4 values.
Sensitivity
analysis
for heat exchanger
stead of the base case value of 3OO”C), T,, is 20°C (instead of 40°C) and F,, is 72 kW/“C (instead of 60 kW/“C). For each of these three changes, they used their sensitivity tables to calculate the effect of each
20
1
change total
S -L ff
/
2,18
o_
\
-lO- Y
3
x,:
14
-20 0
0.2
0.4
0.6
U., For
0.8
1.0
two
HE-2
5. Sensitivity
of network
For
iterations
exact
Fig. 4. Variation of Q values with CLvalue.
Table
457
up the effects to estimate example,
they
found
that
different
temperatures
were
Percentage
change
required
in this
case
to get
of ds.
(in “C) for change
no.
- 50%
- 40%
- 20%
0%
2 3 5 6 8 9 11 12 14 15 17 18 20 21
2 1.24 10.89 4.67 1.56 8.42 2.18 0.85 0.85 7.02 14.78 17.37 39.47 0.00 12.88
t 5.29 7.63 3.27 1.09 5.72 1.48 0.58 0.58 4.76 10.51 12.86 29.00 0.00 11.63
6.33 3.04 1.30 0.43 2.17
0.00 0.00 0.00 0.00
0.00 0.00
0.56 0.22
0.00 0.00 0.00 0.00 0.00 0.00 0.00 O.CNl
0.22 1.81 4.27 5.47 12.35 0.00 6.50
6. Iterative calculation
in CP of stream
no. 16
in CP
K and L no. 1 2 3
2 3 5
6 8 9 11 12 14 15 17 18 20 21 ‘This
problem.
4 5 6 7 8 9 10 11 column
lists values
Exact calculation+
iteration
1
112.4850
~ 146.3585 - 84.9118 _ 36.3906 - 12.1303 _ 36.0422 18.9642 7.4191 7.42 19 ~ 61.8822 - 107.9672 _ 106.9794 _ 72.6382 - 0.0036 - 41.6373
- 106.9794 - 72.0422 - 0.0031 - 30.7579
obtained
the entire network
by solving
20%
40%
~ ~
4.65 2.14 0.92 0.31 1.44 0.37 0.15 0.15 1.20 3.08 4.10 9.39 0.00 - 6.57
-
8.19 3.72 1.59 0.53 2.45 0.64 0.25 0.25 2.05 5.40 7.26 ~ 16.71 0.00 - 12.71
50% -
9.66 4.36 1.87 0.62 2.84 0.74 0.29 0.29 2.38 6.35 8.57 ~ 19.80 0.00 - 15.57
of 4 values (in “C) by eq. (31) tterative
Stream no.
the
~
the
Of the three parameters that are from the base case, two are source temper-
value
Stream
Table
the
change in T, was - lO.l”C. If the network is solved as a new problem with the changed values of parameters, the change in T, was found to be - 9.816”C. It is interesting to see the results obtained using the equations developed in this study. Application of eq. (19X which covers the effect of all parameter changes simultaneously (but uses only the base case matrix inverse), gives #‘\$) = - 9.784”C, which is a much more accurate estimate of the change in T, than that obtained by adding up individual effects. Both these approaches are valid only for small enough changes in parameters. As the changes increase, their accuracy suffers. Application of eq. (31), which represents an iterative approach, for two iterations gives @\I) = - 9.784”C and 4:‘) = - 9.816”C. Thus, only
i=17
lo-
networks
-
85.6214 36.6948 12.2317 36.0422 31.1163 12.1731 12.1777 - 75.5532 - 95.7009
calculation
iteration
with eq. (31)
2
~ 146.3585 - 84.9118 - 36.3906 - 12.1303 - 36.0422 18.9642 7.4191 7.4219 - 61.8822 - 107.9672 _ 106.9794 _ 72.63X2 - 0.0036 - 41.5497 with new parameter
iteration
3
~ 146.3585 - 84.9118 - 36.3906 - 12.1303 - 36.0422 18.9642 7.4191 7.4219 - 61.8822 ~ 107.9672 _ 106.9794 - 72.63X2 - 0.0036 - 41.6373 values as a new
458
R. RATNAM and V. S.
PATWARDHAN
number number
of heat exchangers of streams
atures. It has been indicated earlier that when only source temperatures are changed, the 4 values are strictly linear even for large deviations. The third parameter that was changed was one of the heat capacity flow rates which was increased by only 20%. Therefore, the estimate of 45 obtained by using sensitivity tables was quite accurate.
WA)IF, RIP (uA)/‘Fi matrix defined by eq. (27) vector of unknown temperatures
The case of large deviations
eq. (13) source temperature
Let us now consider what happens when both UA and F values are also varied in addition to source temperatures, also by rather large amounts. This will bring out the utility of eq. (3 1) clearly. Consider a case where (UA), is increased by 300%, (UA), and (UA), are reduced by X0”/ each, F4 is increased by 50%, T, is reduced by 50°C and T,, is reduced by 90°C. These are very large parameter changes indeed. Table 6 shows the results obtained both by eq. (15) (i.e. by considering it as a new problem) and by the iterative application of eq. (3 1). First of all, it may be noted that some of the deviations obtained are larger than 100°C due to the large parameter changes. Tn spite of this, it is seen that just two iterations of eq. (31) are enough to calculate deviations correct to four decimal places. The only exception is Tzl, where a third iteration is required to get all four decimals correct. This example, though it involves impractically large parameter changes, clearly brings out the robustness and the inherent convergence possessed by eq. (31). If one attempts to estimate the deviations in this case by using sensitivity tables and adding up the individual deviations, the results are far from satisfactory (for example, #Jo, #+, &Ii and 41s are estimated as ~ 107.77, 24.29, 10.19 and - 100.31”C respectively, which are far different from the exact values shown in Table 6). This is hardly surprising in view of the large changes in parameters. CONCLUSIONS
The partial linearity inherent in heat exchanger networks can be exploited to conduct the complete sensitivity analysis in a very efficient manner. If the effect of simultaneous changes in several parameters (source temperature, UA values and heat capacity flow rates) on network temperatures is to be estimated, one can use eq. (19) or eq. (31) depending upon the magnitude of the changes. Even for very large changes, the iterative procedure of eq. (31) converges rapidly to the correct network temperatures. NOTATION
A B D F
Fi> F,
square design matrix ve\$x in eq. (13)
in eq. (13)
Ab
heat capacity flow rate defined in Fig. 1
temperatures shown in Fig. 1 defined in eq. (23) overall heat transfer coefficient for a heat exchanger
in
x area
Subscripts b k
base case refers to kth equation log mean value output
lm 0
Superscripts
iteration
1, 2, r Greek El, a2 :
\$
numbers
letters
defined by eqs (6) and (7) defined in eq. (21) vector of deviations in network atures defined by eq. (23)
temper-
RRFERENCES
Calandranis, J. and Stephanopoulos, G., 1986, Structural operability analysis of heat exchanger networks. Chem. Engng Res. Des. 64, 347. Halemane, K. P. and Grossmann,
I. E., 1983, Optimal process design under uncertainty. A.1.Ch.E. J. 29, 425. Kern, D. Q., 1950, Process Heat Transfer.McGraw-Hill, New York. Kotjabasakis, E. and Linnhoff, B., 19X6, Sensitivity tables for the design of flexible processes. Chem. Engng Res. Des. 64, 197.
Mars&e, D. F., Morari, M. and Rudd, D. F., 1982, Design of resilient processing plants-II. Design and control of energy management systems. Chem. Engng Sci. 37, 259. Ratnam, R. and Patwardhan, V. S., 1990, Design and simulation of single and multi-oass heat exchangers. Chew Engng (submitted for pub&ion). Saboo, A. K. and Morari, M., 1983. Design of resilient processing plants-IV. Some new result: on heat exchanger network synthesis. Chem. Enana Sci. 39. 579. Saboo,-A. K., MO&i, M. and Woo&&k, D. C., 1985, Design of resilient processing plants~VIII. A resilience
index for heat exchanger networks. Chem. Engng Sci. 40, 1553. Swaney, R. E. and Grossmann, I. E., 1985a, An index for operational flexibility in chemical process design-I. Formulation and theory. A.1.Ch.E. J. 31, 621. Swaney, R. E. and Grossmann, I. E., 1985b, An index for operational flexibility in chemical process design--II. Computational algorithms. A.1.Ch.E. J. 31, 631.
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http://energyeducation.ca/encyclopedia/Celsius
|
# Celsius
Celsius is the standard unit of temperature in the metric system of units. Celsius is split up into degrees, with one degree being 1/100 of the temperature difference between the boiling and freezing points of water. A change by 1 degree Celsius is equal to a change of 1 Kelvin, however the Kelvin scale is offset by +273.15 degrees (0°C = 273.15 K).
## Fun facts
The Celsius scale was created by Anders Celsius, who was a Swedish astronomer. Originally, Anders set 0°C to be the boiling point of water, and 100°C to be the freezing point![1] It is likely that the scale was reversed to how it currently exists (0°C as the freezing point) by Daniel Ekström, a manufacturer of scientific instruments.[2]
The Celsius scale is occasionally referred to as Centigrade, because there are 100 degrees in the scale between the boiling point of water, and its freezing point.[3]
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|
https://www.freqtrade.io/en/2022.12/deprecated/
|
# Deprecated features¶
This page contains description of the command line arguments, configuration parameters and the bot features that were declared as DEPRECATED by the bot development team and are no longer supported. Please avoid their usage in your configuration.
## Removed features¶
### the --refresh-pairs-cached command line option¶
--refresh-pairs-cached in the context of backtesting, hyperopt and edge allows to refresh candle data for backtesting. Since this leads to much confusion, and slows down backtesting (while not being part of backtesting) this has been singled out as a separate freqtrade sub-command freqtrade download-data.
This command line option was deprecated in 2019.7-dev (develop branch) and removed in 2019.9.
### The --dynamic-whitelist command line option¶
This command line option was deprecated in 2018 and removed freqtrade 2019.6-dev (develop branch) and in freqtrade 2019.7. Please refer to pairlists instead.
### the --live command line option¶
--live in the context of backtesting allowed to download the latest tick data for backtesting. Did only download the latest 500 candles, so was ineffective in getting good backtest data. Removed in 2019-7-dev (develop branch) and in freqtrade 2019.8.
### ticker_interval (now timeframe)¶
Support for ticker_interval terminology was deprecated in 2020.6 in favor of timeframe - and compatibility code was removed in 2022.3.
### Allow running multiple pairlists in sequence¶
The former "pairlist" section in the configuration has been removed, and is replaced by "pairlists" - being a list to specify a sequence of pairlists.
The old section of configuration parameters ("pairlist") has been deprecated in 2019.11 and has been removed in 2020.4.
### deprecation of bidVolume and askVolume from volume-pairlist¶
Since only quoteVolume can be compared between assets, the other options (bidVolume, askVolume) have been deprecated in 2020.4, and have been removed in 2020.9.
### Using order book steps for exit price¶
Using order_book_min and order_book_max used to allow stepping the orderbook and trying to find the next ROI slot - trying to place sell-orders early. As this does however increase risk and provides no benefit, it's been removed for maintainability purposes in 2021.7.
### Legacy Hyperopt mode¶
Using separate hyperopt files was deprecated in 2021.4 and was removed in 2021.9. Please switch to the new Parametrized Strategies to benefit from the new hyperopt interface.
## Strategy changes between V2 and V3¶
Isolated Futures / short trading was introduced in 2022.4. This required major changes to configuration settings, strategy interfaces, ...
We have put a great effort into keeping compatibility with existing strategies, so if you just want to continue using freqtrade in spot markets, there are no changes necessary. While we may drop support for the current interface sometime in the future, we will announce this separately and have an appropriate transition period.
Please follow the Strategy migration guide to migrate your strategy to the new format to start using the new functionalities.
### webhooks - changes with 2022.4¶
#### buy_tag has been renamed to enter_tag¶
This should apply only to your strategy and potentially to webhooks. We will keep a compatibility layer for 1-2 versions (so both buy_tag and enter_tag will still work), but support for this in webhooks will disappear after that.
#### Naming changes¶
Webhook terminology changed from "sell" to "exit", and from "buy" to "entry", removing "webhook" in the process.
• webhookbuy, webhookentry -> entry
• webhookbuyfill, webhookentryfill -> entry_fill
• webhookbuycancel, webhookentrycancel -> entry_cancel
• webhooksell, webhookexit -> exit
• webhooksellfill, webhookexitfill -> exit_fill
• webhooksellcancel, webhookexitcancel -> exit_cancel
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http://mathhelpforum.com/differential-equations/175846-use-reduction-order-solve-problem.html
|
# Math Help - use reduction of order to solve the problem...
1. ## use reduction of order to solve the problem...
y''-4y=2; y1=e^(-2x)
i dont see how my text got yp=1/2
ok so this is what i have so far....
let y2=ue^(-2x)
$\large y^{'}=u^{'}e^{-2x}-2ue^{-2x}$
$\large y^{''}=u^{''}e^{-2x}-4u^{'}e^{-2x}+4ue^{-2x}$
so $\large y^{''}-4y = u^{''}e^{-2x}-4u^{'}e^{-2x}$
$\large e^{-2x}[u^{''}-4u^{'}]=0 ; w=u^{'}$
$\large \int (e^{-4x}w)^{'}=\int 0$
$\large w = \frac{c_{1}}{e^{-4x}}$
$\large \int u^{'}=\int \frac{c_{1}}{e^{4x}}; u=c_{2}e^{4x}$
so $\large y_{2}=c_{2}e^{4x}e^{-2x}\rightarrow y_{2}=c_{2}e^{2x}$
$\large y=c_{1}e^{-2x}+c_{2}e^{2x}$
i have the yc part i just dont know how to get the yp..what am i missing or not getting??
2. x''(t)-4x(t)=2. First find the homogeneous x''(t)-4x(t)=0, characteristic equation m^2-4=0, m1/2=+-2, xh=C1*e^(m1*t)+C2*e^(m2*t)=C1e^(2*t)+C2*e^(-2*t). As we see that a non homogeneous part in start equation is 2, xp must be constant. x=xh+xp. Substitute this in start equation (C1*e^2t+C2*e(-2t)+xp)''-4(C1*e^2t+C2*e(-2t)+xp)=2, xp''=0, -4xp=2, xp=-1/2.
Kind regards,
3. derdack, yes, the problem can be solved that way, but I don't believe it is a god idea to advise a person to ignore the teacher's or text's instructions. Slapmaxwell1 says he was instructed to use "reduction of order". It is not at all uncommon to ask a person to solve a simple problem using a more complicated technique in order to practice that technique.
Slapmaxwell1, yes, letting $y= ue^{2x}$ reduces the left side of the equation to $e^{-2x}(u''- 4u')$ but you appear to have left out the right side of the equation. You have $e^{-2x}(u''- 4u')= 2$ so that $u''- 4u'= 2e^{-2x}$ and, letting w= u', $w'- 4w= 2e^{-2x}$.
That is now a first order equation linear equation. It has $e^{-4x}$ as integrating factor:
$e^{-4x}w'- 4e^{-4x}w= (e^{-4x}w)'= 2e^{-4x}$
4. You are right, but it is completly corect that we have other ways for solving which is important for learner. (John - Beautiful mind) .
5. Originally Posted by derdack
You are right, but it is completly corect that we have other ways for solving which is important for learner. (John - Beautiful mind) .
True, but I was taught reduction of order before your method. The different methods come in their own itme.
-Dan
6. Yes. Both of us are right...
7. i am starting to see why you guys were so pissed that i wasnt using latex...I apologize. learning the commands in beginning is a bit troublesome and take a lil extra time, but its totally worth the effort.
8. ok ok i see it now.
if i let $y_{p}=A$ then $y'=0 , y''=0$
ok so $0-4A=2$ so $A=\frac{-1}{2}$
there for $y_{p}=\frac{-1}{2}$ so $y=y_{c}+y_{p}$ because i found Yc I would just put it all together for my final answer. thanks again!
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https://www.physicsforums.com/threads/general-calculus-question.211283/
|
# General Calculus question
1. Jan 27, 2008
### Obsidian
1. The problem statement, all variables and given/known data
Okay, I have here the original equation that we start out with:
f(x) = -2x + 4
2. Relevant equations
I'm supposed to find the slope of that equation. Which is obvious, since it's -2.
But I was supposed to show how it's consistent with the limit definition of slope, which originally looks like this:
[f(x+h) - f(x)] / h
The way they showed it, was by plugging in (x + h) into the x in -2x + 4. My question is, why exactly did they do that? Sorry if it's a stupid question, but it's been bugging me and I would like to know when to plug in the x + h, and when not to when determining slopes.
Thanks in advance!
2. Jan 27, 2008
### neutrino
Well, the value of the function at the point x+h is -2(x+h) + 4.
f(x) = -2x+4
f(x+h) = -2(x+h) + 4
3. Jan 27, 2008
### sutupidmath
well look first of all the slope of the line at any point in the curve is basically the derivative of that function at that point. Now to fully understand this you need to look at the concept of the derivative. However, look here, f(x)-f(a) is merely the change of the function in the y-axes, while h=x-a is the change in the x-axes. now the slope of a line drawn at a poin in the curve is the limit of the change of the function on y-axes over the change of argument in the x-axes, as x-->a or, as h-->0,
this way:
$$\frac{f(x)-f(a)}{x-a}$$ the limit of this as x--->a or
$$\frac{f(a+h)-f(a)}{h}$$ the limit of this as h-->0
4. Jan 27, 2008
### Newton1Law
f'(x) = limit [f(x+h) - f(x)]/h
(as h->0)
f(x) = -2x+4
f'(x) = limit [f(-2(x+h) + 4) - (-2x + 4)]/h
h -> 0
f'(x) = limit [-2x - 2h+ 4 +2x - 4]/h
h -> 0
f'(x) = limit [ -2 h]/h
h-> 0
f'(x) = limit [-2]
h -> 0
f'(x) = -2
Hope this helps.
5. Jan 27, 2008
### Feldoh
As stupid math said [f(x+h) - f(x)] / h is just the average slope of a function.
However according to the mean value theorem there is some point on a closed interval where the average slope is the the same as the instantaneous rate of change (slope) of the function or:
f'(c) = [f(x+h) - f(x)] / h
Since your function is a line this happens to occur everywhere.
6. Jan 27, 2008
### jambaugh
Wo there! you're invoking a jackhammer to pull a staple. It is just a trivial instantiation of the definition of the derivative. If he does the algebra correctly and invokes the definition and the limit laws correctly (which I think is the point of the exercise) he gets the correct answer.
One key step is that the value of the difference quotient is undefined at h=0 but it is "ok" to cancel h's as one is working inside a limit and you invoke the pertinent limit law (f=g except at x=a then limit of f = limit of g at x=a).
7. Jan 27, 2008
### Feldoh
I was just trying to present another way to look at the problem :)
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http://math.stackexchange.com/questions/206183/what-is-the-coefficient-of-zk-in-zn-1-choose-n-for-1-leq-k-leq-n?answertab=oldest
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# What is the coefficient of $z^k$ in ${z+n-1 \choose n}$ for $1 \leq k \leq n$?
What is the coefficient of $z^k$ in ${z+n-1 \choose n}$ for $1 \leq k \leq n$? Thanks. I'm currently looking into Stirling numbers of the first kind, as it seems there is a connection.
-
We prefer questions not to be entirely contained in titles. – Pedro Tamaroff Oct 2 '12 at 20:56
$\displaystyle {z+n-1 \choose n} = \frac{1}{n!} z^{n\uparrow}$, where I use the notation $z^{n \uparrow}$ for the rising factorial.
On the other hand, $\displaystyle z^{n \uparrow} = (-1)^n (-z)^{n\downarrow} = \sum_k (-1)^{n-k} s(n,k) z^k$, so the coefficient is $\displaystyle \frac{1}{n!} (-1)^{n-k} s(n,k) = \frac{1}{n!} |s(n,k)|$.
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https://dsp.stackexchange.com/questions/602/how-do-window-size-sample-rate-influence-fft-pitch-estimation/610
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# How do window size, sample rate influence FFT pitch estimation?
I am trying to create a pitch-detection program which extracts the frequencies of peaks in a power spectrum obtained from an FFT (fftpack). I am extracting the peak frequencies from my spectrum using Quinn's First Estimator to interpolate between bin numbers. This scheme seems to work well under certain conditions. For example, using a rectangular window function with a window size of 1024 and a sample rate of 16000, my algorithm correctly identifies the frequency of a pure A440 tone as 440.06 with a second partial frequency of 880.1. However, under other conditions, it produces inaccurate results. If I change the sample rate (e.g to 8000) or the window size (e.g. to 2048), it still correctly identifies the first partial as 440, but the second partial is somewhere around 892. The problem becomes even worse for inharmonic tones like those produced by a guitar or piano.
My general question is: In what way do the sample rate, window size, and window function affect frequency estimation of FFT peaks? My assumption was that simply increasing the resolution of the spectrum would increase the accuracy of peak frequency estimation, but this is clearly not my experience (zero padding also does not help). I am also assuming that the choice of window function will not have much effect because spectral leakage should not change the peak location (though, now that I think about it, spectral leakage could potentially influence the interpolated frequency estimate if the magnitudes of bins adjacent to the peak are artificially increased by leakage from other peaks...).
Any thoughts?
## migrated from stackoverflow.comNov 7 '11 at 18:53
This question came from our site for professional and enthusiast programmers.
1. Use a Gaussian window - the Fourier transform of a Gaussian is a Gaussian
2. Log-scale the spectrum to emphasize peaks and turn the Gaussian peaks into parabolic peaks
3. Use parabolic interpolation to find the true peaks.
Note that, as mentioned in §D.1, the Gaussian window transform magnitude is precisely a parabola on a dB scale. As a result, quadratic spectral peak interpolation is exact under the Gaussian window. Of course, we must somehow remove the infinitely long tails of the Gaussian window in practice, but this does not cause much deviation from a parabola, as shown in Fig.3.30.
I estimate 1000.000004 Hz for a 1000 Hz waveform this way: https://gist.github.com/255291#file_parabolic.py
If you're having trouble, plot the spectrum and use your eyes to see why it's not working.
• Thank you! This makes perfect sense. The log of a Gaussian is a parabola, so parabolic interpolation of the peaks in a Gaussian-windowed log spectrum is nearly exact. After implementing this, I am getting consistent FFT peak frequency estimates across different sample rates and window sizes. Huzzah! – willpett Nov 9 '11 at 1:26
• @will.pett: So maybe the problem was caused by "Quinn's First Estimator" more than by the FFT? – endolith Nov 9 '11 at 4:35
• I don't think the interpolation method was entirely to blame because quadratic interpolation also gave me bad results with certain window functions and sample rates. I think it was the combination of the above parameters that was important. I was not using the proper window function and had not log-transformed my spectrum. I bet the most important thing was the log-transform. Probably standard protocol that I was just unaware of. – willpett Nov 9 '11 at 5:46
• @endolith, thanks, got it (questions may follow) – denis Nov 16 '13 at 14:51
First, peak frequency estimation and pitch estimation are two different things. Pitch is a psycho-acoustic phenomenon. People can hear a pitch even with the fundamental frequency completely missing, or relatively weak compared to most other peaks, as in the low notes produced by some instruments.
Second, using no window on an FFT is equivalent to using a rectangular window, which convolves your spectrum with the Sinc function. The Sinc function has lot of humps spread far from the peak which will show up for all frequencies that are not exactly periodic in the FFT length (also know as "spectral leakage"). All this energy leakage from one strong frequency will interfere with the position estimation of other frequency peaks. So a more suitable window function (Hamming or von Hann) might help reduce this interference between peaks.
A longer FFT will reduce the delta frequency between bin centers, which should increase interpolation and thus frequency estimation accuracy for stationary spectrums. However if the FFT is so long that the spectrum changes within the FFT window, all those changed frequencies will be blurred together in a longer FFT.
You definitely need a suitable window function - the effects of spectral leakage vary significantly depending on how the pitch period and FFT window length are related - if you get a large transient between the last and first sample of the FFT window then this will produce very nasty smearing of the spectrum, whereas if you get lucky and this discontinuity is small then the resulting spectrum will be a lot cleaner. This is probably why you are seeing inconsistencies when you change any of your parameters such as FFT size. With a suitable window function you will get a consistent spectrum as the pitch changes.
• I have now tried different window functions (Hamming, Blackman-Harris, Gauss, Weedon-Gauss) and all of them give me wildly inaccurate results under any sample rate / window size conditions (e.g estimating the first partial frequency at 460, 488, and others). Only a rectangular window was able to correctly identify a peak at 440 Hz. Interestingly, this peak is largely invariant with different sample-rate/window-size combinations in a rectangular window, though the second partial is still variable. How do I reconcile these results with your advice? – will.pett Nov 7 '11 at 17:16
• As a side note, I am also using an autocorrelation algorithm to compare with the FFT. This method (which is independent of the window function) gives ~440.4 Hz for the wikipedia tone, while the FFT method gives nearly exactly 440 without a window function. I realize that autocorrelation does not directly estimate the first partial frequency, but rather the psychoacoustic "pitch", but it is still interesting to compare. From experimenting with piano tones, I have noticed that the autocorrelation method consistently overestimates the first partial frequency compared with the FFT method. – will.pett Nov 7 '11 at 17:28
• It's hard to guess what the problems might be without seeing the code etc. Have you tried plotting the power spectrum to see what the peaks actually look like with/without a window function ? This should not only tell you whether your windowing/FFT/etc is behaving correctly but also may give you some insight as to why your pitch estimation algo is giving the results that it does. – Paul R Nov 7 '11 at 20:10
• It is weird, because the window functions do indeed produce cleaner looking spectra, with little smearing. However, the estimates of the peak frequencies are not right. When I use the settings that give me 440 Hz with no windowing, then switch to a Hamming window, I get 444.6 Hz. With a Blackman-Harris window I get 460.9 Hz, and with a Gaussian window I get 446.4 Hz. Is it possible that peak interpolation methods make implicit assumptions about the window function that I might be violating? – willpett Nov 7 '11 at 22:16
• I'm not really familiar with the interpolation methods in the article that you link to - they seem to be using both magnitude and phase information rather than just magnitude, but I wouldn't have thought that windowing would have a significant impact on phase. – Paul R Nov 7 '11 at 22:49
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https://atarnotes.com/forum/index.php?topic=185904.0
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January 21, 2020, 10:20:22 am
AuthorTopic: I have a question on binomials (Read 186 times) Tweet Share
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_.aliciaaa_
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I have a question on binomials
« on: June 10, 2019, 03:44:06 pm »
0
in the expansion of (ax + b)6, the coefficient of x4 is 2160 and the coefficient of x5 is −576. Find a and b.
I don't understand these types of questions so I will really appreciate an explanation
thank you
RuiAce
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Re: I have a question on binomials
« Reply #1 on: June 10, 2019, 06:13:11 pm »
+1
To help build your understanding, recall that the general form of the binomial expansion is
$(a+b)^n = \binom{n}{0}a^n + \binom{n}{1}a^{n-1}b + \binom{n}{2}a^{n-2}b^2 + \binom{n}{3}a^{n-3}b^3 + \dots + \binom{n}{n-2}a^2 b^{n-2} + \binom{n}{n-1}ab^{n-1}+\binom{n}{n}b^n.$
The idea is that each term is of the form $\boxed{\binom{n}{k}a^{n-k}b^k}$. This expression is therefore referred to as the 'general term' of the expansion of $(a+b)^n$.
Whereas in your example, because you're dealing with $(ax+b)^6$, your general term is of the form $\boxed{\binom{6}{k} (ax)^{6-k}b^k}$. And after using your index laws, it rearranges to $\boxed{\binom{6}{k} a^{6-k}b^k x^{6-k}}$.
Since you want to find the term with $x^4$, you first set the power on $x$ equal to 4. This gives you $6-k=4$, so $k=2$. Then, the coefficient is obtained by subbing back in for $k$, but blocking out the $x$'s. So the coefficient of $x^4$ is $\boxed{\binom62 a^4b^2}$. If this is equal to 2160, then you first have
$15 a^4 b^2 = 2160.$
Note that the value of $\binom62$ was computed on the calculator.
You should have a go at repeating the procedure for $x^5$ now and finish off the question. If you're stuck, please provide extra details.
(Note that to fully finish the question, you will need simultaneous equations here.)
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https://algorithmist.com/index.php/UVa_10900
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UVa 10900
Summary
You are a player on a quiz show. In the beginning, you have \$1. For each correct answer this price doubles, but once you give a wrong answer, you lose everything. The game is over either after you decide to stop, or after you answer ${\displaystyle n}$ questions.
Each time you are given a question, you think for a while, and come up with a possible answer. You can also estimate the probability ${\displaystyle p}$ that your answer is correct. Based on this ${\displaystyle p}$ you can decide whether you will stop playing (and take the current price), or try to answer the question.
What is your expected price, if you use an optimal strategy?
Assume that ${\displaystyle p}$ is a random variable uniformly distributed over the interval ${\displaystyle [t,1]}$.
Explanation
First of all, we will explain the last sentence. Take a lot of questions, try to answer each of them, and each time write down the value ${\displaystyle p}$. That sentence says that the numbers you have written down will all come from the interval ${\displaystyle [t,1]}$ and they will be approximately uniformly distributed.
Now, what is the optimal strategy?
Suppose that your current price is ${\displaystyle C}$, and that the probability of answering the current question right is ${\displaystyle p}$. If you keep the price, you will gain ${\displaystyle C}$. If you answer the question, with probability ${\displaystyle p}$ you will have ${\displaystyle C}$ and you will still be in the game with one question less to answer, with probability ${\displaystyle (1-p)}$ you gain nothing and you are out.
If this is the last question, the expected price if you answer the question is ${\displaystyle 2pC}$. If this is more than ${\displaystyle C}$, you should answer the question, otherwise you shouldn't.
Now consider the general case. Let ${\displaystyle f(k)}$ be the answer we seek – the expected price, if you have ${\displaystyle k}$ questions left and play optimally. How to compute it? If you don't answer, you will get ${\displaystyle 2^{n-k}}$ dollars. If you do, you have the probability ${\displaystyle p}$ that you get the price ${\displaystyle f(k-1)}$.
When you will be in this situation, you will know the exact value ${\displaystyle p}$, thus your expected price will be ${\displaystyle \max \left(2^{n-k},p.f(k-1)\right)}$.
But when we compute our answer, we don't know the question you are going to get. What now? We will simply take an "average over all possible values of p". (As there is an infinite number of possible values, the "average" will actually be an integral.)
We get the following recurrence:
• ${\displaystyle f(0)=2^{n}}$
• ${\displaystyle f(k)={1 \over 1-t}\cdot \int _{t}^{1}\max \left(2^{n-k},p.f(k-1)\right)dp}$
Using them, we can compute the values ${\displaystyle f(k)}$ and output the value ${\displaystyle f(n)}$.
Implementations
An easy way of computing ${\displaystyle f(k)}$: split the integral into two parts, on the first part integrate the constant function ${\displaystyle 2^{n-k}}$, on the second part integrate the linear function ${\displaystyle p.f(k-1)}$.
A More Formal Approach
First we define a couple of random variables. Let ${\displaystyle X_{k}}$ denote the amount that you win when you have ${\displaystyle k}$ questions left, and let ${\displaystyle P_{k}}$ denote the probability that you'll answer the next question correctly when you have ${\displaystyle k}$ questions left.
We want to determine ${\displaystyle E(X_{n})}$, which is the expected prize when there are ${\displaystyle n}$ questions left.
We use ${\displaystyle E(X_{k}|P_{k}=p)}$ to denote the conditional expected value of ${\displaystyle X_{k}}$ given that ${\displaystyle P_{k}=p}$. This is just the expression that was derived above.
${\displaystyle E(X_{k}|P_{k}=p)=\max \left(2^{n-k},p.f(k-1)\right)}$
where ${\displaystyle f(k-1)=E(X_{k-1})}$.
Now, as explained above, we don't know the value of ${\displaystyle p}$. The solution above was to "average over all possible values of p". This is the correct thing to do, but here's the formal justification for this step:
There is a theorem from probability theory which says that ${\displaystyle E(X_{k})=E(E(X_{k}|P_{k}))}$. (See, for example, section 7.5.2, "Computing Expectations by Conditioning", in _A First Course in Probability_ by Sheldon Ross, to see why this theorem holds.)
${\displaystyle E(X_{k})=E(E(X_{k}|P_{k}))=\int _{-\infty }^{\infty }E(X_{k}|P_{k}=p)\cdot f_{P_{k}}(p)dp}$
where ${\displaystyle f_{P_{k}}(p)}$ is the density function of ${\displaystyle P_{k}}$. Since ${\displaystyle P_{k}}$ is uniformly distributed over ${\displaystyle t..1}$, it follows that
• ${\displaystyle f_{P_{k}}(p)={1 \over 1-t}}$ for t <= p <= 1 and
• ${\displaystyle f_{P_{k}}(p)=0}$ for p < t or p > 1
Plugging the density function and the conditional expected value into the expression for ${\displaystyle E(X_{k})}$ yields the same results as above:
• ${\displaystyle f(0)=E(X_{0})=2^{n}}$
• ${\displaystyle f(k)=E(X_{k})={1 \over 1-t}\cdot \int _{t}^{1}\max \left(2^{n-k},p.f(k-1)\right)dp}$
Input
1 0.5
1 0.3
2 0.6
24 0.25
30 0.8
0 0
Output
1.500
1.357
2.560
230.138
45517159.608
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https://cs.stackexchange.com/questions/123969/unordered-pairs-in-homotopy-type-theory
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# Unordered pairs in Homotopy Type Theory
It's conceptually simple to state what an "unordered pair" is supposed to be in set theory. Yet, in homotopy type theory I have trouble formalizing this. A first naive try in agda syntax:
data UPair (A : Type ℓ) : Type ℓ where
mkpair : (x y : A) → UPair A
uswap : ∀ a b → mkpair a b ≡ mkpair b a
This fails, since there are actually two different paths between e.g. mkpair 1 2 and mkpair 2 1, that is we have uswap 1 2 and sym (uswap 2 1). Again, these can be forced equal by a one-higher path constructor, but one would have to continue for ever.
Obviously, if A is an n-truncated type, we can stop at some point. Generally truncating at some level fails because it might forget some non-trivial paths in A. Take for example the set-truncation of the above type and A = S¹, the circle, then the path i. mkpair (loop i) base is lost and identified with refl (mkpair base base).
Can we generally write down the type of unordered pairs of a parameter A : Type ℓ? Can the resulting type live inside the universe ℓ?
Clarification:
Let A· = (A , a) be a pointed type. Define UPA· = (UPair A, mkpair a a) as a pointed type. I would then expect Ωₜ UPA· ≡ UPair (Ωₜ A·). These correspond to singleton sets.
Let A∙ = (A, a, b) be a bipointed type with a ≢ b. Then I expect that the map (a ≡ a) × (b ≡ b) → mkpair a b ≡ mkpair b a given by (pa , pb) → (λ i → mkpair (pa i) (pb i)) ∙ uswap a b is an equivalence.
The type of unordered pairs in a type $$A$$ is defined to be $$\sum_{(X:\mathcal{U})}\sum_{(H:\|X\simeq \mathsf{bool}\|)}A^X.$$ In other words, an undordered pair in $$A$$ is simply a map $$X\to A$$ from a type $$X$$ that merely has two elements.
Note that in general, this is not a set, because the type of 2-element types is not a set but a 1-type. The way to think about this is that unordered pairs have some symmetries (swapping the order of the elements in the unordered pairs) that should be taken into account in homotopy type theory.
Note that the type of unordered pairs can also be used to define the type of fully coherent commutative binary operations on a type $$A$$. This type is simply $$\Big(\sum_{(X:\mathcal{U})}\sum_{(H:\|X\simeq\mathsf{bool}\|)}A^X\Big)\to A.$$ In other words, a fully coherent commutative binary operation on $$A$$ is an operation on the unordered pairs of $$A$$.
• Another application of the same idea is the type of non-planar binary trees: it is the inductive type $T$ equipped with a base point $r:T$ and an operation $\mathsf{unordered{-}pairs}(T)\to T$ Apr 12, 2020 at 19:02
• At first sight, this seems like a straightforward definition with the correct paths, at least I think I can see how to define mkpair and a better version of uswap that doesn't have the problems I had. Very insightful. This generalizes to n-tuples (and other container types) where equivalence is permutations?! Apr 12, 2020 at 19:13
• It generalizes indeed. The type of unordered lists of elements in $A$ is defined to be $S(A):=\sum_{X:\mathbb{F}}A^X$ where $\mathbb{F}$ is the type of all merely finite types. The type $S(A)$ should be the free symmetric monoid on $A$, although to state that, you'd have to solve an infinite coherence problem. Apr 12, 2020 at 19:37
• Nevertheless, you can still pretty easily define some of the low-dimensional structure on $S(A)$, that you'd expect from the free symmetric monoid. Apr 12, 2020 at 19:40
The set of unordered pairs of A can be defined using a higher-inductive type with set-truncation, just as you suggested, somewhat like this (I am writing this off the top of my head without verifying it in Agda, but you'll get the point):
data UPair (A : Type ℓ) : Type ℓ where
mkpair : (x y : A) → UPair A
uswap : ∀ a b → mkpair a b ≡ mkpair b a
trunc : ∀ (u v : UPair A) (p q : u ≡ v) → p ≡ q
It is obvious that UPair A is a set (is a $$0$$-type) because trunc directly witnessess this fact. You do not have to add any higher-path constructors.
• Maybe I'm overthinking. This is somewhat unsatisfactory since UPair A ≡ UPair ∥ A ∥₀ for any A, so it is the set of unordered sets (though perfectly good for that). Apr 12, 2020 at 12:15
• If A is not a set, then what do you expect UPair A to be, mathematically speaking? For instance, what is UPair S¹? Apr 12, 2020 at 14:11
• Since the loop space Ω S¹ is Int, I would expect Ω (UPair S¹) to be UPair Int. Apr 12, 2020 at 14:23
• UPair S¹ should be like the torus S¹ x S¹ but you can swap the two directions "up" and "around". Apr 12, 2020 at 14:29
• Naive informal descriptions do not reveal what higher-path structure you might be thinking of. What does this "swap" mean, are you talking about a homotopy pushout of some sort, or what? For instance, would you expect UPair A to have the same truncation level as A? Apr 12, 2020 at 14:37
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https://events.las.iastate.edu/category/event-type/seminar/
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# Category: Seminar
## Mathematical Biology Seminar: Modeling gene regulatory network dynamics at single-cell resolution
Speaker: Adam MacLean, University of Southern California https://g.co/kgs/5y6b2f Abstract: Since single-cell RNA sequencing technologies have become widespread, great efforts have been made to develop appropriate computational methods to learn biological features from high dimensional datasets. Much less effort has gone into the important yet challenging task of inferring dynamics from these genomic data. Here we … Continue reading Mathematical Biology Seminar: Modeling gene regulatory network dynamics at single-cell resolution
Wednesday, April 14, 3:20-4:10pm | Zoom
## Probability, Analysis, and Data Science (PADS) Seminar: Regime-Switching Jump-Diffusion Processes with Countable Regimes
Speaker: Chao Zhu (University of Wisconsin-Milwaukee) Abstract: This work focuses on a class of regime-switching jump diffusion processes, which is a two component Markov processes $(X(t),\Lambda(t))$, where the analog component $X(t) \in R^{d}$ models the state of interest while the switching component $\Lambda(t)\in \{1,2,\dots\}$ can be used to describe the structural changes of the state … Continue reading Probability, Analysis, and Data Science (PADS) Seminar: Regime-Switching Jump-Diffusion Processes with Countable Regimes
Wednesday, April 14, 4:10-5:00pm | Zoom
## Mathematics and Deep Learning (MDL) Collective Seminar: Solving Inverse Problems with Deep Learning
Speaker: Lexing Ying (Stanford University) Abstract: This talk is about some recent progress on solving inverse problems using deep learning. Compared to traditional machine learning problems, inverse problems are often limited by the size of the training data set. We show how to overcome this issue by incorporating mathematical analysis and physics into the design … Continue reading Mathematics and Deep Learning (MDL) Collective Seminar: Solving Inverse Problems with Deep Learning
Friday, April 16, 4:00-5:15pm | Zoom
## Mathematical Biology Seminar
Speaker: Nancy Rodriguez, UC Boulder Title: TBA
Wednesday, April 21, 3:20-4:10pm | Zoom
## Mathematical Biology Seminar
Speaker: Ivana Bozic, University of Washington Title: TBA
Wednesday, April 28, 3:20-4:10pm | Zoom
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https://qiskit.org/documentation/locale/pt_BR/stubs/qiskit.circuit.Delay.html
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# qiskit.circuit.Delay¶
class Delay(duration, unit='dt')[código fonte]
Do nothing and just delay/wait/idle for a specified duration.
Create new delay instruction.
__init__(duration, unit='dt')[código fonte]
Create new delay instruction.
Methods
__init__(duration[, unit]) Create new delay instruction. add_decomposition(decomposition) Add a decomposition of the instruction to the SessionEquivalenceLibrary. Assemble a QasmQobjInstruction broadcast_arguments(qargs, cargs) Validation of the arguments. c_if(classical, val) Add classical condition on register or cbit classical and value val. copy([name]) Copy of the instruction. Special case. Return True .IFF. DEPRECATED: use instruction.reverse_ops(). Return a default OpenQASM string for the instruction. Creates an instruction with gate repeated n amount of times. For a composite instruction, reverse the order of sub-instructions. soft_compare(other) Soft comparison between gates. Return a Numpy.array for the unitary matrix. validate_parameter(parameter) Delay parameter (i.e.
Attributes
decompositions Get the decompositions of the instruction from the SessionEquivalenceLibrary. definition Return definition in terms of other basic gates. duration Get the duration of this delay. label Return instruction label params return instruction params. unit Get the time unit of duration.
add_decomposition(decomposition)
Add a decomposition of the instruction to the SessionEquivalenceLibrary.
assemble()
Assemble a QasmQobjInstruction
broadcast_arguments(qargs, cargs)[código fonte]
Validation of the arguments.
Parâmetros
• qargs (List) – List of quantum bit arguments.
• cargs (List) – List of classical bit arguments.
Yields
Tuple(List, List) – A tuple with single arguments.
Levanta
CircuitError – If the input is not valid. For example, the number of arguments does not match the gate expectation.
c_if(classical, val)[código fonte]
Add classical condition on register or cbit classical and value val.
copy(name=None)
Copy of the instruction.
Parâmetros
name (str) – name to be given to the copied circuit, if None then the name stays the same.
Retorna
a copy of the current instruction, with the name
updated if it was provided
Tipo de retorno
qiskit.circuit.Instruction
property decompositions
Get the decompositions of the instruction from the SessionEquivalenceLibrary.
property definition
Return definition in terms of other basic gates.
property duration
Get the duration of this delay.
inverse()[código fonte]
Special case. Return self.
is_parameterized()
Return True .IFF. instruction is parameterized else False
property label
Return instruction label
Tipo de retorno
str
mirror()
DEPRECATED: use instruction.reverse_ops().
Retorna
a new instruction with sub-instructions
reversed.
Tipo de retorno
qiskit.circuit.Instruction
property params
return instruction params.
qasm()
Return a default OpenQASM string for the instruction.
Derived instructions may override this to print in a different format (e.g. measure q[0] -> c[0];).
repeat(n)
Creates an instruction with gate repeated n amount of times.
Parâmetros
n (int) – Number of times to repeat the instruction
Retorna
Containing the definition.
Tipo de retorno
qiskit.circuit.Instruction
Levanta
CircuitError – If n < 1.
reverse_ops()
For a composite instruction, reverse the order of sub-instructions.
This is done by recursively reversing all sub-instructions. It does not invert any gate.
Retorna
a new instruction with
sub-instructions reversed.
Tipo de retorno
qiskit.circuit.Instruction
soft_compare(other)
Soft comparison between gates. Their names, number of qubits, and classical bit numbers must match. The number of parameters must match. Each parameter is compared. If one is a ParameterExpression then it is not taken into account.
Parâmetros
other (instruction) – other instruction.
Retorna
are self and other equal up to parameter expressions.
Tipo de retorno
bool
to_matrix()[código fonte]
Return a Numpy.array for the unitary matrix. This has been added to enable simulation without making delay a full Gate type.
Retorna
matrix representation.
Tipo de retorno
np.ndarray
property unit
Get the time unit of duration.
validate_parameter(parameter)[código fonte]
Delay parameter (i.e. duration) must be int, float or ParameterExpression.
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|
http://mathhelpforum.com/statistics/185229-another-expectation-through-conditioning-question.html
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# Math Help - Another Expectation through conditioning question
1. ## Another Expectation through conditioning question
(1) A gambler wins each game with probability p. In each of the following cases, determine the expected total number of wins.
(a) The gambler will play n games; if he wins X of these games, then he will play an additional X games before stopping.
(b) The gambler will play until he wins; if it takes him Y games to get this win, then he will play an additional Y games.
I'm having some trouble wrapping my head around this one.
So far, for part A I'm looking at it like this
E[W]=E[W|wins X games]P(wins X games)
That line of thinking gets me
$(xp+np)$ ${n}\choose{x}$ $p^{x}(1-p)^{n-x}$
2. ## Re: Another Expectation through conditioning question
The wording of the question is confusing. Is it saying that if the gambler wins a specific number of games, he'll get to play that many more games? Or is is it saying that every time he wins, he'll get to play an additional game?
3. ## Re: Another Expectation through conditioning question
It's the first way you wrote.
The answer for A. comes out to be np(1+p)
But I'm not exactly sure on how it's found.
I hope that clarifies it a bit.
4. ## Re: Another Expectation through conditioning question
Are you sure that's the answer?
Let W= the number of wins
let X = the event that the gambler wins X of his first n games
$E(W) = E(W|X)P(X) + E(W|X^{c})P(X^{c})$
= $(x+xp) \binom{n}{x} p^{x}(1-p)^{n-x} + E(W|X^{c}) (1- \binom{n}{x} p^{x}(1-p)^{n-x})$
Let Z ~ binom(n,p). Then $E(Z) = \sum_{z=0}^{n} z \binom{n}{z} p^{z}(1-p)^{n-z} = np$
therefore, $E(W|X^{c}) = np - x \binom{n}{x} p^{x}(1-p)^{n-x}$
$E(W) = (x+xp) \binom{n}{x} p^{x}(1-p)^{n-x} + \big( np - x\binom{n}{x}p^{x}(1-p)^{n-x} \big) \big(1- \binom{n}{x} p^{x}(1-p)^{n-x}\big)$
Perhaps with some creative manipulation you can show that the above equals np(1+p), but I doubt it.
5. ## Re: Another Expectation through conditioning question
I agree that the answer I gave seems a bit simple, but that's the answer that the professor gave us. I'll try to get clarification the next time class meets. It seems like much of the class is struggling right now.
6. ## Re: Another Expectation through conditioning question
I didn't calculate $E(W|X^{c})$ correctly. But I still don't get than answer (although it's a bit closer).
$E(W|X^{c}) = E(W|W \ne x) = \sum w P(W=w|W \ne x)$ where w=x is not included in the sum
$= \sum \frac{w P(W=w \cap W \ne x)}{P(W \ne x)}$
$= \frac{1}{P(W \ne x)} \sum w P(W=w)$
$= \frac{np - x \binom{n}{x}p^{x}(1-p)^{n-x}}{1- \binom{n}{x} p^{x} (1-p)^{n-x}}$
so $E(W) = (x+xp) \binom{n}{x} p^{x}(1-p)^{n-x} + np - x \binom{n}{x} p^{x} (1-p)^{n-x}$
$= xp \binom{n}{x} p^{x}(1-p)^{n-x} + np$
7. ## Re: Another Expectation through conditioning question
The professor solved a similar problem in class, but the procedure seems to work properly with these problems as well.
This is how the solution was presented in class:
Let N be the total number of wins
Let X be the number of wins in the first N games
(a) The gambler will play n games; if he wins X of these games, then he will play an additional X games before stopping.
$E[N]=E[E[N|X]]$
$E[N|X]=X+Xp$
So we have,
$E[X+Xp]=E[X]+pE[X]=np+np^2=np(1+p)$
8. ## Re: Another Expectation through conditioning question
We weren't treating X as a random variable.
9. ## Re: Another Expectation through conditioning question
$E(W) = 0 \binom{n}{0} p^{0}(1-p)^{n} + (1+p) \binom{n}{1} p^{1}(1-p)^{n-1} + (2+2p) \binom{n}{2} p^{2}(1-p)^{n-2} + \ldots + (n+np) \binom{n}{n} p^{n}(1-p)^{0}$
$= (1+p) \sum_{k=1}^{n} k \binom{n}{k} p^{k}(1-p)^{n-k}$
$= np(1+p)$
10. ## Re: Another Expectation through conditioning question
Do you have the answer to part (b)?
$E(W) = (1+p)p + (1+2p)(1-p)p + (1+3p)(1-p)^{2}p + \ldots$
$= \Big( p +(1-p)p + (1-p)^{2}p + \ldots \Big) + p \sum_{k=1}^{\infty}k(1-p)^{k-1} p$
$= 1 + \frac{p}{p} = 2$ which is a very strange answer
11. ## Re: Another Expectation through conditioning question
I have $1+\frac{1}{p}$ written down, but it wasn't explained how to do it.
12. ## Re: Another Expectation through conditioning question
$1 + \frac{1}{p}$ is the solution I got first when I wrote
$E(W) = (1+p)p + (2+2p)(1-p)p + (3+3p)(1-p)^{2}p$
$= (1+p) \sum_{n=1}^{\infty}n (1-p)^{n}p = \frac{1+p}{p}$
but $E(W|Y=k) = 1 + kp$ not $k + kp$ like in part (a).
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http://www.cram.com/flashcards/astr-cont-436565
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### 17 Cards in this Set
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conservation of momentum momentum can't change unless external force acts on them -when 2 balls hit the combined momentum after htey hit is the same as before (no external forces) conservation of angular momentum -can be change only by TORQUE (twisting force) -obj can only change its own momentum by transferrings ome to or from another object -earth needs no fuel!! -bc earth's angular speed depends on its distance from the sun its speed must be faster when its closer to the sun (radius is shorter) conservation of energy objects can gain or lose energy only by exchanging energy w other objects = all actions in universe involve exchanges of energy or conversion to another form 3 types of energy kinetic radiative potential kinetic energy objects in motion have kinetic energy potential energy stored energy - can be converted to kinetic or radiative radiative energy energy carried by light -why light can cause changes in matter (warm) thermal energy collective kinetic energy of many individual particals (temperature measure the avg kinetic energy of particals) -higher temp means particles have a higher average kinetic energy) gravitational potential energy depends on its mass and how far it can fall due to gravity (has more when higher up) mass-energy energy contained in mass itself -mass is a form of potential energy E= mc^2 (E= amt of potential energy) gravity extended to kepler's laws kepler's laws are consequences of the laws of motion and the universal law of gravitation KEPLER'S 2ND LAW: -planet moves faster when closer to sun (conservation of angular momentum) KEPLER'S 3RD LAW: -avg orbital speed higher for planets w smaller orbital distance -- --Planets closer to sun have stronger gravitational attraction "epicycle" the SMALL CIRCLE that turns around a bigger circle (as shown in the ptolemaic model) universal law of gravitation -every mass attracts every other mass thru a force called gravity -strength of gravity atrracting 2 objects is proportional to product of their masses (doubling one's mass doulbes force between them) -strength of gravity between 2 objects decreases w/ square of distance between their centers (doulbing their distance weakens the force by 2^2 (4) "spacetime" time dilation (time moves slower when moving faster) argues time and space cannot be seperated -must be consided a SINGLE ENTITY to push mass faster than the speed of light... would require an infinite amt of energy E=mc^2 potential energy (3 types?) 1)GRAVITATIONAL 2)CHEMICAL 3)ELECTRICAL increasing thermal energy? Decreasing thermal energy? increasing thermal energy = -causes bonds to break (dissociation, ionization, -plasma phase) decreasing thermal energy: -forms bonds, makes bonds stronger -
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https://www.physicsforums.com/threads/volume-of-a-sphere-problem.100731/
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# Homework Help: Volume of a sphere problem
1. Nov 20, 2005
### skivail
i need to be able to solve a problem like this for a test on monday. please solve, showing work, so i can trace your steps to teach myself.
a spherical balloon is inflated so that its volume is increasing at the rate of 6ft^3/minute. how fast is the diameter of the balloon increasing when the radius is 1 feet? reminder: volume of a sphere= 4/3 (pi)r^3
2. Nov 20, 2005
### Tide
Just differentiate with respect to time. The left side will be dV/dt and the right side will contain a factor of dr/dt which is rate at which the RADIUS changes. Be sure to rewrite it in terms of the DIAMETER.
3. Nov 20, 2005
### ms. confused
-Substitute (D(t)/2)^3 for r in V=4/3 (pi)r^3.
-When simplified you get pi/6(D(t))^3.
-Differentiate and you get V'= pi/6[3(D(t))^2] [D'(t)] (implicit diff.)
-plug in the numbers--remember any variable with the ' means it's a rate, a unit over time
- I got 3.8197 ft/min. but if you have an answer key go with that.
I really hope this helps! Good luck on your test!
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https://impartiallyderivative.com/category/confidential-computing/
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http://mathhelpforum.com/discrete-math/195328-no-possible-words-print.html
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# No. of possible 'words'
Printable View
• January 15th 2012, 06:15 AM
Punch
No. of possible 'words'
In this question, a 'word' is defined to be any set of letters in a row, whether of not it makes sense. Find how many different 'words' can be made using only 5 letters of the word SYLLABUS
I tried to separate them into 4 cases,
1) all different letters
2) 2 'S'
3) 2 'L'
4)2 'S' and 2 'L'
• January 15th 2012, 01:14 PM
Soroban
Re: No. of possible 'words'
Hello, Punch!
Quote:
In this question, a 'word' is defined to be any set of letters in a row,
whether of not it makes sense. . Find how many different 'words'
can be made using only 5 letters of the word SYLLABUS.
I tried to separate them into 4 cases,
1) all different letters
2) two S's
3) two L's
4) two S's and two L's
An excellent game plan! How far did you get?
We have 8 letters, 6 distinct: . $A,B,LL,SS,U,Y$
1) Five different letters
. . Choose 5 of the 6 letters and permutate them:. $_6P_5 \,=\,720$
2) Two S's: . $S\,S\,\_\,\_\,\_$
. . Choose 3 of the other 5 letters:. $_5C_3 \,=\,10$
. . and permute the 5 letters:. $10\cdot\tfrac{5!}{2!} \,=\,600$
3) Two L's:. $L\,L\,\_\,\_\,\_$
. . Choose 3 of the other 5 letters:. $_5C_3\,=\,10$
. . and permutate the 5 letters:. $10\cdot\tfrac{5!}{2!}\,=\,600$
4) Two S's, two L's:. $S\,S\,L\,L\,\_$
. . Choose 1 of the other 4 letters:. $_4C_1\,=\,4$
. . and permutate the 5 letters:. $4\cdot\tfrac{5!}{2!\,2!}\,=\,120$
There are:. $720 +600 + 600 +120 \:=\:2040$ "words".
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https://en.wikipedia.org/wiki/Carbonic_acid
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# Carbonic acid
Carbonic acid
Names
IUPAC name
Carbonic acid[1]
Other names
Hydroxyformic acid
Hydroxymethanoic acid
Dihydroxycarbonyl
Identifiers
3D model (JSmol)
ChEBI
ChEMBL
ChemSpider
DrugBank
ECHA InfoCard 100.133.015
EC Number
• 610-295-3
25554
KEGG
UNII
• InChI=1S/CH2O3/c2-1(3)4/h(H2,2,3,4)
Key: BVKZGUZCCUSVTD-UHFFFAOYSA-N
• InChI=1/H2O3/c2-1(3)4/h(H2,2,3,4)
Key: BVKZGUZCCUSVTD-UHFFFAOYAU
• O=C(O)O
Properties
H2CO3
Appearance Colorless gas
Melting point −53 °C (−63 °F; 220 K)[2] (sublimes)
Boiling point 127 °C (261 °F; 400 K) (decomposes)
Reacts to form carbon dioxide and water
Conjugate base Bicarbonate, Carbonate
Hazards
NFPA 704 (fire diamond)
Structure
monoclinic
p21/c, No. 14
-
a = 5.392 Å, b = 6.661 Å, c = 5.690 Å
α = 90°, β = 92.66°, γ = 90°[3]
(D2CO3 at 1.85 GPa, 298 K)
204.12 Å3
4 formula per cell
Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa).
In chemistry, carbonic acid is an inorganic compound with the chemical formula H2CO3. As a dilute solution in water, it is pervasive, but the pure compound, a colorless gas, can only be obtained at temperatures around −80 °C. The molecule rapidly converts to water and carbon dioxide in the presence of water, however in the absence of water, against contrary belief, it is quite stable at room temperature.[4][5] The interconversion of carbon dioxide and carbonic acid is related to the breathing cycle of animals and the acidity of natural waters.[6]
In biochemistry and physiology, the name "carbonic acid" is often applied to aqueous solutions of carbon dioxide, which play an important role in the bicarbonate buffer system, used to maintain acid–base homeostasis.[7]
## Chemical equilibria
### Equilibrium constant values
Bjerrum plot for carbonate speciation in seawater (ionic strength 0.7 mol dm−3)
In aqueous solution carbonic acid behaves as a dibasic acid. The Bjerrum plot shows typical equilibrium concentrations, in solution, in seawater, of carbon dioxide and the various species derived from it, as a function of pH.[8][9] The acidification of natural waters is caused by the increasing concentration of carbon dioxide in the atmosphere, which is caused by the burning of increasing amounts of coal and hydrocarbons.[10][11]
Expected change refers to predicted effect of continued ocean acidification.[12] It has been estimated that the increase in dissolved carbon dioxide has caused the ocean's average surface pH to decrease by about 0.1 from pre-industrial levels.
The stability constants database contains 136 entries with values for the overall protonation constants, β1 and β2, of the carbonate ion. In the following expressions [H+] represents the concentration, at equilibrium, of the chemical species H+, etc.
The value of log β1 decreases with increasing ionic strength, ${\displaystyle {\ce {I}}}$. At 25 °C:
${\displaystyle {\ce {CO3^{2-}{+ H+}<=> HCO3^-}}}$ : ${\displaystyle \beta _{1}={\frac {[{\text{HCO}}_{3}^{-}]}{[{\text{H}}^{+}][{\text{CO}}_{3}^{2-}]}}}$
${\displaystyle \log \beta _{1}=0.54I^{2}-0.96I+9.93}$ (selected data from SC-database)
The value of log β2 also decreases with increasing ionic strength.
${\displaystyle {\ce {CO3^{2-}{+ 2H+}<=> H2CO3}}}$ : ${\displaystyle \beta _{2}={\frac {[{\text{H}}_{2}{\text{CO}}_{3}]}{[{\text{H}}^{+}]^{2}[{\text{CO}}_{3}^{2-}]}}}$
${\displaystyle \log \beta _{2}=-2.5I^{2}-0.043I+16.07}$
At ${\displaystyle {\ce {I}}}$=0 and 25 °C the pK values of the stepwise dissociation constants are
pK1 = logβ2 - logβ1 = 6.77.
pK2 = logβ1 = 9.93.
When pH = pK the two chemical species in equilibrium with each other have the same concentration.
Note 1: There are apparently conflicting values in the literature for pKa. Pines et al. cite a value for "pKapp" of 6.35, consistent with the value 6.77, mentioned above.[13] They also give a value for "pKa" of 3.49 and state that
pKa = pKapp − log KD (eqn. 5)
where KD=[CO2]/[H2CO3]. (eqn. 3) The situation arises from the way that the dissociation constants are named and defined, which is clearly stated in the text of the Pines paper, but not in the abstract.
Note 2: The numbering of dissociation constants is the reverse of the numbering of the numbering of association constants, so pK2 (dissociation)= log β1 (association). The value of the stepwise constant for the equilibrium
${\displaystyle {\ce {HCO3- <=> CO3^{2-}{+ H+}}}}$
is given by
pK1(dissociation)1 = log β2 − log β1 (association)
### In non-biological solutions
The hydration equilibrium constant at 25 °C is called Kh, which in the case of carbonic acid is [H2CO3]/[CO2] ≈ 1.7×10−3 in pure water[14] and ≈ 1.2×10−3 in seawater.[15] Hence, the majority of the carbon dioxide is not converted into carbonic acid, remaining as CO2 molecules. In the absence of a catalyst, the equilibrium is reached quite slowly. The rate constants are 0.039 s−1 for the forward reaction and 23 s−1 for the reverse reaction.
In the beverage industry, sparkling or "fizzy water" is usually referred to as carbonated water. It is made by dissolving carbon dioxide under a small positive pressure in water. Many soft drinks treated in the same way make them effervescent.
Significant amounts of molecular H2CO3 exist in aqueous solutions subjected to pressures of multiple gigapascals (tens of thousands of atmospheres), such as can occur in planetary interiors.[16][17] Pressures of 0.6–1.6 GPa at 100 K, and 0.75–1.75 GPa at 300 K are attained in the cores of large icy satellites such as Ganymede, Callisto, and Titan, where water and carbon dioxide are present. Pure carbonic acid, being denser, would then sink under the ice layers and separate them from the rocky cores of these moons.[18]
### In biological solutions
When the enzyme carbonic anhydrase is also present in the solution the following reaction takes precedence.[19]
${\displaystyle {\ce {HCO3^- {+}H^+ <=> CO2 {+}H2O}}}$
When the amount of carbon dioxide created by the forward reaction exceeds its solubility, gas is evolved and a third equilibrium
${\displaystyle {\ce {CO_2 (soln) <=> CO_2 (g)}}}$
must also be taken into consideration. The equilibrium constant for this reaction is defined by Henry's law. The two reactions can be combined for the equilibrium in solution.
${\displaystyle {\ce {HCO3^- {+}H^{+}<=> CO_2(soln) {+}H2O}}}$ : ${\displaystyle {\ce {K_3 = {\frac {[H^+][HCO_3^{-}]}{[CO_2(soln)]}}}}}$
When Henry's law is used to calculate the value of the term in the denominator care is needed with regard to dimensionality.
In physiology, carbon dioxide excreted by the lungs may be called volatile acid or respiratory acid.
## Use of the term carbonic acid
Speciation for a monoprotic acid, AH as a function of pH.
Strictly speaking the term "carbonic acid" refers to the chemical compound with the formula ${\displaystyle {\ce {H2CO3}}}$, however, for historical reasons, dissolved carbon dioxide in extracellular fluid is often referred to as "carbonic acid" in biochemistry literature.
Since pKa1 has a value of ca. 6.8, at equilibrium carbonic acid will be almost 50% dissociated in the extracellular fluid (cytosol) which has a pH of ca. 7.2.
The reaction in which it is produced
HCO3 + H+ ⇌ CO2 + H2O
is fast in biological systems. Carbon dioxide can be described as the anhydride of carbonic acid.
## Pure carbonic acid
Carbonic acid, H2CO3, is quite stable at ambient temperatures as a gas. In the presence of water, it decomposes to form carbon dioxide and water, which further accelerates the decomposition.[5]
Pure carbonic acid is mainly produced in two ways, the proton-irradiation of pure solid carbon dioxide or by the reaction of hydrogen chloride and potassium bicarbonate at 100 K in methanol.[2]
A high-pressure deuterated version of carbonic acid, i.e. D2CO3, has been produced in a hybrid clamped cell (Russian alloy/copper-beryllium) at 1.85 GPa and characterized by neutron diffraction. The molecules, which are planar, form dimers joined by pairs of hydrogen bonds. All three C-O bonds are nearly equidistant at 1.34 Å. More typical C-O and C=O distances are 1.43 and 1.23 Å, respectively. The unusual C-O bond lengths are attributed to delocalized π bonding in the molecule's center, in addition to extraordinarily strong hydrogen bonds, indicated by the O---O separation of 2.13 Å. The shortness of the O---O separation is partially a consequence of the 136° O-H-O, imposed by the doubly hydrogen-bonded 8-membered rings.[6] Longer O---O distances are observed in strong, intramolecular hydrogen bonds, e.g. in dicarboxylic acid, which are above 2.4 Å. This high-pressure modification displays a different diffraction pattern from carbonic acid prepared at ambient pressure, for which the crystal structure is still missing.[20]
## References
1. ^ "Front Matter". Nomenclature of Organic Chemistry : IUPAC Recommendations and Preferred Names 2013 (Blue Book). Cambridge: The Royal Society of Chemistry. 2014. pp. P001–P004. doi:10.1039/9781849733069-FP001. ISBN 978-0-85404-182-4.
2. ^ a b W. Hage, K. R. Liedl; Liedl, E.; Hallbrucker, A; Mayer, E (1998). "Carbonic Acid in the Gas Phase and Its Astrophysical Relevance". Science. 279 (5355): 1332–1335. Bibcode:1998Sci...279.1332H. doi:10.1126/science.279.5355.1332. PMID 9478889.
3. ^ Benz, Sebastian; Chen, Da; Möller, Andreas; Hofmann, Michael; Schnieders, David; Dronskowski, Richard (September 2022). "The Crystal Structure of Carbonic Acid". Inorganics. 10 (9): 132. doi:10.3390/inorganics10090132. ISSN 2304-6740.
4. ^ Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. p. 310. ISBN 978-0-08-037941-8.
5. ^ a b Loerting, Thomas; Tautermann, Christofer; Kroemer, Romano T.; Kohl, Ingrid; Hallbrucker, Andreas; Mayer, Erwin; Liedl, Klaus R.; Loerting, Thomas; Tautermann, Christofer; Kohl, Ingrid; Hallbrucker, Andreas; Erwin, Mayer; Liedl, Klaus R. (2000). "On the Surprising Kinetic Stability of Carbonic Acid (H2CO3)". Angewandte Chemie International Edition. 39 (5): 891–894. doi:10.1002/(SICI)1521-3773(20000303)39:5<891::AID-ANIE891>3.0.CO;2-E. PMID 10760883.
6. ^ a b Sebastian Benz, Da Chen,, Andreas Möller, Michael Hofmann, David Schnieders, Richard Dronskowski (2022). "The Crystal Structure of Carbonic Acid". Inorganics. 10 (9): 132. doi:10.3390/inorganics10090132.{{cite journal}}: CS1 maint: multiple names: authors list (link)
7. ^ Acid-Base Physiology 2.1 – Acid-Base Balance by Kerry Brandis.
8. ^ Pangotra, Dhananjai; Csepei, Lénárd-István; Roth, Arne; Ponce de León, Carlos; Sieber, Volker; Vieira, Luciana (2022). "Anodic production of hydrogen peroxide using commercial carbon materials". Applied Catalysis B: Environmental. 303: 120848. doi:10.1016/j.apcatb.2021.120848. S2CID 240250750.
9. ^ Andersen, C. B. (2002). "Understanding carbonate equilibria by measuring alkalinity in experimental and natural systems". Journal of Geoscience Education. 50 (4): 389–403. Bibcode:2002JGeEd..50..389A. doi:10.5408/1089-9995-50.4.389. S2CID 17094010.
10. ^ Caldeira, K.; Wickett, M. E. (2003). "Anthropogenic carbon and ocean pH". Nature. 425 (6956): 365. Bibcode:2001AGUFMOS11C0385C. doi:10.1038/425365a. PMID 14508477. S2CID 4417880.
11. ^ Sabine, C. L.; et al. (2004). "The Oceanic Sink for Anthropogenic CO2". Science. 305 (5682): 367–371. Bibcode:2004Sci...305..367S. doi:10.1126/science.1097403. hdl:10261/52596. PMID 15256665. S2CID 5607281. Archived from " the original on 6 July 2008. Retrieved 22 June 2021.
12. ^ National Research Council. "Summary". Ocean Acidification: A National Strategy to Meet the Challenges of a Changing Ocean. Washington, DC: The National Academies Press, 2010. 1. Print.
13. ^ Pines, Dina; Ditkovich, Julia; Mukra, Tzach; Miller, Yifat; Kiefer, Philip M.; Daschakraborty, Snehasis; Hynes, James T.; Pines, Ehud (2016). "How Acidic Is Carbonic Acid?". J Phys Chem B. 120 (9): 2440–2451. doi:10.1021/acs.jpcb.5b12428. PMC 5747581. PMID 26862781.
14. ^ Housecroft and Sharpe, Inorganic Chemistry, 2nd ed, Prentice-Pearson-Hall 2005, p. 368.
15. ^ Soli, A. L.; R. H. Byrne (2002). "CO2 system hydration and dehydration kinetics and the equilibrium CO2/H2CO3 ratio in aqueous NaCl solution". Marine Chemistry. 78 (2–3): 65–73. doi:10.1016/S0304-4203(02)00010-5.
16. ^ Wang, Hongbo; Zeuschner, Janek; Eremets, Mikhail; Troyan, Ivan; Williams, Jonathon (27 January 2016). "Stable solid and aqueous H2CO3 from CO2 and H2O at high pressure and high temperature". Scientific Reports. 6 (1): 19902. Bibcode:2016NatSR...619902W. doi:10.1038/srep19902. PMC 4728613. PMID 26813580.
17. ^ Stolte, Nore; Pan, Ding (4 July 2019). "Large presence of carbonic acid in CO2-rich aqueous fluids under Earth's mantle conditions" (PDF). The Journal of Physical Chemistry Letters. 10 (17): 5135–5141. arXiv:1907.01833. doi:10.1021/acs.jpclett.9b01919. PMID 31411889. S2CID 195791860. Retrieved 24 March 2021.
18. ^ G. Saleh; A. R. Oganov (2016). "Novel Stable Compounds in the C-H-O Ternary System at High Pressure". Scientific Reports. 6: 32486. Bibcode:2016NatSR...632486S. doi:10.1038/srep32486. PMC 5007508. PMID 27580525.
19. ^ Lindskog S (1997). "Structure and mechanism of carbonic anhydrase". Pharmacology & Therapeutics. 74 (1): 1–20. doi:10.1016/S0163-7258(96)00198-2. PMID 9336012.
20. ^ Winkel, Katrin; Hage, Wolfgang; Loerting, Thomas; Price, Sarah L.; Mayer, Erwin (2007). "Carbonic Acid: From Polyamorphism to Polymorphism". Journal of the American Chemical Society. 129 (45): 13863–13871. doi:10.1021/ja073594f. PMID 17944463.
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https://mathtuition88.com/2014/10/27/sum-of-cubes-a-maths-tuition/
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# What is tested for A Maths (Additional Maths) Exam
Just to share an A Maths question that is likely to come out for 2014 A Maths Exam. It is the brand new topic just added this year: Sum and difference of cubes.
$\boxed{\alpha^3+\beta^3=(\alpha+\beta)(\alpha^2-\alpha\beta+\beta^2)}$
$\boxed{\alpha^3-\beta^3=(\alpha-\beta)(\alpha^2+\alpha\beta+\beta^2)}$
Attached below is a practice question on Alpha Cube+Beta Cube question that may be likely to come out this year! After all, if it is just added in the syllabus it is highly likely that they will test it.
Alpha Beta Cube Question
Good luck for the exam!
## Maths Tuition
For Mathematics Tuition, contact Mr Wu at:
Email: [email protected]
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https://worldwidescience.org/topicpages/t/tauri+spectral+twins.html
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#### Sample records for tauri spectral twins
1. Spectral Variations of T Tauri stars
Science.gov (United States)
Guenther, E.
1994-02-01
Although it can now be taken for granted that T Tauri stars accrete matter from circumstellar disks, the way in which the matter is ultimately accreted by the star is still under discussion. Boundary layer models, as well as models of magnetic accretion are considered. Since the very inner part of the disk, the star, and the boundary layer or the accretion shock radiate mainly in the optical, it is necessary to investigate this wavelength region. Optical spectra of classical T Tauri stars consist of emission lines superimposed on a late-type photospheric spectrum, but the photospheric lines in T Tauri stars are much weaker than the lines of main sequence stars of the same spectral type. This is generally attributed to the presence of an additional continuum which veils the photospheric spectrum of the star, which may be be the emission of the boundary layer, or the emission of the immediate vicinity of an accretion shock. The aim of this work is to give additional information on the nature of the region that emits the veiling continuum by investigating the correlations between the veiling and line fluxes in time serieses of T Tauri stars. For this work a time series of 27, 117, and 89 spectra of BM And, DI Cep and DG Tau, were taken in 9, 13, and 12 nights, using the Echellette-Spectrograph of the 2.2m telescope on Calar Alto, Spain. These T Tauri stars were selected because of their different of levels of activity. The spectra cover the whole region between 3200Å and 11000Å with a resolution of about Δ λ λ = 3000. Using 32 template stars the spectral types of the stars were determined, which is found to remain unchanged during the whole time series. The wavelengths of all photospheric lines are in agreement with a single doppler shift (+/- 6 km/s), which is taken as the systemic velocity. It is thus assumed that the low excitation lines are indeed the photospheric lines of the star and the veiling is an additional continuum source. The spectrum of the veiling
2. Spectral energy distributions of T Tauri stars - disk flaring and limits on accretion
International Nuclear Information System (INIS)
Kenyon, S.J.; Hartmann, L.
1987-01-01
The Adams et al. (1987) conclusion that much of the IR excess emission in the spectral energy distribution of T Tauri stars arises from reprocessing of stellar radiation by a dusty circumstellar disk is presently supported by analyses conducted in light of various models of these stars' spectra. A low mass reprocessing disk can, however, produce these spectra as well as a massive accretion disk. The detection of possible boundary layer radiation in the optical and near-UV regions poses the strongest limits on accretion rates. Disk accretion in the T Tauri phase does not significantly modify stellar evolution. 85 references
3. Spatial and spectral coherence in propagating high-intensity twin beams
Czech Academy of Sciences Publication Activity Database
Haderka, O.; Machulka, R.; Peřina ml., Jan; Allevi, A.; Bondani, M.
2015-01-01
Roč. 5, Sep (2015), s. 14365 ISSN 2045-2322 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : spatial and spectral coherence * high-intensity twin beams Subject RIV: BH - Optics, Masers, Lasers Impact factor: 5.228, year: 2015
4. How to unveil a T Tauri star
International Nuclear Information System (INIS)
Hartigan, P.; Hartmann, L.; Kenyon, S.; Hewett, R.; Stauffer, J.
1989-01-01
A method for separating the 'veiling' continuum often present in T Tauri stars from the underlying photospheric spectrum is described. Echelle observations from 5100 to 6800 A of the partially veiled T Tauri star BP Tau were analyzed to determine the shape of the veiling spectrum. The residuals of the fit indicate the deviation of the veiling spectrum from a simple continuum and identify the location and strength of any emission-line components. It is shown, by means of goodness-of-fit tests, that the spectrum of BP Tau can be decomposed into a normal stellar spectrum plus a smooth veiling continuum with only a few emission lines superposed. The continuum dominates the veiling spectrum in this spectral region; the veiling does not arise from numerous deep photospheric absorption lines that are filled in by weak emission. 36 refs
5. Receiver sensitivity improvement in spectrally-efficient guard-band twin-SSB-OFDM using an optical IQ modulator
Science.gov (United States)
Chen, Ming; Peng, Miao; Zhou, Hui; Zheng, Zhiwei; Tang, Xionggui; Maivan, Lap
2017-12-01
To further improve receiver sensitivity of spectrally-efficient guard-band direct-detection optical orthogonal frequency-division multiplexing (OFDM) with twin single-side-band (SSB) modulation technique, an optical IQ modulator (IQM) is employed to optimize optical carrier-to-signal power ratio (CSPR). The CSPRs for the guard-band twin-SSB-OFDM signal generated by using dual-drive Mach-Zehnder modulator (DD-MZM) and optical IQM are theoretically analyzed and supported by simulations. The optimal CSPR for the two types of guard-band twin-SSB-OFDM are identified. The simulations exhibit that the error vector magnitude (EVM) performance of the IQM-enabled guard-band twin-SSB-OFDM is improved by more than 4-dB compared to that of the twin-SSB-OFDM enabled by DD-MZM after 80-km single-mode fiber (SMF) transmission. In addition, more than 3-dB and 10 dB receiver sensitivity improvements in terms of received optical power (ROP) and optical signal-to-noise ratio (OSNR) are also achieved, respectively.
6. POST T-Tauri Stars in Galactic Clusters
Science.gov (United States)
Haro, G.
1983-08-01
spectral type and luminosity: the earlier the spectral type, the shorter the vanishing effect. Therefore, if we look for weakened T Tauri features in stellar aggregates of various ages from which the typical and extreme T Tauri stars have already disappeared, we find that the older the aggregate, the later the spectral type in which the last prominent features are detectable. Everything seems to suggest that it is within these possible evolved T Tauri objects that we can find the so-called post-T Tauri stars, and that a good number of flare stars detected in galactic clusters are among them. These clusters are: the Orion stellar aggregate, NOC 2264, the Pleiades, and possibly the flare stars in stellar aggregates of ages equal or superior to 108 years. As I have in the past, I would like to place special emphasis on the genetic relationship between certain flare stars and their T Tauri ancestors, based not only on the very rapid outbursts of the former but also, and primarily, on the fact that these flare stars show spectroscopic characteristics reminiscent of the T Tauri original stars. In other words, the simple fact that a star presents the "flare" phenomenon does not constitute necessary and sufficient proof that it should be regarded as an evolutionary product of a T Tauri star: in addition to the flare-up the spectral types of the investigated objects must present -during maximum and minimum light- clear and reminiscent spectroscopic evidences of the original T Tauri objects; that is, spectral types as late or later than G and some emission lines, at least in H and Call. There are some flare stars in Orion and NGC 2264 which, even during minimum light, can be classified spectroscopically as typical T Tauri stars. In the case of the Pleiades, where undoubtedly there are no T Tauri stars, many of the flare stars show spectral emission lines (H and Call) of great intensity during maximum and of detectable intensity in slit spectrograms of not high dispersion, during
7. Paradoxical gap in the relative ages of T Tauri stars
International Nuclear Information System (INIS)
Weaer, W.B.
1984-01-01
The frequency distribution of T Tauri stars of different Youth (relative age) shows a pronounced gap at 5% of their time to the zero-age main sequence. This gap, which occurs in all of the four major T Tauri associations, is too large to be filled by unclassifiable veiled stars. It is nearly vertical on the Hertzsprung-Russell diagram, is centered near spectral class K5, and lies close to the transition between the convective and radiative tracks of the pre-main-sequence stars
8. Environments of T Tauri stars
International Nuclear Information System (INIS)
Chevalier, R.A.
1983-01-01
The environments of T Tauri stars are probably determined by the interaction of a stellar wind with matter which is falling toward a newly formed star. As shown by Ulrich, the steady infall of cool gas with angular momentum toward the star leads to a density distribution with rhoproportionalr/sup -1/2/ inside a radius r/sub d/ and rhoproportionalr/sup -3/2/ outside r/sub d/. The radius r/sub d/ is determined by the angular momentum of the infalling gas. The expansion of the wind into this medium depends on the parameter α = M/sub w/v/sub w//M/sub in/v/sub in/(r/sub d/), where v/sub in/(r/sub d/) is the free-fall velocity at r/sub d/, M/sub in/ is the mass accretion rate, v/sub w/ is the wind velocity, and M/sub w/ is the mass loss rate. For α 14 cm, v/sub w/ = 150 km s -1 , M/sub in/ = 10 -7 M/sub sun/ yr -1 , and M/sub w/ = 3 x 10 -8 M/sub sun/ yr -1 . The inflow is clumpy. The shocked wind gives the radio emission and nebular emission from T Tauri, and dust within the clumps gives the infrared emission. T Tauri is in a transitory phase in which most of the wind has only recently propagated beyond r/sub d/. The model naturally predicts variable obscuration of T Tauri stars because the infalling clumps move on nonradial trajectories. The infrared emission can vary either because of structural changes in the circumstellar gas or because of variations in the stellar luminosity. Infrared variability should be small at short time scales because of light-travel time effects
9. Twin peak high-frequency quasi-periodic oscillations as a spectral imprint of dual oscillation modes of accretion tori
Science.gov (United States)
Bakala, P.; Goluchová, K.; Török, G.; Šrámková, E.; Abramowicz, M. A.; Vincent, F. H.; Mazur, G. P.
2015-09-01
Context. High-frequency (millisecond) quasi-periodic oscillations (HF QPOs) are observed in the X-ray power-density spectra of several microquasars and low-mass X-ray binaries. Two distinct QPO peaks, so-called twin peak QPOs, are often detected simultaneously exhibiting their frequency ratio close or equal to 3:2. A widely discussed class of proposed QPOs models is based on oscillations of accretion toroidal structures orbiting in the close vicinity of black holes or neutron stars. Aims: Following the analytic theory and previous studies of observable spectral signatures, we aim to model the twin peak QPOs as a spectral imprint of specific dual oscillation regime defined by a combination of the lowest radial and vertical oscillation mode of slender tori. We consider the model of an optically thick slender accretion torus with constant specific angular momentum. We examined power spectra and fluorescent Kα iron line profiles for two different simulation setups with the mode frequency relations corresponding to the epicyclic resonance HF QPOs model and modified relativistic precession QPOs model. Methods: We used relativistic ray-tracing implemented in the parallel simulation code LSDplus. In the background of the Kerr spacetime geometry, we analyzed the influence of the distant observer inclination and the spin of the central compact object. Relativistic optical projection of the oscillating slender torus is illustrated by images in false colours related to the frequency shift. Results: We show that performed simulations yield power spectra with the pair of dominant peaks that correspond to the frequencies of radial and vertical oscillation modes and with the peak frequency ratio equal to the proper value 3:2 on a wide range of inclinations and spin values. We also discuss exceptional cases of a very low and very high inclination, as well as unstable high spin relativistic precession-like configurations that predict a constant frequency ratio equal to 1:2. We
10. Chemistry in T Tauri winds
Energy Technology Data Exchange (ETDEWEB)
Rawlings, J M.C.; Williams, D A; Canto, J
1988-02-15
The chemistry occurring in the winds of T Tauri stars is investigated. On the assumption that the wind is dust-free, then routes to H/sub 2/ are inhibited under the conditions in the wind, and subsequent chemistry does not produce substantial molecular abundances. The major losses to the chemical network lie in the geometrical dilution and collisional dissociation rather than in chemical destruction and photodissociation. Mass loading of the wind with dust and H/sub 2/ may, however, occur. This stimulates the chemistry and may in some circumstances lead to a conversion of approx.1-10 per cent of carbon into CO. This gives a column density of CO which is marginally detectable. A positive detection of CO at high wind velocities would imply that the winds must be cool and that mixing of molecular material from a disc, which may play a role in collimating the wind, or the remnants of a disc, must occur.
11. Applicability of colour index calibrations to T Tauri stars
Science.gov (United States)
Schöning, T.; Ammler, M.
2008-01-01
We examine the applicability of effective temperature scales of several broad band colours to T Tauri stars (TTS). We take into account different colour systems as well as stellar parameters like metallicity and surface gravity which influence the conversion from colour indices or spectral type to effective temperature. For a large sample of TTS, we derive temperatures from broad band colour indices and check if they are consistent in a statistical sense with temperatures inferred from spectral types. There are some scales (for V-H, V-K, I-J, J-H, and J-K) which indeed predict the same temperatures as the spectral types and therefore can be at least used to confirm effective temperatures. Furthermore, we examine whether TTS with dynamically derived masses can be used for a test of evolutionary models and effective temperature calibrations. We compare the observed parameters of the eclipsing T Tauri binary V1642 Ori A to the predictions of evolutionary models in both the H-R and the Kiel diagram using temperatures derived with several colour index scales. We check whether the evolutionary models and the colour index scales are consistent with coevality and the dynamical masses of the binary components. It turns out that the Kiel diagram offers a stricter test than the H-R diagram. Only the evolutionary models of \\cite {BCAH98} with mixing length parameter α=1.9 and of \\cite{DM94,DM97} show consistent results in the Kiel diagram in combination with some conversion scales of \\cite{HBS00} and of \\cite{KH95}.
12. The photosphere of T. Tauri Stars
International Nuclear Information System (INIS)
Calvet, Nuria; Marin, Zaida
1987-01-01
We have calculated the absorption spectrum in the wavelength interval 4880-5025A for a set of models with Teff = 4000K and log g = 3.5 and a chromospheric temperature rise. These models are considered as representative of the atmosphere of T Tauri stars. The position of the temperature minimum goes from 0.1 to 2 gr cm -2 in the models. Populations are in LTE and the two level plus continuum approximation is used for the source function. We have compared the calculated spectra with those observed in the program of rotational velocity determination by Vogel and Kuhi (1981). Differences between the spectrum of T Tauri stars can be understood in first approximation in terms of differences in the position of the temperature minimum. In particular, we find that at the moment of the observation, the minimum in BP Tau was located between 1 and 2 cm -2 and in AA Tau between 0.3 and 0.6 gr cm -2 . (Author)
Science.gov (United States)
Charlemaine, Christiane
2006-12-31
This paper explores the deep roots of closeness that twins share in their youngest age and their effect on their destiny at the adult age. Psychologists believe the bond between twins begins in utero and develops throughout the twins' lives. The four patterns of twinship described show that the twin bond is determined by the quality of parenting that twins receive in their infancy and early childhood. Common problems of adult twins bring about difficulties to adapt in a non-twin world. The nature versus nurture controversy has taken on new life focusing on inter-twin differences and the importance of parent-child interaction as fundamental to the growth and development of personality.
14. Twin RSA
OpenAIRE
Lenstra, Arjen K.; Weger, De; Benjamin, M. M.
2005-01-01
We introduce Twin RSA, pairs of RSA moduli (n, n+ 2), and formulate several questions related to it. Our main questions are: is Twin RSA secure, and what is it good for? © Springer-Verlag Berlin Heidelberg 2005.
15. THE SPITZER INFRARED SPECTROGRAPH SURVEY OF T TAURI STARS IN TAURUS
International Nuclear Information System (INIS)
Furlan, E.; Luhman, K. L.; Espaillat, C.
2011-01-01
We present 161 Spitzer Infrared Spectrograph (IRS) spectra of T Tauri stars and young brown dwarfs in the Taurus star-forming region. All of the targets were selected based on their infrared excess and are therefore surrounded by protoplanetary disks; they form the complete sample of all available IRS spectra of T Tauri stars with infrared excesses in Taurus. We also present the IRS spectra of seven Class 0/I objects in Taurus to complete the sample of available IRS spectra of protostars in Taurus. We use spectral indices that are not significantly affected by extinction to distinguish between envelope- and disk-dominated objects. Together with data from the literature, we construct spectral energy distributions for all objects in our sample. With spectral indices derived from the IRS spectra we infer disk properties such as dust settling and the presence of inner disk holes and gaps. We find a transitional disk frequency, which is based on objects with unusually large 13-31 μm spectral indices indicative of a wall surrounding an inner disk hole, of about 3%, and a frequency of about 20% for objects with unusually large 10 μm features, which could indicate disk gaps. The shape and strength of the 10 μm silicate emission feature suggests weaker 10 μm emission and more processed dust for very low mass objects and brown dwarfs (spectral types M6-M9). These objects also display weaker infrared excess emission from their disks, but do not appear to have more settled disks than their higher-mass counterparts. We find no difference for the spectral indices and properties of the dust between single and multiple systems.
16. T Tauri stars - Wild as dust
International Nuclear Information System (INIS)
Bertout, C.
1989-01-01
T Tauri stars (TTSs), their surroundings, and their common evolution toward the main sequence are discussed. The photospheric properties of TTSs and their solar-type outer atmospheres, recent evidence for circumstellar disks around classical TTSs (CTTSs), and CTTS mass outflows are examined. TTSs are depicted as complex systems whose properties depend mostly on the initial conditions of star formation and on their rotation rates, which appear to control the magnetodynamic activity in the stars. The most exotic traits of CTTSs are primarily due to the disk and its interaction with the star, and the properties of weak-line TTSs (WTTSs) are mainly manifestations of the enhanced solar-type magnetic activity expected from their rotation rates. CTTSs are expected to become WTTSs when their disks dissipate. 217 refs
17. Chemical Compositions of RV Tauri Stars and Related Objects
Science.gov (United States)
Rao, S. S.; Giridhar, S.
2014-04-01
We have undertaken a comprehensive abundance analysis for a sample of relatively unexplored RV Tauri and RV Tauri like stars to further our understanding of post-Asymptotic Giant Branch (post-AGB) evolution. From our study based on high resolution spectra and a grid of model atmospheres, we find indications of mild s-processing for V820 Cen and IRAS 06165+3158. On the other hand, SU Gem and BT Lac exhibit the effects of mild dust-gas winnowing. We have also compiled the existing abundance data on RV Tauri objects and find that a large fraction of them are afflicted by dust-gas winnowing and aided by the present work, we find a small group of two RV Tauris showing mild s-process enhancement in our Galaxy. With two out of three reported s-process enhanced objects belonging to RV Tauri spectroscopic class C, these intrinsically metal-poor objects appear to be promising candidates to analyse the possible s-processing in RV Tauri stars.
18. Twin pregnancy
DEFF Research Database (Denmark)
Sperling, Lene; Tabor, A
2001-01-01
Determination of chorionicity is one of the most important issues in the management of twin pregnancy. Modern ultrasound equipment has made it possible to accurately assess placentation already in the first trimester with the lambda sign. With regard to prenatal diagnosis, it is important to know...... for clinicians caring for twin pregnancies....
19. Disk accretion onto magnetic T Tauri stars
International Nuclear Information System (INIS)
Koenigl, A.
1991-01-01
The dynamical and radiative consequences of disk accretion onto magnetic T Tauri stars (TTS) are examined using the Ghosh and Lamb model. It is shown that a prolonged disk accretion phase is compatible with the low rotation rates measured in these stars if they possess a kilogauss strength field that disrupts the disk at a distance of a few stellar radii from the center. It is estimated that a steady state in which the net torque exerted on the star is zero can be attained on a time scale that is shorter than the age of the youngest visible TTS. Although the disk does not develop an ordinary shear boundary layer in this case, one can account for the observed UV excess and Balmer emission in terms of the shocks that form at the bottom of the high-latitude magnetic accretion columns on the stellar surface. This picture also provides a natural explanation of some of the puzzling variability properties of stars like DF Tau and RY Lup. YY Ori stars are interpreted as magnetic TTS in which the observer's line of sight is roughly parallel to an accretion column. 37 refs
20. HOT GAS LINES IN T TAURI STARS
International Nuclear Information System (INIS)
Ardila, David R.; Herczeg, Gregory J.; Gregory, Scott G.; Hillenbrand, Lynne A.; Ingleby, Laura; Bergin, Edwin; Bethell, Thomas; Calvet, Nuria; France, Kevin; Brown, Alexander; Edwards, Suzan; Johns-Krull, Christopher; Linsky, Jeffrey L.; Yang, Hao; Valenti, Jeff A.; Abgrall, Hervé; Alexander, Richard D.; Brown, Joanna M.; Espaillat, Catherine; Hussain, Gaitee
2013-01-01
For Classical T Tauri Stars (CTTSs), the resonance doublets of N V, Si IV, and C IV, as well as the He II 1640 Å line, trace hot gas flows and act as diagnostics of the accretion process. In this paper we assemble a large high-resolution, high-sensitivity data set of these lines in CTTSs and Weak T Tauri Stars (WTTSs). The sample comprises 35 stars: 1 Herbig Ae star, 28 CTTSs, and 6 WTTSs. We find that the C IV, Si IV, and N V lines in CTTSs all have similar shapes. We decompose the C IV and He II lines into broad and narrow Gaussian components (BC and NC). The most common (50%) C IV line morphology in CTTSs is that of a low-velocity NC together with a redshifted BC. For CTTSs, a strong BC is the result of the accretion process. The contribution fraction of the NC to the C IV line flux in CTTSs increases with accretion rate, from ∼20% to up to ∼80%. The velocity centroids of the BCs and NCs are such that V BC ∼> 4 V NC , consistent with the predictions of the accretion shock model, in at most 12 out of 22 CTTSs. We do not find evidence of the post-shock becoming buried in the stellar photosphere due to the pressure of the accretion flow. The He II CTTSs lines are generally symmetric and narrow, with FWHM and redshifts comparable to those of WTTSs. They are less redshifted than the CTTSs C IV lines, by ∼10 km s –1 . The amount of flux in the BC of the He II line is small compared to that of the C IV line, and we show that this is consistent with models of the pre-shock column emission. Overall, the observations are consistent with the presence of multiple accretion columns with different densities or with accretion models that predict a slow-moving, low-density region in the periphery of the accretion column. For HN Tau A and RW Aur A, most of the C IV line is blueshifted suggesting that the C IV emission is produced by shocks within outflow jets. In our sample, the Herbig Ae star DX Cha is the only object for which we find a P-Cygni profile in the C IV
1. The Surface of V410 Tauri
Science.gov (United States)
Rice, J. B.; Strassmeier, K. G.; Kopf, M.
2011-02-01
We present Doppler images of the weak-lined T Tauri star V410 Tau obtained with two different Doppler-imaging codes. The images are consistent and show a cool extended spot, symmetric about the pole, at a temperature approximately 750 K below the average photospheric value. Smaller cool spots are found fairly uniformly distributed at latitudes below the polar cap with temperatures about 450 K below the average photospheric temperature. Resolution on the stellar surface is limited to about 7° of arc, so structure within these spots is not visible. Also at lower latitudes are hotter features with temperatures up to 1000 K above the photosphere. A trial Doppler image using a TiO molecular feature reproduced the cool polar cap at a temperature about 100 K below the value from the atomic line images. The equatorial features, however, were not properly reproduced since Doppler imaging relies on information in the wings of lines for reconstructing equatorial features, and for V410 Tau these molecular band lines overlap. In 1993, V410 Tau had a large photometric amplitude resulting from the concentration of cool spots on the hemisphere of the star visible at phase 0°, a phenomenon known as preferred longitude. In contrast, the small photometric amplitude observed currently is due to a strong symmetric polar spot and the uniform distribution in longitude of equatorial cool and warm spots. This redistribution of surface features may be the beginning of a slow "flip-flop" for V410 Tau where spot locations alternate between preferred longitudes. Flare events linked to two of the hotter spots in the Doppler image were observed.
2. An optical spectroscopic study of T Tauri stars. I. Photospheric properties
Energy Technology Data Exchange (ETDEWEB)
Herczeg, Gregory J. [Kavli Institute for Astronomy and Astrophysics, Peking University, Yi He Yuan Lu 5, Haidian Qu, Beijing 100871 (China); Hillenbrand, Lynne A. [Caltech, MC105-24, 1200 East California Boulevard, Pasadena, CA 91125 (United States)
2014-05-10
Estimates of the mass and age of young stars from their location in the H-R diagram are limited by not only the typical observational uncertainties that apply to field stars, but also by large systematic uncertainties related to circumstellar phenomena. In this paper, we analyze flux-calibrated optical spectra to measure accurate spectral types and extinctions of 281 nearby T Tauri stars (TTSs). The primary advances in this paper are (1) the incorporation of a simplistic accretion continuum in optical spectral type and extinction measurements calculated over the full optical wavelength range and (2) the uniform analysis of a large sample of stars, many of which are well known and can serve as benchmarks. Comparisons between the non-accreting TTS photospheric templates and stellar photosphere models are used to derive conversions from spectral type to temperature. Differences between spectral types can be subtle and difficult to discern, especially when accounting for accretion and extinction. The spectral types measured here are mostly consistent with spectral types measured over the past decade. However, our new spectral types are one to two subclasses later than literature spectral types for the original members of the TW Hya Association (TWA) and are discrepant with literature values for some well-known members of the Taurus Molecular Cloud. Our extinction measurements are consistent with other optical extinction measurements but are typically 1 mag lower than near-IR measurements, likely the result of methodological differences and the presence of near-IR excesses in most CTTSs. As an illustration of the impact of accretion, spectral type, and extinction uncertainties on the H-R diagrams of young clusters, we find that the resulting luminosity spread of stars in the TWA is 15%-30%. The luminosity spread in the TWA and previously measured for binary stars in Taurus suggests that for a majority of stars, protostellar accretion rates are not large enough to
3. CURVED WALLS: GRAIN GROWTH, SETTLING, AND COMPOSITION PATTERNS IN T TAURI DISK DUST SUBLIMATION FRONTS
Energy Technology Data Exchange (ETDEWEB)
McClure, M. K.; Calvet, N.; Hartmann, L.; Ingleby, L. [Department of Astronomy, The University of Michigan, 500 Church Street, 830 Dennison Building., Ann Arbor, MI 48109 (United States); D' Alessio, P. [Centro de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de México, 58089 Morelia, Michoacán (Mexico); Espaillat, C. [Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Sargent, B. [Center for Imaging Science and Laboratory for Multiwavelength Astrophysics, Rochester Institute of Technology, 54 Lomb Memorial Drive, Rochester, NY 14623 (United States); Watson, D. M. [Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627 (United States); Hernández, J., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Centro de Investigaciones de Astronomía (CIDA), Mérida 5101-A (Venezuela, Bolivarian Republic of)
2013-10-01
The dust sublimation walls of disks around T Tauri stars represent a directly observable cross-section through the disk atmosphere and midplane. Their emission properties can probe the grain size distribution and composition of the innermost regions of the disk, where terrestrial planets form. Here we calculate the inner dust sublimation wall properties for four classical T Tauri stars with a narrow range of spectral types and inclination angles and a wide range of mass accretion rates to determine the extent to which the walls are radially curved. Best fits to the near- and mid-IR excesses are found for curved, two-layer walls in which the lower layer contains larger, hotter, amorphous pyroxene grains with Mg/(Mg+Fe) = 0.6 and the upper layer contains submicron, cooler, mixed amorphous olivine and forsterite grains. As the mass accretion rates decrease from 10{sup –8} to 10{sup –10} M{sub ☉} yr{sup –1}, the maximum grain size in the lower layer decreases from ∼3 to 0.5 μm. We attribute this to a decrease in fragmentation and turbulent support for micron-sized grains with decreasing viscous heating. The atmosphere of these disks is depleted of dust with dust-gas mass ratios 1 × 10{sup –4} of the interstellar medium (ISM) value, while the midplane is enhanced to eight times the ISM value. For all accretion rates, the wall contributes at least half of the flux in the optically thin 10 μm silicate feature. Finally, we find evidence for an iron gradient in the disk, suggestive of that found in our solar system.
4. CURVED WALLS: GRAIN GROWTH, SETTLING, AND COMPOSITION PATTERNS IN T TAURI DISK DUST SUBLIMATION FRONTS
International Nuclear Information System (INIS)
McClure, M. K.; Calvet, N.; Hartmann, L.; Ingleby, L.; D'Alessio, P.; Espaillat, C.; Sargent, B.; Watson, D. M.; Hernández, J.
2013-01-01
The dust sublimation walls of disks around T Tauri stars represent a directly observable cross-section through the disk atmosphere and midplane. Their emission properties can probe the grain size distribution and composition of the innermost regions of the disk, where terrestrial planets form. Here we calculate the inner dust sublimation wall properties for four classical T Tauri stars with a narrow range of spectral types and inclination angles and a wide range of mass accretion rates to determine the extent to which the walls are radially curved. Best fits to the near- and mid-IR excesses are found for curved, two-layer walls in which the lower layer contains larger, hotter, amorphous pyroxene grains with Mg/(Mg+Fe) = 0.6 and the upper layer contains submicron, cooler, mixed amorphous olivine and forsterite grains. As the mass accretion rates decrease from 10 –8 to 10 –10 M ☉ yr –1 , the maximum grain size in the lower layer decreases from ∼3 to 0.5 μm. We attribute this to a decrease in fragmentation and turbulent support for micron-sized grains with decreasing viscous heating. The atmosphere of these disks is depleted of dust with dust-gas mass ratios 1 × 10 –4 of the interstellar medium (ISM) value, while the midplane is enhanced to eight times the ISM value. For all accretion rates, the wall contributes at least half of the flux in the optically thin 10 μm silicate feature. Finally, we find evidence for an iron gradient in the disk, suggestive of that found in our solar system
5. New T Tauri stars in Chamaeleon I and Chamaeleon II
Science.gov (United States)
Hartigan, Patrick
1993-01-01
A new objective prism survey of the entire Chamaeleon I dark cloud and 2/3 of the Chamaeleon II cloud has uncovered 26 new H-alpha emission line objects that were missed by previous H-alpha plate surveys. The new H-alpha emission line objects have similar IR colors and spatial distributions to the known T Tauri stars in these dark clouds, and could represent the very low mass end of the stellar population in these clouds or an older, less active component to the usual classical T Tauri star population. The new H-alpha survey identified 70 percent of the total known Young Stellar Objects (YSOs) in Cha I, compared with 35 percent for IRAS, and 25 percent from the Einstein X-ray survey. Ten of the new objects are weak-lined stars, with H-alpha equivalent widths less than 10 A. Weak-lined T Tauri stars make up about half of the total population of young stars in the Chamaeleon I cloud, a proportion similar to the Taurus-Auriga cloud. Presented are coordinates, finding charts, and optical and IR photometry of the new emission-line objects.
6. The Qingdao Twin Registry
DEFF Research Database (Denmark)
Duan, Haiping; Ning, Feng; Zhang, Dongfeng
2013-01-01
In 1998, the Qingdao Twin Registry was initiated as the main part of the Chinese National Twin Registry. By 2005, a total of 10,655 twin pairs had been recruited. Since then new twin cohorts have been sampled, with one longitudinal cohort of adolescent twins selected to explore determinants of me...
7. X-ray sources in regions of star formation. I. The naked T Tauri stars
International Nuclear Information System (INIS)
Walter, F.M.
1986-01-01
Einstein X-ray observations of regions of active star formation in Taurus, Ophiuchus, and Corona Australis show a greatly enhanced surface density of stellar X-ray sources over that seen in other parts of the sky. Many of the X-ray sources are identified with low-mass, pre-main-sequence stars which are not classical T Tauri stars. The X-ray, photometric, and spectroscopic data for these stars are discussed. Seven early K stars in Oph and CrA are likely to be 1-solar-mass post-T Tauri stars with ages of 10-million yr. The late K stars in Taurus are not post-T Tauri, but naked T Tauri stars, which are coeval with the T Tauri stars, differing mainly in the lack of a circumstellar envelope. 72 references
8. Chandra resolves the T Tauri binary system RW Aur
Energy Technology Data Exchange (ETDEWEB)
Skinner, Stephen L. [CASA, University of Colorado, Boulder, CO 80309-0389 (United States); Güdel, Manuel, E-mail: [email protected], E-mail: [email protected] [Department of Astrophysics, University of Vienna, Türkenschanzstr. 17, A-1180 Vienna (Austria)
2014-06-20
RW Aur is a multiple T Tauri system consisting of an early-K type primary (A) and a K5 companion (B) at a separation of 1.''4. RW Aur A drives a bipolar optical jet that is well characterized optically. We present results of a sensitive Chandra observation whose primary objective was to search for evidence of soft extended X-ray emission along the jet, as has been seen for a few other nearby T Tauri stars. The binary is clearly resolved by Chandra and both stars are detected as X-ray sources. The X-ray spectra of both stars reveal evidence for cool and hot plasma. Surprisingly, the X-ray luminosity of the less-massive secondary is at least twice that of the primary and is variable. The disparity is attributed to the primary whose X-ray luminosity is at the low end of the range for classical T Tauri stars of similar mass based on established correlations. Deconvolved soft-band images show evidence for slight outward elongation of the source structure of RW Aur A along the blueshifted jet axis inside the central arcsecond. In addition, a faint X-ray emission peak is present on the redshifted axis at an offset of 1.''2 ± 0.''2 from the star. Deprojected jet speeds determined from previous optical studies are too low to explain this faint emission peak as shock-heated jet plasma. Thus, unless flow speeds in the redshifted jet have been underestimated, other mechanisms such as magnetic jet heating may be involved.
9. Modeling acardiac twin pregnancies
NARCIS (Netherlands)
de Groot, Rosa; van den Wijngaard, Jeroen P. H. M.; Umur, Asli; Beek, Johan F.; Nikkels, Peter G. J.; van Gemert, Martin J. C.
2007-01-01
Acardiac twin pregnancies are a rare but severe complication of monochorionic twinning, where the acardiac twin lacks cardiac function but nevertheless grows during pregnancy because it is perfused by the pump twin through a set of placental arterioarterial and venovenous anastomoses. Because the
10. Flat spectrum T Tauri stars: The case for infall
Science.gov (United States)
Calvet, Nuria; Hartmann, Lee; Kenyon, S. J.; Whitney, B. A.
1994-01-01
We show that the mid- to far-infrared fluxes of 'flat spectrum' T Tauri stars can be explained by radiative equilibrium emission from infalling dusty envelopes. Infall eliminates the need for accretion disks with non-standard temperature distributions. The simplicity and power of this explanantion indicates that models employing 'active' disks, in which the temperature distribution is a parameterized power law, should be invoked with caution. Infall also naturally explains the scattered light nebulae detected around many flat spectrum sources. To match the observed spectra, material must fall onto a disk rather than the central star, as expected for collapse of a rotating molecular cloud. It may be necessary to invoke cavities in the envelopes to explain the strength of optical and near-infrared emission; these cavities could be produced by the powerful bipolar outflows commonly observed from young stars. If viewed along the cavity, a source may be lightly extincted at visual wavelengths, while still accreting substantial amounts of material from the envelope. Infall may also be needed to explain the infrared-bright companions of many optical T Tauri stars. This picture suggests that many of the flat spectrum sources are 'protostars'-young stellar objects surrounded by dust infalling envelopes of substantial mass.
11. Local protoplanetary disk ionisation by T Tauri star energetic particles
Science.gov (United States)
Fraschetti, F.; Drake, J.; Cohen, O.; Garraffo, C.
2017-10-01
The evolution of protoplanetary disks is believed to be driven largely by viscosity. The ionization of the disk that gives rise to viscosity is caused by X-rays from the central star or by energetic particles released by shock waves travelling into the circumstellar medium. We have performed test-particle numerical simulations of GeV-scale protons traversing a realistic magnetised wind of a young solar mass star with a superposed small-scale turbulence. The large-scale field is generated via an MHD model of a T Tauri wind, whereas the isotropic (Kolmogorov power spectrum) turbulent component is synthesised along the particles' trajectories. We have combined Chandra observations of T Tauri flares with solar flare scaling for describing the energetic particle spectrum. In contrast with previous models, we find that the disk ionization is dominated by X-rays except within narrow regions where the energetic particles are channelled onto the disk by the strongly tangled and turbulent field lines; the radial thickness of such regions broadens with the distance from the central star (5 stellar radii or more). In those regions, the disk ionization due to energetic particles can locally dominate the stellar X-rays, arguably, out to large distances (10, 100 AU) from the star.
12. Analysis of the nebulosities near T Tauri using digital computer image processing
International Nuclear Information System (INIS)
Lorre, J.J.
1975-01-01
Direct plates of T Tauri taken with the 120-inch (3 m) and 36-inch (91 cm) Lick reflectors were digitized and analyzed using digital computer image processing techniques. Luminous emission protrusions extending to as far as 13'' from T Tauri in position angles 170degree, 210degree, and 330degree are shown. These features are variable and may contain layered structure. The complex reflection nebula west of T Tauri (NGC 1555) appears to be an illuminated portion of a much larger dark nebula whose variability is due to obscuring material near the star
13. The Mysterious Dimmings of the T Tauri Star V1334 Tau
Energy Technology Data Exchange (ETDEWEB)
Rodriguez, Joseph E.; Zhou, George; Cargile, Phillip A.; Relles, Howard M.; Latham, David W.; Eastman, Jason; Bieryla, Allyson; Esquerdo, Gilbert A.; Berlind, Perry; Calkins, Michael L.; Vanderburg, Andrew [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Stevens, Daniel J. [Department of Astronomy, The Ohio State University, Columbus, OH 43210 (United States); Osborn, Hugh P. [Department of Physics, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL (United Kingdom); Shappee, Benjamin J. [Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101 (United States); Reed, Phillip A. [Department of Physical Sciences, Kutztown University, Kutztown, PA 19530 (United States); Lund, Michael B.; Stassun, Keivan G. [Department of Physics and Astronomy, Vanderbilt University, 6301 Stevenson Center, Nashville, TN 37235 (United States); Gaidos, Eric [Department of Geology and Geophysics, University of Hawai‘i at Mnoa, Honolulu, HI 96822 (United States); Ansdell, Megan [Institute for Astronomy, University of Hawai‘i at Manoa, Honolulu, HI 96822 (United States); Siverd, Robert J. [Las Cumbres Observatory Global Telescope Network, 6740 Cortona Drive, Suite 102, Santa Barbara, CA 93117 (United States); and others
2017-02-20
We present the discovery of two extended ∼0.12 mag dimming events of the weak-lined T Tauri star V1334. The start of the first event was missed but came to an end in late 2003, and the second began in 2009 February, and continues as of 2016 November. Since the egress of the current event has not yet been observed, it suggests a period of >13 years if this event is periodic. Spectroscopic observations suggest the presence of a small inner disk, although the spectral energy distribution shows no infrared excess. We explore the possibility that the dimming events are caused by an orbiting body (e.g., a disk warp or dust trap), enhanced disk winds, hydrodynamical fluctuations of the inner disk, or a significant increase in the magnetic field flux at the surface of the star. We also find a ∼0.32 day periodic photometric signal that persists throughout the 2009 dimming which appears to not be due to ellipsoidal variations from a close stellar companion. High-precision photometric observations of V1334 Tau during K2 campaign 13, combined with simultaneous photometric and spectroscopic observations from the ground, will provide crucial information about the photometric variability and its origin.
14. The Mysterious Dimmings of the T Tauri Star V1334 Tau
International Nuclear Information System (INIS)
Rodriguez, Joseph E.; Zhou, George; Cargile, Phillip A.; Relles, Howard M.; Latham, David W.; Eastman, Jason; Bieryla, Allyson; Esquerdo, Gilbert A.; Berlind, Perry; Calkins, Michael L.; Vanderburg, Andrew; Stevens, Daniel J.; Osborn, Hugh P.; Shappee, Benjamin J.; Reed, Phillip A.; Lund, Michael B.; Stassun, Keivan G.; Gaidos, Eric; Ansdell, Megan; Siverd, Robert J.
2017-01-01
We present the discovery of two extended ∼0.12 mag dimming events of the weak-lined T Tauri star V1334. The start of the first event was missed but came to an end in late 2003, and the second began in 2009 February, and continues as of 2016 November. Since the egress of the current event has not yet been observed, it suggests a period of >13 years if this event is periodic. Spectroscopic observations suggest the presence of a small inner disk, although the spectral energy distribution shows no infrared excess. We explore the possibility that the dimming events are caused by an orbiting body (e.g., a disk warp or dust trap), enhanced disk winds, hydrodynamical fluctuations of the inner disk, or a significant increase in the magnetic field flux at the surface of the star. We also find a ∼0.32 day periodic photometric signal that persists throughout the 2009 dimming which appears to not be due to ellipsoidal variations from a close stellar companion. High-precision photometric observations of V1334 Tau during K2 campaign 13, combined with simultaneous photometric and spectroscopic observations from the ground, will provide crucial information about the photometric variability and its origin.
15. ON THE TRANSITIONAL DISK CLASS: LINKING OBSERVATIONS OF T TAURI STARS AND PHYSICAL DISK MODELS
International Nuclear Information System (INIS)
Espaillat, C.; Andrews, S.; Qi, C.; Wilner, D.; Ingleby, L.; Calvet, N.; Hernández, J.; Furlan, E.; D'Alessio, P.; Muzerolle, J.
2012-01-01
Two decades ago 'transitional disks' (TDs) described spectral energy distributions (SEDs) of T Tauri stars with small near-IR excesses, but significant mid- and far-IR excesses. Many inferred this indicated dust-free holes in disks possibly cleared by planets. Recently, this term has been applied disparately to objects whose Spitzer SEDs diverge from the expectations for a typical full disk (FD). Here, we use irradiated accretion disk models to fit the SEDs of 15 such disks in NGC 2068 and IC 348. One group has a 'dip' in infrared emission while the others' continuum emission decreases steadily at all wavelengths. We find that the former have an inner disk hole or gap at intermediate radii in the disk and we call these objects 'transitional disks' and 'pre-transitional disks' (PTDs), respectively. For the latter group, we can fit these SEDs with FD models and find that millimeter data are necessary to break the degeneracy between dust settling and disk mass. We suggest that the term 'transitional' only be applied to objects that display evidence for a radical change in the disk's radial structure. Using this definition, we find that TDs and PTDs tend to have lower mass accretion rates than FDs and that TDs have lower accretion rates than PTDs. These reduced accretion rates onto the star could be linked to forming planets. Future observations of TDs and PTDs will allow us to better quantify the signatures of planet formation in young disks.
16. Peculiarities and Variations in the Optical Spectrum of the RV Tauri-type Star R Sct
Directory of Open Access Journals (Sweden)
Kipper Tõnu
2013-06-01
Full Text Available We analyzed some new high resolution optical spectra of the semiregular RV Tauri-type star R Sct. Fundamental parameters were found to be Teff = 4500 K, log g = 0.0 and ξt = 4.0 km s−1. The results of chemical analysis show that R Sct is a metal-poor star with [Fe/H]≈ −0.5. The carbon content with respect to iron is significantly larger than in the Sun, [C/Fe]=0.84, but there is an evident deficiency of heavy elements. We found no tight correlation of the chemical abundances on the condensation temperatures of elements. This means that in R Sct the depletion by condensation into dust does not work, with possible exception of Ca and Sc. The luminosity derived from the Hipparcos parallax corresponds to a tip of the red-giant branch or slightly above it. Thus it is possible that R Sct evolved off the early-AGB when it has not yet experienced the third dredge-up in thermal pulses, or it is still located on AGB. The peculiarities of spectral features (emissions, line-splitting and the complicated time-variable radial velocities were also studied.
17. High-resolution TNG spectra of T Tauri stars. Near-IR GIANO observations of the young variables XZ Tauri and DR Tauri
Science.gov (United States)
Antoniucci, S.; Nisini, B.; Biazzo, K.; Giannini, T.; Lorenzetti, D.; Sanna, N.; Harutyunyan, A.; Origlia, L.; Oliva, E.
2017-10-01
Aims: We aim to characterise the star-disk interaction region in T Tauri stars that show photometric and spectroscopic variability. Methods: We used the GIANO instrument at the Telescopio Nazionale Galileo to obtain near-infrared high-resolution spectra (R 50 000) of XZ Tau and DR Tau, which are two actively accreting T Tauri stars classified as EXors. Equivalent widths and profiles of the observed features are used to derive information on the properties of the inner disk, the accretion columns, and the winds. Results: Both sources display composite H I line profiles, where contributions from both accreting gas and high-velocity winds can be recognised. These lines are progressively more symmetric and narrower with increasing upper energy which may be interpreted in terms of two components with different decrements or imputed to self-absorption effects. XZ Tau is observed in a relatively high state of activity with respect to literature observations. The variation of the He I 1.08 μm line blue-shifted absorption, in particular, suggests that the inner wind has undergone a dramatic change in its velocity structure, connected with a recent accretion event. DR Tau has a more stable wind as its He I 1.08 μm absorption does not show variations with time in spite of strong variability of the emission component. The IR veiling in the two sources can be interpreted as due to blackbody emission at temperatures of 1600 K and 2300 K for XZ Tau and DR Tau, respectively, with emitting areas 30 times larger than the central star. While for XZ Tau these conditions are consistent with emission from the inner rim of the dusty disk, the fairly high temperature inferred for DR Tau might suggest that its veiling originates from a thick gaseous disk located within the dust sublimation radius. Strong and broad metallic lines, mainly from C I and Fe I, are detected in XZ Tau, similar to those observed in other EXor sources during burst phases. At variance, DR Tau shows weaker and
18. Herbig-Haro objects and T Tauri nebulae
International Nuclear Information System (INIS)
Boehm, K.H.
1975-01-01
The empirical information about Herbig-Haro objects and T Tauri nebulae is summarized. We emphasize especially the importance of the spectroscopic and spectrophotometric data. Relative and (preliminary) absolute emission line fluxes are presented and discussed. We consider the radial velocity data and the detection of a faint blue continuum in Herbig-Haro objects as important from a theoretical point of view. The direct interpretation of the emission line spectra is simple and leads to values of the electron temperature, electron density, density inhomogeneities, filling factors, degree of ionization and chemical abundances. The relevant procedures are discussed in some detail. The possible role of the Herbig-Haro objects in the early phases of stellar evolution is discussed. (orig./BJ) [de
19. PLANETARY SYSTEM FORMATION IN THE PROTOPLANETARY DISK AROUND HL TAURI
Energy Technology Data Exchange (ETDEWEB)
Akiyama, Eiji; Hasegawa, Yasuhiro; Hayashi, Masahiko; Iguchi, Satoru, E-mail: [email protected], E-mail: [email protected] [National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 (Japan)
2016-02-20
We reprocess the Atacama Large Millimeter/Submillimeter Array (ALMA) long-baseline science verification data taken toward HL Tauri. Assuming the observed gaps are opened up by currently forming, unseen bodies, we estimate the mass of such hypothetical bodies based on the following two approaches: the Hill radius analysis and a more elaborate approach developed from the angular momentum transfer analysis in gas disks. For the former, the measured gap widths are used for estimating the mass of the bodies, while for the latter, the measured gap depths are utilized. We show that their masses are comparable to or less than the mass of Jovian planets. By evaluating Toomre’s gravitational instability (GI) condition and cooling effect, we find that the GI might be a mechanism to form the bodies in the outer region of the disk. As the disk might be gravitationally unstable only in the outer region of the disk, inward planetary migration would be needed to construct the current architecture of the observed disk. We estimate the gap-opening mass and show that type II migration might be able to play such a role. Combining GIs with inward migration, we conjecture that all of the observed gaps may be a consequence of bodies that might have originally formed at the outer part of the disk, and have subsequently migrated to the current locations. While ALMA’s unprecedented high spatial resolution observations can revolutionize our picture of planet formation, more dedicated observational and theoretical studies are needed to fully understand the HL Tauri images.
20. Pulsed Accretion in the T Tauri Binary TWA 3A
Energy Technology Data Exchange (ETDEWEB)
Tofflemire, Benjamin M.; Mathieu, Robert D. [Department of Astronomy, University of Wisconsin–Madison, 475 North Charter Street, Madison, WI 53706 (United States); Herczeg, Gregory J. [The Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871 (China); Akeson, Rachel L.; Ciardi, David R. [NASA Exoplanet Science Institute, IPAC/Caltech, Pasadena, CA 91125 (United States)
2017-06-20
TWA 3A is the most recent addition to a small group of young binary systems that both actively accrete from a circumbinary disk and have spectroscopic orbital solutions. As such, it provides a unique opportunity to test binary accretion theory in a well-constrained setting. To examine TWA 3A’s time-variable accretion behavior, we have conducted a two-year, optical photometric monitoring campaign, obtaining dense orbital phase coverage (∼20 observations per orbit) for ∼15 orbital periods. From U -band measurements we derive the time-dependent binary mass accretion rate, finding bursts of accretion near each periastron passage. On average, these enhanced accretion events evolve over orbital phases 0.85 to 1.05, reaching their peak at periastron. The specific accretion rate increases above the quiescent value by a factor of ∼4 on average but the peak can be as high as an order of magnitude in a given orbit. The phase dependence and amplitude of TWA 3A accretion is in good agreement with numerical simulations of binary accretion with similar orbital parameters. In these simulations, periastron accretion bursts are fueled by periodic streams of material from the circumbinary disk that are driven by the binary orbit. We find that TWA 3A’s average accretion behavior is remarkably similar to DQ Tau, another T Tauri binary with similar orbital parameters, but with significantly less variability from orbit to orbit. This is only the second clear case of orbital-phase-dependent accretion in a T Tauri binary.
1. PLANETARY SYSTEM FORMATION IN THE PROTOPLANETARY DISK AROUND HL TAURI
International Nuclear Information System (INIS)
Akiyama, Eiji; Hasegawa, Yasuhiro; Hayashi, Masahiko; Iguchi, Satoru
2016-01-01
We reprocess the Atacama Large Millimeter/Submillimeter Array (ALMA) long-baseline science verification data taken toward HL Tauri. Assuming the observed gaps are opened up by currently forming, unseen bodies, we estimate the mass of such hypothetical bodies based on the following two approaches: the Hill radius analysis and a more elaborate approach developed from the angular momentum transfer analysis in gas disks. For the former, the measured gap widths are used for estimating the mass of the bodies, while for the latter, the measured gap depths are utilized. We show that their masses are comparable to or less than the mass of Jovian planets. By evaluating Toomre’s gravitational instability (GI) condition and cooling effect, we find that the GI might be a mechanism to form the bodies in the outer region of the disk. As the disk might be gravitationally unstable only in the outer region of the disk, inward planetary migration would be needed to construct the current architecture of the observed disk. We estimate the gap-opening mass and show that type II migration might be able to play such a role. Combining GIs with inward migration, we conjecture that all of the observed gaps may be a consequence of bodies that might have originally formed at the outer part of the disk, and have subsequently migrated to the current locations. While ALMA’s unprecedented high spatial resolution observations can revolutionize our picture of planet formation, more dedicated observational and theoretical studies are needed to fully understand the HL Tauri images
2. Monochorionic twin pregnancies
NARCIS (Netherlands)
Hack, K.E.A.
2008-01-01
Following widespread application of assisted reproductive technology modalities and the increased age of motherhood, the incidence of twin gestations has increased markedly. Twins are either monozygotic or dizygotic. Dizygotic (i.e. fraternal) twins result from the fertilization of two different
3. The wind and the magnetospheric accretion onto the T Tauri star S Coronae Australis at sub-au resolution
Science.gov (United States)
Gravity Collaboration; Garcia Lopez, R.; Perraut, K.; Caratti O Garatti, A.; Lazareff, B.; Sanchez-Bermudez, J.; Benisty, M.; Dougados, C.; Labadie, L.; Brandner, W.; Garcia, P. J. V.; Henning, Th.; Ray, T. P.; Abuter, R.; Amorim, A.; Anugu, N.; Berger, J. P.; Bonnet, H.; Buron, A.; Caselli, P.; Clénet, Y.; Coudé Du Foresto, V.; de Wit, W.; Deen, C.; Delplancke-Ströbele, F.; Dexter, J.; Eckart, A.; Eisenhauer, F.; Garcia Dabo, C. E.; Gendron, E.; Genzel, R.; Gillessen, S.; Haubois, X.; Haug, M.; Haussmann, F.; Hippler, S.; Hubert, Z.; Hummel, C. A.; Horrobin, M.; Jocou, L.; Kellner, S.; Kervella, P.; Kulas, M.; Kolb, J.; Lacour, S.; Le Bouquin, J.-B.; Léna, P.; Lippa, M.; Mérand, A.; Müller, E.; Ott, T.; Panduro, J.; Paumard, T.; Perrin, G.; Pfuhl, O.; Ramirez, A.; Rau, C.; Rohloff, R.-R.; Rousset, G.; Scheithauer, S.; Schöller, M.; Straubmeier, C.; Sturm, E.; Thi, W. F.; van Dishoeck, E.; Vincent, F.; Waisberg, I.; Wank, I.; Wieprecht, E.; Wiest, M.; Wiezorrek, E.; Woillez, J.; Yazici, S.; Zins, G.
2017-12-01
Aims: To investigate the inner regions of protoplanetary discs, we performed near-infrared interferometric observations of the classical T Tauri binary system S CrA. Methods: We present the first VLTI-GRAVITY high spectral resolution (R 4000) observations of a classical T Tauri binary, S CrA (composed of S CrA N and S CrA S and separated by 1.̋4), combining the four 8m telescopes in dual-field mode. Results: Our observations in the near-infrared K-band continuum reveal a disc around each binary component, with similar half-flux radii of about 0.1 au at d 130 pc, inclinations (i = 28 ± 3° and i = 22 ± 6°), and position angles (PA = 0°± 6° and PA = –2°± 12°), suggesting that they formed from the fragmentation of a common disc. The S CrA N spectrum shows bright He I and Brγ line emission exhibiting inverse P Cygni profiles, typically associated with infalling gas. The continuum-compensated Brγ line visibilities of S CrA N show the presence of a compact Brγ emitting region whose radius is about 0.06 au, which is twice as big as the truncation radius. This component is mostly tracing a wind. Moreover, a slight radius change between the blue- and red-shifted Brγ line components is marginally detected. Conclusions: The presence of an inverse P Cygni profile in the He I and Brγ lines, along with the tentative detection of a slightly larger size of the blue-shifted Brγ line component, hint at the simultaneous presence of a wind and magnetospheric accretion in S CrA N.
4. THE HERSCHEL DIGIT SURVEY OF WEAK-LINE T TAURI STARS: IMPLICATIONS FOR DISK EVOLUTION AND DISSIPATION
International Nuclear Information System (INIS)
Cieza, Lucas A.; Olofsson, Johan; Henning, Thomas; Harvey, Paul M.; Evans, Neal J. II; Najita, Joan; Merín, Bruno; Liebhart, Armin; Güdel, Manuel; Augereau, Jean-Charles; Pinte, Christophe
2013-01-01
As part of the 'Dust, Ice, and Gas In Time (DIGIT)' Herschel Open Time Key Program, we present Herschel photometry (at 70, 160, 250, 350, and 500 μm) of 31 weak-line T Tauri star (WTTS) candidates in order to investigate the evolutionary status of their circumstellar disks. Of the stars in our sample, 13 had circumstellar disks previously known from infrared observations at shorter wavelengths, while 18 of them had no previous evidence for a disk. We detect a total of 15 disks as all previously known disks are detected at one or more Herschel wavelengths and two additional disks are identified for the first time. The spectral energy distributions (SEDs) of our targets seem to trace the dissipation of the primordial disk and the transition to the debris disk regime. Of the 15 disks, 7 appear to be optically thick primordial disks, including 2 objects with SEDs indistinguishable from those of typical Classical T Tauri stars, 4 objects that have significant deficit of excess emission at all IR wavelengths, and 1 'pre-transitional' object with a known gap in the disk. Despite their previous WTTS classification, we find that the seven targets in our sample with optically thick disks show evidence for accretion. The remaining eight disks have weaker IR excesses similar to those of optically thin debris disks. Six of them are warm and show significant 24 μm Spitzer excesses, while the last two are newly identified cold debris-like disks with photospheric 24 μm fluxes, but significant excess emission at longer wavelengths. The Herschel photometry also places strong constraints on the non-detections, where systems with F 70 /F 70,* ∼> 5-15 and L disk /L * ∼> 10 –3 to 10 –4 can be ruled out. We present preliminary models for both the optically thick and optically thin disks and discuss our results in the context of the evolution and dissipation of circumstellar disks.
5. Musical Interests and Talent: Twin Jazz Musicians and Twin Studies/Twin Research: Loss of a Preterm Multiple; Conjoined Twin Conception; Depression in Fathers of Twins; Twin-to-Twin Transfusion Syndrome/Twin News: High-Achieving Twins; Twin Children of a Tennis Star; Conjoined Twin Separation; Twin Delivery to a Giant Panda.
Science.gov (United States)
Segal, Nancy L
2017-12-01
Findings from twin studies of musical interests and talent are reviewed as a backdrop to the lives and careers of twin jazz musicians, Peter and Will Anderson. The Anderson twins exemplify many aspects of twin research, namely their matched musical abilities, shared musical interests, and common career. This overview is followed by reviews of studies and case reports of bereavement in families who have lost a preterm multiple birth infant, the conception of conjoined twins following in vitro fertilization (IVF), depression in fathers of twins, and twin-to-twin transfusion incidence in monochorionic-diamniotic IVF twin pairs. Twins highlighted in the media include high-achieving identical female twins with nearly identical academic standing, tennis star Roger Federer's two sets of identical twin children, surgical separation of craniopagus conjoined twins, and the rare delivery of twins to a 23-year-old giant panda.
6. SPECTROPOLARIMETRY OF THE CLASSICAL T TAURI STAR BP TAU
International Nuclear Information System (INIS)
Chen, Wei; Johns-Krull, Christopher M.
2013-01-01
We implement a least-squares deconvolution (LSD) code to study magnetic fields on cool stars. We first apply our code to high-resolution optical echelle spectra of 53 Cam (a magnetic Ap star) and three well-studied cool stars (Arcturus, 61 Cyg A, and ξ Boo A) as well as the Sun (by observing the asteroid Vesta) as tests of the code and the instrumentation. Our analysis is based on several hundred photospheric lines spanning the wavelength range 5000 Å to 9000 Å. We then apply our LSD code to six nights of data on the Classical T Tauri Star BP Tau. A maximum longitudinal field of 370 ± 80 G is detected from the photospheric lines on BP Tau. A 1.8 kG dipole tilted at 129° with respect to the rotation axis and a 1.4 kG octupole tilted at 104° with respect to the rotation axis, both with a filling factor of 0.25, best fit our LSD Stokes V profiles. Measurements of several emission lines (He I 5876 Å, Ca II 8498 Å, and 8542 Å) show the presence of strong magnetic fields in the line formation regions of these lines, which are believed to be the base of the accretion footpoints. The field strength measured from these lines shows night-to-night variability consistent with rotation of the star
7. SPECTROPOLARIMETRY OF THE CLASSICAL T TAURI STAR BP TAU
Energy Technology Data Exchange (ETDEWEB)
Chen, Wei; Johns-Krull, Christopher M., E-mail: [email protected], E-mail: [email protected] [Department of Physics and Astronomy, Rice University, Houston, TX 77005 (United States)
2013-10-20
We implement a least-squares deconvolution (LSD) code to study magnetic fields on cool stars. We first apply our code to high-resolution optical echelle spectra of 53 Cam (a magnetic Ap star) and three well-studied cool stars (Arcturus, 61 Cyg A, and ξ Boo A) as well as the Sun (by observing the asteroid Vesta) as tests of the code and the instrumentation. Our analysis is based on several hundred photospheric lines spanning the wavelength range 5000 Å to 9000 Å. We then apply our LSD code to six nights of data on the Classical T Tauri Star BP Tau. A maximum longitudinal field of 370 ± 80 G is detected from the photospheric lines on BP Tau. A 1.8 kG dipole tilted at 129° with respect to the rotation axis and a 1.4 kG octupole tilted at 104° with respect to the rotation axis, both with a filling factor of 0.25, best fit our LSD Stokes V profiles. Measurements of several emission lines (He I 5876 Å, Ca II 8498 Å, and 8542 Å) show the presence of strong magnetic fields in the line formation regions of these lines, which are believed to be the base of the accretion footpoints. The field strength measured from these lines shows night-to-night variability consistent with rotation of the star.
8. The Effect of Substrate Emissivity on the Spectral Emission of a Hot-Gas Overlayer
Science.gov (United States)
2015-12-30
The spectral radiosity , denoted by Js(0, λ, Ts, Tsurf) accounts for both the emitted spectral energy and the reflected spectral energy from the...spectral intensity emitted from the window is given by I(λ, Twin) = εwinI(λ, Twin)BB where εwin is the spectral emissivity. The spectral radiosity incident... radiosity , one determines that the window contributes 6.1% reflected radiation to the observed signal from the anode. Figure 9. Anode-Window Geometry
9. Perinatal hepatic infarction in twin-twin transfusion.
LENUS (Irish Health Repository)
O'Sullivan, M J
2012-02-03
We report a case of a twin pregnancy which was complicated by a twin-twin transfusion in which the recipient twin was noted to have an intra-abdominal echogenic mass. This twin died at two days of age of hepatic infarction. The donor twin was healthy at birth, at thirty weeks\\' gestation, and did not have any subsequent problems. Fetal intra-abdominal echogenicity may be a marker of hepatic infarction.
10. The Brazilian Twin Registry.
Science.gov (United States)
Ferreira, Paulo H; Oliveira, Vinicius C; Junqueira, Daniela R; Cisneros, Lígia C; Ferreira, Lucas C; Murphy, Kate; Ordoñana, Juan R; Hopper, John L; Teixeira-Salmela, Luci F
2016-12-01
The Brazilian Twin Registry (BTR) was established in 2013 and has impelled twin research in South America. The main aim of the initiative was to create a resource that would be accessible to the Brazilian scientific community as well as international researchers interested in the investigation of the contribution of genetic and environmental factors in the development of common diseases, phenotypes, and human behavior traits. The BTR is a joint effort between academic and governmental institutions from Brazil and Australia. The collaboration includes the Federal University of Minas Gerais (UFMG) in Brazil, the University of Sydney and University of Melbourne in Australia, the Australian Twin Registry, as well as the research foundations CNPq and CAPES in Brazil. The BTR is a member of the International Network of Twin Registries. Recruitment strategies used to register twins have been through participation in a longitudinal study investigating genetic and environmental factors for low back pain occurrence, and from a variety of sources including media campaigns and social networking. Currently, 291 twins are registered in the BTR, with data on demographics, zygosity, anthropometrics, and health history having been collected from 151 twins using a standardized self-reported questionnaire. Future BTR plans include the registration of thousands of Brazilian twins identified from different sources and collaborate nationally and internationally with other research groups interested on twin studies.
11. JHKL photometry of three Herbig-Haro jet sources and a nebulous T Tauri star
International Nuclear Information System (INIS)
Vrba, F.J.; Rydgren, A.E.; Zak, D.S.; Computer Sciences Corp., Baltimore, MD; Rensselaer Polytechnic Institute, Troy, NY)
1985-01-01
Infrared sources have been detected at the positions of the Herbig-Haro jet sources HH 30, DG Tau B, and Haro 6-5 B in the Taurus dark cloud complex. The colors of these Herbig-Haro jet sources in the 1-4 micron wavelength range are comparable to those of the dustiest T Tauri stars, while the K magnitudes corrected for likely interstellar extinction are actually somewhat fainter than those oftypical T Tauri stars in this region. These observations are consistent with the view that these Herbig-Haro jet sources are low-mass premain-sequence stars. The nebulous T Tauri star Haro 6-5 was also observed and found to show both a large infrared excess and an intrinsic-polarization of about 3 percent in visible light. Thus this star seems to resemble HL Tau and DG Tau, which have been suggested as examples of young stars with circumstellar disks. 17 references
12. Conjoined (Siamese) Twins in Zambia
African Journals Online (AJOL)
year-old Zambian multiparous mother gave birth to a set of twins with two heads ... (symmetric or mirror image) but one twin attached with an incomplete foetus is known as hetropagtrs. (asymmetrical). Thoracopagus twins (joined at the chest).
13. The reduced kinome of Ostreococcus tauri: core eukaryotic signalling components in a tractable model species.
Science.gov (United States)
Hindle, Matthew M; Martin, Sarah F; Noordally, Zeenat B; van Ooijen, Gerben; Barrios-Llerena, Martin E; Simpson, T Ian; Le Bihan, Thierry; Millar, Andrew J
2014-08-02
The current knowledge of eukaryote signalling originates from phenotypically diverse organisms. There is a pressing need to identify conserved signalling components among eukaryotes, which will lead to the transfer of knowledge across kingdoms. Two useful properties of a eukaryote model for signalling are (1) reduced signalling complexity, and (2) conservation of signalling components. The alga Ostreococcus tauri is described as the smallest free-living eukaryote. With less than 8,000 genes, it represents a highly constrained genomic palette. Our survey revealed 133 protein kinases and 34 protein phosphatases (1.7% and 0.4% of the proteome). We conducted phosphoproteomic experiments and constructed domain structures and phylogenies for the catalytic protein-kinases. For each of the major kinases families we review the completeness and divergence of O. tauri representatives in comparison to the well-studied kinomes of the laboratory models Arabidopsis thaliana and Saccharomyces cerevisiae, and of Homo sapiens. Many kinase clades in O. tauri were reduced to a single member, in preference to the loss of family diversity, whereas TKL and ABC1 clades were expanded. We also identified kinases that have been lost in A. thaliana but retained in O. tauri. For three, contrasting eukaryotic pathways - TOR, MAPK, and the circadian clock - we established the subset of conserved components and demonstrate conserved sites of substrate phosphorylation and kinase motifs. We conclude that O. tauri satisfies our two central requirements. Several of its kinases are more closely related to H. sapiens orthologs than S. cerevisiae is to H. sapiens. The greatly reduced kinome of O. tauri is therefore a suitable model for signalling in free-living eukaryotes.
14. Mid-infrared interferometric variability of DG Tauri: Implications for the inner-disk structure
Science.gov (United States)
Varga, J.; Gabányi, K. É.; Ábrahám, P.; Chen, L.; Kóspál, Á.; Menu, J.; Ratzka, Th.; van Boekel, R.; Dullemond, C. P.; Henning, Th.; Jaffe, W.; Juhász, A.; Moór, A.; Mosoni, L.; Sipos, N.
2017-08-01
Context. DG Tau is a low-mass pre-main sequence star, whose strongly accreting protoplanetary disk exhibits a so-far enigmatic behavior: its mid-infrared thermal emission is strongly time-variable, even turning the 10 μm silicate feature from emission to absorption temporarily. Aims: We look for the reason for the spectral variability at high spatial resolution and at multiple epochs. Methods: Infrared interferometry can spatially resolve the thermal emission of the circumstellar disk, also giving information about dust processing. We study the temporal variability of the mid-infrared interferometric signal, observed with the VLTI/MIDI instrument at six epochs between 2011 and 2014. We fit a geometric disk model to the observed interferometric signal to obtain spatial information about the disk. We also model the mid-infrared spectra by template fitting to characterize the profile and time dependence of the silicate emission. We use physically motivated radiative transfer modeling to interpret the mid-infrared interferometric spectra. Results: The inner disk (r 1-3 au) spectra show a crystalline silicate feature in emission, similar to the spectra of comet Hale-Bopp. The striking difference between the inner and outer disk spectral feature is highly unusual among T Tauri stars. The mid-infrared variability is dominated by the outer disk. The strength of the silicate feature changed by more than a factor of two. Between 2011 and 2014 the half-light radius of the mid-infrared-emitting region decreased from 1.15 to 0.7 au. Conclusions: For the origin of the absorption we discuss four possible explanations: a cold obscuring envelope, an accretion heated inner disk, a temperature inversion on the disk surface and a misaligned inner geometry. The silicate emission in the outer disk can be explained by dusty material high above the disk plane, whose mass can change with time, possibly due to turbulence in the disk. Based on observations made with the ESO Very Large
15. EVIDENCE FOR AN FU ORIONIS-LIKE OUTBURST FROM A CLASSICAL T TAURI STAR
International Nuclear Information System (INIS)
Miller, Adam A.; Poznanski, Dovi; Silverman, Jeffrey M.; Kleiser, Io K. W.; Cenko, S. Bradley; Bloom, Joshua S.; Filippenko, Alexei V.; Hillenbrand, Lynne A.; Kasliwal, Mansi M.; Ofek, Eran O.; Quimby, Robert M.; Covey, Kevin R.; Rojas-Ayala, Barbara; Muirhead, Philip S.; Law, Nicholas M.; Dekany, Richard G.; Rahmer, Gustavo; Hale, David; Smith, Roger; Nugent, Peter
2011-01-01
We present pre- and post-outburst observations of the new FU Orionis-like young stellar object PTF 10qpf (also known as LkHα 188-G4 and HBC 722). Prior to this outburst, LkHα 188-G4 was classified as a classical T Tauri star (CTTS) on the basis of its optical emission-line spectrum superposed on a K8-type photosphere and its photometric variability. The mid-infrared spectral index of LkHα 188-G4 indicates a Class II-type object. LkHα 188-G4 exhibited a steady rise by ∼1 mag over ∼11 months starting in August 2009, before a subsequent more abrupt rise of >3 mag on a timescale of ∼2 months. Observations taken during the eruption exhibit the defining characteristics of FU Orionis variables: (1) an increase in brightness by ∼>4 mag, (2) a bright optical/near-infrared reflection nebula appeared, (3) optical spectra are consistent with a G supergiant and dominated by absorption lines, the only exception being Hα which is characterized by a P Cygni profile, (4) near-infrared spectra resemble those of late K-M giants/supergiants with enhanced absorption seen in the molecular bands of CO and H 2 O, and (5) outflow signatures in H and He are seen in the form of blueshifted absorption profiles. LkHα 188-G4 is the first member of the FU Orionis-like class with a well-sampled optical to mid-infrared spectral energy distribution in the pre-outburst phase. The association of the PTF 10qpf outburst with the previously identified CTTS LkHα 188-G4 (HBC 722) provides strong evidence that FU Orionis-like eruptions represent periods of enhanced disk accretion and outflow, likely triggered by instabilities in the disk. The early identification of PTF 10qpf as an FU Orionis-like variable will enable detailed photometric and spectroscopic observations during its post-outburst evolution for comparison with other known outbursting objects.
16. Twin anemia polycythemia sequence
NARCIS (Netherlands)
Slaghekke, Femke
2014-01-01
In this thesis we describe that Twin Anemia Polycythemia Sequence (TAPS) is a form of chronic feto-fetal transfusion in monochorionic (identical) twins based on a small amount of blood transfusion through very small anastomoses. For the antenatal diagnosis of TAPS, Middle Cerebral Artery – Peak
17. The Danish Twin Registry
DEFF Research Database (Denmark)
Skytthe, Axel; Ohm Kyvik, Kirsten; Vilstrup Holm, Niels
2011-01-01
Introduction: The Danish Twin Registry is a unique source for studies of genetic, familial and environmental factors on life events, health conditions and diseases. Content: More than 85,000 twin pairs born 1870-2008 in Denmark. Validity and coverage: Four main ascertainment methods have been emp...
18. Twin Pregnancy with Gastroschisis in Both Twins
Directory of Open Access Journals (Sweden)
Hui-Fen Kao
2007-12-01
Conclusion: The cause of gastroschisis is unknown, although possible exogenous causes have been studied. The diagnosis of gastroschisis in twin pregnancy is always in late gestation. Therefore, maternal serum alpha feto-protein screening and a detailed prenatal ultrasound evaluation are recommended in multifetal pregnancies.
19. The Curious Case of PDS 11: A Nearby, >10 Myr Old, Classical T Tauri Binary System
Energy Technology Data Exchange (ETDEWEB)
Mathew, Blesson; Manoj, P. [Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Colaba, Mumbai 400005 (India); Bhatt, B. C.; Sahu, D. K.; Muneer, S. [Indian Institute of Astrophysics, Koramangala, Bangalore 560034 (India); Maheswar, G., E-mail: [email protected] [Aryabhatta Research Institute of Observational Sciences (ARIES), Nainital 263002 (India)
2017-05-01
We present results of our study of the PDS 11 binary system, which belongs to a rare class of isolated, high Galactic latitude T Tauri stars. Our spectroscopic analysis reveals that PDS 11 is an M2–M2 binary system with both components showing similar H α emission strengths. Both the components appear to be accreting and are classical T Tauri stars. The lithium doublet Li i λ 6708, a signature of youth, is present in the spectrum of PDS 11A, but not in PDS 11B. From the application of lithium depletion boundary age-dating method and a comparison with the Li i λ 6708 equivalent width distribution of moving groups, we estimated an age of 10–15 Myr for PDS 11A. Comparison with pre-main sequence evolutionary models indicates that PDS 11A is a 0.4 M {sub ⊙} T Tauri star at a distance of 114–131 pc. PDS 11 system does not appear to be associated with any known star-forming regions or moving groups. PDS 11 is a new addition, after TWA 30 and LDS 5606, to the interesting class of old, dusty, wide binary classical T Tauri systems in which both components are actively accreting.
20. Bipolar molecular outflows: T Tauri stars and Herbig-Haro objects
International Nuclear Information System (INIS)
Choe, S.U.
1984-01-01
The relations of Herbig-Haro objects to the observed bipolar molecular outflows with T Tauri stars are studied. An evaporation disk model is proposed to obtain the shape of the disk where gas evaporates and to explain the collimation of the central T Tauri wind. In this case the collimation angle is about 10 0 . The collimated T Tauri wind making a form of de Laval nozzle viscously interacts with the surrounding medium. This interaction enhances the second collimation (about 40 0 ) of the resulting flow, mixing stellar and disk winds with external molecular gas. These viscous outflows are observed in the bipolar molecular outflow of the T Tauri stars. It is also proposed in the model that a Kelvin-Helmholtz instability in the throat of the de Laval nozzle produces clumps, which can be accelerated by the ram pressure of the collimated wind up to the wind speed. The clumps eventually pass through a shock in the outlfow, which results from its encounter with the ambient cloud. The clumps are then moving faster than the surrounding flow. These clumps are identified with Herbig-Haro objects
1. Neonatal status of twins
Directory of Open Access Journals (Sweden)
Božinović Dragica
2012-01-01
Full Text Available Multiple pregnancy is a pregnancy where more than one fetus develops simultaneously in the womb, as a result of the ovulation and fertilization of more than one egg. It is relatively rare in humans and represents the rest of the phylogenetic stages. The most common are twins and they indicate the development of two fetuses in the womb. The frequency of twin pregnancies is about 1%. Multiple pregnancies belong to a group of high-risk pregnancies because of the many complications that occur during the pregnancy: higher number of premature deliveries, bleeding, early neonatal complications and higher perinatal morbidity and mortality. Such pregnancies and infants require greater supervision and monitoring. The aim of this study was to determine the percentage of baby twins born at the maternity ward of the General Hospital in Prokuplje and their morbidity and mortality. Data on the total number of deliveries, number of twins, parity and maternal age, gestational age, body weight of twins, method of delivery, Apgar score and perinatal mortality were collected and statistically analyzed by means of retrospective analysis of operative birth and neonatal protocol for 6 years (2005 of 2010. Out of 4527 mothers who gave birth 43 were pairs of twins, or 0.95% of women gave birth to twins. These babies are more likely born by Caesarean section, but delivered with slightly lower birth weight.
2. TIME VARIABILITY OF EMISSION LINES FOR FOUR ACTIVE T TAURI STARS. I. OCTOBER–DECEMBER IN 2010
International Nuclear Information System (INIS)
Chou, Mei-Yin; Takami, Michihiro; Karr, Jennifer L.; Shang Hsien; Liu, Hauyu Baobab; Manset, Nadine; Beck, Tracy; Pyo, Tae-Soo; Chen, Wen-Ping; Panwar, Neelam
2013-01-01
We present optical spectrophotometric monitoring of four active T Tauri stars (DG Tau, RY Tau, XZ Tau, RW Aur A) at high spectral resolution (R ∼> 1 × 10 4 ), to investigate the correlation between time variable mass ejection seen in the jet/wind structure of the driving source and time variable mass accretion probed by optical emission lines. This may allow us to constrain the understanding of the jet/wind launching mechanism, the location of the launching region, and the physical link with magnetospheric mass accretion. In 2010, observations were made at six different epochs to investigate how daily and monthly variability might affect such a study. We perform comparisons between the line profiles we observed and those in the literature over a period of decades and confirm the presence of time variability separate from the daily and monthly variability during our observations. This is so far consistent with the idea that these line profiles have a long-term variability (3-20 yr) related to episodic mass ejection suggested by the structures in the extended flow components. We also investigate the correlations between equivalent widths and between luminosities for different lines. We find that these correlations are consistent with the present paradigm of steady magnetospheric mass accretion and emission line regions that are close to the star.
3. TIME VARIABILITY OF EMISSION LINES FOR FOUR ACTIVE T TAURI STARS. I. OCTOBER-DECEMBER IN 2010
Energy Technology Data Exchange (ETDEWEB)
Chou, Mei-Yin; Takami, Michihiro; Karr, Jennifer L.; Shang Hsien; Liu, Hauyu Baobab [Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan (China); Manset, Nadine [Canada-France-Hawaii Telescope, 65-1238 Mamalahoa Hwy, Kamuela, HI 96743 (United States); Beck, Tracy [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Pyo, Tae-Soo [Subaru Telescope, 650 North Aohoku Place, Hilo, HI 96720 (United States); Chen, Wen-Ping; Panwar, Neelam [Institute of Astronomy, National Central University, Taoyuan County 32001, Taiwan (China)
2013-04-15
We present optical spectrophotometric monitoring of four active T Tauri stars (DG Tau, RY Tau, XZ Tau, RW Aur A) at high spectral resolution (R {approx}> 1 Multiplication-Sign 10{sup 4}), to investigate the correlation between time variable mass ejection seen in the jet/wind structure of the driving source and time variable mass accretion probed by optical emission lines. This may allow us to constrain the understanding of the jet/wind launching mechanism, the location of the launching region, and the physical link with magnetospheric mass accretion. In 2010, observations were made at six different epochs to investigate how daily and monthly variability might affect such a study. We perform comparisons between the line profiles we observed and those in the literature over a period of decades and confirm the presence of time variability separate from the daily and monthly variability during our observations. This is so far consistent with the idea that these line profiles have a long-term variability (3-20 yr) related to episodic mass ejection suggested by the structures in the extended flow components. We also investigate the correlations between equivalent widths and between luminosities for different lines. We find that these correlations are consistent with the present paradigm of steady magnetospheric mass accretion and emission line regions that are close to the star.
4. SUSY meets her twin
Energy Technology Data Exchange (ETDEWEB)
Katz, Andrey [Theory Division, CERN,CH-1211 Geneva 23 (Switzerland); Département de Physique Théorique and Center for Astroparticle Physics (CAP),Université de Genève,24 quai Ansermet, CH-1211 Genève 4 (Switzerland); Mariotti, Alberto [Theoretische Natuurkunde and IIHE/ELEM, Vrije Universiteit Brussel,and International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Pokorski, Stefan [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,ul. Pasteura 5, PL-02-093 Warsaw (Poland); Redigolo, Diego [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University,Tel-Aviv 69978 (Israel); Department of Particle Physics and Astrophysics, Weizmann Institute of Science,Rehovot 7610001 (Israel); Ziegler, Robert [Institute for Theoretical Particle Physics (TTP), Karlsruhe Institute of Technology,Engesserstraße 7, D-76128 Karlsruhe (Germany)
2017-01-31
We investigate the general structure of mirror symmetry breaking in the Twin Higgs scenario. We show, using the IR effective theory, that a significant gain in fine tuning can be achieved if the symmetry is broken hardly. We emphasize that weakly coupled UV completions can naturally accommodate this scenario. We analyze SUSY UV completions and present a simple Twin SUSY model with a tuning of around 10% and colored superpartners as heavy as 2 TeV. The collider signatures of general Twin SUSY models are discussed with a focus on the extended Higgs sectors.
5. THE HERSCHEL DIGIT SURVEY OF WEAK-LINE T TAURI STARS: IMPLICATIONS FOR DISK EVOLUTION AND DISSIPATION
Energy Technology Data Exchange (ETDEWEB)
Cieza, Lucas A. [Institute for Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822 (United States); Olofsson, Johan; Henning, Thomas [Max Planck Institute fuer Astronomie, Koenigstuhl 17, D-69117 Heidelberg (Germany); Harvey, Paul M.; Evans, Neal J. II [Department of Astronomy, University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712-1205 (United States); Najita, Joan [National Optical Astronomy Observatory, 950 N. Cherry Avenue, Tucson, AZ 86719 (United States); Merin, Bruno [Herschel Science Centre, European Space Astronomy Centre, ESA, P.O. Box 78, E-28691 Villanueva de la Canada, Madrid (Spain); Liebhart, Armin; Guedel, Manuel [Department of Astronomy, University of Vienna, Tuerkenschanzstr. 17, A-1180 Vienna (Austria); Augereau, Jean-Charles; Pinte, Christophe, E-mail: [email protected] [UJF-Grenoble 1/CNRS-INSU, Institut de Planetologie et d' Astrophysique (IPAG) UMR 5274, BP 53, F-38041 Grenoble cedex 9 (France)
2013-01-10
As part of the 'Dust, Ice, and Gas In Time (DIGIT)' Herschel Open Time Key Program, we present Herschel photometry (at 70, 160, 250, 350, and 500 {mu}m) of 31 weak-line T Tauri star (WTTS) candidates in order to investigate the evolutionary status of their circumstellar disks. Of the stars in our sample, 13 had circumstellar disks previously known from infrared observations at shorter wavelengths, while 18 of them had no previous evidence for a disk. We detect a total of 15 disks as all previously known disks are detected at one or more Herschel wavelengths and two additional disks are identified for the first time. The spectral energy distributions (SEDs) of our targets seem to trace the dissipation of the primordial disk and the transition to the debris disk regime. Of the 15 disks, 7 appear to be optically thick primordial disks, including 2 objects with SEDs indistinguishable from those of typical Classical T Tauri stars, 4 objects that have significant deficit of excess emission at all IR wavelengths, and 1 'pre-transitional' object with a known gap in the disk. Despite their previous WTTS classification, we find that the seven targets in our sample with optically thick disks show evidence for accretion. The remaining eight disks have weaker IR excesses similar to those of optically thin debris disks. Six of them are warm and show significant 24 {mu}m Spitzer excesses, while the last two are newly identified cold debris-like disks with photospheric 24 {mu}m fluxes, but significant excess emission at longer wavelengths. The Herschel photometry also places strong constraints on the non-detections, where systems with F {sub 70}/F {sub 70,*} {approx}> 5-15 and L {sub disk}/L {sub *} {approx}> 10{sup -3} to 10{sup -4} can be ruled out. We present preliminary models for both the optically thick and optically thin disks and discuss our results in the context of the evolution and dissipation of circumstellar disks.
6. Preparing for Twins
Science.gov (United States)
7. The 16th International Twin Congress: Highlights from Madrid/Twin Research: Twin Study of Partner Aggression; ABO Incompatibility in Dizygotic Twins; Growth Discordance in a Monoamniotic Twin Pair; Quick Note on Twin Implantation/In the Media: Long-Lost Twins Found; NASA Twin Experiment; Twin Brothers and the Las Vegas Attack; Retired Twin Airline Pilots; Twin Film Clips.
Science.gov (United States)
Segal, Nancy L
2018-02-01
Highlights from the 16th International Twin Congress, held in Madrid, Spain from November 16-18, 2017, are presented. The Twin Congress, formerly held every three years, now takes place biennially with a single-day meeting organized during the off years. This meeting is the largest gathering of scientific twin researchers, medical personnel, and representatives of multiple birth organizations in the world. This overview is followed by reviews of recent twin research and commentary concerning partner aggression, ABO incompatibility in dizygotic twins, growth discordance in a monoamniotic twin pair and twin implantation. The article closes with summaries of timely topics in the media, namely a father's finding of his long-lost twin children, early results from the NASA twin experiment, twin brothers at the center of the October 2017 Las Vegas attack, retired twin airline pilots, and clips from recent films with twin-based themes.
8. THE SPITZER c2d SURVEY OF WEAK-LINE T TAURI STARS. III. THE TRANSITION FROM PRIMORDIAL DISKS TO DEBRIS DISKS
International Nuclear Information System (INIS)
Wahhaj, Zahed; Cieza, Lucas; Koerner, David W.; Case, April; Stapelfeldt, Karl R.; Chapman, Nicholas; Padgett, Deborah L.; Brooke, Tim; Keller, James R.; MerIn, Bruno; Evans, Neal J.; Harvey, Paul; Sargent, Anneila; Van Dishoeck, Ewine F.; Allen, Lori; Blake, Geoff; Mundy, Lee; Myers, Philip C.
2010-01-01
We present 3.6 to 70 μm Spitzer photometry of 154 weak-line T Tauri stars (WTTSs) in the Chamaeleon, Lupus, Ophiuchus, and Taurus star formation regions, all of which are within 200 pc of the Sun. For a comparative study, we also include 33 classical T Tauri stars which are located in the same star-forming regions. Spitzer sensitivities allow us to robustly detect the photosphere in the IRAC bands (3.6 to 8 μm) and the 24 μm MIPS band. In the 70 μm MIPS band, we are able to detect dust emission brighter than roughly 40 times the photosphere. These observations represent the most sensitive WTTSs survey in the mid- to far-infrared to date and reveal the frequency of outer disks (r = 3-50 AU) around WTTSs. The 70 μm photometry for half the c2d WTTSs sample (the on-cloud objects), which were not included in the earlier papers in this series, those of Padgett et al. and Cieza et al., are presented here for the first time. We find a disk frequency of 19% for on-cloud WTTSs, but just 5% for off-cloud WTTSs, similar to the value reported in the earlier works. WTTSs exhibit spectral energy distributions that are quite diverse, spanning the range from optically thick to optically thin disks. Most disks become more tenuous than L disk /L * = 2 x 10 -3 in 2 Myr and more tenuous than L disk /L * = 5 x 10 -4 in 4 Myr.
9. Twin-twin transfusion syndrome: etiology, severity and rational management
NARCIS (Netherlands)
van Gemert, M. J.; Umur, A.; Tijssen, J. G.; Ross, M. G.
2001-01-01
The twin-twin transfusion syndrome is a serious complication of monochorionic twin pregnancies. Partly as a result of an inadequate understanding of the pathophysiology of the syndrome, there is a lack of consensus in clinical management. We sought to review the available information on the etiology
10. Ionization ratios and elemental abundances in the atmosphere of 68 Tauri
Science.gov (United States)
Aouina, A.; Monier, R.
2017-12-01
We have derived the ionization ratios of twelve elements in the atmosphere of the star 68 Tauri (HD 27962) using an ATLAS9 model atmosphere with 72 layers computed for the effective temperature and surface gravity of the star. We then computed a grid of synthetic spectra generated by SYNSPEC49 based on an ATLAS9 model atmosphere in order to model one high resolution spectrum secured by one of us (RM) with the échelle spectrograph SOPHIE at Observatoire de Haute Provence. We could determine the abundances of several elements in their dominant ionization stage, including those defining the Am phenomenon. We thus provide new abundance determinations for 68 Tauri using updated accurate atomic data retrieved from the NIST database which extend previous abundance works.
11. The character and behaviour of circumstellar shells at T Tauri stars
International Nuclear Information System (INIS)
Goetz, W.
1988-01-01
T Tauri stars are extremely young low-mass stars in the pre-main sequence stage. A brief review of investigations made at the Sonneberg observatory concerning the character and the behaviour of circumstellar shells at T Tauri stars is given. They lead to the construction of a shell model on the basis of observational facts. The idea rests upon the causal connection between the gas and dust shell phenomenon and the cosmogonic mass loss of the stars, which is the connecting link between the stars and their shells and which appears in the early phase of the pre-main sequence stage and decreases, like the accompanying shell phenomena, during the evolution of the stars. (author)
12. Anencephaly with incomplete twinning (diprosopus).
Science.gov (United States)
Riccardi, V M; Bergmann, C A
1977-10-01
A case of diprosopus with anencephaly is presented. It is suggested that such concurrence of neural tube defects and incomplete twinning corroborates the notion that a single pathogenetic mechanism may be common to both neural tube defects and monozygotic twinning.
13. New upper limit to the coronal line emission from the T Tauri star RU Lupi
Energy Technology Data Exchange (ETDEWEB)
Gahm, G F [Stockholm Observatory (Sweden); Lago, M T.V.T. [Universidade do Porto (Portugal). Grupo de Matematica Aplicada; Penston, M V [ESTEC, European Space Agency, Villafranca Satellite Tracking Station, Madrid, (Spain)
1981-05-01
A high dispersion AAT spectrogram sets an upper limit on the (Fe x) emission line lambda 6374.5 A in the T Tauri star RU Lupi. The intensity of any 10/sup 6/ K corona in this star is less than 600 times that of the Sun compared to a chromosphere and transition region of 3 x 10/sup 3/ to 2 x 10/sup 5/ K gas 10/sup 6/ times stronger than the Sun's. The important theoretical implications are noted.
14. Relativistic twins or sextuplets?
International Nuclear Information System (INIS)
Sheldon, Eric
2003-01-01
A recent study of the relativistic twin 'paradox' by Soni in this journal affirmed that 'A simple solution of the twin paradox also shows anomalous behaviour of rigidly connected distant clocks' but entailed a pedagogic hurdle which the present treatment aims to surmount. Two scenarios are presented: the first 'flight-plan' is akin to that depicted by Soni, with constant-velocity segments, while the second portrays an alternative mission undertaken with sustained acceleration and deceleration, illustrated quantitatively for a two-way spacecraft flight from Earth to Polaris (465.9 light years distant) and back
15. Relativistic twins or sextuplets?
CERN Document Server
Sheldon, E S
2003-01-01
A recent study of the relativistic twin 'paradox' by Soni in this journal affirmed that 'A simple solution of the twin paradox also shows anomalous behaviour of rigidly connected distant clocks' but entailed a pedagogic hurdle which the present treatment aims to surmount. Two scenarios are presented: the first 'flight-plan' is akin to that depicted by Soni, with constant-velocity segments, while the second portrays an alternative mission undertaken with sustained acceleration and deceleration, illustrated quantitatively for a two-way spacecraft flight from Earth to Polaris (465.9 light years distant) and back.
16. Imaging of conjoined twins
Energy Technology Data Exchange (ETDEWEB)
McHugh, Kieran [Great Ormond Street Hospital for Children, Department of Radiology, London (United Kingdom); Kiely, Edward M.; Spitz, Lewis [Great Ormond Street Hospital for Children, Department of Surgery, London (United Kingdom)
2006-09-15
The incidence of conjoined twins is estimated to be around 1 in 250,000 live births. There is a distinct female predominance. In this paper the imaging of conjoined twins both antenatally and postnatally is reviewed, in particular taking into consideration recent advances with multidetector CT. Accurate counselling of parents regarding the likely outcome of the pregnancy and the likelihood of successful separation is dependent on good prenatal imaging with ultrasound and MRI. Planning of postnatal surgical separation is aided by accurate preoperative imaging which, depending on the conjoined area, will encompass many imaging modalities, but often relies heavily on CT scanning. (orig.)
17. Imaging of conjoined twins
International Nuclear Information System (INIS)
McHugh, Kieran; Kiely, Edward M.; Spitz, Lewis
2006-01-01
The incidence of conjoined twins is estimated to be around 1 in 250,000 live births. There is a distinct female predominance. In this paper the imaging of conjoined twins both antenatally and postnatally is reviewed, in particular taking into consideration recent advances with multidetector CT. Accurate counselling of parents regarding the likely outcome of the pregnancy and the likelihood of successful separation is dependent on good prenatal imaging with ultrasound and MRI. Planning of postnatal surgical separation is aided by accurate preoperative imaging which, depending on the conjoined area, will encompass many imaging modalities, but often relies heavily on CT scanning. (orig.)
18. Residual Gas and Dust around Transition Objects and Weak T Tauri Stars
Energy Technology Data Exchange (ETDEWEB)
Doppmann, Greg W. [W. M. Keck Observatory, 65-1120 Mamalahoa Hwy., Kamuela, HI 96743 (United States); Najita, Joan R. [National Optical Astronomy Observatory, 950 N. Cherry Avenue, Tucson, AZ 85719 (United States); Carr, John S., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Naval Research Laboratory, Code 7213, Washington, DC 20375 (United States)
2017-02-20
Residual gas in disks around young stars can spin down stars, circularize the orbits of terrestrial planets, and whisk away the dusty debris that is expected to serve as a signpost of terrestrial planet formation. We have carried out a sensitive search for residual gas and dust in the terrestrial planet region surrounding young stars ranging in age from a few to ∼10 Myr. Using high-resolution 4.7 μ m spectra of transition objects (TOs) and weak T Tauri stars, we searched for weak continuum excesses and CO fundamental emission, after making a careful correction for the stellar contribution to the observed spectrum. We find that the CO emission from TOs is weaker and located farther from the star than CO emission from nontransition T Tauri stars with similar stellar accretion rates. The difference is possibly the result of chemical and/or dynamical effects (i.e., a low CO abundance or close-in low-mass planets). The weak T Tauri stars show no CO fundamental emission down to low flux levels (5 × 10{sup −20} to 10{sup −18} W m{sup −2}). We illustrate how our results can be used to constrain the residual disk gas content in these systems and discuss their potential implications for star and planet formation.
19. Identification and analysis of OsttaDSP, a phosphoglucan phosphatase from Ostreococcus tauri.
Directory of Open Access Journals (Sweden)
Julieta B Carrillo
Full Text Available Ostreococcus tauri, the smallest free-living (non-symbiotic eukaryote yet described, is a unicellular green alga of the Prasinophyceae family. It has a very simple cellular organization and presents a unique starch granule and chloroplast. However, its starch metabolism exhibits a complexity comparable to higher plants, with multiple enzyme forms for each metabolic reaction. Glucan phosphatases, a family of enzymes functionally conserved in animals and plants, are essential for normal starch or glycogen degradation in plants and mammals, respectively. Despite the importance of O. tauri microalgae in evolution, there is no information available concerning the enzymes involved in reversible phosphorylation of starch. Here, we report the molecular cloning and heterologous expression of the gene coding for a dual specific phosphatase from O. tauri (OsttaDSP, homologous to Arabidopsis thaliana LSF2. The recombinant enzyme was purified to electrophoretic homogeneity to characterize its oligomeric and kinetic properties accurately. OsttaDSP is a homodimer of 54.5 kDa that binds and dephosphorylates amylopectin. Also, we also determined that residue C162 is involved in catalysis and possibly also in structural stability of the enzyme. Our results could contribute to better understand the role of glucan phosphatases in the metabolism of starch in green algae.
20. The Placenta in Twin-to-Twin Transfusion Syndrome and Twin Anemia Polycythemia Sequence.
Science.gov (United States)
Couck, Isabel; Lewi, Liesbeth
2016-06-01
Twin-to-twin transfusion syndrome (TTTS) and twin anemia polycythemia sequence (TAPS) are complications unique to monochorionic twin pregnancies and their shared circulation. Both are the result of the transfusion imbalance in the intertwin circulation. TTTS is characterized by an amniotic fluid discordance, whereas in TAPS, there is a severe discordance in hemoglobin levels. The article gives an overview of the typical features of TTTS and TAPS placentas.
1. Dialysis for twins
DEFF Research Database (Denmark)
Gramkow, Ann-Maria; Aarup, Michael; Andersen, L. L. T.
2014-01-01
A 32-year-old woman with known stage-4 chronic kidney disease due to lupus nephritis presented with twin pregnancy after in vitro fertilization at a gestational age of 24 weeks + 3 days because of imminent preterm labour. Repeated ultrasound evaluations confirmed intrauterine growth restriction...
2. Anaesthesia for conjoined twins
African Journals Online (AJOL)
draw~ver patient system consisting of a paediatric. "Ambu" bag and "Paedivalven drawing oxygen-en- riched air through a halothane vaporiser. Oxygen was supplied from an electric oxygen concentrator which can give 2 litres of 95% oxygen per minute. This apparatus has been described I. Mter 3 minutes the Sa02 of Twin ...
3. Sleep Terrors in Twins
Directory of Open Access Journals (Sweden)
J Gordon Millichap
2008-12-01
Full Text Available In an attempt to clarify the genetic and environmental causes of sleep terrors in childhood, reasearchers in Canada followed 390 pairs of monozygotic and dizygotic twins by assessing the frequency of sleep terrors at 18 and 30 months of age using a questionnaire administered to the biological mothers.
4. Sleep Terrors in Twins
OpenAIRE
J Gordon Millichap
2008-01-01
In an attempt to clarify the genetic and environmental causes of sleep terrors in childhood, reasearchers in Canada followed 390 pairs of monozygotic and dizygotic twins by assessing the frequency of sleep terrors at 18 and 30 months of age using a questionnaire administered to the biological mothers.
5. The USC Adult Twin Cohorts: International Twin Study and California Twin Program.
Science.gov (United States)
Cozen, Wendy; Hwang, Amie E; Cockburn, Myles G; Hamilton, Ann S; Zadnick, John; Mack, Thomas M
2013-02-01
The study of twin subjects permits the documentation of crude heritability and may promote the identification of specific causal alleles. We believe that at the current time, the chief research advantage of twins as subjects, especially monozygotic twins, is that the commonality of their genetic and cultural identity simplifies the interpretation of biological associations. In order to study genetic and environmental determinants of cancer and chronic diseases, we developed two twin registries, maintained at the University of Southern California: The International Twin Study (ITS) and the California Twin Program (CTP). The ITS is a volunteer registry of twins with cancer and chronic disease consisting of 17,245 twin pairs affected by cancer and chronic disease, respectively, ascertained by advertising in periodicals from 1980-1991. The CTP is a population-based registry of California-born twin pairs ascertained by linking the California birth records to the State Department of Motor Vehicles. Over 51,000 individual California twins representing 36,965 pairs completed and returned 16-page questionnaires. Cancer diagnoses in the California twins are updated by regular linkage to the California Cancer Registry. Over 5,000 cancer patients are represented in the CTP. Twins from both registries have participated extensively in studies of breast cancer, melanoma, lymphoma, multiple sclerosis, systemic lupus erythematosus, diabetes mellitus type 1, mammographic density, smoking, and other traits and conditions.
6. Twin-twin transfusion syndrome - diagnosis and prognosis
Directory of Open Access Journals (Sweden)
Hajrić-Egić Amira
2003-01-01
Full Text Available Twin-twin transfusion syndrome is a serious complication of monozygotic, monochorionic, diamniotic twins resulting from transplacental vascular communications. In this syndrome blood is thought to be shunted from one twin - donor,who develops anaemia,growth retardation and oligoamnios, to the other twin - recipient,who becomes plethoric,macrosomic and develops polyhydroamnios. The incidence of twin-twin transfusion syndrome ranges from 5-15% of all twin pregnancies. If this condition develops in the second trimester, it is usually associated with spontaneous abortion and death of one or both fetuses before viability. Developing the syndrome in the third trimester has better perinatal outcome. Mortality rates ranging from 56%-100%, depending on gestational age and severity of the syndrome. The ultrasound criterias for diagnosis, in this study,were the presence of twins of the same sex with discordant growth, with oligohydroamnios in one twin sac and polyhydroamnios in the other one, one placenta and thin membrane between twins. The present study shows clinical course of 14 cases and value of Doppler ultrasound to analyze the usefulness of umbilical artery blood flow velocimetry for predicting the risk of twin-twin transfusion syndrome. 14 twin pregnancies with twin-twin transfusion syndrome were diagnosed during the last four years period and prospectivelly followed. 9 cases were diagnosed before the completion od 28 weeks of gestation.The mean gestational age was 21,6_+4,2 weeks at diagnosis and 23,2+_3,6 weeks at delivery. 5 cases were diagnosed after 28 weeks of gestation. The mean gestational age in this group was 29,6+_2,1 weeks at diagnosis and 33+_3,3 weeks at delivery. The survival rate in this study was 29%(8/28.9 cases ended in spontaneous abortion between 18th and 27th weeks of pregnancy (table 1 and 5 in premature labor (table 2.There were 7 intrauterine death (5 at admission and 2 few days after admission and 13 neonatal deaths
7. Brazilian Twin Registry: A Bright Future for Twin Studies/Twin Research: Twin Study of Alcohol Consumption and Mortality; Oxygen Uptake in Adolescent Twins/In the News: Superfecundated Twins In Vietnam; Adolescent Twin Relations; Twin and Triplet Co-Workers; A Special Twin Ultrasound; Monozygotic Twins With Different Skin Color; Identical Twin Returns from Space.
Science.gov (United States)
Segal, Nancy L
2016-06-01
The establishment of the Brazilian Twin Registry for the study of genetic, social, and cultural influences on behavior is one of eleven newly funded projects in the Department of Psychology at the University of São Paulo. These 11 interrelated projects form the core of the university's Center for Applied Research on Well-Being and Human Behavior. An overview of the planned twin research and activities to date is presented. Next, two recent twin studies are reviewed, one on the relationship between alcohol consumption and mortality, and the other on factors affecting maximal oxygen uptake. Twins cited in the media include the first identified superfecundated twins in Vietnam, adolescent twin relations, twins and triplets who work together, monozygotic twins with different skin tones and a co-twin control study that addresses the effects of space travel.
8. Sleep-EEG in dizygotic twins discordant for Williams syndrome.
Science.gov (United States)
Bódizs, Róbert; Gombos, Ferenc; Szocs, Katalin; Réthelyi, János M; Gerván, Patrícia; Kovács, Ilona
2014-01-30
Reports on twin pairs concordant and discordant for Williams syndrome were published before, but no study unravelled sleep physiology in these cases yet. We aim to fill this gap by analyzing sleep records of a twin pair discordant for Williams syndrome extending our focus on presleep wakefulness and sleep spindling. We performed multiplex ligation-dependent probe amplification of the 7q11.23 region of a 17 years old dizygotic opposite-sex twin pair discordant for Williams syndrome. Polysomnography of laboratory sleep at this age was analyzed and followed-up after 1.5 years by ambulatory polysomnography. Sleep stages scoring, EEG power spectra and sleep spindle analyses were carried out. The twin brother showed reduced levels of amplification for all of the probes in the 7q11.23 region indicating a typical deletion spanning at least 1.038 Mb between FKBP6 and CLIP2. The results of the twin sister showed normal copy numbers in the investigated region. Lower sleep times and efficiencies, as well as higher slow wave sleep percents of the twin brother were evident during both recordings. Roughly equal NREM, Stage 2 and REM sleep percents were found. EEG analyses revealed state and derivation-independent decreases in alpha power, lack of an alpha spectral peak in presleep wakefulness, as well as higher NREM sleep sigma peak frequency in the twin brother. Faster sleep spindles with lower amplitude and shorter duration characterized the records of the twin brother. Spectra show a striking reliability and correspondence between the two situations (laboratory vs. home records). Alterations in sleep and specific neural oscillations including the alpha/sigma waves are inherent aspects of Williams syndrome.
9. Reared-Apart Chinese Twins: Chance Discovery/Twin-Based Research: Twin Study of Media Use; Twin Relations Over the Life Span; Breast-Feeding Opposite-Sex Twins/Print and Online Media: Twins in Fashion; Second Twin Pair Born to Tennis Star; Twin Primes; Twin Pandas.
Science.gov (United States)
Segal, Nancy L
2017-04-01
A January 2017 reunion of 10-year-old reared-apart Chinese twin girls was captured live on ABC's morning talk show Good Morning America, and rebroadcast on their evening news program Nightline. The twins' similarities and differences, and their participation in ongoing research will be described. This story is followed by reviews of twin research concerning genetic and environmental influences on media use, twin relations across the lifespan and the breast-feeding of opposite-sex twins. Popular interest items include twins in fashion, the second twin pair born to an internationally renowned tennis star, twin primes and twin pandas.
10. Thermodynamics of twinning
International Nuclear Information System (INIS)
Mueller, I.; Zak, G.
1995-01-01
The quasiplastic hysteresis occuring in shape memory alloys is associated with twinning in tension and compression, i.e. a conversion of one martensitic variant into antoher one. It shows the phenomena of internal elasticity and internal yield, heretofore studied extensively in pseudoelasticity. This paper presents experimental evidence of such phenomena and it offers partial explanation in identifying the onset of yield as an instability phenomenon due to coherency. That conjecture is motivated from a previous consideration of pseudoelasticity. (orig.)
11. Monozygotic twins with discordant intestinal rotation
International Nuclear Information System (INIS)
Smith, Vance L.; Nwomeh, Benedict C.; Long, Frederick
2006-01-01
Previous case reports have suggested a strong concordance of intestinal malrotation among identical twins. This has led to the recommendation that the asymptomatic twin undergo screening when malrotation is discovered in the identical sibling. We present a case of monozygotic twins in which one twin presented with intestinal malrotation with midgut volvulus while the other twin was found to have normal gastrointestinal anatomy. (orig.)
12. Monozygotic twins with discordant intestinal rotation
Energy Technology Data Exchange (ETDEWEB)
Smith, Vance L.; Nwomeh, Benedict C. [Ohio State University College of Medicine and Public Health, Department of Pediatric Surgery, Columbus Children' s Hospital, Columbus, OH (United States); Long, Frederick [Ohio State University College of Medicine and Public Health, Department of Radiology, Columbus Children' s Hospital, Columbus, OH (United States)
2006-04-15
Previous case reports have suggested a strong concordance of intestinal malrotation among identical twins. This has led to the recommendation that the asymptomatic twin undergo screening when malrotation is discovered in the identical sibling. We present a case of monozygotic twins in which one twin presented with intestinal malrotation with midgut volvulus while the other twin was found to have normal gastrointestinal anatomy. (orig.)
13. Illustrations of the twin paradox
International Nuclear Information System (INIS)
Rebhan, E.
1985-01-01
In order to provide a more intuitive understanding of the twin paradox, several illustrations of this are presented. In one of these, each of the twins is equipped with a lamp whose monochromatic light can be observed by the other. In other illustrations the travelling twin uses an Einstein train instead of a space ship, all the cars of the train and all stations along the route of the train being equipped with clocks. (author)
14. Abundâncias químicas de estrelas T Tauri fracas
Science.gov (United States)
Rojas, G. A.; Gregorio-Hetem, J.
2003-08-01
15. Holographic twin Higgs model.
Science.gov (United States)
Geller, Michael; Telem, Ofri
2015-05-15
We present the first realization of a "twin Higgs" model as a holographic composite Higgs model. Uniquely among composite Higgs models, the Higgs potential is protected by a new standard model (SM) singlet elementary "mirror" sector at the sigma model scale f and not by the composite states at m_{KK}, naturally allowing for m_{KK} beyond the LHC reach. As a result, naturalness in our model cannot be constrained by the LHC, but may be probed by precision Higgs measurements at future lepton colliders, and by direct searches for Kaluza-Klein excitations at a 100 TeV collider.
16. Holographic Twin Higgs Model
Science.gov (United States)
Geller, Michael; Telem, Ofri
2015-05-01
We present the first realization of a "twin Higgs" model as a holographic composite Higgs model. Uniquely among composite Higgs models, the Higgs potential is protected by a new standard model (SM) singlet elementary "mirror" sector at the sigma model scale f and not by the composite states at mKK , naturally allowing for mKK beyond the LHC reach. As a result, naturalness in our model cannot be constrained by the LHC, but may be probed by precision Higgs measurements at future lepton colliders, and by direct searches for Kaluza-Klein excitations at a 100 TeV collider.
17. X-shooter spectroscopy of FU Tauri A
Science.gov (United States)
Stelzer, B.; Alcalá, J. M.; Scholz, A.; Natta, A.; Randich, S.; Covino, E.
2013-03-01
We have analyzed a broad-band optical and near-infrared spectrum of FU Tau A, which is a presumed young brown dwarf in the Taurus star forming region that has intrigued both theorists and observers by its overluminosity in the Hertzsprung-Russell (HR) diagram with respect to standard pre-main sequence evolutionary models. FU Tau A is brighter than any other Taurus member of the same or similar spectral type, and various phenomena (accretion, activity, binarity) have been put forth as possible explanations. The new data, obtained with the X-shooter spectrograph at the Very Large Telescope, include an unprecedented wealth of information on stellar parameters and simultaneously observed accretion and outflow indicators for FU Tau A. We present the first measurements of gravity (log g = 3.5 ± 0.5), radial velocity (RV = 22.5 ± 2.9 km s-1), rotational velocity (vsini = 20 ± 5 km s-1), and lithium equivalent width (EWLi = 430 ± 20 mÅ) for FU Tau A. From the rotational velocity and the published period we infer a disk inclination of i ≳ 50°. The lithium content is much lower than theoretically expected for such a young very low-mass object, adding another puzzling feature to this object's properties. We determine the mass accretion rate of FU Tau A from comparison of the luminosities of 20 emission lines to empirical calibrations from the literature and find a mean of log Ṁacc [M⊙/yr] = -9.9 with standard deviation σ = 0.2. The accretion rate determined independently from modeling of the excess emission in the Balmer and Paschen continua is consistent with this value. The corresponding accretion luminosity is too low to make a significant contribution to the bolometric luminosity. Strong magnetic activity affecting the stellar parameters or binarity of FU Tau A, both combined with extreme youth, may be responsible for its position in the HR diagram. The existence of an outflow in FU Tau A is demonstrated through the first detection of forbidden emission lines
18. Turbulent mixing layers in supersonic protostellar outflows, with application to DG Tauri
Science.gov (United States)
White, M. C.; Bicknell, G. V.; Sutherland, R. S.; Salmeron, R.; McGregor, P. J.
2016-01-01
Turbulent entrainment processes may play an important role in the outflows from young stellar objects at all stages of their evolution. In particular, lateral entrainment of ambient material by high-velocity, well-collimated protostellar jets may be the cause of the multiple emission-line velocity components observed in the microjet-scale outflows driven by classical T Tauri stars. Intermediate-velocity outflow components may be emitted by a turbulent, shock-excited mixing layer along the boundaries of the jet. We present a formalism for describing such a mixing layer based on Reynolds decomposition of quantities measuring fundamental properties of the gas. In this model, the molecular wind from large disc radii provides a continual supply of material for entrainment. We calculate the total stress profile in the mixing layer, which allows us to estimate the dissipation of turbulent energy, and hence the luminosity of the layer. We utilize MAPPINGS IV shock models to determine the fraction of total emission that occurs in [Fe II] 1.644 μm line emission in order to facilitate comparison to previous observations of the young stellar object DG Tauri. Our model accurately estimates the luminosity and changes in mass outflow rate of the intermediate-velocity component of the DG Tau approaching outflow. Therefore, we propose that this component represents a turbulent mixing layer surrounding the well-collimated jet in this object. Finally, we compare and contrast our model to previous work in the field.
19. Clumpy molecular clouds: A dynamic model self-consistently regulated by T Tauri star formation
International Nuclear Information System (INIS)
Norman, C.; Silk, J.
1980-01-01
A new model is proposed which can account for the longevity, energetics, and dynamical structure of dark molecular clouds. It seems clear that the kinetic and gravitational energy in macroscopic cloud motions cannot account for the energetic of many molecular clouds. A stellar energy source must evidently be tapped, and infrared observations indicate that one cannot utilize massive stars in dark clouds. Recent observations of a high space density of T Tauri stars in some dark clouds provide the basis for our assertion that high-velocity winds from these low-mass pre--main-sequence stars provide a continuous dynamic input into molecular clouds. The T Tauri winds sweep up shells of gas, the intersections or collisions of which form dense clumps embedded in a more rarefied interclump medium. Observations constrain the clumps to be ram-pressure confined, but at the relatively low Mach numbers, continuous leakage occurs. This mass input into the interclump medium leads to the existence of two phases; a dense, cold phase (clumps of density approx.10 4 --10 5 cm -3 and temperature approx.10 K) and a warm, more diffuse, interclump medium (ICM, of density approx.10 3 --10 4 cm -3 and temperature approx.30 K). Clump collisions lead to coalescence, and the evolution of the mass spectrum of clumps is studied
20. V819 TAU: A RARE WEAK-LINED T TAURI STAR WITH A WEAK INFRARED EXCESS
International Nuclear Information System (INIS)
Furlan, E.; Forrest, W. J.; Manoj, P.; Kim, K. H.; Watson, Dan M.; Sargent, B. A.
2009-01-01
We use Spitzer data to infer that the small infrared excess of V819 Tau, a weak-lined T Tauri star in Taurus, is real and not attributable to a 'companion' 10'' to the south. We do not confirm the mid-infrared excess in HBC 427 and V410 X-ray 3, which are also non-accreting T Tauri stars in the same region; instead, for the former object, the excess arises from a red companion 9'' to the east. A single-temperature blackbody fit to the continuum excess of V819 Tau implies a dust temperature of 143 K; however, a better fit is achieved when the weak 10 and 20 μm silicate emission features are also included. We infer a disk of sub-μm silicate grains between about 1 AU and several 100 AU with a constant surface density distribution. The mid-infrared excess of V819 Tau can be successfully modeled with dust composed mostly of small amorphous olivine grains at a temperature of 85 K, and most of the excess emission is optically thin. The disk could still be primordial, but gas-poor and therefore short-lived, or already at the debris disk stage, which would make it one of the youngest debris disk systems known.
1. A radio survey of weak T Tauri stars in Taurus-Auriga
International Nuclear Information System (INIS)
O'neal, D.; Feigelson, E.D.; Mathieu, R.D.; Myers, P.C.
1990-01-01
A multi-epoch 5 GHz survey of candidate or confirmed weak T Tauri stars in the Taurus-Auriga molecular cloud complex was conducted with the Very Large Array. The stars were chosen from those having detectable X-ray or chromospheric emission, and weak-emission-line pre-main-sequence stars found by other means. Snapshots of 99 VLA fields containing 119 candidate stars were obtained with a sensitivity of 0.7 mJy; most fields were observed on two or three dates. Nine radio sources coincident with cataloged stars were found. One may be an RS CVn binary system; the other eight are pre-main-sequence stars. Three of the detected stars - HD 283447, V410 Tau, and FK X-ray 1 - were previously known radio sources. Five new detections are Herbig's Anon 1, Hubble 4, HDE 283572, Elias 12, and HK Tau/c. At least five of the sources are variable, and no linear or circular polarization was found. Several lines of evidence suggest that the radio-detected weak T Tauri stars are quite young, perhaps younger on average than nondetected stars. 54 refs
2. Voice similarity in identical twins.
Science.gov (United States)
Van Gysel, W D; Vercammen, J; Debruyne, F
2001-01-01
If people are asked to discriminate visually the two individuals of a monozygotic twin (MT), they mostly get into trouble. Does this problem also exist when listening to twin voices? Twenty female and 10 male MT voices were randomly assembled with one "strange" voice to get voice trios. The listeners (10 female students in Speech and Language Pathology) were asked to label the twins (voices 1-2, 1-3 or 2-3) in two conditions: two standard sentences read aloud and a 2.5-second midsection of a sustained /a/. The proportion correctly labelled twins was for female voices 82% and 63% and for male voices 74% and 52% for the sentences and the sustained /a/ respectively, both being significantly greater than chance (33%). The acoustic analysis revealed a high intra-twin correlation for the speaking fundamental frequency (SFF) of the sentences and the fundamental frequency (F0) of the sustained /a/. So the voice pitch could have been a useful characteristic in the perceptual identification of the twins. We conclude that there is a greater perceptual resemblance between the voices of identical twins than between voices without genetic relationship. The identification however is not perfect. The voice pitch possibly contributes to the correct twin identifications.
3. Twin Studies of Atopic Dermatitis
DEFF Research Database (Denmark)
Elmose, Camilla; Thomsen, Simon Francis
2015-01-01
Aim. The aim of this study was to conduct a systematic review of population-based twin studies of (a) the concordance and heritability of AD and (b) the relationship between AD and asthma and, furthermore, to reinterpret findings from previous twin studies in the light of the emerging knowledge a...
4. Hypertensive disorders in twin pregnancy
NARCIS (Netherlands)
J.G. Santema (Job); E. Koppelaar (Elin); H.C.S. Wallenburg (Henk)
1995-01-01
textabstractObjective: To compare the incidence and severity of pregnancy-induced hypertensive disorders in twin pregnancy and in singleton gestation. Study design: Case-control study in the setting of a University Hospital. Each pregnancy of a consecutive series of 187 twin pregnancies attending
5. Ferrobielastic twinning in irradiated quartz
International Nuclear Information System (INIS)
Shiau, S.M.
1986-01-01
6. Oliver Sacks: Our Correspondence About Twins/Twin Research: Vanishing Twins Syndrome; Discordant Sex in MZ Twins; Pregnancy Outcomes in IVF and ICSI Conceived Twins/Print and Media: Superfetated Twins; Twins Discordant for Smoking; Twins in Fashion; Yale University Twin Hockey Players; Conjoined Twin-Visiting Professor.
Science.gov (United States)
Segal, Nancy L
2017-08-01
The late neurologist and author, Oliver Sacks, published an insightful 1986 review of Marjorie Wallace's book, The Silent Twins, in the New York Times. Taking exception to his assertion about Sir Francis Galton, I wrote a letter to the Times' editor. The letter was unpublished, but it brought a wonderful response from Sacks himself that is reproduced and examined. Next, brief reviews of twin research concerning the vanishing twin syndrome (VTS), discordant sex in a monozygotic (MZ) twin pair, and multiple pregnancy outcomes from assisted reproductive technology (ART) are presented. This section is followed by popular coverage of superfetated twins, smoking-discordant co-twins, twins in fashion, Yale University twin hockey players, and a visiting professor who was a conjoined twin.
7. C2D spitzer-IRS spectra of disks around T tauri stars : II. PAH emission features
NARCIS (Netherlands)
Geers, V. C.; Augereau, J. -C; Pontoppidan, K. M.; Dullemond, C. P.; Visser, R.; Kessler-Silacci, J. E.; Evans, N. J.; van Dishoeck, E. F.; Blake, G. A.; Boogert, A. C. A.; Lahuis, F.; Merin, B.
Aims. We search for Polycyclic Aromatic Hydrocarbon (PAH) features towards young low-mass (T Tauri) stars and compare them with surveys of intermediate mass (Herbig Ae/Be) stars. The presence and strength of the PAH features are interpreted with disk radiative transfer models exploring the PAH
8. Minimal mirror twin Higgs
Energy Technology Data Exchange (ETDEWEB)
Barbieri, Riccardo [Institute of Theoretical Studies, ETH Zurich,CH-8092 Zurich (Switzerland); Scuola Normale Superiore,Piazza dei Cavalieri 7, 56126 Pisa (Italy); Hall, Lawrence J.; Harigaya, Keisuke [Department of Physics, University of California,Berkeley, California 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory,Berkeley, California 94720 (United States)
2016-11-29
In a Mirror Twin World with a maximally symmetric Higgs sector the little hierarchy of the Standard Model can be significantly mitigated, perhaps displacing the cutoff scale above the LHC reach. We show that consistency with observations requires that the Z{sub 2} parity exchanging the Standard Model with its mirror be broken in the Yukawa couplings. A minimal such effective field theory, with this sole Z{sub 2} breaking, can generate the Z{sub 2} breaking in the Higgs sector necessary for the Twin Higgs mechanism. The theory has constrained and correlated signals in Higgs decays, direct Dark Matter Detection and Dark Radiation, all within reach of foreseen experiments, over a region of parameter space where the fine-tuning for the electroweak scale is 10-50%. For dark matter, both mirror neutrons and a variety of self-interacting mirror atoms are considered. Neutrino mass signals and the effects of a possible additional Z{sub 2} breaking from the vacuum expectation values of B−L breaking fields are also discussed.
9. A Computational Discriminability Analysis on Twin Fingerprints
Science.gov (United States)
Liu, Yu; Srihari, Sargur N.
Sharing similar genetic traits makes the investigation of twins an important study in forensics and biometrics. Fingerprints are one of the most commonly found types of forensic evidence. The similarity between twins’ prints is critical establish to the reliability of fingerprint identification. We present a quantitative analysis of the discriminability of twin fingerprints on a new data set (227 pairs of identical twins and fraternal twins) recently collected from a twin population using both level 1 and level 2 features. Although the patterns of minutiae among twins are more similar than in the general population, the similarity of fingerprints of twins is significantly different from that between genuine prints of the same finger. Twins fingerprints are discriminable with a 1.5%~1.7% higher EER than non-twins. And identical twins can be distinguished by examine fingerprint with a slightly higher error rate than fraternal twins.
10. Therapeutic modalities of twin to twin transfusion syndrome
Directory of Open Access Journals (Sweden)
Šulović N.
2015-01-01
Full Text Available Twin to twin transfusion syndrome (TTTTS accounts for approximately 10% of monochorionic twin pregnancies and, if left untreated, is associated with high morbidity and mortality rate. A net transfusion of blood flow from one fetus (donor twin to the other (recipient twin via placental vascular anastomoses has been supposed as the major etiology of TTTTS. The donor twin becomes hypovolemic and oliguria, oligohydramnios, and a variable degree of growth restriction develop, whereas the recipient twin manifests polyuria, polyhydramnios, and hydrops in response to hypervolemia. TTTTS can be treated by either serial amniocentesis or selective fetoscopic laser coagulation of the communicating vessels. The rationale for removal of large volumes of amniotic fluid is to prevent preterm delivery secondary to polyhydramnios and to improve fetal circulation by reducing pressure on the chorionic plate. On the other hand, the goal of laser therapy is to occlude vascular anastomoses, thereby interrupting intertwin blood exchange. Although laser treatment is associated with increased survival rate and reduced neurologic complications, compared with amnioreduction, it requires highly specialized centers, whereas serial amniocentesis has the advantage of being performed worldwide. Therefore, the optimal treatment for pregnancies complicated with TTTTS is still controversial.
11. Antenatal management of twin-twin transfusion syndrome and twin anemia-polycythemia sequence.
Science.gov (United States)
Slaghekke, Femke; Zhao, Depeng P; Middeldorp, Johanna M; Klumper, Frans J; Haak, Monique C; Oepkes, Dick; Lopriore, Enrico
2016-08-01
Twin-twin transfusion syndrome (TTTS) and twin anemia polycythemia sequence (TAPS) are severe complications in monochorionic twin pregnancies associated with high mortality and morbidity risk if left untreated. Both diseases result from imbalanced inter-twin blood transfusion through placental vascular anastomoses. This review focuses on the differences in antenatal management between TTTS and TAPS. Expert commentary: The optimal management for TTTS is fetoscopic laser coagulation of the vascular anastomoses, preferably using the Solomon technique in which the whole vascular equator is coagulated. The Solomon technique is associated with a reduction of residual anastomosis and a reduction in post-operative complications. The optimal management for TAPS is not clear and includes expectant management, intra-uterine transfusion with or without partial exchange transfusion and fetoscopic laser surgery.
12. Discussing the low fraction of disk-bearing T Tauri stars discovered near to the Sh2-296 nebula
Science.gov (United States)
Gregorio-Hetem, Jane
2015-08-01
A multiband study has been developed by our team in the direction of young star clusters associated to the Sh2-296 nebula aiming to unveil the star formation history of this galactic molecular cloud that shows a mixing of different age stellar groups. A sample of 58 pre-main sequence stars has been recently discovered by us in this region (Fernandes et al. 2015, MNRAS in press), based on optical spectral features. Only 41% of the sample shows evidence of IR excess revealing the presence of circumstellar disks. It is interesting to note that the targets were revealed by their strong X-ray emission, typically found in T Tauri stars (TTs) (Santos-Silva et al. 2015, in preparation) . In this case, it would be expected a larger number of disk-bearing stars and also the fraction of circumstellar emission (fc = Ldisk/Ltotal ) should be more significant in these objects. However, we verified that only 12% of the sample has fc > 30%. This low fraction is quite rare compared to most young star-forming regions, suggesting that some external factor has accelerated the disc dissipation. In the present work we explore the circumstellar structure of a subsample of 8 TTs associated to Sh2-296. The TTs were selected on the basis of their high circumstellar emission, which is estimated by SED fitting that uses near- to mid-IR data extracted from available catalogues (WISE, AKARI, MSX). The circumstellar characteristics are confronted to interstellar environment by comparing the stellar spatial distribution with 12CO maps (Nanten Survey, Fukui et al. ). Most of the TTs are projected against moderate molecular emission (33 Jy), but some of them are found in regions of lower levels of gas distribution (3.8 Jy). The similarities and differences found among the studied objects are discussed in order to better understand the formation and evolution of protostellar disks of the selected sample and their role in the star formation scenario nearby Sh2-296
13. Twin Higgs Asymmetric Dark Matter.
Science.gov (United States)
García García, Isabel; Lasenby, Robert; March-Russell, John
2015-09-18
We study asymmetric dark matter (ADM) in the context of the minimal (fraternal) twin Higgs solution to the little hierarchy problem, with a twin sector with gauged SU(3)^{'}×SU(2)^{'}, a twin Higgs doublet, and only third-generation twin fermions. Naturalness requires the QCD^{'} scale Λ_{QCD}^{'}≃0.5-20 GeV, and that t^{'} is heavy. We focus on the light b^{'} quark regime, m_{b^{'}}≲Λ_{QCD}^{'}, where QCD^{'} is characterized by a single scale Λ_{QCD}^{'} with no light pions. A twin baryon number asymmetry leads to a successful dark matter (DM) candidate: the spin-3/2 twin baryon, Δ^{'}∼b^{'}b^{'}b^{'}, with a dynamically determined mass (∼5Λ_{QCD}^{'}) in the preferred range for the DM-to-baryon ratio Ω_{DM}/Ω_{baryon}≃5. Gauging the U(1)^{'} group leads to twin atoms (Δ^{'}-τ^{'}[over ¯] bound states) that are successful ADM candidates in significant regions of parameter space, sometimes with observable changes to DM halo properties. Direct detection signatures satisfy current bounds, at times modified by dark form factors.
14. The nature of pseudo-twinning modes on the basis of a twin classification scheme
International Nuclear Information System (INIS)
Singh, Jung B.; Sundararaman, M.; Krishnan, M.
2011-01-01
Pseudo-twins can form in ordered structures under high stress conditions. These twins are defined by lattice sites that are at twin positions but are incorrectly occupied by different species of atoms. The present note discusses if it is possible to further classify pseudo-twins into different modes based on the nature of associated twinning elements.
15. Twins and Kindergarten Separation: Divergent Beliefs of Principals, Teachers, Parents, and Twins
Science.gov (United States)
Gordon, Lynn Melby
2015-01-01
Should principals enforce mandatory separation of twins in kindergarten? Do school separation beliefs of principals differ from those of teachers, parents of twins, and twins themselves? This survey questioned 131 elementary principals, 54 kindergarten teachers, 201 parents of twins, and 112 twins. A majority of principals (71%) believed that…
16. The classical twin study and beyond
NARCIS (Netherlands)
Boomsma, D.I.; Busjahn, A.; Peltonen, L.
2002-01-01
Twin studies have been a valuable source of information about the genetic basis of complex traits. To maximize the potential of twin studies, large, worldwide registers of data on twins and their relatives have been established. Here, we provide an overview of the current resources for twin
17. Monochorionic twin pregnancies: a systematic approach to ...
African Journals Online (AJOL)
Complications unique to these pregnancies include Twin-To-Twin Transfusion Syndrome (TTTS), Twin Polycythaemia Anaemia Sequence (TAPS), Selective Intrauterine Growth Restriction (sIUGR) and death of the co-twin. Adhering to a systematic and objective approach of management, can lead to early recognition and ...
18. Ülehomme on õpetajate päev - milline oli teie parim õpetaja? / Toomas Edur, Tauri Tallermaa, Irene Käosaar...[jt.
Index Scriptorium Estoniae
2009-01-01
Küsimusele vastavad Rahvusooper Estonia balleti kunstiline juht Toomas Edur, koolitaja Tauri Tallermaa, haridus- ja teadusministeeriumi osakonnajuhataja Irene Käosaar, Tartu Karlova Gümnaasiumi direktor Undel Kokk ja näitleja Andrus Vaarik
19. Peak effect in twinned superconductors
International Nuclear Information System (INIS)
Larkin, A.I.; Marchetti, M.C.; Vinokur, V.M.
1995-01-01
A sharp maximum in the critical current J c as a function of temperature just below the melting point of the Abrikosov flux lattice has recently been observed in both low- and high-temperature superconductors. This peak effect is strongest in twinned crystals for fields aligned with the twin planes. We propose that this peak signals the breakdown of the collective pinning regime and the crossover to strong pinning of single vortices on the twin boundaries. This crossover is very sharp and can account for the steep drop of the differential resistivity observed in experiments. copyright 1995 The American Physical Society
20. Emission-line widths and stellar-wind flows in T Tauri stars
International Nuclear Information System (INIS)
Sa, C.; Lago, M.T.V.T.
1986-01-01
Spectra are reported of T Tauri stars taken with the IPCS on the Isaac Newton Telescope at the Observatorio del Roque de los Muchachos at a dispersion of l7 A mm -1 . These were taken in order to determine emission-line widths and hence flow velocities in the winds of these stars following the successful modelling of the wind from RU Lupi using such data. Line widths in RW Aur suggest a similar pattern to the wind flow as in RU Lupi with velocities rising in the inner chromosphere of the star and then entering a 'ballistic' zone. The wind from DFTau is also similar but velocities are generally much lower and the lines sharper. (author)
1. Optical veiling, disk accretion, and the evolution of T Tauri stars
International Nuclear Information System (INIS)
Hartmann, L.W.; Kenyon, S.J.
1990-01-01
High-resolution spectra of 31 K7-M1 T Tauri stars (TTs) in the Taurus-Auriga molecular cloud demonstrate that most of these objects exhibit substantial excess emission at 5200 A. Extrapolations of these data consistent with low-resolution spectrophotometry indicate that the extra emission is comparable to the stellar luminosity in many cases. If this continuum emission arises in the boundary layers of accreting disks, more than about 30 percent of all TTs may be accreting material at a rate which is sufficiently rapid to alter their evolution from standard Hayashi tracks. It is estimated that roughly 10 percent of the final stellar mass is accreted in the TT phase. This amount of material is comparable to the minimum gravitationally unstable disk mass estimated by Larson and it is speculated that the TT phase represents the final stages of disk accretion driven by gravitational instabilities. 40 refs
2. Spectroscopy of bright Algol-type semi-detached close binary system HU Tauri (HR 1471)
Science.gov (United States)
Parthasarathy, M.
2018-01-01
Radial velocities of the primary component (B8V) of HU Tauri derived from the photographic spectra obtained during January 1974 to December 1974 and spectroscopic orbital elements from the analysis of the radial velocity curve of the B8V primary are given. The H line of the late type secondary component is clearly detected on the photographic spectra taken around the quadratures and radial velocities of the secondary component are derived. The radial velocity semi amplitudes of the primary (K) and secondary (K) are found to be 60 km/sec and 234 km/sec respectively. The mass ratio M/M = K/K is found to be 0.2564. The detection of the H line of the secondary is confirmed from the high resolution spectra that I obtained during 1981 and 1983 at quadratures using the 2.1-m McDonald observatory Otto Struve reflector telescope and high resolution coude Reticon spectrograph.
3. IMAGING THE DISK AND JET OF THE CLASSICAL T TAURI STAR AA TAU
International Nuclear Information System (INIS)
Cox, Andrew W.; Grady, Carol A.; Hammel, Heidi B.; Hornbeck, Jeremy; Russell, Ray W.; Sitko, Michael L.; Woodgate, Bruce E.
2013-01-01
Previous studies of the classical T Tauri star AA Tau have interpreted the UX-Orionis-like photo-polarimetric variability as being due to a warp in the inner disk caused by an inclined stellar magnetic dipole field. We test that these effects are macroscopically observable in the inclination and alignment of the disk. We use Hubble Space Telescope (HST)/STIS coronagraphic imagery to measure the V magnitude of the star for both STIS coronagraphic observations, compare these data with optical photometry in the literature, and find that, unlike other classical T Tauri stars observed in the same HST program, the disk is most robustly detected in scattered light at stellar optical minimum light. We measure the outer disk radius, 1.''15 ± 0.''10, major-axis position angle, and disk inclination and find that the inner disk, as reported in the literature, is both misinclined and misaligned with respect to the outer disk. AA Tau drives a faint jet, detected in both STIS observations and in follow-on Goddard Fabry-Perot imagery, which is also misaligned with respect to the projection of the outer disk minor axis and is poorly collimated near the star, but which can be traced 21'' from the star in data from 2005. The measured outer disk inclination, 71° ± 1°, is out of the range of inclinations suggested for stars with UX-Orionis-like variability when no grain growth has occurred in the disk. The faintness of the disk, small disk size, and detection of the star despite the high inclination all indicate that the dust disk must have experienced grain growth and settling toward the disk midplane, which we verify by comparing the observed disk with model imagery from the literature.
4. Mottled Protoplanetary Disk Ionization by Magnetically Channeled T Tauri Star Energetic Particles
Science.gov (United States)
Fraschetti, F.; Drake, J. J.; Cohen, O.; Garraffo, C.
2018-02-01
The evolution of protoplanetary disks is believed to be driven largely by angular momentum transport resulting from magnetized disk winds and turbulent viscosity. The ionization of the disk that is essential for these processes has been thought to be due to host star coronal X-rays but could also arise from energetic particles produced by coronal flares, or traveling shock waves, and advected by the stellar wind. We have performed test-particle numerical simulations of energetic protons propagating into a realistic T Tauri stellar wind, including a superposed small-scale magnetostatic turbulence. The isotropic (Kolmogorov power spectrum) turbulent component is synthesized along the individual particle trajectories. We have investigated the energy range [0.1–10] GeV, consistent with expectations from Chandra X-ray observations of large flares on T Tauri stars and recent indications by the Herschel Space Observatory of a significant contribution of energetic particles to the disk ionization of young stars. In contrast with a previous theoretical study finding a dominance of energetic particles over X-rays in the ionization throughout the disk, we find that the disk ionization is likely dominated by X-rays over much of its area, except within narrow regions where particles are channeled onto the disk by the strongly tangled and turbulent magnetic field. The radial thickness of such regions is 5 stellar radii close to the star and broadens with increasing radial distance. This likely continues out to large distances from the star (10 au or greater), where particles can be copiously advected and diffused by the turbulent wind.
5. Twin-to-twin transfusion syndrome : from placental anastomoses to long-term outcome
NARCIS (Netherlands)
Lopriore, Enrico
2006-01-01
Twin-to-twin transfusion syndrome (TTTS) is a severe complication of monochorionic twin pregnancies associated with high perinatal mortality and morbidity rates. Placental vascular anastomoses, almost invariably present in monochorionic placentas, are the essential anatomical substrate for the
6. Herschel GASPS spectral observations of T Tauri stars in Taurus. Unraveling far-infrared line emission from jets and discs
NARCIS (Netherlands)
Alonso-Martínez, M.; Riviere-Marichalar, P.; Meeus, G.; Kamp, I.; Fang, M.; Podio, L.; Dent, W. R. F.; Eiroa, C.
2017-01-01
Context. At early stages of stellar evolution young stars show powerful jets and/or outflows that interact with protoplanetary discs and their surroundings. Despite the scarce knowledge about the interaction of jets and/or outflows with discs, spectroscopic studies based on Herschel and ISO data
7. A Powerful Twin Arrives
Science.gov (United States)
1999-11-01
First Images from FORS2 at VLT KUEYEN on Paranal The first, major astronomical instrument to be installed at the ESO Very Large Telescope (VLT) was FORS1 ( FO cal R educer and S pectrograph) in September 1998. Immediately after being attached to the Cassegrain focus of the first 8.2-m Unit Telescope, ANTU , it produced a series of spectacular images, cf. ESO PR 14/98. Many important observations have since been made with this outstanding facility. Now FORS2 , its powerful twin, has been installed at the second VLT Unit Telescope, KUEYEN . It is the fourth major instrument at the VLT after FORS1 , ISAAC and UVES.. The FORS2 Commissioning Team that is busy installing and testing this large and complex instrument reports that "First Light" was successfully achieved already on October 29, 1999, only two days after FORS2 was first mounted at the Cassegrain focus. Since then, various observation modes have been carefully tested, including normal and high-resolution imaging, echelle and multi-object spectroscopy, as well as fast photometry with millisecond time resolution. A number of fine images were obtained during this work, some of which are made available with the present Press Release. The FORS instruments ESO PR Photo 40a/99 ESO PR Photo 40a/99 [Preview - JPEG: 400 x 345 pix - 203k] [Normal - JPEG: 800 x 689 pix - 563kb] [Full-Res - JPEG: 1280 x 1103 pix - 666kb] Caption to PR Photo 40a/99: This digital photo shows the twin instruments, FORS2 at KUEYEN (in the foreground) and FORS1 at ANTU, seen in the background through the open ventilation doors in the two telescope enclosures. Although they look alike, the two instruments have specific functions, as described in the text. FORS1 and FORS2 are the products of one of the most thorough and advanced technological studies ever made of a ground-based astronomical instrument. They have been specifically designed to investigate the faintest and most remote objects in the universe. They are "multi-mode instruments" that
8. Intrinsic polarization changes and the H-alpha and CA II emission features in T-Tauri stars
Science.gov (United States)
Svatos, J.; Solc, M.
1981-12-01
On the basis of the correlation between polarization and emission features observed in certain T-Tauri stars, it is concluded that flaring effects associated with UV and/or X-ray irradiation and with increased magnetic field are responsible for the intrinsic polarization changes in T-Tauri stars. The correlation between emission Ca II lines and polarization degree both in Miras and T-Tau stars is thought to support the contention that the intrinsic polarization changes are due to the irradiation of silicate-like grains. In some T-Tau stars the increase in the magnetic field can be the principal agent causing the polarization increase due to the enhanced orientation of elongated grains.
9. Estimating twin concordance for bivariate competing risks twin data
DEFF Research Database (Denmark)
Scheike, Thomas; Holst, Klaus K.; Hjelmborg, Jacob B.
2014-01-01
For twin time-to-event data, we consider different concordance probabilities, such as the casewise concordance that are routinely computed as a measure of the lifetime dependence/correlation for specific diseases. The concordance probability here is the probability that both twins have experience...... events with the competing risk death. We thus aim to quantify the degree of dependence through the casewise concordance function and show a significant genetic component...... the event of interest. Under the assumption that both twins are censored at the same time, we show how to estimate this probability in the presence of right censoring, and as a consequence, we can then estimate the casewise twin concordance. In addition, we can model the magnitude of within pair dependence...... over time, and covariates may be further influential on the marginal risk and dependence structure. We establish the estimators large sample properties and suggest various tests, for example, for inferring familial influence. The method is demonstrated and motivated by specific twin data on cancer...
10. Growth curves for twins in Slovenia.
Science.gov (United States)
Bricelj, Katja; Blickstein, Isaac; Bržan-Šimenc, Gabrijela; Janša, Vid; Lučovnik, Miha; Verdenik, Ivan; Trojner-Bregar, Andreja; Tul, Nataša
2017-02-01
Abnormalities of fetal growth are more common in twins. We introduce the growth curves for monitoring fetal growth in twin pregnancies in Slovenia. Slovenian National Perinatal Information System for the period between 2002 and 2010 was used to calculate birth weight percentiles for all live born twins for each week from 22nd to 40th week. The calculated percentiles of birth weight for all live-born twins in Slovenia served as the basis for drawing 'growth' curves. The calculated growth curves for twins will help accurately diagnose small or large twin fetuses for their gestational age in the native central European population.
11. Measuring the rotation periods of 4-10 Myr T-Tauri stars in the Orion OB1 association
Science.gov (United States)
Karim, Md Tanveer; Stassun, Keivan; Briceno, Cesar; Vivas, Kathy; Raetz, Stefanie; Calvet, Nuria; Mateu, Cecilia; Downes, Juan Jose; Hernandez, Jesus; Neuhäuser, Ralph; Mugrauer, Markus; Takahashi, Hidenori; Tachihara, Kengo; Chini, Rolf; YETI
2016-01-01
Most existing studies of young stellar populations have focused on the youngest (Investigaciones de Astronomía-Quest Equatorial Survey Team (CIDA-QUEST), the Young Exoplanet Transit Initiative (YETI) and from a Kitt Peak National Observatory (KPNO) campaign. We investigated stellar rotation periods according to the type of stars (Classical or Weak-lined T-Tauri stars) and their locations, to look for population-wide trends. We detected 563 periodic variables and 1411 non-periodic variables by investigating the light curves of these stars. We find that ~ 30% of Weak-line T-Tauri stars (WTTS) and ~ 20% of Classical T-Tauri stars (CTTS) are periodic. Though we did not find any noticeable difference in rotation period between CTTS and WTTS, our study does show a change in the overall rotation periods of stars 4-10 Myr old, consistent with predictions of angular momentum evolution models, an important constraint for theoretical models for an age range for which no similar data existed.
12. Molecular dynamics simulation of albite twinning and pericline twinning in low albite
International Nuclear Information System (INIS)
Li, Bin; Knowles, Kevin M
2013-01-01
Two twinning laws, the albite law and the pericline law, are the predominant growth twinning modes in triclinic plagioclase feldspars such as low albite, NaAlSi 3 O 8 , in which the aluminum and silicon atoms are in an ordered arrangement on the tetrahedral sites of the aluminosilicate framework. In the terminology used formally to describe deformation twinning in a triclinic lattice, these twin laws can be described as Type I and Type II twin laws, respectively, with the pericline twin law being conjugate to the albite twin law. In this study, twin boundaries have been constructed for low albite according to these two twinning laws and studied by molecular dynamics simulation. The results show that suitably constructed twin boundary models are quite stable for both albite twinning and pericline twinning during molecular dynamics simulation. The calculated twin boundary energy of an albite twin is significantly lower than that of a pericline twin, in accord with the experimental observation that albite twinning is the more commonly observed mode seen in plagioclase feldspars. The results of the molecular dynamics simulations also agree with conclusions from the prior work of Starkey that glide twinning in low albite is not favoured energetically. (paper)
13. Nike Twins Seven Seven: Nigerian Batik Artist.
Science.gov (United States)
1987-01-01
Chronicles the personal and professional life of Nike Twins Seven Seven (born 1951), a Nigerian batik artist, and her husband, Twins Seven Seven, a musician-artist, both of whom have received international acclaim. (BJV)
14. Spectral stratigraphy
Science.gov (United States)
Lang, Harold R.
1991-01-01
A new approach to stratigraphic analysis is described which uses photogeologic and spectral interpretation of multispectral remote sensing data combined with topographic information to determine the attitude, thickness, and lithology of strata exposed at the surface. The new stratigraphic procedure is illustrated by examples in the literature. The published results demonstrate the potential of spectral stratigraphy for mapping strata, determining dip and strike, measuring and correlating stratigraphic sequences, defining lithofacies, mapping biofacies, and interpreting geological structures.
15. The Fourth International Network of Twin Registries: Overview from Osaka/Research Reviews: Familial Fraternal Twinning; Twin Study of Masculine Faces; Physical Aggression and Epigenetics; Prenatal Education for Parents of Twins/Current Events: 2016 Guinness Book of World Records; Oldest Living Male Twins; Twins Reunited at Sixty-Nine; Panda Twins; Twins.com.
Science.gov (United States)
Segal, Nancy L
2015-12-01
The 4th International Network of Twin Registries (INTR) Consortium Meeting took place in Osaka, Japan, September 28-29, 2015. The venue was the Osaka Medical Center for Medical Innovation and Translational Research. An overview of presentations and other activities is provided. Next, 1930s research on familial fraternal twinning, preference for masculine faces, physical aggression and epigenetics, and a prenatal education program for parents of multiples are described. Current twin-related events include the 2016 Guinness Book of World Records (GWR), the oldest living male twins, newly reunited twins, the birth of panda twins and a controversial twin-based website.
16. Simulations of stress-induced twinning and de-twinning: A phase field model
International Nuclear Information System (INIS)
Hu Shenyang; Henager, Chuck H.; Chen Longqing
2010-01-01
Twinning in certain metals or under certain conditions is a major plastic deformation mode. Here we present a phase field model to describe twin formation and evolution in a polycrystalline fcc metal under loading and unloading. The model assumes that twin nucleation, growth and de-twinning is a process of partial dislocation nucleation and slip on successive habit planes. Stacking fault energies, energy pathways (γ surfaces), critical shear stresses for the formation of stacking faults and dislocation core energies are used to construct the thermodynamic model. The simulation results demonstrate that the model is able to predict the nucleation of twins and partial dislocations, as well as the morphology of the twin nuclei, and to reasonably describe twin growth and interaction. The twin microstructures at grain boundaries are in agreement with experimental observation. It was found that de-twinning occurs during unloading in the simulations, however, a strong dependence of twin structure evolution on loading history was observed.
17. Remembering Irving I. Gottesman: Twin Research Colleague and Friend Extraordinaire/Research Studies: Face-Lift Technique Comparison in Identical Twins; Raising Preterm Twins; Fetal Behavior in Dichorionic Twin Pregnancies; Co-Bedding and Stress Reduction in Twins/Public Interest: Identical Co-Twins' Same Day Delivery; Teaching Twins in Bosnia; Twin Auctioneers; Sister, the Play.
Science.gov (United States)
Segal, Nancy L
2016-12-01
Dr Irving I. Gottesman, a colleague, friend, and long-time member of the International Society of Twin Studies passed away on June 29, 2016. His contributions to twin research and some personal reflections are presented to honor both the man and the memory. This tribute is followed by short reviews of twin research concerning differences between cosmetic surgical techniques, the rearing of preterm twins, behavioral observations of dichorionic fetal twins, and the outcomes of co-bedding twins with reference to stress reduction. Interesting and informative articles in the media describe identical co-twins who delivered infants on the same day, educational policies regarding twins in Bosnia and the United Kingdom, unusual practices of twin auctioneers, and a theatrical production, Sister, featuring identical twins in the leading roles.
18. HIGH-RESOLUTION OBSERVATIONS OF DUST CONTINUUM EMISSION AT 340 GHz FROM THE LOW-MASS T TAURI STAR FN TAURI
International Nuclear Information System (INIS)
Momose, Munetake; Ohashi, Nagayoshi; Kudo, Tomoyuki; Tamura, Motohide; Kitamura, Yoshimi
2010-01-01
FN Tau is a rare example of a very low-mass T Tauri star that exhibits a spatially resolved nebulosity in near-infrared scattering light. To directly derive the parameters of a circumstellar disk around FN Tau, observations of dust continuum emission at 340 GHz are carried out with the Submillimeter Array (SMA). A point-like dust continuum emission was detected with a synthesized beam of ∼0.''7 in FWHM. From the analysis of the visibility plot, the radius of the emission is estimated to be ≤0.''29, corresponding to 41 AU. This is much smaller than the radius of the nebulosity, 1.''85 for its brighter part at 1.6 μm. The 340 GHz continuum emission observed with the SMA and the photometric data at λ ≤ 70 μm are explained by a power-law disk model whose outer radius and mass are 41 AU and (0.24-5.9) x 10 -3 M sun , respectively, if the exponent of dust mass opacity (β) is assumed to be 0-2. The disk model cannot fully reproduce the flux density at 230 GHz obtained with the IRAM 30 m telescope, suggesting that there is another extended 'halo' component that is missed in the SMA observations. By requiring the halo not to be detected with the SMA, the lower limit to the size of the halo is evaluated to be between 174 AU and 574 AU, depending on the assumed β value. This size is comparable to the near-infrared nebulosity, implying that the halo unseen with the SMA corresponds to the origin of the near-infrared nebulosity. The halo can contain mass comparable to or at most 8 times greater than that of the inner power-law disk, but its surface density should be lower than that at the outer edge of the power-law disk by more than 1 order of magnitude. The physical nature of the halo is unclear, but it may be the periphery of a flared circumstellar disk that is not described well in terms of a power-law disk model, or a remnant of a protostellar envelope having flattened structure.
19. Roentgeno-cephalometric analysis on the twin
Energy Technology Data Exchange (ETDEWEB)
Choi, Hi Sup; Ahn, Hyung Kyu [College of Dentistry, Seoul National University, Seoul (Korea, Republic of)
1972-11-15
The purpose of this investigation can be sought for studying varients between twin by the cephalometric roentgenog raphic technics. The author have applied Down's, Bjork and Sakamoto's technic and measured in various angulations and length of cephalometric points. The results are as follows; 1. No significantly different data were found between twin. 2. There was no differences between normality and twin.
20. Postpartum Mental State of Mothers of Twins
Science.gov (United States)
Brantmüller, Éva; Gyúró, Mónika; Galgán, Kitti; Pakai, Annamária
2016-01-01
Twin birth is a relevant risk factor for postnatal depression (PND). The primary objective of our study is to reveal the prevalence of suspected cases of depression and to identify some background factors among mothers of twins. We applied convenience sampling method within a retrospective, quantitative study among mothers given birth to twins for…
1. Epigenetic Epidemiology of Complex Diseases Using Twins
DEFF Research Database (Denmark)
Tan, Qihua
2013-01-01
through multiple epigenetic mechanisms. This paper reviews the new developments in using twins to study disease-related epigenetic alterations, links them to lifetime environmental exposure with a focus on the discordant twin design and proposes novel data-analytical approaches with the aim of promoting...... a more efficient use of twins in epigenetic studies of complex human diseases....
2. Concordance for multiple sclerosis in Danish twins
DEFF Research Database (Denmark)
Hansen, T; Skytthe, Axel; Stenager, Egon
2005-01-01
The occurrence of multiple sclerosis (MS) in twins has not previously been studied in complete nationwide data sets. The existence of almost complete MS and twin registries in Denmark ensures that essentially unbiased samples of MS cases among twins can be obtained. In this population-based study...
3. Geir Hønneland, Russia and the Arctic: Environment, Identity and Foreign Policy & Leif Christian Jensen, International Relations in the Arctic: Norway and the Struggle for Power in the New North (London/New York: IB Tauris, 2016
Directory of Open Access Journals (Sweden)
Romain Chuffart
2017-03-01
Full Text Available A review of the books: Geir Hønneland, Russia and the Arctic: Environment, Identity and Foreign Policy (London/New York: IB Tauris, 2016; and Leif Christian Jensen, International Relations in the Arctic: Norway and the Struggle for Power in the New North (London/New York: IB Tauris, 2016
4. Sports pairs: insights on athletic talent; research reviews: twins with leukemia; parents and twins.
Science.gov (United States)
Segal, Nancy L
2007-06-01
Twin research exploring genetic and environmental influences on athletic interests and talents is reviewed. Illustrative examples of twin athletes representing a variety of sports activities are presented. This is followed by an overview of twin studies offering critical insights into the onset and progress of leukemia. In the last section, timely events involving twins and parents of twins will be described--each case provides a new look at an old question.
5. Twins and non-twin siblings: different estimates of shared environmental influence in early childhood.
Science.gov (United States)
Koeppen-Schomerus, Gesina; Spinath, Frank M; Plomin, Robert
2003-04-01
Twin studies typically indicate shared environmental influence for cognitive abilities, especially in early childhood. However, across studies, DZ twin correlations tend to be greater than non-twin sibling correlations, suggesting that twin estimates of shared environment are to some extent specific to twins. We tested this hypothesis in a sample of more than 1800 MZ and 1800 same-sex DZ pairs from the Twins Early Development Study (TEDS), a study of twins born in England and Wales in 1994 and 1995. For this analysis, we obtained comparable data from more than 130 same-sex younger siblings of the twins. Twins and their younger siblings were assessed for language, cognitive abilities and behavior problems by their parents at 2 and 3 years of age. For language and cognitive measures at both 2 and 3 years, but not for behavior problems, estimates of shared environment were more than twice as large for twins as compared to non-twin siblings. We conclude that about half of twin study estimates of shared environment for cognitive abilities in early childhood are specific to twins. Although many possibilities exist for explaining the special shared environment effect for twins, we suggest that cognitive-relevant experiences that are not shared by siblings are shared by twins because they are exactly the same age.
6. PHOTO-REVERBERATION MAPPING OF A PROTOPLANETARY ACCRETION DISK AROUND A T TAURI STAR
Energy Technology Data Exchange (ETDEWEB)
Meng, Huan Y. A.; Plavchan, Peter; Ciardi, David [Infrared Processing and Analysis Center, California Institute of Technology, MC 100-22, 770 S. Wilson Ave., Pasadena, CA 91125 (United States); Rieke, George H. [Lunar and Planetary Laboratory and Department of Planetary Sciences, University of Arizona, 1629 E. University Blvd., Tucson, AZ 85721 (United States); Cody, Ann Marie [NASA Ames Research Center, Moffett Field, CA 94035 (United States); Güth, Tina [Department of Physics, New Mexico Institute of Mining and Technology, 801 Leroy Pl., Socorro, NM 87801 (United States); Stauffer, John; Carey, Sean; Rebull, Luisa M. [Infrared Science Archive and Spitzer Science Center, Infrared Processing and Analysis Center, California Institute of Technology, MC 314-6, 1200 E. California Blvd., Pasadena, CA 91125 (United States); Covey, Kevin [Department of Physics and Astronomy, MS-9164, Western Washington University, 516 High St., Bellingham, WA 98225 (United States); Duran-Rojas, Maria C. [Instituto de Astronomía, Universidad Nacional Autónoma de México, Apartado Postal 106, 22800, Ensenada, Baja California, México (Mexico); Gutermuth, Robert A. [Department of Astronomy, University of Massachusetts, Amherst, MA 01003 (United States); Morales-Calderón, María, E-mail: [email protected] [Centro de Astrobiología, Departamento de Astrofísica, INTA-CSIC, P.O. Box 78, E-28691, ESAC Campus, Villanueva de la Cañada, Madrid (Spain); and others
2016-05-20
Theoretical models and spectroscopic observations of newborn stars suggest that protoplantary disks have an inner “wall” at a distance set by the disk interaction with the star. Around T Tauri stars, the size of this disk hole is expected to be on a 0.1 au scale that is unresolved by current adaptive optics imaging, though some model-dependent constraints have been obtained by near-infrared interferometry. Here we report the first measurement of the inner disk wall around a solar-mass young stellar object, YLW 16B in the ρ Ophiuchi star-forming region, by detecting the light-travel time of the variable radiation from the stellar surface to the disk. Consistent time lags were detected on two nights, when the time series in H (1.6 μ m) and K (2.2 μ m) bands were synchronized while the 4.5 μ m emission lagged by 74.5 ± 3.2 s. Considering the nearly edge-on geometry of the disk, the inner rim should be 0.084 au from the protostar on average, with an error of order 0.01 au. This size is likely larger than the range of magnetospheric truncations and consistent with an optically and geometrically thick disk front at the dust sublimation radius at ∼1500 K. The widths of the cross-correlation functions between the data in different wavebands place possible new constraints on the geometry of the disk.
7. THE BIMODALITY OF ACCRETION IN T TAURI STARS AND BROWN DWARFS
International Nuclear Information System (INIS)
Vorobyov, E. I.; Basu, Shantanu
2009-01-01
We present numerical solutions of the collapse of prestellar cores that lead to the formation and evolution of circumstellar disks. The disk evolution is then followed for up to three million years. A variety of models of different initial masses and rotation rates allow us to study disk accretion around brown dwarfs and low-mass T Tauri stars (TTSs), with central object mass M * sun , as well as intermediate- and upper-mass TTSs (0.2 M sun * sun ). Our models include self-gravity and allow for nonaxisymmetric motions. In addition to the self-consistently generated gravitational torques, we introduce an effective turbulent α-viscosity with α = 0.01, which allows us particularly to model accretion in the low-mass regime where disk self-gravity is diminishing. A range of models with observationally motivated values of the initial ratio of rotational-to-gravitational energy yield a correlation between mass accretion rate M-dot and M * that is relatively steep, as observed. Additionally, our modeling reveals evidence for a bimodality in the M-dot - M * correlation, with a steeper slope at lower masses and a shallower slope at intermediate and upper masses, as also implied by observations. Furthermore, we show that the neglect of disk self-gravity leads to a much steeper M-dot - M * relation for intermediate- and upper-mass TTSs. This demonstrates that an accurate treatment of global self-gravity is essential to understanding observations of circumstellar disks.
8. Robustness of circadian clocks to daylight fluctuations: hints from the picoeucaryote Ostreococcus tauri.
Directory of Open Access Journals (Sweden)
Quentin Thommen
Full Text Available The development of systemic approaches in biology has put emphasis on identifying genetic modules whose behavior can be modeled accurately so as to gain insight into their structure and function. However, most gene circuits in a cell are under control of external signals and thus, quantitative agreement between experimental data and a mathematical model is difficult. Circadian biology has been one notable exception: quantitative models of the internal clock that orchestrates biological processes over the 24-hour diurnal cycle have been constructed for a few organisms, from cyanobacteria to plants and mammals. In most cases, a complex architecture with interlocked feedback loops has been evidenced. Here we present the first modeling results for the circadian clock of the green unicellular alga Ostreococcus tauri. Two plant-like clock genes have been shown to play a central role in the Ostreococcus clock. We find that their expression time profiles can be accurately reproduced by a minimal model of a two-gene transcriptional feedback loop. Remarkably, best adjustment of data recorded under light/dark alternation is obtained when assuming that the oscillator is not coupled to the diurnal cycle. This suggests that coupling to light is confined to specific time intervals and has no dynamical effect when the oscillator is entrained by the diurnal cycle. This intriguing property may reflect a strategy to minimize the impact of fluctuations in daylight intensity on the core circadian oscillator, a type of perturbation that has been rarely considered when assessing the robustness of circadian clocks.
9. VizieR Online Data Catalog: UV spectra of classical T Tauri stars (France+, 2014)
Science.gov (United States)
France, K.; Schindhelm, E.; Bergin, E. A.; Roueff, E.; Abgrall, H.
2017-06-01
We present 16 objects from the larger GTO + DAO T Tauri star samples described by Ardila et al. (2013ApJS..207....1A; focusing on the hot gas emission lines) and France et al. (2012, J/ApJ/756/171; focusing on the molecular circumstellar environment). Eleven of the 16 sources were observed as part of the DAO of Tau guest observing program (PID 11616; PI: G. Herczeg), four were part of the COS Guaranteed Time Observing program on protoplanetary disks (PIDs 11533 and 12036; PI: J. Green), and we have included archival STIS observations of the well-studied CTTS TW Hya (Herczeg et al. 2002ApJ...572..310H, 2004ApJ...607..369H), obtained through StarCAT (Ayres 2010, J/ApJS/187/149). The targets were selected by the availability of reconstructed Lyα spectra, as this emission line is a critical component to the intrinsic CTTS UV radiation field (Schindhelm et al. 2012ApJ...756L..23S) and has not been uniformly included in recent studies of the CTTS radiation field (e.g., Ingleby et al. 2011AJ....141..127I; Yang et al. 2012, J/ApJ/744/121). Most of the targets were observed with the medium-resolution FUV modes of COS (G130M and G160M; Green et al. 2012ApJ...744...60G). (2 data files).
10. MAGNETIC FIELD MEASUREMENTS OF T TAURI STARS IN THE ORION NEBULA CLUSTER
International Nuclear Information System (INIS)
Hao Yang; Johns-Krull, Christopher M.
2011-01-01
We present an analysis of high-resolution (R ∼ 50, 000) infrared K-band echelle spectra of 14 T Tauri stars (TTSs) in the Orion Nebula Cluster. We model Zeeman broadening in three magnetically sensitive Ti I lines near 2.2 μm and consistently detect kilogauss-level magnetic fields in the stellar photospheres. The data are consistent in each case with the entire stellar surface being covered with magnetic fields, suggesting that magnetic pressure likely dominates over gas pressure in the photospheres of these stars. These very strong magnetic fields might themselves be responsible for the underproduction of X-ray emission of TTSs relative to what is expected based on main-sequence star calibrations. We combine these results with previous measurements of 14 stars in Taurus and 5 stars in the TW Hydrae association to study the potential variation of magnetic field properties during the first 10 million years of stellar evolution, finding a steady decline in total magnetic flux with age.
11. The effect of chorionicity and twin-to-twin delivery time interval on short-term outcome of the second twin
DEFF Research Database (Denmark)
Hjortø, Sofie; Nickelsen, Carsten; Petersen, Janne
2013-01-01
Abstract Objectives: To investigate the effect of chorionicity and twin-to-twin delivery time interval on short-term outcome in the second twin. Additionally, to investigate predictors of adverse outcome in both twins. Methods: Data included vaginally delivered twins (≥ 36 weeks) from Copenhagen ...
12. Twin methodology in epigenetic studies
DEFF Research Database (Denmark)
Tan, Qihua; Christiansen, Lene; von Bornemann Hjelmborg, Jacob
2015-01-01
of diseases to molecular phenotypes in functional genomics especially in epigenetics, a thriving field of research that concerns the environmental regulation of gene expression through DNA methylation, histone modification, microRNA and long non-coding RNA expression, etc. The application of the twin method...
13. The Danish political twin study
DEFF Research Database (Denmark)
Klemmensen, Robert; Hobolt, Sara B; Dinesen, Peter Thisted
2012-01-01
We compare a recent Danish twin survey on political attitudes and behaviors to a nationally representative survey covering similar topics. We find very similar means and variances for most of our constructed scales of political attitudes and behaviors in the two surveys, although even small...
14. Heteropagus twinning on back -- a case report.
Science.gov (United States)
Debnath, Bidyut; Biswas, Sumitra Kumar
2011-07-01
Heteropagus twins, also called parasitic twins, are malformation of the foetus where the development of one twin is incomplete. They are attached most commonly to the lower chest and upper abdomen. We report a case of heteropagus twin, where the parasite possessed well-formed limb as well as blind ending intestine. It was attached to the back of the host by a broad pedicle. We take this opportunity to classify areas of confusion prevailing regarding twinning, foetus in foetu, teratoma and caudal duplication.
15. Fetal growth disorders in twin gestations.
LENUS (Irish Health Repository)
Breathnach, Fionnuala M
2012-06-01
Twin growth is frequently mismatched. This review serves to explore the pathophysiologic mechanisms that underlie growth aberrations in twin gestations, the prenatal recognition of abnormal twin growth, and the critical importance of stratifying management of abnormal twin growth by chorionicity. Although poor in utero growth of both twins may reflect maternal factors resulting in global uteroplacental dysfunction, discordant twin growth may be attributed to differences in genetic potential between co-twins, placental dysfunction confined to one placenta only, or one placental territory within a shared placenta. In addition, twin-twin transfusion syndrome represents a distinct entity of which discordant growth is a common feature. Discordant growth is recognized as an independent risk factor for adverse perinatal outcome. Intertwin birth weight disparity of 18% or more should be considered to represent a discordance threshold, which serves as an independent risk factor for adverse perinatal outcome. At this cutoff, perinatal morbidity is found to increase both for the larger and the smaller twin within a discordant pair. There remains uncertainty surrounding the sonographic parameters that are most predictive of discordance. Although heightening of fetal surveillance in the face of discordant twin growth follows the principles applied to singleton gestations complicated by fetal growth restriction, the timing of intervention is largely influenced by chorionicity.
16. Using Twins to Better Understand Sibling Relationships.
Science.gov (United States)
Mark, Katharine M; Pike, Alison; Latham, Rachel M; Oliver, Bonamy R
2017-03-01
We compared the nature of the sibling relationship in dyads of varying genetic relatedness, employing a behavioural genetic design to estimate the contribution that genes and the environment have on this familial bond. Two samples were used-the Sisters and Brothers Study consisted of 173 families with two target non-twin children (mean ages = 7.42 and 5.22 years respectively); and the Twins, Family and Behaviour study included 234 families with two target twin children (mean age = 4.70 years). Mothers and fathers reported on their children's relationship with each other, via a postal questionnaire (the Sisters and Brothers Study) or a telephone interview (the Twins, Family and Behaviour study). Contrary to expectations, no mean level differences emerged when monozygotic twin pairs, dizygotic twin pairs, and non-twin pairs were compared on their sibling relationship quality. Behavioural genetic analyses also revealed that the sibling bond was modestly to moderately influenced by the genetic propensities of the children within the dyad, and moderately to substantially influenced by the shared environment common to both siblings. In addition, for sibling negativity, we found evidence of twin-specific environmental influence-dizygotic twins showed more reciprocity than did non-twins. Our findings have repercussions for the broader application of results from future twin-based investigations.
17. Register-based research on twins
DEFF Research Database (Denmark)
Christensen, Kaare; Ohm Kyvik, Kirsten; Holm, Niels V
2011-01-01
Introduction: The Danish Twin Registry (DTR) has for more than 50 years been based on surveys and clinical investigations and over the two last decades also on register linkage. Currently these two approaches are merged within Statistics Denmark. Research topics: Here we report on three major...... groups of register-based research in the DTR that used the uniqueness of twinning. First, we focus on the ''long-term prognosis'' of being a twin compared with being a singleton and show that Danish twins have health trajectories in adulthood similar to singletons, which is a result of interest for twins...... illustrate how the co-twin control method in a register setting can be used to control for the effect of rearing environment and genetic factors in studies of the association between exposures and health. CONCLUSION: The spectrum of register-based twin studies is very wide and have changed in accordance...
18. Is that me or my twin? Lack of self-face recognition advantage in identical twins.
Directory of Open Access Journals (Sweden)
Matteo Martini
Full Text Available Despite the increasing interest in twin studies and the stunning amount of research on face recognition, the ability of adult identical twins to discriminate their own faces from those of their co-twins has been scarcely investigated. One's own face is the most distinctive feature of the bodily self, and people typically show a clear advantage in recognizing their own face even more than other very familiar identities. Given the very high level of resemblance of their faces, monozygotic twins represent a unique model for exploring self-face processing. Herein we examined the ability of monozygotic twins to distinguish their own face from the face of their co-twin and of a highly familiar individual. Results show that twins equally recognize their own face and their twin's face. This lack of self-face advantage was negatively predicted by how much they felt physically similar to their co-twin and by their anxious or avoidant attachment style. We speculate that in monozygotic twins, the visual representation of the self-face overlaps with that of the co-twin. Thus, to distinguish the self from the co-twin, monozygotic twins have to rely much more than control participants on the multisensory integration processes upon which the sense of bodily self is based. Moreover, in keeping with the notion that attachment style influences perception of self and significant others, we propose that the observed self/co-twin confusion may depend upon insecure attachment.
19. Twin Research and the Arts: Interconnections / Twin Research: Twin Studies of Sexual Orientation; A Historical Biological Twin Gem; GWAS Approach to Who Has Twins / Newsworthy: Twins on College Campuses; 'Brainprint': Personal Identification by Brain Waves.
Science.gov (United States)
Segal, Nancy L
2016-08-01
The interrelatedness between twin research and the arts is explored via a new play about a famous case. In the 1960s, identical twin David Bruce Reimer was accidentally castrated as an infant during circumcision to correct a urinary problem. The decision to raise him as a girl, and the consequences of that decision, are explored in the new theatrical production of Boy. Other examples of the arts mirroring science, and vice versa, are described. Next, brief reviews and summaries of twin research on sexual orientation, 1860s' knowledge of placental arrangements and twinning mechanisms, and genes underlying multiple birth conception and fertility related measures are provided. This article concludes with a look at twins on college campuses and the identification of individuals by their brain waves. A correction and clarification regarding my article on the Brazilian Twin Registry in the last issue of THG (Segal, 2016) is also provided.
20. Ventricular strain changes in monochorionic twins with and without twin-to-twin transfusion syndrome.
Science.gov (United States)
Taylor-Clarke, Marisa C; Matsui, Hikoro; Roughton, Michael; Wimalasundera, Ruwan C; Gardiner, Helena M
2013-06-01
The objective of the study was to investigate whether vector velocity imaging (VVI), a non-Doppler speckle tracking ultrasound technology, is feasible in twin pregnancies and can aid management of twin-twin transfusion syndrome (TTTS). Twenty-seven women pregnant with monochorionic diamniotic twins affected by TTTS and 28 monochorionic pregnancies that did not develop TTTS were included in a prospective case-control study at a fetal medicine center. Fetal echocardiograms were recorded with dummy electrocardiography to retain original frame rates when exported for offline speckle tracking analysis using Syngo-VVI software (Siemens Corp, Munich, Germany). Right and left ventricular (LV) free wall Lagrangian strain was measured from the original coordinates. Within-twin pair ventricular strain differences including relationship to Quintero staging and response to laser therapy for TTTS were analyzed by Wilcoxon signed-rank test. The VVI strain measurements could be analyzed in 182 of 200 TTTS and 96 of 112 non-TTTS control ventricles. Within-pair strain was concordant in non-TTTS controls. Recipient LV strain was reduced at all Quintero stages compared with donors (P < .01). Recipient right ventricular strain was reduced only in stages 3 and 4 (P < .01). Strain improved at a median of 2 weeks following successful laser therapy. Intertwin differences in strain were independent of weight discordance. Recipient LV strain is reduced in stages 1 and 2 TTTS. Within-pair strain discordance may distinguish early TTTS from growth discordance and guide timing of and management following treatment. Copyright © 2013 Mosby, Inc. All rights reserved.
1. Deformation twinning: Influence of strain rate
Energy Technology Data Exchange (ETDEWEB)
Gray, G.T. III
1993-11-01
2. Fingerprint recognition with identical twin fingerprints.
Science.gov (United States)
Tao, Xunqiang; Chen, Xinjian; Yang, Xin; Tian, Jie
2012-01-01
Fingerprint recognition with identical twins is a challenging task due to the closest genetics-based relationship existing in the identical twins. Several pioneers have analyzed the similarity between twins' fingerprints. In this work we continue to investigate the topic of the similarity of identical twin fingerprints. Our study was tested based on a large identical twin fingerprint database that contains 83 twin pairs, 4 fingers per individual and six impressions per finger: 3984 (83*2*4*6) images. Compared to the previous work, our contributions are summarized as follows: (1) Two state-of-the-art fingerprint identification methods: P071 and VeriFinger 6.1 were used, rather than one fingerprint identification method in previous studies. (2) Six impressions per finger were captured, rather than just one impression, which makes the genuine distribution of matching scores more realistic. (3) A larger sample (83 pairs) was collected. (4) A novel statistical analysis, which aims at showing the probability distribution of the fingerprint types for the corresponding fingers of identical twins which have same fingerprint type, has been conducted. (5) A novel analysis, which aims at showing which finger from identical twins has higher probability of having same fingerprint type, has been conducted. Our results showed that: (a) A state-of-the-art automatic fingerprint verification system can distinguish identical twins without drastic degradation in performance. (b) The chance that the fingerprints have the same type from identical twins is 0.7440, comparing to 0.3215 from non-identical twins. (c) For the corresponding fingers of identical twins which have same fingerprint type, the probability distribution of five major fingerprint types is similar to the probability distribution for all the fingers' fingerprint type. (d) For each of four fingers of identical twins, the probability of having same fingerprint type is similar.
3. Fingerprint recognition with identical twin fingerprints.
Directory of Open Access Journals (Sweden)
Xunqiang Tao
Full Text Available Fingerprint recognition with identical twins is a challenging task due to the closest genetics-based relationship existing in the identical twins. Several pioneers have analyzed the similarity between twins' fingerprints. In this work we continue to investigate the topic of the similarity of identical twin fingerprints. Our study was tested based on a large identical twin fingerprint database that contains 83 twin pairs, 4 fingers per individual and six impressions per finger: 3984 (83*2*4*6 images. Compared to the previous work, our contributions are summarized as follows: (1 Two state-of-the-art fingerprint identification methods: P071 and VeriFinger 6.1 were used, rather than one fingerprint identification method in previous studies. (2 Six impressions per finger were captured, rather than just one impression, which makes the genuine distribution of matching scores more realistic. (3 A larger sample (83 pairs was collected. (4 A novel statistical analysis, which aims at showing the probability distribution of the fingerprint types for the corresponding fingers of identical twins which have same fingerprint type, has been conducted. (5 A novel analysis, which aims at showing which finger from identical twins has higher probability of having same fingerprint type, has been conducted. Our results showed that: (a A state-of-the-art automatic fingerprint verification system can distinguish identical twins without drastic degradation in performance. (b The chance that the fingerprints have the same type from identical twins is 0.7440, comparing to 0.3215 from non-identical twins. (c For the corresponding fingers of identical twins which have same fingerprint type, the probability distribution of five major fingerprint types is similar to the probability distribution for all the fingers' fingerprint type. (d For each of four fingers of identical twins, the probability of having same fingerprint type is similar.
4. ACCRETION AND MAGNETIC RECONNECTION IN THE CLASSICAL T TAURI BINARY DQ TAU
International Nuclear Information System (INIS)
Tofflemire, Benjamin M.; Mathieu, Robert D.; Ardila, David R.; Akeson, Rachel L.; Ciardi, David R.; Johns-Krull, Christopher; Herczeg, Gregory J.; Quijano-Vodniza, Alberto
2017-01-01
The theory of binary star formation predicts that close binaries ( a < 100 au) will experience periodic pulsed accretion events as streams of material form at the inner edge of a circumbinary disk (CBD), cross a dynamically cleared gap, and feed circumstellar disks or accrete directly onto the stars. The archetype for the pulsed accretion theory is the eccentric, short-period, classical T Tauri binary DQ Tau. Low-cadence (∼daily) broadband photometry has shown brightening events near most periastron passages, just as numerical simulations would predict for an eccentric binary. Magnetic reconnection events (flares) during the collision of stellar magnetospheres near periastron could, however, produce the same periodic, broadband behavior when observed at a one-day cadence. To reveal the dominant physical mechanism seen in DQ Tau’s low-cadence observations, we have obtained continuous, moderate-cadence, multiband photometry over 10 orbital periods, supplemented with 27 nights of minute-cadence photometry centered on four separate periastron passages. While both accretion and stellar flares are present, the dominant timescale and morphology of brightening events are characteristic of accretion. On average, the mass accretion rate increases by a factor of five near periastron, in good agreement with recent models. Large variability is observed in the morphology and amplitude of accretion events from orbit to orbit. We argue that this is due to the absence of stable circumstellar disks around each star, compounded by inhomogeneities at the inner edge of the CBD and within the accretion streams themselves. Quasiperiodic apastron accretion events are also observed, which are not predicted by binary accretion theory.
5. THE PTF ORION PROJECT: A POSSIBLE PLANET TRANSITING A T-TAURI STAR
Energy Technology Data Exchange (ETDEWEB)
Van Eyken, Julian C.; Ciardi, David R.; Von Braun, Kaspar; Kane, Stephen R.; Plavchan, Peter; Akeson, Rachel L.; Beichman, Charles A.; Gelino, Dawn M. [NASA Exoplanet Science Institute, California Institute of Technology, 770 South Wilson Avenue, M/S 100-22, Pasadena, CA 91125 (United States); Bender, Chad F.; Mahadevan, Suvrath [Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 (United States); Brown, Timothy M.; Fulton, Benjamin J.; Shporer, Avi [Las Cumbres Observatory Global Telescope, Goleta, CA 93117 (United States); Crepp, Justin R. [Cahill Center for Astrophysics, California Institute of Technology, Pasadena, CA 91125 (United States); Howard, Andrew W.; Marcy, Geoffrey W. [Department of Astronomy, University of California, Berkeley, CA 94720-3411 (United States); Howell, Steve B. [NASA Ames Research Center, M/S 244-30, Moffett Field, CA 94035 (United States); Szkody, Paula [Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195 (United States); Boden, Andrew F. [Caltech Optical Observatories, California Institute of Technology, Pasadena, CA 91125 (United States); Hoard, D. W., E-mail: [email protected] [Spitzer Science Center, M/S 220-6, California Institute of Technology, Jet Propulsion Laboratory, Pasadena, CA 91125 (United States); and others
2012-08-10
We report observations of a possible young transiting planet orbiting a previously known weak-lined T-Tauri star in the 7-10 Myr old Orion-OB1a/25-Ori region. The candidate was found as part of the Palomar Transient Factory (PTF) Orion project. It has a photometric transit period of 0.448413 {+-} 0.000040 days, and appears in both 2009 and 2010 PTF data. Follow-up low-precision radial velocity (RV) observations and adaptive optics imaging suggest that the star is not an eclipsing binary, and that it is unlikely that a background source is blended with the target and mimicking the observed transit. RV observations with the Hobby-Eberly and Keck telescopes yield an RV that has the same period as the photometric event, but is offset in phase from the transit center by Almost-Equal-To - 0.22 periods. The amplitude (half range) of the RV variations is 2.4 km s{sup -1} and is comparable with the expected RV amplitude that stellar spots could induce. The RV curve is likely dominated by stellar spot modulation and provides an upper limit to the projected companion mass of M{sub p}sin i{sub orb} {approx}< 4.8 {+-} 1.2 M{sub Jup}; when combined with the orbital inclination, i{sub orb}, of the candidate planet from modeling of the transit light curve, we find an upper limit on the mass of the planetary candidate of M{sub p} {approx}< 5.5 {+-} 1.4 M{sub Jup}. This limit implies that the planet is orbiting close to, if not inside, its Roche limiting orbital radius, so that it may be undergoing active mass loss and evaporation.
6. THE PTF ORION PROJECT: A POSSIBLE PLANET TRANSITING A T-TAURI STAR
International Nuclear Information System (INIS)
Van Eyken, Julian C.; Ciardi, David R.; Von Braun, Kaspar; Kane, Stephen R.; Plavchan, Peter; Akeson, Rachel L.; Beichman, Charles A.; Gelino, Dawn M.; Bender, Chad F.; Mahadevan, Suvrath; Brown, Timothy M.; Fulton, Benjamin J.; Shporer, Avi; Crepp, Justin R.; Howard, Andrew W.; Marcy, Geoffrey W.; Howell, Steve B.; Szkody, Paula; Boden, Andrew F.; Hoard, D. W.
2012-01-01
We report observations of a possible young transiting planet orbiting a previously known weak-lined T-Tauri star in the 7-10 Myr old Orion-OB1a/25-Ori region. The candidate was found as part of the Palomar Transient Factory (PTF) Orion project. It has a photometric transit period of 0.448413 ± 0.000040 days, and appears in both 2009 and 2010 PTF data. Follow-up low-precision radial velocity (RV) observations and adaptive optics imaging suggest that the star is not an eclipsing binary, and that it is unlikely that a background source is blended with the target and mimicking the observed transit. RV observations with the Hobby-Eberly and Keck telescopes yield an RV that has the same period as the photometric event, but is offset in phase from the transit center by ≈ – 0.22 periods. The amplitude (half range) of the RV variations is 2.4 km s –1 and is comparable with the expected RV amplitude that stellar spots could induce. The RV curve is likely dominated by stellar spot modulation and provides an upper limit to the projected companion mass of M p sin i orb ∼ Jup ; when combined with the orbital inclination, i orb , of the candidate planet from modeling of the transit light curve, we find an upper limit on the mass of the planetary candidate of M p ∼ Jup . This limit implies that the planet is orbiting close to, if not inside, its Roche limiting orbital radius, so that it may be undergoing active mass loss and evaporation.
7. MN Lup: X-RAYS FROM A WEAKLY ACCRETING T TAURI STAR
International Nuclear Information System (INIS)
Günther, H. M.; Wolk, S. J.; Wolter, U.; Robrade, J.
2013-01-01
Young T Tauri stars (TTS) are surrounded by an accretion disk, which over time disperses due to photoevaporation, accretion, and possibly planet formation. The accretion shock on the central star produces an UV/optical veiling continuum, line emission, and X-ray signatures. As the accretion rate decreases, the impact on the central star must change. In this article we study MN Lup, a young star where no indications of a disk are seen in IR observations. We present XMM-Newton and VLT/UVES observations, some of them taken simultaneously. The X-ray data show that MN Lup is an active star with L X /L bol close to the saturation limit. However, we find high densities (n e > 3 × 10 10 cm –3 ) in the X-ray grating spectrum. This can be well fitted using an accretion shock model with an accretion rate of 2 × 10 –11 M ☉ yr –1 . Despite the simple Hα line profile which has a broad component, but no absorption signatures as typically seen on accreting TTS, we find rotational modulation in Ca II K and in photospheric absorption lines. These line profile modulations do not clearly indicate the presence of a localized hot accretion spot on the star. In the Hα line we see a prominence in absorption about 2R * above the stellar surface—the first of its kind on a TTS. MN Lup is also the only TTS where accretion is seen, but no dust disk is detected that could fuel it. We suggest that MN Lup presents a unique and short-lived state in the disk evolution. It may have lost its dust disk only recently and is now accreting the remaining gas at a very low rate.
8. ACCRETION AND MAGNETIC RECONNECTION IN THE CLASSICAL T TAURI BINARY DQ TAU
Energy Technology Data Exchange (ETDEWEB)
Tofflemire, Benjamin M.; Mathieu, Robert D. [Department of Astronomy, University of Wisconsin–Madison, 475 North Charter Street, Madison, WI 53706 (United States); Ardila, David R. [The Aerospace Corporation, M2-266, El Segundo, CA 90245 (United States); Akeson, Rachel L.; Ciardi, David R. [NASA Exoplanet Science Institute, IPAC/Caltech, Pasadena, CA 91125 (United States); Johns-Krull, Christopher [Department of Physics and Astronomy, Rice University, Houston, TX 77005 (United States); Herczeg, Gregory J. [The Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871 (China); Quijano-Vodniza, Alberto [University of Nariño Observatory, Pasto, Nariño (Colombia)
2017-01-20
The theory of binary star formation predicts that close binaries ( a < 100 au) will experience periodic pulsed accretion events as streams of material form at the inner edge of a circumbinary disk (CBD), cross a dynamically cleared gap, and feed circumstellar disks or accrete directly onto the stars. The archetype for the pulsed accretion theory is the eccentric, short-period, classical T Tauri binary DQ Tau. Low-cadence (∼daily) broadband photometry has shown brightening events near most periastron passages, just as numerical simulations would predict for an eccentric binary. Magnetic reconnection events (flares) during the collision of stellar magnetospheres near periastron could, however, produce the same periodic, broadband behavior when observed at a one-day cadence. To reveal the dominant physical mechanism seen in DQ Tau’s low-cadence observations, we have obtained continuous, moderate-cadence, multiband photometry over 10 orbital periods, supplemented with 27 nights of minute-cadence photometry centered on four separate periastron passages. While both accretion and stellar flares are present, the dominant timescale and morphology of brightening events are characteristic of accretion. On average, the mass accretion rate increases by a factor of five near periastron, in good agreement with recent models. Large variability is observed in the morphology and amplitude of accretion events from orbit to orbit. We argue that this is due to the absence of stable circumstellar disks around each star, compounded by inhomogeneities at the inner edge of the CBD and within the accretion streams themselves. Quasiperiodic apastron accretion events are also observed, which are not predicted by binary accretion theory.
9. Photo-reverberation Mapping of a Protoplanetary Accretion Disk around a T Tauri Star
Science.gov (United States)
Meng, Huan Y. A.; Plavchan, Peter; Rieke, George H.; Cody, Ann Marie; Güth, Tina; Stauffer, John; Covey, Kevin; Carey, Sean; Ciardi, David; Duran-Rojas, Maria C.; Gutermuth, Robert A.; Morales-Calderón, María; Rebull, Luisa M.; Watson, Alan M.
2016-05-01
Theoretical models and spectroscopic observations of newborn stars suggest that protoplantary disks have an inner “wall” at a distance set by the disk interaction with the star. Around T Tauri stars, the size of this disk hole is expected to be on a 0.1 au scale that is unresolved by current adaptive optics imaging, though some model-dependent constraints have been obtained by near-infrared interferometry. Here we report the first measurement of the inner disk wall around a solar-mass young stellar object, YLW 16B in the ρ Ophiuchi star-forming region, by detecting the light-travel time of the variable radiation from the stellar surface to the disk. Consistent time lags were detected on two nights, when the time series in H (1.6 μm) and K (2.2 μm) bands were synchronized while the 4.5 μm emission lagged by 74.5 ± 3.2 s. Considering the nearly edge-on geometry of the disk, the inner rim should be 0.084 au from the protostar on average, with an error of order 0.01 au. This size is likely larger than the range of magnetospheric truncations and consistent with an optically and geometrically thick disk front at the dust sublimation radius at ˜1500 K. The widths of the cross-correlation functions between the data in different wavebands place possible new constraints on the geometry of the disk.
10. Identical twins in forensic genetics
DEFF Research Database (Denmark)
Tvedebrink, Torben; Morling, Niels
2015-01-01
The increase in the number of forensic genetic loci used for identification purposes results in infinitesimal random match probabilities. These probabilities are computed under assumptions made for rather simple population genetic models. Often, the forensic expert reports likelihood ratios, where...... published results accounting for close familial relationships. However, we revisit the discussion to increase the awareness among forensic genetic practitioners and include new information on medical and societal factors to assess the risk of not considering a monozygotic twin as the true perpetrator......, then data relevant for the Danish society suggests that the threshold of likelihood ratios should approximately be between 150,000 and 2,000,000 in order to take the risk of an unrecognised identical, monozygotic twin into consideration. In other societies, the threshold of the likelihood ratio in crime...
11. Einstein and the twin paradox
International Nuclear Information System (INIS)
Pesic, Peter
2003-01-01
Einstein was the first to discuss and resolve the 'twin paradox', which in 1905 he did not consider paradoxical and treated as a consequence of lack of simultaneity. He maintained this view until at least 1914. However, in 1918 Einstein brought forward arguments about accelerated frames of reference that tended to overshadow his initial resolution. His earlier arguments were gradually rediscovered during the subsequent controversy about this 'paradox'
12. Ectodermal dysplasia in identical twins
OpenAIRE
Puttaraju, Gurkar Haraswarupa; Visveswariah, Paranjyothi Magadi
2013-01-01
Hereditary hypohidrotic ectodermal dysplasia (HED) is typically inherited as an X-linked recessive trait, characterized by deformity of at least two or more of the ectodermal structures - hair, teeth, nails and sweat glands. Two cases of hereditary HED involving identical male twins, is being documented for the rarity of its occurrence with special attention given to genetics, pathophysiology, clinical, intraoral manifestations and to the methods to improve the masticatory function, the facia...
Science.gov (United States)
Laursen, Brett; Hartl, Amy C.; Vitaro, Frank; Brendgen, Mara; Dionne, Ginette; Boivin, Michel
2017-01-01
This investigation examines the spread of problem behaviors (substance use and delinquency) between twin siblings. A sample of 628 twins (151 male twin pairs and 163 female twin pairs) drawn from the Quebec Newborn Twin Study completed inventories describing delinquency and substance use at ages 13, 14, and 15. A 3-wave longitudinal actor-partner…
14. Twinning of Polymer Crystals Suppressed by Entropy
Directory of Open Access Journals (Sweden)
Nikos Ch. Karayiannis
2014-09-01
Full Text Available We propose an entropic argument as partial explanation of the observed scarcity of twinned structures in crystalline samples of synthetic organic polymeric materials. Polymeric molecules possess a much larger number of conformational degrees of freedom than low molecular weight substances. The preferred conformations of polymer chains in the bulk of a single crystal are often incompatible with the conformations imposed by the symmetry of a growth twin, both at the composition surfaces and in the twin axis. We calculate the differences in conformational entropy between chains in single crystals and chains in twinned crystals, and find that the reduction in chain conformational entropy in the twin is sufficient to make the single crystal the stable thermodynamic phase. The formation of cyclic twins in molecular dynamics simulations of chains of hard spheres must thus be attributed to kinetic factors. In more realistic polymers this entropic contribution to the free energy can be canceled or dominated by nonbonded and torsional energetics.
15. Twin-Telescope Wettzell (TTW)
Science.gov (United States)
Hase, H.; Dassing, R.; Kronschnabl, G.; Schlüter, W.; Schwarz, W.; Lauber, P.; Kilger, R.
2007-07-01
Following the recommendations made by the VLBI2010 vision report of the IVS, a proposal has been made to construct a Twin Telescope for the Fundamental Station Wettzell in order to meet the future requirements of the next VLBI generation. The Twin Telescope consists of two identical radiotelescopes. It is a project of the Federal Agency for Cartography and Geodesy (BKG). This article summarizes the project and some design ideas for the Twin-Telescope. %ZALMA (2005). Technical Specification for Design, Manufacturing, Transport and Integration on Site of the ALMA ANTENNAS, Doc. ALMA-34.00.00.00.006-BSPE. Behrend, D. (2006). VLBI2010 Antenna Specs, Data sheet. DeBoer, D. (2001). The ATA Offset Gregorian Antenna, ATA Memo #16, February 10. Imbriale, W.A. (2006). Design of a Wideband Radio Telescope, Jet Propulsion Laboratory and S. Weinreb and H. Mandi, California Institute of Technology. Kilger, R. (2007). TWIN-Design studies, Presentation for the IVS board members (internal document),Wettzell. Kronschnabl, G. (2006). Subject: Memo from Bill Petrachenko, E-mail to the Twin-Working Group (in German), July. Lindgren, ETS-Lindgren (2005). The Model 3164-05 Open Boundary Quadridge Horn, Data Sheet. Niell, A., A. Whitney, W. Petrachenko, W. Schlüter, N. Vandenberg, H.Hase, Y. Koyama, C. Ma, H. Schuh, G. Tucari (2006). in: IVS Annual Report 2005, pg. 13-40, NASA/TP-2006-214136, April. Olsson, R., Kildal, P.-S., and Weinreb, S. (2006). IEEE Transactions on Antennas and Propagation, Vol. 54, No. 2, February. Petrachenko, B. (2006). The Case For and Against Multiple Antennas at a Site, IVS Memorandum, 2006-019v01. Petrachenko, B. (2006). IVS Memorandum, 2006-016v01. RFSpin (2004). Double Ridged Waveguide Horn-Model DRH20, Antenna Specifications, Data Sheet. Rohde&Schwarz (2004). SHF Antennas Crossed Log- Periodic Antennas HL024A1/S1, Data Sheet. Rohde&Schwarz (2004). SHF Antennas Log-Periodic Antennas HL050/HL050S1, Data Sheet. Rogers, A.E.E. (2006). Simulations of broadband
16. Anaesthesia for the separation of conjoined twins
Directory of Open Access Journals (Sweden)
Jaya Lalwani
2011-01-01
Full Text Available Thoraco-omphalopagus is one of the most common type of conjoint twins accounting for 74% cases of conjoint twins. We report the anaesthetic management for successful separation of thoraco-omphalopagus conjoint twins, both of them surviving till date. We highlight the responsibility of anaesthesia team in anaesthetising the two individual patients simultaneously, need of careful monitoring and anticipation of complications like massive blood loss, hypotension, hypokalemia, hypoxia and hypercabia. Detailed description of successful management is reported.
17. Gene-Environment Interplay in Twin Models
OpenAIRE
2013-01-01
In this article, we respond to Shultziner’s critique that argues that identical twins are more alike not because of genetic similarity, but because they select into more similar environments and respond to stimuli in comparable ways, and that these effects bias twin model estimates to such an extent that they are invalid. The essay further argues that the theory and methods that undergird twin models, as well as the empirical studies which rely upon them, are unaware of these potential biases...
18. Exotic quarks in Twin Higgs models
Energy Technology Data Exchange (ETDEWEB)
Cheng, Hsin-Chia [Department of Physics, University of California, Davis,One Shields Avenue, Davis, CA 95616 (United States); Jung, Sunghoon [School of Physics, Korea Institute for Advanced Study,85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of); SLAC National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025 (United States); Salvioni, Ennio [Department of Physics, University of California, Davis,One Shields Avenue, Davis, CA 95616 (United States); Tsai, Yuhsin [Department of Physics, University of California, Davis,One Shields Avenue, Davis, CA 95616 (United States); Maryland Center for Fundamental Physics,Department of Physics, University of Maryland,College Park, MD 20742 (United States)
2016-03-14
The Twin Higgs model provides a natural theory for the electroweak symmetry breaking without the need of new particles carrying the standard model gauge charges below a few TeV. In the low energy theory, the only probe comes from the mixing of the Higgs fields in the standard model and twin sectors. However, an ultraviolet completion is required below ∼ 10 TeV to remove residual logarithmic divergences. In non-supersymmetric completions, new exotic fermions charged under both the standard model and twin gauge symmetries have to be present to accompany the top quark, thus providing a high energy probe of the model. Some of them carry standard model color, and may therefore be copiously produced at current or future hadron colliders. Once produced, these exotic quarks can decay into a top together with twin sector particles. If the twin sector particles escape the detection, we have the irreducible stop-like signals. On the other hand, some twin sector particles may decay back into the standard model particles with long lifetimes, giving spectacular displaced vertex signals in combination with the prompt top quarks. This happens in the Fraternal Twin Higgs scenario with typical parameters, and sometimes is even necessary for cosmological reasons. We study the potential displaced vertex signals from the decays of the twin bottomonia, twin glueballs, and twin leptons in the Fraternal Twin Higgs scenario. Depending on the details of the twin sector, the exotic quarks may be probed up to ∼ 2.5 TeV at the LHC and beyond 10 TeV at a future 100 TeV collider, providing a strong test of this class of ultraviolet completions.
19. Numerical Simulation of Twin Nozzle Injectors
OpenAIRE
Milak, Dino
2015-01-01
Fuel injectors for marine applications have traditionally utilized nozzles with symmetric equispaced orifice configuration. But in light of the new marine emission legislations the twin nozzle concept has arisen. The twin nozzle differs from the conventional configuration by utilizing two closely spaced orifices to substitute each orifice in the conventional nozzle. Injector manufacturers regard twin nozzle injectors as a promising approach to facilitate stable spray patterns independent of t...
20. Bilateral Norrie's disease in identical twins.
OpenAIRE
Sukumaran, K
1991-01-01
A case of Norrie's disease in an identical twins is reported. No positive family history was obtained. The couple had no other children. The older of the twins died at the age of 9 months of uncertain cause. To the best of my knowledge this is the first case of Norrie's disease reported in Malaysia. And its occurrence in an identical twins is very rare.
1. Dental twinning anomalies: the nomenclature enigma.
Science.gov (United States)
Killian, C M; Croll, T P
1990-07-01
Dental twinning results from abnormal events in the embryologic development of teeth. This paper describes the impossibility of assigning precise diagnostic terms, such as germination, fusion, macrodontia, and concrescence, to dental twinning anomalies because the entire course of odontogenesis cannot be witnessed. Traditional nomenclature is reviewed and seven cases that exemplify the principle are presented. Modification of nomenclature to describe dental twinning defects is suggested.
2. Twin Loss: Implications for Counselors Working with Surviving Twins.(practice & Theory)
Science.gov (United States)
Withrow, Rebecca; Schwiebert, Valerie L.
2005-01-01
Multiple births are becoming increasingly prevalent due to the use of fertility drugs and women choosing to wait until later life to conceive. With the growth in the twin population, little research has been done to investigate the effects on the grief process when 1 twin dies. Counselors must understand the unique experience of twins to formulate…
3. Problem in twin pregnancy: Findings of prenatal sonography and autopsy
International Nuclear Information System (INIS)
Kim, Jeong Ah; Cho, Jeong Yeon; Song, Mi Jin; Min, Jee Yeon; Lee, Young Ho; Lee, Hak Jong; Chun, Yi Kyeong; Kim, Yee Jeong; Hong, Sung Ran
2001-01-01
Multifetal gestations are high risk pregnancies with higher perinatal morbidity and mortality. Multifetal gestations are subject to unique complications including conjoined twins, twin-to-twin transfusion syndrome (TTTS), acardiac twins, twin embization of co-twin demise and heterotopic pregnancies. Prenatal sonographic diagnosis of types and complications of multifetal gestations is important for antenatal care and prediction of fetal outcome. This study was performed to present the prenatal ultrasonographic findings and pathologic findings of the unique complications of twin pregnancy. Acardia is a lethal anomaly occurring in 1% of monozygotic twin. The acardiac twin has a parasitic existence and depends on the donor (pump) twin for its blood supply via placental anastomoses and retrograde perfusion of umbilical cord. This twin reversed arterial perfusion (TRAP) sequence is a most extreme manifestation on the TTTS. Doppler verification reversed flow in umbilical cord of the acardiac twin confirms the diagnosis.
4. HDE 245059: A WEAK-LINED T TAURI BINARY REVEALED BY CHANDRA AND KECK
International Nuclear Information System (INIS)
Baldovin-Saavedra, C.; Audard, M.; Duchene, G.; Guedel, M.; Skinner, S.L.; Paerels, F. B. S.; Ghez, A.; McCabe, C.
2009-01-01
We present the Chandra High Energy Transmission Grating Spectrometer and Keck observations of HDE 245059, a young weak-lined T Tauri star (WTTS), member of the pre-main-sequence group in the λ Orionis Cluster. Our high spatial resolution, near-infrared observations with Keck reveal that HDE 245059 is in fact a binary separated by 0.''87, probably composed of two WTTS based on their color indices. Based on this new information we have obtained an estimate of the masses of the binary components; ∼3 M sun and ∼2.5 M sun for the north and south components, respectively. We have also estimated the age of the system to be ∼2-3 Myr. We detect both components of the binary in the zeroth-order Chandra image and in the grating spectra. The light curves show X-ray variability of both sources and in particular a flaring event in the weaker southern component. The spectra of both stars show similar features: a combination of cool and hot plasma as demonstrated by several iron lines from Fe XVII to Fe XXV and a strong bremsstrahlung continuum at short wavelengths. We have fitted the combined grating and zeroth-order spectrum (considering the contribution of both stars) in XSPEC. The coronal abundances and emission measure distribution for the binary have been obtained using different methods, including a continuous emission measure distribution and a multi-temperature approximation. In all cases we have found that the emission is dominated by plasma between ∼8 and ∼15 MK a soft component at ∼4 MK and a hard component at ∼50 MK are also detected. The value of the hydrogen column density was low, N H ∼ 8 x 10 19 cm -2 , likely due to the clearing of the inner region of the λ Orionis cloud, where HDE 245059 is located. The abundance pattern shows an inverse first ionization potential effect for all elements from O to Fe, the only exception being Ca. To obtain the properties of the binary components, a 3-T model was fitted to the individual zeroth-order spectra
5. Twin-Foucault imaging method
Science.gov (United States)
2012-02-01
A method of Lorentz electron microscopy, which enables observation two Foucault images simultaneously by using an electron biprism instead of an objective aperture, was developed. The electron biprism is installed between two electron beams deflected by 180° magnetic domains. Potential applied to the biprism deflects the two electron beams further, and two Foucault images with reversed contrast are then obtained in one visual field. The twin Foucault images are able to extract the magnetic domain structures and to reconstruct an ordinary electron micrograph. The developed Foucault method was demonstrated with a 180° domain structure of manganite La0.825Sr0.175MnO3.
6. Ectodermal dysplasia in identical twins
Directory of Open Access Journals (Sweden)
Gurkar Haraswarupa Puttaraju
2013-01-01
Full Text Available Hereditary hypohidrotic ectodermal dysplasia (HED is typically inherited as an X-linked recessive trait, characterized by deformity of at least two or more of the ectodermal structures - hair, teeth, nails and sweat glands. Two cases of hereditary HED involving identical male twins, is being documented for the rarity of its occurrence with special attention given to genetics, pathophysiology, clinical, intraoral manifestations and to the methods to improve the masticatory function, the facial esthetics and psychology of patients affected by this disease.
7. Risk of Oral Clefts in Twins
DEFF Research Database (Denmark)
Grosen, Dorthe; Bille, Camilla; Petersen, Inge
2011-01-01
and heritability. Twins (207 affected/130,710) and singletons (7766 affected/4,798,526) born from 1936 through 2004 in Denmark were ascertained by linkage among the Danish Facial Cleft Database, the Danish Twin Registry, and the Civil Registration System. We computed oral cleft prevalence and prevalence proportion...
8. Fatique life and twinning in alphazirconium
DEFF Research Database (Denmark)
Warren, M.R.; Beevers, C.J.
1970-01-01
stress for {11−21} twinning of ~0.5 kg mm−2 in zirconium containing 0.003 wt pct O. During observations confined to internal grains it was found that increasing grain size and decreasing oxygen content favored the formation of fatigue damage in association with these {11−21} twins. In external grains...
9. Gestation period and twinning in chimpanzees.
Science.gov (United States)
PEACOCK, L J; ROGERS, C M
1959-04-10
The length of the gestation period in 118 births in a colony of chimpanzees was found to be 226.8 days, with a standard deviation of 13.3 and a range of 196 to 260 days. Six pairs of twins were born in 120 parturitions; thus the apparent twinning rate is higher than that in man.
10. Fetal behavior in normal dichorionic twin pregnancy
NARCIS (Netherlands)
Mulder, E. J. H.; Derks, J. B.; de Laat, M. W. M.; Visser, G. H. A.
2012-01-01
Objectives: A prospective study was performed to compare fetal behavioral development in healthy dichorionic twins and singletons, and identify twin intra-pair associations (synchrony) of fetal movements and rest-activity cycles using different criteria to define synchrony. Subjects and methods:
11. Urticaria in monozygotic and dizygotic twins
DEFF Research Database (Denmark)
Thomsen, Simon Francis; van der Sluis, Sophie; Kyvik, Kirsten Ohm
2012-01-01
Aim. To identify risk factors for urticaria, to determine the relative proportion of the susceptibility to urticaria that is due to genetic factors in an adult clinical twin sample, and to further determine whether the genetic susceptibility to urticaria overlaps with the genetic susceptibility...... to atopic diseases. Methods. A total of 256 complete twin pairs and 63 single twins, who were selected from sibships with self-reported asthma via a questionnaire survey of 21,162 adult twins from the Danish Twin Registry, were clinically interviewed about a history of urticaria and examined for atopic...... diseases. Data were analysed with Cox proportional hazards regression and variance components models. Results. A total of 151 individuals (26%) had a history of urticaria, whereas 24 (4%) had had symptoms within the past year. Female sex, HR = 2.09 (1.46-2.99), P = 0.000; hay fever, HR = 1.92 (1...
12. Twins in Ancient Greece: a synopsis.
Science.gov (United States)
2016-01-01
This brief outline associates twins with several aspects of life in Ancient Greece. In Greek mythology twins caused ambivalent reactions and were believed to have ambivalent feelings for each other. Very often, they were viewed as the representatives of the dualistic nature of the universe. Heteropaternal superfecundation, which dominates in ancient myths, explains on one hand, the god-like qualities and, on the other hand, the mortal nature of many twins. An assumption is presented that legends referring to twins might reflect the territorial expansions of Ancient Greeks in Northern Mediterranean, around the Black Sea, in Asia Minor, as well as North East Africa. In conclusion, in Greek antiquity, twins have been used as transitional figures between myth and reality.
13. 'Biracial'-Looking Twins: A New Twin Type?/Twin Research: Twins with Cystic Teratomas; Sleep Quality and Body Mass Index; Previable Membrane Rupture/Print and Online Reports: Twins Born to a Sister Surrogate; NASA Twin Study; African-Cosmopolitan Twin Fashion Inspirations; Triplet Hockey Stars.
Science.gov (United States)
Segal, Nancy L
2017-06-01
Dizygotic (DZ) co-twins born to mothers and fathers from different racial or ethnic backgrounds often resemble one parent much more than the other. As such, these pairs comprise a unique subset of twins for investigating how others' responses to their different looks may affect their personalities and self-esteem. This article describes some of these twin pairs and some challenges of raising them, and suggests ways they may be used in research. Next, recent twin research on cystic teratomas, relations between sleep quality and body mass index, and previable membrane rupture is described. The final section concerns twins, twin studies, and related events in the media, namely: twins born to a sister surrogate, the NASA twin investigation, inspiring African-Cosmopolitan twins in fashion, and triplet Hockey Stars.
14. Highlights from the 15th International Congress of Twin Studies/Twin Research: Differentiating MZ Co-twins Via SNPs; Mistaken Infant Twin-Singleton Hospital Registration; Narcolepsy With Cataplexy; Hearing Loss and Language Learning/Media Mentions: Broadway Musical Recalls Conjoined Hilton Twins; High Fashion Pair; Twins Turn 102; Insights From a Conjoined Twin Survivor.
Science.gov (United States)
Segal, Nancy L
2015-02-01
Highlights from the 15th International Congress of Twin Studies are presented. The congress was held November 16-19, 2014 in Budapest, Hungary. This report is followed by summaries of research addressing the differentiation of MZ co-twins by single nucleotide polymorphisms (SNPs), an unusual error in infant twin-singleton hospital registration, twins with childhood-onset narcolepsy with cataplexy, and the parenting effects of hearing loss in one co-twin. Media interest in twins covers a new Broadway musical based on the conjoined twins Violet and Daisy Hilton, male twins becoming famous in fashion, twins who turned 102 and unique insights from a conjoined twin survivor. This article is dedicated to the memory of Elizabeth (Liz) Hamel, DZA twin who met her co-twin for the first time at age seventy-eight years. Liz and her co-twin, Ann Hunt, are listed in the 2015 Guinness Book of Records as the longest separated twins in the world.
15. The utility of twins in developmental cognitive neuroscience research: How twins strengthen the ABCD research design.
Science.gov (United States)
Iacono, William G; Heath, Andrew C; Hewitt, John K; Neale, Michael C; Banich, Marie T; Luciana, Monica M; Madden, Pamela A; Barch, Deanna M; Bjork, James M
2018-08-01
16. The mobility of growth twins synthesized by sputtering: Tailoring the twin thickness
International Nuclear Information System (INIS)
Velasco, Leonardo; Hodge, Andrea M.
2016-01-01
The current work presents a protean twin thickness contour zone map that illustrates how the nucleation and the mobility of twin boundaries affects the twin thickness of sputtered films. The twin thickness contour zone map can be used as a versatile guide to synthesize fully nanotwinned films with tailored twin thicknesses in materials with a wide range of stacking fault energies. The nucleation and mobility of twin boundaries was studied in four Cu alloys of different compositions (Cu-6wt.%Al, Cu-4wt.%Al, Cu-2wt.%Al, and Cu-10wt.%Ni), having stacking fault energies ranging from 6 mJ/m 2 to 60 mJ/m 2 . The films were synthesized by magnetron sputtering and characterized by transmission electron microscopy, where the twin thickness varied from 2 nm to 35 nm. Our experimental results show that it is possible to control the twin thickness. Three main mechanisms are explained to describe twin nucleation and twin boundary mobility, which are correlated to the interplay of specific sputtering conditions and the deposition temperature.
17. Effect of co-twin gender on neurodevelopmental symptoms: a twin register study.
Science.gov (United States)
Eriksson, Jonna Maria; Lundström, Sebastian; Lichtenstein, Paul; Bejerot, Susanne; Eriksson, Elias
2016-01-01
Autism spectrum disorder (ASD) and attention-deficit/hyperactivity disorder (ADHD) are neurodevelopmental disorders thought to have both genetic and environmental causes. It has been hypothesized that exposure to elevated levels of prenatal testosterone is associated with elevated traits of ASD and ADHD. Assuming that testosterone levels from a dizygotic male twin fetus may lead to enhanced testosterone exposure of its co-twins, we aimed to test the prenatal testosterone hypothesis by comparing same-sex with opposite-sex dizygotic twins with respect to neurodevelopmental symptoms. Neuropsychiatric traits were assessed in a population-based twin cohort from the Child and Adolescent Twin Study in Sweden (CATSS). Parental interviews were conducted for 16,312 dizygotic twins, 9 and 12 years old, with the Autism-Tics, ADHD, and other Comorbidities inventory (A-TAC). Girls with a female co-twin had an increased risk of reaching the cut-off score for ADHD compared with girls with a male co-twin. Both boys and girls with a female co-twin displayed a larger number of traits related to attention deficit and repetitive and stereotyped behaviors than those with a male twin. In girls, this also extended to social interaction and the combined measures for ASD and ADHD, however, with small effect sizes. Our results are reverse to what would have been expected from the prenatal testosterone hypothesis but consistent with a previous study of ASD and ADHD traits in dizygotic twins. The seemingly protective effect for girls of having a twin brother may be an effect of parent report bias, but may also be an unexpected effect of sharing the intrauterine environment with a male co-twin.
18. Probing Signatures of a Distant Planet around the Young T-Tauri Star CI Tau Hosting a Possible Hot Jupiter
Science.gov (United States)
Konishi, Mihoko; Hashimoto, Jun; Hori, Yasunori
2018-06-01
We search for signatures of a distant planet around the two million-year-old classical T-Tauri star CI Tau hosting a hot-Jupiter candidate ({M}{{p}}\\sin i∼ 8.1 {M}Jupiter}) in an eccentric orbit (e ∼ 0.3). To probe the existence of an outer perturber, we reanalyzed 1.3 mm dust continuum observations of the protoplanetary disk around CI Tau obtained by the Atacama Large Millimeter/submillimeter Array (ALMA). We found a gap structure at ∼0.″8 in CI Tau’s disk. Our visibility fitting assuming an axisymmetric surface brightness profile suggested that the gap is located at a deprojected radius of 104.5 ± 1.6 au and has a width of 36.9 ± 2.9 au. The brightness temperature around the gap was calculated to be ∼2.3 K lower than that of the ambient disk. Gap-opening mechanisms such as secular gravitational instability (GI) and dust trapping can explain the gap morphology in the CI Tau disk. The scenario that an unseen planet created the observed gap structure cannot be ruled out, although the coexistence of an eccentric hot Jupiter and a distant planet around the young CI Tau would be challenging for gravitational scattering scenarios. The mass of the planet was estimated to be between ∼0.25 M Jupiter and ∼0.8 M Jupiter from the gap width and depth ({0.41}-0.06+0.04) in the modeled surface brightness image, which is lower than the current detection limits of high-contrast direct imaging. The young classical T-Tauri CI Tau may be a unique system for exploring the existence of a potential distant planet as well as the origin of an eccentric hot Jupiter.
19. Ostreococcus tauri Luminescent Reporter Lines as Biosensors for Detecting Pollution From Copper-Mine Tailing Effluents in Coastal Environments
Directory of Open Access Journals (Sweden)
Carlos Henríquez-Castillo
2018-05-01
Full Text Available Phytoplankton cells are excellent biosensors for environmental monitoring and toxicity assessments in different natural systems. Green algae, in particular, appear to be more responsive to copper (Cu disturbances. This is interesting considering that Cu pollution in coastal environments has increased over the last century, with enormous repercussions to marine ecosystems. Unfortunately, no high-throughput method exists for the environmental monitoring of Cu toxicity in seawater. To assess potential uses as biosensors of Cu pollution, high-throughput screening was performed on five luminescence reporter lines constructed in the green algae Ostreococcus tauri RCC745. The reporter line expressing the iron storage ferritin protein fused to luciferase (Fer-Luc was the most sensitive, responding to Cu concentrations in the μM range. Fer-Luc was also the most sensitive reporter line for detecting toxicity in mining-derived polluted seawater predominantly contaminated by soluble Cu. Nevertheless, the Cyclin-Dependent-Kinase A (CDKA reporter was most suitable for detecting the toxicity of copper-mine tailing effluents containing other metals (e.g., iron. These results highlight that Ostreococcus biosensors can serve as a reliable, inexpensive, and automated, high-throughput laboratory approach for performing seawater analyses of coastal areas subjected to metal disturbances. When challenged with Cu, O. tauri not only evidenced a rapid, transcriptional response for the tested genes, but also showed changes in a broad range of genes, especially as related to the stress response. Overall, the obtained results reinforce that a single biosensor is insufficient when dealing with complex mixtures of toxic compounds in natural environments.
20. Hypothesis test for synchronization: twin surrogates revisited.
Science.gov (United States)
Romano, M Carmen; Thiel, Marco; Kurths, Jürgen; Mergenthaler, Konstantin; Engbert, Ralf
2009-03-01
The method of twin surrogates has been introduced to test for phase synchronization of complex systems in the case of passive experiments. In this paper we derive new analytical expressions for the number of twins depending on the size of the neighborhood, as well as on the length of the trajectory. This allows us to determine the optimal parameters for the generation of twin surrogates. Furthermore, we determine the quality of the twin surrogates with respect to several linear and nonlinear statistics depending on the parameters of the method. In the second part of the paper we perform a hypothesis test for phase synchronization in the case of experimental data from fixational eye movements. These miniature eye movements have been shown to play a central role in neural information processing underlying the perception of static visual scenes. The high number of data sets (21 subjects and 30 trials per person) allows us to compare the generated twin surrogates with the "natural" surrogates that correspond to the different trials. We show that the generated twin surrogates reproduce very well all linear and nonlinear characteristics of the underlying experimental system. The synchronization analysis of fixational eye movements by means of twin surrogates reveals that the synchronization between the left and right eye is significant, indicating that either the centers in the brain stem generating fixational eye movements are closely linked, or, alternatively that there is only one center controlling both eyes.
1. CSI 2264: Probing the inner disks of AA Tauri-like systems in NGC 2264
Science.gov (United States)
McGinnis, P. T.; Alencar, S. H. P.; Guimarães, M. M.; Sousa, A. P.; Stauffer, J.; Bouvier, J.; Rebull, L.; Fonseca, N. N. J.; Venuti, L.; Hillenbrand, L.; Cody, A. M.; Teixeira, P. S.; Aigrain, S.; Favata, F.; Fűrész, G.; Vrba, F. J.; Flaccomio, E.; Turner, N. J.; Gameiro, J. F.; Dougados, C.; Herbst, W.; Morales-Calderón, M.; Micela, G.
2015-05-01
Context. The classical T Tauri star (CTTS) AA Tau has presented photometric variability that was attributed to an inner disk warp, caused by the interaction between the inner disk and an inclined magnetosphere. Previous studies of the young cluster NGC 2264 have shown that similar photometric behavior is common among CTTS. Aims: The goal of this work is to investigate the main causes of the observed photometric variability of CTTS in NGC 2264 that present AA Tau-like light curves, and verify if an inner disk warp could be responsible for their observed variability. Methods: In order to understand the mechanism causing these stars' photometric behavior, we investigate veiling variability in their spectra and u - r color variations and estimate parameters of the inner disk warp using an occultation model proposed for AA Tau. We also compare infrared Spitzer IRAC and optical CoRoT light curves to analyze the dust responsible for the occultations. Results: AA Tau-like variability proved to be transient on a timescale of a few years. We ascribe this variability to stable accretion regimes and aperiodic variability to unstable accretion regimes and show that a transition, and even coexistence, between the two is common. We find evidence of hot spots associated with occultations, indicating that the occulting structures could be located at the base of accretion columns. We find average values of warp maximum height of 0.23 times its radial location, consistent with AA Tau, with variations of on average 11% between rotation cycles. We also show that extinction laws in the inner disk indicate the presence of grains larger than interstellar grains. Conclusions: The inner disk warp scenario is consistent with observations for all but one star with AA Tau-like variability in our sample. AA Tau-like systems are fairly common, comprising 14% of CTTS observed in NGC 2264, though this number increases to 35% among systems of mass 0.7 M⊙ ≲ M ≲ 2.0 M⊙. Assuming random
2. CLASSICAL T TAURI-LIKE OUTFLOW ACTIVITY IN THE BROWN DWARF MASS REGIME
International Nuclear Information System (INIS)
Whelan, E. T.; Ray, T. P.; Podio, L.; Bacciotti, F.; Randich, S.
2009-01-01
Over the last number of years, spectroscopic studies have strongly supported the assertion that protostellar accretion and outflow activity persist to the lowest masses. Indeed, previous to this work, the existence of three brown dwarf (BD) outflows had been confirmed by us. In this paper, we present the results of our latest investigation of BD outflow activity and report on the discovery of two new outflows. Observations to date have concentrated on studying the forbidden emission line (FEL) regions of young BDs and in all cases data have been collected using the UV-Visual Echelle Spectrometer (UVES) on the ESO Very Large Telescope. Offsets in the FEL regions are recovered using spectro-astrometry. Here, ISO-Oph 32 is shown to drive a blueshifted outflow with a radial velocity of 10-20 km s -1 and spectro-astrometric analysis constrains the position angle of this outflow to 240 0 ± 7 0 . The BD candidate, ISO-ChaI 217 is found to have a bipolar outflow bright in several key forbidden lines (V RAD = -20 km s -1 , +40 km s -1 ) and with a P.A. of 193 0 -209 0 . A striking feature of the ISO-ChaI 217 outflow is the strong asymmetry between the red- and blueshifted lobes. This asymmetry is revealed in the relative brightness of the two lobes (redshifted lobe is brighter), the factor of 2 difference in radial velocity (the redshifted lobe is faster) and the difference in the electron density (again higher in the red lobe). Such asymmetries are common in jets from low-mass protostars and the observation of a marked asymmetry at such a low mass ( sun ) supports the idea that BD outflow activity is scaled down from low-mass protostellar activity. Also note that although asymmetries are unexceptional, it is uncommon for the redshifted lobe to be the brightest as some obscuration by the accretion disk is assumed. This phenomenon has only been observed in one other source, the classical T Tauri (CTTS) star RW Aur. The physical mechanism responsible for the brightening of
3. Establishing a Twin Registry in Guinea-Bissau
DEFF Research Database (Denmark)
Bjerregaard-Andersen, Morten; Gomes, Margarida A; Joaquím, Luis C
2013-01-01
represent a powerful tool. Though twin studies have been carried out by the Bandim Health Project for more than 30 years, the renewed registry described here was officially established in 2009 and includes both a cohort of newborn twins and a cohort of young and adult twins. Currently more than 1,500 twins...
4. Twin Delivery: Comparison of Incidence and Foetal Outcome in two ...
African Journals Online (AJOL)
Background: The incidence of twin delivery in Nigeria may have changed, in view of the worldwide increase in the rates of twinning attributed to increasing maternal age and use of fertility therapies. Objective: To determine the current incidence of twin delivery in Benin City and document the foetal outcome in twins.
5. CERN: Ten-Tesla twin
International Nuclear Information System (INIS)
Anon.
1991-01-01
An important step in the development of the high field superconducting magnets for CERN's proposed LHC proton collider came on 21 October when a 1 metre-long model of the proposed twin-dipole magnet produced a field of 10 Tesla in its two o beam apertures at the design temperature of 1.8K. The LHC designers have to plan for proton beams approaching 8 TeV to attain the right conditions for the quarks and gluons hidden deep inside protons to produce new physics. To contain these very high energy protons in the tight track of the 27-kilometre LEP tunnel would need the strongest magnetic bending power ever used in a full storage ring
6. Median mental sinus in twins.
Science.gov (United States)
Ong, S T; Ngeow, W C
1999-05-01
Sinus on the chin can be the result of a chronic apical abscess due to pulp necrosis of a mandibular anterior tooth. The tooth is usually asymptomatic, and a dental cause is therefore not apparent to the patient or the unsuspecting clinician. Not infrequently, the patient may seek treatment from a dermatologist or general surgeon instead of a dentist. Excision and repair of the fistula may be carried out with subsequent breakdown because the dental pathology is not removed. This paper reports the presence of median mental sinus of dental origin in twins. One case healed following root canal therapy while the other required both root canal therapy and surgery to eliminate the infection.
7. Undiagnosed xiphopagus twins: a perinatal malady
Directory of Open Access Journals (Sweden)
Gowri Dorairajan
2012-02-01
Full Text Available Conjoined twins are a very rare entity. It is associated with poor survival rate in the presence of vital organ sharing. The entity can be diagnosed as early as the first trimester. A conjoined twin diagnosed late in labor is a malady with high perinatal mortality and maternal morbidity. We present one such case of xiphopagus twins. The management of a case diagnosed late in labor can be very challenging. Such obstetric challenges can be avoided by a meticulous early scan with a high index of suspicion, especially in the absence of separating membrane while scanning multiple pregnancies.
8. Attractiveness Differences Between Twins Predicts Evaluations of Self and Co-Twin
Science.gov (United States)
Principe, Connor P.; Rosen, Lisa H.; Taylor-Partridge, Teresa; Langlois, Judith H.
2012-01-01
One of the most consistent findings in psychology shows that people prefer and make positive attributions about attractive compared with unattractive people. The goal of the current study was to determine the power of attractiveness effects by testing whether these social judgments are made where attractiveness differences are smallest: between twins. Differences in facial attractiveness predicted twins’ evaluations of self and their co-twin (n = 158; 54 male). In twin pairs, the more attractive twin judged their less attractive sibling as less physically attractive, athletic, socially competent, and emotionally stable. The less attractive twin did the reverse. Given that even negligible differences in facial attractiveness predicted self and co-twin attitudes, these results provide the strongest test yet of appearance-based stereotypes. PMID:23467329
9. Marital status and twins' health and behavior: an analysis of middle-aged Danish twins
DEFF Research Database (Denmark)
Osler, Merete; McGue, Matt; Lund, Rikke
2008-01-01
mass index (BMI), depression symptoms, self-rated health, cognitive function, physical activity, smoking, and alcohol intake. RESULTS: Among all 2350 individual twins, men who were divorced/widowed or never married had higher depression scores, lower cognitive test scores, lower physical activity....../widowed twin had higher average depression scores and was more likely to be a smoker. Never married twins had lower physical activity scores and never married male twins had higher BMI and higher depression scores than their married co-twin. CONCLUSION: This study suggests that the relationships of adult...... divorce with depression and smoking in Danish twins are due to the stressful effects of marital dissolution, but that marital differences in other health and behavioral outcomes are most consistent with selection effects related to genetic or rearing environmental factors....
10. Pump Spectral Bandwidth, Birefringence, and Entanglement in Type-II Parametric Down Conversion
Directory of Open Access Journals (Sweden)
Daniel Erenso
2009-01-01
Full Text Available The twin photons produced by a type-II spontaneous parametric down conversion are well know as a potential source of photons for quantum teleportation due to the strong entanglement in polarization. This strong entanglement in polarization, however, depends on the spectral composition of the pump photon and the nature of optical isotropy of the crystal. By exact numerical calculation of the concurrence, we have shown that how pump photons spectral width and the birefringence nature of the crystal directly affect the degree of polarization entanglement of the twin photons.
11. Molecular dynamics simulation of deformation twin in rocksalt vanadium nitride
International Nuclear Information System (INIS)
Fu, Tao; Peng, Xianghe; Zhao, Yinbo; Li, Tengfei; Li, Qibin; Wang, Zhongchang
2016-01-01
We perform molecular dynamics simulation of nano-indentation with a cylindrical indenter to investigate the formation mechanism of deformation twin in vanadium nitride (VN) with a rocksalt structure. We find that the deformation twins occur during the loading stage, and subsequently conduct a systematic analysis of nucleation, propagation and thickening of a deformation twin. We find that the nucleation of a partial dislocation and its propagation to form a stacking fault are premise of deformation twin formation. The sequential nucleation and propagation of partial dislocation on adjacent parallel {111} planes are found to cause the thickening of the deformation twin. Moreover, the deformation twins can exist in VN at room temperature. - Highlights: • MD simulations of indentation are performed to study the deformation twin in VN. • The deformation twins can occur in VN during the loading stage. • The nucleation, propagation and thickening of a deformation twin are analyzed. • The deformation twins can exist in VN at room temperature.
12. Cohort Profile : The National Academy of Sciences-National Research Council Twin Registry (NAS-NRC Twin Registry)
NARCIS (Netherlands)
Gatz, Margaret; Harris, Jennifer R.; Kaprio, Jaakko; McGue, Matt; Smith, Nicholas L.; Snieder, Harold; Spiro, Avron; Butler, David A.
The National Academy of Sciences-National Research Council Twin Registry (NAS-NRC Twin Registry) is a comprehensive registry of White male twin pairs born in the USA between 1917 and 1927, both of the twins having served in the military. The purpose was medical research and ultimately improved
13. Intragranular twinning, detwinning, and twinning-like lattice reorientation in magnesium alloys
International Nuclear Information System (INIS)
Wu, Wei; Gao, Yanfei; Li, Nan; Parish, Chad M.; Liu, Wenjun; Liaw, Peter K.; An, Ke
2016-01-01
Deformation twinning plays a critical role on improving metals or alloys ductility, especially for hexagonal close-packed materials with low symmetry crystal structure. A rolled Mg alloy was selected as a model system to investigate the extension twinning behaviors and characteristics of parent-twin interactions by nondestructive in situ 3D synchrotron X-ray microbeam diffraction. Besides twinning-detwinning process, the “twinning-like” lattice reorientation process was captured within an individual grain inside a bulk material during the strain reversal. The distributions of parent, twin, and reorientated grains and sub-micron level strain variation across the twin boundary are revealed. A theoretical calculation of the lattice strain confirms that the internal strain distribution in parent and twinned grains correlates with the experimental setup, grain orientation of parent, twin, and surrounding grains, as well as the strain path changes. The study suggests a novel deformation mechanism within the hexagonal close-packed structure that cannot be determined from surface-based characterization methods.
14. Twin Cities Metro Hybrid Landcover 2000 (Raster)
Data.gov (United States)
Minnesota Department of Natural Resources — The Hybrid Landcover is an attempt to clean up the University of Minnesota Remote Sensing Lab's 2000 LandSat Land Cover for the Twin Cities 7-county metropolitan...
15. Twin Screw Mixer/Fine Grind Facility
Data.gov (United States)
Federal Laboratory Consortium — The 40-mm Twin-Screw Mixer/Extruder (TSE) pilot plant is a continuous, remotely operated, flexible facility that can significantly enhance safety and environmental...
16. Prevention of preterm delivery in twin pregnancy
DEFF Research Database (Denmark)
Rode, Line; Tabor, Ann
2014-01-01
The incidence of twin gestation has increased markedly over the past decades, mostly because of increased use of assisted reproductive technologies. Twin pregnancies are at increased risk of preterm delivery (i.e. birth before 37 weeks of gestation). Multiple gestations therefore account for 2...... sequelae such as abnormal neurophysiological development in early childhood and underachievement in school. Several treatment modalities have been proposed in singleton high-risk pregnancies. The mechanism of initiating labour may, however, be different in singleton and twin gestations. Therefore......, it is mandatory to evaluate the proposed treatments in randomised trials of multiple gestations. In this chapter, we describe the results of trials to prevent preterm delivery in twin pregnancies....
17. Having Twins? How to Stay Healthy
Science.gov (United States)
... at night between bathroom breaks. Proper nutrition and hydration is important for your twin pregnancy, as is ... Pregnancy to Preschool (Copyright © 2010 American Academy of Pediatrics) The information contained on this Web site should ...
18. Micromechanics of twinning in a TWIP steel
International Nuclear Information System (INIS)
Rahman, K.M.; Jones, N.G.; Dye, D.
2015-01-01
The deformation behaviour of a TWinning Induced Plasticity (TWIP) steel was studied at quasi-static strain rates using synchrotron X-ray diffraction. A {111} RD and {200} RD texture developed from the earliest stages of deformation, which could be reproduced using an elasto-plastic self consistent (EPSC) model. Evidence is found from multiple sources to suggest that twinning was occurring before macroscopic yielding. This included small deviations in the lattice strains, {111} intensity changes and peak width broadening all occurring below the macroscopic yield point. The accumulation of permanent deformation on sub-yield mechanical cycling of the material was found, which further supports the diffraction data. TEM revealed that fine deformation twins similar to those observed in heavily deformed samples formed during sub-yield cycling. It is concluded that twinning had occurred before macroscopic plastic deformation began, unlike the behaviour traditionally expected from hexagonal metals such as Mg
19. Micromechanics of twinning in a TWIP steel
Energy Technology Data Exchange (ETDEWEB)
Rahman, K.M., E-mail: [email protected] [Department of Materials, Royal School of Mines, Imperial College London, Prince Consort Road, London SW7 2BP (United Kingdom); Jones, N.G. [Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS (United Kingdom); Dye, D. [Department of Materials, Royal School of Mines, Imperial College London, Prince Consort Road, London SW7 2BP (United Kingdom)
2015-05-21
The deformation behaviour of a TWinning Induced Plasticity (TWIP) steel was studied at quasi-static strain rates using synchrotron X-ray diffraction. A {111} RD and {200} RD texture developed from the earliest stages of deformation, which could be reproduced using an elasto-plastic self consistent (EPSC) model. Evidence is found from multiple sources to suggest that twinning was occurring before macroscopic yielding. This included small deviations in the lattice strains, {111} intensity changes and peak width broadening all occurring below the macroscopic yield point. The accumulation of permanent deformation on sub-yield mechanical cycling of the material was found, which further supports the diffraction data. TEM revealed that fine deformation twins similar to those observed in heavily deformed samples formed during sub-yield cycling. It is concluded that twinning had occurred before macroscopic plastic deformation began, unlike the behaviour traditionally expected from hexagonal metals such as Mg.
20. Cooperative Research Twin Trawl Sweep Comparison Study
Data.gov (United States)
National Oceanic and Atmospheric Administration, Department of Commerce — The "Twin-Trawl Sweep Efficiency Study" was intended to compare the sweep efficiency and selectivity of the NEFSC standardized bottom trawl to that of a standardized...
1. Diabetes and Menopause: A Twin Challenge
Science.gov (United States)
Diabetes and menopause: A twin challenge Diabetes and menopause may team up for varied effects on your body. Here's what to ... to stay in control. By Mayo Clinic Staff Menopause — and the years leading up to it — may ...
2. Strong crystal size effect on deformation twinning
DEFF Research Database (Denmark)
Yu, Qian; Shan, Zhi-Wei; Li, Ju
2010-01-01
plasticity. Accompanying the transition in deformation mechanism, the maximum flow stress of the submicrometre-sized pillars was observed to saturate at a value close to titanium’s ideal strength9, 10. We develop a ‘stimulated slip’ model to explain the strong size dependence of deformation twinning......Deformation twinning1, 2, 3, 4, 5, 6 in crystals is a highly coherent inelastic shearing process that controls the mechanical behaviour of many materials, but its origin and spatio-temporal features are shrouded in mystery. Using micro-compression and in situ nano-compression experiments, here we...... find that the stress required for deformation twinning increases drastically with decreasing sample size of a titanium alloy single crystal7, 8, until the sample size is reduced to one micrometre, below which the deformation twinning is entirely replaced by less correlated, ordinary dislocation...
3. Infantile Perineal Protrusion in Two Monochorionic Twins
Directory of Open Access Journals (Sweden)
Paola Cavicchioli
2014-11-01
Full Text Available Case Report - Two female monochorionic-monoamniotic twins showed the same kind of infantile perineal protrusion (IPP at birth. Lesions in both twins progressively healed until resolution in 6 weeks' time; none of the twins have manifested, till date, alvus disturbances. Discussion and Literature Review - A literature review numbers approximately 100 reports of IPP. This condition has been classically classified into three categories: congenital/familiar (i.e., female sex, positive parental history of IPP, acquired (mainly due to constipation, and associated with lichen sclerosus et atrophicus. Conclusions and Final Remarks - This case report describes, for the first time, the presence of IPP in monochorionic-monoamniotic twins, supporting the existence of hereditary/genetic factors in the developing of this condition.
4. Ferromagnetic and twin domains in LCMO manganites
International Nuclear Information System (INIS)
Jung, G.; Markovich, V.; Mogilyanski, D.; Beek, C. van der; Mukovskii, Y.M.
2005-01-01
Ferromagnetic and twin domains in lightly Ca-doped La 1-x Ca x MnO 3 single crystals have been visualized and investigated by means of the magneto-optical technique. Both types of domains became visible below the Curie temperature. The dominant structures seen in applied magnetic field are associated with magneto-crystalline anisotropy and twin domains. In a marked difference to the twin domains which appear only in applied magnetic field, ferromagnetic domains show up in zero applied field and are characterized by oppositely oriented spontaneous magnetization in adjacent domains. Ferromagnetic domains take form of almost periodic, corrugated strip-like structures. The corrugation of the ferromagnetic domain pattern is enforced by the underlying twin domains
5. X-ray sources in stars formation areas: T Tauri stars and proto-stars in the rho Ophiuchi dark cloud
International Nuclear Information System (INIS)
Grosso, Nicolas
1999-01-01
This thesis studies from large to small scales, X-ray sources in the rho Ophiuchi dark cloud. After some background on the formation of the low-mass young stars (Chapter 1), Chapter 2 takes an interest in the T Tauri star population. Chapter 3 tackles the search of the magnetic activity at the younger stage of protostar, presenting a powerful X-ray emission from an IR protostar, called YLW15, during a flare, and a quasi-periodic flare of the same source; as well as a new detection of another IR protostar in the ROSAT archives. It ends with a review of protostar detections. Some IR protostar flares show a very long increasing phase. Chapter 4 links this behaviour with a modulation by the central star rotation. The standard model of jet emission assumes that the central star rotates at the same speed that the inner edge of its accretion disk. This chapter shows that the observation of the YLW15 quasi-periodic flare suggests rather that the forming star rotates faster than its accretion disk, at the break up limit. The synchronism with the accretion disk, observed on T Tauri stars, must be reach progressively by magnetic breaking during the IR protostar stage, and more or less rapidly depending on the forming star mass. Recent studies have shown that T Tauri star X-ray emission could ionize the circumstellar disk, and play a role in the instability development, as well as stimulate the accretion. The protostar X-ray emission might be higher than the T Tauri star one, Chapter 5 presents a millimetric interferometric observation dedicated to measure this effect on YLW15. Finally, Chapter 6 reassembles conclusions and perspectives of this work. (author) [fr
6. Spectral Imaging by Upconversion
DEFF Research Database (Denmark)
Dam, Jeppe Seidelin; Pedersen, Christian; Tidemand-Lichtenberg, Peter
2011-01-01
We present a method to obtain spectrally resolved images using upconversion. By this method an image is spectrally shifted from one spectral region to another wavelength. Since the process is spectrally sensitive it allows for a tailored spectral response. We believe this will allow standard...... silicon based cameras designed for visible/near infrared radiation to be used for spectral images in the mid infrared. This can lead to much lower costs for such imaging devices, and a better performance....
7. Buoyant Helical Twin-Axial Wire Antenna
Science.gov (United States)
2016-11-15
February 2017 The below identified patent application is available for licensing. Requests for information should be addressed to...300169 1 of 9 BUOYANT HELICAL TWIN-AXIAL WIRE ANTENNA CROSS REFERENCE TO OTHER PATENT APPLICATIONS [0001] This application is a divisional...application and claims the benefit of the filing date of United States Patent Application No. 14/280,889; filed on May 19, 2014; and entitled “Twin-Axial
8. Magnetic resonance in multiple sclerose twins
International Nuclear Information System (INIS)
Polman, C.H.; UitdeHaag, B.M.J.; Koetsier, C.J.; Valk, J.; Lucas, C.J.
1989-01-01
Magnetic resonance imaging (MR) examinations were performed in a series of 7 twin sets (4 monozygotic and 3 dizygotic) and one triplet set who were clinically discordant for multiple sclerosis (MS). MRI abnormalities were detected in a number of the unaffected members of the nonzygotic twin pairs. The authors discuss the possible implications of their findings for the present view on the aetiology of MS. (author). 3 refs.; 1 fig.; 1 tab
9. Screening and Invasive Testing in Twins
Directory of Open Access Journals (Sweden)
Giovanni Monni
2014-07-01
Full Text Available Prenatal screening and testing for trisomy 21 in twin pregnancies poses a number of challenges: the exact estimate of the a priori risk of trisomy 21, the choice of prenatal screening test and/or invasive techniques to employ for the diagnosis and the impact of the result on the options of treatment in case of discordant results within a twin pair or among multiples. These different aspects are discussed below while recognizing that many issues remain unresolved.
10. Spectral Decomposition Algorithm (SDA)
Data.gov (United States)
National Aeronautics and Space Administration — Spectral Decomposition Algorithm (SDA) is an unsupervised feature extraction technique similar to PCA that was developed to better distinguish spectral features in...
11. Laying the ghost of twin paradox
Directory of Open Access Journals (Sweden)
Popović Marko
2009-01-01
Full Text Available Someone's true age is not written in his ID, but in his biomarkers. Aging process is not caused by time passing, but by thermodynamically laws. Entropy, extent of metabolic reaction, and temperature are Lorentz invariant, so these facts make twin paradox impossible because there is no way for one twin to age slower than the other even if the time in his frame is dilated. Entropy is the function of state, not time. So as much as standard thermodynamics concerns, the path between two points in space is equivalent to the path between two states. Whether the point B is reached by moving faster using the longer way (with time dilatation, or slower by using shortcut (without time dilatation, the state of the system after completing the road should be the same. This is supported by the fact that when two twins reach the same space-time point (point B in which the state parameters are the same. If we use entropy as an age parameter, then both twins have the same entropy value and are exactly the same biological age. Therefore, the twin paradox is a logical mistake based on wrong first premise. Bergson symmetry is not necessary any more to explain the impossibility of twin paradox.
12. Imperfect twinning: a clinical and ethical dilemma.
Science.gov (United States)
Denardin, Daniela; Telles, Jorge Alberto B; Betat, Rosilene da Silveira; Fell, Paulo Renato K; Cunha, André Campos da; Targa, Luciano Vieira; Zen, Paulo Ricardo G; Rosa, Rafael Fabiano M
2013-09-01
OBJECTIVE To review the history, epidemiology, etiology, gestational aspects, diagnosis and prognosis of imperfect twinning. DATA SOURCES Scientific articles were searched in PubMed, SciELO and Lilacs databases, using the descriptors "conjoined twins", "multiple pregnancy", "ultrasound", "magnetic resonance imaging" and "prognosis". The research was not delimited to a specific period of time and was supplemented with bibliographic data from books. The description of conjoined twins is legendary. The estimated frequency is 1/45,000-200,000 births. These twins are monozygotic, monochorionic and usually monoamniotic. They can be classified by the most prominent fusion site, by the symmetry between the conjoined twins or by the sharing structure. The diagnosis can be performed in the prenatal period or after birth by different techniques, such as ultrasound, magnetic resonance imaging and echocardiography. These tests are of paramount importance for understanding the anatomy of both fetuses/children, as well as for prognosis and surgical plan determination. CONCLUSIONS Although imperfect twinning is a rare condition, the prenatal diagnosis is very important in order to evaluate the fusion site and its complexity. Hence, the evaluation of these children should be multidisciplinary, involving mainly obstetricians, pediatricians and pediatric surgeons. However, some decisions may constitute real ethical dilemmas, in which different points should be discussed and analyzed with the health team and the family.
13. The Mid-Atlantic Twin Registry, revisited.
Science.gov (United States)
Lilley, Emily C H; Silberg, Judy L
2013-02-01
The Mid-Atlantic Twin Registry (MATR) is a population-based registry of more than 56,000 twins primarily born or living in Virginia, North Carolina, and South Carolina. The MATR employs several methods of ascertaining twins, and devotes considerable resources to tracking and maintaining communication with MATR participants. Researchers may utilize the MATR for administration of research services including study recruitment, collection of DNA, archival data set creation, as well as data collection through mailed, phone, or online surveys. In addition, the MATR houses the MATR Repository, with over 1,200 blood samples available for researchers interested in DNA genotyping. For over 35 years MATR twins have participated in research studies with investigators from diverse scientific disciplines and various institutions. These studies, which have resulted in numerous publications, have covered a range of topics, including the human microbiome, developmental psychopathology, depression, anxiety, substance use, epigenetics of aging, children of twins, pre-term birth, social attitudes, seizures, eating disorders, as well as sleep homeostasis. Researchers interested in utilizing twins are encouraged to contact the MATR to discuss potential research opportunities.
14. Twin birth order, birthweight and birthweight discordance: any relationship
Directory of Open Access Journals (Sweden)
Onyiriuka A.N.
2010-12-01
Full Text Available Background: It is widely believed that in twin pairs, at birth, the first-born weigh more than the second-born but this concept has been challenged. Objective: To assess the truthfulness of this common concept that first-born twins are usually heavier than their second-born siblings at birth. Methods: In a series of 104 sets of live-born twins, the birth weights of first-born twins were compared with those of their second-born siblings, after controlling for gender. Their intra-pair birthweight differences were determined and twin pairs whose birthweight difference was 15% or more were designated as discordant. Results: Twin I was heavier than Twin II in 61.5% of cases while Twin II was heavier than Twin I in 28.9% of cases. Twins I and II had equal birthweights in 9.6% of cases. Comparing the mean birthweight of the first-born-male twin with that of second-born- male twin, it was 2515+427g (95% Confidence Interval, CI=2402-2628 versus 2432 +435g (95% CI=2321-2543 p>0.05. The mean birthweight of first-born-female twin was 2326+445g (95% CI=2214-2439 while that of the second-born-female twin was 2325+501g (95% CI=2197-2453 p>0.05. When the birthweight difference exceeded 750g, the probability that Twin I will be heavier than Twin II was 83.3% (5 of 6. Conclusion: Although the first-born twin was more often heavier than their second-born siblings, either could weigh more or less at birth. The larger the birthweight difference between growth-discordant twin pair, the greater the probability that the heavier twin would be delivered first
15. Familial aggregation of atrial fibrillation: a study in Danish twins
DEFF Research Database (Denmark)
Christophersen, Ingrid Elisabeth; Ravn, Lasse Steen; Budtz-Joergensen, Esben
2009-01-01
BACKGROUND: Heritability may play a role in nonfamilial atrial fibrillation (AF). We hypothesized that a monozygotic (MZ) twin whose co-twin was diagnosed with AF would have an increased risk of the disease compared with a dizygotic (DZ) twin in the same situation. METHODS AND RESULTS: A sample......-free survival times, we compared the time span between occurrences of disease in MZ and DZ twins. The unaffected twin was included when his or her twin-sibling (the index twin) was diagnosed with AF. After adjustment for age at entry, MZ twins had a significantly shorter event-free survival time (hazard ratio......, 2.0; 95% CI, 1.3 to 3.0), thereby indicating a genetic component. Using biometric models, we estimated the heritability of AF to be 62% (55% to 68%), due to additive genetics. There were no significant differences across sexes. CONCLUSIONS: All the analyses of twin similarities in the present study...
16. Twin probes for space geodesy
International Nuclear Information System (INIS)
Bertotti, B.
1978-01-01
The twin probe method, proposed by Bertotti and Colombo (1972) to get rid of nongravitational forces in interplanetary space, can be applied to a near-Earth orbit to eliminate the atmospheric drag. Two equal pairs of probes, each pair consisting of two passive, small and dense spheres of equal surface and different masses, are flown on a circular orbit at an altitude of about 300 km. Each pair determines the motion of an ideal point which feels only the gravitational forces. They are separated by a distance d of (100/200) km and are tracked from a spacecraft or the Space Shuttle, flying at the same altitude. The relative motion of the two ideal points is reconstructed and yields a measurement of the fine structure of the Earth gravitational field, corresponding to a harmonic order l approximately a/d (a is the radius of the Earth). The tracking can be done by laser ranging to the four spheres, covered by corner reflectors; Doppler ranging is more convenient for higher values of l and can also be used. The accuracy in the compensation of the non-gravitational forces and in the measurements one needs for a given l are discussed in detail. (author)
17. Effect of maternal smoking on birth weight of twins: a study from the Dutch Twin Register
NARCIS (Netherlands)
Orlebeke, J.F.; Boomsma, D.I.; van Baal, G.C.M.; Bleker, O.P.
1994-01-01
Since twins weigh about 20% less than singletons at birth, maternal smoking may be a more severe risk for them than for singletons. Therefore, the effect of maternal smoking during pregnancy on birth weight was investigated in a group of 5376 twins. All necessary information was collected by a
18. Art for twins: Yorùbá artists and their statues/twin research studies: twins' education and conceptions; diurnal preference; inherited eye diseases; ultrasound counseling when twins are conjoined/popular twin reports: twin sisters (the film); rare pregnancy; diet test; French twins reared apart and reunited.
Science.gov (United States)
Segal, Nancy L
2014-06-01
The Yorùbá of Nigeria are well known for their high twinning rate and the statues they create to commemorate deceased twins. An impressive collection of this artwork was displayed at the University of California's Fowler Museum in Los Angeles between October 13, 2013 and March 2, 2014. An overview of this exhibit is provided. Next, twin research on maternal education and conception, diurnal preference, inherited eye diseases, and ultrasound counseling for couples with conjoined twins are briefly summarized. This article concludes with a discussion of media-based items related to twins. The topics include an award-winning twin film, a rare pregnancy, a diet test, and the separation and chance reunion of monozygotic female twins.
19. Attachment to the Romantic Partner and Sibling: Attachment Hierarchies of Twins and Non-Twin Siblings
Directory of Open Access Journals (Sweden)
Sascha Schwarz
2015-12-01
Full Text Available Previous studies have shown that romantic partners and siblings are important attachment figures. This study compares the attachment to the romantic partner with the attachment to the sibling as a function of the participant’s sibling type among monozygotic (MZ twins, dizygotic (DZ twins, and non-twin (NT siblings. The results show that MZ twins prefer their sibling to their romantic partner whereas DZ twins are equally attached to their sibling and romantic partner. In contrast, NT siblings are more attached to their romantic partner compared to their sibling. These results indicate that genetic relatedness has profound impact on a person’s attachment hierarchy and the relative rank of the romantic partner and the sibling.
20. Relationship between refractive error and ocular biometrics in twin children: the Guangzhou Twin Eye Study.
Science.gov (United States)
Wang, Decai; Liu, Bin; Huang, Shengsong; Huang, Wenyong; He, Mingguang
2014-09-01
A cross-sectional study was conducted to explore the relationship between refractive error and ocular biometrics in children from the Guangzhou twin eye study. Twin participants aged 7-15 years were selected from Guangzhou Twin Eye Study. Ocular examinations included visual acuity measurement, ocular motility evaluation, autorefraction under cycloplegia, and anterior segment, media, and fundus examination. Axial length (AL), anterior chamber depth (ACD), and corneal curvature radius were measured using partial coherence laser interferometry. A multivariate linear regression model was used for statistical analysis. Twin children from Guangzhou city showed a decreased spherical equivalent with age, whereas both AL and ACD were increased and corneal curvature radius remained unchanged. When adjusted by age and gender, the data from 77% of twins presenting with spherical equivalent changes indicated that these were caused by predictable variables (R2 = 0.77, P biometrics. Refractive status is largely determined by axial length as the major factor.
1. Indigenous Manufacturing realization of TWIN Source
Science.gov (United States)
Pandey, R.; Bandyopadhyay, M.; Parmar, D.; Yadav, R.; Tyagi, H.; Soni, J.; Shishangiya, H.; Sudhir Kumar, D.; Shah, S.; Bansal, G.; Pandya, K.; Parmar, K.; Vuppugalla, M.; Gahlaut, A.; Chakraborty, A.
2017-04-01
TWIN source is two RF driver based negative ion source that has been planned to bridge the gap between single driver based ROBIN source (currently operational) and eight river based DNB source (to be operated under IN-TF test facility). TWIN source experiments have been planned at IPR keeping the objective of long term domestic fusion programme to gain operational experiences on vacuum immersed multi driver RF based negative ion source. High vacuum compatible components of twin source are designed at IPR keeping an aim on indigenous built in attempt. These components of TWIN source are mainly stainless steel and OFC-Cu. Being high heat flux receiving components, one of the major functional requirements is continuous heat removal via water as cooling medium. Hence for the purpose stainless steel parts are provided with externally milled cooling lines and that shall be covered with a layer of OFC-cu which would be on the receiving side of high heat flux. Manufacturability of twin source components requires joining of these dissimilar materials via process like electrode position, electron beam welding and vacuum brazing. Any of these manufacturing processes shall give a vacuum tight joint having proper joint strength at operating temperature and pressure. Taking the indigenous development effort vacuum brazing (in non-nuclear environment) has been opted for joining of dissimilar materials of twin source being one of the most reliable joining techniques and commercially feasible across the suppliers of country. Manufacturing design improvisation for the components has been done to suit the vacuum brazing process requirement and to ease some of the machining without comprising over the functional and operational requirements. This paper illustrates the details on the indigenous development effort, design improvisation to suits manufacturability, vacuum brazing basics and its procedures for twin source components.
2. Monozygotic twins discordant for ROHHAD phenotype.
Science.gov (United States)
Patwari, Pallavi P; Rand, Casey M; Berry-Kravis, Elizabeth M; Ize-Ludlow, Diego; Weese-Mayer, Debra E
2011-09-01
Rapid-onset obesity with hypothalamic dysfunction, hypoventilation, and autonomic dysregulation (ROHHAD) falls within a group of pediatric disorders with both respiratory control and autonomic nervous system dysregulation. Children with ROHHAD typically present after 1.5 years of age with rapid weight gain as the initial sign. Subsequently, they develop alveolar hypoventilation, autonomic nervous system dysregulation, and, if untreated, cardiorespiratory arrest. To our knowledge, this is the first report of discordant presentation of ROHHAD in monozygotic twins. Twin girls, born at term, had concordant growth and development until 8 years of age. From 8 to 12 years of age, the affected twin developed features characteristic of ROHHAD including obesity, alveolar hypoventilation, scoliosis, hypothalamic dysfunction (central diabetes insipidus, hypothyroidism, premature pubarche, and growth hormone deficiency), right paraspinal/thoracic ganglioneuroblastoma, seizures, and autonomic dysregulation including altered pain perception, large and sluggishly reactive pupils, hypothermia, and profound bradycardia that required a cardiac pacemaker. Results of genetic testing for PHOX2B (congenital central hypoventilation syndrome disease-defining gene) mutations were negative. With early recognition and conservative management, the affected twin had excellent neurocognitive outcome that matched that of the unaffected twin. The unaffected twin demonstrated rapid weight gain later in age but not development of signs/symptoms consistent with ROHHAD. This discordant twin pair demonstrates key features of ROHHAD including the importance of early recognition (especially hypoventilation), complexity of signs/symptoms and clinical course, and importance of initiating comprehensive, multispecialty care. These cases confound the hypothesis of a monogenic etiology for ROHHAD and indicate alternative etiologies including autoimmune or epigenetic phenomenon or a combination of genetic
3. The Project TALENT Twin and Sibling Study.
Science.gov (United States)
Prescott, Carol A; Achorn, Deanna Lyter; Kaiser, Ashley; Mitchell, Lindsey; McArdle, John J; Lapham, Susan J
2013-02-01
Project TALENT is a US national longitudinal study of about 377,000 individuals born in 1942-1946, first assessed in 1960. Students in about 1,200 schools participated in a 2-day battery covering aptitudes, abilities, interests, and individual and family characteristics (Flanagan, 1962; www.projectTALENT.org). Follow-up assessments 1, 5, and 11 years later assessed educational and occupational outcomes. The sample includes approximately 92,000 siblings from 40,000 families, including 2,500 twin pairs and 1,200 other siblings of twins. Until recently, almost no behavior genetic research has been conducted with the sample. In the original data collection information was not collected with the intent to link family members. Recently, we developed algorithms using names, addresses, birthdates, and information about family structure to link siblings and identify twins. We are testing several methods to determine zygosity, including use of yearbook photographs. In this paper, we summarize the design and measures in Project TALENT, describe the Twin and Sibling sample, and present our twin-sib-classmate model. In most twin and family designs, the 'shared environment' includes factors specific to the family combined with between-family differences associated with macro-level variables such as socioeconomic status. The school-based sampling design used in Project TALENT provides a unique opportunity to partition the shared environment into variation shared by siblings, specific to twins, and associated with school- and community-level factors. The availability of many measured characteristics on the family, schools, and neighborhoods enhances the ability to study the impact of specific factors on behavioral variation.
4. Diabetes and perinatal mortality in twin pregnancies.
Directory of Open Access Journals (Sweden)
Zhong-Cheng Luo
Full Text Available BACKGROUND: Diabetes in pregnancy has been associated with a paradoxically reduced risk of neonatal death in twin pregnancies. Risk "shift" may be a concern in that the reduction in neonatal deaths may be due to an increase in fetal deaths (stillbirths. This study aimed to clarify the impact of diabetes on the risk of perinatal death (neonatal death plus stillbirth in twin pregnancies. METHODS: This was a retrospective cohort study of twin births using the largest available dataset on twin births (the U.S. matched multiple birth data 1995-2000; 19,676 neonates from diabetic pregnancies, 541,481 from non-diabetic pregnancies. Cox proportional hazard models were applied to estimate the adjusted hazard ratios (aHR of perinatal death accounting for twin cluster-level dependence. RESULTS: Comparing diabetic versus non-diabetic twin pregnancies, overall perinatal mortality rate was counterintuitively lower [2.1% versus 3.3%, aHR 0.70 (95% confidence intervals 0.63-0.78]. Individually, both stillbirth and neonatal mortality rates were lower in diabetic pregnancies, but we identified significant differences by gestational age and birth weight. Diabetes was associated with a survival benefit in pregnancies completed before 32 weeks [aHR 0.55 (0.48-0.63] or with birth weight =2500 g [aHR 2.20 (1.55-3.13]. CONCLUSIONS: Diabetes in pregnancy appears to be "protective" against perinatal death in twin pregnancies ending in very preterm or very low birth weight births. Prospective studies are required to clarify whether these patterns of risk are real, or they are artifacts of unmeasured confounders. Additional data correlating these outcomes with the types of diabetes in pregnancy are also needed to distinguish the effects of pre-gestational vs. gestational diabetes.
5. Sonographic monitoring of complications and anomalies in twin gestations
International Nuclear Information System (INIS)
Coleman, B.G.; Grumbach, K.; Arger, P.H.; Mintz, M.C.; Arenson, R.L.; Mennuti, M.T.; Gabbe, S.G.
1986-01-01
One hundred sixty-eight twin gestations were evaluated to assess the role of US in the diagnosis of obstetric complications and anomalies. US revealed the following complications: symptomatic polyhydramnios (eight cases), myomas (seven), placenta previa (three), and abruption (five). Fetal anomalies included twin-twin transfusion syndrome (two), acardiac anomaly (two), chromosomal abnormality (two), anencephaly (one), hydrocephaly (one), and conjoined twins (two). In 26 gestations intrauterine fetal demise or neonatal death involved one or both twins for a total of 42 deaths, constituting a mortality of 12.5%. No maternal deaths occurred. The impact of sonographic monitoring on the obstetric management of twin gestations is emphasized
6. Twin pregnancy possibly associated with high semen quality
DEFF Research Database (Denmark)
Asklund, Camilla; Jensen, Tina Kold; Jørgensen, Niels
2007-01-01
BACKGROUND: Recent studies found an association between a long waiting time to pregnancy (TTP) and reduced probability of twinning and a reduced dizygotic (DZ) twinning rate in subfertile men. However, it remains unsolved whether semen quality is associated with twin offspring. We therefore studied...... the semen quality in a group of fathers of naturally conceived twins. METHODS: In this study, 37 fathers of DZ twins and 15 fathers of monozygotic (MZ) twins participated, and 349 normal fertile men served as a reference group. All men delivered a semen sample, underwent a physical examination and completed...... points higher than the reference group (P semen quality than the reference group, which supports...
7. A twin study of body dysmorphic concerns.
Science.gov (United States)
Monzani, B; Rijsdijk, F; Anson, M; Iervolino, A C; Cherkas, L; Spector, T; Mataix-Cols, D
2012-09-01
Dysmorphic concern refers to an excessive preoccupation with a perceived or slight defect in physical appearance. It lies on a continuum of severity from no or minimal concerns to severe concerns over one's appearance. The present study examined the heritability of dysmorphic concerns in a large sample of twins. Twins from the St Thomas UK twin registry completed a valid and reliable self-report measure of dysmorphic concerns, which also includes questions about perceived body odour and malfunction. Twin modelling methods (female twins only, n=3544) were employed to decompose the variance in the liability to dysmorphic concerns into additive genetic, shared and non-shared environmental factors. Model-fitting analyses showed that genetic factors accounted for approximately 44% [95% confidence intervals (CI) 36-50%] of the variance in dysmorphic concerns, with non-shared environmental factors and measurement error accounting for the remaining variance (56%; 95% CI 50-63%). Shared environmental factors were negligible. The results remained unchanged when excluding individuals reporting an objective medical condition/injury accounting for their concern in physical appearance. Over-concern with a perceived or slight defect in physical appearance is a heritable trait, with non-shared environmental factors also playing an important role in its causation. The results are relevant for various psychiatric disorders characterized by excessive concerns in body appearance, odour or function, including but not limited to body dysmorphic disorder.
8. Characterization of Gastric Microbiota in Twins.
Science.gov (United States)
Dong, Quanjiang; Xin, Yongning; Wang, Lili; Meng, Xinying; Yu, Xinjuan; Lu, Linlin; Xuan, Shiying
2017-02-01
Contribution of host genetic backgrounds in the development of gastric microbiota has not been clearly defined. This study was aimed to characterize the biodiversity, structure and composition of gastric microbiota among twins. A total of four pairs of twins and eight unrelated individuals were enrolled in the study. Antral biopsies were obtained during endoscopy. The bacterial 16S rRNA gene was amplified and pyrosequenced. Sequences were analyzed for the composition, structure, and α and β diversities of gastric microbiota. Proteobacteria, Firmicutes, Bacteroidetes, Actinobacteria, and Fusobacteria were the most predominant phyla of gastric microbiota. Each individual, twins as well as unrelated individuals, harbored a microbiota of distinct composition. There was no evidence of additional similarity in the richness and evenness of gastric microbiota among co-twins as compared to unrelated individuals. Calculations of θ YC and PCoA demonstrated that the structure similarity of gastric microbial community between co-twins did not increase compared to unrelated individuals. In contrast, the structure of microbiota was altered enormously by Helicobacter pylori infection. These results suggest that host genetic backgrounds had little effect in shaping the gastric microbiota. This property of gastric microbiota could facilitate the studies discerning the role of microbiota from genetic grounds in the pathogenesis.
9. Yoruba customs and beliefs pertaining to twins.
Science.gov (United States)
Leroy, Fernand; Olaleye-Oruene, Taiwo; Koeppen-Schomerus, Gesina; Bryan, Elizabeth
2002-04-01
The Yoruba are an important ethnic group mainly occupying Southwestern Nigeria. Mainly for genetic reasons, this very large tribe happens to present the highest dizygotic twinning rate in the world (4.4 % of all maternities). The high perinatal mortality rate associated with such pregnancies has contributed to the integration of a special twin belief system within the African traditional religion of this tribe. The latter is based on the concept of a supreme deity called Olodumare or Olorun, assisted by a series of secondary gods (Orisha) while Yoruba religion also involves immortality and reincarnation of the soul based on the animistic cult of ancestors. Twins are therefore given special names and believed to detain special preternatural powers. In keeping with their refined artistic tradition, the Yoruba have produced numerous wooden statuettes called Ibejis that represent the souls of deceased newborn twins and are involved in elaborate rituals. Among Yoruba traditional beliefs and lore some twin-related themes are represented which are also found in other parts of the world. Basic features of the original Yoruba beliefs have found their way into the religious traditions of descendants of African slaves imported in the West Indies and in South America.
10. Separation surgery for total vertical craniopagus twins.
Science.gov (United States)
Goh, Keith Y C
2004-08-01
A pair of conjoined twins aged 11 months underwent investigations, followed by surgical separation in Singapore General Hospital in April 2001. They were joined at the skull vertex and facing in opposite directions. Radiological investigations including cerebral angiography, magnetic resonance imaging and computerized tomographic scans were performed, leading to the diagnosis of total vertical craniopagus. There were two separate brains, with separate arterial circulations, but with a common superior sagittal sinus. Tissue expanders were inserted in the subgaleal space for 6 months of scalp expansion prior to surgery. Pre-operative planning involved the use of virtual reality equipment and life-sized polymer models of the conjoined skulls and brains. Surgical separation of the twins was achieved after approximately 100 h of operating time, using intraoperative image guidance, microsurgical techniques and intraoperative neurophysiologic monitoring. Reconstruction of the dura, calvarium and scalp was performed with artificial dura, absorbable plates and split skin grafts. Postoperative complications included focal cortical infarction, meningitis, and hydrocephalus. Despite these complications, the twins recovered satisfactorily and were discharged to their home country within 6 months. The 3-month outcome was minor disability in one twin and severe developmental delays in the other. Separation surgery is possible for complex cranially-conjoined twins but requires detailed planning and extensive surgical management.
11. A Possible Twin: The 1960s Twin Study Revisited/Twin Research: Twin-to-Twin Heart Transplantation; Distinguishing Monozygotic Twins; Twin Conceptions via Oocyte Donation; Factors Affecting Craniofacial Traits/In the Media: Triplet Delivery in the UK; Conjoined Twins and the Concept of Self; Colombian Twin Trainers; Skin Grafting to Save an Identical Co-Twin; Lack of Physical Flaws in Dolly the Cloned Sheep; Possible Conjoined Twins of Opposite-Sex; Passing of the Remaining Twin From the World's Longest Separated Pair.
Science.gov (United States)
Segal, Nancy L
2018-04-01
This article begins with the story of a 51-year-old Los Angeles, California man, Justin Goldberg, whose daughter caught a glimpse of his striking look-alike at a popular market. Many people have so-called doppelgängers, but this occurrence is especially intriguing - the individual in question, born in New York City in the mid-1960s to an unwed mother, was an adoptee placed by the Louise Wise Adoption Agency. This agency, under the guidance of a prominent psychiatrist, decided to place twins in separate homes. Some of these twin children were part of a controversial child development study that was hidden from them and their parents. Next, recent and current twin research on heart transplantation, distinguishing monozygotic co-twins, twin conceptions via oocyte donation and factors affecting craniofacial traits are summarized. The article concludes with highlights on twins in the media, specifically, a triplet delivery in the United Kingdom, self-concept and consciousness in conjoined twins, Colombian twin trainers, skin grafting to save an identical co-twin, lack of physical flaws in Dolly the cloned sheep, possible opposite-sex conjoined twins, and the passing of the remaining twin from the world's longest separated pair.
12. Analysis of 45-years of Eclipse Timings of the Hyades (K2 V+ DA) Eclipsing Binary V471 Tauri
Science.gov (United States)
Marchioni, Lucas; Guinan, Edward; Engle, Scott
2018-01-01
V471 Tau is an important detached 0.521-day eclipsing binary composed of a K2 V and a hot DA white dwarf star. This system resides in the Hyades star cluster located approximately 153 Ly from us. V471 Tau is considered to be the end-product of common-envelope binary star evolution and is currently a pre-CV system. V471 Tau serves as a valuable astrophysical laboratory for studying stellar evolution, white dwarfs, stellar magnetic dynamos, and possible detection of low mass companions using the Light Travel Time (LTT) Effects. Since its discovery as an eclipsing binary in 1970, photometry has been carried out and many eclipse timings have been determined. We have performed an analysis of the available photometric data available on V471 Tauri. The binary system has been the subject of analyses regarding the orbital period. From this analysis several have postulated the existence of a third body in the form of a brown dwarf that is causing periodic variations in the system’s apparent period. In this study we combine ground based data with photometry secured recently from the Kepler K2 mission. After detrending and phasing the available data, we are able to compare the changing period of the eclipsing binary system against predictions on the existence of this third body. The results of the analysis will be presented. This research is sponsored by grants from NASA and NSF for which we are very grateful.
13. CHANDRA AND XMM-NEWTON X-RAY OBSERVATIONS OF THE HYPERACTIVE T TAURI STAR RY TAU
Energy Technology Data Exchange (ETDEWEB)
Skinner, Stephen L. [Center for Astrophysics and Space Astronomy (CASA), Univ. of Colorado, Boulder, CO 80309-0389 (United States); Audard, Marc [Dept. of Astronomy, University of Geneva, Ch. d’Ecogia 16, CH-1290 Versoix (Switzerland); Güdel, Manuel, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Dept. of Astrophysics, Univ. of Vienna, Türkenschanzstr. 17, A-1180 Vienna (Austria)
2016-07-20
We present results of pointed X-ray observations of the accreting jet-driving T Tauri star RY Tau using Chandra and XMM-Newton . We obtained high-resolution grating spectra and excellent-quality CCD spectra and light curves with the objective of identifying the physical mechanisms underlying RY Tau’s bright X-ray emission. Grating spectra reveal numerous emission lines spanning a broad range of temperature superimposed on a hot continuum. The X-ray emission measure distribution is dominated by very hot plasma at T {sub hot} ∼ 50 MK, but higher temperatures were present during flares. A weaker cool plasma component is also present as revealed by low-temperature lines such as O viii. X-ray light curves show complex variability consisting of short-duration (∼hours) superhot flares accompanied by fluorescent Fe emission at 6.4 keV superimposed on a slowly varying (∼one day) component that may be tied to stellar rotation. The hot flaring component is undoubtedly of magnetic (e.g., coronal) origin. Soft- and hard-band light curves undergo similar slow variability implying that at least some of the cool plasma shares a common magnetic origin with the hot plasma. Any contribution to the X-ray emission from cool shocked plasma is small compared to the dominant hot component but production of individual low-temperature lines such as O viii in an accretion shock is not ruled out.
14. Label-free quantitative analysis of the casein kinase 2-responsive phosphoproteome of the marine minimal model species Ostreococcus tauri.
Science.gov (United States)
Le Bihan, Thierry; Hindle, Matthew; Martin, Sarah F; Barrios-Llerena, Martin E; Krahmer, Johanna; Kis, Katalin; Millar, Andrew J; van Ooijen, Gerben
2015-12-01
Casein kinase 2 (CK2) is a protein kinase that phosphorylates a plethora of cellular target proteins involved in processes including DNA repair, cell cycle control, and circadian timekeeping. CK2 is functionally conserved across eukaryotes, although the substrate proteins identified in a range of complex tissues are often different. The marine alga Ostreococcus tauri is a unicellular eukaryotic model organism ideally suited to efficiently study generic roles of CK2 in the cellular circadian clock. Overexpression of CK2 leads to a slow circadian rhythm, verifying functional conservation of CK2 in timekeeping. The proteome was analysed in wild-type and CK2-overexpressing algae at dawn and dusk, revealing that differential abundance of the global proteome across the day is largely unaffected by overexpression. However, CK2 activity contributed more strongly to timekeeping at dusk than at dawn. The phosphoproteome of a CK2 overexpression line and cells treated with CK2 inhibitor was therefore analysed and compared to control cells at dusk. We report an extensive catalogue of 447 unique CK2-responsive differential phosphopeptide motifs to inform future studies into CK2 activity in the circadian clock of more complex tissues. All MS data have been deposited in the ProteomeXchange with identifier PXD000975 (http://proteomecentral.proteomexchange.org/dataset/PXD000975). © 2015 The Authors. PROTEOMICS Published by Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
15. Perfil de temperatura dos funis magnetosféricos de estrelas T Tauri com aquecimento alfvênico
Science.gov (United States)
Vasconcelos, M. J.
2003-08-01
Estrelas T Tauri Clássicas são objetos jovens circundados por discos de gás e poeira e que apresentam uma intensa atividade magnética. Seu espectro mostra linhas de emissão alargadas que são razoavelmente reproduzidas nos modelos de acresção magnetosférica. No entanto, o perfil de temperatura dos funis magnéticos é desconhecido. Aquecimento magnético compressional e difusão ambipolar foram considerados para estas estruturas, porém as temperaturas obtidas não são suficientes para explicar as observações. Neste trabalho, examinamos o aquecimento gerado pelo amortecimento de ondas Alfvén através de quatro mecanismos, os amortecimentos não-linear, turbulento, viscoso-resistivo e colisional como função da freqüência da onda. Inicialmente, a temperatura é ajustada para reproduzir as observações e o grau de turbulência requerido para que o mecanismo seja viável é calculado. Os resultados mostram que este é compatível com os dados observacionais. Apresentam-se, também, resultados preliminares do cálculo auto-consistente do perfil de temperatura dos funis, levando-se em conta fontes de aquecimento Alfvênica e fontes de resfriamento.
16. Role of local absorption on the X-ray emission from MHD accretion shocks in classical T Tauri stars
Directory of Open Access Journals (Sweden)
Bonito
2014-01-01
Full Text Available Accretion processes onto classical T Tauri stars (CTTSs are believed to generate shocks at the stellar surface due to the impact of supersonic downflowing plasma. Although current models of accretion streams provide a plausible global picture of this process, several aspects are still unclear. For example, the observed X-ray luminosity in accretion shocks is, in general, well below the predicted value. A possible explanation discussed in the literature is in terms of significant absorption of the emission due to the thick surrounding medium. Here we consider a 2D MHD model describing an accretion stream propagating through the atmosphere of a CTTS and impacting onto its chromosphere. The model includes all the relevant physics, namely the gravity, the thermal conduction, and the radiative cooling, and a realistic description of the unperturbed stellar atmosphere (from the chromosphere to the corona. From the model results, we synthesize the X-ray emission emerging from the hot slab produced by the accretion shock, exploring different configurations and strengths of the stellar magnetic field. The synthesis includes the local absorption by the thick surrounding medium and the Doppler shift of lines due to the component of plasma velocity along the line-of-sight. We explore the effects of absorption on the emerging X-ray spectrum, considering different inclinations of the accretion stream with respect to the observer. Finally we compare our results with the observations.
17. Water Formation and Destruction by 'Super' X-ray Flares from a T-Tauri Star in a Protoplanetary Disk
Science.gov (United States)
Waggoner, Abygail R.; Cleeves, L. Ilsedore
2018-01-01
We present models of H2O chemistry is protoplanetary disks in the presence of 'super' X-ray flares emitted by a T-Tauri star. We examine the time-evolving chemistry of H2O at radial locations from 1 to 20 AU at various vertical heights from the mid-plane to the surface of the disk. We find the gas-phase H2O abundance can be enhanced in the surface (Z/R ≥ 0.3) by more than a factor of approximately 3 - 5 by strong flares, i.e., those that increase the ionization rate by a factor of 100. Dissociative recombination of H3O+ , H2O adsorption onto grain, and photolysis of H2O are found to be the three dominant processes leading to a change in H2O abundance. We find X-ray flares have predominantly short- term (days) effects on gaseous H2O abundance, but some regions show a long-term (for the duration of the test about 15 days) decrease in gaseous H2O due to adsorption onto grains, which results in an increase (up to 200%) in ice H2O in regions where ice H2O is 10-8 abundance no are response in the ice is observed.Thanks to the National Science Foundation for funding this research as a part of the Smithsonian Astrophysical Observatory Research Experience for Undergraduates (SAO REU).
18. Low twinning rate and seasonal effects on twinning in a fertile population, the Hutterites
Science.gov (United States)
Nonaka, K.; Miura, T.; Peter, K.
1993-09-01
This paper analyzes from the mid 18th century to 1987 the birth records of the “Dariusleut,” one of the three subgroups of the Hutterite population. The aim of this study is to describe several aspects of the twinning rate in a fertile population. The overall rate of twinning was 0.90%:103 twins among all 11492 maternities. The rate peaked at the 7th birth order and at the maternal age of 40 years and over. Until the mid 19th century when the Hutterites lived in Russia, the twinning rate was higher (1.5%), and it decreased during the migration period in the second half of the 19th century (0.7%). After the group had settled in the USA and Canada, the population maintained a twinning rate of 1.0% until 1965. After 1965 the rate decreased to 0.7%, partly due to a decline in fertility among women aged 30 years and over. There was a significant seasonal variation: the twinning rate decreased to 0.5% in May July compared to 1.2% for the other three seasons during the years up to 1965 ( P<0.01), while more recent mothers did not show such a seasonal variation. The incidence of twin births in this population seems to have been influenced by environmental factors, which would change their effect seasonally and secularly.
19. Increased risk of abortion after genetic amniocentesis in twin pregnancies
DEFF Research Database (Denmark)
Palle, C; Andersen, J W; Tabor, A
1983-01-01
Forty-seven twin pregnancies among 3676 patients who had a genetic amniocentesis between 1973 and 1979, are reported. The detection rate of twins at the time of amniocentesis was 62 per cent. Five (17 per cent) of the 29 women with detected twin pregnancy aborted spontaneously, these are compared...... in at least one sac aborted, while 3 of 20 twin pregnancies with one puncture in each sac aborted (15 per cent). One of 18 (6 per cent) twin pregnancies, where only one sac was punctured, because the twin pregnancies were undetected, aborted. Amniocentesis of both sacs in twin pregnancies seems associated...... with an increased risk of spontaneous abortion. The indications for amniocentesis in twin pregnancies should be critically evaluated....
20. Aging and communication in the twin paradox
International Nuclear Information System (INIS)
De Wolf, David A
2016-01-01
The twin paradox of the special theory of relativity has given rize to a large body of literature discussing its implications. In its standard form, the traveler changes velocity only at the destination of the trip, so that he appears to perceive an improbably instantaneous and non-continuous change in age of the stationary twin. In this work, a smooth velocity/acceleration profile is used that allows the abrupt velocity-change case as a limit. All gravitational effects are ignored in this treatment. Aside from mutual perception of simultaneous clock times in an accelerating frame, constant communication of clock times between the twins by means of (digital) light signals is shown to be possible, in principle if not in practice. (paper)
1. On the theory of twinning plane superconductivity
International Nuclear Information System (INIS)
Mishonov, T.M.
1988-01-01
The thermodynamic potential of the superconducting layer in the twinning plane (TP) vicinity for the type I superconductors is found. The corrections to the surface tension in powers of the Ginsburg-Landau parameter κ are obtained. The corresponding states law for the supercooling field for the type I twinning plane superconductivity (TPS) is obtained, as well as the critical field law for the type II TPS. A review of experimental and theoretical works on TPS and some similar systems is given. The conditions for the Berezinski-Kosterlitz-Thouless transition for the proximity effect are discussed, as well as the possible mechanisms for the conducting phase transition TPS in Nb and the pinning forces close to the twinning plane. The obtained order parameter distribution can be used for description of the superlattices from normal and superconducting metals as well. 6 figs., 44 refs
Energy Technology Data Exchange (ETDEWEB)
O’Malley, P.D.; Bardayan, D.W.; Kolata, J.J.; Hall, M.R.; Hall, O.; Allen, J. [Physics Department, University of Notre Dame, Notre Dame, IN 46556 (United States); Becchetti, F.D. [Physics Department, U. Michigan, Ann Arbor MI 48109 (United States)
2016-06-01
TwinSol, a pair of coupled, superconducting solenoids, was one of the first devices capable of producing beams of radioactive nuclei at energies near the Coulomb barrier. A primary beam from University of Notre Dame (UND) tandem accelerator is used to bombard a primary target producing a secondary beam in flight. TwinSol is used to gather, separate, and focus the recoils. Since it was commissioned at the UND in 1997, at least 58 publications have reported data from its use and there have been hundreds of collaborators from many different countries that use this device. Currently, plans are in place at the UND to provide several upgrades to TwinSol, including a multi-cell gas production target and the possible addition of a third solenoid. Upgrades currently in progress will be discussed along with future plans.
3. Early prenatal diagnosis of ischiopagus conjoined twins
Directory of Open Access Journals (Sweden)
Ahmet Mete Ergenoğlu
2014-03-01
Full Text Available Introduction: Conjoined twins are very rare and the incidence of them vary about 1/50,000 and 1/100,000. They are named according to the joint parts. Embryos are conjoined at the level of ischium in ischiopagus. A case of ischiopagus will be presented in this article. Case: A twenty-seven year old women who is 9-10 weeks pregnant with a history of 1 abortus applied to the Ege University Department of Obstetrics and Gynecology for routine follow-up. Ultrasonography revealed a twin pregnancy but the embryos were attached at the pelvic region. 3D Doppler sonography confirmed the diagnosis of ischiopagus tetrapus. The patient's decision of termination of pregnancy is concluded at Perinatology Council of the clinic. Conclusion: Ischiopagus conjoined twins are very rare. Early prenatal diagnosis will prevent the maternal complications during the termination of the pregnancy.
4. Conjoined twins detected in the first trimester: A review
Directory of Open Access Journals (Sweden)
Chih-Ping Chen
2011-12-01
Full Text Available Conjoined twinning occurs in 1 in 100 sets of monozygotic twins, 1 in 50,000 gestations or 1 in 250,000 live births. With the advent of ultrasound technology, prenatal diagnosis of conjoined twins is possible. This article provides a comprehensive review of conjoined twins detected in the first trimester including fetal gender, maternal age, parity, types of fusion, related ultrasound abnormalities, perinatal outcome and association with assisted reproduction.
5. Dichorionic Diamniotic Twin Pregnancy Discordant for Bladder Exstrophy
Directory of Open Access Journals (Sweden)
William Tu
2009-01-01
Full Text Available A 38 year-old woman presented with a dichorionic diamniotic twin pregnancy at gestational age of 32 weeks concerning for an abdominal wall mass in one of the twins. Initial ultrasound evaluation was suspicious for an omphalocele, but the affected twin was found to have bladder exstrophy at birth. This illustrates the difficulties of accurate prenatal diagnosis of bladder exstrophy in a twin pregnancy at a late gestation.
6. A note on twin-singleton differences in asthma
DEFF Research Database (Denmark)
Thomsen, Simon Francis; Kyvik, Kirsten Ohm; Backer, Vibeke
2008-01-01
Twins constitute a valuable resource for genetic studies of asthma. However, critics argue that twins are 'special' in terms of prenatal environment and upbringing and therefore nonrepresentative. In respect to asthma a small range of studies report differential morbidity in twins compared...... with singletons. We review some of the possible explanations for these findings and conclude that results from twin studies of asthma can be extrapolated to the general population....
7. Testicular cancer in twins: a meta-analysis.
Science.gov (United States)
Neale, R E; Carrière, P; Murphy, M F G; Baade, P D
2008-01-15
In a meta-analysis of testicular cancer in twins, twins had a 30% increased risk (estimate 1.31, 95% CI 1.1-1.6), providing indirect support for the hypothesis that in utero hormone variations influence risk of testicular cancer. The summary-estimate for dizygotic twins was 1.3 (1.0-1.7) and for monozygotic or same sex twins 1.4 (1.2-1.8).
8. Needle twins and right-angled twins in minerals: comparison between experiment and theory
Science.gov (United States)
Salje, E.K.H.; Buckley, A.; Van Tendeloo, G.; Ishibashi, Y.; Nord, G.L.
1998-01-01
Transformation twinning in minerals forms isolated twin walls, intesecting walls with corner junctions, and wedge-shaped twins as elements of hierarchical patterns. When cut perpendicular to the twin walls, the twins have characteristic shapes, right-angled and needle-shaped wall traces, which can be observed by transmission electron microscopy or by optical microscopy. Theoretical geometries of wall shapes recently derived for strain-related systems should hold for most displacive and order-disorder type phase transitions: 1) right-angled twins show curved junctions; 2) needle-shaped twins contain flat wall segments near the needle tip if the elastic behaviour of the mineral is dominated by its anisotroyp; 3) additional bending forces and pinning effects lead to curved walls near the junction that make the needle tip appear more blunt. Bent right-angled twins were analyzed in Gd2(MoO4)3. Linear needle tips were found in WO3, [N(CH3)4]2.ZnBr4 CrAl, BiVO4, GdBa2Cu3O7, and PbZrO. Parabolic tips occur in K2Ba(NO2)4, and GeTe whereas exponential curvatures appear in BaTiO3, KSCN, Pb3(PO4)2, CaTiO3, alkali feldspars, YBa2Cu3O7, and MnAl. The size and shape of the twin microstructure relates to its formation during the phase transition and the subsequent annealing history. The mobility of the twin walls after formation depends not only on the thermal activation but also on the structure of the wall, which may be pinned to impurities on a favorable structural site. Depinnign energies are often large compared with thermal energies for diffusion. This leads to kinetic time scales for twin coarsening that are comparable to geological time scales. Therefore, transformation twins that exhibit needle domains not only indicate that the mineral underwent a structural phase transition but also contain information about its subsequent geological history.
9. Cord entanglement in monoamniotic twin pregnancies
DEFF Research Database (Denmark)
Lyndrup, J; Schouenborg, Lars Øland
1987-01-01
Monoamniotic twin pregnancy involves a heavy risk of fatal umbilical cord entanglement. Two cases are reported. In the first case, both twins were found dead in the 36th week, and the monoamnionicity was recognized at birth. In the second case, the monoamnionicity was discovered during an ultraso...... an ultrasound examination, and cord entanglement was suspected in the 35th week on the basis of a non-stress test (NST) with variable decelerations. Cesarean section was performed and two healthy children were delivered....
10. Conjoined twins: scientific cinema and Pavlovian physiology.
Science.gov (United States)
Krementsov, Nikolai
2015-01-01
Through the lens of a 1957 documentary film, "Neural and humoral factors in the regulation of bodily functions (research on conjoined twins)," produced by the USSR Academy of Medical Sciences, this essay traces the entwined histories of Soviet physiology, studies of conjoined twins and scientific cinema. It examines the role of Ivan Pavlov and his students, including Leonid Voskresenkii, Dmitrii Fursikov and Petr Anokhin, in the development of "scientific film" as a particular cinematographic genre in Soviet Russia and explores numerous puzzles hidden behind the film's striking visuals. Crown Copyright © 2015. Published by Elsevier Ltd. All rights reserved.
11. Conjoined twins: implications for blastogenesis.
Science.gov (United States)
Machin, G A
1993-01-01
fail to develop (interaction aplasia) because of conflicting migrational pathways or abnormal concentrations of morphogens in and around the neoaxes. 8. Where the cardiovascular system is discordantly expressed in dicephalus and thoracopagus twins, the right heart is more severely malformed, depending on the degree of interaction of the two embryonic septa transversa. 9. The septum transversum provides mesenchymal components to the heawrt and liver; the epithelial components (derived fro the foregut[s]) may vary in number from the number of mesenchymal septa transversa contributing to the liver of the CT embryo.(ABSTRACT TRUNCATED AT 400 WORDS)
12. Near-ultraviolet Excess in Slowly Accreting T Tauri Stars: Limits Imposed by Chromospheric Emission
Science.gov (United States)
Ingleby, Laura; Calvet, Nuria; Bergin, Edwin; Herczeg, Gregory; Brown, Alexander; Alexander, Richard; Edwards, Suzan; Espaillat, Catherine; France, Kevin; Gregory, Scott G.; Hillenbrand, Lynne; Roueff, Evelyne; Valenti, Jeff; Walter, Frederick; Johns-Krull, Christopher; Brown, Joanna; Linsky, Jeffrey; McClure, Melissa; Ardila, David; Abgrall, Hervé; Bethell, Thomas; Hussain, Gaitee; Yang, Hao
2011-12-01
Young stars surrounded by disks with very low mass accretion rates are likely in the final stages of inner disk evolution and therefore particularly interesting to study. We present ultraviolet (UV) observations of the ~5-9 Myr old stars RECX-1 and RECX-11, obtained with the Cosmic Origins Spectrograph and Space Telescope Imaging Spectrograph on the Hubble Space Telescope, as well as optical and near-infrared spectroscopic observations. The two stars have similar levels of near-UV emission, although spectroscopic evidence indicates that RECX-11 is accreting and RECX-1 is not. The line profiles of Hα and He I λ10830 in RECX-11 show both broad and narrow redshifted absorption components that vary with time, revealing the complexity of the accretion flows. We show that accretion indicators commonly used to measure mass accretion rates, e.g., U-band excess luminosity or the Ca II triplet line luminosity, are unreliable for low accretors, at least in the middle K spectral range. Using RECX-1 as a template for the intrinsic level of photospheric and chromospheric emission, we determine an upper limit of 3 × 10-10 M ⊙ yr-1 for RECX-11. At this low accretion rate, recent photoevaporation models predict that an inner hole should have developed in the disk. However, the spectral energy distribution of RECX-11 shows fluxes comparable to the median of Taurus in the near-infrared, indicating that substantial dust remains. Fluorescent H2 emission lines formed in the innermost disk are observed in RECX-11, showing that gas is present in the inner disk, along with the dust. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile.
13. Deformation twinning in zinc-aluminium single crystals after slip
International Nuclear Information System (INIS)
Lukac, P.; Kral, F.; Trojanova, Z.; Kral, R.
1993-01-01
Deformation twinning in Zn-Al single crystals deformed by slip in the basal system is examined. The influence of temperature and the content of aluminium in zinc on the twinning stress is investigated in the temperature range from 198 to 373 K. It is shown that the twinning stress rises with increasing temperature and increases with the concentration of Al atoms. (orig.)
14. Heritability of psoriasis in a large twin sample
DEFF Research Database (Denmark)
Lønnberg, Ann Sophie; Skov, Liselotte; Skytthe, A
2013-01-01
AIM: To study the concordance of psoriasis in a population-based twin sample. METHODS: Data on psoriasis in 10,725 twin pairs, 20-71 years of age, from the Danish Twin Registry was collected via a questionnaire survey. The concordance and heritability of psoriasis were estimated. RESULTS: In total...
15. Perinatal Mortality Among Twins In Lagos University Teaching ...
African Journals Online (AJOL)
Background: Perinatal mortality rate is reported to be higher in twins than in singletons. More than two decades ago, Abudu and Agarin reported a twinning rate of 21.1/1000 maternities and perinatal mortality rate of 142.6/1000 among twins in Lagos. Objective: To determine the current perinatal mortality rate and risk factors ...
16. New theory for crack-tip twinning in fcc metals
Science.gov (United States)
Andric, Predrag; Curtin, W. A.
2018-04-01
Dislocation emission from a crack tip is a necessary mechanism for crack tip blunting and toughening. In fcc metals under Mode I loading, a first partial dislocation is emitted, followed either by a trailing partial dislocation ("ductile" behaviour) or a twinning partial dislocation ("quasi-brittle"). The twinning tendency is usually estimated using the Tadmor and Hai extension of the Rice theory. Extensive molecular statics simulations reveal that the predictions of the critical stress intensity factor for crack tip twinning are always systematically lower (20-35%) than observed. Analyses of the energy change during nucleation reveal that twin partial emission is not accompanied by creation of a surface step while emission of the trailing partial creates a step. The absence of the step during twinning motivates a modified model for twinning nucleation that accounts for the fact that nucleation does not occur directly at the crack tip. Predictions of the modified theory are in excellent agreement with all simulations that show twinning. Emission of the trailing partial dislocation, including the step creation, is predicted using a model recently introduced to accurately predict the first partial emission and shows why twinning is preferred. A second mode of twinning is found wherein the crack first advances by cleavage and then emits the twinning partial at the new crack tip; this mode dominates for emission beyond the first twinning partial. These new theories resolve all the discrepancies between the Tadmor twinning analysis and simulations, and have various implications for fracture behaviour and transitions.
17. Emergency separation of a xipho-omphalopagus twin in a ...
African Journals Online (AJOL)
Emergency separation of a xipho-omphalopagus twin in a developing country. RM Shukla, B Mukhopadhyay, KC Mandal, K Saha, D Roy, PP Mukherjee. Abstract. Female conjoined twins (thoraco-omphalopagus) were delivered by emergency caesarean section in a private nursing home. On examination, one of the twins ...
18. Obstetric outcome of twin pregnancies in Jos, Nigeria | Mutihir ...
African Journals Online (AJOL)
Obstetric outcome of twin pregnancies in Jos, Nigeria. JT Mutihir, VC Pam. Abstract. Objectives: The objectives of the study were to determine the incidence, maternal and foetal outcome of twin delivery in Jos, Nigeria. Methodology: All consecutive twin deliveries between August 2003 and November 2004 were studied.
19. Pelvic ventral hernia repair in a pygopagus conjoint twin | Bhullar ...
African Journals Online (AJOL)
Pelvic ventral hernia repair in a surviving conjoint twin with multiple congenital anomalies that make surgery a challenge. Conjoint twins are a rare. The incidence is reported to be in the range of 1/50 000 to 1/100 000 live births. Of the conjoint twins, 40% are stillborn and an additional one-third die within 24 h of birth.
20. Influences on achieving motor milestones: A twin-singleton study
NARCIS (Netherlands)
Brouwer, S.I.; van Beijsterveldt, C.E.M.; Bartels, M.; Hudziak, J.; Boomsma, D.I.
2006-01-01
In order to determine if twinning impacted achievement of motor milestones the attainment of early motor milestones in twins was examined and compared to published data from singletons of the same age from the same culture and birth years. We examined the influence of twinning, sex, zygosity and
1. Twin Specific Risk Factors in Primary School Achievements
NARCIS (Netherlands)
de Zeeuw, L.E.J.; van Beijsterveldt, C.E.M.; de Geus, E.J.C.; Boomsma, D.I.
2012-01-01
The main aim of this study was to examine twin specific risk factors that influence educational achievement in primary school. We included prenatal factors that are not unique to twins, except for zygosity, but show a higher prevalence in twins than in singletons. In addition, educational
2. Twin-Core Fiber-Based Mach Zehnder Interferometer for Simultaneous Measurement of Strain and Temperature
Science.gov (United States)
Kowal, Dominik; Urbanczyk, Waclaw; Mergo, Pawel
2018-01-01
In this paper we present an all-fiber interferometric sensor for the simultaneous measurement of strain and temperature. It is composed of a specially fabricated twin-core fiber spliced between two pieces of a single-mode fiber. Due to the refractive index difference between the two cores in a twin-core fiber, a differential interference pattern is produced at the sensor output. The phase response of the interferometer to strain and temperature is measured in the 850–1250 nm spectral range, showing zero sensitivity to strain at 1000 nm. Due to the significant difference in sensitivities to both parameters, our interferometer is suitable for two-parameter sensing. The simultaneous response of the interferometer to strain and temperature was studied using the two-wavelength interrogation method and a novel approach based on the spectral fitting of the differential phase response. As the latter technique uses all the gathered spectral information, it is more reliable and yields the results with better accuracy. PMID:29558386
3. Spectral gamuts and spectral gamut mapping
Science.gov (United States)
Rosen, Mitchell R.; Derhak, Maxim W.
2006-01-01
All imaging devices have two gamuts: the stimulus gamut and the response gamut. The response gamut of a print engine is typically described in CIE colorimetry units, a system derived to quantify human color response. More fundamental than colorimetric gamuts are spectral gamuts, based on radiance, reflectance or transmittance units. Spectral gamuts depend on the physics of light or on how materials interact with light and do not involve the human's photoreceptor integration or brain processing. Methods for visualizing a spectral gamut raise challenges as do considerations of how to utilize such a data-set for producing superior color reproductions. Recent work has described a transformation of spectra reduced to 6-dimensions called LabPQR. LabPQR was designed as a hybrid space with three explicit colorimetric axes and three additional spectral reconstruction axes. In this paper spectral gamuts are discussed making use of LabPQR. Also, spectral gamut mapping is considered in light of the colorimetric-spectral duality of the LabPQR space.
4. Infant mortality in twin pregnancies following in-utero demise of the co-twin
Directory of Open Access Journals (Sweden)
Boubakari Ibrahimou
2015-09-01
Conclusions: Risks for all mortality types were lower among converted co-twins than their unconverted or same-quantile counterparts. The lower neonatal and higher post-neonatal mortality among black require future research.
5. Nature versus nurture: identical twins and bariatric surgery.
Science.gov (United States)
Hagedorn, Judith C; Morton, John M
2007-06-01
Genetics and environment both play a role in weight maintenance. Twin studies may help clarify the influence of nature vs nurture in weight loss. We present the largest U.S. experience with monozygotic (MZ) twins undergoing bariatric surgery. We retrospectively reviewed the charts of four sets of MZ twins who underwent Roux-en-Y gastric bypass (RYGBP) surgery and laparoscopic adjustable gastric band (LAGB) placement at three different institutions. BMI and co-morbidities were examined pre- and postoperatively, and laboratory values were recorded. All four sets of twins are female, live together, and have similar professions. Twin cohort 1 had near identical weight loss patterns after open RYGBP surgery in 1996 (preop 146/142 kg; 2 years 82/82; and 10 years 108/107). Twin cohort 1 also both underwent cholecystectomies within the first year postoperatively. Twin cohort 2 underwent laparoscopic RYGBP surgery and also required cholecystectomies in the first postoperative year. Cohort 2 also experienced nearly identical weight loss at 1 year (36.7% vs 37.0% BMI loss). Twin cohort 3 underwent LAGB placement with two different surgeons with differing amounts of weight loss at 6 months (6.5% vs 15.7% BMI loss). Finally, twin cohort 4 underwent laparoscopic RYGBP with 2-year BMI loss of 39% vs 34%. In twin cohort 4, the twin who lost less weight lived apart from her twin and extended family, and her weight loss was less than the twin living with her family. Two sets of MZ twins had identical responses to bariatric surgery. The other two sets of identical twins had differential weight loss results, possibly due to differences in surgical approach and social support. While genetics do exert a strong influence on weight loss and maintenance, this case series demonstrates the potential effect of social support and postoperative management upon postoperative weight loss in the presence of identical genetics.
6. Characterization of the matrix-twin interface of a (1 0 -1 2) twin during growth
Czech Academy of Sciences Publication Activity Database
Ostapovets, Andriy; Serra, A.
2014-01-01
Roč. 94, č. 25 (2014), s. 2827-2839 ISSN 1478-6443 R&D Projects: GA MŠk(CZ) EE2.3.30.0063 Grant - others:Catalan Government(ES) AGAUR2014SGR 1644; Spanish Secretariat of Research, Development and Innovation(ES) FIS2012-39433-C02-02 Institutional support: RVO:68081723 Keywords : twinning * twin boundaries * disconnections Subject RIV: BM - Solid Matter Physics ; Magnetism; BM - Solid Matter Physics ; Magnetism (FZU-D)
7. A phenomenological study on twin screw extruders
NARCIS (Netherlands)
Janssen, L.P.B.M.
1976-01-01
Although more and more twin screw extruders are being used in the polymer industry, the theoretical background is relatively undeveloped. The literature abounds in contradictions and often informs the reader that all extrusion problems can be solved if a certain new design is considered. The
8. Craniofacial duplication (diprosopus) in a twin.
Science.gov (United States)
Changaris, D G; McGavran, M H
1976-07-01
A fused, double-faced (diprosopus), anencephalic monster was born prematurely as one of twins after 30 weeks of gestation. We will describe the autopsy findings and summarize the literature concerning the diprosopus defect. Factors other than fetal environment may contribute to its pathogenesis.
9. Determinants of monozygotic twinning in ART
DEFF Research Database (Denmark)
Hviid, Kathrine Vauvert R; Malchau, Sara Sofia; Pinborg, Anja
2018-01-01
BACKGROUND: The incidence of monozygotic twins (MZT) after ART appears to be higher than the incidence after spontaneous conceptions contradicting the aim of ART to avoid multiple pregnancies because of the associated risks. OBJECTIVE AND RATIONALE: The aim was to study the frequency of MZT after...
10. Identical Twin Primigravid Sisters -Spontaneous Labour and ...
African Journals Online (AJOL)
We report 2 cases of identical twin sisters, the older sibling getting married 14 months earlier but both got pregnant for their first child at about the same time and were managed by the same Obstetrician and fell into spontaneous labour within a few hours of each other. Both were delivered by emergency caesarean section ...
11. Prenatal Sonographic Diagnosis of Acardiac Twins
Energy Technology Data Exchange (ETDEWEB)
Kim, Jeong Ah; Song, Mi Jin [Cheil General Hospital, Sungkyunkwan University School of Medicine, Seoul (Korea, Republic of)
2006-09-15
This study was performed to present the prenatal sonographic findings and the associated abnormalities of acardiac twins. Seven cases of acardiac twins were reviewed retrospectively. Prenatal ultrasonography was performed in all patients at a gestational age between 12 and 27 weeks (mean 17.6 weeks). Autopsy was performed in four cases. The sonographic and autopsy findings were reviewed to report the associated abnormalities of the acardiac and donor fetuses. The diagnosis of acardiac twins was made on the basis of ultrasonography (n=6) or autopsy (n=1). The associated abnormalities of the acardiac fetuses were single umbilical artery (SUA) (n=5), abdominal wall defect (n=4), club feet (n=4), scoliosis (n=1), cleft lip and palate (n=1), digital anomaly (n=1), and umbilical cord cyst (n=1). In four of the donor fetuses, sonographic abnormalities were found. Autopsy was performed in three of the four cases to reveal hydropic change (n=2), diaphragmatic hernia (n=1) and multiple structural abnormalities of interventricular septal defect, polydactyly, club feet and SUA (n=1). Intrauterine fetal death occurred in five donors and follow-up was lost in the remaining two. Meticulous sonography enables the diagnosis of acardiac twins at an early gestational age and can reveal the associated abnormalities of the donor fetus as well as the acardiac fetus
12. INTEGRATED TWIN TOWERS DAN ISLAMISASI ILMU
Directory of Open Access Journals (Sweden)
Syaifuddin Syaifuddin
2013-05-01
Full Text Available This paper shows some idea as follows: First, integrated design of the Twin Towers as the changing action from IAIN to UIN Sunan Ampel. The religion and general knowledge’s position of Twin Towers’ integrated design is not mixed into one, but it works individually, and at the certain time are united in mutual dialogue. Second, Islamize design is done in order to criticize the general knowledge which has western sources and are secular, materialistic, and individualistic. In the process to Islamize the knowledge, Islamic knowledge tries to intervene the general knowledge in order to filter it so the knowledge will be Islamized. Consequently, to Islamize knowledge is to give an Islamic concept into general knowledge. Third, there are the similarities and differences between integrated design knowledge based on Islamic knowledge and integrated Twin Towers. The difference is in its epistemology process. The similarity is in the curriculum (ontology and objective (axiology. In the curriculum, the examined knowledge is religion and general knowledge. While the objective, Islamize knowledge and integrated Twin Towers aims to integrate religion and general knowledge, to dialogue, to communicate, and to synergy, so it can be a knowledge which is intact-integral-integrative.
13. Prenatal Sonographic Diagnosis of Acardiac Twins
International Nuclear Information System (INIS)
Kim, Jeong Ah; Song, Mi Jin
2006-01-01
This study was performed to present the prenatal sonographic findings and the associated abnormalities of acardiac twins. Seven cases of acardiac twins were reviewed retrospectively. Prenatal ultrasonography was performed in all patients at a gestational age between 12 and 27 weeks (mean 17.6 weeks). Autopsy was performed in four cases. The sonographic and autopsy findings were reviewed to report the associated abnormalities of the acardiac and donor fetuses. The diagnosis of acardiac twins was made on the basis of ultrasonography (n=6) or autopsy (n=1). The associated abnormalities of the acardiac fetuses were single umbilical artery (SUA) (n=5), abdominal wall defect (n=4), club feet (n=4), scoliosis (n=1), cleft lip and palate (n=1), digital anomaly (n=1), and umbilical cord cyst (n=1). In four of the donor fetuses, sonographic abnormalities were found. Autopsy was performed in three of the four cases to reveal hydropic change (n=2), diaphragmatic hernia (n=1) and multiple structural abnormalities of interventricular septal defect, polydactyly, club feet and SUA (n=1). Intrauterine fetal death occurred in five donors and follow-up was lost in the remaining two. Meticulous sonography enables the diagnosis of acardiac twins at an early gestational age and can reveal the associated abnormalities of the donor fetus as well as the acardiac fetus
14. Gene-Environment Interplay in Twin Models
Science.gov (United States)
Hatemi, Peter K.
2013-01-01
In this article, we respond to Shultziner’s critique that argues that identical twins are more alike not because of genetic similarity, but because they select into more similar environments and respond to stimuli in comparable ways, and that these effects bias twin model estimates to such an extent that they are invalid. The essay further argues that the theory and methods that undergird twin models, as well as the empirical studies which rely upon them, are unaware of these potential biases. We correct this and other misunderstandings in the essay and find that gene-environment (GE) interplay is a well-articulated concept in behavior genetics and political science, operationalized as gene-environment correlation and gene-environment interaction. Both are incorporated into interpretations of the classical twin design (CTD) and estimated in numerous empirical studies through extensions of the CTD. We then conduct simulations to quantify the influence of GE interplay on estimates from the CTD. Due to the criticism’s mischaracterization of the CTD and GE interplay, combined with the absence of any empirical evidence to counter what is presented in the extant literature and this article, we conclude that the critique does not enhance our understanding of the processes that drive political traits, genetic or otherwise. PMID:24808718
15. Monozygotic twins of different apparent sex
Energy Technology Data Exchange (ETDEWEB)
Yokota, Yukifumi; Fujino, Nobuyuki; Sato, Yoshiaki; Matsunobu, Akira; Tadokoro, Mamoru [Sagamihara Kyodo Hospital (Japan); Akane, Atsushi [Kansai Medical College, Osaka (Japan); Matsuura, Nobuo; Maeda, Tohru [Kitasato Univ. (Japan); Nakahori, Yutaka; Nakagome, Yasuo [Univ. of Tokyo (Japan)
1994-10-15
We report on twins of unlike sex who shared a 45,X/46,X, +mar karyotype. The mar chromosome was found to be Yq- by DNA analysis. Marker studies, including 8 VNTR loci, yielded a probability of monozygosity of 0.99999996. 16 refs., 1 fig., 1 tab.
16. Management of Conjoined Twins During Neonatal Period
African Journals Online (AJOL)
HussamHassan
Background/Purpose: Conjoined twins are rare and complex anomalies of the newborn. ... The short term postoperative follow up revealed uneventful course of 6 children resulting from ... sex and karyotype 3. ... revealed vertebral bodies, brain tissue occupying the ... continued for 8 hours during which the right and left.
17. A Proper Perspective on the Twin Deficits
Science.gov (United States)
1989-05-01
deficit twins, the relation between them, and their consanguine parentage. The trade deficit or, to be more accurate, the current account deficit, is...In general, there is a small negative, but statistically significant, relationship between the size of the federal deficit in one year and the
18. Twinning anisotropy of tantalum during nanoindentation
Energy Technology Data Exchange (ETDEWEB)
Goel, Saurav, E-mail: [email protected] [School of Mechanical and Aerospace Engineering, Queen' s University, Belfast, BT9 5AH (United Kingdom); Beake, Ben [Micro Materials Limited, Willow House, Yale Business Village, Ellice Way, Wrexham LL13 7YL (United Kingdom); Dalton Research Institute, Manchester Metropolitan University, Manchester, M15GD (United Kingdom); Chan, Chi-Wai [School of Mechanical and Aerospace Engineering, Queen' s University, Belfast, BT9 5AH (United Kingdom); Haque Faisal, Nadimul [School of Engineering, Robert Gordon University, Garthdee Road, Aberdeen AB10 7GJ (United Kingdom); Dunne, Nicholas [School of Mechanical and Aerospace Engineering, Queen' s University, Belfast, BT9 5AH (United Kingdom)
2015-03-11
Unlike other BCC metals, the plastic deformation of nanocrystalline Tantalum (Ta) during compression is regulated by deformation twinning. Whether or not this twinning exhibits anisotropy was investigated through simulation of displacement-controlled nanoindentation test using molecular dynamics (MD) simulation. MD data was found to correlate well with the experimental data in terms of surface topography and hardness measurements. The mechanism of the transport of material was identified due to the formation and motion of prismatic dislocations loops (edge dislocations) belonging to the 1/2〈111〉 type and 〈100〉 type Burgers vector family. Further analysis of crystal defects using a fully automated dislocation extraction algorithm (DXA) illuminated formation and migration of twin boundaries on the (110) and (111) orientation but not on the (010) orientation and most importantly after retraction all the dislocations disappeared on the (110) orientation suggesting twinning to dominate dislocation nucleation in driving plasticity in tantalum. A significant finding was that the maximum shear stress (critical Tresca stress) in the deformation zone exceeded the theoretical shear strength of Ta (Shear modulus/2π~10.03 GPa) on the (010) orientation but was lower than it on the (110) and the (111) orientations. In light of this, the conventional lore of assuming the maximum shear stress being 0.465 times the mean contact pressure was found to break down at atomic scale.
19. Uses of the Twins UK genetic database.
Science.gov (United States)
Spector, Tim D
2007-11-01
Tim Spector is a Professor of Genetic Epidemiology at King's College London and Director of the Twin Research and Genetic Epidemiology Unit at St Thomas' Hospital, London. Professor Spector graduated from St Bartholomew's Hospital Medical School, London, in 1982. After working in General Medicine, he completed a MSc in Epidemiology, and his MD degree at the University of London in 1989. He founded the UK Twins Registry of 10,000 twins in 1993, which is one of the largest collections of genotype and phenotype information on twins worldwide, whose breadth of research has expanded to cover a wide range of common complex traits many of which were previously thought to be mainly due to aging and the environment. He has published over 350 research articles on common diseases. He has written several original articles on the genetics of a wide range of diseases and traits including back pain, acne, inflammation, obesity, memory, musical ability and sexuality. He is the principal investigator of the EU Euroclot and Treat OA study, and a partner in five others. He has written several books, focusing on osteoporosis and genetics and, in 2003, he published a popular book on genetics: Your Genes Unzipped.
20. Analysis of metabolomics data from twin families
NARCIS (Netherlands)
Draisma, Hermanus Henricus Maria
2011-01-01
Metabolomics is the comprehensive analysis of small molecules involved in metabolism, on the basis of samples that have been obtained from organisms in a given physiological state. Data obtained from measurements of trait levels in twin families can be used to elucidate the importance of genetic and
1. Prenatal diagnosis of chorionicity in twins.
LENUS (Irish Health Repository)
Hassan, T
2012-02-01
The aim of this audit was to assess the accuracy of transabdominal ultrasound scan in predicting chorionicity in twin pregnancies in our unit. The presence or absence of lambda sign, T-sign, dividing membrane thickness and number of placentae were used to determine chorionicity. We retrospectively analysed these antenatal markers in 268 sets of twins delivered over a 5 year period and compared it with the postpartum placental histology and neonatal gender. Of 268 twin deliveries, 204 (76%) had both chorionicity and placental histology to compare. 67 of 84 (80%) were correctly diagnosed antenatally as monochorionic and 137 of 151 (91%) as dichorionic. In 31 cases (15%) the ultrasound diagnosis of chorionicity didn\\'t match placental histology. Seventeen were thought to be monochorionic antenatally but were confirmed dichorionic on placental histology. Overall chorionicity was correctly diagnosed in 171\\/204 (84%) using transabdominal ultrasound scan (USS) in all trimesters. However the sensitivity and specificity of USS was much higher for dichorionic twins when carried out before 14 weeks of gestation.
2. Digital Twin concept for smart injection molding
Science.gov (United States)
Liau, Y.; Lee, H.; Ryu, K.
2018-03-01
Injection molding industry has evolved over decades and became the most common method to manufacture plastic parts. Monitoring and improvement in the injection molding industry are usually performed separately in each stage, i.e. mold design, mold making and injection molding process. However, in order to make a breakthrough and survive in the industrial revolution, all the stages in injection molding need to be linked and communicated with each other. Any changes in one stage will cause a certain effect in other stage because there is a correlation between each other. Hence, the simulation should not only based on the input of historical data, but it also needs to include the current condition of equipment and prediction of future events in other stages to make the responsive decision. This can be achieved by implementing the concept of Digital Twin that models the entire process as a virtual model and enables bidirectional control with the physical process. This paper presented types of data and technology required to build the Digital Twin for the injection molding industry. The concept includes Digital Twin of each stage and integration of these Digital Twin model as a thoroughgoing model of the injection molding industry.
3. Association between the birth of twins and parental divorce.
Science.gov (United States)
Jena, Anupam B; Goldman, Dana P; Joyce, Geoffrey
2011-04-01
Mothers of multiple births face higher rates of postpartum depression, yet evidence on the marital consequences of multiple births is limited. We examined the association between twin births and parental divorce. We used the 1980 U.S. Census to identify a large sample of mothers with and without twin births. The goal was to estimate multivariate logistic models of the association between birth of twins and divorce adjusting for race, age at marriage and first birth, and college education. We examined whether the association was affected by maternal education, age and sex composition of twins, and family size. Twins at first birth were associated with greater parental divorce compared with singletons (odds ratio, 1.08; 95% confidence interval, 1.01-1.16; absolute risk 13.7% with twins compared with 12.7%; P=.02). The association was statistically greater among mothers not attending college (14.9% with twins compared with 13.3%; P=.01) compared with those with some college (10.4% with twins compared with 10.5%; P=.34); those with children older than 8 years (15.6% with twins compared with 13.5%; P<.01) compared with younger children (10.6% with twins compared with 10.8%; P=.42); and those with at least one twin girl (13.8% with twins compared with 12.6%; P=.03) compared with twin boys (12.1% with twins compared with 12.5%, P=.38). Mothers with four or more children had a larger association between birth of twins and divorce (15.4% for mothers with twins at fourth birth compared with 11.3% for all other mothers with four or more children; P<.01) compared with mothers with twins at first birth (13.7% for twins at first birth compared with 12.7%; P=.02). Health consequences of twin births for children and mothers are well known. Twin births may be associated with longer-term parental divorce. Specific groups, namely mothers not completing college and mothers who already have more children, may be at higher risk. II.
4. The morphology of the sella turcica in monozygotic twins
DEFF Research Database (Denmark)
Brock-Jacobsen, Mette T; Pallisgaard, Carsten; Kjaer, Inger
2009-01-01
of 42 twin pairs (18 male and 24 female pairs, aged 18-23 years) comprised the material. Sella turcica measurements from non-twins aged 6-21 years were used as normal reference. Length, depth and diameter of the sella turcica were measured and controlled by re-measurements. Pearson's correlation...... showed that the size of the sella turcica may be partly similar and partly dissimilar within the pair of monozygotic twins. Statistical evaluation of the data showed correlations between length, depth and diameter of the sella turcica between the two twin individuals in the same twin pair. Differences...
5. Mid-infrared coincidence measurements on twin photons at room temperature
DEFF Research Database (Denmark)
Mancinelli, M.; Trenti, A.; Piccione, S.
2017-01-01
Quantum measurements using single-photon detectors are opening interesting new perspectives in diverse fields such as remote sensing, quantum cryptography and quantum computing. A particularly demanding class of applications relies on the simultaneous detection of correlated single photons...... pave the way to quantum measurements in the MIR by the demonstration of a room temperature coincidence measurement with non-degenerate twin photons at about 3.1 mu m. The experiment is based on the spectral translation of MIR radiation into the visible region, by means of efficient up-converter modules...
6. Conjoined twin piglets with duplicated cranial and caudal axes.
Science.gov (United States)
McManus, C A; Partlow, G D; Fisher, K R
1994-06-01
Twins with doubling of the cranial and caudal poles, yet having a single thorax, are rare. One set of diprosopus, dipygus porcine conjoined twins was studied. In addition to the conjoining anomaly, these twins also exhibited ambiguous internal reproductive features. The twins had two snouts, three eyes, a single thorax, and were duplicated from the umbilicus caudally. Radiography indicated a single vertebral column in the cervical region. The vertebral columns were separate caudally from this point. There was a total of six limbs--one pair of forelimbs and two pairs of hindlimbs. Many medial structures failed to develop in these twins. Medial cranial nerves V-XII were absent or displaced although apparently normal laterally. The medial palates were present but shortened, whereas the medial mandibular rami had folded back on themselves rostrally to form a midline mass between the two chins. Each twin had only one lateral kidney and one lateral testis. Medial scrotal sacs were present but devoid of a testis. There was a midline, "uterine"-like structure which crossed between the twins. However, histological analysis of this structure revealed it to be dysplastic testicular tissue. The relationship between the abnormal reproductive features in these twins and the conjoining is unclear. The anatomy of these twins, in addition to the literature reviewed, illustrates the internal anatomical heterogeneity of grossly similar conjoined twins. A review of the literature also suggests that conjoined twinning may be more common in swine than was previously suspected.
7. Time trends in the natural dizygotic twinning rate.
Science.gov (United States)
Derom, Catherine; Gielen, Marij; Peeters, Hilde; Frijns, Jean-Pierre; Zeegers, Maurice P A
2011-08-01
The natural dizygotic (DZ) twinning rate has been proposed as a reliable and useful measure of human fecundity, if adjusted for maternal age at twin birth. The aim of this study was to analyze age-adjusted trends in natural DZ twinning rates over the past 40 years using data from the 'East Flanders Prospective Twin Survey (EFPTS)'. This study involved 4835 naturally conceived twin pregnancies between 1969 and 2009 from the population-based Belgian 'EFPTS'. Age-adjusted trends in the incidence of natural DZ twin pregnancies were calculated using a generalized linear model with Poisson distribution. Both the natural DZ twinning rates and maternal age at twin birth increased in a linear fashion from 1969 to 2009. When age-adjusted, we found that the trend in the natural DZ twinning rate was stable during the whole time period. According to our population-based data and after age-adjustment, a stable natural DZ twinning rate could be observed over the last four decades. Under the assumption that the spontaneous DZ twinning rate is a sensor of fecundity, this indicates a stable 'high' fecundity for this population.
8. Conjoined twins – role of imaging and recent advances
Directory of Open Access Journals (Sweden)
Rishi Philip Mathew
2017-12-01
Full Text Available Introduction: Conjoined twins are identical twins with fused bodies, joined in utero. They are rare complications of monochorionic twinning. The purpose of this study is to describe the various types of conjoined twins, the role of imaging and recent advances aiding in their management. Material and methods: This was a twin institutional study involving 3 cases of conjoined twins diagnosed over a period of 6 years from 2010 to 2015. All the 3 cases were identified antenatally by ultrasound. Only one case was further evaluated by MRI. Results: Three cases of conjoined twins (cephalopagus, thoracopagus and omphalopagus were accurately diagnosed on antenatal ultrasound. After detailed counseling of the parents and obtaining written consent, all the three cases of pregnancy were terminated. Delivery of the viable conjoined twins was achieved without any complications to the mothers, and all the three conjoined twins died after a few minutes. Conclusion: Ultrasound enables an early and accurate diagnosis of conjoined twins, which is vital for obstetric management. MRI is reserved for better tissue characterization. Termination of pregnancy when opted, should be done at an early stage as later stages are fraught with problems. Recent advances, such as 3D printing, may aid in surgical pre-planning, thereby enabling successful surgical separation of conjoined twins.
9. A SPITZER IRS STUDY OF INFRARED VARIABILITY IN TRANSITIONAL AND PRE-TRANSITIONAL DISKS AROUND T TAURI STARS
International Nuclear Information System (INIS)
Espaillat, C.; Furlan, E.; D'Alessio, P.; Sargent, B.; Muzerolle, J.; Nagel, E.; Calvet, N.; Watson, Dan M.
2011-01-01
We present a Spitzer IRS study of variability in 14 T Tauri stars in the Taurus and Chamaeleon star-forming regions. The sample is composed of transitional and pre-transitional objects which contain holes and gaps in their disks. We detect variability between 5 and 38 μm in all but two of our objects on timescales of 2-3 years. Most of the variability observed can be classified as seesaw behavior, whereby the emission at shorter wavelengths varies inversely with the emission at longer wavelengths. For many of the objects we can reasonably reproduce the observed variability using irradiated disk models, particularly by changing the height of the inner disk wall by ∼20%. When the inner wall is taller, the emission at the shorter wavelengths is higher since the inner wall dominates the emission at 2-8 μm. The taller inner wall casts a larger shadow on the outer disk wall, leading to less emission at wavelengths beyond 20 μm where the outer wall dominates. We discuss how the possible presence of planets in these disks could lead to warps that cause changes in the height of the inner wall. We also find that crystalline silicates are common in the outer disks of our objects and that in the four disks in the sample with the most crystalline silicates, variability on timescales of 1 week is present. In addition to explaining the infrared variability described above, planets can create shocks and collisions which can crystallize the dust and lead to short timescale variability.
10. NARROW Na AND K ABSORPTION LINES TOWARD T TAURI STARS: TRACING THE ATOMIC ENVELOPE OF MOLECULAR CLOUDS
Energy Technology Data Exchange (ETDEWEB)
Pascucci, I.; Simon, M. N. [Lunar and Planetary Laboratory, The University of Arizona, Tucson, AZ 85721 (United States); Edwards, S. [Five College Astronomy Department, Smith College, Northampton, MA 01063 (United States); Heyer, M. [Department of Astronomy, University of Massachusetts, Amherst, MA 01003-9305 (United States); Rigliaco, E. [Institute for Astronomy, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich (Switzerland); Hillenbrand, L. [Department of Astronomy, California Institute of Technology, Pasadena, CA 91125 (United States); Gorti, U.; Hollenbach, D., E-mail: [email protected] [SETI Institute, Mountain View, CA 94043 (United States)
2015-11-20
We present a detailed analysis of narrow Na i and K i absorption resonance lines toward nearly 40 T Tauri stars in Taurus with the goal of clarifying their origin. The Na i λ5889.95 line is detected toward all but one source, while the weaker K i λ7698.96 line is detected in about two-thirds of the sample. The similarity in their peak centroids and the significant positive correlation between their equivalent widths demonstrate that these transitions trace the same atomic gas. The absorption lines are present toward both disk and diskless young stellar objects, which excludes cold gas within the circumstellar disk as the absorbing material. A comparison of Na i and CO detections and peak centroids demonstrates that the atomic gas and molecular gas are not co-located, the atomic gas being more extended than the molecular gas. The width of the atomic lines corroborates this finding and points to atomic gas about an order of magnitude warmer than the molecular gas. The distribution of Na i radial velocities shows a clear spatial gradient along the length of the Taurus molecular cloud filaments. This suggests that absorption is associated with the Taurus molecular cloud. Assuming that the gradient is due to cloud rotation, the rotation of the atomic gas is consistent with differential galactic rotation, whereas the rotation of the molecular gas, although with the same rotation axis, is retrograde. Our analysis shows that narrow Na i and K i absorption resonance lines are useful tracers of the atomic envelope of molecular clouds. In line with recent findings from giant molecular clouds, our results demonstrate that the velocity fields of the atomic and molecular gas are misaligned. The angular momentum of a molecular cloud is not simply inherited from the rotating Galactic disk from which it formed but may be redistributed by cloud–cloud interactions.
11. NARROW Na AND K ABSORPTION LINES TOWARD T TAURI STARS: TRACING THE ATOMIC ENVELOPE OF MOLECULAR CLOUDS
International Nuclear Information System (INIS)
Pascucci, I.; Simon, M. N.; Edwards, S.; Heyer, M.; Rigliaco, E.; Hillenbrand, L.; Gorti, U.; Hollenbach, D.
2015-01-01
We present a detailed analysis of narrow Na i and K i absorption resonance lines toward nearly 40 T Tauri stars in Taurus with the goal of clarifying their origin. The Na i λ5889.95 line is detected toward all but one source, while the weaker K i λ7698.96 line is detected in about two-thirds of the sample. The similarity in their peak centroids and the significant positive correlation between their equivalent widths demonstrate that these transitions trace the same atomic gas. The absorption lines are present toward both disk and diskless young stellar objects, which excludes cold gas within the circumstellar disk as the absorbing material. A comparison of Na i and CO detections and peak centroids demonstrates that the atomic gas and molecular gas are not co-located, the atomic gas being more extended than the molecular gas. The width of the atomic lines corroborates this finding and points to atomic gas about an order of magnitude warmer than the molecular gas. The distribution of Na i radial velocities shows a clear spatial gradient along the length of the Taurus molecular cloud filaments. This suggests that absorption is associated with the Taurus molecular cloud. Assuming that the gradient is due to cloud rotation, the rotation of the atomic gas is consistent with differential galactic rotation, whereas the rotation of the molecular gas, although with the same rotation axis, is retrograde. Our analysis shows that narrow Na i and K i absorption resonance lines are useful tracers of the atomic envelope of molecular clouds. In line with recent findings from giant molecular clouds, our results demonstrate that the velocity fields of the atomic and molecular gas are misaligned. The angular momentum of a molecular cloud is not simply inherited from the rotating Galactic disk from which it formed but may be redistributed by cloud–cloud interactions
12. Prospective risk of fetal death in uncomplicated monochorionic twins.
LENUS (Irish Health Repository)
2012-03-01
A retrospective cohort study was carried out in a university teaching hospital to determine the prospective risk of unexpected fetal death in uncomplicated monochorionic diamniotic (MCDA) twin pregnancies after viability. All MCDA twins delivered at or after 24 weeks\\' gestation from July 1999 to July 2007 were included. Pregnancies with twin-twin transfusion syndrome, growth restriction, structural abnormalities, or twin reversed arterial perfusion sequence were excluded. Of the 144 MCDA twin pregnancies included in our analysis, the risk of intrauterine death was 4.9%. The prospective risk of unexpected intrauterine death was 1 in 43 after 32 weeks\\' gestation and 1 in 37 after 34 weeks\\' gestation. Our results demonstrate that despite close surveillance, the unexpected intrauterine death rate in uncomplicated MCDA twin pregnancies is high. This rate seems to increase after 34 weeks\\' gestation, suggesting that a policy of elective preterm delivery warrants evaluation.
13. Structures and growth textures of Japanese twin boundaries in quartz
Science.gov (United States)
Momma, K.; Nagase, T.; Kudoh, Y.; Kuribayashi, T.
2008-12-01
Growth textures and atomic configurations of Japanese twin boundaries in quartz were studied by the observation of natural samples and by computational simulations. Samples used in this study are collected from Narushima, Nagasaki Prefecture, Japan. The samples were first polished, and then etched by hydrofluoric acid for several minutes. The etched figures were observed by phase-contrast reflection microscopy and scanning electron microscopy. From these observations, high concentration of Brazil twin lamellae is found near the composition plane of Japanese twin. Observations of cathode luminescence images reveal that the development of Brazil twin lamellae at {112×2} composition plane of Japanese twin is directly related to the preferential growth of Japanese twin along the composition plane. Atomic configurations at {112×2} composition planes of Japanese twin were simulated by using molecular dynamics simulations and the energy minimization method. The simulated structures proved that {112×2} or {1×1×22} composition planes are the only composition planes that do not introduce unsatisfied bonding between Si and O atoms. When the composition plane is different from these planes, some kind of defect structures, like dislocations, are inevitably introduced. In the case of Brazil twin, screw dislocations are also known to be incorporated where orientation of Brazil twin boundary changes from one orientation to another. On the other hand, in the case where Brazil twin boundaries intersect with {112×2} composition planes of Japanese twin, we found that structures are kept coherently without any unsatisfied bonding. This result means that {112×2} composition planes of Japanese twin are the crystallographic sites having more than one possible stacking structures. Observations in this study indicate that {112×2} composition plane of Japanese twin serves as a source of Brazil twin during the course of crystal growth.
14. 'Twin2twin' an innovative method of empowering midwives to strengthen their professional midwifery organisations.
Science.gov (United States)
Cadée, Franka; Perdok, Hilde; Sam, Betty; de Geus, Myrte; Kweekel, Liselotte
2013-10-01
midwives need professional support from a national midwifery organisation to be able to provide the services that are by regulatory mechanisms and accreditation expected of them. Not all midwives in the world are united in a professional organisation. The aim of this project was to strengthen the midwifery organisations of Sierra Leone and the Netherlands. During the process of the project it was realised that the development of a platform of exchange at organisational level would be enhanced by introducing personal exchange between individual midwives. In response to this new insight the original project plan was adjusted by incorporating the twin2twin method. twin2twin is a feminist methodology of mutual exchange between twenty pairs of midwives from different organisations (in this case Sierra Leone and the Netherlands). The method can be distinguished by 10 specific steps. It was developed, used and (re)evaluated through focus group discussions, storytelling and written evaluations. twinning of organisations was strengthened by adding a human component to the process. With the use of the 'twin2twin' method, midwives were encouraged to invested in a professional and personal bond with their 'twin sister'. This bond was independent and went beyond the relatively short four year project period. Through personal engagement and mutual exchange of knowledge and skills, midwives empowered each other to build and strengthen their midwifery organisations both in Sierra Leone and the Netherlands. (Empowerment refers to the expansion in people's ability to make strategic life choices in a context where this ability was previously denied to them (Narayan, 2005); organisational empowerment includes processes and structures that enhance members' skills and provides them with the mutual support necessary to effect community level change (Zimmerman, 1995).). despite challenges we are convinced that twin2twin can be of additional benefit for the success of other projects
15. X-ray stars observed in LAMOST spectral survey
Science.gov (United States)
Lu, Hong-peng; Zhang, Li-yun; Han, Xianming L.; Shi, Jianrong
2018-05-01
X-ray stars have been studied since the beginning of X-ray astronomy. Investigating and studying the chromospheric activity from X-ray stellar optical spectra is highly significant in providing insights into stellar magnetic activity. The big data of LAMOST survey provides an opportunity for researching stellar optical spectroscopic properties of X-ray stars. We inferred the physical properties of X-ray stellar sources from the analysis of LAMOST spectra. First, we cross-matched the X-ray stellar catalogue (12254 X-ray stars) from ARXA with LAMOST data release 3 (DR3), and obtained 984 good spectra from 713 X-ray sources. We then visually inspected and assigned spectral type to each spectrum and calculated the equivalent width (EW) of Hα line using the Hammer spectral typing facility. Based on the EW of Hα line, we found 203 spectra of 145 X-ray sources with Hα emission above the continuum. For these spectra we also measured the EWs of Hβ, Hγ, Hδ and Ca ii IRT lines of these spectra. After removing novae, planetary nebulae and OB-type stars, we found there are 127 X-ray late-type stars with Hα line emission. By using our spectra and results from the literature, we found 53 X-ray stars showing Hα variability; these objects are Classical T Tauri stars (CTTs), cataclysmic variables (CVs) or chromospheric activity stars. We also found 18 X-ray stars showing obvious emissions in the Ca ii IRT lines. Of the 18 X-ray stars, 16 are CTTs and 2 are CVs. Finally, we discussed the relationships between the EW of Hα line and X-ray flux.
16. Personality and birth order in monozygotic twins adopted apart: a test of Sulloway's theory; Research Reviews: twin births and cancer risk in mothers, male sexual dysfunction, twin study of ultimatum game behavior; Human Interest: 'The Land of Twins', twin-like reunion-I, twin-like reunion-II.
Science.gov (United States)
Segal, Nancy L
2008-02-01
A brief overview of Sulloway's (1996) theory of birth order and personality is presented. A reared apart twin approach for testing his personality findings regarding openness to experience and conscientiousness in first borns and later borns is described. This is followed by summaries of three recent twin studies. The topics include cancer risk in mother of twins, sexual dysfunction in males and responder behavior during ultimatum games. This article concludes with a discussion of twinning rates and rituals among the Yoruba of western Nigeria, and descriptions of two unusual reunions between siblings and twins.
17. The embedded young stars in the Taurus-Auriga molecular cloud. I - Models for spectral energy distributions
Science.gov (United States)
Kenyon, Scott J.; Calvet, Nuria; Hartmann, Lee
1993-01-01
We describe radiative transfer calculations of infalling, dusty envelopes surrounding pre-main-sequence stars and use these models to derive physical properties for a sample of 21 heavily reddened young stars in the Taurus-Auriga molecular cloud. The density distributions needed to match the FIR peaks in the spectral energy distributions of these embedded sources suggest mass infall rates similar to those predicted for simple thermally supported clouds with temperatures about 10 K. Unless the dust opacities are badly in error, our models require substantial departures from spherical symmetry in the envelopes of all sources. These flattened envelopes may be produced by a combination of rotation and cavities excavated by bipolar flows. The rotating infall models of Terebey et al. (1984) models indicate a centrifugal radius of about 70 AU for many objects if rotation is the only important physical effect, and this radius is reasonably consistent with typical estimates for the sizes of circumstellar disks around T Tauri stars.
18. Do assisted-reproduction twin pregnancies require additional antenatal care?
Science.gov (United States)
Jauniaux, E; Ben-Ami, I; Maymon, R
2013-02-01
Iatrogenic twinning has become the main side-effect assisted reproduction treatment. We have evaluated the evidence for additional care that assisted-reproduction twins may require compared with spontaneous twins. Misacarriages are increased in women with tubal problems and after specific treatments. Assisted-reproduction twin pregnancies complicated by a vanishing twin after 8 weeks have an increased risk of preterm delivery and of low and very low birthweight compared with singleton assisted-reproduction pregnancies. Monozygotic twin pregnancies occur at a higher rate after assisted reproduction treatment and are associated with a higher risk of perinatal complications. The incidence of placenta praevia and vasa praevia is increased in assisted-reproduction twin pregnancies. Large cohort studies do not indicate a higher rate of fetal congenital malformations in assisted-reproduction twins. Overall, assisted-reproduction twins in healthy women assisted-reproduction twins is only increased in women with a pre-existing medical condition such as hypertensive disorders and diabetes and most of these risks can be avoided with single-embryo transfer. Following the birth of the first IVF baby, rumours started to spread in both the medical literature and the media about the long-term health effects for children born following assisted reproduction treatment. However, after more than 30 years, the most common complications associated with IVF treatment remain indirect and technical such as the failure of treatment and ovarian hyperstimulation. Iatrogenic twinning has become the main side-effect of assisted reproduction treatment and the increasing number of twin pregnancies, in particular in older women, has generated numerous debates on the need for additional healthcare provision. In this review, we have evaluated the evidence for additional care that assisted-conception twin pregnancies may require compared with spontaneous twin pregnancies. Twin pregnancies are
19. Cervical column morphology and craniofacial profiles in monozygotic twins.
Science.gov (United States)
Sonnesen, Liselotte; Pallisgaard, Carsten; Kjaer, Inger
2008-02-01
Previous studies have described the relationships between cervical column morphology and craniofacial morphology. The aims of the present study were to describe cervical column morphology in 38 pairs of adult monozygotic (MZ) twins, and compare craniofacial morphology in twins with fusions with craniofacial morphology in twins without fusion. Visual assessment of cervical column morphology and cephalometric measurements of craniofacial morphology were performed on profile radiographs. In the cervical column, fusion between corpora of the second and third vertebrae was registered as fusion. In the twin group, 8 twin pairs had fusion of the cervical column in both individuals within the pair (sub-group A), 25 pairs had no fusions (subgroup B), and in 5 pairs, cervical column morphology was different within the pair (subgroup C), as one twin had fusion and the other did not. Comparison of craniofacial profiles showed a tendency to increased jaw retrognathia, larger cranial base angle, and larger mandibular inclination in subgroup A than in subgroup B. The same tendency was observed within subgroup C between the individual twins with fusion compared with those without fusion. These results confirm that cervical fusions and craniofacial morphology may be interrelated in twins when analysed on profile radiographs. The study also documents that differences in cervical column morphology can occur in individuals within a pair of MZ twins. It illustrates that differences in craniofacial morphology between individuals within a pair of MZ twins can be associated with cervical fusion.
20. Twin specific risk factors in primary school achievements.
Science.gov (United States)
de Zeeuw, Eveline L; van Beijsterveldt, Catherina E M; de Geus, Eco J C; Boomsma, Dorret I
2012-02-01
The main aim of this study was to examine twin specific risk factors that influence educational achievement in primary school. We included prenatal factors that are not unique to twins, except for zygosity, but show a higher prevalence in twins than in singletons. In addition, educational achievement was compared between twins and their nontwin siblings in a within-family design. Data were obtained from parents and teachers of approximately 10,000 twins and their nontwin siblings registered with the Netherlands Twin Register. Teachers rated the proficiency of the children on arithmetic, language, reading, and physical education, and reported a national educational achievement test score (CITO). Structural equation modeling showed that gestational age, birth weight, and sex were significant predictors of educational achievement, even after correction for socioeconomic status. Mode of delivery and zygosity did not have an effect, while parental age only influenced arithmetic. Mode of conception, incubator time, and birth complications negatively affected achievement in physical education. The comparison of educational achievement of twins and singletons showed significantly lower ratings on arithmetic, reading, and language in twins, compared to their older siblings, but not compared to their younger siblings. Low gestational age and low birth weight were the most important risk factors for lower educational achievement of twins in primary school. It seems that the differences observed between twins and their nontwin siblings in educational achievement can largely be explained by birth order within the family.
1. Phase field modeling of twinning in indentation of transparent crystals
International Nuclear Information System (INIS)
Clayton, J D; Knap, J
2011-01-01
Continuum phase field theory is applied to study elastic twinning in calcite and sapphire single crystals subjected to indentation loading by wedge-shaped indenters. An order parameter is associated with the magnitude of stress-free twinning shear. Geometrically linear and nonlinear theories are implemented and compared, the latter incorporating neo-Hookean elasticity. Equilibrium configurations of deformed and twinned crystals are attained numerically via direct energy minimization. Results are in qualitative agreement with experimental observations: a long thin twin forms asymmetrically under one side of the indenter, the tip of the twin is sharp and the length of the twin increases with increasing load. Qualitatively similar results are obtained using isotropic and anisotropic elastic constants, though the difference between isotropic and anisotropic results is greater in sapphire than in calcite. Similar results are also obtained for nanometer-scale specimens and millimeter-scale specimens. Indentation forces are greater in the nonlinear model than the linear model because of the increasing tangent bulk modulus with increasing pressure in the former. Normalized relationships between twin length and indentation force are similar for linear and nonlinear theories at both nanometer and millimeter scales. Twin morphologies are similar for linear and nonlinear theories for indentation with a 90° wedge. However, in the nonlinear model, indentation with a 120° wedge produces a lamellar twin structure between the indenter and the long sharp primary twin. This complex microstructure is not predicted by the linear theory
DEFF Research Database (Denmark)
Gran, Fredrik; Jakobsson, Andreas; Jensen, Jørgen Arendt
2009-01-01
. The methods can also provide better quality of the estimated power spectral density (PSD) of the blood signal. Adaptive spectral estimation techniques are known to pro- vide good spectral resolution and contrast even when the ob- servation window is very short. The 2 adaptive techniques are tested......In this paper, 2 adaptive spectral estimation techniques are analyzed for spectral Doppler ultrasound. The purpose is to minimize the observation window needed to estimate the spectrogram to provide a better temporal resolution and gain more flexibility when designing the data acquisition sequence...... and compared with the averaged periodogram (Welch’s method). The blood power spectral capon (BPC) method is based on a standard minimum variance technique adapted to account for both averaging over slow-time and depth. The blood amplitude and phase estimation technique (BAPES) is based on finding a set...
3. Chronic Idiopathic Neutrophilia in Two Twins
Directory of Open Access Journals (Sweden)
Roberto Miniero
2014-01-01
Full Text Available Neutrophilia in adults refers to an alteration in the total number of blood neutrophils that is in excess of about 7500 cells/μL. This definition is restrictive in childhood as neutrophil count is age-dependent. Chronic Idiopathic Neutrophilia (CIN refers to a condition that persists for many years in individuals who appear otherwise healthy. CIN is rarely mentioned in scientific literature and in academic books of hematology; only few words are dedicated to this topic. We report a case study of two twins with CIN followed from the first year of life to 24 years of age. To the best of our knowledge this is the first case report of two twins with CIN followed through a long period of time. We believe that our observation may contribute to better understand and characterize this hematologic abnormality.
4. The TwinEBIS setup: Machine description
Energy Technology Data Exchange (ETDEWEB)
Breitenfeldt, M. [CERN, Geneva 23 CH-1211 (Switzerland); Mertzig, R. [CERN, Geneva 23 CH-1211 (Switzerland); Technische Universität Dresden, 01069 Dresden (Germany); Pitters, J. [CERN, Geneva 23 CH-1211 (Switzerland); Technische Universität Wien, 1040 Vienna (Austria); Shornikov, A. [CERN, Geneva 23 CH-1211 (Switzerland); GANIL, Bd. Becquerel, BP 55027, 14076 Caen Cedex 05 (France); Wenander, F., E-mail: [email protected] [CERN, Geneva 23 CH-1211 (Switzerland)
2017-06-01
TwinEBIS is an Electron Beam Ion Source (EBIS) recently made operational at CERN. The device is similar in construction to the REXEBIS charge breeder operating at the ISOLDE facility. After relocation of the solenoid from the Manne Siegbahn Laboratory (MSL) Stockholm, TwinEBIS was commissioned at CERN and serves as a test bench dedicated to manipulation of low-energy highly charged ions. In this paper we give an overview of the setup and present advanced numerical simulations of the electron optics. In addition, the alignment procedure of the solenoid magnetic field is described and measurement results are presented. Results from cathode investigations, electron beam tests and ion extraction modulation are presented in a follow-up paper.
5. Twin-twin transfusion syndrome: cerebral ischemia is not the only fetal MR imaging finding
Energy Technology Data Exchange (ETDEWEB)
Kline-Fath, Beth M. [University of Cincinnati Medical Center, Department of Radiology, Cincinnati Children' s Hospital Medical Center, Cincinnati, OH (United States); Cincinnati Children' s Hospital, Department of Radiology, Cincinnati, OH (United States); Calvo-Garcia, Maria A.; O' Hara, Sara M.; Racadio, Judy M. [University of Cincinnati Medical Center, Department of Radiology, Cincinnati Children' s Hospital Medical Center, Cincinnati, OH (United States); Crombleholme, Timothy M. [University of Cincinnati Medical Center, Department of Surgery, Cincinnati Children' s Hospital Medical Center, Cincinnati, OH (United States)
2007-01-15
Twin-twin transfusion syndrome (TTTS) is a complication of monochorionic/diamniotic twin pregnancies. An imbalance of blood flow occurs through placental anastomoses, causing potentially significant morbidity and mortality in both twins. Although the sonographic findings of TTTS are well documented, we believe that MR imaging is a valuable adjunct. We describe the fetal MR imaging findings associated with TTTS. From 2003 to 2005, 37 consecutive MR imaging studies were performed on multiple-gestation pregnancies. Of the 37, 25 were consistent with TTTS, correlated and confirmed by sonographic criteria. MR fetal abnormalities were documented. Cerebral ischemia, which could not be demonstrated by sonography, was delineated well by MR imaging. New findings noted on fetal MR imaging were enlargement of cerebral venous sinuses in both twins, dilatation of the renal collecting system in the recipient, lung lesions in the recipient and cerebral malformations in the donor. MR imaging is an important adjunct in TTTS imaging. Its benefit over sonography is its clear definition of cerebral pathology, which is important for intervention and counseling. The new findings, particularly in the urinary tract and cerebral venous sinuses, also help support the diagnosis of TTTS and might reveal additional consequences of the altered hemodynamics that occur in TTTS. (orig.)
6. Twin-twin transfusion syndrome: cerebral ischemia is not the only fetal MR imaging finding
International Nuclear Information System (INIS)
Kline-Fath, Beth M.; Calvo-Garcia, Maria A.; O'Hara, Sara M.; Racadio, Judy M.; Crombleholme, Timothy M.
2007-01-01
Twin-twin transfusion syndrome (TTTS) is a complication of monochorionic/diamniotic twin pregnancies. An imbalance of blood flow occurs through placental anastomoses, causing potentially significant morbidity and mortality in both twins. Although the sonographic findings of TTTS are well documented, we believe that MR imaging is a valuable adjunct. We describe the fetal MR imaging findings associated with TTTS. From 2003 to 2005, 37 consecutive MR imaging studies were performed on multiple-gestation pregnancies. Of the 37, 25 were consistent with TTTS, correlated and confirmed by sonographic criteria. MR fetal abnormalities were documented. Cerebral ischemia, which could not be demonstrated by sonography, was delineated well by MR imaging. New findings noted on fetal MR imaging were enlargement of cerebral venous sinuses in both twins, dilatation of the renal collecting system in the recipient, lung lesions in the recipient and cerebral malformations in the donor. MR imaging is an important adjunct in TTTS imaging. Its benefit over sonography is its clear definition of cerebral pathology, which is important for intervention and counseling. The new findings, particularly in the urinary tract and cerebral venous sinuses, also help support the diagnosis of TTTS and might reveal additional consequences of the altered hemodynamics that occur in TTTS. (orig.)
7. Introduction to spectral theory
CERN Document Server
Levitan, B M
1975-01-01
This monograph is devoted to the spectral theory of the Sturm- Liouville operator and to the spectral theory of the Dirac system. In addition, some results are given for nth order ordinary differential operators. Those parts of this book which concern nth order operators can serve as simply an introduction to this domain, which at the present time has already had time to become very broad. For the convenience of the reader who is not familar with abstract spectral theory, the authors have inserted a chapter (Chapter 13) in which they discuss this theory, concisely and in the main without proofs, and indicate various connections with the spectral theory of differential operators.
8. Aberrant twinning (diprosopus) associated with anencephaly.
Science.gov (United States)
Moerman, P; Fryns, J P; Goddeeris, P; Lauweryns, J M; Van Assche, A
1983-10-01
A case of Monocephalus diprosopus, associated with craniorachischisis and duplication of most of the foregut derivates is presented. The major part of the cardiovascular system remained single but the heart exhibited severe defects, including a complete persistent atrioventricular canal, transposition of the great arteries and atresia of the pulmonary valve. This report further supports the hypothesis that certain-types of incomplete twinning and neural tube defects may be caused by a single teratogenic mechanism.
9. Optical Properties of Rotationally Twinned Nanowire Superlattices
DEFF Research Database (Denmark)
Bao, Jiming; Bell, David C.; Capasso, Federico
2008-01-01
We have developed a technique so that both transmission electron microscopy and microphotoluminescence can be performed on the same semiconductor nanowire over a large range of optical power, thus allowing us to directly correlate structural and optical properties of rotationally twinned zinc...... a heterostructure in a chemically homogeneous nanowire material and alter in a major way its optical properties opens new possibilities for band-structure engineering....
10. Arterio-venous flow between monochorionic twins determined during intra-uterine transfusion
NARCIS (Netherlands)
van Gemert, Martin J. C.; van den Wijngaard, Jeroen P. H. M.; Lopriore, Enrico; Pasman, Suzanne A.; Vandenbussche, Frank P. H. A.
2008-01-01
Twin-twin transfusion syndrome (TTTS) is a severe complication of monozygotic (identical) twin fetuses sharing one single (monochorionic) placenta. TTTS is caused by a net inter-twin transfusion of blood through placental anastomoses, from one twin (the donor) to the other (the recipient), which
11. Emergency separation of a xipho-omphalopagus twin in a developing country
Directory of Open Access Journals (Sweden)
Shukla R
2010-01-01
Full Text Available Female conjoined twins (thoraco-omphalopagus were delivered by emergency caesarean section in a private nursing home. On examination, one of the twins was dead and was threatening the survival of the surviving twin (twin A. An emergency separation was performed to salvage the surviving twin.
12. The Impact of Preschool Twins' Physical Difficulties on Parental Perceptions towards Separation, Closeness and Friendship
Science.gov (United States)
Markodimitraki, Maria; Linardakis, Michalis; Kypriotaki, Maria; Manolitsis, George
2016-01-01
The aims of this study were to: (a) provide descriptive data of twins with physical difficulties among 120 Greek twins of preschool age; and (b) to investigate the impact of twins' health condition on parental perceptions towards twins' separation, closeness and friendship. The administration of School Policy for Twins and Higher Multiples…
13. IVF twins: buy one get one free?
Science.gov (United States)
Ismail, Laura; Mittal, Monica; Kalu, Emmanuel
2012-10-01
There has been an overall increase in the incidence of multiple pregnancies and assisted reproduction technology is largely responsible for this rise. Although twins may appeal to couples undergoing in vitro fertilisation (IVF), they have been associated with serious health consequences to the babies, their mothers and the family unit, as well as having massive financial implications for the National Health Service. Transfer of more than one embryo during IVF is mainly responsible for IVF twins, and elective transfer of a single embryo at a time with cryopreservation of surplus embryos for later transfer has been shown to be an effective strategy to minimise the risk of twins without compromising IVF success rates. Factors that will impact on the success of the policy of elective single embryo transfer (eSET) include improvement in embryo selection for transfer, better cryopreservation techniques and adequate state funding for IVF. However, in implementing the policy of eSET it is important that each case is assessed on an individual basis since in some situations (e.g. in older women) the transfer of two embryos may be more cost effective. Adequate and continuous education of all stakeholders is essential if the policy of eSET is to be successful in the UK.
14. Twins: prevalence, problems, and preterm births.
Science.gov (United States)
Chauhan, Suneet P; Scardo, James A; Hayes, Edward; Abuhamad, Alfred Z; Berghella, Vincenzo
2010-10-01
The rate of twin pregnancies in the United States has stabilized at 32 per 1000 births in 2006. Aside from determining chorionicity, first-trimester screening and second-trimester ultrasound scanning should ascertain whether there are structural or chromosomal abnormalities. Compared with singleton births, genetic amniocentesis-related loss at births is higher (0.9% vs 2.9%, respectively). Selective termination for an anomalous fetus is an option, although the pregnancy loss rate is 7% at experienced centers. For singleton and twin births for African American and white women, approximately 50% of preterm births are indicated; approximately one-third of these births are spontaneous, and 10% of the births occur after preterm premature rupture of membranes. From 1989-2000, the rate of preterm twin births increased, for African American and white women alike, although the perinatal mortality rate has actually decreased. As with singleton births, tocolytics should be used judiciously and only for a limited time (births. Administration of antenatal corticosteroids is an evidence-based recommendation. Copyright © 2010 Mosby, Inc. All rights reserved.
15. Anorexia and Bulimia Nervosa in Same-Sex and Opposite-Sex Twins : Lack of Association With Twin Type in a Nationwide Study of Finnish Twins
NARCIS (Netherlands)
Raevuori, Anu; Kaprio, Jaakko; Hoek, Hans W.; Sihvola, Elina; Rissanen, Aila; Keski-Rahkonen, Anna
2008-01-01
Objective: The authors tested the hypothesis that either prenatal feminization or masculinization hormone influences in utero or later socialization affects the risk for anorexia and bulimia nervosa and disordered eating in members of opposite-sex twin pairs. Method: Finnish twins (N=2,426 women,
16. A tale of twin Higgs: natural twin two Higgs doublet models
International Nuclear Information System (INIS)
Yu, Jiang-Hao
2016-01-01
In original twin Higgs model, vacuum misalignment between electroweak and new physics scales is realized by adding explicit ℤ 2 breaking term. Introducing additional twin Higgs could accommodate spontaneous ℤ 2 breaking, which explains origin of this misalignment. We introduce a class of twin two Higgs doublet models with most general scalar potential, and discuss general conditions which trigger electroweak and ℤ 2 symmetry breaking. Various scenarios on realising the vacuum misalignment are systematically discussed in a natural composite two Higgs double model framework: explicit ℤ 2 breaking, radiative ℤ 2 breaking, tadpole-induced ℤ 2 breaking, and quartic-induced ℤ 2 breaking. We investigate the Higgs mass spectra and Higgs phenomenology in these scenarios.
17. A tale of twin Higgs: natural twin two Higgs doublet models
Energy Technology Data Exchange (ETDEWEB)
Yu, Jiang-Hao [Amherst Center for Fundamental Interactions, Department of Physics,University of Massachusetts Amherst,710 North Pleasant St., Amherst, MA 01002 (United States)
2016-12-28
In original twin Higgs model, vacuum misalignment between electroweak and new physics scales is realized by adding explicit ℤ{sub 2} breaking term. Introducing additional twin Higgs could accommodate spontaneous ℤ{sub 2} breaking, which explains origin of this misalignment. We introduce a class of twin two Higgs doublet models with most general scalar potential, and discuss general conditions which trigger electroweak and ℤ{sub 2} symmetry breaking. Various scenarios on realising the vacuum misalignment are systematically discussed in a natural composite two Higgs double model framework: explicit ℤ{sub 2} breaking, radiative ℤ{sub 2} breaking, tadpole-induced ℤ{sub 2} breaking, and quartic-induced ℤ{sub 2} breaking. We investigate the Higgs mass spectra and Higgs phenomenology in these scenarios.
18. Functional characterization of the NhaA Na+/H+ antiporter from the green picoalga Ostreococcus tauri.
Science.gov (United States)
Dawut, Keatisuda; Sirisattha, Sophon; Hibino, Takashi; Kageyama, Hakuto; Waditee-Sirisattha, Rungaroon
2018-07-01
Transmembrane ion transport is a critical process in the cellular response to salt stress. Among the known functional membrane transporters that are involved in the salt stress response, Na + /H + antiporters have been extensively studied. These ubiquitous membrane proteins are crucial for salt tolerance and are associated with the regulation of internal pH, cell volume, morphogenesis, and vesicular trafficking. Molecular and functional analyses of Na + /H + antiporters have been characterized among taxa but little is known about algal Na + /H + antiporters. Here, we analyzed putative Na + /H + antiporters from the complete genome sequence of the marine picoalga Ostreococcus tauri. At least 10 putative Na + /H + antiporters belonging to the SOS1, NHX, and KEA/Kef families were found. Surprisingly, a bacterial type NhaA sequence (OtNhaA) was also found. Topological modeling of OtNhaA predicted 12 possible transmembrane segments with a long N-terminus. The full-length (FL_OtNhaA) and N-terminal truncated (ΔN112_OtNhaA) versions of OtNhaA were constructed, expressed in the salt-sensitive mutant Escherichia coli TO114, and functionally characterized. Complementation analysis revealed that FL_OtNhaA- and ΔN112_OtNhaA-expressing cells exhibited increased tolerance to high NaCl concentrations up to 700 mM. Antiporter activity assays showed that both FL_OtNhaA and ΔN112_OtNhaA proteins predominantly exhibited Na + /H + and Ca 2+ /H + antiporter activities at alkaline pH conditions. Intriguingly, the ΔN112_OtNhaA exhibited higher Na + /H + and Ca 2+ /H + antiporter activities compared to FL_OtNhaA. Kinetic analysis revealed that FL_OtNhaA has a high affinity for Na + and Ca 2+ ions with a K m of 1.1 ± 0.23 mM for Na + (at pH 8.5) and a K m of 0.3 ± 0.07 mM for Ca 2+ (at pH 8.5). Since NhaA has shown striking diversity among taxa, our results provide insight into the functional properties of the algal NhaA Na + /H + antiporter. These results will
19. Coffee and smoking as risk factors of twin pregnancies
DEFF Research Database (Denmark)
Morales-Suárez-Varela, Maria M; Bech, Bodil Hammer; Christensen, Kaare
2007-01-01
their prepregnancy weight and height, coffee and alcohol intake, smoking habits, and potential confounding factors at early stages of pregnancy. We identified smoking (> 10 cigarettes/day) as a possible determinant of twinning, particularly for dizygotic twinning rates (same sex) and furthermore corroborated......Twinning rates have changed substantially over time for reasons that are only partly known. In this study we studied smoking, coffee and alcohol intake, and their possible interaction with obesity as potential determinants of twinning rates using data from the Danish National Birth Cohort between...... 1996 and 2002. We identified 82,985 pregnancies: 81,954 singleton and 1031 twins. For the twins we had data to classify 121 as monozygotic, 189 dizygotic (same sex), 313 dizygotic (opposite sex) but, 408 were of the same sex but with unknown zygosity. All mothers were interviewed about...
20. Atopic diseases in twins born after assisted reproduction
DEFF Research Database (Denmark)
Jäderberg, Ida; Thomsen, Simon F; Kyvik, Kirsten Ohm
2012-01-01
Jäderberg I, Thomsen SF, Kyvik KO, Skytthe A, Backer V. Atopic diseases in twins born after assisted reproduction. Paediatric and Perinatal Epidemiology 2012; 26: 140-145. We examined the risk of atopic diseases in twins born after assisted reproduction. Data on atopic diseases and assisted...... reproduction in 9694 twin pairs, 3-20 years of age, from the Danish Twin Registry were collected via multidisciplinary questionnaires. The risk of atopic diseases in twins born after assisted reproduction was compared with the risk in twins born after spontaneous conception using logistic regression...... and variance components analysis. Children born after assisted reproduction did not have a different risk of atopic outcomes (adjusted odds ratios [95% confidence intervals] for asthma: 0.95 [0.85, 1.07], P = 0.403; hay fever: 1.01 [0.86, 1.18], P = 0.918; and atopic dermatitis: 1.02 [0.81, 1.11], P = 0...
1. Quality of life in unaffected twins discordant for affective disorder
DEFF Research Database (Denmark)
Vinberg, Maj; Bech, Per; Kyvik, Kirsten Ohm
2007-01-01
-Risk twins) and without (the control group/Low-Risk twins) a co-twin history of affective disorder were identified through nationwide registers. The aim of the present study was to investigate the hypothesis that a genetic liability to affective disorder is associated with a lower perception of quality......BACKGROUND: The disability and hardship associated with affective disorder is shared by the family members of affective patients and might affect the family member's quality of life. METHOD: In a cross-sectional, high-risk, case-control study, monozygotic (MZ) and dizygotic (DZ) twins with (High...... of life. RESULTS: Univariate analyses showed that quality of life in all domains was impaired for the 121 High-Risk twins compared to the 84 Low-Risk twins. In multiple regression analyses, the differences remained significant after adjustment for sex, age, marital status and years of education. Adjusted...
2. Effect of twinning plane on superconductor magnetic properties
International Nuclear Information System (INIS)
Buzdin, A.I.; Kuptsov, D.A.
1989-01-01
Effect of twinning planes on pinning of the Abrikosov vortices in superconductors of the second order with the Ginsburg-Landau parameter, κ >> 1, is considered. The modified Ginsburg-Landau functional, where the effect of superconducting properties improvement near the twinning plane is taken into account by adding the additional δ-function component, is used to descibe superconductivity of twinning plane. Force of interaction of a vortex filament and the twinning plane is calculated. It is shown that in case of the twinning plane opaque to electrons, additional attractive force, being analogous to that occurring in the problem on the surface Been-Livingston barrier, affects the vortex filament. The results can explain anisotropy of vortex pinning observed in the periodic twinning structure in high-temperature superconductors
3. Hydride formation on deformation twin in zirconium alloy
Energy Technology Data Exchange (ETDEWEB)
Kim, Ju-Seong [Korea Atomic Energy Research Institute, 989-111 Daedeokdaero, Yuseong-gu, Daejeon, 305-353 (Korea, Republic of); Kim, Sung-Dae [Korea Institute of Material Science (KIMS), 797 Changwondaero, Changwon, Gyeongnam, 642-831 (Korea, Republic of); Yoon, Jonghun, E-mail: [email protected] [Department of Mechanical Engineering, Hanyang University, 1271 Sa3-dong, Sangrok-gu, Ansan-si, Gyeonggi-do, 426-791 (Korea, Republic of)
2016-12-15
Hydrides deteriorate the mechanical properties of zirconium (Zr) alloys used in nuclear reactors. Intergranular hydrides that form along grain boundaries have been extensively studied due to their detrimental effects on cracking. However, it has been little concerns on formation of Zr hydrides correlated with deformation twins which is distinctive heterogeneous nucleation site in hexagonal close-packed metals. In this paper, the heterogeneous precipitation of Zr hydrides at the twin boundaries was visualized using transmission electron microscopy. It demonstrates that intragranular hydrides in the twinned region precipitates on the rotated habit plane by the twinning and intergranular hydrides precipitate along the coherent low energy twin boundaries independent of the conventional habit planes. Interestingly, dislocations around the twin boundaries play a substantial role in the nucleation of Zr hydrides by reducing the misfit strain energy.
4. Twins with omphalocele in Denmark (1970-1989)
DEFF Research Database (Denmark)
Bugge, Merete
2010-01-01
Seven pairs of twins, two monozygotic (MZ), two dizygotic (DZ), and three like-sex pairs of unknown zygosity are described. The twin pairs were all discordant for omphalocele except for one pair of conjoined twins. The 8 infants with omphalocele represent 3.1% of the 253 infants with omphalocele......, ascertained in an almost complete nationwide data set of live- and stillborn infants with abdominal wall defects in two decades in Denmark (1970-1989). The occurrence of twins with omphalocele was not significantly different from the occurrence of twins in the Danish population in the same period. To our...... knowledge this is the first report of the occurrence of twins with omphalocele in a systematic nationwide epidemiological study....
5. Adolescent idiopathic scoliosis in twins: a population-based survey
DEFF Research Database (Denmark)
Andersen, Mikkel O; Thomsen, Karsten; Kyvik, Kirsten O
2007-01-01
STUDY DESIGN: A questionnaire-based identification of adolescent idiopathic scoliosis (AIS) patients in a twin cohort. OBJECTIVE: The purpose of this study was to establish a scoliosis twin cohort to provide data on the heritability of AIS. SUMMARY OF BACKGROUND DATA: The etiology of AIS is still...... environmental factors. METHODS: All 46,418 twins registered in the Danish Twin Registry born from 1931 to 1982 were sent a questionnaire, which included questions about scoliosis. A total of 34,944 (75.3%) representing 23,204 pairs returned the questionnaire. RESULTS: A subgroup of 220 subjects considered...... of monozygotic and dizygotic pairs was significantly different (P scoliosis in 1 twin whose other twin has scoliosis is smaller than believed up until now....
6. Confined Blood Chimerism in Monochorionic Dizygotic Twins Conceived Spontaneously
Directory of Open Access Journals (Sweden)
Takashi Kanda
2013-05-01
Full Text Available Traditionally, monochorionicity has been regarded as synonymous with monozygosity. However, several recent cases of monochorionic dizygotic twins have shown that monochorionic twins can be dizygous. We report a rare case of monochorionic diamnionic, gender-discordant twins who were conceived spontaneously. Initially, a monochorionic placenta was diagnosed by ultrasonography at 8 weeks of gestation and then confirmed by pathology after delivery. The twins had different genders. A comparison of cytogenetic analyses using peripheral blood lymphocytes and skin fibroblasts revealed that chimerism was confined to blood cells. We have experienced two cases of monochorionic dizygotic twins since 2003. These cases suggest that monochorionic dizygotic twins are not as rare as previously thought.
7. On Longitudinal Spectral Coherence
DEFF Research Database (Denmark)
Kristensen, Leif
1979-01-01
It is demonstrated that the longitudinal spectral coherence differs significantly from the transversal spectral coherence in its dependence on displacement and frequency. An expression for the longitudinal coherence is derived and it is shown how the scale of turbulence, the displacement between ...... observation sites and the turbulence intensity influence the results. The limitations of the theory are discussed....
8. Deformation twinning in irradiated ferritic/martensitic steels
Science.gov (United States)
Wang, K.; Dai, Y.; Spätig, P.
2018-04-01
Two different ferritic/martensitic steels were tensile tested to gain insight into the mechanisms of embrittlement induced by the combined effects of displacement damage and helium after proton/neutron irradiation in SINQ, the Swiss spallation neutron source. The irradiation conditions were in the range: 15.8-19.8 dpa (displacement per atom) with 1370-1750 appm He at 245-300 °C. All the samples fractured in brittle mode with intergranular or cleavage fracture surfaces when tested at room temperature (RT) or 300 °C. After tensile test, transmission electron microscopy (TEM) was employed to investigate the deformation microstructures. TEM-lamella samples were extracted directly below the intergranular fracture surfaces or cleavage surfaces by using the focused ion beam technique. Deformation twinning was observed in irradiated specimens at high irradiation dose. Only twins with {112} plane were observed in all of the samples. The average thickness of twins is about 40 nm. Twins initiated at the fracture surface, became gradually thinner with distance away from the fracture surface and finally stopped in the matrix. Novel features such as twin-precipitate interactions, twin-grain boundary and/or twin-lath boundary interactions were observed. Twinning bands were seen to be arrested by grain boundaries or large precipitates, but could penetrate martensitic lath boundaries. Unlike the case of defect free channels, small defect-clusters, dislocation loops and dense small helium bubbles were observed inside twins.
9. [Early prenatal diagnosis of diprosopic syncephalic joined twins].
Science.gov (United States)
Picaud, A; Nlome-Nze, A R; Engongha-Beka, T; Ogowet-Igumu, N
1990-06-01
The authors summarize the case of diprosopic syncephalic joined twins diagnosed at 22 weeks of pregnancy by ultrasonography performed because of hydramnios. The rate of separation anomalies of monozygotic twins is assessed by a review of the literature: from 1 to twenty to fifty thousands for joined twins to 1 per cent fifty thousand to fifteen millions for diprosopus. The etiology is the result of a late division of the egg between D12 and D16. Often an encephalic diprosopic joined twins cause elevated levels of maternal serum alpha protein. Early ultrasonography permits to consider a vaginal therapeutic abortion.
10. Conjoined twins: morphogenesis of the heart and a review.
Science.gov (United States)
Gilbert-Barness, Enid; Debich-Spicer, Diane; Opitz, John M
2003-08-01
Five cases of conjoined twins have been studied. These included three thoracopagus twins, one monocephalus diprosopus (prosop = face), and one dicephalus dipus dibrachus. The thoracopagus twins were conjoined only from the upper thorax to the umbilicus with a normal foregut. These three cases shared a single complex multiventricular heart, one with a four chambered heart with one atrium and one ventricle belonging to each twin with complex venous and arterial connection; two had a seven chambered heart with four atria and three ventricles. The mono-cephalus diprosopus twins had a single heart with tetralogy of Fallot. The dicephalus twins had two separate axial skeletons to the sacrum, two separate hearts were connected between the right atria with a shared inferior vena cava. Thoracopagus twinning is associated with complex cardiac malformations. The cardiac anlagen in cephalopagus or diprosopus are diverted and divided along with the entire rostral end of the embryonic disc and result in two relatively normal shared hearts. However, in thoracopagus twins the single heart is multiventricular and suggests very early union with fusion of the cardiac anlagen before significant differentiation. Cardiac morphogenesis in conjoined twins therefore appears to depend on the site of the conjoined fusion and the temporal and spatial influence that determines morphogenesis as well as abnormally oriented embryonic axes. Copyright 2003 Wiley-Liss, Inc.
11. Twinning interactions induced amorphisation in ultrafine silicon grains
Energy Technology Data Exchange (ETDEWEB)
Cao, Y. [School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 2052 (Australia); Zhang, L.C., E-mail: [email protected] [School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 2052 (Australia); Zhang, Y. [School of Mechatronics Engineering, Harbin Institute of Technology (China)
2016-03-21
Detailed transmission electron microscopy analysis on a severely deformed Al-Si composite material has revealed that partial dislocation slips and deformation twinning are the major plastic deformation carriers in ultrafine silicon grains. This resembles the deformation twinning activities and mechanisms observed in nano-crystalline face-centred-cubic metallic materials. While deformation twinning and amorphisation in Si were thought unlikely to co-exist, it is observed for the first time that excessive twinning and partial dislocation interactions can lead to localised solid state amorphisation inside ultrafine silicon grains.
12. Pregnancy outcome of monochorionic twins: does amnionicity matter?
Science.gov (United States)
Dias, Thiran; Contro, Elena; Thilaganathan, Basky; Khan, Hina; Zanardini, Cristina; Mahsud-Dornan, Samina; Bhide, Amar
2011-12-01
To compare the fetal loss rate of monochorionic (MC) twin pregnancies according to their amnionicity. A retrospective review of all MC pregnancy outcomes in a tertiary centre. Pregnancy outcomes were compared for monochorionic monoamniotic (MCMA) versus monochorionic diamniotic (MCDA) pregnancies. 29 MCMA and 117 MCDA twin pregnancies were identified. The overall fetal loss rate was significantly higher in MCMA (23/52, 44.2%) compared to MCDA pregnancies (28/233, 12%, Chi squared = 30.03, p fetal survival rate in MCDA twins were significantly higher than in MCMA twins (Log-rank Chi-squared = 27.9, p fetal losses in some MCMA twins. After exclusion of identifiable causes, the difference in fetal survival was not significant in the two groups (Log-rank chi-squared = 0.373, p = .54). The loss rate for MCMA twins is high and occurs mainly due to discordant congenital abnormality, conjoint twins or twin reversed arterial perfusion (TRAP) sequence. Although the fetal loss rate in MCDA is lower than in MCMA pregnancies, the majority of fetal loss in MCDA pregnancies cannot be predicted at the first scan at presentation. The data of this study questions the widespread policy of a difference in the scheduling of elective delivery for MCMA and MCDA twins.
13. Quality of life in unaffected twins discordant for affective disorder
DEFF Research Database (Denmark)
Vinberg, Maj; Bech, Per; Kyvik, Kirsten Ohm
2006-01-01
BACKGROUND: The disability and hardship associated with affective disorder is shared by the family members of affective patients and might affect the family member's quality of life. METHOD: In a cross-sectional, high-risk, case-control study, monozygotic (MZ) and dizygotic (DZ) twins with (High......-Risk twins) and without (the control group/Low-Risk twins) a co-twin history of affective disorder were identified through nationwide registers. The aim of the present study was to investigate the hypothesis that a genetic liability to affective disorder is associated with a lower perception of quality...
14. Two sets of twins with selective mutism: neuropsychological findings.
Science.gov (United States)
Gray, Robert M; Jordan, Catherine M; Ziegler, Richard S; Livingston, Ronald B
2002-03-01
Neuropsychological data are reviewed from two sets of dizygotic twins presenting with selective mutism characterized by situation specific anxiety, extreme passive behavior, lack of responsivity, lack of peer interaction, and a chronic course of selective mutism. Both sets of twins had a history of prematurity and delayed speech development. One set of twins presented with normal intelligence and normal receptive language skills but with expressive language and oral motor sequencing difficulties. The second set of twins presented with Verbal IQ deficits and significant receptive and expressive language deficits. A summary of current conceptualizations regarding etiology and treatment of selective mutism is provided.
15. Temperature dependence of work hardening in sparsely twinning zirconium
International Nuclear Information System (INIS)
Singh, Jaiveer; Mahesh, S.; Roy, Shomic; Kumar, Gulshan; Srivastava, D.; Dey, G.K.; Saibaba, N.; Samajdar, I.
2017-01-01
Fully recrystallized commercial Zirconium plates were subjected to uniaxial tension. Tests were conducted at different temperatures (123 K - 623 K) and along two plate directions. Both directions were nominally unfavorable for deformation twinning. The effect of the working temperature on crystallographic texture and in-grain misorientation development was insignificant. However, systematic variation in work hardening and in the area fraction and morphology of deformation twins was observed with temperature. At all temperatures, twinning was associated with significant near boundary mesoscopic shear, suggesting a possible linkage with twin nucleation. A binary tree based model of the polycrystal, which explicitly accounts for grain boundary accommodation and implements the phenomenological extended Voce hardening law, was implemented. This model could capture the measured stress-strain response and twin volume fractions accurately. Interestingly, slip and twin system hardness evolution permitted multiplicative decomposition into temperature-dependent, and accumulated strain-dependent parts. Furthermore, under conditions of relatively limited deformation twinning, the work hardening of the slip and twin systems followed two phenomenological laws proposed in the literature for non-twinning single-phase face centered cubic materials.
16. [Twin pregnancy as the risk factor for neonatal intraventricular hemorrhage].
Science.gov (United States)
Wieczorek, Aleksandra I; Krasomski, Grzegorz
2015-02-01
The aim of this study was to find the perinatal risk factors of intravenricular hemorrhage in twin neonates. A retrospective analysis of 203 twin pregnancies and deliveries between 2003 and 2009 was performed. Then data according birth state and neonatal complications in 406 twins were analyzed. Twin outcome was compared with the outcome of 105 singletons born at the same time and at the same gestational age as twins. Intraventricular hemorrhage was diagnosed in 116/406 (29%) of twins. IVH was found two times more often in the analyzed group than in singletons born at the same gestational age (29% vs. 18%, p = 0,03). In 96% I and II grade hemorrhage was diagnosed and in 4% III and IV grade hemorrhage in the Papille scale was found. 1) Intraventricular hemorrhage is found more often in twins than in singleton neonates born at the same gestational age. 2) IVH in twins correlate with preterm birth and low birth weight. IVH occur more often in twins with birth weight discordance and with too small maternal weight gain.
17. Increased risk of type 2 diabetes in elderly twins
DEFF Research Database (Denmark)
Poulsen, Pernille; Grunnet, Louise G; Pilgaard, Kasper
2009-01-01
OBJECTIVE: Genetic susceptibility, low birth weight (LBW), and aging are key etiological factors in the development of type 2 diabetes. LBW is common among twins. It is unknown whether twin status per se is associated with risk of type 2 diabetes, and valid concordance rates of type 2 diabetes...... in twins on a lifetime perspective are lacking. RESEARCH DESIGN AND METHODS: A clinical study was done on a population-based cohort of same-sex elderly monozygotic (MZ) and dizygotic (DZ) twins (n = 297) and singleton control subjects (C) (n = 71) including measures of anthropometry and glucose tolerance...
18. Twin reversed arterial perfusion sequence is more common than generally accepted
NARCIS (Netherlands)
Gemert, M.J. van; Wijngaard, J.P. van den; Vandenbussche, F.P.H.A.
2015-01-01
BACKGROUND: Approximately 75% of monozygotic twin pregnancies share one monochorionic placenta where placental anastomoses are virtually always present to connect the two fetoplacental circulations. These anastomoses cause several serious complications such as acardiac twinning. Acardiac twins lack
19. Twin reversed arterial perfusion sequence is more common than generally accepted
NARCIS (Netherlands)
van Gemert, Martin J. C.; van den Wijngaard, Jeroen P. H. M.; Vandenbussche, Frank P. H. A.
2015-01-01
Approximately 75% of monozygotic twin pregnancies share one monochorionic placenta where placental anastomoses are virtually always present to connect the two fetoplacental circulations. These anastomoses cause several serious complications such as acardiac twinning. Acardiac twins lack a functional
20. Neurological impairment in a surviving twin following intrauterine fetal demise of the co-twin: a case study.
Science.gov (United States)
Forrester, K R; Keegan, K M; Schmidt, J W
2013-01-01
It has been established that twin pregnancies are at an increased risk for complications, including the risk of morbidity or mortality for one or both of the infants. Cerebral palsy and other associated neurological deficits also occur at higher rates in twin pregnancies. This report examines two cases of intrauterine demise of one twin with subsequent survival of the co-twin. In both cases, the surviving infant suffered significant neurological sequelae. Impairments observed in these two cases include multicystic encephalomalacia and periventricular leukomalacia as well as the subsequent development of cerebral palsy. This case study explores the predisposing factors, incidence, pathophysiology, consequences, and future research implications of these findings.
1. Birth size and gestational age in opposite-sex twins as compared to same-sex twins
DEFF Research Database (Denmark)
Jelenkovic, Aline; Sund, Reijo; Yokoyama, Yoshie
2018-01-01
It is well established that boys are born heavier and longer than girls, but it remains unclear whether birth size in twins is affected by the sex of their co-twin. We conducted an individual-based pooled analysis of 21 twin cohorts in 15 countries derived from the COllaborative project of Develo......It is well established that boys are born heavier and longer than girls, but it remains unclear whether birth size in twins is affected by the sex of their co-twin. We conducted an individual-based pooled analysis of 21 twin cohorts in 15 countries derived from the COllaborative project....... In girls, birth size was not associated (5 g birth weight; 95% CI -8 to -18 and -0.089 cm birth length; 95% CI -0.202 to 0.025) with the sex of the co-twin. Gestational age was slightly shorter in boy-boy pairs than in boy-girl and girl-girl pairs. When birth size was standardized by gestational age......, the magnitude of the associations was attenuated in boys, particularly for birth weight. In conclusion, boys with a co-twin sister are heavier and longer at birth than those with a co-twin brother. However, these differences are modest and partly explained by a longer gestation in the presence of a co...
2. Estimation of spectral kurtosis
Science.gov (United States)
Sutawanir
2017-03-01
Rolling bearings are the most important elements in rotating machinery. Bearing frequently fall out of service for various reasons: heavy loads, unsuitable lubrications, ineffective sealing. Bearing faults may cause a decrease in performance. Analysis of bearing vibration signals has attracted attention in the field of monitoring and fault diagnosis. Bearing vibration signals give rich information for early detection of bearing failures. Spectral kurtosis, SK, is a parameter in frequency domain indicating how the impulsiveness of a signal varies with frequency. Faults in rolling bearings give rise to a series of short impulse responses as the rolling elements strike faults, SK potentially useful for determining frequency bands dominated by bearing fault signals. SK can provide a measure of the distance of the analyzed bearings from a healthy one. SK provides additional information given by the power spectral density (psd). This paper aims to explore the estimation of spectral kurtosis using short time Fourier transform known as spectrogram. The estimation of SK is similar to the estimation of psd. The estimation falls in model-free estimation and plug-in estimator. Some numerical studies using simulations are discussed to support the methodology. Spectral kurtosis of some stationary signals are analytically obtained and used in simulation study. Kurtosis of time domain has been a popular tool for detecting non-normality. Spectral kurtosis is an extension of kurtosis in frequency domain. The relationship between time domain and frequency domain analysis is establish through power spectrum-autocovariance Fourier transform. Fourier transform is the main tool for estimation in frequency domain. The power spectral density is estimated through periodogram. In this paper, the short time Fourier transform of the spectral kurtosis is reviewed, a bearing fault (inner ring and outer ring) is simulated. The bearing response, power spectrum, and spectral kurtosis are plotted to
3. From monster to twin reversed arterial perfusion: a history of acardiac twins.
Science.gov (United States)
2010-05-01
A human being born without heart and head, i.e., the acardius/acranius malformation, has been described since antiquity. Superstition and fear made it a mystical disorder, a sign of God's wrath. The inquisition ruled that acranic infants should not be baptized and located the soul in the brain. Acardia was not associated with twin gestation until the reports of Mery in 1720 and Winslow in 1740. In 1850, Meckel identified the pathogenetic mechanism as reversed perfusion due to large arterio-arterial and veno-venous anastomoses; he believed the heart would fail to develop or arrest during development, and the acardiac fetus would be maintained by arterial perfusion from the pump twin. In 1859, Claudius articulated that after normal initial development, the heart degenerates when reversed flow in the aorta leads to thrombosis. Today, it is assumed that both mechanisms may exist. With the advent of prenatal ultrasound diagnosis and radiofrequency ablation of the acardiac twin's circulation, it became possible to save the pump twin.
4. Birth weight in opposite sex twins as compared to same sex dizygotic twins
NARCIS (Netherlands)
Orlebeke, J.F.; van Baal, G.C.M.; Boomsma, D.I.; Neeleman, D.
1993-01-01
The question addressed in the present report is whether the large birth weight differences in dizygotic twin pairs of opposite sex (DZos), especially in 'male first' couples - observed by Blickstein and Weissman (Blickstein I, Weissman A. Birth weight discordancy in male-first and female-first pairs
5. Spectrally accurate contour dynamics
International Nuclear Information System (INIS)
Van Buskirk, R.D.; Marcus, P.S.
1994-01-01
We present an exponentially accurate boundary integral method for calculation the equilibria and dynamics of piece-wise constant distributions of potential vorticity. The method represents contours of potential vorticity as a spectral sum and solves the Biot-Savart equation for the velocity by spectrally evaluating a desingularized contour integral. We use the technique in both an initial-value code and a newton continuation method. Our methods are tested by comparing the numerical solutions with known analytic results, and it is shown that for the same amount of computational work our spectral methods are more accurate than other contour dynamics methods currently in use
CERN Document Server
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
7. Initiation and strain compatibility of connected extension twins in AZ31 magnesium alloy at high temperature
Energy Technology Data Exchange (ETDEWEB)
Liu, Xiao, E-mail: [email protected] [Key Laboratory of High Temperature Wear Resistant Materials Preparation Technology of Hunan Province, Hunan University of Science and Technology, Xiangtan, Hunan 411201 (China); State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan 410082 (China); Zhu, Biwu [Key Laboratory of High Temperature Wear Resistant Materials Preparation Technology of Hunan Province, Hunan University of Science and Technology, Xiangtan, Hunan 411201 (China); Huang, Guangjie [College of Materials Science and Engineering, Chongqing University, Chongqing, Chongqing 400045 (China); Li, Luoxing, E-mail: [email protected] [State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan 410082 (China); Xie, Chao [Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211 (China); Tang, Changping [Key Laboratory of High Temperature Wear Resistant Materials Preparation Technology of Hunan Province, Hunan University of Science and Technology, Xiangtan, Hunan 411201 (China)
2016-12-15
Uniaxial compression tests were carried out at 350 °C and a strain rate of 0.3 s{sup −1} on as-extruded AZ31 magnesium alloy samples. At a true strain of − 0.1, extension twin pairs in a grain and twin chains across adjacent grains were detected. The orientation of selected twins and their host grains were determined by electron backscattered diffraction (EBSD) techniques. The Schmid factors (SFs), accommodation strains and geometric compatibility factors (m{sup ′}) were calculated. Analysis of the data indicated that the formation of twin pair and twin chain was related to the SF and m{sup ′}. Regarding to twin chain across adjacent grains, accommodation strain was also involved. The selection of twin variants in twin chain was generally determined by m{sup ′}. When the twins required the operation of pyramidal slip or twinning in adjacent grain, the corresponding connected twins with a relative high m{sup ′} were selected in this adjacent grain. - Highlights: •The formation of paired twins is studied during high temperature deformation. •The initiation of twinning in twin pair and twin chain obeys the Schmid law. •The twin variants' selection in twin chain is related to the geometric compatibility factor. •The accommodation strain plays an important role on the formation of twin chain.
8. Twin correlations of telomere length metrics
DEFF Research Database (Denmark)
Hjelmborg, Jacob B; Dalgård, Christine; Möller, Sören
2015-01-01
variation among adults. A number of studies have estimated the heritability of LTL, but none has assessed the heritability of age-dependent LTL attrition. METHODS: We examined the heritability of LTL dynamics based on a longitudinal evaluation (an average follow-up of 12 years) in 355 monozygotic and 297...... dizygotic same-sex twins (aged 19-64 years at baseline). RESULTS: Heritability of LTL at baseline was estimated at 64% (95% CI 39% to 83%) with 22% (95% CI 6% to 49%) of shared environmental effects. Heritability of age-dependent LTL attrition rate was estimated at 28% (95% CI 16% to 44%). Individually...
9. Reliable actuators for twin rotor MIMO system
Science.gov (United States)
Rao, Vidya S.; V. I, George; Kamath, Surekha; Shreesha, C.
2017-11-01
Twin Rotor MIMO System (TRMS) is a bench mark system to test flight control algorithms. One of the perturbations on TRMS which is likely to affect the control system is actuator failure. Therefore, there is a need for a reliable control system, which includes H infinity controller along with redundant actuators. Reliable control refers to the design of a control system to tolerate failures of a certain set of actuators or sensors while retaining desired control system properties. Output of reliable controller has to be transferred to the redundant actuator effectively to make the TRMS reliable even under actual actuator failure.
10. [Gestational diabetes insipidus during a twin pregnancy].
Science.gov (United States)
De Mesmay, M; Rigouzzo, A; Bui, T; Louvet, N; Constant, I
2013-02-01
Gestational diabetes insipidus is an uncommon clinical disease whose prevalence is approximately two to three pregnancies per 100,000. It may be isolated or associated with preeclampsia. We report a case of gestational diabetes insipidus in a twin pregnancy, originally isolated during two months, and secondarily complicated by HELLP-syndrome. We recall the specific pathophysiology of polyuric-polydipsic syndrome during pregnancy and summarize its various causes. Finally, we discuss the indications, in case of isolated gestational diabetes insipidus, of treatment by dDAVP. Copyright © 2013. Published by Elsevier SAS.
11. Asymptotically Free Natural Supersymmetric Twin Higgs Model
Science.gov (United States)
2018-05-01
Twin Higgs (TH) models explain the absence of new colored particles responsible for natural electroweak symmetry breaking (EWSB). All known ultraviolet completions of TH models require some nonperturbative dynamics below the Planck scale. We propose a supersymmetric model in which the TH mechanism is introduced by a new asymptotically free gauge interaction. The model features natural EWSB for squarks and gluino heavier than 2 TeV even if supersymmetry breaking is mediated around the Planck scale, and has interesting flavor phenomenology including the top quark decay into the Higgs boson and the up quark which may be discovered at the LHC.
12. EXOSAT observations of V471 Tauri - a 9.25 minute white dwarf pulsation and orbital phase dependent X-ray dips
International Nuclear Information System (INIS)
Jensen, K.A.; Swank, J.H.; Petre, P.; Guinan, E.F.; Sion, E.M.; Navy, E. O. Hulburt Center for Space Research, Washington, DC; Villanova Univ., PA)
1986-01-01
New results obtained from a 28 hr continuous observation of V471 Tauri with the EXOSAT satellite are reported. The detection of soft X-ray fluxes from both the white dwarf and the K dwarf, the discovery of a 9.25 minute pulsation from the white dwarf, and the discovery of orbital phase-related soft X-ray dips are discussed. The dips may be correlated with the triangular Lagrangian points of the binary orbit. The X-ray flux from the white dwarf is consistent with thermal models for a white dwarf photosphere with T(eff) of about 35,000 K, log g = 8.0-8.5, and log N(H) = 18.65 + or - 0.2. 25 references
13. Spectral unmixing: estimating partial abundances
CSIR Research Space (South Africa)
Debba, Pravesh
2009-01-01
Full Text Available techniques is complicated when considering very similar spectral signatures. Iron-bearing oxide/hydroxide/sulfate minerals have similar spectral signatures. The study focuses on how could estimates of abundances of spectrally similar iron-bearing oxide...
14. Rectangular spectral collocation
KAUST Repository
Driscoll, Tobin A.; Hale, Nicholas
2015-01-01
Boundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon
15. Vowel Inherent Spectral Change
CERN Document Server
Assmann, Peter
2013-01-01
It has been traditional in phonetic research to characterize monophthongs using a set of static formant frequencies, i.e., formant frequencies taken from a single time-point in the vowel or averaged over the time-course of the vowel. However, over the last twenty years a growing body of research has demonstrated that, at least for a number of dialects of North American English, vowels which are traditionally described as monophthongs often have substantial spectral change. Vowel Inherent Spectral Change has been observed in speakers’ productions, and has also been found to have a substantial effect on listeners’ perception. In terms of acoustics, the traditional categorical distinction between monophthongs and diphthongs can be replaced by a gradient description of dynamic spectral patterns. This book includes chapters addressing various aspects of vowel inherent spectral change (VISC), including theoretical and experimental studies of the perceptually relevant aspects of VISC, the relationship between ar...
16. Gender Differences in Mother-Neonate Twin Interaction.
Science.gov (United States)
Riese, Marilyn L.
To investigate differences in mothers' interaction patterns with their neonate twins based on birth order, relative size at birth, or gender, 37 neonate twins and their mothers were observed during the first 10 minutes of a feeding in a hospital nursery. Time-sampling recordings were made of maternal behaviors related to proximal stimulation,…
17. A twin-family study of general IQ
NARCIS (Netherlands)
Leeuwen, M; van den Berg, Stéphanie Martine; Boomsma, D.I.
2008-01-01
In this paper we assess the presence of assortative mating, gene¿environment interaction and the heritability of intelligence in childhood usinga twin family design with twins, their siblings and parents from 112 families. We evaluate two competing hypotheses about the cause of assortativemating in
18. Genetic influences on dietary variety - Results from a twin study
NARCIS (Netherlands)
Scheibehenne, Benjamin; Todd, Peter M.; van den Berg, Stéphanie Martine; Hatemi, Peter K.; Eaves, Lindon J.; Vogler, Christian
2014-01-01
The heritability of variety seeking in the food domain was estimated from a large sample (N = 5,543) of middle age to elderly monozygotic and dizygotic twins from the “Virginia 30,000” twin study. Different dietary variety scores were calculated based on a semi-quantitative food choice questionnaire
19. Consequences of vanishing twins in IVF/ICSI pregnancies
DEFF Research Database (Denmark)
Pinborg, Anja Bisgaard; Lidegaard, Ojvind; la Cour Freiesleben, Nina
2005-01-01
Spontaneous reductions are a possible cause of the increased morbidity in IVF singletons. The aim of this study was to assess incidence rates of spontaneous reductions in IVF/ICSI twin pregnancies and to compare short- and long-term morbidity in survivors of a vanishing co-twin with singletons...
20. Quantitative XRD analysis of {110} twin density in biotic aragonites.
Science.gov (United States)
Suzuki, Michio; Kim, Hyejin; Mukai, Hiroki; Nagasawa, Hiromichi; Kogure, Toshihiro
2012-12-01
{110} Twin densities in biotic aragonite have been estimated quantitatively from the peak widths of specific reflections in powder X-ray diffraction (XRD) patterns, as well as direct confirmation of the twins using transmission electron microscopy (TEM). Influence of the twin density on the peak widths in the XRD pattern was simulated using DIFFaX program, regarding (110) twin as interstratification of two types of aragonite unit layers with mirrored relationship. The simulation suggested that the twin density can be estimated from the difference of the peak widths between 111 and 021, or between 221 and 211 reflections. Biotic aragonite in the crossed-lamellar microstructure (three species) and nacreous microstructure (four species) of molluscan shells, fish otoliths (two species), and a coral were investigated. The XRD analyses indicated that aragonite crystals in the crossed-lamellar microstructure of the three species contain high density of the twins, which is consistent with the TEM examination. On the other hand, aragonite in the nacre of the four species showed almost no difference of the peak widths between the paired reflections, indicating low twin densities. The results for the fish otoliths were varied between the species. Such variation of the twin density in biotic aragonites may reflect different schemes of crystal growth in biomineralization. Copyright © 2012 Elsevier Inc. All rights reserved.
1. Frequency of twinning in Kwara State, North-Central Nigeria
African Journals Online (AJOL)
O.A. Iyiola
2012-10-05
Oct 5, 2012 ... Results: Frequencies of twin births of 37.60, 35.01, and 35.9 per 1000 deliveries were recorded for. UITH, OHI and ... Recent work showed that the twinning birth rate in the ..... Health Statistics Data Brief, January 2012; No. 80.
2. Determinants of Perinatal Mortality in Twins at Ibadan | Olayemi ...
African Journals Online (AJOL)
Context: Twinning being a very important high-risk condition in our environment requires detailed study. There are several studies reviewing factors in twin perinatal mortality in our environment but there is a need to ascertain the relative contributions of each of these factors. Objectives: To assess the relative contributions of ...
3. Diecephalic thoraco-omphalopagus conjoined twins: case report ...
African Journals Online (AJOL)
We present a case report of conjoined twins discovered at 17 weeks gestation on routine trans-abdominal ultrasound in a 27 year old woman. The twins were joined at the chest and upper abdomen. They shared a heart, liver, sternum and diaphragm. The patient opted for termination of the pregnancy which was performed ...
4. Twin deliveries in Sacred Heart Catholic Hospital Obudu ...
African Journals Online (AJOL)
Background: Twin pregnancy is associated with increased risk of obstetric complications as well as increased perinatal mortality rate. The study aims to determine the incidence and outcome of twin pregnancy in a rural/semi urban hospital which provide secondary level obstetric services in South- south Nigeria. Method: ...
5. A twin-family study of general IQ.
NARCIS (Netherlands)
van Leeuwen, M.; van den Berg, S.M.; Boomsma, D.I.
2008-01-01
In this paper we assess the presence of assortative mating, gene-environment interaction and the heritability of intelligence in childhood using a twin family design with twins, their siblings and parents from 112 families. We evaluate two competing hypotheses about the cause of assortative mating
6. The Prenatal Environment in Twin Studies: A Review on Chorionicity
NARCIS (Netherlands)
Marceau, K.; McMaster, M.T.; Smith, T.F.; Daams, J.G.; van Beijsterveldt, C.E.M.; Boomsma, D.I.; Knopik, V.S.
2016-01-01
A literature search was conducted to identify articles examining the association of chorionicity (e.g., whether twins share a single chorion and thus placenta or have separate chorions/placentas) and genetics, psychiatry/behavior, and neurological manifestations in humans twins and higher-order
7. Management of Conjoined Twins During Neonatal Period | Ali ...
African Journals Online (AJOL)
Background/Purpose: Conjoined twins are rare and complex anomalies of the newborn. It is reported in 1/50.000 to 1/100.000 live births. The aim of the study was to summarize the experiences gained during separation of 5 sets of conjoined twins with presentation of literature review. Materials & Methods: During the period ...
8. Monozygotic twins with CAPN5 autosomal dominant neovascular inflammatory vitreoretinopathy.
Science.gov (United States)
Rowell, Hannah A; Bassuk, Alexander G; Mahajan, Vinit B
2012-01-01
The purpose of this study was to describe the clinical findings in a set of monozygotic twins with autosomal dominant neovascular inflammatory vitreoretinopathy (ADNIV) over a 23-year period. A pair of female twins were examined between 26 and 49 years of age. The concordance and discordance of their clinical features were determined. The CAPN5 gene was sequenced using genomic DNA. Both twins of an affected father demonstrated Stage I ADNIV with mild vitreous cells and a negative b-wave on electroretinography. Genetic analysis confirmed a guanine to thymine nucleotide (c.728G>T, pArg243Leu) mutation in the CAPN5 gene. Over the course of 23 years, each twin progressed to stage III disease, showing posterior uveitis, cystoid macular edema, intraocular fibrosis, early retinal neovascularization, retinal degeneration, and cataract. Disease progression varied moderately between each twin and was asymmetrical between eyes. Twin A had 20/70 and 20/125 in the right and left eye, respectively, and underwent vitrectomy surgery and intravitreal injections with bevacizumab for recurrent cystoid macular edema. Twin B maintained 20/20 and 20/40 in the right and left eye, respectively without intervention. There was asymmetry between the eyes and some discordance in the rate of disease progression in these monozygotic twins with ADNIV. The overall high disease concordance suggests genetic factors play a major role in clinical manifestations in CAPN5 vitreoretinopathy.
9. A twin-case study of developmental number sense impairment
NARCIS (Netherlands)
Davidse, Neeltje J.; de Jong, Maria T.; Shaul, Shelley; Bus, Adriana G
2014-01-01
The current study reports on 9-year-old monozygotic twin girls who fail to make any progress in learning basic mathematics in primary education. We tested the hypothesis that the twins' core maths problems were deficits in number sense that manifested as impairments in approximate and small number
10. Gut microbiomes of Malawian twin pairs discordant for kwashiorkor
Science.gov (United States)
Kwashiorkor, an enigmatic form of severe acute malnutrition, is the consequence of inadequate nutrient intake plus additional environmental insults. To investigate the role of the gut microbiome, we studied 317 Malawian twin pairs during the first 3 years of life. During this time, half of the twin ...
11. Twin boundary cavitation in aged type 304 stainless steel
International Nuclear Information System (INIS)
Sikka, V.K.; Swindeman, R.W.; Brinkman, C.R.
1975-10-01
A transition from grain to twin boundary cavitation was observed in aged-and-creep-tested type 304 stainless steel. Evidence of twin boundary cavitation has also been observed for unaged material under certain test conditions. This same behavior was also found in aged type 316 stainless steel. Several possible reasons have been suggested for the absence of frequently observed grain boundary cavitation
12. Case of twin pregnancy complicated by idiopathic thrombocytopenic ...
African Journals Online (AJOL)
2016-05-09
May 9, 2016 ... Idiopathic thrombocytopenic purpura (ITP) is an acquired thrombocytopenia without other clear cause of thrombocytopenia. It is not common in a singleton pregnancy and less common in twin pregnancy. We report a 33‑year‑old ITP pluripara whose first pregnancy was uneventful. She carried twin ...
13. EXTENDED MAGNETOSPHERES IN PRE-MAIN-SEQUENCE EVOLUTION: FROM T TAURI STARS TO THE BROWN DWARF LIMIT
Energy Technology Data Exchange (ETDEWEB)
Gomez de Castro, Ana I.; Marcos-Arenal, Pablo [Grupo de Investigacion Complutense AEGORA, Universidad Complutense de Madrid, 28040 Madrid (Spain)
2012-04-20
Low-mass pre-main-sequence stars, i.e., T Tauri stars (TTSs), strongly radiate at high energies, from X-rays to the ultraviolet (UV). This excess radiation with respect to main-sequence cool stars (MSCSs) is associated with the accretion process, i.e., it is produced in the extended magnetospheres, in the accretion shocks on the stellar surface, and in the outflows. Although evidence of accretion shocks and outflow contribution to the high-energy excess have been recently addressed, there is not an updated revision of the magnetospheric contribution. This article addresses this issue. The UV observations of the TTSs in the well-known Taurus region have been analyzed together with the XMM-Newton observations compiled in the XEST survey. For the first time the high sensitivity of the Hubble Space Telescope UV instrumentation has allowed measurement of the UV line fluxes of TTSs to M8 type. UV- and X-ray-normalized fluxes have been determined to study the extent and properties of the TTS magnetospheres as a class. They have been compared with the atmospheres of the MSCSs. The main results from this analysis are (1) the normalized fluxes of all the tracers are correlated; this correlation is independent of the broad mass range and the hardness of the X-ray radiation field; (2) the TTS correlations are different than the MSCS correlations; (3) there is a very significant excess emission in O I in the TTSs compared with MSCSs that seems to be caused by recombination radiation from the disk atmosphere after photoionization by extreme UV radiation; the Fe II/Mg II recombination continuum has also been detected in several TTSs and most prominently in AA Tau; and (4) the normalized flux of the UV tracers anticorrelates with the strength of the X-ray flux, i.e., the stronger the X-ray surface flux is, the weaker the observed UV flux. This last behavior is counterintuitive within the framework of stellar dynamo theory and suggests that UV emission can be produced in the
14. Spectrally selective glazings
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-08-01
Spectrally selective glazing is window glass that permits some portions of the solar spectrum to enter a building while blocking others. This high-performance glazing admits as much daylight as possible while preventing transmission of as much solar heat as possible. By controlling solar heat gains in summer, preventing loss of interior heat in winter, and allowing occupants to reduce electric lighting use by making maximum use of daylight, spectrally selective glazing significantly reduces building energy consumption and peak demand. Because new spectrally selective glazings can have a virtually clear appearance, they admit more daylight and permit much brighter, more open views to the outside while still providing the solar control of the dark, reflective energy-efficient glass of the past. This Federal Technology Alert provides detailed information and procedures for Federal energy managers to consider spectrally selective glazings. The principle of spectrally selective glazings is explained. Benefits related to energy efficiency and other architectural criteria are delineated. Guidelines are provided for appropriate application of spectrally selective glazing, and step-by-step instructions are given for estimating energy savings. Case studies are also presented to illustrate actual costs and energy savings. Current manufacturers, technology users, and references for further reading are included for users who have questions not fully addressed here.
15. Heredity In Sarcoidosis - A Registry-Based Twin Study
DEFF Research Database (Denmark)
Sverrild, Asger; Backer, Vibeke; Kyvik, Kirsten Ohm
2008-01-01
BACKGROUND: Sarcoidosis is a multiorgan, granulomatous, inflammatory disease with unknown aetiology. Familial clustering of cases and ethnic variation in the epidemiology suggests a genetic influence on the disease susceptibility. AIM: This paper reports twin concordance and heritability estimates...... of sarcoidosis in order to assess the overall contribution of genetic factors to the disease susceptibility. METHODS: Monozygotic and dizygotic twins enrolled in either the Danish or the Finnish population-based, national Twin Cohorts (61,662 pairs in total) were linked to diagnostic information on sarcoidosis.......012. Compared to the general population we found an 80-fold increased risk of developing sarcoidosis in co-twins of affected monozygotic brothers or sisters. The increased risk in dizygotic twins was on the other hand only 7-fold. Aetiological model fitting gave a heritability of sarcoidosis of 0.66 (95% CI 0...
16. Twinning in muskox and the cytogenetic investigation of a freemartin
Directory of Open Access Journals (Sweden)
N. J. Reindl
1993-12-01
Full Text Available The occurrence of twinning has been documented for muskox in both wild and captive populations. Of two known captive twin births only one set survived beyond 120 days. In both cases the twins were male-female pairs and both females showed abnormal sexual development. Two sets of stillborn twins have also been recorded. All four stillborn fetuses were female and none showed anomalies of the reproductive tract upon post-mortem examination. Blood cultures from the surviving male and female twins revealed that both were chimeric, indicating the admixture of fetal blood. Fibroblast cultures were normal for the respective sex of each individual. The freemartin heifer had anatomical abnormalities of the clitoris as well as the secondary sex characteristics of a male.
17. Cognitive function in unaffected twins discordant for affective disorder
DEFF Research Database (Denmark)
Christensen, Maj Vinberg; Kyvik, Kirsten Ohm; Kessing, Lars Vedel
2006-01-01
. Cognitive performance of 203 High-Risk and Low-Risk twins was compared. RESULTS: Healthy twins discordant for unipolar disorder showed lower performance on almost all measures of cognitive function: selective and sustained attention, executive function, language processing and working and declarative memory...... impairment found seemed to be related to genetic liability, as the MZ High-Risk twins showed significant impairment on selective and sustained attention, executive function, language processing and working and declarative memory, whereas the DZ High-Risk twins presented with significantly lower scores only......, and also after adjustment for demographic variables, subclinical symptoms and minor psychopathology. Healthy twins discordant for bipolar disorder showed lower performance on tests measuring episodic and working memory, also after adjustment for the above-mentioned covariables. The discrete cognitive...
18. Disease-Concordant Twins Empower Genetic Association Studies
DEFF Research Database (Denmark)
Tan, Qihua; Li, Weilong; Vandin, Fabio
2017-01-01
and ordinary healthy samples as controls. We examined the power gain of the twin-based design for various scenarios (i.e., cases from monozygotic and dizygotic twin pairs concordant for a disease) and compared the power with the ordinary case-control design with cases collected from the unrelated patient...... concordant for a disease, should confer increased power in genetic association analysis because of their genetic relatedness. We conducted a computer simulation study to explore the power advantage of the disease-concordant twin design, which uses singletons from disease-concordant twin pairs as cases...... population. Simulation was done by assigning various allele frequencies and allelic relative risks for different mode of genetic inheritance. In general, for achieving a power estimate of 80%, the sample sizes needed for dizygotic and monozygotic twin cases were one half and one fourth of the sample size...
19. Aspects of narcissism and symbiosis, or, essential neurosis of twins.
Science.gov (United States)
Kahn, Charlotte
2012-06-01
Following a brief introduction I address the relationships of twins from five different perspectives: the Intimate Connection, the Mirror Image and Complementarity, Object- and Self-Representation, Self and Object or Rivalry, and Intersubjective Communication. This approach attempts to understand twin relationships and the individual development of twins in terms of their intense mutual dependence, akin to infantile symbiosis, and in terms of narcissism. In their similarity to each other, twins may choose each other as love objects even as they see themselves in the other. That is, a twin may "love what he himself is" or "someone who was once part of himself." This "type of object-choice … must be termed 'narcissistic'" (Freud, 1914, pp. 90, 88). Such "cathexis of an undifferentiated self-object" is considered to be "primary narcissism" (Burstein, 1977, p. 103). Hoffer (1952) describes primary narcissism as "the lack of all qualities discriminating between self and not-self, inside and outside" (p. 33).
20. Salivary cortisol in unaffected twins discordant for affective disorder
DEFF Research Database (Denmark)
Vinberg, Maj; Bennike, Bente; Kyvik, Kirsten Ohm
2008-01-01
. In conclusion, a high genetic liability to affective disorder was associated with a higher evening cortisol level, but not with awakening cortisol level. Future prospective family, high-risk and twin studies are needed to decide whether abnormalities in the HPA axis can be identified as an endophenotype......Dysfunction in the hypothalamic-pituitary-adrenal (HPA) axis has been proposed as a biological endophenotype for affective disorders. In the present study the hypothesis that a high genetic liability to affective disorder is associated with higher cortisol levels was tested in a cross......-sectional high-risk study. Healthy monozygotic (MZ) and dizygotic (DZ) twins with (High-Risk twins) and without (Low-Risk twins) a co-twin history of affective disorder were identified through nationwide registers. Awakening and evening salivary cortisol levels were compared between the 190 High- and Low...
1. Seasonality in twin birth rates, Denmark, 1936-84.
Science.gov (United States)
Bonnelykke, B; Søgaard, J; Nielsen, J
1987-12-01
A study was made of seasonality in twin birth rate in Denmark between 1977 and 1984. We studied all twin births (N = 45,550) in all deliveries (N = 3,679,932) during that period. Statistical analysis using a simple harmonic sinusoidal model provided no evidence for seasonality. However, sequential polynomial analysis disclosed a significant fit to a fifth order polynomial curve with peaks in twin birth rates in May-June and December, along with troughs in February and September. A falling trend in twinning rate broke off in Denmark around 1970, and from 1970 to 1984 an increasing trend was found. The results are discussed in terms of possible environmental influences on twinning.
DEFF Research Database (Denmark)
Christensen, Kaare; Petersen, Inge; Skytthe, Axel
2006-01-01
deviations for twins and singletons (8.02 v 8.02 and 1.05 v 1.06) despite the twins weighing on average 908 g (95% confidence interval 886 to 930 g) less than the singletons at birth. Controlling for birth weight, gestational age at birth, age at test, and parents' age and education confirmed the similarity......OBJECTIVES: To determine whether twins in recent cohorts show similar academic performance in adolescence to singletons and to test the effect of birth weight on academic performance in twins and singletons. DESIGN: Follow-up study. SETTING: Denmark. PARTICIPANTS: All twins (n=3411) and a 5% random...... sample of singletons (n=7796) born in Denmark during 1986-8. MAIN OUTCOME MEASURES: Test scores in ninth grade (age 15 or 16), birth weight, gestational age at birth, parents' age, and parents' education. RESULTS: Ninth grade test scores were normally distributed, with almost identical mean and standard...
3. Genetic susceptibility to bilateral tinnitus in a Swedish twin cohort
DEFF Research Database (Denmark)
Maas, Iris Lianne; Brüggemann, Petra; Requena, Teresa
2017-01-01
PURPOSE: Genetic contributions to tinnitus have been difficult to determine due to the heterogeneity of the condition and its broad etiology. Here, we evaluated the genetic and nongenetic influences on self-reported tinnitus from the Swedish Twin Registry (STR). METHODS: Cross-sectional data from...... the STR was obtained. Casewise concordance rates (the risk of one twin being affected given that his/her twin partner has tinnitus) were compared for monozygotic (MZ) and dizygotic (DZ) twin pairs (N = 10,464 concordant and discordant twin pairs) and heritability coefficients (the proportion of the total...... variance attributable to genetic factors) were calculated using biometrical model fitting procedures. RESULTS: Stratification of tinnitus cases into subtypes according to laterality (unilateral versus bilateral) revealed that heritability of bilateral tinnitus was 0.56; however, it was 0.27 for unilateral...
4. Conjoined Twins: Philosophical Problems and Ethical Challenges.
Science.gov (United States)
2016-02-01
5. The spontaneous ℤ_2 breaking Twin Higgs
International Nuclear Information System (INIS)
Beauchesne, Hugues; Earl, Kevin; Grégoire, Thomas
2016-01-01
The Twin Higgs model seeks to address the little hierarchy problem by making the Higgs a pseudo-Goldstone of a global SU(4) symmetry that is spontaneously broken to SU(3). Gauge and Yukawa couplings, which explicitly break SU(4), enjoy a discrete ℤ_2 symmetry that accidentally maintains SU(4) at the quadratic level and therefore keeps the Higgs light. Contrary to most beyond the Standard Model theories, the quadratically divergent corrections to the Higgs mass are cancelled by a mirror sector, which is uncharged under the Standard Model groups. However, the Twin Higgs with an exact ℤ_2 symmetry leads to equal vevs in the Standard Model and mirror sectors, which is phenomenologically unviable. An explicit ℤ_2 breaking potential must then be introduced and tuned against the SU(4) breaking terms to produce a hierarchy of vevs between the two sectors. This leads to a moderate but non-negligible tuning. We propose a model to alleviate this tuning, without the need for an explicit ℤ_2 breaking sector. The model consists of two SU(4) fundamental Higgses, one whose vacuum preserves ℤ_2 and one whose vacuum breaks it. As the interactions between the two Higgses are turned on, the ℤ_2 breaking is transmitted from the broken to the unbroken sector and a small hierarchy of vevs is naturally produced. The presence of an effective tadpole and feedback between the two Higgses lead to a sizable improvement of the tuning. The resulting Higgs boson is naturally very Standard Model like.
6. Secular trends in gestational age and birthweight in twins.
Science.gov (United States)
Gielen, M; van Beijsterveldt, C E M; Derom, C; Vlietinck, R; Nijhuis, J G; Zeegers, M P A; Boomsma, D I
2010-09-01
In recent decades, the overall rate of preterm births has increased. The aim of the present study was to examine whether this trend is also seen for multiple gestations. More specifically, we examined if there has been a decrease in gestational age for live born monozygotic (MZ) and dizygotic (DZ) twins and if there has been a simultaneous change in birthweight. The contributions of fertility treatments and Caesarean sections were taken into consideration. All analyses were carried out in two large European twin cohorts. Cross-sectional study of 6310 live born twin pairs, born between 1964-2007, from the Belgian East Flanders Prospective Twin Survey and 14,712 twin pairs, born between 1990-2006, from the Netherlands Twin Register. Multiple regression analyses were performed with gestational age as outcome variable, and multilevel analysis with birthweight as outcome variable. All analyses were performed with and without adjustment for zygosity, parity, maternal age, mode of conception and delivery and, for the analyses of birthweight, gestational age. Gestational age decreased in a linear fashion from 1964 to 2007 with a decrease of 0.25 days per year in a similar way for MZ and DZ twins. Changes in birthweight depended on gestational age: up to 32 weeks, birthweight decreased and after 32 weeks birthweight increased. The frequency of infertility treatment and Caesarean sections, primiparity and advanced maternal age increased over the years, but none of these factors influenced the secular trends in gestational age and birthweight. The decrease in gestational age and change in birthweight in twins are sources of concern, especially for very preterm twins, for whom birthweight decreased. For twins born after 32 weeks, an increase in birthweight was observed and this is very likely the explanation for the decrease in gestational age.
7. Trends in the obstetric features and management of twin pregnancies.
LENUS (Irish Health Repository)
Smith, K E
2010-03-01
There are no reports outlining the trends in obstetric features and clinical management of twin pregnancies in an Irish obstetric population. The aim of this study was to investigate these factors for all twin pregnancies delivered during the 19 year period between 1989 and 2007, at Galway University Hospital (GUH). There were 52,199 infants delivered at GUH, of which 1594 infants (3.05% of births) were twins, related to 797 twin pregnancies. The overall incidence of twin pregnancies was 1.52%, increasing from 0.8%-1.0% in the early years of the study to 1.7-1.8% in the latter years of the study (P<0.001). There was a significant increase in incidence of twins born to mothers aged 30-39 years, alongside a significant reduction to mothers aged 20-29 years (P<0.01). The caesarean section rate overall was 41.5% (331\\/797), of which 54% (n=179) were elective, and 46% (n=152) were emergency, representing an emergency caesarean section rate of 19.1% of all twin pregnancies, and of 24.6% after exclusion of elective caesarean sections. The caesarean section rate for twins increased from 30% in 1989 to greater than 50% in the latter years of the study (P<0.01), related largely to a significant increase in elective caesarean sections (P<0.01). The combined vaginal-caesarean delivery rate was remarkably low at 0.75% of all twin pregnancies, and 1% after exclusion of elective caesarean sections. The preterm delivery rates were 4.1% (<32 weeks), and 16.3% (<36 weeks), with an overall perinatal mortality rate of 37 per 1000. These findings highlight the altered demographic and clinical aspects of twin pregnancies in an Irish obstetric population.
8. Recurrent twin-twin transfusion syndrome after selective fetoscopic laser photocoagulation: a systematic review of the literature.
LENUS (Irish Health Repository)
Walsh, C A
2012-11-01
Selective fetoscopic laser photocoagulation (SFLP) is now the treatment of choice for twin-twin transfusion syndrome (TTTS). The incidence of recurrent TTTS following SFLP has been inconsistently reported across different studies. We performed a systematic review of TTTS recurrence following SFLP.
9. Spatio-spectral characterization of twin-beam states of light for quantum state engineering
Czech Academy of Sciences Publication Activity Database
Allevi, A.; Lamperti, M.; Jedrkiewicz, O.; Galinis, J.; Machulka, R.; Haderka, Ondřej; Peřina Jr., J.; Bondani, M.
2014-01-01
Roč. 12, 7-8 (2014), s. 1560027 ISSN 0219-7499 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : parametric down conversion * coherence properties * photon statistics Subject RIV: BH - Optics, Masers, Lasers Impact factor: 0.877, year: 2014
10. Neurodevelopmental outcome at 2 years in twin-twin transfusion syndrome survivors randomized for the Solomon trial.
Science.gov (United States)
van Klink, Jeanine M M; Slaghekke, Femke; Balestriero, Marina A; Scelsa, Barbara; Introvini, Paola; Rustico, Mariangela; Faiola, Stefano; Rijken, Monique; Koopman, Hendrik M; Middeldorp, Johanna M; Oepkes, Dick; Lopriore, Enrico
2016-01-01
The preferred treatment for twin-twin transfusion syndrome is fetoscopic laser coagulation of inter-twin vascular anastomoses on the monochorionic placenta. Severe postoperative complications can occur when inter-twin vascular anastomoses remain patent including twin-anemia polycythemia sequence or recurrent twin-twin transfusion syndrome. To minimize the occurrence of residual anastomoses, a modified laser surgery technique, the Solomon technique, was developed in which the entire vascular equator is coagulated. In the Solomon randomized controlled trial (NTR1245), the Solomon technique was associated with a significant reduction in twin-anemia polycythemia sequence and recurrence of twin-twin transfusion syndrome when compared with the standard laser surgery technique. Although a significant improvement in perinatal outcome was shown after the Solomon technique, the clinical importance should also be ascertained with long-term follow-up evaluation of the surviving children. The purpose of this study was to compare the long-term neurodevelopmental outcome in surviving children with twin-twin transfusion syndrome who were included in the Solomon randomized trial and treated with either the Solomon technique or standard laser surgery technique. Routine standardized follow-up evaluation in survivors, at least 2 years after the estimated date of delivery, was performed at 2 of the 5 centers that participated in the Solomon trial: Buzzi Hospital Milan (Italy) and Leiden University Medical Center (The Netherlands). The primary outcome of this follow-up study was survival without long-term neurodevelopmental impairment at age 2 years. Neurodevelopmental impairment was defined as cerebral palsy, cognitive and/or motor development score of neurodevelopmental impairment) was detected in 95 of 141 cases (67%) in the Solomon group and in 99 of 146 cases (68%) in the standard group (P = .92). Neurodevelopmental impairment in long-term survivors who were included for follow
11. Does anemia-polycythemia complicating twin-twin transfusion syndrome affect outcome after fetoscopic laser surgery?
Science.gov (United States)
Donepudi, R; Papanna, R; Snowise, S; Johnson, A; Bebbington, M; Moise, K J
2016-03-01
Twin anemia-polycythemia sequence (TAPS) can occur as a unique disease or as a complication of twin-twin transfusion syndrome (TTTS). Middle cerebral artery (MCA) Doppler studies are not currently part of the routine evaluation of monochorionic twins since they are not used in the Quintero staging system. As such, the true incidence of TAPS is unknown. We aimed to compare the characteristics and outcomes of twin pregnancies with TTTS complicated by spontaneous anemia-polycythemia vs those with TTTS alone. This was a secondary analysis of data collected prospectively from a cohort of 156 consecutive patients undergoing fetoscopic laser surgery for TTTS, between October 2011 and August 2014. TAPS was defined as discordance in the preoperative MCA peak systolic velocity (PSV), with one twin fetus having MCA-PSV ≤ 1.0 multiples of the median (MoM) and the other having MCA-PSV ≥ 1.5 MoM. Maternal demographics as well as preoperative, operative and postoperative variables were analyzed. Included in the final analysis were 133 patients with complete records: 11 cases with TTTS with anemia-polycythemia and 122 cases with TTTS alone. There was no difference in maternal body mass index, gestational age (GA) at procedure, rate of preterm prelabor rupture of membranes or GA at delivery between the two groups. Patients with TTTS and anemia-polycythemia were more likely to be older (P = 0.03) and parous (P = 0.04) and had a significantly lower number of placental anastomoses (P = 0.01). The dual live-birth rate was similar for both groups (P = 0.76). Cases of TTTS with anemia-polycythemia were more likely to be found in parous and older women and were characterized by fewer vascular anastomoses. TTTS with anemia-polycythemia was not associated with worse perinatal outcome after laser therapy. Copyright © 2015 ISUOG. Published by John Wiley & Sons Ltd. Copyright © 2015 ISUOG. Published by John Wiley & Sons Ltd.
12. Do MZ twins have discordant experiences of friendship? A qualitative hypothesis-generating MZ twin differences study
Science.gov (United States)
Moran, Nicola; Plomin, Robert
2017-01-01
Using a qualitative monozygotic (MZ) twin differences design we explored whether adolescent MZ twins report discordant peer relationships and, if so, whether they perceive them as causes, consequences or correlates of discordant behaviour. We gathered free-response questionnaire data from 497 families and conducted in-depth telephone interviews with 97 of them. Within this dataset n = 112 families (23% of the sample) described discordant peer relationships. Six categories of discordance were identified (peer victimisation, peer rejection, fewer friends, different friends, different attitudes to friendship and dependence on co-twin). Participants described peer relationship discordance arising as a result of chance occurrences, enhanced vulnerability in one twin or discordant behaviour. Consequences of discordant peer relationships were seen as discordance in self-confidence, future plans, social isolation, mental health and interests. In all cases the twin with worse peer experiences was seen as having a worse outcome. Specific hypotheses are presented. PMID:28727730
13. The neonatal outcome in twin versus triplet and quadruplet pregnancies
Directory of Open Access Journals (Sweden)
Fatemeh Nasseri
2009-02-01
Full Text Available
• BACKGROUND: To assess the risk of neonatal mortality and morbidity in twin, triplet and quadruplet pregnancies.
• METHODS: In a retrospective study, the neonatal outcome of all twin, triplet and quadruplet gestations delivered from October 2001 to September 2006 was reviewed. The neonatal outcome of triples and quadruplets was compared with a matched group of twins for gestational age.
• RESULTS: During a 5-year period, 511 sets of twin pregnancies, 42 sets of triplet and 5 sets of quadruplet pregnancies were studied. The mean of gestational age for twins, triplets and quadruplets were 33.92 ± 3.5 weeks, 30.92 ± 3.8 weeks and 31.60 ± 2.0 weeks, respectively, (P = 0.0001. Triplets and quadruplets weighed less than twins, (P = 0.0001. Neonatal mortality was 13.5% for twins, 26.8% for triplets and 30% for quadruplets. In vitro fertilization, use of ovulation induction agents, and cesarean delivery in the women with triplet and quadruplet were significantly higher than in those with twin pregnancies, (P = 0.0001. The mean age of mothers with triplets and quadruplets was significantly higher than with twins (P = 0.026. There was not a significant difference in respiratory and non-respiratory short outcomes between triplets, quadruplets and twins when matched for gestational age. Apgar score at 1 and 5 minutes was significantly lower in triplets and quadruplets than twins. There was no influence of birth order on neonatal mortality of triplet pregnancy. Neonatal mortality of triplet births was significantly decreased over the 5 years of the study period.
• CONCLUSIONS: Triplets and quadruplets have a similar neonatal outcome as twins when matched for gestational age. There is no influence of birth on the neonatal mortality of triplet pregnancy. It appears that outcome is mainly dependent on gestational age.
• KEYWORDS: Neonatal
• Successful fetoscopic laser coagulation for twin-to-twin transfusion syndrome under local anaesthesia.
LENUS (Irish Health Repository)
Cooley, S
2011-06-01
A review of the efficacy and outcome of fifteen fetoscopic laser ablations under local anaesthesia for twin to twin transfusion syndrome (TTTS) in the National Maternity Hospital Dublin was undertaken. The mean gestation at laser was 19.7 weeks (range 16-25 weeks) with a mean gestation at delivery of 29.1 weeks (range 20-35 weeks). The overall liveborn birth rate was 79% (22 infants) and one pregnancy was still ongoing. There were four neonatal deaths secondary to complications of prematurity. The surviving eighteen infants (64%) undergo regular paediatric review. The procedure was performed successfully in all cases with local anaesthesia. In no case was there maternal discomfort that warranted the procedure to be abandoned and good visual access of the vascular anastamoses was obtained in all cases. Local anaesthesia therefore offers a safe effective anaesthetic option for fetoscopic laser coagulation in monochorionic pregnancies complicated by TTTS.
• BayesTwin: An R Package for Bayesian Inference of Item-Level Twin Data
Directory of Open Access Journals (Sweden)
Inga Schwabe
2017-11-01
Full Text Available BayesTwin is an open-source R package that serves as a pipeline to the MCMC program JAGS to perform Bayesian inference on genetically-informative hierarchical twin data. Simultaneously to the biometric model, an item response theory (IRT measurement model is estimated, allowing analysis of the raw phenotypic (item-level data. The integration of such a measurement model is important since earlier research has shown that an analysis based on an aggregated measure (e.g., a sum-score based analysis can lead to an underestimation of heritability and the spurious finding of genotype-environment interactions. The package includes all common biometric and IRT models as well as functions that help plot relevant information or determine whether the analysis was performed well. Funding statement: Partly funded by the PROO grant 411-12-623 from the Netherlands Organisation for Scientific Research (NWO.
• The ethics of separating conjoined twins: two arguments against.
Science.gov (United States)
Kallberg, Luke
2018-02-01
I argue that the separation of conjoined twins in infancy or early childhood is unethical (rare exceptions aside). Cases may be divided into three types: both twins suffer from lethal abnormalities, only one twin has a lethal abnormality, or neither twin does. In the first kind of case, there is no reason to separate, since both twins will die regardless of treatment. In the third kind of case, I argue that separation at an early age is unethical because the twins are likely to achieve an irreplaceably good quality of life-the goods of conjoinment-that separation takes away. Evaluation of this possibility requires maturation past early childhood. Regarding the second type, I point out that with conceivable but unrecorded exceptions, these cases will consistently involve sacrifice separation. I present an argument that sacrifice separation is unethical, but in some cases a moral dilemma may exist in which separation and refraining from separation are both unethical. Perhaps in such cases a decision can be made on non-moral grounds; however, the possibility of such a decision serves not to mitigate but to underscore the fact that the separation is unethical. My conclusion, which applies to all three types of cases, is that it is unethical to separate conjoined twins before their developing personalities give some reliable indication as to whether they desire separation and whether they will achieve those goods of conjoinment.
• Has the "Equal Environments" assumption been tested in twin studies?
Science.gov (United States)
Eaves, Lindon; Foley, Debra; Silberg, Judy
2003-12-01
A recurring criticism of the twin method for quantifying genetic and environmental components of human differences is the necessity of the so-called "equal environments assumption" (EEA) (i.e., that monozygotic and dizygotic twins experience equally correlated environments). It has been proposed to test the EEA by stratifying twin correlations by indices of the amount of shared environment. However, relevant environments may also be influenced by genetic differences. We present a model for the role of genetic factors in niche selection by twins that may account for variation in indices of the shared twin environment (e.g., contact between members of twin pairs). Simulations reveal that stratification of twin correlations by amount of contact can yield spurious evidence of large shared environmental effects in some strata and even give false indications of genotype x environment interaction. The stratification approach to testing the equal environments assumption may be misleading and the results of such tests may actually be consistent with a simpler theory of the role of genetic factors in niche selection.
• CRISS power spectral density
International Nuclear Information System (INIS)
Vaeth, W.
1979-04-01
The correlation of signal components at different frequencies like higher harmonics cannot be detected by a normal power spectral density measurement, since this technique correlates only components at the same frequency. This paper describes a special method for measuring the correlation of two signal components at different frequencies: the CRISS power spectral density. From this new function in frequency analysis, the correlation of two components can be determined quantitatively either they stem from one signal or from two diverse signals. The principle of the method, suitable for the higher harmonics of a signal as well as for any other frequency combinations is shown for the digital frequency analysis technique. Two examples of CRISS power spectral densities demonstrates the operation of the new method. (orig.) [de
• Parametric Explosion Spectral Model
Energy Technology Data Exchange (ETDEWEB)
Ford, S R; Walter, W R
2012-01-19
Small underground nuclear explosions need to be confidently detected, identified, and characterized in regions of the world where they have never before occurred. We develop a parametric model of the nuclear explosion seismic source spectrum derived from regional phases that is compatible with earthquake-based geometrical spreading and attenuation. Earthquake spectra are fit with a generalized version of the Brune spectrum, which is a three-parameter model that describes the long-period level, corner-frequency, and spectral slope at high-frequencies. Explosion spectra can be fit with similar spectral models whose parameters are then correlated with near-source geology and containment conditions. We observe a correlation of high gas-porosity (low-strength) with increased spectral slope. The relationship between the parametric equations and the geologic and containment conditions will assist in our physical understanding of the nuclear explosion source.
• Photovoltaic spectral responsivity measurements
Energy Technology Data Exchange (ETDEWEB)
Emery, K.; Dunlavy, D.; Field, H.; Moriarty, T. [National Renewable Energy Lab., Golden, CO (United States)
1998-09-01
This paper discusses the various elemental random and nonrandom error sources in typical spectral responsivity measurement systems. The authors focus specifically on the filter and grating monochrometer-based spectral responsivity measurement systems used by the Photovoltaic (PV) performance characterization team at NREL. A variety of subtle measurement errors can occur that arise from a finite photo-current response time, bandwidth of the monochromatic light, waveform of the monochromatic light, and spatial uniformity of the monochromatic and bias lights; the errors depend on the light source, PV technology, and measurement system. The quantum efficiency can be a function of he voltage bias, light bias level, and, for some structures, the spectral content of the bias light or location on the PV device. This paper compares the advantages and problems associated with semiconductor-detector-based calibrations and pyroelectric-detector-based calibrations. Different current-to-voltage conversion and ac photo-current detection strategies employed at NREL are compared and contrasted.
1. Investigating Unique Environmental Influences of Parenting Practices on Youth Anxiety: A Monozygotic Twin Differences Study
Science.gov (United States)
Chen, Jie; Yu, Jing; Zhang, Jianxin
2016-01-01
The associations between parenting practices and adolescent anxiety symptoms were examined in both individual and monozygotic (MZ) twin differences levels. Participants were 804 pairs of Chinese MZ adolescent twins aged 10-18 years (M = 13.57, SD = 2.67, 52% females). Twins' anxiety symptoms were assessed by self- and parent-reports. Twins also…
2. The Heritability of Dry Eye Disease in a Female Twin Cohort
NARCIS (Netherlands)
Vehof, Jelle; Wang, Bin; Kozareva, Diana; Hysi, Pirro G.; Snieder, Harold; Hammond, Christopher J.
PURPOSE. We estimated the relative importance of genes and environment in dry eye disease (DED) using a classic twin study. METHODS. A large sample of 3930 female monozygotic and dizygotic twins from the UK Adult Twin Registry (TwinsUK) was questioned about the presence of a DED diagnosis and about
3. Twin's Birth-Order Differences in Height and Body Mass Index From Birth to Old Age
DEFF Research Database (Denmark)
Yokoyama, Yoshie; Jelenkovic, Aline; Sund, Reijo
2016-01-01
of age was 397,466. As expected, first-born twins had greater birth weight than second-born twins. With respect to height, first-born twins were slightly taller than second-born twins in childhood. After adjusting the results for birth weight, the birth order differences decreased and were no longer...
4. Strain rate sensitivity and evolution of dislocations and twins in a twinning-induced plasticity steel
International Nuclear Information System (INIS)
Liang, Z.Y.; Wang, X.; Huang, W.; Huang, M.X.
2015-01-01
The present work investigated the effect of strain rates (10 −3 to 10 3 s −1 ) on the deformation behaviour of a twinning-induced plasticity (TWIP) steel. The strain rate sensitivity was studied in terms of instantaneous strain rate sensitivity (ISRS) and strain rate sensitivity of work-hardening (SRSW). While ISRS concerns the instantaneous flow stress change upon strain rate jump, SRSW deals with the subsequent modification in microstructure evolution, i.e. change of work-hardening rate. The present TWIP steel demonstrates a positive ISRS which remains stable during deformation and a negative SRSW, i.e. lower work-hardening rate at higher strain rate. Synchrotron X-ray diffraction experiments indicate that the negative SRSW should be attributed to the suppression of dislocations and deformation twins at high strain rate. This unexpected finding is different to conventional face-centred cubic (fcc) metals which generally show enhanced work-hardening rate at higher strain rate. A constitutive model which is strain rate- and temperature-dependent is developed to explain the stable ISRS and the negative SRSW. The modelling results reveal that the stable ISRS should be attributed to the thermally-activated dislocation motion dominated by interstitial carbon atoms and the negative SRSW should be due to the suppression of the dislocations and deformation twins caused by the adiabatic heating associated with high strain rate deformation
5. Twin-twin transfusion syndrome: neurodevelopment of infants treated with laser surgery
Directory of Open Access Journals (Sweden)
Denise Campos
2016-04-01
Full Text Available ABSTRACT Objective To assess the neurodevelopmental functions of survivors of twin-twin transfusion syndrome (TTTS treated by fetoscopic laser coagulation (FLC, during the first year of life, comparing them to a control group; and to verify the influence of specific variables on neurodevelopment. Method This was a prospective, longitudinal study. The sample comprised 33 monochorionic diamniotic twins who underwent FLC for treatment of TTTS and 22 full-term infants of single-fetus pregnancies. Bayley Scales of Infant and Toddler Development Screening Test were used for evaluation. Prenatal, perinatal and postnatal information were obtained. Results There was an increased frequency of infants in the TTTS group with inadequate performance compared to the control group. The identified variables (fetal donor, low economic income and cardiorespiratory disease negatively impacted expressive communication and fine motor skills. Conclusion Although through follow-up is recommended in all TTTS survivors, particular attention is required for the high-risk group as defined in this study.
6. Socio-psycho-historical observation on the twin
International Nuclear Information System (INIS)
Watanabe, Shoji; Satow, Yukio; Ueoka, Hiroshi; Munaka, Masaki; Kurihara, Minoru
1980-01-01
The so-called ''twin control study'', mainly on the monozygotic twins one of which was A-bomb exposed and the other was non-exposed were carried out. Sampling was conducted utilizing the materials as follows: 1) The survey on casualities of A-bomb exposed families in Hiroshima which was undertaken in 1946. 2) The survey of A-bomb survivors in 1965. 3) A-bomb exposed family survey conducted between 1973 to 1975. 4) Investigations of A-bomb victims exposed in the proximal areas from the hypocenter. From the above mentioned materials 470 pairs were selected, of which 220 were exposed. Among them 172 pairs were twins of the same sex. Female and male pair were also employed. In one case they were exposed, while the others were nonexposed. Two pairs were examined under the following methods: 1) Depth interview to ascertain familial casualities with reference to the family life cycle. 2) Socio-historical research. 3) Motoaki's Jinkaku Shindan Kensa (Modified Rorschach test by H. Motoaki), and T.A.T. test. Results obtained were summarized as follows: 1) Both pairs of twins were similar appearance, and also personality traits, and had a strong feeling of companionship for each other. 2) In family relationships, the persons studied were very conscious of the role expectations of elder and younger siblings in the twin pairs. 3) Through depth interview and projective test, A-bomb exposed pairs still showed deep psychological stresses, resulting from the A-bomb disaster. 4) Both among the exposed twins and within the nonexposed control group twin siblings had a close feeling of companionship for each other. However, nonexposed twins could not understand the psychological experience of twins who had been subjected to the atomic disaster. (author)
7. The Child and Adolescent Twin Study in Sweden (CATSS).
Science.gov (United States)
Anckarsäter, Henrik; Lundström, Sebastian; Kollberg, Linnea; Kerekes, Nora; Palm, Camilla; Carlström, Eva; Långström, Niklas; Magnusson, Patrik K E; Halldner, Linda; Bölte, Sven; Gillberg, Christopher; Gumpert, Clara; Råstam, Maria; Lichtenstein, Paul
2011-12-01
The Child and Adolescent Twin Study in Sweden (CATSS) is an ongoing longitudinal twin study targeting all twins born in Sweden since July 1, 1992. Since 2004, parents of twins are interviewed regarding the children's somatic and mental health and social environment in connection with their 9th or 12th birthdays (CATSS-9/12). By January 2010, 8,610 parental interviews concerning 17,220 twins had been completed, with an overall response rate of 80%. At age 15 (CATSS-15) and 18 (CATSS-18), twins and parents complete questionnaires that, in addition to assessments of somatic and mental health, include measures of personality development and psychosocial adaptation. Twin pairs in CATSS-9/12 with one or both twins screening positive for autism spectrum disorders, attention deficit/hyperactivity disorder, tic disorders, developmental coordination disorder, learning disorders, oppositional defiant disorder, conduct disorder, obsessive-compulsive disorder, and/or eating problems have been followed with in-depth questionnaires on family, social environment and personality, and subsequently by clinical assessments at age 15 together with randomly selected population controls, including 195 clinically assessed twin pairs from the first 2 year cohorts (CATSS-15/DOGSS). This article describes the cohorts and study groups, data collection, and measures used. Prevalences, distributions, heritability estimates, ages at onset, and sex differences of mental health problems in the CATSS-9/12, that were analyzed and found to be overall comparable to those of other clinical and epidemiological studies. The CATSS study has the potential of answering important questions on the etiology of childhood mental health problems and their role in the development of later adjustment problems.
8. Monozygotic twins with CAPN5 autosomal dominant neovascular inflammatory vitreoretinopathy
Directory of Open Access Journals (Sweden)
Rowell HA
2012-12-01
Full Text Available Hannah A Rowell,1,2 Alexander G Bassuk,3,4 Vinit B Mahajan1,21Omics Laboratory, 2Department of Ophthalmology and Visual Sciences, 3Department of Pediatrics, 4Department of Neurology, University of Iowa, Iowa City, IA, USABackground: The purpose of this study was to describe the clinical findings in a set of monozygotic twins with autosomal dominant neovascular inflammatory vitreoretinopathy (ADNIV over a 23-year period.Methods: A pair of female twins were examined between 26 and 49 years of age. The concordance and discordance of their clinical features were determined. The CAPN5 gene was sequenced using genomic DNA.Results: Both twins of an affected father demonstrated Stage I ADNIV with mild vitreous cells and a negative b-wave on electroretinography. Genetic analysis confirmed a guanine to thymine nucleotide (c.728G>T, pArg243Leu mutation in the CAPN5 gene. Over the course of 23 years, each twin progressed to stage III disease, showing posterior uveitis, cystoid macular edema, intraocular fibrosis, early retinal neovascularization, retinal degeneration, and cataract. Disease progression varied moderately between each twin and was asymmetrical between eyes. Twin A had 20/70 and 20/125 in the right and left eye, respectively, and underwent vitrectomy surgery and intravitreal injections with bevacizumab for recurrent cystoid macular edema. Twin B maintained 20/20 and 20/40 in the right and left eye, respectively without intervention.Conclusion: There was asymmetry between the eyes and some discordance in the rate of disease progression in these monozygotic twins with ADNIV. The overall high disease concordance suggests genetic factors play a major role in clinical manifestations in CAPN5 vitreoretinopathy.Keywords: autosomal dominant neovascular inflammatory vitreoretinopathy, ADNIV, CAPN5, calpain-5, monozygotic twins
9. Tidal effects in twin-degenerate binaries
International Nuclear Information System (INIS)
Campbell, C.G.
1984-01-01
The tidal velocity field is calculated for an initially non-rotating low mass white dwarf secondary in a twin-degenerate binary. These motions are used to find the tidal torque on the secondary, to first order in the orbital frequency, and an expression is derived for the synchronization time. For a lobe-filling secondary the synchronization time has a weak dependence on the mass and luminosity of the star, and for the binary G61-29 is found to be of the same order as the estimated lifetime of the system. It is emphasized, however, that tidal excitation of non-radial oscillatory modes in the secondary may significantly shorten the synchronization time. (author)
10. Twin paradox in de Sitter spacetime
International Nuclear Information System (INIS)
Boblest, Sebastian; Wunner, Guenter; Mueller, Thomas
2011-01-01
The 'twin paradox' of special relativity offers the possibility of making interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline of a uniformly accelerated observer in de Sitter spacetime and the communication between the travelling observer and an observer at rest. This paper is intended to give graduate students who are familiar with special relativity and have some basic experience of general relativity a deeper insight into accelerated motion in general relativity, into the relationship between the proper times of different observers and the propagation of light signals between them, and into the use of compactification to describe the global structure of a relativistic model.
11. The story of antimatter matter's vanished twin
CERN Document Server
2018-01-01
Each elementary particle contained within every known substance has an almost identical twin called its antiparticle. Existing data clearly indicate that equal numbers of particles and antiparticles were initially created soon after the birth of the universe. Despite this, all objects around us, as well as all the stars in all the known galaxies, are made of particles, while antiparticles have almost completely vanished. The reasons behind this disappearance are not yet fully known. Uncovering them will allow us to not only penetrate much deeper into the structure of matter, but also to understand the secret mechanisms that determine the genesis and development of our immense universe. That is why explaining the mystery of the missing antimatter is currently considered to be one of the main tasks of particle physics. This book tells the story of all the achievements in solving the problem of the missing antiparticles including the latest developments in the field. It is written by Prof. Guennadi Borissov, an...
12. Cesarean Section for the Second Twin
DEFF Research Database (Denmark)
Engelbrechtsen, Line; Nielsen, Elise Hoffmann; Perin, Trine
2013-01-01
deliveries. Data were extracted from medical records, a fetal medicine software program (Astraia), and the National Birth Registry. Short-term poor neonatal outcome was measured as a 5-minute Apgar score ≤ 7, umbilical cord pH ≤ 7.10, and admission to neonatal intensive care unit for more than 3 days....... RESULTS: Vertex-nonvertex fetal presentations were more prevalent in combined deliveries than vaginal deliveries (OR 4.4, 2.5-7.8). Nonvertex second twins born by combined delivery had a higher risk of Apgar score ≤ 7 and umbilical cord pH ≤ 7.10 compared with vaginal delivery, unadjusted OR 6.2 (2...
13. Dancing Twins: Stellar Hierarchies That Formed Sequentially?
Science.gov (United States)
Tokovinin, Andrei
2018-04-01
This paper draws attention to the class of resolved triple stars with moderate ratios of inner and outer periods (possibly in a mean motion resonance) and nearly circular, mutually aligned orbits. Moreover, stars in the inner pair are twins with almost identical masses, while the mass sum of the inner pair is comparable to the mass of the outer component. Such systems could be formed either sequentially (inside-out) by disk fragmentation with subsequent accretion and migration, or by a cascade hierarchical fragmentation of a rotating cloud. Orbits of the outer and inner subsystems are computed or updated in four such hierarchies: LHS 1070 (GJ 2005, periods 77.6 and 17.25 years), HIP 9497 (80 and 14.4 years), HIP 25240 (1200 and 47.0 years), and HIP 78842 (131 and 10.5 years).
14. Spectral analysis by correlation
International Nuclear Information System (INIS)
Fauque, J.M.; Berthier, D.; Max, J.; Bonnet, G.
1969-01-01
The spectral density of a signal, which represents its power distribution along the frequency axis, is a function which is of great importance, finding many uses in all fields concerned with the processing of the signal (process identification, vibrational analysis, etc...). Amongst all the possible methods for calculating this function, the correlation method (correlation function calculation + Fourier transformation) is the most promising, mainly because of its simplicity and of the results it yields. The study carried out here will lead to the construction of an apparatus which, coupled with a correlator, will constitute a set of equipment for spectral analysis in real time covering the frequency range 0 to 5 MHz. (author) [fr
International Nuclear Information System (INIS)
Kwon, Sung Duck; Lee, Keun Hyun; Kim, Bo Ra; Yoon, Suk Soo
2004-01-01
Ultrasonic backward radiation profile is frequency-dependent when incident region has deptional gradient of acoustical properties or multi-layers. Until now, we have measured the profiles of principal frequencies of used transducers so that it was not easy to understand the change of the frequency component and spectrum of backward radiation from the profile. We tried to measure the spectral backward radiation profiles using DFP(digital filer package) Lecroy DSO. The very big changes in the shape and pattern of spectral backward radiation profiles leads to the conclusion that this new try could be very effective tool to evaluate frequency dependent surface area.
16. Solar Twins and the Barium Puzzle
International Nuclear Information System (INIS)
Reddy, Arumalla B. S.; Lambert, David L.
2017-01-01
Several abundance analyses of Galactic open clusters (OCs) have shown a tendency for Ba but not for other heavy elements (La−Sm) to increase sharply with decreasing age such that Ba was claimed to reach [Ba/Fe] ≃ +0.6 in the youngest clusters (ages < 100 Myr) rising from [Ba/Fe] = 0.00 dex in solar-age clusters. Within the formulation of the s -process, the difficulty to replicate higher Ba abundance and normal La−Sm abundances in young clusters is known as the barium puzzle. Here, we investigate the barium puzzle using extremely high-resolution and high signal-to-noise spectra of 24 solar twins and measured the heavy elements Ba, La, Ce, Nd, and Sm with a precision of 0.03 dex. We demonstrate that the enhanced Ba ii relative to La−Sm seen among solar twins, stellar associations, and OCs at young ages (<100 Myr) is unrelated to aspects of stellar nucleosynthesis but has resulted from overestimation of Ba by standard methods of LTE abundance analysis in which the microturbulence derived from the Fe lines formed deep in the photosphere is insufficient to represent the true line broadening imposed on Ba ii lines by the upper photospheric layers from where the Ba ii lines emerge. Because the young stars have relatively active photospheres, Ba overabundances most likely result from the adoption of a too low value of microturbulence in the spectrum synthesis of the strong Ba ii lines but the change of microturbulence in the upper photosphere has only a minor affect on La−Sm abundances measured from the weak lines.
17. Solar Twins and the Barium Puzzle
Energy Technology Data Exchange (ETDEWEB)
Reddy, Arumalla B. S.; Lambert, David L., E-mail: [email protected] [W.J. McDonald Observatory and Department of Astronomy, The University of Texas at Austin, Austin, TX 78712-1205 (United States)
2017-08-20
Several abundance analyses of Galactic open clusters (OCs) have shown a tendency for Ba but not for other heavy elements (La−Sm) to increase sharply with decreasing age such that Ba was claimed to reach [Ba/Fe] ≃ +0.6 in the youngest clusters (ages < 100 Myr) rising from [Ba/Fe] = 0.00 dex in solar-age clusters. Within the formulation of the s -process, the difficulty to replicate higher Ba abundance and normal La−Sm abundances in young clusters is known as the barium puzzle. Here, we investigate the barium puzzle using extremely high-resolution and high signal-to-noise spectra of 24 solar twins and measured the heavy elements Ba, La, Ce, Nd, and Sm with a precision of 0.03 dex. We demonstrate that the enhanced Ba ii relative to La−Sm seen among solar twins, stellar associations, and OCs at young ages (<100 Myr) is unrelated to aspects of stellar nucleosynthesis but has resulted from overestimation of Ba by standard methods of LTE abundance analysis in which the microturbulence derived from the Fe lines formed deep in the photosphere is insufficient to represent the true line broadening imposed on Ba ii lines by the upper photospheric layers from where the Ba ii lines emerge. Because the young stars have relatively active photospheres, Ba overabundances most likely result from the adoption of a too low value of microturbulence in the spectrum synthesis of the strong Ba ii lines but the change of microturbulence in the upper photosphere has only a minor affect on La−Sm abundances measured from the weak lines.
18. Pygopagus Conjoined Twins: A Neurophysiologic Intraoperative Monitoring Schema.
Science.gov (United States)
Cromeens, Barrett P; McKinney, Jennifer L; Leonard, Jeffrey R; Governale, Lance S; Brown, Judy L; Henry, Christina M; Levitt, Marc A; Wood, Richard J; Besner, Gail E; Islam, Monica P
2017-03-01
Conjoined twins occur in up to 1 in 50,000 live births with approximately 18% joined in a pygopagus configuration at the buttocks. Twins with this configuration display symptoms and carry surgical risks during separation related to the extent of their connection which can include anorectal, genitourinary, vertebral, and neural structures. Neurophysiologic intraoperative monitoring for these cases has been discussed in the literature with variable utility. The authors present a case of pygopagus twins with fused spinal cords and imperforate anus where the use of neurophysiologic intraoperative monitoring significantly impacted surgical decision-making in division of these critical structures.
19. Dissecting complex phenotypes using the genomics of twins
DEFF Research Database (Denmark)
Tan, Qihua; Ohm Kyvik, Kirsten; Kruse, Torben A
2010-01-01
of human diseases. Besides, twins not only serve as ideal samples for disease gene mapping using conventional genetic markers but also represent an excellent model for associating DNA copy number variations, a structural genetic marker, with human diseases. It is believed that, with the rapid development...... in biotechniques and new advances in bioinformatics, the unique samples of twins will make new contributions to our understanding of the nature and nurture in complex disease development and in human health. This paper aims at summarizing the new uses of twins in current genetic studies and suggesting novel...
20. Genetic Influences on Pulmonary Function: A Large Sample Twin Study
DEFF Research Database (Denmark)
Ingebrigtsen, Truls S; Thomsen, Simon F; van der Sluis, Sophie
2011-01-01
Heritability of forced expiratory volume in one second (FEV(1)), forced vital capacity (FVC), and peak expiratory flow (PEF) has not been previously addressed in large twin studies. We evaluated the genetic contribution to individual differences observed in FEV(1), FVC, and PEF using data from...... the largest population-based twin study on spirometry. Specially trained lay interviewers with previous experience in spirometric measurements tested 4,314 Danish twins (individuals), 46-68 years of age, in their homes using a hand-held spirometer, and their flow-volume curves were evaluated. Modern variance...
1. Validation of Quench Simulation and Simulation of the TWIN Solenoid
CERN Document Server
Pots, Rosalinde Hendrika
2015-01-01
For the Future Circular Collider at CERN a multi-purpose detector is proposed. The 6T TWIN Solenoid, a very large magnet system with a stored energy of 53 GJ, is being designed. It is important to protect the magnet against quenches in the system. Therefore several existing quench protection systems are evaluated and simulations have be performed on quenches in the TWIN Solenoid. The simulations on quenches in the TWIN Solenoid have been performed with promising results; the hotspot temperatures do not exceed 120 K and layer to layer voltages stay below 500 V. Adding quench heaters to the system might improve the quench protection system further.
2. Association between obesity and asthma in a twin cohort
DEFF Research Database (Denmark)
Thomsen, SF; Ulrik, Charlotte Suppli; Kyvik, KO
2007-01-01
Background: Obesity is linked to asthma in a yet poorly understood manner. We examined the relationship between obesity and asthma in a population-based sample of twins. Methods: From the cohorts born between 1953 and 1982, who were enrolled in The Danish Twin Registry, a total of 29 183 twin ind...... to obesity and asthma were significantly correlated only in females, r = 0.28 (0.16-0.38). Conclusions: Obese subjects have an increased risk for asthma, which in females seems partly because of common genes....
3. Estimating heritability for cause specific mortality based on twin studies
DEFF Research Database (Denmark)
Scheike, Thomas; Holst, Klaus Kähler; von Bornemann Hjelmborg, Jacob
2014-01-01
the Danish twin registry and discuss how to define heritability for cancer occurrence. The key point is that this should be done taking censoring as well as competing risks due to e.g. death into account. We describe the dependence between twins on the probability scale and show that various models can...... be used to achieve sensible estimates of the dependence within monozygotic and dizygotic twin pairs that may vary over time. These dependence measures can subsequently be decomposed into a genetic and environmental component using random effects models. We here present several novel models that in essence...
4. A proof of the conjecture on the twin primes
Energy Technology Data Exchange (ETDEWEB)
Zuo-ling, Zhou [Department of Lingnan college, Sun Yat-sen University GuangZhou, GuangDong, 510275 (China)
2016-06-08
In this short note, we have proved the conjecture on twin primes using some thoughts of the set theory. Firstly, using the original sieve method and a new notation(concept)introduced by myself, the conjecture on twin primes is summed up as an elementary successive limit, afterwards we form a subsequence of positive integers,and using it,we prove that the successive limits are commutative and complete the proof of the conjecture on twin primes We also give a more straightforward proof of the conjecture.
5. Heritability of retinal vascular fractals: a twin study
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
. The retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficents. Falconer´s formula and quantitative genetic models were used to determine the genetic component of variation. Results: The retinal...... for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, p=0.0002) in monozygotic twins than in dizygotic twins (0.108, p=0.46), corresponding to a heritability h2 for the fractal dimension of 0.79. In quantitative genetic models, 54% of the variation was explained...
6. Twinning in Zircon: Not a High-Pressure Phenomenon
Science.gov (United States)
Jones, G. A.; Moser, D.; Shieh, S. R.; Barker, I.
2017-12-01
Microtwins in zircon are commonly found in shocked terrestrial and extraterrestrial samples and are potentially important for shock history and crater reconstruction. Twinning is easily observed with both the optical microscope and variety of electron beam techniques. Twinning as a deformation mechanism is consistent with the high strain rates generated during impact. No constitutive relationships, or even general limits on the physical conditions required for twinning in zircon are known, however. Present speculation on the critical quantity for twin formation, i.e. 10s of GPa of shock pressure (Moser et al. 2011, Timms et al., 2012), has no basis in the underlying mechanisms of twin nucleation, which are related to the motion of dislocations. This erroneous value is due to conflation of twinning sensu stricto with a phase transformation to reidite. Reidite occurs as twin-like lamellae occupying the {112} planes which are thought to be a mirror plane for twinning. We review the crystallographic theory of twinning in zircon. We then evaulate several theories on the nucleation of twins along with their necessary stresses involved. Our aim is to show that shock microtwins in zircon can be a `low pressure' shock phenomenon. This 'low pressure' hypothesis is supported by natural samples. These zircons are from the lower crust nearly 80 km from the centre of the Vredefort impact structure—the most distal zircon shock microstructures yet found in the lithosphere. Twins are present in 10% of the zircon grains greater than 50 µm in diameter. As an extensive, 'low pressure' phenomenon, twins are an easily recognized and potentially widespread record of Earth's impact history.Moser, D.E., Cupelli, C. L., Barker, I., Flowers, R. M., Mowman, J. R., Wooden, J. and Hart, R. (2011) New zircon shock phenomena and their use for dating and […] analysis of the Vredefort dome, Canadian Journal of Earth Sciences 48(2), 117-139.Timms, N.E., Reddy, S. M., Healy, D., Nemchin, A. A
7. Monozygotic twins with Marfan's syndrome and ascending aortic aneurysm.
Science.gov (United States)
Redruello, Héctor Jorge; Cianciulli, Tomas Francisco; Rostello, Eduardo Fernandez; Recalde, Barbara; Lax, Jorge Alberto; Picone, Victorio Próspero; Belforte, Sandro Mario; Prezioso, Horacio Alberto
2007-08-01
Marfan's syndrome is a hereditary connective tissue disease, in which cardiovascular abnormalities (especially aortic root dilatation) are the most important cause of morbidity and mortality. In this report, we describe two 24-year-old twins, with a history of surgery for lens subluxation and severe cardiovascular manifestations secondary to Marfan's syndrome. One of the twins suffered a type A aortic dissection, which required replacement of the ascending aorta, and the other twin had an aneurysmal dilatation of the ascending aorta (46mm) and was prescribed medical treatment with atenolol and periodic controls to detect the presence of a critical diameter (50mm) that would indicate the need for prophylactic surgery.
8. Anorexia and bulimia nervosa in same-sex and opposite-sex twins: lack of association with twin type in a nationwide study of Finnish twins.
Science.gov (United States)
Raevuori, Anu; Kaprio, Jaakko; Hoek, Hans W; Sihvola, Elina; Rissanen, Aila; Keski-Rahkonen, Anna
2008-12-01
The authors tested the hypothesis that either prenatal feminization or masculinization hormone influences in utero or later socialization affects the risk for anorexia and bulimia nervosa and disordered eating in members of opposite-sex twin pairs. Finnish twins (N=2,426 women, N=1,962 men with known zygosity) from birth cohorts born 1974-1979 were assessed at age 22 to 28 years with a questionnaire for eating disorder symptoms. Based on the questionnaire screen, women (N=292), men (N=53), and their cotwins were interviewed to assess diagnoses of anorexia nervosa and bulimia nervosa (per DSM-IV and broad criteria). In women from opposite-sex twin pairs, the prevalence of DSM-IV or broad anorexia nervosa was not significantly different than that of women from monozygotic pairs or same-sex dizygotic pairs. Of the five male anorexia nervosa probands, only one was from an opposite-sex twin pair. Bulimia nervosa in men was too rare to be assessed by zygosity; the prevalence of DSM-IV or broad bulimia nervosa did not differ in women from opposite- versus same-sex twin pairs. In both sexes, the overall profile of indicators on eating disorders was rather similar between individuals from opposite- and same-sex pairs. The authors found little evidence that the risk for anorexia nervosa, bulimia nervosa, or disordered eating was associated with zygosity or sex composition of twin pairs, thus making it unlikely that in utero femininization or masculinization or socialization effects of growing up with an opposite-sex twin have a major influence on the later development of eating disorders.
9. Incidence of spontaneous twin anemia-polycythemia sequence in monochorionic-diamniotic twin pregnancies: Single-center prospective study.
Science.gov (United States)
Yokouchi, Tae; Murakoshi, Takeshi; Mishima, Takashi; Yano, Hiroko; Ohashi, Madoka; Suzuki, Takashi; Shinno, Takashi; Matsushita, Mitsuru; Nakayama, Satoru; Torii, Yuichi
2015-06-01
The purpose of this study was to prospectively estimate the incidence of spontaneous twin anemia-polycythemia sequence (TAPS) in monochorionic-diamniotic twin pregnancies. We prospectively examined umbilical cord hemoglobin (Hb) and reticulocyte count of consecutive monochorionic-diamniotic twin pregnancies delivered at Seirei Hamamatsu General Hospital from December 2006 to September 2013. We excluded cases of twin-twin transfusion syndrome, intrauterine fetal demise, and missing data (Hb and reticulocyte count missing from the medical record). TAPS was diagnosed using the postnatal criteria of intertwin Hb difference >8.0 g/dL and reticulocyte count ratio >1.7. Acute feto-fetal hemorrhage was defined as Hb difference >7 g/dL and reticulocyte count ratio <1.7. A total of 185 monochorionic-diamniotic twin pregnancies were included in this study. Three fulfilled the diagnostic criteria for postnatal TAPS, and one fulfilled the diagnostic criteria for acute feto-fetal hemorrhage. The incidence of spontaneous TAPS in monochorionic-diamniotic twin pregnancies was 1.6% (3/185) at Seirei Hamamatsu General Hospital. © 2014 The Authors. Journal of Obstetrics and Gynaecology Research © 2014 Japan Society of Obstetrics and Gynecology.
10. Education in Twins and Their Parents Across Birth Cohorts Over 100 years: An Individual-Level Pooled Analysis of 42-Twin Cohorts.
Science.gov (United States)
Silventoinen, Karri; Jelenkovic, Aline; Latvala, Antti; Sund, Reijo; Yokoyama, Yoshie; Ullemar, Vilhelmina; Almqvist, Catarina; Derom, Catherine A; Vlietinck, Robert F; Loos, Ruth J F; Kandler, Christian; Honda, Chika; Inui, Fujio; Iwatani, Yoshinori; Watanabe, Mikio; Rebato, Esther; Stazi, Maria A; Fagnani, Corrado; Brescianini, Sonia; Hur, Yoon-Mi; Jeong, Hoe-Uk; Cutler, Tessa L; Hopper, John L; Busjahn, Andreas; Saudino, Kimberly J; Ji, Fuling; Ning, Feng; Pang, Zengchang; Rose, Richard J; Koskenvuo, Markku; Heikkilä, Kauko; Cozen, Wendy; Hwang, Amie E; Mack, Thomas M; Siribaddana, Sisira H; Hotopf, Matthew; Sumathipala, Athula; Rijsdijk, Fruhling; Sung, Joohon; Kim, Jina; Lee, Jooyeon; Lee, Sooji; Nelson, Tracy L; Whitfield, Keith E; Tan, Qihua; Zhang, Dongfeng; Llewellyn, Clare H; Fisher, Abigail; Burt, S Alexandra; Klump, Kelly L; Knafo-Noam, Ariel; Mankuta, David; Abramson, Lior; Medland, Sarah E; Martin, Nicholas G; Montgomery, Grant W; Magnusson, Patrik K E; Pedersen, Nancy L; Dahl Aslan, Anna K; Corley, Robin P; Huibregtse, Brooke M; Öncel, Sevgi Y; Aliev, Fazil; Krueger, Robert F; McGue, Matt; Pahlen, Shandell; Willemsen, Gonneke; Bartels, Meike; van Beijsterveldt, Catharina E M; Silberg, Judy L; Eaves, Lindon J; Maes, Hermine H; Harris, Jennifer R; Brandt, Ingunn; Nilsen, Thomas S; Rasmussen, Finn; Tynelius, Per; Baker, Laura A; Tuvblad, Catherine; Ordoñana, Juan R; Sánchez-Romera, Juan F; Colodro-Conde, Lucia; Gatz, Margaret; Butler, David A; Lichtenstein, Paul; Goldberg, Jack H; Harden, K Paige; Tucker-Drob, Elliot M; Duncan, Glen E; Buchwald, Dedra; Tarnoki, Adam D; Tarnoki, David L; Franz, Carol E; Kremen, William S; Lyons, Michael J; Maia, José A; Freitas, Duarte L; Turkheimer, Eric; Sørensen, Thorkild I A; Boomsma, Dorret I; Kaprio, Jaakko
2017-10-01
Whether monozygotic (MZ) and dizygotic (DZ) twins differ from each other in a variety of phenotypes is important for genetic twin modeling and for inferences made from twin studies in general. We analyzed whether there were differences in individual, maternal and paternal education between MZ and DZ twins in a large pooled dataset. Information was gathered on individual education for 218,362 adult twins from 27 twin cohorts (53% females; 39% MZ twins), and on maternal and paternal education for 147,315 and 143,056 twins respectively, from 28 twin cohorts (52% females; 38% MZ twins). Together, we had information on individual or parental education from 42 twin cohorts representing 19 countries. The original education classifications were transformed to education years and analyzed using linear regression models. Overall, MZ males had 0.26 (95% CI [0.21, 0.31]) years and MZ females 0.17 (95% CI [0.12, 0.21]) years longer education than DZ twins. The zygosity difference became smaller in more recent birth cohorts for both males and females. Parental education was somewhat longer for fathers of DZ twins in cohorts born in 1990-1999 (0.16 years, 95% CI [0.08, 0.25]) and 2000 or later (0.11 years, 95% CI [0.00, 0.22]), compared with fathers of MZ twins. The results show that the years of both individual and parental education are largely similar in MZ and DZ twins. We suggest that the socio-economic differences between MZ and DZ twins are so small that inferences based upon genetic modeling of twin data are not affected.
11. Socio-psycho-historical observation on the twin. Sampling methods and case study of the atomic bomb exposed twins
Energy Technology Data Exchange (ETDEWEB)
Watanabe, S; Satow, Y; Ueoka, Hiroshi; Munaka, M; Kurihara, M [Hiroshima Univ. (Japan). Research Inst. for Nuclear Medicine and Biology
1980-07-01
The so-called ''twin control study'', mainly on the monozygotic twins one of which was A-bomb exposed and the other was non-exposed were carried out. Sampling was conducted utilizing the materials as follows: 1) The survey on casualities of A-bomb exposed families in Hiroshima which was undertaken in 1946. 2) The survey of A-bomb survivors in 1965. 3) A-bomb exposed family survey conducted between 1973 to 1975. 4) Investigations of A-bomb victims exposed in the proximal areas from the hypocenter. From the above mentioned materials 470 pairs were selected, of which 220 were exposed. Among them 172 pairs were twins of the same sex. Female and male pair were also employed. In one case they were exposed, while the others were nonexposed. Two pairs were examined under the following methods: 1) Depth interview to ascertain familial casualities with reference to the family life cycle. 2) Socio-historical research. 3) Motoaki's Jinkaku Shindan Kensa (Modified Rorschach test by H. Motoaki), and T.A.T. test. Results obtained were summarized as follows: 1) Both pairs of twins were of similar appearance and personality traits, and had a strong feeling of companionship for each other. 2) In family relationships, the persons studied were very conscious of the role expectations of elder and younger siblings in the twin pairs. 3) Through depth interviews and projective tests, A-bomb exposed pairs still showed deep psychological stresses, resulting from the A-bomb disaster. 4) Both among the exposed twins and within the nonexposed control group twin siblings had a close feeling of companionship for each other. However, nonexposed twins could not understand the psychological experience of twins who had been subjected to the atomic disaster.
12. Spectral Ensemble Kalman Filters
Czech Academy of Sciences Publication Activity Database
Mandel, Jan; Kasanický, Ivan; Vejmelka, Martin; Fuglík, Viktor; Turčičová, Marie; Eben, Kryštof; Resler, Jaroslav; Juruš, Pavel
2014-01-01
Roč. 11, - (2014), EMS2014-446 [EMS Annual Meeting /14./ & European Conference on Applied Climatology (ECAC) /10./. 06.10.2014-10.10.2014, Prague] R&D Projects: GA ČR GA13-34856S Grant - others:NSF DMS-1216481 Institutional support: RVO:67985807 Keywords : data assimilation * spectral filter Subject RIV: DG - Athmosphere Sciences, Meteorology
13. Mechanical spectral shift reactor
International Nuclear Information System (INIS)
Sherwood, D.G.; Wilson, J.F.; Salton, R.B.; Fensterer, H.F.
1981-01-01
A mechanical spectral shift reactor comprises apparatus for inserting and withdrawing water displacer elements from the reactor core for selectively changing the water-moderator volume in the core thereby changing the reactivity of the core. The apparatus includes drivemechanisms for moving the displacer elements relative to the core and guide mechanisms for guiding the displayer rods through the reactor vessel
14. Mechanical spectral shift reactor
International Nuclear Information System (INIS)
Sherwood, D.G.; Wilson, J.F.; Salton, R.B.; Fensterer, H.F.
1982-01-01
A mechanical spectral shift reactor comprises apparatus for inserting and withdrawing water displacer elements from the reactor core for selectively changing the water-moderator volume in the core thereby changing the reactivity of the core. The apparatus includes drive mechanisms for moving the displacer elements relative to the core and guide mechanisms for guiding the displacer rods through the reactor vessel. (author)
15. Objective assessment of facial skin aging and the associated environmental factors in Japanese monozygotic twins
OpenAIRE
Ichibori, Ryoko; Fujiwara, Takashi; Tanigawa, Tomoko; Kanazawa, Shigeyuki; Shingaki, Kenta; Torii, Kosuke; Tomita, Koichi; Yano, Kenji; Sakai, Yasuo; Hosokawa, Ko
2014-01-01
Twin studies, especially those involving monozygotic (MZ) twins, facilitate the analysis of factors affecting skin aging while controlling for age, gender, and genetic susceptibility. The purpose of this study was to objectively assess various features of facial skin and analyze the effects of environmental factors on these features in MZ twins. At the Osaka Twin Research Center, 67 pairs of MZ twins underwent medical interviews and photographic assessments, using the VISIA® Complexion Analys...
16. 2.5D global-disk oscillation models of the Be shell star ζ Tauri. I. Spectroscopic and polarimetric analysis
Science.gov (United States)
Escolano, C.; Carciofi, A. C.; Okazaki, A. T.; Rivinius, T.; Baade, D.; Štefl, S.
2015-04-01
Context. A large number of Be stars exhibit intensity variations of their violet and red emission peaks in their H i lines observed in emission. This is the so-called V/R phenomenon, usually explained by the precession of a one-armed spiral density perturbation in the circumstellar disk. That global-disk oscillation scenario was confirmed, both observationally and theoretically, in the previous series of two papers analyzing the Be shell star ζ Tauri. The vertically averaged (2D) global-disk oscillation model used at the time was able to reproduce the V/R variations observed in Hα, as well as the spatially resolved interferometric data from AMBER/VLTI. Unfortunately, that model failed to reproduce the V/R phase of Br15 and the amplitude of the polarization variation, suggesting that the inner disk structure predicted by the model was incorrect. Aims: The first aim of the present paper is to quantify the temporal variations of the shell-line characteristics of ζ Tauri. The second aim is to better understand the physics underlying the V/R phenomenon by modeling the shell-line variations together with the V/R and polarimetric variations. The third aim is to test a new 2.5D disk oscillation model, which solves the set of equations that describe the 3D perturbed disk structure but keeps only the equatorial (i.e., 2D) component of the solution. This approximation was adopted to allow comparisons with the previous 2D model, and as a first step toward a future 3D model. Methods: We carried out an extensive analysis of ζ Tauri's spectroscopic variations by measuring various quantities characterizing its Balmer line profiles: red and violet emission peak intensities (for Hα, Hβ, and Br15), depth and asymmetry of the shell absorption (for Hβ, Hγ, and Hδ), and the respective position (i.e., radial velocity) of each component. We attempted to model the observed variations by implementing in the radiative transfer code HDUST the perturbed disk structure computed with a
17. A Simple Spectral Observer
Directory of Open Access Journals (Sweden)
Lizeth Torres
2018-05-01
Full Text Available The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm for time-frequency analysis because is a method that can compute on the fly the Fourier transform (FT of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1 the reconstruction of a simple periodical signal, (2 the approximation of both a square and a triangular signal, (3 the edge detection in signals by using the Fourier coefficients, (4 the fitting of the historical Bitcoin market data from 1 December 2014 to 8 January 2018 and (5 the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT, which is a well-known method for time-frequency analysis.
18. Hemoglobin Differences in Uncomplicated Monochorionic Twins in Relation to Birth Order and Mode of Delivery.
Science.gov (United States)
Verbeek, Lianne; Zhao, Depeng P; Te Pas, Arjan B; Middeldorp, Johanna M; Hooper, Stuart B; Oepkes, Dick; Lopriore, Enrico
2016-06-01
To determine the differences in hemoglobin (Hb) levels in the first 2 days after birth in uncomplicated monochorionic twins in relation to birth order and mode of delivery. All consecutive uncomplicated monochorionic pregnancies with two live-born twins delivered at our center were included in this retrospective study. We recorded Hb levels at birth and on day 2, and analyzed Hb levels in association with birth order, mode of delivery, and time interval between delivery of twin 1 and 2. A total of 290 monochorionic twin pairs were analyzed, including 171 (59%) twins delivered vaginally and 119 (41%) twins born by cesarean section (CS). In twins delivered vaginally, mean Hb levels at birth and on day 2 were significantly higher in second-born twins compared to first-born twins: 17.8 versus 16.1 g/dL and 18.0 versus 14.8 g/dL, respectively (p < .01). Polycythemia was detected more often in second-born twins (12%, 20/166) compared to first-born twins (1%, 2/166; p < .01). Hb differences within twin pairs delivered by CS were not statistically or clinically significant. We found no association between inter-twin delivery time intervals and Hb differences. Second-born twins after vaginal delivery have higher Hb levels and more often polycythemia than their co-twin, but not when born by CS.
19. Prospective risk of stillbirth and neonatal complications in twin pregnancies
DEFF Research Database (Denmark)
Cheong-See, Fiona; Schuit, Ewoud; Arroyo-Manzano, David
2016-01-01
OBJECTIVE: To determine the risks of stillbirth and neonatal complications by gestational age in uncomplicated monochorionic and dichorionic twin pregnancies. DESIGN: Systematic review and meta-analysis. DATA SOURCES: Medline, Embase, and Cochrane databases (until December 2015). REVIEW METHODS: ...
20. Twin Ritual (Kamta Bulikur): The Significance of Traditional Music in ...
African Journals Online (AJOL)
2016-12-16
Dec 16, 2016 ... to contain the emotional reactions created by the beliefs in the ... Figure 1: Map of Nigeria showing Buraland shaded grey in the northeast ..... physical, bodily, appearance of twins in composing the lyrics for the praise songs.
1. Twinning structures in near-stoichiometric lithium niobate single crystals
International Nuclear Information System (INIS)
Yao, Shuhua; Chen, Yanfeng
2010-01-01
A near-stoichiometric lithium niobate single crystal has been grown by the Czochralski method in a hanging double crucible with a continuous powder supply system. Twins were found at one of the three characteristic growth ridges of the as-grown crystal. The twin structure was observed and analyzed by transmission synchrotron topography. The image shifts ΔX and ΔY in the transmission synchrotron topograph were calculated for the 3 anti 2 anti 12 and 0 anti 222 reflections based on results from high-resolution X-ray diffractometry. It is confirmed that one of the {01 anti 1 anti 2} m planes is the composition face of the twin and matrix crystals. The formation mechanism of these twins is discussed. (orig.)
2. Spontaneous unilateral Twin Ectopic Pregnancy: A case report
Directory of Open Access Journals (Sweden)
هادی اریا منش
2017-03-01
Full Text Available Abstract Aim & Objective: Twin pregnancy in the tube is a few and due to more frequent use of ovulatory medicine and increased maternal mortality rate. In this article, we report a case of untitled twin ectopic pregnancy. Case study: The pregnant women was a 28 year-old to had a history infertility, PCOD, Abortion and cortege, too have one 5 years girl by CS and Mild cramp pain in both abdominal lower quadrants and metroreghia . That have not treatment by projection. The ultra-sonography showed a twin pregnancy uterus with a moderate amount of fluid in pelvic cavity was seen. And do salpanjectimy surgery. Conclusion: We report one Untitled Spontaneous Twin Ectopic Pregnancy, is necessary any pregnant woman with positive BhCG and metrorhoghia must be considered for Ectopic pregnancy. To decrease maternal mortality rate. Key words:
3. Maternal 25-hydroxyvitamin d and preterm birth in twin gestations.
LENUS (Irish Health Repository)
Bodnar, Lisa M
2013-07-01
To assess whether there was an independent association between maternal 25-hydroxyvitamin D concentrations at 24-28 weeks of gestation and preterm birth in a multicenter U.S. cohort of twin pregnancies.
4. Adult glucose metabolism in extremely birthweight-discordant monozygotic twins
DEFF Research Database (Denmark)
Frost, M; Petersen, I; Brixen, K
2012-01-01
Low birthweight (BW) is associated with increased risk of type 2 diabetes. We compared glucose metabolism in adult BW-discordant monozygotic (MZ) twins, thereby controlling for genetic factors and rearing environment....
5. Two wide-angle imaging neutral-atom spectrometers (TWINS)
International Nuclear Information System (INIS)
McComas, D.J.; Blake, B.; Burch, J.
1998-01-01
Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS) is a revolutionary new mission designed to stereoscopically image the magnetosphere in charge exchange neutral atoms for the first time. The authors propose to fly two identical TWINS instruments as a mission of opportunity on two widely-spaced high-altitude, high-inclination US Government spacecraft. Because the spacecraft are funded independently, TWINS can provide a vast quantity of high priority science observations (as identified in an ongoing new missions concept study and the Sun-Earth Connections Roadmap) at a small fraction of the cost of a dedicated mission. Because stereo observations of the near-Earth space environs will provide a particularly graphic means for visualizing the magnetosphere in action, and because of the dedication and commitment of the investigator team to the principles of carrying space science to the broader audience, TWINS will also be an outstanding tool for public education and outreach
6. Outcomes of preterm premature rupture of membranes in twin pregnancies.
Science.gov (United States)
Trentacoste, Stephanie V; Jean-Pierre, Claudel; Baergen, Rebecca; Chasen, Stephen T
2008-08-01
To describe outcomes in twin pregnancies with preterm premature rupture of membranes (PPROM). Dichorionic twin pregnancies complicated by PPROM at premature rupture of membranes (PROM), latency from PROM to delivery, and infection were examined. In 49 twin pregnancies, the median gestational age at PROM was 31 weeks with a median latency between PROM and delivery of 0 days (interquartile range 0-6). Latency intervals of >or=2 and >or=7 days were achieved by 40.8% and 22.4%, respectively. PPROM at or= 2 days (70.6% vs. 25.0%) and >or=7 days (47.1% vs. 9.4%). There was a significant relationship between latency and clinical and histologic signs of infection. After 30 weeks, most twin pregnancies with PPROM delivered within 2 days. Infection appears to be a consequence rather than a cause of PPROM in most cases.
7. Infertility, infertility treatment and twinning: the Danish National Birth Cohort
DEFF Research Database (Denmark)
Zhu, Jin Liang; Basso, Olga; Obel, Carsten
2007-01-01
BACKGROUND: We have previously observed that an increasing time to pregnancy (TTP) is associated with a reduced frequency of twin deliveries in couples not receiving infertility treatment. By using updated information, we assessed the frequencies of dizygotic (DZ) and monozygotic (MZ) twin...... deliveries as a function of infertility (TTP > 12 months), as well as infertility treatment. METHODS: From the Danish National Birth Cohort (1997-2003), we identified 51 730 fertile couples with TTP 12 months and 5163 infertile couples who conceived after treatment. Information on zygosity, available...... for part of the cohort (1997-2000), was based on standardized questions on the similarities between the twins at the age of 3-5 years. RESULTS: Compared with fertile couples, the frequency of DZ twin deliveries was lower for infertile couples conceiving naturally (odds ratio 0.4, 95% confidence interval 0...
8. The 1600 Å Emission Bump in Protoplanetary Disks: A Spectral Signature of H{sub 2}O Dissociation
Energy Technology Data Exchange (ETDEWEB)
France, Kevin [Laboratory for Atmospheric and Space Physics, University of Colorado, 600 UCB, Boulder, CO 80309 (United States); Roueff, Evelyne; Abgrall, Hervé, E-mail: [email protected] [LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, F-92190, Meudon (France)
2017-08-01
The FUV continuum spectrum of many accreting pre-main sequence stars, Classical T Tauri Stars (CTTSs), does not continue smoothly from the well-studied Balmer continuum emission in the NUV, suggesting that additional processes contribute to the short-wavelength emission in these objects. The most notable spectral feature in the FUV continuum of some CTTSs is a broad emission approximately centered at 1600 Å, which has been referred to as the “1600 Å Bump.” The origin of this feature remains unclear. In an effort to better understand the molecular properties of planet-forming disks and the UV spectral properties of accreting protostars, we have assembled archival FUV spectra of 37 disk-hosting systems observed by the Hubble Space Telescope -Cosmic Origins Spectrograph. Clear 1600 Å Bump emission is observed above the smooth, underlying 1100–1800 Å continuum spectrum in 19/37 Classical T Tauri disks in the HST -COS sample, with the detection rate in transition disks (8/8) being much higher than that in primordial or non-transition sources (11/29). We describe a spectral deconvolution analysis to separate the Bump (spanning 1490–1690 Å) from the underlying FUV continuum, finding an average Bump luminosity L (Bump) ≈ 7 × 10{sup 29} erg s{sup −1}. Parameterizing the Bump with a combination of Gaussian and polynomial components, we find that the 1600 Å Bump is characterized by a peak wavelength λ {sub o} = 1598.6 ± 3.3 Å, with FWHM = 35.8 ± 19.1 Å. Contrary to previous studies, we find that this feature is inconsistent with models of H{sub 2} excited by electron -impact. We show that this Bump makes up between 5%–50% of the total FUV continuum emission in the 1490–1690 Å band and emits roughly 10%–80% of the total fluorescent H{sub 2} luminosity for stars with well-defined Bump features. Energetically, this suggests that the carrier of the 1600 Å Bump emission is powered by Ly α photons. We argue that the most likely mechanism
9. Birth weight, sex, and celiac disease: a nationwide twin study
Directory of Open Access Journals (Sweden)
Kuja-Halkola R
2017-11-01
Full Text Available Ralf Kuja-Halkola,1 Benjamin Lebwohl,1,2 Jonas Halfvarson,3 Louise Emilsson,4–6 Patrik K Magnusson,1 Jonas F Ludvigsson1,2,7,8 1Department Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden; 2Department of Medicine, Celiac Disease Center, Columbia University Medical Center, Columbia University, New York, NY, USA; 3Department of Gastroenterology, Faculty of Medicine and Health, Örebro University, Örebro, Sweden; 4Department of Health Management and Health Economy, Institute of Health and Society, University of Oslo, Oslo, Norway; 5Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA, USA; 6Centre for Clinical Research, Vårdcentralen Värmlands Nysäter, County Council of Värmland, Värmland, 7Department of Pediatrics, Örebro University Hospital, Örebro, Sweden; 8Division of Epidemiology and Public Health, School of Medicine, City Hospital, University of Nottingham, Nottingham, UK Objective: Earlier research suggests that birth weight may be associated with celiac disease (CD, but the direction of association has been unclear potentially due to confounding effect from genetic and intrafamilial factors. Through within-twin analyses, we aimed to minimize confounding effects such as twins that share genetic and early environmental exposures.Materials and methods: Using the Swedish Twin Registry, we examined the birth weight of 146,830 twins according to the CD status. CD was defined as having villous atrophy according to a small intestinal biopsy reports.Results: The prevalence of diagnosed CD was 0.5% (n=669, and we included 407 discordant pairs of CD–non-CD twins. Comparing the 669 CD patients with non-CD twins, the association between birth weight and future CD was not statistically significant (odds ratio [OR] per 1000 g increase in birth weight: 1.16; 95% confidence interval [CI]=0.97–1.38. In males, the association was positive and statistically significant (OR=1.50; 95% CI
10. Risk of chronic bronchitis in twin pairs discordant for smoking
DEFF Research Database (Denmark)
Meteran, Howraman; Thomsen, Simon Francis; Harmsen, Lotte
2012-01-01
It is well known that smoking is a major risk factor for lung disease and respiratory symptoms. We examined the association between smoking and the risk of chronic bronchitis in a large twin sample.......It is well known that smoking is a major risk factor for lung disease and respiratory symptoms. We examined the association between smoking and the risk of chronic bronchitis in a large twin sample....
11. Prenatal x-ray exposure and childhood cancer in twins
International Nuclear Information System (INIS)
Harvey, E.B.; Boice, J.D. Jr.; Honeyman, M.; Flannery, J.T.
1985-01-01
A case-control study was conducted to investigate the relation between prenatal exposure to x-rays and childhood cancer, including leukemia, in over 32,000 twins born in Connecticut from 1930 to 1969. Twins as opposed to single births were chosen for study to reduce the likelihood of medical selection bias, since twins were often exposed to x-rays to diagnose the twin pregnancy or to determine fetal positioning before delivery and not because of medical conditions that may conceivably pre-dispose to cancer. Each of 31 incident cases of cancer, identified by linking the Connecticut twin and tumor registries, was matched with four twin controls according to sex, year of birth, and race. Records of hospitals, radiologists, and private physicians were searched for histories of x-ray exposure and other potentially important risk factors. Documented prenatal x-ray exposures were found for 39 per cent of the cases (12 of 31) and for 26 per cent of the controls (28 of 109). No other pregnancy, delivery, or maternal conditions were associated with cancer risk except low birth weight: 38 per cent of the cases as compared with 25 per cent of the controls weighed under 2.27 kg at birth. When birth weight was adjusted for, twins in whom leukemia or other childhood cancer developed were twice as likely to have been exposed to x-rays in utero as twins who were free of disease (relative risk, 2.4; 95 per cent confidence interval, 1.0 to 5.9). The results, though based on small numbers, provide further evidence that low-dose prenatal irradiation may increase the risk of childhood cancer
12. Epigenetic signature of birth weight discordance in adult twins
DEFF Research Database (Denmark)
Tan, Qihua; Nielsen, Morten Frost Munk; Heijmans, Bastiaan T
2014-01-01
between birth weight and adult life health while controlling for not only genetics but also postnatal rearing environment. We performed an epigenome-wide profiling on blood samples from 150 pairs of adult monozygotic twins discordant for birth weight to look for molecular evidence of epigenetic signatures...... profiling did not reveal epigenetic signatures of birth weight discordance although some sites displayed age-dependent intra-pair differential methylation in the extremely discordant twin pairs....
13. There are two twin shadows, but einstein is one
Directory of Open Access Journals (Sweden)
Popović Marko E.
2012-01-01
Full Text Available 2011 is the international year of chemistry, and it is exactly 100 years past after the P. Langevin promotion of “twin paradox” problem. The hundred year old problem still demands its solution. Twin paradox, established by a physicist, has been representing a nightmare for philosophers, physicists, chemists, and biologists until these days. After a hundred years, it is time to try to close this page in long history of misunderstanding of the special relativity. This analysis has three main assumptions. First, biological systems are a part of physical world and therefore they behave in accordance to the physical laws according to Schrödinger. Second, according to Von Bertalanffy the biological systems are open thermodynamic systems. Because of that the approach of non-equilibrium thermodynamics was used for analyzing the twin paradox. Third, rise of entropy is according to Hyflick strongly connected with aging. Entropy can be taken as a measure of cell age or even human age according to Silva et al. and Gladyshev. So entropy invariance strongly suggests that both twins should be the same age, so there is a potential problem for twin paradox with the second law. The only possible influence of relativity on the chemical reaction rate is time dilatation. However time flow does not cause the aging process, so time dilatation cannot have any influence on it. So, after detailed analysis, it is concluded that there is no twin paradox in reality. Both twins will be exactly in same thermodynamic state and bio-logical age. The traveler twin will notice time dilatation, but this relativistic effect has no influence on the aging process.
14. The identical-twin transfusion syndrome: a source of error in estimating IQ resemblance and heritability.
Science.gov (United States)
Munsinger, H
1977-01-01
Published studies show that among identical twins, lower birthweight is associated with lower adult intelligence. However, no such relation between birthweight and adult IQ exists among fraternal twins. A likely explanation for the association between birthweight and intelligence among identical twins is the identical twin transfusion syndrome which occurs only between some monochorionic identical twin pairs. The IQ scores from separated identical twins were reanalysed to explore the consequences of identical twin transfusion syndrome for IQ resemblance and heritability. Among 129 published cases of identical twin pairs reared apart, 76 pairs contained some birthweight information. The 76 pairs were separated into three classes: 23 pairs in which there was clear evidence of a substantial birthweight differences (indicating the probable existence of the identical twin transfusion syndrome), 27 pairs in which the information on birthweight was ambiguous (?), and 26 pairs in which there was clear evidence that the twins were similar in birthweight. The reanalyses showed: (1) birthweight differences are positively associated with IQ differences in the total sample of separated identical twins; (2) within the group of 23 twin pairs who showed large birthweight differences, there was a positive relation between birthweight differences and IQ differences; (3) when heritability of IQ is estimated for those twins who do not suffer large birthweight differences, the resemblance (and thus, h2/b) of the separated identical twins' IG is 0-95. Given that the average reliability of the individual IQ test is around 0-95, these data suggest that genetic factors and errors of measurement cause the individual differences in IQ among human beings. Because of the identical twin transfusion syndrome, previous studies of MZ twins have underestimated the effect of genetic factors on IQ. An analysis of the IQs for heavier and lighter birthweight twins suggests that the main effect of the
15. Birth order, gestational age, and risk of delivery related perinatal death in twins: retrospective cohort study
Science.gov (United States)
Smith, Gordon C S; Pell, Jill P; Dobbie, Richard
2002-01-01
Objective To determine whether twins born second are at increased risk of perinatal death because of complications during labour and delivery. Design Retrospective cohort study. Setting Scotland, 1992 and 1997. Participants All twin births at or after 24 weeks' gestation, excluding twin pairs in which either twin died before labour or delivery or died during or after labour and delivery because of congenital abnormality, non-immune hydrops, or twin to twin transfusion syndrome. Main outcome measure Delivery related perinatal deaths (deaths during labour or the neonatal period). Results Overall, delivery related perinatal deaths were recorded for 23 first twins only and 23 second twins only of 1438 twin pairs born before 36 weeks (preterm) by means other than planned caesarean section (P>0.99). No deaths of first twins and nine deaths of second twins (P=0.004) were recorded among the 2436 twin pairs born at or after 36 weeks (term). Discordance between first and second twins differed significantly in preterm and term births (P=0.007). Seven of nine deaths of second twins at term were due to anoxia during the birth (2.9 (95% confidence interval 1.2 to 5.9) per 1000); five of these deaths were associated with mechanical problems with the second delivery following vaginal delivery of the first twin. No deaths were recorded among 454 second twins delivered at term by planned caesarean section. Conclusions Second twins born at term are at higher risk than first twins of death due to complications of delivery. Previous studies may not have shown an increased risk because of inadequate categorisation of deaths, lack of statistical power, inappropriate analyses, and pooling of data about preterm births and term births. What is already known on this topicIt is difficult to assess the wellbeing of second twins during labourDeliveries of second twins are at increased risk of mechanical problems, such as cord prolapse and malpresentation, after vaginal delivery of first twins
16. ON THE OBSERVATION AND SIMULATION OF SOLAR CORONAL TWIN JETS
Energy Technology Data Exchange (ETDEWEB)
Liu, Jiajia; Wang, Yuming; Zhang, Quanhao [CAS Key Laboratory of Geospace Environment, School of Earth and Space Sciences, University of Science and Technology of China, NO. 96, Jinzhai Road, Hefei, Anhui 230026 (China); Fang, Fang [Laboratory for Atmospheric and Space Physics, University of Colorado at Boulder, 1234 Innovation Drive, Boulder, CO 80303 (United States); McIntosh, Scott W.; Fan, Yuhong [High Altitude Observatory, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307 (United States)
2016-02-01
We present the first observation, analysis, and modeling of solar coronal twin jets, which occurred after a preceding jet. Detailed analysis on the kinetics of the preceding jet reveals its blowout-jet nature, which resembles the one studied in Liu et al. However, the erupting process and kinetics of the twin jets appear to be different from the preceding one. Lacking detailed information on the magnetic fields in the twin jet region, we instead use a numerical simulation using a three-dimensional (3D) MHD model as described in Fang et al., and find that in the simulation a pair of twin jets form due to reconnection between the ambient open fields and a highly twisted sigmoidal magnetic flux, which is the outcome of the further evolution of the magnetic fields following the preceding blowout jet. Based on the similarity between the synthesized and observed emission, we propose this mechanism as a possible explanation for the observed twin jets. Combining our observation and simulation, we suggest that with continuous energy transport from the subsurface convection zone into the corona, solar coronal twin jets could be generated in the same fashion addressed above.
17. Evidence of genetic susceptibility to infectious mononucleosis: a twin study.
Science.gov (United States)
Hwang, A E; Hamilton, A S; Cockburn, M G; Ambinder, R; Zadnick, J; Brown, E E; Mack, T M; Cozen, W
2012-11-01
Infectious mononucleosis is a clinical manifestation of primary Epstein-Barr virus infection. It is unknown whether genetic factors contribute to risk. To assess heritability, we compared disease concordance in monozygotic to dizygotic twin pairs from the population-based California Twin Program and assessed the risk to initially unaffected co-twins. One member of 611 and both members of 58 twin pairs reported a history of infectious mononucleosis. Pairwise concordance in monozygotic and dizygotic pairs was respectively 12·1% [standard error (s.e.)=1·9%] and 6·1% (s.e.=1·2%). The relative risk (hazard ratio) of monozygotic compared to dizygotic unaffected co-twins of cases was 1·9 [95% confidence interval (CI) 1·1-3·4, P=0·03], over the follow-up period. When the analysis was restricted to same-sex twin pairs, that estimate was 2·5 (95% CI 1·2-5·3, P=0·02). The results are compatible with a heritable contribution to the risk of infectious mononucleosis.
18. Nephrolithiasis in identical twins: the impact of nature vs nurture.
Science.gov (United States)
Haleblian, George E; Cantor, David A; Sur, Roger L; Assimos, Dean G; Preminger, Glenn M
2007-09-01
To assess possible underlying metabolic abnormalities in three sets of monozygotic twins, to evaluate the interplay among the factors of kidney stone formation, a complex multifactorial process influenced by environmental, genetic and anatomical factors. Three sets of identical twins with either cystine or calcium oxalate stones were identified. Demographic data, medical histories and the results of 24-h urine testing, with samples collected on self-selected diets, were reviewed and analysed. The cystinuric twins had very similar cystine excretion rates, while stone activity was significantly more pronounced in one. Metabolic abnormalities were concordant in one set of twins with calcium oxalate stones, both being hypercalciuric and hyperuricosuric. However, metabolic abnormalities were discordant in the other pair, one twin with hypercalciuria and the other with hypocitraturia. Two of the three pairs had low urinary volume. These results support previous observations that environmental, genetic and potentially, anatomical factors play roles in kidney-stone formation. Additional controlled studies of monozygotic stone-forming twins might help to define the interplay between environmental and genetic factors, and allow the identification of susceptibility genes involved in stone generation.
19. Microplastic processes developed in pure Ag with mesoscale annealing twins
International Nuclear Information System (INIS)
Al-Fadhalah, Khaled Jabr Hasan; Li, Chun-Ming; Beaudoin, A.J.; Korzekwa, D.A.; Robertson, I.M.
2008-01-01
The impact of annealing twin boundaries with a high residual defect content on the mechanical response of polycrystalline fine- and coarse-grained (2 and 20 μm) silver was investigated through transmission electron microscopy and modeling. Besides an increase in the yield strength, the fine-grained material exhibited an inflection in the stress-strain curve after initial yield. Static and dynamic TEM studies revealed that the annealing twin boundaries acted as sources of perfect dislocations, partial dislocations and deformation twins; as barriers to the propagation of these dislocations; and as annihilation sites for dislocations. With increasing strain and as the twin boundaries were penetrated by dislocations, they contributed less to the overall mechanical properties. Based on these observations, equations for the evolution of mobile and forest dislocation densities are posed, depicting boundary sources and dislocation-dislocation interactions, respectively. The deformation response is modeled by computing the aggregate response of matrix-twin composite grains in the viscoplastic self-consistent scheme, which permits consideration of compatibility and equilibrium requirements across the twin boundaries. This work highlights the significant role boundaries play in generating the dislocations that control the macroscopic mechanical response
20. Microplastic processes developed in pure Ag with mesoscale annealing twins
Energy Technology Data Exchange (ETDEWEB)
Al-Fadhalah, Khaled Jabr Hasan [Mechanical Engineering Department, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: [email protected]; Li, Chun-Ming [Alcan Rolled Products-Ravenswood, LLC. P.O. Box 68, Century Road, Ravenswood, WV 26164 (United States)], E-mail: [email protected]; Beaudoin, A.J. [Department of Mechanical Science and Engineering, University of Illinois, 1206 West Green Street, Urbana, IL 61801 (United States)], E-mail: [email protected]; Korzekwa, D.A. [Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545 (United States); Robertson, I.M. [Department of Materials Science and Engineering, University of Illinois, 1304 W. Green Street, Urbana, IL 61801 (United States)], E-mail: [email protected]
2008-11-15
The impact of annealing twin boundaries with a high residual defect content on the mechanical response of polycrystalline fine- and coarse-grained (2 and 20 {mu}m) silver was investigated through transmission electron microscopy and modeling. Besides an increase in the yield strength, the fine-grained material exhibited an inflection in the stress-strain curve after initial yield. Static and dynamic TEM studies revealed that the annealing twin boundaries acted as sources of perfect dislocations, partial dislocations and deformation twins; as barriers to the propagation of these dislocations; and as annihilation sites for dislocations. With increasing strain and as the twin boundaries were penetrated by dislocations, they contributed less to the overall mechanical properties. Based on these observations, equations for the evolution of mobile and forest dislocation densities are posed, depicting boundary sources and dislocation-dislocation interactions, respectively. The deformation response is modeled by computing the aggregate response of matrix-twin composite grains in the viscoplastic self-consistent scheme, which permits consideration of compatibility and equilibrium requirements across the twin boundaries. This work highlights the significant role boundaries play in generating the dislocations that control the macroscopic mechanical response.
1. Twin edge colorings of certain square graphs and product graphs
Directory of Open Access Journals (Sweden)
R Rajarajachozhan
2016-04-01
Full Text Available A twin edge $k\\!$-coloring of a graph $G$ is a proper edge $k$-coloring of $G$ with the elements of $\\mathbb{Z}_k$ so that the induced vertex $k$-coloring, in which the color of a vertex $v$ in $G$ is the sum in $\\mathbb{Z}_k$ of the colors of the edges incident with $v,$ is a proper vertex $k\\!$-coloring. The minimum $k$ for which $G$ has a twin edge $k\\!$-coloring is called the twin chromatic index of $G.$ Twin chromatic index of the square $P_n^2,$ $n\\ge 4,$ and the square $C_n^2,$ $n\\ge 6,$ are determined. In fact, the twin chromatic index of the square $C_7^2$ is $\\Delta+2,$ where $\\Delta$ is the maximum degree. Twin chromatic index of $C_m\\,\\Box\\,P_n$ is determined, where $\\Box$ denotes the Cartesian product. $C_r$ and $P_r$ are, respectively, the cycle, and the path on $r$ vertices each.
2. Reciprocal Longitudinal Associations Between Adolescent Twin Gambling and Delinquency.
Science.gov (United States)
Vitaro, Frank; C Hartl, Amy; Laursen, Brett; Brendgen, Mara; Dionne, Ginette; Boivin, Michel
2015-12-01
This study examined sibling influence over gambling involvement and delinquency in a sample of 628 twins (151 male dyads, 163 female dyads). Self-reports of gambling involvement and delinquency were collected for each twin at ages 13, 14 and 15 years. Results revealed evidence of between-twin influence. Higher levels of an adolescent's delinquency predicted an increase in his or her co-twin's delinquency from age 13 to age 14 and from age 14 to age 15. In contrast, gambling behavior was unaffected by the co-twin's gambling involvement. Within-twins, higher initial levels of delinquency predicted a subsequent increase in gambling behavior from age 13 to age 14 and again from age 14 to age 15, and higher initial levels of gambling involvement predicted an increase in delinquency from age 14 to age 15. Between and within siblings effects are discussed in light of the scant literature on (a) sibling influence on gambling, and (b) the links between gambling and delinquency.
3. The Impact of Twin Birth on Early Neonatal Outcomes.
Science.gov (United States)
Fumagalli, Monica; Schiavolin, Paola; Bassi, Laura; Groppo, Michela; Uccella, Sara; De Carli, Agnese; Passera, Sofia; Sirgiovanni, Ida; Dessimone, Francesca; Consonni, Dario; Acaia, Barbara; Ramenghi, Luca Antonio; Mosca, Fabio
2016-01-01
This study aims to describe the impact of twin birth, chorionicity, intertwin birth weight (BW) discordance and birth order on neonatal outcomes. We performed a hospital-based retrospective study on 2,170 twins (6.4% of all live births) and 2,217 singletons inborn 2007 to 2011. Data on neonatal characteristics, morbidities, and mortality were collected and compared. Univariate and multiple (adjusted for gestational age [GA] and gender) linear random intercept regression models were used. Overall, 62.3% of twins were born premature. At multiple regression, twins were similar to singletons for neonatal morbidities, but they were more likely to have lower BW and to be born by cesarean delivery. Monochorionic twins had lower GA and BW compared with dichorionic ones and were more likely to develop respiratory distress syndrome (odds ratio [OR], 1.7), hypoglycemia (OR, 3.3), need for transfusion, (OR, 3.4) but not brain abnormalities. Moderate and severe BW discordance were associated with longer length of stay and increased risk for morbidities but not for death. Birth order had no effects. Prematurity was the most common outcome in twins and accounted for the apparently increased risk in morbidities. Monochorionicity was confirmed as risk factor for lower GA and neonatal morbidities. BW discordance may play a role in developing neonatal complications and needs to be further investigated. Thieme Medical Publishers 333 Seventh Avenue, New York, NY 10001, USA.
4. On the Observation and Simulation of Solar Coronal Twin Jets
Science.gov (United States)
Liu, Jiajia; Fang, Fang; Wang, Yuming; McIntosh, Scott W.; Fan, Yuhong; Zhang, Quanhao
2016-02-01
We present the first observation, analysis, and modeling of solar coronal twin jets, which occurred after a preceding jet. Detailed analysis on the kinetics of the preceding jet reveals its blowout-jet nature, which resembles the one studied in Liu et al. However, the erupting process and kinetics of the twin jets appear to be different from the preceding one. Lacking detailed information on the magnetic fields in the twin jet region, we instead use a numerical simulation using a three-dimensional (3D) MHD model as described in Fang et al., and find that in the simulation a pair of twin jets form due to reconnection between the ambient open fields and a highly twisted sigmoidal magnetic flux, which is the outcome of the further evolution of the magnetic fields following the preceding blowout jet. Based on the similarity between the synthesized and observed emission, we propose this mechanism as a possible explanation for the observed twin jets. Combining our observation and simulation, we suggest that with continuous energy transport from the subsurface convection zone into the corona, solar coronal twin jets could be generated in the same fashion addressed above.
5. Decreasing prematurity in twin gestations: predicaments and possibilities.
Science.gov (United States)
Zork, Noelia; Biggio, Joseph; Tita, Alan; Rouse, Dwight; Gyamfi-Bannerman, Cynthia
2013-08-01
The twin birth rate has been steadily increasing in the United States over the past 10 years attributable in large part to the increased use of reproductive technologies. Despite advancements in the prevention of preterm labor for singletons, the overall rate of preterm birth has decreased only minimally. Several interventions to prevent preterm birth in twins have been studied, but none has proven effective. Inpatient bedrest has not been shown to be effective and can cause significant maternal morbidity. Although intramuscular 17α-hydroxyprogesterone caproate is effective in decreasing the risk of recurrent preterm delivery in singletons, neither it nor cerclage is effective in twin gestations, even in those with a short cervix. However, small trials, subgroup analyses, and a meta-analysis suggest that vaginal progesterone and the Arabin cervical pessary may reduce rates of preterm birth in twins of mothers with a short cervix. Given the current lack of effective therapies to prevent preterm birth in twins, large multicenter trials are needed to assess the effectiveness of vaginal progesterone and pessary in twins of mothers with a short cervix.
6. Family and twin studies on methacholine hypersensitivity
Directory of Open Access Journals (Sweden)
Robert G Townley
1998-01-01
Full Text Available Essentially all asthmatics demonstrate a marked sensitivity to inhaled methacholine and histamine, termed non-specific bronchial (airway hyperresponsiveness (BHR. Airway hyperresponsiveness is a characteristic not only of asthmatics, but can be found in many persons with allergic rhinitis as well as in members of asthmatics' families. The presence of BHR usually precedes the development of clinically identifiable asthma. In recent years there has been an emphasis on inflammation, inducing hyperresponsiveness. However, these factors increase airway hyperresponsiveness by a magnitude of only three-fold compared with normal subjects. The important question is not why asthmatics respond, but why normal subjects do not. The normal subjects are quite able to maintain normal airway function in the presence of high concentrations of methacholine or histamine in vivo but not in vitro, suggesting the presence of protective mechanisms in vivo that are either lacking in, or are less effective in, the asthmatic subjects. There is a strong correlation between the degree of airway hyperresponsiveness and the severity of asthma. In order to determine whether methacholine sensitivity could be used as a potential genetic marker, we studied 750 subjects from 53 asthma families and 26 control families. The best sensitivity and specificity is at 200 breath units. Only 6% of the allergic rhinitis subjects showed a high positive response, but 30% overlapped with asthmatics in that they reacted with 200 breath units or less. There was a group of non-atopic subjects from asthma families who responded by 200 breath units, but there was a significantly lower percentage from normal families. Being from an asthma family is a risk factor in terms of subsequent development of asthma and increased airway reactivity. The parent data suggest that airway reactivity is transmitted to succeeding generations. Studies of twins have revealed that the concordance of asthma is higher in
7. Identification of promising Twin Hub networks : Report of Work Package 1 of the Intermodal rail freight Twin hub Network Northwest Europe - project (final report)
NARCIS (Netherlands)
Kreutzberger, E.D.; Konings, J.W.; Meijer, S.; Witteveen, C.; Meijers, B.M.; Pekin, E.; Macharis, C.; Kiel, J.; Kawabata, Y.; Vos, W.
2014-01-01
This report is the first deliverable of the project Intermodal Rail Freight Twin Hub Network Northwest Europe. We call its subject Twin hub network and the organisational entity to carry out the actions the Twin hub project. The project is funded by INTERREG NWE (programme IVb). Its work started in
8. Clinical Factors Associated With Presentation Change of the Second Twin After Vaginal Delivery of the First Twin.
Science.gov (United States)
Panelli, Danielle M; Easter, Sarah Rae; Bibbo, Carolina; Robinson, Julian N; Carusi, Daniela A
2017-11-01
To identify clinical factors associated with a change from vertex to nonvertex presentation in the second twin after vaginal birth of the first. We assembled a retrospective cohort of women with viable vertex-vertex twin pregnancies who delivered the presenting twin vaginally. Women whose second twin changed from vertex to nonvertex after vaginal birth of the first were classified as experiencing an intrapartum change in presentation. Characteristics associated with intrapartum presentation change in a univariate analysis with a P value ≤.10 were then evaluated in a multivariate logistic regression model. Four-hundred fifty women met inclusion criteria, of whom 55 (12%) had intrapartum presentation change of the second twin. Women experiencing intrapartum presentation change were more likely to be multiparous (69% compared with 47%, Ppresentation of the second twin between the most recent antepartum ultrasonogram and the ultrasonogram done on admission to labor and delivery (11% compared with 4%, P=.04). In an adjusted analysis, multiparity and gestational age less than 34 weeks were significantly associated with presentation change (adjusted odds ratio [OR] 2.9, 95% CI 1.5-5.6 and adjusted OR 2.6, 95% CI 1.1-5.9, respectively). Women with intrapartum presentation change were more likely to undergo cesarean delivery for their second twin (44% compared with 7%, Ppresentation. Twenty of the 24 (83%) cesarean deliveries performed in the intrapartum presentation change group were done for issues related to malpresentation. Multiparity and gestational age less than 34 weeks are associated with intrapartum presentation change of the second twin.
9. Hybrid spectral CT reconstruction.
Directory of Open Access Journals (Sweden)
Darin P Clark
Full Text Available Current photon counting x-ray detector (PCD technology faces limitations associated with spectral fidelity and photon starvation. One strategy for addressing these limitations is to supplement PCD data with high-resolution, low-noise data acquired with an energy-integrating detector (EID. In this work, we propose an iterative, hybrid reconstruction technique which combines the spectral properties of PCD data with the resolution and signal-to-noise characteristics of EID data. Our hybrid reconstruction technique is based on an algebraic model of data fidelity which substitutes the EID data into the data fidelity term associated with the PCD reconstruction, resulting in a joint reconstruction problem. Within the split Bregman framework, these data fidelity constraints are minimized subject to additional constraints on spectral rank and on joint intensity-gradient sparsity measured between the reconstructions of the EID and PCD data. Following a derivation of the proposed technique, we apply it to the reconstruction of a digital phantom which contains realistic concentrations of iodine, barium, and calcium encountered in small-animal micro-CT. The results of this experiment suggest reliable separation and detection of iodine at concentrations ≥ 5 mg/ml and barium at concentrations ≥ 10 mg/ml in 2-mm features for EID and PCD data reconstructed with inherent spatial resolutions of 176 μm and 254 μm, respectively (point spread function, FWHM. Furthermore, hybrid reconstruction is demonstrated to enhance spatial resolution within material decomposition results and to improve low-contrast detectability by as much as 2.6 times relative to reconstruction with PCD data only. The parameters of the simulation experiment are based on an in vivo micro-CT experiment conducted in a mouse model of soft-tissue sarcoma. Material decomposition results produced from this in vivo data demonstrate the feasibility of distinguishing two K-edge contrast agents with
10. Hybrid spectral CT reconstruction
Science.gov (United States)
Clark, Darin P.
2017-01-01
Current photon counting x-ray detector (PCD) technology faces limitations associated with spectral fidelity and photon starvation. One strategy for addressing these limitations is to supplement PCD data with high-resolution, low-noise data acquired with an energy-integrating detector (EID). In this work, we propose an iterative, hybrid reconstruction technique which combines the spectral properties of PCD data with the resolution and signal-to-noise characteristics of EID data. Our hybrid reconstruction technique is based on an algebraic model of data fidelity which substitutes the EID data into the data fidelity term associated with the PCD reconstruction, resulting in a joint reconstruction problem. Within the split Bregman framework, these data fidelity constraints are minimized subject to additional constraints on spectral rank and on joint intensity-gradient sparsity measured between the reconstructions of the EID and PCD data. Following a derivation of the proposed technique, we apply it to the reconstruction of a digital phantom which contains realistic concentrations of iodine, barium, and calcium encountered in small-animal micro-CT. The results of this experiment suggest reliable separation and detection of iodine at concentrations ≥ 5 mg/ml and barium at concentrations ≥ 10 mg/ml in 2-mm features for EID and PCD data reconstructed with inherent spatial resolutions of 176 μm and 254 μm, respectively (point spread function, FWHM). Furthermore, hybrid reconstruction is demonstrated to enhance spatial resolution within material decomposition results and to improve low-contrast detectability by as much as 2.6 times relative to reconstruction with PCD data only. The parameters of the simulation experiment are based on an in vivo micro-CT experiment conducted in a mouse model of soft-tissue sarcoma. Material decomposition results produced from this in vivo data demonstrate the feasibility of distinguishing two K-edge contrast agents with a spectral
11. Noncommutativity from spectral flow
Energy Technology Data Exchange (ETDEWEB)
Heinzl, Thomas; Ilderton, Anton [School of Mathematics and Statistics, University of Plymouth, Drake Circus, Plymouth PL4 8AA (United Kingdom)
2007-07-27
We investigate the transition from second- to first-order systems. Quantum mechanically, this transforms configuration space into phase space and hence introduces noncommutativity in the former. This transition may be described in terms of spectral flow. Gaps in the energy or mass spectrum may become large which effectively truncates the available state space. Using both operator and path integral languages we explicitly discuss examples in quantum mechanics (light-front) quantum field theory and string theory.
12. Mechanical spectral shift reactor
International Nuclear Information System (INIS)
Wilson, J.F.; Sherwood, D.G.
1982-01-01
A mechanical spectral shift reactor comprises a reactive core having fuel assemblies accommodating both water displacer elements and neutron absorbing control rods for selectively changing the volume of water-moderator in the core. The fuel assemblies with displacer and control rods are arranged in alternating fashion so that one displacer element drive mechanism may move displacer elements in more than one fuel assembly without interfering with the movement of control rods of a corresponding control rod drive mechanisms. (author)
13. Evolution of Matrix-Twin Interfaces of (1 0 -1 2) Twin in Magnesium
Czech Academy of Sciences Publication Activity Database
Ostapovets, Andriy; Serra, A.
2015-01-01
Roč. 128, č. 4 (2015), s. 661-663 ISSN 0587-4246. [ISPMA13 - International Symposium on Physics of Materials /13./. Praha, 31.08.2014-04.09.2014] R&D Projects: GA MŠk(CZ) EE2.3.30.0063; GA MŠk(CZ) ED1.1.00/02.0068 Grant - others:Spanish Secretariat of Research, Development and Innovation (ES) FIS2012-39433-C02-02 Institutional support: RVO:68081723 Keywords : twinning * magnesium * computer simuations Subject RIV: JG - Metallurgy Impact factor: 0.525, year: 2015
14. Cross-scale observations of the 2015 St. Patrick's day storm: THEMIS, Van Allen Probes, and TWINS
International Nuclear Information System (INIS)
Goldstein, J.
2016-01-01
In this paper, we present cross-scale magnetospheric observations of the 17 March 2015 (St. Patrick's Day) storm, by Time History of Events and Macroscale Interactions during Substorms (THEMIS), Van Allen Probes (Radiation Belt Storm Probes), and Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS), plus upstream ACE/Wind solar wind data. THEMIS crossed the bow shock or magnetopause 22 times and observed the magnetospheric compression that initiated the storm. Empirical models reproduce these boundary locations within 0.7 R E . Van Allen Probes crossed the plasmapause 13 times; test particle simulations reproduce these encounters within 0.5 R E . Before the storm, Van Allen Probes measured quiet double-nose proton spectra in the region of corotating cold plasma. About 15 min after a 0605 UT dayside southward turning, Van Allen Probes captured the onset of inner magnetospheric convection, as a density decrease at the moving corotation-convection boundary (CCB) and a steep increase in ring current (RC) proton flux. During the first several hours of the storm, Van Allen Probes measured highly dynamic ion signatures (numerous injections and multiple spectral peaks). Sustained convection after ~1200 UT initiated a major buildup of the midnight-sector ring current (measured by RBSP A), with much weaker duskside fluxes (measured by RBSP B, THEMIS a and THEMIS d). A close conjunction of THEMIS d, RBSP A, and TWINS 1 at 1631 UT shows good three-way agreement in the shapes of two-peak spectra from the center of the partial RC. A midstorm injection, observed by Van Allen Probes and TWINS at 1740 UT, brought in fresh ions with lower average energies (leading to globally less energetic spectra in precipitating ions) but increased the total pressure. Finally, the cross-scale measurements of 17 March 2015 contain significant spatial, spectral, and temporal structure.
15. Speech recognition from spectral dynamics
Carrier nature of speech; modulation spectrum; spectral dynamics ... the relationships between phonetic values of sounds and their short-term spectral envelopes .... the number of free parameters that need to be estimated from training data.
16. Risk of epilepsy in opposite-sex and same-sex twins
DEFF Research Database (Denmark)
Mao, Yanyan; Ahrenfeldt, Linda Juel; Christensen, Kaare
2018-01-01
Background: There is a complex interaction between female and male sex hormones and the risk of epilepsy. Whether prenatal exposure to higher levels of sex hormones affects the development of epilepsy in childhood or later in life is not well known. The sex hormone environment of fetuses may...... be affected by the sex of the co-twin. We estimated the risk of epilepsy for twins with an opposite-sex (OS) co-twin compared with twins with a same-sex (SS) co-twin. Methods: From the Danish Twin Registry, we identified OS female twins (n = 11,078), SS female twins (n = 19,186), OS male twins (n = 11...
17. Genetic contribution to the relationship between social role function and depressive symptoms in Japanese elderly twins: a twin study.
Science.gov (United States)
Nishihara, Reiko; Inui, Fujio; Kato, Kenji; Tomizawa, Rie; Hayakawa, Kazuo
2011-03-01
Social role function is the capacity to maintain interpersonal relationships and is essential for being independent in the community. Limitations in social role function often coexist with depressive symptoms, suggesting a possible common mechanistic basis. We investigated whether the observed association between these traits is mainly a result of genetic or environmental influences. In 2008, a questionnaire was sent to 745 male twins aged 65 years and older. Our sample included 397 male twins. The number of monozygotic twins was 302, and dizygotic was 95. Among the twin pairs for whom data were available for both twins, 75 twin pairs (150 individuals) were monozygotic and 28 pairs (56 individuals) were dizygotic. Social role function was assessed using the Tokyo Metropolitan Institute of Gerontology Index of Competence. Depressive symptoms were measured by the 15-item version of the Geriatric Depression Scale. Relative importance of genes and environments for the phenotypes was calculated using structural equation analyses. Our results show that genetic influence was the major contributor to the relationship between social role function and depressive symptoms, and non-shared environmental influence was important for overall variation in each trait. We concluded that focusing on a non-shared environment is an essential approach for maintaining social role function and psychological well-being. It is suggested that treatments specific to depressive symptoms are more effective than indirect intervention targeting social role function. © 2011 The Authors. Psychogeriatrics © 2011 Japanese Psychogeriatric Society.
18. Late language emergence in 24-month-old twins: heritable and increased risk for late language emergence in twins.
Science.gov (United States)
Rice, Mabel L; Zubrick, Stephen R; Taylor, Catherine L; Gayán, Javier; Bontempo, Daniel E
2014-06-01
This study investigated the etiology of late language emergence (LLE) in 24-month-old twins, considering possible twinning, zygosity, gender, and heritability effects for vocabulary and grammar phenotypes. A population-based sample of 473 twin pairs participated. Multilevel modeling estimated means and variances of vocabulary and grammar phenotypes, controlling for familiality. Heritability was estimated with DeFries-Fulker regression and variance components models to determine effects of heritability, shared environment, and nonshared environment. Twins had lower average language scores than norms for single-born children, with lower average performance for monozygotic than dizygotic twins and for boys than girls, although gender and zygosity did not interact. Gender did not predict LLE. Significant heritability was detected for vocabulary (0.26) and grammar phenotypes (0.52 and 0.43 for boys and girls, respectively) in the full sample and in the sample selected for LLE (0.42 and 0.44). LLE and the appearance of Word Combinations were also significantly heritable (0.22-0.23). The findings revealed an increased likelihood of LLE in twin toddlers compared with single-born children that is modulated by zygosity and gender differences. Heritability estimates are consistent with previous research for vocabulary and add further suggestion of heritable differences in early grammar acquisition.
19. Variant selection of primary, secondary and tertiary twins in a deformed Mg alloy
International Nuclear Information System (INIS)
Mu, Sijia; Jonas, John J.; Gottstein, Günter
2012-01-01
Samples of magnesium alloy AZ31 were deformed in plane strain compression in a channel die at 100 °C and a strain rate of 5 × 10 −3 s −1 . The initial texture was favorably oriented for extension twinning. At a true strain of ε = −0.11, many primary extension twins were observed to consume their parent grains completely. Furthermore, numerous secondary contraction twins formed within the primary extension twins and some tertiary extension twins grew within the secondary contraction twins. The orientations of the parent grains and all three generations of twins were measured. The twin variants selected during each of the three stages of twinning were determined by electron backscatter diffraction techniques and the absent potential twin variants were also identified. The way in which the selected primary extension twins grow so as to consume the parent grains and contact all the neighboring grains is explained in terms of the accommodation strains imposed on the neighboring grains. The analysis shows that the primary twin selected is not necessarily the variant with the highest Schmid factor but the one that requires the least accommodation work in most of the neighboring grains. The same principle was found to hold for the secondary and tertiary twins. By contrast, potential high Schmid factor twins that required the consumption of appreciable accommodation energy did not form. A Taylor simulation produced similar results and indicates that the accommodation strain concept is consistent with the principle of the minimization of plastic work.
20. Monozygotic twin discordant for Down syndrome: mos 47,XX,+21/46,XX and 46,XX.
Science.gov (United States)
Choi, Sun Ah; Ko, Jung Min; Shin, Choong Ho; Yang, Sei Won; Choi, Jin Sun; Oh, Sun Kyung
2013-08-01
Monozygotic twins, developed from a single zygote, are almost identical in clinical phenotype and concordant karyotypes. Monozygotic twins with discordant karyotypes are thought to be quite rare. Here, we report monochorionic-diamniotic twins discordant for Down syndrome. On findings of prenatal ultrasonography, nuchal translucency thickness was different between twins, and suggested that one of the twins was at high risk for having chromosomal abnormalities including Down syndrome. The twins were monochorionic-diamniotic; therefore, chorionic villi sampling of the common placenta was performed. The karyotype of the chorionic villi cells was 46,XX, and pregnancy was maintained. After delivery, dysmorphic clinical features suggesting Down syndrome were found in one of the twins, while the other twin showed a morphologically normal appearance. Karyotypes of peripheral blood leukocytes were repeatedly normal in the dysmorphic twin; however, the karyotype of skin fibroblasts from the dysmorphic twin indicated Down syndrome mosaicism; 47,XX,+21[99]/46,XX[2]. The karyotype of skin fibroblasts from the morphologically normal twin was 46,XX. Monozygosity of the twins was confirmed by a short tandem repeat analysis using 16 polymorphic markers. A mitotic nondisjunction followed by the twinning would explain the discordant karyotypes between monozygotic twins.
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https://www.physics-in-a-nutshell.com/article/29/rotating-frame-of-reference
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Physics in a nutshell
$\renewcommand{\D}[2][]{\,\text{d}^{#1} {#2}}$ $\DeclareMathOperator{\Tr}{Tr}$
# Rotating Frame of Reference
## Newton's 2nd Law
The derivation of the Navier-Stokes equations is based on Newton's second law: It is assumed that the kinematics of a particle is determined by the particle's interaction with its physical environment. Every acceleration (change of velocity) is caused by an external force. If one on the other hand knows all relevant forces, the acceleration can be calculated and also the trajectories (by integrating the acceleration twice).
### Non-Inertial Frames of Reference
However, this approach is strictly speaking not valid in non-inertial (accelerated) frames of reference (as for instance the rotating earth). In these, additional accelerations are observed which are not due to actual physical forces as stated by Newton's laws. So, Newton's 2nd law cannot be applied directly to determine the equations of motion!
This issue can be fixed by considering a coordinate transformation between the observer's (accelerated) and any inertial frame of reference (in which Newton's 2nd law applies). Then one can simply apply Newton's 2nd law in the inertial frame and replace the inertial acceleration with other quantities that can be measured directly by the observer.
## Coordinate Representation, Change of Basis, Rotation Matrix
Consider two cartesian coordinate system: One is inertial ($\text{in}$) and the other one ($\text{rot}$) rotates with respect to the first one with constant angular velocity: \begin{align} \Omega = \frac{\D{\varphi}}{\D{t}} \label{eq:Omega} \end{align} Without loss of generality, the $z$-axes of both systems can be chosen to be aligned parallel to the axis of rotation. Then the relative orientation between the two coordinate systems is given by the angle $\varphi (t)$ that is spanned by the respective $x$- or $y$-axes.
Depending on the choice of the coordinate system, any vector $\vec{a}$ can be specified by its coordinates with respect to the corresponding basis. In general, these differ for the different coordinate systems but are related by a transformation matrix $R$ (and its inverse $R^{-1}$): \begin{align} \left[ \vec{a} \right]_\text{rot} &= R \;\;\;\cdot \left[ \vec{a} \right]_\text{in} \label{eq:R} \\ \left[ \vec{a} \right]_\text{in}\; &= R^{-1} \cdot \left[ \vec{a} \right]_\text{rot} \label{eq:R^T} \end{align} Here \begin{align} \left[ \vec{a} \right]_\text{rot} := \begin{pmatrix} x_\text{rot} \\ y_\text{rot} \\ z_\text{rot} \end{pmatrix} \quad \text{and} \quad \left[ \vec{a} \right]_\text{in} := \begin{pmatrix} x_\text{in} \\ y_\text{in} \\ z_\text{in} \end{pmatrix} \end{align} are the coordinate representations of the position vector $\vec{a}$ with respect to the rotating basis ($\text{rot}$) and the inertial one ($\text{in}$).
## Rotation Matrix
The transformation matrix $R$ depends on the angle of rotation $\varphi (t)$ and contains the coordinates of the rotational unit vectors with respect to the inertial basis: \begin{align} R &= \begin{pmatrix} \left[ \hat{x}_\text{rot} \right]_\text{in} & \left[ \hat{y}_\text{rot} \right]_\text{in} & \left[ \hat{z}_\text{rot} \right]_\text{in} \end{pmatrix} \\[2ex] &= \begin{pmatrix} \cos\varphi & -\sin\varphi & 0 \\ \sin\varphi & \cos\varphi & 0 \\ 0 & 0 & 1 \end{pmatrix} \end{align} As it is characteristic for a rotation matrix, \begin{align} R^{-1} = R^T \end{align} since $R R^{T} = \mathbb{I}$ (as you can easily verify). Thus, instead of calculating the inverse laboriously, one can simply take the transpose.
### Useful Relations
At this point it is convenient to calculate two more expressions which will be needed later: \begin{align} \frac{\D{R}}{\D{t}} &\stackrel{\eqref{eq:Omega}}{=} \frac{\D{R}}{\D{\varphi}} \underbrace{\frac{\D{\varphi}}{\D{t}}}_{:= \Omega} = \Omega \cdot \begin{pmatrix} -\sin\varphi & -\cos\varphi & 0 \\ \cos\varphi & -\sin\varphi & 0 \\ 0 & 0 & 0 \end{pmatrix} \label{eq:dRdT} \\[2ex] \frac{\D{R}}{\D{t}} \cdot R^T &\stackrel{\eqref{eq:dRdT}}{=} \Omega \cdot \begin{pmatrix} -\sin\varphi & -\cos\varphi & 0 \\ \cos\varphi & -\sin\varphi & 0 \\ 0 & 0 & 0 \end{pmatrix} \cdot \begin{pmatrix} \cos\varphi & \sin\varphi & 0 \\ -\sin\varphi & \cos\varphi & 0 \\ 0 & 0 & 1 \end{pmatrix} \\ &= \Omega \cdot \begin{pmatrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ \Omega \end{pmatrix} \times \\ &= \vec{\Omega} \times \label{eq:Omegax} \end{align} The penultimate step may be a bit surprising. It has to be understood in a sense of an operator equation that is completely meaningful only when being applied to a dummy vector. So if you apply both operators to an arbitrary vector, you'll notice that the result is the same.
Accordingly, one finds: \begin{align} \frac{\D{R^T}}{\D{t}} \cdot R = - \vec{\Omega} \times \label{eq:-Omegax} \end{align}
## Time Derivatives
When the origins of the coordinates systems coincide, then the position vector $\vec{r}$ is independent of the particular coordinate system, since it connects this common origin with a particle's location in space (which is also independent of the frame of reference).
### Velocities
This is a bit different for velocities and accelerations: They are defined as the change of the coordinates of a position vector in a particular coordinate system. A vector which is at rest in the rotating frame rotates with non-zero velocity in the inertial one. Therefore, we will use another (inner) index for velocities and accelerations indicating the frame of reference in which them are defined. The resulting velocity vector can however be represented as an arrow in space, which in turn can be given either with respect to the inertial or rotating basis (indicated by the outer index). \begin{align} \left[ \vec{v}_\text{rot} \right]_\text{rot} & := \frac{\D{}}{\D{t}} \left[ \vec{r} \right]_\text{rot} \stackrel{\eqref{eq:R}}{=} \frac{\D{}}{\D{t}} \left( R \cdot \left[ \vec{r} \right]_\text{in} \right) \\[1ex] &= \frac{\D{R}}{\D{t}} \cdot \left[\vec{r}\right]_\text{in} + \underbrace{ R \cdot \underbrace{ \frac{\D{}}{\D{t}} \left[ \vec{r} \right]_\text{in} }_{= \left[ \vec{v}_\text{in} \right]_\text{in}} }_{ = \left[ \vec{v}_\text{in} \right]_\text{rot} } \\ &\stackrel{\eqref{eq:R^T}\eqref{eq:R}}{=} \underbrace{ \frac{\D{R}}{\D{t}} R^T }_{\vec{\Omega}\times} \cdot \left[\vec{r}\right]_\text{rot} + \left[ \vec{v}_\text{in} \right]_\text{rot} \\ &\stackrel{\eqref{eq:Omegax}}{=} \vec{\Omega} \times \left[ \vec{r} \right]_\text{rot} + \left[ \vec{v}_\text{in} \right]_\text{rot} \end{align} Analogously: \begin{align} \left[ \vec{v}_\text{in} \right]_\text{in} & := \frac{\D{}}{\D{t}} \left[ \vec{r} \right]_\text{in} \\ &= -\vec{\Omega} \times \left[\vec{r}\right]_\text{in} + \left[ \vec{v}_\text{rot} \right]_\text{in} \label{eq:vRotIn} \end{align}
These expressions can now also be stated in coordinate-independent form:
The velocities in the inertial and rotating frame of reference are related by:[1] \begin{align} \vec{v}_\text{rot} = \vec{\Omega} \times \vec{r} + \vec{v}_\text{in} \end{align}
Thus, the two velocities $\vec{v}_\text{rot}$ and $\vec{v}_\text{in}$ differ by a term $\vec{\Omega} \times \vec{r}$ which accounts for the relative motion of the coordinate systems which respect to each other. It appears because the transformation matrix $R(\varphi (t) )$ is a function of time and therefore the order of the time derivative operator ($\frac{\D{}}{\D{t}}$) and the change of basis operators ($R$,$R^T$) cannot just be reversed. Instead, the product rule has to applied which creates the additional term.
#### Accelerations
For the accelerations one can proceed in an analogous way as before with the velocities: \begin{align} \left[ \vec{a}_\text{rot} \right]_\text{rot} &:= \frac{ \D{} }{ \D{t} } \left[ \vec{v}_\text{rot} \right]_\text{rot} \stackrel{\eqref{eq:R}}{=} \frac{ \D{} }{ \D{t} } \left( R \cdot \left[ \vec{v}_\text{rot} \right]_\text{in} \right) \\[1ex] &\stackrel{\eqref{eq:vRotIn}}{=} \frac{ \D{} }{ \D{t} } \left[ R \cdot \left( \left[ \vec{v}_\text{in} \right]_\text{in} + \vec{\Omega} \times \left[ \vec{r} \right]_\text{in} \right) \right] \\[2ex] &= \frac{ \D{R} }{ \D{t} } \left[ \vec{v}_\text{in} \right]_\text{in} + R \frac{ \D{} }{ \D{t} } \left[ \vec{v}_\text{in} \right]_\text{in} + \frac{ \D{R} }{ \D{t} } \vec{\Omega} \times \left[ \vec{r} \right]_\text{in} + R \cdot \vec{\Omega} \times \frac{ \D{} }{ \D{t} } \left[ \vec{r} \right]_\text{in} \\[2ex] &= \underbrace{ \frac{ \D{R} }{ \D{t} } R^T }_{ \vec{\Omega} \times } \left[ \vec{v}_\text{in} \right]_\text{rot} + \left[ \vec{a}_\text{in} \right]_\text{rot} + \underbrace{ \frac{ \D{R} }{ \D{t} } R^T }_{\vec{\Omega} \times} \vec{\Omega} \times \left[ \vec{r} \right]_\text{rot} + \vec{\Omega} \times \left[ \vec{v}_\text{in} \right]_\text{rot} \\[2ex] &= 2 \cdot \vec{\Omega} \times \left[ \vec{v}_\text{in} \right]_\text{rot} + \vec{\Omega} \times \left( \vec{\Omega} \times \left[ \vec{r} \right]_\text{rot} \right) + \left[ \vec{a}_\text{in} \right]_\text{rot} \end{align} In coordinate-independent notation this reads:
In the case of time-independent rotation vector $\vec{\Omega}$ the accelerations within the inertial and rotating frame of reference are related by: \begin{align} \vec{a}_\text{rot} = \underbrace{ 2 \cdot \vec{\Omega} \times \vec{v}_\text{in} }_\text{Coriolis} + \underbrace{ \vec{\Omega} \times \left( \vec{\Omega} \times \vec{r} \right) }_\text{centrifugal} + \vec{a}_\text{in} \end{align} The two additional terms are referred to as the Coriolis- and centrifugal acceleration respectively.[2] [3]
## References
[1] Pijush K. Kundu, Ira M. Cohen Fluid Mechanics Academic Press 2002 (ch. 12) [2] D. J. Tritton Physical Fluid Dynamics Oxford University Press 2006 (ch. 16.2) [3] Pijush K. Kundu, Ira M. Cohen Fluid Mechanics Academic Press 2002 (ch. 12)
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https://annals.math.princeton.edu/1995/141-2/p01
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# The isomorphism problem for hyperbolic groups I
### Abstract
Using canonical representatives in hyperbolic groups and the decidability of the Diophantine theory of free semigroups with paired alphabet, we solve the isomorphism problem for hyperbolic groups with no (essential) small action on a real tree. The solution enables computation of the outer automorphism group of such groups and implies the homeomorphism problem for “weakly geometric” 3-manifolds, closed hyperbolic manifolds, and negatively curved ones of dimension $\ge 5$. In a continuation paper [Sel], we combine structural results on hyperbolic groups and their automorphisms obtained in [Se2] with the procedure described in this paper to give a complete solution to the isomorphism problem for (torsion-free) hyperbolic groups.
Zlil Sela
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https://www.physicsforums.com/threads/special-relativity-momentum.211901/
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# Special Relativity(momentum)
1. Jan 29, 2008
### Winzer
1. The problem statement, all variables and given/known data
A particle of rest mass 1.30 MeV/c2 and kinetic energy 2.70 MeV collides with a stationary particle of rest mass 2.50 MeV/c2. After the collision, the particles stick together. Find the speed of the first particle before the collision
2. Relevant equations
$$KE=(1-\gamma)mc^2$$
3. The attempt at a solution
I am positive this is the right equation to use but I keep getting the wrong answer.
I don't know why!
2. Jan 29, 2008
### joelperr
Show us what you have so far, and we can go from there. That might be one of the equations that will be used, but you need to show some sort of attempt at a solution instead of simply stating that you're getting an incorrect answer.
3. Jan 29, 2008
### Winzer
fine.
That equation goes to:$$c*\sqrt(1-(\frac{E_rest}{KE-E_rest})^2)$$
I converted 1.30 MeV/c^2=2.314E-30 kg, included in E rest
and 2.70 MeV=4.325E-13 J, for KE
I get: 1.11E8 m/s
oh $$E_rest=mc^2$$
4. Jan 29, 2008
### joelperr
The best way to proceed is to write down the relevant equations for the conservation of momentum and conservation of energy:
$$E_{1} + E_{2} = E_{final}$$
$$\textbf{p}_{1} + 0 = \textbf{p}_{final}$$
Initially, the first particle has kinetic and rest mass energy, and the second particle has only rest mass energy (note that we are doing everything in the lab frame). The end product only has one 'particle', with a modified kinetic energy and rest mass energy. For momentum, the only change from initial to final is that the final combined 'particle' has more mass.
Use $$E^2 - \textbf{p}^2c^2 = m^2c^4$$ and then solve for the momentum of the final particle.
This problem can be solved in a few lines if you use 4-vector notation, and in a few more lines if you do everything component-wise.
Last edited: Jan 29, 2008
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https://id.scribd.com/document/341724012/mikhailov-partial-differential-equations-pdf
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Anda di halaman 1dari 408
B. rr.
Mnxa:HJIOB
V. P. MIKHAILOV
PARTIAL
DIFFERENTIAL
EQUATIONS
Translated from the Russian
by
P. C. Sinha, Cand. Sc.
MIR PUBLISHERS
MOSCO\V
First published 1978
Revised from the 1976 Russian edition
Ha ane.~tuiic'noJI HBbtne
@ .Hap;aTeJibCTBO HayKa, 1976
English translation, Mir Publishers, 1978
CONTENTS
Preface 7
CHAPTER I
INTRODUCTION. CLASSIFICATION OF EQUATIONS.
FORMULATION OF SOME PROBLEMS
1. The Cauchy Problem. Kovalevskaya's Theorem 12
2. Classification of Linear Differential Equations of the Second Order 31
3. Formulation of Some Problems 34
Problems on Chapter I 41
Suggested Reading on Chapter I 41
CHAPTER II
THE LEBESGUE INTEGRAL AND SOME QUESTIONS
OF FUNCTIONAL ANALYSIS
1. The Lebesgue Integral 42
2. Normed Linear Spaces. Hilbert Space 64
3. Linear Operators. Compact Sets. Completely Continuous Operators 72
4. Linear Equations in a Hilbert Space 85
5. Selfadjoint Completely Continuous Operators 94
CHAPTER III
FUNCTION SPACES
1. Spaces of Continuous and Continuously Differentiable Functions 101
2. Spaces of Integrable Functions 104
3. Generalized Derivatives 111
6 CONTENTS
4. Spaces Hk(Q) 121
5. Properties of Functions Belonging to H 1 (Q) and H1(Q) 135
6. Properties of Functions Belonging to Hk(Q) 149
7. Spaces cr, 0 and C2s, 8 Spaces HT, 0 and H2 8 , 8 155
8. Examples of Operators in Function Spaces 161
Problems on Chapter III 166
Suggested Reading on Chapter III 168
CHAPTER IV
ELLIPTIC EQUATIONS
1. Generalized Solutions of Boundary-Value Problems. Eigenvalue Prob-
lems 169
2. Smoothness of Generalized Solutions. Classical Solutions 208
3 Classical Solutions of Laplace's and Poisson's Equations 232
Problems on Chapter IV 261
Suggested Reading on Chapter IV 264
CHAPTER V
HYPERBOLIC EQUATIONS
1. Properties of Solutions of Wave Equation. The Cauchy Problem for
Wave Equation 266
2. Mixed Problems 284
3. Generalized Solution of the Cauchy Problem 328
Problems on Chapter V 339
Suggested Reading on Chapter V 341
CHAPTER VI
PARABOLIC EQUATIONS
1. Properties of Solutions of Heat Equation. The Cauchy Problem for
Heat Equation 342
2. Mixed Problems 362
Problems on Chapter VI 388
Suggested Reading on Chapter VI 390
Index 391
PREFACE
This book has developed from courses of lectures given by the
author over a period of years to the students of the Moscow Physico-
Technical Institute. It is intended for the students having basic
knowledge of mathematical analysis, algebra and the theory of
ordinary differential equations to the extent of a university course.
All the necessary information can be found, for instance, in the
following textbooks: S.M. Nikolsky, A Course of Mathematical
Analysis, 2 vols., Mir Publishers, Moscow, 1977; A. I. Mal'cev,
Foundations of Linear Algebra, W. H. Freeman, San Francisco,
1963; L. S. Pontryagin, Ordinary Differential Equations, Pergamon
Press, Oxford, 1964.
Except Chapter I, where some general questions regarding partial
differential equations have been examined, the material has been
arranged so as to correspond to the basic types of equations. The
central role in the book is played by Chapter IV, the largest of all,
which discusses elliptic equations. Chapters V and VI are devoted
to the hyperbolic and parabolic equations.
The method used in this book for investigating the boundary value
problems and, partly, the Cauchy problem is based on the notion
of generalized solution which enables us to examine equations with
variable coefficients with the same ease as the simplest equations:
Poisson's equation, wave equation and heat equation. Apart from
discussing the questions of existence and uniqueness of solutions of
the basic boundary value problems, considerable space has been
devoted to the approximate methods of solving these equations:
8 PREFACE
Ritz's method in the case of elliptic equations and Galerkin's
method for hyperbolic and parabolic equations.
Information regarding function spaces, in particular, S. L. Sobo-
lev's embedding theorems, necessary for such arrangement of subject
matter is contained in Chapter III. It is not assumed on the part
of the reader that he is familiar with the required portions of the
theory of functions and functional analysis; these have been treated
in Chapter II which is of auxiliary nature.
Problems have been given on all the chapters except Chapter II.
The majority of them are intended to deepen and broaden the con-
tents of respective chapters; precisely with the same aim have the
lists of suggested reading been supplied. For exercises we recommend
the following books: V. S. Vladimirov et al., A Collection of Problems
on Equations of Mathematical Physics, Nauka, Moscow, 1974 (in
Russian); B. M. Budak, A. A. Samarskii and A. N. Tikhonov, A Col-
lection of Problems on Mathematical Physics, Pergamon Press, Oxford,
1964; M. M. Smirnov, Problems on Equations of Mathematical Physics,
Pergamon Press, Oxford.
In conclusion the author expresses his sincere thanks to V. S. Vla-
dimirov for his constant interest in this book, and toT. I. Zelenyak,
I. A. Kipriyanov and S. L. Sobolev who, having gone through the
is especially indebted to his colleagues A. K. Gushchin and L.A. Mu-
ravei with whom he had fruitful discussions that led to considerable
improvement in the book.
V. ill! ikhailov
July 1975
CHAPTER I
INTRODUCTION.
CLASSIFICATION OF EQUATIONS.
FORMULATION OF SOME PROBLEMS
Differential equations are those equations where the unknowns
are functions of one or more variables and which contain not only
these functions but their derivatives as well. If the unkno\vns are
functions of several variables (not less than two), then the equations
are called partial differential equations. We shall deal with only
such equations, and shall consider a single partial differential
efluation in one unknown function.
A partial differential equation containing derivatives of the un-
known function u with respect to the variables x1 , , Xn is said
to be of Nth-order if it contains at least one Nth-order derivative
and does not contain derivatives of higher orders, that is, the equa-
tion
au au a2u a2u aNu)
<J> ( .1'1 : Xn, U, -{)-, ,-a-, ""J2 aa ... , --ri" =0. (1)
Xl Xn Xl Xl X2 axn
Eq. (1) is said to be linear if <1>, as a function of u, :u , ... , aN;:,
xl axn
is linear. Henceforth we shall consider linear equation of the second
order, that is, equation of the form
n n
a2u ""' au
"'Q
LJ aii (x) axiax. + LJ ai (x) axi +a (x) u = f (x); (2)
i,j=1 J i=i
here x = (x1 , , xn) The functions aii (x), i, j = 1, ... , n,
ai (x), i = 1, ... , n and a (x) are called coefficients of Eq. (2)
and f (x) the free term.
Let Rn denote an n-dimensional Euclidean space, and let x =
= (x1 , , Xn) be a point of Rn, I x I = (x~ + ... +
x~) 1 i 2
As usual, by a region in Rn or an n-dimensional region we mean an
open connected (nonempty) set of points of Rn. In what follows,
unless stated otherwise, all the regions are assumed to be bounded.
10 PARTIAL DIFFERENTIAL EQUATIONS
Let Q be an n-dimensional region. A set E c Q is said to be strictly
interior with respect to Q, E ~ Q, if E c Q, where E is the closure
(in the sense of distance in Rn) of E.
The set of functions having in Q continuous partial derivatives
up to order k, k being a nonnegative integer, is denoted by C"- (Q),
while its subset consisting of those functions whose all the partial
derivatives up to order k are continuous in Q by C"- (Q). For the
sets co (Q) and co ((J) of functions which are continuous in Q and Q
respectively, we shall also use the notation C (Q) and C (Q). We
designate by coo (Q) the set of functions which belong to each of
ck (Q), k=-..oO, i, ... , that .
IS, C""(Q)= n ck (Q),
00
-
and by C""(Q)
1<=0
the set of functions belonging to each of C~~-
(Q), k=O, i, ... , that
00
is, Coo (Q) = n C"(Q).
k=O
A function f(x) is said to have compact support in Q if there
exists a subregion Q' ~ Q such that /(x) = 0 in Q '"- Q'. The set
C"- (Q) is composed of all the functions belonging to C"- (Q) and
having compact support, and the intersection of all these sets is
denoted by coo (Q) : C""(Q) = n c"- (Q).
k=O
Let a= (a 1 , , an) be a vector with nonnegative integer com-
ponents, and put I a I= a 1 + ...
+an. If f (x) E C"- (Q), then the
a!++anf
partial derivative a a1 an
will be often denoted for brevity by
iJx 1 axn
Daj. The first- and second-order derivatives will also be written as
fx.,' fx.x
,. j
. For the gradient Ux 1 , .. , fx n ) of a function f E C 1(Q)
we use the notation V f (x).
By an (n- i)-dimensional closed surfaceS we shall mean a bound-
ed and closed (n - i)-dimensional surface, without edge, of class
C"- for a certain k > 1, that is, a connected, bounded and closed
surface (S = S) lying in Rn and having the following property:
for any point x0 E S there exist an (n-dimensional) neighbourhood
Uxo of it and a function Fxo (x) E C"- (Ux 0 ) such that VFx 0 (x 0} =/= 0
so that the set S nUxo is described by the equation Fxo (x} = 0.
(That is, all the points of the set S n
Uxo satisfy the equation
F xo (x) = 0 and any point of U xo satisfying the equation F xo (x} = 0
belongs to S .)
The boundary of Q will be denoted by iJQ. In what follows, without
further qualification, the boundaries of regions in question are as-
sumed to consist of a finite number of disjoint closed (n - i)-dimen-
sional surfaces (of class C1}. By I Q I we indicate the volume of Q.
INTROD"CCTION 11
We note that if an (n - i)-dimensional closed surface S belongs
to the class Ck, then for a point x0 on it there exists a small neigh-
bourhood U~o such that the intersectionS n
U~ is uniquely project-
ed onto an (n- i)-dimensional region Dxo, with boundary of class
Ck, which lies in one of the coordinate planes, that is, for some
i, i = 1, ... , n, the surface is described by the equation x; =
= (jlxo (x1, . . . , X;-1, Xi+1 . , Xn), (X1, ... , X;-1, Xi+1
. . , Xn) E Dxo, and (jlxo E Ck (D ...,o). The intersection s U~o will n
be called a simple piece (or piece) of the surface S.
Since S is bounded and closed, one may choose a finite subcover
from the cover { U~, x E S} of S. The collection of simple pieces
S 11 , S N corresponding to such a finite cover will be called the
cover of the surface S by simple pieces.
By an (n - i)-dimensional surface S of class Ck, k >-
i, we shall
mean a connected surface which can be covered by a finite number
of (n-dimensional) regions Ub i = 1, ... , N, so that each of the
sets S; = S n
U;, i = i, ... , N, is uniquely projected onto an
(n- i)-dimensional region D; having boundary of class Ck and lying
in one of the coordinate planes, that is, for some p = p (i), p =
= 1, ... , n, the surface is represented by the equation Xp =
= <:p; (x1, . . . , Xp_1, Xp+ 1 , , Xn), (x1, ... , Xp_1, Xp+ 1, ... ) E
E D;, and cp; E Ck (D ;) . The collection of surfaces S b which are
simple pieces of S, corresponding to such a cover U1 , , UN
of Swill be called a cover of S by simple pieces. Henceforth an (n - i)-
dimensional surface will mean an (n - i)-dimensional surface of
class ck for a certain k i. >-
We denote by Q'\ 6 > 0, the region obtained by taking the
union over all x 0 EQ of balls {jx-xol<6}: Q6 = U {lx-xol<6};
xOEQ
Q ~ Q6 Qf, 6 > 0, denotes the set containing all the points of
Q whose distance from the boundary oQ exceeds 6; Q6 ~ Q; for
sufficiently small 6 > 0, Q6 is a region. We shall show that for an
arbitrarily small enough 6 > 0 there exists in Rn an infinitely
differentiable function ~~~ (x) which equals unity in Q6 and vanishes
outside Q612 . The function ~ll (x) will henceforth be called 6-slicing
function (or, simply, slicing function) for the region Q. Before con-
structing the function ~ 6 (x), we introduce an important notion of the
averaging kernel.
Suppose that w1 (t) is an infinitely differentiable and nonnegative
even function of a single variable t (-oo < t < +oo) which van-
ishes for I t I>- i, and is such that
j wt(l x I) dx = ~ wdl x I) dx = 1. (3)
Rn ]xf<1
12 PARTIAL DIFFERENTIAL EQUATIONS
For (1) 1 (t) we may take, for instance, the function
_t_e- 1 ~ 12 , o~ 1 t I < 1 ,
(l)f(t)= { Cn
o, 1 ti~1,
where the constant Cn has been chosen so as to satisfy (3). Let h be
any positive number. The function
1
(l)h (I X I)= hn wi(I X ilk)
is called the averaging kernel (of radius h). The averaging kernel
wh (I x I) has the following obvious properties:
(a) (l)h (I X I) ECoo (Rn), Wh (x) ~0 in Rn,
(b)(l)h(ixi)=O for lxi~h,
(c)) (l)h(lxl)dx=1,
Rn
(d) for any a=(a1 , ,an), lai~O, and for all xERn
IDawh (I X I) I~ Cafhn+lal,
where Ca is a positive constant independent of h.
Let (l)h (I x I) be an arbitrary averaging kernel. It is directly
verified that for sufficiently small 6 > 0 the function
So (x) = r
Q36/'
W/)j4 <I X- y I) dy
is a slicing function for the region Q; moreover, s
6 (x) satisfies in Rn
the inequalities 0 ~ ~ 6 (x) ~ 1.
1. Formulation of the Cauchy Problem. In a region Q of the
n-dimensional space Rn (Q is not necessarily bounded, and, in partic-
ular, may coincide with the whole of Rn), we consider a linear
differential equation of the second order
n "
Xu= i,~i aiJ (x) UxixJ + i~i ai (x) Uxi +a (x) u = f (x), (1)
where the coefficients and the free term are assumed to be sufficiently
smooth complex-valued functions. We denote by A(x) the matrix
II aii (x) II, i, j = 1, ... , n, which is composed of the coefficients
of the highest derivatives; at no point of Q, A(x) is a null matrix.
INTRODUCTION 13
When n = 1, Eq. (1) is an ordinary differential equation which
can be written as (a 11 =1= 0)
u" + b (x) u' + c (x) u = g (x). (2)
In this case the simplest problem is the Cauchy problem which con-
sists in finding the solution of this equation that satisfies for some
x = x0 the initial conditions u (x 0) = u 0 , u'(x0 ) = u 1
We shall now formulate an analogous problem for the partial
differential equation (1). We take a sufficiently smooth (of class
C2 ) (n - i)-dimensional surface S lying in Q that is given by the
equation
F (x) = 0, (3)
where F (x) is a real-valued function and I V F I =I= 0 for all x E S.
Suppose that in Q there is given a vector field l (x) = (Z1 (x), ...
. . . , ln (x)), where li (x), i = 1, ... , n, are real-valued functions
belonging to C1 (Q), 1 l 12 = l~ + ... + z;
> 0, such that for no
x E S the vector l (x) is tangent to the surface S, that is,
aF
az
I _ ill
8-
(l, 'V F) I =I= 0
8
(In what follows, we shall be interested in the values of the field
l (x) on S only.)
We take an arbitrary point x0 ES, and consider Eq. (!)ina suf-
ficiently small neighbourhood U of this point. (Let U be a ball of
sufficiently small radius with centre at x0 .) Let S 0 denote the inter-
section s n u.
Let u, u E C2 (U), be a solution of Eq. (1) in U, and let u 0 (x)
au
be the value of u on S 0 and u 1 (x) the value of Tz on S 0 :
ujs 0 =Uo(x), (4)
We shall show that for a partial differential equation, in contrast
to an ordinary differential equation, u 0 and u 1 cannot be, generally
speaking, arbitrary (smooth) functions.
Since V F(x 0 ) =1= 0, one of the components of V F (x0 ) is not zero;
suppose, for example, Fx n (x0 ) =1= 0. We assume the neighbourhood U
to be so small that Fx n (x) =I= 0 in U and Eq. (3) may be written as
Xn = <p (x'), X1 = (x1 , , , Xn-1),
where <p (x') is a smooth function. We denote by Fn (x) the function
F (x) and by Fi (x) the functions xi - x~, i = 1, ... , n - 1, and
14 PARTIAL DIFFERENTIAL EQUATIONS
consider one-to-one mapping
Y; = F; (x), i= 1, ... , n, (6)
of the region U in to a neighbourhood V of the origin- the image
of the point xo. Let 1:: denote the image of Sa lying in the plane
Yn = 0: 1:: = V n {y' = (y1 , , Yn-t) E Rn-1 , Yn = 0}. The function
n
u (x (y)) is denoted by v (y). Since Ux. ~ Vy Fpx. and
= p=i Ux.x. =
I p I l J
n n
~
= p,q=i Vy y Fpx. Fqx.
p q I J
+ p=i
~ Vy Fpx;x .,
p J
in new variables Eq. (1) has
the form
n n
i,~i ~u(Y) Vyiyj+~1 ~;(y) Vv;+~(y) V=f1(y), (1')
where ~ii (y) are elements of the square matrix II (A (x (y)) X
X VF; (x (y)), VF 1 (x (y))) II, in particular,
~nn (y (x)) = (A (x) 'V F(x), 'V F(x)). (7)
Conditions (4) and (5) respectively become
v ll: = Vo (y') (8)
and
('Vyv, 1-(y))jl:=v~(y'), (5')
where v0 (y') = u0 (y', c:p (y')), v; (y') = u 1 (y', c:p (y')), and the vec-
tor 1- (y (x)) = ( 0~1 , , o:zn ) , x E S 0 ; moreover,
oFn oF
---az = Tl ..,P 0 on S 0
We shall first show that the value of the vector vv on the surface 1::
is uniquely determined by v0 and v;. In fact, the derivatives
vv,b i = 1, ... , n- 1, are computed from (8): vv,I:E = Vovt i =
= 1, ... , n - 1, and according to (5')
(9)
n-1
where v1 (y ') =oF oF; )
"'V Vov; at
1 ( V 1'(Y') - LJ
7if i=1
Clearly, the conditions (8), (5') and (8), (9) are equivalent.
We now consider the values on 1:: of the second derivatives of
v(y). First, we note that by (8) and (9) the values on 1:: of all the
second derivatives, except Vy n y n , of v (y) are uniquely determined
by the functions v 0 and v 1 To find the value of Vy n y n on 1::, we use
l~TRODUCTION 15
Eq. (1'). Noting (7), by ('1') we obtain
(A (x (y)) Y'xF (x (y)), Y'xF (x (y))) Vynyn
n- 1 n-1 n
=f1 (y)- s
i, i=l
~ijVy.y.-
1 J
2;
i=i
~inVy.y
1 n
- 2; ~;Vy.-~V
i=1 1
(1")
If the function (A (x) V' F, V' F) =1= 0 on the surface S 0 , then the
function (A (x (y)) V' xF (x (y)), V' xF (x (y))) does not vanish on ~,
and therefore also in V (the neighbourhood U is assumed to be small).
In this case Eq. (1") inr can be written as
n-1 n-1 n
Vy 11 =
n n
~ '\'ijVy.y.
i,j=1 z J
+ i=l
2; '\'inVy.y
' n
--!- 2i
i=i
'\'iVy.+ '\'V
z
+h. (10)
Setting Yn = 0 in (10), we obtain the value of u11 n un on~.
Hence, if (A(x) VF, V'F) =!= 0 on S 0 all the derivatives of u (x)
up to second order are uniquely determined on S 0
However, if at some point x E S 0 (A (x) vF (x), VF (:;)) = 0,
then at the corresponding pointy (A (x (y)) V' xF (x (Y)), V' xF (x (y))) =
= 0. Then at the point ythe equality (t") connects the known quanti-
ties v (i/), v11i (ij), uu;Yj {y), i = 1, ... , n, j = 1, ... , n -, 1.
Tlms the values of v0 and its derivatives up to second order and those
of u1 and its derivatives of first order at the pointy, and hence the
x
values at the point of u 0 and u 1 and their corresponding derivatives
are subject to some relation, that is, they cannot be, generally speak-
ing, arbitrary.
A point x on the surface S of class C1 and given by the equation
F = 0 (F is a real-valued function, vF =1= 0 on S) is called the char-
acteristic point for Eq. (1) if at this point
(A(x) VF(x), VF(x)) = 0.
The surfaceS is called a characteristic surface for Eq. (1) or character-
istic (for) of Eq. (t) if all its points are characteristic points.
In this section we shall study the Cauchy problem for Eq. ('1), that
is, the problem of finding solution of (1) satisfying conditions (4)
and (5) with given functions u 0 and u 1 in the case when the surface S
does not contain characteristic points.
The case when the surface S contains characteristic points is far
more difficult. As it was shown, if the point x 0 E S is a characteristic
point, then there are (smooth) functions u 0 and u 1 such that Eq. (1)
has no smooth solution (in c~ (U)) in any neighbourhood of this
point that satisfies conditions (4) and (5) on S 0 = S U. It is easy n
to see that if U+ is one of the parts into which S 0 divides [) (it is
16 PARTIAL DIFFERENTIAL EQUATIONS
assumed that U is a ball of sufficiently small radius with centre at
x 0 ), then there is no solution in C2 ( U+ U S 0 ) too which satisfies con-
ditions (4) and (5) on S 0 If still a smooth solution exists, it may not
be unique.
Suppose, for example, n = 2. In a disc U with the origin as its
centre let us consider the equation
Ux 1 x 2 = f (x),
for which the line x 2 = 0 is a characteristic (to this form is trans-
formed the wave equation Ux,x, - ux.x, = / 1 by a change of variab-
les). It is easy to see that for the existence in U of a smooth solution
(belonging to C2 ( U)) of this equation that satisfies the conditions,
u lx.=O = u 0 (x1), ux.lx.=O = u 1 (x1) it is necessary and sufficient
that dul (x 1 ) =f (x1 , 0). Furthermore, if this condition is satisfied,
xl
then the solution can be expressed in the form
x1 ~2
u (xt, x2)= Jdtj f(t, 2)d2+uo(xt)+g(x2),
0 0
where g is a twice continuously differentiable arbitrary function
satisfying the conditions g (0) = 0, ddg (O) = u 1 (0).
x2
If S is a characteristic surface, then there may be situations where
the problem for Eq. (1) should be posed in analogy with the Cauchy
problem for an ordinary differential equation not of the second order
but of the first order. Thus, for example, for the equation (again
n = 2)
f (x)
Ux,x,- Ux 2 =
(the heat equation) having the line x 2 = 0 as a characteristic in
Chap. VI we shall study the problem (the Cauchy problem) of finding
a solution of this equation in the half-plane x 2 > 0 satisfying only
one condition (4): uJx.=O = U 0 (x1).
We shall now consider the problem (1), (4), (5) in the case where the
surface S does not contain characteristic points. Let Q be an n-dimen-
sional region, and let S be an (n - i)-dimensional surface given by
Eq. (3) that lies in Q and divides Q into two disjoint regions Q+ and
Q-, that is, Q~S = Q+ U Q-, Q+ n Q- = 0. Suppose that Eq. (1)
is given in Q (that is, the coefficients and the free term of Eq. (1)
are defined in Q), and a vector field l (x) = (l1 (x), ... , ln (x)),
I l (x) / > 0 on S, is defined on S that is nowhere tangent to S. Let
there be given two functions u 0 (x) and u 1 (x). Suppose that S does
not contain characteristic points of Eq. (1), that is, on S
(A(x) VF, VF) =I= 0. (11)
INTRODUCTION 17
It is required to find a function u (x) belonging to C2 (Q) and satis-
fying Eq. (1) in Q together with initial conditions (4) and (5) on S.
This problem will be called the noncharacteristic Cauchy problem.
The given! functions, that is, the coefficients and the free term of
Eq. (1), the function F of (3), the vector function land the functions
u 0 and u 1 will be referred to as the data of the problem.
We shall assume that the data of the problem (1), (4), (5) are
infinitely differentiable: the coefficients and the free term of Eq. (1)
and the function F (x) of (3) belong to C00 (Q), while the functions
l 1 (x), ... , ln(x), u 0 (x), u1 (x) belong to C00 (S) (that is, the func-
tions l 1 (x (y)), ... , u 1 (x(y)), where x = x (y) is a mapping, defi-
ned by (6), of a neighbourhood U of any point xO E S into a neighbour-
hood V of the origin, are infinitely differentiable in an (n - i)-
dimensional region ~ = V n {y' E Rn _1 , Yn = 0}). We also assume
that there is a solution u (x) of the problem (1), (4), (5) that is
infinitely differentiable in Q.
As shown above, all the derivatives of u (x) up to second order are
determined uniquely on S in terms of the data of the problem. We
shall show that on the surface S all the derivatives of u (x) of any
order are uniquely determined in terms of the data of the problem.
Since in this case the mapping (6) of the neighbourhood U of any
point xo E S into the neighbourhood V of the origin is given by func-
tions Fi (x), i = 1, ... , n, that are infinitely differentiable in U,
as a consequence of mapping (6) the problem (1), (4), (5) in U (by
this we mean the problem of finding in U a solution of Eq. (1) satis-
fying the initial conditions u I So = u 0 (x), !~ I so = u1 (x), where
80 = U nS) is replaced by an equivalent problem (8)-(10) for the
function v (y) in V with infinitely differentiable data. And because
there exists a solution u (x) of thelproblem (1), (4), (5) that is infi-
nitely differentiable in U, the problem (8)-(10) has also an infinitely
differentiable solution v(y) = u(x (y)) in V. To establish this asser-
tion, it suffices to show that all the derivatives D~v (y) are uniquely
determined on ~ in terms of the data of.l.the problem (8)-(10).
For any a'= (a 1 , , an- 1), I a' I~ 0, the values of
the derivatives D<a.',O>v(y) and D<a.',1>v(y) on~ are determined
directly from (8) and (9):
D<a.', O)v I:!:= Da' Vo, D<a', 1)v 1:!: = Da'v1.
If Va denotes the value of the function ~I Dav (a!= a 11 . ani)
at the origin:
(12)
:!-0594
18 PARTIAL DIFFERENTIAL EQUATIONS
then Va:, o and Va:, 1, Ia' I ~ 0, are uniquely determined in terms
of v0 and v1 :
1 Drr.' Vo Iv'=O
Vrr.,o= (a)'l (13)
1 Dtz! Vt Iy'=O
Vrr., 1 = (CG')! (14)
((a') I= a1l . an-1!).
To find the value of n<rr.', 2> v (y), I a' I )::. 0, on ~, we use (10).
Differentiating (10) with respect to y19 , Yn-l and setting Yn = 0,
we obtain
Ia' I ~0,
where the function H 1 (y) is defined in V by the formula
n-1 It- 1
H 1 (y) =. ~ '\'tJ (y) Vy 1y 1
t,J=i
+ .~
~=1
"?in (y) Vv 1un
n
+ i=1
~ Yt (y) v, +Y (y) v+ h (y)
1
(in which v (y) is the solution of the problem (8)-(10)). Now n<rr.', O)Hdl!
is a function (which is linear with known coefficients) of known quan-
tities D<li' .o>vl:!: and n<v'' 1 >v11: for 0 ~ I ~' I ~ I a' I+ 2, 0 ~
~ I y' I ~ I a' I + 1. Therefore, on ~, all the derivatives
n<rr.', 2 >v (y), I a' I)::. 0, are uniquely determined in terms of the
data of the problem, and, in particular,
Va, 2 = (2! (a')!t 1D<rr.', 0>H1 (y) 111=0 I a' I~ 0.
We assume that for some k)::. 2 all the derivatives n<a' n-1)v (y),
1 a' I ::> 0, have been uniquely determined on ~ in terms of the
data of the problem. We now find the derivative n<a', n>v (y) l1:.
1 a' 1 ::> 0. For this, we differentiate in V Eq. (10) a 1 times with
respect to y1 , , an _1 times with respect to Yn _1 and k - 2 times
with respect to Yn and then set Yn = 0. This yields
D<a',n)v (y) i.:E=D<a', k-2)fl1 (y) 1.:!:
Now D<a', P.-21H 1 Jl: is a function (linear with known coefficients)
of already-known quantities D<f3'. i)v j1:, 0 ~ i ~ k-1 (0 ~I WI~
~I a' I+ 2 for 0 ~ i ~ k-2 and 0 ~I WI~ I a' I+ 1 for i = k-1).
Hence all the derivatives D<a', h>v, Ia' I ~ 0, are uniquely deter-
mined on ~ in terms of the data of the problem, and, in
particular,
Vrr., h =((a')! k!t 1 D<a' h- 2 >H1 (y) lv=O (15)
This proves the assertion.
INTRODUCTION 19
Remark. Let v (y) be any infinitely differentiable function in V.
Consider the following infinitely differentiable function in V:
n-1 n-1 n
H (y) = Vt; 11 lln- ~ "YiiVliY.- ~ "YinVYIJ - ~ YiVy.- yv- h, {16)
i, i=1 t J i=1 t n i=1 t
It follows from the above discussion that if the values of the function
v (y) and its derivatives satisfy conditions (12), where the numbers
Va., / a I ~ 0, are defined by (13)-(15), then
DaH (y) IY=O = 0 for all a, Ia I > Ct. (17)
Thus we have shown that if the surfaceS does not contain character-
istic points, then the data of the problem uniquely determine on S
all the derivatives of the infinitely differentiable solution of the
problem (1), (4), (5). Hence the solution of the problem (1), (4),
(5) is unique in the class of functions that are uniquely determined
by their values and those of all their derivatives on S. One of such
classes is the class of analytic functions. Later in this section we
shall show that in the class of analytic functions the problem (1),
(4), (5) is solvable with analytic data.
It should be noted that in contrast to the case of an ordinary differ-
ential equation, the analyticity condition of the data in such
a generality (if no additional conditions are imposed on the coeffi-
cients of Eq. (1)) is, in a definite sense, necessary for the solvability
of the problem. The1following example, due to H. Lewy, shows that
a partial differential equation with infinitely differentiable coeffi-
cients and free term may not, in general, have a solution.
Example 1. The differential equation
(18)
does not have twice continuously differentiable solutions in any
neighbourhood of the origin (in R 3) if the real-valued function f (x 3}
is not analytic.
To prove this statement, it is obviously enough to check that the
equation
(19)
does not have continuously differentiable solutions in any neigh-
bourhood of the origin.
Suppose, on the contrary, that in the cylinder Q = {x: x~ < +
< R 2 , I x 3 I < H} for some R > 0 and H > 0, there is a solution
u (x) belonging to C1 (Q) of Eq. (19) with a real-valued function~
I (x 3) that is nonanalytic on the interval I x 3 I< H. Then in the1
parallelepiped II = {0 < p < R, 0 < <p < 2n, I x 3 I< H} the'
function u 1 (p, <p, x 8) = u (pcos <p, psin <p, x 3 ) is a solution of
2
20 PARTIAL DIFFERENTIAL EQUATIONS
the equation
u 1peicp +i u~cp eicp + 2ipei<J)u1x, = f (x 3 ),
where u 1 E C1 (ll) and u1 (p, 3) 1 0, x == u (p, 2n, x
3). Integrating
this equation (for fixed p and x 3 ) with respect to {() E (0, 2n), we
find that in the rectangle K 1 = {0 < p < R, I x 3 I< H} the
function
2n
Uz (p, xa) = ~ Ut (p, qJ, x 3 ) eicp dqJ,
0
u 2 (p, x 3) EC1 (K1), satisfies the equation
Uzp + ; + 2ipu2x = 2nf (xa)
2
1
Therefore the function
v (r, Xa) = Vr Uz <Vr' xa)
belonging to C1 (K 2 ) n
C(K 2 ), where K 2 is the rectangle
{0 < r < R 2 , I x 3 I < H}, is a solution of the equation
Vr +
ivx 3 = nf (x 3)
in K 2 , or, which is the same, is a solution of the equation
Xa Xs
(u(r, x 3 )+in ~ f()d)r+i (v(r, x 3 )+in) /(~)d):~:.=0.
0 0
But the last equation is the Cauchy-Riemann equation for the func-
tion
Xa
0
Hence the function w (r, x 3) as a function of the complex variable
r+ ix 3 , w (r, x 3) = g (r +
ix 3), is analytic in K 2 and continuous
in K 2 Since Re glr=O = 0, by the principle of symmetry the func-
tion g (r +ix 3 ) can be continued analytically into the rectangle
K 3 = {I r I< R 2 , I x 3 I< H}, and, in particular, is analytic in
Xo
x 3 on the segment {r = 0, I x 3 I < H}. But glr=O = in ) f () d;
0
consequently, for I x 3 I < H the function f (x 3) is also analytic,
Let us note that the plane x1 = 0, for example, does not contain
characteristic points for Eq. (18). Thus for any initial functions the
INTRODUCTION 21
Cauchy problem for Eq. (18) (with initial conditions given on the
plane x 1 = 0) does not have solutions in any neighbourhood that
contains the origin.
2. Analytic Functions of Several Variables. Let Q be a region in
the n-dimensional space Rn and g (x) a complex-valued function
defined in Q.
The function g (x) is said to be analytic at the point x 0 E Q if in
a neighbourhood U of this point it can be represented as an absolutely
convergent power series
00 00 00
C!Gt=O a,=O an=O
a
where a=(a 1 , , an), (x-x 0)a=(x 1 -x~)a ... (xn-X~)an.
The function g (x) is said to be analytic in a region if it is analytic
at every point of this region.
Let the function g (x) be analytic at the point x 0 E Q. Then in the
cube Kn(x0 ) = {I xi- x~ I< R, i = 1, ... , n}, R > 0, this
function is represented by an absolutely convergent (in Kn(x0 ))
series (20). Since a power series that converges absolutely in Kn(x 0)
converges uniformly in any strictly interior subregion K of the cube
KR(x 0 ), K ~ Kn(x0 ), together with all its derivatives, the function
g(x) E Coo(K), and, consequently, g (xj E Coo(Kn(x 0)). Moreover,
it is evident that ga = :, Dag(x0 ), where a! = a 1 ! ... an!, that is,
the series (20) is the Taylor series of g (x) at the point x 0 Hence it
follows that a function which is analytic in the region Q is uniquely
determined in all of Q by its own value and the values of all its
derivatives at an arbitrary point of Q; in particular, if the function
vanishes together with all its derivatives at a point of Q, then g (x) =
= 0 in Q.
Let us show that if the function g (x) is analytic at the point x 0 E Q,
then it is also analytic in some neighbourhood of this point. For this
it is enough to prove that if KR(x 0 ) is a cube in which g (x) is repre-
sented by the (absolutely convergent) series (20), then g (x) is analy-
tic in the cube KR; 4 (x 0).
Since the series (20) is absolutely convergent in K n(x0 ), it fol-
lows that for any p E (0, R)
hI ga Ipial< oo. (21)
a
22 PARTIAL DIFFERENTIAL EQUATIONS
We take an arbitrary point x 1 E KR 14 (x 0 }. Then for all x E KRrs(x1)
we have
an
. X ( ~ c:n (xn -x~)Pn (x~-x~)an-Pn)
Pn=O n
a, an
= ~ ~ . . . ~ gaG~: .. c:n
a p 1=0 Pn=O n
X (x1-xf)P (Xn -x!)Pn (xl- x~)a,-p, . (x~ -x~)an -Pn.
Since for all x EKRts(x1) and any a= (at. . , an), p =
=(Ptt ... , Pn), Pi ~a;, i=1, ... , n,
I ga Ca,p, CPan (Xt-Xtt}p' .. (Xn-Xn
1 O)a n -p n I
n
~I g&: 12ial ( ~ )'PI ( ~ )lai-IPI =I ga I ( ~ )laJ21;1
and since by (21) the series
~ ~I ga I ( ~ ) 1a;1 2 ~ 1 =2n ~I ga I ( ~ ) 1a 1< oo.
a p a
it }ollows that the function g (x) is represented in KRts(x 1) by
an absolutely convergent series
g(x)=~ g~(x-x 1 )P,
p
00 00
W h ere ~
~gp =
. . ~
~ a, (Xtt -Xt0) a,- p .. Cpan (Xnt -XnO)a. n -p n.
ga CP'
a,=v, an=Pn n
Therefore the function g(x) is analytic at the point x 1 , and hence
in KR/4(x0) because xl EKR 14 (x0) is arbitrary. The assertion is
proved.
A real-valued function g (x) = ~ 'ia. t
(x - x 0 which is analytic at
a
x 0 is called majorant at x 0 of the function g (x} (of (20)) if for all a,
I a I >- 0, I ga. I ~ ia
Let {ga, I a I):. 0} be a complex number sequence for which
there is a real number sequence (ga, I a I):. 0} such that for all a,
I a I ):. 0, I ga. I ~ ga. and the series ~ 'ia (x - x 0t converges abso-
a
lutely in a neighbourhood of the point x0 Then it is evident that
INTRODUCTION 23
the funstion g (x) = ~ ga. (x- x0Y~ is analytic at the point x 0 ,
a
and the function g(x) = ~a ia (x- x )a is its majorant at x
0 0
It is also evident that any function which is analytic at the point
x 0 has a majorant (at x0). As a majorant for the function g (x) of (20)
one can take, for example, the function ~ I ga. I (x- x 0 )~. A majo-
a
rant of g (x) from (20) can also be constructed as follows. Suppose
that the series (20) converges absolutely in the cube KR(x 0 ) for
some R > 0. Take some p from the interval (0, R). In view of (21),
there is a positive M such that I ga I pial :::::;;; M, that is, I ga I : : :; ;
:::::;;; Mfplal for all a. = (a.1 , , a.n) This means that a majorant
of the function g (x) at the point x 0 is the function
- ~ M (x-xO)a M
g(x)=~ pial = {1 - x 1 ;x~) ... ( 1 _xn;x?, )"
The function, with any N > 1,
- M
g (x) = 1 _ (x 1 - x~) + ... + (xn-1 -x?,_1) + N (xn- x?,)
p
is also a majorant of g(x) at the point x 0 , since for all a.=
MNan (I a 1)1
=(exit ... ,a.n), >lgal
p1a. 1a!
3. Kovalevskaya's Theorem. In this subsection we shall study
the Cauchy problem in the class of analytic functions, that is, we
shall consider solutions of the problem (1), (4), (5) that are analytic
in Q or in its subregion Q' containing the surfaceS. We shall assume
that the data of the problem (1), (4), (5) are analytic, that is, we
shall assume that the coefficients and the free term of Eq. (1) and the
function F in (3) (defining S) are analytic in Q, and the functions
l 1 (x), ... , ln (x), u 0 (x), u 1 (x) are analytic on S (that is, the fun-
ctions l1 (x (y)), ... , ln (x (y)), u 0 (x (y)), u 1 (x (y)), where x (y),
given by formula (6), is the mapping of some neighbourhood U of
an arbitrary point x 0 E S into a neighbourhood V of the origin, are
analytic in an (n- i)-dimensional region ~ = v n
{y' ERn-It
Yn = 0}). We recall that the solution of the problem, the coeffic-
ients and free term of Eq. (1) and the initial functions are complex-
valued, whereas the components l1 (x), ... , ln (x) of the vector
l (x) and the function F (x) are real-valued. We shall assume that S
does not contain characteristic points for Eq. (1).
First of all, we shall prove a local theorem regarding the existence
and uniqueness of the solution of this problem.
24 PARTIAL DIFFERENTIAL EQUATIONS
Theorem 1 (Kovalevsbya). Let the data of the problem (1), (4),
(5) be analytic, and let the surface S not contain characteristic points
for Eq. (1). Then for any point x 0 E S there is a neighbourhood U xo
of this point where this problem has an analytic solution. Moreover,
there cannot be more than one analytic solution of this problem in any
neighbourhood of xD.
We recall (Subsec. 1) that by problem (1), (4), (5) in the region
U x 0 we mean the problem of finding solution u(x) of Eq. (1) in U xo
satisfying the initial conditions ulso = u 0 , ~~ lso = u 1 , where S 0 =
n
= s uxo; moreover, the neighbourhood u xo is supposed to be
so small that the surface S 0 divides it into two disjoint regions.
Let x 0 be an arbitrary point on S. We consider one-to-one map-
ping (6) of a sufficiently small neighbourhood U of this point into
a neighbourhood V of the origin-the image of x 0 Since the data of
the problem (1), (4), (5) and the functions F;(x), i = 1, ... , n - 1,
are analytic, the Cauchy problem (1), (4), (5) in U transforms under
this mapping to an equivalent problem (8)-(10) (in V) with analytic
data. For the proof of Theorem 1, it is enough to show that we can
find a neighbourhood V of the origin where the problem (8)-(10)
has an analytic solution v (y) and that this solution is unique.
We start by proving the uniqueness. Suppose that in a neighbour-
hood V1 of the origin there is an analytic solution v (y) of the prob-
lem (8)-(10). As v (y) E C""(V1), it follows from considerations of
Subsec. 1 that the values on the surface ~ of all the derivatives
Da. v, I ex I :> 0, are determined uniquely by the data of the problem.
In particular, all the values Da.v (0), I ex I :> 0, are uniquely determi-
ned. Hence (see Subsec. 2) the solution v (y) is uniquely determined
by the data of the problem in V1 This establishes the uniqueness.
Now we prove the existence of a solution. First, we note that
it is enough to prove the existence of a function v (y) that is analytic
at the origin (it is also analytic in a neighbourhood V of the origin,
by the properties of analytic functions; see Subsec. 2) and is a solu-
tion of the problem (8H 10) in V.
According to (12)-(15) (see Subsec. 1), the quantities Vrz, I ex I> 0,
are (uniquely) determined by the data of the problem (8)-(10). We
shall show that the formal power series
(22)
is an analytic function at the origin. Then the sum of this series,
denoted by v (y), which converges absolutely in a neighbourhood V
of the origin will be the desired solution.
In fact, it follows from (13) that the value of the function v (y', 0)
analytic in y' and the values of all its derivatives with respect to
y 1 , . . , Yn - 1 for y' = 0 coincide with corresponding values for the
INTRODUCTION 25
function v0 (y') which is analytic in y'. Consequently, v (y', 0) ==
== Vo (y')on 2: = v n
{y' E Rn-1 Yn = 0}. Similarly, from (14)
we obtain v11 n (y', 0) ==
v1 (y') on 2:. That the function v (y) satis-
fies Eq. (10) in V can be verified in the following manner. Let us
consider a function H (y) which is analytic in V and is defined by
(16), where for v (y) we take the analytic function (22) which is
under consideration. In view of the choice of quantities Va, I a I :>- 0,
by Remark in Subsec. 1, equalities (17) hold, that is, the function
H (y) and all its derivatives at the origin vanish. Accordingly,
H (y) is analytic in V, and H (y) = 0. This means that v (y) satis-
fies Eq. (10) in V.
Thus we must prove that the series (22) converges absolutely in
some neighbourhood of the origin. For this (see Subsec. 2) it is
enough to show that this series has majorants at the origin.
The Cauchy problem (in V)
n-1 n
.~ :Yin;;;,t"n + t=1
Yi 1v"i"; + t=1 .~ :Yivvi + yv + h,
V /Yn=O = ilo (y'), (S)
;Yn 1Yn=0 = ;1 (y') (9)
with analytic data will be referred to as a majorant problem for the
problem (8)-(10) if the data of the former are majorants at the origin
for corresponding data of the problem (8)-(10).
If the problem (8)-(fO) has an analytic solution
V(y) = ~ Vaya,
a
at the origin, then this solution is a major ant there; for the series
(22) and, consequently, (22) represents an analytic function at the
origin.
In order to prove this statement, we must check the validity of
the inequalities I Va I ~ Va for all a, I a I :>- 0. According to the
definition of the majorant problem, the functions ;;0 and ul are
majorants at the origin of functions u 0 and u 1 , respectively. There-
fore ,(see (13) and (14)) I Va, ol ~ Va, o and I Va,1 I~ Va, 1 for
all a , I a' I >
0.
Now assume that for some k~1 we have already established
the inequalities /va /-<:va,s for all s, O<;:s<;:k-1, and all a',
/a'/~0. We shall demonstrate that then lva, 11 1-<:va,k,ja'I~O.
According to (15)
11-2
Va,11= ~
113'i~la'l+1
Cfi',II-1Vfi',ll-1 + =O
~ ~
lll'i~la'l+2
CJi,sVW,s+ha,l.,
26 PARTIAL DIFFERENTIAL EQUATIONS
and
where
ha',k= (a')1I kl n<a',k>h(O),
1 n<a', k)h (0),
(a') I kl
the constants cw. s are linear combinations with nonnegative coef-
ficients of values at the origin of derivatives of the coefficients in
Eq. (10), while~. s are the same linear combinations of co_Erespond-
ing (nonnegative!) derivatives of the coefficients of Eq. (10). Since
(8)-(tO) is a majorant problem for the problem (8)-(10), it follows that
lha',k l~ha',k and lc~.sl~cw,s Hence IVa,kl~va',k
Thus for the proof of absolute convergence of the series (22) in
some neighbourhood of the origin it is enough to construct the
majorant problem (S)-(10) which has an analytic solution at the
origin. While constructing the majorant problem, it is more conve-
nient to deal with homogeneous initial conditions (8) and (9):
v lun=o= 0, (8o)
Vy n lu n =O =0. (9 0 )
We note that for the proof of the existence of the analytic solu-
tion of the problem (8)-(10) it is enough to show the existence of the
analytic solution w (y) of the following problem with homogeneous
initial conditions:
n-1 n-1 n
w11 11 - L] "YiJWy.y- L] YinWy.y- L] yiwy.-yw-h'=O,
n n i, j=1 1 i i=1 ' n i=1 '
W /vn=O = 0,
Wu n lu n =0 = 0,
where
n-1 n-1 n
h'=h-w~ n 11 n + .~
3=1
"YiJW~ill 1 + ,L] "YinW~illn + ,L] YiW~i + yw',
=1 =1
w' (y) = Vo (y') + YnVi (y').
Indeed, it is easy to see that if w is an analytic solution of this prob-
lem, the function v = w + w', is the analytic solution of the prob-
lem (8)-(10).
INTRODUCTION 27
Consequently, we can regard the initial conditions (8) and (9)
as homogeneous, that is, it suffi.ces to construct a majorant problem
for the problem (8 0), (9 0), (to). Since the coefficients and the free
term of Eq. (10) are analytic at the origin, as (see Subsec. 2) Eq. (10)
of the majorant problem we can take the following equation
M
v 11 Y = ------:------:---~N
"-" 1- lft + + pYn-1 + Yn
X (
n-1
~
-
V ViY
n-1
-
J + ~ ~J::iYn + ~
- + -+ 1/\
n
Vyi V (10)
i, j=i i=1 i=i
for some p>O, M>O and arbitrary N-;;::::1. Let us consider solu-
tions;;= Y ('Y.J) of Eq. (10) that depend only on Yt++Yn-t+NYn 11-
P
All such solutions are solutions of the ordinary differential equa-
tion
Y" = AY' +B (Y +1) (23)
a-'Y] '
h A _Mp(n-1+N) B-Mp 2
1 _M(n-1)2_(n-1)M _
w ere - N2 ' - N2 ' a - N2 N
Choose N so large that the number a is positive, 0 <a< 1.
Consider the solution Y 0 (YJ) of (23) that satisfies the homogeneous
initial conditions Y 0 (0) = Y 0(0) = 0. Since the coefficients of
Eq. (23) are analytic when n = 0 (even when I 'YJ I< a), it is easy
to see that Y 0 (YJ) is also analytic at zero.* Since all the derivatives
1-
of the function -a-'Y] are positive at the point 'YJ = 0, by (23)
dll~~~O) ~0 for all k=O, 1, ....
Thus the function ; (y) = Y 0 ( Yt + +Yn-t +NYn) which is ana-
P_
lytic at the origin is a solution of Eq. (tO), and all its deriva-
* It can be most easily exhibited in the following manner. Consider the
equation
y=_1_ (AY'+ B(Y+1))
a-'Y] a-'Y] '
whose coefficients are majorants (since 0 < a < 1) of the corresponding coef-
ficients of Eq. (23). Eq. (23) is the Euler's equation for the function Y 1. +
- - 1
The solution of Eq. (23) Y 0 ('Y]) = crl-cr2
[cr1 (1- 'Y]Ia)a- cr 2 (1 - 'Y]/a)cr')-
- 1 satisfying the initial conditions Y (0) = Y' (0) = 0, where cr1 =
= [1- A+ Y(1- A)2 +
4B)/2, cr 2 = [1- A - V(1- A) 2 4B)/2, is +
analytic at zero and is a majorant of the function Y 0 (f]) at the point 'YJ = 0.
28 PARTIAL DIFFERENTIAL EQUATIONS
tives are nonnegative at the origin. Consequently, we have construct-
ed an analytic solution of the Cauchy problem which is a majorant
problem for the problem (8 0), (9 0), (10) at the origin. I *
The following proposition is a consequence of Theorem 1.
Theorem 2. Let the data of the problem (1), (4), (5) be analytic,
and let the surface S not have characteristic points. Then there is
a region Q' (Q' c Q) containing S in which this problem has an analytic
solution, and this problem cannot have more than one analytic solution
in any region containing S.
First of all we note that the statement regarding uniqueness of
the solution follows directly from Theorem 1 and the properties
of analytic functions.
We shall now prove the existence of the solution. According t()
Theorem 1, for every point x 0 on the surface S there is a neighbour-
hood of this point where the problem (1), (4), (5) is uniquely solvable.
It is easy to see that by contracting each of the neighbourhoods
U xo, x 0 E S, it is possible to obtain a cover { U~o, x 0 E S} for the
surface S which has the following property: if the intersection of
any two neighbourhoods is not empty, then it is an open set each
of connected components of which contains points of S (that is.
this intersection can be expressed as a union of not more than a count-
able number of disjoint regions each of which contains points of S).
In fact, in U x0 consider the ball {I x - x 0 I < r 0 } of sufficiently
small radius r0 = r0 (x0 ) > 0 such that the angle between normals
to S at any two points of the intersection of this ball with S is less
than n/4. Let us take for U~o the region {x: x = x1 + tn (x'), x1 E
n
E s {I X - x 0 I< ro/4}, t E (-<'>o, <'>o)}, where n (x1) is normal
to S at the point x1 ; moreover, we assume 6 0 = 6 0 (x 0) < r 0 /4 to be
so small that through every point of this region there passes only
one normal to the surface s n {I X - x 0 I < r 0} (that is, correspond-
ing to each point x E U~o there is only one point x1 (x) belonging to
s n {I X - x 0 I < r 0} such that X lies on the straight line
{x: x = x 1 +n (x 1) t, t E R 1 }). It is evident that the cover
{u~~, x 0 E S} for the surface S is the desired one.
Since for every x 0 E S U~o c U xo, the problem (1), (4), (5) has
a unique analytic solution in U~o; let it be denoted by Uxo (x). Note
that if x 0 and x1 are two arbitrary points on s and U~o n u~l =I= 0.
then Uxo (x) = Uxl (x) in U~o n
u~l. Consequently, it is possible to
define the analytic function u (x) by the equality u (x) = Uxo (x)
for x E U~o in the region Q' = U U~o, Q' c Q. The function
xOES
u(x) is the desired analytic solution inQ' of the problem (1), (4), (5). I
INTRODUCTION 29
When the surface S does not contain characteristic points, the
Cauchy problem, as Kovalevskaya's theorem shows, for the second-
order partial differential equation which was formulated in Sub-
sec. 1 in analogy with the Cauchy problem for ordinary second-order
differential equation is in fact analogous to it in a definite sense.
The well-known Cauchy theorem in the theory of ordinary differen-
tial equations states that the ordinary differential equation (2)
whose coefficients and the free term are analytic on the interval
a< x < b has in a neighbourhood of the point xO, a< x0 < b,
where the initial conditions are prescribed, a unique analytic solu-
tion satisfying these initial conditions. Kovalevskaya's theorem gene-
ralizes the Cauchy theorem to the case of partial differential equa-
tions: if the surface S where the initial conditions are prescribed does
not have characteristic points and the data of the problem (1), (4),
(5) are analytic, then the problem (1), (4), (5) has a unique solution
in some "neighbourhood" of S.
Nevertheless, the Cauchy problem for an ordinary differential
equation and the Cauchy problem for a partial differential equation,
and more so, the theory of ordinary differential equations and that of
partial differential equations are not totally analogous- the case
of partial differential equations is far more complicated.
In Subsec. 1 it was shown that when there are characteristic points
on the surfaceS, the existence of an analytic (even twice continuously
differentiable) solution of the Cauchy problem cannot be guaranteed:
if x0 E S is a characteristic point for Eq. (1), then there are smooth,
even analytic, initial functions u 0 and u 1 such that the problem (1),
(4),(5) has no solution (belonging to C2 (U)) in any neighbourhood U
of this point. Moreover, it was noted that if S is a characteristic
surface, then there may be cases where the Cauchy problem must be
formulated in analogy with the f1rst-order ordinary differential
equation. (For example, for the equation Ux,x, - ux, = f (x), for
which the straight line x 2 = 0 is a characteristic, the Cauchy problem
will be examined in Chap. VI. The problem is to find a solution
of this equation in the half-plane x 2 > 0 satisfying one initial con-
dition uix,=O = u 0 (x1 ).) In this case also, as the following example,
due to Kovalevskaya, shows, the analyticity of the data of the
problem does not guarantee the existence of an analytic solution.
Example 2. The equation
has no analytic solution at the origin satisfying the initial condition
1
uj x,= o=i+"
Xf
30 PARTIAL DIFFERENTIAL EQUATIONS
It is directly verified that if the analytic solution of this problem
at the origin exists:
then the coefficients Ua. a. have the form u 28 ~ = {Z~+ Zk)! ( -1)k..-~>
" '" ( s)! k!
and U2s+1, It= 0, where s>=O, k>=O. But the above series does not
converge in any neighbourhood of the origin since it diverges, for
example, at any point (0, x 2 ) when x 2 =1= 0.
As is well-known, the solution of the Cauchy problem for ordinary
differential equation (2) depends continuously on the initial data.
The following example, due to Hadamard, shows that, generally
speaking, partial differential equations do not have this property.
Example 3. Consider the Cauchy problem in the disc
Q = {x~ +xi< 1}:
Ux 2 x 2 = - Ux,x, t
u Ix..- o -- un o-
= e- Vneinx, '
Ux /x.-o = Un f = 0,
where n is a natural number (the straight line ~ = 0, obviously~
does not contain characteristic points for the equation ux.x. =
= -ux,x,) As is easy to check, the solution of this problem (unique
in the class of analytic functions) is of the form u = un(x) =
= e- vn cosh nx2 einx,. Consequently' for any point X = (xl' x2) of the
disc Q, not lying on the initial line x 2 = 0, Jun(x) 1-+ oo as n-+ oo
in spite of the fact that Un, 0 (x1 ) -+ 0 ( Jun, 0 I = e- Yn) and even fo~
dku
any k :;;> 1 --+ 0, as n-+ oo, uniformly on [-1, 1].
dx 1
What is more, it is well known that any ordinary differential
equation (2) with continuous coefficients and free term on some inter-
val has always a solution (on all of this interval). However, for
partial differential equations in such a general situation, which we
considered up-to-now, the similar statement does not hold: as shown
by Lewy's example (Subsec. 1), there are linear partial differential
equations of the second order that have no solution in any neigh-
bourhood of a given point; what is more, no conditions regarding
smoothness of coefficients (and even analyticity of coefficients) can
be imposed which would guarantee the existence of the solution with
any smooth (even infinitely differentiable) free term. Consequently,
in order to study nonanalytic solutions of linear second-order partial
differential equations, it is necessary to impose additional condi-
tions on the structure of the equation. In the next section we shall
select some classes of equations which will be the subject of our
study in the sequel.
INTRODUCTION 31
2. CLASSIFICATION OF LINEAR DIFFERENTIAL
EQUATIONS OF THE SECOND ORDER
We consider a linear partial differential equation of the second
order
n n
i, ]=1 =1
in an n-dimensional region Q.
The coefficients ail (x), i, j = 1, ... , n, are assumed to be
real-valued, and the solutions of Eq. (1) are assumed to belong
to C2 (Q). The matrix A (x) =II a11 (x) II composed of the coefficients
of highest derivatives of the operator : can be taken as symmet-
ric. In fact, ~ a,,ux.x.
l }
= ~ aijUx.x1
l.a
+
~ a;jUx.x1, where ai; =
't' '-
= ~ (aiJ+aif), aij= ~ (aii-aJ;). S.ince Ux 1re1 =ux1x1, it follows
= =
that ~ aiiux1x1 0, hence ~ aiJux1x1 ~ ajjUx1x1, where II aij (x>:ll
is symmetric.
Let x 0 be an arbitrary point of Q, and "-t (x0}, , An (x0 ) the
eigenvalues (evidently, real) of the matrix A (x0}. The number of
positive eigenvalues is denoted by n+ = n+ (x0), while that of nega-
tive eigenvalues by n_ = n_ (x0} and the number of zero eigenvalues
by n 0 = n 0 (x 0); n = n+ n-_ +
n0 +
Eq. (1) is called an equation of elliptic type at the point x 0 (or sim-
ply, elliptic at the point x0) if n+ = n or n_ = n. This equation is
said to be elliptic on the set E, E c: Q, if it is elliptic at every point
of this set. An example of elliptic equation in Rn is Poisson's equation
11u=f,
()2 ()2
where 11=-::>2+ .. +~ is the Laplace operator.
vX 1 vXn
Eq. (1) is said to be hyperbolic at the point x 0 E Q (or an equation of
the hyperbolic type at x 0) if n+ = n - 1 and n_ = 1, or if n+ = 1 and
n_ = n- 1. If the equation is hyperbolic at every point of the
set E, E c: Q, then it is said to be hyperbolic on E. An example of the
equation that is hyperbolic in the whole of space Rn of variables
x 1 , , Xn is the wave equation
Ux 1 x 1 + + Ux x
n-1 n-1
- Ux n xn =f.
Eq. (1) is termed ultra-hyperbolic at the point x 0 if n 0 = 0 and
1 < n+ < n - 1. Eq. (1) is ultra-hyperbolic on E, E c: Q, if it is
ultra-hyperbolic at each point of E. The equation
is ultra-hyperbolic in all of R,.
32 PARTIAL DIFFERENTIAL EQUATIONS
Eq. (1) is designated parabolic (or, an equation of the parabolic
type) at the point x 0 E Q if n 0 > 0. Eq. (1) is said to be parabolic on
the set E c Q if it is parabolic at every point of E. The heat equation
Ux,x, + + Ux x
n-1 n-1
- Ux n = f (x)
provides an example of the equation that is parabolic in the whole
space Rn of variables .t1 , , Xn
Of course, an equation need not be of the same type at all points
Qf a region. For example, Chapligin's equation (n = 2)
Ux,x, + T (xt) Ux x 1 1 = f (x),
where the function: T(x1) > 0 for x1 > 0, T(x1) < 0 for
x 1 < 0, and T(x1) = 0 for x 1 = 0, is elliptic for x1 > 0, hyper-
bolic for x1 <(O.and parabolic for x1 = 0.
We recall that (see Sec. 1.1 *) the surface S lying in Q and given
by the equation P(x) = 0 (the real-valued function F E C1 (Q) and
*
1V' F I 0 on S) is called the characteristic surface (characteristic)
for Eq. (1) if for all points x E S ,'
(A(x) VF, VF) = 0. (2)
If Eq. (1) is elliptic in Q, then the matrix A(x) is positive- or nega-
tive-defmite at each point x E Q. This means that (2) holds only
when 1VFI = 0. Hence elliptic equations do not have characteristic
surfaces (what is more, no surface S contains a characteristic point
of the elliptic equation).
If Eq. (1) is hyperbolic in Q, then it can be shown that a character-
istic surface can be made to pass through every point of Q. For
example, for the wave equation Ux 1x 1 Ux x+ ... +
n-1 n-1
= Ux n x n
Eq. (2) has the form
F'i,+ ... +P;n-1 -F;n =0. (2')
This equation is, in particular, satisfied by the function (x- x 0 , m) =
= (xl - xn + ... +
ml (Xn - X~) mn, Where X0 iS an arbitrary
point of Rn and the vector m = (m1 , , mn), I m I = 1, is subject
to the condition m: + ... + m~_ 1 = m;. Eq. (2') is also satisfied
by the function (xl - xn + ... +
2 (Xn -1 - X~-t) 2 - (Xn - X~) 2 ,
where x 0 is an arbitrary point of Rn. Hence the plane (x- x 0 , m) =
= 0 and the canonical surface (x1 - x~) 2 + ... +
(xn _1 - x~-1) 2 =
= (xn - x~) 2 are characteristics for the wave equation.
For the heat equation Ux,x, + ... Ux x
n-1 n-1
+
= Ux n Eq. (2)
is of the form
F~,+ ... +F~ n-1 =0.
* Here and in what follows the first number will denote the section and the
second its subsection.
INTRODUCTION 33
It is evident that any solution of this equation has the form F =
= <t> (x,.,), where <t> is an arbitrary continuously differentiable func-
tion (<t>' =fo 0). Thus the characteristics for the heat equation are
the planes Xn = const.
Let xo be a point of the region Q. We denote by y = y (x)(Yi =
=y;(x 1 , ,xn), i=1, ... ,n) a transformation which maps
one-to-one a neighbourhood U of the point x 0 into the neighbour-
hood V of the corresponding point yo, yo= y (xO), and by x = x (y)
the inverse transformation. We shall assume that the functions
Yi(x) E C2 (U), i = 1, ... , n, and that the Jacobian matrix J (x) =
=II ~~~ II of the transformation y = y (x) is nonsingular, that is,
the Jacobian of transformation det J(x) =I= 0 in U. Let v (y) denote
the function u (x (y)). Since
n n n
Ux. = ~ Vy,Yhx 1.,
-
Ux.x 1 -
..,
2.; ~
Vyky Ykx.Ysx.+ ..:.J Vy,Vkx.x.,
I k=i " I k, 8=1 S I J k=i " I J
Eq. (1), as a result of the change of variables, assumes the form
11
~
k, s=i
a,.. (x (y)) Vykys = F (y, v, \7v), (3)
n
where i,.. (x) = ~ ail (x) Y~<xYsx. and F ~s a function that does
i, j=i I J
not depend on the second derivatives of v. Since the matrices A(x)=
= II a,..(x) II and A(x) = II au (x) II are related by A(x) = J AJ*,
by a well-known theorem of algebra the numbers of positive, nega-
tive and zero eigenvalues of A (x) coincide with the corresponding
numbers for the matrix A(x). This implies that at any point y E V
Eq. (3) is of the same type as Eq. (1) at the corresponding point
x E U. Hence the above classification of second-order equations is
invariant under smooth one-to-one nondegenerate transformations
of independent variables. This fact can be utilized for simplifying
Eq. (1).
Let us take an arbitrary point x 0 E Q. It is known that for the
matrix A(x 0) there exists a nonsingular matrix T = T(x 0 ) =
= II tu II such that
n_ 0
-~~
Oo
34 PARTIAL DIFFERENTIAL EQUATIONS
We effect a linear change of variables y = T (x 0) x. Since the Jacobian
matrix of this transformation is T, Eq. (1), under this transformation,
reduces to (2) in which the matrix of coefficients of highest deriva-
tives is TA(x) T*. This implies that for x = x 0 Eq. (3) has the form
Vy,y, + +
Vyn+Y14- Vyn++iYrt++i- - Vyn++n-Yn++n- = F1,
where the function F 1 does not depend on second derivatives of v.
This form is called the canonical form of Eq. (1) at the point x 0
Hence for any point x = x 0 E Q we can find a nonsingular linear
transformation of independent variables which reduces Eq. (1)
to the canonical form at the point x = x 0 Since the transformation
depends only on the values of the coefficients of highest derivatives
in (1) at x = x 0 , in the case when the coefficients are constants in Q
the resulting linear transformation reduces Eq. (1) to the canonical
form at each point of Q (in the region Q).
3. FORMULATION OF SOME PROBLEMS
In this section we shall examine some physical problems which lead
to problems in partial differential equations.
1. Problems of the Equilibrium and Motion of a Membrane.
Let us consider the problem of determining the equilibrium position
of a membrane (a thin elastic plate) which is subject to the action
of a system of forces.
We shall assume that in any admissible position the membrane
is a surface lying in the space (x, u) = (x1 , x 2 , u) that projects
uniquely onto a region Q of the plane x10x 2 , and is given by the equa-
tion u = u (x), x E Q, where the function u (x) E C1 (Q). If u =
= cp (x), x E Q, is any admissible position of the membrane, then
we assume that any other admissible position u = u (x) is obtained
from the position u = cp (x) in such a manner that every point of
the membrane is displaced parallel to the Ou-axis.
Suppose that the external force acting on the membrane is directed
parallel to the Ou-axis and has continuous density / 1 (x, u) equal
to f (x) - a (x) u (the membrane is subject to the force with density
f (x), x E Q, and to the resistance force of the elastic medium whose
density is a (x) u is proportional to the displacement and opposite
in sign, a (x) :;;? 0 is the elasticity coefficient of the medium). The
work done by this force in displacing the membrane from the position
cp (x) to the position u (x) is given by
u(x}
.\ J / (x, u) du dx = ) [/ (x) (u (x)- cp (x))
1
Q cp(x) Q
- a~x) (u 2 (x)-cp 2 (x))]dx.
INTRODUCTION 35
Besides this, the membrane is subject to the internal elastic force.
We assume that the work done by this force in displacing the mem-
brane from the position ep (x) to the position u (x) is equal to
- .l k (x>[ V 1 + I Vu 1 V 1 +I vep / Jdx
2 - 2
(the work done by this force with regard to the element (x1 , x1 + ~x1 ) x
X (x 2 , x 2 +
~x 2 ) of Q is proportional to the change in the surface
area of that part of the membrane which is projected onto this ele-
ment; the coefficient k (x) > 0 is called the tension of the membrane).
If at the points of the boundary of the membrane a force is applied
with linear density g1 (x, u) = g1 (x) - a 1 (x) u (a 1 (x) :;;? 0 is the
coefficient of elastic fastening of the boundary), then the work done
by this force in displacing the membrane from the position ep (x) to the
position u (x) is given by
J [g1 (x) (u (x)- ep (x))- c\(x) (u2 (x)- ep 2 J
(x)) dS.
{IQ
Thus, in the position u (x), the potential energy of the membrane is
U(u)=U(ep)+ J[k(x)(V1+/Vu/ 2- V1+/Vepj 2
Q
+ ~ (u2-ep2)-f(u-ep)]dx+ J [i (u 2-ep2)-gdu-ep)]ds,
aQ
where U (ep) is the potential energy of the membrane in the posi-
tion ep.
To simplify the problem, we assume that the gradient of the func-
tion u (x) is small for all the admissible positions u (x) which the
membrane can have, and we neglect the terms of the order l vu !4
Then the potential energy of the membrane in position u becomes
U (u) '= U (ep) + J[ ~ (j Vu /2-/ 'Yep 2) + ; (u ep f (u- ep) Jdx
j 2- 2) -
Q
+ J [ ~1 (u2-ep2)-gt(u-ep) JdS.
aQ
If u is the equilibrium position of the membrane, then, by the
principle of virtual displacements, the polynomial (in t)
P (t) = U (u +tv)
=U(u)+t[j (k'Vu'Vv+auv-fv)dx+) (a 1uv-g 1v)dS]
Q aQ
+ ~ [ J (k/Vv/ 2 +av 2 )dx+ Ja v 1 2 dS]
Q ao
3
36 PARTIAL DIFFERENTIAL EQUATIONS
has, for any admissible v, a stationary point for t = 0. Hence
dPd~O) = 0, that is, for all v E C1 (Q) the function u (x) describing
the equilibrium position of the membrane satisfies the integral
identity
I (kV'uVv+auv) dx+ JI (JtUvdS= Jr fvdx+ l gtvdS.
~
(1)
Q iJQ Q iJQ
If the boundary of the membrane is fixed (tightly stretched), then
all the admissible positions u of the membrane satisfy the condition
u loQ = <p loQ (2)
In this case the potential energy of the membrane in any position
u is (neglecting the terms of the order I vu 14)
U(u)=U(<p)+ .\ [~ (1Vuj 2 -IV<pj 2 +; (u -<p )-f(u-<p)]dx.
2 2
Q
Let u be the equilibrium position of the tightly stretched mem-
brane. Then for any function v E C1 (Q) satisfying the condition
v loQ = 0 (3)
the function u + tv satisfies condition (2) for all t. Therefore for
all such v the polynomial
P(t)=U(u+tv)=U(u)+t) (kVuVv+auv-fv)dx
Q
+ ~ ) (k IVv l2 +av 2 ) dx
Q
has a minimum when t = 0. This means that for all v E C1 (Q) satis-
fying (3) the function u (x) which describes the position of a tightly
stretched membrane satisfies the integral identity
Q Q
(4)
It will be shown in Chap. V that under suitable conditions on
the given functions k, a, a 1 , f, g1 , and in the case of a tightly
stretched membrane also on <JlloQ the integral identities (1) and (4)
determine unique functions u (x) subject to the condition (2). Further-
more, it will be shown that if the boundary aQ is sufficiently smooth,
then the functions u (x) belong to C2 (Q).
However, assuming here that u (x) E C2 (Q}, k (x) E C 1 (Q),
k (x)> k 0 > 0, a (x) E C (Q), a 1 (x) E C (aQ), g 1 E C (aQ), <p E
E C (aQ), we shall obtain local conditions, in place of integral iden-
tities (1} and (4}, that must be satisfied by the desired function u (x)
INTRODUCTION 37
J k'Vu'Vvdx=- J vdiv(k'Vu)dx+ J k !~ vdS
Q Q iJQ
for any v E C1 (Q}, we can rewrite (1) and (4), respectively, in the
form
J (div(k'Vu)-au+f)vdx- J (k :~ +cr 1u-g 1 ) vdS=O (1')
Q ~
and
\ (div(k'Vu)-au+f)vdx=O. (4')
Q
Because the function div (kVu) - au +f is continuous, from (4')
we obtain
div (kVu) - au +f = 0, x E Q, (5)
which together with the boundary condition (2) gives the required
local conditions that must be satisfied by the function u (x) in the
case of a tightly stretched membrane. The problem of finding the
solution of Eq. (5) satisfying the boundary condition (2) is called
the first boundary-value problem (the Dirichlet problem) for Eq. (5).
Since the function v (x) in (1') is an arbitrary function belonging
to C1 (Q), we find, in particular, that for v satisfying condition (3)
u (x) in this case also satisfies Eq. (5). Therefore the identity (1')
may be written as
J (k
BQ
~~ +a1u - g 1 ) v dS = 0.
Because any function in C1 (8Q) admits of an extension into Q
which belongs to C1 (Q) (see Sec. 4.2, Chap. III), the last identity
yields the boundary condition
- au
an+ O"U I-
8Q-g, (6)
>
where a = cr 1 /k 0, g = g1/k.
The problem of finding a solution of Eq. (5) satisfying the boundary
condition (6) is called the third boundary-value problem for Eq. (5).
When a ==0, the third boundary-value problem is known as the
second boundary-value problem (the Neumann problem). In this case
the boundary condition becomes
(7)
38 PARTIAL DIFFERENTIAL EQUATIONS
Hence the equilibrium position of a membrane is described by the
solution of Eq. (5) satisfying some boundary condition. Eq. (5)
is elliptic and is called the equation of equilibrium for the membrane.
We shall nowinvestigate the problem of the motion of a membrane.
Let u (x, t) define the position of the membrane at a given time t.
Then the function u 1 (x, t) and u 11 (x, t) (these derivatives are
assumed to exist) define the velocity and acceleration of the mem-
brane at a point x EQ. Suppose that at a certain (initial) time moment
t = t 0 the position ofthe membrane and its velocity are given, that is,
u lt=to = 'i'o''(x), X E Q, (8)
Ut /t=to = 'i't (x), {9)
The conditions (8) and (9) are referred to as initial conditions.
By the D'Alembert's principle, the equation of motion of the
membrane is the equilibrium equation (5) in which f (x) has been
replaced by the function -p (x) Utt + f (x, i) ( -p (x) Utt is the
density of the force of inertia at the point x, p (x) > 0 is the
density of the membrane at the point x, and f (x, t) is the density
of the external force which, generally speaking, depends on t):
div (kVxu) -au+ f (x, t) - p (x) Utt = 0, x E Q, t > t 0 (10)
As in the static case, the boundary conditions have the form (2),
(6) or (7), depending on the conditions defined on the boundary 8Q
and are fulfilled for all values of time t >
t 0 in question. The pro-
blems of finding a solution of Eq. (10) subject to conditions (2),
(8), (9); (7), (8), (9); (6), (8), (9) are called, respectively, the first,
second and third mixed problems for Eq. (10).
Hence the motion of the membrane is described by the solution
of Eq. (10) satisfying the initial and some boundary conditions.
Eq. (10) is hyperbolic (in the three-dimensional space) and is called
the equation of motion of a membrane.
When the membrane is expanded infinitely (Q = R 2 ), the func-
tion u (x, t) describing the motion of the membrane for all x E R 2
and t > t 0 is the solution of Eq. (10) and satisfies initial conditions
(8) and (9). In this case we say that u (x, t) is a solution of the ini-
tial-value problem (the Cauchy problem) for Eq. (10).
If the coefficients in Eqs. (10) and (5) are constants: k (x) k, ==
p (x) = p, and a (x) = 0, then these equations are called, respec-
tively, the wave equation
a\ Utt-~U= f(xk t), xEQ, t>t 0 , (10')
a= V ~ , and Poisson's equation
~U= _ f(x) xEQ. (5')
k '
INTRODUCTION 39
In the case of one space variable, Eq. (10') has the form
1 U t t - Uxx = f (x,k t)
/i2 ' X
E(a, t'R) ' t > t O (10")
It describes the motion of a string situated over the interval (a, ~).
When x = (x1 , x 2 , x 3 ), the equation
_1_ _ A _ f (x, t)
a2 Utt o.U- k ' xEQ, ( 10"')
describes the motion of a gas in a region Q (the function u (x, t)
characterizes, for example, small deviations at the point x E Q at
time t in the pressure of gas from the constant pressure). The quan-
tity a in this case is the velocity of sound propagation in the gas.
2. The Problem of Heat Conduction. Suppose that a substance
in the three-dimensional region Q has the density p (x) > 0, heat
capacity c (x) > 0, and the coefficient of heat conduction k (x) > 0.
Let u (x, t) denote the temperature at x E Qat a given timet. Assum-
ing that the temperature at the initial time t = t 0 is known:
u (x, t) lt=to = 'o (x), xEQ; (11)
it is required to determine it for t > t 0
Let Q' be a subregion of Q. By Newton's law, the amount of heat
passing through the boundary oQ' into Q' in an interval of time
(t 1 , t 2 ), t 0 :::::;;; t 1 < t 2 , is equal to
~r2 I au
- J d.r: J k (x) a; dS,
tt aQ'
where n is the normal to oQ' which is outward with respect to Q'.
If the source of heat is present in Q with a given density f (x, t),
then the increase in the amount of heat in Q' in an interval of time
(t1 , t 2 ) is equal to
f2 f2
) dt) f(x,t)dx-) dt J k(x),:~ dS
tt Q' tt aQ'
and therefore the equation of heat balance in Q' has the form
tz t2
- J dt J k (x) ;~ dS + Jdt Jf (x, t) dx
tt aQ' tt Q'
=) c (x) p (x) (u (x, t 2) - u (x, t 1)) dx.
Q'
40 PARTIAL DIFFERENTIAL EQUATIONS
12
Noting that u (x, t 2 ) - u (x, t 1) = ) ~~ dt and using the Ostrograd-
11
skii's formula, we obtain
12
I! Q'
If the integrand is continuous in Q, then, because Q' and the inter-
val of time (t 1 , t 2 ) are arbitrary, the last equation is equivalent to
the differential equation
c (x) p (x) ~~ - div (k (x) Vu) = f (x, t}, x EQ, t > t0 (12)
This equation is of parabolic type (in a four-dimensional space of
the variables x 1 , x 2 , x 8 , t). When the functions c (x), p (x) and k (x)
are constants, Eq. (12) is called the heat equation:
_1_ u -!1u = f (x, t) (12')
a2 t cp '
where a 2 = ...!!__.
cp
It should be emphasized that Eq. (12) holds only for t > t 0 and
only for the interior points of Q. The behaviour of the function
u (x, t) for t = t 0 is given by the initial condition (11), and for
x E fJQ u (x, t) should be subject to some additional conditions.
This is motivated by the concrete physical problem establishing
heat relation of Q with the external medium.
In the simplest case, the value of the temperature u (x, t) is given
on the boundary oQ:
u !aQ = / 0 (x,it) (13)
for all values of t under consideration. In this case the temperature
is described by the solution u (x, t) of Eq. (12) satisfying the condi-
tions (11) and (13).
If the density q0 (x, t) of the heatj flow through the boundary
is known, then, by Newton's law, the boundary condition is of
the form
~f)u
k (x),-;;- I=
un aQ
q 0 (x, t). (14)
If the temperature u 0 (x, t) of the medium external to Q is given,
and the density q0 (x, t) of the heat flow through the boundary fJQ
is proportional to the difference in temperatures u!aQ and u 0 laQ,
then the boundary condition is of the form
(15)
SUGGESTED READING ON CHAPTER I 4t
where k 1 (x) > 0 is the coefficient of heat exchange of the body with
the surrounding medium.
The problem of finding solutions of Eq. (12) satisfying the condi-
tions (11), (13); (11), (14); (11), (15) are called, respectively, the-
first, second, and third mixed problems for Eq. (12).
When the substance occupies the whole of R 3 , Q = R 3 , the
temperature u (x, t) satisfies Eq. (12) for t > t 0 and the initial con-
dition (11) for t = t 0 In this case we say that u(x, t) is the solu-
tion of the initial value problem (the Cauchy problem) for Eq. (12).
PROBLEMS ON CHAPTER I
1. Let a surface S of class C2 divide the region Q into two disjoint regions.
Q+ and Q-, and let the function u(x) belong to C1 (Q) n C2 (Q+ U S) n C2 (Q- US)
and satisfy in Q+ and Q- the second-order linear differential equation
n n
2j aij(x)ux.x.+ 2.,";ai(x)ux.+a(x)u=f(x) (1)'
i, j=i I ] i=1 I
when coefficients and free term are continuous in Q. Show that if for a neigh-
bourhood U x of a point x 0 E S the function u(x) does not belong to C2 ( U x),
then x 0 is a characteristic point for Eq. (1).
2. Suppose that in a two-dimensional region Q there is given the second-
order linear differential equation (1) whose coefficient and free term are analytic,
and suppose that the two lines L 1 and L 2 which intersect at a point x 0 E (J are
characteristics for this equation. Show that the problem (the Goursat problem)
has a unique solution u(x) of Eq. (1) satisfying the conditions uiL, = u1 and
uiL, = u2 , where the functions u1 and u 2 are analytic, in a neighbourhood of
the point x 0 in the class of analytic functions (u1 (x 0 ) = u2 (x 0 )).
3. Suppose that a second-order linear differential equation with continuous
coefficients is given in a region Q. Show the following.
If the equation is elliptic (hyperbolic) at a point of Q, then it is also elliptic
(hyperbolic) in a neighbourhood of this point.
If there are two points in Q at one of which the equation is elliptic and at the
other is hyperbolic, then there is a point in Q where the equation is parabolic.
Petrovskii, I. G. Lectures on Partial Differential Equations, lnterscience
Publishers, New York, 1954.
Sobolev, S. L. Partial Differential Equations of Mathematical Physics, Addi-
Tikhonov, A. N. and Samarskii, A. A. Equations of Mathematical Physics~
Nauka, Moscow, 1972 (Engl. transl.: Pergamon Press, Oxford).
Mass., 1962.
Vladimirov, V. S. Equations of Mathematical Physics, Nauka, Moscow, 1971
(in Russian).
Vladimirov, V. S. Methods of the Theory of Functions of Several Complex
Variables, Nauka,'" Moscow, 1964 (in Russian).
CHAPTER II
THE LEBESGUE INTEGRAL
AND SOME QUESTIONS
OF FUNCTIONAL ANALYSIS
1. THE LEBESGUE INTEGRAL
The notion of an integral and that of an integrable function asso-
dated with it are fundamental for mathematical analysis. Due to
the need of applied sciences, and of mathematics itself, these ideas
have undergone radical changes during the course of their develop-
ment. To solve some problems, it was enough to know how to inte-
grate continuous or even analytic functions, while for other pro-
blems it became necessary to enlarge these sets and sometimes even
consider the set of all functions which are integrable in the sense
of Riemann. What is more, in order to express mathematically anum-
ber of phenomena even the set of Riemann-integrable functions is
not rich enough. Naturally, this set was not sufficient even for the
need of mathematics itself.
In particular, some processes are described approximately by means
of a sequence of "well-behaved" functions fk(x), k = 1, 2, ... ,
whose convergence c.an be asserted only in some integral sense. Thus,
for example, the sequence fk(x), k = 1, 2, ... , may have one of
the following properties: J I fk- fm I dx--+ 0 as m, k--+ oo (the
sequence is fundamental in the mean), J (fk- /m) 2 dx--+ 0 (the
sequence is fundamental in the mean square) or, in more complicated
cases, the integrals containing derivatives of the functions converge
to zero (the sequence is fundamental in the energy). These properties,
in particular when the sequence is fundamental in the mean square,
may not guarantee convergence in the ordinary sense: the sequence
may not converge at any point. However, we can still show (it will
be done below) that there exists a unique function to which this
sequence converges in a definite sense (in the mean square). This
function, generally speaking, is nonintegrable in the sense of Rie-
mann, therefore the integral in the definition of convergence must
he understood in some wider sense-in the sense of Lebesgue.
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 43
1. Set of Measure Zero. A set E c Rn is said to be a set of (n-dimen-
sional) measure zero if it can be covered by a countable system of
(n-dimensional) open cubes the sum of whose volumes (total vol-
ume) is arbitrarily small, that is, for a given e > 0 we can find a count-
00
i=1
00
total volume of these cubes 2J I Ki I < e, where I Ki I is the
i=1
volume of the cube K;, i = 1, 2, ....
It readily follows from the definition that the set composed of
a countable number of points has measure zero. The intersection
and union of a countable number of sets of measure zero are sets
of measure zero. The smooth surfaces of dimension k < n are also
sets of measure zero.
The following criterion will prove useful in what follows.
Lemma 1. A set E is a set of measure zero if and only if it can be
covered by a countable system of cubes having finite total volume so that
every point is covered by infinitely-many sets of these cubes.
First, suppose that the covering mentioned in Lemma 1 exists.
Deleting from it a finite number of cubes with maximum volumes,
we can make the total volume of the remaining covering arbitrarily
small. This means that E is a set of measure zero. Conversely, if E
is a set of measure zero, then it can be covered by a countable system
of cubes with total volume less than 2-" for any integer k :>- 1. The
required covering is obtained by taking the union over k = 1, 2, ...
of these covers. I
If a property holds for all the points x of a set G except, possibly,
for the set of measure zero, then we say that this property holds
for almost all points x E G, almost everywhere in G, a.e. (in G). Thus,
the Dirichlet's function X (x) which equals 1 at points whose all coor-
dinates are rational and vanishes elsewhere, vanishes a.e. in Rn.
Let Q be a region of Rn. Together with the functions defined every-
where in Q (that is, having finite value at every point of Q), we shall
also consider functions that are defined a.e. in Q, that is, functions
which are undefined on a set of measure zero. The functions f + g,
f. g (f and g are defined a.e.) are defined at those points where both
the functions f and g are defined.
2. Measurable Functions. Let Q be a region of the space Rn. A se-
quence of functions (defined a.e. in Q) fk (x), k = 1, 2, ... , is
said to converge a.e. in Q if for almost all x 0 E Q the number sequence
of values of these functions at the point x 0 has a (finite) limit. A func-
tion f(x) is called the limit of an a.e. convergent sequence fk(x),
k = 1, 2, ... , fk(x)-+ f(x) a.e. in Q, as k-+ oo, if for almost
all x 0 E Q lim fk(x 0 ) = f(x 0 ). It is evident that if two functions
1<--+oo
44 PARTIAL DIFFERENTIAL EQUATIONS
f (x) and g (x) are limits of the same sequence of functions, that
converges a.e., they coincide a.e.
A function f (x) is said to be measurable in Q if it is the limit of an
a.e. convergent sequence of functions in C (Q).
Let us note some of the obvious properties of measurable functions.
Any linear combination of measurable functions is measurable;
the function / 1 / 2 is measurable if so are / 1 and / 2 Together with f
the function If I is also measurable. If the functions / 1 , / 2 ,
are measurable, then so are max (/ 1 (x)), min (/ 1 (x)), and
i~h i~h
lim fh (x) (the limit is understood in the sense of a.e.). Since
h-+oo
sup (fh (x)) = lim max (/ 1 (x)) and inf (fh (x)) = lim min(f 1(x)),
II 1<--.oo i.;;;h k h-+oo i~h
it follows that these functions are also measurable provided so are
fh, k = 1, 2, .... If the derivative of a measurable function exists
a.e., it is also measurable.
It follows from the definition that a function f (x) belonging to
C (Q) is measurable. An arbitrary function f (x) belonging to C (Q)
is also measurable, because it can be expressed as the limit of a se-
quence of functions belonging to C (Q) that converges in Q: f (x) =
= lim f (x) ~o (x), where ~6 (x) is the slicing function for the
6-+0
region Q (see Chap. I).
3. Lebesgue Integral of Nonnegative Functions. We shall often
consider sequences fh (x), k = 1, 2, ... , of measurable functions.
that are monotone nondecreasing (nonincreasing) a.e. in Q, that is,
the sequences which, for all k >-
1, satisfy the inequalities
>-
/1<+ 1 (x) fh (x) (/H 1 (x) ~ fh (x)) a.e. in Q. If such a sequence of
functions is bounded a.e. (that is, for almost all x 0 E Q the number
sequence f~t (x0), k . 1, 2, ... , is bounded), then it converges a.e.
to some function. We shall denote this as follows: /11. t f a.e. as
k-+ oo if the sequence is monotone nondecreasing, and fR t f a.e.
as k -+ oo if the sequence is monotone nonincreasing.
A function f (x) which is nonnegative a.e. in Q is said to be Lebes-
gue-integrable in Q (over Q) if there is a monotone nondecreasing se-
quence of functions fh (x), k = 1, 2, ... , in C (Q) which converges
to f (x) a.e. in Q and is such that the sequence of (Riemann) integrals
~ fh (x) dx ~ C, k = 1, 2, ... , is bounded above. The exact
Q
upper bound of the set { ~ fh (x) dx, k = 1, 2, ... } is called the
Q
Lebesgue integral of the function f (x):
(L) ) f dx =sup ) !11. (x) dx =lim \ fh (x) dx. (1)
Q h Q h-.oo Q
LEBESGUE INTEGRAl,. QUESTIONS OF FUNCTIONAL ANALYSIS 45
Let us show that if the function f(x) nonnegative a.e. in Q is
Lebesgue-integrable, then for any monotone nondecreasing sequence
of functions fi.(x), k = 1, 2, ... , in C(Q) that converges a.e.
to f the sequence of integrals i
Q
fi. (x) dx, k = 1, 2, ... , is bounded
above and sup \ fi.(x) dx = (L) j'
f dx, that is, the Lebesgue integral
Q h Q
is independent of the choice of the approximating sequence.
Before proving the above statement, we shall demonstrate that
if f,.(x), k = 1, 2, ... , is an arbitrary sequence of functions in
C(Q) such that f,. t f a.e. as k--+ oo (f (x) 0 a.e.), then >-
sup Jf,.(x) dx >- 0, and hence for any a.e. nonnegative function
" Q
i(x) that is Lebesgue-integrable
(L) ) f dx~O. (2)
Q
Let f,.(x) t f(x) a.e. as k--+ oo. Take an arbitrary 8 > 0. The
set E consisting of points where the sequence /,., k = 1, 2, ... ,
does not converge to for where f < 0 is a set of measure zero, hence
it can be covered by a countablesetofopen cubes {Kh i = 1, 2, ... }
with total volume less than 8. Let K denote the union of all the
cubes of this cover. For any point x 0 E Q"--.K f,.(x 0 ) t f(x 0 ) 0 as >-
k--+ oo, therefore, there is anN= N (x 0) such that fN (x 0) >-e.
Since the function f [\" (x) E C (ij), the last inequality holds also in the
interSeCtiOn lj xo n Q Of the Set Q With an Open CUbe lj xO Centred at
the point x 0 Because the sequence is monotone, the inequalities
j,.(x) > - 8 also hold in Uxo n Q for all k N. The aggregate >-
{Ux, x E Q"--.K} U {Ki, i = 1, 2, ... } of open sets covers the
set Q, and, since Q is closed, from this cover we can select a finite
s
subcover Uxt, ... ,Ul, Ki,, ... ,Ki. Put K'=UKi Since
X S j=f J
t K' I< e and there exists an N 0 such that for all x EQ'-..K' c
l -
c(UU:x:.) nQ we have f,.(x)>- 8 for all k~N0 , it follows
j=l J
that for these k
Jf,.(x)dx= J /,.(x)dx+ Jf,.(x)dx~-8lQI+A 1 8
.q Q"'-K' K'
= 8 (At -I Q I),
46 PARTIAL DIFFERENTIAL EQUATIONS
where I Q I is the volume of Q, A 1 = min f1 (x). Since e > 0 is
xEQ
arbitrary, the last inequality yields (2).
Now suppose that f (x) is an arbitrary a.e. nonnegative Lebesgue-
integrable function, and let fR_ (x), k = 1, 2, ... , fk t f a.e. as
k -+ oo, be a sequence of functions in C (Q) for which the sequence of
integrals is bounded. Taking an arbitrary sequence of functions
fi. (x), k = 1, 2, ... , in C (Q) such that fi. (x) t f (x) a.e. as
k-+ oo, we shall show that
lim r f!tdx=lim r t~~.dx.
k->oo ~ k->oo ~
Consider the sequence f~t- j;,, k= 1, 2, ... , with arbitrary m.
Since, as k-+ oo, f~~.- f:.n t f- t:.n;;;::,o a.e. in Q, it follows that
~~~ _\ (!~~.- t:.n) dx = !~~ Jf~t dx- _\ t:.n dx?;;O. Hence the sequence
Q Q Q
\ t:.ndx, m=1, 2, ... ,is bounded and lim
Q m->oo
Jt:.ndx~lim Q\ fkdx,
Q k->oo
and, because the reverse inequality obviously holds, the assertion
is established.
Let us consider a cube containing the region Q and sides parallel
to the coordinate planes, and decompose it by planes parallel to
the sides into a finite number of parallelepipeds. The nonempty
intersection of an open parallelepiped of the resulting decomposition
with the region Q will be called a cell (of decomposition of Q), and
the aggregate of all the cells the decomposition II of Q. A measurable
function f (x) is called step-function in Q if it assumes only constant
values inside each cell of a decomposition II of Q.
By the integral of a step-function we shall obviously mean the
sum of volumes of all the cells multiplied by the value of the function
in the corresponding cell.
Lemma 2. For every monotone nondecreasing sequence of functions
f~t (x), k = 1, 2, ... , inC (Q) there exists an a.e. monotone nonde-
creasing sequence f(,. (x), k = 1, 2, ... , of step-functions such that
fl, (x) ~ !~~. (x), k = 1, 2, ... , a.e., and f~t (x) -fit (x)-+ 0 a.e.
as k-+ oo.
Proof. Since the function f~t (x) is uniformly continuous, we can
find a number 811. > 0 such that I fk (x') - !~~. (x") I < 2-k for any
points x', x" E Q satisfying I x' - x" I< 6~~., k = 1, 2, . . .. We
denote by Il 1 a decomposition of Q with maximum diameter of the
cell ~ 61 . The step-function 1; (x), which is equal to min / 1 (x)
x{k
in every cell K of the decomposition Il 1 , has the property that
0 ~ / 1 (x) - 1; (x) ~ 2- 1 for almost all x E Q. By taking finer decom_
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 47
position of ITl we can construct a new decomposition IT2 with maxi-
mum diameter of the cell ~ 62 The step-function f2 (x), which is
equal to min f 2 (x) in every cell K of IT 2 , satisfies the inequalities
xEK
0::::;;: f 2 (x) - f2 (x) ~ 2-z for almost all x E Q. Furthermore, f2 (x) ::;>
::;> f~ (x) a.e. in Q. Continuing this process, we obtain for any k ::;> 1
a decomposition ITk of Q and together with it a step-function f',_ (x)
having the properties that 0 ~ fk (x) - fl. (x) < 2-k, fl. (x) ~ fl. _1 (x)
for almost all x E Q. Hence f(, (x) ~ fk (x) a.e. in Q, and a.e. in Q
the sequence fk (x)- fl. (x), k = 1, 2, ... , has a limit equal to
zero. I
Lemma 2'. For any sequence of step-functions fl. (x), k = 1, 2, ... ,
which is monotone nondecreasing a.e. in Q, there exists a monotone
nondecreasing sequence of functions fk(x), k = 1, 2, ... , in C (Q)
such that fk(x) ~ fi, (x) a.e. and /',. (x) - fk (x)--+ 0, as k--+ oo,
a. e. in Q.
Proof. Evidently, it suffices to establish the lemma for /1 (x) ::;> 0
a.e.
Consider the function /1. (x) (f1 (x) ::;> 0 a.e. implies that fi,(x) ::;> 0
a.e.), and let the corresponding decomposition ITh of a cube contain-
ing Q (a 0 denotes the length of the side of the cube) consist of mk cells
(when the decomposition ITk of Q corresponding to f/, does not con-
tain more than mk cells). Take .Sk =min {a;, 2nan 11mk 2k},
0
where
ak is the length of the smallest of all sides of all the parallelepipeds,
the cells of decomposition IT/,, and let sEk (x), 0 ~ sEk (x) ~ 1'
where sEk is the slicing function (see Introduction, Chap. I) for
the pth cell of decomposition IT/,, (.Skis chosen so that the total vol-
mk
ume of the intersection of parallelepipeds, where 2] s~k (x) < 1'
p=i
with Q does not exceed 2-~<).
mk
Let '~IJR(x) denote the function //,(x) 2] s~~< (x). It is easy to see
P=i
that 'ljll< (x) E C(Q), 'ljlk(x) ~ /l,(x) a.e., and /h(x) - 'ljlk(x)--+ 0,
ask--+ oo, a.e. Then the functions fk(x) = max 'ljlm(x), which are
m~h
continuous in Q, satisfy a.e. the inequalities fk(x) ~ //,(x), k =
= 1, 2, ... , and /l.(x)- fk(x)--+ 0, ask--+ oo, a. e. I
Lemmas 2 and 2' immediately imply the following proposition.
Theorem 1. In order that a function f(x) nonnegative a.e. in Q may
be Lebesgue-integrable over Q, it is necessary and sufficient that there-
exist an a.e. monotone nondecreasing sequence fk(x), k = 1, 2, .. ~
48 PARTIAL DIFFERENTIAL EQUATIONS
which converges to f (x) a.e., of step-functions with bounded sequence of
integrals. Furthermore, (L) J
f dx = sup
Q
/11 dx.
k
J
Q
Lemma 3. A monotone nondecreasing sequence of functions in
C (Q) having bounded sequence of integrals converges a.e. in Q.
It follows from Lemma 2 that in order to prove Lemma 3 it suf-
fices to establish the following proposition: If the sequence of step-
functions fk, k = 1, 2, ... , is monotone nondecreasing a.e. and
the sequence of their integrals is bounded, then the sequence fk,
k = 1, 2, ... , converges a.e. in Q.
Let us cover the boundary 8Q (8Q E Ct, see Introduction, Chap. I)
by a finite number of closed cubes K 1 , , K 1 with sufficiently
l
small total volume so that the set Q' = Q'-.. U Ki is a region. Evi-
i=i
dently, it is enough to show that an a.e. monotone nondecreasing
sequence of step-functions / 11 , k = 1, 2, ... , converges a.e. in the
polyhedron Q'.
Consider an arbitrary function / 11 (x) from this sequence, and let II 11
be the corresponding decomposition of the polyhedron Q'.
Let S denote the union of sides of all such polyhedra which belong
to at least one of the decompositions II 11 , k = 1, 2, ... , and let~
denote the aggregate of all the points x of the set Q' "-._ S at which
the number sequence / 11 (x), k = 1, 2, ... , is unbounded. Because S
is a set of measure zero, it is enough to show that ~ is a set of mea-
sure zero.
Taking an arbitrary e > 0, we denote by ~~~. e the set which
.consists of (a finite number) of cells of the decomposition II 11 on
which fk(x)-;;;:,1/e. Since c;;:, f fk(x)dx;;:,-IAtliQ'I + f-1 ~k.e ,,
Q'
where A 1 is the least value that the function / 1 (x) assumes on the
.cells of the decomposition II 1 (! 11 (x) ~A 1 a.e. in Q'), it follows
that !~ 11 ,e/::=:;;e (C+IA 1 IIQ/). Since
00 00
11=1 1!=1
the set ~ is covered by a countable system of polyhedra; further-
more, the total volume of these polyhedra does not exceed
e(C +I A1 ll Q / ), because, in view of the fact that the sequence
of step-functions f 11 (x), k=1, 2, ... , is monotone a.e., for any
N-1 _
N-;;;:,1 ~t,eU U (~k+t,e"-._~l!,e)C~N.e and hence
1!=1
N-1
l~t.el+ ~ /~k+t,e"-..~k.el::::;;I~N. eJ::=:;;e(C+IAti!QI).
11=1
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 49
But then the set 0 can be covered by a countable system of open
cubes with total volume less than 2e (C + I A1 I I Q 1). I
4. Lebesgue-Integrable Functions. Any real-valued function f(x)
can be expressed as
f (x) = J+ (x) - f- (x), (3)
where the functions J+ (x) = max (! (x), 0) and f- (x) =
= max (-f(x), 0) are nonnegative.
The function f (x) is said to be Lebesgue-integrable over Q if the
functions f+ (x) and f- (x) in (3) are Lebesgue-integrable over Q. The
integral of f (x) is defined by
(L) J. f dx = (L) .\ r d.x- (L) ) f- dx. (4)
Q Q Q
Let A(Q) denote the set of functions that are Lebesgue-integrable
over Q. From the definition of A(Q) it follows that the function
C1fdx) + C 2/ 2 (x) E A(Q) if the functions /;(x) E A(Q) and Ct
are any constants, i = 1, 2. Furthermore,
(L) f
Q
(Ct/ 1 + Czfz) dx = C!(L) )
Q
ft dx + Cz (L) ) f2 dx.
Q
Therefore, in particular, If (x) I = f+ (x) f- (x) E A (Q) if +
f(x) E A(Q), that is, a Lebesgue-integrable function is absolutely
integrable. Since If I + f = 2f+ >-
0 and If I - f = 2f- 0, >-
inequality (2) implies
I<L)) fdxJ~(L)) lfldx (5)
Q Q
for f E A(Q).
For functions f 1 , i 2 in A (Q) satisfying the inequality f 1 ~ f 2 for
almost all x E Q, by the same inequality (2) we have the inequality
(L) ) / 1 dx~(L)
Q
f/
Q
2 dx. (6)
1
The functions max (ft(x), f 2 (x)) = 2 (/1 +/ + 2 Ii1 - f 2 I) and
min (/1 (x), f 2 (x)) = ; (/1 + f 2 - I i 1 - f 2 I) belong to A(Q) if so
do the functionsi 1 andf 2 , and therefore also max (ft{x), ... , fm(x))E
E A (Q), min (/1 (x), ... , fm (x)) E A (Q), if fi (x) E A (Q), i =
= 1, ... , m.
Theorem 6. In order that an a.e. nonegative function i(x) which
is Lebesgue-integrable over Q may vanish a.e., it is necessary and
sufficient that (L) \ f dx = 0.
Q
4-0594
50 PARTIAL DIFFERENTIAL EQUATIONS
Proof. If f (x) = 0 a.e. in Q, then the sequence fh(x), k =
= 1, 2, ... , of functions that are identically zero in Q has the
property that fh (x) t f (x), ask-+- oo, a.e. in Q. Therefore, by
definition, (L) J f dx = 0.
Q
Conversely, suppose that (L) Jf dx = 0. Then there exists a se-
Q
quence of functions fk(x), k = 1, 2, ... , in C(Q) such that
fk(x) t f(x), ask-+- oo, a. e. Now consider the sequence f~(x),
k = 1, 2, .... Evidently, ft. (x) E C(Q), k = 1, 2, ... , and
ft. (x) t f (x), ask-+- oo, a.e., thereby implying that 0 ~ J
ft. (x) dx ~
Q
= 0 for
(0
~ (L) .\ f dx = 0, that is ft. (x) all k :;;> 1, which, in turn,
0
yields that f = 0 a.e. I
5. Comparison of Riemann and Lebesgue Integrals. If a function
f (x) is Riemann-integrable (it should be recalled that Riemann
integral is defined only for bounded functions), then, as is known,
there exist two sequences fl., f~, k = 1, 2, ... , of step-functions,
with fk, k = 1, 2, ... , a.e. monotone nondecreasing and f'h, k =
= 1, 2, ... , a.e. monotone nonincreasing, that converge to j (x)
a.e. and are such that the sequences of their integrals have a common
limit equal to the Riemann integral of f(x). In the more "economical"
process of constructing a Lebesgue integral, it is enough to have
(in view of Theorem 1) only the first of these sequences (the bounded
function f (x) can, by adding an appropriate contant, be assumed
nonnegative).
Hence if a function f (x) is Riemann-integrable, then it is also Le-
besgue-integrable and the two integrals coincide. Henceforth the letter
L before the integral sign will be dropped, and an integral will always
mean a Lebesgue integral, while an integrable function will mean
a function belonging to i\ (Q).
The set of bounded functions belonging to i\ (Q) is larger than
the set of Riemann-integrable functions, because, for instance, the
Dirichlet function x (x) E i\ (Q) is bounded but not Riemann-inte-
grable.
Furthermore, in the construction of the Lebesgue integral of
f (x) it was not assumed that the function is bounded; for example,
the unbounded function I x 1-a for 0 <a< n belongs to i\ (I xI <1).
In Courses of Analysis the idea of Riemann integral is extended to
unbounded functions (improper integrals). It can be easily shown
that an absolutely Riemann-integrable (in the improper sense) func-
tion f(x) belongs to A(Q) and that its Lebesgue integral coincides
with the improper Riemann integral.
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 51
Let us note that in regions of dimension not less than 2 all the
improper Riemann-integrable functions are absolutely integrable
in the improper sense. Therefore only in the one-dimensional case the
existence of improper Riemann integral of a function may not
imply its integrability in the sense of Lebesgue. An example of
this is the function __!_
X
sin_.!._
.1:
defmed on (0, 1).
6. Sufficient Conditions for Lebesgue-Integrability. Levy's Theo-
rem. We shall now establish a relationship between measurability
and integrability of a function. By definition, an integrable function
is measurable; however, as illustrated by the function I x 1-a, a> n,
defined in the ball {I x I < 1 }, not every measurable function is inte-
grable. Let us establish some sufficient conditions for integrability.
For this, we shall require theorems on the passage to limit under the
integral sign, which are also important in their own right.
First, we examine monotone f'equences of functions and prove a theo-
rem which states that the set of integrable functions is "closed" with
respect to monotone limit processes.
Theorem 3 (B. Levi). An a.e. monotone sequence of functions
fk (x), k = 1, 2, ... , integrable over Q with bounded sequence of inte-
grals converges a.e. in Q to an integrable function f (x), and
~~~ .\ ik dx = .l f dx. (7)
Q Q
Proof. It is enough to prove the theorem for a monotone nondecreas-
ing sequence. By changing the sign of all the functions, the case of
a monotone non increasing sequence can be reduced to the previous case.
So, let fk (x), k = 1, 2, ... , be an a.e. monotone nondecreasing
sequence of integrable functions. Without loss of generality, we may
assume that fk (x)::;;? 0 a.e., k = 1, 2, ... (otherwise, instead of the
sequence fk (x), k = 1, 2, ... , we would consider the sequence
F k (x) = fk (x) - / 1 (x), k = 1, 2, ... , consisting of a.e. nonnega-
tive functions).
For every k ::;;? 1, we examine the sequence of functions fkm (x),
m = 1, 2, ... , in C (Q), fkm (x) t fk (x), as m--+ oo, a.e. in Q.
The functions cpm (x) = max (/;m (x)), m = 1, 2, ... , belong to
i:::;m
C (Q) and have the following properties:
(a) cpm (x) ~ cpm+l (x),
(b) fkm (x) ~ cpm (x) ~ fm (x) for k ~ m (the second inequality
holds a.e.),
(c) .\ cpm(x)dx~) fm(x)dx~C,
Q Q
(d) i fkm(x)dx~ ,I\
J
cpm(x)dx for k~m.
Q Q
52 PARTIAL DIFFERENTIAL EQUATIONS
From (a), (c) and Lemma 3, we find that crm t f, as m--+ oo, a.e.
in Q, where f is a measurable function. Passing to limit as m--+ oo
in the left inequality of (b) and using the right inequality of (b),
we obtain, for all k, cpk (x) :::::;; fk (x) :::::;; f (x) a.e. in Q. Then, as
k--+ oo, fk (x)--+ f (x) a.e. in Q and f (x) ::):- 0 a.e. in Q. Hence
f (x) E A (Q) and f f dx =
Q
f cpk (x) dx. Taking the limits,
lim
k-+oo Q
Q Q m->oo Q
for every k, that is, f f dx
Q
= lim
m-+oo Q
f fm dx. I
By means of Levi's theorem the following sufficient condition for
integrability of a function is establislied.
Theorem 4 (Fatou's Lemma). If the sequence fk(x), k = 1, 2, ... ,
of a.e. nonnegative integrable functions converges a.e. to a function
f(x) and f fkdx:::::;; A, k = 1, 2, ... , then f (x) is indegrable and
Q
J f dx:::::;; A.
Q
Proof. Consider the integrable functions 'mk (x) = min (ji (x))
m,;i:;::;k
with m :::::;; k. In view of the fact that as k--+ oo 'mk(x) t 'm (x) =
= in (fi (x)) a.e. and 0:::::;; 'mk (x):::::;; fm (x) a.e., the inequality
i~m
(6) and Levi's theorem imply that 'm (x) E A (Q) and 0:::::;;
~ .\ 'm (x) dx :::::;; Jf m (x) dx :::::;; A. The assertion of the theorem
Q Q
now follows from Levi's theorem, since a.e. 'm (x) t f (x) as m--+ oo. I
Another sufficient condition for a function to belong to the set
A (Q) is contained in the following theorem.
Theorem 5. If a function f (x) is measurable and I f (x) J :::::;; g (x)
a.e., where g (x) is an integrable function, then f (x) is also integrable.
Thus a measurable function with integrable modulus is integrable,
and, in particular (the region Q is bounded!), every bounded (that is,
I f (x) I :::::;; const a.e. in Q) measurable function is integrable.
Proof of Theorem 5. Since the function f (x) is measurable, there
is a sequence of integrable (in fact, of even continuous in Q)
functions fk (x), k = 1, 2, ... , which converges to f (x) a.e.
in Q. The sequence of integrable functions f~ (x) =
= max (-g (x), min (ik (x), g (x))), k = 1, 2, ... , also converges
to f (x) a.e. and has an additional property that I fl, (x) l :::::;; g (x)
a.e., k = 1, 2, .... Then the sequence fi. (x) + g(x), k = 1, 2, ... ,
is composed of a.e. nonnegative functions, converges a.e. to f g, +
LEBESGl;E INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 53
and for all k ~ (fi. +g) dx ~ 2 f g dx. By Fatou's lemma, f +
Q Q
+ g E A (Q), thereby implying f E A (Q). I
From Levi's theorem and Theorem 5 we obtain the following
result.
Corollary. If /,. (x) E A (Q), k = 1, 2, ... , and the series
00 00
I
~ 1 If" I dx < oo, then the series ~ ik (x) converges a. e. in Q
k=i Q k=i
m
absolutely (that is, the sequence~ lfk(x)/, m=1, 2, ... , con-
k=1
00
verges a.e.), and the function f(x)= ~ fk(x)EA(Q).
k=1
7. Lebesgue's Theorem on Passage to Limit under the Integral
Sign. One of the fundamental results of the theory of Lebesgue inte-
gration is the following theorem, due to Lebesgue, regarding the
passage to limit under the integral sign.
Theorem 6 (Lebesgue). Let the sequence of measurable functions
fk (x), k = 1, 2, ... , converge a.e. in Q to a function f (x), and let
I fk (x) I~ g (x) a.e., k = 1, 2, ... , where g (x) is integrable. Then
f (x) is also integrable and
lim ) fk dx
k-+oo Q
=) f dx. Q
(7)
Proof. By Theorem 5, the functions fk (x), k = 1, 2, ... , are
integrable.
Consider the measurable functions IPs (x) =sup (fk (x)) and 'IJJs (x) =
ll';;>s
= inf (fk (x)), s = 1, 2, .. .. Since a.e. I IPs (x) I~g (x) and I 'IJJs (x) / ~
k';;>s
~g (x), s = 1, 2, ... , the functions IPs (x) and 'IJJs (x), s = 1, 2, ... ,
are also integrable. But, as S-+ oo, IPs (x) t f (x) and 'IJJs (x) t f (x)
a.e. which, according to Levi's theorem, implies that f (x) E A (Q)
and ) f dx =lim ) IPs dx =lim \ 'IJJs dx. Now (7) is a consequence
Q S-+00 [Q S-+00 Q '
of the obvious inequalities 'IJJs (x) ~f s (x) ~IPs (x) a.e., s = 1, 2, .. . . I
The relation (7) may not hold if the majorant of the sequence is
not an integrable function. For instance, the sequence fk (x) =
= k 2 1xI" (1 - 1x 1), k = 1, 2, ... , where O'n is the surface area of
On
unit sphere in the n-dimensional space, defined in the ball Q =
54 PARTIAL DIFFERENTIAL EQUATIONS
{I x I < 1} tends to zero everywhere in Q but ) fk dx =
Q
k2
(k+n)(k+n+1)-.1 as k-+oo.
Lebesgue's theorem yields the following result.
Theorem 7. Suppose that for some s >-
0 the function f(x, y), X=
= (x1 , . , Xn) E Q c Rn, Y = (y1 , , Ym) E Q c Rm, belongs
to the space c (Q) for almost all x E Q, and for all y EQ and I a I ~
~ s I D~ f (x, y) I ~ g (x) for almost all x E Q, where the function
g (x) is integrable ouer Q. Then J
f (x, y) dx E c (Q).
Q
8. Change of Variables under the Integral Sign. As regards the
change of independent variables, the Lebesgue integral behaves
exactly like a Riemann integral.
Suppose that the transformation
Y = Y (x) (y; = Yi (x1 , , Xn), i = 1, ... , n) (8)
that is continuously differentiable in the region Q maps Q one-to-one
into the region Q'. First of all, we shall show that this transforma-
tion maps a set of measure zero into a set of measure zero.
Indeed, let E, E c Q, be a set of measure zero. Since the union of
a countable number of sets of measure zero is a set of measure zero,
it is enough to show that under transformation (8) the image of the
set E 6 = E n Qr, with sufficiently small 6 > 0, is a set of measure
zero.
Let e > 0 be arbitrary. The set E 6 can be covered by a countable
set of cubes with total volume less than e. We may assume that all
the cubes of this cover have diameters less than 6/2, thereby implying
that all of them belong to Q612 Since every cube, with diameter d,
of this system is mapped by (8) into a region with diameter d' ~
~ d Vn max I VYi I = Cd, the image of the set E 6 can be covered
1!'Si~n
xEQ6/2
by a countable system of cubes whose total volume is less than
en <Vnte. This proves the assertion.
Theorem 8. Let the transformation (8), which is continuously differ-
entiable in Q and has a nonvanishing Jacobian J(x) in Q, map Q one-
to-one into Q'. In order that a function f (y) may belong to A (Q') it is
necessary and sufficient that the function f (y (x)) I J (x) I belong to
A (Q). Furthermore,
Jf (y) dy f f (y (x)) I J (x) Idx.
= (9)
Q' Q
Proof. The inverse transformation corresponding to (8) maps Q'
one-to-one into Q, is continuously differentiable in Q', and has a
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 55
non vanishing Jacobian in Q'. Therefore it suffices to establish
Theorem 8 only in one direction, and we may confine to the case
where f (y) is a.e. nonnegative in Q'.
Let f (y) be an a.e. nonnegative function integrable over Q', and
let !R. (y), k = 1, 2, ... , be a sequence of functions in C (Q'),
JR. (y) t f (y), ask-+ oo, a.e. in Q'. Consider the following sequence
of continuous functions in Q': ji, (y) = !R. (y) ~ (kp (y)), k = 1, 2, ... ,
where the function s
(t) defined over [0, oo) equals zero for 0 ~
~ t ~ 1/2, 2t- 1 for 112 < t < 1, 1 for t :> 1, and p (y) is the
distance of y E Q' from the boundary fJQ' (p (y) E C (Q')).
Obviously, for any k fi. (y) ~ !R. (y) ~ f (y) a.e. in Q' (this implies
that the sequence ~ f/c. dy, k = 1, 2, ... , is bounded) and, as
Q
k-+ oo, ji, (y) tf (y) a.e. in Q'. Hence
lim \ ti. (y) dy = r f (y) dy.
Q'
ll-00 ~
Since the functions fi. (y) are continuous in Q', we have
) //, (y) dy = ~ fl. (y (x)) I J (x) I dx, k = 1, 2, . . . . Hence the
Q' l,J
function f (y (x)) I J (x) I, being the limit of a monotone nondecreas-
ing sequence of functions !R. (y (x)) I J (x) I, k = 1, 2, ... , in
C (Q) that converges a.e. in Q, is integrable over Q and relation (9)
holds. I
Remark. Theorem 8 readily implies that if in Q the inequalities
Co~ I J (x) I ~ cl, where Co and cl are some positive constants,
hold, then a necessary and sufficient condition for the function f (y)
to be integrable over Q' is that the function f (y (x)) be integrable
over Q. i\Ioreover, we have the inequalities
Q Q Q
9. Measurable Sets. Integrals over Measurable Sets. Consider
a subset E of Q. The function XE (x) equal to 1 for x E E and zero
for x E Q'""E is called the characteristic function of the set E.
A set E is called measurable if its characteristic function is mea-
surable. The measure of a measurable set E (mes E) is defmed by the
relation
mes E = ) XE (x) dx. (11)
Q
(The integral on the right side exists in view of Theorem 5.)
56 PARTIAL DIFFERENTIAL EQUATIONS
If Q' is a subregion of Q, then it is measurable, since XQ (x) =
= lim ~~~ (x), where ~ 6 (x) is the slicing function for_Q'. Further,
6-->0
roes Q' = I Q' 1.
The sets of measure zero defined in Subsec. 1 are measurable, and
they are the only sets with zero measure (according to the definition
just given). To prove this statement, it suffices to use Theorem 2 of
Subsec. 4.
If Eisa measurable subset of Q and f (x) is integrable over Q, then
by definition we consider this function to be also integrable over E,
and the integral is defined by
E Q
(Again, in view of Theorem 5, the integral on the right-hand side
exists.)
If Eisa subregion Q' of Q, then, as is easy to see, these new defini-
tions of integrability and of integral over Q', of course, do not con-
tradict the respective defmitions (Subsec. 4) given directly for Q'.
10. Absolute Continuity of an Integra). The following property
is known as absolute continuity of the Lebesgue integral.
Theorem 9. Let a function f (x) be integrable over Q. Then for any
e > 0 there is a 6 > 0 such that for an arbitrary measurable set E c Q,
roes E < 6, the inequality
1 r fax
E
1 <e (13)
holds.
Proof. In view of the inequality (5), it is enough to prove the
theorem for If (x) I, .that is, we may assume that f (x) >
0 a.e. in Q.
Taking an arbitrary e > 0, we choose a function fe (x) EC (Q)
such that f(x)~fe(x)~O a.e. in Q and 0~ ~ fdx- J fedx~e/2.
Q Q
I
Then J fdx=
I
J fXEdx= J (f-fe)xEdx+)r fe"f.Edx~T+MemesE,
~ e
E Q Q Q
where Me= rna~ fe (x). Hence (13) follows if we set 6 = e/(2111 e) I
xEQ
11. Relationship between Multiple and Iterated Integrals. We
shall now discuss the question of reducing a Lebesgue multiple
integral to an iterated integral, and simultaneously the question
of interchanging the order of integration.
Let Qn be an n-dimensional bounded region in variables x =
= (x1 , , xn) and Qm an m-dimensional bounded region in va-
riables y = (y1 , , Ym). We consider a function f (x, y) in the
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 57
bounded region Qm+n = Qm X Qn of (m +
n)-dimensional space
in variables (x,- y).
Theorem 10 (Fubini). Let the junction f (x, y) be integrable over
Qm+n Then f (x, y) is integrable with respect to y E Qm for almost all
x E Qn, is integrable with respect to x E Qn for almost all y E_..Qm, the-
junctions rt (x, y) dy and ) t (x, y) dx are integrable with respect
~m Qn
to x E Qn and y E Qm, respectively, and
) fdxdy=) dx j fdy= f dy) fdx. (14}
Qm+n Qn Qm Qm ~n
It is, of course, enough to prove Fubini's theorem (see Subsec. 9)
for the case where Qn is the cube Kn = {I xi I< a, i = 1, ... , n},
Qm is the cube Km ={I Yi I< a, i = 1, ... , m}, and Qm+n is.
the cube Km+n = {I xi I< a, I Yi I< a, i = 1, ... , n, j =
= 1, ... , m} for some a > 0. Before proving the above theorem,
we shall establish the following assertion.
Lemma 4. Let E be a set of (m +
n)-dimensional measure zero
situated in Km+n and let E 2 (x) and E 1 (y) be its m- and n-dimension-
al sections by the planes x = x
andy= y,
respectively. Then for almost
all x E Kn the set E 2 (x) has m-dimensional measure zero and for almost
ally E Km the set E 1 (y) has n-dimensional measure zero.
By Lemma 1 (Subsec. 1), the set E can be covered by a countable
system of cubes with finite total volume in such a manner that every
point of the set belongs to infinitely-many cubes. We may assume
that the sides of these cubes are parallel to coordinate planes. The
series formed by integrals of characteristic functions Xk (x, y) of
these cubes converges. Since i
Xk (x, y) dx dy = ) dx Xk dy, f
Km+n J(n J(m
according to Corollary to Theorems 3 and 5 (Subsec. 6) the series.
composed of integrals ~ Xk (x, y) dy converges for almost all x. This,
J(m
in turn, means that for almost all x the set E 2 (x) is covered by a count-
able system of m-dimensional cubes with finite total volume in a
manner such that each of the points lies in infinitely-many such
cubes. I
Proceeding now to the proof of Fubini's theorem, we first note
that we can confine to the case f (x, y) >
0 a.e. in Km+n
Take a sequence of functions fk (x, y), k = 1, 2, ... , inC (Km+n}
such that fk (x, y) t f (x, y) a.e. in Km+n Denote by E a set having-
(m + n)-dimensional measure zero such that for all (x, y) E Km+n ~ E'
the sequence fk (x, y) converges monotonically to f (x, y).
58 PARTIAL DIFFERENTIAL EQUATIONS
Jdxj"fk(x,y)dy= J fk(x,y)dxdy-+ f fdxdy
Kn J(m Km+n Km+n
By Levi's theorem, monotone sequence Fk (x) = ~ fk (x, y) dy,
Km
.k = 1, 2, ... , of functions belonging to C (Kn) converges a.e. in
Kn to a function F (x) integrable over K 11 , and
.\ Fdx=;~~ ~ Fdx)dx= ) fdxdy. (15)
Kn Kn Km+n
x
Let us take an arbitrary point E Kn at which the number sequence
Fk (x), k = 1, 2, ... , converges to F (x) and the set E 2 (r) (the
intersection of E with the plane x = X) has m-dimensional measure
zero. According to Lemma 4, the set of points of Kn not satisfying
these properties has n-dimensional measure zero. The sequence
fk (x, y), k = 1, ... , converges monotonically for ally E Km ""'Eix)
(consequently, a.e. in Km) to f (x, y). Levy's theorem asserts that
f(x, y)EA(Km), and, as k-+oo,
f fk (::i", y) dy t \ f (x, y) dy. ( 1G)
Km Km
Hence the functions ~ f (x, y) dy and F (x) coincide a.e. in K 11 I
Km
In what follows, we shall often make use of the following propo-
sition which is a consequence of Fubini's theorem.
Corollary. If f (x, y) is measurable in Om+n is a.e. nonnegative,
and if one of the iterated integrals in (14) exists (that is, for instance,
for almost all x f (x, y) is integrable with respect to y and the function
\ f dy is integrable with respect to x), then the function f (x, y) is
Qm
integrable over Om+n and hence the second iterated integral also exists
and (14) holds.
To establish this, it suffices to verify that f (x, y) E A (Qm+n)
The sequence fk (x, y) = min (f (x, y), k), k = 1, 2, ... , has the
property that fk (x, y) t f (x, y) a.e. in Om+n
) fk (x, y)dxdy= j dx f t,, (x, y)dy,~f dx ~ fdy
Qm+rt Qn Qm Qn Qm
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 59
(the equality here has been written on the basis of Fubini's theorem
as applied to a measurable and bounded, and hence integrable over
Qm+n function fk (x, y)). The fact that f (x, y) E A (Qm+n) now
follows from Levi's theorem.
12. Integrals of the Potential Type. Let a function p (x) be meas-
urable and bounded a.e. in Q, I p (x) I ~ M a.e. Then for every
.x E Rn the function u (x) = \ p (y) dya' a< n, is defined and is
Q lx-yl
known as integral of the potential type.
Let us show that u (x) E C (Rn) For a ~ 0 it is obvious, so let
a> 0. We first note that for any points x 0 and x and any 6 > 0
we have the inequality
Q
~M rJ ( I x0 - +
1 1 ) dy
/xO-Y/<li
Y Ia I x- Y Ia
-f-M Qn{J-YI">li} llxO~yla lx~yla 'dy. (17)
Fix x 0 and take an arbitrary e > 0. Since for a?O and x :I= x 0
1 1 1
inf -? sup a,
YE{/x-yf<:O}!l{ixO-yf>li} I x-y Ia 6a YE{/x-yf>li}!l{/xO-yf<li} I x-y I
and mes{(Jx-yJ<6) n (Jx 0 -yl>6)}=mes{(/x-yl>6)n
n(/x0 -y/<6)}, it follows that
r dy:::;:::: r dy
J
/xO-yf<li
I X- Y Ia """""" J
fxO-yf<li
I x0 -
Y Ia
Hence
J
r ( lxO-yla
1 + 1
/x-yla
) dy ~ 2 r
J
dy
lxO-yla
= const 6n-a.
xO-yf<6
1 fxO-yf<O
Accordingly, we can find (and fix) a 6 > 0 so that the first term on
the right-hand side of (17) is less than e/2.
The function F (x, y) =I 1
I xO-y Ia
1
I x-y Ia
I is continuous on
the closed set Q = { I X - x 0 I ~ ~ ' y E Q n ( I y - x 0 I ? 6)} and
F (x, y) lx=xo = 0. Therefore an 'l"J, 0 < 'll < M2, can be found such
e -
that F (x, y) < 2M I Q I whenever I X - x 0 I< 'll for all y E Q n
n(ly-x 0 l?6). Accordingly, if lx-x 0 l<'l"J, the second term
in (17) also does not exceed e/2. Then, for I x- x 0 I< 'll
l u (x0 ) - u (x) I< e, that is, u (x) is continuous.
60 PARTIAL DIFFERENTIAL EQUATIONS
Now assume n- a> 1. We shall demonstrate that in this case
u (x) is continuously differentiable in Rn and that
()
UxiX=JPY
f ( ) fJxifJ ( lx-yla
1 ) d f ( ) Yi-Xi d
y=aJpy lx-yla+2 y.
Q Q
.
S1nce IYi-Xi+Z ,___
:::::::::
1 . 1
+i , ~ =
. . th e same
, ... , n, arguing 1n
I x-y Ia I x-y Ia
way as above for u (x), we conclude that the functions
Q
are continuous in Rn. Further, by Fubini's theorem, for any i.
i = 1, ... , n,
xi xi
\ Uj (x) dxi =a J\ dxi f p (y) ____:Y::..:_i_X.:.,-i-;;- dy
J J I x-y la+2
x? x~ Q
xi xi
=a f p (y) dy f ____::.Y.:._i-----:X.::..,-i-,;- dxi
J J lx-yja+ 2
= f
J
p (y) dy f fJfJ. (
J x,
1
lx-yl
a) dxi
Q X~ Q X~
=u(x)-u(x 1 , ,'xi-i xL Xi+i , Xn)
Therefore
Uj (x) = U:x.i (x), i= 1, ... , n,
establishing the assertion.
In exactly the same way, it can be shown that if n - a> s, s is
an integer, then u (x) has continuous derivatives up to order s,
and that
Dau (x) = I p (y) D~ 1 a dy
~ I x-y I
for all a = (a1 , , an), I a I ~ s.
We remark that the function
u!{x)= J p(y)ln/x-y/dy,
Q
called logarithmic potential, is (n - 1) times continuously differen-
tiable in Rn and for all a, I a I ~ n - 1,
Daui(x)= ~ p(y)D~lnjx-yidy.
Q
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 61
13. Lebesgue Integral of Complex-Valued Functions. Suppose that
the function f (x) defined in the region Q is complex-valued:
f (x) = Ref (x) + i Im f (x).
The function f (x) is called measurable in Q if so are the functions
Re f and Im f , while f (x) is integrable in Q if both Re f and
Im f are integrable in Q. In this case the integral off (x) is defined
by the relation
f fdx= J\
.
Refdx+i \ lmfdx.
Q Q Q
Since ~ (IRe f I I Imf I)~ If I~ IRe f I
+ +
I Im f 1. in order
that the measurable function f (x) be integrable it is necessary and
sufficient that the function 1 f (x) 1 be integrable.
14. Lebesgue Integral on an (n-1)-Dimensional Surface. Let
S be an (n - i)-dimensional surface (of class C 1), and let Sm, m =
N
= i, 2, ... , N, be a cover of S by simple pieces, S = U Sm
m=1
(see Chap. I, Introduction). Every simple piece Sm is described by
the equation
Xp = IPm (xtt , Xp-1 Xp+tt , Xn),
(Dm, the projection of Sm onto the coordinate plane Xp = 0, i ~
~ p = p (m) ~ n, is an (n - i)-dimensional region having boun-
dary of class C1).
Formula (i8) provides a one-to-one correspondence between
the points (x1 , , Xp _ 1 , Xp+t, . , Xn) of the set i5 m and the
points (x1 , , Xp _ 1 , Xp, , Xn) of Sm: with every point
(xl, ... , XP-l IPm (xl, ... , XP-1 Xp+l , Xn), Xp+t, , Xn) E
E Sm is associated a point (x1 , x 2 , , Xp- 1 , Xp+t , Xn) E Dm
{its projection onto the plane xp = 0).
Suppose that the set E is contained in Sm for some m, m = i, ...
. . . , N. Let lS denote its original in Dm under the above mapping.
We shall say that E is a set of surface measure zero if lS is a set of
{n - i)-dimensional measure zero.
A set E belonging to S is called a set of surfaces of measure zero
if each of the sets E n
Sm, m = i, ... , N, is a set of surface mea-
sure zero.
It can be easily shown that the property of the set E c S being
a set of surface measure zero is independent of the choice of the
cover sl, ... , SN of the surfaces.
62 PARTIAL DIFFERENTIAL EQUATIONS
The notion of a set of measure zero permits us to introduce, in
complete analogy with the case of n-dimensional region (see Sub-
sees. 1-4), the concept of a.e. convergence on S and the related con-
cepts of measurable and Lebesgue-integrable functions on S.
A function defined on S is called measurable (on S) if it is the
limit of a sequence of functions in C (S) that converges a.e. on S.
The nonnegative function f (x) defined on S is said to be (Le-
besgue) integrable on S if it is the limit of a monotone nondecreasing
sequence, con verging a. e. on S, of functions fR (x), k = 1, 2, ... ,
continuous on S for which the sequence of surface (Riemann) inte-
grals is bounded above: j" fn. (x) dS ~ C, k = 1, 2, . . . . The (Le-
s
besgue) surface integral off (x) is defined by
s h R->CJO
A real-valued function f (x) defined on S is said to be Lebesgue-
integrable over S if the nonnegative functions j+ (x) = max (f (x), 0)
and f- (x) = max (- f (x), 0) are Lebesgue-integrable; in this case
,\ t as =
s
fs r as - Is t- ds.
Let the function f be defined on a surface S, and let S 1 , . . , S .v
be a cover of S by simple pieces. Suppose that fm (x1 , . , Xp<m> _1 ,.
Xp<m>+ 1, ... , Xn) defined on Dm denotes the function f (x1, . . .
., Xp<m>-1 cpm (x1, ., Xp<m>-1 Xp<ml+1 ., Xn), Xp<m>+1
... , Xn)
We shall show that the function f is measurable if and only if all
the functionsr, m = 1, ... , N, are measurable; f is integrable over S
if and only if each of the functions ris integrable over Dm, m =
= 1, . . . , N; furthermore
N
\" fdS= ~ ~ rV1+/Y'cpmj 2 dxt ... dxp<mHdxp<mHtdxn, (19)
J
s m=ln;,
m-1
where D; =D 1 , and D;,, m > 1, is the projection of Sm"" U
i=i
St
onto the plane Xp<m> = 0.
If f is measurable (integrable), then, clearly, so is each of the
functions fm, m = 1, ... , N.
Let us show that if all the functions fm, m = 1, ... , N, are
integrable, then so is f (assertion regarding measurability is estab-
lished similarly); this we shall do assuming (this is no loss of
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 63
generality) that j,. and hence, all r,
m = 1, ... , N, are nonneg-
ative a.e. (on S and correspondingly on Dm)
For each m, m = 1, ... , N, take a monotone nondecreasing
sequence f'l:, k = 1, 2, ... , of nonnegative functions in C (Dm)
converging a.e. (in Dm) to the function fm. We examine the sequence
Ilk, k = 1, 2, ... , of decompositions of an (n- i)-dimensional
cube K containing Dm: Il 1 is decomposition of K into 2n-l equal sub-
cubes with sides equal to half that of K, the decomposition I1 2 is
obtained by taking finer divisions of I1 1 in which every cell (cube)
of decomposition Il 1 is divided into 2n-l equal subcubes, and so on.
For all m = 1, ... , N, k = 1, 2, ... , we denote by D'm, h a closed
set composed of (a finite number of) closures of all the cells of decom-
position Ih contained in D;,., and by f?: a function continuous in Dm
which vanishes in Dm ~D'm, h and in D'm, h equals the function
f'l: ~ (krm, h), where ~ (t) = 0 for 0 < t < 1/2, ~ (t) = 2t- 1
for 1/2 .:C t ~ 1, ~ (t) = 1 for t > 1, and r m, h is the distance between
the point (x1 , . , Xp<m> _1 , Xp<m>+I, ... , Xn) E D'm, h and the boun-
dary of D'm, h Clearly, for all m, m = 1, ... , N, the sequence
f,r'(, k = 1, 2, ... , is monotone nondecreasing a.e. in D;,. and con-
verges to r. ;::::m
We define a function fh, m=1, ... , N, k=1, 2, ... , con-
tinuous on S as follows:
for xESm
for xE S"-..Sm
N ~
and put fh = 2J Jr':, k = 1, 2, Clearly, each of the functions
m=1
fh, k= 1, 2, ... , is continuous on S and
N N
~ r ~~nds
I fhdS= m=1~ I tr:dS= m=!Sm
S S
N
2
m=!Dm
N
~ \ ff': V 1 +I V<pm j2 dx1 .. dxp<mH dxp<m>+i .. dxn. (20}
m=! n'm
Furthermore, as k-+ oo, fh t f a.e. on S. Since the function
rVt+IV<pml 2 , m=1, ... , N, is integrable on D;,., (20) implies
that the sequence Jf h dS, k = 1, 2, ... , is bounded. Consequently,
s
PARTIAL DIFFERENTIAL EQUATIONS
j is integrable over S. Passing to the limit, as k --+ oo, in (20),
we obtain (19).
From what has been just proved/ it readily follows that all the
properties that were established earlier for an n-dimensional region
also hold for functions measurable and continuous over S.
1. Linear Spaces. A set ~ is called a linear space if on its ele-
ments the operations of addition and multiplication by real (complex)
numbers are defined and the resulting elements also belong to ~and
have the following properties:
(a) f1 +f2 = /2 f1, +
(b) (f1 + f2) +fa = f1 + (f2 +fa),
(c) there is an element o in~ such that 0-f = o for any f E ~.
(d) (c1 +c 2 ) f = ctf cJ, +
(e) c U1 + f2) = cft + cf2,
(f) (c1 c 2 ) f = c1 (c 2f),
(g) 1 f = f
for any f, f 1 , E ~ and any real (complex) numbers c, c1 , . . . .
Depending on whether the numbers by which the elements of ~
are multiplied are real or complex, the space ~ is designated as
a real or a complex linear space. For definiteness, in this chapter we
shall consider only complex linear spaces. All the definitions and
results are easily carried over to the case of a real linear space.
A subset of the linear space ~ which itself constitutes a linear
space is called a linear manifold in ,!T.
Let fm, m = 1, 2, ... , be a countable (or finite) system of ele-
ments of the linear space ~- A set composed of elements of the form
ctf1 + ... + c,fk for all possible k and arbitrary complex c1 ,
. . . , c, is a linear manifold in !T and is called linear manifold
spanned by the elements f,, k = 1, 2, .... The elements f 1, ... , fm
Qf .'F are linearly independent if c1f 1 + ... +cmfm = o holds only
for c1 = ... = Cm = 0; otherwise f 1, . . . , fm are linearly depen-
dent. When the set of elements of ~ is infinite, it is linearly inde-
pendent if every finite subset of it is linearly independent.
A linear manifold is finite-dimensional (n-dimensional) if it has n
linearly independent elements and the aggregate of any of its (n + 1)
elements is linearly dependent.
The linear manifold spanned by linearly independent elements
j,, k = 1, ... , n, of 9F is n-dimensional.
A linear manifold is called infinite-dimensional if one can find in
it a linearly independent subset composed of infinite number of
elementf'..
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 65
2. N ormed Linear Spaces. The space ~ is a normed linear space
if to each element f of this space we can assign the quantity II f II =
= II f lis: (norm of f) having the following properties:
(a) II cf II = I c I II f II for any complex c and any f E !F,
(b) II /1 + !2 II ~ II /1 II + II /2 II for any li E ~. i = 1, 2 (the
triangle inequality),
(c) II t II :;> o, where II t II = o if and only if t = o.
In a normed linear space one can introduce the notion of distance
II / 1 - / 2 II between two elements / 1 and / 2 as well as that of con-
vergence.
The sequence fm, m = 1, 2, ... , of elements of ~ is called
fundamental if II h - fm II~ 0 ask, m ~ oo.
The sequence fm, m = 1, 2, ... , of elements of ~ is said to
converge totE tiT Um ~ t as m ~ oo, or lim lm =f) if II lm - 1 11~
m->oo
~o as m~ oo.
A sequence cannot converge to two different elements, for if
II fm - I II~ o and II fm - g II~ o as m ~ oo, then II t - g II=
= II I - fm + fm- g II-< II lm- I II+ II lm- g II~ o as m ~ oo,
that is, II t - g II = o, implying t = g.
If lm ~ f, then II fm II~ II I II (continuity of the norm). Indeed, by
the triangle inequality, II fm II ~ II fm - I II + II t II and II I II ~
~ II lm - I II + II fm 11. Consequently, I II fm II - II f II I~
~ II fm - f II ~ 0 as m ~ oo.
If the sequence converges Um ~ /), then it is fundamental, since
II f,,- fm II = II l k - I+ I - lm II~ II lk- I II +
+ II I - lm II~ 0 ask, m ~ oo.
The converse, generally speaking, does not hold.
A normed linear space is called complete if corresponding to every
fundamental sequence of its elements there is an element of this
space to which this sequence converges.
A complete normed linear space B is known as Banach space.
A linear manifold in a Banach space B that is complete in the
norm of B (and hence is itself a Banach space with the same norm)
is called a subspace of B. The linear manifold spanned by a finite
number of elements of B is a subspace of B.
If oJft is a linear manifold in B, then the set wit obtained by adding
to c4t all those elements which are limits of all the fundamental
sequences of elements of &It (in B every fundamental sequence has
a limit) is known as the closure (in B) of manifold c!t.
The closure oJft of a linear manifold oJft is clearly a linear mani-
fold. Let us show that it is closed. To this end, let fk, k = 1, 2, ... ,
be a fundamental sequence of elements of oft, and put I = lim lk
k->oo
5-0594
66 PARTIAL DIFFERENTIAL EQUATIONS
We show that f E aJt. By the definition of (!If/, for any k = 1, 2, ... ,
there is an element fi. E elft such that II fi. - fk II < 1/k, therefore
II I - !J; II = II f - fk +
fk - fi. II :::;;; II I - fk II 1/k-+ o +
as k -+ oo, that is f = lim fi., implying f E elft.
k__,.oo
Thus the closure of a linear manifold in B is a subspace.
The closure of a linear manifold spanned by the elements /,10
k = 1, 2, ... , is called a subspace spanned by these elements.
A set o!t' c: B is bounded if there is a constant C such that II/ II::=;;; C
for all f E o!t'.
The set e!lt' c: B is said to be everywhere dense in B if for any f E B
there is a sequence fi., k = 1, 2, ... , of elements of elft' that con-
verges to f.
A Banach space B is separable if it contains an everywher&
dense countable set.
3. The Scalar Product. Hilbert Space. We say that a scalar product
is introduced in a linear space H if with every pair of elements hH
h 2 E E there is associated a complex quantity (h1, h 2) (the scalar
product of these elements) with the following properties:
(a) (h 1 , h 2) = (h 2 , h 1) (in particular, (h, h) is a real number),
(b) (hl + h2, h) = (hl, h) +
(h2, h),
(c) for any complex c (ch 1 , h 2) = c (h 1 , h 2),
(d) (h, h) >-0, where (h, h) = 0 if and only if h = o.
Let us establish the important inequality, known as Bunyakov-
skii's inequality,
I (hl, h2) 12:::;;; (hl, hl) (h2, h2), (1)
which holds for arbitrary h 1 , h 2 in H. When h 2 = o, the inequali-
ty (1) is obvious, so let h 2 =1= o. For any complex t 0 ::=;;; (h 1 + th 2 ,
h1 +th2) = (h 1 , h 1). +
t (h 1 , h 2 ) +
t (h17 h 2 ) + I t 12 (h 2, h 2 ). If we
- (ht. h2) h' . l't
pu t t - - (h , h ) , t 1s mequa 1 y ecomes 1 , h) b (h 1 -
l(ht. h2)12 ........
(h , h ) -7'
2 2 2 2
>- 0, equivalent to (1).
The scalar product generates a norm II h II = V (h, h) in H.
Properties (a) and (c) of a norm are apparently satisfied. To show that
(b) (the triangle inequality) is also satisfied, we make use of the
Bunyakovskii's inequality
II hl + h2 11 2 = II hl 11 2 (hH h2)+ (h2, hl) +
II h2 ll 2 +
+
:::;;; Hh1 W 211hl llllh2ll llh2ll = (1lh1
2 + llh2ll) 2 II+
A linear space with a scalar product that is complete in the norm
generated by this scalar product (that is, is a Banach space in this
norm) is called a Hilbert space.
Apart from the convergence (in norm), it proves convenient to
introduce one more type of convergence in a Hilbert space. A se-
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 67
quence hm, m = 1, 2, ... , in His said to converge weakly to an ele-
ment h E H if lim (hm, f) = (h, f) for any f E H.
m.... oo
Let us show that a sequence cannot converge weakly to different
elements of H. Assume that there are two elements h, h' E H such
that lim (hm, f) = (h, f) and lim (hm, f) = (h', f) for any
m~oo m~~
f E H. Then for all f EtH (h - h', f) = 0 and, in particular, with
f = h - h' we have (h- h', h - h') = 0, implying h = h'.
If a sequence hm E H, m = 1, 2, ... , converges to hE H, then
it converges to it weakly as well. Indeed,
I (hm, f) - (h, f) I = I (hm - h, f) I
~ II hm- h 1111 f II-+ 0 as m-+ oo.
4. Hermitian Bilinear Forms and Equivalent Scalar Products.
A Hermitian bilinear form W is said to be defined on a Hilbert space H
if with every pair of elements h 1 , h 2 E H there is associated a complex
number W (h 1 , h 2 ) with the following properties:
(a) W (h 1 + h 2 , h) = W (h 1 , h) +
W (h 2 , h),
(b) W (ch 1 , h 2) = cW (h 1 , h 2 ),
(c) W (h 1 , h 2) = W (h 2 , h 1 )
for arbitrary h, h 1 , h 2 E H and arbitrary complex c.
The function W (h, h) defined on H is called quadratic form cor-
responding to the Hermitian bilinear form W (h 1 , h 2). By Property
(c), the quadratic form corresponding to a Hermitian bilinear form
is real-valued.
An example of Hermitian bilinear form defined on H is the scalar
product and the correspondingiquadratic form is the square of the
norm generated by the scalar product.
If/a quadratic form corresponding to a Hermitian bilinear form
has the property that W (h, h) :;> 0 for all h E II and W (h, h) = 0
for h = o only, then the bilinear form W (h 1 , h 2 ) can be taken as
the (new) scalar product in H: W (h 1 , h 2) = (h1 , h 2)', and the result-
ing (new) norm is defined by II h' II = VW (h, h).
The norm II II' is said to be equivalent to the norm II II if there-
exist constants C1 > o, C 2 > o such that II h II' ~ C1 II h II, II h II~
~ C 2 II h II' for any element hE H. Two scalar products (,)and (, )"
are said to be equivalent if so are the norms generated by them.
If the norm II II' is equivalent to the norm II II, then the set n
is a Hilbert (that is, a complete) space also with respect to th~
scalar product ( , )'.
In fact, let the sequence hk, k = 1, 2, ... , of elements of H be
fundamental in the norm II II': II hk - hs II' -+ 0 as k, s-+ oo;
this sequence is also fundamental in the norm II II, since II hk - hsll ~
~ C2 II hk - h 8 II'. Because H is complete in the norm II IJ, there
exists an element h E H to which the sequence in question con.:.
5*
68 PARTIAL DIFFERENTIAL EQUATIONS
verges: II hk - h II -+ 0 as k-+ oo. But the sequence converges to h
in the norm II II' also, since II hk - h II' ~ C1 II hk - h II, and the
conclusion follows.
5. Orthogonality. Orthonormal Systems. Two elements h 1 , h 2 E H
:are orthogonal (h 1 _l h 2 ) if (h 1 , h 2) = 0. An element h is said to be
-orthogonal to a setH' c H if (h, h') = 0 for all h' E H'. Two sets H'
and H" in H are orthogonal (H' _l H") if (h', h") = 0 for all h' E H',
h" EH".
If h E II is orthogonal to a set H' that is everywhere dense in H,
then h = o. Indeed, let hi,, k = 1, 2, ... , be a sequence of ele-
ments of H' and hi,-+ h ask-+ oo. Since (h),, h) = 0 for all k :;;?:- 1
and by weak convergence (hi,, h)-+ II h W, it follows that II h II = 0,
implying h = o.
An element hE H is normalized if II h II = 1, and a set H' c H
is called orthonormal (orthonormal system) if its elements are norma-
lized and are mutually orthogonal. An orthonormal set is, obvious-
ly, linearly independent.
A countably infinite (or finite) linearly independent set of ele-
ments hk, k = 1, 2, ... , can be transformed into a countably
infinite (or finite) orthonormal set in the following manner (Gramm-
Schmidt's method):
h2-(h 2 , e 1 ) e 1
II h2- (h2, e1l e1 II ' ... '
(according to the supposition that the set hk, k = 1, 2, ... , is
linearly independent, hn- (hn, e1 ) e 1 - . - (hn, en-1 ) en- 1 =I= o
for any n :;;?:- 2). .
6. Fourier Series with Respect to an Arbitrary Orthonormal
System. Suppose that f is an arbitrary element of H and e1 , ,
en, ... a countable orthonormal system in H (if His fmite-dimension-
al, one must take an orthonormal system consisting of a finite
number of elements). Denoting by Hp, for some p :;;?:- 1, the subspace
spanned by the elements e1 , . , ep, we try to find in Hp an ele-
ment which is closest (in the norm of H) to the element f. Since any
p
element of Hp is of the form ~ Crer with certain constants c1 , , Cp,
r=1
the problem reduces to determining constants cu , Cp such
p
that the quantity 61 p (!; c1 , , cp) = II f - ~ c.,.e.,. 11 2 attains
~1
its minimum.
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 69
The quantities fk = (f, ek), k = 1, 2, .. , are called Fourier
coefficients off with respect to the system e1 , e2 , . . . . Since
p p
r=1 r=1
p p p
=II f 11 2 - ~ Crfr- ~ Cr/r+ ~ / Cr 1
2
r=1 r=1 r=!
p p
= ~ I Cr- f r l2 - 2 + 1/ f W'
~ Ifr 1
r=1 r=1
the quantity 6kP (!; c1 , , cp) attains its minimum only when
Cr=/ 7 , r=1, ... , p, and this minimum, denoted by 6kp(f), is
p
equal to 1/ f // 2 - ~ I fr 12 :
r=1
p
6kp U) =II t 11 2 - ~ I fr
r=!
r (2)
p p
ilf- ~ Crer I/~ /if-~ frer //
r=t r=1
for all c1 , , Cp, describing the minimal property of Fourier coef-
ficients; the equality is attained only for Cr = fr, r = 1, ... , p.
Denoting by fP the unique element closest to f in the subspace H P:
we have
(3)
The element fP is called the projection of f onto the subspace H p
Equality (2) implies that for any f EH and any p ~ 1,
p 00
~
r=1
I fr J 2 ~1/ f 1/ 2 Accordingly, the number sequence ~
r=1
I fr \2 con-
verges and Bessel's inequality
00
r=1
~ lfr/ 2 ~1/fiJ 2
holds.
Lemma 1. Let fk, k = 1, 2, ... , be a sequence of complex num-
bers and ek, k = 1, 2, ... , an orthonormal system in H. In order
00
k=t
00
sary and sufficient that the number series ~ If r 12 converge.
r=1
70 PARTIAL DIFFERENTIAL EQUATIONS
p 00
Proof. Let Sp = L; . vL...: f rer.
frer be the partial sum of the senes
r=t r=t
p p
For p>q we have the equality IISp-Sqii 2 =JI q+t
L; frer IJ 2= L; lfrl 2
q+i
which implies that convergence of L; I fr /2 is necessary as well
as sufficient for the sequence of its partial sums to be fundamen-
tal, and hence for convergence of series in question, since H
is complete. I
Let f be any element of Hand fk, k = 1, 2, ... , its Fourier coef-
ficients with respect to the orthonormal system ek, k = 1, 2, ....
The series
00
L; fkek
k=i
is called Fourier series of f with respect to the system ek, k =
= 1, 2, ....
Lemma 1 and Bessel's inequality yield the following result.
Lemma 2. The Fourier series of any element f E H with respect to
an arbitrary orthonormal system converges in the norm of H.
Lemma 2 establishes the existence of an element E II to which T
the Fourier series of f converges. A natural question can be asked:
Is 1 = f for all f E II?
In the general case, unless additional conditions are imposed on the
system e1 , e2 , besides its orthonormality, the answer to above
question is in negative.
7. Orthonormal Basis. It follows from (2) that for any f E H the
quantity flk (f) decreases when p increases. Therefore a priori there
are two case~ to be examined:
(a) for all f E H fl'Jr (f)-+ 0 asp-+ oo,
(b) there is an ele~ent I E H for which 61 (f) -+ c > 0 asp -+ oo.
When (a) holds, for any I E H we have, hy (3),
p
lim L; lkek
I= P-+oo k=i
or, which is the same
co
I= L; l,.eJ&, (4)
k=1
that is, in case (a) the Fourier series of an element I converges (in
the metric of H) to f. Furthermore, for any IE H we have
co
(5)
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 71
00
(f, g)= ~ f1tgk, (5')
11=1
true for all f, g E H.
Equality (5) is a consequence of (2). To establish (5') we first
note that the series on the right side converges absolutely, because
i.ts general term has a majorant which is the general term of a con-
- 1
vergent series: I fk g1l. I~ 2 (I/,~. 1z +
I g 11 12 ). Further, by (4)
p
(f, g)= lim (fP, g)= lim ( ~ fke1l., g)
p~oo p~oo k=1
p p 00
=lim ~ fk (ell., g)= lim ~ fkg1l. = ~ fkgk,
p~oo 11=1 p~oo 11=1 11=1
as desired.
In case (b), there is an element f E H whose Fourier series con-
verges (by Lemma 2 of the preceding Subsection) to 1=1= f, that is, the
element h = f -1 =1= o. Hence
00
f=h+ ~ f11.e11.,
k=i
where h =1= o and h is orthogonal to the subspace spanned by the
system e1 , e2 ,
We again return to case (a) in which we are basically interested.
A countable orthonormal system e1 , e 2 , is called complete
or an orthonormal basis for the space H if any element f E H can be
expanded in a Fourier series (4) with respect to this system.
The aforementioned discussion leads to the following assertion.
Lemma 3. For an orthonormal system e1 , e 2 , to be an orthonor-
mal basis for H it is necessary and sufficient that the Parseval-Steklov
equality (5) hold for any element f E H or (5') hold for any two elements
j and g of H.
Lemma 4. For an orthonormal system e1 , e 2 , to be an orthonor-
mal basis for H it is necessary and sufficient that the linear manifold
spanned by this system constitute an everywhere dense set in H.
If the system e1 , e2 , is an orthonormal basis for H, then every
element f E H is approximated in the norm of H as closely as one
pleases by the partial sums of its Fourier series which are linear
combinations of this system. This shows that the condition is neces-
sary.
To show that the condition is sufficient, take an arbitrary element
j E H. For an e > 0 we can find a number p = p(e) and numbers
p
c1 (e), ... , cp(e) such that II f - ~ ck(e) ek II< e. Since the
11=1
72 PARTIAL DIFFERENTIAL EQUATIONS
that
which shows that f has a Fourier expansion (4). 1
Theorem 1. In a separable Hilbert space there is an orthonormal
basis.
Proof. Let h;, h;, ... be a set everywhere dense in H. By h 1 denote
the first nonvanishing element h/., (h; = ... = h/.,_1 = o), by h 2
the first nonvanishing element of the set hk,+ 1 , hk,+z . . . that
forms with h 1 a pair of linearly independent elements, and so on.
The countable (or finite) system h 1 , h 2 , is linearly independent
and the linear combinations of the elements of this system are every-
where dense in H. We can transform the system h 1 , h 2 , (Sub-
sec. 5) into a countable orthonormal system of elements e1 , e2 ,
whose linear combinations are also dense in H. By Lemma 4, this
system is an orthonormal basis for H. 1
3. LINEAR OPERATORS. COMPACT SETS.
COMPLETELY CONTINUOUS OPERATORS
1. Operators and Functionals. Let B 1 and B 2 be Banach spaces and
B' a set lying in B 1 An operator A (operator A from B 1 into B 2 ) is
s;id to be defined on B; if to every element f E s; there corresponds
an element g E B 2 : g = Af. The set B; is called the domain of defini-
tion of A and is denoted by D A D A = B;, while the set of elements
of the form Aj, f ED A is known as its rangeR A c B 2
The operator A is a functional if the space B 2 is a set of complex
numbers (the modulus of a complex number is taken as a norm of this
set). The functionals will commonly be denoted by l.
Simplest examples of operators are the operator 0, the null ope-
rator, and (for B 1 = B 2 ) the identity operator I defined as follows:
Of= o for all IE D 0 , If= I for all IE Dr.
An operator A is said to be continuous on an element f E D A if it
111 aps a sequence fk, k = 1, 2, ... , of elements of D A converging
to fin the norm B 1 into a sequence A/", k = 1, 2, ... , that converges
to AI in the norm B 2 Operator A is continuous on the set E c D A
(in particular, on D A) if it is continuous on every element fEE. An
operator A that is continuous on D A will be referred to as continuous.
The operator A is linear if D A is a linear manifold and
+
A(c1f 1 +
cJ 2 ) = c1 A/1 c2 A/ 2 for any elements /i ED A and
numbers c;, i = 1, 2.
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 73
The null element of B 1 is mapped by the linear operator A into
the null element of B 2 , because
Ao = A(Of) = OAf = o
(f is any element of D A)
For a linear operator A to be continuous it is necessary and sufficient
that it be continuous on the null element (or, generally, on some element
of D A)
The necessity of this condition is apparent. To show that it is
sufficient as well, let fk, k = 1, 2, ... , be a sequence of elements
of D A that converges to fED A Since gk = fk- j, k = 1, 2, ... ,
is a sequence of elements of D A converging to zero, it follows that
Agk-+ o as k-+ oo, thereby implying Afk-+ Aj ask-+ oo. 1
Let A;, i = 1, 2, be linear operators from B 1 into B 2 , D A 1 = D A 2,
and let c;, i = 1, 2, be certain numbers. We define a new operator
A = c1A 1 + c 2 A 2 as follows: for any fED A= DA, = DA 2, Aj =
+
= c1 A 1 j c 2 Ad. Operator A is also linear.
Thus the operations of addition and multiplication by complex
numbers are defined on the set of linear operators with common do-
mains of definition. It is easily seen that this set is a linear space.
A linear operator A is said to be bounded if there is a constant
C > 0 such that II Aj IIB 2 ~ C II f liB, for all f E D A or, what is
the same, II Aj IIB 2 ~ C for all fED A satisfying II f liB, = 1.
The exact upper bound of the values of Cis known as the norm of A
and is denoted by II A 11.
We can show that
JIAIJ=supiiA/IJB2 = sup IIA!IIB2 (1)
tEDA IJ!IIB, tEDA
II IIIB,=1
Put a = sup II Aj IIB2111 f liB'" For all f ED A II Aj IIB2IIIfiiBt~
fED A
~ a, therefore II A II ~ a. To establish the reverse inequality, we
note that, by the definition of exact upper bound, for every e > 0
there is an element /e ED A such that II Afe IIB 2/II /e IIB 1 :;;>a- e.
This implies that II A II :;;> a - e for any e > 0, that is, II A II :;;> a.
Hence II A II = a.
In particular, when A is a bounded linear functional, A = l,
its norm is given by
IIli i, -sup
- _IZ/_1_-
II f II - sup Jlf. I
IED1 B1 !ED1
II f IIB 1=1
Note that the set of bounded linear operators with common domains-
of definition is a linear manifold in the space of all the linear opera-
tors with the same domains of defmition. The norm defined above
74 PARTIAL DIFFERENTIAL EQUATIONS
for a bounded linear operator satisfies all the axioms of being a
norm. It can be easily shown that this normed space is complete
(that is, it is a Banach space).
The following proposition establishes a connection between the
notions of boundedness and continuity for linear operators.
For a linear operator A to be continuous it is necessary and sufficient
that it be bounded.
Sufficiency. Let the sequence f 1u k= 1, 2, ... , in DA converge
{in B 1) to !EDA. Since IIAf~t-AfiiBz=IIA(fk--f)IIBz<::IIAIIx
Xllf~t-!IIB 1 ~0 as k~oo, it follows that Af~t~Af, as k~oo,
in B 2
Necessity. Assume the contrary, that is, A is unbounded. Then
there is a sequence fi., k = 1, 2, ... , of elements of D A such that
II Ali. IIB2 > k II /i. IIB11 but this contradicts the continuity of A,
because the sequence fk = fh./(k II /1. IIB1), k = 1, 2, ... , belonging
to D A converges in B 1 to zero, while the sequence Afk, k = 1, 2, ... ,
-cannot converge to Ao = o since II Af~t II B. :;> 1. I
A bounded linear operator A whose domain of definition D A is
-everywhere dense in B 1 can always be assumed to be defined on the
whole of B 1, by redefining it on B 1~D A as follows. Let f be an ele-
ment of B 1 ~D A and fk, k = 1, 2, ... , a sequence of elements of
D A that converges to f in the norm of B 1 (D A is everywhere dense
in B 1 ). Since A is bounded, the sequence Afk, k = 1, 2, ... , of
-elements of B 2 is fundamental in B 2 , and because B 2 is complete,
the sequence A/It, k = 1, 2, ... , has a limit in B 2 We show that
this limit is independent of the choice of the sequence fk, k =
= 1, 2, . . .. In fact, let /1.., k = 1, 2, ... , be another sequence
1Jf D A converging to f. Then II A/h. - Afk IIB 2 = II A (fl. - iR) IIB2 =
= II A II II fl.- ik IIB1 ~ 0 ask~ oo; accordingly, the limit depends
only on the element f. We take this as the value At of A on f. The
.extension of A obtained in this manner, and referred to as the exten-
sion with respect to continuity, is a bounded linear operator defmed
on the whole of B 1.
If A 1, A 2 are linear operators for which RA 2 c: DA 1 , then the
linear operator A 1 A 2 on DA 2 with range in RA 1 is defined as follows:
A 1 AJ = A1 (AJ). If A 1 and A 2 are bounded, then so is A 1A 2 and
IIA1A2 II:::;; II A1 II II Az 11.
Suppose that the equation A/ = g has a unique solution fED A
for every g E R A This means that on R A an operator, denoted by
A -l, is defined which with every g E R A associates the unique f E D A
such that Af =g. The operator A-lis called inverse of A. Clearly,
DA-t = RA, RA-1 = DA, A-1A =I, AA-1 =I; and A-1 is linear
provided so is A.
2. Riesz's Theorem. An example of a bounded linear functional
defined on a Hilbert space H is provided by the scalar product: if we
fix an arbitrary element hE H, then (f, h) is (with respect to f)
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 75
a bounded linear functional (boundedness is a consequence of Bunya-
kovskii's inequality). The most striking feature is that any bounded
linear functional defined on H (or, by the results of Subsec. 1, on
a set everywhere dense in H) may be expressed as a scalar product
by a proper choice of h E H. Namely, the following important asser-
tion holds.
Theorem 1 (F. Riesz). For every L:Junded linear functional defined
en a Hilbert space H there is a unique element h E H such that for
all t EH
l (f) = (f, h). (2)
We shall prove this theorem only for a separable Hilbert space H
(only for such. spaces will this theorem be used in this book).
Proof. Let e1o e 2 , , en, . be an orthonormal basis for H (such
00
a basis exists, by Theorem 1, Sec. 2), and let ~ fke,. be the
11.=1
p
Fourier expansion of some fEH. Since, as p-HX>, ~ j,.e,.-+f,
~=1
by the continuity of l
p p 00
l (f)= lim l ( ~ fke,.) =lim ~ fkl (ek) = ~ j,."ii~~., (3)
p-.oo k=1 p-.oo k=1 11.=1
where h,.=l(ek), k=1,2, ....
p
Consider the element hP = ~ h,.e~~.. Since JZ (hP) I< Iilii II hP II
k=i
p p
(l is bounded) and l (hP) = 2} hkl (e,.) = 2} I hk 12 =II hP w, we have
k=1 k=1
p 00
11.=1 11.=1
00
k=1
00
series 2} hkek converges in the norm of H to an element hE H
k=1
(hk are Fourier coefficients of h).
Substituting fk = (!, ek) into (3) and again making use of the
.JO 00
continuity of l, we obtain (2): l (f)= 2} (!, h,.e~~.) = (!, 2] hken) =
k=1 11.=1
=(!,h).
Apart from representation (2) if there is another representation
for l: l (f) = (f, h'), then for all f E H (f, h - h') = 0, implying
h = h'. 1
76 PARTIAL DIFFERENTIAL EQUATIONS
Let us note that, when proving Theorem 1, we have established
that II h II ~ II z 11. The reverse inequality II z II ~ II h II follows.
from (2) and the Bunyakovskii's inequality. Thus liZ II = II h 11.
3. Adjoint Operator. Suppose that H is a Hilbert space and A
a linear operator from H into H which is defined on a set D A every-
where dense in H (operator A is, generally speaking, not bounded).
Let D A* denote a set of elements of H satisfying the following
condition: for any g ED A* there is an element h E H such that
for all fED A
(Aj, g) = (f, h).
The set D A* is nonempty, because the null element of H belongs
to it: when g = o, h = o.
We show that to every element g ED A* there corresponds only one
h E H. Assume the contrary, that is, to a g ED A* let there corres-
pond two elements h, h' of H. Then for all fED A (f, h - h') = 0,
implying h = h' (recall that D A is everywhere dense in H).
Thus an operator, denoted by A*, is defined on D A*: to every ele-
ment g E D A* there corresponds a unique element h = A* g E H
such that
(Aj, g)= (f, A*g) (4)
for any f E D A- Operator A* is called adjoint of A. Its domain of defi-
nition is the set D A* consisting of those elements of H for which (4)
holds for all f E D A
If g 1 , g 2 are arbitrary elements of D A* and c1 , c2 arbitrary complex
numbers, then for any fED A (4) yields
(f, c1 A*g1 + c A*g
2 2) = c (f,
1 A*g1) + c2 (f, A*g 2 )
c;.
.= (A!, gt) + ~ (Af, g2) = (Af, ctgt + c2g2)
which implies that c g + c g
1 1 2 2 E D A* (that is, D A* is a linear mani-
fold) and A* (c1 g1 + c2 g 2 ) = c1 A *g 1 +c2 A * g 2 Thus the operator
A* is linear.
Now suppose that A is bounded. By Subsec. 1, it can be assumed
to be defined on all of H. Take an arbitrary element g E H. The linear
functional l (f) = (Af, g) is bounded, because I l (f) I ~ IIA/ II X
x II g II~ (II A II II g II) II f 11. By Riesz's theorem (Subsec. 2},
there is a (unique) element hE H such that l (f) = (Af, g) = (f, h) =
= (f, A *g). Hence (4) holds for all g E H, that is, D A* = H.
Let us show that A* is bounded and that II A* II = II A 11. Set-
ting in (4) f = A* g for any g E H, we obtain
II A*g 11 2 = (AA*g, g)~ II A (A*g) 1111 g II
~ (II A II II g II) II A* g 11.
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 77
Therefore II A* g \\ ~ II A \\ II g \\, that is, A* is bounded and
II A* \\ ~ \\A 11. Setting in (4) g = Af for any f E H, we similarly
Dbtain II A* II>- II A 11. Hence II A* II= II A \\.
Summarizing, the adjoint operator A* of a bounded linear opera-
tor A is defined on the whole space, is linear, is bounded and its
norm equals that of A.
It can be easily shown that (A*)* = A, (cA )* = cA * (c is a com-
plex number), (A +
B)* = A* +
B*, (AB)* = B* A*.
4. Matrix Representation of a Bounded Linear Operator. While
proving Riesz's theorem, it was established that a bounded linear
functional defined on a separable Hilbert space is completely deter-
mined by its values on an orthonormal basis for this space. Same is
the case with bounded linear operators.
Let A be a bounded linear operator acting from a separable Hilbert
space H into H. Let D A = Hand e1 , , en, ... an orthonormal
basis for H.
The infinite matrix au = (Ae;, ei) = (e;, A *et), i >- 1, j >- 1
will be called matrix representation of A in the basis e1 , , en, ..
Since (A*eh e;) =au, i = 1, 2, ... , are the Fourier coefficients
Df A *ei, by the Parseval-Steklov equality (equality (5), Sec. 2. 7)
00
the series 2J \au
i=1
\2 converges and for all j = 1, 2, ... we have the
inequality
00
~ laiilz=i!A*ej!lz<IIA*li2=11AIIz. (5)
i=i
00
Take an arbitrary element fEH, and let f=~fkekbeits
k=i
Fourier series expansion. Since Af EH, its Fourier coefficients
00 00 00
(Ah = (Aj, ei) =(A ~ fie;, ei) = ~ fi (Aei, ei) = ~ fiaii, (6)
i=i i=i i=i
j = 1, 2, . . . . The series on the right side of (6) converges abso-
lutely, because its general term fiai! does not exceed the general term
{- ( \ fi \2 + I a;i \2 ) of a convergent series. Substituting the values
00
i=i
we obtain
00 00
Af = ~ (~ a;J/;) ei. (7)
j=i i=i
78 PARTIAL DIFFERENTIAL EQUATIONS
Thus, for any f E H, the element Af E H can be determined cor-
responding to f by means of only the matrix (ail) This means that
the matrix (ail) completely defines the operator A.
If (ail) is the matrix representation of A in the basis e1 , e 2 ,
and (afj) is the corresponding representation of the adjoint opera-
tor A*, then
ati=(A*et, e1)=(e 1 , Ae1)=a1t for all i~1, j~1.
Operator A is designated as finite-dimensional (n-dimensional)
if it maps a Hilbert space H into ann-dimensional subspace of it.
Suppose that Hn is a subspace of H spanned by the elements e1 ,
. . . , en. For the bounded linear operator A to map H into Hn it is
necessary and sufficient that aii = 0 for j > n, i >- 1. This state-
ment is an immediate consequence of (6) and (7).
5. Selfadjoint Operators. Operators of Orthogonal Projection.
A bounded linear operator from a Hilbert space H into H which is
defined on H is termed selfadjoint if A = A*.
With a selfadjoint operator A we can associate a Hermitian bili-
near form W (f, g) = (Af, g) and the corresponding quadratic form
(Af, n. These forms are called, respectively, bilinear and quadratic
forms of operator A. The quadratic form of a selfadjoint operator is
real-valued. A selfadjoint operator A is said to be nonnegative if
(A/, f) >- 0 for all f E H. A nonnegative operator A is positive if
(Af, f) = 0 only for f = o.
The matrix representation (ail) of a selfadjoint operator satisfies
a
(when His separable) the property: ati = 1io i, j = 1, 2, ....
Suppose that e1 , e2 , is an orthonormal basis for a separable
Hilbert space H and ei,, ... , eik . . . is a countable (or finite) sub-
set of it, while ej,, ... , eik, ... , a subset of the basis, is complement
of the chosen subset. Let ~r, ffi" denote, respectively, the sub-
spaces spanned by the elements ei 11 , k = 1, 2, ... , and eit,,
k = 1, 2, .... Subspace ffi' (ffi") is the aggregate of elements of H
that are orthogonal to all the elements eik' k = 1, 2, ... (ei 11
k = 1, 2, ... ). Equivalently, the subspace ffi' Ol1") is the set
of all the elements of H having the property that in their Fourier
expansions with respect to the basis ek, k = 1, 2, ... , the Fourier
coefficients of the elements ej11 , k = 1, 2, ... (ei 11 , k = 1, 2, ... )
vanish (that is, the corresponding terms do not appear in the expan-
sions). The subspaces ffi' and m" are orthogonal, ~r _Lffi".
With an arbitrary f E H, whose Fourier expansion is of the form
~fkek, we associate the elements
00 00
(8)
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS i9
Since, by Bessel's inequality and Lemma 1 (Sec. 2.6), the series in
(8) converge in the norm of H, they define on H two operators P'
and P". These are linear with range Rp = ~r, Rr = m".
Operators P' and P" are known as operators of orthogonal projec-
tion of H onto the subspaces m' and ffi", respectively (for the sake
of brevity, these operators will be referred to as projection operators).
A projection operator is bounded and its norm is unity. In fact.
00 00
since for all /EH IIP'/11 =11!'11
2 2= ~ l/;kl 2 <;: ~ likl 2 =/lf/l 2 , we
k=1 k=1
have II P' II-< 1. But P' ei 1 = ei 1 which implies II P' /1 = 1.
A projection operator is selfadjoint, because (P'j, h) =
00 00 00
= ( ~ /;ke;h, h)= ~ /;k (eih' h)= ~ h/i;k = (/, P'h) for any I and
11.=1 k=1 k=1
hE H.
From equality (8) it follows that for any I E H
I= I I= P' I+ P"I, I= P' + P", (9)
wh.ere P'l Em', P"l Em". Furthermore,
II I W= II P'l+ P"f 11 2 =II P'f 11 2 + II P"f W+ (P'j, P"f)
+ (P"j, P'f) =II P'l 11 2 + II P"f 11 2 , (10)
because m' __L m".
6. Compact Sets. Let H be a Hilbert space. A set !11ft c: His called
compact in H if any (infinite) sequence of its elements contains
a subsequence that is fundamental in H.
Lemma 1. A compact set is bounded.
Proof. Suppose oJft is unbounded. We claim that it cannot be
compact. Taking any one of its elements 1\ we denote by a ball s,.
of radius 1 with centre at f\ that is, the set of those f E H for which
II f - f' II < 1. Because alt is unbounded, the set atft. 1 = atft "'- S 1,
is nonempty. We take any f E allt 1 (II f - Jlll >
1). Since tJII[ 2 =
= allt 1 ~St is also nonempty, there is an element f 3 E atft such that
II j3 - f 1 II> 1, II 13 - f 2 II> 1. Continuing in this manner, we
obtain a sequence t, k = 1, 2, ... , of elements of alit satisfying
the inequality II f; - fi II > 1 for all i, j, i =I= j. This sequence does
not contain any fundamental subsequence. Hence atft cannot be
compact. I
Lemma 2. For a set atft of a finite-dimensional (n-dimensional)
Hilbert space H to be compact it is necessary and sufficient that it be
bounded.
That the condition of boundedness is necessary follows from
Lemma 1. We shall show that it is sufficient also.
Since alit is bounded, II f II-< C for all IE alt. Consequently, the
Fourier coefficients fi = (!, ei), i = 1, ... , n, in the expansion
80 PARTIAL DIFFERENTIAL EQUATIONS
f= / 1e 1 + ... +
f nen of an element f E!J!It* satisfy the inequalities
lfil=/(f,ei)/</lfll//ei/1=1/f/I<C. Hence for any sequence
jk, k=1, 2, ... , of elements of aJt the sequence (!~, ... , f~),
k= 1, 2, ... , of n-dimensional vectors, where f~ = (fk, ei), is bound-
ed. From it, by the Bolzano-Weirstrass theorem, one can choose
a fundamental subsequence (f~s, ... , /~8 ), s = 1, 2, ... :
1 /2
I f ks1 - jkP + ...
+ /t"sn - jkP
n /2 -+- 0 as s, p-+- oo.
1 e1 +
The correspon d ing sequence f ks = t"s ... + j"sn en, s = 1, 2, ... ,
is fundamental in H, because
ll f s_ f p 11 2 = I1! 8 - f1P 12 + ... +I Ins_ fnP 12 -+- 0 as s, p-+- oo.
h k h h k k
I
7. A Theorem on Compactness of Sets in a Separable Hilbert
Space. Suppose that H is an infinite-dimensional separable Hilbert
space and e1 , , en, ... an orthonormal basis for it.
First of all we note that not every bounded set in H is compact.
For instance, any bounded set containing the orthonormal basis is
noncompact because no fundamental subsequence can be selected
from the sequence ek, k = 1, 2, ... , since II ei - ei II = V2,
i =1= j. In particular, the set {II f II :s; 1} (the closed unit ball) is
noncompact in the infinite-dimensional space.
Let P~ denote the projection operator which maps H onto the
n-dimensional subspace Hn spanned by the elements e1 , . . , en,
and put P~ = I - P~. For any f E H and arbitrary n 1 we have >-
(see (9))
f = P~f+P~f. (11)
n oo
where P~f = 2J fkek,
1<=1
~~ = ~
k=n+1
fkek. Then (11) yields
(12)
n oo
where 1/P~fl/ 2 = ~ /fk/ 2 , IIP~f/1 2 = ~ /fk/ 2 , which implies that
k=! h=n+1
for any f E H the number II sequence P~f /1 2 ,
n = 1, 2, ... , being
monotone nonincreasing, tends to zero as n-+- oo.
Theorem 2. For the set oJft c H (H is a separable Hilbert space) to
be compact it is necessary and sufficient that it be bounded and for any
e > 0 there be ann = n (e) such that II P~f II :s; e for all f E alit.
In other words, for the compactness of a/It it is necessary and
sufficient that it be bounded and "almost finite-dimensional".
Sufficiency. Let II f II :s; C for all f E ell. We consider an arbitrary
sequence/", k = 1, 2, ... , of elements of !J!It. Setting e = 1, we
* With respect to some orthonormal basis e1 , , en.
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 81
have II P~.f' II~ 1 for all k, where n1 = n (1). Since II P~, !h. II ~
~ Iilli ~ C for all k (P~ is defined in (11)), the set P~, JR., k =
= 1, 2, ... , is bounded in the ncdimensional space Hn, From
this space, according to Lemma 2 (Subsec. 6), one can choose a fun-
damental subsequence and from the latter a subsequence P~, f1 8 ,
s = 1, 2, ... , having the property that II P~, / 1 8 - P~, / 1 P II ~ 1
for all s and p :;;> 1. Then, taking into account (12), for the subse-
quence f1 1 , , / 1 8 , we have the inequalities
II 11 ' s - 11 ' p11 2 =II P~/ s-P~/ p11 2 + II P:t;l '-P';./'p 11 2
-<1 + (II Pn/ II+ II Pn/ P II ) <5,
2
true for all p and s.
Take a number n 2 = n (112) corresponding to e = 1/2. The se-
quence P~/ 1 , , P~/ ', . . . belongs to Hn, and is bounded;
hence from it a subsequence P~.f , s = 1, 2, ... , can be selected
II-<
for which II P~.l 2 ' s - P~.f 2 ' P 1/2 for all p and s.
In view of (12), we have II1 2 ' 8 -I 2 'PII 2 =IIP~.f 2 ' 8 -P~/PII 2 +
-<! +!
+II P';.,l 2 ' '-P;.fP 11 2 = ~ for all s, p; and so on. For
e=1li we can find ni=n(1/i) and from the subsequence P~.fi-i,,
s = 1, 2, ... , we can choose a subsequence P~ f ', s = 1, '2, ... ,
such that JJP~/'-P~/PII-<11i for all s, p. Noting (12), for
'
the subsequence l' ', s = 1, 2, ... , we have Ill'' -<
-l P IJ 2
-<1li 2 +4/i 2 =5/i 2 for all s, p.
The diagonal sequence I' 8 , s = 1, 2, ... , is a subsequence of
the initial sequence and is such that II fP. P - f s II ~ 5/i2 for all
p, s :;;> i, that is, it is fundamental.
Necessity. The necessity of boundedness of the set oJt was proved
in Lemma 1 (Subsec. 6). We shall establish the necessity of the
second condition in the hypothesis.
Suppose that Jt is compact but nevertheless there is an e 0 > 0
such that for any n II P';.F II>- Eo for some r E o/lt.
Taking arbitrary n 1 , we find a corresponding Jnt E olft such that
II P';.,Jnt II:;;> E 0 On the basis of [n 1 we choose a number n 2 > n1
such that II P';.jn 1 II < E 0/2 (this is possible, since for any fixed
f E H, II P'hf II~ 0 as k ~ oo). Corresponding to n 2 we choose
jn 2E olft such that II P;.,tn 2 II :;;> E 0 , and on the basis of ln 2we choose
an n 3 such that II P';.,ln2 II < E 0 /2, and so on. Thus, we obtain a se-
quence Jnl<, k = 1, 2, ... , of elements of olt for which the inequa-
lities
hold.
6-0594
82 PARTIAL DIFFERENTIAL EQUATIONS
We show that this sequence cannot contain a fundamental sub-
sequence. Indeed, in view of (12) and the fact that II P~f II is mono-
tone with respect to n, we have for any k > s
Corollary. Let oJft be a set in the separable Hilbert space H.
Consider a family of sets o/lt 8 c H, e > 0, having the following
property: for any f E oJft an element f' = f' (e) can be found in each
oJ!t 8 , e > 0, such that II f' - f II ~ e. If for some sequence ek- 0 as
k - oo, ek > 0, all the sets r!ltek are compact, then oJft is compact.
Consider an arbitrary ek of this sequence. Since (!Jt 8 k is compact,
we can find an n = n ( ek) such that II P';.f II ~ ek for all f E elf{ ek.
But then for any f E oit, II P~f II = II P~ (f- f') +
P~f' II~
~ II P;, (f- f') II +
II P~f' II ~ II f - f' II +
ek ~ 2ek if f' ts an
element of oJftek such that II f - f' II~ ek. Since ek- 0, by Theo-
rem 2 the set &It is compact.
8. Weak Compactness. A set oJft in the Hilbert space H is called
weakly compact if from any (infinite) sequence of its elements one
can construct a subsequence that converges weakly to an element
of H (not necessarily belonging to o!lt).
Theorem 3. Any bounded subset of a Hilbert space is weakly com-
pact.
In fact, boundedness is not only suffteient but also necessary
for the set to be weakly compact; however, we shall not prove the
necessity and confine only to the proof of sufficiency in the case of
a separable Hilbert space.
Proof. Let ek, k = 1, 2, ... , be an orthonormal basis for H and
c!/t a bounded set in H: II f II ~ C for all f E &It. Consider an arbitrary
sequence J'<, k = 1, 2, ... , of elements of c!/t. Since for all k llfkll ~
~ C, the number sequence (f"-, e1), k = 1, 2, ... , is bounded:
I (/, e1 ) I ~ II fh II II e1 II~ C; hence from the sequence fk, k =
= 1, 2, ... , one can select a subsequence fl, k, k = 1, 2, ... ,
such that the number sequence (! 1 k, e1} converges to some a 1 :
(! 1 k, e1 ) - a 1 as k - oo. The number sequence (! 1 h, e2 ) is also
bounded; this means that from the sequence j 1 h, k = 1, 2, . . . ,
a subsequence p.~<, k = 1, 2, ... , may be chosen such that (! 2 " e2 )
converges to a a 2 ask- oo, and so on.
We shall show that the diagonal sequence fk, h, k = 1, 2, ... ,
is weakly convergent. First, let us note that for any s >
1 (jh, 11 , e8 ) -
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 83
-+ a 8 ask-+ oo. Hence for any m:;;? 1
m m m
(l", h G;e;)= ~ adf"", e;)-+ ~ jcr1! 2 as k-+oo.
i=1 i=i i=!
m m m
Since I(!'' 11 , .Lj a;e;) 1
t=!
2 <"Ill' 11 W.~ Icrd 2 <" C2 .2j Icr;j 2 ,
t=1 t=!
we have
m oo
i=t i=!
00
i=!
00
f E H and II f 11 2 = Li I O; 12 It will be shown that the sequence
i=!
f" 11 , k= 1, 2, ... , converges weakly to f.
Let g be any element of H. Taki.ng an e > 0, we choose s=s(e)
00
such that ~ I gi 12 -<e2 By the generalized Parseval-Steklov
i=s+1
equality (equality (5') in Sec. 2.7), we obtain
00 s
IU""-f,g)l=ilj ((l", e;)-o;)gJ-< 2j IU"", e;)-o;jjg;J
i=1 i=i
00 00
+ i=s+! (13)
i=s+!
Furthermore,
00 00 00
(~ Jo;jjg;J) 2 -< ~ lcr;\2 1: jg;l <"1l/ll2 2 e2 ,
i=s+i i=s+1 i=s+i
00 00 00
( ~ I (!II, n, e;) II g;j)2-< ::>-} I(!''", e;) lz 2.; Ig;jz-<czez.
i=s+i i=s+ 1 i=s+ 1
By the definition of numbers o ;, the first term in the right side of
(13) can also be made < e if k:;;? k 0 (e) for some k 0 (e). Thus-
1(/"" - /, g) I ~ e + e (C + II f II) for k:;;? k 0 (e). I
9. Completely Continuous Operators. Let H bea Hilbert space.
A linear operator A acting from H into H and defmed on H is said
to be completely continuous if it maps a bounded set into a compact
set.
If A 1 and A 2 are completely continuous operators, then so is the
operator c1 A 1 +
c2 A 2 with arbitrary constants c1 , c2 If the operator
A is completely continuous and the operator B defined on His bound-
ed, then the operators AB and BA are also completely continuous.
From Lemma 1 (Subsec. 6) it follows that a completely continuous
operator is bounded. However, not every bounded operator is com~
pletely continuous. For instance, the identity operator I acting
6*
84 PARTIAL DIFFERENTIAL EQUATIONS
in an infinite-dimensional Hilbert space cannot be completely
continuous, for it maps a noncompact set-the orthonormal basis-
into itself.
A finite-dimensional bounded operator is completely continuous;
this fact is a consequence of Lemma 2 (Subsec. 6). The following
l"esult is a direct generalization of this assertion.
Theorem 4. For a bounded linear operator A defined on a separable
Hilbert space Hand acting from H into H to be completely continuous,
it is necessary and sufficient that for any e > 0 it is possible to find an
integer n = n(e) and linear operators A 1 and A 2 , where A 1 is n-dimen-
sional and II A 2 II ~ e, such that
A = A1 +A 2 (14)
Thus completely continuous operators are those operators which
are "almost finite-dimensional".
Necessity: In view of (11) (see Subsec. 7), for any f E H and any
n > 0 we have the representation
A/= P~A/ + P~Af (A=P~A+P~A). (15)
Since A is completely continuous, given an e > 0 an n = n(e) can
be found such that II P~A II~ e. Indeed, by Theorem 2, II P~Af II =
= II f II II P~A(f/11 I II) II~ e II f II, because the boundedness of
{f/11 f II} implies the compactness of {A (fill f II)}. Since P~A is
n-dimensional, the necessity is established.
Sufficiency. Let fh, k = 1, 2, ... , be an arbitrary bounded se-
quence '~in H, II fh II~ C, k = 1, 2, . . .. We shall demonstrate
that fundamental subsequence can be extracted from the sequence
Af, k = 1, 2, . . .. Choosing an e > 0 from the set {1, 1/2, ...
. . . , 1/i, ... }, for e = 1/i we can find ni = n (1/i) and operators
Af and A~ such that A = A1 + A~, where Af is n;-dimensional and
II A~ II~ 1/i. Then II Ai II= II A - A~ II~ II A II+ II A~ II~
~ II A II + 1. The set AVh, k = 1, 2, ... , is bounded in the
n 1-dimensional space, therefore (Lemma 2, Subsec. 6) from it a
fundamental subsequence A~f1, k, k = 1, 2, ... , can be chosen. The
sequence f1, It, k = 1, 2, ... , has the property: II A~1, It II ~
~II A~ II II f 1h II~ 1C. The sequence A~ft.~t, k = 1, 2, ... , is
a bounded sequence of the n 2-dimensional space, therefore there is
a corresponding fundamental subsequence A~f2 h, k = 1, 2, ....
This subsequence satisfies the inequality II A~2 h II ~ II A~ll II P It II~
1
~ 2 C, and so on.
The diagonal sequence f1 1 , f 2 , has the following obvious
properties: the sequence AtfR., ", k = 1, 2, ... , is fundamental
for any i, because for k >- i fit, It are elements of the sequence fi, ~t,
k = 1, 2, . . .. Further, II AJfh, It II ~ C/i for all i. Let us show
that the sequence Afh, ~t, k = 1, 2, ... , is fundamental. Take an
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 85
e > 0 and fix i > 1/e. Since Atf" h, k = 1, 2, ... , is a fundamen-
tal sequence, for sufficiently large k, s we have
II At" k- Aj" s II~ II A1 u" k- r II+ II A~ (fh, k- r II
8) 8)
~e+ /1 A~l "II+ 1/ A~t s /l~e+ 2C/i~(1 + 2C) e.
as required. I
Theorem 4 yields, in particular, the following result.
Suppose that the linear operator A acting from a separable Hilbert
space li into li and defined on the whole H is completely continuous.
Then its adjoint A* is also completely continuous.
Indeed, the representation (14) generates the representation A* =
=A~+ A~, where II A: II = II A 2 II~ e. Accordingly, the above
assertion will have been established if it is shown that A~ is a finite-
dimensional operator.
Let RA, be an n-dimensional subspace of li and e1 , , en an
n
i=!
n
= .L; (f, A~e;)e;. Consequently, for any f, gEH we have
i=!
n n
i=l
g; = (f, ~ g;Aie;),
i=!
that is,
n
(!, A!g) =(Ad, g)(!, l~ g;Afe;).
i=l
n
Hence for all g Eli Aig = ~ g;A!e;. This means that H.Af is a
i=l
subspace spanned by the elements A!e 1 , , ATen, that is, AT is
fini te-d imen sional.
4. LINEAR EQUATIONS IN A HILBERT SPACE
The results of this section are true for any Banach space; nonethe-
less, we shall confine our discussion only to a separable Hilbert
space H.
1, Contracting Linear Operator. A linear operator A acting from li
into li and defined on H is called a contraction if II A II < 1.
Lemma 1. If A is a contraction from H into H, then there is an
operator (I - A)- 1 from H into H which is defined on H, and
II(/- Atl II~ 1_! II A II
86 PARTIAL DIFFERENTIAL EQUATIONS
To prove this, we consider the equation
(I -A) f = g (1)
and show that for any g E H it has a unique solution given by the
00
series f = ~ A kg (A 0 = I) which converges in H.
k=O
The last series converges, because H is complete and the partial
m
sums gm =~A kg constitute a fundamental sequence: for, p > m
k=O
II gp-gm II= II APg-j- +Am+tgll<;ll APgll + +IIAm+tgll
<ligiJ <II All m+t + ... )=l!gii 1II _A 11llm+l
AII -+0 as m, p-+oo.
The element f E H is a solution of (1), since (I - A)f =
= (g + Ag + ... ) - (Ag +A 2 g + ... )
= g.
This solution is unique. In fact, assume that there are two solu-
tions It and / 2 of Eq. (1). Then the element f = ft - / 2 is the solu-
tion of the homogeneous equation f = Af; accordingly, it satisfies
II t II = II At II :::;;: II A II II t 11. Hence t = o, that is It = / 2
Thus the operator (I- At1 exists, is defined on the whole H,
is bounded, because for all gEH li(I-At 1gll=llg+-Ag-j- ...
. . . +Amg+ .. II<JI:g II (1+11 A 11+ ... )= 1~jll~ II ,and 11(1-Attll <
1
< 1-IIAII. I
Remark. Under the hypothesis of Lemma 1 the bounded opera-
tor (I - A *)- 1 also exists, since II A* II = II A II < 1, and
(I - A *)-1 = ((I - A)-1]*.
To prove this relation, we take arbitrary f', g' E H and construct
(Lemma 1) corresponding f, g E H such that (I - A) f = f',
(I - A*) g = g'.
Since f = (I - A)- 1 f' and g = (I - A *)- 1 g', the relation
((I - A) f, g) = (f, (I - A*) g) can be written as (f' ,(I -A *)- 1g')=
= ((I - A)-tf', g'), whence the desired relation follows.
2. Equation with a Completely Continuous Operator. We consider
Eq. (1) without the assumption that the norm of A is small. Instead
we assume that A is completely continuous.
By Theorem 4, Sec. 3.9, (1) can be written as (I - A 2 ) f - Atf =
= g, where At is an n-dimensional operator and II A 2 II :::;;: e < 1.
Put h = (I- 4 2 ) f. By Lemma 1, the operator I -~A 2 has a bound-
ed inverse (I - A 2 )- 1 defmed on H;
(I - A 2) I = h, I = (I - A 2 )- 1 h. (2)
Eq. (1) for h can be expressed in the form
h - A 1 ( I - A 2 )- 1h = g. (3)
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 87
Let A* be adjoint of A. The equation
(/-A*)!*= g* (1*)
is referred to as adjoint of Eq. (1). The relation A = A 1 A2 +
implies A* = Ar +At. In view of the Remark to Lemma 1, the
operator (/-A;) has a bounded inverse(/- A;t1 = [(/-A 2 )- 1 ]*
defined on H,
(/ - A;)- 1g* = z*, g* = (/ - Ai) z*. (2*)
Eq. (1 *) can be written in the form
(/-A~)!*- Art* = g*.
Applying to it the operator (/ - Ait\ we obtain the equivalent
equation
(3*)
where the operator [(/ - A 2 )- 1 ]* A~ is adjoint of the operator
A 1 (/ - A 2 )- 1 (in Eq. (3)).
The operator A 1 (/ - A 2 )- 1 is clearly n-dimensional, therefore,
its matrix representation (a; 1) in the corresponding orthonormal
basis e~~., k = 1, 2, ... (the subspace spanned by the elements
e1 , e2 , , en coincides with R A,(I -A.)-' satisfies the property that
aii = 0 for i >1, j >
n + 1 (see Sec. 3.4), and formula (5) of
Sec. 3.4 yields, for any j,
00
2J I aii 12 -< II At (/- A2t1 1/ 2
i=l
By formula (7), Sec. 3.4, Eq. (3) can be expressed in the form
Lhiei- ~L h;aiiei = ~g1 e 1 which, in view of the linear inde-
; j i j
pendence of the system e1 , e2 , , is equivalent to a system of algeb-
raic equations for the Fourier coefficients h1 , . . , hm, ... of the
desired element h:
00
h1 - ~ a; 1h; = g,,
i=1
Since the coefficients h 1 are known when j > n:
h1 = g" j > n, (4)
the last system reduces to the system of algebraic equations
n oo
h,-~aiJh;=g 1 + ~ a; 1g;, j=1, ... ,n, (5)
i=1 i=n+t
for h 1, j-<n.
88 PARTIAL DIFFERENTIAL EQUATIONS
Similarly, Eq. (3*) can be replaced by an equivalent algebraic
system of equations for determining Fourier coefficients fJ , j =
= 1, 2, ... , of the element /* in terms of the Fourier coefficients
zj, j = 1, 2, ... , of the element z* = (/- Ai)- 1 g*. For jj,
j ~ n, we obtain the linear algebraic system
n
I i* - "LJ -aii !*i = z;* ' j= 1, ... , n, (5*)
i=1
while /j, j > n, are determined uniquely in terms of jj, j ~ n, by
the formulas
n
ff=zj+ ~ ajdT. j>n. (4*)
i=1
3. Fredholm's First Theorem. The matrices of systems (5) and
(5*) are Hermitian conjugate, therefore moduli of their determi-
nants are equal. Hence if one of these systems is solvable with any
free term, that is, the corresponding determinant does not vanish,
then the same property is possessed by the second of these systems,
and the solutions of these systems are determined uniquely. In
particular, the corresponding homogeneous systems have only
trivial solutions. Or if one of the homogeneous systems (5) or (5*)
has only a trivial solution (accordingly, the corresponding determi-
nant does not vanish), then so has the other, and the systems (5)
and (5*) are solvable (uniquely) with any free term.
Eqs. (1) and (1*) also have the same property.
In fact, assume that Eq. (1) (or Eq. (1 *)) is solvable with any g
(or g*) of H; or, in view of (2) (or (2*)) what amounts to the same
thing, Eq. (3) (or (3*)) is solvable with any g (or z*) of H. In particu-
lar, it has a solution for any g (or z*) of the subspace spanned by the
elements e1 , , en. Consequently, the system of Eqs. (5) (or (5*))
is solvable with any right-hand side. That is, the determinant of the
system does not vanish, and the homogeneous systems (5) and (5*)
have only trivial solutions. Then, in view of (4) and (4*), the homo-
geneous equations (1) and (1 *) have only trivial solutions.
Conversely, suppose that one of the homogeneous equations (1)
or (1 *) has only a trivial solution. Then the corresponding homoge-
neous system (5) or (5*) has only a trivial solution. Consequently,
the determinants of both the systems do not vanish. That is, the
nonhomogeneous systems (5) and (5*) have (unique) solutions for
any free term. Then, in view of (4) and (4*), Eqs. (1) and (1*) are
(uniquely) solvable with any free term belonging to H. This implies
that the inverse operators (/ - A)- 1 and (/ - A *)- 1 exist and are
defined on H.
Let us show that these operators are bounded.
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 89
Suppose that the system (5) is uniquely solvable (the determinant
of matrix in (5) is nonvanishing) and that (h 1 , , hn) is its solu-
tion. From Cramer's rule it follows that there exists a constant
C > 0, independent of the free term in (5), such that
n n oo
~ lhti 2<:C2
!=1
LJ
j=1
/gt+ ~ aiigij 2.
i=n+1
(6)
Since
n oo n oo oo
~ I gt+ ~ aijgi 12 <:2
j=1 i=n+1
LJ (I gt 12 + i=n+1
j=1
~ Igd 2)
LJ I aij 12 i=n+1
-<II g 11 2 (2+ 2n II At(/ -A2t1 W) = c: llg 11 2,
we have
n
.h I hi 12-< (CC1) 2li g 11 2
3=1
and
n oo
llhll2= .LJ Jhtl2+.3=n+1
3=1
2j JgtJz<:(1+C2C~)llgiJ2=C;llgJJ2.
Consequently, in view of (2)
II f II ~ c3 II g II, (7)
where the constant C3 > 0 does not depend on g. This in turn means
that the operator(/ - A)- 1 and, hence also, the operator(/ - A *)- 1
are bounded: II (/- A)- 1 = II (/-A *t1 II~ C 3
Thus we have established the following assertion.
Theorem 1 (Fredholm's First Theorem). Let A be a completely
continuous linear operator from H into H which is defined on H. If one
of the Eqs. ( 1) or (1*) has a solution for any free term, then the other
also has a solution for any free term, and these solutions are unique,
that is, the homogeneous equations (1) (g = o) and (1*) (g* = o) have
only trivial solutions.
If one of the homogeneous equations (1) (g = o) or (1*) (g* = o)
has only a trivial solution, then so has the other equation. Eqs. (1) and
(1 *) are uniquely solvable with any free terms, that is, the operators
(/ - A)- 1 and (I - A *t 1 exist and are defined on H, and these
operators are bounded.
4. Fredholm's Second Theorem. Note that the ranks of matrices
B = II bu II, where bit = 6u - au, i, j = 1, ... , n ({)ii = 0
when i =I= j, {)ii = 1), and B* = II b1i II in the systems (5) and (5*)
are the same. Therefore the homogeneous systems (5) and (5*) have
always the same number k :;:;:;; n of linearly independent solutions.
PARTIAL DIFFERENTIAL EQUATIONS
Then, by (2), (4) and (4*), the sets of all solutions of homogeneous
equations (1) and (1 *) also contain exactly k linearly independent
elements.
Thus we have the following result.
Theorem 2 (Fredholm's Second Theorem). If the homogeneous
equation (1) (A is a completely continuous operator from H into Hand
defined on H) has nontrivial solutions, then only a finite number of
them are linearly independent. The homogeneous equation (1*) has also
the same number of linearly independent solutions.
5. Fredholm's Third Theorem. We now examine the question of
solvability of Eq. (1) when the homogeneous equation (1) may have
nontrivial solutions. By Fredholm's Second Theorem, the homoge-
neous equation (1) has only a finite number of linearly independent
solutions: fl, ... , l. The same number of linearly independent
solutions has also the homogeneous equation (1*): f 1*, ... , f"*
'The system jl, .. . ,f" (as also the system f 1*, ... , fk*) can be
assumed to be orthonormal.
Theorem 3 (Fredholm's Third Theorem.) For Eq. (1) with a com-
pletely continuous operator A from H into H and defined on H to have
a solution, it is necessary and sufficient that the element g be orthogonal
to all the solutions of the homogeneous equation (1 *).
Among all the solutions of Eq. (1) there is a unique solution f that
is orthogonal to all the solutions of the homogeneous equation (1).
Any other solution of Eq. (1) is expressed as a sum of this solution and
some solution of the homogeneous equation (1). Solution f satisfies the
inequality (7) in which the constant does not depend on g.
Proof. Suppose that thel solution of Eq. (1) exists, then, by (2},
Eq. (3) as well as the system (5) also !have solutions.
Let the rank of the matrix B = II bu II, where bu = 6u - au,
i, J = 1, ... , n, be n - k. Then the subspace Rn _, of the n-dimen-
sional vector space spanned by the vectors Bi = (bil, . . . , bin},
i = 1, ... , n, forming columns of B, is of dimension n- k. Since
n
the homogeneous system (5*): ~ ~dt = 0, j = 1, ... , n, can be
i=1
written in the form (!*, Bi) = 0, i = 1, ... , n, it follows that
the solutions of the homogeneous system (5*) constitute a k-dimen-
sional subspace, denoted by R~_,, orthogonal to the subspace
Rn-k
By the Kronecker-Kapelli theorem, for the system (5) to have
a solution it is necessary and sufficient that the ranks of B and the
augmented matrix obtained by adjoining to B the column consisting
of free terms of (5) coincide, that is, the vector constituted by free
terms should belong to the space Rn -k or, what is the same, should
be orthogonal to RLk
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 91
Noting that any solution f* of the homogeneous equation (1 *)
is of the form
f* = f!et + + f~en + f~+!en+i + . .,
where the vector 7* U:, ... , f~) is the solution of the homoge-
=
n
neous system (5*) and Jj = ~ aJdt when j > n, and expressing
i=l
the condition of orthogonality of vectors f* and the right side of
(5) as follows
n oo n oo
0 = ~ (gj + 2J U;jgi) fj = ~~ gJf1 + 2J g}f =c (g, /*),
j=! i=n+! j=! i=n+!
we fmd that if the solution of the nonhomogeneous equation (1)
exists, then the element g must be orthogonal to all the solutions of
the homogeneous equation (1 *).
Conversely, if the element g is orthogonal to all the solutions f*
of the homogeneous equation (1 *), then the vector with components
00
gi + 1
i~n+!
aug" j = 1, ... , n, is orthogonal to all the solutions
J* of the homogeneous system (5*). Consequently, system (5) and
together with it Eqo (1) have solutions.
Let / 0 be a solution of the nonhomogeneous equation (1) and
jl, 0 0, lk be an orthonormal system of solutions of the homogeneous
equation (1). Then the element I = / 0 - (/ 0 , jl) 11 - o -
- (/ 0 , fk) Jk is also a solution of Eq. (1), and it is orthogonal to all
the solutions of the homogeneous equation (1)0 Such a solution is
unique: for if there were one more such solution 7, then their differ-
ence~ f - T, being a solution of the homogeneous equation (1),
would be orthogonal to all the solutions of the homogeneous equa-
tion (1) including itself, that is, f - 7 = o.
If f' is any solution of the nonhomogeneous equation (1), then
f' - 1 = !" is a solution of the homogeneous equation (1), that is,
+
f' = t f"o
We shall now establish inequality (7). Suppose that h is an ele-
ment of H corresponding, according to (2}, to the element f. This
means that h is a solution of Eq. (3) which satisfies k equations:
0 = (/, /i) = ((/ - A2)-th, li) = (h, (/ - A;)-lji),
i = 1, .. 0' k. (8)
Since the augmented matrix of system (5) has the same rank n - k
as the matrix B, some of k equations in the system (5) are linear
combinations of the remaining n - k equations. Therefore if we de-
92 PARTIAL DIFFERENTIAL EQUATIONS
lete these k equations, the resulting system will be equivalent to the
system (5).
Thus n-dimensional vector (h 1 , , hn) is a solution of the
linear system of n equations (n - k equations of (5) and k equa-
tions of (8)) whose coefficients do not depend on the right-hand side
of (5). Moreover, since the element f is unique, it follows that
(h 1 , . . , hn) is a unique solution of this system, that is, the deter-
minant of the resulting system is not zero. Then the vector
(h 1 , , hn) can be obtained by Cramer's rule. Therefore inequal-
ity (6) holds for it, which readily yields the desired inequality (7). I
6. Eigenvalues and Eigenelements of a Completely Continuous
Operator. A quantity 'A is called an eigenvalue of a linear operator A
acting from H into H if there is an element f E H such that f =1= o
and Af = 'Af; the element f is termed eigenelement of the operator A.
The quantity 1-L = 1/'A, 'A =1= 0, is called the characteristic 1:alue.
Since together with f the element cf for any constant c =1= 0 is also
an eigenelement corresponding to the eigenvalue 'A, the eigenelements
can be assumed normalized by, for instance, the condition, II f II = 1.
The maximum number of linearly independent eigenelements
corresponding to the given characteristic value (eigenvalue) is
called the multiplicity of this characteristic value of the eigenvalue.
If there is an infinite number of linearly independent eigenelements
corresponding to a characteristic value (eigenvalue), the multiplic-
ity of the characteristic value (of the eigenvalue) is infinite.
Suppose that the operator A defined on the whole H is completely
continuous. Then the operator !-LA, where 1-L is a complex number,
is also completely continuous. The following assertions are a con-
sequence of Theorems 1, 2 and 3.
For the equation
f - !-LA!= g (1')
to have a solution for all g E H, it is necessary and sufficient that !l
should not be a characteristic value of A (that is, 1/!-L should not be an
eigenvalue). If 1-L is a characteristic value, then it is of finite multiplicity
and "it is characteristic value of the operator A* with the same multiplic-
ity. In order that Eq. (1') may be solvable in this case, it is necessary
and sufficient that the element g be orthogonal to all the eigenelements
of A* that correspond to the eigenvalue 1/[t. In this case the solution
of Eq. (1') is unique, and this solution is orthogonal to all the eigen-
elements of A corresponding to the eigenvalue 11!-L.
These are precisely the assertions that are usually referred to as
Fredholm's Theorems.
7. Fredholm's Fourth Theorem. We shall establish some prop-
erties of characteristic values of a completely continuous operator.
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 93
Theorem 4 (Fredholm's Fourth Theorem). For any M > 0 the
disc {I f.l I < M} of the complex plane can contain only a finite number
of characteristic values of a completely continuous operator acting
from H into H with domain of definition H or, equivalently, only a
finite number of eigenvalues can lie outside the disc {I /. , I < 1/M}.
Proof. Assume the contrary, that is, let the disc {I f.l I < M}
contain an infinite number of characteristic values f.t 1 , , f.tn ... ,
f.l; =F f.t 1 , i =F j. Let e; be some eigenelement corresponding to the
characteristic value f.lt> i = 1, 2, ....
We shall demonstrate that for any n~1 the system e1 , , en
is linearly independent. When n= 1, this assertion is trivial.
Let it be also true for n -1 elements. Assume that e 1 , , en
are linearly dependent. Then en= c1e1 + ... +
Cn-ten-t for some
constants c1, ... , cn-t not all zero. But Aen=-e~=c 1 ~+ ...
!ln !11
... +cn-ten-l ;accordingly,c 1 (1-~)e 1 + ... +cn- 1 (1-~) X
!ln-1 !11 !ln-1
X en-t=O, which is impossible, since 1-Y..!!..=foO, k=1, ... , n-1.
flk
Let SRn be the subspace spanned by the elements e1 , , e11
From what has been shown above, it follows that SR 1 c ~U 2 c ...
. . . c SRn c ... and SRn =F SRn_ 1 for any n. Therefore, for any n
an element In E SRn can be found such that In J.... SRn_1 , II In II = 1.
Since the set / 1 , / 2 , , fn, ... is bounded and the operator A
is completely continuous, a fundamental subsequence can be chosen
from the set Aft, ... , Afn, ....
We shall demonstrate that this, in fact, cannot be done, which
will be the contradiction required for the proof of the theorem.
For arbitrary integers m, n, m < n, Afn - Afm = - 1- In+
!ln
+-1
!ln
1
(f.tnAf n- f n)- Afm = - f n +an,
!ln
where an E SRn-1 because
Afm ESRm C ffin-1 and f.tnAfn- fn = flnA (ctet + ... + cnen)- (ctet +
fll
)e
... + cnen) = c1 ( ~ -1 1+ ... + Cn-t ( ~ -1 )en-t E SRn-t There-
fln-1
fore 1/ Afn- Afm Jl =II
:n fn +an~~~ I 111n 1 11 fn II = 11 :n I~! , that
is, the sequence A/1, Af2 , , Afn, ... cannot contain a funda-
mental subsequence. I
Theorem 4 implies that the set of characteristic values of a completely
continuous operator is at most countable (it may even be empty!). The
characteristic values, if they exist, can be arranged in the order of non-
decreasing moduli
f.l1' f.l2' ' (9)
I f.l; I ::::;;; I f.l;+ 1 I, i = 1, 2, ... ; moreover, every characteristic value
in the sequence (9) is counted as many times as its multiplicity. The
94 PARTIAL DIFFERENTIAL EQUATIONS
set (9) may contain a finite number of elements (in particular, it
may be empty) or infinitely-many elements. In the latter case
I ~k I -+ oo as k -+ oo. (10)
With the sequence (9) is associated the sequence of corresponding eigen-
elements
(11)
which is linearly independent.
It will be proved in the following section that for a selfadjoint
completely continuous operator A =F 0 the sets (9) and (11) are
nonempty.
OPERATORS
1. Eigenvalues and Eigenelements of a Selfadjoint Completely
Continuous Operator. Let A be a bounded selfadjoint linear opera-
tor from H into H. Since for all f, II f II = 1, I (Af, f) I~ II A II,
it follows that on the unit sphere II f II = 1 there exist exact upper
and lower bounds of the quadratic form (Af, f) associated with the
operator A: m = in (Af, f), M = sup (A/, f); furthermore,
11111=1 11111=1
I m I ~ II A 11. M ~ II A II, m ~ (Af, f)~ M.
If f is an arbitrary nonzero element of EJ, then the element
fill f II belongs to the unit sphere; consequently, m = }~J <~j 11 ;),
M=s1~E(~j 11 ;), and hence the inequalities mllfii 2 <(Af, f)<
<M II f 1/ 2 hold for all f EH.
Since the quadratic form of operator A is real-valued, all its
eigenvalues (characteristic values) are real: if "A is an eigenvalue and f
the corresponding eigenelement, that is, Af = "Aj, then 'A =
= (Af, f)/11 f 11 2 Therefore, m ~ ').. ~ M.
The eigenelements / 1 and / 2 of operator A corresponding to different
eigenvalues "A1 and "A 2 are orthogonal. In fact, scalar multiplication
of the relations Af1 = "A1/ 1 and Af2 = "A 2/ 2 by f 2 and f 1 , respectively,
and subsequent subtraction yield (Aft, f 2 ) - (f1 , A/ 2 ) =
= ("A1 - "A 2 ) (f1 , f 2 ). This implies (f1 , f 2 ) = 0, since (A/1 , f 2 ) =
= (f1 , Af2 ) and A.1 =I= "A2.
Lemma 1. For the number M = sup (Af, f) to be an eigenva-
11 t II= 1
lue and fo the corresponding eigenelement (it is assumed that II fo II = 1)
of a selfadjoint bounded operator A from H into H, it is necessary and
sufficient that (Af 0 , f 0 ) = M.
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 95
Similarly, for the number m = inf (A/, f) to be an eigenvalue
II f II= 1
and / 0 the corresponding eigenelement (it is assumed that II / 0 II = 1)
of the operator A, it is necessary and sufficient that (A/ 0 , / 0 ) = m.
Proof. If M is an eigenvalue and / 0 any corresponding eigenele-
ment of the operator A, then A/ 0 = M/ 0 Therefore (A/ 0 , / 0 ) =
= M (/0 , / 0 ) = M, which proves the necessity part of the lemma.
To prove the sufficiency, let (A/ 0 , / 0 ) = M for some / 0 , II / 0 II = 1.
or, equivalently, (M/ 0 - A/0 , / 0 ) = 0. Since for all I in H 0 ~
~ M II f 112 - (Af, f) = (Mf- A/, f), it follows that for an arbit-
rary q> in H and any complex t (M (/0 +
tq>) - A (/0 +
tq>), / 0 +
+ t q>) :.?:- 0, that is, t (M/ 0 - A/ 0 , cp) +
t (M/ 0 - A/ 0 , cp) +
+ I t 12 (Mcp- Acp, cp) :.?:- 0. Putting in this inequality t = -aeia.
where a = arg (M/0 - A/0 , cp) and cr is real, we obtain the inequali-
ty -2cr I (M/ 0 - A/ 0 , cp) I +
cr 2 (Mcp- Acp, cp) :.?:- 0, true for all
real cr. This inequality implies (M/ 0 - A/ 0 , cp) = 0, and, since cp is
arbitrary, M/ 0 - A/ 0 = 0.
The second part of the lemma follows from the first part if instead
of A one considers the operator -A. I
Lemma 2. If the operator A acting from H into H is selfadjoint and
completely continuous, then the quantity M = sup (A/, f) (similarly,
11/11= 1
the quantity m = inf (Af, f)), if different from zero, is an eigenvalue
IIIII= 1
of this operator.
Proof. Suppose M =1= 0. We consider the Hermitian bilinear from
(Mf- A/, g),/, g E H, and the corresponding quadratic form (Mf-
- Af, f). For all I in H (Mf - Af, fs) :.?:- 0.
We shall demonstrate that there is a nonzero element f 0 such that
(M/ 0 - A/ 0 , / 0 ) = 0. Then Lemma 2 will follow from Lemma 1.
Assume that no such / 0 exists. Then (Mf- A/, f), f E H, can van-
ish only when f = o. Therefore the bilinear form (Mf- Af, g)
can be taken as a new scalar product in H. This means that for any
j, g in H Bunyakovskii's inequality
I(M/- Af, g) 12 ~ (Mf- Af, f) (Mg- Ag, g) (1)
holds.
From the definition of M as the exact upper bound of the quadra-
tic form (Af, f) on the unit sphere II f II = 1 it follows that there is a
sequence / 1 , / 2 , , II li II = 1, i = 1, 2, ... , for which
(Afn, fn)--+ M or
(Mfn - Afn, fn)--+ 0, n--+ oo.
Putting in (1) f = fn, g = Mfn - Afn, we obtain II Mfn - Afn 11 4 ~
~(Min- Afn, In) (M 2 fn- 2MAfn + A 2/n, Mfn- Afn) ~
~ (Mfn - Afn, fn) (I M I +
II A 11) 3 Therefore, in view of (2), it
follows that the sequence Mfn - Afn--+ 0 as n--+ oo. Since the ope-
rator A is completely continuous and the sequence / 1 , / 2,
96 PARTIAL DIFFERENTIAL EQUATIONS
(II/; II = 1) is bounded, the sequence Af1 , Af 2 , is compact.
This means that a convergent subsequence can be chosen from it;
we assume that it coincides with A/1 , A/ 2 , Then the sequence
M/1 , Mf 2 , , and together with it (M =1= 0) also the sequence
ft> / 2 , , converges. If the limit of the sequence ft, / 2 , is
denoted by f 0 , then, evidently, II / 0 II = 1, and by (2) (M/ 0 -
-Afo.to) = 0. I
Theorem 1. For every nonzero selfadjoint completely continuous oper-
ator A from H into H (H is a Hilbert space) one of the quantities
1111 A II = 11 sup I (A/, f) I is the first (smallest in absolute
U/11=1
value) characteristic value f.1 1 , and Ill = 11M if M > I m I, where
M = sup (Af, f), m = inf (A/, f), f..l 1 = 1/m if M < I m 1.
II f II = 1 II f II =1
If M = I m I, then both the quantities 11m and 1/ M are characteristic
values, smallest in absolute values, of the operator A.
All the elements fo for which (A/ 0 , / 0)/11 / 0 11 2 = M when M >
> I m I or (Af 0 , / 0 )/11 / 0 112 = m when M < I m I, and only they,
are eigenelements corresponding) to f.1 1 If M= I m I, then eigenele-
ments corresponding to the characteristic value 11M are only those f G
for which (Af 0 , / 0 )/11 fo 11 2 = M, while eigenelements corresponding to
the characteristic value 11m are only those f 0 for which (Af 0 , / 0 )/11 fo W=
=m.
In particular, if the operator A is nonnegative, then
f..lt=-1- = 1 = inf - 1 -=inf 11/11 2
til A II sup (Af, /) 11111=1 (Af, /) tEH (A/, /)
11111=1
and the; eigenelements corresponding to f.1 1 , normalized by the condition
II f II = 1, are only those elements / 0 , II / 0 II = 1, where the quadratic
form (Af, f) attains its upper bound on the unit sphere. ,
Proof. To establish Theorem 1, it suffices, in view of Lemmas 1
and 2, to demonstrate that IIAII =N, where N =sup I (A/, f) I=
11111=1
=max (I m I, M). As shown above, N::::;;; II A II, so that it remains
only to establish the reverse inequality II A II ::::;;; N.
Since for any g E H I(Ag, g) I ::::;;; N II g 11 2 and since (A (f1 + / 2),
f1 + /2) = (Afi, / 1) +
(A/ 2, / 2) + 2Re (A/1, f 2 ), we have for any
f1, f2 E H
I Re (Aft, /2) I= 41 I (AUt+ f2), It+ f2)- (AUt- /2), It- /2) I
-< ! <I (AUt+ fa), ft + f2) I+ I(AUt- /2), fc- /2) I)
-<:(II It+ f2ll 2+ II It- /2 !1 2) = ~ <II tdl 2 + II /21! 2)
Putting in this inequality ft=YNf, / 2 = :N Af, where f is an
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 97
arbitrary element of H, we have IJ Af 11 2 <: ~ (N II f 11 2 +
Af 11 2 ) , ! II
whence it follows that IIAfii-<NHfll Accordingly, IIAII<:N. I
Thus the sets
(3)
(4)
of characteristic values and corresponding eigenelements of a self-
adjoint completely continuous operator A =I= 0 are not empty. In
this case all the characteristic values are real and the system of eigen-
elements can be assumed to be orthonormal, since eigenelements
corresponding to different characteristic values are orthogonal and
the finite number of linearly independent eigenelements corresponding
to a given characteristic value can be orthonormalized.
Let A be a completely continuous selfadjoint operator acting from
H into H. By Hn we denote the subspace of H consisting of elements
f that are orthogonal to the first n eigenelements of the operator A:
(/, et) = 0, i = 1, ... , n.
For any f in Hn, the element Af is also in Hn, since (A/, e1) =
= (f, Ae 1) =..!. (f, e1) = 0 for all i = 1, ... , n. This means that
the operator A~'can be regarded as an operator acting from the Hil-
bert space Hn into Hn. And it is, of course, selfadjoint and completely
continuous. Its characteristic values and the corresponding eigen-
elements coincide with the characteristic values f.Ln+I f.Ln+ 2, and
the corresponding eigenelements en+I en+z ... of the operator A
acting from H into H. Therefore Theorem 1, applied to the operator
A from Hn into Hn, yields
1 1
If.Ln+i I= sup I (A/, /) I sup 1(A/, /) I"
11/11=1 }1/11=1
IEHn ( 't)=O
i=1, ,n
If the operator A is nonnegative, then
1
inf llfJII
f.tn+t = --su-p--,(,....,A,..,./,-/""") (/, 't)=O (A/, /)
(5)
111(1=1
(/, 't)=O i=i, .. . , n
i=1, . , n
2. Fourier Expansion with Respect to Eigenelements of a Self-
adjoint Completely Continuous Operator. Consider the orthonormal
system (4) which consists of the eigenelements of a selfadjoint com-
pletely continuous operator A from H into H, A =1= 0. Let Pn be
the operator of orthogonal projection onto the subspace spanned by
the elements e1 , , en, and let the operator An = A - API\ =
=A ( I - Pn).
7-0594
98 PARTIAL DIFFERENTIAL EQUATIONS
The operator An is linear and bounded: II An II ~ II A 11.
The operator Pn commutes with the operator A, because for any
f EH
APnf =A Utet + + fnen) = ftAet + . + fnAen
=lLet+. .+A en= (f, .!..L) et+ ... + (f, 2)'en
Itt lln ll1 lln '
= (f, Aet) et + ... + (!, Aen) en =(Af, et) et+ ... +(Af, en) en=PnAf.
Since the operators A and Pn commute and are selfadjoint, the oper-
ator APn is selfadjoint: (APn)* = P!A * = PnA = APn. Accord-
ingly, the operator An is also selfadjoint.
Furthermore, the operator An as the sum of two completely con-
tinuous operators, the operator A and the finite-dimensional operator
APn = PnA, is completely continuous.
For any IE H
n
Anf=Af- ~ Aek. (6)
.LJ Ilk
11=1
The quantities 1-Ln+l ... and the elements en+l .. are char-
acteristic values and corresponding eigenelements of the operator
An- Indeed, since (ep, ek) = 0, k =F p, using (6) we have Anep =
n
= A ep -
~ (ep, elt)
LJ ek = ep f . . . ._
- or p ~ n
+ 1.
k=1 Ilk llp
The operator An has no other characteristic values. Assume, on
the contrary, that 11 and e are the characteristic value and eigenele-
ment, !l-Ane = e, fL =F fLP p :;;? n +
1. Scalar multiplication of the
last equality by ek, k ~ n, yields (e, ek) = f.t(Ane, ek) = 11 (e,
Anek) = 0, since Anek = o when k ~ n. Therefore, noting (6),
Ane = Ae, that is, fLAe = e. Thus fL is the characteristic value and e
is the eigenelement of the operator A. But all the characteristic
values of A are contained in sequence (3) and since e _L ek, k =
= 1, ... , nit follows that fL coincides with one of I-Lk k:;;? n +1.
Since fln+l is characteristic value, smallest in absolute value, of
the operator An, Theorem 1 yields
1
I ftn+t I = Jl An If (7)
If the sequences (3) and (4) are finite and contain m elements, then,
according to Theorem 1, Am= 0, since it has no characteristic val-
ues. In this case A = APm is a finite-dimensional operator, that is,
for any f E H
(8)
LEBESGUE INTEGRAL. QUESTIONS OF FUNCTIONAL ANALYSIS 99
When the sequences (3) and (4) are infinite, (7) and relation (10)
of the preceding section imply that II An II-+ 0 as n-+ oo. This
means that for any /EH IIAn/ll:s::;IIAnllll/11-+0 as n-+oo,that
is, for any f E H
00 00
A/= lim APnf = ~ ~ e,. = ~ (Af)ke,.. (9)
n-+oo 11=1 ./JR. 11=1
We have thus established the following important theorem.
Theorem 2 (Hilbert-Schmidt). If A is the selfadjoint completely
continuous operator from H into Hand f is an arbitrary element of H,
then the element Af has Fourier expansion (9) (or (8)) with respect to
the system (4).
In our later discussions we shall require some corollaries of the
Hilbert-Schmidt theorem.
00
According to Lemma 2, Sec. 2.6, the Fourier series ~ j,.e,. of
11=1
any element f E H with respect to the orthonormal system (4)
00 00
converges in H; consequently, A ~ f~~.e,. = ~ j,.Ae,.. But j,.Ae,. =
11=1 11=1
= j,.!!!:... = (/, Ae11 ) e11 '--= (Aj, e~~.) e11 = (Af)k e11 Therefore by (9) we have
flR.
00
11=1
If the operator A has an inverse A -1, then (10) yields
00
!= 2} f~~.e,.
k=1 ~
for any element f E H. This means that in this case the system (4) is
an orthonormal basis for the space H. Thus we have proved the
following result.
Corollary 1. If the selfadjoint completely continuous operator A
from H into H has an inverse, then the system (4) is an orthonormal
basis for the space H. .
In the general case, from (10) we can only conclude that for any
element f E H there exists an element e 0 E H, Ae 0 = 0, such that
00
!=eo+ 2} f 11 e11 (11)
11=1
The set m
containing the elements g E H for which Ag = 0 is a
subspace of H; any nonzero element of is an eigenelement of the m
operator A corresponding to the zero eigenvalue. If the space H is
assumed separable, a countable orthonormal basis e;, e;, ... (con-
7*
tOO PARTIAL DIFFERENTIAL EQUATIONS
sisting of eigenelements of the operator A corresponding to the zero
eigenvalue) can be constructed in 91. Then, by (11), for any f E H
we have the expansion
where fh = (!, ek)
Thus we have proved
Corollary 2. For any selfadjoint completely continuous operator A
from the separable (Hilbert) space H into H there exists an orthonormal
basis for H whose elements are the eigenelements of the operator A.
CHAPTER III
FUNCTION SPACES
In the preceding chapter we introduced the notions of Banach and
Hilbert spaces. These notions were based only on the relationships
between elements: it was enough to introduce the operations of
addition of elements and multiplication by numbers, norm or cor-
responding scalar product that satisfy some definite axioms. The
nature of elements of these spaces was not at all important, and the
general results obtained in the last chapter are applicable to all the
spaces irrespective of the elements they are composed of. However,
for the theory of differential equations these general properties are
far from sufficient. In the investigation of partial differential equa-
tions it is natural to consider function spaces, that is, spaces whose
elements are, for our purposes, functions of n real variables. In the
present chapter we shall introduce some function spaces and obtain
assertions regarding mutual telationships between them that enable
us to conclude from some properties of their elements various other
properties.
1. SPACES OF CONTINUOUS AND CONTINUOUSLY
DIFFERENTIABLE FUNCTIONS
1. Normed Spaces C(Q) and Ck(Q). We consider the set C (Q)
of all the functions that are continuous in Q (Q is a bounded region
in the space Rn). Let us first note that this set is a linear space. It
can be directly verified that the functional max If (x) I defined on
xeQ
C(Q) satisfies all the axioms for being a norm (see Sec. 2.2.,
Chap. II): max I cf I =I c I max If I; I /1 (x) + !2 (x) I~ I /1 (x) I+
xEQ xEQ
+ I / 2 (x) I for all x E Q, therefore maxi / 1 (x) + / 2 (x) I~
xEQ
102 PARTIAL DIFFERENTIAL EQUATIONS
=:::;;;max l/1(x) I+ max l/2(x); max 1/(x) I:::>Oandmaxjf(x)l=
xeQ xeQ xeQ xEQ
=0 only when f(x) = 0. Thus in C(Q) we may introduce the norm
II f llc(Q) =rna! If (x) /. (1)
xeQ
The convergence in norm (1) coincides with uniform convergence in Q.
The space C(Q) with norm (1) is Banach space, because, by the
Cauchy criterion, any sequence of functions in C (Q) that is funda-
mental in norm (1) converges uniformly to a function belonging
to C(Q).
Since, by Weirstrass's theorem, every function continuous in Q
is the limit of a sequence of polynomials that converges uniformly
in Q (that is, in the norm (1)), the set of all the polynomials is every-
where dense in C(Q). But, in turn, an arbitrary polynomial can be
expressed as the limit of the sequence of polynomials with rational
coefficients that converges uniformly in Q. Therefore the countable
set of all polynomials with rational coefficients is also everywhere
dense in C(Q). This means that the space C(Q) is separable.
0
We consider in C(Q) the set C(Q) containing all the functions that
vanish on the boundary 8Q of Q. Clearly, C(Q) is a linear manifold
in C (Q). This manifold is closed (in the norm (1)), because the limit
of a sequence of functions in C(ij} converging uniformly in Q is a
function belonging to C(Q); accordingly, C(Q) is a subspace of the
space C(Q).
Next, in C(Q) consider the subsets~ C"(Q), k = 1, 2, ... , con-
sisting of the functions whose all the derivatives up to order k are
continuous in Q. The set C"(Q) is a linear space. What is more, in
C"(Q) one may introduce the norm
lal~ll xEQ
Convergence in this norm means the uniform convergence in Q of
the Hunctions and all their derivatives up to order k. Evidently,
C"(Q) is a Banach space (with norm (2)).
Let (J)h (I x - y I) be some averaging kernel (see Chap. I, Intro-
duction) and f E C(Q). With h > 0, consider the function
fh (x) = Jf (y) (J)h (I x- y /) dy, (3)
Q
FUNCTION SPACES 103
Functions fh (x), h > 0, are called the average functions for the
function f(x) (the averaging functions for /(x)). From the Property (a)
of an averaging kernel and Theorem 7, Sec. 1. 7, Chap. II, it follows
that f,.(x) E coo(Rn) for any h > 0. Further, fh(x) =0 outside
Qh (Qh is the union of balls {I x - x 0 I< h} taken over all x0 E Q).
Let us show that if f E C (Q), then h (x) converges to f (x), as
h-+ 0, uniformly on any strictly interior subregion Q' of Q, Q' ~ Q.
In fact, for sufficiently small h (less than the distance between fJQ'
and fJQ) by Properties (b), (c) and (a) of the averaging kernel we
have, for x E Q',
'lfdx)- I (x) I= I
jx-yl<h
J I (y) roh (lx-y J) dy-f (x) J
fx-yf<h
roh (lx- yl) dy I
::;; max lf(y)-f(x)!
lx-yj,;;;h
J
jx-yJ<h
roh(lx-yJ)dy= max !f(y)-f(x)l
lx-yl,;;;h
Therefore, by uniform convergence of f(x) in Q, we obtain
II fh- I llc<Q'l -+0 as h-+0.
Since for f ECk(Q), with x EQ' and sufficiently small h,
D~ ih (x) = J f (y) D~roh (I x - y I) dy
Q
-1)1at Jf (y) D~roh (jx- y I) dy
= (
Q
= JD~f(y)roh(!x-yl)dy,
Q
the above assertion implies that
if I E c~t (Q), then for any Q' ~ Q
llh-fllck<<h -+0 as h-+0.
2. Formulas of Integration by Parts. Suppose that in the region Q
(the boundary fJQ E C1) there is defined a vector A(x) = (A 1 (x), .. .
. . . , An(x)); whose components A;(x)'"'EC(Q) n
C1 (Q), i = 1, .. .
. . . , n. From the Course of Analysis it is known that if the func-
.
t wn d"tv A( x ) =-a-
aAt ... +-a-+
aAn 1s. contmuous
. .
1n Q-, or even
Xt Xn
integrable over Q, then the following formula, known as Ostrograd-
.skii' s formula, holds:
J divA (x)
Q
dx = JA (x) n (x) dS,
aQ
(4)
104 PARTIAL DIFFERENTIAL EQUATIONS
where n is the unit vector normal to the boundary iJQ and directed
outwards with respect to Q.
Let u(x) E C2 (Q) n C1 (Q), v E C1 (Q}, and let the function ~u =
= div (Vu) be integrable over Q. Since v ~u = V div (Vu) =
= div (vVu) - vuvv (VuVv = Ux1Vx 1 + ... + Ux n Vx n }, by Ostro-
Q OQ Q
(5)
because Vu n laQ = :~ laQ .
If both the functions u and v belong to C2 (Q) n C1 (Q) and the
functions flu and ~v are integrable over Q, then, apart from for-
mula (5}, we also have
Jullv dx Ju :: dS - JVvVu dx.
Q
=
OQ Q
(5')
Subtraction of (5') termwise from (5) yields
J(vllu-ullv)dx=) (v !~ -u :: )ds.
Q oQ
(6)
2. SPACES OF INTEGRABLE FUNCTIONS
As shown above, the set of continuous functions in Q is a Banach
space with the norm max If (x)l. Nevertheless, it often proves
xEQ
convenient to consider on this set integral norms, for example,
J
}1 f (x) I dx or ( I f (x) 12 dx)l/2 (it is easy to see that they satisfy
Q Q
all the axioms of a norm). We examine the space with norm
J I f (x) I dx whose elements are continuous functions in Q. This
Q
normed space is incomplete. In fact, from the definition of Lebesgue
integral it follows that for any function f(x) integrable over Q there
is a sequence fm(x) of functions continuous in Q which converges to
f(x) in this norm: }1 f m (x) - f (x) I dx -- 0 as m -- oo. This
Q
means that if we wish to obtain a complete normed (Banach) space
with the norm ) I f (x) I dx which would contain all the functions
Q
FUNCTION SPACES 105-
continuous (or even infinitely differentiable) in Q, we must include
all those functions which are integrable over Q. But then the func-
tional ~I j(x) I dx ceases to be a norm-it does not satisfy the last
Q
axiom (see Sec. 2.2, Chap. II) of a norm, since ) I f(x) I dx = 0 for
Q
all f(x) = 0 a.e. in Q. However, according to Theorem 2, Sec. 1.4~
J
Chap. II, I f(x) I dx = 0 only for functions f(x) that vanish a.e.
Q
in Q. Therefore, for the last axiom of the norm to be satisfied, we
must identify all the functions that vanish a.e. in Q. For this we
may consider as the elements of the space either classes of functions-
each of which contains all the functions that are equal a.e. or else,
equivalently, may introduce a new definition of equality of functions:
functions are equal if their values coincide almost everywhere. Since
it is more convenient to operate with functions than with classes of
functions, in the sequel we shall regard functions equal if their
values coincide for almost all (not necessarily for all) x in Q. Since
in such a definition of equality of functions the functions remain un-
changed when their values change arbitrarily on any fixed set of
measure zero, in this case it is natural to assume that the functions-
are defined almost everywhere. If a function f vanishes almost every-
where, we take it as the zero function. Similarly, if a function
coincides almost everywhere with an everywhere defined continuous
function, we regard it as a continuous function, while f is contin-
uously differentiable up to order k if it coincides almost everywhere
with a function that is everywhere defined and is continuously differ-
entiable up to order k. In accordance with the abovementioned no-
tion of equality, we shall assume that the space Ck(Q), k >-0, con-
tains also the functions defined almost everywhere in Q and con-
tinuously differentiable up to order k. That is, a function f(x) be-
longs to Ck(Q) if it coincides almost everywhere with a function
which is defined at all points of Q and is continuous in Q together
with all its derivatives up to order k. Further, by the value of an
element of the space C(Q) (and, more so, of functions in Ck(Q)) at
some point we shall mean the value at this point of the continuous
function defined everywhere that coincides with this element almost
everywhere in Q.
1. Spaces L 1 (Q) and L 2 (Q). Consider the set of complex-valued
functions that are integrable over Q. Obviously, it is a linear space
(also in the new sense of equality of functions), and the functional
~ I f(x) I dx satisftes all the axioms of a norm. This linear space
Q
106 PARTIAL DIFFERENTIAL EQUATIONS
Q
(1)
The set of complex-valued measurable functions (recall that func-
tions coinciding a. e. are identified) the squares of whose moduli are
integrable over Q will be denoted by L 2 (Q). Let us demonstrate
that L 2 (Q) is a linear space. Let c1 , c2 be arbitrary numbers, and
j 1 (x), 12 (x) arbitrary functions in L 2 (Q). Since the measurable
function c111 (x) + cJ 2 (x) satisfies the inequality I cJf1 (x) +
+ c212 (x) 12 :< 2 I c1 12 I II(x) 12 +
2 ! c2 12 I l 2 (x) 12 , by Theorem 5,
Sec. 1.6, Chap. II, the function I ctf1 (x) + cJ 2 (x) 12 is integrable,
which implies that cJi1 (x) + cJ 2 (x) E L 2 (Q).
The function l 1 (x) l 2 (x), where l 1 (x), l 2 (x) E L 2 (Q), is integrable,
because it is measurable and I l 1 (x) l 2 (x) I~ (I l 1 (x) 12 ! +
+ I I 2 (x) 12). Therefore with the pair of functions 11 and I 2 one can
associate the quantity
(f,, 12)L.(Q) = J l,(x) l2(x) dx. (2)
Q
It is easily checked that formula (2) defines a scalar product in
L 2 (Q). The norm generated by this scalar product is of the form
II I IIL.<Q> = ( J I l(x) 1 dx)
2 112
(3)
Q
Since I I I= I I 11 ~ ; (II 12 +
1), we find that when the region
Q is bounded the function l(x) belonging to L 2 (Q) also belongs to
1 (Q). This means that L 2 (Q) c L 1 (Q) for a bounded region. In
this case it is also evident that C(Q) c L 2 (Q) c L 1 (Q).
Theorem 1. 1 (Q) is a Banach space with norm (1). L 2 (Q) is a
Hilbert space with scalar product (2).
To prove this theorem, it suffices to establish that the spaces L 1 (Q)
and L 2 (Q) are complete in the respective norms.
1. Let the sequence lk, k = 1, 2, ... , of functions in L 1 (Q) be
fundamental in L 1(Q), that is, for any e > 0 there is a number
N(e) such that II fk - lm II Lt<Q> e for all k, m <
N(e). Choose >
e = 2-k for some integer k, and let N k denote the number N(2-k)
such that Nk ~ Nk+I Then for m Nk we have >
II1Nk-lmiiL,(Q)<2-k, (4)
and, in particular, II INk- !Nk+li\L,cQ> < 2-k. Hence the series
00
~ 1
..::..1 II IN k - IN k+l IlL (Q)
1
converges. This, in view of Corollary to
k=l
FUNCTION SPACES 107
00
Sec. 1.6, Chap. II, means that the series ~ (/Nk -INk) converges
11=1 +l
a. e. in Q to a function belonging to L 1(Q), which, in turn,
means that the sequence INk , k = 1, 2, ... , converges, as k-+ oo,
a.e. in Q to a function IE L 1( Q):
INk(x)-+ l(x), k-+ oo.
We shall show that II lm - I II Lt(Q) -+ 0 as m-+ oo. Indeed, for
m > Nr, k >
r the inequality (4) implies
I lm-INki!L,(Q) ::s;; 111m- INri/L,(Q)+ I11Nr- INki/L,(Q) ::s;; 22-r=2 1-r.
Letting k-+ oo in this inequality, we obtain, by Fatou's lemma
(Theorem 4, Sec. 1.6, Chap. II), the inequality II lm- I II Lt(Q) ::s;;
>
:s;: 21 -r which is true for all m N r For sufficiently large m the
number r can be chosen large enough, therefore II lm - I II Lt(Q) -+ 0
as m-+ oo. Thus the space L 1 (Q) is complete.
2. Suppose that the members of the sequence l 11 (x), k = 1, 2, ... ,
belong to L 2 (Q) and that the sequence is fundamental in the norm
L 2 (Q). As in the proof of the first part of this theorem, a number
sequence N 1 ::s;; N 2 ::s;; ... ::s;; N k ::s;; . . . can be found such that
(4')
for all m ~ N~~,, and, in particular, II INk+l- IN~~,IIL.<Q> < 2-k.
An application of Bunyakovskii's inequality gives II 1Nk+ 1 -
- IN~~,I!L,<Q> ::s;; VfQIII IN~~,+l- INk IIL,(Q) < VfQT 2-11., therefore there
is a function l(x)EL 1(Q) such that IN~~,(x)-+l(x), as k-+oo,
a.e. in Q. This means that 11Nkl2 -+l// 2 , as k-+oo, a.e. in Q.
Furthermore,
1
II INk 1/L,(Q} ::s;; II INk- IN,IIL,(Q) +II IN.l!L,(Q) ::s;; 2+ II IN, IIL,(Q)
Hence, by Fatou's lemma, l(x) E L 2 (Q).
Let us show that II lm - I II L,(Q)-+ 0 as m-+ oo. Form> Nr and
k~r inequality (4') implies
II lm- INk IIL,(Q) -< II lm- /Nr IIL,(Q) +II INr- INk 1/L,(Q) ::s;; 2i-r.
Letting k-+ oo in this inequality and again using Fatou's lemma, we
conclude that II fm- I II<L,Q) :s;; 21 -r for all m >
Nr. And since
with sufficiently large m, r can be chosen sufficiently large, we obtain
II fm- I IIL,(t_.)-+ 0 as m-+ oo. I
Remark. We remark that in proving Theorem 1 we have at the
same time established the following assertion.
108 PARTIAL DIFFERENTIAL EQUATIONS
From every sequence of functions converging to a function f in L 1 (Q)
or in L 2 (Q) a subsequence can be chosen that converges to f a.e.
2. Denseness of the Set O(Q) in L 1 (Q) and L 2 (Q). Separability
of L 1 (Q) and L 2 (Q). Continuity in the Mean of Elements of L 1 (Q)
and L 2 (Q).
Theorem 2. The set of functions continuous in Q is everywhere dense
in L 1 (Q) and L 2 (Q).
1. Let f(x) E L 1 (Q). With no loss of generality this function can
be assumed real-valued and nonnegative. Then by the definition of
integrability of f(x), there exists a sequence !11.(x), k = 1, 2, ... ,
of functions continuous in Q having the property that f11.(x) t f(x)
a.e. in Q and J /11. dx-+ JI dx
Q Q
as lc-+ oo. Since JI f -
Q
!11. I dx =
= r
Q
( j - fk) dx, it follows that II I - fk IIL,(Q)-+ 0 as lc-+ oo, as
required.
2. Let f(x) E L 2 (Q) which is again assumed real-valued and
nonnegative. Since f(x) E L 1 (Q), we can find a monotone nondecreas-
ing sequence fk, k = 1, 2, ... , of functions belonging to C(Q) that
converges to f a.e. in Q. The functions /11.(x) can be additionally
assumed to be nonnegative, for, if necessary, this sequence can be
replaced by the sequence f't.(x), k = 1, 2, . . .. But then t:(x)t
t f(x), as k-+ oo, a.e. in Q. By the definition of the integral of
f(x) Jt: dx-+ Jf
Q Q
dx, that is, II /11. lll.<Q> -+ II I lll.<Q> Since /,d ~
~ f 2 , by Lebesgue's theorem (Theorem 6, Sec. 1.7, Chap. II)
lim (fk, /)L.<Q> = II I llt.<Qh which implies that II h - I lll.<Q> =
k .... oo
= II /11. lll.<Q>- 2 (/71., /)L1 (Q) + II I lll.<Q>-+ 0 as k-+ oo. I
Note that if a sequence of functions in C(Q) converges to a fun-
ction in the norm of C (Q), it also converges to it in the norms of
L 1 (Q) and L 2 (Q). Consequently, any function continuous in Q can
be approximated by a sequence of polynomials with rational coeffic-
ients in the norms of L 1 (Q) and L 2 (Q). Then Theorem 2 implies
that the countable set of polynomials with rational coefficients is
everywhere dense in L 1 (Q) and L 2 (Q). We have the following result.
Theorem 3. L 1 (Q) and L 2 (Q) are separable spaces.
A function f(x) belonging to L 2 (Q) (and extended outside Q by
assigning to it the value zero) is called continuous in the mean (square)
or in the norm of L 2 (Q) if for a given e > 0 a 6 > 0 can be found such
that II f(x + z) - f(x) IIL1 (Q) < e for all z, I z I < 6.
A function f(x) belonging to L 1 (Q) (and extended as being equal to
zero outside Q) is called continuous in the mean or in the norm of
FUNCTION SPACES 109
L 1 (Q) if for a given e > 0 a 6 > 0 can be found such that
II f(x + z) - f(x) IIL1(Q) < e for all z, I z I < 6.
Theorem 2 implies the following result.
Theorem 4. Any function belonging to L 2 (Q) is continuous in the
mean (square). Any function belonging to L 1(Q) is continuous in the
mean.
Proof. Let f E L 2 (Q) (the proof is exactly the same when f E
E L 1 (Q)). Consider a large number a > 0 so that Q ~ Sa, where Sa
is the ball {I x I < a}. Since f(x) E L 2 (Q), the function F(x},
which is equal to f(x) when x E Q and vanishes when x E S 24 "-._Q,
belongs to L 2 (S 2 a). Take an arbitrary e > 0. By Theorem 2, there is
a function F(x) which is continuous in S 2a and satisfies the inequali-
ty II F(x) - Jf(x) IIL.<S2a> < e/3. By multiplying F(x) by a prop-
erly chosen slicing function for the region Sa, it can be assumed
that F(x) == 0 for x ES 2 a"-._Sa. Therefore for I z I~ a, II F(x + z)-
- F(x + z) IIL,(S1 a) = II F(x) - F(x) IIL,(S > ~ e/3. Since the
- a_
function F(x) is uniformly continuous in S 2a, there is a 6 > 0
(ti <a) such that II F(x + z) - F(x) IIL,(s24 > ~ e/3 whenever
I z I < 6. This means that for I z I < 6
Ill (x + z)- f (x) IIL.<Q> =II F (x + z)- F (x) IIL,(s2a>
~ /1 F (x + z)- F (x + z) IIL.<s 24>+II F (x + z)- F (x) lk.<s24>
+II F (x)- F (x) IIL,(B 24 ) ~ ~ + : + : =e. I
3. Averaging of Functions Belonging to L 1 (Q) and L 2 (Q). As in
the case of functions belonging to C(Q}, averaging functions can
also be defined for functions belonging to L 1 (Q) and L 2 (Q).
Let ffih(l x - y I) be some averaging kernel (Chap. I, Introduc-
tion), and let f(x) E L 1(Q). The function
fh(x)= Jf(y)ffih(ix-yj)dy, h>O, (5)
Q
is called the average function for the function f (averaging function
for f).
By the Property (a) of an averaging kernel and Theorem 7, Sec. 1.7,
Chap. II, fh(x) E C""(Rn) for h > 0. Further, fh(x) =
0 beyond Qh.
Theorem 5. If f(x) E L 1 (Q) (L 2 (Q)), then II h - f IIL,(Q)-+ 0
(II h - f IIL,(Q)-+ 0) as h-+ 0.
Proof. Both the assertions are proved exactly in the same way,
therefore we examine, for example, the case when f E L 2 (Q). The
function f is assumed extended outside Q by assigning to it the value
zero. Successive applications of Properties (b) and (c) of an averag-
110 PARTIAL DIFFERENTIAL EQUATIONS
ing kernel, Bunyakovskii's inequality and Property (d) of the
averaging kernel yield
I fh(x)- f (x) 12
- J lx-Yi<h
f(y) wh(l x- Y J) dy- f(x)
J
lx-YI<h
~ ~ w~(l x- Y J) dy ) I f(y)- f(x) 12 dy
lx-yl<h lx-yl<h
~~
const i1 I f(x + z)- f(x) J2 dz.
lz!<:h
By the Corollary of Fubini 's theorem (Sec. 1.11, Chap. II)
Q !zl<h
2 (6)
lzl<h Q
Take any e > 0. By the theorem on continuity in the mean (Theo-
rem 4), a 8 > 0 can be found such that II /(x z) - /(x) IIL.(Q) < +
< e whenever I z I ~ h < 8. Therefore for such h the inequality (6)
implies llfh - f IIL.(Q) ~ const e. I
Remark. It should be noted that the proof of Theorem 5 nowhere
uses the fact that the averaging kernel is nonnegative. Consequently,
if the averaging function fh(x) for f(x) is defined by the formula (5),
where wh ( I x - y I) = hn 1 w -h-
1
(lz-yl)
and w1 t), -- (X)< t < CXl, (
is an infinitely differentiable even function that vanishes for I t I 1 >
and is such that J
~ 1 ( I x I) dx = 1 (compare with the definition of
Rn
the averaging kernel given in Introduction, Chap. 1), then Theorem 5
remains valid in this case also.
Theorem 6. The set C00 (Q) is everywhere dense in L 1 (Q) and in
L2 (Q).
Proof. Let f(x) E L 2 (Q) (the case f E L 1 (Q) is disposed of similar-
ly), and fix any e > 0. By the theorem on absolute continuity of a
Lebesgue integral (Theorem 9, Sec. 1.10, Chap. II), there is a 8 > 0
such that J
If 12 dx < e2 /4. This means that the function F(x)
Q'o...Qa
with compact support in Q which belongs to L 2 (Q) and equals f(x)
when x E Q6 and vanishes when x E Q',.Q 6 , satisfies the inequality
II F - f IIL,(Q) ~ e/2. By Theorem 5, a h 0 > 0 can be found such
FUNCTION SPACES 111
that II F h - F IIL.(Q) ~ e/2 for all 0 < h ~ h 0 The averaging
function F h for the function F with compact support belongs to
(:oo(ij) for sufficiently small h and
111-Fhi/L.<Ql ~ llf-FI/L.<QJ+IIF-FhliL.(Q) ~~+~=e. I
Since for any k ~ 0 C""(Q) c Ck(Q) c L 2 (Q), it] follows that
for all k :;> 0 {;k(Q) are everywhere dense in L 2 (Q).~
4. Linear Spaces L 1 , 10 c, L 2 , Joe The set of functions that are
integrable over any strictly interior subregion Q' of Q, Q' ~ Q, are
denoted by Lt, Ioc(Q).
The set of funcUons that are measurable in Q and the squares of
whose moduli are integrable over any strictly interior subregion Q'
of Q, Q' ~ Q, is denoted by L 2, Ioc(Q).
It is clear that L 1 , Ioc(Q) and L 2 , Ioc(Q) are linear spaces. Further,
L1(Q) c L 1 , Ioc(Q) and L 2(Q) c L 2, Ioc(Q). The function (1 - ~ x l)m'
for example, belongs to L 1 , Ioc( I x I < 1) and L 2 , Ioc( I x I < 1)
for any m, and at the same time it belongs to L 1 ( I x I < 1) only
when m < 1 and to L 2 (1 x I< 1) only when m < 1/2.
3. GENERALIZED DERIVATIVES
1. Simplest Properties of Generalized Derivatives. Suppose that a
continuous function f(x) in Q has continuous derivative fx.(x)
I
in Q.
Then for any function g(x) E C1 (Q)
Q Q
It turns out that the derivative fx.I off is completely determined
by the last equality: it can be easily shown that if for a continuous
function f(x) there exists a continuous function ht(x) such that
Q
Jfgxi dx = - .\
Q
h;gdx (1)
for any g(x) E b(Q), then the function f(x) has in Q the derivative
fxi and fxt = ht for all x E Q. Thus by means of identity (1) a defini-
tion of the derivative of f(x) can be given that is equivalent (in the
class of continuous functions) to the usual definition. If in (1) the
continuity condition of f(x) and ht(x) is dropped and instead it is
required that they be integrable or their squares be integrable (the
112 PARTIAL DIFFERENTIAL EQUATIONS
latter is more convenient for us) and the integrals in (1) are under-
stood in Lebesgue sense, then we enlarge the class of functions for
which the notion of derivative can be introduced; the function hi is
ealled the generalized derivative off with respect to xi in Q.
Let a = (a1 , , an) be a vector with nonnegative integral
eomponents. A function F(x) E L 2, loc(Q) is called ath general-
ized derivative (g.d.) in Q of a function f(x) E L 2, 10c(Q) if
J/(x) Dag (x) dx = :- (i)lttl Jja(x) g (x) dx (2)
Q Q
for any g(x) E Cltti(Q).
We shall first show that a function f(x) can have only one g.d.
F(x) (recall that functions are considered equal if they coincide a.e.).
In fact, let f't(x) and f:(x) be two g.d. of f(x). For an arbitrarily
fixed subregion Q', Q' ~ Q, and an arbitrary function g(x) E
E Clai(Q') the identity (2) yields ~ iff: - f:) g dx = 0. But
Q'
j~ - r: E L 2 (Q'), therefore, by Theorem 6, Subsec. 3 of the previous
section, ff - f': = 0 a.e. in Q', which means that this holds a.e.
also in Q.
Let f(x) E bai(Q). By Ostrogradskii's formula we have
J/(x) Dag (x)
Q
dx = ( -i)lal J
Q
Daj(x) g (x) dx (3)
for any g(x) E Cfai(Q). That is, the function f(x) has g.d. F(x)
equal to Dat(x). In particular, the function f(x) which is equal to a
constant (a.e.) in Q has each g.d. F(x) = 0, I a I > 0.
In the sequel g.d. F of a function twill be denoted by nat. The
generalized derivatives, primarily the first-and second-order deri-
vatives, will also be denoted by fx 1, fx 1x1 , .. and:;,, a:,~xJ, ... .
Since for smooth functions g(x) the derivative a~fafg a does not
iJx1 iJxnn
depend on the order of differentiation, it follows from the uniqueness
of a generalized derivative and formula (2) that a generalized deriv-
ative also does not depend on the order of differentiation.
The definition of g.d. also implies that if the functions fi(x), i =
= 1, 2, have g.d. na.ti, then the function ctf1 +
c.j 2 , with any con-
stants ch has g.d. Da (ctf1 +
c.j2 ) = c 1Daft +
c 2Da/ 2
Example 1. The function f(x) = 1x 1 1 has in the ball Q =
= {I x I< 1} first generalized derivatives fx 1 = sign x1 , fx 1 = 0,
i = 2, ... , n.
FUNCTION SPACES 113
In fact, for any g(x) E C1 (Q)
JI x.!"gx,dx= i xtix,dx- j xtix,dx,
Q Q+ Q-
n n
where Q+ = Q (x1 > 0), Q- = Q (x1 < 0). Applying Ostrograd-
skii's formula, we have (x1g = 0 on 8Q and also for x 1 = 0)
.\ l x 1 Igx, dx = -
Q
Jgdx + ) gdx = - Jsign x
Q+ Q- Q
1 g dx.
Therefore g.d. with respect to x 1 of the function I x1 I exists and is
equal to the function sign x1 Since for i 2 >-
Jlxtlix dx=)1 (lxt)g)x 1 dx=0=- JOgdx,
Q Q Q
the function I x1 I has generalized derivatives with respect to x 1, i =
= 2, ... , n, equal to zero.
Note that the function I x1 I has no classical derivative with re-
spect to x 1 in Q (the derivative does not exist for x1 = 0).
Example 2. The function f(x) = sign x1 has in the ball Q =
= {I x I < 1} first generalized derivatives fx.l = 0, i = 2, ... , n,
but has no generalized derivative fx 1 The existence of g.d. fx 1 , i =
= 2, ... , n, is established in the same manner as in Example 1.
Let us show that f has no g.d. with respect to x1 . Suppose, on the
contrary, that there is a function ffi E L 2, Ioc(Q) which is a general-
ized derivative of f with respect to x1 Then for any g(x) E C1 (Q)
Q Q
1
Q+ q-
=2 \ g dx2 ... dxn. (4)
Qnt;,.=o>
This equality, first of all, implies that ffi = 0 (a.e.) in Q. In fact,
substituting in (4) an arbitrary g(x) E C1 (Q) vanishing in Q-, we
have J
ffig dx = 0, which implies that ffi = 0 (a.e.) in Q+. Analog-
Q+
ously, it can be shown that ffi = 0 (a.e.) in Q-. Accordingly, for any
J
g(x) E Ct(Q), ffig dx = 0, that is, J
g (x) dx 2 dxn = 0, but
Q Qntx,=O} _
this cannot hold for an arbitrary function g(x) E C1 (Q).
In contrast to the corresponding classical derivative, the general-
ized derivative Daf is defined by (2) globally, at once in all of Q.
8-0594
114 PARTIAL DIFFERENTIAL EQUATIONS
However, in every subregion Q' c Q also the junction nat will be
g.d. of the function t, since the function g(x), belonging to C'lrx.I(Q')
and extended outside Q' by assigning to it the value zero, belongs to
Clrx.I(Q) (this property was, in fact, used while proving the unique-
ness of a g.d.). Therefore iff (x) has in Q g.d. nat and j(x) = c (a.e.)
in Q' c Q, then nat = 0 (a.e.) in Q'. In particular, g.d. (if it exists)
of a function /(x) having compact support in Q (that is, for some
Q", Q" ~ Q, f(x) = 0 a.e. in Q"-..Q") has compact support in Q,
and therefore belongs to L 2 (Q).
Suppose that the function /(x) belonging to L 2 , Ioc(Q) has g.d.
nat = F and the function F(x) has g.d. nrF = G. Then there
exists g.d. na+r>j and na+r>j = G.
Indeed, suppose g(x) E ba+r>I(Q). Since nr>g E bai(Q), we
have
i
Q
tna+r>g dx = ( -1)1rx.l
Q
Jnatnr>g dx
= ( -1)1rx.l) FDf\g dx = ( -1)1rx.I+Jf\1 JnfiFg dx = ( -1)1a+f'>l r Gg dx,
Q Q Q
as required.
In contrast to the classical derivative, the generalized derivative
nat is defined at once for order I a I without assuming the existence
of corresponding derivatives of lower orders. Let us show that the
derivatives of lower orders may not, in fact, exist.
Example 3. In the ball Q = {I x I< 1} consider the function
t(x) = cp(x1 ) + cp(x 2 ), where cp(x1 ) = sign x1 The results of
Example 2 show that /(x) has no generalized derivatives fx, and fx.
Nevertheless, we shall now show that the generalized derivative
fx,x, exists. Taking an arbitrary g(x) E C2 (Q), we have
Q Q
1 2
Q
Since
Jcp (xt) gx,x dx
Q
2 = - J
Qntx,<O}
gx,x 2 dX + J
Qntx,>O}
g x,x. dx = 0
and, similarly, Jcp(x )gx,x dx=0, it follows that
2 1
Jlix,x, dx = 0= J0 gdx.
Q Q
Thus the generalized derivative fx,x. exists and is equal to zero.
FUNCTION SPACES f15
2. Generalized Derivatives and Averaging Functions. A Criterion
for the Existence of Generalized Derivatives. Let f(x) E L 2 (Q),
and roh be some averaging kernel, and let
fh(x)= ~ roh(ix-yi)f(y)dy, h>O,
Q
be the averaging function for the function f(x), fh(x) E Coo(Rn)
Lemma 1. If the function f(x) E L 2 (Q) has a generalized deriva-
tive nat E L 2 (Q), then for any point y E Q
(nat)h (y) = nafh (y) (5)
with sufficiently small h > 0, and for any subregion Q' ~ Q
II nat"- nat ilr.,<Q'> ~ o (6)
ash~ 0.
If in addition to the above, the function f(x) has compact support in
Q (and is extended outside Q by assigning to it the value zero), then
formula (5) holds for all y EQ for sufficiently small h > 0, and
II nat h- nat IIL,(Q) ~ 0 as h ~ 0. (7)
Proof. Taking in (2) for g(x) the averaging kernel ro"( I x - y 1),
y E Q, with sufficiently small h > 0 (h is less than the distance be-
tween y and the boundary 8Q) and applying Theorem 7, Sec. 1. 7,
Chap. II, we obtain formula (5)
(Daf)h(Y)=(-1)\al ~ f(x)n~roh(ix-yi)dx
Q
= ~ f(x) n~roh (i x- y i) dx = n~f h(Y).
Q
If Q' ~ Q, there exists a h 0 > 0 such that when h :::;;; h 0 formula (5)
holds for all y E Q'. If f(x) has compact support (in this case nat
also has compact support and belongs to L 2 (Q)), again there is a
h 0 > 0 such that when h:::;;; h 0 formula (5) holds for all y E Q. There-
fore relations (6) and (7) follow from Theorem 5, Sec. 2.3.
Corollary. If all the first-order g.d. of a function f are zero, then
f = const.
In fact, in a subregion Q' ~ Q Ux.h l
= 0, i = 1, ... , n, for
sufficiently small h. By (5), (fh)x.l = 0, i = 1, ... , n, that is,
fh = const = c (h) in Q' for such h. Since II fh - f IIL2(Q') =
= II c(h)- f IIL2(Q') ~ 0 ash~ 0 (Theorem 5, Sec. 2.3), it follows that
II c (h1) - c (h 2 ) IIL2(Q') = I c (h 1) - c (h 2 ) I VTQ'T ~ 0 as h 1 , h 2 -+
~ 0. Consequently, c(h) = fh converges uniformly in Q' (and more
so in L 2 (Q')) to some constant, that is, f = const, in Q', and there-
fore also in Q.
8*
116 PARTIAL DIFFERENTIAL EQUATIONS
By means of Lemma 1 the following criterion for the existence of
generalized derivative of f E L 2 (Q) is established.
Theorem 1. For the existence of g.d. nat of a function f E L 2 (Q) it
is necessary and sufficient that for any subregion Q' ~ Q there exist
constants C(Q') and h 0 (Q') such that II nath IIL2 (Q') ~ C (Q') for
all h < h 0 (Q').
Proof. The necessity has been proved in Lemma 1.
Sufficiency. Consider a system of regions Q1 ~ Q2 ~ ~
~ Qm ~ ... ~ Q such that any point x E Q belongs to some Qi
(and therefore to all Qj. j > i). Since for h < ho (Ql) II nath IIL2(Q1) ~
~ C(Q 1), the set {nath} is weakly compact for such h (Theo-
rem 3, Sec. 3.8, Chap. II). Therefore a sequence of values of h,
h 1 , 1 , . . . , h 1 , '" t 0 as k-+ oo, can be found such that the
sequence of functions nath 1 , k' k = 1, 2, ... , converges weakly in
L 2 (Q 1 ). Similarly, from the sequence h 1 , k k = 1, 2, ... , one may
choose a subsequence h 2 , k k = 1, 2, ... such that the sequence of
functions najh 2 , k' k = 1, 2, ... , converges weakly in L 2 (Q 2 );
and the weak limit of this sequence in Q1 coincides, of course, with
the weak limit of the sequence nathl, k k = 1, 2, ... , and so forth.
The diagonal sequence nathk, k' k = 1, 2, ... , converges weakly to
some function ro(x) E L 2 , Joc(Q) in the space L 2 (Qi) for any i =
= 1, 2, .... Then for any Q' ~ Q nathh, k converges weakly to w
in L 2 (Q').
Consider an arbitrary function g E CJa.J (Q), and let Q' be the
region beyond which g(x) = 0, Q' ~ Q. For all k = 1, 2, ... , we
have
) Dafhk,kgdx=(-1)iat) fhk,knagdx,
Q Q
where the integration is, in fact, not over entire Q but over Q'. Since
the sequence nafhk, k' k = 1, 2, ... , converges weakly in L 2 (Q') to
the function w and the sequence hk, k' k = 1, 2, ... , converges
strongly (and therefore also weakly) to the function/, we may pass
to the limit as k-+ oo in the last identity:
) wg dx = ( -1)1aJ ) tnag dx.
Q Q
This means that f has generalized derivative nat equal to the func-
tion ro. I
3. Existence of Generalized Derivative in the Union of Regions.
As noted in Subsec. 1, if nat is g.d. of a function fin Q, then it is
g.d. of this function in any subregion Q' c Q also. In the present
subsection we shall prove the following assertion.
FUNCTION SPACES 117
Theorem' 2. If a junction f has g.d. Da.j in regions Q 1 and Q 2 and
if Q 1 U Q 2 = Q is also a region (that is, a connected set), then g.d.
Da.j exists in Q.
Proof. Take an arbitrary point x E Q. Let Sp(x) be the ball of
radius p > 0 with centre at x, and let p1 = min I x - y I, p2 =
yEoQ,
= min I x - y I If x E Q 1 ""'Q 2 , then Sp,J 2 (x) ~ Q 1 , while if
YECIQo
X E Qz""-Ql, then Sr./2(x) ~ Qz; however, if X E Ql n Q2 and
p = min (p 1 , p2 ), then Sr/ 2 (x) ~ Q1 and SpJ 2 (x) ~ Q 2
Let all the points of Q be divided into two classes: the first class
contains all the points of QI""' Q2 and those points of QI n Q2 for
which PI< p2 , p = PI and the second class contains the remaining
points, that is, all the points of Q 2 ""-QI as well as those points of
Ql n Q2 for which P2 :s;; PI p = P2
In this way, Q is covered by the balls Sr12 (x): if x belongs to the
first class, then p = PI and if x belongs to the second class, then
P = P2
Let Q' be any strictly interior subregion of Q, Q' ~ Q. From the
cover of Q' by the balls Sr12 (x) one can choose a finite subcover.
A part of the balls of this subcover having centres at the points of
the first class constitutes an open set Q; ~ Q 1 , while the remaining
ones constitute an open set Q; ~ Q2. Thus for Q' there are two open
sets Q; and Q; having the following prcJperties: (a) Qi, i = 1, 2, is
the sum of a finite number of balls, (b) Q' belongs to the region
Q; U Q; and Q~ ~ QI, Q; ~ Q2. Since g.d. Dr:r.j exists in Q 1 and Q2 ,
by Theorem 1 there are constants C(Q;), C(Q;), h 0 (Q;) and ,h 0 (Q;)
such that for h < h 0 = min (h 0 (Q;), ho(Q;)), II Da.fh IIL.<Qi> :s;;
:s;; C(Q;), II Da.fh IIL.cQ2l :s;; C(Q;), where h is the averaging func-
tion for f in Q. Hence
II Dajh iiLQ') :s;; II Dafh IILQ{) +II nath11L<Q2) :s;; cf (Q;)
+q (Q;) = Cz (Q')
for all h < h 0 Therefore, by Theorem 1, the function f has g.d.
Daj of ath order in Q that coincides, of course, with Dr:r.j in QI and
Q2. I
4. A Connection Between Generalized Derivatives and Finite-
Difference Ratios. Let f(x) have compact support in Q and belong
to L 2 (Q). We extend this function outside Q by assigning to it the
value zero and consider for h =1= 0 the difference ratio
{j~j(x)= f(xll ... , xlt-l x~t+h~ Xk+I , Xn)-f(x), (8)
k = 1, ... , n. Clearly, for all h =I= 0, 6~/(x) E L 2 (Q). If the func-
tion g(x) E L 2 (Q) (and is extended as being equal to zero outside
118 PARTIAL DIFFERENTIAL EQUATIONS
Q), then for sufficiently small I h I (less than the distance between
the boundaries of Q and Q', outside which I = 0) the formula of
"integration by parts" holds:
(6~1, g)L2 (Q)
=!) Q
(/(xt, ... , xll-1 xll + h, xll+ 1, .. , Xn)- l(x)) g(x) dx
Q
Theorem 3. Let the function f(x) with compact support in Q belong
to L 2 (Q).
(a) I I g .d. I xh. exists for some k = 1, ... , n, then for all sufficient-
ly small I h I, h =I= 0, II 6~/ IlL. (Q) ~ II I xll IlL. (Q) and
116~/- fxlli!L.<Ql -o as h - 0. (10)
(b) If there is a constant C > 0 such that for all sufficiently small
I h I, h =I= 0, II
6~/ IlL. (Q) ~ C, then the function f has g.d. fxh in Q,
and the inequality II f xh IIL,(Ql ~ C as well as relation (10) hold.
Proof of (a). Suppose first f E Ct(Q). With no loss of generality
xn+n
one can take k=n. Then {j~f=h
1 \
j
at(x' s)
as'n n dn, where, as usual,
xn
x' = (x 1 , , Xn-t). Therefore (suppose h > 0, for definiteness)
xn+n xn+n
I {j~f(x) 12-< ;2 ( J I at(~~~ sn) Idn r-< ! ~ I rat(~~~ Sn) 12 dn,
xn xn
whence it follows that
+fJ I6nf(x)
n ,
12 dx n . . . .- __!:_h Y'J ' dx nxnt
~ J
I at(x',
8n
~n) 12 dt::n = +fJ I at(x'.OXnxn) 12 dx n
-oo -00 -00
Integration with respect to x' E Rn-i yields
(11)
Further,
xn+h
6~/(x)-fxn(x)=! J
xn
iJf(x', Xn) ) d't
iJ Xn 'on
Hence
+oo
J(c5~/(x)- fxn(x)) dxn
-oo
2
= ! I d1]
h
0
r(
+oo
-oo
iJf(x' ~=: + 1]) - of (~:n Xn) ) 2 dxn.
Integrating with respect to x' E Rn_ 1 , we have
h
II c5nf-
h
I Xn 112L,(Q)-..::::
::;:: _!_ rd r(
h J 1} j
iJf(x'' Xn +11)
iJXn
aj(x', Xn) ) 2 d
iJXn X. (12)
0 Q
Inequalities (11) and (12) established for the time being only for
functions f E C1 (Q) are also true for functions in L 2 (Q) having com-
pact support and g.d. f xn in Q. To show this, it suffices to approxi-
mate f(x) by its averaging function with a sufficiently small aver-
aging radius p, use for this last function inequalities (11) and (12)
(the averaging function has compact support in Q) and then take
the limit as p--+ 0.
Thus the first inequality in (a), coinciding with (11), is proved.
To prove relation (10), we apply the theorem on continuity in the
mean (square) of functions belonging to L 2 (Q) (Theorem 4, Sec. 2.2),
which implies that for a given e > 0 a c5 = c5(e) can be found such
that
r ( iJf(x', Xn + tj) _ iJf(x', Xn) ) 2 dx <,_ g2
J &n &n
Q
whenever Ill I :::.:;; I h I :::.:;; c5. Therefore (12) yields the inequality
jic5~/- fxniiL<Q>:::.:;; e 2 whenever I h I< c5. This proves Propo-
sition (a).
Proof of (b). By Theorem 3, Sec. 3.8, Chap. II, the set {c5~/} with
small I h I is weakly compact in L 2 (Q). Accordingly, a sequence
120 PARTIAL DIFFERENTIAL EQUATIONS
6~ /, p = 1, 2, ... , hp-+- 0 asp-+- oo, can be chosen that con-
vci-ges weakly to some function w E L 2 (Q); moreover, II w IIL.(Q) ~ C.
Further, in view of (9), (6~Pf, g)L,(Q) = - (/, 6h_hPg)L,(Q) for any
g(x) E Ct(Q). When p-+- oo, the left side of this identity tends to
(w, g) and the right side, by Lebesgue theorem, to -(/, gxk). There-
fore g.d. fxk exists and fxk = w. I
In the sequel the following proposition will also be used.
Let Q be a simply connected region in Rn which contains the ori-
gin and is symmetrical with respect to the plane Xn = 0 (that is,
if x = (x', Xn) belongs to Q, then (x', -xn) also belongs to Q), and
let 6 > 0 be a small number so that Q6 is a region. We denote
Q+ = Q n {Xn >
0}, Q- = Q n {Xn < 0},
(Q6)+ = Q6 n {xn > 0}.
Theorem 4. Let f(x) E L 2 (Q+) and f(x) = 0 in Q+"'-(Q6)+.
(a) If for some k < n g.d. fxk exists in Q+, then for all sufficiently
small I h I, h =F 0,
and
(10')
(b) If there is a constant C > 0 such that for all sufficiently small
I h I, h =F 0, II 6~/ IIL,(Q+)-<C, k < n, then g.d. fxk exists in Q+,
and II fxk IIL.(Q+) ~ C and relation (10') holds.
In Q we defme a function F(x) as follows: F(x) = f(x) in Q+ and
F(x) = f (x', -xn) in Q-. Clearly, FE L 2 (Q) and F(x) = 0 outside
Qc5. Moreover, II 6~FIIL<o> = 2 II 6~/ lll.<o+> k < n, o < I h I< 6.
Proof of (a). Suppose that the function f has g.d. fxk in Q+. We
shall first show that the function F has g.d. Fxk in Q. In fact, con-
sider an arbitrary function g(x) E C1 (Q) and with any 6 > 0 the
even function S6(xn) E C1( - oo, +
oo), S6(-xn) = S6(xn), sat-
isfying the inequality I S6(xn) I ~ 1 for all Xn, and equal to 1
when Xn :;;> 6 and to zero when 0 ~ x, ~ 6/2.
The equality
J F(x) gxk(x) S6(xn) dx
Q
= 1f(x)gxk(x)\;6(xn)dx +) f(x', -Xn)gxk(x)\;o(xn)dx
Q+ Q-
=) f(x) a!h. (S6(Xn) (g (:z.l, Xn) + g(x', - Xn)]) dx
Q+
FUNCTION SPACES 121
and definition of g.d. of I in Q+ (the function so(xn) (g(x', Xn) +
+ g(x', -xn)) E C1 (Q+)) imply
Q
Q+
Q+ Q-
Letting here 6-+ 0, by Lebesgue theorem we find that the func-
tion which is equal to fxk(x) in Q+ and to fxk (x', -xn) in Q-
is g.d. Fxk in Q of F, and II Fxk IIL<Q) = 2/1 fxk lli.<Q+)
By Theorem 3, II6~F IIL,(Q)-< II F xk i/L,(Q), therefore /16~/ lli.<Q+) =
= ; JI6~F lli.(Q)-< ; Jl F xk /Jl,(Q) =/Ifxk //L,(Q+). Since II 6~F- F xk lii.<Q) =
= ; II 6~/- f xk lii.<Q+) and II 6~F -- F xk //L,(Q)-+ 0 as h-+ 0, we find
that II 6~!-fxki/L,(Q+)-+0 as h-+0. This proves Proposition (a).
Proof of (b). Suppose that II 6:VIIL,(Q+)-<C, k < n, for all suf-
ficiently small I h I, h =I= 0. Then for all such h II 6~F lll.<Q) ~
~ 2C 2 By Theorem 3, g.d. Fxk exists in Q and II Fxk lll,(Q) ~
~ 2 C2 , which means that g.d. fxk exists in Q+ and II fxk lli.<Q+) ~
~ C2 and (10') holds. 1
4. SPACES Hk(Q)
1. Linear Space H~ocUJ). Hilbert Space Hk(Q). The set of func-
tions belonging to L2, Joc(Q) and having all generalized derivatives
up to order k, k :> 1, (belonging to L 2 , Joc(Q)) will be denoted by
H~oc(Q). By Hk(Q) we shall denote a subset of Htoc(Q) whose ele-
ments belong to L 2 (Q) together with all the generalized derivatives
up to order k. When k = 0, Hfoc(Q) and Hk(Q) will mean Lz, Joc(Q}
and L 2 (Q), respectively: Hfoc(Q) = L2,Ioc(Q), H 0 (Q) = L 2 (Q).
It is clear that Htoc(Q) and Hk(Q) are linear spaces. Let us show
that Hk(Q) is a Hilbert space with the scalar product
(f, g)Hk(Q) = ~ JDafDa:-g dx. (1)
trxl~k Q
1.22 PARTIAL DIFFERENTIAL EQUATIONS
in the norm
generated by scalar product (1).
Let fm, m = 1, 2, ... , be a sequence of elements of Hk(Q) that
is fundamental in the norm (2):
/lfs-fml/~k(Q)= ~ \ IDafs-Dafml 2 dx-rO as m., S-roo.
ial""k Q
Then for any a, Ia I~ k, when m, s -r oo
) !Da/ 8 -Dafml 2 dx-r0, (3)
Q
and, in particular (when a = 0),
Q
'Since L 2 (Q) is complete, (4) implies the existence of a function
j E L 2 (Q) to which the sequence fm, m = 1, 2, ... , converges (in
L 2 (Q)), and (3) implies the existence, for any a, I a I ~ k, of a
function r E L 2 (Q) to which the sequence Dafm, m = 1, 2, ... ,
converges (in L 2 (Q)).
Since each of the functions fm(x) has all generalized derivatives
up to order k belonging to L 2 (Q), it follows that for any a, I a I ~ k,
Um, Dag)L 2 (Q) = ( -1)lal (Dafm, g)L2 (Q)
for any g E (;k(Q). Letting m -r oo in this identity (strong conver-
gence implies weak convergence), we find that the function f is
ath g.d. of f. So f E Hk(Q) and II fm - f IIHk(Q) -r 0 as m -roo,
which proves the statement.
Remark. Sometimes it becomes convenient to consider the set of
all real-valued functions belonging to Jlk(Q), k = 0, 1, ...
(H 0 (Q) = L 2 (Q)). This set is, of course, a (real) Hilbert space with
the scalar product (1). It will be referred to as the real Hk(Q)
-space and the same notation will be used for it.
Let us note some of the properties of spaces Hk(Q).
1. If the region Q' c Q and f E Hk(Q), then f E Hk(Q').
2. If f (Hk(Q) and a(x) E Ck(Q), then af E Hk (Q). In this case
any generalized derivative Da(af), I a I ::( k, is computed accord-
FUNCTION SPACES 123
ing to the usual rule of differentiating the product of functions.
In particular, (af)x. = ax.f + afx., i = 1, ... , n.
3. If f E Hk(Q) and' fh(x)
' is the' averaging function for /, then
for any subregion Q', Q' ~ Q, II h - f IIHk(Q')-+ 0 ash-+ 0. If, in
addition, the function f has compact support in Q, then
11 /, - f IIHk(Ql -+ 0 as h-+ 0.
4. If f E Hk(Q) and has compact support in Q, then a function
equal to f in Q and to zero outside Q belongs to Hk(Q') for any
Q', Q' ::::>Q.
Properties 1-4 are a direct consequence of the definition of spaces
Hk(Q) and the properties of generalized derivatives.
5. Let the transformation y = y(x) (y, = Yi(x 1 , , Xn), i =
= 1, ... , n) map one-to-one the region Q onto the region Q, and
let x = x(y) (xi = xi(y 1 , . , Yn), i = 1, ... , n) be the corres-
ponding inverse transformation. Suppose that for some k ::;> 1
Yi(x) E Ck(Q), xi (y) E Ck(Q), i = 1, ... , n. Then in order that
the function F(x) = f(y(x)), where f(y) is a function defmed in
Q, may belong to the space Hk(Q) it is necessary and sufficient that
f(y) should belong to Hk(Q). Derivatives of F(x) are calculated
according to the usual rule of differentiating a composite function.
For example, the first derivatives are given by the formulas
i = 1, ... , n. (5)
Moreover, there are constants C1 and C 2 depending on functions
Yi(x), i = 1, ... , n, such that (a) II F IIHk(Q) ~ cl II f IIHk(Q)'
(b) 11 1 IIHk<g> ~ c2 II F IIHii<Q>'
The inverse transformation x = x(y) satisfies the same conditions
as the transformation y = y(x), therefore we confine our proof to
the sufficiency part and the inequality (a).
Let k=1, and f(y)EH 1(Q). By Remark to Theorem 8, Sec. 1.8,
n
Chap. II, the function F(x) and the functions Fi(x) = ~. fv(y(x)) x
- J
i=1
ay.
X ax~' i=1, ... , n, belong to L 2 (Q). If/,(y) is the averaging
function for f (y), then the function F(h, x) = f,(y (x)) belongs
n
to Ci(Q-), an d aF(h, x ) - " '
axi - .:....l
I hyi (y (x.)) ayj
ax;, "-1 ,
t- ... , n.
j=1
Let the subregion Q' ~ Q and Q' be its image, then Q' ~ Q.
Since, as h-+ 0, II f, - f IIL.(Q) -+ 0 and II fhvi - fvi IIL.(Q') -+ 0,
124 PARTIAL DIFFERENTIAL EQUATIONS
i = 1, ... , n, by Remark to Theorem 8, Sec. 1.8, Chap. II,
II F(h, x) - F(x) I1L,(Q)--+- 0 and II Fxit(h, x) - Ft(x) IIL,(Q')--+-
--+- 0, i = 1, ... , n, ash--+- 0, for any Q' ~ Q. This means that
in the equalities (F(h, x), gxi(x))L,(Q) = - (Fx;(h, x), g(x))L,(Q)
i = 1, ... , n, where g is any function in C1(Q) (Q' is chosen so
that g = 0 in Q""-Q') one can pass to the limit as h--+- 0:
(F, gx)L,(Q) = - (F;, g)L,(Q) Therefore F has all the first gener-
alized derivatives belonging to L 2 (Q), that is, F belongs to H 1 (Q);
the relations (5) hold, and therefore inequality (a) also holds when
k=1.
Suppose now k = 2. We have already proved that F(x) E H 1 (Q)
and formulas (5) hold. By Property 2, the right-hand sides of (5),
being the function of y, belong to H 1 (Q). Then the functions Fx 1 (x)
also belong to H 1 (Q). Consequently, F E H 2 (Q) and inequality (a)
holds for k = 2. Regarding third derivatives as the derivatives of
second derivatives and so forth, we see that the assertion is true for
any k.
The following property will be used in Subsec. 2.
6. If the region Q is a rectangular parallelepiped, then C (Q) 00
(and hence Ck(Q)) is an everywhere dense set in Hk(Q).
It suffices to establish this assertion for the parallelepiped lla =
={I Xt I< a;, i = 1, ... , n}, where a == (a 1 , . , an), ai > 0,
i = 1, .... n.
Take any function f E Hk(lla) and any e > 0. Whatever be a,
0 ~ Ia I < k, the function Daf E L 2 (lla), therefore, by Theorem 2,
Sec. 2.2, there is a function C~Ja(x) E C(lla) such that II Daf -
- fPa IIL,(IIa) < e.
In the parallelepiped Daa ={I Xt I< aia, i = 1, ... , n} where
a> 1, Da ~ Daa consider the function Fa(x) = f(x/a). By Prop-
erty 4, Fa E Hk(lla 0 ), and hence Fa E Hk(lla) Since
II Da Fa(x)- fPa(x) I/L2(IIal
-<II Da Fa(x)- Cl'a(x/a) IIL,(IIaa> +II fPa (x)- fPa (x/a) 1/L.crra>
II DaFa(x) - fPa(x/a) IIL,(IIa a )
= IJ-111
aa
Daf.(xla)- fPa (x/a) I L,(IIaal -<II (1--111 ) Daf (x/a) I L,(ITaa>
aa
FUNCTION SPACES 125
it follows that
JljDcx;Fa( X)- (jlcx;(X) /IL 1 (Ilal
<;anf 2 ( 1---k-) II Dal 1/L.(ITal + anf~e + /1 (jlcx;(X)- CVa(x/a) IIL (ITa)
1
a
Therefore for any a, 0<;1 a j<;k,
ll Dal(x)- DaF a(x) IIL.(IIa>< II Dal- (jlcx; !IL.(IIa) +II D~ Fa- (jla I!L.ma>
~e(1 +anf2)+anf2 ( 1- )al) IIDafi!L.ma>+ll (jla(x)-cpa(x/a) lk.ma>
The function (jla(x) EC(fla), which means that II (jla(x)-cpa(x/a) IIL.(lla)-+
-+ 0 as a-+ 1. Therefore a a= a 0 > 1 can be found such that for
all ~a, O~j a I ~k, II Dal(x) -DaFa0 (x) IIL,<IIa><3e. Consequently,
II f-Fao lln'\na ,<;Ce.
Take now the averaging function (Fa 0 h(x) for the function
Fa 0 (x)EHk(Daa 0 ). By Property 3, /I(Fa 0 )h-Faolisllm l-+0 as h-+0,
thereby implying that a number h = h0 can be f~und such that
II (Faoh~-Fa'o llnk(II ,<;e. The function (Faoho (x) E ceo (Da) and
a
II (Faoho- I llsk(Ila) <II (Fao)ho- F ao lln'\rra)
+IIFao-lllsk(rra,<;(C+1)e. I
2. On Extension of Functions. Suppose that a function l(x) is
defined in a region Q and the region Q' contains Q. A function F(x)
defined in Q' and coinciding with l(x) in Q is called extension of
f(x) into Q'. Note first that every function l(x) has an extension.
For example, F(x) can be taken as zero in Q' ""'Q. When l(x) E
E L 2 (Q), we already used such an extension above. However, if
f(x) is a smooth function in Q, for example, IE Hk(Q) (or f E
E Ck(Q)) for some k >
1, then it is natural to seek its extension
F(x) in the class of functions that are as much smooth in Q': be-
longing to Hk(Q') (or to Ck(Q')). We shall demonstrate that under
definite conditions on the boundary of Q such extensions are possible.
Suppose first that Q' is the cube Ka with side 2a > 0, Ka =
={I Yi I< a, i = 1, ... , n} (independent variables here will be
denoted by y1 , , Yn) and Q -is the parallelepiped K~ = K a n
f1 {Yn > 0}. The extension Z(y) of a function z(y) E Ck(K~) into
K-;. = Ka n {Yn < 0} is defined as follows:
k+i
Z(y) = 2j A;z(y', - Ynli), (6)
i=1
126 PARTIAL DIFFERENTIAL EQUATIONS
where y' = (y 1 , . , Yn-1) and A 1 , . , Ak+ 1 is the solution of the
linear algebraic system of equations
h+t
2j (-1/i) 5 A;=1, S=0, . .. , k. (7}
i=1
Note that when y E K~. the points (y', - Ynli) in (6) lie in K~ for
all i = 1, ... , k +
1. The determinant (Vandermonde's determin-
ant) of the system (7) does not vanish, therefore the system (7)
has a unique solution A 1 , . , Ah+t
For any y0 = (y 0 ' ' 0) E Ka n
{Yn = 0}, the function Z(y) is
taken equal to lim z(y). Thus the function Z(y) is defined on
y .... y
yEK~
entire Ka. Since z(y) E Ck(K~), by (6) Z(y) E Ck(K~). We shall
first show that Z(y) E C(Ka).
Passing to the limit in (6) as y ~ y0 , y E K~, and taking into
account (7), we have
k+t k+1
lim Z(y) = 2j A; lim z(y) = ~ A ;Z (y 0 ) = Z(yo),
y-.yo i=1 y-.yo i=1
YEK~ y<=K~
which means that Z(y) E C(Ka)
For any vector a = (a 1 , . . , an), Ia I~ k, with integer com-
ponents, by (6) we have, for y E K~,
h+t
Da'Z(y)= ~ A;(-1/it'nDaz(y', -yn/i). (8)
i=1
Letting y ~ y 0 , y E K~. in (8), we obtain
lim DaZ(y) =lim Da.Z(y)
y-.yo y-.yo
yEK~ YEK~
for all possible a such that I a I = 1. Then at the points in the plane
Ka n{Yn = 0} all the first derivatives of Z(y) exist, and they coin-
cide with corresponding limiting values. Therefore Z(y) E C1 (Ka).
Repeating these arguments and using (7), we find that Z (y) E
E cz(Ka) for all l ~ k.
For any a, I a I ~ k, the relation (8) yields, for all y E K;.,
h+i k+t
I DaZ(y) 12 <: ~ Af . 2~ ~ I Daz(y', - Ynli) 12
i=1 ' n i=1
h+t
=Co~ I Daz(y', - Ynli) j2
i=1
Integration with respect to y EK~ gives
k+1
) I Daz 12 dy<Co ~ ~ I Daz (y', -yn/i) 12 dy
K~ i=1 K~
k+i
=C 0 ~ i ~ 1Daz(y)! 2 dy<C' j JDaz(y)l 2 dy.
i=i x~n<Yn<afi) K~
Since Z(y) = z(y) when y E K~, it follows that
~ I DaZ(y) 12 dy = I I DaZ(y) 12 dy +J I DaZ(y) 12 dy
Ka K~ K~
. ~C" j I Daz(y) J2 dy ..
K~
Summing these inequalities over all a, Ia I~ k, we obtain the
inequality
(9)
where the constant C1 > 0 does not depend on the function z(y).
Thus an extension Z(y) E Ck(Ka) has been obtained for the func-
tion z(y) E Ck(.Kiz) and for this extension inequality (9) holds.
Suppose now that the function z(y) E Hk(K~). By Property 6 of
the previous subsection, there is a sequence z8 (y), s = 1, 2, ... , of
functions in Ck(K~) converging to z(y) in the norm Hk(K~):
II Z 8 - z IIHk<d>-+ 0 as s-+ oo. Denote by Zs (y) the extension of
Zs(Y) into Ka obtained in abovementioned manner, Z 8 (y) E Ck(Ka).
From (9) follows the inequality II Zs- Zp IIHk(Ka) ~ cl II Zs-Zp IIHk(K;i:)'
which shows that the sequence of functions Z 8 , s = 1, 2, ... , is
fundamental in the norm Hk(Ka) This means that there is a func-
tion Z(y) E Hk(Ka) to which this sequence conYerges in the norm
Hk(Ka) Since Z(y) = z(y) for y E K~, the function Z(y) is an
extension into Ka of the function z(y). The function Z(y) clearly
sa tisf1es inequality (9).
Thus the following result has been established.
Lemma 1. For any function z(y) E Hk(K~) (Ck(K~)) there is an
extension Z(y) E Hk(Ka) (Ck(Ka)), and inequality (9) holds.
Note that since equalities (6) hold for Z 8 (y), s = 1, 2, ... , and
Z 8 -+ z in Hk(K~) and z .. -+ Z in Hk(K;), it follows that this equal-
ity also holds for Z(y).
Lemma 2. Suppose that the function f(x) E Hk(Q) (or Ck(Q))
and for any point ~ E a Q there is a function F;(x) defined in the ball
128 PARTIAL DIFFERENTIAL EQUATIONS
Sr() ={I x - ; I< r} oj radius r = r(;) > 0 such that F;(x) =
= n
f(x) for X E Q Sr() and F,(x) E Hk(Sr(S)) (Ck(Sr())) (the
junction F~(x) will be referred to as the extension of f(x) into the ball
Sr()). Suppose further that inequality
1: Fr. 11Hk(Sr<w-<C211 f llHk(Q)' (10)
v:here the constant C 2 does not depend on f(x), holds.
Then for any p > 0 there is an extension F(x) into the region QP*
<Jf the function f(x) having the properties: F(x) E Hk(QP) (Ck(QP)),
F(x) = 0 outside QP12 , there is a constant C 3 > 0 depending only on
Q and the number p such that
II F llHk(QP)~Call f IIHk(Q)" (11)
Proof. According to the hypothesis, for any point E Q there
~xists a ball S7 ( ; ) , r = r(;), in which either the function f (x) E
E Hk(S 7 ( ; ) ) (Ck(r (S))) itself is defined if E Q or else its exten-
sion of the same class. Assume that r() < p. The aggregate of
balls S 7 ; 3 () for all possible ; E Q covers the set Q; accordingly
{recall that the region Q is bounded), from thi~ cover a finite sub-
~over S 7 ,;a(x1), , SrN; 3 (xN), where ri = r(xt), can be chosen.
Let the function Si(x) E Coo(~n), Si(x) = 1 in S r 1ta(x;) and
ei(x) = 0 outside the ball s T/2(x\),l
i = 1, ... , N. We denote by
ai(x) the function 1 - Si(x), i = 1, ... , N, and construct the
functions
1' 1(x) = 8 1(x), "1'2(x) = a 1 (x) 82 (x), ... ,
"r'i(x) = a 1(x) ... ai_ 1 (x) Si(x), i<: N.
It is clear that yj(x) E Coo(Rn),
"r'i(x) = 0 in U Sr .fa(xj) (12)
J<i J
and
(13)
Further,
y 1 (x) + ... +'Vi (x) = (1-a 1 (x)) +a 1 (x) (1-a2 (x))
+ ... +ai (x) ... ai-t (x) (1-ai (x)) = 1-a1 (x) ... a; (x),
therefore
"r't (x) + ... + '\'i (x) = 1 (14)
for xE U S 7 .; 3 (xJ), and, in particular, for xESr.;a (xi).
J<:;i J '
* QP is the union over all x 0 E Q of the halls {I x - x 0 I < p }.
FUNCTION SPACES 129
We defme functions /i (.li), i = 1, ... , N, for all x ERn in the
following manner: in Sr.l (x') the function. / 1 (x) coincides with
either
f (x) or its extension Fxi (x) into Sr. (x'), outside Sr. (x') the func-
' I
tion /1 (x) = f (x) if x E Q or / 1 (x) = 0 if x Ef Q.
By (13) and Properties 2 and 4 of the preceding subsection, the
function "Vi (x) fi (x) E Hk (QP) (Ck (t)P)). Therefore the function
N
F (x) = 2j / 1 (x) "Vi (x) (15)
i=1
belongs to Hk (QP) (Ck (QP)).
Let x be a point of Q and Sr 1; 3 (x 1) the first hall of the chosen finite
subcover containing this point. As f 1 (x) = f (x) for all i = 1, ... , N
l
and by (12) "Vi (x) f (x) = 0 when i > l, so F (x) = ~ "Vi (x) f (x) =
i=1
= f (x) in view of (14). This means that the function F (x) given
by (15) is an extension off (x). The relation F (x) =
0 outside QP12
is a consequence of (13) and (15), because r 1 < p, i = 1, ... , N.
Inequality (11) readily follows from (10) and (15). I
Theorem 1 (on extension). Let Q and Q' be bounded regions, Q ~
~ Q', and 8Q E Ck. Then any function f (x) E Hk (Q) (Ck (Q)) has an
extension F (x) EHk (Q') (Ck (Q')) into Q' with compact support.
Moreover,
(16)
where the constant C >0 depends only on Q and Q'.
s
Proof. Take an arbitrary point E 8Q. In some neighbourhood Ua
of this point the equation of 8Q can be expressed (if necessary, by
redesignating the variables) in the form Xn = <p (x 1, ... , Xn _1)
with <p (xl, ... , Xn-1) E ck (D), where (n- 1)-dimensional region
D is the projection of 8Q n Ua onto the plane Xn = 0. It is assumed
that Xn > <p in Q n Ua. The change of variables
y;=x 1 - 1 , i=1, .. ,n-1, Yn=Xn-<p(x 1 , vXn-1) (17)
maps Ua one-to-one onto some neighbourhood Q of the origin which is
expressed in terms of the variables y 1 , , Yn Let Ka be the cube
{I y 1 I< a, i = 1, ... , n} lying in Q and V~ its original under the
transformation (17). The image of Q n Vi, is then the parallelepiped
K~ = Ka n {Yn > 0} and the function I (x) defined in Q n Vi, be-
comes the function z (y) = f (Y 1 +s
1, ... , Yn-1 +
Sn-1 Yn +
+ +
+ <p (yl St, ., Yn- 1 Sn-1)) belonging to Hk (K~) (Ck (1(~)),
by Property 5 of the preceding subsection.
9-0594
130 PARTIAL DIFFERENTIAL EQUATIONS
By Lemma 1, there is an extension Z (y) of z (y) into the cube Ka.
By the inverse transformation of (17)
Xi=Yi+Si> i=1, ... , n-1, Xn=Yn+<p(yt+St, .. , Yn-t+Sn-t)
this extension generates extension F~ (x) of f (x) from Q Vi into n
Vi, and, more so, into the ball Sr (s), contained in Vi, of radius r =
= r (s) > 0 with centre at the point . :Moreover (see Property 5.
Subsec. 1),
II F ~ 1/Hk<Sr<m-< II FsiiHk<Ui>-< c311 z IIHk(Ka)'
II z IIHk<x+a >-< C~oll f IIHk<u~ nQ>-< C~o II f IIHk<Q>'
~
where the constants C 3 and C,. depend only on the function <p (x1 ,
. . . , Xn_ 1 ) from (17) and its derivatives up to order k. These ine-
qualities and (9) imply (10). The conclusion of the theorem now fol-
lows from Lemma 2 if p is taken less than the distance between the
boundaries 8Q and 8Q' of Q and Q'. I
Remark. The extension F (x) into Q' of the function f (x) belong-
ing to Hk (Q), obtained in the above proof, satisfies not only the
inequality (16) but also the inequalities
II F IIH"(Q')-<: C !If IIHs(Q)
for all s ~ k.
So far the functions were extended from a given region into some
wider region. In the sequel we shall have to use the smooth extension
of a function from the boundary.
Suppose that a continuous function f (x) is defined on the bound-
ary 8Q of the region Q. A function F (x) continuous in Q is called
extension into Q of the function f (x) if for all x E 8Q F(x) = f (x).
The following result holds.
Theorem 2. If the boundary 8Q E Ck for some k 1, then any>
function f (x) E c~t (8Q) has an extension F (x) into Q which belongs
to Ck (Q). Moreover,
II F llck(Q>-< C II f lick(aQ>'
where the constant C > 0 does not depend on f.
Proof. Since 8Q E Ck, for any point s E 8Q there is a number p =
= p (s) > 0 such that a portion of the boundary 8Q n Sp (s)
(Sp (s) denotes the ball with radius p and centre at the point s) is
uniquely projected into a region D 6 in some coordinate plane, the
plane Xn = 0, say, (it can be always achieved by redesignating the
variables) and let the equation of the surface 8Q n Sp (s) have the
form Xn = <p (x'), x' E D6, where <p (x') E ck (D-s)
Choose a sufficiently small number r = r (s} > 0 so that the
s'
(n-1)-dimensional ball {I x'- I< r} ~ D~. Then the function
FUNCTION SPACES 131
F~ (x) = f (x', qJ (x')) (independent of Xn) of n variables is defined
on the closed ball S 7 (),belongs to ell. (Sr ()) and coincides with f
on aQ nSr (). Moreover II Fdci!.(Sr(s))<e ()II f llcl!.(iJQ)' where the
constant e () does not depend on f.
The set of balls S713 () covers the boundary oQ for all E oQ.
From this set we choose a finite c~ver of the boundary Sr,/ 3 (x1),
. . , SrN/ 3 (xN), where r 1 = r (x')~
For any i = 1, ... , N, we define the function f 1 (x) as follows:
in the ball Sr. (xi) take it equal to Fxi (x), outside Sr. (xi) take it
equal to zero if' X~ oQ and equal to f (x) if X E oQ. Then' for all i =
= 1, ... , N the functions f; (x) y; (x), where y 1 (x) is the function
constructed in the proof of Lemma 2, belong to e11. (Rn), and hence
to e11. (Q). Hence the function
N
F (x) = ~ y 1 (x) f 1 (x)
i=1
also belongs to ell. (Q).
Take an arbitrary x E oQ and assume that Sr 113 (x1) is the first
ball of the selected finite cover of the boundary containing this
point. Since for all i = 1, ... , N f 1 (x) = f (x), relations (12) and
l
(14) imply that F (x) = 21 'Vi (x) f (x)
i=1
= f (x). Thus the function
F (x) belonging to ell. (Q) is an extension of f (x). The desired esti-
mate is a consequence of corresponding inequalities for the functions
Fxi (x). I
3. Denseness of Coo (q) in HI!. ( Q). Spaces HI!.( Q). Let the boundary
oQ of Q belong to the class ell..
Theorem 3. The set of functions eoo(Q) (and hence e11.(Q)) is every-
where dense in the space HI!. (Q).
Proof. Consider any region Q' for which Q is strictly interior,
Q ~ Q'. Let f (x) be any function belonging to HI!. (Q). By Theorem 1
of the preceding subsection, there is an extension F (x) belonging to
HI!. (Q') off (x) from Q into Q'. By Property 3 (Subsec. 1), -
il F h - f IIHI!.(Q) = II F h - F l1H11.(Q) -
0 as h- 0,
where Fh (x) is the averaging function for F (x). Since Fh (x) E
E Coo (Q), the conclusion of the theorem follows.
The set Cl!. (Q) is a linear manifold in HI!. (Q). From Theorem 3 it
follows that if the boundary oQ E C11 ' then the closure of the set
Ck (Q) in the norm HI!. (Q) coincides with HI!. (Q).
Let S be an (n - i)-dimensional surface lying in Q. The subset
c~ (Q) of functions belonging to ell. (Q) that vanish on the intersec-
9
132 PARTIAL DIFFERENTIAL EQUATIONS
tion of Q with some neighbourhood of S (every function has its own
neighbourhood) is also a linear manifold in H" (Q). The closure of
C~ ({j) in the norm of Hk (Q) is a subspace of H" (Q); this will be de-
"k
noted by Hs (Q).
k
(Q) will be denoted by H k (Q)
0 0
When S = 8Q, the subspace HaQ
(the norm in ifk (Q) is the norm of Hk (Q)). Theorem 6, Sec. 2.3,
implies that for k = 0 the subspace fik (Q) = ifo (Q) coincides with
the space H 0 (Q) = L 2 (Q). In Subsec. 1 of the next section it will
be shown that fik (Q) does not coincide with H" (Q) when k 1. >
If the region Q is contained in Q', Q c Q', then any function
f (x) in ck
(Q) extended as being equal to zero in Q' ""- Q belongs to
Ck (Q'). Therefore from the definition of ifk it follows that the func-
tion f (x) belonging to fik (Q) and extended as being equal to zero
into Q' "'- Q belongs to fik (~').
4. Separability of Space H (Q). It is assumed that the boundary
iJQ of Q belongs to the class ck.
Theorem 4. The space Hk (Q) is separable.
Proof. Consider first the cube K = {I xi I < n, i = 1, ... , n }.
The countable system of functions (2ntnf 2ei(m, x), where m =
= (m1 , , mn), mi = 0, +1, +2, ... , i = 1, ... , n, (m, x) =
= m 1x 1 + ... +
mnXn, is orthonormal in L 2 (K). Any function
f (x) E L 2 (K) has a Fourier series expansion
00
1 "" f ei(m, x) = 1 "" ")1 f ei(m, X) (18)
(2:n:)n/2 LJ m (2:rt)n/2 LJ ~ m '
m s=O s~lml<s+i
(f (x) ei(m, x))
where fm = ' 2
12 L (K) are Fourier coefficients of f (x) and
(2:rt)n
I m 12 = mi + ... + m~.
f (x) EC"" (K). First note that for all m
Let
I fm 1-< (2;c)n12 ll f llc(K) =Co. (19)
Put m' = (m 1, ... , mn- 1). x' = (x 1, ... , Xn-t), K' = {I xi[< n,
i=1, ... ,n--1}cRn-t If mn=/=0, then
f
m
= 1
(2:rt)n/2
j' f (x) ei(m, x) dx
K ~
= Jr ei(m',x')dx' ( Jr f(x' ' Xn )eixnmndX n )
1
(2n)n/2
K' -~
= 1 ( - ___
1_ )p r 8Pf (x) ei(m, x) dx
(2n)n/2 lmn ~ ax~
FUNCTION SPACES 133
for any natural p, whence it follows that I fm I< (Z:n:)n;~~~~~cPcR>
accordingly, by (19),
II I llcP(K) 2P (2:n:)n/Z c~
lfml< (i+lmni)P = (1+1mni)P
for any natural p.
Apart from this inequality, the inequalities
C'
lfml< (1+l~if)P - i=1, ... , n-1,
also hold, and therefore also the inequalities
C'
lfmJ<C~m~nC1+J 1mii)P}= (1+m_axl~ii)P" (20)
Since m~x I mi I~ v; I mI. from (20)
c~
'
Cp
(21)
I fm I< ( 1
)P < (1+1 m I)P
1+Vn!ml 1
true for all m and any natural p. Take p = n 2. The number of +
terms in the summation ~ f mei(m, x), which is equal to the
s,;jmJ<s+1
number of points m with integer coordinates in the annular region
s ~ Im I< s +
1, does not exceed the number of such points in
the cube with side 2 (s +
1), that is, does not exceed (2s 1))n. +
Therefore
I ~
Ll
f
m
ei(m, x) 1./ ~
~
LJ
If I~ cn+22n (1+s)n
m '"""' (1 +s)n+2
Cn+zzn
(1 +s)2 '
s,;Jml<s+1 s,;)m)<s+i
which means that the series (18) converges uniformly in K.
Taking p = n +
3, we find that for any r, 1 ~ r ~ n,
I ~
Ll
.
lmr me
j i(m, x) I~ Cn+32n (1 +s)n+l -
-..:::: (1+s)n+3 -
Cn+s2n
(1+s)2
s~lmi<s+l
Therefore the series obtained from (18) by termwise differentiation
with respect to Xr, r = 1, ... , n, converges uniformly inK. It can
be similarly shown that the series obtained from (18) by termwise
differentiation l times, l = 2, 3, ... , converge uniformly in K.
Denote the sum of (18) by g (x):
g (x) = (2:n:~n/2 ~ fmei(m, x).
m
134 PARTIAL DIFFERENTIAL EQUATIONS
We have shown that g (x) E C"" (K). This means that also the
function q> (x) = g (x) - f (x) E C"" (K). Let us show that q> (x) =
= 0 inK.
ei(m, x)
(
Since g (x), ) =fm, for all m
(2n)n12 L 2(K)
K
Having fixed an arbitrary m' = (m1 , . , mn _1), we write this
equality in the form
I
:rt
-:rt K'
Since the function lllm' (xn) = J
K'
q> (x'' Xn) ei(m'' x') dx'' which is
infinitely differentiable with respect to Xn, I Xn I ~ :rt, is orthogonal
in the space with the scalar product, L 2 (-:rt, :rt}, to the functions
eimnxn for all mn = 0, +1, +2, ... , it follows that for any m'
'Pm' (xn) = 0 for all Xn, I Xn I ~ :rt. Let m" = (m1, . . . , mn _2),
x" = (xl, ... , Xn-2), K" = K' n {xn-1 = 0}. For any fixed m",
any Xn, I Xn I~ :rt, and all mn_1 = 0, +1, ... , we have
0= I q> (x', Xn) ei(m' x') dx'
K'
:rt
= Jr etxn-tmn-1
r
d Xn-1 J qJ <X, , Xn-1, Xn >et< x.. ' m"> dX, ,
-:rt K"
which- implies
J q> (x", Xn-1 Xn) ei(m", xn) dx" = 0
K"
for any Xn-1 , Xn, I Xn- 1 I ~ :rt, I Xn I~ :rt and all m". Continuing in
this manner, we find that q> (x) = 0 in K.
Thus it has been established that any function f (x) E C"" (K)
has series expansion (18) that converges uniformly together with
derivatives of any order in K. Evidently, this holds for any cube
Ka = {I xi I< a, i = 1, ... , n}.
We now turn to the proof of the theorem. Take a number a> 0 so
large that Q ~ Ka. By Theorem 1, Subsec. 2, any function f (x) E
E Hk (Q) has extension F (x) E Hk (Ka) with compact support in
Ka. Any such function F (x) can be approximated, according to
Property 3, Subsec. 1, in the norm of Hk(Ka) by averaging functions
FUNCTION SPACES 135
F h (x), which are infinitely differentiable and for sufficiently small h
have compact supports in Ka.
As shown above, every function F h (x) (for sufficiently small h)
can be approximated uniformly in Ka together with all the deriva-
tives (and therefore also in the norm of Hk (Ka)) by partial sums of
its Fourier series. Consequently, any function F h (x) can be approx-
imated in the norm of Hk (Q) by a linear combination of the system
.:rr
e' a (m, x)
with coefficients whose real and imaginary parts are ratio-
nal numbers. Thus we have constructed a countable set which is
.everywhere dense in Hk (Q). I
5. PROPERTIES OF FUNCTIONS BELONGING
0
TO H 1 (Q) AND H 1 (Q)
1. Trace of Functions. Let Q be a region in Rn and S a smooth
(n - i)-dimensional surface lying in Q. If in Q there is given a func-
tion f (x) defined at every point (that is, if the equality of functions
is understood as the equality of their values at every point), then
we can consider the value of this function on S. That is, we can con-
sider the function f ixes defined at every point of S whose values for
all x E S coincide with the value off (x). If we consider a function
defined a.e. in Q (that is, functions are considered equal if they coin-
cide a.e.), then the value off on a fixed surface S is determined not
uniquely: since mes S = 0, the function can assume any value.
Nevertheless, one can speak, in a definite sense, of values on
(n - i)-dimensional surfaces of an almost everywhere defined func-
tion as well.
For the sake of simplicity, assume that the surface S = S (xn) is
the intersection of a region Q with the plane Xn = const. Then,
according to Fubini's theorem*, for almost all Xn.the function f
has the value f ixES(xn) on S (xn) which is defined almost every-
where on S (naturally, the equality of functions of (n- i) variables
is understood as equality of their values a.e. in the sense of (n- i)-
dimensional measure). Moreover, it is apparent that for almost all
.Xn the value on S (xn) of a function continuous in Q is a continuous
function on S (xn), whereas for almost all Xn the value on S (xn) of
a function belonging to L 2 (Q) belongs to L 2 (S (xn)).
In the investigation of solutions of differential equations, condi-
tions are often prescribed which must be satisfied by the solution on
some fixed (n - i)-dimensional surface, for instance, on 8Q (the
boundary conditions). Therefore we must generalize the meaning
* More precisely, according to Lemma 4, Sec. 1.11, Chap. II.
136 PARTIAL DIFFERENTIAL EQUATIONS
of the value on an (n - i)-dimensional surface S of an a.e. defined
function-the idea of the trace of a function on S. For an a.e. defmed
function satisfying some smoothness conditions this idea can be
introduced uniquely. In particular, this is easily presented for a
continuous function in iJ
By the trace f Is of a function f E C (Q) on an (n - i)-dimensional
surface S we mean the value on this surface of a function defined at
every point and continuous in Q that coincides with f almost every-
where (that is, by the trace on S of a continuous function is meant
its value extended uniquely with respect to continuity on S). As
usual, here the equality of functions defined on S is understood as
a.e. equality in the sense of (n - i)-dimensional measure.
The notion of the trace of a function on S can also be introduced
for functions belonging to certain spaces with integral norms; in
particular, for functions in spaces Hk (Q) with k ::;;> 1. Since for
k ::;;> i all Hk (Q) are contained in H 1 (Q), it is enough to introduce
this notion for functions belonging to H 1 (Q).
LetS be a surface of class C1 (see Chap. I, Introduction) lying in
Q, and let S 1 be its simple piece that is projected uniquely onto a
region D in the plane {xn = 0} and having the equation
Xn = cp (x'), where x' = (x1 , , Xn_ 1), cp (x') E C1 (D).
The region Q is bounded, therefore it can be assumed enclosed in
a cube {0 <xi< a, i = i, ... , n} for some a> 0. Suppose first
that f (x) belongs to C1 (Q), and equate it to zero outside Q. Accord-
ing to Newton-Leibnitz formula
({l(x')
f(x)lsr=f(x', cp(x'))=
Jr 8f(x', sn)
8n
ds n
0
({l(x') a
lfls~l2-<cp(x') ) / 8/(;~nsn) /2dsn-<a JI af{;~nn) j2dsn
0 0
Multiplying this inequality by Vi + cp~1 + ... + cp;n_ 1 and
integrating over D, we obtain
II f lli.<sl) = JIf ls1l2
81
dS t -<C 2!1 f llff<Ql (i)
where the constant C > 0 does not depend on the function f.
Since the surface S can be covered by a finite number of simple
pieces, pieces of type S 1 (that possibly project onto other coordinate
FUNCTION SPACES 137
planes), we find, summing the respective inequalities (1), that
II I I!L,(S)-< c II I IIHl(Q)' (2)
where the constant C > 0 does not depend on the function f.
The inequality (2) also holds for any function f (x) E C1 (Q). To
show this, it suffices to use Theorem 1, Sec. 4.2, on extension (assum-
ing, of course, oQ E C1 ) and inequality (2) for a function belong-
ing to C 1 and having compact support.
Suppose now that f E H 1 (Q). From Theorem 3, Sec. 4.3, it
follows that there is a sequence of functions /p (x), p = 1, 2, ... ,
in C1 (Q) which converges to f in the norm of H 1 (Q). For the-
function /p - /q inequality (2) assumes the form
II /p- /q lk,<s>-<C II /p- /q IIHl(Q) (3}
Since II /p - /q IIH(Q)-+ 0 asp, q-+ oo, it follows that also
II /p - /q IIL,(S)-+ 0 asp, q-+ oo. This means that the sequence of
traces /pIs of functions /p on S is fundamental in L 2 (S). Since
L 2 (S) is complete, there is a function fs (x) E L 2 (S) to which the
sequence of traces/pIs converges asp-+ oo. Passing to the limit,
as p-+ oo, in (3), we obtain
II /q- Is IIL,(S)-<C II /q- f IJHl(Q) (4}
Let us show that the function fs (x) does not depend on the choice-
of the sequence fk (x), k = 1, 2, ... , which approximates f (x) in
the norm of H 1 (Q). Indeed, let fk (x), k = 1, 2, ... , be another
sequence of functions in C 1 (Q} for which II f - fk IIH'<Q>-+ 0 as
k-+ oo, and let f s (x) be the limit in the norm of L 2 (S) of the se-
quence fk Is , k = 1, 2, . . . . Then
II f s- fs IIL.<s>-< II f s-fq lk.<s> + II f q -fq 1/L.<s> + IJfq -fs lk.<s>
-<C ( Jl / - /q 1/Hl(Q) +II /q -fq IIHl(Q) + llfq-fs IIHl(Q))~
by the inequalities (3) and (4). Since, when q-+ oo, the right-hand
side of the last inequality tends to zero, we have Is = fs.
The function fs (x) (as an element of L 2 (S)) will be called the
trace of the function f (x) E H 1 (Q) on the surface S and will be denoted
by f Is (II f Is IIL.<S> will be denoted by II f IIL,(S))
Thus the trace of a function is defined for any element f E H 1 (Q).
We now show that the notion of the trace is, in fact, a generaliza-
tion of the notion of the value of a function on an (n-1)-dimension-
al surface. Assume for the sake of simplicity that S = S (xn) is
the intersection of the region Q with the plane Xn = const, and that
the function f E H 1 (Q). Consider a sequence of functions fm (x), m =
= 1, 2, ... , in C1 (Q) which converges to f in the norm of H 1 (Q).
By definition, the trace f ls<xn> for each Xn is the limit in L 2 (S (.r n)}
138 PARTIAL DIFFERENTIAL EQUATIONS
{)f the sequence of functions fml S(x n l Since the sequence fm, m =
= i, 2, ... , converges in L 2 (Q) to f, a subsequence fmk' k = i, ... ,
can be chosen, in view of Remark to Theorem i, Sec. 2.i, that con-
verges to f a.e. in Q. This means that for almost all Xn the sequence
fmk ls<xnl' k = i, 2, ... , converges to the value of f on S (xn)
almost everywhere in the sense of (n - i)-dimensional measure.
Consequently, the trace and value off on S (xn) coincide for almost
all Xn.
Thus we have the notions of the trace on S of a function continuous
in Q and that of a function belonging to H 1 (Q). It is claimed that if
.a function f belongs to C (Q) and to H 1 (Q}, then its trace as the trace
{)f a function in C (Q) (denoted by f Is) and that of a function in
H 1 (Q) (denoted by f Is) coincide. In fact, the function f can be extend-
ed, by Theorem i, Sec. 4.2, into Q', Q ~ Q', in such a way that
its extension F will belong to C (Q1 ) and to H 1 (Q'). Consider the
averaging functions Fh (x) for the function F. Since Fh-+ F ash-+
--+ 0 in both the norms of C (Q) (see Sec. 1.i) and H 1 (Q) (see Sec. 4.i,
Property 3), we find that, ash-+ 0, Fh(x) Is-+ f Is in the norm of
C (S) and F h (x) Is-+ f Is in the norm of L 2 (S); accordingly,
tIs= f Is
The trace f Is of a function f (x) E H~ (Q) (the definition of this
space is given in Sec. 4.3) is zero, since the function f Is is the limit
in the norm of L 2 (S) of functions vanishing on S (of traces on S of
functions in C~ (Q)). In particular, the trace f laQ of a function
j (x) E H1 (Q) is zero. By the way, this establishes the assertion of
Subsec. 3 of. the preceding section which states that Hk (Q) =I= Jik (Q)
fork::;:? i: the function equal to i belonging to any Hk (Q), k::;:? i, is
continuous in Q, therefore its trace on oQ is i; hence this function
does not belong to ifk (Q) for any k ::;:? 1.
The trace f Is of a function f E H 1 (Q) satisfies the inequality (2).
To establish this, it is enough to pass to the limit, asp-+ oo, in the
inequality (2) written for the functions fp (x) (fp (x) E C1 (Q), II fp-
- f II Hl (Ql -+ 0 as p -+ oo) .
. It was assumed so far that the boundary oQ E C1 However, when
S ~ Q, for the definition of the trace on S of a function and the
proof of inequality (2) this restriction can be done away with. In-
deed, in this case there is a region Q' ~ Q such that oQ' E C1 and
SEQ'.
Thus we have proved the follo:wing theorem.
Theorem 1. Suppose that a.n (n - i)-dimensional surface S of class
C 1 either belongs to Q', Q' ~ Q, or instead S c: Q and,. in addition,
FUNCTION SPACES 139
iJQ E C1 . Then any function f (x) E H 1 (Q) has on this surface the trace
j Is belonging to L 2 (S), and the inequality (2) holds.
Let f (x) E HR. (Q), k > 1. Since any generalized derivative Da.f
of order I a I < k belongs to H 1 (Q), this derivative has, by Theo-
rem 1, the trace Da.f Is belonging to L 2 (S) on any (n- 1) - dimen-
sional surfaceS of class C1 Moreover, the inequalities
1/ Da.f lbcs><C II fiiHia.l+ 1cQ><C II f IIHR.<Q> (5)
hold with constant C > 0 independent of the function f.
2. The Formula of Integration by Parts. Let the functions f (x)
and g (x) belong to H 1 (Q) and oQ E C1 . Then for any i = 1, ... , n
the formula of integration by parts holds:
.\ fxig dx =
Q
J
aQ
fgni dS- J
Q
fgxi dx, (6)
where ni = cos (n, xi) is cosine of the angle between outward normal
n to the surface oQ and the xi-axis, and the functions f and g pres-
ent under the integral sign over oQ are traces of functions f and g
on oQ. Thus, so far as the applicability of formula (6) is concerned,
functions belonging to H 1 (Q) behave just like functions in C1 (Q).
To prove (6), consider (Theorem 3, Sec. 4.3) the sequences fp (x)
and gP (x), p = 1, 2, ... , of functions in C1 (Q) which converge,
respectively, to the functions f (x) and g (x) in the norm of H 1 (Q).
Formula (6) holds for functions /p and gp:
Jfpxigq dx Jf pgqni dS- ~ f pgqxi dx.
=
Q CiQ Q
Letting here p-+ oo and q-+ oo (and noting that II /p- f II L,(CIQ)-+
--+ 0, II gq - g II L,(CIQ)-+ 0), the relation (6) follows.
It readily follows from (6) that if g E H 1 (Q) and the components
fi (x), i = 1, ... , n, of a vector f (x), f (x) = (ft (x), . . . , fn (x)),
belong to H 1 (Q), then the relation
Q
.\ gdivfdx= J
CIQ
g(fn)dS- J Q
f-Vgdx (7)
holds.
3. Properties of Traces of Functions Belonging to H 1 ( Q ). A Crite-
rion for Membership of the Subspace H1 (Q). Let f 0 b~ a sufficiently
small (that is, contained in a ball of sufficiently small radius _r 0 )
simple piece of a surface of class C1 lying in Q, and let r 0 be uniquely
projected into a region D in the coordinate plane {xn = 0}, Xn =
= cp (x'), x' ED, cp (x') E C1 (D), is the equation of.f 0 ,
Let f 0 denote the. surface {x' E D, Xn = cp (x') +
6} and Qo the
region {x' ED, cp (x') < Xn < cp (x') +
6} when 6 > 0 or the re-
140 PARTIAL DIFFERENTIAL EQUATIONS
gion {x' ED, cp (x') +
6 < Xn < cp (x')} when 8 < 0. Note that for-
sufficiently small I 8 I (and sufficiently small r 0 ) at least one of the-
regions Q+ 1t'l 1 or Q_ 161 is contained in Q.
Let x E Q 6 c Q. Then for any function f E C1 (Q) we have
r
(l)(X')+t'l
~(x')
whence it follows that
r I at (~:nXn) r I
Ql(x')+ll
If (x'' Cjl (x') + 6)- f (x'' Cjl (x')) 1 2 -<;: I~'~ dxn
Ql(x')
Multiplication of this inequality by V 1 + cpx~ + ... + cp;n-i and
integration over D yield
II f (x6) - f (x0 ) IIL,(ro)-< c vm II f IIH1(Qc5), (8)
where x 0 =(x', cp(x'))Er0 , x 6 =x6 (x 0 )=(x', cp(x')+l>)Er 6 , and
C2 =max V 1 Cjl~. + + +
Cjl~n-1
x'ED
l t is obvious that, apart from inequality (8), there also holds the
inequality
(9)
Approximating the function f E H 1 (Q) by functions of class
C (Q) and using the definition of the trace of a function belonging to
1
H 1 (Q), we find that inequalities (8) and (9) hold for all the functions
belonging to H 1 (Q).
These inequalities express a definite continuity of traces on sur-
faces r 6 of functions belonging to H 1 (Q) depending on the dis-
placements of these surfaces.
If the trace on r 0 of a function f is zero, f lro = 0, then (9) im-
plies the inequality
II f lli.<r6>-<C2 cS II f llk<o.s>-<C2p II f llhl(911 J
for any p and 6, 0 < 8 ::::;:;; p ~ p 0 , where Po is such that Qp 0 c Q
(for the sake of definiteness, we take p 0 > 0). Integrating the last
inequality with respect to 8 E (0, p) and using the absolute contin-
uity of the integral, we find that
II f IIL,(OP) = o (p) as p--+ 0. (10)
Thus we have proved that if f E H 1 (Q), f lro = 0 and QP c Q
(in particular, r 0 may be a piece of the boundary 8Q), then (10)
holds.
FUNCTION SPACES 141
Lemma 1. If f E H 1 (Q) and its trace on the boundary f laQ= 0,
then
(11)
Proof. Since the boundary oQ E Cl, for every point y E oQ there
is a ballS 2r (y) of radius 2r, r = r (y) > 0, with centre at this point
SUCh that a piece Of the boundary 0Q n s 2T (y) iS projeCted Uniquely
onto an (n - i)-dimensional region D 2r (y) lying in one of the coor-
dinate planes, say the plane {xn = 0}. The equation of the piece
n
.QQ S2r (y) is of the form Xn = (jl (x'), x' E D2r (y), (jl (x') E
E C1 (D 2r (y)). Denote by f 0 = f 0 (y) the surface oQ n Sr (y), and
by f 6 = f 6 (y) and !211 = Q 6 (y) the "parallel" surface and the cor-
responding region constructed with respect to r 0 in the manner
described above. Choose 60 = 60 (y) so small in absolute value that
the region Q/10 = Q/10 (y) C Q n s 2T (y)
Since the distance bet ween oQ "'-. S 2 r (y) and Q60 (y) is positive
s
.and the distance between oQ n 2T (y) and r 6 (y)' where 8 E (0, <'lo)
if 6 0 > 0 and 8 E (6 0 , 0) if 6 0 < 0, is obviously greater than y I 8 I
with some constant y = y (y), 0 < y < 1, a Yo =Yo (y), 0 <Yo<
< 1, can be found such that for all such 8
inf lx-~I>Yol<'ll. (12)
xEoQ
;Er6
From the cover of oQ by the balls S r (y), y EoQ, we choose
a finite subcover Sr t (x 1), ... , Sr N (xN). Then there exists a num-
her 61 > 0, 61 < min 160 (xm) 1, such that
1~m~N
(13)
Furthermore, by (12), for all 6, 0 < 8 < 61 , and m = 1, ... , N
(Q "'-. Qy,6) nQ6o(xm) (xm) C QO.sign 6o (xm) (xm), (14)
where y1 = min Yo (xm).
1~m~N
The inclusions (13) and (14) imply that for any f E H 1 (Q) the
inequalities
N
~ II f II~ 2(Q6s1gn6
.::::;: m=1 m (xm))
0(x)
hold for 0 < 8 < 61 Since f laQ = 0, (11) now follows from the last
inequality and the relation (10). I
142 PARTIAL DIFFERENTIAL EQUATIONS
Theorem 2. In order that a function belonging to H 1 (Q) may belong
0
to the subspace H 1 (Q) it is necessary and sufficient that its trace on the
boundary of the region be zero.
Proof. That the condition is necessary is obvious, so we confine
ourselves to the proof of sufficiency. Let f E H 1 (Q) and f IBQ = 0.
Take an arbitrary e > 0. Lemma 1 and Theorem 9, Sec. 1.10,
Chap. II, on the absolute continuity of an integral imply the exist-
ence of a small 6 = 6 (e) such that
II I IIL,(Q"-Qo> < e6, II f I!Hl(Q"-Qo> <e.
Since for a function I E H 1 (Q) there is (Theorem 3, Sec. 4.3; note
that aQ E C1) a sequence of functions /p (x), p = 1, 2, ... , in
C1 (Q) converging to fin the norm of H 1 (Q) (and more so in the norm
of H 1 (Q"'-..Qo)), a number N = N (6) = N (6 (e)) can be found such
that
II f-IN IIHl(Q} < e,
II f N IIL.<Q"-Q11 >< 2e6, (15)
II f N IIHl(~Qo> < 2e.
Consider the function
~o(x)= J ffi0/3(1x-yl)dy,
Qo/2
where ffip (I x - y I) is an averaging kernel. The properties of the
averaging kernel imply that ~o (x) E C 00 (Rn), ~o (x) = 1 for x E
E Q 5ots, and more so for x E Q0 , ~o (x) = 0 outside Qots, that is,
~o (x) E (;oo (Q). What is more, for all x E Rn 0 ~o (x) ~ 1, <
I V~o I ~ C/6 where the constant C > 0 does not depend on 6.
By (15) we have
If N- f N~o i!Hl(Q} = II f N-I N~O IIHl(Q"-Qo>
-< (II IN (1-~o) lllz<Q"-Qo>+ Ill VIN I (1- ~o) +I IN II V~o 1111.cQ',Q11 >) 112
-< (II IN llt.cQ"-Qo> + 2111 VI N lllt.cQ,Q 11 >+ 211 IN I V'~o llli.cQ,Q 0>) 112
2C2 I1tN 112L CQ"-Qo> ) 1/2 -<e( 8 +8c2 ) 1/2 = c1e.
-< ( 8e 2 + 62 2
The functions I moce>> (x) ~oce> (x) belong to b (1}) and
II f moce>> (x) ~oce> (x)- I (x) IIHl(Q}-< II f- I N<O<e IIHl(Q}
+II I NCfl(e)) - f N10(E))~0(E) IIHl(Q} < (1 + ct) 8.
Accordingly, f (x) E Ifl (Q). I
FUNCTION SPACES 143
4. On Compactness of Sets in L 2 (Q).
Theorem 3. A set bounded in H 1 (Q) is compact in L 2 (Q).
Proof. Let a set aft be bounded in H 1 (Q}, that is, for all f E aft
II!IIHl(Q)<C. (16}
Suppose first that aft c lfl (Q). We extend all the functions be-
longing to aft outside Q by putting them equal to zero. I~ the case-
under consideration the extended functions belong to H 1 (Q') for
any region Q' ::::> Q.
If fh (x) is an averaging function for f (x) E uJft, then inequality (6),,
Sec. 2.3, holds:
lzl<h Q
The function f (x) E C1 (()), also extended outside Q by assigning
to it the value zero, satisfies for any vector z the identity /(x+z)-
1 1
- f (x) =) df (xd-:-tz) dt =) ("\// (x+ tz) Z) dt, thereby yielding
0 0
1
lf(x+z)-f(x)l 2 <lzl 2 ) I"'Vf(x+tz)j 2 dt
0
and hence
)'If (x+z)- f (x) 12 dx<l z 12 11 f llhl(Q) (18)
Q
The inequality (18) also holds for any f E aft; this can be proved
by the usual limiting process.
It follows from (17) and (18) that
ll!h-flli.<Q><Collfllffl(Q) ~: ) dz<C:h 2 ,
lzl<h
where the constant C1 is independent, in view of (16), of both h
and f.
If it is now shown that for any fixed h > 0 the set all h consisting
of averaging functions fh (x) for all f (x) E aft is compact in C (Q}
(and therefore in L 2 (Q}}, the assertion of the theorem will follow
from Corollary of Theorem 2, Sec. 3.7, Chap. II.
According to Property (d) of the averaging kernel (see Chap. I~
Introduction), we have
I ih (x) I<~~ ) I I (x) I dx<C~ II I /IL.<Q><C~ II I IIHI<Q><const
Q
1.44 PARTIAL DIFFERENTIAL EQUATIONS
and
I ~~~ j< h:~l JIf (x) I dx<:const, i = 1, ... , n,
Q
where, by (16), the constant does not depend on f. Now an applica-
tion of Arzela's theorem shows that the set {fh (x)} = o!th * is com-
pact in C (Q).
Suppose now that a!f c H 1 (Q). Denote by cl/t' the set of functions
F (x) belonging to H 1 (Q') obtained by extension, according to
Theorem 1, Sec. 4.2, of functions f (x) belonging to olt into some
region Q', Q <.e Q'. Since II F IIH(Q') ~ const II f IIH(Q) with con-
stant independent off, the set o!t' is bounded in H 1 (Q'). By what has
been proved just now, it is compact in L 2 (Q'). Hence the set oJt is
.compact in L 2 (Q). I
5. On Compactness of the Set of Traces of Functions Belonging to
Hl (Q).
Theorem 4. If a set of functions is bounded in H 1 (Q), then the set
,of their traces on the (n - i)-dimensional surface r c Q of class C1
is compact in L 2 (f).
Proof. Let the set olt be bounded in H 1 (Q) and let oltr be the set of
traces on r of functions belonging to olt. We denote by r:di' the set
.bounded in H 1 (Q') that consists of extensions into Q' 2) Q of func-
tions belonging to olt (Theorem 1, Sec. 4.2, iJQ E C1).
Let r 0 be the part of the surface r which is uniquely projected
into a region D in the plane {xn = 0}, and let Xn = cp (x'), x' ED,
.be the equation of r 0 , cp (x') E C 1 (D). There exists a 6 > 0 such
that the region Q 26 = {x' E D, cp (x') < Xn < cp (x') 26} lies +
in Q'.
* Suppose that the set ~ of continuous functions in Q is uniformly bounded
.and equicontinuous: 11 g lie - ~ const for all g E ~ and for any e > 0 there
is a 6 = 6 (e) > 0 such th~~)for all g E~I g (x') - g (x") I < e for arbitrary
x', x" in Q satisfying I x' - x" I < 6 (in our case 'WI= oJt h and equicontinuity
-{)f oJth follows from uniform boundedness of derivatives). Let us show that the
set SJJl is compact in C (Q).
Let {gk} be an arbitrary infinite sequence of functions belonging to SJJl. For
-every natural m take a finite set of points {x:;'}. q = 1, ... , p (m), in 7j
-!SO that for every x E Q there is a point in this set that is at a distance less than
,1') (2-m) from x. From the sequence {gk} we choose a subsequence {gk 1} converg-
ing at every point of the set {x~}; then II g, 1 - gliiiC(Q) < 32-1 for k1 , l1 ;;;;,.
~ N 1 From the sequence {gk 1} choose a subsequence {gk 2} converging at every
point of the set {x~}, and so forth. Thus for every m there is a sequence {g,m}
with the property that II g" - g1 lie - < 3 2-m for km, lm;;;;,. Nm Evident-
m
m ((J)
ly, the diagonal sequence {gm } is fundamental in C (Qi.
m
FUNCTION SPACES 145
For any function I (x) E C1 (Q') and any points X = (x'' Xn) Er0
and (x', Yn) E Q 26 we have
Yn
I (x', Yn)- I (x) = ) of<~~~ ;n> d~n.
xn
which yields
xn+26
II (x) 1-<21 t (x'' Yn) 1+ 46
2 2 r I at<;~~ ;n) 2
1 d~n
U ~+U
6
2dyn + 462
Yn) 1 r l of(~~~
xn
;n) [2d~n
and then integrate the resulting inequality over r 0 with respect to x
(that is, multiply it by V 1 +
cp~ + ... +
cp xn-1
2 and integrate
over D) to have
ro Q' Q'
r
5 ) I /1 2dS-< const ( 2 ) I t 12dx + 46 2 I V/ 12dx) .
Since the surface f can be divided into a finite number of pieces
of r 0 type and for each of such pieces the inequality just established
holds, summing these inequalities we obtain
II t lli.<r>-< ~i II I lli.<Q'> + c;<'>ll t 111Il<Q'>
where the constants c; and c; are independent of both f and 6. By
the usual technique, it is found that this inequality is true not only
for any f E C1 (Q') but also for any function belonging to H 1 (Q').
By Remark to the theorem on extension (see Sec. 4.2), the last
inequality yields the inequality
II f lli.<r>-< ~~ II f lli.<Q> + C2<'>IIJ/ llkl(Q) (19)
true for any I E H 1 (Q).
By Theorem 3 (of the preceding subsection), the set oJt is compact
in L 2 (Q). Therefore from any infinite sequence of elements of the
set oJt a subsequence /p, p = 1, 2, ... , can be chosen which is
fundamental in L 2 (Q): given e > 0 anN can be found such that for
all p :>- N and q :>- N II /p - /q IIL,(Q) < e. But then the sequence
of traces /p 18 , p = 1, 2, ... , will be fundamental in L 2 (S},
because the inequality (19) applied to fp - /q and the inequality (16)
10-0594
146 PARTIAL DIFFERENTIAL EQUATIONS
imply, for all p, q > N,
II fp- fq lli.<Q>-< c.{! + c2~ II f p- /q llkl(Q)<,e (Ct + 4CzC 2) = C3e,
provided we take ~ = e. I
6. Equivalent Norms in Spaces H 1 ( Q) and IJ.l( Q). Suppose that in
a region Q, 8Q E C\ there is defined a real symmetric matrix
P(x) = (pii(x)), i, j = 1, ... , n, continuous in Q. This means
that the real-valued functions Pti(x) E C (Q) and Pii = p ih i,
j = 1, ... , n. Suppose further that a real-valued function q (x) E
E C (Q) is defined in Q, while the real-valued function r (x) E
E C (8Q) is defined on 8Q.
On H 1 {Q) we define the Hermitian bilinear form (see Sec. 2.4,
Chap. II)
n
W (f, g)= J~ PtJfxi"ix,dx+ ~ q{gdx+ ) rfgdS (20)
Q i, 5=1 Q iJQ
(in the rightmost integral, of course, f = fliJq, g = claq}.
Theorem 5. If the matrix P (x) is positive-definite, that is, for any
complex vector ~ = (~ 1 , , ~n) and for all x E Q
n n
. ~ PiJ (x) ~~~J~'\' .~ I~~ 1
2 (21)
,,,=1 t=1
with constant y > 0, the functions q (x) >
0 on Q, r (x) 0 on 8Q>
and either q (x) ;= 0 or r (x) =#- 0, then the bilinear form (20) defines on
H 1 (Q) a scalar product equivalent to the scalar product
(f, C)Hl(Ql = ) (VfVg.+ {g) dx. (22)
Q
Proof. According to the definition (see Sec. 2.4, Chap. II), for the
proof of this theorem it is enough to establish the existence of two
constants cl > 0 and c2
> 0 such that the inequalities
W(f, f)<,C: II f 1/kl(Q) II f llkl(Q)<,C~W(f,~f) (23)
hold for all f E H {Q).1
First note that by the hypothesis all the three terms in the expres-
sion for W(f, f) (in (20) g = f) are nonnegative.
Since
n n
J~
Q i, j=t
PtJfxlxi dx<,A J ~i=1 lfx II f%j Idx
Q i,
1
<,An JIVfl dx<,Anllfllki(Q)
Q
2
FUNCTION SPACES 147
Q
where A 1 = II q llc(Ql' and according to inequality (2) of Subsec. 1,
) r If 1
2 dS -<:Azll f lli.<8QJ-<:C2 Azll f lihi(Qlt
8Q
where A 2 = II r llc(8Q) the first of inequalities (23) holds with the
constant q =An+ A 1 +
A 2 C2
We shall establish the second inequality in (23). Supposing, on
the contrary, that there is no such constant C~, a function fm(x) E
>
EH 1 (Q) can be found for any integer m 1 such that II fm llki(Ql >
> mW (fm, fm) or, equivalently, a funetion gm (x) E H 1 (Q) (gm =
= fmlll fm IIHI(Q)) can be found su~h that
(24)
= ~ ~ PiJgmxi"imxidx+) qjgmj 2 dx+ ~ rjgmj 2 d8<11m.
Q i, i=l Q oQ
This inequality implies that each of the three terms in W(gm, gm)
is less than 1/m, therefore (using the inequality (21)) the following
inequalities hold:
Q Q fJQ
By virtue of (24), the sequence gm, m = 1, 2, ... , is bounded in
H 1(Q); accordingly (Theorem 3, Subsec. 4), from it a subsequence
can be chosen which is fundamental in L 2 (Q). With no loss of gen-
erality, it can be assumed that the sequence gm, m = 1, 2, ... ,
itself is fundamental in L 2 (Q), that is, II gm- gP IIL,{Q) ~ 0 as..
m, p ~ oo. Since, by the first inequality in (25),
II gm- g p !lhl(Q) =II gm- g p 1/t,(Q) +Ill V' (gm- g p) lllt.(Q)
-<II gm- gp lli.<o> + 2111 Vgm lllt.<o> + 2111 'Vgp Illi.<o>
-<:II gm- gp llt.(Q) + ;,Y + :Y 1
it follows that II gm- gp IIH<Q> ~ 0 as m, p ~ oo, that is, the
sequence gm, m = 1, 2, ... , is fundamental in H 1 {Q) as well.
Thus this sequence converges in the norm of H 1 (Q) to an element
10*
148 PARTIAL DIFFERENTIAL EQUATIONS
g E H 1 (Q). Letting m--+ oo in (24) and (25), we obtain the fol-
lowing relations:
(a) II g IIHI<Ql = 1,
(b) ) 1Vgl 2 dx=0,
Q
~c) Jq gI 12 dx = 0,
Q
{d) ) rjg/ 2 dS=0.
aQ
The relations (b) and (a) imply that g = const = 1/VTQI in Q
and glaQ= 1/VTQi on oQ, which contradicts (c) if q (x) =1= 0 or
(d) if r (x) =I= 0. I
Let P (x) = p (x) E, where E is the identity matrix. Theorem 5
has the following corollary.
Corollary. The bilinear form
W(f, g)=) (pVfVg+qfg}dx+
Q
J
aQ
r(x)fgdS,
where p (x) E C (Q), q (x) E C (Q), r (x) E C (oQ), p (x) const > 0,>
q (x) >
0 in Q, r (x) >
0 on oQ and either q (x) =;t= 0 in Q or r(x) =1= 0
on oQ, defines in H 1 (Q) a scalar product equivalent to the scalar pro-
duct (22).
Theorem 6. If the matrix P (x) is positive-definite and the function
q (x) >
0 in Q, then the Hermitian bilinear form
n
Wt(f, .g)= ~ Piifx.fJx.dx+ Jr qfgdx
JI ..... l}
Q i, j=1 <J
defines a scalar product in H1 (Q) which is equivalent to the scalar pro-
duct (22).
Proof. Since ffl (Q) c H 1 (Q), it follows from Theorem 5 that a
scalar product equivalent to the scalar product (22) can be defined in
/[1 (Q) by means of the bilinear form (20) with r (x) 1 on oQ and =
q (x) >0 in Q. But for the functions f (x) and g (x) belonging to
H (Q) the values of bilinear forms W and W1 coincide.
1 I
Let P (x) = p (x) E. Theorem 6 implies the following result.
Corollary. The bilinear form
W (f, g)= ~ (pVfVg+ qfg) dx,
Q
FUNCTION SPACES 149
where p (x) E C (Q), q (x) E C (Q), p (x) >-
const > 0, q (x) 0 in Q, >-
defines a scalar product in ffl (Q) equivalent to the scalar product (22).
In particular, the scalar product
(!' g)'o
Hl(Q)
= j r vr+:ii dx
Q
is equivalent to the scalar product (22).
The last assertion readily yields Steklov's inequality
Q
6. PROPERTIES OF FUNCTIONS BELONGING
TO Hk(Q)
In this section we shall examine mutual relationship between the
spaces Hk (Q) and C1 (Q). It will be demonstrated that if a function
belongs to Hk (Q) for sufficiently large k, then it will also belong to
C1 (Q) (that is, the function can be so modified on a set of measure
zero that it becomes continuous in Q together with all the deriva-
tives up to order l).
To obtain this result, it is necessary to represent a sufficiently
smooth function in Q in terms of the integral over Q of a combination
of its derivatives.
1. Representation of Functions by Means of Integrals.
Theorem 1. Let the function f(x) E C2 (Q) and let the space have
dimension n >-2. Then for any point x E Q the following identity
holds:
f(x)=) U(x-s)~/(s)ds+ \ (t(s) au~~l~>- a;~~> U(x-s)) dS~,
Q ;Q
(1)
where
-
1
(n-2) a n J x 1n 2
when n> 2,
U(x)= { 1 1 (2)
--ln- when n=2,
2~ JxJ
150 PARTIAL DIFFERENTIAL EQUATIONS
and on = 2:n:nf 2 /l' (n/2) is the surface area of the (n - i)-dimensional
unit sphere*.
Proof. The function U (x - ~) (called the fundamental solution
for the Laplace operator) as a function of ~ satisfies for =1= x the
relation L\,U(~o1': - x) = ( a~a2 + ... +
a2 ) U (~o1': - x) = 0 , as can
a,fi
be checked by direct differentiation.
Fix a point x E Q and take e > 0 so small that the ball {I ~ - x I~
~ ~::}c Q. In the region Q8 = Q"'-{1 x - I~, e} Green's for-
mula (see Sec. 1.2)
) ~/()U(x-~)d= J(U(-x) a~~)-/(~) au~~x) )dS;
OQ
)
Qe
1~-x(=e
holds for the function u (~ - x) (regarded as a function of s) and
any function f (~) E C2 (Q).
a a
As an; = - a I ~-xI on the sphere I- xI= e, the second term
on the right side of (3) has the form (when n > 2)
- i \ at() dS + 1 f I (t) dS
(n-2) O'nen 2 J
16-xl=e
an ' O'nen 1 J
(6-x(=8
'o ;
= f (x) + O'n!n 1 ) (f (~)- f (x)) dSf.
(!i-xJ=8
-
1
( n- 2) O'n8n-2
J at()
-,
un-dS,=f(x)+O(e),
4
()
"-xl=8
since the surface area of the sphere I~- xI= e is crnen-t, and for
1~-x!=e /(S)-/(x)=O(e) and Ia~~) 1-<const.
The function U ( - x) is integrable over Q, therefore the limit,
as e-+- 0, of the left-hand side of (3) is equal to the integral over Q
of the function U ( - x) ~~ (6). Letting e-+- 0 in (3) and using
(4), we obtain (1) when n > 2. When n = 2, the above proof re-
The representation (1) holds in one-dimensional case also (Q=(a, b)).
b
The identity f (x) ; Jl x-61 I"() liS++(/ (a)+ f (b))- ; ((a-x) f' (a)+
a
+(b-x) f' (b)), which is easily verified, can be put in form (1) if we intro-
duce the function U (x-6)= ~ I x-6 J. However, we won't have occasions
to use the identity (1) when n = 1.
FUNCTION SPACES 151
mains valid, the only difference being that the second term on the
right side of (3), in contrast to (4), is now f (x) + 0 (e ln e). I
2. Continuity and Continuous Differentiability of Functions Be-
longing to H 14 (Q). In Theorem 1, any function f E C2 (Q) was
expressed in terms of integral over Q of its second derivatives. If the
function is still more smooth, f E C14 ({j), k > 2, then, along with
representation (1), there are representations in terms of derivatives
of order k. To obtain such representations, we require the following
simple result.
Lemma 1. Let n >
3. Then for any:(real))1 the function
u11 (x) = I (!'~~~~;: n)
ln I xl
when fL =I=- 2, fL =I=- n,
(In Ix 1)/(n- 2) when fL = -2,
satisfies the equation l\u 11 = I x I" for all x E Rn, x =I= 0.
That the lemma is true can be seen by direct calculation.
Let the function f E C2 (Q). By formula (1), we have for all x E Q
f (x) =) U (x-6) M (6) l6.
Q
In particular, when n = 2
f (x) = 2~ J&f (6) ln Ix- 61 d6,
Q
(5)
when n=3
(6)
when n>3
f (x) = -
1
(n-2) O"n
r llf <s)
J I x-~ ln-i d6. (7)
Q
Suppose that n = 4, and the function f (x) E C3 (Q). Integration of
(7) by parts yields, on using the relation I~~~ 1 ~ ~ L1; ln I x - 6 I
(Lemma 1)
f(x)= 4 !, ) ML1;lnlx-6ld6= 4~, ~ Y'(L1/(6))V;lnlx-6ld6. (8)
Q Q
152 PARTIAL DIFFERENTIAL EQUATIONS
When n = 5, the relation (7) and the identity I x - l- 3 =
1 1
= -2 Y'; 1x-s 1 (Lemma 1) yield the representation
f(x)= 2!a5) L\f(s)L1; lx~sl ds
Q
1 r . 1
(9)
= - 23a& J Y' (M (s)) Y'; I x-s I ds
Q
for the function f (x) E C3 (Q). and so on. Suppose that f (x) E
E C2P (Q), p >
2. Then for n > 4p - 3 the identities
1 C' ,1P-1 1 1
I x-s I"P-" = 4p-2 ' I x-s 12p-2' I x-s l"p-3
=
C'4p - 1 L\P-1
,
1
...,..,-x----::-s""'l2:-p...,..1
which follow from Lemma 1, and (7) yield
r
f (x) = Cf.p-2 J 1x-s I2P_2 ds when
!!Pt (!;)
n = 4p-2 (10~ap-z)
Q
and
1x_{ 14p-2 C4pdr ( Jx-~l2p-2), lx-~l4p-1 =C4p+1L\r { Jx-~J2P 1)
for n > 4p - 1, p > 2, we have, by (7),
f (x) = Cf.p .\ Y' (I~.Pj (S)) V'6 ( 1x-~ 12P 2 ) ds when n = 4p, (104p)
Q
and
f (x) = Cl.P+i ~
Q
Y' (,1Pf (s)) Y'; ( I x-: 12p 1 ) ds when n=4p+ 1 (104p+t)
for j E d.!P+I (ij}, p > 2, where Ci, Ci are absolute constants.
Since jv6 lx~sl/= lx-~ls+l, s~1, the relations (6), (8), (9),
(104p-2)-(104p+t) yield the inequalities
lf(x)I-<C"P-2 Jr Jx-si
1 !!Pt (s) 1
2P 2 ds for n=4p-2, p>1, (114p-z)
Q
jf(x)j-<C"p- 1 JI lx-si
I !!pf (s)2P I 1 -
ds for n-4p--1, p~1, (11 ~op-1 )
0
FUNCTION SPACES 153
for all f E C2 P (Q) and the inequalities
i 1v~P/ (~)I
lf(x)I-<C4 p J lx-~I 2 P 1 d for n=4p, p~1,
Q
r I v~Pj (~)
if(x)I-<C4p+1 J lx-~/ 2P d for n=4p+1, p~1,
Q
for all f E C2P+l (Q), where C, are absolute constants.
From (5), by means of Bunyakovskii's inequality, we obtain
II (x) 1-< 2~ ( JIMl
Q
2 df 12 {) lln I x-Wd
Q
f 12
-<CIIfllH2<Q> n-=2,
from (114p- 2 )
I I (x) 1-< C4p-2 ( J ~Pf d f JI x-~~14p
Q
I 12
12
(
Q
4 r 12
and similarly from (11 4p _1)-(114p+ 1)
I I (x) 1-<C II f IIH2P(Q)' n=4p-1~3,
where the constant C depends on n and the region Q.
Thus the inequality
llfllc(Q">~clltll [~]+ 1 (12)
H 2 (Q)
[2:]+1
holds for all f E C 2 (Q), n ::;> 1, where the constant does not de-
pend on f. For n = 1, this inequality readily follows from the repre-
sentation
b
f(x)= ~ Jsign(x-s)f'(s)d~
a
for any function f (x) E (;t
(Ia, bl) .
1+1+[2:] -
If the function f E C 2 (Q) for some l > 0, then, apart from
(12), it also satisfies the inequality
H 2 (Q)
where the constant C 1 > 0 does not depend on f.
154 PARTIAL DIFFERENTIAL EQUATIONS
Indeed, for any vector a = (a 1 , . , an) with nonzero integer
components, I a I ~ l, by (12) we have
Jl Daf llc<m-<C II Daf II 1+[!:.] -<C II f II i+lal+[!:.]
H 2 (Q) H 2 (Q)
-<CII/11 1+1+[!:.] .
H 2 (Q)
Summing these inequalities over all a, I a I ~ l, we obtain the
inequality (13).
o1+1+l ~ 1
Suppose now f EH (Q) and fm (x), m = 1, 2, ... , IS
.1+1+[~1 -
a sequence of functions in C 2 (Q) that converges to f in the
1+1+[!:.1
norm of H 2 (Q). By (13)
H 2 (Q)
as m, s-+ oo, that is, fm, m = 1, 2, ... , is a fundamental sequence
in the norm of C1 (Q). This means that the limit function f belongs
to C1 (Q). Passing to the limit, as m-+ oo, in the inequality
II fm llcz(-Q) ~ C II fm II n , we see that the inequality (13)
H
1+1+[2] (Q)
0 1+1+[~1
holds for any f EH 2 (Q).
1+1+[~1
Let f E H 100 2 (Q). Take any subregion Q' ~ Q and construct
the function ~ (x) EC"" (Q) which is equal to 1 in Q'. The function
o1+1+[!:.1 _
f ~ E H 2 (Q), so it belongs to C1(Q), which means that f be-
longs to C1 (Q'). Since Q' is arbitrary, f belongs to C1 (Q). Thus we
have proved the following assertion.
!+1+[ ~]
Theorem 2. A function belonging to the space Htoc (Q) belongs
1+1+[!:.1
2 (Q) c: C1(Q).
to the space C1(Q), that is H 1oc
!+1+(~1 !+1+( ~ 1
Suppose now that I E H 2 (Q) and let oQ E C . Then
by the theorem on extension for (any) region Q', Q' 2> Q, there exists
1+1+[~1
a function F belonging to iJ 2 (Q') that coincides in Q with /;
moreover, II F II n ~ C' II f II n , where the constant
H1+1+(2-)(Q') H!+i+(T](Q)
FUNCTION SPACES 155
C' does not depend on f. The function F E C1(Qi) and satisfies the
inequality II F llcz(Q')-.<C" II F II 1 + 1 +[~] (inequality (13) for the
H 2 (Q')
function F in Q'). Accordingly, f EC1 (Q) and the inequality
II f llct<cr>-<C'C" II f II I+Hl~l
H 2 (Q)
holds. Thus we have shown the following theorem.
1+1+[~] 1+1+[..!:..] -
Theorem 3. If aQ EC 2 , then H 2 (Q) c C 1 (Q).
Moreover, the inequality (13), where C>O does not depend on f,
1+1+[..?!..]
holds for any function f EH 2 ( Q).
We have so far examined function spaces (Ck, Hk, k = 0, 1, ... )
composed of functions whose differentiability properties were the
same with respect to all the independent variables: for example, the
space Hk consists of all the functions belonging to L 2 whose all the
generalized derivatives up to order k belong to L 2 In the theory of
differential equations one has to use also sets composed of functions
whose differentiability properties differ with respect to different
variables. In particular, the spaces of functions introduced below
will be used in Chap. VI on parabolic equations.
Let D be a bounded region in the space Rn (x = (x 1 , , Xn) is a
point in Rn) and QT ={xED, 0 < t < T} a cylinder of height
T > 0 in the space Rn+l = Rn X {- oo < t < oo }.
1. Banach Spaces or 0 ( QT) and 0 2" s <<h>
We denote by cr 0(QT),
where the integer r >
1, the set of all functions f (x, t) that are
- aett+ .. -+ttn/
continuous in QT together with the derivatives for all
ax~ 1 ax~n
(nonnegative integers) a 1 , , an, a 1 + ... +
an :::;;:; r.
We let C 2" 8 (QT), where the integer s 1, denote the set of>
functions f (x, t) that are continuous in QT together with the deriva-
attt+ ttn+Pt
tives et 11 for all (nonnegative integers) a 1 , , an, ~.
ax1 1 ax~n at
a1 + ... +an +
2~ :::;;:; 2s.
When r = 0 and s = 0, the spaces cr 0 (QT) and C 28' s (QT) will
mean the space C0 0 (QT) = C (QT)
156 PARTIAL DIFFERENTIAL EQUATIONS
It is clear that the set C7 ' 0 (QT), r >- 0, is a Banach space with
the norm
while the set C 28 ' (QT), s >- 0, is a Banach space with the norm
II I llc2, (o ) = ~ max I oat+ . +an+f3f
a a f3
I
T al+ .. +an+2f3~2s QT oxil ... oxnnot
2. Hilbert Spaces Hr, 0 ( QT) and H 2" "( QT). We denote by H 7 ' 0(QT)
where the integer r >-
1, the set of all functions l(x, t) that together
0 at+ ... +anf
with the generalized derivatives for all (nonnegative inte-
iJx~~ ... i}x~n
gers) a 1 , , an, a 1 + ... +
an:::;;; r, belong to L 2 (QT) Simi-
larly, H 28 8(QT), where the integer s >-
1, denotes the set of all
functions I (x, t) that together with the generalized derivatives
oal+ . +an+f3f
a a
ox 11 oxn n ot
13 for all (nonnegative integers) a 1 , , c.tn, ~. a1 + ..
... + an + 2~ :::;;; 2s, belong to L 2 (QT)
The space H7 0 (QT) with r = 0 and the space H 28 8 (QT) with s =
= 0 will mean the space H 0 0 (QT) = L 2 (QT)
The following properties of the sets H 7 0 (QT) and H 28 (QT) are
an immediate consequence of their definitions.
1. The set H 7 0 (QT), r >-
0, is a Hilbert space with the scalar
product
while the set H 28 (QT), s >- 0, is a Hilbert space with the scalar
product
(!, g) H2s, s(QT)
a 1+ ... +an= r' ::=;;;r.
FUNCTION SPACES 157
al+ . . +an+llt
4 If f (X, t) E H 28 8(Q T ) ' then a E H2(s-s'), 8-B' (QT)
axial ... axnan at II
'
for a 1+ ... +an+2~<2s', where s'<s.
We shall now show that if the boundary aD of the region D is
sufficiently smooth, then the functions belonging to nr. 0 (QT) and
H 28 8 (QT) can be extended into a wider (than QT) region while
preserving the smoothness. Namely, we shall prove the following.
5. Suppose that D' is an arbitrary region in Rn such that D ~ D',
and t 0 , t 1 are any numbers satisfying the inequalities to< 0, t1 > T.
Let Q;o, tl denote the cylinder {xED', t 0 < t < t 1 }. If aD E cr,
r >- 1, then for any function f E nr, 0 (QT) there is an extension
F E nr,o (Qto, tt) whose support is compact in Qto, t' Moreover, the
inequality
(1)
where the positive constant C does not depend on f, holds. If aD E
E C2S, s >-
1, then for any function f E H 28 8 (QT) there is an exten-
sion F E H 2 " 8 (Qio, tl) with compact support in Qt, ,.; moreover the
inequality
(2)
where the constant C > 0 does not depend on f, holds.
The desired extension F of a function f belonging to Hr, 0 (QT) or
to H 28 8 (QT) is obtained in two stages: first, f is extended to F 1
through the curved surface of the cylinder QT into a wider cylinder
Qi- = {xED', 0 < t < T} of the same height T, and then the
function F 1 is extended through the top {x ED', t = T} and base
{x E D', t = 0} of the cylinder Q'.r.
To construct the function F 1 , we employ the same technique as
the one used in extending into D' a function belonging to Hk (D)
(see Sec. 4.2). We use the extension constructed there of functions
belonging to a rectangular parallelepiped.
Let lla. T a> 0, denote the rectangular parallelepiped {I xi I <
< a, i = 1, ... , n, 0 < t < T} and ll~. T, ll;;, T the rectangular
parallelepipeds {I xi I< a, i = 1, ... , n- 1, 0 < Xn <a, 0 <
< t < T} and {I xi I< a, i = 1, ... , n - 1, -a< Xn < 0,
0 < t < T}, respectively. Suppose that the function z (x, t) E
E Ck (fi,i, T) for some k >-
1. The extension Z (x, t) of the function
z (x, t) into the parallelepiped lla, T is defined in the parallelepiped
11~. T in the following manner:
k+1
Z (x, t) = ~ Aiz { x', - xt , t) , (3)
i=1
1.58 PARTIAL DIFFERENTIAL EQUATIONS
where x' = (x1 , , Xn- 1) and A 1 , . , Ak+ 1 is the solution of
the linear algebraic system
(-+r=1.
k+i
i=i
While proving Lemma 1 in Sec. 4.2, it was established that
k -
Z (x, t) E C (TI 0 , r), and for any rx1 , , tXn, ~. rx 1 0, ... , >
~ > 0, rx 1 + ... + tXn +
~ ~ k,
I aa+ .+an+llz
a, an II
II -<.C II aa+
81la
.. +llz rr
1 atll '
8xl ... 8xn 8t L.(ITa, T) I L.(II~, T)
where the constant C > 0 does not depend on z. Therefore for any
r~k
(4)
and for any s, 2s-<.k,
II Z IIH2' '<IIa, T )-<. C II Z IIH (II+a,T) 28 8 (5)
where the constant C > 0 does not depend on z.
Since the set Coo (TI~. T) and hence also the set C" (TI!, T) is
everywhere dense in the space nr, 0 (TI~. T) and in H (TI!, T) for 2"'
any k ;;;;::: r or k> 2s, respectively (this is proved in exactly the
same way as analogous assertions regarding the space H" (D), see
Property 6, Sec. 4.1), and since these spaces are complete, it follows
from what has been said above that any function z belonging to
nr, 0 (TI!, T) or to H 2" 8 (TI!, T) has an extension z into ITa, T that
belongs to nr,o(rra, T) or to H 2''(I1a,T), respectively; moreover,
the function Z is defined in lla, T by (3), and the inequality (4) or
inequality (5) respectively holds. Arguing exactly in the same way
as in the proof of Theorem 1 (Sec. 4.2), we obtain the function
F 1 (x, t) which is the extension off (x, t) into the cylinder QT; fur-
thermore, iff E W. 0 (Qr), then F 1 E H" 0 (QT) and the inequality
II F IIHr, o(QT>-<. Ctil f IIH" o(QT)
holds; if f E H 2" "(Qr), then F 1 E ll 2'' (QT) and the inequality
II F tiiH2s, '<Q:f>-<. C21/ f I/H 2" '<Qr>
holds (the constants C1 , C 2 > 0 do not depend on/). What is more,
F 1 = 0 in QT"'Q'T, where Q'T = {xED", 0 < t < T} and D" is a
region in Rn such that D ~ D" ~ D'.
We shall now construct the required extension F of f into the
cylinder Q!o, tl
FUNCTION SPACES 159
When IE Hr, 0 (QT), for F we take the function equal to F 1 . in
QT and to zero in Q!o, 11"'-QT Evidently, F belongs to Hr, 0 (Qio, 11),
its support is compact in Qio, 11, and it satisfies the inequality (1).
When IE H 28 8(QT), then we define its extension F into the
cylinder Qio, t' by putting F = ~ (t) F 2 (x, t), where ~ (t) E C"" X
T+t 1
X(-oo, +oo), ~(t)=1 for tE(O, T), ~(t)=O forjt>-
2-
and for t < ~ , while the funetion F 2 (x, t) is equal to F 1 (x, t)
s+1
in QT, to ~ AiFd x, :~ ) in {xED', t0 < (< 0} fand to
i=1
+1
"'AF
LJ i 1 ( x, T- t-.T
, ti-T
T ) 1'n {xED', T < t < t 1}, where
i=1
A;, ... , A~+t is the solution of the linear algebraic system of
equations
a+1
~ Ai (
i=1
t;o r= 1, p = 0, ... , s while A:, ... , A:. 1 is the
solution of the system
s+1
~ Ai(-
i=1
i(/'-T) r = 1, p=O, ... , s.
Evidently, the function FE H 2' (Qi. 1,), has compact support in
Qlo, t'' and satisfies the inequality (2).
Property 5 coupled with Lemma 1, Sec. 3.2, readily implies the
following assertion (the corresponding assertion regarding the space
Hk was obtained in Sec. 4.3).
6. If the boundary aD E cr, r >
1, then the set coo (QT) is every-
where dense in Hr,o (QT) If an E C21 , s >
1, then the set C00 (QT) is
everywhere dense in H 28 (QT)
7. Let I (x, t) E H 1 0 (QT) and S be an (n- i)-dimensional sur-
face of class C 1 lying in D; in particular, S may coincide with the
By r;,T we denote the cylindrical surface {xES, 0 < t < T};
the curved surface faD, T = {x E an, 0 < t < T} of the cylinder
Qr Will be denoted by f T
By Property 6 (aD E C 1), there is a sequence of functions fk, k =
= 1, 2, ... , in C1 (QT) such that lim II lk - I IIH1, o{Q > = 0. Since
k .... oo T
the functions lk (x, t), k = 1, 2, ... , regarded as functions of x,
belong to C1 (D) for any t E [0, T], the inequalities
//lk-fsilL<s>-<C 2 l/fk-fsl/h'<D> k, s=1, 2, ... , (6)
160 PARTIAL DIFFERENTIAL EQUATIONS
hold for any t E [0, T] in which the positive constant C depends only
on the region D and the surface S (see inequality (3), Sec. 5.1). In-
tegration of (6) with respect to t E (0, T) yields the inequalities
II fk- fslk.<rs, T>-<.C II fk- fsiiHt,o(QT)' k, S= 1, 2, ....
Since fk, k = 1, 2, ... , is a fundamental sequence in Il1 0(QT),
the last inequalities imply that the sequence of values fk l<x, t)Ers. T
k = 1, 2, ... , of these functions On f s ,T is fundamental in
L 2 (r s. T> Accordingly, there exists a function frs.T E L 2 (fs. T) to
which the sequence fklcx.t>ers,T' k=1, ... , converges in
L 2 (fs,T), and by repeating the arguments of Sec. 5.1, it can be
easily shown that the function fr 8 ,T does not depend on the choice
of the sequence fk, k = 1, 2, ... , which approximates the function f.
It is natural to call the function /r 8 .T the trace of function f (be-
longing to H 1 0 (QT)) on the cylindrical surface r s. T and denote it
by /Irs, T.
As in Sec. 5.1, it is easily shown that
II f IIL.(rs, T>-<. C II f IIH1, o(QT)
(here II f IIL,(rs, T> = II f llr8, T IIL.(rs, T>), where the constant
C > 0 does not depend on f.
Note that if oft is a bounded set of functions in H 1 0 (QT), then,
by the last inequality, the set &It' of traces of these functions on
r s. T is bounded in L 2 (rs. T) but, in contrast to the case of the
space H 1 (QT), is not compact.
The above notion of trace enables us to extend the formula of
integration by parts to functions belonging to H 1 0 (QT). Namely,
for any two functions f and g in H 1 0 (QT) there holds the formula
of integration by parts (Ostrogradskii 's formula)
r
QT
f.,igdxdt= ftgnidSdt-
rT QT
fg.,idxdt,r
where ni is the ith component of the n-dimensional (unit) vector
which is outward normal to the surface 8D, i = 1, 2, ... , n, and
the functions f and g present under the integral sign over the curved
SUrface f T of the cylinder QT are traces of functions f and g On f T
This formula can be easily proved (compare Sec. 5.2) by approximat-
ing in H 1 0 (QT) the functions f and g by functions belonging to
C 1 (QT)
Iff E Hr,o (QT), r ?:- 1, then any derivative of this function with
respect to x1 , , Xn of order less than r has the trace on the
FUNCTION SPACES 161
curved surfacer T of the cylinder QT. Iff E H 28 8 (QT), s :;> 1, then any
aa:+ .. . +a:n+ilt
derivative a:
oxl l .
tl , a 1 + ...
ox'i;,n ot
+ ctn + 2~ < 2s, has the
trace on the curved surface r T of the cylinder QT.
8. EXAMPLES OF OPERATORS IN FUNCTION
SPACES
1. Integral Operators. Fredholm Integral Equation. Let Q be a
bounded region in the n-dimensional space Rn. On Q X Q we consi-
der the measurable function K (x, y). Assume that the function f (y)
is such that K (x, y) f (y) E L 1 (Q) for almost all x E Q (for instance,
f = 0). With every such function f (y) we associate a function
g (x) = ) K (x, y) f (y) dy. (1)
Q
This mapping can be regarded as an operator (linear, obviously)
from L 1 (Q) into L 1 (Q), from L 2 (Q) into L 2 (Q), from C (Q) into
C (Q) and so on. The function K (x, y) is referred to as kernel of
this operator. Of course, this operator may not be defined on the
whole space, for example, for the operator from C (Q) into C (Q) the
domain of definition is the set of all those functions in C (Q) for
which g(x) E C (Q). However, if the kernel K (x, y) E C (Q X Q),
then, as can be easily seen, this operator is defined everywhere (in
L 1 (Q), L 2 (Q), C (Q)) and is bounded.
We shall examine the operator defined by formula (1) with the ker-
nel K (x, y) = K 0 (x, y) I x - y 1-a:, where K 0 (x, y) E C (Q X Q)
and 0 < a < n, regarded as an operator from C (Q) into C (Q) and
as an operator from L 2 (Q) into L 2 (Q); in both cases it will be de-
noted by K:
g = Kj. (2)
The operator K is called the Fredholm integral operator. According
to the results of Sec. 1.12, Chap. II, for any function f E C (Q) the
function g E C (Q). This means that the operator K from C (Q)
into C (Q) is defined on the whole of C (Q).
Since the functions J
I K (x, y) I dy and I K (x, y) I dx are j
Q Q
continuous in Q, they are bounded, that is,
A= max { m~x ) I K (x, y) Idx, m~x ) I K (x, y) Idy} < oo. (3)
IIEQ Q xEQ Q
11-0594
162 PARTIAL DIFFERENTIAL EQUATIONS
Because for any point x E Q
lg(x)l-<1/IIIC(Q) ~ IK(x, y)jdy-<A/Ifi/C(Q)'
Q
so II g 1/c(Q)-<A II f llc(Q)' which implies that the operator K from
C (Q) into C (Q) is bounded and /1 K 11-<A.
Let I (x) E L 2 (Q). The functions If (y) 12 ) I K (x, y) I dx and
Q
I I K (x, y) Idx belong to L (Q) (the latter even to
1 C(Q)), therefore~
Q
by Corollary to Fubini's theorem, the functions K (x, y) It (y) r~
and K (x, y) belong to L 1 (Q X Q). This means that the function
K (x, y) f (y) also belongs to L 1 (Q X Q), since IK (x, y) f (y)J-<
+
-< I K (~, Y) I I K (x' Y~ II f (y} 12 Then by Fubini 's theorem the
functions g (x) =) K (x, y) f (y) dy, I I K (x, y) Idy and I IK (x, y) jx
Q Q Q
xj f (y) /2 dy belong to LdQ). For almost all x EQ we have the
inequality
jg(x)j 2 -< )IK(x, y)jdy )IK(x, y)/lf(y)jZdy
Q Q
-<A \IK(x, y)l/f(y)/ 2 dy~
Q
implying that g (x) E L 2 (Q). Integrate this inequality over Q and
apply Fubini's theorem to obtain
llglii.<Q>-<A) dx )IK(x, y)l/f(y)/ 2 dy
Q Q
=A ) II (y) /2 ( .\I K (x, y) Idx ) dy-<A 2 11 I lli.<Ql
Q Q
Thus the operator K from L 2 (Q) into L 2 (Q) is defined on the
whole of L 2 (Q), is bounded and II K II< A.
Lemma 1. The operator K acting from L 2 (Q) into L 2 (Q) is com-
pletely continuous. The operator K acting from C (Q) into C (Q) is
completely continuous.
Proof. 1. We first consider the operator K acting from L 2 (Q) into
L 2 (Q). The function K N (x, y) defined for any N > 0 as follows
K(x, y) when jx-yi~N- 1
{
KN(x, y)= K 0 (x, y)Na when /x-y/<N- 1
FUNCTION SPACES 163
belongs to C (Q X Q). Since for any point x E Q we have the in-
equality
)!K(x, y)-KN(x, y)ldy
(.J
where B = II K 0 II c (QxQ> and O'n is the surface area of the (n- i)-
dimensional unit sphere, given an e > 0 we can find anN such that
rna!
xfQ Q
JI K(x, y)-KN(x, y) jdy< ~
Because [KN(x, y) E C(Q X Q), there is a polynomial P(x, y) such
that IP(x,y)-KN(x,y)l< 21 eQI for all (x, y)EQxQ. This
implies that
rna! ~IK(x, y)-P(x, y)jdy<;:m~ )!K(x, y)-KN(x, y)dy
xEQ Q xEQ Q
+m~
XEQ Q
JIKN(x, y)-P(x, y) I dy < ~ + ~ =e. (4)
YEQ Q
The polynomial P(x, y) and the function G(x, y) = K(x, y) -
_ P(x, y) = Ko(x, y)-P(x, y) I x-y Ia: can be regarded as kernels of
lx-yla:
integral operators of the type (2); we denote them by P and G, res-
pectively. Moreover, we have the relation
K = P + G,
and, by (4) and (4'), the estimate
II G II< E.
11*
164 PARTIAL DIFFERENTIAL EQUATIONS
Thus the operator K has been expressed as the sum of an operator
G with arbitrarily small norm and the finite-dimensional operator P
(this operator transforms L 2 (Q) into the set of polynomials whose
degrees do not exceed that of P(x, y)). Therefore, by Theorem 4,
Sec. 3.9, Chap. II, the operator K is completely continuous.
2. We now examine the operator K acting from C(Q) into C(Q).
Because K is bounded, it maps a bounded set alt in C(Q) into a
bounded set rvft'. According to the results of Sec. 1.12, Chap. II,
given an e.> 0 a 6 > 0 can be found such that
\ IK(x', y)-K(x", y) I dy <e. whenever I x'- x" I< 6. There-
~re for I x' - x" I < 6
{ g (x') -g (x") 1-<) I K (x', y) -K (x", Y) II f (y) I dy -<e. II f 1/c(Q)'
Q
Thus the set rvft' of functions continuous in Q is uniformly bound-
ed and equi-continuous. Hence, by Arzela 's theorem, this set is
compact. I
The equation lj) = fLKIP +
f, where f1 is a complex parameter and
K the Fredholm integral operator, that is, the equation
IP(x) = f1 ) K(x, y) IP(Y) dy + f(x), (5)
Q
is known as the Fredholm integral equation (of the second kind).
We shall examine Eq. (5) in L 2 (Q) (f E L 2 (Q) and the desired
solution IP will be sought in L 2 (Q)).
In view of Lemma 1, Fredholm's theorems (Sees. 4.3-4.7, Chap. II)
are applicable to Eq. (5). In particular, if f1 is not a characteristic
value of the operator K (such numbers are at most countable), there
exists a bounded operator (/ - fLK) -1, that is Eq. (5) has a unique
solution lj) E L 2 (Q) with any free term f E L 2 (Q).
:-:--:---:-
If the kernel K (x, y) is such that K (x, y) = K (y, x), the operator
K from L 2 (Q) into L 2 (Q) is selfadjoint.
In fact, by Fubini's theorem,
(KIP, ')L.<Ql=) JK(x, y)qJ(y)dy'(x)dx
Q Q
Q Q
= J1P (y) ( J K (y, x) ' (x) dx) dy = (IP, K')L,(Q)
Q Q
for any lj), 'P E Lz(Q).
FUNCTION SPACES 165
Therefore all the results obtained in Sec. 5 of Chap. II for a gen-
eral completely continuous selfadjoint operator are also true for the
operator K. In particular, all the eigenvalues and characteristic
values of K are real and there exists an orthonormal basis composed
of eigenfunctions of this operator for the space L 2 (Q) (Corollary 2 to
Theorem 2, Sec. 5.2, Chap. II).
2. Differential Operators. Suppose that in an n-dimensional region
Q there is defined a bounded measurable function aa(x) for every
vector a = (a1 , , an), with the integers a;> 0, i = 1, ... , n,
I a 1:~ k, where k > 1. A linear operator acting from L 2 (Q) into
L 2 (Q) that associates with the function I the function
(6)
is called the linear differential operator (from L 2 (Q) into L 2 (Q)).
It will be assumed that the operator :t is of order k, that is, at least
one of the coefficients aa(x) is different from zero for I a I = k (the
set where aa(x) =1= 0 is not a set of measure zero).
The operator :t is, of course, not defined on the whole of L 2 (Q).
Nevertheless, the set of functions I for which expression (6) makes
sense (Dal is the generalized derivative) contains Hk(Q). Accord-
ingly, Hk (Q) can be taken as the domain of definition of :t.
If all the functions aa(x), I a I ~ k, are continuous in Q, for-
mula (6) also defines a linear operator from C(Q) into C(Q) (the
linear differential operator from C(Q) into C(Q)). In this case as
the domain of definition of :t one can take Ck(Q).
A particular case of :t acting from L 2 (Q) into L 2 (Q) (from C(Q)
into C(Q)) is the operator Da, I a I = k, that associates with I in
lJk(Q) (Ck (Q)) its generalized (classical) derivative. The operator
Da from L 2 (Q) into L 2 (Q) is unbounded, because the sequence
lm(x) = eim(x,+. +xn), m = 1, 2, ... , of functions in Hk (Q)
which is bounded in L 2 (Q) (II lm IIL.(Q) = VTQT, m = 1, 2, ... ) is
mapped into the sequence gm(x) = (im) 1aleim(x,+. .+xn>, m =
= 1, 2, ... , unbounded in L 2 (Q) (II gm IIL.(Q) = mla I YTQI-+ oo
as m-+ oo).
It can be similarly shown that the operator :t, k >
1, from L 2 (Q)
into L 2 (Q) is also unbounded, and so are the operators Da and Z
from C(Q) into C(Q).
If :t is regarded as an operator from Hk(Q) into L 2 (Q) or from
Ck(Q) into C(Q), then it is bounded, because for any I E Hk(Q)
(Ck(Q))
II Zl IIL,(Q)<:const II f IIHk<Q> (II Z/ IIC(Q)<:const II I llck(Q)).
166 PARTIAL DIFFERENTIAL EQUATIONS
PROBLEMS ON CHAPTER III
1. A ball S = {II x II < 1} in a Banach space is said to be strictly convex
if for any points x and y, x =I= y, on the unit sphere II x II = II y II = 1 and any
a E (0, 1) the point ax+ (1 -a) yES, that is, II ax+ (1 -a) y II < 1.
Is the unit ball strictly convex in spaces C(Q), L1 (Q), L 2 (Q)?
2. Let x he a point on the unit sphere in C(Q) (L 1 (Q)). Find the set of all
points yon the unit sphere such that all the points of the segment ax (1 - a)y,+
0 <: a <: 1, lie on this sphere.
3. The set Cl< (Q) is a linear manifold in CI<(Q}. Denote by b(Q) the clo-
sure of this set in the norm rna~ ~ l Dal (x) j: b (Q) = Cl< (Q). What func-
xEQ I a !~k
tions is b (Q) composed of?
4. Show that if iJQ ECl<, then W"'(Q) is everywhere dense in CI<(Q).
Let B be a Banach space, and a~lt, Jlf' its subspaces. We say that B is the
direct sum of &'It and .;V': B = &'/t(J)Jll' if any element I of B is uniquely expressed
as the sum h+l2 , where 11 ~&'It and 12 E Jlf'. If the Hilbert space H = &'lt(J).;V"
and &'It j_ .;11, then &'It (.Jf(') is called orthogonal complement of .J/(' (&'It) in H.
5. Express Cl<([a, b]) as a direct sum of the subspace Ck([a, b)) and a sub-
space .Jlf'. Find the dimension of ,jf/.
6. The set of functions belonging to L 2 (Q) that vanish (a.e.) in Q', Q' c Q,
is a subspace of L 2 (Q). Find its orthogonal complement.
7. Consider the function I (x) = ra!p in the plane x = (x1 , x2 ) = (r cos !p,
r sin !p), 0 <: !p < 2n. For what a does the function 1 belong to H 1 (Q}, where Q
is (a) the disc {r < 1}, (b) {r < 1, !p =I= 0}?
8. Suppose that the sequence of functions lm(x), m = 1, 2, .. , in Cl< (Q)
converges weakly in L 2 (Q) to a function I and the sequence Dalm, m = 1, 2, ... ,
for some a = (a1 , , an}, I a I = k, is bounded in L2 (Q). Show that I has
generalized derivative Dal.
9. Suppose that the sequence of functions lm(x), m = 1, 2, . , in C1 (Q)
converges weakly in L 2 (Q), and the sequences 881m, i=1, . , n, m = 1, 2, ... ,
. Xi
are bounded in L 2 (Q). Show that the sequence lm,m = 1, 2, . , converges
strongly in L 2 (Q). Give an example of a sequence that satisfies the formulated
conditions but is not compact in H 1 (Q).
10. Show that if the sequence of functions lm(x}, m = 1, 2, ... , in Cl< (Q),
k ~ 1, converges weakly in L 2 (Q) to a function I and for all a = (a1 , , an),
I a I = k, II Dalm IIL,(Q) <: const, m = 1, 2, ... , then (a) f E HI<(Q), (b) the
sequence fm m = 1, 2, ... , converges to f strongly in Hl<-1 (Q).
11. Prove that for any function f(x) E HI< (K) (f(x) E Cl< (K)), where K is an
n-dimensional cube, there is an extension F(x}, with compact support, into
a wider region Q, Q 2> K, that belongs to Hk(Q) (Ck(Q)), and satisfies the
inequality II FIIHII.(Q) <: C II f IIHII.(K)' where the constant C > 0 does not
depend on f.
12. Let x 0 be a point in a region Q of the n-dimensional space Rn, n > 1.
Show that the closure of the linear manifold of functions that are continuously
differentiable in 7j and vanish in some neighbourhood (different for different
functions) of x 0 coincides with H 1 (Q).
FUNCTION SPACES i67
i3. Show that the set H1 (a, b) of all functions I E H 1 (a, b) for which l(a) =
= 1 (b) is a subspace of the space H 1 (a, b). Show that ifl(a, b) c ifl(a, b) c
c H 1 (a, b). Find the orthogonal complement of W(a, b) in H1 (a, b) and that
()[ H1 (a, b) in H 1 (a, b), and construct orthonormal bases for the spaces H1 (a, b),
Ifl(a, b) and H 1 (a, b).
Let a function IE L 2 (K), where K is the cube {I x1 I <a, i = i, ... , n}.
According to Fubini's theorem, for almost all Xn = ~ E (-a, a) the function
l(x 1 .~) is defined and belongs to L 2 (K 1 ) , where K 1 is the (n - i)-dimensional
eube {I x 1 I < a, t = i, ... , n - 1 }. This function will be referred to as the
value of I on the section K n
{xn = ~}. Similarly, for almost all x' = ~I E K.
a function 1(~ 1 , xn) is defined and belongs to L 2 (-a, a). This function will be
referred to as the value of I on the section K n
{x 1 = ~I}.
For a function IE H 1 (K) there exists the trace flxn=s for all xn = ~ E
~ [-a, a], belonging to L 2 (K 1 ).
i4. Prove that if IE H 1 (K), then for almost all ~ E K 1 its value 1(~ 1 , xn)
()n the section K n{x 1 = ~I} belongs to the space H 1 ( -a, a), for almost all
~ E (-a, a) its trace llnn=s and its value l(x 1 , ~)on the section K n {xn = ~}
belong to H 1 (K 1 ).
i5. Prove that the set of traces of all functions in H 1 (Q) on an (n - i)-di-
mensional surface S c Q does not coincide with L 2 (S).
i6. Prove the following assertions:
(a) If I E H 1 (Q), then I I I also belongs to H 1 (Q),
(b) If the functions fi, ... , IN belong to H 1 (Q), then the functions
max (/1 , , IN) and min (fi, ... , IN) also belong to H 1 (Q).
17. We shall say that a function l(x) belongs to the class ca(Q) for some a,
0 <a< 1, if for any strictly interior subregion Q 1 , Q 1 ~ Q, there is a constant
C = C(Q 1 ) such that for all points X 1 , x" in Q 1 the inequality I l(x 1 ) - l(x")'l ~
~ C I x 1 - x" Ia holds. If this inequality holds with some constant C for all
1
X x" in Q, then we say that the function I (x) belongs to the class ca(Q).
'
PI +1 (Q)
Show that if IE H 102c (Q is an n-dimensional region}, then IE ca (Q)
[~] +1 [~] +1
for any a<[n/2J+i-n/2, and if IE H 2 (Q} or IE H 2 (Q) and
[~] +1 . -
iJQEC 2 , then IECa(Q) for any a<[n/2]+1-n/2.
k+1+ [~] (
i8. Prove that any bounded set in H 2 (Q) Q is ann-dimensional re-
gion, iJQ E C
k+1+ [~1-)
2 is compact in Ck(Q).
-
i9. Suppose that the functions k(x), a(x), p(x) belong to C(Q), a(x) E C(iJQ),
k (x) > 0, a (x) ;;;;;;: 0, p (x) ;;;;;;: 0 in Q, a (x) ;;;;;;: 0 on aQ. Show that the bilinear
form
Q Q
J
Q
pg dx)
with a + p \$ 0 and the bilinear form
W2 (!,g)= J
Q
(kVtvi+alg) dx+ ( J
aQ
at dS) ( J
aQ
ag dS)
168 PARTIAL DIFFERENTIAL EQUATIONS
when either a \$ 0 or a \$ 0 defined on H 1 (Q) determine scalar products in
Hl(Q) which are equivalent to the scalar product
(!, g)Hco>=) (V/Vi+{i> dx.
Q
20. Suppose that the function k(x) E C2 ([0, 1]) and k(x) > 0 for x > 0.
By Hk(O, 1) denote the completion of the set of functions in C1 ([0, 1]) vanishing
1
for x = 1 in the norm generated by the scalar productl ~ k(x) /'(x) g'(x) dx.
0
Prove that Hk(O, 1) c 2 (0, 1) if and only if lim k(x) x-2 > 0.
X-++0
21. Show that the scalar products (/, g)'= ) ~ Da/Dag dx and (/,g)"=
Q )al~k
= ) ~ Da/Dag dx are equivalent in the space Hk(Q).
Q rar=k
22. Let f E 2 (0, 1). The linear functional lt(u) = (/, u)L.(Q) is bounded in
Hk(O, 1) for any k >
0. By Riesz's theorem, there exists (a unique) element
FEHk(O, 1) such that lt(u)=(F, u)ok for all uEHk(O, 1). Find F and
H (0, 1)
show that FE Hk(O, 1) n H2k(O. 1). (For scalar product take (a) (!,g)=
1 1
= J /ck>gck>dx, (b) (/, g)= .\ (J'k>iJ<k> +/g) dx, where f k)= dkf
dxk
)
0 0
Besov, 0. V., Il'in, V. P. and Nikol'skii, S.M. Integral Representations ~
Functions and Embedding Theorems, Moscow, Nauka, 1975 (in Russian).
Nikol'skii, S.M. Approximation of Functions of Several Variables and Embed-
ding Theorems, Springer-Verlag, 1975.
Sobolev, S. L. Some Applications of Functional Analysis in Mathematical
Soc. R. I., 1963).
CHAPTER IV
ELLIPTIC EQUATIONS
1. GENERALIZED SOLUTIONS OF BOUNDARY-VALUE
PROBLEMS. EIGENVALUE PROBLEMS
1. Classical and Generalized Solutions of Boundary-Value Problems.
Suppose that in an n-dimensional region Q there is given the elliptic
equation
:t;u =
div (k(x) vu) - a(x) u = f(x), (1}
whose coefficients are real-valued and satisfy the conditions
a(x) E C(Q), k(x) E C1 (Q), k(x) >k > 0 0 for all x E Q.
The function u(x) and the free term f(x) of the equation may be,
in general, complex-valued.
A function u(x) belonging to C 2 (Q) n C(Q) is called a (classical)
solution of the first boundary-value problem or the Dirichlet problem
for Eq. (1) if it satisfies Eq. (1) in Q and the condition
u iaQ = <p(x), (2)
where q;(x) is a given function, on the boundary fJQ.
The function u(x) E C2 (Q) n C1 (Q) is called a (classical) solution
of the third boundary-value problem for Eq. (1) if it satisfies Eq. (1}
in Q and on the boundary fJQ the condition
( :~ +a(x) u} lao= q;(x), (3)
where a(x) E C(fJQ) and <p(x) are given functions. It will be as-
sumed that a(x) >
0.
If the function a (x) in (3) is identically zero, then the third bound-
ary-value problem is termed the second boundary-value problem or
the Neumann problem.
When n = 1, Eq. (1) becomes an ordinary differential equation
:u ==
(k(x) u')' - a(x) u = f(x). (1 1)
t70 PARTIAL DIFFERENTIAL EQUATIONS
The region Q in this case is an interval (a, ~), while the boundary
conditions of the first and third boundary-value problems are, res-
pectively, of the form
and
>
where c:p 0 , c:p 1 , a 0 >
0, a 1 0 are some given constants.
Suppose that the function u(x) is a classical solution in Q of the
first boundary-value problem (1), (2). We multiply (1) by an arbit-
rary function v(x) E Ct(Q) and integrate the resulting identity
over Q. By means of Ostrogradskii's formula, we obtain
Q
J(k'Vu v;+auv) dx=- Jf;dx Q
(4)
(the integral over the boundary fJQ vanishes, because v has compact
support).
If we additionally assume that the partial derivatives of the solu-
tion Ux.l E L 2 (Q), i = 1, ... , n, that is, that u(x) E H 1 (Q) and
f(x) E L 2 (Q), then the integral identity (4) holds not only for all
v(x) E C1(Q) but also for all v E H1 (Q). To see this, we consider
any function v E ifl(Q) and a sequence of functions v11 (x), k =
= 1, 2, ... , in b(Q) that converges to v in the norm of H 1 (Q). The
identity (4) holds for each of v,.. (x). Letting in this k - oo, we find
that the identity (4) holds for v also.
Thus, iff E L 2 (Q), the classical solution u of the problem (1), (2)
belonging to the space H 1 (Q) satisfies the integral identity (4) for
all v E H1 (Q).
We introduce the following definition.
A function u E H 1(Q) is called the generalized solution of the prob-
.lem (1), (2) with f E L 2 (Q) if it satisfies the identity (4) for all v E
E IP(Q) and the boundary condition (2). In the boundary condi-
tion (2), the equality is understood as the equality of elements of
L 2 (fJQ), and uioQ is the trace of u.
Note that the above definition of a generalized solution is not a
,complete generalization of the corresponding classical notion,
because in order that a classical solution u(x) be a generalized solu-
tion it should be subject to additional conditions of "integral char-
acter", namely, it must be such that u E H 1 (Q) and Zu E L 2 (Q),
where : is the operator in (1).
In an analogous manner one can introduce the notion of general-
ized solution of third (second) boundary-value problem for Eq. (1).
ELLIPTIC EQUATIONS 171
Suppose that the function u(x) is a classical solution of the third
boundary-value problem (1), (3). Assume that the right-hand side
j(x) of Eq. (1) belongs to L 2 (Q) and the function <p(x) present in the
boundary condition (3) belongs to L 2 (aQ). We multiply (1) by an
arbitrary function v (x) E H 1(Q) and integrate the resulting identity
-over Q. Then Ostrogradskii's formula yields the integral identity
) (kVu V'v + auv) dx+ l kauv dS = - Jfv dx + ~ k<pv dS, (5)
Q fJQ Q oQ
which is satisfied by the classical solution u(x) for all v(x) E H 1(Q).
We now introduce the following definition.
The function u E H 1(Q) is termed a generalized solution of the
third (second, if a (x) = 0) boundary-value problem for Eq. (1) with
f E L 2 (Q), <p E L 2 (aQ), if it satisfies (5) for all v E H 1(Q).
In defining the generalized solutions the functions v in identities
{4) and (5) were assumed to be complex-valued, but they may as
well be assumed real-valued. Indeed, if the function u E H 1 (Q)
satisfies, for example, the identity (4) for all complex-valued func-
tions v E IJl(Q), then it obviously satisfies the same identity for
0
all real-valued v E H 1(Q). Conversely, if the function u E H 1 (Q)
satisfies (4) for all real-valued v E H1 (Q), then the same identity
holds also for any complex-valued v = Re v
0
+ i Im v belonging to
H 1 (Q), because it holds for functions Rev and Im v belonging to
0
fll(Q).
Note that we have, in fact, already encountered (Sec. 3.1, Chap. I)
generalized solutions of boundary-value problems for Eq. (1) (in
the two-dimensional case) in deriving the equilibrium conditions of
a membrane: the integral identities (4) and (5) appearing in the
definition of generalized solutions coincide with the identities (4)
and (1) of Sec. 3.1, Chap. I.
The definitions of generalized solutions of boundary-value problems
for Eq. (1) apply equally well to one-dimensional case. A function
u E H 1(a, ~) satisfying the boundary conditions (2 1 ) (from Theo-
rem 3, Sec. 6.2, Chap. III, it follows that u E C([a, ~])) is a general-
ized solution of the first boundary-value problem for Eq. (1 1 ) if for
any v E H1(a, ~)
~ ~
J (ku';' + auv) dx = - ' tv dx.
172 PARTIAL DIFFERENTIAL EQUATIONS
A function u E H1 (a, ~) is a generalized solution of the third (sec-
ond) boundary-value problem for Eq. (1 1) if for any v E H 1 (a, ~)
~
J(ku't? + GUV) dx + k (~) <J1U (~) V(~) + k (a) <JoU (a);- (a)
a
~
The present section is devoted to the study of generalized solu-
tions of boundary-value problems. Since the generalized solutions
are elements of the Hilbert space H 1 (Q), the general results of
Chap. II will be widely used.
The investigation of classical solutions of the boundary-value
problems is a considerably more difficult problem and it is natural to
divide this into two simpler problems: first, the generalized solution
is constructed, and then by establishing (under appropriate condi-
tions) its smoothness it is shown to be a classical solution. The smooth-
ness of generalized solutions will be proved in the next section.
2. Existence and Uniqueness of Generalized Solution in the Sim-
plest Case. To examine the questions of existence and uniqueness of
generalized solutions of boundary-value problems, it is convenient to
(that is, cp = 0). By definition, a generalized solution of the bound-
ary-value problem (1), (2) with cp = 0 is the function u E ifl(Q)
satisfying for all v E Ffl(Q) the integral identity (4):
Q
) (k'Vu Vv+auv) dx=-
Q
Jf;dx.
The generalized soiution of the third (second) boundary-value prob-
lem (1), (3) with cp = 0 is the function u E H 1 (Q) satisfying for all
v E H 1 (Q) the integral identity
,\ (k'Vu '\Tv+ auv) dx + ) kauv dS = - ) /;- dx. (6)
Q ~ Q
Suppose that a(x) :> 0 in Q. Then, by Theorem 6, Sec- 5.6,
Chap. III, a scalar product
(u, v). = \ (k'Vu Vv+ auv) dx, (7)
H'(Q) d
equivalent to the usual scalar product ( (u, v) = ) (Vu "1/v + uV} dx}
Q
can be introduced in the space /Jl(Q). Using this, the identity (4)
ELLIPTIC EQUATIONS 173
may be put in the form
(u,v). =-(f,v)L,(Q) (8)
H(Q)
For a fixed f E L 2 (Q) (f, v)L,(Q) is a linear functional on H1(Q},
v E H1(Q). Since
I (f' V)L,(Q) 1-< II f I!L.(Q) II v IIL,(Q)-< c II f IIL,(Q) II v "H(Q)
in which the positive constant C does not depend on f and v, this
functional is bounded and its norm does not exceed C II f IIL,(Q)
By Riesz's theorem (Theorem 1, Sec. 3.2, Chap. II), there is a
function F 1 in if1 (Q) such that (f, v)L,(Ql = (F1 , v).Hl(Q) for all v E
E H1 (Q). Such a function is unique and satisfies the inequality
II F 1 IIHl(Q) ~ C II f IIL2(Ql Accordingly, in FJl(Q) there is a unique
function u = F 1 satisfying the identity (8).
Thus we have proved the following theorem.
Theorem 1. If a(x) >
0 in Q, then for any f E L 2 (Q) there exists
a unique generalized solution u of the problem (1}, (2) (with <p = 0).
J~foreover,
(9)
where the positive constant C does not depend onf.
If a (x) > 0 and at least one of the functions a(x) or a(x) does
not vanish identically, then, by Corollary to Theorem 5, Sec. 5.6,
Chap. III, the scalar product
(u, v)H<Q>= ~(k'Vu'V;-+auv)dx+ ~kauvdS, (10)
G aq
-equivalent to the usual scalar product, can be introduced in H 1 (Q).
Therefore identity (6) can be rewritten as
(u, V)H(Q)= -(f, V)L,(Q) (11)
Since for a fixed f E L 2 (Q) the functional (f, v)L,(Ql which is li-
near in v E H 1 (Q}, is bounded: I (/, v)L,(Ql I ~ II f IIL,(Q) II v IIL,(Q) :::;;:
~ C II f IIL,(Ql II v IIHl(Ql where the constant C > 0 does not depend
<>n for v, by Riesz's theorem there is a unique function F 2 in H 1 (Q)
such that (j, v)L,(Q) = -(F 2 , v)Hl(Q) for any v E H 1 (Q), and
II F 2 IIHl(Q) ~ C II f IIL2<Ql Therefore in H 1 (Q) there exists a unique
function u = F 2 satisfying (11).
Thus we have proved the following theorem.
Theorem 2. lf a(x) >0 in Q and at least one of the functions a(x)
<Jr a(x) does not vanish identically, then for any f E L 2 (Q) there
174 PARTIAL DIFFERENTIAL EQUATIONS
exists a unique generalized solution u of the problem (1), (3) (with
<p = 0). Moreover,
(12)
where the positive constant C does not depend on f.
Remark. If f is a real-valued function, then the solutions of the
boundary-value problems obtained in Theorems 1 and 2 are also
real-valued. Indeed, let u = Re u + i Im u be the generalized
solution of one of these boundary-value problems. Since the coef-
ficients of the equation and the function f are real-valued, from (4)
(or (6)) it follows that the function Re u is also a generalized solu-
tion of the same problem (the function v in (4.) and (f.) may te con-
sidered real-valued). The uniqueness of the solution implies that
u =He u.
3. Eigenfunctions and Eigenvalues. A nonzero function u(x) is
called an eigenfunction of the first boundary-value problem for the
operator Z = div (k(x) V) - a(x) if there exists a number A such
that the function u (x) is a classical solution of the following problem:
Xu = J..u, x E Q, (13)
ulaQ = 0. (14)
The number A is called the eigenvalue (corresponding to the eigen-
function u(x)).
It is obvious that to every eigenfunction there corresponds only
one eigenvalue but not vice-versa. In particular, if u(x) is an eigen-
function, then so is the function cu(x) for any constant c =t= 0 cor-
responding to the same eigenvalue. Accordingly, we may consider
eigenfunctions normalized, for instance, by the condition ll u !IL,(Q) =
=1.
Let A be an eigenvalue and u(x) an eigenfunction of the first
boundary-value problem, and let u(x) E ffl(Q). Multiplying (13)
v
by .an arbitrary E ffl(Q) and integrating the resulting equation
over Q, we obtain the integral identity
Q Q
which is satisfied by u for all v E H1(Q).
A nonzero function u E ifl(Q) is called the generalized eigen-
function of the first boundary-value problem for the operator Z if there
is a number A such that the function u satisfies the integral identity
(15) for all v E H1 (Q); the number A is called the eigenvalue (corres-
ponding to the generalized eigenfunction u).
ELLIPTIC EQUATIONS 175
It will he assumed that II u IIL.<Q> = 1.
A nonzero function u(x) is called the eigenfunction of the third
(second) boundary-value problem for the operator :t = div (k(x) V) -
- a(x) if there is a number lv (the eigenvalue corresponding to u(x)}
such that u(x) is a classical solution of the following problem
Zu='Au, xEQ,
( ~~ + a(x) u) [OQ = 0.
As is easy to see, the eigenfunction of the third (second) boundary'-
value problem satisfies for all v E H 1 (Q) the integral identity
J(kvuvv+auv)dx+ JkauvdS=-'AJuvdx. (16)'
Q oQ Q
A nonzero function u E H 1 (Q) is called the generalized eigenfunc-
tion of the third (second) boundary-value problem for the operator :t
if there is a number "A (the eigenvalue corresponding to u) such that.
the function u satisfies the identity (16) for all v E H 1 (Q).
It will be assumed that II u IIL.(Q) = 1.
The further consideration in this section will be confined to gen--
eralized eigenfunctions and their corresponding eigenvalues. It will
be convenient to regard the identities (15) and (16) defining the gen-
eralized eigenfunctions as identities in the scalar products in
spaces L 2 (Q) and ifl(Q) or H 1 (Q), respectively.
Put m = min a(x) (here it is not assumed that a(x) >-
0). Then,
xeQ
the function
-a(x) = a(x) - m + 1 >- 1 in Q.
Therefore a scalar product (equivalent to the usual scalar product)
in H1 (Q) can be defined by the formula
(u, v)o
H(Q)
= Jl(kVuVv+auv)dx, (17)
Q
while in H 1(Q) by
(u, v)H(Q) = J(kVuVv + auv) dx + ) kauv dS. (18)
Q aQ
Then (15) and (16) can be rewritten as
(u, v)oH(Q) =(-'A-m+1)(u, v)L,(Q) (19)
and
(u, v)H<Ql = (-'A-m+ 1) (u, v)L,(Q) (20)
We shall first prove the following assertions.
176 PARTIAL DIFFERENTIAL EQUATIONS
Lemma 1. There is a bounded linear operator A acting from L 2 (Q)
into iP(Q) with the domain of definition L 2 (Q) such that for all v E
E ffl(Q) the following relation holds:
(u, v)L.CQ> =(Au, v) o (21)
H(Q)
The operator A has an inverse A - 1 . If A is regarded as an operator
from H1 (Q) into H1 (Q), it is selfadjoint, positive and completely
continuous.
Lemma 1'. There is a bounded linear operator A' acting from
L 2 (Q) into H 1 (Q) with the domain of definition L 2 (Q) such that for
all v E H 1(Q) the following relation holds:
(u, V)L,(Q) = (A'u, V)H(Q) (21')
The operator A' has an inverse A' - 1 . If A' is regarded as an operator
jrom H 1 (Q) into H 1(Q), it is selfadjoint, positive, and completely
continuous*.
We shall prove Lemma 1; Lemma 1' is proved in the same way.
Proof of Lemma 1. For any (fixed) function u E L 2 (Q) the function-
al l(v) = (u, v)L,(Q) which is linear in v, v E ffl(Q), is bounded,
because
ll (v) I= I(u, v)L.cQ> 1-< II u IIL,(Q) II v IlL.<~><:: C II u lk.co> II v IIH<Q> .
Therefore, by Riesz's theorem, there exists a unique function U E
0
E H 1 (Q), II U IIIft(Q) = Ill II:::;:; C II u IIL.(Q) such that l(v) =
0
= (U, v)o
H(Q)
for all v E H 1 (Q). This means that on L 2 (Q) an oper-
ator A is defined (which is obviously linear): Au = U, for which
{21) holds. Since II Au lloH(Q) :::;:; C II u IIL.CQh the operator A from
0
L 2 (Q) into H 1 (Q) is bounded. If for ~orne u E L 2 (Q) Au = 0, then,
by (21), (u, v)L.<Q> = 0 for all v E H 1 (Q), that is, u = 0. This im-
plies that the operator A - 1 exists.
The operator A from Ffl(Q) into ifl(Q) is selfadjoint, as can be
seen from (21): (Au, v)o = (u, v)L,(Q) = (v, u)L,(Q) =
H(Q)
= (Av, u)o
H(Q)
= (u, Av) 1
H (Q)
; (21) also implies that the operator A
is positive.
* The form of operators A and A' depends, of course, on the scalar product
defined in ifl(Q) and H 1 (Q), respectively. Here scalar products (17) and (18)
are used.
ELLIPTIC EQUATIONS 177
0 0
Let us show that A as an operator from H 1 (Q) into H 1 (Q) is
completely continuous. Consider an arbitrary set of functions bound-
o
ed in H 1(Q). By Theorem 3, Sec. 5.4, Chap. III, this set is com-
pact in L 2 (Q). This means that from any of its infinite subsets we
can choose a sequence U 8 , s = 1, 2, ... , which is fundamental in
0
L 2 (Q). Since the operator A fmm L 2 (Q) into H 1 (Q) is bounded,
and hence continuous, the sequence Au8 , s = 1, 2, ... , is funda-
H
mental in 1 (Q). I
By Lemma 1, the identity (1?) can be written in the form of an
operator equation in the space H 1 (Q):
+ m- 1) Au =
0
Similarly, (20) can be written, using Lemma 1 ', as an operator
equation in the space H 1(Q}:
-(A-+ m -1)A'u = u, u E H 1 (Q). (22')
Thus the number A, is an eigenvalue of the first (third) boundary-
value problem for the operator: and u is the corresponding genera-
lized eigenfunction if and only if - (A- + m - 1) is the character-
istic value of the completely continuous selfadjoint operator A
0 0
from H 1 (Q) into H 1 (Q) (A' from H 1 (Q) into lfl(Q)) and u is the
corresponding eigenelement.
Therefore from the results of Sec. 5, Chap. II it follows that there is
at most a countable set of eigenvalues of the first (third) boundary-
value problem; this set does not have finite limit points; all the
eigenvalues are real; to every eigenvalue there corresponds a fmite
number (the multi~licity of the eigenvalue) of mutually orthogonal
eigenfunctions in H 1 (Q) (in H 1 (Q)); the eigenfu~ctions correspond-
ing to different eigenvalues are orthogonal in lfl(Q) (in H 1 (Q)).
Note that corresponding to each eigenvalue A, of the f1rst (third)
boundary-value problem one can choose exactly k, k being the mul-
o
tiplicity of A, mutually orthogonal real eigenfunctions in H 1 (Q)
(in H 1 (Q)). Let u '~ Re u -+- i Im u be the eigenfunction corres-
ponding to the eigenvalue A. Since A, and the coefficients k(x) and
a(x) are real, the functions Re u and lm u, as follows from (15) or
(ifi), are also eigenfunctions corresponding to the same A, (the func-
ti-on v in (15) or (Hi) may be considered real-valued). It is not dif-
ficult to check that the inaximum number of mutually orthogonal
real eigenfunctions is k.
Let
12--0594
178 PARTIAL DIFFERENTIAL EQUATIONS
be the sequence of all the eigenvalues of the first (third) boundary-
vahle problem for the operator : in which each eigenvalue is re-
peated according to its multiplicity. Let
(24)
be a system of mutually orthogonal generalized eigenfunctions
0
(II U 6 IILi(Q) = 1) in H 1 (Q) (H 1 (Q)); each Us corresponds to the
eigenva ue "-s:
-(As+ m- 1) Au8 = u., s = 1, ... , (25)
for the first boundary-value problem and
-(As+ m- 1) A'u 8 = U 8 , s = 1, . , (25')
for the third boundary-value problem.
Scalar! multiplication in H1 (Q) (H1 (Q)) of (25) ((25')) by u 8
gives, in view of (21) ((21')),
llusWH(Q)
rr"= -(A8 +m-1)llualll.(Q)= -(A 8 +m-1), (26)
II Uallk(Q) = - (A 8 + m-1) II Uslli,(Q) =-(As+ m-1), (26')
which may be written (the scalar products in H1 (Q) and H 1 (Q) are
defined by formulas (17) and (18)) in the form
~kl'VU 8 j 2 dx+) (a+l..s)lusl2 dx=0 (27)
Q Q
Q OQ
(27')
for the third boundary-value problem.
It follows from equality (27) that for all s = 1, 2,
'-.<-m= -min a(x). (28)
xeQ
Similarly, from (27') it follows that for all s = 1, 2,
<
A8 -m= -min a(x), (28')
xEQ
and for all s = 1, ... strict inequality holds if either a(x) ;: const
or cr(x) :f= 0. If, however, a(x) == 0 (the second boundary-value
problem) and a(x) == const, a(x) =
m, then among the eigenvalues
of the second boundary-value problem there is one that equals - m
and the corresponding eigenfunction is equal to const = 11VTQI.
This eigenvalue has multiplicity 1, because, by (27'), all the eigen-
ELLIPTIC EQUATIONS i79
functions corresponding to it satisfy the relation Jk I vu 12 dx =
Q
= 0, that is, are constants.
It follows from (26) ((26')) that the system
,/
y 1-m-jA.1
ul
' ... ' ,/
Us
y 1-m-1.. 8 . . ..
H
is orthonormal in 1 (Q) (in H 1(Q)). By Corollary 1 to Theorem 2,
Sec. 5.2, Chap. II, this system is an orthonormal basis for ifl(Q) (for
H 1 (Q)). And since the space H1 (Q) (H1 (Q)) is infinite-dimensional,
it follows that the set (24), and therefore also (23), is infinite. Hence
'A.~- oo ass~ oo.
Scalar multiplication in H1 (Q) (H1 (Q)) of (25) ((25')) by ub
j =!= s, and the use of (21) ((21')), gives the identity -('A.+ m-1) X
x (u., ui)L.<Q> = 0, that is, the system (24) is orthonormal in
L 2 (Q). As the linear manifold spanned by the system (24) (and
therefore by the system (24)) is everywhere dense in ifl(Q) (H1 (Q)),
it is also everywhere dense in L 2 (Q). Accordingly, the system (24)
is an o'fthonormal basis for L 2 (Q), that is, any element f E L 2 (Q)
can be expanded in a convergent Fourier series in L 2 (Q):
(29)
and the Parseval-Steklov equality holds:
""
2J It.12
lrt IIL.<Q> = a=t
Suppose that the function f E H1 (Q) (H 1 (Q)). It can be expa:nded
in a Fourier series with respect to the orthonormal b~is (24) that
converges in ifl(Q) (H1 (Q)):
00
= ~ ( J' Y Us A. ) - V Us (30)
s=1. 1-m- s .H'{Q) 1-m-l..s
for the first boundary-value problem (/ E H1 (Q)) and
00
!= ~ (t, (30')
a=t
180 PARTIAL DIFFERENTIAL EQUATIONS
for the third boundary-value problem (f E H 1(Q)). Moreover, the
following Parseval-Steklov equalities hold:
00
~I (t.
s=1
and
00
s=!
The series (30) ((30')), of course, converges to f in the norm of
L 2 (Q) also. A comparison of this series with the series (29) shows
that Is=(/, Us)L 1 (Q) = (1, Vi -m- o
1
Us ')., s )H(Q) Vi -m- ').,
s
(Is=
- (f
- 1
us
V1-m-'J.,s
)
H(Q)
V 1-m-A
1 ) Therefore
8
00
s=!
00
2J '-sl fs/ 2 ),
(II I llh(Q) =(1-m) II I lli.<Q>- s=!
whence it follows, in view of (28), that
;JO 00 00
~ lfsl 2
h As/ls/ 2 +2/m/ s=i
2J l'-sllfsl 2 -<- s=i
s=i
-<II t IIA:,<Ql + (21 m I+ Im -11 ) II t llt.<Q>
and similarly (in view of (28')) that
00
s=i
2
00
.6i I'-.II Is / -<C !If IIA,<ol'
2 (31)
ELLIPTIC EQUATIONS 181
where As, s = 1, 2, ... , are eigenvalues of the fHst boundary-value
problem with f E ifl (Q), and the inequality
00
2J I As II fs P~<: c II f 1111-<Q),
s=l
(32)
where A8 , s = 1, 2, ... , are eigenvalues of the third boundary-
value problem with f E H 1 (Q). The constant C in (31) and (32) does
not depend on f. Thus we have proved the following theorem.
Theorem 3. The eigenvalues A1 , A2 , of the first or third (second)
boundary-value problem for the operator : = div (k(x) V) - a(,x)
are real and As -+ - oo as s-+ oo. When a(x) =I= const, the eigenval-
ues of the first and third, with a =1= 0, boundary-value problems as well
as those of the second boundary-value problem (a = 0) satisfy the ine-
quality As< -min a(x) for all s = 1, 2, ... , When a(x) is a
xEQ
constant, a (x) = m, the eigenvalues of the second boundary-value
problem satisfy the inequality As ~ - m, s = 1, 2, . . . , and there is
an eigenvalue that is equal to -m whose multiplicity is 1 and to which
there corresponds the generalized eigenfunction 1/VTQT. The gener-
alized eigenfunctions u 1 (x), u 2 (x), ... of the boundary-value prob-
lems under consideration constitute an orthonormal basis for L 2 (Q),
that is, any function f E L 2 (Q) can be expanded in a Fourier series
(29) which converges in L 2 (Q). When f E ]Jl(Q), the series (29) in
terms of the generalized eigenfunctions of the first boundary-value
problem converges in ]Jl(Q) and the inequality (31) holds. When f E
E H 1 (Q), the series (29) in terms of the generalized eigenfunctions of
the third (second) boundary-value problem converges in H 1(Q) and
the inequality (32) holds.
4. Variational Properties of Eigenvalues and Eigenfunctions. The
operator A defined by the relation (21) and acting from ]Jl(Q) into
iJl(Q) is selfadjoint, completely continuous and positive (Lemma 1),
therefore, by Theorem 1, Sec. 5.1, Chap II, its first characteristic
value, obviously positive, is
2 2
_ . f II f llii<Q) = 1. nf II f llii'<Q)
I-tt- 1on (Af, f) o II f 11 2
IEH 1 (Q) Ht(Q) IEH'(Q) L.(Q)
(the norm of f in ifl(Q) is defined corresponding to the SC!J.lar pro-
duct (17)). The functional II f IIA<Q/11 f IIL<Q) assumes the value fA- 1
when f = u 1 , where u 1 is the f1rst eigenelement of the operator A ..
Therefore the first eigenvalue of the first boundary-value problem
1.82 PARTIAL DIFFEREN'riAL EQUATIONS
for the operator : is given by
2 ) (k I V/l 2 +a I If') d31
~ - - m +1- loll
"'t -
f ll/llk<Q>--
11/112 -
1"nf
0
Q
['
(33)
/EH'(Q) L,(Q) /EH'(Q) j lfl2 dz
Q
and the exact lower bound of the functional
~ (k IV/ 12 +a I f 12) dx /) I !1 2 dx
Q Q
on the space fit (Q) is attained through the first eigenfunction u1
The results of Sec. 5.1, Chap. II, imply that (k+ 1)th character-
z
istic value flk+t of the operator A is equal to inf ll/ll.ff<Q>
/EH(Q) 11/II}.,(Q)
(/, Ui)Hl(Q)=O
i=t, k
Since, according to (21), (!, ui).fl<Q> = f.tt (/, Aut).ff<Q> = f.tt (/, Ut)L,(Ql
i = 1, 2, ... , it follows that ~-
21
11/llkt(Q)
f.tk+t = inf
11/lli.(Q)
/EH'(Q)
(I, u 1)L,(Q)=O
i=1, . h.
Thus the (k + 1)th eigenvalue of the first boundary-value problem
for the operator X is given by
2
11/llk(Q)
"-k+t = -m+ 1- inf
11/lli,(Q)
teil<Q>
(/, ui)L,(Q)=O
i=i, ... , R
S (kJV/I 2 +aJ/J 2)dz
Q
inf (34)
teH(Ql
(!, ut>L,(Q)=O
i=i, .. , R
The functional
J (kiV/I 2 +al/l2)dx/) I fl 2 dx
Q Q
attains its exact lower bound through the eigenfunction uk+ 1 on the
subspace of the space Jp (Q) that is composed of all the functions
orthogonalJin the space with the scalar product, L 2 (Q), to the eigen-
functions u 1 , , uk of this boundary-value problem.
ELLIPTIC EQUATIONS 183
In exactly the same manner, for the third (second) boundary-
value problem for the operator Z
At = - m + 1- inf 11 1 11 ~'<Q>
/EH(Q) II f IIL.(Q)
~ (kjVfl 2 +alfl 2 )dx+ S kaJfl 2 dS
=- inf Q l'Q (33')
/EH 1 (Q) s I f 1 dx
2
Q
~ (klVfl 2 +alfl 2 )dx+ ~ kalfl 2 dS
Q BQ
inf (34')
/EH 1 (Q)
(/, ui)Lo(Q)=O
i=1, . , h.
The exact lower bound of the functional
~ (k!V/I 2 +alfl 2 )dx+ ~ kalfl 2 dS
Q BQ
~ It 12 dx
Q
on H 1 (Q) is attained through the first eigenfunction u 1 The exact
lower bound of this functional is attained through the (k 1)th +
eigenfunction u11.+1 on the subspace of H 1 (Q) consisting of all the
elements orthogonal to the space with the scalar product, L 2 (Q}, to
the eigenfunctions u 1 , , u11. of the respective boundary-value
problem.
Formulas (33) and (33') can be combined into one:
~ (k IV/ l2 +a I I 12 ) dx+ S ka II 12 dS
At= -in Q BQ (33")
/EG S If 12 dx
Q
moreover, 1.1 is the first eigenvalue of the third (second, if a 0) =
boundary-value problem for the operator Z if G = H 1 (Q), and 1.1
is the first eigenvalue of the first boundary-value problem if G =
= ifl(Q) (when f E
ifl(Q), the integral ka I f 12 dS = J 0) .
BQ
Similarly, formulas (34) and (34') can be combined into one:
~ (kjV/I 2 +alfl 2 )dx+ S kajfl 2 dS
Q BQ
inf (34")
lEG
(/, ui>L.(Q)~Il
i=1, . . h.
184 PARTIAL DIFFEREN:TIAL EQUATIONS
Sometimes the application of formulas (34), (34'), (34") in finding
the (k -t- 1)th eigenvalue AH 1 becomes difficult as they depend on
the knowledge of the preceding eigenfunctions u 1, . . . , uh. A form-
ula for calculating A7<+ 1 will be obtained below which is free from
this defect.
We take arbitrary k functions cp 1 , , cpk belonging to L 2 (Q)
and denote by R (cp1 , , cph) the subspace of ffl (Q) which con-
sists of functions f that are orthogonal to the functions cp 1 , . , cpk
in the space with the scalar product, L 2(Q): (f, (Ps)L,(Q) = 0, s =
= 1, ... , k. Let
2
. . II I lhh<Q>
d(cpt, .. , qJk)= -m-t-1- mf 11/112 '
/ER(<i'J, .. , cpk) L.(Q)
and let dk+ 1 be the exact lower bound of the number set {d (cpi>
... , cpk)} taken over all the possible systems of functions qJ 1 ,
, (jlk belonging to L 2 (Q):
(q>l, q>k)
q> 8EL 2(Q)
s=i, ... , h
We shall show that dk+ 1 = A-k+ 1 , where A-lt+ 1 is the (k + 1)th
eigenvalue of the first boundary-value problem for the operator :.
Since d (u 1 , . . , uh) = Alt+ 1 (formula (34)), it follows that
dk+ 1 ::::;;; A,k+l We shall now establish the reverse inequality. To do
this, it is enough to construct for an arbitrary fixed choice of the
system cp 1 , . . , cpk a function f in R (cp 1 , . . . , cpk) such that
II f IIL,(Q) = 1 and
II f IIA<Q) < - AHt- m + 1.
The function f will be sought in the form
k+l
f=~f.u., fs = (/, Us)L 1 (Q).
s=l
Then the conditions f E R(qJ1, ... , cp1,) and II f IIL,(Q) = 1 become
h+l
(/, CJ)p)L,(Q)= 2J
s=l
f.(u., CJ)p)L,(Q)=O, p=1, ... , k, (35)
k+l
111.1 2 =1.
11/IIL<Ql= s=l (36)
Since the linear system (35) regarding the vector (/1 , . , fk+I) is a
homogeneous system of k equations in k -t- 1 unknowns, it has always
a nontrivial solution. It is always possible to satisfy the normalizing
ELLIPTIC EQUATIONS 185
h+1 h+1
II I IIA1(Q) = 5~ I 1./2 11 Us IIAs(Q) = .J 11 /..1 2 ( - lv.-m + 1)
h+1
-< ~ =1
/lsl 2 (-/vh+1-m+1)=-A-h+t-m+1
(recall that 'A1 ;::?: 'A 2 > ... > 'AH 1),
it follows that I is the desired
function.
Thus the (k + 1)th eigenvalue of the first boundary-value problem
for the operator Z is given by the formula
AJt+t = inf ( - m+ 1- inf II f 11~1<Q>)
(QJ 1 .. Qlh) !EEP(Ql II f llt,(Ql
QJ 8 ELz(Q) (/, QJ;)L,(Q)=O
s=i, ... , h i=i, ... , h
2
II fllihQ>
= -m+1- sup inf
(Qll' . <Ph) fEll1(Q) 11/lli,(Q)
<PsEL.(Q) (!, <P;)L.(Q)=O
s=i' . , k i=i' .. ' k
) (k I Vf 12 -f-a If 12 ) dx
Q
(37)
t:xpressing the so-called minimax property of the eigenvalues.
Exactly in the same manner the formula for (k + 1)th eigenvalue
of the third (and second) boundary-value problem for the operator
Z is established:
~
II.Jt+t = - m
+
1- sup . f
m II f II}P(Q)
II 1 IIL.(Q)
2
(<Pl . '<Ph) IEH1(Q)
<P EL 2 (Q) (/, <P;)L 2 (Q)=0
s=f. .. . , h i=!, ... , h
S (k1Vfl 2 -f-alfl 2 )dx-f- S kalfl 2 dS
Q OQ
sup in (37')
(<PI' .. '<Ph) /EH1(Q)
<PEL,(Q) (! <P;)L 2 (Q)=0
i=i, ... ,h i=i, ... ,k
Formulas (37) and (37') can be combined into one:
~ (k I Vf 12 -f-a If 12 ) dx-f- ~ ka If 12 dS
Q OQ
(37'')
186 PARTIAL DIFFERENTIAL EQUATIONS
in which A,H 1 is the (k + 1)th eigenvalue of the first boundary-value
problem for the operator div (k(x) V) - a(x) if G = H1 (Q), and
A,H 1 is the (k + 1)th eigenvalue of the third (second, if cr = 0)
boundary-value problem if G = H 1(Q).
The minimax property of eigenvalues furnishes a possible way of
-comparing the eigenvalues of various boundary-value problems.
Theorem 4. 1. Let A,t A,~X, A,~II be the kth eigenvalues of the first,
.second, and third (for some cr ::;? 0) boundary-value problems for the
-operator Z = div (k(x) V) - a(x). Then A,~ :::;:;; A,~II :::;:;; A,l1 for all
k = 1, 2, ....
2. Let A,lt be the kth eigenvalue of the first, second or third (for some
a = a' ::;? 0) boundary-value problems for the operator Z' =
= div (k'(x) V) - a'(x), and let A,~ be the kth eigenvalue of the
first, second or third (for some cr = cr"::;? 0) boundary-value problems
for the operator Z" = div (k"(x) V) - a"(x). If k' ::::;:;; k", a' :::;:;; a"
in Q and in the case of the third boundary-value problem a' :::;:;; cr" on
;)Q, then Att::;? A,~ for all k = 1, 2, ....
3. Let Q' be a subregion of the region Q, Q' c Q, and 'A.k(Q), 'A.k(Q')
be the kth eigenvalues of the first boundary-value problem for the opera-
tor Z = div (k (x) V) - a (x) in Q and Q', respectively. Then
:Ak(Q) ::;? 'A.k(Q') for all k = 1, 2, ....
Proof. Let k > 1. Since the value of the functional present in
{37") after the sign inf in the case of the third boundary-value prob-
lem (cr ::;? 0) is not less than its value for the second boundary-
value problem (cr = 0) and the set G in both cases is the same, G =
= H 1(Q), it follows that 'A.~II:::;:;; A.l1. The inequality A.~:::;:;; 'Alii also
follows from (37"), because the set G over which inf is taken in the
-case of the third boundary-value problem is wider than the set G
for the first boundary-value problem: H 1 (Q) ::::> ifl(Q).
Assertion 1 for k = 1 follows from (34)". ,
2. Assertion 2 follows from (37") (for k > 1) and from (34")
{when k = 1), because the value of the functional appearing after
the inf sign for the operator Z" is not less than the corresponding
value for the operator Z'.
3. Since the set ifl(Q) contains the set Ffl(Q) of functions belong-
ing to H1 (Q) and vanishing on Q"'.Q', we have for k > 1
J..k(Q) = - sup in T(f)
(q>1' q>k-1) IEH(Q)
q>sEL,(Q) (I q>s)L,(Q)=O
s=1, , lt-1 s=1, . , lt-1
~ - sup inf T(f)
(q>1' q>k-1) ..2..
q> EL.(Q) (f /EH'(Q) -0
s=1,8 , k-1 q>s)L.(Q)-
s=1, .. , It-
ELLIPTIC EQUATIONS 187
sup inf T(f) = A.k(Q'),
(q>l, !llk-1> teH<Q'>
!llsEL,(Q') (f, !lls>L.(Q')=O
s=1, , k-1 s=1, ,k-1
where
~ (k I Vf 12 + a If j 2) dx
T(f) = ....:::.Q--=-----
S I /1 11 dx
Q
If k= 1, then
A.1(Q) = - inf T(f)?;:- inf T(f) = A. 1(Q'). I
teH<Q> te!i.cQ>
5. Asymptotic Behaviour of Eigenvalues of the First Boundary-
Value Problem. We first consider the eigenvalues of the first bound-
ary-value problem for the Laplace operator ~ (of the operator: =
= div (kV') - a with k = 1, a = 0) in the cube K 1 = {0 < X; < l,
i = 1, ... , n} with side l > 0. The generalized eigenfunction
u(x), corresponding to the eigenvalue A., of the first boundary-value
problem for the operator ~ in K 1 is defined to be a function belong-
ing to H1 (K 1) which satisfies the identity
1V'u V'v
Kz
dx = - A. ) uvdx
Kz
for all v EH 1(K 1).
It can be easily verified that the function Um, . mn (x) =
n
= ( T2 )n/2 fl sin -z-'
nmx-' with integers m 1 > 0, ... , mn > 0 is an
i=1
eigenfunction of the boundary-value problem under discussion; the
ll
7
corresponding eigenvalue is - 11 (m: + ... + m~). The system
of functions um, ... mn(x) for all integers m; > 0, i = 1, ... , n,
is orthonormal in L 2 (K 1). Since any function belonging to L 2 (K z)
and orthogonal to all um, ... mn is zero (this is proved just as the
corresponding assertion in Sec. 4.4, Chap. III, for the system of
functions um, ... mn = exp {i (m 1x 1 + ... +
mnxn)} in the cube
{I X; I< n, i = 1, ... , n}), this system constitutes an orthonor-
mal basis for L 2 (K 1), and accordingly contains all the eigenfunctions
of the first boundary-value problem for the operator ~ in K 1
Thus there is a one-to-one correspondence between the set of all
the eigenfunctions of the problem in question and the set of all the
points (m1 , , mn) with positive integer coordinates, and there-
fore also the set of all the cubes Km, ...mn = {m; - 1 ~ x; ~ m;,
i = 1, .. , n }. And the eigenvalue corresponding to the function
188 PARTIAL DIFFERENTIAL EQUATIONS
Um, . mn(x) is equal to the square of the distance from the point
(m 1 , , mn) to the origin multiplied by -n 2 /Z 2 Thus the multi-
plicity of the eigenvalue 'A equals the number of points with integer
coordinates lying on a sphere of radius V -'A l/:rr. In particular, the
2
7
number - 2 n is the first eigenvalue; its multiplicity is 1. The cor-
.
respon d mg
etgen f unc t"wn IS
u (x )
1 1 = (T
2 )' n/2 sm-l-
. :n:x 1 .
... srn -:n:xn
l-.
The next eigenvalue is - 7: (n + 3); its multiplicity is n. The
corresponding eigenfuctions are u1 . 1 , 2 , 1 .. 1 (x) =
'-.--'
(f) n; 2
X
i-1
. :n:x llXi- . 2:n:xi llXi+l :n:xn i
X Slll -l-1 ... Sin - l -1 Sin - l - Sln-l- ... Sin -l-, ~ = , ... , n.
Let N(p) denote the number of eigenvalues (having regard to
the multiplicity) which do not exceed some p > 0 in absolute
value. N(p) is equal to the number of points (m, ... , mn) with
positive integer coordinates for which mi + ... m;-< p or, + !:
what is the same, is equal to the volume of a solid M Vii" lin com-
posed of all the cubes Km, ... mn for which mi + ... + m; < : 2 p.
Since MVillfncSViilln={lxl< ~ Vr, xi~O, i=1, ... , n},
N(p)-<J SYPI/nl = ;nnn ~: p"/ 2 On the other hand, for p>n 7:
n:n: 2 a
M v'Pl!n =:J S V"PI;n- Vii therefore for p > ---y2, N(p) ~ znnn X
X e~p- Vnf
Let the eigenvalues be numbered, as usual, in increasing order:
0 > 'A 1 ~'A 2 > ... (every eigenvalue in this sequence occurs
according to its multiplicity). Consider any eigenvalue 'A. of multi-
plicity p 8 , Ps > 1, and assume that 'As-p8, . , 'A., , 'As +p"8 for
some p; >0, p;> 0, p; + +
p; 1 = Ps are all the eigenvalues
equal to 'A .
The number Ps is equal to the volume of the solid composed
of the cubes Km, ... mn whose vertices (m 1 , , mn) lie on a sphere
I 'As 11 12 with the origin as the centre. This solid is
contained in sl ~. 11/21/n '-.__S I~. 11/21/n- Yn' so Ps-< 2~~n [ ( ~ I 'As I) n/ 2 -
- ( ~ I"'1- Vn) n;z J.
In particular, noting that 'A 8 -+-oo as S-+oo, we find that
l"liD I A PsJnf2 =
0.
s-..ao :s
ELLIPTIC EQUATIONS 1R9
From the definition of the function N (p) it follows that
s+ p; = N(l A8 j). Accordingly, :;n ( ll;sl- V1i)n/Z -<:s+ p;~
-<: :2n ( ll;s I r 12 And since O-<: p:-<:p., the ratio s/1 As lnf 2 has a
limit that equals ::n
lnf 2 :rr,-nf2 Therefore (recalling that ... -<:"'z~
-<:A 1 <0) there are constants C0 and Ct> O<Co-<:Ct> such that
(38)
for all s = 1, 2,
Since the eigenvalues do not depend on the coordinate system
chosen, the inequalities (38) for the eigenvalues of the first boundary-
value problem for the Laplace operator continue to hold if the cube
K 1 is replaced by any other cube with side l. It is easy to see that
the eigenvalues of the first boundary-value problem for the operator
k0 11 - a 0 , where k 0 > 0 and a 0 are constants, in a cube with side l
are -k 0 7: (m~ + ... + m;)- a 0 , where m 1 , , mn are posi-
tive integers. Thus the inequalities (38), with some constants C0
and C1 (depending on k 0 ) hold also for them for all s, starting with
some s 0 (depending on k 0 and a 0 ).
We now examine the general case.
Theorem 5. Let 'A 8 , s = 1, 2, ... , be the eigenvalues of the first
boundary-value problem for the operator X = div (k(x) V) - a(x)
in the region Q. There exist constants C 0 and C1 , 0 < C0 ~ C1 , and a
number s0 such that the inequalities
(39)
hold for all s?;:: s0
Proof. Suppose that ~s and As are eigenvalues of the first bound-
ary-value problem in Q for the operators Z = div (kV)- a= k/1.- a
and X=k/1.-a, respectively, where k=maxk(x), k=mink(x),
- ~ - ~
a= max a(x), a= min a(x). Then, by Assertion 2 of Theorem 4,
xEQ - xEQ
ts-<:As-<:As for s = 1, 2, ....
By K' and K" we denote the cubes such that K' c Q c K", and
by ~ and A; the eigenvalues of the first boundary-value problem for
the operator X in K' and the operator X in K", respectively. By
Assertion 3 of Theorem 4, 1; ~ X. and 'A; :> A8 for all s. The con-
clusion of the theorem now follows from the fact that starting with
SQ]'H~ s = s0 the inequalities (39) hold for~~ and ~~ I
190 PARTIAL DIFFERENTIAL EQUATIONS
6. Solvability of Boundary- Value Problems in the Case of Homo-
geneous Boundary Conditions. In Subsec. 2, we examined the question
of existence and uniqueness of generalized solutions of the first
and third (second) boundary-value problems for Eq. (1) under the
assumption that a(x) >
0 in Q. Now the general case will be dis-
cussed.
Let m = min a(x). The identities (4) and (6) can be written
:x:eQ
in the form
(u, v)H(Q) + (m-1) (u, v)L,(Q) = - (/, v)L,(Q> (4'}
(u, V)H(Q)+(m-1)(u, V)L,(Q)= -(j, V}L,(Q)t (6'}
where the scalar products in Ffl(Q) and H 1 (Q) are defined by for-
mulas (17) and (18). By Lemma 1, Sec. 1.3, the identity (4') is equiv-
alent to the operator equation
u + (m - 1) Au = - Af (40}
in the space H1 (Q), while the identity (6'), by Lemma 1', to the
operator equation
u + (m- 1) A'u = -A'f (40'}
in the space H 1 (Q) (recall that AfE ifl(Q}, A'f E H 1 (Q}). The oper-
ator A from H1 (Q) into H1(Q) (A' from /J 1 (Q) into H 1 (Q)) is
completely continuous. Therefore for the investigation of Eq. (40)
((40')) Fredholm's theorems can be applied (Theorems 1-4, Sees. 4.3-
4.7, Chap. II).
(1) If the number -m + 1 is not a characteristic value of the
operator A (A'), then by Fredholm's first theorem Eq. (40) ((40'}) is
uniquely solvable with any f E L 2 (Q}, and the inequality II u llw<Q> ~
~ cl II At IIHl(Q) ~ c II I lb<Q> (II u IIHl(Q) ~ c II I IIL2(Q)) holds,
where the constant C > 0 does not depend on f. Since -m + 1 is a
characteristic value of the operator A (A') if and only if zero is an
eigenvalue of the first (third) boundary-value problem for the opera-
tor :, we have established the following theorem.
Theorem 6. For any f E L 2 (Q), there exists a unique generalized
solution u(x) of each of the boundary-value problems (1), (2) and (1),
(3) with homogeneous boundary conditions (q> = 0), provided that zera
is not an eigenvalue for the operator :.Moreover, the inequality
ll u IIH(Q)< c II f IIL,(Q)
where the constant C > 0 does not depend on f, holds.
(2) If -m + 1 is a characteristic value of A (A') (then, of course,
m =1= 1), we use Fredholm's third theorem. In this case, in order
ELLIPTIC EQUATIONS i9t
that Eq. (40) ((40')) be solvable it is necessary and sufficient that the-
equality (Af, up)Hl(Ql = 0 ((A'f, up)Hl(Q) = 0) hold for all the eigen-
functions up of the operator A (A') corresponding to the character-
istic value -m + 1. Eq. (40) ((40')) has a unique solution u which
is orthogonal in H1 (Q) (H 1 (Q)) to all the functions up, and for this-
solution the inequality II u ll.ff 1 (Ql ~ C II f IIL2(Ql (II u IIHl(Q) ~
~ C II f IIL.(Q)) holds in which the constant C > 0 does not depend
on /. Any other solution of Eq. (40) ((40')) is expressed as the sum
of the solution u and a linear combination of the functions uw
From the definition of operators A and A' ((21) and (21'), respec-
tively) it follows that orthogonality in H1 (Q) (H1 (Q)) of functions
A/ (A'f) and up is equivalent to that of functions f and up in L 2 (Q)
What is more, the orthogonality in H 1 (Q) (H 1 (Q)) of the solution u
of Eq. (40) ((40')) to the eigenfunction Up is equivalent to their ortho-
gonality in L 2 (Q), because, in view of (21) ((21'))
(u, Up).ff(Ql =(1-m) (Au, Up).ff,(Q)- (Af, Up)HI(Q)
({u, Up)H(Q) =(1-m) (u, Up)L1 (Q))
We thus have the following result.
Theorem 7. If zero is an eigenvalue of the first or third (second)
boundary-value problem for the operator :, the necessary and sufficient
conditions for the problem (1), (2) or (1), (3) with homogeneous bounda-
ry conditions ( q> = 0) to have a generalized solution are the following:
(/, up)L.<Q> = 0 for all generalized eigenfunctions up of the respective
problem corresponding to the zero eigenvalue. The problem (1), (2) or
(1), (3) (with q> = 0) has a unique solution u which is orthogonal to all
the eigenfunctions: (u, up)L.<Q> = 0. This solution satisfies the in-
equality
II u IIH(Q)-<C II f IIL.(Q)
where the constant C > 0 does not depend on f. Any other solution is
expressed as a sum of this solution u and a linear combination of the
functions uw
From Theorem 3 it follows that zero is an eigenvalue of the second
boundary-value problem (a= 0) for the operator : when a== 0;
the eorresponding unique eigenfunction is 11VTQ"T. Therefore Theo-
rem 7, in particular, implies
Theorem 8. For the problem
div (k(x) vu) = f' :: laQ = 0,
192 PARTIAL DIFFERENTIAL EQUATIONS
to have a generalized solution it is necessary and sufficient that
\ fdx=O.
Q
Under this condition, there is a unique solution u satisfying the condi-
tion j
u dx = 0, and this solution satisfies the inequality
Q
II u IIH(Q)-< c II f IIL.(Q),
where the constant C > 0 does not depend on f. Any other generalized
u u
solution of this problem can be expressed as = u + c1 , where c1 is a
constant.
Remark. If f is a real-valued function, then the solutions described
in Theorem 6 are also real-valued. This assertion is proved just as the
corresponding assertion in Remark at the end of Subsec. 2. The solu-
tions mentioned in Theorems 7 and 8 could also be considered real-
valued, provided, of course, all the corresponding eigenfunctions
are taken real-valued and one considers their linear combinations
with real coefficients only.
7. First Boundary- Value Problem for the General Elliptic Equa-
lion. The results of the foregoing subsections are easily extended to
the case of more general elliptic equations. To illustrate it, we con-
sider the following boundary-value problem:
n n
Zu= 2} (atj{x)ux.)x.+ 2} a 1(x)ux.+a(x)u=f(x), xEQ, (41)
i, j=1 ' J i=1 '
u laQ = 0, (42)
where the real-valued coefficients au(x) E C1 (Q), a 1(x) E C1 (Q),
a(x) E C (Q), i, j = 1, ... , n; the matrix II a;; (x) II is assumed to
be symmetric and posi ti ve-defini te (ellipticity of Eq. (41)), that is,
it satisfies the inequality
n n
LJ au(xHti~'\'
i, j=1
~ t
i=1
(43)
with a constant y > 0 for any real vector ( 1 , . , sn) and any
point x E Q.
The classical solution u(x) of the problem (41), (42) is defined in
the usual manner: this is a function \Vhich belongs to C2 (Q) n C(Q)
and satisfies (41) and (42). By means of Ostrogradskii's formula, it is
easily seen that iff E L 2 (Q), .the classical solution of the problem (41),
(42) belonging to i'fl(Q) satisfies for all v
E fii(Q) the integral iden-
tity
n
~ ~ UtjUxi;;xJ dx
Q i,i=t
n n
+ ~ u[~ atVxi+(~ Uixi-a) v]dx=- ~ fvdx. (44)
Q i=i i=i Q
JJ
The function u E 1 (Q) is called a generalized solution of the
0
problem (41), (42) if for all v E H 1(Q) it satisfies the integral iden-
tity (44) with f E L 2 (Q).
According to Theorem 6, Sec. 5.6, Chap. III, we can define in
H (Q) a scalar product
1
n
(u, v)H<Q> = ) ~ atiUxijx1 dx
Q i, i=i
which is equivalent to the usual scalar product. In view of this, the
identity (44) can be written as
n n
(u, v).ff,(Q)+(u, -~ a 1 vx 1 +(~ aix1 -a)vh.<Q>= -(!, v)L.(Q) (45)
1=1 t=i
Lemma 2. 1. For any functions a 0 (x), a 1 (x), ... , an(x) contin-
uous in Q there exists a bounded linear operator A acting from L 2 (Q)
into ift (Q) and defined on the whole L 2 (Q) such that
n
(u, i~t aiv"1 +aovh.<Q>=(Au, v)H<Q>
0
for all v E H 1 (Q).
2. The operator A regarded as an operator from H1(Q) into H1(Q) is
completely continuous.
Proof. Since for a fixed u EL 2 (Q) the linear functional l (v) =
n
= (u, ~ a 1vx. +aovh.<Ql (vE /Ji(Q)) defined on Ffl(Q) is hounded:
i=1 '
n
ll (v) 1~11 u IIL,(Q) II.~
t=i
atVx 1 +aov /k.<Q>~C II u IIL,(Ql II v IIH:<Q>' where
the constant C > 0 depends only on II a 1 llc<Q>' i = 0, 1, ... , n, by
Riesz's theorem there is a unique element U EH1(Q) such that
l(v)=(U, v)H:cQ> for all vE Fft(Q), and IIUIIAcQ>=IIlii~C llu IIL,<Q>
This means that an operator A (obviously, linear) is defined on
13-0594
194 PARTIAL DIFFERENTIAL EQUATIONS
L 2 (Q) that maps L 2 (Q) into H1(Q): Au= U. This operator is
bounded, IIAII~C, and for any uE L 2 (Q) and vEH 1(Q) the identity
n
(u, i~i a;vx 1 + a0 v)L,(Q) =(Au, v)H(Q)
holds.
0
Let us demonstrate that A regarded as an operator from H 1 (Q)
into ]Jl(Q) is completely continuous. Take any bounded set in JJI (Q).
This set is compact in L 2 (Q), by Theorem 3, Sec. 5.4, Chap. III.
Therefore from any infinite sequence of its elements a subsequence-
can be chosen which i~ fundamental in L 2 (Q). Since A as an opera-
tor from L 2 (Q) into H 1 (Q) is bounded (and therefore continuous).
0
it maps this subsequence into a fundamental sequence in H 1(Q). Ac-
cordingly, the operator A from H1 (Q) into H1 (Q) is completely
continuous. I o o
The linear functional (/, v)L,((,!) defined on H 1 (Q) (v E H 1 (Q))
is bounded: I(/, v)L,(Q) I~ C II f IIL,(Q) II vII , therefore Riesz's H(Q)
0
theorem guarantees the existence of a unique element F E H 1 (Q)
I
such that for all v E H 1 (Q) (f, v)L,(Q) = (F, v)H(Q)' and II F IIH(Q) ~
~ c II t IJL;(Q) n
Thus, by means of Lemma 2 (put a 0 = ~ aix. -a), the integ-
i=i I
.0
in the form of an operator equation in the space H 1 (Q):
u+Au=F, (46}
n
Lemma 3. If ; L a.ix 1- a;;;;:;:: 0 in Q, then the homogeneous equa-
i=t
tion (46) has only a trivial solution.
Proof. Let u denote the solution of the equat'ion u +Au= 0. Scalar
multiplication in H1(Q)' of this equation by u gives IJuW.
+ 2 H(Q)
+(Au, u) H(Q) = 0, whiC:tJ, 1mphes .that. II u lln<Q> + Re (Au, u)H<Q> = 0.
'
Since Re a 1ux 1u =
'- 1 .
2 (a; Ju f>x 1 -
, ,
~ '
Tax lu 12
t '
and u laQ = 0, it follows
ELLIPTIC EQUATIONS 195
that
n n
Re(Au, u)H(Q)=Re) {~ a!uxJi+ (~ aix;-a) JuJ 2 ) dx
Q i=1 i=1
n n
= ) { ~ ; (a;! u J2)x; + ( ; ~ aix;- a) I u 12 ) dx
Q i=1 i=1
n
= J (; ~ aix;-a) I u J 2 dx~O.
Q i=1
<
Hence II u IIA<Q> 0, that is, u = 0. I
Lemma 3 coupled with Fredholm's first theorem yields the follow-
ing
n
Theorem 9. If {- ~ aix1 - a >- 0 in Q, then the generalized solution
i=1
of the problem (41), (42) exists for any f E L 2 (Q) and is unique.
8. Generalized Solutions of Boundary- Value Problems with Non-
homogeneous Boundary Conditions. Let us first examine the problem
(1), (2). We recall that the generalized solution of this problem is
defined to be a function u E H 1(Q) satisfying the integral identity (4)
and whose trace on the boundary 8Q equals the boundary function <p.
The definition of a generalized solution imposes a natural condi-
tion on the boundary function <p. This function must be required to
have an extension into Q which belongs to H 1(Q). In the sequel it
will be assumed that this condition is fulfilled, otherwise the general-
ized solution of the problem (1), (2) cannot exist. From the theorem
on traces of functions belonging to H 1 (Q) it follows that <p must be-
long to the space L 2 (8Q), but this is not enough for the function to
have an extension into Q by means of a function which belongs to
H 1 (Q); what is more, even its continuity is not enough for \his pur-
pose. We shall return to this problem at the end of this subsection
where we obtain a necessary and sufficient condition for such an
extension in the case of a circle.
Note that such an extension c>xists when 'P E C 1 (8Q). By Theo-
rem 2, Sec. 4.2, Chap. III, there follows the existence of a function
Cl>(x) in C1 (Q), and more so in H 1(Q), such that Cl>loq = <p and
II Cl> IIH(Q):::;; C1 ll <p llct<aQh where the constant C1 > 0 do~s not
depend on <p.
Thus, suppose that there is a function Cl> E lfl(Q) such that
Cl>IBQ = <p. With the aid of the substitution u- Cl> = w, the prob-
lem of finding the generalized solution u reduces to that of finding
13
196 PARTIAL DIFFERENTIAL EQUATIONS
a function wE H 1 (Q) which satisfies the integral identity
f
Q
(kV'wVv + awv) dx = -)
Q
(kV<DVv + a<Dv +tV) dx (4')
for cdl 1 E H 1(Q).
Note that if <DE H 2 (Q) (when oQ E C2 , for this it is enough that
cp E C 2 (8Q)), the identity (4') can be written as
.\ (kvwvv+awv)dx=- .l Tvdx,
Q Q
where / = f- div (kV<D) + a<D, that is, the problem reduces to
the one investigated in Subsecs. 2 and 4.
As in Subsec. 2, we confine ourselves to the case when a(x) :> 0
in Q. Introducing in ifl(Q) the scalar product according to formu-
la (7), identity (4') can be written in the form
(w, v)H(QJ = l(v),
where l(v) = - ~ (kv<Dvv + a<Dv + fv) dx is a linear functional
Q
defined on fP(Q) (v E Ffl(Q)). Since
jl (v) I< II fi!L,(QJ II v IIL,(QJ +max k (x) Ill V<D IIIL,(<JJ Ill V'v IIIL,(Q)
xf:.Q
+ m~a (x) II<D IIL,<QJ II v IIL,(QJ~C2 (II/ IIL,<Q> +II <D IIH<o>) II v IIA<Q>'
xEQ
where the constant C 2 > 0 depends only on the coefficients k and a,
the functional l is bounded and Ill II,::;:; c2 (II t IIL,(Q) + II <D IIH(Q)).
Therefore by the Riesz theorem there is a unique function w in
H (Q)
1 which satisfies (4') and is such that II w II H(Q) c = Ill II ~
,::;:; c2
(II t IlL,(() + II <D IIH(C.,)) Then the function u = w + <D is a
generalized solution of the problem (1), (2). Furthermore,
II u IIH<o>~ c3 (II t IIL,<Q> +II <D IIH<Q>>
where the constant C 3 > 0 does not depend on f or <D, and hence
II u IIH<Q> .;;c (!I I I!L,<Q> + inf
<I>f fll(Q)
II <D IIH<Q>), (47)
<I> laQ='P
where the constant does not depend on f or qJ. If the boundary func-
tion f~ E C1 (8Q), these inequalities imply the inequality
llnliH<O> <::;; C (II fiiL,(Ql +II qJjb(aQJ) (47')
ELLIPTIC EQUATIONS 197
Let us show that the above solution is unique. Indeed, if there is
another generalized solution u', then the difference u - u' be- u=
longs to /Jl(Q) and, by virtue of (4), satisfies the integral identity
j (k;;iuvv + ai:;V} dx = 0 for all v E Ffl(Q). Since the left-hand
Q
side of this identity is the scalar product in Ffl(Q) of functions u
and v, it follows that = 0. u
Thus we have proved the following assertion.
Theorem 10. If a(x) >
0 in Q and <p is the boundary-value of a
function belonging to H 1 (Q), then there exists a unique solution u of
the problem (1), (2). This solution satisfies the inequality (47), and thus
also the inequality (47') with <p E C 1 (8Q).
Remark. As can be easily verified, the set&!/ of functions <p defined
on 8Q which are traces of some functions <ll belonging to H 1 (Q) is a
Banach space with the norm II <p ll&~t: = inf II <ll IIH(Q) In view
<l>EH'(Q)
<I>ioQ=IJ>
of this, inequality (47) can be written in the form
II u IIH<ol< C (II I IIL,(Q) +II <p llaAz}.
Next we consider the problem (1), (3). We recall that a function
u E H 1 (Q) is called the generalized solution of this problem if it
satisfies the integral identity (5) for all v E H 1 (Q). In this case it is
assumed that the boundary function <p E L 2 (8Q).
Theorem 11. If a(x) >
0 in Q and either a(x) 0 in Q or a(x)
=I= 0 on 8Q, then for all f E L 2 (Q) and <p E L 2 (8Q) there exists a
unique generalized solution u of the problem (1), (3). Moreover,
II u IIH(Q)<' C (II I IIL,(Q) +II <p IIL,(oQ)), (48)
where the constant C > 0 does not depend on f or <p.
Proof. By means of formula (10), we introduce in H 1 (Q) a scalar
product equivalent to the usual scalar product. Then the integral
identity (5) can be written in the form
(u, v)H(Q) = l(v),
where
l (v) = - JliJ dx + .l kcp7; dS
Q oQ
is a linear functional on (v EH 1 (Q)).
H 1 (Q)
By Theorem 1, Sec. 5.1, Chap. III,
ll(v) I.:::;;;: II I IIL,(Q) II v IIL,(Q) +max k(x) II <p IIL,(oQ) II v I!L,(oQ)
xEQ
1.98 PARTIAL DIFFERENTIAL EQUATIONS
where the constant C > 0 does not depend on f, cp or v. Therefore
the functional l(v) is bounded and Ill II ~ C~(ll f IIL,(QJ + II cp IIL,(aQJ)
Accordingly, by Riesz's theorem, there is a unique function u in
H 1 (Q) satisfying the identity (5); moreover, II u IIH<O> = Ill II ~
~ c (II f IIL,(Q) + II .IP IIL,(iJQJ) I
Now suppose that a(x) = 0 in Q and a(x) ==
0 on fJQ in the prob-
lem (1), (3). In~H 1 (Q) we deftne the scalar product
(u, v)a<Q>= ~ (kVuVv+uv)dx (49)
Q
equivalent to the usual scalar product. Then the integral identity (5)
deftning the generalized solution of the second boundary-value prob-
lem for the operator div (kV) assumes the form
(u, v)a<Q>- (u, v)L 2 (QJ = l(v), (50)
where
l(v)=- f fvdx+ .l kcpvdS (51)
Q OQ
is a linear functional on H 1 (Q) (v E H 1(Q)). Since, by Theorem 1,
Sec. 5.1,~Chap. III,
ll (v) 1~11 /IIL,(QJ II viiL,(Ql +maxk (x) II IPIIL,(aQ) II viiL,(BQ)
xEQ
-<.C' (II f IIL,(Q) +II cp IIL.(BQ)) II v IIH(Q)
where. the constant C' > 0 does not depend on f, cp or v, the function-
al l (Ll) is bounded and Ill II~ C' (II/ IIL,(QJ + II cp IIL.(aQ>) Accord-
ing to Riesz's theorem, there exists a unique element F' in H 1 (Q)
such that for all v E H 1 (Q)
l(v) = (F', v)a(QJ (52)
and
II F' lla(Q)~C' (II f IIL,(QJ +II cp IIL,(BQJ) (53)
By Lemma 1', Subsec. 3 (the scalar product in H 1 (Q) is defined by
the formula (49)), there is a bounded operator A' from L 2 (Q) into
H 1 (Q), with L 2 (Q) as the domain of definition, such that
(u, v)L,(QJ = (A'u, v)a(Q) (54)
for all v EH 1 (Q). If A' is regarded as an operator from H 1 (Q) into
H 1 (Q), it is selfadjoint and completely continuous.
With the aid of (52) and (54), the identity (50) can be replaced by
an equivalent operator equation in the space H 1 (Q):
u- A'u = F'. (55)
ELLIPTIC EQUATIONS 199
Since for the function u 1 (x) == const = ,r 1
r IQ I
there holds the
relation; (u1, v)L.<Q> = (u1, v)H(Q) (the scalar product in H 1(Q) is
defined by the formula (49)) for any v E H 1 (Q), it follows from (54)
that (A 'u1 , v)H<Q> = (u 1 , v)L.(Ql = (u1 , v)H<Q> This means that
the number 1 is a characteristic value of the operator A' and u 1 =
= ,r 1 is the corresponding eigenfunction. Since any eigenfunc-
r I Q It
tion u; of the operator A' corresponding to the characteristic value 1
satisfies the equality (u;, u;)H<Q> = (A 'u;, u;)H(Ql = (u;, u;)L.<Ql
this eigenfunction satisfies
) kl vu; IZdx=O.
Q
Accordingly, u; = const, that is, the number 1 is a nonrepeated
characteristic value of the operator A'.
According to Fredholm's third theorem, in order that Eq. (55) be
solvable it is necessary and sufficient that the function F' be orthogo-
nal in }H1 (Q) to the function u 1 = ,r 1 : ( F', , 1 1 ) = 0.
y IQI y I Q I H(Q)
This condition is equivalent, in view of (52), (51), to the condition
-r Q
fdx+ r
oQ
kcpdS =0. (56)
When this condition is fulfilled, Eq. (55) has a unique solution u
which is orthogonal in H 1 (Q) to constant functions. This is a gener-
alized solution of the problem under consideration. And, in view of
(53), the inequality (48) holds, where the constant C does not depend
on f or cp. All other solutions differ from u by constant terms. Since
for functions in H 1 (Q) the condition of orthogonality to constant
functions in the scalar product (49) is equivalent to that of orthogo-
nality to constant functions in L 2 (Q) with a scalar product, we have
established the following result.
Theorem 12. For the existence of a generalized solution of the prob-
lem div (k(x) Vu) = f, 88 u j = cp it is necessary and sufficient that
n aQ
equality (56) hold. The generalized solution u is orthogonal to constant
functions in L 2 (Q) with a scalar product, is unique and satisfies the
inequality t(48). All other generalized solutions of the problem differ
from the function u by constants.
Remark. If f and cp are real-valued functions, then so are the
solutions described by Theorems 10-12.
In the investigation of the first boundary-value problem for
Eq. (1) with nonhomogeneous boundary condition there arose the
following problem: Under what conditions the function cp E L 2 (oQ)
200 PARTIAL DIFFERENTIAL EQUATIONS
has an extension into the region Q belonging to H 1 (Q). As shown
above, a sufficient condition for this is that the function cp belong to
the space C1 (iJQ). Now we shall obtain a necessary and sufficient
condition for the case when Q is a disc.
Let Q(n = 2) be the disc {I xI= p < 1}, x = (x1 , 'x 2) =
= (p cos 8, p sin 8). On the circle iJQ = {p = 1} we consider a real-
valued function cp belonging to the (real) space L 2 (iJQ), cp(8) E:
E L 2 (0, 2n). The Fourier expansion of cp(8), which converges in the
norm of L 2 (0, 2n), is of the form
00
cp(8) = ~o + ~ (alt cos k8 + bk sin k8),
k=1
where
2n
ak=! I cp(8)cosk8d8,
0
k=O, 1, ... ,
2n
bit= ! Jcp(8) sin k8 dO, k = 1, 2, ... ,
0
are its Fourier coefficients.
According to the Parseval-Steklov equality,
00
a~ ~ 1
2 + .:::J (ak + bk) = n IliP IIL.(O,
2 2
< oo. 2
2:rt) (57)
k=1
The following result holds.
Theorem 13. For the function cp(8) E L 2 (0, 2n) to be a trace on the
circle {I x I = 1} of a function belonging to H 1 ( I x I < 1) it is nec-
essary and sufficient that the series
00
ll=i
2j k(a~ + b~) (58)
converge.
By (57), the sequences alt, bk, k = 1, 2, ... , are bounded. There-
oo
fore the function ~ (ak -
k=i
ib~t) zk, where z = x1 + ix 2, is ana-
lytic in the disc {I z I < 1 }. This means that the function
00
k=i
= ~o +~ pk(ak cos k8 + bn sin k8) (59)
k=1
ELLIPTIC EQUATIONS 201
belongs to Coo ( 1 x I < 1), and the series (59) as well as those ob-
tained from it by termwise differentiation converge absolutely and
uniformly in the disc {I xI< r} for any r < 1.
To prove Theorem 13, we shall require the following result.
Lemma 4. In order that the function w(x) defined by the series (59)
may belong to the space H 1 ( I x I < 1) it is necessary and sufficient
that the series (58) converge.
Proof. By wm(x) we denote the partial sum of the series (59)~
m
wm(x)= ~o + ~ pk(akcoske+bksinke).
1<=1
Since all the functions of the system pk cos ke, pk sin ke, k =
= 0, 1, ... , are mutually orthogonal in L 2 (1 x I< 1) and
II pk cos ke lli.<ixf<1) = II pk sin ke lli.oxi<O = 2 (k~ i) , k = 1, 2, ... ~
for any p and q, q > p, we have
q
n a:+b:
llwq-wplli.oxl<t)= 2 ~ k+1
l<=p+1
Therefore the convergence of the series (57) implies that of the se-
quence Wm (x), m = 1, 2, ... , in L 2 (1 x I< 1). Accordingly, the-
function w E L 2 (1 x I< 1), and the series (59) converges to it in
L2 (I X I< 1).
Assume that the series (58) converges. Then (for q > p)
JxT<1
1 2:rt
=)pdp) [(wq-wp) + 2 (wqp-Wpp) 2 + :2 (wqa-wpa) 2 ] de
0 0
q
-~ ~
- 2 Ll
l<=p+1
asp, q-+ oo. That is, the sequence Wm, m = 1, 2, ... , converges.
in H 1 (1 x I< 1). Consequently, wE H 1 (1 x I< 1).
Suppose now that wE H 1 (1 x I< 1). Since for any r < 1 the
sequence of norms
m = 1, 2, ..
202 PARTIAL DIFFERENTIAL EQUATIONS
being monotone nondecreasing, converges, as m-+ oo, to II w llhl(ixJ<rh
the inequality
m
S k( a:+ b:) r 1t <~II Wm llkl(lxi<rl <;: ~ II w llkl(lxl <r) <;: +11:w l!kl(ixl<i l
2
k=i
h'Jlds for all r< 1 and all m. Consequently, the partial sums of the
series (58) are bounded:
m
~ k(a:+b:)<-!t-IJwllhl(ixl<ih m=1, 2, ... ,
h=i
that is, the series (58) converges. I
Proof of Theorem 13. That the condition is sufficient is an immedi-
ate consequence of Lemma 4, because, if the series (58) converges,
the function w in (59) belongs to H 1(1 x I< 1) and its trace on the
circle { l.x I = 1} is <p.
We shall, prove the necessity. Assume that there is a function
E H 1 (1 x I< 1) for :~hich <Pioxl=il = <p. Then, by Theorem 10,
the first boundary-value problem for Eq. (1) with boundary func-
tion <p has a generalized solution belonging to H 1 ( I x I < 1). Let u
be the generalized solution of the first boundary-value problem for
Eq. (1)i with k ==
;1, a= f =
0, satisfying the condition u luxJ=1} =
= <p. It will be shown in Sec. 2.2 that the function u belongs to
Coo( I x I < 1) and] satisfies the equation Llu = 0 in the disc {I x I<
< 1}. We use this result, and expand the function u(x) = u(p, 8)
with fixed (p E (0, 1) in a uniformly and absolutely convergent
Fourier series in 8:
00
lt=1
where
21t
Ult(P)=+) u(p,8)cosk8d8, k=0,1, ... ,
0
21t
Vlt(p)= { ) u(p, 8)sink8d8, k=1, 2, ....
0
The functions U~t(P) (and Vlt(p)), k = 0, 1, ... , are infinitely
differentiable for 0 < p < 1 and are bounded as p -+ + 0. Since
u E H 1(1 x 1< 1), by the theorem on the traces of functions belong-
ing to H 1 (1 x I< 1) we have, as p-+ 1 - 0,
21t 21t
) (u(p, 8)- <p(8)) cos k8 dB -+ 0 ( ) (u(p, 8)- <p(8)) sin kB da -+ 0)
" 0
ELLIPTIC EQUATIONS 203
for all k = 0, 1, . . .. This means that all the functions Uk(p)
(V~t(P)) are left-continuous at the point p = 1 and Uh (1) =
= ah (Vh (1) = b~t), k = 0, 1, ....
Since for pE(O, 1)~u=Upp+_!_ up+~uaa=O, for such p
P iP
2n 2n
UJ.(p) = f -~ upp (p,
0
a) cos ke de= - :P ) up cos w de
0
2n
1 )~ 1 k 2
--2 u 66 cosked9= - - Uk+- U~t, k=O, 1, ...
np p p2
0
This means that for any k = 0, 1, ... the function U~t(P) satisfies
the ordinary (Euler's) differential equation y" + ..!.p
y' - p y = 0 k:
for 0 < p < 1. The general solution of this equation is of the form
Bpk + Cp-k, k =1= 0, and B +
C In p when k = 0, where B and C
are arbitrary constants, therefore U h (p) = ahpk, k = 0, 1, ....
It is similarly shown that V~t(P) = bhpk, k = 1, 2, ....
Thus the function u belonging to H 1 (1 x I< 1) coincides with the
function win (59). And then, by Lemma 4, the series (58) converges. I
Let us utilise this theorem in constructing the function <p (e)
continuous on the circle {p = 1} . which cannot be extended into
the disc {I x I< 1} by a function belonging to H 1 (1 x I< 1). Put
Since this series is uniformly convergent, the function <p E
E C(l xI= 1). But at the same time, in view of Theorem 13, it can-
not be the trace of any function belonging to H 1 ( I x I < 1), because
00
the series (58) (which has the form ~ k 8 (k~) 2 ) for it diverges.
k=l
9. Variational Method for Solving Boundary- Value Problems.
Let H' be any subspace of the real space H 1 (Q); in particular, H'
may coincide with the whole H 1 (Q). We shall assume that a scalar
product is defined in H' that is equivalent to the usual scalar pro-
duct in H 1 (Q).
We take a real function f E L 2 (Q) and on H' consider the func-
tional
E(v) =II v Ilk+ 2 (!, v)L,(Q)t (60)
204 PARTIAL DIFFERENTIAL EQUATIONS
Since I (f, v)L,(QJ I~ II f llL,(Ql /1 v IIL.(Ql ~ C II f /k.<Ql I/ v llw, for all
vEH'
E (v)~// v /Iii -2/(f, v)L,(QJ /~1/ v /Iii -2C /1 v 1/w 1\ f /lr.,(Q)
C2 /l f /IL<Ql~- C2 ll f I/1.<QJ
=-(II u /h- C 1/ f //r. <QJ) 2 -
This means that the range of values of the functional E on H' is
bounded below. Let d = d(H') denote the exact lower bound of the
functional E on H':
d = inf E(v).
vEH"
A function u in H' is said to realize the minimum of the functional E
on H' if
E(u) =d. (61)
Like the number d, the function u, of course, depends on the choice
of the subspace H'.
By the definition of the exact lower bound, there is a sequence
of functions Vm, m = 1, 2, ... , in H' for which
lim E (vm) =d. (62)
m~-oo
Any such sequence is called a minimizing sequence for the func-
tional E on H'.
Lemma 5. For any subspace H' of the space H 1 (Q) (in particular,
H' may coincide with the whole H'(Q)) there is a unique function u
in H' realizing the minimum of the functional Eon H'. Any minimiz-
ing sequence for the functional E on H' converges to this function in
the norm of H 1 (Q).
Proof. Suppose that a sequence Vm, m = 1, 2, ... , of elements
in H' is a minimizing sequence for the functional E on H'. Then
given an e > 0 a number N = N(e) can be found such that for all
m';;:>N
d ~ E(vm) ~ d B. + (63)
Since I'
Vm; Vs 11:. = !11 Vm 1/ii +!II Vsllk ~ (vm, Vs)w, it fol-
lows that
II Vmt~IJ:.+II Vm;-Vs 11:.= ~ (1/vmllif+l/vsllk).
Taking into account (60), the last relation yields
I Vm;-Vs 11:.= ~ (l!vm/lii+I/vsl/h)-11 VmtVs ,,:.
= ~ (E(vm)+E(v 8 ))-E ( vmtVs).
ELLIPTIC EQUATIONS 205
But E ( vm tvs } ~d. and the functions Vm and V8 satisfy inequal-
ities (63) for m, s ~ N; this implies that
O<ll vm;Vs 1:.< ~ (d+e+d+e)-d=e
for all m, s >
N. Since e > 0 is arbitrary, this means that the se-
quence under consideration is fundamental in H 1 (Q). Consequently,
there is a function u in H' to which this sequence converges in the
norm of H 1(Q), but then II V 8 llw--+ II u llw and (f, V 8 )L,(Ql--+
--+ (f, u)L,<Q as s--+ oo. Accordingly, E(vs)--+ E(u). The equality
(61) now follows from the relation (62).
We shall now show that the function u realizing the minimum of
the functional E on H' is unique. Suppose that there are two such
functions u 1 and u 2 Then the sequence u 1 , u 2 , u 1 , u 2 , is a min-
imizing sequence for the functional E on H' and does not converge
in H', which contradicts the assertion just established. I
We now set forth the Ritz method for constructing a minimizing
sequence for the functional E. In H' take an arbitrary linearly inde-
pendent system of functions 'Pin k = 1, 2, ... , whose linear hull is
everywhere dense in H'. When H' = H 1 (Q), for such a system one
can take the set of all monomials x'X = x( 1 x;;~, where a is
any n-dimensional vector with nonnegative integer components.
We denote by R11. the k-dimensional subspace of H' c H 1(Q)
spanned by qJ 1, , 'Pin and find the element which realizes the
minimum of the functional E on R~~. (such an element exists, by
Lemma 5). Since any element in R~~. can be expressed in the form
+ ... +
c1qJ 1 ck'Pk with some real constants ch this problem is
equivalent to that of finding the minimum of the function
F(c 1, .. , c~~.) = E(cl'Pt + ... + Ck'Pk)
k k
o= 2J CjC j ( !p;, 'Jlj}H' + 2 .-l ci(f, 1Jli)L2 (Q)
i, i=1 i=l
with respect to cl! . . . , c~~..
The vector (c 1 , , ck) where the function F attains its minimum
is a solution of the system of linear equations aF = 0 i = 1
aci ' '
.. , k, that is, of the system
k
2J
j=1
('Pi> 'PJ)H'cJ + (!, 'Pi)L,(Q) = 0, i = 1, ... , k. (64)
The determinant of the system (64), called Gram's determinant of
the system qJ 1 , , 'Pk is not zero. Indeed, if it were zero, the li-
near dependence of its rows would imply the existence of constants
slt , ~~~.. I s1 I + ... + I ~~~. I =I= o, such that s1 (1Jl1, 'Jlj)w+ . . .
206 PARTIAL DIFFERENTIAL EQUATIONS
+ ~" (cp", cp1) H' = 0 for all j = 1, ... , k. This would mean
that the function 1 cp 1 + ... + ~k'Pk is orthogonal to all the func-
tions 'PI ... , cp", that is, ~IIPI + ... +
the linear independence of the system 'PI ... , 'Pk
Thus the linear system (64) has always a unique solution c~,
... , c:. Then the function
VI!.= C1" 'Pi+ + Ch'Pk
k (65}
belonging to R" realizes the minimum of the functional E on R".
The sequence of functions v", k = 1, 2, ... , is called the Ritz
sequence for the functional E with respect to the system 'PI cp 2, ....
Lemma 6. The Ritz sequence v~~., k = 1, 2, ... , of the functional E
with respect to an arbitrary linearly independent system of functions:
'Pk k = 1, 2, ... , whose linear hull is everywhere dense in H' is a
minimizing sequence for the functional E on H'. The sequence v 1u
k = 1, 2, ... , converges in the norm of H 1 (Q) to a function u which
realizes the minimum of E on H'.
Proof. As RIc R 2 c ... c R11. c ... c H',
E(v 1}-;;:::: E(v2 }-;;:::: ~ E(vh);;::: . .. -;;::::d. (66)
Since the linear hull of the system 'Pk k = 1, 2, ... , is everywhere
dense in H', for any e > 0 we can find numbers k = k (e) and
c; (e), ... , c;. (e) such that 1\ Ue- u 1\w :!( e, where Ue =
= c;(e) 'PI + ... + c/. (e) 'Pk belongs to R". Then (60) yields
+
E(ue) =II ueljk 2 (f, Ue}L,(Q) =II Ue- u + U 1/k
+ +
2 (f, u 8 - u u)L,(Q) = E(u) E(ue- u) + + 2 (ue- u, u)w
-<d+ I E(ue-U) 1+211 Ue-U llw II U llw -<d+ II Ue-U Ilk
+ 2C II f lk.<Q) II Ue- U llw + 211 Ue- U llw II U llw
-<d+e2 +2C II fliL.<Q>e+ 211 u llw e-<d+ Cte
with a constant CI > 0. As the minimum of Eon R" is attained on
the function v", (66) implies that d :!( E(v.) :!( E(v") :::;;: d + C1 e
for all s >
k. This means that E(v 8 ) -+ d as s-+ oo. The convergence
of the sequence v., s = 1, 2, ... , to the function u follows from
Lemma 5. I
We shall now establish an important property of the function u
which realizes the minimum of the functional E on H'. Take any
function v E H' and any real number t. The function Wt = u + tv
belongs to H', therefore the polynomial (in t) P(t) = E(w 1} =
= E (u) + 2t ((u, v)w + (/, v)L;.(Q)) + t 2 II v Ilk >
d for all t E
E (- oo, + oo). Moreover, PtO) = E(u) = d. This means that
a:; /t=O =2 ((u, v}w + (f, v)L,(Q)) =0.
ELLIPTIC EQUATIONS 207
Thus any function u in H' realizing the minimum of E on H'
satisfies the identity
(67)
for all v E H'.
The manner in which the scalar product equivalent to""the scalar
product in H 1 (Q) is defined in H' was so far immaterial.
Let H' = H 1(Q). Take functions k(x) E C {Q), k(x) k0 = >-
= const > 0, a(x) E C (Q), a(x) >-
0 in Q and o (x) E C(8Q),
o(x) >- 0 on 8Q, and assume that either a(x) = 0 in Q or o(x) =
== 0 on 8Q. We define a scalar product in H 1 (Q) by the formula (10):
(u, v)HI(Q) = ~ (k \lu \lv + auv) dx + f ko uv dS.
Q aQ
Then identity (67) coincides with the identity (6):
Q a~ Q
defining the generalized solution of the third or second (if o = 0)
boundary-value problem for Eq. (1) (with homogeneous boundary
conditions).
If H' = Ffl(Q) and the scalar product in ifl(Q) is defined by the
formula (7):
(u, v) HI(Q) = f (k \lu \lv + auv) dx
Q
(k (x), a (x) E C (Q), k (x) >-
k 0 > 0, a (x) >-
0), then the identity
(67) coincides with the identity (4) defining the generalized solution
of the first boundary-value problem for Eq. (1) (with homogeneous
boundary condition).
Thus the following result has been established.
Theorem 14. There is a unique function u in H 1 (Q) which realizes:
the minimum of the functional E on H 1 (Q). If the scalar product in
H 1 (Q) is defined by (10), then this function is a generalized solution of
the third or second (if o =
0) boundary-value problem for Eq. (1) (with
homogeneous boundary condition).
0
There is a unique function u in H 1 (Q) realizing the minimum of the-
functional E on ifl(Q). If the scalar product in }JI(Q) . is defined by
formula (7), then this function is a generalized solution of the first
boundary-value problem for Eq. (1).
Theorem 14 provides an alternative method, the variational meth-
od, different from the one employed in Theorems 1 and 2 for estab-
lishing the existence and uniqueness of generalized solutions of the
208 PARTIAL DIFFERENTIAL EQUATIONS
boundary-value problems examined in Subsec. 2, and indicates the
variational significance of generalized solutions.
If the subspace H' coincides with H 1(Q)(Ffl(Q)) and the scalar
product, equivalent to the usual scalar product, is defined there by
the formula (10) ((7)), then, by Lemma 6 and Theorem 14, the Ritz
sequence Vft, k = 1, 2, ... , for the functional E on H 1(Q) u'b(Q))
converges in H 1(Q) to the generalized solution of the third (first)
boundary-value problem for Eq. (1). That is, the Ritz sequence may
be regarded as an approximation to the generalized solution of the
boundary-value problem for Eq. (1).
Thus we have the following result.
Theorem 15. The Ritz sequence for the functional E defined on
H (Q) or on ifl(Q) (the scalar product is defined by (10) or (7)) con-
1
structed with respect to any linearly independent system of func-
tions whose linear hull is everywhere dense in H 1(Q) or ffl(Q), res-
pectively, converges in H 1(Q) to the generalized solution of the cor-
responding boundary-value problem (third or first) for Eq. (1).
2. SMOOTHNESS OF GENERALIZED SOLUTIONS.
CLASSICAL SOLUTIONS
In the preceding section we examined the question of solvability
of basic boundary-value problems for the second-order elliptic
equations. We shall now investigate the smoothness of solutions of
these problems.
We shall assume that the data of the problem under consideration
are real-valued. Then, as noted in Sec. 1, the generalized solutions
of these problems are also real-valued. Accordingly, by solutions in
the sequel we shall mean, unless otherwise stated, real-valued fun-
ctions-the elements of real spaces C11 (Q) or Hk(Q), k = 0, 1, 2, ....
In the investigation of smoothness of generalized solutions it is
advantageous to consider the one-dimensional case separately, since
the results obtained in this case are, in general, not true for n > 1.
Moreover, the investigation in this case is far more simpler. In par-
ticular, when n = 1, the generalized solutions of the boundary-
value problems (they belong to the space H 1 (a, ~)) are continuous
functions on [a, ~), by Theorem 3, Sec. 6.2, Chap. III. The question
of extension of a function defined on the boundary into the region
by a function in H 1(a, ~) is also easily solved in the one-dimensional
case: if ll>lx=a = c:p 0 , ll>lx=Jl = c:p 1 , then for such an extension one
can take the linear function d> = x ( <ft- q o) acp 1 - ~ff'o
~-a ~-a
ELLIPTIC EQUATIONS 209
1. Smoothness of Generalized Solutions in the One- Dimensional
Case. We recall that in the classical formulation the boundary-
value problems for the equation
Xu == (ku')' - au = f, x E (a, ~), (1)
consist in finding the solution u(x) of this equation which satisfies
the following conditions: in the case of the first boundary-value
problem u(x) EC2 (a, ~) C([a, ~]) andn
U ix=a = IJlo, U \x=~ ='Pt. (2}
in the case of the third (second) boundary-value problem u(x) E
E C2 (a, ~) nC1([a, ~]) and
+
(- Ux Uou) ix=a = IJlo, (ux 01U) \x=~ = 'P1 ( 3) +
Here k(x) E ~]), a(x) E C([a, ~]) and f(x) are given func-
C1 ([a,
tions with k(x) >-
k 0 > 0; a 0 , a 1 , IJlo, qJ 1 are given constants.
The generalized solution of the problem (1), (2) (f E L 2 (a, ~)) is
the function u(x)E H 1 (a, ~) satisfying the integral identity
~ ~
a a
for all v E lfl(a, ~) and the boundary conditions (2).
The generalized solution of the problem (1), (3) (f E L 2 (a, ~)) is
the function u(x) E H 1(a, ~) satisfying the integral identity
~
) (ku'v' + auv) dx + k(~) a1 u(~) v(~) + k(a) a u(a) v(a) 0
a
fl
= - )" fv dx + k(~) qJ 1 v(~) + k(a) qJ v(a)
0 (5)
a
for all v E H 1 (a, ~).
The following auxiliary proposition holds.
Lemma 1. If f E C([a, ~]), then the function u(x) E H 1 (a, ~)
satisfying the integral identity (4) for all v E lfl(a, ~) belongs to
the space C 2 ([a, ~]) and is a solution of Eq. (1) in the interval (a, ~).
Proof. Since the function u(x) E C([a, ~]) (H 1(a, ~) c C([a, ~j)),
X
0
X 1]
the function u 0 (x) = ) k ~~) ) (f() +a() u(~)) d. By the condi-
o 0
tions imposed on k(x), the function u 0 (x) E C2 ([a, ~]), and, more-
14-0594
210 PARTIAL DIFFERENTIAL EQUATIONS
over, is a solution on (a, ~) of the differential equation (ku~)' =
= f(x) +
a(x) u(x). Therefore the function u 0 (x) satisfies for any
v Eif1(a, ~) the identity
r (ku~v' +
~
a
auv) dx = - r
~
a
fv dx,
which means that the function u 1 = u - u 0 belonging to H 1 (a, ~)
satisfies the integral identity
~
Jku;v dx
a
= 0, v CH 1(a, ~),
thereby implying that on (a, ~) the function ku; has a generalized
derivative equal to zero. Consequently, ku; = const, that is, u 1 E
E C2 (!a, ~]). Therefore also u(x) E C2 ([a, ~]).
~ ~
Since J
a
ku'v' dx=- J(ku')'vdx
a
for all v E iJl(a, ~), (4) im-
plies that the function (ku')' - a(x) u(x) - f(x) continuous on
[a, ~] is orthogonal (in L 2 (a, ~) with a scalar product) to any func-
tion belonging to H1 (a, ~). Therefore the function u(x) is a solu-
tion of Eq. (1) in (a, ~). I
The generalized solution u(x) of any of the first, second or third
boundary-value problems belongs to H 1 (a, ~) and for it identity (4)
holds for all v E Ffl(a, ~). Therefore, by Lemma 1, u(x) E C2 ([a, ~])
and u(x) is the solution of Eq. (1) in (a, ~).
Thus we have shown that iff E C([a, ~]), the generalized solutions
of the boundary-value problems under discussion have continuous
derivatives up to order 2 on [a, ~] and satisfy Eq. (1). Moreover, it
is evident that in the case of the first boundary-value problem the
function u(x) satisfies the boundary conditions (2). In the case of
the third (second) boundary-value problem,
a
~
f ku'v' dx = - r
~
a
(ku')' v dx + k(~) u' (~) v(~)- k(a) u'(a) v(a)
for any v (x) E H 1 (a, ~). If account is taken of (5), this gives
k(~) (u'(~) + a 1 u(~)- cp 1) v(~) + k(a) ( - u' (a)+ a u(a)- cp0 ) v(a) =
0 0
for any v(~) and v(a) (recall that for any v(a) and v(~) there is a
function v(x) in H 1 (a, ~) assuming the values v(a) and v(~) at
x = a and x = ~). Hence the function u(x) satisfies the boundary
conditions (3).
ELLIPTIC EQUATIONS 211
Thus we have proved the following theorem.
Theorem 1. If the function f(x) E C(la, ~)), then the generalized
solutions of the first, second and third boundary-value problems for
Eq. (1) belong to C2 (la, ~]) and are classical solutions of the corres-
ponding problems.
Suppose that u 8 (x) is a generalized eigenfunction of, for example,
the third (second) boundary-value problem for the operator :. This
means that u 8 (x) E H 1 (a, ~), and hence u.(x) E C([a, ~]), and
satisfies the equality
f3
~ (ku~v' + au.v) dx + k(~) cr 1 u 8 (~) v(~) + k(a) a0 u 8 (a) v(a)
a
f3
=-A.)u.vdx,
a
where A8 is an eigenvalue, for all v E H 1 (a, ~). By Theorem 1, the
function u.(x) belongs to C2([a, ~]) and is a classical solution of the
equation
:u = (ku')'- au= A8 u, xE(a,~), (6)
satisfying the homogeneous boundary conditions (3), that is, u.(x) is
a classical eigenfunction of the third (second) boundary-value pro-
blem for the operator :.
It is similarly shown that the generalized eigenfunction u 8 (x) of
the first boundary-value problem belongs to C2 ([a, ~]) and is a
classical eigenfunction of the same problem.
Let us show that the eigenvalues of any of the boundary-value
problems are nondegenerate. Assume that there is an eigenvalue A8
of, for example, the third boundary-value problem to which there
correspond two linearly independent eigenfunctions u<v and u< 2 >.
We know that the general solution of Eq. (6) is of the form
+
C1 u< 1 > C 2 u< 2 >, where C 1 and C 2 are arbitrary constants. This means
that any solution of Eq. (6) must satisfy the boundary condition
u'(a) - a 0 u(a) = 0, because this boundary condition is satisfied
by both the functions u< 1 > and u< 2 >. But there is a solution of Eq. (6)
that does not satisfy this condition, for example, the solution with
initial conditions u(a) = 0, u'(a) = 1.
Thus we have established the following result.
Theorem 2. The generalized eigenfunctions of the first, second and
third boundary-value problems for the operator : belong to C 2 ([a, ~])
and are classical eigenfunctions of the corresponding problems. All the
eigenvalues are nondegenerate.
2. Interior Smoothness of Generalized Solutions. We shall now
examine the question of smoothness of generalized solutions of bound-
ary-value problems when n > 1. In order that the essential points
14*
212 PARTIAL DIFFERENTIAL EQUATIONS
do not get lost in technical details, we confine our discussion to a
particular case of Eq. (1) of the preceding section, and investigate
the smoothness of the generalized solutions of the boundary-value
problems for Poisson's equation (k =
1, a= 0)
t1u =f. (7)
We recall that the generalized solution of the first boundary-value
problem for Eq. (7) is a function u(x) in H 1 (Q) satisfying the integ-
ral identity
J Vu Vv dx = - J fv dx
Q Q
(8)
for all v E Ifl(Q) and the boundary condition u iaQ = <p (the func-
tion f E L 2 ( Q) and <p is the trace of a function <t> belonging to H 1 ( Q),
that is, there is a function <t> E H 1(Q) such that <I> laQ = <p).
The generalized solution of the third (second) boundary-value
problem for Eq. (7) is a function u(x) E H 1 (Q) satisfying the in-
tegral identity
Q ~ Q ~
for all v E H 1 (Q) (the function f E L 2 (Q) and <p E L 2 (8Q)).
The results of the preceding section imply that the generalized
solution u(x) of the first boundary-value problem exists, is unique
and satisfies the inequality
u;uiiHl(Q)<C(II'fiiL.(Q)+ inf II<DIIHl(Q))' (10)
(ci>EHl(Q)
ci>IaQ=IP
where the constant C does not depend on f or <p.
The generalized solution u(x) of the third boundary-value prob-
lem with a >
0, a =I= 0, also exists, is unique and satisfies the in-
equality
II u IIHl(Q) <c(II f lk,(Q) +II <p IIL,(c'lQ)), (11)
where the constant C does not depend on f or t:p.
In the case of the second boundary-value problem (a = 0) the
condition of its solvability is assumed fulfilled: - .\ f dx + .\ <p dS =
Q oQ
= 0. Then the second boundary-value problem has a unique general-
ized solution u(x) in the class of functions which are orthogonal to
the constant functions with respect to L 2 (Q) with a scalar product,
and for this solution inequality (11) holds. Because all other gener-
alized solutions differ from u(x) by constant terms, we may confine
ourselves to the function u(x) in investigating the smoothness of
generalized solutions of the second boundary-value problem.
ELLIPTIC EQUATIONS 213
n
Lemma 2. Suppose that f E L 2 (Q) H~oc(Q}, k = 0, 1, 2, ... ,
and the function u E H 1 (Q) and satisfies the integral identity (8) for
all v E jfl(Q). Then u E H~;;c2 (Q) and for any pair of subregions Q~
and Q" of Q, such that Q' ~ Q" (f; Q, the inequality
II u 11Hk+2(Q') ~ c (II t "Hk(Q") +II u IIHl(Q")) ( 12)
holds with a positive constant C = C(k, Q', Q").
Proof. Let Q', Q" be arbitrary subregions of Q _such that Q' ~
~ Q" ~ Q. By 6 > 0 we denote the distance between\the bounda-
ries 8Q' and 8Q", and consider the function ~(x) such that ~(x) E
E Coo(Rn), ~(x) = 1 in Q6 (and thus in Q'), ~(x) = 0 outside Q26n
For function v (x) in identity (8) take the function ~(x) v 0 (x),
where v 0 (x) is any function in H 1 (Q") ex~ended as being equal to
zero outside Q" (obviously, ~(x) v 0 (x) E H 1 (Q)). Since vu vv =
= Vu V(~vo) = Vu(V~Vo +
~Vvo) = Vu V~Vo V(~u)Vvo - +
- u V~ Vv 0 , the identity (8) assumes the form
JVU Vv dx = JFv dx + Ju V~ Vv
0 0 0 dx, (13 0)
Q" Q" Q"
where the function
U(x) = ~(x) u(x) (14)
belongs to H 1 (Q"), vanishes outside Q26; 3 and coincidesrwith u(x)
in Q6, and the function
F(x) = - g - vu v~ (15)
belongs to L 2 (Q") and vanishes outside Q26!3
Note that the integration in (13 0) is, in fact, over Q26; 3 Therefore
this identity is true not only for any v 0 E H 1(Q") but also for any
v 0 E H 1(Q6 12) (extended arbitrarily outside Q012 , as an element of
L2(Q")).
Take any function v1 (x) belonging to H 1 (Q") and extended as
being equal to zero outside Q". For any i = 1, 2, ... , nand any h,
0 < I h I < fJ/2, the finite-difference ratio
V1 (x 1 , , Xi-l Xj-h, Xi+l , Xn)-Vt(X)
-h
belongs to H 1 (Q6;2) n L2(Q"). Put in (13o) Vo = {)~hvl(x)
for some i = 1, 2, ... , n and some h, 0 < I h I< fJ/2. The for-
mula of "integration by parts" ((9), Sec. 3.4, Chap. III} yields the
- dentity
} V6~U Vv 1 dx= - J F6~hVt dx+) 6~ (u V~) Vv dx. 1 (16 0)
Q" Qz~;a Q"
214 PARTIAL DIFFERENTIAL EQUATIONS
We shall first prove the lemma for k = 0. From (15) it readily
follows that
II F IIL,(Q") ~C'(Q'' Q") (II f IIL,(Q") +II u IIHl(Q"))
Therefore from (16 0 ), by means of Theorem 3, Sec. 3.4, Chap. III,
we obtain the inequalitie!'
Q"
<.C (Q', Q") (II f IIL,(Q"l +II u IIHI(Q")) Ill V'v1II/L,(Q")
Putting v1 = 6f, U ( U is assumed extended as being zero outside Q),
we find that
Ill yr6~U IIIL,(Q")< c (Q'' Q") (II f IIL,(Q") +II u IIHl(Q"))
for all i = 1, 2, ... , n, 0 < I h I< 6/2.
In view of Theorem 3, Sec. 3.4, Chap III, the last inequality
implies that U E H 2 (Q") and II U IIH2(Q"l ~ C(Q', Q") (II f IIL,(Q"l +
+ II u IIHI(~") ). Because U = u in Q', it follows that u E H 2 (Q')
and the inequality (12) holds for k = 0. Thus u E H[oc(Q),
since Q' is any subregion of Q.
Now let f E H'{b"6 1 (Q). Suppose that u has the following properties:
u E H'{b"6 2 (Q) for any pair of subregion Q1 and Q 2 of Q such that
Q1 ~ Q 2 ~ Q, u satisfies the inequality (12) for k = m:
II U 11Hm+2(Qt)<.C (m, Q1, Q2) (IJ f 1/Hm(Q,) +II U IIHI(Q,)), (12m)
and for any a, I a I ~ m, i = 1, 2, ... , n and 0 < I h I< 6!2 the
identity
) V'6~(DaU) '\7Vm+1 dx
Q"
=- ) Da F6~hVm+1 dx + .\ 6h (Da(u \7~)) Y'Vm+i dx,
Qzota Q'
where Vm+l is any function in H 1(Q"), holds. Note that the above
properties have already been established for m = 0.
According to the above hypotheses, (14) and (15) imply that
DaU E H 2 (Q") and DaF E H 1(Q"), therefore, by Theorem 3, Sec. 3.4,
Chap. Ill, we may pass to the limit, as h-+ 0, in (16 111 ). Thus for
any a, I a I = m, i = 1, 2, ... , n, we obtain the equality
J\ V' DaU x.Y'Vm+i dx =
l
-
J\ . l dx + J\ Da(u V'~)x.l
Da F(vm+i)x. Y'vm+1 dx,
Q" Q'~f>l :J Q"
ELLIPTIC EQUATIONS 215
f VDaUxiVVm+t dx= ' DaFxym+t dx+ fDa (uVs)xiVVm+1 dx (13m+t)
Q" Q" Q"
for all Vm+I E H 1 (Q") (the function Da F vanishes outside Qzli/ 3 ). This
equality coincides with (13 0) if we replace there Da U xi by U, Da F xi
by F, Da(uVs)xi by uVs and Vm+ 1 by v 0 Moreover, DaU xi E
E H 1(Q"), vanishes outside Qzli/a and coincides with Daux; in Q6,
while Da F xi E L 2 (Q") and vanishes outside Qzli/a. Since the in-
tegration in (13m+t) is, in fact, taken over Q2e,13 , in the last
equality we can put Vm+ 1 (x) = 6~hVm+ 2 (x), j = 1, 2, ... , n,
0 < I h I < 6/2, where Vm+2 is an arbitrary function in H 1(Q").
This results in
~ V6~(DaUxi) Vvm+2 dx
Q"
= - \" DaFxi6~hVm+2 dx+ i 6~ (Da(u Vs)x) Vvm+ 2dx. (16m+t)
~" ~"
Using the inequality (12m) (with Q 1 = Q'26f 3 , Q2 = Q"), from (15)
we obtain
11 F l/Hm+I 1Q") <: C1 (JJ f JIHm+I(Q") +II u 11Hm+2(Qze,; 3 ))
~C2 (J/ I 1/Hm+I<Q") + 1/ u IIHl(Q"))
Setting in (16m+ 1 } Vm+2 = 6~ (DaUx;) and again using Theorem 3,
Sec. 3.4, Chap. Ill, we find that u E Hf:.2(Q) and the inequality (12)
holds for u(x) for k = m + 1. I
As a corollary to Lemma 2, we have the following result.
Corollary. Suppose that f E L 2 (Q), and the function u E H 1(Q)
and satisfies the integral identity (8) for all v E H1(Q). Then the func-
tion u(x) satisfies Eq. (7) (a.e.) in Q.
We must show that the sum of the generalized second derivatives
Ux,x, + ... + Uxnxn (the existence of these derivatives has just
been established) equals f a.e. in Q. As v(x) in (8) we take an arbitra-
ry function belonging to ffl (Q'), Q' ~ Q, extended outside Q' by
assigning to it the value zero. Since u E H 2 (Q'), the Ostrogradskii's
formula yields that )' (lw - f) v dx = 0, whence it follows that
Q'
du- f = 0 (a.e.) in Q', and hence (a.e.) in Q.
The generalized solutions u(x) of the first, second and third bound-
ary-value problems for Eq. (7) satisfy the hypotheses of Lemma 2
216 PARTIAL DIFFERENTIAL EQUATIONS
as well as the inequality (10) or (11) (the solution u(x) of the second
boundary-value problem is assumed orthogonal in L 2 (Q) to constant
functions), therefore from Lemma 2 and Theorem2, Sec. 6.2, Chap. III,
the following result follows.
Theorem 3. Iff E L 2 (Q) n H~oc(Q), k >
0, then the generalized
solutions u(x) of the first, second and third boundary-value problems
for Eq. (7) belong to H~0~ 2 (Q) and satisfy Eq. (7) (a.e.) in Q. Forany
subregions Q' and Q" of Q, Q' ~ Q" ~ Q, there exists a positive constant
C depending on Q', Q" and k such that
II u llu~<+ 2 <Q'J ~C( 1/ f 1/uk(Q"J + 1/ f //Lz(QJ + <l>EJil(Q)
in 1/ <D IIII (QJ
1 )
<I>iaQ='P
for the first boundary-value problem and
II u 1/uk+z<Q') < c <II t \\uk(Q"> +II t lk,<Q> +II rp lk,<aQJ)
for the second and third boundary-value problems (in the case of the
second boundary-value problem it is assumed that .\ u dx = 0).
Q
If k?;::; [ T ]-1, then u(x)ECk+i-l;J(Q). In particular, if
IE L2(Q) n C"(Q), then u(x) E Coo(Q).
Theorem 3 implies that the smoothness of generalized solutions of
boundary-value problems for Eq. (7) in the interior of Q does not
depend on the type of boundary conditions nor on the smoothness of
the boundary or on that of boundary functions. The interior smooth-
ness depends only on the smoothness of the right-hand side f(x)
of the equation. The result obtained above is utmost precise: the
smoothness of the solution is higher than that of the right-hand side
by a number equal to the order of the equation.
Remark. For the one-dimensional case it was shown, in particular,
that if the right-hand side of Eq. (7) is continuous, then the general-
ized solutions have continuous derivatives up to order 2. Analogous
result does not hold for the multi-dimensional case. Later (Subsec. 3
of the next section) an example will be given of a function f(x)
continuous in Q such that the generalized solution of the fi.rst bound-
ary-value problem for the Poisson equation (7) does not belong to
C2(Q) (it belongs, of course, to HFoc(Q)).
3. Smoothness of Generalized Solutions of Boundary- Value Prob-
lems. In the preceding subsection the interior smoothness of general-
ized solutions was established, that is, we established that the
solutions belong to the spaces Hfoc(Q) or C1(Q) for some k and l.
Here we shall examine the smoothness of generalized solutions of
boundary-value problems in the whole of Q, that is, the question of
ELLIPTIC EQUATIONS 217
the solutions being contained in the spaces Hh(Q) or C 1(Q). Natu-
rally, the smoothness of solutions "right up to the boundary" depend&
on the smoothness of the boundary as well as that of boundary func-
tions.
It will be assumed that the boundary aQ E C11 +2 for some k 0. >-
We first examine the case of homogeneous boundary conditions.
The generalized solutions of the first or second boundary-value prob-
lems* with homogeneous boundary conditions (the function cp, the
right-hand side in the boundary conditions, is zero) for Eq. (7) are
functions belonging to the spaces H1 (Q) or H 1 (Q) and satisfying the
integral identity (8) for all v belonging to ifl(Q) or to H 1 (Q), respec-
tively (in the case of the second boundary-value problem the func-
tions f and u are assumed orthogonal to constant functions in L 2 (Q)}
with a scalar product.
Theorem 4. If f E H 11 (Q) and aQ E C11 +2 for certain k >-
0, then
the generalized solutions u(x) of the first and second boundary-value
problems with homogeneous boundary conditions for the Poisson equa-
tion (7) belong to H 11 +2 (Q) and satisfy (in the case of the second bounda-
ry-value problem it is assumed that \ u dx = 0) the inequality
'
Q
II u 11Hk+2(Q)'<: c II I IIHit(Q)' ( 17)
where the constant C > 0 does not depend on f**.
Proof. Let x 0 be an arbitrary point on the boundary aQ. Let the
system of coordinates be chosen in such a way that the point x~t
becomes the origin and the normal to the boundary at this point is
directed along the Oxn-axis. We take a small number r = r(x0 ) such
that the portion of the boundary aQ n
(I X I < 4r) is a connected
set which is uniquely projected along the Oxn-axis onto a region D
in the plane Xn = 0; the equation of the surface aQ n(
I X I < 4r}
has the form
Xn = 'ljJ(x'), x' = (x 1 , , Xn_ 1) ED,
where the function '(x') belongs to C11 +2 (D) and satisfies '(0) = o,
'x 1(0) = . . = 'x n-1 (0) = 0 as well as the inequalities
l'xii-<: 21n, i=1, ... ,n-1, x'(D. (18}
* For the sake of simplicity, we confine our discussion to the solutions of
the first and second boundary-value problems. The investigation of smoothness
of generalized solutions of the third boundary-value problem with certain
conditions on the function a(x) (of (9)) can be carried out by the same method.
** For the function u(x) which is a generalized solution of the third boundary-
value problem for Eq. (7) with homogeneous boundary conditions the following-
result holds: if f E HII(Q), aQ E Ck+ 2 and a(x) E Ck+1 (8Q) (a ;:;:. 0) for some
k ;:;:. 0, then u(x) E Hk+ 2 (Q) and satisfies the inequality (17).,
218 PARTIAL DIFFERENTIAL EQUATIONS
. Then the region Q = Q n (I X I < 3r), and thus also its subregion
Q' = Q n( I X I< r) are projected along the Oxn-axis into D.
Let r denote the common part of the boundaries of Q and Q, r =
= aQ n ( I X I < 3r), and by r 0 the remaining part~of the boundary
Q. The set of functions in H 1 (Q) whose traces on rare zero will be
denoted by Ht(Q).
Suppose that the function s(x) E C (Rn), s(x) = 1 when I X I <
00
=
< r, s(x) 0 when I X I > 2r. Then for any function Vo(x) in
Ht(Q)(H1 (Q)) the function v(x), which is equal to s(x) Vo(x) in Q
and to zero at the remaining points of Q, belongs to H1 (Q) (H1 (Q)).
Substituting v(x) into (8), we obtain, as in the preceding subsection,
~ VUV'vodx=) Fv 0 dx+ Ju'Vs'Vv 0 dx, (19)
Q Q Q
where the function v 0 is an arbitrary function in Ht(Q) in the case of
the first boundary-value problem, while for the second boundary-
value problem v 0 is an arbitrary function in H 1 (Q), and the func-
tions F(x) and U(x) are determined by (14) and (15) with s(x) just
introduced. Evidently, U(x) E H 1 (Q) and F(x) E L 2 (Q).
The transformation
Y;=X;, i=1, ... , n-1, Yn=Xn-'(x') (20)
maps the regions Q and Q' onto certain regions w and w' with the
identity Jacobian.
!Jn
lJ y
x' !!'
Fig. 1
The images of surfaces f and f 0 are denoted by y and y 0 , respec-
tively. The functions U(x), u(x), ... defined in Q are mapped by
transformation (20) into functions U(y), u(y), . . . defined in w
(the same notation is retained). Moreover, U(y) = u(y) in w'
and for some 8 > 0 the functions U(y) and F(y) vanish at points of
w w
the set w "'-. 6 , where 6 is a subregion of w which consists of those
points whose distance from y 0 is greater than 8.
ELLIPTIC EQUATIONS 219
Since for x E Q(y E ffi) U xi = Uy1 - Uyn 'l'xi for i = 1, ... , n -
- 1 and Ux n = Uy n , we see that
n
(J)
=
(J) (J)
~
i, j=1
AijUytVoyi dy
n
+ ~ ~ Bti~vpvov; dy, (21 0)
(J) i, .i=l
n-1
whereA;n=Ant='l'x. fori=1, ... ,n-1, Ann=-~ ljl~., Aij=O
' i=1 '
for remaining i and j; Bti=6;i-Ai.i, 6ii=0 for i=Fj, 6tt=1,
i=1, ... ,n. Evidently, .AiiECk+1 (w), BtiECk+t(ffi) for all i andj;
furthermore, by (18),
1
!Aii(Y)!<-zn i,j=1,2, ... ,n, yEffi. (22)
Since the functions U(y) and F(y) vanish in ffi ~6/2, equality
(21 0 ) holds not only for any v0 (y) in H~(ffi) or in H 1 (ffi) but also for
any v0 (y) in H~(wo;2) (arbitrarily extended outside wo; 2 as a func-
tion belonging to 2( ffi}} or in H 1 ( ~; 2 ) (arbitrarily extended outside
ro0;2 as a function belonging to L 2(ffi)), respectively.
Consider any function v1 (y) belonging to H{-( ffi) (H1 ( ffi}} and
xtended outside ffi by assigning to it the value zero, and in (21 0)
set v 0 = 6~hv1 for a certain l < n and 0 < I h I < 6/2 (the function
Vo(Y) belongs, obviously, to H~(Wo;2) L2(ffi) and to H 1 (wo;2) n n
n L 2(ffi), respectively). The identity (21 0 ) then becomes
r v y(6~U) v
(J)
yVt dy = _ r F6~hVt
(J)
dy
n n
+J ~ 6~(AtPvi) Vtyi dy +) ~ 6~(Bii~vp) V1yi dy (23o)
(J) i, j=1 (J) i, j=i
(note that the integration here is taken not over whole ffi but only
over its subregion roo;z; accordingly, all the expressions under the
220 PARTIAL DIFFERENTIAL EQUATIONS
From Theorem 4, Sec. 3.4, Chap. III, it follows that
If (J)
F6 1-hVt dy l-<11 F I!L,(w) JJ Vty 1 JJL,(w)-<:ll F JJL,(w) II JY'vtii!L,(w) (24o}
In order to estimate the second integral in the right-hand side
of (23 0 ), we break it into two terms
n n
f
(J)
,:S 6~ (AuU v) Vty 1 dy = ~ L
i, :i=1 (J) i, :i=l
(Aii)h 6h U yiVty 1 dy
n
(J) i, :i=i
Here we have used the identity
6~ (fg) = gh6hf + f6hg,
where g~(y) = g(y 1 , , Yz-1 , Yz + h, Yz + 1 , Yn), true for
arbitrary functions f and g.
Using (22), the first term is estimated as follows:
n n
I~ ,:S (AiJ)~6~UyiVty 1 dy 1-<
(J) i, :i=1
1
2n f (,:S J6~Uyi J)
(J) i=1
n n
X ( :s I
:i=1
Vtyj I) dy-<: 21n f Vn ( :s
(J) i=1
(6hUvl f 12
(26 0 )
The second term in (25 0))s estimated together with the third integ-
ral in the right-hand side of (23 0 ). Since the functions A 11 and B 11
are continuously differentiable in ro,
n n
j J ,:S
(J) i, :i=1
(6kAu) UyiVtv 1 dy+)
(J)
,:S
i, :i=i
6h (Biisvp) v1v1 dy I
-<: Ctil U JJHl(Q) Ill Y'Vt JllL,(w)-<: C1 JJ U JJHl(Q) JIJV'vt IJJL,(wh (27 o)
where the constant C1 does not depend on u or v1
Taking into account (24 0 )-(27 0), from (23 0 ) we have
If Y' (6~U)
(J)
Y'Vt dy 1-< (II FJ!,(w) + ~ IJJ V'6~U IJJL,(w)
+ Ctil u l!Hl(Q)) JJJ Y'Vt JJ!L,(oo) (28o)
ELLIPTIC EQUATIONS 221
Putting in this inequality v1 = 6hU and using the inequality
II F(y) IJL,(w) =II F(x) IIL,(!'l)-< C2(11 f IIL,(Q) +II U IIHl(Q)), (29o)
(the constant C 2 depends only on the function ~. that is, only on the
region Q) which follows from (15), and the inequality (10) or (11),
where cp = 0 (then in (10) inf II <D IIH(Q)= 0), we obtain the esti-
mate
l=1, ... ,n-1,
which in turn implies that (Theorem 4, Sec. 3.4, Chap. III) all the
second-order generalized derivatives of U except Uy n yn belong to
L 2 (ro) and the inequality IIUviYi IIL,(w):::;;; C II f IIL,(Q) holds for
them. This means that for the corresponding derivatives of the func-
tion u(y) the inequalities
II uYiYj IIL,<w'):::;;;c II t IIL,(Q)
hold.
To estimate Uy n v n in ro 1 , we may use Corollary to Lemma 2, accord-
ing to which 11xu = f a.e. in Q, and thus a.e. in Q 1 In the new vari-
ables this equation has the form
n-1 n-1 n-1
11yu(y)- 2 2}
i=i
Uy yn'Px
t t
+ Uy n yn i=i
h 'i-1 ~.- Uy n i=i
1
~ lfxx = t t
f (y),
whence for all y E ro 1
n-1
(1 ;2J "'~;) UYnYn
+ t=1
n-1 n-1 n-1
= f(y) ~ UYiYn 'i'xi- h UYiYi + Uyn h 'i'xixi
+ 2 i=1 (30)
i=1 i=1
Since 'i' E C11.+2 (D) for k :> 0, it follows that Uy y
n n
E L 2 (ro 1
) and
II uYnYn IIL,(w'):::;;; const 1/ f 1/L,(Q)
Thus it is established that for any point x 0 E BQ we can find posi-
tive numbers r = r(x0 } and c = C(x0) such that u(x) E lJ2 (Q n
n (I X - X 0 I< r(x0 ))) and
II U IIH2(Qn(/x-xOJ<r(xO))) :::;;;C(x0 ) II f IIL,(Q)
From the cover of the boundary BQ by the sets aQ n (I X - x 0 I <
< r (x 0 )) fl?r all pos!'lible x 0 E aQ, we choose a finite subcover aQ n
n (I X - x' I< r (x1 )), i = 1, 2, ... , N. Then there is a number
N
6o > 0 such that Q""-Qoo c u Q n (I X -
i=1
xi I< r (xi)).
222 PARTIAL DIFFERENTIAL EQUATIONS
Therefore u(x) E H 2 (Q"-..Qo.) and II u IIH (Q'-Oo,l c l II f IIL,(Q) 2 <
where C1 is a positive constant. But by Theorem 3, u(x) E H 2 (Q 6 .;~)
<
and llu IIH<o6, 12 ) C 2 II f IIL,(Q) Therefore u EH 2 (Q) and II u IIH(Q) <
:::;:; C II f IIL,(Qh where the constant C > 0 does not depend on f.
This proves Theorem 4 for k = 0.
Now let k be any natural number.By the theorem on interior smooth-
ness of generalized solutions (Theorem 3), it is enough to establish,
as in the case when k = 0, that for any boundary point x 0 there are
numbers r = r(x0 ) > 0 and C = C(x0 ) > 0 such that u(x) E
n
EHk+ 2 (Q (lx- x 0 I< r)) and
II U IIHk+2<Qn(fx-xOJ<r)) ~ C II f IIHk(Q)
(the point x 0 may be taken as the origin and the axis Oxn directed
along the normal to oQ at this point). In view of smoothness of the
transformation (20) (smoothness of the boundary), for this it suffices
to show that u(y) E Hk+ 2 (ro') and llui1Hk+2(w'l ~ C II f IIHk(Ql"
We have already established that u(y) E H 2 (ro'), II u IIH(w') <
< C II f IIL,(Ql and, furthermore, the relation (23 0 ) holds. Using
the device adopted in the proof of Lemma 2 of the preceding subsec-
tion, we shall show that for any m = 1, 2, ... , k u(y) E nm+ 2 (ro')
<
II u 11Hm+2(w') C II f IIHm(Q) and the equality
) V (6~Da"U) Vvm+i dy
(!)
n
(!) (!) i, i=1
n
(!) i, i=1
holds for all a= (a1 , . an_ 1 , 0), I a I< m, l = 1, ... , n - 1,
0
0 < I h I< 6/2, Vm+l E H~(ro) in the case of the first boundary-
value problem and Vm+l E H 1 (ro) in the case of the second bounda-
ry-value problem. We shall prove this for m = 1.
In (23 0) we pass on to the limit as h-+ 0, and integrate by parts
the first term of the right-hand side of the resulting equality. This
yields
n
JVU Yz Vv dy = J F y v dy + J ~
Cil
1
Cil
1 1
Cil i, j=1
(AiiU y)y 1 v 1Yj dy
n
+J ~ (Bii~Yju)y 1 Vtyi dy, (21t)
Cil i, i=1
ELLIPTIC EQUATIONS 223
which is true for all v1 in H~( ro) in the case of the first boundary-
value problem and in H 1 ( ro) for the second boundary-value problem.
The identity (21 1) for Uy 1 differs from the identity (21 0) for U in
merely that the functions F, A;jUy., B;/~y.u have been replaced
! }
by Fy 1, (AiiUY)Yz (Bii~Y;u)y 1 , respectively, and the function
v 0 by the function v1 with the same properties.
Setting in (21 1) v1 (y) = 6B_hv 2 (y), s < n, 0 < I h I < 6/2, where
v 2 (y) is an arbitrary function in Ht(ro) (H1 (ro)) extended as being
equal to zero outside ro, we obtain the identity analogous to (23 0 )
) V(6~Uy)Vv 2 dy=- f Fyl--hv2dy 3
w w
n n
+j ~ 6/,((AiiUY;)y 1)(v2)yidy+ j L 6/,((Bu~yp)y 1 )(v2)y;dy.
(I) i, j=1 w i, j=i
As in the previous case, we estimate the integrals in the right-
hand side of (23 1 ). Just as in (24 0 ), we have (since u E H 2 (Q) and
>
f E Hk(Q), k 1, by (15) FE H 1 (Q), and because 1jJ E ck+ 2 (D).
F(y) E H 1 ( ro))
Analogously to (25 0 ), the second integral in the right-hand side of
(23 1) is divided into two parts:
"1'1
00 i, i=i
n
= j ~ (Aii)/, 6~U YiYz (v2)yi dy
w i, j=i
n
+j ~ [6~ (Au) U YiYz + 6/, (Aijyp Yi)] (v2)yj dy. (25 1)
w i, i=1
Using (22), we estimate the first term in (25 1):
n
w i, i=1
~+Ill V6~U y1 IIIL (w) Ill Vv2II/L (w)
2 2 (261}
"224 PARTIAL DIFFERENTIAL EQUATIONS
Since the functions Aii and Bii belong to Ck+1 (w), k :;> 1, the
sum of the second integral in (25 1) and the third integral in the right-
.hand side of (231) is estimated in the following manner:
n
w i, 3=1
n
(J) i, i=i
In view of (241)-(27 1), (23 1) yields the inequality
:1) V6~U111 'VIJ2 dyl
(J)
l=1, ... , n-1, s=1, . .. , n-1.
:Setting in this inequality v 2 (y) = 6~U 111 (y), and using the estimate
II F 1/Hl(w) :s;; C (I/ f IIHl(Q) +II U IIH2(Q))
which follows from (15), and the estimate (17) already established
for k = 0, we obtain
Ill V6hU y 1 /IIL.<w> :s;;const II f f/Hl(Ql
s, z= 1, ... , n -1, o< I h 1< 612.
This means that in ro' there exist generalized derivatives u11 p 11111 s
,
p = 1, 2, ... , n, s, l = 1, ... , n- 1 which belong to L 2 (ro') and
satisfy the inequality II Uy p 11111 s II :s;; const II f IIH<Q>
To estimate the remaining third order derivatives uYpYnYn'
p = 1, 2, ... , n, we use the identity (30). Differentiating it with
respect to YP for p < n, we find that for all such p uYpYnYn EL2(ro')
and that II uYpYnYn IIL.<w') :s;;C II f IIHl(Q)' Further, differentiating (30)
with respect to Yn we find that UYnYnYn E L?..(ro') and II UYnYnYn IIL.(w')~
:s;; c II f 1/Hl(Q)
Thus we have shown that u(y) E H 3 (ro'), II u /IHs(w'l :s;; C II f IIHl(Q)
and the identity (23 1) holds foralll, s=1, ... , n-1, O<lhl<
< 6/2 and v2 E i/~ (ro) (v2 E H 1 (ro)). Repeating this process m times,
m ~k, we find that u E Hm+ 2(ro'), /1 u l/Hm+2(w') :s;;c II f 1/Hm(Q) and
identity (23m) holds. I
We shall now see in what sense the generalized solutions under
-consideration satisfy the boundary conditions. For the case of the
ELLIPTIC EQUATIONS 225
first boundary-value problem, it immediately follows from the
definition (u E Ffl(Q)) that the solution has a trace on oQ that is
equal to zero: u laQ = 0.
We shall now demonstrate that in the case of the second boundary-
value problem the solution satisfies the boundary condition in the
following sense: VuiOQn = 0, where n is outward normal vector
to aQ, In I = 1, and VulryQ isJ a vector whose components Uxi laQ,
t = f, ... , n, are the traces on fJQ of functions Ux 1 belonging to
Hl(Q).
In fact, since u E' lP(Q), an application of Ostrogradskii 's for-
mula to (8) yields the identity
~ (Vun) v dS ~"J ''(du- f) vdx,
iJQ ~j
valid for any v E H 1(Q) (here Vun = Vulaqn). Since du = f
a.e. in Q, we have
) (Vun) vdS = 0,
iJQ
implying the desired identity, because, by Theorem 2, Sec. 4.2,
Chap. Ill, the set of traces vj 8q of functions in H 1(Q) is everywhere
dense in L 2 (8Q).
In the sequel, the expression Vu jaq n will be denoted by :~ laQ.
Note that if u E C1(Q) nH 2 (Q), then the function fjau
n
I
iJQ
as an ele-
ment of L 2 (8Q) coincides with the normal derivative :~ of u on
the boundary oQ. The notation 0
n 8Q
u I
is natural also in the sense
that there is a function in H (Q) whose trace on oQ coincides
I
1
w1th -8aun iJQ
Thus, if aQ E C2 , the generalized solution of the second** boundary-
value problem satisfies the boundary condition
!'on!_I 8Q
=0
* It suffices to construct such a function in Q"-._Qo for some 6 > 0. SiliCa
<)Q E C2 , for any point x E Q'-..,Qo with sufficiently small 6 > 0 there is a unique
point y = y(x) E oQ, I y - x I < 6, such that the vector y - x is directed
along the normal n(y) to:the~boundary oQ at the pointy. The function V'u(x) X
X n(y(x)) belongs to H 1 (Q"-._Q 6 ) and its trace on oQ V'u(x) n(y(x)) laQ =
= V'u loQ n(x) = f)u
'an
I
oQ.
** For the case of the third boundary-value problem the generalized so-
lution satisfies the boundary condition ( :: +au) laQ =0.
t 5-0594
226 PARTIAL DIFFERENTIAL EQUATIONS
From Theorems 4 and 3 and Theorems 2 and 3 of Sec. 6.2, Chap. III,
the following result, in particular, follows.
Pl+1 l~l+1
Theorem 5. Let f EH 2 (Q). If aQ EC 2 , then the generalized
solution of the first boundary-value problem for Eq. (7) with homogeneous
boundary condition is a classical solution of this problem. When aQ E
EcG1 + 2 ' the generalized solution of the second boundary-value problem
for Eq. (7) with homogeneous boundary condition is a classical solution
of this problem.
We now examine the question of smoothness of the generalized
solutions in the whole region when the boundary conditions are
nonhomogeneous. We confine our discussion to the first boundary-
value problem.
Suppose that u(x) is a generalized solution of the first boundary-
value problem, that is, it belongs to H 1(Q) and for all v E H1 (Q)
satisfies the integral identity (8) as well as the boundary condition
u laQ = cp.
Assume that for a certain k:)::. 0 f E Hk(Q), aQ E Ck+ 2 , and that
the boundary function cp is the trace on aQ of some function <l> in
H 11 +2 (Q) (in order that cp be the trace on aQ of a function in Hk+ 2(Q)
it is sufficient, by Theorem 2, Sec. 4.2., Chap. Ill, that it belong to
ck+ 2 (aQ)). Let us show that then u E Hk+ 2 (Q).
0
Consider the function z = u - <1>. It is clear that z E H 1(Q)
and satisfies for all v E H1 (Q) the integral identity
Q ,Q Q
or, by Ostrogradskil's formula, equivalently the integral identity
JVzVvdx=- Jf vdx, 1
Q Q
where f 1 = f - ~<1>. Since the function f 1 E Hk(Q), z E Hk+ 2 (Q) by
Theorem 4. Hence the generalized solution u = z +
<l> E Hk+ 2 (Q),
establishing the assertion.
4. Smoothn!'ss of Generalized Eigenfunctions. Let u(x) be gener-
alized eigenfunction of the first, second or third boundary-value
problem for the Laplace operator and A. .the corresponding eigen-
E
value. Then for any v H 1 (Q) .
I VuVvdx= -A. Juvdx,
Q Q
ELLIPTIC EQUATIONS 227
which coincides with the identity (8) for f = 'Au. Since 'Au E H 1(Q)
and hence AU E 2 (Q), Theorem 3 implies that u E nroc(Q) and
~u ='Au (31)
a.e. in Q. Thus the function 'Au appearing on the right-hand side of
(28) belongs to Htoc(Q) n L 2 (Q). Therefore another application of
Theorem 3 shows that u E Hfoc (Q), and so forth.
Consequently, u E Hfoc(Q) for any k. Theorem 2, Sec. 6.2,
Chap. III, u(x) E coo(Q).
Thus the following result is established.
Theorem 6. The generalized eigenfunctions of the first, second and
third boundary-value problems for the Laplace operator are infinitely
differentiable in Q and satisfy Eq. (31).
The smoothness of generalized eigenfunctions in the whole region
is determined by the smoothness of the boundary.
Theorem 7. If 8Q E Ck for some k >- 2, then any eigenfunction
u(x) of the first or second boundary-value problem for the Laplace opera-
tor belongs to Hk(Q) and satisfies th(corresponding boundary condition
{ u iaQ = 0 and ~~ JaQ = 0 for the first and second boundary-value prob-
lems, respectively ) . Then the generalized eigenfunctions of the first
boundary-value problem when k>- [ ~ J+ 1 and of the second bounda-
ry-value problem when k>- [ ~ J+
2 are classical eigenfunctions *.
Proof. Since 8Q E C2 and . u E H 1 (Q) c: L 2 (Q), u E H 2 (Q) by
Theorem 4. If 8Q E C3 , then, by Theorem 4, u E H 3 (Q). When
8Q E C4, the inclusion u E H 2 (Q) implies that u E H 4 (Q), and so
forth. Thus we find that u E E'"(Q), provided iJQ E Ck.
What is more, by Theorem 6, the generalized eigenfunctions be-
long to C"" (Q) and satisfy Eq. (31).
If k';;::: [ ~ J+ 1, then, by Theorem 3, Sec. 6.2, Chap. Ill, u E
ECk-[;1- 1 (Q) c: C(Q), while u E C1{Q) i~ k>-[; J+2. Conseq-
uently, the results of Sec. 5.1, Chap. III, imply that the eigenfunc-
tion u of the first boundary-value problem satisfies for k>- [ ; J+
+1 the boundary condition u iaQ =l 0 in the classical sense, and
For the third boundary-value problem the following assertion holds:
If BQ E Ck and a(x) E Ck-l(BQ) for some k ;a. 2, then any eigenfunction u(x)
of the third boundary-value problem for the Laplace operator belongs to Hk(Q).
Moreover, {~~+au) laQ =0, and if k >[; ]+2,thenthegeneralizedeigenfunc-
tions of the third boundary-value problem are classical eigenfunctions.
228 PARTIAL DIFFERENTIAL EQUATIONS
the eigenfunction u of the second boundary-value problem satisfies
for k > [; J+ 2 the boundary condition !~ /aQ = 0 in the classical
sense. I
5. On Series Expansions in Eigenfunctions. Let u 1 , u 2 , denote
the system of all the generalized eigenfunctions of the first (second)
boundary-value problem for the Laplace operator, and A. 1 , A. 2 ,
the corresponding system of eigenvalues. As shown above (Theorem 3,
Sec. 1.3), the system u 8 , s = 1, 2, ... , is an orthonormal basis for
L 2 (Q). This means that any function I E L 2 (Q) can be represented
by a convergent Fourier series in L 2 (Q) with respect to any of these
systems:
00
m=i
Suppose that the function I E'Hit(Q) for some k >
1. Its Fourier
series in eigenfunctions of the first and second boundary-value prob-
lems, of course, converge to it in L 2 (Q). However, in the norm of
H"(Q) or even in the norms of Hh' (Q), 0 < k' < k, these series, gener-
ally speaking, do not converge. For instance, the Fourier series of
:Q
the function I 0 (x) = 1 in with respect to the system of eigenfunc-
tions of the first boundary-value problem cannot converge in the
norm of H"(Q) for any k >
1. Indeed, if this series converged in the
norm of H 1 (Q), it would converge only to l 0 (x), but this is impossible,
because the sum of any series of elements of H1 (Q) which converges
in !Jl(Q) must belong to H1 (Q).
In order that the Fourier series of any function I in Hh(Q) may
converge to it in H"(Q), the function f must be subjected to some
boundary conditions.
Note that for the Fourier series (32) of a function I with respect to
the system of eigenfunctions of the first boundary-value problem for
the Laplace operator to converge in the norm of H 1 (Q) it is sufficient
(Theorem 3, Sec. 1.3) and as shown just now, necessary that I E
E jJl(Q).
We denote by H':z(Q), k: 1, the subspace of H"(Q) consisting of
all the functions t for whi
r1t- tj
l-2-
/ aQ=O, ... , !l. l!aQ=O.
BY H~(Q) we shall mean the space L 2 (Q). Note that by Theorem 2,
Sec. 5.~. Chap. Ill, H}o(Q) = ifl(Q).
ELLIPTIC EQUATIONS 22.9
By H~(Q), k >-
2, we designate the subspace of Hk(Q) consisting
of all the functions f for which
a .~ [ ~ 1- 1 f/aQ=O.
at I =0, ... , -a
-an 8Q n
By H~ (Q) we shall mean the space L 2 (Q) and by Hf (Q) the
space H 1 (Q).
Lemma 3. Suppose that fJQ E Ck for a certain k >-
1. Then there is
a constant C > 0 such that any function f E H'2; (Q) or f E Hj,.(Q)
orthogonal to constant functions in L 2 (Q) with a scalar product satisfies
the inequality
(33)
h-1
II I lln"<Q>~c li ~-2-/ IIH<Q> (33')
if k is odd.
Proof. We first consider the case of even k, k = 2p. The lemma
will be proved by induction on p. We shall establish (33) for p = 1.
Suppose that f E H~ (Q) (H~ (Q)). Let F denote the function M.
Then f(x) ~atisfieR Poisson's equation
M=F (34)
a.e. in Q. Moreover, by the definition of H'\$ (Q) (Hjr-(Q)) u /aQ = 0
-
au I(jQ-
( fin 0) .
Multiplying (34) by an arbitrary function v E ifl(Q) and applying
Ostrogradskii's formula, we find that u is a generalized solution of
the first (second) boundary-value problem'for Eq. (34). Now inequali-
ty (33) for k = 2 follows from Theorem 4. -
Assume that the inequality (33) has been established for k = 2p,
and let f E H~+ 2 (Q) (Hj; 2 (Q)). Since in this case the function
F = M belongs to HY) (Q) (H:;y. (Q)).
II F IIH2P<Q> ~C1 II ~PF 1/L,<Q> =, ci II ~P+if /IL,<Q>
But f(x) is a generalized solution of the first (second) boundary-
value problem for Eq. (34), therefore Theorem 4 yields
II f I/H2p+2<Q> ~C2II F IIH2P<Q> ~c 11 ~P+it 1/L.<Ql.
230 PARTIAL DIFFERENTIAL EQUATIONS
We now consider the case of odd k. For k = 1 the inequality (33')
is trivial. Assuming that it has]been proved fork= 2p - 1, p 1, >
we shall establish the same for k = 2p + 1. Let f E HJE+ 1 (Q)
(H}+ 1 (Q)). Then F(x) = l1f Ef!~- 1 (Q) (H}- 1 (Q)). By Theorem 4
and by induction, we obtain
11 f IIH2p+1<Q> ~C2II F 11~2p-i<Q> ~c II dP-iF llul<Q> = c II dPf llul<Q> 1
We can now prove the following result.
Theorem 8. Assume that the boundary aQ E Ck, k 1. In order >
that the function f may be expanded in a Fourier series (32), converging
in the norm of Hk(Q), with respect to the system of eigenfunctions of the
first (second) boundary-value problem for the Laplace operator it is
necessary and sufficient that f belong to H'Jzy (Q) (Hy (Q)). If f E
00
EH'fty (Q) (H~;r (Q)), rthe series ~ f: I As I" ~converges and there is
s=t
a constant C > 0, independent of f, such that
,oo
s=t
Proof. From the identity (31) and Theorem 7 it follows that if
oQ E Ck, then the generalized eigenfunctions of the first (second)
boundary-value problem for the JLaplace operator belong to H'Jzy (Q)
(Hy (Q)). Therefore if the Fourier series of the function f E H"(Q)
with respect to the eigenfunctions of the first (second) boundary-value
problem convergesJn the norm of H"(Q), then f EH2;(Q) (Hy(Q)).
This proves the necessity part.
We now suppose that f E H2; (Q) (Hf (Q)), and establish the in-
equality (35). First assume that k is even, k = 2p, p 1. Let 'Ys >
denote the Fourier coefficients of dPf : 'Ys = (dPf, u 8 )L,(Ql An
application of Green's formula yields
'Ya = (dPf, U8 )L,(Q) = (dP-if, dU8 )L,(Q) = A8 (dP-if, U8 )L,(Q)
= ... =A"f(f, U 8 )L,(Q)=A~f 8 , s=1, 2,
;oo
Since dPfEL 2 (Q), it follows thatJ 2] -y; = lidPfJii.<Q> hence
8=1
00 k
~ f~ I A8 IIi= II d 2 f IIi.<~> which, obviously, implies the inequal-
s=t
ity (35). When k=2p+1, the function dPfEH 1(Q) (H 1 (Q)).
ELLIPTIC EQUATIONS 231
00
Therefore, by Theorem 3, Sec. 1.3, the inequality ~ I'~ I "'- I ~
8=1
~C llt'J.Pf llhl(Ql holds, thereby implying the inequality (35).
By Sm(x) we denote the partial sum of the series (32). Evidently,
S~-E H~(Q) (Hy(Q)) for all m = 1, 2, ....
In view of (33) and (35) (assume that m > i~1), we have for
k = 2p
II Sm-Si II~"<Ql~C II !:o.P (Sm-S;) 1/L<Q>
m m m
=CII ~ A-!'f.u.JJi.<Q>=C ~ A-;P(f=C 2J A-~f~-+0
s=i+1 s=i+1 s=i+1
as m, i-+ oo. This means that the series (32) converges to I in H"(Q).
When k = 2p + 1, the proof is similarly carried out by applying
the inequality (33'). I
Theorem 9. If the boundary aQ of the region Q belongs to C"
for a certain k~ [ ~ J+
1, then any function f EH~ (Q) (H~(Q))
has a Fourier series expansion (32) with respect to eigenfunctions
of the first (second) boundary-value problem for the Laplace operator
k-[..!:.]-1 -
converging in the space C 2 (Q).
Proof. Theorem 3, Sec. 6.2, Chap. III, implies that the space
k-[..!:.]-1 -
C 2 (Q) contains the function f(x) and all the eigenfunctions
u 8 (x) as well as all the partial sums Sm(x) of the series (32).
Moreover, the inequality IJSm-Sdl k-[..!:.]_ 1_ ~CIJSm-SdJH,.(Ql'
c 2 (Q)
where the constant C does not depend on m or i, holds. By Theo-
rem 8, II Sm - si llnk(Q)-+ 0 as m, i-+ oo, therefore
liSm-Sdl ~t-[~]- 1 _ -+0 as m, i-+oo, thereby implying that
c 2 {Q)
k-[2:.] -1 -
the series (32) converges in C 2 (Q). I
6. Generalizations. The method applied in Subsecs. 2 and 3 to
investigate the smoothness of generalized solutions of boundary-
value problems for Poisson's equation is equally suitable for inves-
tigating the smoothness of generalized solutions of boundary-value
problems for more general equations. For instance, suppose that
u(x) is a generalized solution of the first boundary-value problem
:u = div (k(x)Vu) - a(x) u = j, X E Q,
u laQ = 0 (36)
UEL2(Q), jk(x)EC 1 (Q), :a(x)EC(Q), k(x)~k0 >0).
232 PARTIAL DIFFERENTIAL EQUATIONS
If k(x) E CP+l (Q), a(x) E jCP(Q) and ! f(x) E L2(Q) n Hfoc(Q)
for some p >- 0, then u(x) E Hfo"6 2 (Q). In particular, every general-
ized eigenfunction of the first boundary-value problem for the operator
: belongs to Hfo"6 2 (Q).
If, in addition, the boundary aQ E CP+ 2 and f EW(Q), then
u(x) E HP+ 2 (Q); in particular, every generalized eigenfunction of
the first boundary-value problem for the operator X belongs to
W+2(Q).
Totally analogous results hold also for the generalized solutions
of the second and third boundary-value problems for Eq. (36) and
the corresponding eigenfunctions for the operator :t.
3. CLASSICAL SOLUTIONS OF LAPLACE'S
AND POISSON'S EQUATIONS
1. Harmonic Functions. Potentials. A real-vah1ed fnnction u(x) is
termed harmonic in a region Q (or in an open set) in the space Rn if
it is twice continuously differentiable in Q and satisfies the Laplace
equation
ll.u = 0 (1)
at every point x EQ.
An equivalent definition of a harmonic function can easily be giv-
en in terms of Hk spaces (as usual, functions are considered equal if
they coincide almost everywhere).
A function u(x) belonging to Htoc(Q), where Q is a region in Rn
is called harmonic in Q if it satisfies the integral identity
) V'u V'vdx= 0 (2)
Q
for all v E H 1 (Q) having compact support in Q (that is, equal to zero
a.e. in Q""' Q' for a certain Q' (: Q).
If u (x) E C2 (Q) is harmonic in Q, then it obviously belongs to
Hto~(Q). Multiplying (1) by an arbitrary v E H 1 (Q) with compact
support in Q and integrating the resulting identity over Q, we find.
by means of Ostrogradskii's formula, that u satisfies the integral
identity (2).
Suppose now that u E Hfoc(Q) and satisfies the integral identity (2)
for all v belonging to H 1 (Q) and having compact support in Q.
Take an arbitrary strictly interior subregion Q' of Q. Since u E H 1 (Q')
;;d satisfies the identity:) r '\i'U'\i'Vdx =iO for all v E H1 (Q'), u E
Ill .l
" Q'
E Coo (Q') by Lemma 2, Sec. 2.2, and Theorem 2, Sec. 6.2, Chap. III.
What is more, u satisfies Eq. (1) in Q' (see Corollary to Lemma 2 of
Jhe preceding section). Since Q' is arbitr11ry, the function u (x) belong\$
ELLIPTIC EQUATIONS
to C00 (Q) and satisfies Eq. (1) in Q, that is, is harmonic.
If a function u harmonic in Q is twice continuously differentiabl&
in Q, then, integrating (1) over and using Ostrogradskii's formulap
we obtain the identity
f r
0= J /).udx=.l div(Vu)dx= ]'a~ dS
a I' r'~(3)
:Ql lQ fJQ
which will be frequently used in the sequel.
Let ~ be any point in Rn, and let r = I x - 1- Since ().j =
= frr + n r 1 /r for a function f dependin~only on r, the harmonic
function u depending only on r satisfies the ordinary differential
equation Urr + n - 1 Ur = 0. The general solution of this equation
r
on the half-liner> 0 has the form 7:~2 +
c1 if n > 2 and c0 ln r +
+ c1 if n = 2, where c0 and c1 are arbitrary constants. Therefore all
the functions harmonic in the entire space except at the point x =
and depending only on I x - I have the form I x-c~ 1n_ 2 C1 if +
n > 2, and c0 In I x - ~ I +
c1 if n = 2 (c 0 and c1 are arbitrary
constants).
The function
1
U(x-<)~{ (n-2)
1
2n
O"n I x-6Jn-~ '
In lx-~1, n=2,
(4)
harmonic in Rn ""'- {x = }, where an is the surface area of the unit
sphere, is called the fundamental solution of the Laplace equation.
This function plays a basic role in the study of solutions of the-
Laplace and Poisson equations.
For any measurable function p 0 () bounded in Q the function
uiJ(x) = ) U(x-~) p0 () d, (5)
Q1
which is defined for all x, is called the volume potential with densi-
ty p,.
Far any function p1 () and p 2 () integrable over oQ the functions-
8Q
u2(x) = r aU(x-~) P2() dS~,
~an~
(7}
aQl
234 PARTIAL DIFFERENTIAL EQUATIONS
which are defi.ned,)for all x ERn '---._8Q, are, respectively, referred to as
potentials of simple and double layers with densities p1 and p 2
We have already encountered the potentials (5), (6) and (7). In
Sec. 6.1, Chap. III (Theorem 1}, it was established that any function
u(x) E C2 (Q) can be expressed as a sum of three terms: the volume
potential with density ~u. the potential of simple layer with density
- :~ and the potential of double layer with density u:
Q aQ
u(x) = J ( au~:~ s) u(s)- a;~s) U (x- s)) dS~j (9)
aQ
for any x E Q.
Lemma 1. The potentials of single and double layers are harmonic
in Rn '---._8Q.
Proof. Let x 0 be any point inRn '---._8Q, and let t5 > 0 be the distance
from this point to aQ. The integrand functions in (6) and (7) regarded
s
as functions of , E aQ, belong to L 1 (8Q) for all x lying in the ball
{I x - x 0 I< 6/2} and belong to C""(l x - x 0 I~ 6/2) for almost
s
all EaQ if they are regarded as functions of x. Furthermore, for all
s E aQ and x in:the ball {I x - x 0 I< 6/2} the estimates ID~U (x-
- s) I~ c, In: c
au~:~s) I~ hold in which a = (al, ... , an) is
arbitrary and the constant C > 0 depends only on t5 and a. Therefore
j"i)~U(x-s) P1(6)1~C I P1(6) I I
I Da
X
au(x-)
anG
(!:):I C.C"'f!jlP2 (!::)I
P2 "' I ~ "'
'
Then, by Theorem 7, Sec. 1.7, Chap. II, the functions u 1(x) and
u 2 (x) are infi.nitely differentiable in the ball {I x - x 0 I < 6/2} and
Dau 1(x) = ~ p1(6) D~U(x-6) dS6
aQ
and
ELLIPTIC EQUATIONS 235
for any a. In particular,
Llu1 =) pt(6) Ll:P (x-6) dS~ =0
aQ
and
Ll~ (x) = ) Pz (6) a~ LlxU (x- s) dS~ = 0,
lJQ ~
because Llx.U (x - s) = 0 when X =I= S
Lemma 2. If Po (6) E C'L (Q), then the volume potential u 0 (x)
n
belongs to C2 (Q) C1 (Q) and satisfies Poisson's equation Llu 0 = Po
for all x E Q.
Proof. Since the function p 0 is measurable and bounded in Q,
it follows (see Sec. 1.12, Chap. II) that u 0 E C1 (Q) and
auo = r au (x-~) (1::) rre = - r 'aU (x-~)' (f:) dt . 1
axi j axi Po.,...,.., J la~i ,Po"' ..,, ~= ' ... , n.
Q Q
If p 0~(s) EIC 1 (Q), then, by Ostrogradskii's formula,
-:~; =
Q
~ U (x-s) ~~ d6- raQ
U (x-) Po (s) ni (6) dS~,
/'-..
where the function n 1 (s) = cos (n, s;) is continuous on iJQ.
The first term~on the right-hand side of this identity is the volume
potential with density ~~; which is continuous in Q, thereby imply-
ing that~this term belongs to C1 (Q). The second term is the potential
of the simple layer with density p 0 n 1 continuous on iJQ, and, accord-
ingj to Lemma 1, belongs to c>O (Q). Therefore Uo E C1(Q) n
n C2 (Q). Take an arbitrary function \jJ E C2 (Q) with compact sup-
port in Q. Since 'i'laQ = ~ j = 0, by (8)
un aQ
(x) =) u (x-s) Ll (s) d (tO)
~Q
for all x E Q. Applying Green's formula to the funcdons 'lj> and u 0
and using successively Fubini 's theorem (Theorem 10, Sec. 1.11,
Chap. II) and the identity (10), we obtain
) \jl(x) Llu0 (x)dx = ) Ll\jl(x) u 0 (x)dx
Q Q
=) Ll(x) () p(x-s) Po(6) d) dx
Q Q
= ) Po(s) ( ) U (x- s) d \jl(x)dx ) d6 = ~ 'l'(s) p0 (s) ds.
Q Q Q
236 PARTIAL DIFFERENTIAL EQUATIONI5
Thus for any function ' E C2 (Q) with compact support in Q the
identity,
J
'i-1 (x) (~u 0 (x)- Po (x)) dx = 0
lQ
holds, implying that ~u 0 = Po in Q. I
2. Principal Properties of Harmonic Functions. We shall now
establish some of the important properties of harmonic functions.
Theorem 1. (First Mean Value Theorem). Let u (x) be a harmonic
function in Q and x any point of Q. Then for any r, 0 < r < d, where
d is the distance of X from the boundary oQ,
) u (S) dS~. (11)
Jx-~l=r
Proof. Since u() E C2 (I s-
x I ~ r), formula (9) is applicable
to this function in the region {I - x 1< r}. By this formula
for n > 2 (for n = 2, the argument is analogous),
()=
U X
r
j
1 au(~) dS
(n-2).<Tnrn 2 an !;
JG-Xl=r
r u(~)
J (n-2)crn
Js-xJ=r~
1 \ au(~) dS
- (n-2)crnrn-i J an t
/i-xl=r
+ cr)n-1 J u() dS~,
JE-xJ=r
because on the sphere { I- xI= r}
o 1 a 1
I ;-x 1n-2 I ~-x In 2 (n-2) (n-2)
an~ a16-x 1 - 1 x-6Jn-1 rn-1
Formula (11) now follows from (3) 1.
Theorem 2 (Second Mean Value Theorem). Let u(:c) be a harmonic
function in Q and :c any point of Q. Then for any r, 0 < r < d, where
d i& the distance from X to the boundary oQ,
u(x) =-.;..- \
<Tnr .I
u() d. (12)
IG-xJ<r]
Proof. According to Theorem 1, the identity
O'nPn-1u(x) = J u() dS,
1;-x1 =P
ELLIPTIC EQUATIONS 237
holds for any p, 0 < p <d. Integrating this with respect top from 0
to'r, we'obtain (12). I
Theorems 1 and .2 are referred to as mean value theorems because
the right-hand sides in (11) and (12) are the average values of the
function u over the sphere {I G- x I = r} and over the ball
{I - x I < r}, respectively ( O'nrn-l is the surface area of this sphere
and CJ';;n the volume of the ball) .
As shown ~above, a function which is harmonic in Q is infinitely
differentiable in Q. The following result often proves useful in the
study of harmonic functions.
Lemma 3. Let the junction u(x) be harmonic in Q and be bounded:
I u(x) l ~ M. Then any derivative Dau (x) of order I a I = k, k =
= 1,~2, .. , at the noint x E Q satisfies the inequality
IDau (x) 1-<:M ( ~ )" k". (13)
where {) is the distance from the point X to the boundary aQ.
Proof. This lemma will be proved by induction on k.
Suppose first that k = 1. We shall demonstrate that : u,.i I ~
~ Mn/6 for all t = 1, .. , n. Since the function u,. is harmonic
in Q, by Theorem 2, for any 6' < 6,
u,..(x)=~
t CJnu JI u~.d=~
t CJnu JI u()cosaidS~,
1';-xi<O' 1;-xf=O'
where a 1 is the angle between the vector - x and the Oi axis.
Therefore
!u,..(x)l-<:
t
:,n
CJnu JI j'u()ldSa-<:M :.n crn6m- 1 =Mn/6'.
CJnu
1~-xi=O'
The desired inequality follows from this by passing to the limit as
1')'-+ 6.
Assume that the lemma has been proved for all derivatives Dau,
where I a I ~ k - 1, k::.? 2. Let us prove the inequality (13).
Take two balls {I- xI< 6'} and { I -xI< 6'/k} with
eentre at the point x (<'>' is any positive number less than 6). By the
induction hypothesis the following inequality holds for any point
ill the ball { I- x I< 6'/k} and any ~. I~ I = k - 1: 1
Thus for any ~. ! ~ I = k - 1, the harmonic function D~u() is
:bounded in the ball {I - x I < <'>' /k} by a constant M ( ;, ) h-i k"--1.
238 PARTIAL DIFFERENTIAL EQUATIONS
Then, by what has been just established, for the first derivatives of
this function we have ,
I (D~u (s)hi I<M ( ;, r-Hkl!-i~( ()~! = M ) ( ;, r kll, i = 1, ... 'n.
That is, for any a, I a I = k, we have I Dau I ~ M ( ;, ) "k".
Letting 6'-+ 6 in this inequality, we obtain the inequality (13). I
Let us take up some of the applications of Lemma 3.
Theorem 3. From any infinite set of harmonic functions in Q that are
bounded in'Q by the same constant a sequence can be chosen which con-
verges uniformly on any strictly interior subregion of~ Q.
Proof. Let ID1 be an infinite set of harmonic functions u (x) in Q
which are' bounded in Q by the same constant: I u (x) I ~ M. Con-
sider a sequence of regions Q1 , Q 2 , , such that Q1 c: Q2 c: ... ;
Qi ~ Q, i = 1, 2, ... ; u Qi
i=1
= Q.
The set ID1 consists of functions belonging to C(Q 1 ) and bounded
on Q1 by the same constant. By Lemma 3, there is a constant C > 0,
depending only on Q1 , such that for all functions u in ID1 1 vu I ::::;;: C
for x E Q1 Therefore the set ID1 is equicontinuous in Q1 According
to Arzela 's theorem, it is possible to choose a sequence u 11 , u 12 ,
from ID1 which converges uniformly in Oto Since this sequence is
uniformly bounded and, by Lemma 3, is equicontinuous in Q2 ,
a subsequence u 21 , u 22 , can be selected from it which converges
uniformly in Q., and so forth. It is apparent that the diagonal se-
quence uw u 22 , is the desired sequence. I
Theorem 4. Suppose that a sequence u 1 (x), u 2 (x), ... of harmonic
functions in Q converges to u(x) uniformly in any strictly interior
subregion of Q. Then the function u(x) is harmonic in Q and for any
a = (a 1 , , an) the sequence Dau1 , Dau 2 , converges to Dau
uniformly in any strictly interior subregion of Q.
Proof. Let Q' be any strictly interior subregion of Q. Then the
function u (x) E C (Q'). Take any region Q" such that Q' ~ Q" ~ Q.
It is clear that each Um (x) is bounded in Q". According to Lemma 3,
for any a there is a constant C > 0, depending only on Q', Q" and
I a I, such that
II Da (Um- Us} lbQ') <: C II Um- Us lbzy')
for all m, s = 1, 2, .... Since llum- Us llc(Q")-+ 0 as m, S-+ oo, all
the sequences D aum, m = 1, 2, ... , are fundamental in the norm of
C(Q'). This means that the function u (x) E Coo(Q') and for any
all Daum- Dau llc(ih-+ 0 as m-+ oo.
ELLIPTIC EQUATIONS 239
Passing to the limit as m-+ oo in the equation ~um = 0, x E Q',
we find that ~u = 0 in Q', that is, u(x) is harmonic in Q' and hence
also in Q. I
Theorem 5. A function which is harmonic in Q is analytic there.
Proof. Let the function u(x) be harmonic in Q. Take any point
x0 in Q, and let 6 > 0 denote the distance between' this point and
the boundary aQ and 86/4 (x0) denote the ball {I X - x 0 I < 6/4 }.
The function u(x) E C(Q6; 2), therefore it is bounded in Q612 ; let
M = max I u(x) I
~EQ6/2
Since the distance from any point of the ball Sr,14 (x0) to the bound-
ary 8Q6;2 is not less than 6/4, by Lemma 3 for any point x in
8o;4 (x 0) and any a= (a1 , , an) the inequality
IDau !-<M (4n/6)1all a 11a1
kk+1/2 1
holds. Since lim = ,,~ (Stirling's formula), there is
k-+oo k! ek r 2;n;
a constant C > 0 such that 0 ~ Cekk!, and hence I a llal ~ Celal (I a I)!
for all natural k.
If in the identity (x 1 + ... +
Xn)k = ~ (I ~ 11 )! xa, which is
laJ=h
true for any natural 'k, we set x 1 = ... = Xn = 1, we obtain the
identity nk = h (I a I )!/a! which implies the inequality (I al)!/a! ~
Lai=k
-< nlal. Therefore for all x E8r, 14 (xO) and all a
1Daui-<CM(4n2e/6)iala!. (14)
From the inequality (14) it follows first of all that the Taylor
series
a
of function u(x) converges absolutely in the ball 8 = { I x - x0 I <
< 4 : 2 e } , therefore the sum of this series is an analytic function in \$.
Let us show that this series converges to u(x) in the ball 8' =
= {I x - x0 I < 8 : 3 e}. For this it is enough to demonstrate that
the remainder term in the Taylor's formula
240 PARTIAL DIFFERENTIAL EQUATIONS
for function u, where I a I<, 1, approaches zero as N - 00 at
every point of S'. Since for x E S' the point 'x0 +;a (x - x 0 ) also
lies in S', and thus in the ball S 514 (x0), we ftnd, in view of (14),
that for all x E S'
I R N (x) .1
-< ~c-(4n2e)N(t))N
LJ M -&- 8n3e
CM N_CCM
(2n)N n - y -<
lai=N
Hence RN (x)- 0 as N - oo.
Since the point x 0 E Q is arbitrary, the function u(x) is analytic
in Q. I
In the two-dimensional! case,, apart from Theorem 5 establishing
the analyticity of a harmonic function as a function of two variables
x 1 , x 2 , a deeper result holds that connects harmonic functions with
analytic functiJns of a single complex variable z = x 1 +
ix 2 For
simplicity, we confine our discussion to a simply connected region.
Theorem 6. For the function u(xu x 2 ) to be harmonic in a simply
connected region Q it is necessary and sufficient that there exist an ana-
lytic function f(z) in Q, z = x1 +
ix 2 , such that u(x1 , x 2) = Re f(z).
Sufficiency. Suppose that f(z) is analytic in Q. Then the functions
u(.x1 , X 2 ) = Re f(x 1 + ix 2 ) and v(x 1 , x 2 ) = Im f(x 1 +
ix 2 ) in Q
are infinitely differentiable and they satisfy Cauchy-Riemann equa-
tions:
(15)
Differentiating the first of equations (15) with respect to x 1 and the
second with respect to x 2 and adding them, we see that ~u = 0, that
is u is a harmonic function.
Necessity. Assume that the function u is harmonic in Q, and con-
sider the function
v_(x) = ) - u,, dx 1 + Ux,;dx 2 ,
L(xO,~x)~
where x 0 = (x~, x~) is a fixed point of Q, x = (x1 , x 2 ), and L(x6 , x)
is any rectifiable 'curve joining the points x 0 and x and lying in Q
(since Q is a simply connected region, Green's formula yields that
the function v does not depend on the contour L). The function
v(x) E C1 (Q) and satisfies conditions (15). Consequently, the function
f = u + iv is an analytic function of x 1 ix 2 in Q. I +
Remark 1 .The analytic function f(z) corresponding to the harmo-
nic function u(xu x 2) is defined up to a pure arbitrary constant.
Indeed, suppose that ft(z) = u + iv1 and f 2 (z) = u + iv 2 are two
analytic functions inQ for which Re ft = Re f 2 = u. Then the func-
tion ft - f 2 = iv, where the (real) function v = v1 - v2 , is analytic
in Q. In view of the Cauchy-Riemann equations, Dx, = Vx, = 0, that
is,- v 2 = v1 + c, where c is any real constant. Accordingly, f.Jz) =
+
= f 1 (z) ic. I
ELLIPTIC EQUATIONS 241
Remark 2. An assertion analogous to that of Theorem 6 holds also
for any region Q. In this case the analytic function f of x1 + ix 2
in Q, constructed corresponding to the function u harmonic in Q,
may be multiple-valued. For instance, to the function In I z I harmo-
nic in the annulus {1 < I z I< 2} there corresponds a multiple-
valued function In z = In I z I + i arg (x1 + ix 2 ) (z = x1 + ix 2 )
analytic in this annulus.
Corollary. Suppose that the function z' = F(z) = F 1 (x1 , x 2 ) +
+
+iF 2 (x1 , x 2 ), z = x1 ix 2 , analytic in a simply connected region Q maps
Q one-to-one onto another simply connected region Q' of the complex
plane z' = x; + ix;. If the function u' (x') is harmonic in Q', then
the function u(x) = u'(F1 (x), F 2 (x)) is harmonic in Q.
In fact, let the function f'(z') analytic in Q' be such that u'(x') =
= Re f'(z'). Since the function /(z) = f'(F(z)) is analytic in Q,
the function u(x) = u' (F1 (x), F 2 (x)) = Re f'(z') = Re /(z) is
analytic in Q.
The following important property of harmonic functions, a con-
sequence of a mean value theorem, is referred to as the maximum
principle.
Theorem 7 (The maximum principle). Let a function u(x) harmonic
in Q be continuous in Q. Then either u(x) = const in Q or
min u(:r) < u(x) <max u (x) (16)
xeoQ xeoQ
for all x E Q.
Proof. Put M = max u(x). Let us show that if the right-hand
xEQ
inequality in (16) is violated at a point in Q, then the function u(x) =
= const = Min Q. Indeed, assume that there is such a point. Then
in QAthere is a point x0 at which u = M. Taking any point y in Q,
we shall demonstrate that u(y) = M. Join the points y and x 0 by
a polygonal line L (without self-intersection) lying wholly in Q.
By d > 0 denote the distance between L and 8Q. We cover L by
a finite number of balls S; ={I x - xi I<~}. i=O, 1, ... , N,
with centres at xi E L n S;_1 , i = 1, ... , N. The point x 0 is the
centre of the ball S 0 and the pointy E SN.
By the second mean value theorem (Theorem 2),
u(x 0 ) = crn(~ 2 )n ) u(x) dx,
Jx-xOJ<d/2
that is,
r (u(x) -u(xO)) dx = 0.
So
Since the integrand function u(x) - u(x 0) is nonpositive u(x) =
= u(x0 ) = M in S 0 , and, in particular, u(x1 ) = M. Repeating the
16-0594
242 PARTIAL DIFFERENTIAL EQUATIONS
same arguments for the point x1 and the ball S 1 , it can be shown that
u(x) = Min S 1 , and, in particular, u(x2) = M, and so on. Finally
we find that u(x) =Min SN, and, in particular, u(y) = M.
Thus it is established that either u(x) = const in Q or the right-
hand inequality in (16) holds for all x in Q. Applying this result to
-u(x), we obtain that either u(x) = const in Q or the left-hand
inequality in (16) holds for all x in Q. I
Corollary. It readily follows from Theorem 7 that a function u(x)
harmonic in Q and continuous in Q satisfies the inequality
II u !lc(Q)-< If u llc(aQ). (17)
Theorem 8. Let the functions uh(x), k = 1, 2, ... , belong to C(Q)
and be harmonic in Q. If the sequence uh laQ, k = 1, 2, ... , converges
uniformly on aQ, then the sequence UJt,k = 1, 2, ... , converges uni-
formly in Q to a function harmonic in Q.
Proof. In fact, we have by formula (17)
II Us- Um IIC(Q)-< II Us- Um lbaQ)
for all sand m. Since the sequence U~tlaQ, k = 1, 2, ... , converges
uniformly on iJQ, II U8 - Um llc(8Q)-+ 0 as m, s-+ oo; hence llus-
-um llc{Q>-+ 0 as m, s-+ oo. The completeness of the space C(Q)
implies that there is a continuous function u(x) to which the sequence
uh (x), k = 1, 2, ... , converges uniformly in Q. That the function
u (x) is harmonic in Q follows from Theorem 4. I
3. On Classical Solutions of the Dirichlet Problem for Poisson's
Equation. Let us recall that a function u (x) is called the classical
solution of the Dirichlet problem (the first boundary-value problem)
for Poisson's equation
11u = f, X E Q, (18)
ulaQ = q:>, (19)
if u(x) E C2(Q) nC (Q) and satisfies (18) and (19).
First of all we shall establish uniqueness of the solution.
Theorem 9. The Dirichlet problem for Poisson's equation cannot
have more than one classical solution.
Proof. Let u1 (x) and u 2 (x) be two solutions of the problem (18),
(19). Then the function u(x) = u 1 (x) - u 2 (x) is harmonic in Q,
continuous in Q and vanishes on iJQ. Therefore, by the inequality (17),
u = 0 in Q, that is, u1 = u 2 I
The existence of the classical solution of the problem (18), (19)
was established in Subsec. 3 of the preceding section under the assump-
(;.]+t [~]+1 [-~-+1]
tion that aQ E C 2 , I EH 2 (Q), q:> E C 2 (iJQ). We have,
ELLIPTIC EQUATIONS 243
in fact, established there a stronger result: under the assumptions
made regarding aQ, f and <p the generalized solution u of the problem
l~]+3 [-i]+1
(18), (19) belongs to the space H1oc (Q) n H (Q). This, in
view of the embedding theorem, implies that u(x) E C2 (Q) n C(Q),
that is, is a classical solution. But the conditions of functions being
[~]+3 l;]+1
contained in the spaces H Joe (Q) and H (Q) are more stronger
than their being contained in the spaces C2 (Q) and C(Q), respec-
tively. Therefore it seems plausible that the classical solutions exist
under milder conditions on aQ, f and <p.
Theorem 10. If aQ E C2 , f E C1 (Q), <p E C (aQ), then the problem
(18), (19) has a classical solution.
We start by proving Theorem 10 for the case of homogeneous equa-
tion (18), that is, for the problem (1), (19).
Lemma 4. If aQ E C2 and <p E C (aQ), then the problem (1), (19)
has a classical solution.
[_:;z- ]+1
Proof. Suppose first that aQ E C . Since <p E C (8Q), there
{.2:]+1
exists a sequence of functions <pll, k = 1, 2, ... , in C 2 (8Q)
converging uniformly on aQ to the function <p. (Indeed, the continu-
ous extension of <p into Q can be approximated in C(Q) by functions
belonging to C""(Q) and their values on the boundary belong to
l ~ ]+1
C (8Q).) But for any <pll there is a function ull(x) harmonic in Q
which is a classical solution of the problem (1), (19) with this bound-
ary function. By Theorem 8, the sequence ull (x), k = 1, 2, ... ,
converges uniformly in Q. Moreover, the limit function u (x) is
harmonic in Q, continuous in Q and satisfies the boundary condition
(19), that is, is a classical solution of the problem (1), (19).
Assume now that aQ E C2 By <I> denote the continuous extension
into Q of the boundary function <p, and set M = max 1<1> (x) I Take
xEQ
a sequence of regions Q;, i = 1, 2, ... , having the following prop-
"" [~]+1
erties: Q; ~ QH 1 for all i = 1, 2, ... ; U Q; = Q; aQ; E c 2 ,
i=1
i = 1, 2, .... By what has been proved, for any i = 1, 2, ... there
exists in Qi a classical solution v;(x) of the problem (1), (19) satis-
fying the boundary condition v;iaQ. = <lllaQ. Moreover, for all
i = 1, 2, , , , I I
max I v; (x) I<M.
xeQi
16*
244 PARTIAL DIFFERENTIAL EQUATIONS
Let u 1(x) denote a function defined in Q that is equal to v 1(x) in
Q1 and vanishes outside Q1, i = 1, 2, .... By Theorem 3, the sequence
of functions u 2 (x), u 3 (x), ... harmonic in Q 2 contains a subsequence
Uw u 12 , which converges uniformly in Q1 The sequence Uw
u 12 , is composed of functions harmonic in Q3 (if the function
u 2 (x}, possibly contained in this, is rejected). Therefore, according
to Theorem 3, from it a subsequence u 21 , u 22 , can be chosen which
converges uniformly in Q2 , and so forth.
Consider the diagonal sequence uw u 22 , , uPP .... The corres-
ponding subsequence of the sequence of regions Qm, m = 1, 2, ... ,
will be denoted by Q1;, i = 1, 2 ... : the function uii equals v11 in
Qii and vanishes outside Qii. The sequence (uPP p = 1, 2, ... ,
converges, obviously, in Q and this convergence is uniform
on any Qii. Consequently, by Theorem 4, the limit function
u(x) is harmonic in Q. What is more, I u(x) I ~ M for all x E Q.
We shall show that u(x) is continuous in Qand satisfies the bound-
ary condition (19), that is, u (x) is a classical solution of the prob-
lem (1), (19).
Take an arbitrary point x 0 E fJQ. Since fJQ E C2 , there are a point
x 1 ~ Q and a number r > 0 such that the ball {I x- x 1 I< r} touch-
ing the boundary fJQ at x 0 does not contain points of Q and the
sphere {I x - x1 I = r} has only one common point x 0 with fJQ.
Fix an e > 0. Since <D(x) is continuous at x 0 , a number 6 = 6(e) >
> 0 can be found such that I <l>(x) - <l>(x0) I < e for all points of
the ball {I x - x 0 I < 6} lying in Q. Since for x =1= x1 the harmonic
function
1 1
w(x) = rn-2 - I x-xijn-2
(for the sake of definiteness the case n > 2 is considered; when n = 2,
w (x) = - ln r + ln I x - x1 I) is nonnegative for all x EQ and
vanishes at only one point x 0 in Q, we can find a C = C (6) > 0 such
that. the inequalities
<D(x0) - e - Cw(x) < <l>(x) < <l>{x0 ) + e + Cw(x)
hold for all x E Q.
The functions Upp(x) + Cw(x) and Upp(x)- Cw(x) are harmonic
in QPP continuous in Qpp and (upp + Cw) laQpp =(<I>-+- Cw) laQpp>
> <'D(x0 ) - e and (upp - Cw) laQpp = (<I> - Cw) laQpp < <D {x0 ) +e.
Therefore, according to the maximum principle, upp(x) +Cw(x)>
+
> cD(xO)- e and Upp(x)- Cw(x) < <D(xO) e in QPP that is,
<l>(xO)- 8- Cw(x)<: Upp(x)<:<D(xO) + e + Cw(x)
ELLIPTIC EQUATIONS 245
for all x EQpp Accordingly, for any x EQ
<I>(xO) - e - Cw(x)-:(u(x)-:( <I>(xO) + e + Cw(x).
Since w (x)-+ 0 as x-+ xo, these inequalities, in turn, imply that
X-+XO X-+xO
whence it follows, as e > 0 is arbitrary, that u(x) is continuous at
the point x 0 and u(x 0) = <I>(x0 ) = cp(x0). I
Proof of Theorem 10. Consider the function u 0 (x) = ) U(x-
Q
- y) f(y) dy, which is a volume potential with density f. Applying
Lemma 2, we find that Uo(x) E C2 (Q) n
C 1 (Q) and is a solution of
Eq. (18) in Q. According to Lemma 4, there exists a classical solution
v(x) of the problem Llv = 0 in Q, vlaQ = cp - u 0 laQ Then the
function u = u 0 + vis a classical solution of the problem (18), (19). I
By means of Theorem 10, we can establish the following important
property of harmonic functions.
Theorem 11 (On removal of singularity). Let the function u(x) be
harmonic in the region Q"'-. {x0 }, where x0 is a point of Q. If u(x) =
= o (U (x- x 0 )), as x-+ x 0 , where U is the fundamental solution of
the Laplace equation, then lim u (x) = A exists and the function u(x)
X-~>oX 0
redefined at x 0 by A is harmonic in Q.
Proof. Consider the ball SR(x0) = {I x - x0 I< R} lying strictly
inside Q. Let the function v(x), satisfying the boundary condition
v las R (x) = u las R<x), be the classical solution of the Dirichlet prob-
lem for the Laplace equation in the ball SR(x 0). The function
u(x) - v(x) = w(x) is harmonic in S R(x 0) "'-. { x0 } and w los R<x) =
= 0. To establish the theorem, it suffices to show that at every point
of the set SR(x0)"'-. {x0 } the function w = 0: in this case the function
u(x) coincides with v(x) for all x E SR(x 0 )"'-. {x0 }, and, consequently,
the function u (x) redefined at the point x0 by A = v(x 0) coincides
with the harmonic function v(x) throughout the ball SR(x0).
With arbitrary e > 0, consider the two functions
e
z(x) = I x-xo In 2 + w(x)
(to be definite, let the dimension of the space be n > 2; when
n = 2, z(x) = e ln I xZ::.xo I w(x)). The functions z(x) are
harmonic in S R(xO) "- {xO} and z(x) lasR(xO) = e/ Rn-z > 0. Since, by
hypothesis, u(x) = o ( I x-!o In 2 ) as x-+xo, we have z(x) hx-xOf=p=
246 PARTIAL DIFFERENTIAL EQUATIONS
= e
pn- 2 + e
w lix-xOJ=p = pn- 2 + o ( pn-1 )
Therefore z (x)IJx-xOf=P > 0
2
for sufficiently small p > 0. According to the maximum principle,
z(x)>O for all x in the spherical annulus P-<lx-xoi-<R. Let
xi be any point in SR(x~)"{xo}. This point belongs to the spherical
annulus P-<1 x-x0 1-<R for sufficiently small p. Consequently,
z (xi)> 0, that is, I w (xi) I< 8 , implying w (xi) = 0
I xi-xO ln-2
since e > 0 is arbitrary. I
In Theorem 10 the existence of a classical solution of the Dirichlet
problem (18), (19) has been established for any f E C1 (Q), <p E
E C (iJQ), iJQ E C 2 It can be asked whether for the solvability ofthis
problem it is enough to require merely that f E C(Q). The condition
that f E C1 (Q) is really more than what is required: it can be shown
that for the solvability of the problem it is enough to assume that
the function f satisfies in Q the Holder condition with some positive
exponent *. But, as demonstrated by the following example, this
condition cannot be replaced by the condition that f E C(Q).
In the ball Q = {I x I < R} of radius R < 1 consider Poisson's
equation
/1 x~-xf ( n+2 1 )
u = 21 x 12 (-In 1x 1) 112 + 2 (-In 1xI )312 ' (20)
where the function on the right-hand side (set zero at the origin) is
continuous in Q. The function
u(x)=(x:-x~)(-lnlxl) 112 (21)
n
belongs to C(Q) C (Q"' {0}) (the point {0} is the origin) and, as
00
is easily verified, s~tisfies in Q"' {0} the equation (20) as well as
the boundary condition
(22)
Nevertheless, the' function u(x) cannot be a classical solution of
the problem (20), (22): since
xf (xf-x~)
hm
lxJ-+0
Ux 1x 1 = hm
lxl-+0
(
2 ( -ln IxI)
1/2
+ lx1 4 (-lnlxl)
112
2xf x~-x~
IX r 2 (-In IX 1) 1 ' 2 21 1 (-lnl xi )1' 2
X 2
it follows that u(x) ~ C2 (Q).
* A function f(x) is said to satisfy in Q the Holder condition with some expo-
nent a > 0 if there is a constant M such that I f(x') - f(x") I M I x' -x" Ia <
for any points x', x" of Q.
ELLIPTIC EQUATIONS 247
Let us show that the problem (20), (22) has no classical solution
at all.
Assume, on the contrary, that the classical solution v(x) of this
problem exists. Then the funcion w(x) = u(x) - v(x) is harmonic
and bounded in Q"--.. {0}. According to the theorem on removal of
singularity, the function w(x) may be redefined at the origin so that
it will become harmonic in Q and therefore belong to C2 (Q). There-
fore, in particular, the (finite) limit lim Wx,x, exists. The existence of
(xi-0
finite limit lim Vx,x, follows from the fact that v(x) belongs to
I X l-0
C 2 (Q). Accordingly, the finite limit lim
!xi-0
Ux,x, = lim
lxi-O
Wx,x, +
+ I limi-0 Vx,x,
X
must exist. This contradiction establishes the assertion.
We have more than once used the formula (8) expressing an arbi-
trary function u(x) in C2 (Q) in terms of the values in Q of its Laplace
au
operator and the values u and an on the boundary 8Q. In the sequel
we shall require another formula of the same sort.
First of all note that for an arbitrary function u(x) E C2 (Q) and
any point y~ Q the following formula holds:
Q
oQ
where U(y- ~)is the fundamental solution of the Laplace equation.
To prove this identity, it is enough to apply Green's formula to
the functions u(~) and U(y - ~) in Q:
~ [ u(~) L\6U (y- ~) - U (y- ~) L\u(~)] d~
Q
and use the fact that the function U(y - s) regarded as a function
s
of is harmonic in Q.
Now take any points x E Q, y ~ Q, and consider a function d(y)
continuous outside Q. Multiplying (23) by d(y) and subtracting the
resulting identity from (8), we find that for any function u E C2 (Q)
248 PARTIAL DIFFERENTIAL EQUATIONS
the representation
u(x) = \ [U(x-)-d(y)U(y-)]L\u()d
Q
+) [a~~) (d(y)U(y-)-U(x-))
aQ
holds for all x E Q, y ~ Q and any function d(y) which is continuous
outside Q.
It may be shown that under fairly wide assumptions regarding
region Q there exists a transformation y = y(x) which associates
with every point x E Q a point y ~ Q and there is a function
d(y(x)) such that
d(y(x)) U(y(x) - ) - U(x - ) 0, E iJQ (25)==
for all x E Q. Formula (24) gives then representation in Q of an arbi-
trary function u(x) EC 2 (Q) in terms of its value on the boundary
and the value of the Laplace operator of this function in Q. We shall
confine our discussion to the case when Q is a ball; in this case it is
possible to find explicit expressions for the functions y(x) and
d(y(x)).
Thus, suppose that Q = {I I< R}, and, to be definite, let the
dimension of the space be n > 2. Then the condition (25) assumes
the form
1 d(y(x)) _ O
I y(x)- In 2 = ' lsl=R,
or, if b denotes d1 f<n- 2>, the form
1 b(y(x))
lx-1 jy(x)-sl '
lsi=R. (26)
The mapping y = y(x) will be sought in the form
y = a(x) x, (27)
where the function a(x) is to be determined. The identity (26) will
hold if the functions a(x) and b(y(x)) are connected by the relation
I y(x)- 12 == b (y(x))
2 I x- 12 , I I = R,
or by
(a2 (x)- b2 (y(x))) j x j2 + (1- b (y(x))) R
2 2
= 2 (x, )(a(x)- b (y(x))), 2 lsi=R.
Set b(y(x)) = I~ 1 , a(x) = b2 (y(x)) = 1~2 1 . Then the identity (26)
ELLIPTIC EQUATIONS 249
holds and for any x E Q the point
R2
y = y(x) =a(x) x = JXT2 x (28)
is situated outside Q because I y I = R 2 /l x I> R for I x I< R.
For the sphere { Is I= R} the normal is given by n; = Th- = ~
therefore
a (
an;
1
lx-1n 2
)
=
( 1
'V; lx-;;ln-2 'n; =
) n-2
lx-sln (x-, n;)
(n-2) (x-~, ~) (n-2) ((x, E)-R 2 ) ( 29 )
= Rlx-1n = Rlx-~ln
Analogously _aa (111 y (x)- sln- 2) is computed. Therefore, by (26).
n;
we have for IsI = R
a ( 1 bn-2(y (x)) )
an; 1x- 1n-2 - 1 y (x)-~ 1n 2
=
(n-2)
Rlx-~ln
[
(x, s)-R-
2 (y (x), ~)-R2
b2(y(x))
J_ Rlx-~ln
1 12-R2
-
x2
(n- ).
Thus, if u(x) E C2 (1 x I~ R), for any point x, I x I< R, we
have the equality
u(x)=) PR(x,)u(S)dS 6- ) GR(a,s)du(S)d, (30)
l;i=R lsi<R
where
(31)
and
(32}
Exactly in the same manner the representation (30) is established
in the two-dimensional case, n = 2. The function PR (x, s) has the
form (31) and
GR(x, s) -z;tln
- 1 I II~-I I:~2
X
R x-1
X I. (32'}
The function PR(x, s)
defined for I I = R, I X I ~ R, by formu- s
la (31) is called the Poisson kernel for the first boundary-value problem
(the Dirichlet problem) for the Laplace operator in the ball {I x I <
<R}.
The function Gn(x, s)
defined for I I ~ R' I X I ~ R' by formula s
(32) when n > 2 or by (32') when n = 2 is known as Green's function
250 PARTIAL DIFFERENTIAL EQUATIONS
of the fi.rst boundary-value problem (the Dirichlet problem) for the
Laplace operator in the ball {I xI< R}.
Lemma 5. The function GR(x, 6) defined in the region { x =I= 6,
x =I= 6R 2 /I 6 12 } of the space R 2n by formula (32) when n > 2 or by
(32') when n = 2 is continuous there and has the following properties:
(a) GR(x, 6) == 0 for I x I = R,
(b) GR(x, 6) = GR (6, x),
(c) GR(x, 6) is a harmonic function of x and of 6,
(d) for lx I~ R, I 6 I~ R 0 ~ GR(x, 6) ~ 1/(crn I x-6 ln-2 ) for
1 2R
n >2 and 0 ~ GR(x, 6) ~-2--nln lx-~l for n = 2.
Proof. Property (a) of the function GR(x, 6) follows at once from
{32) (or from (32') if n = 2).
For any points x and 6 the identity I R2 6 - x I 6 12 I 2 I x I 2 =
= I R 2 x - 6 I x 12 12 I 6 12 holds, whence it readily follows that the
condition 6 = xR 2 /I x 12 is equivalent to the condition x = 6R 2 /I61 2 ;
therefore if the point (x, 6) (in R 2 n) belongs to the domain of defini-
tion of the function GR (x, 6), then so does the point (6, x). Further-
more, the same identity implies the identity I x 1I R2x~l x 12_ ~I
= I~ II R2~~ ~ l2 - x I hence also the identity GR(x, 6) = GR(6, x).
1
This proves Property (b).
It follows from (32) (from (32') if n = 2) that the function GR(x, 6)
is a harmonic function of S Since the function GR(x, 6) is symmetric
'(Property (b)), it is also a harmonic function of x. This proves Proper-
ty (c).
The right-hand inequality in Property (d) for n > 2 follows from
{32). To prove this for n = 2, note that for I x I ~ R, I 6 I ~ R
I x I I 6 - R 2xl I x 12 I = I 6 I x I - R 2 xl I x II ~ I 6 II x I + R2
. 2R 2
-<
-< 2R Therefore for
2 I x I ~ R, I 6 I ~ R 0 < In I x I I ~ _ R2xfl x 121 1
and hence
We shall now establish the left-hand inequalities in (d).
First take x = 0. By virtue of Property (b), GR(O, 6) = GR(6, 0),
therefore GR (0, 6) = :n (I~ ~n-2- R!-2) ~ 0 if n > 2 and GR(O, 6) =
= 2~ln 1~ 1 ~0ifn=2.
Now take any point x0 , 0 < I x 0 I< R, and the ball {I 6- x 0 I<
< e} of radius e, 0 < e < R- I x 0 1, lying in the ball {I 6 I< R}.
According to Properties (a) and (b), GR (x0 , 6) = 0 when I 6 I = R.
ELLIPTIC EQUATIONS 251
~ crin ( en~2 - (R -I ~o l)n 2) > 0 if n > 2
and
G ( o t)=_!_l _!..+_1 l jxOII-R2xOjjxOI21
R X ' 'o 23t n e 2n .n R
~ 2~ {ln++ln(R-jx0 1))>0 if n=2.
Therefore, by the maximum principle, the function G8 (x 0 , )harmon-
ic in is positive in {I I< R}"'-{1 - x 0 I~ 8}. From this
inequality the left-hand inequality in (d) follows, since 8 > 0 is
arbitrarily small. I
The integral representation (30) has been obtained under the
assumption that u (x) E C2 (I x 1 ~ R). Lemma 5 enables us to
obtain the same representation with conditions of u relaxed.
Lemma 6. Let the function u(x) E C(l X I~ R) n C2 (1 X I< R),
and let the function ~u(x) be bounded in the ball {I x I < R }. Then
representation (30) holds for any point x, I x I < R.
Proof. Let x 0 be any point of the ball {I xI< R} and p 0 , p be
numbers such that I x 0 I< p 0 ~ p < R. Since u(x) E C2 (1 x I~ p),
in view of (30) for all x, 1 x 1< p, and, in particular, for x = x 0 ,
we have
u(x0 ) = ) p p(x 0 ' s) u() dS 6- ) Gp(x0 ' ) ~u() d. (33)
161=P lsi<P
In (33), in the integral over the sphere { 1 1 = p} we change the
variables by putting = ~ p:
f
JsJ=p
Pp(x0 , ) u() dS 6 = (~ r-i )
11JJ=R
Pp( x 0 , jf) u ( ji) dSw
Since the function (p/R)n-lpP (x 0 , YJp/R) u (YJp/R) is continuous in
the variables YJ 1 , , 'Yln p on the set {I 11 I = R, Po~ p ~ R}
and (p/R)n- 1 Pp(x0 , YJp/R) u(YJpiR)-+ PR (x 0 , YJ) u (11) as p-+ R,
we obtain
lim i
p-+R J
Jsi=P
Pp(x 0 , ) u() dSt =
Jr
lsi=R
PR(x 0 , ) u() dSt. (34)
Next consider the second term on the right-hand side of (33). Let
Gp(x0 , ) denote the function equal to Gp(x0 , ) for I I < p and
252 PARTIAL DIFFERENTIAL EQUATIONS
to zero for I ~ I> p. Then
\ Gp (x 0 , ~)Au (s) ds= j Gp (x 0 , ~)Au(~) d.
l~i<P 16/<R
Clearly, Gp(x )-+ 0, ) asp-+ R for all =I= x 0 , I I< R.
Gn(x0 , s
Further, by Property (d) of Lemma 5, the function Gp(x 0 , ) Au()
has a majorant independent of p and integrable in the ball {I I <
<R}:
and
where M = sup I Au (x) 1. Therefore, according to the Lebesgue
lxi~R
theorem,
lim j Gp(x 0 , ) Au(~) ds = j GR(x 0 , ) Au (s) ds. (35)
p-+R I~ i<P lsi<R
Letting p -+ R in (33) and noting (34) and (35), we obtain the
representation (30) for any point of the ball {I x I < R}.
It follows from Lemma 6 that the classical solution (if it exists) of
the Dirichlet problem
Au=f, !xl<R,
(36)
u lux J=R} = <p,
where the function <p is continuous on the sphere {I x I = R} and the
function f is bounded and continuous in the ball {I x I < R }, can be
expessed in the form
u(x) = J Pn(x, s) <p (s) dS~- J Gn(x, s) /(s) ds. (37)
ls/=R lsi<R
Note that these conditions (as illustrated by the above example) do
not guarantee the existence of a classical solution.
According to Theorem 10, in order that a classical solution of the
problem (36) may exist it is enough to require that f(x) E C1 ( I x I ~
~ R). Thus Theorem 10 in conjunction with Lemma 6 yields the
following result.
Theorem 12. If f(x) E C1(1 x I ~ R) and P(X) E C(l x I = R)
then a classical solution of the Dirichlet problem (36) exists and can be
represented in the form (37).
Remark. Let Q be a simply connected region in the (x1 , x 2 )-plane,
and let z' = F (z), z = x 1 +
ix 2 , z' = x; +
ix; be a function analytic
ELLIPTIC EQUATIONS 253
in Q and continuously differentiable (with respect to x 1 , x 2) in Qthat
performs a one-to-one mapping of Q onto the disc {I z' I < R} of
radius R(R = I F(z) lzeaQ)
By u (z) = u(x1 , x 2) we denote a classical solution of the Dirichlet
problem
!1u = 0, z E Q,
(38)
u lzeaQ = q>(z),
where q> (z) E C(8Q), and by u' (z') = u'(x~, x;) a classical solution
of the Dirichlet problem
!1u' = 0, I z' I < R,
u' l<iz'i=Rl = 1jJ (z'),
where 1jl(z') = q>(F _1 (z')) (F _1 (F(z)) = z, z E Q).
By Theorem 12
u
, ( ')
z = 2nR
1 r
J
R2 -I z' 12 'I' ('1"')
I z' -~' 12 'Y "'
I d'r'"' I
li.'I=R
From the uniqueness theorem regarding the classical solution of
the Dirichlet problem (Theorem 9) and Corollary to Theorem 6 it fol-
lows that u(z) = u(F _1 (z')) = u'(z'). Hence the solution of the
problem (38) has the form
u(z) =
1
2nR
r
J
R2-IF(z)l2
1F(z)- F(~) 12
,
I F (\;)I rp(\;) I d\;
I
aQ
= _1 r
2n J
IF(~) 12 -I F(z) 12 I r;~g
JF(1;;)-F(z)j2
I q>(\;) Id\; I
aQ
4. Harmonic Functions in Unbounded Regions. Let Q be an un-
bounded region of the space Rn, and let its complement Rn "-.,Q contain
at least one interior point; we take this point as the origin.
Consider a one-to-one mapping
x' = I ; 12 (39)
of the region Rn "--., {0} onto itself. This mapping is known as the
inversion mapping (with respect to the sphere {I x 1= 1 }); we have
already used this in the preceding subsection. Under the mapping
(39) the sphere {I x I = 1} is transformed into itself, the region
{0 < I x I < 1} into the region {I x I > 1} and vice-versa. It is
clear that the inverse of mapping (39) has the form
lx'
x=l?l2'
that is, is also an inversion mapping.
254 PARTIAL DIFFERENTIAL EQUATIONS
As a result of the inversion mapping, the rigion Q is transformed
into a bounded region Q'. Note that the origin becomes a boundary
point of Q'. When. the boundary aQ is unbounded, the origin is a bound-
ary point of the set Q' also. If, however, aQ is bounded, that is, if
Q is exterior to some bounded set, then the origin is an isolated
boundary point of Q', and therefore is an interior point of the set Q'.
Let a function u (x) be defined in the region Q. The function
u'(x') defined in Q' by the relation
'( ')
u X = Ix'1ln-2 U
{ x' )
Ix' 12 (40)
is known as the Kelvin transform of the function u.
It follows from (39) and (40) that
u(x) =I x ~n- 2 u'C ; 12 ), (41}
that is, the transformation inverse to (40) is also a Kelvin transfor-
mation.
Lemma 7. If a function u(x) is harmonic in the region Q, then the
function u' (x') is harmonic in the region Q'.
Proof. Let Q; be any strictly interior subregion of Q', and let Q1
be its original under the inversion mapping. Then Q1 is a strictly
interior bounded subregion of Q. Since the function u is harmonic in
Q1 and belongs to C2 (Q 1), by formula (9) for all x E Q1
u(x)=) [ 1 x~~~in-2+v(6) a:~ Cx-~ln 2)]ds,,
t
BQ,
where 1.1. (6) = (n -~) .Un auiJ(~)
n
I ,
BQ 1
W
v (6) = - (nu- Un BQ are con tin-
1
uous functions on aQ 1 (to be definite, we are ta ing the case
n > 2; when n = 2, arguments are exactly the same). Therefore,
by (40),
u'(x') = ~ [ fl;~) n 2
BQ, I x' ln-21 jX'"j2 -~I
+v(6) 0~.( ;, n_ 2 )JdS,
~ 1:c' jn-2 1 j"X'j2 _ ~ 1
(42}
for all x' E Q;.
From Property (c) in Lemma 5 of the preceding subsection it
follows that the function Ix' 1z-n j"'?l2-
x'
I
6~2-n , and hence the func-
tion a:~ {I x' 1z-n j 1;' 12 - 6~ 2 -n) are harmonic functions of x' for
ELLIPTIC EQUATIONS 255
I:: 12 + . Thus the integrand function in (42) and any of its
derivatives with respect to x' are jointly continuous in , x' and
are harmonic functions of x' for 6E oQ 1 and x' E Q' (the condition
1 ;; 12 ~oQ 1 is equivalent to the condition x' ~aQ;).
Consequently, for any point x1 E Q; the identity (42) can be differ-
entiated under the integral sign with respect to x' any number of
times, and, moreover, L1u' = 0. Since Q; is arbitrary, the conclusion
of lemma follows.
Thus, by means of Lemma 7, the investigation of harmonic func-
tions in an unbounded region whose complement contains interior
points is reduced to that of harmonic functions in a bounded region.
Let the complement Rn ~Q of the region Q in Rn be bounded.
A harmonic function u(x) defined in Q is called regular at infinity if
u(x) = o (1) when n > 2 or u(x) = o (In I x I) when n = 2 as
I X 1-+ 00.
Suppose that the complement of Q contains interior points (this
includes, as above, the origin). As a result of inversion mapping (39)
the region Q is transformed into a bounded region Q' having an iso-
lated boundary point, the origin. If the harmonic function defined in
Q is regular at infinity, then, by (40), the Kelvin transform u'(x') of
this function is, as x' -+ 0, o (I x' 12 -n) if n > 2 and o (In I x' I) if
n = 2, that is, as x'-+ 0, u'(x') = o (U(x')), where U is the funda-
mental solution of the Laplace equation. Then, according to the
theorem on removal of singularity, lim u'(x') = A exists and the
x',.....Q
function u'(x') redefined at the origin by A (the same notation
u'(x') is used) is harmonic in the region Q~ = Q' U {0}.
Thus we have obtained the following result.
Lemma 8. Let the function u(x) be harmonic in an unbounded region
Q whose complement is bounded and contains interior points, and let
this function be regular at infinity. Then its Kelvin transform is har-
monic in Q~.
According to Theorem 5, the function u' (x') is analytic in x' in
Q' U {0}. Therefore, in particular, there is a number R 0 such that
the function u'(x') has a Taylor series expansion
u' (x') = ~ Aa.x'a.
a
in the ball {I x' I< R 0 } that converges (together with all the deriv-
atives) absolutely (and uniformly); here Aa. = :I
Da.u' (0), A 0 =A~
But then, in view of (39) and (41), for all x, I x I> 1/R 0 ,
xa.
u(x)-"" A
- L..J a. I x J21ttl+n-2 1
(43}
a
256 PARTIAL DIFFERENTIAL EQUATIONS
where the series on the right-hand side of this equality converges for
I x I > 1/R 0 absolutely and uniformly together with all its deriva-
tives.
Let T(x) denote the function u(x) - 1~~- 2 , that is, for I xI>
xrx.
> 1/R0 T(x) = ~ Aa. 2 /rx.l+n- 2 Since for any ex= (ex 1 , , exn)
/c.t/>1 IX I
Dau = Drx. I x1~- 2 + DaT (x) and since I DaTI< I x ln~Jaj-!, where Ca.
is a positive constant, it follows that
(44)
In particular,
I
U
A0 I const
(x) -I x ln-2 -<:I x ln-1 '
(45)
Iv n
U
_A 0 (2-n)x,/const
I X In ~ I X In .
The assertions established just now regarding the behaviour for
large I x I of the function u(x) harmonic in Q and regular at infinity
in the case when the complement of Q is bounded and contains in-
terior points remain always valid if the complement of Q is bounded
(in particular, Q may coincide with the whole Rn) Indeed, since we
are interested in the values of the function u(x) for sufficiently large
I x I only, it may be assumed to be defined only on Q1 = {I x I>
> R 1 }, which is a subregion of Q for sufficiently large R 1 And Q1 is
the complement of the set {I x I ~ R 1 } for which the origin is an
interior point.
Thus we have proved the following result.
Theorem 13. Let the complement of a region Q be bounded. Then for
any function u(x) harmonic in Q and regular at infinity there is a con-
stant R > 0 such that for all x, I x I > R, the function u(x) has a series
expansion (43) which converges absolutely and uniformly together with
all its derivatives, and the inequalities (44) hold.
From Theorem 13 it follows, in particular, that if the function
u (x) is harmonic in an n-dimensional, n > 2, region Q, which is
exterior of a bounded set, and decreases at infinity, then it decreases
not slower than the fundamental solution of the Laplace equation,
and, moreover, the limit of u (x) I x ln-2 exists as I x I-+ oo. When
n = 2, the function u (x) harmonic in Q which grows slower than the
fundamental solution is, in fact, bounded, and its limit exists as
I X I-+ oo.
Remark. u;the complement of Q is unbounded, then for a function
u(x) which is harmonic in Q and satisfies the condition
u(x) = o (1) as I x I-+ oo, x EQ, for n > 2
ELLIPTIC EQUATIONS 257
or
u (x) = o (In Ix I) as I x 1-+ oo, :t E Q, for n = 2,
the conclusions of Theorem 13 are, generally speaking, not true. For
instance, when n = 2, the function arg (x1 +
ix 2 ) is harmonic and
bounded in R 2 ""- {x2 = 0, x1 >
0} but does not have a limit as
I X 1-+ 00.
Suppose that a function u (x) is harmonic throughout the space Rn.
We shall say that u(x) is semibounded if it is bounded above or be-
low, that is, if for all x E Rn the inequality u(x) M or u(x) ~ M >
holds, respectively, with some constant M.
Theorem 14. A semibounded function which is harmonic in Rn is
constant.
Proof. Since for a function u(x) bounded above the function
-u(x) is bounded below, it suffices to establish the theorem for the
case u(x) >
M in Rn. In this case the harmonic function v(x) =
= u(x)- M >
0 in Rn. The theorem will be proved if we show that
v(x) = const.
Take an arbitrary point x 0 E Rn and the ball {I x I < R} of radius
R > I x 0 I The Dirichlet problem for the Laplace equation in the
ball {I x I < R} with boundary function v 111 x I=R} has a unique
classical solution, so for all x, I x I < R,
v(x) = J Pn(x, ~) v(~) dS~,
l~l=R
where- Pn(x, ~) is the Poisson kernel of the Dirichlet problem for the
Laplace equation in the ball {I x I < R} (formula (31)). In particu-
lar, for x = x 0 we have
v(x0 )= J
l~i=R
Pn(x0 ,~)v(~)dS~=R 2 ;n1; 012 J
i!ii=R
Jx~~~lndS~.
Since for I ~ I= R
R - I X0 I ~ I X0 - 6 I ~ R + I X 0 I,
we have (note that the function v (6) > 0)
1 f (R2-j xo 12) Rn-2
GnRn 1 J v(~) dS ~ (R +I xo lln <;;. v(xO)
lsi=R
or, in view of the first mean value theorem,
Rn-2 (R2 -I xo j2) Rn-2 (R2-I xo j2)
(R+I xo i)n v(O)<;;.v(xO)<;;_ (R-1 xo I" v (0).
17-0594
258 PARTIAL DIFFERENTIAL EQUATIONS
Letting R--+ oo in this inequality, we find that v(x0 ) = v(O).
Consequently, since the point x 0 is arbitrary, v(x) const. I=
Corollary. If the function u(x) harmonic in Rn satigfies the inequal-
ity I u(x) I ~ C(1 + I x l)k, where C is a constant and k a non-
negative integer, for all x ERn, then u(x) is a polynomial of degree not
exceeding k.
Proof. When k = 0, this result is contained in Theorem 14. As-
sume that k > 0, and take an arbitrary number R > 1. By Lemma 3.
Subsec. 2, for any ex = (ex1 , , exn), I ex I = k
max I Dau /<. kk ( ~ ) k max I u(x) I
~ER ~EU
<. C0( ~ r+
(1 2R)Il <. C0( ~ r
(3Rt= C (3kn)".
From this inequality it follows that for any ex, I ex I = k, the func-
tion Da.u harmonic in Rn is bounded in Rn. According to Theorem 14,
the functions Dau, I ex I = k, are constant in Rn. Consequently,
u(x) is a polynomial of degree not exceeding k. I
We have established above some properties of harmonic functione
in unbounded regions. It was shown, in particular, that the Kelvin
transformation reduces the investigation of a harmonic function in
an unbounded region (whose complement contains interior points)
to that of a harmonic function in a bounded region.
Let us now examine boundary-value problems for the Laplace
equation in unbounded regions. First of all note that for an unbounded
region the usual conditions on the solution (imposed in the case of
a bounded region) are not enough to guarantee its uniqueness.
For instance, all the functions c In r, c(r1t - r-k) cos ke, c(r1t -
-r-") sin ke, k = 1, 2, ... , where c is any constant, x1 = r cos e,
x 2 = r sine, are harmonic in the region {r > 1} c R 2 , continuous
in its closure and vanish on the boundary {r = 1 }. Therefore in
defining a solution some additional condition characterizing its
behaviour at infinity should naturally be imposed.
N
Let the region Q = Rn ""'- U Q,. where Q1, i = 1, ... , N, are
i=i
bounded regions with disjoint boundaries.
A function u(x) E C2 (Q) is called the (classical) solution tJf the
Dirichlet problem for the Laplace equation in Q:
~u=O, x EQ,
(46)
uloQ= <p
if it is harmonic in Q, continuous in Q, satisfies the boundary condi-
tion in (46) and is reglilar at infinity.
ELLIPTIC EQUATIONS 259
A function u (x) E C2 (Q) is called the (classical) solution of the
third boundary-value problem for the Laplace equation in Q:
~u = 0, x E Q,
tf it is harmonic in Q, continuously differentiable in Q, satisfies the
boundary condition in (47) and is regular at infinity.
If a = 0, the third boundary-value problem is designated the
second boundary-value problem or the Neumann problem.
Let Q' denote a bounded region which is the image of the region Q
under the inversion mapping (the origin is an interior point of the
complement of Q).
Assume that u(x) is a solution of the problem (46). It follows
from Lemma 8 that the function u'(x'), the Kelvin transform of
u (x) (redefined with respect to continuity at the origin), is harmonic
in Q~ = Q' U {0}. Furthermore, it is clear that u' (x') E C (Q~) and
u'(x') I x'EliQ~ = cp'(x'), where cp'(x') = 1/ 1n_ 2 cp ( 1 ; , ' 12 ) This
means that u'(x') is a classical solution of the Dirichlet problem
for the Laplace equation in the (bounded) region Q~ with boundary
function cp' (x').
Conversely, if u' (x') is a classical solution of the Dirichlet problem
for the Laplace equation in Q~ with boundary function cp'(x'), then
the function u(x), its Kelvin transform, is harmonic in Q, continu-
ous in Q, satisfies the boundary condition u lvo = cp and is clearly
regular at infinity, that is, u(x) is a classical solution of the prob-
lem (46).
Therefore the existence and uniqueness theorems rega:rding classi-
cal solution of the Dirichlet problem in a bounded region (Theo-
rems 9 and 10) imply the following result.
Theorem 15. There exists a unique classical solution of the Dirichlet
problem (46) with any continuous boundary function cp.
The Kelvin transformation similarly reduces the investigation of
the third boundary-value problem in an unbounded region Q to that
in a bounded region Q~. We confine to the proof of the uniqueness
theorem.
Theorem 16. The third boundary-value problem, with a(x) ~ 0,
a (x) 0, for the Laplace equation in Q cannot have more than one
solution.
The second boundary-value problem for the Laplace equation in Q
cannot have more than one solution when n > 2, while in the case n = 2
the solution (if it exists) is determined up to a constant term.
Proof. Suppose that the third (second) boundary-value problem has
two solutions u 1 (x) and u 2 (x). Then the function u(x) = u 1(x) -
17*
260 PARTIAL DIFFERENTIAL EQUATIONS
-u 2 (x) is harmonic in Q, continuously differentiable in Q, satisfies the
boundary condition ( :~ +au) laQ = 0 and is regular at infinity.
We take a number R > 0 so large that the region { 1 x 1 > R} is
contained in Q' and in the region QR = Q {I X I < R} apply n
Green's formula
0= f ul1u dx = - .\ I Vu 12 dx +) !: u dS
QR QR oQ
+ ) !~ u dS = -- f I vu 12 dx- .\ au2 dS + ) !~ u dS.
ixl=R QR oQ ixi=R
This yields the identity
QR CJQ Jxi=R
un {lxJ=R}
=0 {R!-1)
when n > 2 and ~u I
un {JxJ=R}
= 0 { R\ ) when n = 2. Therefore
.\ :: u dS = 0 ( R!- 2 ) if n > 2
lxi=R
and
\ !.:!:. u dS = 0 ( _!_) if n = 2.
' on
lxl=R
R
Passing to the limit in (48) as R-+ co, we obtain
~
Q
I Vu 12 dx + Jcru dS
oQ
2 = 0
Since a > 0, this identity is equivalent to two identities
J Vu
Q
1 12 dx = 0 and f cru dS = 0.
oQ
2 (49)
The first identity in (49) implies that u = c 0 = const in Q. If
n > 2, we find, noting the regularity of u (x) at infinity, c0 = 0,
that is, u 1 = u 2 in Q.
If n = 2 and cr(x) >
0, a(x) =f= 0 (the third boundary-value prob-
lem), then the relation c 0 = 0 is a consequence of the second identi-
ty in (49).
==
If, however, n = 2 and cr(x) 0 (the second boundary-value prob-
lem), then the function u(x) =
c 0 , with an arbitrary constant c 0 ,
is harmonic and regular in Q and satisfies the homogeneous boundary
condition un l
~u oQ = 0. I
PROBLEMS ON CHAPTER IV 2&1
PROBLEMS ON CHAPTER IV
1. Show that a function u(x) belonging to L 2 , loc(Q) and satisfying the
identity ) u dV dx = (\ for all v E C (Q) is harmonic in Q.
00
Q
2. Complete the set of fnnctions belonging to L 2 (Q) and harmonic in Q in
the norm of L 2 (Q).
3. Suppose that the function u E Hloe(Q) n C (Q) and iJQ E C2 Prove that
I ,
u E H :l)(Q) provided du E L 2 (Q).
Note that the result of Problem 3 implies that the classical solution of the
Dirichlet problem for Poisson's equation du = /, u laQ = 0 with right-hand
side f belonging to L 2 (Q) is a generalized solution and even a solution ahnost
everywhere. Accordingly, the classical eigenfunctions of the first boundary"value
problem for tho Laplace operator are generalized eigenfunctions.
4. Let iJQ E C2 On the set of all functions u(x) EC2 (Q) nC(Q) such that
,iu(x) E L2 (Q), we define a scalar product S ,iu ,i~ dx. Complete this set in the
Q I
norm generated by this scalar product.
5. Suppose that the boundary iJQ of a region Q belongs to Ck. Establish
the following results.
(a) In the Hilbert space H~ (Q) the following scalar products equivalent to
the usual scalar product may be defined:
for even k,
and
00
(f, grH:z,(Q) = s=t
k ~ fsg siAal"-,
where / 8 = (f, u 8 )L.(Q) while Us and A8 are sth eigenfunction and the correspond-
ing eigenvalue of the Dirichlet problem for the Laplace operator in Q.
(b) In the Hilbert space H
(Q) one may introduce the following scalar
products equivalent to the usual scalar product:
' { (dk/2/, ,ik/2g)L.(Q)+(f, g)L.(Q) for even k,
(/,g) k =
H Ar(Q)
,;v
(,i<k-t)/ 2 / ,i(k-t)/ 2g)
'
g)
H(Q)
+<!' L 2 (Q)
for odd k,
and
00
(f, g)" k = 2} Isis (I As I"+ 1),
H .J/1-(Q) s=1
where / 8 = (/, us)L,(Q) while us and As are sth eigenfunction and the correspond-
ing eigenvalue of the Neumann problem for the Laplace operator in Q.
6. Suppose that a function u(x) E C(Q'>, and for any point x E Q there is a
number r=r(x)>O such that the ball S,(x)={l~-x/<r}c:Q and u(x)=
= C1n:n-l ) u (~) dS~. Show that u(x) is harmonic in Q.
ilS,(x)
262 PARTIAL DIFFERENTIAL EQUATIONS
7. Suppose that the function u(x) E C1 (Q) and J:~ dS =0 for any sphere
s
S lying in Q. Show that u(x) is harmonic in Q.
8. Show that the first eigenvalue of the first boundary-value problem for
the Laplace operator in the region Q, iJQ E C2 , is nondegenerate and the corre-
sponding eigenfunction does not vanish in Q.
9. Show that a function u(x) E C2 (Q) and satisfying in Q the Helmholtz
equation ~u + A.u = 0, where A. is a constant, is analytic in Q.
Note that the result of Problem 9 implies that eigenfunctions of any
boundary-value problem for the Laplace operator in 0 are analytic in Q.
10. Let A.k(Q1 ) and A.k(Q 2 ) be kth eigenvalues of the first boundary-value
problem for the Laplace operator in regions Q1 and Q2 , Q1 (f; Q2 Prove that
A.k (Ql) < A.k (Q 2) for all k = 1, 2, ....
11. Let L2 ( iJQ) ( iJQ is the boundary of an n-dimensional region Q) be the
subspace of the space L 2 (iJQ) that contains all the functions orthogonal (in
L 2 (iJQ) with a scalar product) to constant functions. For any function 'ljl(x) E
E L 2(iJQ) there exists a unique generalized solution u(x) of the Neumann prob-
lem for the Laplace equation in Q with boundary function 'ljJ whoso trace on
oQ ui 6 Q = cp E L2 (iJQ). Thus an operator A is defined on L 2 (oQ) that asso-
ciates with every function 'ljJ E L2 (iJQ) a function cp E L 2 (iJQ): A'ljl = cp.
Establish the following results.
(a) The eigenvalues A.k, k = 1, 2, ... , of the operator A are positive;
the eigenfunctions ek, Aek = A.kek, k = 1, 2, ... , constitute an ortlionormal
basis for L2 ( iJQ).
(b) There exists a generalized solution uk(x) of the Dirichlet problem for
the Laplace equation in Q with boundary function y;;- ek, k = 1, 2, ....
The system uk (x), k= 1, 2, ... , constitutes an orthonormal basis for the
space with scalar product .\ Vu v; dx which consists of all the harmonic
Q
functions in Q belonging to H 1 (Q) whose trace on iJQ lies in L 2 (iJQ).
00
(c) For any function 'ljJ E L2 (8Q) the series ~ 'ljlk lft.k uk(x), where'ljlk =
k=i
= ('ljl, ek) L,(BQ) converges in H 1 (Q) and represents a generalized solution
of the Neumann problem for the Laplace equation in Q with the boundary
function 'ljl.
(d) Let cp E L 2 (iJQ). In order that there may exist a generalized solution
u (x) of the Dirichlet problem for the Laplace equation in Q with boundary
00
A.k
k=i
'Pk = (q>, e11 )L,(BQ) converge. Moreover, u(x) =I a~ I ) cp dS + ~ cpkuk (x).
{)Q h=i
(e) Find the eigenvalues and eigenfunctions of the operator A when the
region Q is the disc { 1 x 1 < 1} (a two-dimensional case), and show that the
condition of part (d) in this case coincides with the condition in Theorem 13,
Sec, 1.8.
12. In order that the function f(cp) defined on the boundary {r = 1} of
the unit disc {r < 1} in the plane xi = r cos !p, x 2 = r sin cp and belonging
to L 2 (0, 2:rt) may be the boundary va ue of some function in HI (r < 1) it is
PROBLEMS ON CHAPTER IV 263
2n 2n
necessary and sufficient that the integral J ~! J (! (q:> + t) - f (q:>)) 2 dq:>
0 0
converge.
A function u(x) E C' (Q) nC (Q)
1 satisfying the equation
~2 u = f, x E Q, (1)
and the boundary conditions
(2)
is called the classical solution of the Dirichlet problem for the equation ~ 2 u = f
in Q. A function u (x) E C' (Q) n
C2 (Q) satisfying Eq. (1) and the boundary
conditions
u laQ = 0, ~u l 0 q = 0 (3)
is known as the classical solution of the Riquet problem for the equation ~2 u =
= f in Q.
Let the function f E 2 (Q). A function u belonging to H2 (Q) and satisfying
the integral identity
J
Q
!l.u!l.v dx= Jtv
Q
ax (4)
for all v E H2 (Q) is called the generalized solution of the Dirichlet problem (1),
(2). A function u belonging to H~(Q) and satisfying the integral identity (4)
for all v E H~(Q) is designated as the generalized solution of the Riquet prob-
lem (1), (3).
13. Let aQ E C2 Prove the following results.
(a) The classical solutions u(x) of the problems (1), (2) and (1), (3) belong
ing to C4 (Q) are generalized solutions of these problems.
(b) The generalized solutions of the problems (1), (2) and (1), (3) exist
for all f E L 2 (Q) and are unique.
Let Q be a ball of radius R: Q = { I X I < R }. By sl denote the hemisphere
(I X I= R}n {zl > 0} and by s2 the hemisphere {I X I= R} n {xl::;;;;; 0}.
A function u(x) belonging to C2 (Q) n C1 (Q U S 1 ) n C(Q) and satisfying
Poisson's equation
!l.u = f, X E Q, (5)
and the boundary condition
-au j =0, (6)
an St
is termed the classical solution of the problem (5), (6).
By lP(Q) denote the subspace of the space H 1 (Q) which contains all the
functions u E H 1 (Q) whose trace on S 2 is zero. Let f E L 2 (Q). By a generalized
solution of the problem (5), (6) is meant the function u E fil(Q) which satisfies
the integral identity
~ VuVvdx=- Jfvdx
Q Q
for all v E Hl(Q).
264 PARTIAL DIFFERENTIAL EQUATIONS
14. Prove that for any function f E L 2 (Q) the generalized solution of the
problem (5), (6) exists and is unique.
Let Q be a bounded two-dimensional region with boundary 8Q E C3 , and
let l(x) be a twice continuously differentiable vector defined on 8Q, I l(x) I = 1.
that makes an angle a:(x), 1 a:(x) 1 < ~ , with the (outward) normal vector
to aQ (a (x) = (n-:l)). A function u(x) belonging to C1 (Q) nC2 (Q) and satis-
fying the equation
!J.u- u = f, X E Q, (7)
asJ well as the boundary condition
au
al
IaQ-
-0 (8)
is called the classical solution of the directional derivative problem (7), (8).
Let A (x) be a function belonging to C2 (Q) whose value on the boundary
(Q is tan a:(x). Let f E L 2 (Q). By a generalized solution of the problem (7), (8)
is meant a function u E Jll(Q) satisfying the integral identity
2 1 2) dx
Q Q
for all v E H 1 (Q).
15. Prove the following assertions.
(a) A classical solution of the problem (7), (8) is a generalized solution.
=
(b) If a:(x) const, then for any f E L 2 (Q) there exists a unique genera-
lized solution of the problem (7), (8); this solution does not depend on the method
of extending the function tan a:(x) by A (x) into Q.
Agmon, S., Douglis, A. and Nirenberg, L. "Estimates near the boundary
for solutions of elliptic partial differential equations satisfying general boundary
conditions 1-11", Comm. Pure Appl. Math. 12 (1959) 623-727; 17 (1964) 35-92.
Bers, L., John, F. and Shechter, M. Partial Differential Equations, Wiley,
New York, 1963.
Bitsadze, A. V. Boundary-value Problems for Second-order Elliptic Equations,
North-Holland, Amsterdam, 1968.
Courant, R. and Hilbert, D. Methods of Mathematical Physics, Interscience,
New York, 1962.
Il 'in, V. A. "On the convergence of expansions in eigenfunctions of the Lap-
lace operator", Uspekhi Mat. Nauk 13: 1 (1958), 87-180 (in Russian).
John, F. Plane Waves and Spherical Means Applied to Partial Differential
Equations, Interscience, New York, 1955.
Keldysh, M. V. "On the solvability and stability of the Dirichlet problem",
Uspekhi Mat. N auk 8 (1941), 171-292 (in Russian).
Keldysh, M. V. "On the completeness of the system of eigenfunctions of cer-
tain classes of nonselfadjoint linear operators", U spekhi Mat. N auk 26: 4
(1971), 15-41 (in Russian).
Krylov, N. M. and Bogolyubov, N. N. "Application de la methode de l'algo-
rithme variational a la solution approchee des equations differentielles aux
SUGGESTED READING ON CHAPTER IV 265
derivees partielles du type elliptique," lzv. Akad. Nauk SSSR, Otd. Fiz. Mat.
N auk (1930), 43-71, 105-114.
Lavrent'ev, M. A. Variational Method in the Boundary-value Problems for
the System of Equations of the Elliptic Type, Izd. Akad. Nauk SSSR, 1962
(in Russian).
Lavrent'ev, M. M. "On the Cauchy problem for the Laplace equation",
lzv. Akad. Nauk SSSR, Ser. Matem., 20 (1956), 819-842 (in Russian).
Lavrent'ev, M.A. and Lyusternik, L. A. A Course of Calculus of Variations,
Gostekhizdat, Moscow, 1950 (in Russian).
Ladyzhenskaya, 0. A. Boundary-value Problems of Mathematical Physics,
Nauka, Moscow, 1973 (in Russian).
Ladyzhenskaya, 0. A. and Ural 'tseva N. N. Linear and Quasi linear Equations
of Elliptic Type, Academic Press, New York, 1968.
Miranda, K. Partial Differential Equations of Elliptic Type, Springer, Berlin,
1955.
Petrovskii, I. G. Lectures on Partial Differential Equations, Interscience,
New York, 1954.
Sobolev, S. L. Partial Differential Equations of Mathematical Physics, Addi-
Sobolev, S. L. Some Applications of Functional Analysis in Mathematical
Math. Soc., R. I. 1963).
Steklov, V. A. On Asymptotic Behaviour of Solutions of Linear Differential
Equations, Kharkov Univ .. Press, Kharkov, 1956 (in Russian).
Tikhonov, A. N. and Samarskii, A. A. Equations of Mathematical Physics,
Nauka, Moscow, 1972 (Engl. transl.: Pergamon Press, Oxford).
Vekua, I. N. New Methods for Solution of Elliptic Equations, North-Holland,
Amsterdam, 1967.
Vekua, I. N. "On metaharmonic functions", Proceedin~s of the Tbilisi Math.
Inst., XII (1943), 105-174 (in Russian).
Vladimirov, V. S. Equations of Mathematical Physics, Nauka, Moscow, 1971
(in Russian).
CHAPTER V
HYPERBOLIC EQUATIONS
In this chapter we shall study the Cauchy problem and the mixed
problems for a hyperbolic equation of the form
Utt - div (k (x)Vu (x, t)) + a (x) u (x, t) = I (x, t).
Here (x, t) = (xtt ... , Xn, t) is a point of the (n +i)-dimensional
space Rn+t x ERn, t E Rtt Vv (x, t) = ( :;1 , , ::n } and
div (w1 (x, t), ... , Wn (x, t)) = iJwa 1
xl
+ .. + 00wn Xn
; by fl.v (x, t) we
{)2v {)2v
shall mean div Vv (x, t) = + ... + -
-0 2 The data of the prob-
0 2
xl Xn
lem will be assumed real-valued functions and we shall examine
only real-valued solutions of these problems. Therefore Hk, Ck,
k = 0, 1, ... , will henceforth mean corresponding real spaces.
1. PROPERTIES OF SOLUTIONS OF WAVE EQUATION.
THE CAUCHY PROBLEM FOR WAVE EQUATION
1. Properties of the Solutions of the Wave Equation. Let us exa-
mine the simplest hyperbolic equation of the second order, the wave
equation,
n
Ou (x, t) = Utt -fl.u = Uu- .~
t=1
Ux 1x 1 =I (x, t). (1)
First of all we shall obtain some special solutions of the homogene-
ous wave equation (Du = 0) depending only on til x 1. The func-
tion v(x, t) = w (tfl x I) which for I x I =F 0 is a solution of the homo-
geneous wave equation satisfies the ordinary differential equation
d2w dw
{z2 -1) dz 2 +(3-n)zdz=O.
HYPERBOLIC EQUATIONS 267
The general solution of this equation in each of the intervals (-oo,
-1) (-1, +1), (+1, +oo) is given by the formula
Ct fII z -11_
2
n-3
2_ dz + c2 ,
where c1 and c2 are arbitrary constants. This, in particular, implies
that for 0 < I x I<- t (z = til x I< -1) the function v(x, t)
has the form
v(x t)-c In lt+Vt2-lxl21 +c when n= 2,
' - t lxl 2
t
v(x, t) = c1 TXT+ c2 when n= 3,
and so on.
By Kx, t', to we shall denote the cone {I x - x' I < t' - t,
t 0 < t < t'} of "height" t' - t 0 with vertex at the point (x', t'), by
rx',t',tO its lateral surface {I X - x' I = t'- t, t 0 ~ t ~ t'},
which is a characteristic (see Sec. 2, Chap. I) for the wave equation,
by Dx,t,t the base of the cone {I x - x' I< t'- t 0 , t = t 0 }
and by Sx', t', to the boundary of the base which is the sphere
{I x- x' I = t' - t 0 , t = t 0 }.
Let (x 1 , t 1) be a point of Rn+t K the cone Kx, t. 1o, t 0 < t 1 , and
D = Dx, t, t the base of this cone (see Fig. 2). We shall demon-
strate that if the function u(x, t) is sufficiently smooth in K U D,
then its value at any point (x, t) of the cone K is determined by the
value of Ou in the cone Kx, 1, t and those of u and u 1 on the base
of this cone i5 x, t, t
Consider first the case of three space variables, n = 3. It is as-
sumed that u(x, t) E C2 (K) n C1(K U D) and ou E C(K U D). Let
(~, 't) be any point of K and 8 any positive number less than 't - t 0,
0 < 8 < 't - t 0 By K 8 denote the region {8 < I x - ~ I < 't - t,
t 0 < t < ' t - 8} lying inK. The boundary of K 8 is divided into three
s
parts: re = {I X - I = ' t - t, t 0 ~ t ~ ' t - 8 }, De = {8 <
< I x - ~ I< ' t - t0 , t = t 0 }, '\'e = {I x - ~ I = 8, t 0 ~ t <
< ~- 8}.
t-'1:
We examine the special solution, depending only on I x- 1 , of
the homogeneous wave equation:
t-'1:
v(x-~, t-'t)= lx-sl +1. (2)
268 PARTIAL DIFFERENTIAL EQUATIONS
Since the functions u(x, t) and v(x - , t - 't) belong to C1 (K8),
3
V 0 U-U 0 V=- ~
i-=1
(Ux.V-UVx.)x.
' l l
+ (UtV- UVt)t
in K 8
Integrating this equality over K 1 and taking into account that
0 v = 0 in K 8 , we obtain, by Ostrogradskii 's formula,
3
Jv 0 u dx dt= ) [- ~ (ux;v-uvx;) n; + (u,v-uvt) n 4 ] dS
~ ~u~u~ ~1
=lre+lv8 +lv8 , (3)
where n = (n 1, n 2, n 8, nil) is a unit vector normal to:-aKe directed
outwards, and Ir,e
lv,8
lve are integrals over fe, De, '\'e
Fig. 2
Consider the integral over f 8 It follows from (2) that vire = 0.
Furthermore, since _.
(
'Vv= t-'t') 16-xl3 '
s-x
Vt= lx-1
1
(4)
and the I r 1 ( Xt-61 x2-2 Xa-6s
'1) =
norma on e n= 'V2 lx-1 ' lx-sl' lx-1
= J2 ( :-;, 1 ). we have
~
3
( )
LJ Vx;ni -vtn!o
I _'V2
I'-
1 ( (x-, x-!;)
jx-13 - jx-1
1 ) _
=0.
i=1 8
HYPERBOLIC EQUATIONS 269
Consequently,
3 3
re i=1 i=1
Since the normal on De is n= (0, 0, 0, -1), we have by (2)
and (4)
I
De
= ~ u(x, tO) dx
lz-61
+ r
J
( lz-61 1) Ut (x, t;O) dx.
't-tO
s<l x- l<'f-1 e<l x-"<'f-1
Since the functions u(x, t 0) and u 1(x, t 0) are continuous (u E
E C1(K UD)), the limit of the integral In exists as e-+ 0 and
. I _
1tm ~ u(x, tO) d
D-
8 .... 0 e
I x-.,!:1 X
Jx-6 <'f-1
Jx-~)<'f-1
On the surface l'e the normal _n = ( j":~~f ,0) = ( 6--;z , 0),
therefore, taking (4) into account, we J:>ave
'f-8 'f-8
Ive=- ) dt ) ;~ vdSx+ ) dt f
I x-~ 1=8
!: udSx
t I x-"=8 t
'f- 'f-
= - ) ( t 8 't + 1 ) dt f ;: dS x +) t 82 't dt f u dS x
t lx-iJ=e t Jx-iJ=a
Since for lx-6J=e, t 0 :=;;;t:=;;;-r-e the inequalities I!~ I:=;;;M
and I u(x, t)- u(6, t) I:=;;;Me, where M is a certain constant
(M = max I \luI), hold, it follows that
Jx-H::::'f-t
f 0 !St~'t'
I ) !: dSxj:=;;;4ne M
Jx-6)=
2
and
dSx- ) u(6, t) dSxl
llxJJ=e u(x, t) l:x-;J=e
Therefore the limit of the integral I y B exists as e -+ 0 and
:ao PARTIAL DIFFERENTIAL EQUATIONS
1:
lim/y =4n; I (t-T) u (~, t) dt. (7)
e-o 8 J
t
Passing to the limit in (3) as e -+ 0 and taking (5), (6), (7) intc>
account, we find that for any point (~, 't) of K
1:
4n) (t-T) u(~, t) dt=- ( 1u;~~o~ dx
t lx-!ii<t-1
)
lx-Ef<1:-t0
c:=~, t)ut(x,t')dx
1:
t0 lx-61<1:-t
Differentiate this identity with respect to 't:
1:
) u (~, t) dt = 4n (1:1-to) ) u(x, t 0 ) dS x
t I x-1; 1=1:-1
0 u(z, t) d
lz-sl x.
whence we have
u(, T) = :. { 4n(-r:1"-to) ) u(x, to) dSx)
I x-; 1==-t-1
1:
+! ) dt j t I x-6 I=T-t
0 u(z, t) dS
lz-~1 x:
Since
T 1:-t
f dt lx-61=1:-t
.l o u(z, t) dS - lo d'A I 0 u(z, 1:-A.) dS
lz-sl x- J J !z-sl x
t lx-61=~
0 u(z, -I z-s I) d
- ~
lx-6 <1:-t 0
lz-sl x.
HYPERBOLIC EQUATIONS 271
for any point (x, t) of the cone Kx, t,t the following Kirchhoff
formula holds:
u(x, t)= :t {4n(t~to) \
I x-;r=t-t
u(~, to)dS;)
+ 4n (/- t 0 J u 1 (~, to) dS~
+_1
4n
I x-~ l=t-t
lx-' <t-t 0
l 0 u(!;, t-1 ~-~1 )pd~ - (8)
I~- I., ,
Since
1
4n (t-tO) Jr u(~, to) dS;
t-tO
= ~ S u(x + T} (t- to), to) dSTJ
I x-~ l=t-1 111 1=1
it follows that
:t ( 4n (t~tO) f u(~, to) dS;)
lx-ai=t-t
= 4~ ) u(x+rt)(t-t0 ), t 0 )dSTJ
I TJ l=!l
+ t 4nto J (V'u(x + Tl (t- to), to)' rt):ds TJ
I TJ 1=1
4n(t~t0)2 lx-~L-t [u(~, to)+(~-x)V'u(~, to)]dS~.
Therefore Kirchhoff's formula can be written in the form
lx-;l=f-! 0
I x-~l=f-! 0
+ _1_ r D u(, t-1 ~-I) d~ (9)
J 1~-1
4n
I x-' l<f-! 0
Formulas (8) and (9) show that the value of the function u at any
point (x, t) of K is expressed in terms of values of ou in Kx, t, t and
of u and Ut in Dx, t, , Note that the value of the function u at
the point (x, t) E K is determined (when n = 3) by the values of the
function 0 u not on the whole cone Kx, t, t but merely on its lat-
eral surface r x, t, t and those of u, u 1 and vu not on the whole
base Dx, t, t but only on its boundary, the sphere Sx, t, t In
272 PARTIAL DIFFERENTIAL EQUATIONS
particular, if at some point (x, t) E K D u =. 0 on r x, t, t' and u =
= Ut = I vu I = 0 on S,, t, t' then at this point u(x, t) = 0.
The above fact at once implies the following theorem, true for
n = 3, which states that the solution u of Eq. (1) in the cone Kxt, tl, to=
= K is uniquely determined by the values of u and u 1 on the base
Dxt, 11, to = D of this cone.
Theorem 1. Suppose that the functions u 1(x, t) and u2 (x, t)
belong to C2(K) nC1(K uD), D Ut = D Uz in K and Ut(x, t 0 ) In=
- ( tO) ID aul (x,
- u2 x,
0 I-
at t ) v- au2 at I
(x, t 0)
v Th en u 1 =Uz
- ln K
0
Proof. Indeed. the function u = ul - Uz belongs to C2 (K) n
n C (K u D), ou = 0
1 inK and for XED u(x, t 0) = Ut(X, t 0 ) = 0.
u(x, t) = 0 inK, that is, u 1(x, t)
From (9) it follows that u 2 (x, t) ==
in K. I
For any number of space variables, the corresponding representa-
tion and the proof of Theorem 1 can be obtained by the same method.
If the function u(x, t) E C2 (K) n C1 (K U D), the function ou
and all its derivatives with respect to the space variables up to order
m = max ( [ ; J-1, 0) are continuous in K UD, u (x, t 0) E C [ ; ] (D)
and u 1(x, t 0) E cm(D), then the value of u(x, t) at any point (x, t) E
EK is expressed in terms of the function ou (and its derivatives with
respect to space variables up to order m) in Kx, t, 1o and the
functions u and u 1 (and their derivatives up to order [ ; J and m,
respectively) in D:x:, 1, 1o. For instance, for n > 3 the representation
is obtained in exactly the same manner as for the case n = 3; as
a special solution v(x- , t - -r), with 1; ~I < - 1, of the homo-
z n-3
geneous wave equation we have to take the function) ({? - 1)_2_ d~,
-1
t-1:
Z=jx-61"
Note that in the case of even n, n :>- 2, the value of the function u
at the point (x, t) is determined by the values of the function D u
(and its derivatives with respect to space variables) on the whole cone
K:x:, t, to and those of the functions u and u 1 (and their derivatives
with respect to the space variables) on the whole base Dx, 1, to. In
the case of odd number of variables n > 3, the value of u at the
point (x, t) is deftned, as in the case n = 3, by the values of the func-
tion ou and its derivatives with respect to the space variables only
on the lateral surface r x, t, to of the cone and those of u, u 1 and
their derivatives with respect to the space variables only on the
boundary S,, t, 1o of the base.
HYPERBOLIC EQUATIONS 273
For two and one space variables the corresponding representations
together with the proof of Theorem 1 are most easily obtained di-
rectly from formula (9) (or (8)).
Suppose that a function u(x, t), x =(xi, x 2 ), is defined in the
cone K = Kxt, 1', t, xi= (x~, x~), and belongs to C2 (K) nCi(K uD),
D = Dx, t, t and 0 u = Utt- Ux,x,- Ux,x, E C(K UD). The function
u(x, t) may be regarded as a function of four variables x 1 , x2 , x3 ,
t, which is independent of x 3 , defined in the four-dimensional cone
1 .~
K x1. ~ tt , to in which x~ is arbitrary; moreover, u (xi, x 2 , t) E
x2, xa,
E cz (Kxl. xt x!, t 1 , t 0 ) nCi (Kxl. xl, xl. t\ t0 uDxl. x~. xl. t 1 , to), and Utt-
- Ux,x, - Ux,x,- Ux,x, E C ( K l. ... , 1o U D xl. ... , to). For all points
(x 1 , x 2 , t) belonging to K, by formula (9) we have
"
u(x 1 , x 2 , t)
= 4n:(t~to)z
(Xt- St) 2 +(x,-
f
s>'+(x,- 6a) 2=(t- 1) 2
[u(~t ~2 t 0 )
Since
f
(x,- St) 2 +(x,- sz)'+(xa- l;a) 2 =P 2
g (~h ~2) as,
=2p f g(~r. ~2)dsrdsz (iO)
(x,-!;,)'+(x.-s.)'<P' Y P2-(.:z:t-6t) 2-(.:z:2-z) 2 '
it follows that
u (, tO)+(~-x)V'u (,tO) d6
v (t-t0)2-l.:z:- 12
where 6 = (~ 1 , ~ 2 ), x = (x1 , x 2 ), and the point (x, t) is any point in
the cone Kx, t, to This formula gives the desired representation of
the function when n = 2.
18-0594
274 PARTIAL DIFFERENTIAL EQUATIONS
Note that for any point (x, t) in the cone K
1 I u (6, t 0}+(6-x)V'u (6, t 0 ) d
2n(t-tO) J
fx-61<1-1
V(t-to)2-jx-612
a ( 1 I u(6, tO) ds )
=at z;t J
lx-sf<t-t
V (t-t0)2-j x-6 j2 .
Therefore representation (11) can be written in the form
u (x t) -- ~ (-1- I u(6, tO) d )
' - ot 2n J
I x-61<1-1
V(t-t0)2-I x-6 12
+ 1 i Ut (s, t 0} ds
2n J V<t-tO)Z-jx-12
I x-6 l<t-t
t-t
+-2n1- Jr dp Jr o u <s. t-p) d.
V p2-jx-612
(12)
o lx-~I<P
Formula (12) is referred to as Poisson's formula. Similarly, for n = 1
the corresponding representation is easily obtained from formula (11)
(or (12)). If u(x, t) E C 2 (K) n
C 1 (K U D), where K = Kx, t, to
(triangle {t- t 1 < x - x 1 <- t t1, +
t 0 < t < t 1 }), D =
= Dxt, tl, to (interval (x1 t 0 - tl, x1 + t 1 - t 0)), and Ou = +
= u 11 - Uxx E C(K U D), then the value of the function u at any
point (x, t) E K is given by the following D'Alembert formula:
x-1+ t
u (x, t) = u(x-t+to, tO)t u(x+t-to, t 0) +~ ) Ut(, to) d
x-t+t 0
t x+t-1:
+~ JdT: J D u(, T) d, (x, t) EKx, t, t (13)
t0 x-t+'T:
2. The Cauchy Problem for the Wave Equation. For brevity, we
shall denote the set of points {x ERn, t > t 0 }, {x ERn, t t 0 }, >-
{x ERn, t ~ t ~ t }, {x ERn, t = t } by {t > t }, {t
0 1 0 0 t 0 }, >-
{t 0 ~ t ~ t 1 }, {t = t 0 }, respectively, and the spaces Ck({t > t 0 }),
>-
ck ({ t t 0 }) by ck (t > t 0) and Ch(t t 0). >-
A function u (x, t) belonging to C2 (t > 0) C 1 (t 0) is called n >-
the (classical) solution of the Cauchy problem for the wave equation in
the half-space {t > 0} if for all x ERn, t > 0 it satisfies the equation
0 u = f, (14)
and for t = 0 the initial conditions
u lt=O = cp (x),
(15)
Ut lt=O = 'iJ (x),
with!functions <p, 'iJ and f given.
HYPERBOLIC EQUATIONS 275
According to Theorem 1 of the preceding subsection, the solution
u(x, t) of the problem (14), (15) is uniquely determined in any cone
Kx, t, 0 (x 1 E Rn, t 1 > 0), and hence in the whole half-space
{t > 0}, by the given functions j, cp and 'ljl. Thus we have the fol-
lowing theorem.
Theorem 2. The Cauchy problem (14), (15) cannot have more than
one solution.
We now proceed to discuss the question of existence of a solution
of the Cauchy problem.
Assume that the solution u(x, t) of the problem (14), (15) exists.
The results of the foregoing subsection imply that if f E C (t :?> 0),
then in the case of three space variables (n = 3) the solution is
given by Kirchhoff's formula
u(x, t) = a(1
at 4 nt Jr cp() dSs ) + 4:rtt1 Jr '() dS;
lx-~l=t IX-GI=t
+ _1_
4:rt
I
J
f('f., t-lx-'f.l>dt xER
lx-~1 ':> 3
t>O
,
(16)
lx-61<t
in the case of two space variables (n = 2) by Poisson's formula
u (x, t) = ~ ( 21:n ) V t2~;i :~; 12} + 21:n ) y t2~~) ::_; 12
jx-6l<t lx-61<t
t
+ 2~ld-c l' J(',t-t)d', xER2 , t>O, (17)
J0 J
IX-i;l<'t
r:2-lx-'f.l2
while in the case of a single space variable (n = 1) by D'Alembert's
formula
x+t
u(x, t) = <p(x+t)t<p (x-t) +~ ) ' () d
x-t
t x+'t
+~ I dr:
0
)
X-'t
f (, ) d, X E Rt. t > 0. (18)
In view of this, the proof of the existence of the solution of the prob-
lem (14), (15) reduces to obtaining conditions under which the
function u (x, t) given by the corresponding representation is a solu-
tion of this problem.
Consider first the case of three space variables (n = 3). The fol-
lowing assertion holds.
If cp E C3 (R 3), 'ljJ E C2 (R 3) and the junction f and all its derivatives
with respect to x 1 , x 2 , x 3 up to second order are continuous in {t :;> 0},
then the junction u defined by Kirchhoff's formula (16) is a solution of the
18*
276 PARTIAL DIFFERENTIAL EQUATIONS
problem (14), (15); moreover, for any point (X, T) E {t ::> 0},
II u llc<iZX, T, o>:::;;;II (jlllc(oX, T,
>+TIll V'qJIIIC(nX,
o T, o
>
T2
+ T lllJJ I!C(v.X, T,o l + -2 II I llc(KX, T' 0
)" (19)
Remark. From formula (19) it follows that if the function f is
bounded in {0 < t < T}, the function 1jJ is bounded in R 3 , and the
function qJ is bounded in R 3 together with all its first derivatives,
then the solution u of the problem (14), (15) is bounded in {0 < t <
< T} and
T2
sup Jul:::;;supJqJJ+TsupiV'qJJ+TsupJ'tjJI+y sup 1/l.
{O<t<T} R3 R3 Ra {O<t<T}
ug(x, t, -r) = 4 ~t J g(, -r) dS,, x ER 3 , t > 0, T > 0, (20)
I x-:-6 l=t
where g(x, -r) E C('l' ::> 0). When the function g does not depend on
the parameter -r, g (x, -r) = g(x), the function ug(x, t, -r) will be
denoted by Ug(x, t).
Lemma 1. If the function g(x, -r) and all its derivatives with respect
to x1 , x 2 , x 3 up to order k, k=O, 1, ... , belong to C(.- ::;?:- 0), then
the function ug(x, t, -r) and all its derivatives with respect to x 1 , x 2 , x 3 ,
t up to order k are continuous on the set {x E R 3 , t ~ 0, T ::;?:- 0}. When
k ::;?:- 2, the function ug (x, t, -r) for any 't ::> 0 satisfies in {t > 0} the
equation D Ug = 0 and the conditions Ug lt=O = 0, /).ug lt=O = 0,
Ugt lt=O = g (x, T).
Proof. The first assertion of the lemma follows from the identity
Ug(X, t, -r)= 4~ J g(x+trJ, -r)dS'Il. (21)
I 'II 1=1
It also follows from (21) that uglt=O = 0. Since for k ::> 2
/).ug(X, t, T)= 4~ J ().g(x+trJ, -r:)dS'Il, (22)
ITJ 1=1
!lug lt=O =0.
Differentiation of (21) with respect to t yields
aug 1 r
Tt = 4il J g(x + trJ, -r:) dSTJ
ITJ 1=1
+ 4~ J (V'g(x+trJ, T), rJ)dSTJ, (23)
ITJ 1=1
HYPERBOLIC EQUATIONS 277
whence it follows that
Ugt lt=O
= hm Tt =lin
aug 1 r
J g (x, -r) dSTJ = g (x, -r).
t-+O I TJ 1=1
Since
4:n ) (Vg(x+trJ,-r),rJ)dSTJ
11] 1=1
=-t- r ag (x+tTJ, 't) dS =-1- r ag (1;, 't) dS.
4:rt J anT] TJ 4:rtt J an ~
I TJ 1=1 I x-6 l=t
1 I d (E -r)dt= I(x, t, 't)
4:nt J g -' "' 4:nt '
I x-6 1<1
where I (x, t, -r) = ) dg (, ,;) d, (23) may be expressed in the
I x- l<t
form
which yields
() 2 ug 1 1 aug 1 ai I
ijt2 = - +T Tt + 4:rtt at- 4:rtt
t2 Ug 2
ug 1 { ug 1 ) 1 ai I 1 ai
= -t2+T -t-+ 4:nt + 4:nt Tt- 4:nt 2 = 4:nt at
= 4 ~t ) dg (, ,;) dS 6 = 4~ ) dg (x + tf), -r) dSTJ. (24)
I x- l=t 111 1=1
It follows from (24) and (22) that Ugtt = dug. I
The second term on the right-hand side of (16) is (x, t), so by u"'
Lemma 1 ( E C2 (R 3 }) it belongs to C2 (t 0), is a solution of the >-
homogeneous wave equation and satisfies the initial conditions
uiPit=O = 0,
aurp
The first term on the right-hand side of (16) is ---at . Since <p E
OUrp
homogeneous wave equation
0 ( :t Urp )= :t 0 Urp = 0
and satisfies the initial conditions
aurp
---at I
t=O = <p, 7ft
a ( au<P )
--at I
t=O = dUrp it=O = 0.
278 PARTIAL DIFFERENTIAL EQUATIONS
We denote the third term on the right-hand side of (16) by F (x, t)
and transform it as follows:
F(x t) = _1_ r /(~. t-1 x-E I) ds
' 4n J
Jx-~l<t
lx-~1
t
= -1
4n Jr ~
p Jr t<s. t-p) as~
0 Jx-1=p
t t
- ) (4n(;-T)
0
)
lx- ~l=t -'t
!(6, T)dS~ )dT= JG(x,
0
t, T)dT,
where G(x, t, T) = u1(x, t - T, T). According to Lemma 1, the
function G (x, t, T) and all its derivatives with respect to x1 , x 2 , x 3 , t
up to second order are continuous on the set {x E R 3 , t ::;> 0, 0 ~
~ T ~ t} and for any T ::;> 0
Gtt-flG=O fort? T,
G lt='t = 0, Gtlt=-r = f (x, T).
t
Then the function F(x, t) = ) G(x, t, 't) dT is continuous in {t ::;> 0}
0
together with first derivative with respect to t and all the deriva-
tivesJtwith respect to x 1 , x 2 , x 3 up to second order. And since
t t
F 1 = G l-r=t +) Gt(x, t, T) d't = ) G1 (x, t, T) dT,
0 0
FE C2(t ? 0). Furthermore,
t
fl.F(x, t) = \ fl.G(x, t, 't) dT
'o
and
t t
Ftt=Gtl-r=t+) Gtt(x, t, 't)dT=f+ \ fl.G(x, t, 't)dT.
0 ~
Consequently, the function F (x, t) satisfies the equation OF = f
and homogeneous boundary conditions Flt=O = 0, Ft!t=O = 0.
Thus we have shown that the function
t
u(x, t) =
au<p (x, t)
at + uw(x, t) + Jr u1(x, t-T, T)
d
T
0
defined by formula (16) is a solution of the problem (14), (15).
HYPERBOLIC EQUATIONS 279
We shall now establish the inequality (19). Suppose that (X, T)
is any point of the half-space {t > 0}. By formula (20), for any
point (x, t) of the cone Kx. T, 0 and arbitrary T > 0
I ug(x, t, T) I ~ t max I g(, T) / ~ T max I g(, T) I (25)
lx-61=t lx-!;i=t
Consequently,
II u.p llc(I( >~ T max max 1\jJ () I
X, T, 0 (x, t)EKx, T, 0 \X-sl=t
= T max
ix-XI~T
I \jJ I = T Jl \jJ llc(v
X, T, o
> (26)
and
T
1/ JuJ(x,
0
t-T, T)dT II C(K- x. T. o> ~ ~r (t-T) lx-sl=t-'t
max /!(, T)/dT
T
~II f llc(K X, T, o> S
O
2
(T- T) dT = ~ 1/ f llc<K >
X, To 0
(27)
Similarly, by (23),
jj o~cp /lc(:K X, T, o> ~ II qJ llc(vX, T, o>+TIll Y'qJ lllc(v X, T, o>. (28)
The inequality (19) follows immediately from (26)-(28).
Note that the assumptions regarding the functions qJ, \jJ and f
under which the existence of a solution of the Cauchy problem has
been established cannot be relaxed in some definite sense. The fol-
lowing example shows that the assumption qJ E C2 (R 3) is not enough
for the existence of a solution of the problem (14), (15).
Suppose that the function qJ depending only on I x I, qJ(x) =
= a (I x 1), belongs to C2 (R 3). Let there exist a solution u(x, t)
of the problem (14), (15) with this function qJ(x) and the functions
lj7 =0 and f =
0. Then by (16)
u(x, t) = :t (4~t )
jx-!;l=t
a (I!) dS;).
Let I x 1=F 0. Since for all points on the sphere {I x - I = t}?
I 2 I = I X 12 + t2 + 2 I X I t cos e, where e is the angle between
the vectors x and - x, we have
)
x-61 =t
2:rt :rt
= (l. I dqJ I a <V t +I
0 0
2 X 21+ 21 X I t cos 8) sine de
+1 t+lxl
=2nt 2 ) a(Vt 2 +/xl 2 +2lx!tt..)dl.= z;t ) pa(p)dp.
-1 lf-lxll
280 PARTIAL DIFFERENTIAL EQUATIONS
Therefore
Hlxl
u(x, t)=! ( 21 1xl ) pa(p)dp)
l!-lxll
1
= 2TXT ((t +I xI) a (t +I xI)- (t -I xI) a (j t -I x II))
= 21 txl (a(t+lxl)-a(lt-lxll))+ ~ (a(t+jxl)+a(lt-lxiJ)).
This implies that u(O, t) = ta'(t) a(t), because the solution +
is continuous. And since the function u(O, t) E C2 (t > 0), the
function a( I x I) must belong to C3 ( I x I > 0) which, of course,
does not follow from the assumption that <p belongs to C2 (R 3 ).
Next we consider the case n = 2. We shall show that if <p(x1 , x 2 ) E
E C3 (R 2 ), ' (x1 , x 2 ) E C2 (R 2 ) and the function f(x 1 , x 2 , t) is con-
tinuous in {t:;;? 0} together with all the derivatives up to second order
with respect to x1 , x 2 , then the function u(x1 , x 2 , t) given by Poisson's
formula (17) is a solution of the problem (14), (15). Further, for any
point (X, T) of the half-space {t > 0} the inequality (19) holds.
According to formula (10), for any x 3
a ( :n;t
u(x 1, x2, t) = Tt 4
1 Jr <p(s 1 , 2) dS ~)
S 1(x 1 , x,, x 3 )
t
+ 4~t )
S 1(x 1 , x 2 , Xo)
lJl (1, 2) dS; + 4~ J ~-r
0
)
S't(x1 , x 2 , x 3 )
(17')
where Sp (x1 , x 2 , x 3 ) is a sphere of radius p centred at (x1 , x 2 , x 3 ):
(x1 - s1 ) 2 + (x 2 - s
2 ) 2 + (x 3 - 3 ) 2 = p2 s
As just now estab-
lished, the function appearing in the right-hand side of the identi-
ty (17') is a solution of the problem: Utt - Ux,x, - Ux,x, - Ux,x, =
= f (x1 , x 2 , t) in {t > 0}, u lt=O = <p (x1 , x 2), Ut lt=O = ljJ (x1 , X2)
and inequality (19) holds for it. And since the function u does not
depend on x 3 , it is a solution of the problem (14), (15) with n = 2.
For the case n = 1, it can be directly verified that the function
u (x, t) defined by D'Alembert's formula (18) is a solution of the prob-
lem (14), (15) if <p E C2 (R 1 ), ljJ E C1 (R 1 ) and the junction f(x, t)
is continuous in {t :;;> 0} together with its first derivative with respect
to x. Further, for all points (X, T) of the half-plane {t > 0} the fol-
lowing inequality holds:
T2
II u llc(.Kx, T, 0 ) ~II <p llc(ox, T, 0 ) + Til' /1 c(i5x, T, ol +Til f lbRx, T, 0)
(Kx,T.o is the triangle {t+X- T<x< T +X- t, O<t<T}
and Dx, r, ={X- T < x <X+ T, t = 0} its base).
0
HYPERBOLIC EQUATIONS 281
When the number of space variables is greater than three (n > 3),
it is established, just like for the case n = 3, that if cp E cl ~ ]+ 2 (Rn),
n
[-]+!
'iJ E C 2 (Rn) and the function f is continuous on the set {t 0} >
together with its derivatives up to order [ ; + 1 with respect to J
x 1 , , Xn, then the function u given by the corresponding repre-
sentation is a solution of the problem (14), (15).
Theorem 3. If cp(x) E cm+ 3 (Rn), "(x) E cm+ 2 (Rn) and the junc-
tion f(x, t) is continuous in {t >
0} together with its derivatives up
to order m+2 with respect to x 1 , . , Xn, where m=max ( [ ; ]-1, 0),
then there exists a solution u(x, t) of the problem (14), (15). Further,
for any point (X, T) of the half-space {t > 0} the inequality
holds with a constant C depending only on T.
As already noted in the preceding subsection, Poisson's formula
in the case n = 2 or the corresponding representation in the case
of even n > 2 implies that the value of the solution of the Cauchy
problem (14), (15) at the point (x, t), t > 0, depends only on the
values of the function f (in the case n > 2, also on the values of its
derivatives with respect to the space variables) in the whole cone
Kx, t. 0 as well as on the values of the initial functions cp and 'iJ (and
the values of their derivatives) on the whole base Dx, t, 0 of this
cone. In the case of any odd n >
3 (as in the case n = 3) the value
of the solution at the point (x, t) depends on the values of function/,
and in the case n > 3 also on the values of its derivatives with
respect to space variables only on the lateral surface r x. t. 0 of the
cone Kx, t, 0 and on the values of the initial functions cp and 'iJ and
their derivatives only on the boundary of the base, the sphere Sx. t. 0 ,
of the cone.
Due to this, the cone Kx, t, 0 in the case of even number of space
variables n >2 and the conical surface r x, t. 0 in the case of odd
n > 3 are referred to as the region of dependence on the right-hand
side of the equation of the solution of the Cauchy problem (14), (15)
at the point (x, t). Likewise, the ball Dx. t, 0 lying on the initial
plane in the case of even n >
2 and the boundary, the sphere S x. t. 0 ,
of the ball in the case of odd n >
3 are known as the region of depen-
dence on the initial data of the solution of the Cauchy problem at the
point (x, t).
282 PARTIAL DIFFERENTIAL EQUATIONS
When n = 1, from D'Alembert's formula (18) it follows that
the solution of the Cauchy problem at the point (x, t) depends only
on the values of the function f in the triangle Kx. t, 0 , on the values
of the initial function \jJ on the base of this triangle D x. t, 0 and
on the values of function QJ on the boundary of the base, the points
(x + t, 0) and (x - t, 0).
Suppose that for some R > 0 the initial functions qJ and \jJ vanish
for I x I:?:- R, while the function f vanishes for I x I + t > R.
Then the solution u of the Cauchy problem vanishes at all points
(x, t) E {I x I :?:- R + t, t :?:- 0}, because the cone Kx, t, 0 for such
(x, t) does not have common points with the set {I x I + t < R, t > 0}
and its base Dx. t, 0 does not have common points with the ball
{I x I< R, t = 0}. (Even when f vanishes only for I x I:?:- R + t,
this assertion remains valid.)
In the case of even number of space variables the set {I x I~ R + t,
t :?:- 0} is, generally speaking, maximal possible set where u = 0.
For instance, with n = 2, if the function \jJ is taken positive in the
disc {I x I < R} and the functions QJ and f vanish, then it follows
from Poisson's formula that u(x, t) > 0 for all (x, t) E {I x I <
< R + t, t> 0}.
When the number of space variables is odd, n :?:- 3, the function
u(x, t) vanishes not only on the set {I x I :?:- R + t, t :?:- 0} but
also on the set {I x I::::;;:; t - R, t :?:- R}, because for (x, t) E
E {I x I::::;;:; t - R, t :?:- R} the conical surface r x. t, 0 does not have
common points with the set {I x I + t < R, t > 0} while the bound-
ary of the base Sx, t, 0 does not have common points with the ball
{lxi<R,t=O}. The set G={lxi:?:-R+t, t:>-O}U
U { I x I : : ; :; t - R, t :?:- R} is, generally speaking, the maximal
possible set where u = 0. For instance, with n = 3, if the function
'Jl (x) > 0 for I x I < R and the functions QJ and f vanish, then
from Kirchhoff's formula it follows that u(x, t) > 0 on the region
{II x I-t I< R, t > 0}, the complement of G.
If the right-hand side f(x, t) of the equation (14) is defined not
in the whole half-space {t > 0} but only in the strip {0 < t < T} =
= IIr for some T > 0, then we consider the Cauchy problem for
Eq. (14) in the strip IIr.
A function u(x, t) belonging to C2 (0 < t < T) n C1 (0 ::::;;:; t < T)
is called the solution of the Cauchy problem (14), (15) in the strip 11r
if for all points (x, t) E IIr it satisfies Eq. (14) and for t = 0 the
initial conditions (15). For the Cauchy problem in a strip there are,
of course, existence and uniqueness theorems, analogous to corre-
sponding theorems concerning the Cauchy problem in a half-space.
The Cauchy problem in the strip IIr cannot have more than one
solution and in the case of n = 3, for instance, in order that the
Cauchy problem in the strip IIr may have a solution it is sufficient
that QJ E C3 (R 3 ), \jJ E C2 (R 3 ) and the function f be continuous in
HYPERBOLIC EQUATIONS 283
{0 ~ t < T} together with all its derivatives up to second order
with respect to the variables x1 , x 2 , x 3 Moreover, the solution of the
problem is represented in ITT by Kirchhoff's formula.
Apart from considering the Cauchy problem in the half-space
{t > 0}, we may also study the Cauchy problem in the half-spaces
{ t > t 0 } or {t < t 0 } for any t 0 A function u (x, t) belonging to the
space C 2 (t > t 0)n >
C 1 (t t 0) is called the solution of the Cauchy
problem in the half-space {t > t 0 } for the wave equation if in {t > t 0 }
it satisfies the equation D u = f and for t = t 0 the initial conditions
ult=t = <p, utlt=t = lJl. Exactly similar is the definition of the solu-
tion of the Cauchy problem in the half-space {t < t 0 }. The Cauchy
problem in the half-space {t > t 0 } reduces to a Cauchy problem
in the half-space {t > 0} by changing t to t - t 0 Similarly, the
Cauchy problem in the half-space {t < t 0 } transforms to a Cauchy
problem in the half-space {t > 0} by replacing t by t 0 - t. If one
changes t to t!a (a is a positive constant), the Cauchy problem in
the half-space {t > 0} for the equation ~ a
u 11 - ~u = f is trans-
formed to the Cauchy problem (14), (15).
Let D be an n-dimensional region in the plane {t = 0}, and
let the region Q lying in the half-space {t > 0} be formed of the
points (x, t) which are vertices of cones Kx, t, 0 whose bases (balls
Dx, t. 0 ) lie in D. If, in particular, D is the ball {I x - x 0 I< R},
then the region Q is the cone Kx, R, o; if Dis the cube {I xi - x? I<
<a, i = 1, ... , n}, then Q is a pyramid whose base is this cube
and vertex is at the point (x 0 , a); if D is the entire plane {t = 0},
Q is the half-space {t > 0}.
A function u(x, t) belonging to C2 (Q) n C1 (Q U D) is called
the solution of the Cauchy problem in Q for the wave equation if it
satisfies in Q the equation ou = f and for t = 0, xED, the initial
conditions u lt=O = <p, utlt=O = lJl.
Theorem 1 of the preceding subsection immediately yields a
uniqueness theorem for the Cauchy problem in Q: the Cauchy prob-
lem in Q cannot have more than one solution.
It is easily seen that the existence theorem, Theorem 3, is also
valid for the case under consideration. For instance, with n = 3,
a solution of the Cauchy problem in Q exists provided <p E C3 (D),
lJl E C2 (D) and the function f is continuous in Q U D together with
its derivatives up to second order with respect to space variables.
The solution u (x, t) is given by Kirchhoff's formula (16).
Note that the solution of the Cauchy problem (14), (15) in the
half-space {t > 0} in Q coincides with the solution of the Cauchy
problem in Q for Eq. (14) with initial functions <p and lJl considered
only on D.
284 PARTIAL DIFFERENTIAL EQUATIONS
2. MIXED PROBLEMS
1. Uniqueness of the Solution. Let D be a bounded region of the
n-dimensional space Rn (x = (x1 , . ; Xn) is a point in this space).
In the (n + i)-dimensional space Rn+t = Rn X {-oo < t < +oo}
we consider a bounded cylinder Or = {xED, 0 < t < T} of
height T > 0. We denote by rr the lateral surface {x E an,
0 < t < T} of the cylinder Or and by D't its intersection {xED,
t = T} with the plane t = -c; in particular, the top of Or is Dr =
= {xED, t = T}, while its base is D 0 = {xED, t = 0}.
In the cylinder Or with T > 0, we examine the hyperbolic equa-
tion
Zu = Utt - div (k(x) vu) +
a(x) u =f (x, t), (1)
where k(x) E C 1(D), a(x) E C(JJ), k(x) >-
k 0 = const > 0.
A function u (x, t) belonging to the space C2 (0r) n C 1 (0r U
U rr U D 0 ) that satisfies in Or Eq. (1), onD 0 the initial conditions
U lt=O = cp, (2)
Ut lt=O = ", (3)
and On f r one Of the boundary COnditions
u lrr=X
or
(:~+au) lrT =x,
where a, a function continuous on r T is called (classical) solution
of the first or, correspondingly, the third mixed problem for Eq. (1).
If a = 0 on r r the third mixed problem is known as the second
mixed problem.
Since the case of nonhomogeneous boundary conditions is easily
reduced to that of homogeneous boundary conditions, further consid-
eration will be confined to the homogeneous boundary conditions
uJrT=O (4)
and
(5)
We shall assume that the coefficient a(x) in Eq. (1) is nonnegative
in Or, while the function a in the boundary condition (5) depends
only on x, a = a(x), and is nonnegative on r r
Suppose that the function u(x, t) is a solution of either of the
problems (1)-(4) or (1), (2), (3), (5), where the right-hand side f(x, t)
of Eq. (1) belongs to L 2 (0r) Take any 6, 0 < 6 < T. Multiply (1)
by a function v(x, t) belonging to C1 (Qr _6 ) and satisfying the
HYPERBOLIC EQUATIONS 285
condition
=0vJDT-Il (6)
and
|
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|
http://math.stackexchange.com/questions/167360/proof-for-members-of-ideals/167537
|
# proof for members of ideals
If $I$ is an ideal, could you show that if $x\in I$ and $y\notin$ I, then $x+y \notin I$? It seems like an intuitively obvious statement and yet my rigor is failing me. So if you could show me all the steps of the proof that would be much appreciated.
-
If $x + y \in I$ and $x\in I$ then $x + y - x = y \in I$ contradiction. – Tobias Kildetoft Jul 6 '12 at 6:38
This is really a fact about groups. – Dylan Moreland Jul 6 '12 at 6:38
@Tobias Perhaps you could write that as an answer so the question can be marked as answered? – Alex Becker Jul 6 '12 at 6:41
Assume for the sake of contradiction that $x\in I$, $y\not\in I$ and $x+y\in I$. Since $I$ is a subgroup of the additive group of the ring, we have that $y = (x+y) - x \in I$ which is a contradiction. As mentioned by Dylan Moreland, this is a general fact about subgroups of any group.
-
Another way which I find useful in dealing with things like this: Suppose that $x \in I$, $y \notin I$ but $x + y \in I$. Then saying that $x + y \in I$ implies that $x + y = m$ for some $m \in I$. Rearrange to write $y = x - m$. Now $x \in I$ and $m \in I$. Since $I$ is an ideal and $m \in I$ we must have
$$(-1)\cdot m = -m$$
being in $I$. Furthermore $I$ being closed under addition means that $x + (-m) = x - m \in I$. However recall $y = x-m$ so this means $y \in I$ which contradicts the assumption that $y \notin I$.
$\hspace{6in}$ Q.E.D.
-
This is a special case of the following complementary view of a subgroup.
Theorem $\$ Let $\rm\,G\,$ be a nonempty subset of an abelian group $\rm\,H,\,$ with complement set $\rm\,\bar G = H\backslash G.\,$ Then $\rm\,G\,$ is a subgroup of $\rm\,H\iff G + \bar G\, =\, \bar G.$
Proof $\$ $\rm\,G\,$ is a subgroup of $\rm\,H\iff G\,$ is closed under subtraction, so, complementing
$\begin{eqnarray} & &\ \ \rm G\text{ is a subgroup of }\, H\ fails\\ &\iff&\ \rm\ G\ -\ G\ \subseteq\, G\,\ \ fails\\ &\iff&\ \rm\ g_1\, -\ g_2 =\,\ \bar g\ \ \ for\ some\ \ g_1,g_2\in G,\ \ \bar g\in \bar G\\ &\iff&\ \rm\ g_2\, +\ \bar g\ \ =\,\ g_1\ for\ some\ \ g_1,g_2\in G,\ \ \bar g\in \bar G\\ &\iff&\ \rm\ G\ +\ \bar G\ \subseteq\ \bar G\ \ fails\qquad\ {\bf QED} \end{eqnarray}$
Instances of this are ubiquitous in concrete number systems, e.g. below. For many further examples see some of my prior posts here.
-
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|
http://afp.theoremproving.org/entries/matrix_tensor/
|
# Tensor Product of Matrices
T.V.H. Prathamesh
18 January 2016
### Abstract
In this work, the Kronecker tensor product of matrices and the proofs of some of its properties are formalized. Properties which have been formalized include associativity of the tensor product and the mixed-product property.
BSD License
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https://worldwidescience.org/topicpages/s/strong+economic+growth.html
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#### Sample records for strong economic growth
1. Strong economic growth driving increased electricity consumption
International Nuclear Information System (INIS)
Tiusanen, P.
2000-01-01
The Finnish economy is growing faster today than anyone dared hope only a few years ago. Growth estimates for 2000 have already had to be raised. This strong level of economic growth has been reflected in electricity consumption, which has continued to increase, despite the exceptionally warm winter. A major part of this increased electricity usage has so far been met through imports. The continued growth in electricity imports has largely been a result of the fact that the good water level situation in Sweden and Norway, together with the mild winter, has kept electricity prices exceptionally low on the Nordic electricity exchange. The short period of low temperatures seen at the end of January showed, however, that this type of temperature fluctuation, combined with the restrictions that exist in regard to transfer capacity, can serve to push Nordic exchange electricity prices to record levels. This increase in price also highlights the fact that we are approaching a situation in which capacity will be insufficient to meet demand. A truly tough winter has not been seen since the Nordic region's electricity markets were deregulated. The lesson that needs to be learnt is that Finland needs sufficient capacity of her own to meet demand even during particularly cold winters. Finland used 77.9 billion kWh of electricity last year, up 1.6% or 1.3 billion kWh on 1998. This growth was relatively evenly distributed among different user groups. This year, electricity consumption is forecast to grow by 2-3%
2. Intellectual property: A strong determinant of economic growth
Directory of Open Access Journals (Sweden)
Munmun Rai
2009-01-01
Full Text Available The returns from almost all human endeavors can ultimately be translated into monetary gains. The past few years have seen increased attention paid to the strengthening of intellectual property rights due to globalization. The development of Intellectual property rights (IPR over the years has invariably brought an upsurge in the outlook of nations toward the aspect of societal and cultural growth, this being said with the preliminary assumption that economic growth has been the most affected realm and that it requires a separate spectrum of analysis. The artifacts between the IP regime and the national economy can be easily interpreted by the fact that India′s independence had itself brought an era where the enactment of the national IP laws were considered to stand on the touchstone of the market economy. The aim of the present article is to investigate the impact of a strong IP regime on the economic development of a nation and also a light is raised into Indian economy, and the creation of an efficient innovative system is discussed. A strong relation of the IPR with the pharma and biotech sectors has been discussed. Undoubtedly, the Intellectual property (IP systems must be developed so as to bring in socioeconomic well-being. The fact that a strong IPR actually provokes IPR infringements in many developing nations also seems to be an issue that needs to be analyzed while understanding the need of the former. The trade-off between unfair competition laws and IP also assumes importance of high magnitude and hence needs to be particularly emphasized. With the growing recognition of IPR, the importance of worldwide forums on IPR has been realized. Companies, universities, and industries want to protect their IPR internationally. In order to reach this goal, countries have signed numerous agreements and treaties.
3. Intellectual property-A strong determinant of Economic Growth
Directory of Open Access Journals (Sweden)
Love k Singh
2009-12-01
Full Text Available
The returns from almost all human endeavors can ultimately be translated into monetary gains. The past few years
have seen increased attention to the strengthening of intellectual property rights due to globalization. The development
of Intellectual property rights (IPR over the years has invariably brought an upsurge in the outlook of
nations towards the aspect of societal and cultural growth, this being said with the preliminary assumption that
economic growth has been the most affected realm and that it requires a separate spectrum of analysis. The artifacts
between the IP regime and the national economy can be easily interpreted by the fact that India’s independence
had itself brought an era where the enactment of the national IP laws were considered to stand on the touchstone
of the market economy. The aim of the present paper is to investigate the impact of strong IP regime in the
economic development of a nation and also a light is raised into Indian economy and creation for an efficient
innovating system is discussed. A strong relation of IPR wity pharma sector and biotech sector has been discussed.
Undoubtedly, IP systems must be developed so as to bring in socio-economic well-being. The fact that
strong IPR actually provoke IPR infringements in many developing nations also seems to be an issue which needs
to be analyzed while understanding the need of the former. The trade-off between unfair competition laws and IP
also assumes importance of high magnitude and hence needs to be particularly emphasized. With the growing
recognition of IPR, the importance of world wide forums on IPR is realized. Companies, universities, and industries
want to protect their IPR internationally. In order to reach this goal, countries have signed numerous agreements
and treaties.
4. Human Capital and Economic Growth - How Strong is the Nexus?
Directory of Open Access Journals (Sweden)
Marinko Škare
2016-08-01
Full Text Available The link between human capital and economic growth still remains unexplained because of the measurement issues connected to the human capital stock. This study investigates the link between human capital stock and economic growth using inclusive wealth index and ratio of engaged to actively disengaged employees as proxy for human capital stock. Data from the global workplace and inclusive wealth reports are used in order to provide an international comparison of the link between human capital and inclusive wealth. Cross country comparison show human capital largerly contribute to the inclusive wealth formation. Formal education is important but also motivating working environment is needed to achieve sustainable economic growth. The finding further indicates that standard human capital growth model should be revised taking into the account variables addressing sustainable growth (not just growth and environmental variables (work conditions affecting human capital stock. Countries encouraging investments in the development of individuals both through formal education and inspiring work environments achieve higher sustainable economic growth
5. Intellectual Properties Rights-A strong determinant of economic growth in agriculture
Directory of Open Access Journals (Sweden)
Love Kumar Singh
2010-01-01
Full Text Available In the past few decades the subject of intellectual property rights (IPRs has occupied center stage in debates about globalization, economic development and poverty elimination. This study concerns the strengthening of IPRs in the plant breeding industry and its effect on agriculture in India. In India, most of the population relies on agricul-ture for its livelihood. India is self-sufficient in wheat and paddy, but deficient in other agricultural products. Pat-ents are good indicators of research and development output. Patent analysis makes it possible to map out the trend of technological change and life cycle of a technology - growth, development, maturity and decline. Patent infor-mation and patent statistical analysis have been used for examining present, technological status and to forecast future trends. One can determine the directions of corporate R&D and market interests by analyzing patent data. The present study is an attempt to analyze patents granted in India in the field of agriculture and importance of biotechnology-based innovations in agriculture
6. Intellectual Properties Rights-A strong determinant of economic growth in agriculture
Directory of Open Access Journals (Sweden)
Manju Chaudhary
2010-03-01
Full Text Available
In the past few decades the subject of intellectual property rights (IPRs has occupied center stage in debates about globalization, economic development and poverty elimination. This study concerns the strengthening of IPRs in the plant breeding industry and its effect on agriculture in India. In India, most of the population relies on agriculture for its livelihood. India is self-sufficient in wheat and paddy, but deficient in other agricultural products. Patents are good indicators of research and development output. Patent analysis makes it possible to map out the trend of technological change and life cycle of a technology – growth, development, maturity and decline. Patent information and patent statistical analysis have been used for examining present, technological status and to forecast future trends. One can determine the directions of corporate R&D and market interests by analyzing patent data. The present study is an attempt to analyze patents granted in India in the field of agriculture and importance of biotechnology-based innovations in agriculture
7. Ecological economics and economic growth.
Science.gov (United States)
Victor, Peter A
2010-01-01
Boulding's 1966 paper on the economics of spaceship Earth established the framework for ecological economics and an understanding of economic growth. In ecological economics, economies are conceptualized as open subsystems of the closed biosphere and are subject to biophysical laws and constraints. Economic growth measured as an increase in real gross domestic product (GDP) has generally been associated with increases in the use of energy and materials and the generation of wastes. Scale, composition, and technology are the proximate determinants of environmental impacts. They are often reduced to two: scale (GDP) and intensity (impact per unit GDP). New work described in this paper defines "green" growth as intensity that declines faster than scale increases. Similarly, "brown" growth occurs when intensity declines more slowly than increases in scale, and "black" growth happens when both scale and intensity increase. These concepts are then related to the environmental Kuznets curve, which can be understood as a transition from brown to green growth. Ecological economics provides a macroperspective on economic growth. It offers broad policy principles, and it challenges the primacy of economic growth as a policy objective, but many important questions remain.
8. <strong>Neuroeconomics and Health Economics/>
DEFF Research Database (Denmark)
Larsen, Torben
2009-01-01
Objective: Neuroeconomics integrates economics, psychology and neuroscience. Recently, this line of research is summarized in a neuroeconomic model (NeM) which addresses the rehabilitation of important chronic conditions from a new angle as surveyed in this study. Data and Method: Firstly, Ne......://www.integratedhomecare.eu/ . III. In-depth-relaxation is evidenced as the result of regular practice of medical meditation comprising various practical meditation settings by NGOs whereof some are rooted in the religious tradition while other aim to be post-religious. Medical meditation combines savings on health care costs...... with de-stressing benefits as reduced anxiety, less use of stimulants and a reduction of blood pressure which in all increase life-expectancy. Conclusion: Neuroeconomics helps economists to identify dominant health economic interventions that may be overlooked by traditional discipålines [i] This part...
9. Earthquakes and economic growth
OpenAIRE
Fisker, Peter Simonsen
2012-01-01
This study explores the economic consequences of earthquakes. In particular, it is investigated how exposure to earthquakes affects economic growth both across and within countries. The key result of the empirical analysis is that while there are no observable effects at the country level, earthquake exposure significantly decreases 5-year economic growth at the local level. Areas at lower stages of economic development suffer harder in terms of economic growth than richer areas. In addition,...
10. Quality, Export and Economic Growth
DEFF Research Database (Denmark)
1998-01-01
in an international context. The paper, therefore, addresses the complicated interactions between economic growth, export performance and quality. The contribution of the paper, compared to other growth accounting research, is the inclusion of quality data, quality being a significant mirror of technological...... development. The countries covered by the research represent a wide variation in terms of economic development, from poor LDC's to the most developed industrial nations. The empirical results reveal a probable strong relationship between quality/price and export growth as well as economic growth. This new...
11. Population growth and economic growth.
Science.gov (United States)
Narayana, D L
1984-01-01
This discussion of the issues relating to the problem posed by population explosion in the developing countries and economic growth in the contemporary world covers the following: predictions of economic and social trends; the Malthusian theory of population; the classical or stationary theory of population; the medical triage model; ecological disaster; the Global 2000 study; the limits to growth; critiques of the Limits to Growth model; nonrenewable resources; food and agriculture; population explosion and stabilization; space and ocean colonization; and the limits perspective. The Limits to Growth model, a general equilibrium anti-growth model, is the gloomiest economic model ever constructed. None of the doomsday models, the Malthusian theory, the classical stationary state, the neo-Malthusian medical triage model, the Global 2000 study, are so far reaching in their consequences. The course of events that followed the publication of the "Limits to Growth" in 1972 in the form of 2 oil shocks, food shock, pollution shock, and price shock seemed to bear out formally the gloomy predictions of the thesis with a remarkable speed. The 12 years of economic experience and the knowledge of resource trends postulate that even if the economic pressures visualized by the model are at work they are neither far reaching nor so drastic. Appropriate action can solve them. There are several limitations to the Limits to Growth model. The central theme of the model, which is overshoot and collapse, is unlikely to be the course of events. The model is too aggregative to be realistic. It exaggerates the ecological disaster arising out of the exponential growth of population and industry. The gross underestimation of renewable resources is a basic flaw of the model. The most critical weakness of the model is its gross underestimation of the historical trend of technological progress and the technological possiblities within industry and agriculture. The model does correctly emphasize
12. Strong growth for Queensland mining
Energy Technology Data Exchange (ETDEWEB)
1990-10-01
The Queensland mining industry experienced strong growth during 1989-90 as shown in the latest statistics released by the Department of Resource Industries. The total value of Queensland mineral and energy production rose to a new record of $5.1 billion, an increase of 16.5% on 1988-89 production. A major contributing factor was a 20.9 percent increase in the value of coal production. While the quantity of coal produced rose only 1.1 percent, the substantial increase in the value of coal production is attributable to higher coal prices negotiated for export contracts. In Australian dollar terms coal, gold, lead, zinc and crude oil on average experienced higher international prices than in the previous year. Only copper and silver prices declined. 3 tabs. 13. Environmentally Sustainable Economic Growth Directory of Open Access Journals (Sweden) Stelian Brad 2016-05-01 Full Text Available Economic growth and sustainable development are important issues for social prosperity. Sustainable development strives for moderate and responsible use within the economic activity of the limited resources of our planet, whereas economic growth does not limit the resource exploitation and energy, being mainly focused on productivity increase. From this perspective, both conceptual and operational contradictions occur between the two pillars of prosperity. This paper looks to these contradictions and proposes some streams of intervention such as economic growth and environmental sustainability to operate in harmony. A structured framework for innovative problem solving is considered in this respect. Results of this research show that it is possible to induce smart measures in the economic system for directing businesses towards new paradigms where economic growth is possible without negative effects on environmental sustainability. 14. FDI- Economic Growth Nexus DEFF Research Database (Denmark) Bujac, Andreea Ioana; Corado Cretu, Emanuel 2017-01-01 Conducting a systematic literature review on the topic of FDI and Economic Growth and investigating this relationship, along with the determinants of an economy that attract FDI and the externalities resulting from Foreign activities, it is found that FDI does have a positive effect on a host...... country’s economic growth but only with the preexistence of certain determinants which facilitate the absorption capacity of the host country on reaping the spillover effects (externalities) of FDI. Lastly, a framework was built to illustrate the interaction between FDI, Determinants and condition...... of the host economy, barriers to growth, economic growth and externalities.... 15. Armenia's Economic Growth Sustainability OpenAIRE Hayakawa, Tatsuji 2015-01-01 Armenia enjoyed 15 years of uninterrupted high economic growth prior to the global financial crisis in 2009. Investment, particularly in the mining and metallurgy sectors, played a key role as a driver of economic growth. Remittances，mostly from Russia, had an effect in sustaining consumption and boosting construction. Armenia has shown some weaknesses in the external sector, due to demands for natural gas, mineral products, machinery, and equipment. Armenia's exports and FDI suffer from the ... 16. Economic growth, ecological economics, and wilderness preservation Science.gov (United States) Brian Czech 2000-01-01 Economic growth is a perennial national goal. Perpetual economic growth and wilderness preservation are mutually exclusive. Wilderness scholarship has not addressed this conflict. The economics profession is unlikely to contribute to resolution, because the neoclassical paradigm holds that there is no limit to economic growth. A corollary of the paradigm is that... 17. Strong industrial base vital for economic revival CERN Multimedia 2001-01-01 At the inauguration of a 2-day conference on nuclear technology in Islamabad, the chairman of PAEC said that Pakistan needs to develop a strong industrial base and capability to export equipment to improve the economic condition of the country. He descibed how Pakistan has already had a breakthrough with the export of equipment to CERN, Geneva (1 page). 18. DETERMINANTS OF ECONOMIC GROWTH OpenAIRE Bartosz Totleben 2013-01-01 The article is examines the impact of macroeconomic indicators, in particular: human capital, government spending, innovation, political and social stability, on economic growth. In total 12 different indicators describing the economical, political and social conditions are taken into account. The study considers 102 countries between years 1960 and 2012 and two methods of estimation are performed: generalized method of moments (GMM) and fixed effects (FE). The results show the positive impac... 19. Economic Growth, Economic Freedom, and Governance OpenAIRE Cebula, Richard; Ekstrom, Marcus 2008-01-01 This exploratory study examines the impact of various forms of economic freedom and various dimensions of governance, as well as a number of economic factors, on economic growth among OECD nations. Empirical estimation finds that the natural log of per capita purchasing-power-parity adjusted real GDP in OECD nations is positively impacted by business freedom, monetary freedom, trade freedom, and property rights security. Economic growth is found to be negatively affected by perceived governme... 20. Entrepreneurial Diversity and Economic Growth NARCIS (Netherlands) I. Verheul (Ingrid); A.J. van Stel (André) 2007-01-01 textabstractMost studies investigating the relationship between entrepreneurship and economic growth treat entrepreneurs as a homogeneous group. This study investigates the impact of entrepreneurial diversity on national economic growth. Using data for 36 countries participating in the Global 1. Economic growth and business cycles NARCIS (Netherlands) Canton, E.J.F. 1997-01-01 This thesis contains five essays on economic growth and business cycles. The main focus is on the interaction between economic growth and the cycle: is cyclical variability good or bad for the long-run rate of economic growth? The introduction aims to provide some empirical evidence for an 2. Economic Growth Models Transition Directory of Open Access Journals (Sweden) Coralia Angelescu 2006-03-01 Full Text Available The transitional recession in countries of Eastern Europe has been much longer than expected. The legacy and recent policy mistakes have both contributed to the slow progress. As structural reforms and gradual institution building have taken hold, the post-socialist economics have started to recover, with some leading countries building momentum toward faster growth. There is a possibility that in wider context of globalization several of these emerging market economies will be able to catch up with the more advanced industrial economies in a matter of one or two generations. Over the past few years, most candidate countries have made progress in the transition to a competitive market economy, macroeconomic stabilization and structural reform. However their income levels have remained far below those in the Member States. Measured by per capita income in purchasing power standards, there has been a very limited amount of catching up over the past fourteen years. Prior, the distinctions between Solow-Swan model and endogenous growth model. The interdependence between transition and integration are stated in this study. Finally, some measures of macroeconomic policy for sustainable growth are proposed in correlation with real macroeconomic situation of the Romanian economy. Our study would be considered the real convergence for the Romanian economy and the recommendations for the adequate policies to achieve a fast real convergence and sustainable growth. 3. Economic Growth Models Transition Directory of Open Access Journals (Sweden) Coralia Angelescu 2006-01-01 Full Text Available The transitional recession in countries of Eastern Europe has been much longer than expected. The legacy and recent policy mistakes have both contributed to the slow progress. As structural reforms and gradual institution building have taken hold, the post-socialist economics have started to recover, with some leading countries building momentum toward faster growth. There is a possibility that in wider context of globalization several of these emerging market economies will be able to catch up with the more advanced industrial economies in a matter of one or two generations. Over the past few years, most candidate countries have made progress in the transition to a competitive market economy, macroeconomic stabilization and structural reform. However their income levels have remained far below those in the Member States. Measured by per capita income in purchasing power standards, there has been a very limited amount of catching up over the past fourteen years. Prior, the distinctions between Solow-Swan model and endogenous growth model. The interdependence between transition and integration are stated in this study. Finally, some measures of macroeconomic policy for sustainable growth are proposed in correlation with real macroeconomic situation of the Romanian economy. Our study would be considered the real convergence for the Romanian economy and the recommendations for the adequate policies to achieve a fast real convergence and sustainable growth. 4. Does FDI influence economic growth in Albania? Directory of Open Access Journals (Sweden) Aurel Koroci 2018-03-01 Full Text Available Foreign direct investment (FDI has been viewed as a power affecting economic growth (EG directly and indirectly during the past few decades. Foreign direct investment (FDI in developing countries brings economic development and enhances the international competitiveness of domestic enterprises. It is argued in the existing literature that foreign direct investment (FDI influences economic growth through technology diffusion, human capital formation, etc. FDI accounts for the largest and most important proportion of foreign capital in Albania, which undoubtedly plays an important role in the Albania’s economic development growth. However, as the country’s FDI increases, and in this paper I want to make an empirical research how the FDI has influenced the economic growth of the country. The findings revealed that there is a strong positive relationship between the FDI inflows and the GDP for the studied period which covers 1995 to 2012, thus a positive effect on the economic growth. 5. Strong sustainability in Nepal: A structural economics approach Science.gov (United States) Devkota, Surendra R. example of a poor country moving along a path toward strong sustainability. To this end, a sincere intervention at the social and natural capital along with economic growth is necessary. Poverty alleviation efforts should target the socio-economically deprived households by enriching their human capital. Since community based social structures, such as the forest user groups, are already setting an example of strong sustainability, such community based social capital initiatives should be encouraged by granting rights and other resources to augment further economic activities like harnessing hydropower that may eventually transform the socio-ecological-economic system. 6. Electricity regulation and economic growth OpenAIRE Costa, M. Teresa (Maria Teresa), 1951-; Garcia-Quevedo, Jose; Trujillo-Baute, Elisa 2018-01-01 The main objective of this paper is to analyse the effect of electricity regulation on economic growth. Although the relationship between electricity consumption and economic growth has been extensively analysed in the empirical literature, this framework has not been used to estimate the effect of electricity regulation on economic growth. Understanding this effect is essential for the assessment of regulatory policy. Specifically, we assess the effects of two major areas of regulation, rene... 7. Corporate Stability and Economic Growth OpenAIRE He, Kathy S.; Morck, Randall; Yeung, Bernard 2003-01-01 Greater instability in a country's list of top corporations is associated with faster economic growth. This faster growth is primarily due to faster growth in total factor productivity in industrialized countries, and faster capital accumulation in developing countries. These findings are consistent with the view that economic growth is more closely tied to the rise of new large firms than to the prosperity of established large firms. Although a stable list of leading corporations is highly c... 8. Technical Education and Economic Growth Indian Academy of Sciences (India) First page Back Continue Last page Graphics. Technical Education and Economic Growth. Technical Education and Economic Growth. Review of the Present Status. Expanding no.s and impairment of quality; Faculty shortage; Grim situation at Masters and PhD levels; Regional imbalance; Absence of International flavour ... 9. Human Development and Economic Growth OpenAIRE Ranis, Gustav 2004-01-01 Recent literature has contrasted Human Development, described as the ultimate goal of the development process, with economic growth, described as an imperfect proxy for more general welfare, or as a means toward enhanced human development. This debate has broadened the definitions and goals of development but still needs to define the important interrelations between human development (HD) and economic growth (EG). To the extent that greater freedom and capabilities improve economic performan... 10. SECTORAL SHARES AND ECONOMIC GROWTH DEFF Research Database (Denmark) Ahmad, Nisar; Naveed, Amjad; Naz, Amber 2013-01-01 believe that structural change is an unimportant side effect of the economic development. On the contrary, economists associated with the World Bank and some others posit that growth is brought about by the changes in sectoral composition. The objective of this study is to empirically test...... the relationship between sectoral shares and economic growth by using the panel data for 20 developed countries. The results of the granger causality suggest that both services and agriculture sectors do granger cause economic growth, whereas industrial sector does not granger cause growth. Reverse causality does...... not hold for any of the three sectors. The results of Barro and Non-Barro regressions along with the set of control variables have suggested that services sector is negatively affecting growth, whereas both industrial and agriculture shares are positively affect economic growth.... 11. Sociological explanations of economic growth. Science.gov (United States) Marsh, R M 1988-01-01 Even if questions of how resources are distributed within and between societies are the main concern, it is necessary to continue to grapple with the issue of the causes of economic growth since economic growth and level of development continue to be among the most important causes of inequality, poverty, unemployment, and the quality of life. This paper's dependent variable is the economic growth rate of 55 less developed countries (LDCs) over 2 time periods. 1970-78 and 1965-84. The causal model consists of control variables--level of development and domestic investment in 1965--and a variety of independent variables drawn from major sociological theories of economic growth published during the last 3 decades. Multiple regression analysis shows that, net of the effects of the 2 control variables, the variables which have the strongest effect on economic growth are: 1) direct foreign investment, which has a negative effect, 2) the proportion of the population in military service, and 3) the primary school enrollment ratio, both of which have positive effects on economic growth. On the other hand, variables drawn from some theories receive no empirical support. The mass media of communications, ethnolinguistic heterogeneity, democracy and human rights, income inequality, and state-centric theory's key variable, state strength, all fail to show any significant impact on economic growth rates when the control variables and the significant independent variables are held constant. The theoretical implications of these findings are discussed. 12. Structural modelling of economic growth: Technological changes Directory of Open Access Journals (Sweden) Sukharev Oleg 2016-01-01 Full Text Available Neoclassical and Keynesian theories of economic growth assume the use of Cobb-Douglas modified functions and other aggregate econometric approaches to growth dynamics modelling. In that case explanations of economic growth are based on the logic of the used mathematical ratios often including the ideas about aggregated values change and factors change a priori. The idea of assessment of factor productivity is the fundamental one among modern theories of economic growth. Nevertheless, structural parameters of economic system, institutions and technological changes are practically not considered within known approaches, though the latter is reflected in the changing parameters of production function. At the same time, on the one hand, the ratio of structural elements determines the future value of the total productivity of the factors and, on the other hand, strongly influences the rate of economic growth and its mode of innovative dynamics. To put structural parameters of economic system into growth models with the possibility of assessment of such modes under conditions of interaction of new and old combinations is an essential step in the development of the theory of economic growth/development. It allows forming stimulation policy of economic growth proceeding from the structural ratios and relations recognized for this economic system. It is most convenient in such models to use logistic functions demonstrating the resource change for old and new combination within the economic system. The result of economy development depends on starting conditions, and on institutional parameters of velocity change of resource borrowing in favour of a new combination and creation of its own resource. Model registration of the resource is carried out through the idea of investments into new and old combinations. 13. Innovation, resources and economic growth International Nuclear Information System (INIS) Curzio, A.Q.; Fortis, M.; Zoboli, R. 1994-01-01 The book is concerned with the following items: 1. Technological Creativity and Institutions, 2. Innovation at Work in an Historical-Economic Perspective: Energy and Industrial Materials, 3. Scientific Revolutions and Strategies of Economic Supremacy: Advanced Materials and Biotechnologies, 4. Economic Growth and Agro-Food Policies in Key Problem Regions: Former USSR and LDCs, 5. Economic Growth and Natural Resources at Risk: Climate Change, Forests and Water and in Conclusion: Innovation and Resources in a Global Policy Perspective. Only one chapter have regard to energy problems: Energie efficient technologies: past and future perspectives. (UA) 14. Blue Growth and Economics Directory of Open Access Journals (Sweden) Phoebe eKoundouri 2015-11-01 Full Text Available Oceans and seas represent over 70% of the earth's surface. Furthermore, living aquatic resources can provide a significant contribution to food, energy and bio-based products. However, marine ecosystems are subject to increasing pressures and competing usages, resulting from resources over-exploitation and pollution. In order to produce efficient marine management plans, it is essential to consider the total economic value provided by the marine ecosystems. In this review, we are focusing on the Marine Framework Strategy Directive and the European Marine Spatial Planning that are established for the protection and efficient use of the marine area. We present the ecosystem services approach with regards to the marine ecosystem and propose economic methods that capture the marine ecosystem’s total economic value in relation to the opportunity cost of marine space. Values should be used to guide policy makers following the European directives and initiatives. 15. Traffic fatalities and economic growth Science.gov (United States) 2003-04-01 As countries develop death rates usually fall, especially for diseases that affect the young and result in substantial life-years lost. Deaths due to traffic accidents are a notable exception: the growth in motor vehicles that accompanies economic gr... 16. Retail payments and economic growth OpenAIRE Hasan, Iftekhar; De Renzis, Tania; Schmiedel , Heiko 2012-01-01 This paper examines the fundamental relationship between retail payments and overall economic growth. Using data from across 27 European markets over the period 1995–2009, the results confirm that migration to efficient electronic retail payments stimulates overall economic growth, consumption and trade. Among different payment instruments, this relationship is strongest for card payments, followed by credit transfers and direct debits. Cheque payments are found to have a relatively low macro... 17. Institutions, Entrepreneurship, and Economic Growth DEFF Research Database (Denmark) Bjørnskov, Christian; Foss, Nicolai Juul 2016-01-01 sample limitations, omitted variable biases, causality issues, and response heterogeneity. We argue that theories in management research, such as the resource-based view, transaction cost economics, and strategic entrepreneurship theory, can fill some of the conceptual and theoretical gaps.......We review the literature that links institutions, entrepreneurship, and economic growth outcomes, focusing in particular on empirical research. Most of the literature has an economics orientation, but we also review relevant literature from other social sciences, including management research... 18. City Population Growth and Economic Growth DEFF Research Database (Denmark) Freire-Gibb, L. Carlos 2008-01-01 This article looks at the relationship between city population growth (intimately related to population proximity), and economic development. The hypothesis is that wherever dynamic and inclusive networks exist, there are more opportunities for economic development in this place. When these types...... of networks choose a tool (project, policy) to implement in the city, success will be more likely. Furthermore, virtuous circles will arise. The author gives an overview of two historical cases in urban growth, in Europe (1200-1800) and the U.S.A. (1800 to today).... 19. ECONOMIC GROWTH – COSTS AND DEVELOPMENT DISCREPANCES OpenAIRE Ion Bucur 2007-01-01 The economic growth shows an ascending tendency of the economic evolution over a long period of time, having favorable social and economic effects. Each economic growth factor acts simultaneous trough three dimensions. 20. Linking Ethics and Economic Growth DEFF Research Database (Denmark) Foss, Nicolai Juul 2012-01-01 Hunt (2012) builds on his work concerning ethics and resource-advantage theory to link personal ethical standards, societal norms, and economic growth but offers few details concerning the precise mechanisms that link ethics and growth. This comment suggests a number of such mechanisms – for exam...... – for example, the influence of prevailing ethical norms on the aggregate elasticity of substitution and, therefore, total factor productivity and growth.... 1. Political Instability and Economic Growth OpenAIRE Alberto Alesina; Sule Ozler; Nouriel Roubini; Phillip Swagel 1992-01-01 This paper investigates the relationship between political instability and per capita GDP growth in a sample of 113 countries for the period 1950-1982. We define ?political instability? as the propensity of a government collapse, and we estimate a model in which political instability and economic growth are jointly determined. The main result of this paper is that in countries and time periods with a high propensity of government collapse, growth is significantly lower than otherwise. This ef... 2. The role of energy in economic growth. Science.gov (United States) Stern, David I 2011-02-01 This paper reviews the mainstream, resource economics, and ecological economics models of growth. A possible synthesis of energy-based and mainstream models is presented. This shows that when energy is scarce it imposes a strong constraint on the growth of the economy; however, when energy is abundant, its effect on economic growth is much reduced. The industrial revolution released the constraints on economic growth by the development of new methods of using coal and the discovery of new fossil fuel resources. Time-series analysis shows that energy and GDP cointegrate, and energy use Granger causes GDP when capital and other production inputs are included in the vector autoregression model. However, various mechanisms can weaken the links between energy and growth. Energy used per unit of economic output has declined in developed and some developing countries, owing to both technological change and a shift from poorer quality fuels, such as coal, to the use of higher quality fuels, especially electricity. Substitution of other inputs for energy and sectoral shifts in economic activity play smaller roles. © 2011 New York Academy of Sciences. 3. Reduced Deforestation and Economic Growth OpenAIRE Patrick Doupe 2014-01-01 The clearing of forests for agricultural land and other marketable purposes is a well-trodden path of economic development. With these private benefits from deforestation come external costs: emissions from deforestation currently account for 12 per cent of global carbon emissions. A widespread intervention in reducing emissions from deforestation will affect the paths of agricultural expansion and economic growth of lower income nations. To investigate these processes, this paper presents a ... 4. Energy, economic growth, and human welfare International Nuclear Information System (INIS) Schurr, S.H. 1984-01-01 The subject is covered in sections, entitled: economic growth and human welfare; world-wide economic growth; economic growth and energy consumption; assessing the future; caution advised; energy supply and economic growth; supply as constraint; sound policies needed. (U.K.) 5. Exhaustible resources and economic growth International Nuclear Information System (INIS) Campbell, H.F. 1984-09-01 This study examines the effect of a booming natural resource sector on regional economic growth, with particular attention to the impact of regional government policy on mineral rent taxation and the allocation of resource revenues. The author's approach is first to document the relevant theory and then apply it to the case of the uranium industry in Saskatchewan 6. Knowledge Spillovers and Economic Growth NARCIS (Netherlands) A.J. van Stel (André); H.R. Nieuwenhuijsen 2002-01-01 textabstractThe importance of knowledge spillovers for achieving innovation and economic growth is widely recognized. It is not straightforward which type of spillovers is most effective: intra-sectoral spillovers or inter-sectoral spillovers. We investigate this controversy using a model of 7. Financial Liberalization and Economic Growth NARCIS (Netherlands) Bumann, S.; Hermes, N.; Lensink, B.W. 2013-01-01 This study provides a systematic analysis of the empirical literature on the relationship between financial liberalization and economic growth by conducting a meta-analysis, based on 441 t-statistics reported in 60 empirical studies. We focus on explaining the heterogeneity of results in our sample 8. Intangible capital and economic growth NARCIS (Netherlands) Chen, Wen 2016-01-01 Modern economic growth stems in good part from investments in knowledge-based intangible assets, such as research and development (R&D), organisational know-how, product design, branding and marketing. By capitalising expenditures on these intangibles as business investments, this thesis 9. ECONOMIC gROWTH, GLOBALIZATION AND TRADE OpenAIRE Nuno Carlos LEITÃO 2012-01-01 The purpose of this article is to investigate the relationship between economic growth, globalization and trade. The manuscript uses the assumptions of the economic growth exogenous and endogenous models. It introduces new proxies for explain the economic growth as in intra-industry trade, foreign direct investment and globalization index. The results indicate that economic growth is a dynamic process. The intra-industry has a positive impact on economic growth. This paper confirms relevan... 10. Economic growth and gender equality | IDRC - International ... International Development Research Centre (IDRC) Digital Library (Canada) And conversely, does gender equality impact economic growth? ... change and growth in the economy on women's employment opportunities and the type ... sectors and their overall effect on development outcomes, such as economic growth ... 11. Exports and economic growth in Nigeria Directory of Open Access Journals (Sweden) Goodly Otto 2016-09-01 Full Text Available Nigeria is an oil dependent economy, over 90 per cent of its exports receipts in recent years flow from petroleum but this sector is currently affected by local challenges, which include insecurity, oil thefts, sabotage and an unfriendly operational environment. These challenges are generating loses for the major producers and encouraging capital flight but amidst this situation, the economy is said to be having an impressive growth. This paradox informed this research. The study was designed to see the nexus between exports and economic growth in Nigeria. Using data from the Central Bank of Nigeria spanning 1980-2011, the study with the aid of OLS regression analysis found a strong relationship between Exports and economic growth in Nigeria. Nigeria will be better served if it diversifies its export base. It must also create structures that lead to better redistribution of export incomes within the local economy. 12. World economic growth pushing LNG use International Nuclear Information System (INIS) Brown, R.L.; Clary, R. 1997-01-01 Natural gas, especially liquefied (LNG), is in position to participate in the energy growth now being triggered by strong worldwide economic growth, increasingly open markets, and expanding international trade. Natural gas is abundant, burns cleanly, and is highly efficient in combined-cycle, gas-turbine power plants. Moreover, the comparative remoteness of much of the resource base to established and emerging markets can make LNG a compelling processing and transportation alternative. Discussed here are the resource distribution and emerging market opportunities that can make LNG attractive for monetizing natural-gas reserves 13. Population growth and economic development. Science.gov (United States) Corbridge, S 1989-01-01 The Malthusian and neo-Malthusian approaches to the role of population growth in economic development and resource depletion are briefly outlined. Three arguments are then presented that emphasize demographic determinism, empirical evidence, and cause and effect. The author concludes that non-coercive family planning programs may have a role to play in countries that are unable to reduce inequalities, particularly for the poor and for women. 14. Poverty, governance and economic growth Directory of Open Access Journals (Sweden) Kefi Mohamed Karim 2013-07-01 Full Text Available The objective of this paper is to study the effect of governance and povrety on economic growth of a set of eight developing countries during the period 2000-2009, using a dynamic and static panel data model and a simultaneous equations model. The key findings generated from these three empirical tests stipulate a negative effect of governance on povrety and a positive effect of political instability and corruption on poverty 15. Economic growth in a politically fragmented world Czech Academy of Sciences Publication Activity Database Jeong, Byeongju 2014-01-01 Roč. 42, č. 2 (2014), s. 402-416 ISSN 0147-5967 Institutional support: PRVOUK-P23 Keywords : economic integration * economic growth * intergenerational bargain Subject RIV: AH - Economics Impact factor: 1.170, year: 2014 16. Economic growth in a politically fragmented world Czech Academy of Sciences Publication Activity Database Jeong, Byeongju 2014-01-01 Roč. 42, č. 2 (2014), s. 402-416 ISSN 0147-5967 Institutional support: RVO:67985998 Keywords : economic integration * economic growth * intergenerational bargain Subject RIV: AH - Economics Impact factor: 1.170, year: 2014 17. Relationship Between Education Expenditure And Economic Growth ... African Journals Online (AJOL) The empirical part of the result shows that there is unidirectional relationship between education and economic growth with causality running from education expenditure to economic growth. The result therefore suggests that policy makers should boost expenditure on education as it will further improve economic growth in ... 18. Energy taxation and economic growth International Nuclear Information System (INIS) Seymour, Adam; Mabro, Robert. 1994-01-01 These two linked articles look at the relationship between policies aimed at taxing various energy sources and economic growth in the country, raising such taxes in order to decide how such fiscal policy can best serve the needs of developing nations. It is argued that, while many developing nations seek to protect internal energy markets by taxing imported petroleum products, a policy of domestic energy prices being set at the same level as their international equivalent costs is more consistent with the efficient management of long-term structural adjustment programmes. (UK) 19. Pakistan strong industrial base urged for economic progress CERN Multimedia 2001-01-01 A conference organized by Pakistan Nuclear Society urged that Pakistan should develop a strong industrial base and capability to export equipment for economic progress. The chairmen of PAEC pointed out that Pakistan is already showing remarkable progress in export of science-related equipment to CERN. He also asked scientists to wage a war against Pakistans inability to acquire indigenous technology (1 page). 20. Is Urban Economic Growth Inclusive in India? OpenAIRE Tripathi, Sabyasachi 2013-01-01 This paper measures the overall inclusive growth of a city by considering changing trends in the key economic variables based on ‘Borda ranking’ and establishes a relationship between city economic growth and overall city inclusive growth. By using data of 52 large cities in India, this paper finds that higher urban economic growth is associated with an increase in urban inequality, a reduction in urban poverty, and a lower level of overall inclusive growth of a city. 1. ECONOMIC GROWTH AND EQUALITY IN REDUCING POVERTY Directory of Open Access Journals (Sweden) Zaenal Muttaqin 2016-02-01 Full Text Available In some developing countries, the instrument to alleviate the poverty is by using the economic growth. So, the increasing in investment, infrastructure development, and macroeconomics stability always be priority from developing countries. In this article explain that economic growth is not the important factor to alleviate the poverty, because equality sometimes is more important rather than the economic growth. In this context, its measure by inequality growth trade off index (IGTI. This method is to measure the influence of economic growth to reducing the inequality, with this method every country can measure which one is better to reducing the poverty whether the economic growth or equality. With this method, Laos in 2000 show that economic growth is more important than equality, but in the same year in Thailand show that equality is more important than economic growth.DOI: 10.15408/sjie.v1i1.2592 2. What are the "ingredients" for economic growth? OpenAIRE Wolla, Scott A. 2013-01-01 Is there a recipe for economic growth? Perhaps some Miracle-Gro for the economy? If only it were that easy. While the exact recipe is a mystery, economists have identified some of the key ingredients. This month’s newsletter discusses the role that economic institutions play in fostering long-term economic growth. 3. REFERENCE MODELS OF ENDOGENOUS ECONOMIC GROWTH OpenAIRE GEAMĂNU MARINELA 2012-01-01 The new endogenous growth theories are a very important research area for shaping the most effective policies and long term sustainable development strategies. Endogenous growth theory has emerged as a reaction to the imperfections of neoclassical theory, by the fact that the economic growth is the endogenous product of an economical system. 4. Economics of Sustainable Development. Competitiveness and Economic Growth Directory of Open Access Journals (Sweden) Dorel AILENEI 2011-02-01 Full Text Available Economic growth is one of the most important issues of humanity. Both in national economies and world economy, recession and prosperity periods are regularly succeeding with different amplitudes. But beyond these fluctuations and their effects, the results are important: performance and economic growth. Because of the problematical issue of economic growth, the authors are trying to critically reflect on the economic growth concept and on its implications on the praxis area. Although there is a large literature about economic growth modeling, it is intriguing that there still are some serious obstacles for conceptualization and praxis. Only the simple fact that the economic growth process needs serious thinking on the time dimension is sufficient for understanding the real difficulties of this problematical issue. As for the economic growth praxis, a clear analysis of the interests system within an economy is needed. Without trying to find miraculous solutions for the economic growth issue, the authors suggest a clear and correct analysis of this important subject. 5. ICTs, Economic Growth and Poverty | IDRC - International ... International Development Research Centre (IDRC) Digital Library (Canada) ICTs, Economic Growth and Poverty ... new information and communication technologies (ICTs) as a lever for economic and social development. ... Socially equitable climate action is essential to strengthen the resilience of all people, without ... 6. REMITTANCES AND ECONOMIC GROWTH IN TURKEY Directory of Open Access Journals (Sweden) Huseyin KARAMELIKLI 2015-07-01 Full Text Available Savings are one of the important determinants beyond the theories of economic growth. Therefore remittances and foreign direct investment inflows have importance for the countries having insufficient savings. This study examines the relationship between economic growth, remittances, foreign direct investment inflows and gross domestic savings in Turkey during the period 1974-2013 by using Autoregressive Distributed Lag approach. We found that remittances, foreign direct investment and gross domestic savings had positive impact on economic growth. 7. On the relationship between economic freedom and economic growth NARCIS (Netherlands) Haan, Jakob de; Sturm, Jan-Egbert 1999-01-01 Often it is maintained that economic freedom may further high levels of economic growth. This paper compares various indicators for economic freedom. It is concluded that although these measures differ somewhat in their coverage, they show similar rankings for the countries covered. Some elements in 8. 150 Years of Italian CO2 Emissions and Economic Growth DEFF Research Database (Denmark) Annicchiarico, Barbara; Bennato, Anna Rita; Chini, Emilio Zanetti This paper examines the relationship between economic growth and carbon dioxide emissions in Italy considering the developments in a 150-year time span. Using several statistical techniques, we find that GDP growth and carbon dioxide emissions are strongly interrelated, with a dramatic change... 9. Financial Development, Environmental Quality and Economic Growth Directory of Open Access Journals (Sweden) Shushu Li 2015-07-01 Full Text Available In this study, the relationships between financial development, environmental quality and economic growth are studied based on data from 102 countries over the period 1980–2010 using the generalized method of moments (GMM estimation. The econometric results show the following three basic conclusions: First, both financial development and environmental quality have a significant impact on economic growth and should be included in the production function of the economic growth model as important variables. Second, there is a significant and robust “inverted U-shaped” relationship between financial development and economic growth; with the improvement of the level of financial development, economic growth would first increase and then decrease, which is consistent with the results of previous studies. Third, there is also a significant and robust “inverted U-shaped” relationship between economic growth and carbon emissions, indicating that there exists a “critical point” at which achieving economic growth comes at the expense of environmental quality, and after passing the critical point, the deterioration of environmental quality will lead to a significant slowdown in economic growth. In addition, the econometric analysis in this paper also shows that there was a mutually promoting and strengthening relationship between financial development and environmental quality. Specifically, the degree of financial development can further strengthen the promoting effect of environmental quality on economic growth; meanwhile, an improvement in environmental quality can also strengthen the promoting effect of financial development on economic growth. Financial development and environmental quality could influence economic growth through strengthening the marginal product effects of capital and labor, which further indicates the that both financial and environmental factors play an important role in modern economic development. 10. Why higher economic growth cannot always enhance human development OpenAIRE Ahmed, Md Montasir 2017-01-01 This paper studies why higher economic growth cannot always enhance human development. In general, these two dimensions have a strong and positive relationship, but some countries appear unable to balance this relationship. As a consequence, there are some countries with high economic growth but sluggish human development progress. This paper studies how other factors besides GDP – women labor force participation, urbanization, and inequality - are correlated to human development. I construct... 11. Regional Economic Growth; Socio-Economic Disparities among Counties Directory of Open Access Journals (Sweden) Salih Özgür SARICA 2014-12-01 Full Text Available State level economy has always been relying on its major metropolitan area’s economic success. So, such metropolitan agglomerations have been considered the only agents that can foster the state’s economic standing as if other economic places do (or may not have significant contribution to the regional economy. In contrast, as some major cities enhance their economic well-being and agglomerate in specialized sector, the rest of the region lose their economic grounds or stay constant by widening the economic gap among cities. Therefore, an institutional approach can help to establish new regional arrangements to substitute all economic places to coordinate each other and succeed the economic growth as part of state government by reducing the disparities. In this sense, this study builds upon the inquiry that seeks the impacts of some economic disparities among economic places (counties on the performances of state level regional economy. 12. [Economic growth with zero population growth and with declining population]. Science.gov (United States) Kurz, R 1982-05-01 The effects of both zero population growth and a declining population on economic growth are considered. Although the neoclassical theory of economic growth leads to optimistic results in such cases, the author suggests that this theory cannot be used as a basis for political action. The need for further research into the economic effects of a stationary or declining population is stressed. (summary in ENG) 13. Determinants of economic growth in BRIC countries OpenAIRE Rajjev K. Goel 2011-01-01 We study economic growth in four emerging economies - Brazil, Russia, India, and China (BRIC). Questions addressed are: (a) How do medium term growth determinants differ from short term determinants? (b) What are differences between growth effects of aggregate versus disaggregated exports? And (c) Does lower institutional quality hinder growth? Results show that while BRIC nations have higher growth, there are significant within-group differences. China and Russia mostly showed higher growth,... 14. ECONOMIC GROWTH THEORIES, CONCEPTUAL ELEMENTS, CHARACTERISTICS Directory of Open Access Journals (Sweden) Florina, POPA 2014-11-01 Full Text Available The approach of economic growth involves understanding the concept and growth factors, respectively, analysing the growth theories, their trend in the context of the development of economic and social life. The economic growth signifies a process aimed at increasing activities in the national economy, expressed by macroeconomic indicators, respectively, the dynamics of the overall Gross Domestic Product or per inhabitant. It can appreciate that, in the short term, this process signifies phases of economic prosperity and on the long-term, expresses an upward trend, a consequence of the succession of increases and decreases. The study presents some elements which outlines the concept of economic growth, that is, definitions, meanings and the main characteristics of the theories of growth, as well as some of its determinant factors. Also, it gives a brief overview of the main theories of economic growth, as they have evolved over time, in line with the economic reality dynamics and the development of the instruments of economic analysis, starting from the classical theories to the new theories and models of economic growth of the modern age. 15. Electrification, economic growth and uranium power International Nuclear Information System (INIS) Starr, C. 1982-01-01 It is argued that the expanded use of nuclear power is essential to provide a substantial portion of the electricity necessary for world economic growth. However, obstacles to this growth arise not from the technology but rather from the inadequacies of our industrial, political, and economic institutions needed to manage this new energy system effectively, nationally and internationally. (U.K.) 16. CORRELATION BETWEEN ECONOMIC GROWTH AND UNEMPLOYMENT Directory of Open Access Journals (Sweden) Savu Mihaela 2013-06-01 Full Text Available The mankind progress is built on economic growth.Yet, the high rates of economic growth must be properly used and correlated with other macroeconomic indicators in order to get the aimed effects.At the Romanian economic level, there is an inverse ratio connection between the gross domestic product and the unemployed number, a connection of low intensity.The correlation of these two indicators was established using parametric and nonparametric methods of analyzing the statistic connection using the informatic soft. Setting the recession function allows us to calculate the unemployed number depending on the forecasting of the economic growth in Romania. 17. TOURIST ARRIVALS AND ECONOMIC GROWTH IN SARAWAK OpenAIRE Lau, Evan; Oh, Swee-Ling; Hu, Sing-Sing 2008-01-01 This study empirically investigates the comovements and the causality relationship between tourist arrivals and economic growth in Sarawak during the period of 1972 to 2004. The empirical evidence clearly shows that the long run causality running from tourist arrivals to economic growth in the estimation period. As one of the income generator for Sarawak, the findings are consistent with economic theory and proffer important policy conclusions. 18. Energy and economic growth in industrializing countries Energy Technology Data Exchange (ETDEWEB) Samouilidis, J E; Mitropoulos, C S 1984-07-01 This paper investigates some aspects of the interrelated paths of economic growth and energy demand, in the case of an industrializing economy, through the use of numerous econometric models. Translog functions have helped establish that income and price elasticities of energy, two critical parameters in the energy-economy interaction, exhibit falling trends with time. The value share of the industrial sector is strongly associated with both energy demand and energy intensity. Any increase in the former will lead to amplified increases in the latter, rendering the continuation of past trends in industrial expansion questionable under conditions of high energy costs. Substitution among capital, labor and energy does take place, though to a limited extent, as indicated by the aggregate measure of energy/non-energy substitution elasticity. All findings appear to suggest that energy policymaking, in an industrializing country like Greece, will be of low effectiveness until certain structural changes in the economy are realized. 19. Bioenergy, Pollution, and Economic Growth International Nuclear Information System (INIS) Ankarhem, Mattias 2005-01-01 This thesis consists of four papers: two of them deal with the effects on the forest sector of an increase in the demand for forest fuels, and two of them concern the relation between economic growth and pollution. Paper [I] is a first, preliminary study of the potential effects on the Swedish forest sector of a continuing rise in the use of forest resources as a fuel in energy generation. Sweden has made a commitment that the energy system should be sustainable, i.e., it should be based on renewable resources. However, an increasing use of the forest resources as an energy input could have effects outside the energy sector. We consider this in a static model by estimating a system of demand and supply equations for the four main actors on the Swedish roundwood market; forestry, sawmills, pulpmills and the energy sector. We then calculate the industries' short run supply and demand elasticities. Paper [II], is a development of the former paper. In this paper, we estimate the dynamic effects on the forest sector of an increased demand for forest fuels. This is done by developing a partial adjustment model of the forest sector that enables short, intermediate, and long run price elasticities to be estimated. It is relevant to study the effects of increased demand for forest fuels as the Swedish government has committed to an energy policy that is likely to further increase the use of renewable resources in the Swedish energy system. Four subsectors are included in the model: forestry, sawmills, pulpmills and the energy industry. The results show that the short run elasticities are fairly consistent with earlier studies and that sluggish adjustment in the capital stock is important in determining the intermediate and long run responses. Simulation shows that an increase in the demand for forest fuels has a positive effect on the equilibrium price of all three types of wood, and a negative effect on the equilibrium quantities of sawtimber and pulpwood. In paper [III] a 20. Bioenergy, Pollution, and Economic Growth Energy Technology Data Exchange (ETDEWEB) Ankarhem, Mattias 2005-04-15 This thesis consists of four papers: two of them deal with the effects on the forest sector of an increase in the demand for forest fuels, and two of them concern the relation between economic growth and pollution. Paper [I] is a first, preliminary study of the potential effects on the Swedish forest sector of a continuing rise in the use of forest resources as a fuel in energy generation. Sweden has made a commitment that the energy system should be sustainable, i.e., it should be based on renewable resources. However, an increasing use of the forest resources as an energy input could have effects outside the energy sector. We consider this in a static model by estimating a system of demand and supply equations for the four main actors on the Swedish roundwood market; forestry, sawmills, pulpmills and the energy sector. We then calculate the industries' short run supply and demand elasticities. Paper [II], is a development of the former paper. In this paper, we estimate the dynamic effects on the forest sector of an increased demand for forest fuels. This is done by developing a partial adjustment model of the forest sector that enables short, intermediate, and long run price elasticities to be estimated. It is relevant to study the effects of increased demand for forest fuels as the Swedish government has committed to an energy policy that is likely to further increase the use of renewable resources in the Swedish energy system. Four subsectors are included in the model: forestry, sawmills, pulpmills and the energy industry. The results show that the short run elasticities are fairly consistent with earlier studies and that sluggish adjustment in the capital stock is important in determining the intermediate and long run responses. Simulation shows that an increase in the demand for forest fuels has a positive effect on the equilibrium price of all three types of wood, and a negative effect on the equilibrium quantities of sawtimber and pulpwood. In paper 1. Coal consumption and economic growth in Taiwan International Nuclear Information System (INIS) Yang, H.Y. 2000-01-01 The purpose of this paper is to examine the causality issue between coal consumption and economic growth for Taiwan. The co-integration and Granger's causality test are applied to investigate the relationship between the two economic series. Results of the co-integration and Granger's causality test based on 1954--1997 Taiwan data show a unidirectional causality from economic growth to coal consumption with no feedback effects. Their major finding supports the neutrality hypothesis of coal consumption with respect to economic growth. Further, the finding has practical policy implications for decision makers in the area of macroeconomic planning, as coal conservation is a feasible policy with no damaging repercussions on economic growth 2. Export and Economic Growth in the West Balkan Countries Directory of Open Access Journals (Sweden) Florentina Xhelili Krasniqi 2017-09-01 Full Text Available The aim of this paper is to explore the effects of exports and other variables (foreign direct investment, remittances, capital formation, and labour force on economic growth in West Balkan countries (Albania, Kosovo, Macedonia, Montenegro, Bosnia and Herzegovina and Serbia. This study utilizes a strongly balanced panel data over the 2005-2015 period for Western Balkan countries using the ordinary least squares method (OLS, ie Pooled regression model to evaluate the parameters. The relationship between export and economic growth has turned to be statistically significant and positively related for the countries under the study. Results also indicate the statistically significant positive relationship between economic growth and other variables included in the model such is remittances, capital formation, and labor. The relationship between economic growth and foreign direct investment has turned out to be statistically insignificant and negatively related. 3. Fiscal Policy and Economic Growth in Nigeria Directory of Open Access Journals (Sweden) Sylvia Uchenna Agu 2015-11-01 Full Text Available This article aims at determining the impact of various components of fiscal policy on the Nigerian economy. We simply used descriptive statistics to show contribution of government fiscal policy to economic growth, and to ascertain and explain growth rates, and an ordinary least square (OLS in a multiple form to ascertain the relationship between economic growth and government expenditure components after ensuring data stationarity. Findings revealed that total government expenditures have tended to increase with government revenue, with expenditures peaking faster than revenue. Investment expenditures were much lower than recurrent expenditures evidencing the poor growth in the country’s economy. Hence, there is some evidence of positive correlation between government expenditure on economic services and economic growth. Therefore, in public spending, it is important to note that the effectiveness of the private sector depends on the stability and predictability of the public incentive framework, which promotes or crowds out private investment. 4. Entrepreneurship Education and Economic Growth DEFF Research Database (Denmark) Pedersen, Jonna; Lindquist, Carl Rickard . This paper addresses the presumptions behind the project. The presumptions in relation to entrepreneurship demonstrate that the effort should target both growth entrepreneurs and SMEs in a wide sense; there is a need for growth entrepreneurs with ambitions to generate breakthrough innovation as well... 5. An Accounting Method for Economic Growth OpenAIRE Hongchun Zhao 2012-01-01 As Chari et al. (2007) indicate, many growth theories explaining frictions in real economies are equivalent to a competitive economy, with some exogenous taxes. Using this idea, I developed an accounting method for identifying fundamental causes of economic growth. A two-sector neoclassical growth model with taxes is used as a prototype economy, and its equilibrium conditions define wedges. These wedges endogenously determine the long run growth rate, which is exogenous and not correlated wit... 6. Corruption and economic growth with non constant labor force growth Science.gov (United States) Brianzoni, Serena; Campisi, Giovanni; Russo, Alberto 2018-05-01 Based on Brianzoni et al. [1] in the present work we propose an economic model regarding the relationship between corruption in public procurement and economic growth. We extend the benchmark model by introducing endogenous labor force growth, described by the logistic equation. The results of previous studies, as Del Monte and Papagni [2] and Mauro [3], show that countries are stuck in one of the two equilibria (high corruption and low economic growth or low corruption and high economic growth). Brianzoni et al. [1] prove the existence of a further steady state characterized by intermediate levels of capital per capita and corruption. Our aim is to investigate the effects of the endogenous growth around such equilibrium. Moreover, due to the high number of parameters of the model, specific attention is given to the numerical simulations which highlight new policy measures that can be adopted by the government to fight corruption. 7. Investor Protections and Economic Growth OpenAIRE Haidar, Jamal Ibrahim 2009-01-01 Using objective measures of investor protections in 170 countries, I establish that the level of investor protection matters for cross-country differences in GDP growth: countries with stronger protections tend to grow faster than those with poor investor protections. 8. EVIDENCE ON EMPLOYMENT RATE AND ECONOMIC GROWTH Directory of Open Access Journals (Sweden) Cornelia VĂCEANU 2014-11-01 Full Text Available This paper explores a causal relationship between employment rate and economic growth for European Union countries, in general, and produces a structural assessment of employment on the background of labour market dynamics. Economic growth is the key in economic theory and the main source of well-being and quality of life. Since the 2008 financial crisis, most European countries have experienced job shortage and unemployment problem, but today's European economic outlook is strengthening on the bases of a GDP growing momentum. Empirical data shows, regardless the GDP's moderate positive trend, the employment rate did not increase enough. Given this, the present analysis address the question: to what extent the employment rate is affected by economic growth? 9. The economic growth of oil countries International Nuclear Information System (INIS) Arbod, G. 2007-02-01 The literature tries to apprehend the weakness of the economic growth of oil culminates by the assumption of ousted growth factors. In the Dutch Disease models the non-oil exporting sector would be ousted whereas in the analyses in terms of economic policies it would be the efficient economic policies. We consider the phenomenon through the growth theories, the oil income being regarded as an additional exogenous income for the economy. In this manner the growth dynamic of oil countries, even the most unfavourable, can be modelled without utilizing any concept of economic inefficiency. The last part of our work is devoted to the Saudi economy. After having developed a macro-econometric model, and using scenarios of oil prices, we lead a forecasted analysis of this economy. (author) 10. Growth and Economic Opportunities for Women | IDRC ... International Development Research Centre (IDRC) Digital Library (Canada) GrOW works with research teams around the world to generate evidence on ... Growth and Economic Opportunities for Women ... IDRC “unpacks women's empowerment” at McGill University Conference ... Careers · Contact Us · Site map. 11. Public Debt, Corruption and Sustainable Economic Growth Directory of Open Access Journals (Sweden) Eunji Kim 2017-03-01 Full Text Available There are many studies that look into the relationship between public debt and economic growth. It is hard to find, however, research addressing the role of corruption between these two variables. Noticing this vacancy in current literature, we strive to investigate the effect of corruption on the relationship between public debt and economic growth. For this purpose, the pooled ordinary least squares (OLS, fixed effects models and the dynamic panel generalized method of moments (GMM models (Arellano-Bond, 1991 are estimated with data of 77 countries from 1990 to 2014. The empirical results show that the interaction term between public debt and corruption is statistically significant. This confirms the hypothesis that the effect of public debt on economic growth is a function of corruption. The sign of the marginal effect is negative in corrupt countries, but public debt enhances economic growth within countries that are not corrupt, i.e., highly transparent. 12. Islam and Economic Growth in Malaysia National Research Council Canada - National Science Library bin 2003-01-01 .... This thesis discusses nation building by fusing Islam, pluralism, democracy, and modernity. It argues that Malaysia's religious tolerance and adherence to western development models fostered economic growth since its independence... 13. Stages of growth in economic development Czech Academy of Sciences Publication Activity Database Kejak, Michal 2003-01-01 Roč. 27, č. 5 (2003), s. 771-800 ISSN 0165-1889 Institutional research plan: CEZ:AV0Z7085904 Keywords : growth * human capital * development Subject RIV: AH - Economics Impact factor: 0.690, year: 2003 14. Public Debt and Economic Growth in Malaysia OpenAIRE Siew-Peng Lee; Yan-Ling Ng 2015-01-01 Public debt in the Malaysia increased because of fiscal expansions. This study examines whether public debt contributed to the economic growth in Malaysia over the period 1991 to 2013. It also examines whether other indicators of debt burden, such as budget deficit, budget expenditure, and external debt service and government consumption, have an impact on economic growth. The results of this study are consistent with the existing literature that found a negative association between diet and ... 15. Essays on industrial structure and economic growth International Nuclear Information System (INIS) Nordaas, Hildegunn Kyvik 1997-01-01 The book is a thesis submitted for the degree of dr. polit. at the University of Bergen. It has chapters on economic development and industrial structure, trade and growth with static and dynamic economies of scale, terms of trade and economic growth in a world of constrained capital mobility, how liberalization of trade in services may conserve natural reserves, some reasons why capital does not flow from rich to poor counties and finally on South African manufacturing industries - catching up or falling behind 16. FINANCIAL INTERMEDIATION, ENTREPRENEURSHIP AND ECONOMIC GROWTH OpenAIRE Wenli Cheng 2007-01-01 This paper presents a simple general equilibrium model of financial intermediation, entrepreneurship and economic growth. In this model, the role of financial intermediation is to pool savings and to lend the pooled funds to an entrepreneur, who in turn invests the funds in a new production technology. The adoption of the new production technology improves individual real income. Thus financial intermediation promotes economic growth through affecting individuals’ saving behaviour and enabl... 17. HEALTH, EDUCATION AND ECONOMIC GROWTH IN MALAYSIA OpenAIRE Rahmah Ismaila and Doris Padmini Selvaratnamb 1999-01-01 Human capital is vital for the development of a country. Investment in human capital ranges from basic needs expenditure to education and health provision. Economic growth is often used to measure the progress and development of a country. Today other indicators are used to emphasize physical quality of life, for example, education, health and basic needs provision. Using a simultaneous equation model, this paper estimates the relationship between economic growth and human capital variables i... 18. Impact of Globalisation On Economic Growth in Romania: An Empirical Analysis of Its Economic, Social and Political Dimensions Directory of Open Access Journals (Sweden) Olimpia Neagu 2017-04-01 Full Text Available The paper analyses the link between globalisation and economic growth in Romania for a time span of 24 years. Data from World Bank were used in an econometrical model in order to highlight the impact of globalisation, expressed by the KOF globalisation index and its components (economic, social and political globalisation indices on economic growth rate. A statistical strong and positive link is found between GDP per capita dynamics and overall globalisation index as well as between GDP growth rate and economic and political globalisation, except the social dimension of globalisation which has a negative impact on economic growth in Romania for the time span 1990-2013. 19. Energy consumption and economic growth Energy Technology Data Exchange (ETDEWEB) Brookes, L G 1972-10-01 A mathematical model relating Gross National Product (GNP) per capita to useful energy consumed per capita is demonstrated to predict the shift in this relationship actually experienced in the U.K. and the U.S. over a period of years. World GNP growths in the recent past are used to forecast GNP growth to the year 2030 and also (via the model) the necessary fuel consumption for such growth; likewise, potential production of fossil fuels (exclusive of tar sands and oil shale) is shown to 2030, based on two different assumptions about total world reserves. Fossil fuel ceases to meet world requirements for energy at some time between 1985 and 1995. The most likely candidate for filling the gap is nuclear power. 20. Institutions and economic growth : summary and synthesis NARCIS (Netherlands) Szirmai, A. 2013-01-01 This paper provides a summary, overview and synthesis of the findings of the second phase of the AFD/Maastricht Graduate School of Governance research project on institutions and economic growth. The point of departure for this research project is that the diversity of longrun patterns of economic 1. Global warming and economic growth International Nuclear Information System (INIS) Gonand, Frederic 2015-01-01 The macro-economic impacts of climate change and of policies to reduce carbon content should be moderate on a global basis for the planet - a few hundredths of a % of world GDP on an annual basis, but significant for some regions (Asia-Pacific notably). The probability of extreme climatic events justifies with effect from today the implementation of measures that will carry a cost in order to limit global warming. (author) 2. Equity, Economic Growth and Lifestyle DEFF Research Database (Denmark) Meyer, Niels I; Nørgaard, Jørgen; Hvelplund, Frede 2011-01-01 sources (RES) in the supply sector and energy efficiency in the demand sector. Much less attention has been given to potential changes in life style and to alternative economic and social systems. This chapter will focus on non-technological strategies for mitigation of global warming including...... such questions as national and international equity, “limits to growth”, alternative employment policies, military and security policy and alternatives to traditional GDP as the dominant indicator of welfare and of sound development.... 3. Government expenditure and economic growth nexus: Wagner's law ... African Journals Online (AJOL) The Granger causality test was performed within vector error correction model and the results revealed strong support for both Wagner's law and Keynesian hypothesis when ... Wagner's law was only supported in one instance where causality runs from economic growth to development expenditure from domestic sources. 4. Foreign direct investment, financial development and economic growth NARCIS (Netherlands) Hermes, Niels; Lensink, Robert 2000-01-01 FDI may help to raise economic growth in recipient countries. Yet, the contribution FDI can make may strongly depend on the circumstances in the recipient countries. This paper argues that the development of the financial system of the recipient country is an important precondition for FDI to have a 5. Cultural diversity and economic growth DEFF Research Database (Denmark) Ager, Philipp; Brückner, Markus 2013-01-01 We exploit the large inflow of immigrants to the US during the 1870–1920 period to examine the effects that within-county changes in the cultural composition of the US population had on output growth. We construct measures of fractionalization and polarization to distinguish between the different... 6. Financial development, uncertainty and economic growth NARCIS (Netherlands) Lensink, B.W. By performing a cross-country growth regression for the 1970-1998 period this paper finds evidence for the fact that the impact of policy uncertainty on economic growth depends on the development of the financial sector. It appears that a higher level of financial development partly mitigates the 7. Export Specialisation and Local Economic Growth NARCIS (Netherlands) Naude, Wim; Bosker, Maarten; Matthee, Marianne This paper aims to provide empirical evidence on whether export specialization or diversification is better for local economic growth. Using export data from 354 magisterial districts of South Africa for 1996 and 2001 we estimate spatial growth regressions that include measures of the degree of 8. Conflict Between Economic Growth and Environmental Protection Energy Technology Data Exchange (ETDEWEB) Czech, Bryan 2012-01-09 The conflict between economic growth and environmental protection may not be reconciled via technological progress. The fundamentality of the conflict ultimately boils down to laws of thermodynamics. Physicists and other scholars from the physical sciences are urgently needed for helping the public and policy makers grasp the conflict between growth and environmental protection. 9. Economic Growth and Government Spending Nexus: Empirical ... African Journals Online (AJOL) The results highlight the need for policy makers to shift public outlays towards investment in physical infrastructure which will stimulate growth and consequently improve fiscal sustainability as opposed to recurrent expenditure. Keywords: Economic Growth, Fiscal Policy, Cointegration, Causality, Wagner' Law ... 10. Education and Economic Growth in Nigeria: A Granger Causality ... African Journals Online (AJOL) FIRST LADY expenditures on education, primary school enrolment and economic growth. The tests revealed ..... force possessed a positive and significant impact on economic growth through factor ..... Export and Economic Growth in Namibia: A Granger ... 11. Money Supply, Interest Rate, and Economic Growth in Cameroon: A ... African Journals Online (AJOL) Money Supply, Interest Rate, and Economic Growth in Cameroon: A Time Series ... the impacts of money and interest rate on economic growth and development. ... Money Supply, Interest Rates, Economic growth, Co-integration and Inflation. 12. Clean versus Dirty Economic Growth OpenAIRE Palokangas, Tapio 2012-01-01 This document considers an economy with many regions and two engines of growth: horizontal R&D, which increases the number of polluting product lines; and vertical R&D, which improves productivity in these lines. Pollution in any region decreases welfare in all regions. Any group of regions can form a jurisdiction where a common policy maker controls pollution. Large jurisdictions, which can better internalize externality through pollution, perform vertical R&D. Because jurisdictions face dec... 13. Green attitude and economic growth OpenAIRE Ott, Ingrid; Soretz, Susanne 2015-01-01 We analyse the interdependence between green attitude and equilibrium development of environmental quality in an endogenous growth model. Individuals take only part of their impact on pollution into account, hence there is a negative externality of capital accumulation on environmental quality. Increasing wealth or increasing pollution enhance green attitude and reduce the externality, because individuals care more about the environment if their income is higher or if pollution is more obviou... 14. Local Decentralisation and Economic Growth in Nigeria Directory of Open Access Journals (Sweden) Hammed Adetola Adefeso 2014-06-01 Full Text Available The current global drive towards devolution of financial resources and responsibilities has been increasingly justified on the basis that greater transfers of these financial resources and responsibilities to sub-central governments are theoretically expected to deliver greater economic efficiency in the provision of public goods and services and hence greater economic growth. There is a mixed result on these theoretical expectations across earlier empirical literatures. Using the instrumental variables (IV technique of analysis with the recent data from Nigeria for the period 1970-2013, this study found no robust significant effect of the decentralisation of spending or revenue on growth of real GDP per capital in Nigeria. The implication of this to the policy makers is that when it comes to the determinants of improved economic activities, decentralisation either fiscal expenditure or revenue side would not be instrumental to economic growth possibly because of existence of endemic corruption among politicians in Nigeria. 15. Competitiveness and Economic Growth in Romanian Regions Directory of Open Access Journals (Sweden) Simionescu Mihaela 2016-12-01 Full Text Available Considering the fact that Romanian economy competitiveness is not based on innovation and investment in human capital, this study makes an empirical evaluation of the impact of occupation and unemployment in Romanian counties on the economic growth. The approach based on panel vector-autoregressive (panel VAR models indicated a negative impact of occupation and activity rate in 42 Romanian counties on the economic growth during 2006-2014. On the other hand, the real economic growth was achieved at high unemployment rates. These results are contrary to previous studies in literature and are due to a structural economic crisis and to lack of labour productivity and investment in human capital. Further policy measures should focus on structural unemployment decrease, more skilled labour force according to labour market needs, lifelong learning, higher performance and quality of education system, promotion of social inclusion, poverty control. 16. Determinants of economic growth: will data tell? OpenAIRE Ciccone, Antonio; Jarociński, Marek 2008-01-01 Many factors inhibiting and facilitating economic growth have been suggested. Will international income data tell which matter when all are treated symmetrically a priori? We find that growth determinants emerging from agnostic Bayesian model averaging and classical model selection procedures are sensitive to income differences across datasets. For example, many of the 1975-1996 growth determinants according to World Bank income data turn out to be irrelevant when using Penn World Table data ... 17. How does political instability affect economic growth? OpenAIRE Aisen, Ari; Veiga, Francisco José 2011-01-01 The purpose of this paper is to empirically determine the effects of political instability on economic growth. Using the system-GMM estimator for linear dynamic panel data models on a sample covering up to 169 countries, and 5-year periods from 1960 to 2004, we find that higher degrees of political instability are associated with lower growth rates of GDP per capita. Regarding the channels of transmission, we find that political instability adversely affects growth by lowering the rates of pr... 18. Renewable Resources, Capital Accumulation, and Economic Growth OpenAIRE Wei-Bin Zhang 2011-01-01 This paper proposes a dynamic economic model with physical capital and renewable resources. Different from most of the neoclassical growth models with renewable resources which are based on microeconomic foundation and neglect physical capital accumulation, this study proposes a growth model with dynamics of renewable resources and physical capital accumulation. The model is a synthesis of the neoclassical growth theory and the traditional dynamic models of renewable resources with an alterna... 19. Value function in economic growth model Science.gov (United States) Bagno, Alexander; Tarasyev, Alexandr A.; Tarasyev, Alexander M. 2017-11-01 Properties of the value function are examined in an infinite horizon optimal control problem with an unlimited integrand index appearing in the quality functional with a discount factor. Optimal control problems of such type describe solutions in models of economic growth. Necessary and sufficient conditions are derived to ensure that the value function satisfies the infinitesimal stability properties. It is proved that value function coincides with the minimax solution of the Hamilton-Jacobi equation. Description of the growth asymptotic behavior for the value function is provided for the logarithmic, power and exponential quality functionals and an example is given to illustrate construction of the value function in economic growth models. 20. Trade Liberalisation and Economic Growth in Macedonia Directory of Open Access Journals (Sweden) Mano-Bakalinov Viktorija 2016-12-01 Full Text Available The objective of this paper is to explore the effects of trade on Macedonian economic growth. The autoregressive distributed lag (ARDL model is applied on yearly data over the period of 1993-2014. Empirical investigation reveals that an increase of population and openness demonstrate a positive and significant effect on Macedonian economic growth. Given other diverging findings, this suggests that the relationship between trade reforms and growth through the productivity function may vary across transition economies. Nevertheless, the findings of this paper indicate that policies focusing on market liberalisation and opening the economy to trade have a positive effect on Macedonian economic growth, both in the short run and the long run. 1. The Key to Promoting Economic Growth Institute of Scientific and Technical Information of China (English) 2009-01-01 The low contribution of consumption to economic growth has become a source of anxiety for Chinese economic officials. With a sharp decline in exports as a result of the international financial crisis, the Chinese Government hopes that consumption will become a new engine of economic growth. The aim of promoting domestic demand is very clear in the 4-trillion-yuan ($586-billion) economic stimulus package the government approved last fall. How should we assess the present situation of consumption in China and its future course? At the Global Think Tank Summit held in Beijing on July 4, Ma Jiantang, Commissioner of the National Bureau of Statistics, Wang Guangqian, President of the Central University of Finance and Economics, and Yuan Yue, Chairman of the Board of Horizon Research Consultancy Group, shared their opinions.
2. Oil prices and economic growth
International Nuclear Information System (INIS)
Babusiaux, D.; Lescaroux, F.
2006-01-01
There is no limit to the sources of hydrocarbons (whether pumped out of the earth or produced in factories) for the next few decades, but there is and will be a need for increasingly complex and costly techniques as the usual sources of petroleum run out. Does this mean that prices will keep on rising? Probably, since environmental costs must be added onto direct costs. The mining of oil out of 'tar sands', for example, or the production of hydrocarbons by the chemical industry will have a significant impact owing to the emission of greenhouse gases. If prices do rise in the short or middle term, the cause will have to do more with the calendar of investments than with the availability of energy and its costs. In the long run however, price hikes are not all that certain. A few points for analyzing and predicting the macro-and micro-economic effects of fluctuating oil prices are discussed. (author)
3. Energy Distribution and Economic Growth
DEFF Research Database (Denmark)
Dalgaard, Carl-Johan Lars; Strulik, Holger
2011-01-01
This research examines the physical constraints on the growth process. In order to run, maintain and build capital energy is required to be distributed to geographically dispersed sites where investments are deemed profitable. We capture this aspect of physical reality by a network theory....../2 and 3/4, depending on the efficiency of the network. Together with an energy conservation equation, capturing instantaneous aggregate demand for electricity, we are able to provide a metabolic-energetic founded law of motion for capital per capita that is mathematically isomorphic to the one emanating...... of electricity distribution. The model leads to a supply relation according to which feasible electricity consumption per capita rises with the size of the economy, as measured by capital per capita. Specifically, the relation is a simple power law with an exponent assigned to capital that is bounded between 1...
4. Institutions, Technological Change and Economic Growth
Directory of Open Access Journals (Sweden)
David Corderí Novoa
2005-01-01
Full Text Available Theories of economic growth try to explain variations in per capita income across countries by differences in capital accumulation and productivity. However, many scholars consider that integrating institutions into economic theory and economic history is an essential step in improving explanations of why some societies are richer than others. This paper develops the empirical and theoretical case that differences in institutions are the fundamental cause of differences in technological change (productivity, hence in economic growth. First, I give a definition of institutions and how they influence economic performance, from a New Institutional Economics point of view. Then, I introduce the theoretical framework based on the economics of ideas and endogenous growth models. Finally, I argue that R&D expenditures -a proxy for technological change- will vary across countries depending on some measures of institutional quality. In the end, this paper finds that stronger institutions (measured by an aggregate of institutional quality encourage greater R&D expenditures. At a disaggregate level, the rule of law is positively correlated and the regulatory burden is negatively correlated with R&D expenditures. Human capital level (measured by the tertiary and primary school enrolment rates has also a significant positive impact in R&D expenditures.
5. Energy efficiency, sustainability and economic growth
International Nuclear Information System (INIS)
Ayres, Robert U.; Turton, Hal; Casten, Tom
2007-01-01
This paper explores two linked theses related to the role energy in economic development, and potential sources of increased energy efficiency for continued growth with reduced greenhouse gas (GHG) emissions. The first thesis is that, while reduced GHG emissions are essential for long-term global sustainability, the usual policy recommendation of increasing energy costs by introducing a carbon tax may be relatively ineffective under current market structures and have an unnecessarily adverse impact on economic growth. Our second thesis is that there exists a practical near-term strategy for reducing GHG emissions while simultaneously encouraging continued technology-driven economic growth. Moreover, this strategy does not require radical new technologies, but rather improved regulation or-more precisely-better deregulation of the electric power sector. In respect to the first of our two theses, this paper addresses a deficiency in neoclassical economic growth theory, in which growth is assumed to be automatic, inevitable and cost-free. We challenge both the assumption that growth will continue in the future at essentially the same rate ('the trend') as it has in the past, and the corollary that our children's children will inevitably be richer and better able to afford the cost of repairing the environmental damages caused by current generations [Simon et al., The state of humanity. Cambridge MA: Blackwell Publishers Ltd.; 1995
6. Exploring economic structure and drivers of economic growth in Botswana
Directory of Open Access Journals (Sweden)
Patricia Lindelwa Makoni
2015-12-01
Full Text Available This article set out to analyse the economic structure and main economic drivers in Botswana. Botswana, a country in sub-Saharan Africa, is a relatively small economy, hugely dependent on its diamond mineral wealth. Concerns have arisen in recent years that the diamond deposits will soon be depleted and the country therefore needs to embark on a diversification programme to broaden its economic base. In order to understand the Botswana economy, its economic structure and current domestic sectorial performance were evaluated, as well as its trends in imports and exports. An analysis of the data shows that, regardless of the awareness of the sensitivity to external shocks of commodity prices, as well as the obvious future depletion of diamond reserves, the Botswana economy continues to rely on diamonds, at the expense of attracting international capital flows to enhance and maintain sustainable economic growth, through investments in agriculture, manufacturing and tourism. It is therefore recommended that the Government of Botswana becomes proactive and implements recommended policies to diversify its economy, so that it can sustain or improve its economic growth by becoming a prime destination of international capital and domestic private sector investment, thereby increasing employment and trade opportunities.
7. Economic growth - environmental protection - quality of life
International Nuclear Information System (INIS)
Kumm, J.
1975-01-01
This is an investigation into the assumption that uncontrolled economic growth puts a burden on the natural environment and lowers the quality of life. This analysis of the natural, technical, economic, and social environment answers the following questions: 1) which development will production and consumption take up to the year 2000; 2) extent of environmental burden to be expected as a result thereof; 3) influence of needs and valid standard of values thus prevailing; 4) administrative measures for environmental policies; 5) influence of environmental policies on the quality of life; 6) possibility of economic growth while the natural environment is sufficiently protected at the same time. The man-environment model presented elucidates the interrelations between economic development and the natural and social environment; it checks the effectiveness of alternate environmental protection measures. (HP) [de
8. Global economic growth and expected returns around the world: The end-of-the-year effect
DEFF Research Database (Denmark)
Møller, Stig Vinther; Rangvid, Jesper
2017-01-01
Global economic growth at the end of the year strongly predicts returns from a wide spectrum of international assets, such as global, regional, and individual-country stocks, FX, and commodities. Global economic growth at other times of the year does not predict international returns. Low growth...
9. Budget Deficits Effects on Economic Growth
Directory of Open Access Journals (Sweden)
L.C.Risti
2013-06-01
Full Text Available The budget deficit can not be analyzed autarchically, as it affects all the macroeconomic processes and, is itself influenced by all other macroeconomic indicators. Most analyses and studies on public finance and budget balance measure the impact that budgetary deficits accumulation has on economy. Therefore, the present paper aims at following and analyzing the mutual impact between budget deficit and another economic macro indicator, namely the economic growth.
10. INNOVATIVE ASPECTS OF ECONOMIC GROWTH (THE REGION
Directory of Open Access Journals (Sweden)
Sergei A. Orekhov
2014-01-01
Full Text Available Principles of implementation of innovativetechnologies are positioned as a priorityarea for development in the managementof economic processes in the modernRussian economy. Declares that they are the economic growth of the country. This paper discusses the practice of building existing schemes of organization ofthe economy, which is why the definingelement of this process is the businessclass passengers - is the situation quitedependent and extremely nekomfortnomsituation.
11. Global Marine Fisheries with Economic Growth
OpenAIRE
Sugiawan, Yogi; Islam, Moinul; Managi, Shunsuke
2017-01-01
This study explores the state of global marine fisheries and empirically analyzes its relationship to economic factors. We apply the pooled mean group estimator method to examine 70 fishing countries for the period of 1961-2010. We use both catch and the estimated size of stock as proxies for marine ecosystems. Our results confirm that economic growth initially leads to the deterioration of marine ecosystems. However, for a per capita income level of approximately 3,827 USD for the catch mode...
12. Economic Growth, Climate Change, and Obesity.
Science.gov (United States)
Minos, Dimitrios; Butzlaff, Iris; Demmler, Kathrin Maria; Rischke, Ramona
2016-12-01
Human and planetary health as well as economic growth are firmly interlinked and subject to complex interaction effects. In this paper, we provide an overview of interlinkages between economic growth, climate change, and obesity focusing on recent advances in the literature. In addition to empirical findings, we discuss different theoretical frameworks used to conceptualize these complex links and highlight policy options and challenges. We conclude that policies addressing both climate change and obesity simultaneously are particularly promising and often suitable for ensuring sustainable development.
13. Employment, energy, and economic growth in Australia
Energy Technology Data Exchange (ETDEWEB)
Andrews, J
1979-09-01
The author examines the complex relationships between energy use, employment opportunities, and economic growth as they apply to the Australian economy and concludes that state and federal governments should collaborate to analyze the employment impacts of the various energy strategies. He sees the need for changes in the political and economic environment as well as in the way energy is used before Australia can return to full employment. While low or zero energy growth policies would not, by themselves, solve the unemployment problem, most new jobs have been created in the labor-intensive service industries. 25 references. (DCK)
14. RELATIONSHIP BETWEEN ECONOMIC GROWTH AND HUMAN CAPITAL
Directory of Open Access Journals (Sweden)
Mihaela Tania SANDU
2010-02-01
Full Text Available Recognizing the importance of infl uence exerted by human capital oneconomic growth of a country, to base decisions regarding the need to invest in such type of capital there are conducted studies and used different models for analysis related to a series of macroeconomic and demographic indicators.We present the main indicators and dynamics of human capital, placedin the economic context of Romania, with reference, in bringing out statistics data, to an average period of time (between 1994-2008 characterized at macroeconomic level, both by recession and economic growth periods. There were also highlighted indicators and dynamics, both at national and individual level.
15. Role of vaccination in economic growth.
Science.gov (United States)
Quilici, Sibilia; Smith, Richard; Signorelli, Carlo
2015-01-01
The health of a population is important from a public health and economic perspective as healthy individuals contribute to economic growth. Vaccination has the potential to contribute substantially to improving population health and thereby economic growth. Childhood vaccination programmes in Europe can offer protection against 15 important infectious diseases, thus preventing child fatalities and any serious temporary and permanent sequelae that can occur. Healthy children are more able to participate in education, thus preparing them to become healthy and productive adults. Vaccination programmes can also prevent infectious diseases in adolescents, thus allowing them to continue their development towards a healthy adulthood. Protecting adults against infectious diseases ensures that they can fully contribute to productivity and economic development by avoiding sick leave and lower productivity. Vaccination in older adults will contribute to the promotion of healthy ageing, enabling them to assist their familiy with, for instance, childcare, and also help them avoid functional decline and the related impacts on health and welfare expenditure. Effective vaccination programmes for all ages in Europe will thus contribute to the European Union's 2020 health and economic strategies. Indeed, beyond their impact on healthcare resources and productivity, reductions in mortality and morbidity also contribute to increased consumption and gross domestic product. Therefore, assessment of the value of vaccines and vaccination needs to consider not just the direct impact on health and healthcare but also the wider impact on economic growth, which requires a macroeconomic analysis of vaccination programmes.
16. Does inequality in health impede economic growth?
Science.gov (United States)
Grimm, Michael
2011-01-01
This paper investigates the effects of inequality in health on economic growth in low and middle income countries. The empirical part of the paper uses an original cross-national panel data set covering 62 low and middle income countries over the period 1985 to 2007. I find a substantial and relatively robust negative effect of health inequality on income levels and income growth controlling for life expectancy, country and time fixed-effects and a large number of other effects that have been shown to matter for growth. The effect also holds if health inequality is instrumented to circumvent a potential problem of reverse causality. Hence, reducing inequality in the access to health care and to health-related information can make a substantial contribution to economic growth.
17. Parameters of Economic Growth in Kosovo
Directory of Open Access Journals (Sweden)
Shkumbin Misini
2016-01-01
Full Text Available This paper analysis the macroeconomic components that influenced macroeconomic growth in a country, more concretely, the focus will be on the measurement of components that affected economic growth under nominal GDP, in Kosovo. We intend to found out which component of nominal GDP has the biggest and the lowest influence on economic growth. Thus, in order to measure it, GDP components must be analysed: consumption measurement, investments measurement, government expenditures measurement and export measurement. These parameters will be measured by analysing their importance in relation to one another, and the major influence on the growth of nominal GDP. The paper includes a graphic analysis of nominal GDP in relation to consumption, investments, governmental expenses and export.
18. 136 Tax Revenue, Stock Market and Economic Growth of Pakistan
Directory of Open Access Journals (Sweden)
2014-10-01
Full Text Available The purpose of this paper is to examine the effects of capital market and fiscal policy influences in determining the nexus of economic growth in Pakistan from July 2003 to July 2012. The authors utilize ADF unit root test, Johansen Cointegration test, VECM test, Granger causality test and variance decomposition analysis to test the relationship among tax revenue, stock market and economic growth in Pakistan. Granger causality analysis is used to answer questions whether “Does tax revenue cause the economic growth?” or “Does tax revenue cause the capital market?”. The results demonstrate that there is a bidirectional casualty between tax revenue and economic growth; and a unidirectional causality from capital market to tax revenue. The estimated result shows that growth of Pakistan economy is strongly contributed from the high collection of direct tax revenue and the development of financial market activity. The findings of this paper have important implications to current and potential investors in Pakistan economy to understand the economic condition of Pakistan and to assist them in making their investment decision.
19. Does the Euro enhance Economic Growth?
DEFF Research Database (Denmark)
Dreyer, Johannes Kabderian; A. Schmid, Peter
2016-01-01
of economic integration in Europe. The aim of this article is to investigate whether the EU and EZ memberships enhance growth of their members. In order to perform our empirical analysis, we apply an augmented Solow growth model using convergence analysis and the panel Generalized Method of Moments (GMM...... interesting to new potential EZ members, such as some of the Central Eastern European Countries (CEE), who are about or in the process to join the common currency club....
20. Borderplex Economic Growth: Chicken, Egg, or Scrambled?
OpenAIRE
Fullerton, Thomas; Molina, Angel; Ibarreche, Santiago
2007-01-01
Regional debates over which metropoitan economy is the dominant growth pole in multi-city areas can be intense. Such discourse is frequently voiced with regard to economic expansion in the El Paso, Texas, USA - Ciudad Juarez, Chihuahua, Mexico borderplex economy. To date, no empirical analyses have been carried out to address that question. Granger causality tests are applied to various cross-border data to shed light on that question and others regarding the nature of regional growth in t...
1. Industrial Employment, Investment Equipment and Economic Growth
OpenAIRE
Dellas, Harris
2000-01-01
The industrialization of labour is the main engine of growth during the early stages of economic development. In less developed countries, equipment investment has played a less important role than non-equipment investment; and it has only proved growth enhancing when it either encountered a substantial industrial labour force or fostered a large increase in the share of industrial employment. These findings draw attention to the effects of investment on the composition of the labour force; a...
2. Gender Equality and Economic Growth in Brazil
OpenAIRE
Pierre-Richard Agénor; Otaviano Canuto
2013-01-01
This note studies the long-run impacts of policies aimed at fostering gender equality on economic growth in Brazil. After a brief review of gender issues in Brazil, this note describes a framework for quantifying the growth effects of gender-based policies in developing economies. The analysis is based on a computable overlapping generations (OLG) model that accounts for the impact of acce...
3. Social and economic growth of developing nations
International Nuclear Information System (INIS)
Gregersen, H.M.; Laarman, J.G.
1989-01-01
This paper reports on social and economic growth of developing nations. Trees and forests are often of immeasurable importance to developing countries of the world. To be of value, however, effective and efficient institutions, programs, and policies must be designed and focused on such resources. Forest economics and policy researchers can contribute much to such activities. To be most effective, forest economics research should be designed to improve understanding of social forestry, watershed management, and nontimber forest outputs; enhance ability to effectively address environmental consequences of forestry development; heighten skill in guiding development of industrial forestry enterprises; and improve effectiveness of international aid for forestry development. Guided by such strategic directions, forest economics research can contribute much to the economic and social well-being of developing nations
4. Relationship between Economic Freedom and Pro-poor Growth: Evidence from Pakistan (1995-2010
Directory of Open Access Journals (Sweden)
Khalid ZAMAN
2011-07-01
Full Text Available The relationship between economic freedom and pro-poor growth is examined in Pakistan from 1995-2010. The concept of pro-poor growth is derived from the literature of Kakwani and Pernia (2000 and Kakwani and Son (2003. The domino effect shows that there is a strong link between economic freedom indicators and pro-poor growth. Econometric analysis proves a strong relationship between economic freedom, poverty reduction and income inequality. Results reveal that larger the business freedom and / or trade freedom, greater the economic growth. This will ultimately reduce poverty in the country.
5. Demographics, political power and economic growth.
Science.gov (United States)
Holtz-eakin, D
1993-01-01
"Growth theory may be used to predict the response of saving, capital formation, and output growth to large demographic shifts. Such large shifts would also be expected to alter the demand for government services and the desired levels of taxation in the population. This paper extends the overlapping-generations model of economic growth to predict the evolution of government tax and spending policy through the course of a major demographic shift. Simulations suggest that this approach may yield valuable insights into the evolution of policy in the United States and other industrialized economies." excerpt
6. Does Economic Growth Reduce Childhood Undernutrition in Ethiopia?
Science.gov (United States)
Biadgilign, Sibhatu; Shumetie, Arega; Yesigat, Habtamu
2016-01-01
Policy discussions and debates in the last couple of decades emphasized efficiency of development policies for translating economic growth to development. One of the key aspects in this regard in the developing world is achieving improved nutrition through economic development. Nonetheless, there is a dearth of literature that empirically verifies the association between economic growth and reduction of childhood undernutrition in low- and middle-income countries. Thus, the aim of the study is to assess the interplay between economic growth and reduction of childhood undernutrition in Ethiopia. The study used pooled data of three rounds (2000, 2005 and 2010) from the Demographic and Health Surveys (DHS) of Ethiopia. A multilevel mixed logistic regression model with robust standard errors was utilized in order to account for the hierarchical nature of the data. The dependent variables were stunting, underweight, and wasting in children in the household. The main independent variable was real per capita income (PCI) that was adjusted for purchasing power parity. This information was obtained from World Bank. A total of 32,610 children were included in the pooled analysis. Overall, 11,296 (46.7%) [46.0%-47.3%], 8,197(33.8%) [33.2%-34.4%] and 3,175(13.1%) [12.7%-13.5%] were stunted, underweight, and wasted, respectively. We found a strong correlation between prevalence of early childhood undernutrition outcomes and real per capita income (PCI). The proportions of stunting (r = -0.1207, peconomic growth substantially reduced stunting [β = -0.0016, SE = 0.00013, pEconomic growth reduces child undernutrition in Ethiopia. This verifies the fact that the economic growth of the country accompanied with socio-economic development and improvement of the livelihood of the poor. Direct nutrition specific and nutrition sensitive interventions could also be recommended in order to have an impact on the massive reduction of childhood undernutrition in the country.
7. Human Capital Composition and Economic Growth
Science.gov (United States)
Tsai, Chun-Li; Hung, Ming-Cheng; Harriott, Kevin
2010-01-01
The objective of this paper is to analyze the effect of various compositions of human capital on economic growth. We construct alternative measures of human capital composition using five fields of study. In each instance, the measure represents the number of graduates in the respective field as a percentage of all graduates. The measures are as…
8. Economic growth, sectoral structure and unemployment
NARCIS (Netherlands)
de Groot, H.L.F.
1998-01-01
This thesis consists of three parts that deal with the relationship between the relative wealth of nations, economic growth, and the sectoral structure of economies. In the first part, the focus is on the relative stagnancy of Europe versus the USA in terms of productivity levels and unemployment.
9. House Price, House Quality and Economic Growth
NARCIS (Netherlands)
De Vries, P.; Boelhouwer, P.J.
2010-01-01
The literature on housing markets suggest that periods of economic growth are characterised by a demand for better housing quality and increasing prices. The basic principles of the theory are that the short-run price fluctuations occur due to market imperfection, while over the long term, causality
10. Education for Economic Growth: A Critical Investment.
Science.gov (United States)
Hunt, James B., Jr.
1984-01-01
Declaring that a "national emergency" exists in American education, the author outlines "Action for Excellence" recommendations developed by the Task Force on Education for Economic Growth, of which he was chairman, and discusses accomplishments in educational reform in the state of North Carolina, where he is governor. (JBM)
11. Renewable Resources, Capital Accumulation, and Economic Growth
Directory of Open Access Journals (Sweden)
Wei-Bin Zhang
2011-01-01
Full Text Available This paper proposes a dynamic economic model with physical capital and renewable resources. Different from most of the neoclassical growth models with renewable resources which are based on microeconomic foundation and neglect physical capital accumulation, this study proposes a growth model with dynamics of renewable resources and physical capital accumulation. The model is a synthesis of the neoclassical growth theory and the traditional dynamic models of renewable resources with an alternative approach to household behavior. The model describes a dynamic interdependence among physical accumulation, resource change, and division of labor under perfect competition. Because of its refined economic structure, our study enables some interactions among economic variables which are not found in the existing literature on economic growth with renewable resources. We simulate the model to demonstrate the existence of equilibrium points and motion of the dynamic system. Our comparative dynamic analysis shows, for instance, that a rise in the propensity to consume the renewable resource increases the interest rate and reduces the national and production sector’s capital stocks, wage rate and level of the consumption good. Moreover, it initially reduces and then increases the capital stocks of the resource sector and the consumption and price of the renewable resource. The stock of the renewable resource is initially increased and then reduced. Finally, labor is redistributed from the production to the resource sector.
12. public procurement, governance and economic growth
African Journals Online (AJOL)
GRACE
(2003: 2), ―strong procurement management in the public sector is a tool for achieving political, economic and social goals‖. Thus .... professionalism in the public sector procurement system (Section 4, PPA, 2007). The functions and powers of the ..... K., Bose, N. and Haque, M.E. (2004). Public Expenditures, Bureaucratic.
13. Three essays on energy and economic growth
Science.gov (United States)
Peach, Nathanael David
2011-12-01
This dissertation explores the relationship between energy and economic growth. Chapter Two, Three, and Four examine the interaction of energy-related measures and economic outcomes by applying different methodologies across various spatial dimensions. Chapter Two shows that increases in energy consumption are necessary for increases in state level economic growth to occur. Chapter Three estimates a simultaneous supply and demand energy market at the state level. This system allows for estimates of structural elasticities to be obtained. Findings indicate that energy supply is considerably more elastic than energy demand. Energy demand is found to be determined by responses to short run shocks rather than long run processes. Chapter Four estimates the impact of changes in various elements of governance and institutional quality impact genuine investment within an economy. Increases in democracy are predicted to decrease genuine investment in energy-rich nations. The dissertation concludes with Chapter Five.
14. The Impact of FDI on the Economic Growth of Serbia
Directory of Open Access Journals (Sweden)
Miloš Parežanin
2016-05-01
Full Text Available This paper analyzes the impact of foreign direct investment on the economic growth of the Republic of Serbia. The aim is to analyze the effects of the economic crisis on foreign direct investment impact on the economic performance of the Serbian economy. This paper analyzes the period of 2000 - 2014, using the Inward FDI Performance Index and Pearson’s coefficient of simple linear correlation. The period before the economic crises (2000-2007 and the period after the beginning of the economic crisis (2008-2014 are analyzed separately, in order to observe the linear correlation between FDI and economic growth. The results of the research speak in favor of the existence of a strong and statistically significant correlation between FDI and observed macroeconomic indicators in the period of 2000-2007. The second sub-period was characterized by an absence correlation between FDI inflows and all the observed macroeconomic indicators. The results for the period of 2008-2014 can be explained by the effects of the global crisis on the Serbian economy and the deterioration of all macroeconomic indicators in the given period. Effects of the crisis on the Serbian economy were very strong.
15. Economic institutions and economic growth: Empirical evidence from the Economic Community of West African States
Directory of Open Access Journals (Sweden)
Lazarus Z. Wanjuu
2017-12-01
Background: Economic institutions are considered as the fundamental cause of economic growth. Economic institutions affect economic growth through allocation of resources like physical and human capital. Unfortunately, there is dearth of empirical studies showing the impact of economic institutions on growth of the Economic Community of West African States (ECOWAS. Aim: This study investigates the impact of economic institutions on economic growth of the ECOWAS. Setting and method: The study applied cause and effect relationship. The study used econometric research techniques of unit root and co-integration tests to establish the time series properties of the data; the vector error correction and co-integration regression models to estimate the population parameters. The research data comprised data obtained from the United Nations Conference on Trade and Development (UNCTAD, the Transparency International (TI and Heritage Foundation databases. The variables employed were the real gross domestic product (GDP per capita (RGDPPC, corruption perception index (CPI, property rights protection (PROPRGT, private investment per capita (INVESPC, government expenditure per capita (GOEXPPC and trade openness (TRAOPN. Results: The results of the data analysed showed that economic institutions represented by the property rights index engender RGDPPC growth in ECOWAS. The CPI could not stimulate RGDPPC growth in ECOWAS. The results also show that all the other variables stimulated growth except trade openness. Conclusion: The study concludes that good economic institutions, private investments, and government intervention by providing security, economic and social infrastructural facilities are conducive for economic growth in the ECOWAS region. The study recommended that more efforts be made at curbing corruption in the region
16. Electrification, economic growth and uranium power
International Nuclear Information System (INIS)
Starr, C.
1983-01-01
The worldwide growth of uranium power plant capacity is obviously dependent on both the growth of electrification and the competitive status of uranium power. In this paper the thesis is developed that expanded use of uranium power is essential to provide a substantial portion of the electricity necessary for world economic growth. Further, the case is made that the obstacles to this expansion arise not from the technology, but rather from the inadequacies of our industrial, political, and economic institutions to manage this new energy system effectively, nationally and internationally. Data are presented on the relation between electricity consumption and GNP; percentage of primary energy used for electricity; energy price ratio; relative generation costs of U, coal and oil-fired power plants; generating costs and capacity factors of conventional and uranium power plants. (U.K.)
17. Human Capital Investment and Economic Growth in Nigeria ...
African Journals Online (AJOL)
Human Capital Investment and Economic Growth in Nigeria. ... relationship between investment in education, health and economic growth in Nigeria, ... in order to accelerate growth and liberate Nigerians from the vicious cycle of poverty, the ...
18. IMPACTS OF FOREIGN INVESTMENT ON ECONOMIC GROWTH IN TRANSITION COUNTRIES
Directory of Open Access Journals (Sweden)
Siniša Bosanac
2016-12-01
Full Text Available The current global economic crisis raises many questions and the most important imperative is to find solutions and recover the world economy. Neoliberalism as a cause of the crisis has shown fundamental shortcomings and proved that the market is an imperfect self-regulating system. At the present time in the media, politicians and some economists mention foreign direct investment (FDI as a life-saving solution for economic problems and economic growth. The analysis of the economic indicators proved that FDI cannot be, to the necessary extent, a generator of economic growth and that development of each country should be based on endogenous components. The development of critical thinking and questioning of the neoliberal concept, especially with today's time distance through comparisons of indicators such as economic growth, absence of inflation, employment and the export-import ratio, has revealed major systemic defects of the market fundamentalist policies. A strong indicator and argument to this thesis is particularly evident in the industrial production indexes, in the number of industrial workers and in the share of industry in GDP of transition countries.
19. Economic growth and energy consumption in Algeria: a causality analysis
International Nuclear Information System (INIS)
Cherfi, S.
2011-01-01
The purpose of this study is to review the causal link in the Granger sense, between energy consumption and economic growth in Algeria, to determine its implications for economic policy. The analysis was done based on Granger static and causality tests using statistical data on per capita primary energy consumption and gross domestic product per inhabitant in Algeria, over the 1965-2008 period. The results of the survey show that there is, in Algeria, a strong link between energy consumption per inhabitant and GDP per inhabitant. The results also suggest the lack of a long term impetus (no co-integration) between energy consumption and economic growth. In addition, there is a one-way causal link between GDP and energy consumption, i.e. the prior GDP data provides a better forecast of energy consumption level, but not the contrary. In other words, GDP explains consumption, not the contrary. (author)
20. Export and Economic Growth in the West Balkan Countries
OpenAIRE
Florentina Xhelili Krasniqi; Rahmije Mustafa Topxhiu
2017-01-01
The aim of this paper is to explore the effects of exports and other variables (foreign direct investment, remittances, capital formation, and labour force) on economic growth in West Balkan countries (Albania, Kosovo, Macedonia, Montenegro, Bosnia and Herzegovina and Serbia). This study utilizes a strongly balanced panel data over the 2005-2015 period for Western Balkan countries using the ordinary least squares method (OLS), ie Pooled regression model to evaluate the parameters. The rela...
1. Transport Infrastructure and Economic Growth: Spatial Effects
Directory of Open Access Journals (Sweden)
2015-09-01
Full Text Available The author specifies an empirical framework of neoclassical growth model in order to examine impact of transport infrastructure on economic growth in Russian regions during period of 2000-2013. Two different effects of infrastructure are considered. First, infrastructure is viewed as part of region’s own production function. Second, infrastructure generates spillover effect on adjacent regions’ economic performance which can be negative or positive. Results imply that road infrastructure has a positive influence on regional growth, but sign of railroad infrastructure coefficient depends on whether or not congestion effect is considered. Negative spillover effect is shown to exist in the case of road infrastructure. This apparently means that rapid road infrastructure development in some regions moves mobile factors of production away from adjacent regions retarding their economic development. The spillover effect of railroad infrastructure is significant and negative again only if congestion effect is considered. The results of estimation for the Far East and Baikal Regions separately demonstrate no significant effect of both types of infrastructure for economic performance and negative spillover effect of road infrastructure
2. Does Political Ideology Affect Economic Growth?
DEFF Research Database (Denmark)
Bjørnskov, Christian
2005-01-01
This paper asks the question whether political ideology affects economic growth. Voters may demand inefficient levels of redistribution and government intervention, and they may care too little for aspects that really matter for the economy. Their norms and perceptions of society might, via...... their political ideology, affect economic performance. The paper presents evidence suggesting that rightwing societies have grown faster in the last decades than other democratic societies. Further analysis suggests that these societies develop better legal systems and less government intervention, which in turn...
3. How Does Social Trust Affect Economic Growth?
DEFF Research Database (Denmark)
Bjørnskov, Christian
Social capital in the form of generalized trust has been shown to be a determinant of economic growth in a number of studies. Other studies have explored other consequences of trust, such as its effects on governance, corruption, education and investment. This paper connects the two strands...... of literature by estimating the effects of trust on growth through a set of potential transmission mechanisms directly. It does so by modelling the process using a three-stage least squares estimator on a sample of countries for which a full data set is available. The results indicate that trust affects...
4. Economic analyses of rapid population growth.
Science.gov (United States)
Birdsall, N
1989-01-01
"Discussion of the macroeconomic consequences of rapid population growth is organized into three schools: pessimists, optimists, and the recent revisionists. For the revisionists, differing views are presented about the pervasiveness and relevance of market failures, such as the negative externalities of childbearing, and about the ability of families and institutions to adjust rapidly to changes brought on by rapid population growth. A welfare economics approach is used to review the merits of various public policies to reduce fertility, including public financing of family planning services and taxes and incentives associated with childbearing." The focus is on developing countries. excerpt
5. Exports, capital formation and economic growth in South Africa ...
African Journals Online (AJOL)
In South Africa the export sector is frequently accorded a special role in encouraging faster economic growth. Nonetheless, a question that remains unresolved is whether higher export growth indeed leads to higher economic growth and what particular role exports may play within the overall economic growth process of the ...
6. Bank Liquidity, Market Participation, and Economic Growth
OpenAIRE
Mattana, Elena; Panetti, Ettore
2012-01-01
We report evidence that bank liquidity ratios (liquid assets as a percentage of total assets) decrease during the process of economic development. To reconcile this observation with (i) the increasing importance of financial markets and (ii) the increasing direct participation of individual investors in them, we build a neoclassical growth model with banks and markets. In this environment, banks engage in cross-subsidization of the impatient depositors to keep up with the competitive pressure...
7. Boosting Economic Growth Through Advanced Machine Vision
OpenAIRE
2012-01-01
In this chapter, we overview the potential of machine vision and related technologies in various application domains of critical importance for economic growth and prospect. Considered domains include healthcare, energy and environment, finance, and industrial innovation. Visibility technologies considered encompass augmented and virtual reality, 3D technologies, and media content authoring tools and technologies. We overview the main challenges facing the application domains and discuss the ...
8. Economic growth, biodiversity loss and conservation effort.
Science.gov (United States)
2003-05-01
This paper investigates the relationship between economic growth, biodiversity loss and efforts to conserve biodiversity using a combination of panel and cross section data. If economic growth is a cause of biodiversity loss through habitat transformation and other means, then we would expect an inverse relationship. But if higher levels of income are associated with increasing real demand for biodiversity conservation, then investment to protect remaining diversity should grow and the rate of biodiversity loss should slow with growth. Initially, economic growth and biodiversity loss are examined within the framework of the environmental Kuznets hypothesis. Biodiversity is represented by predicted species richness, generated for tropical terrestrial biodiversity using a species-area relationship. The environmental Kuznets hypothesis is investigated with reference to comparison of fixed and random effects models to allow the relationship to vary for each country. It is concluded that an environmental Kuznets curve between income and rates of loss of habitat and species does not exist in this case. The role of conservation effort in addressing environmental problems is examined through state protection of land and the regulation of trade in endangered species, two important means of biodiversity conservation. This analysis shows that the extent of government environmental policy increases with economic development. We argue that, although the data are problematic, the implications of these models is that conservation effort can only ever result in a partial deceleration of biodiversity decline partly because protected areas serve multiple functions and are not necessarily designated to protect biodiversity. Nevertheless institutional and policy response components of the income biodiversity relationship are important but are not well captured through cross-country regression analysis.
9. Energy consumption and economic growth: Evidence from Cameroon
International Nuclear Information System (INIS)
Fondja Wandji, Yris D.
2013-01-01
The aim of this paper is to study the nature of the relationship between energy consumption and economic growth in Cameroon through a three-step approach: (i) Study the stationarity of the chronic, (ii) test of causality between variables and (iii) estimate the appropriate model. The study concludes in a non-stationarity of the series. Using the data in first difference, the Granger causality test yields a strong evidence for unidirectional causality running from OIL to GDP. Cointegration tests also show that these two series are co-integrated and the Error Correction Model (ECM) reveals that every percentage increase in Oil products consumption increases economic growth by around 1.1%. This result confirms the intuition that an economic policy aimed at improving energy supply will necessarily have a positive impact on economic growth. On the other side, a lack of energy is a major bottleneck for further economic development in Cameroon. - Highlights: • The series of GDP, ELECTRICITY, OIL and BIOFUELS are integrated of order 1. • The Granger causality test yields a unidirectional causality running from OIL to GDP. • No causal link between GDP and ELECTRICITY, and no more between GDP and BIOFUELS. • Cointegration tests also show that only OIL and GDP are co-integrated. • Every percentage increase in OIL increases GDP by around 1.1%
10. Factor-structure of economic growth in E-commerce
Institute of Scientific and Technical Information of China (English)
吴隽; 刘洪久; 栾天行
2003-01-01
In order to analyze the factors having effect on economic growth of E-commerce, the economic growthprocess of E-commerce is divided into three stages; growth stage, stabilization stage and re-growth stage. Thesethree different stages are analysed using several economic growth theories, a set of factor-structure is proposedfor each stage of the economic growth process of E-commerce.
11. Sociopolitical Instability and Economic Growth Empirical Evidence from Sri Lanka
OpenAIRE
Changsheng Xu; Santhirasegaram Selvarathinam; Wen X. Li
2007-01-01
Sociopolitical instability severely affects economic growth in short and long run. This study analyzes that sociopolitical instability measured by proxy measure; annual growth rate of tourist arrivals in Sri Lanka during 1960-2005 adversely affects economic growth. Our empirical findings based on ordinary lease square econometric estimation, show that sociopolitical instability negatively and significantly affect economic growth. Reduction of economic growth rate (-0.032) due to the sociopoli...
12. Geography, demography, and economic growth in Africa.
Science.gov (United States)
Bloom, D E; Sachs, J D
1998-01-01
This paper presents the effects of climate, topography, and natural ecology on public health, nutrition, demographics, technological diffusion, international trade and other determinants of economic development in Africa. The goal of this paper is to emphasize the need for intensified research on the issues at the intersection of ecology and human society. Geography was given emphasis because of three reasons: the minimal gain from another recitation of the damage caused by statism, protectionism and corruption to African economic performance; negligence of the role of natural forces in shaping economic performance; and tailoring of policies to geographical realities. The paper also discusses the general problems of tropical development and the focus of Africa's problems in worldwide tropical perspectives; demographic trends in Africa; use of standard cross-country growth equations with demographic and geographic variables, to account for the relative roles of geography; and the future growth strategies and the need for urban-based export growth in manufacturing and services. Lastly, the authors provide a summary of conclusions and discuss the agenda for future research.
13. Relationship of Economic Growth with Tourism Sector
Directory of Open Access Journals (Sweden)
Abdul Holik
2016-06-01
Full Text Available This research aims to analyze the impact of foreign tourists towards the economic growth. It was conducted from 1995 until 2012 on five ASEAN member countrie: Indonesia, Malaysia, Thailand, Philippines, and Singapore. It used the quantitative method; it is one-way random effect of panel regression. The data, which is functioned as dependent variables, were taken from WDI (World Development Indicator of the World Bank for the Gross Domestic Product (GDP. Meanwhile, the data of revenue from the foreign tourist visit (Rec, the number of foreign tourist arrival (Arr, and the exchange rate (Xrate are functioned as the independent variables. Based on the research result, there is evidence that international tourism can increase the economic growth in those countries. The three independent variables have a positive and significant impact to the dependent variables. Based on the findings, the governments of five ASEAN member countries should be able to maintain the sustainability of tourism sector in order to be stronger and to have global market-orientation. In fact, tourism services can support the economic growth because the potential of those ASEAN countries cannot be taken lightly.
14. Relationship of Economic Growth with Tourism Sector
Directory of Open Access Journals (Sweden)
Abdul Holik
2016-06-01
Full Text Available This research aims to analyze the impact of foreign tourists towards the economic growth. It was conducted from 1995 until 2012 on five ASEAN member countrie: Indonesia, Malaysia, Thailand, Philippines, and Singapore. It used the quantitative method; it is one-way random effect of panel regression. The data, which is functioned as dependent variables, were taken from WDI (World Development Indicator of the World Bank for the Gross Domestic Product (GDP. Meanwhile, the data of revenue from the foreign tourist visit (Rec, the number of foreign tourist arrival (Arr, and the exchange rate (Xrate are functioned as the independent variables. Based on the research result, there is evidence that international tourism can increase the economic growth in those countries. The three independent variables have a positive and significant impact to the dependent variables. Based on the findings, the governments of five ASEAN member countries should be able to maintain the sustainability of tourism sector in order to be stronger and to have global market-orientation. In fact, tourism services can support the economic growth because the potential of those ASEAN countries cannot be taken lightly.
15. Energy scarcity and economic growth reconsidered
International Nuclear Information System (INIS)
Uri, N.D.
1995-01-01
The analysis in this paper is concerned with the effect of energy scarcity on economic growth in the United States. After defining the notion of scarcity and introducing two measures of scarcity, unit costs and relative energy price, changes in the trend in resource scarcity for natural gas, bituminous coal, anthracite coal, and crude oil over the most recent three decades are investigated. Each of the energy resources became significantly more scarce resources during the decade of the 1970s in the Malthusian Stock Scarcity and Malthusian Flow Scarcity sense. Unit costs exhibit a similar change for natural gas and crude oil but not for bituminous coal and anthracite coal. The situation reversed itself during the 1980s. Natural gas, bituminous coal, anthracite coal, and crude oil all became significantly less scarce resources during the decade of the 1980s than they had been during the 1970s. That is, the increase in scarcity as measured by relative energy prices observed during the decade of the 1970s was not reversed completely during the 1980s for natural gas and crude oil. Unit costs for natural gas and crude oil demonstrate analogous patterns and test results. Given that change has taken place, it has implications for future economic growth to the extent resource scarcity and economic growth are interrelated. (author)
16. Effects of Credit on Economic Growth, Unemployment and Poverty
Directory of Open Access Journals (Sweden)
Mangasa Augustinus Sipahutar
2016-06-01
Effect of credit on economic growth, unemployment and poverty provides evidence from Indonesia on the role of banks credit for promoting economic growth and reducing both unemployment and poverty. To document the link between banks credit and economic growth, we estimate a VAR model and variance decompositions of annual GDP per capita growth rates to examine what proxy measures of banks credit are most important in accounting for economic growth over time and how much they contribute to explaining economic growth. We also estimate an ECM to document the relationship between banks credit to both unemployment and poverty. This paper revealed bi-direction causality between banks credit and economic growth. Banks credit promotes economic growth and economic growth affects credit depth and financial development. Furthermore, banks credit is a growth accelerating factor on Indonesian economic growth. Banks credit is an endogenous growth and a good predictor on Indonesian economy. Our estimation model explained that credit allocated by banks increases business escalation to the real sectors then promotes economic growth, decreases unemployment rate through increasing in labor demanded, increases income and then decrease poverty. This overall transmission mechanism just occurred through presence of banks credit by increasing money supply to the real sectors, promotes growth and social welfare. Keywords : banks credit, economic growth, growth accelerating factor, poverty, unemployment JEL Classification : E51, E52, E58
17. The role of human capital formation in the transition to modern economic growth, 1300-1900
NARCIS (Netherlands)
de Pleijt, A.M.|info:eu-repo/dai/nl/375805621
2016-01-01
Economic models of the Industrial Revolution increasingly emphasize the key role of human capital in promoting economic growth, and empirical studies have shown that education is a strong predictor of per capita GDP. Contrary to the theory, however, economic historians have described the role of
18. SUSTAINABLE ECONOMIC GROWTH AND ECO-EFFICIENCY
Directory of Open Access Journals (Sweden)
Mariana\tLUPAN
2015-06-01
Full Text Available The current economic and social contexts have brought forth the issues regarding growth and sustainability. The concept of growth has always been linked to an increase in consumption levels, and this inevitably led to pressures on the environment and on the resources that support human activity. Given these circumstances, the question whether we can avoid an environmental disaster while maintaining economic growth, has become more stringent. We chose to approach this aspect by examining the concept of eco-efficiency, a concept that embodies aspects of both economic efficiency and environmental efficiency. Eco-efficiency can be regarded as the effectiveness with which resources are used in order to create products and services that satisfy human needs. Based on this idea, the last decade has produced an increasing number of studies on eco-efficiency and how it can be measured and implemented in the production of goods and services, but also in the field regarding demand patterns. An analysis regarding the aspects of eco-efficiency at the macro level of the Romanian economy is in line with the current environmental concerns, thus I have chosen to cover these questions, as well as the evolution of the locale economy towards a more sustainable development. The outcome of the examined aspects shows that, in spite of an increase in eco-efficiency levels, energy and material consumption and emissions have increased. This raises the question if measuring economic and environmental efficiency by reporting to the GDP value is becoming obsolete and if there is a need to revaluate eco-efficiency indicators in order to measure the transition to a greener and more sustainable development from different points of view.
19. Global warming, energy use, and economic growth
Science.gov (United States)
Khanna, Neha
The dissertation comprises four papers that explore the interactions between global warming, energy use, and economic growth. While the papers are separate entities, they share the underlying theme of highlighting national differences in the growth experience and their implications for long-term energy use and climate change. The first paper provides an overview of some key economic issues in the climate change literature. In doing so, the paper critically appraises the 1995 draft report of Working Group III of the Intergovernmental Panel on Climate Change. The focus is the choice of a pure rate of time preference in the economic modeling of climate change, abatement costs differentials between developed and developing countries, and contrasting implications of standard discount rates and value of life estimates for these two country groups. The second paper develops a global model that takes account of the depletion of oil resources in the context of a geo-economic model for climate change. It is found that in the presence of non-decreasing carbon and energy intensities and declining petroleum availability, the carbon emissions trajectory is much higher than that typically projected by other models of this genre. Furthermore, by introducing price and income sensitive demand functions for fossil fuels, the model provides a framework to assess the effectiveness of fuel specific carbon taxes in reducing the COsb2 emissions trajectory. Cross-price substitution effects necessitate unrealistically high tax rates in order to lower the projected emissions trajectory to the optimal level. The economic structure of five integrated assessment models for climate change is reviewed in the third paper, with a special focus on the macroeconomic and damage assessment modules. The final paper undertakes an econometric estimation of the changing shares of capital, labour, energy, and technical change in explaining the growth patterns of 38 countries. Production elasticities vary by
20. Natural Hazards, Poverty Traps versus Economic Growth
Science.gov (United States)
Netti, Dr.
2012-04-01
Governments, even in developed countries, devote too scarce resources to coping (ex-ante) with natural hazards; as a consequence of this short-sightedness, (ex-post) direct and indirect effects of catastrophic events deeply compromise the economic growth. Protective measures against natural hazards mean complex choices involving the opinions of multidisciplinary groups of experts in the fields of ecology, civic and geotechnical engineering, geology, meteorology, law and economics. Moreover, tools and choices affect different stakeholders: politicians, producers, consumers, taxpayers and voters. Complementarity between informed rationality and democracy need to be recognized and guaranteed as too often the perceptions of the majority of the stakeholders involved about natural hazards are not consistent with any objective information about the catastrophic event. The interaction between strict budget constraints, extremely high degrees of uncertainty, risk-aversion and credit rationing, trade-off between democracy and rationality, are the main causes of potential 'poverty traps'. First of all we believe that the 'reconstruction output' to be included in GDP as an ex-post effect of a natural hazard is a forced investment much more effective in crowding-out other consumption and investment and less effective for growth than investments aiming at increasing, ex-ante, the resiliency of the economy. Keynes' 'Animal Spirits' are embedded in positive expectation for future gains especially if not concentrated in reconstruction procurement sectors but spread across different sectors of the economy. The increased demand for reconstruction goods and services may act in both directions depending on the phase of the business cycles in which the economy is. Risk premiums for risk-averter investors increase in consequence of a natural hazard event; this restrict budget constraints and strengthen credit rationing. A mere replacement effect of the destroyed capital by a more
1. Economic Growth and Sustainable Housing: An Uneasy Relationship
DEFF Research Database (Denmark)
Buch-Hansen, Hubert
2017-01-01
Book review of: "Economic Growth and Sustainable Housing: An Uneasy Relationship" by Jin Xue (Routledge, 2014)......Book review of: "Economic Growth and Sustainable Housing: An Uneasy Relationship" by Jin Xue (Routledge, 2014)...
2. Dynamic analysis of savings and economic growth in Nigeria ...
African Journals Online (AJOL)
Dynamic analysis of savings and economic growth in Nigeria. ... a trivariate dynamic Granger causality model with savings, economic growth and foreign ... It is recommended that in the short run, policies in Nigeria should be geared towards ...
3. On climate change and economic growth
International Nuclear Information System (INIS)
Fankhauser, Samuel; Tol, Richard S.J.
2005-01-01
The economic impact of climate change is usually measured as the extent to which the climate of a given period affects social welfare in that period. This static approach ignores the dynamic effects through which climate change may affect economic growth and hence future welfare. In this paper we take a closer look at these dynamic effects, in particular saving and capital accumulation. With a constant savings rate, a lower output due to climate change will lead to a proportionate reduction in investment which in turn will depress future production (capital accumulation effect) and, in almost all cases, future consumption per capita. If the savings rate is endogenous, forward looking agents would change their savings behavior to accommodate the impact of future climate change. This suppresses growth prospects in absolute and per capita terms (savings effect). In an endogenous growth context, these two effects may be exacerbated through changes in labour productivity and the rate of technical progress. Simulations using a simple climate-economy model suggest that the capital accumulation effect is important, especially if technological change is endogenous, and may be larger than the direct impact of climate change. The savings effect is less pronounced. The dynamic effects are more important, relative to the direct effects, if climate change impacts are moderate overall. This suggests that they are more of a concern in developed countries, which are believed to be less vulnerable to climate change. The magnitude of dynamic effects is not sensitive to the choice of discount rate
4. FISCAL POLICY'S INFLUENCE ON ECONOMIC GROWTH IN THE EUROPEAN UNION
OpenAIRE
MIHAIU Diana Marieta; OPREANA Alin
2012-01-01
In this paper we study the impact of the fiscal policy on the economic growth for European Union, for the period 2000-2009. This subject represents a very debated problem in the economic literature. Our findings shows that, from the analysis of correlation between economic growth rate and total rate of taxation, there is generally an inverse relationship, meaning that an increase in the tax rate adversely affects economic growth. Continuing the analysis of the correlation between economic gro...
5. THE INFLUENCE OF GLOBALIZATION ON ECONOMIC GROWTH IN ROMANIA
Directory of Open Access Journals (Sweden)
PAUL BOGDAN ZAMFIR
2015-12-01
Full Text Available In this paper we propose to emphasize the structural changes involved by globalization process who generate a semnificative influence on the economic growth in Romania. Thus, on this background it is important to point out that even though the phenomenon of globalization represents manny opportunities for Romanian economic growth, nevertheles, our country must regard at the same time all the systemic risks that are involved in this process. From this perspective, an important role has the activity of romanian small and medium sized enterprises that through its specific creates jobs and contributes substantially to growth in Romania. In terms of risks, for our country is necessary to develop effective mechanisms of self-defense against involved economic dangers. Also, should not be ignored that the quality of European Union member offers for Romania a strong base and in the same time the chance to benefit from the positive effects of the single market and the opportunities offered by the global market. In this framework, Romanian economy is not exempted from stiff competition in the field of trade in goods and services from countries like China or India who succeed through competition, to "break down trade barriers" of economic blocs. More than that, Romanian high tech industry can take advantage for themselves from the positive effects of globalization process by penetrating on third country markets.
6. Does Economic Growth Reduce Childhood Undernutrition in Ethiopia?
Directory of Open Access Journals (Sweden)
Full Text Available Policy discussions and debates in the last couple of decades emphasized efficiency of development policies for translating economic growth to development. One of the key aspects in this regard in the developing world is achieving improved nutrition through economic development. Nonetheless, there is a dearth of literature that empirically verifies the association between economic growth and reduction of childhood undernutrition in low- and middle-income countries. Thus, the aim of the study is to assess the interplay between economic growth and reduction of childhood undernutrition in Ethiopia.The study used pooled data of three rounds (2000, 2005 and 2010 from the Demographic and Health Surveys (DHS of Ethiopia. A multilevel mixed logistic regression model with robust standard errors was utilized in order to account for the hierarchical nature of the data. The dependent variables were stunting, underweight, and wasting in children in the household. The main independent variable was real per capita income (PCI that was adjusted for purchasing power parity. This information was obtained from World Bank.A total of 32,610 children were included in the pooled analysis. Overall, 11,296 (46.7% [46.0%-47.3%], 8,197(33.8% [33.2%-34.4%] and 3,175(13.1% [12.7%-13.5%] were stunted, underweight, and wasted, respectively. We found a strong correlation between prevalence of early childhood undernutrition outcomes and real per capita income (PCI. The proportions of stunting (r = -0.1207, p<0.0001, wasting (r = -0.0338, p<0.0001 and underweight (r = -0.1035, p<0.0001 from the total children in the household were negatively correlated with the PCI. In the final model adjustment with all the covariates, economic growth substantially reduced stunting [β = -0.0016, SE = 0.00013, p<0.0001], underweight [β = -0.0014, SE = 0.0002, p<0.0001] and wasting [β = -0.0008, SE = 0.0002, p<0.0001] in Ethiopia over a decade.Economic growth reduces child undernutrition in
7. Medical Tourism and Its Implication on Malaysia's Economic Growth
OpenAIRE
Tang, Chor Foon
2015-01-01
Policymakers in the developed and developing countries already heading toward medical tourism to stimulate economic growth. Nonetheless, the actual impact of medical tourism on economic growth remains ambiguous. Although medical tourism may spur economic growth via its impact on foreign currency earnings, investments, tax revenue, and employment opportunities, it may also leave numerous negative externalities that either direct or indirectly harmful the process of economic growth. Undeniably,...
8. Electricity consumption and economic growth: evidence from Korea
International Nuclear Information System (INIS)
Yoo, Seung-Hoon
2005-01-01
This paper investigates the short- and long-run causality issues between electricity consumption and economic growth in Korea by using the co-integration and error-correction models. It employs annual data covering the period 1970-2002. The overall results show that there exists bi-directional causality between electricity consumption and economic growth. This means that an increase in electricity consumption directly affects economic growth and that economic growth also stimulates further electricity consumption
9. India's refining prospects linked to economic growth
International Nuclear Information System (INIS)
Lewis, E.
1996-01-01
International investors assess refining ventures in India the same way they do comparable projects elsewhere in the world: according to their expectations about investment returns. By that standard, India's appeal is mixed, although its need for some measure of additional refining capacity seems certain. The success of future refinery investments will depend heavily on the government's commitment to policies allowing the economy to grow faster than the population. Unless accompanied by economic growth, expected increases in the population will not automatically raise demand for petroleum products. Decisions about investments in India's refining sector, therefore, must carefully weigh market fundamentals, the business environment, and likely investment performance. This paper reviews the market for the various products and predicts new economic trends
10. Political regime change, economic liberalization and growth accelerations
NARCIS (Netherlands)
Jong-A-Pin, Richard; De Haan, Jakob
We examine whether the type of political regime, regime changes, and economic liberalization are related to economic growth accelerations. Our results show that growth accelerations are preceded by economic liberalizations. We also find that growth accelerations are less likely to happen the longer
11. End-of-the-Year Economic Growth and Time-varying Expected Returns
DEFF Research Database (Denmark)
Møller, Stig Vinther; Rangvid, Jesper
. To explain these results, we show as the second main fi?nding of our paper that economic growth and growth in economic confidence (consumer con?dence and business con?dence) are strongly correlated during the fourth quarter, but not during the other quarters. In summary, we therefore show that when economic......We show that macroeconomic growth at the end of the year (fourth-quarter or December) strongly predicts the returns of the aggregate market, small- and large-cap stocks, portfolios sorted on book-to-market and dividend yields, bond returns, and international stock returns, whereas economic growth...... during the rest of the year does not predict returns. End-of-the-year economic growth rates contain considerably more information about expected returns than standard variables used to predict returns, are robust to the choice of macro variables, and work in-sample, out-of-sample, and in subsamples...
12. End-of-the-year economic growth and time-varying expected returns
DEFF Research Database (Denmark)
Møller, Stig Vinther; Rangvid, Jesper
. To explain these results, we show as the second main fi…nding of our paper that economic growth and growth in economic confidence (consumer con…dence and business con…dence) are strongly correlated during the fourth quarter, but not during the other quarters. In summary, we therefore show that when economic......We show that macroeconomic growth at the end of the year (fourth-quarter or December) strongly predicts the returns of the aggregate market, small- and large-cap stocks, portfolios sorted on book-to-market and dividend yields, bond returns, and international stock returns, whereas economic growth...... during the rest of the year does not predict returns. End-of-the-year economic growth rates contain considerably more information about expected returns than standard variables used to predict returns, are robust to the choice of macro variables, and work in-sample, out-of-sample, and in subsamples...
13. Directed Technical Change and Economic Growth Effects of Environmental Policy
DEFF Research Database (Denmark)
Kruse-Andersen, Peter Kjær
2016-01-01
A Schumpeterian growth model is developed to investigate how environmental policy affects economic growth when environmental policy also affects the direction of technical change. In contrast to previous models, production and pollution abatement technologies are embodied in separate intermediate...... unambiguously directs research efforts toward pollution abatement technologies and away from production technologies. This directed technical change reduces economic growth and pollution emission growth. Simulation results indicate that even large environmental policy reforms have small economic growth effects....... However, these economic growth effects have relatively large welfare effects which suggest that static models and exogenous growth models leave out an important welfare effect of environmental policy....
14. Development of Technology Transfer Economic Growth Metrics
Science.gov (United States)
Mastrangelo, Christina M.
1998-01-01
The primary objective of this project is to determine the feasibility of producing technology transfer metrics that answer the question: Do NASA/MSFC technical assistance activities impact economic growth? The data for this project resides in a 7800-record database maintained by Tec-Masters, Incorporated. The technology assistance data results from survey responses from companies and individuals who have interacted with NASA via a Technology Transfer Agreement, or TTA. The goal of this project was to determine if the existing data could provide indications of increased wealth. This work demonstrates that there is evidence that companies that used NASA technology transfer have a higher job growth rate than the rest of the economy. It also shows that the jobs being supported are jobs in higher wage SIC codes, and this indicates improvements in personal wealth. Finally, this work suggests that with correct data, the wealth issue may be addressed.
15. Economic growth and greenhouse gas emissions
Energy Technology Data Exchange (ETDEWEB)
Ansuategi, Alberto [Environment Department, University of York, York (United Kingdom); Escapa, Marta [Foundations of Economic Analysis Department, University of the Basque Country, Bilbao (Spain)
2002-01-01
Recent empirical research has examined the relationship between certain indicators of environmental degradation and income, concluding that in some cases an inverted U-shaped relationship, which has been called an environmental Kuznets curve (EKC), exists between these variables. Unfortunately, this inverted U-shaped relationship does not hold for greenhouse gas emissions. One explanation of the absence of EKC-like behavior in greenhouse gas emissions is that greenhouse gases are special pollutants that create global, not local, disutility. But the international nature of global warming is not the only reason that prevents de-linking greenhouse gas emissions from economic growth. The intergenerational nature of the negative impact of greenhouse gas emissions may have also been an important factor preventing the implementation of greenhouse gas abatement measures in the past. In this paper we explore the effect that the presence of intergenerational spillovers has on the emissions-income relationship. We use a numerically calibrated overlapping generations model of climate-economy interactions. We conclude that: (1) the intertemporal responsibility of the regulatory agency, (2) the institutional capacity to make intergenerational transfers and (3) the presence of intergenerationally lagged impact of emissions constitute important determinants of the relationship between economic growth and greenhouse gas emissions.
16. [Analysis of grey correlation between energy consumption and economic growth in Liaoning Province, China.
Science.gov (United States)
Wang, Li; Xi, Feng Ming; Wang, Jiao Yue
2016-03-01
The contradiction between energy consumption and economic growth is increasingly prominent in China. Liaoning Province as one of Chinese heavy industrial bases, consumes a large amount of energy. Its economic development has a strong dependence on energy consumption, but the energy in short supply become more apparent. In order to further understand the relationship between energy consumption and economic growth and put forward scientific suggestions on low carbon development, we used the grey correlation analysis method to separately examine the relevance of economic growth with energy consumption industries and energy consumption varieties through analy sis of energy consumption and economic growth data in Liaoning Province from 2000 to 2012. The results showed that the wholesale and retail sector and hotel and restaurant sector were in the minimum energy consumption in all kinds of sectors, but they presented the closest connection with the economic growth. Although industry energy consumption was the maximum, the degree of connection between industry energy consumption and economic growth was weak. In all types of energy consumption, oil and hydro-power consumption had a significant connection with economic growth. However, the degree of connection of coal consumption with economic growth was not significant, which meant that coal utilization efficiency was low. In order to achieve low carbon and sustainable development, Liaoning Province should transform the economic growth mode, adjust industry structure, optimize energy structure, and improve energy utilization efficiency, especially promote producer services and develop clean and renewable energy.
17. Green economic growth premise for sustainable development
Directory of Open Access Journals (Sweden)
Carmen Lenuţa TRICĂ
2013-01-01
Full Text Available Accelerating the global issues such as natural resource depletion, damage to the natural environment, economic and financial crises and consumption growth led to the shift of the development paradigm from consumption to sustainable development and recognition of the new path, namely green economy.At the European level a number of international organizations discussed issues of transition to green economy (EC, UNEP, OECD. In 2008, UNEP launched “Green Economy Initiative to Get the Global Markets Back to Work”, aiming to mobilize and re-focuse the global economy towards.This is the twin challenge of moving towards a green economy: radically reducing the footprint of developed countries, while simultaneously raising levels of social and material well being in developing countries.Without public intervention, the related market failures (i.e. market prices that do not fully reflect the environmental degradation generated by economic activity may delay or even prevent the development of environmentally-friendly technologies.Furthermore, in sectors such as electricity, network effects arising from existing infrastructures create additional barriers to the adoption of alternative sources of power, further hampering incentives to invest in new technologies.Given that the transition to a green economy requires increasing of investment in economic sectors that contribute to enhancing of natural capital and reduce environmental risks, we intend to analyze the main measures taken by Romania to ensure transition to green economy.
18. Financial sector and economic growth in the Republic of Croatia 1995-2005
Directory of Open Access Journals (Sweden)
Novotny Damir
2006-01-01
Full Text Available Financial sector in the Republic of Croatia had a strong growth between 1995 2005.g. Liberalization of financial sector in 1999 led to an increase in bank foreign debt, which resulted in a strong increase in foreign currency reserves and appreciation of the national currency. The growth of the financial sector and credit expansion have been allocated in favour of private and public consumption, but not in industry investments. GDP growth didn't have the same momentum as financial aggregates. Economic growth, after a contraction in 1999 was within the average of global economic growth. Relying on neoclassical growth model, government and central bank didn't put in place the needed set of pro-active policies. Factor allocation was solely through private bank channels financing private consumption. If the sustainable economic growth and new employment are to be major macroeconomic goals, a new macroeconomic paradigm as combination of neclassical and neokeynesians approach will be needed.
19. Sustainable Economic Growth: a Perspective for Macedonia
Directory of Open Access Journals (Sweden)
Sevil Rexhepi
2013-09-01
Full Text Available Retrospective analysis shows that since 1990’s, ex-socialist economies were in transition. This process was multidimensional and had deep roots. In most transition economies, output (GDP is determined by the availability of labour, capital and their productivity (TFP. Hence, these indicators are not generating the business cycles, which is typical for market economies in the long-term. At this point, it is vital to understand the reasons of low-level of capital accumulation in transition economies in order to find opportunities to make better use of physical, human and social capital. Furthermore, it is observed that in these economies, institutions needed to be re-established or the rules of the game needed to be changed to regulate incentive structures that will lead to growth. The main objective of this research is to identify the peculiarity of economic growth in Macedonia and to examine if achieving smart growth in long-term is possible; which is supported by fundamental notions of sustainable development.
20. Economic growth factors system: theoretical and methodological aspect
OpenAIRE
H.Ya. Hlukha
2014-01-01
The aim of the article. The main objective of the article is to create theoretical grounds to build the system of economic growth factors, to modernize their classification, to define exogenous and endogenous factors, to analyze them within the state economic policy structure. The results of the analysis. The article focuses on economic growth factors theoretical studies: - economic growth factors classification characteristics have been highlighted; - various approaches to determine...
1. Causality tests between stock market development and economic growth in West African Monetary Union
Directory of Open Access Journals (Sweden)
Maman Tachiwou ABOUDOU
2009-12-01
Full Text Available This paper examines the causal relationship between stock market development and economic growth for the West African Monetary Union economy over the last decade or so. By applying the techniques of unit–root tests and the long–run Granger noncausality test proposed by Toda and Yamamoto (1995, the causal relationships between the real GDP growth rate and two stock market development proxies are tested. The results are in line with the supply leading hypothesis in the sense that there is strong causal flow from the stock market development to economic growth. A unidirectional causal relationship is also observed between real market capitalization ratio and economic growth.
2. How robust is the relationship between economic freedom and economic growth?
NARCIS (Netherlands)
Sturm, JE; De Haan, J
Using various indicators for economic freedom, it is shown that increases in economic freedom are robustly related to economic growth. This conclusion holds even if the impact of outlying observations is taken into account. The level of economic freedom is not related to growth.
3. Financial Management and Economic Growth: The European Countries Experience
Directory of Open Access Journals (Sweden)
Nuno Carlos LEITÃO
2012-12-01
Full Text Available The purpose of this research is to investigate the impact of financial development on economic growth applied to European Countries. The initial GDP per capita is negatively correlated with growth of real GDP per capita. Our study shows that there is convergence within European Countries for the period 1990-2009. This paper confirms relevant theoretical hypothesis as international trade and saving encourage the economic growth. The inflation has a negative impact on economic growth as previous studies.
4. The Relationship Among Poverty, Economic Growth, and Inequality Revisited
OpenAIRE
Lonnie K. Stevans; David N. Sessions
2008-01-01
It has been shown in prior research that increased economic growth reduces poverty. Authors have also found that the effect of growth in Gross Domestic Product (GDP) on poverty growth has either diminished or remained unchanged over time, and economic expansion in the 1980s in the United States had no affect on poverty. Using a formal error-correction model, we find that increases in economic growth are significantly related to reductions in the poverty rate for all families. Specifically, GD...
5. Social Capital, Economic Growth and Transition Economies
DEFF Research Database (Denmark)
Svendsen, Gert Tinggaard
1998-01-01
transactions to take place without third-party enforcement. Theory and lessons from empirical evidence lead to three general recommendations for building social capital in the future: First, the state must withdraw and minimize its role in the economy so to leave room for voluntary organization and free......Summary: What does social capital mean and how can it be built? Social capital is considered as a new production factor which must be added to the conventional concepts of human and physical capital. Social capital is productive because it increases the level of trust in a society and allows more......-trade. Second, state withdrawal should be combined with efforts to increase economic growth and gain popular support for the implementation of reforms. Third, voluntary groups, beneficial to the economy, should not be institutionalized to prevent them from turning into harmful rent-seeking groups....
6. Correlations between Labor Employment and Economic Growth
Directory of Open Access Journals (Sweden)
Sfichi Elena Daniela
2017-01-01
Full Text Available The main objectives of macroeconomic policy for most governments are: a high level of labouremployment, price stability and high rate of economic growth. As far as I walk in life, I learnsomething new, everywhere I go, I find something that fascinates me. This is why this subject hasan influence over me, I wonder every day why people find a job to maintain with such difficulty andwhy they are so lazy when they hear about work. This type of behaviour leads to a huge increase ofunemployment, because people leave their courage under an invisible line and create a fakepersonality where they hide saying that they can’t do what society wants. In case that increasinginflation is obvious, unemployment is decreasing and people are trying to find something to do, towork, because inflation also leads to some actions which affect directly the unemployed ones.
7. SUSTAINABLE ECONOMIC GROWTH THROUGH EXTERNAL TRADE
Directory of Open Access Journals (Sweden)
Valentina Vasile
2016-12-01
Full Text Available A country’s economic growth is directly influenced by the external trade activity, which is considered by the majority of economists as one of the main engines of a country. How international trade can contributes to a sustainable development of a country depends broadly on the economic policies as well as on global and regional strategies to support the actions for this objective. The high level political meeting of United Nations Organization’s Member States in September 2015 has as aim the adoption of 2030 Agenda for Sustainable Development, which includes global economic, social and environmental goals. Any strategy or global policy influences, of course, in a direct way the international trade activities, by how these measures affect or determine relations between states to achieve the sustainable development objectives. Being involved in all sectors of economic and social life to achieve these noble goals, foreign trade is of course on the list of key areas as well as on the list of the domains being influenced by the global strategy adopted in the framework of the largest summit of its kind in the history of the United Nations. The aim of this paper is to provide an overview of external trade activity of Romania, taking into account the characteristics of companies involved in exports and imports of goods in Romania as well as to identify the key areas to be further developed for a sustainable development of national economy based on export activity. Romania's sustainable development can be achieved in the medium and long term by complementary and converging actions such as increased expenditure on research and development field, attracting as a priority the Greenfield investments, increasing productivity of national capital (human, natural, technological or ensure the efficiency at microeconomic and macroeconomic level. Increasing the share of products and activities using a small amount of energy and material resources but which
8. Climate indices strongly influence old-growth forest carbon exchange
Science.gov (United States)
Sonia Wharton; Matthias Falk
2016-01-01
We present a decade and a half (1998â2013) of carbon dioxide fluxes from an old-growth stand in the American Pacific Northwest to identify ecosystem-level responses to Pacific teleconnection patterns, including the El Niño/Southern Oscillation (ENSO). This study provides the longest, continuous record of old-growth eddy flux data to date from one of the longest running...
9. Predicting economic growth with stock networks
Science.gov (United States)
Heiberger, Raphael H.
2018-01-01
Networks derived from stock prices are often used to model developments on financial markets and are tightly intertwined with crises. Yet, the influence of changing market topologies on the broader economy (i.e. GDP) is unclear. In this paper, we propose a Bayesian approach that utilizes individual-level network measures of companies as lagged probabilistic features to predict national economic growth. We use a comprehensive data set consisting of Standard and Poor's 500 corporations from January 1988 until October 2016. The final model forecasts correctly all major recession and prosperity phases of the U.S. economy up to one year ahead. By employing different network measures on the level of corporations, we can also identify which companies' stocks possess a key role in a changing economic environment and may be used as indication of critical (and prosperous) developments. More generally, the proposed approach allows to predict probabilities for different overall states of social entities by using local network positions and could be applied on various phenomena.
10. Electricity consumption and economic growth in seven South American countries
International Nuclear Information System (INIS)
Yoo, Seung-Hoon; Kwak, So-Yoon
2010-01-01
This paper attempts to investigate the causal relationship between electricity consumption and economic growth among seven South American countries, namely Argentina, Brazil, Chile, Columbia, Ecuador, Peru, and Venezuela using widely accepted time-series techniques for the period 1975-2006. The results indicate that the causal nexus between electricity consumption and economic growth varies across countries. There is a unidirectional, short-run causality from electricity consumption to real GDP for Argentina, Brazil, Chile, Columbia, and Ecuador. This means that an increase in electricity consumption directly affects economic growth in those countries. In Venezuela, there is a bidirectional causality between electricity consumption and economic growth. This implies that an increase in electricity consumption directly affects economic growth and that economic growth also stimulates further electricity consumption in that country. However, no causal relationships exist in Peru. The documented evidence from seven South American countries can provide useful information for each government with regard to energy and growth policy.
11. Management of business economic growth as function of resource rents
Science.gov (United States)
Prljić, Stefan; Nikitović, Zorana; Stojanović, Aleksandra Golubović; Cogoljević, Dušan; Pešić, Gordana; Alizamir, Meysam
2018-02-01
Economic profit could be influenced by economic rents. However natural resource rents provided different impact on the economic growth or economic profit. The main focus of the study was to evaluate the economic growth as function of natural resource rents. For such a purpose machine learning approach, artificial neural network, was used. The used natural resource rents were coal rents, forest rents, mineral rents, natural gas rents and oil rents. Based on the results it is concluded that the machine learning approach could be used as the tool for the economic growth evaluation as function of natural resource rents. Moreover the more advanced approaches should be incorporated to improve more the forecasting accuracy.
12. Justifying the Ivory Tower: Higher Education and State Economic Growth
Science.gov (United States)
Baldwin, J. Norman; McCracken, William A., III
2013-01-01
As the U.S. continues to embrace a comprehensive plan for economic recovery, this article investigates the validity of the claim that investing in higher education will help restore state economic growth and prosperity. It presents the findings from a study that indicates that the most consistent predictors of state economic growth related to…
13. Shocks in economic growth=shocking effects for food security?
NARCIS (Netherlands)
Kavallari, A.; Fellmann, T.; Hubertus Gay, H.
2014-01-01
The recent economic and financial turmoil raises the question on how global economic growth affects agricultural commodity markets and, hence, food security. To address this question, this paper assesses the potential impacts of faster economic growth in developed and emerging economies on the one
14. Effects of Credit on Economic Growth, Unemployment and Poverty
OpenAIRE
Sipahutar, Mangasa Augustinus
2016-01-01
Abstract Effect of credit on economic growth, unemployment and poverty provides evidence from Indonesia on the role of banks credit for promoting economic growth and reducing both unemployment and poverty. To document the link between banks credit and economic growth, we estimate a VAR model and variance decompositions of annual GDP per capita growth rates to examine what proxy measures of banks credit are most important in accounting for economic growth over time and ho...
15. SPORTS INDUSTRY – A POTENTIAL NEW SOURCE OF ECONOMIC GROWTH
Directory of Open Access Journals (Sweden)
Marian STAN, PhD Student, Free International University of Moldova
2016-08-01
Full Text Available The aim of the paper is to study the impact of sports industry on the economic growth of a country, with a further perspective for the Republic of Moldova. The novelty consists in the necessity of a wider research of the activities of sports organizations and their impact on the economic activities within a country, as there are existing worldwide examples that could serve as a strong argument in this case. The results were achieved using the following methods: statistical, analytical, comparison, etc. Understanding that modernization of the sport industry is necessary for any country, including the Republic of Moldova could result in the determination of the linkage between sports and further development of the country.
16. Fertilizing growth: Agricultural inputs and their effects in economic development.
Science.gov (United States)
McArthur, John W; McCord, Gordon C
2017-07-01
This paper estimates the role of agronomic inputs in cereal yield improvements and the consequences for countries' processes of structural change. The results suggest a clear role for fertilizer, modern seeds and water in boosting yields. We then test for respective empirical links between agricultural yields and economic growth, labor share in agriculture and non-agricultural value added per worker. The identification strategy includes a novel instrumental variable that exploits the unique economic geography of fertilizer production and transport costs to countries' agricultural heartlands. We estimate that a half ton increase in staple yields generates a 14 to 19 percent higher GDP per capita and a 4.6 to 5.6 percentage point lower labor share in agriculture five years later. The results suggest a strong role for agricultural productivity as a driver of structural change.
17. Remarks on economic growth and energy demand
International Nuclear Information System (INIS)
Mueller, W.
1979-01-01
An energy policy according to the principles of decoupling is impossible without an increase in reasonable and profitable power application. It is also impossible without increased nuclear energy. Energy policy according to the principles of decoupling connects the natural growth tendency of a liberally arranged industry with the natural limits of the production factor 'nature'. Energy policy is the very sphere where tomorrow's necessities must be planned today. If in long range, a constant level of energy production struturised different from today's can be assumed, then this is future-bound. For it takes into consideration today tomorrow's necessities. This is the only guarantee we have for our industry to be able to grow tomorrow. On the basis of historical experience, an economic system will believe in the goal of a constant energy supply just as it was believing in abounding in energy up to day. The structure of the growth might change in long term. But accepting the thoughts of decoupling, progress will come. (orig./HP) [de
18. Modelling of strongly coupled particle growth and aggregation
International Nuclear Information System (INIS)
Gruy, F; Touboul, E
2013-01-01
The mathematical modelling of the dynamics of particle suspension is based on the population balance equation (PBE). PBE is an integro-differential equation for the population density that is a function of time t, space coordinates and internal parameters. Usually, the particle is characterized by a unique parameter, e.g. the matter volume v. PBE consists of several terms: for instance, the growth rate and the aggregation rate. So, the growth rate is a function of v and t. In classical modelling, the growth and the aggregation are independently considered, i.e. they are not coupled. However, current applications occur where the growth and the aggregation are coupled, i.e. the change of the particle volume with time is depending on its initial value v 0 , that in turn is related to an aggregation event. As a consequence, the dynamics of the suspension does not obey the classical Von Smoluchowski equation. This paper revisits this problem by proposing a new modelling by using a bivariate PBE (with two internal variables: v and v 0 ) and by solving the PBE by means of a numerical method and Monte Carlo simulations. This is applied to a physicochemical system with a simple growth law and a constant aggregation kernel.
19. Analysis of domestic debt: implication for economic growth in Nigeria
African Journals Online (AJOL)
This paper principally analysed the importance of domestic debt on economic growth of Nigeria. The objective of the study is to investigate the relationship between government domestic debt and economic growth and policy that is likely to improve private sector investment and break growth resistance problem.
20. Market-oriented institutions and policies and economic growth : A critical survey
NARCIS (Netherlands)
De Haan, J; Lundstrom, S; Sturm, JE
This paper surveys recent evidence suggesting that market-oriented institutions and policies are strongly related to economic growth, focusing on studies using the economic freedom (EF) indicator of the Fraser Institute. This index is critically discussed. Also various serious shortcomings of
1. Foreign direct investment and economic growth: A theoretical framework
Directory of Open Access Journals (Sweden)
Edmore Mahembe
2014-05-01
Full Text Available The relationship between FDI and economic growth has attracted considerable attention over the years. Despite the important role played by FDI in economic growth, a number of policy-makers have not fully understood the theoretical linkage between FDI and economic growth. The aim of this paper, therefore, is to review the theoretical literature on the relationship between FDI and economic growth in a stylized fashion. The theoretical literature reviewed in this study show that FDI is a key contributor to the economic growth of the host country. FDI affects economic growth through two broad channels: (i FDI can encourage the adoption of new technologies in the production process through technological spillovers; and (ii FDI may stimulate knowledge transfers, both in terms of labour training and skill acquisition, and also by introducing alternative management practices and better organisational arrangements.
2. Gender Factors and Inclusive Economic Growth: The Silent Revolution
Directory of Open Access Journals (Sweden)
Laura Cabeza-García
2018-01-01
Full Text Available The gender factors that trigger economic growth in both high- and low-income countries were investigated in this study. To address these gender factors, four characteristic dimensions of gender inclusion were considered: education, access to the labor market, fertility, and democracy. The relationship between economic growth and gender factors was analyzed in a sample of 127 countries. Value and robustness were added to the results using dynamic models applied to panel data while accounting for endogeneity. We conclude that high fertility in women has negative effects on economic growth. However, when women have greater access to secondary education and the labor market in conditions of equality, the effects are positive. Similarly, the access of women to active political participation has significant effects on economic growth. Overall, this study helps identify which gender factors may promote inclusive economic growth, which is economic growth achieved when both men and women are incorporated in equal conditions.
3. Macroeconomic Determinants of Economic Growth: A Review of International Literature
Directory of Open Access Journals (Sweden)
Chirwa Themba G.
2016-12-01
Full Text Available The paper conducts a qualitative narrative appraisal of the existing empirical literature on the key macroeconomic determinants of economic growth in developing and developed countries. Much as other empirical studies have investigated the determinants of economic growth using various econometric methods, the majority of these studies have not distinguished what drives or hinders economic growth in developing or developed countries. The study finds that the determinants of economic growth are different when this distinction is used. It reveals that in developing countries the key macroeconomic determinants of economic growth include foreign aid, foreign direct investment, fiscal policy, investment, trade, human capital development, demographics, monetary policy, natural resources, reforms and geographic, regional, political and financial factors. In developed countries, the study reveals that the key macroeconomic determinants that are associated with economic growth include physical capital, fiscal policy, human capital, trade, demographics, monetary policy and financial and technological factors.
4. The Services Sector and Economic Growth in Mauritius. A Bounds ...
African Journals Online (AJOL)
Nafiisah
stability of the relationship between services sector development and economic ... sector on the economic growth of the small island economy of Mauritius. ...... significant structural instability (The figures are presented in the Appendix). 6.
5. Temperature impacts on economic growth warrant stringent mitigation policy
Science.gov (United States)
Moore, Frances C.; Diaz, Delavane B.
2015-02-01
Integrated assessment models compare the costs of greenhouse gas mitigation with damages from climate change to evaluate the social welfare implications of climate policy proposals and inform optimal emissions reduction trajectories. However, these models have been criticized for lacking a strong empirical basis for their damage functions, which do little to alter assumptions of sustained gross domestic product (GDP) growth, even under extreme temperature scenarios. We implement empirical estimates of temperature effects on GDP growth rates in the DICE model through two pathways, total factor productivity growth and capital depreciation. This damage specification, even under optimistic adaptation assumptions, substantially slows GDP growth in poor regions but has more modest effects in rich countries. Optimal climate policy in this model stabilizes global temperature change below 2 °C by eliminating emissions in the near future and implies a social cost of carbon several times larger than previous estimates. A sensitivity analysis shows that the magnitude of climate change impacts on economic growth, the rate of adaptation, and the dynamic interaction between damages and GDP are three critical uncertainties requiring further research. In particular, optimal mitigation rates are much lower if countries become less sensitive to climate change impacts as they develop, making this a major source of uncertainty and an important subject for future research.
6. Agglomeration Economies, Economic Growth and the New Economic Geography in Mexico
OpenAIRE
Alejandro Diaz-Bautista
2005-01-01
The present study of regional economic growth in Mexico is based on the new economic geography, where distance plays an important role in explaining urban regional economic growth. The results show that distance to the northern border of Mexico and labor migration between states of Mexico, after the passage of NAFTA are important factors that explain the regional state growth and agglomerations in Mexico between 1994 and 2000. The results also indicate that job growth and FDI are not signific...
7. Economic Recovery: Sustaining U.S. Economic Growth in a Post-Crisis Economy
Science.gov (United States)
2010-07-22
Mankiw , Principles of Economics (Ft. Worth, Dryden Press, 1998), p556, and Robert J. Barro, “Are Government Bonds Net Wealth?” Journal of Political...CRS Report for Congress Prepared for Members and Committees of Congress Economic Recovery: Sustaining U.S. Economic Growth in a Post...2. REPORT TYPE 3. DATES COVERED 00-00-2010 to 00-00-2010 4. TITLE AND SUBTITLE Economic Recovery: Sustaining U.S. Economic Growth in a Post
8. Institutions, regulatory role and economic growth of national economies
Directory of Open Access Journals (Sweden)
2008-12-01
Full Text Available In the present time, characterized by the rapid disturbances in all time more connected global economy, territorially as well as structurally, the role of the state’s influence and responsibility with the adequate institutional addresses and procedures, defined in larger context, becomes the essential point not only of the further growth but also of the existing relations viability. It is simply because the encirclement does not function on the principle of status quo situation any more. Therefore, the role and significance of institutions, adequate regulatory role of these addresses, in the context of demand of permanent and stable economic growth, are of particular interest in the creation of this model. This analysis gains in importance studying the realized accelerated economic growth of states from some parts of the world, notably in the period after WW II. This question turned out to be exceptionally essential during the analysis of national strategies of accelerated economic growth (catch up strategy. On the other side of analysis are the transition period and the processes realized on the territory of the East and Central European states up to 1990 that were under the strong influence of the USSR. The attempts and mistakes in the quest for adequate balance of the market role were initially indoctrinated and led by the predominant conviction that the principles of Washington consensus will lead up to accelerated and efficient change of the entire structure of national economies and new frames for future behaviour. The problems that appeared very soon led to the establishment of significantly more balanced first the understanding and then to establishing significantly, more appropriate concept of balance and complementarity of market development with the permanently present role and responsibility of the state in this process and on this road.
9. Understanding the Drivers of Economic Growth: Grounding Endogenous Economic Growth Models in Resource-Advantage Theory
OpenAIRE
Hunt, Shelby D.
2012-01-01
Foss (2012) provides an informed and informative comment on my article “Trust, Personal Moral Codes, and the Resource-Advantage Theory of Competition: Explaining Productivity, Economic Growth, and Wealth Creation” (Hunt, 2012). In general, his comment is highly supportive of both the theory and the arguments developed in my article. He does, however, raise certain issues that need to be addressed. These issues relate to the concept of total factor productivity, the role of institutions in pro...
10. ENTREPRENEURSHIP SUPPORT OF ECONOMIC GROWTH IN CHINA (I
Directory of Open Access Journals (Sweden)
2015-02-01
Full Text Available Economic growth over the past three decades in China has captured the interest of the whole world. Many nations, governments, business and science look admiringly to "Chinese miracle". The performance of this country is the more remarkable as it includes, besides the effort to go beyond a developing country and the transition from a communist economy to the market economy. "Chinese development model", whereof spoken more and more in this period is unclear due to some nuances not really classical approach to development paradigm, which focuses on promoting democracy, human rights privatization, liberalization and the fight against corruption. Through the new model, some authors, starting from high authority of the state over property and finances, assigns to it a key role in economic growth. From their point of view, the strong boom of the private sector in China is the result of the opening provided by the state and not as a prerequisite for development. This perception is unpopular but other authors who argue that "the Chinese success had as basic ingredients exactly private entrepreneurship, private property, financial and even political reforms, though not always apparent at first glance." This study made a brief foray into Chinese entrepreneurship development, opening new possibilities of deepening towards understanding how it managed to contribute to the development and growth of the country.
11. Does education engender cultural values that matter for economic growth?
OpenAIRE
Prosper F. Bangwayo-Skeete; Afaf H. Rahim; Precious Zikhali
2009-01-01
Empirical research has shown that cultural values matter for economic growth and has specifically identified the achievement motivation as an aspect of culture that engenders economic growth. If specific cultural values engender economic growth, how then can societies promote them? This paper attempts to answer this question using the 2005 wave of the World Values Survey data for 43 countries. We test the contention that education significantly impacts the relative importance an individual pl...
12. The South African tax mix and economic growth
OpenAIRE
AH de Wet; NJ Schoeman; SF Koch
2014-01-01
The research reported in this paper suggests that government fiscal policy can influence economic growth through alterations in the tax mix and the overall size of government spending. The authors estimate the impact on economic growth of changes in fiscal policy via government expenditure, direct taxation and indirect taxation. The results show that economic growth is negatively affected by increases in the size of government, as reflected in its expenditures and direct tax revenues, alth...
13. Economic growth and carbon emission control
Science.gov (United States)
Zhang, Zhenyu
The question about whether environmental improvement is compatible with continued economic growth remains unclear and requires further study in a specific context. This study intends to provide insight on the potential for carbon emissions control in the absence of international agreement, and connect the empirical analysis with theoretical framework. The Chinese electricity generation sector is used as a case study to demonstrate the problem. Both social planner and private problems are examined to derive the conditions that define the optimal level of production and pollution. The private problem will be demonstrated under the emission regulation using an emission tax, an input tax and an abatement subsidy respectively. The social optimal emission flow is imposed into the private problem. To provide tractable analytical results, a Cobb-Douglas type production function is used to describe the joint production process of the desired output and undesired output (i.e., electricity and emissions). A modified Hamiltonian approach is employed to solve the system and the steady state solutions are examined for policy implications. The theoretical analysis suggests that the ratio of emissions to desired output (refer to 'emission factor'), is a function of productive capital and other parameters. The finding of non-constant emission factor shows that reducing emissions without further cutting back the production of desired outputs is feasible under some circumstances. Rather than an ad hoc specification, the optimal conditions derived from our theoretical framework are used to examine the relationship between desired output and emission level. Data comes from the China Statistical Yearbook and China Electric Power Yearbook and provincial information of electricity generation for the year of 1993-2003 are used to estimate the Cobb-Douglas type joint production by the full information maximum likelihood (FIML) method. The empirical analysis shed light on the optimal
14. Strong sales growth in 2006: + 21 per cent
Energy Technology Data Exchange (ETDEWEB)
NONE
2007-07-01
Paris, February 14, 2007 - The Gaz de France group today reported record consolidated sales of euro 27,642 million in 2006, up 21 per cent compared with 2005. Under average weather conditions and comparable accounting methods, sales increased by 24 per cent versus 2005. This growth results primarily from an overall increase in European energy prices notwithstanding the slight decrease in prices towards the end of the year. The group also benefited from an increase in volumes and from the integration of new operations. After a colder first half of the year compared to that of the previous year, the autumn of 2006 was particularly warm. This had a negative impact on sales growth (there was a 12 billion kWh decrease between 2005 and 2006). The sales generated by the group's international activities increased by 33 per cent to a total of euro 10,839 m in 2006 and now account for almost 40 per cent of the group's overall sales. In this context, the group confirmed at the board meeting held on January 23, 2007 that it would reach the targets set for 2006, namely: - Growth in EBITDA above 20 per cent, e.g. in excess of euro 5 billion, - Net income of more than euro 2.2 billion.
15. Strong sales growth in 2006: + 21 per cent
International Nuclear Information System (INIS)
2007-01-01
Paris, February 14, 2007 - The Gaz de France group today reported record consolidated sales of euro 27,642 million in 2006, up 21 per cent compared with 2005. Under average weather conditions and comparable accounting methods, sales increased by 24 per cent versus 2005. This growth results primarily from an overall increase in European energy prices notwithstanding the slight decrease in prices towards the end of the year. The group also benefited from an increase in volumes and from the integration of new operations. After a colder first half of the year compared to that of the previous year, the autumn of 2006 was particularly warm. This had a negative impact on sales growth (there was a 12 billion kWh decrease between 2005 and 2006). The sales generated by the group's international activities increased by 33 per cent to a total of euro 10,839 m in 2006 and now account for almost 40 per cent of the group's overall sales. In this context, the group confirmed at the board meeting held on January 23, 2007 that it would reach the targets set for 2006, namely: - Growth in EBITDA above 20 per cent, e.g. in excess of euro 5 billion, - Net income of more than euro 2.2 billion
16. Investment in Education and Economic Growth in Nigeria: 1981 ...
African Journals Online (AJOL)
PROF. O. E. OSUAGWU
2013-12-01
Dec 1, 2013 ... Keywords: Education, Government Investments, Economic growth, Health, Government ..... poor countries, using agricultural output as .... expectancy takes into account mortality, but .... (Akaike Information Criterion) and SBC.
17. An Analysis of energy consumption and economic growth of Cobb-Douglas production function based on ECM
Science.gov (United States)
Guo, Wei-wei
2018-02-01
Energy is one of the important factors affecting economic growth, the motive force of the economic development of countries in the world, essential for the world economic development and people’s living material resources, an important resource of the relationship between the national economies. The paper sums up the evaluation and literatures on energy consumption and economic growth at home and abroad, thinks “southern talk” as the energy consumption and economic growth in the time division, makes a series of empirical tests on the relationship between total energy consumption and economic growth in China from 1978 to 1991 and from 1992 to 2016.The results show that total energy consumption is a one-way causal relationship between economic growths in china, Economic growth has a strong dependence on energy, there is a co-integration relationship between energy consumption and economic growth. However, economic growth depends on the energy consumption decreased year by year in China, The way of economic growth is changing from the extensive economic growth mode to intensive mode of economic growth.
18. Growth and Economic Opportunities for Women: Strengthening ...
International Development Research Centre (IDRC) Digital Library (Canada)
Asian outlook: New growth dependent on new productivity. There is no doubt that Canada is tying its future growth prospects to Asia. View moreAsian outlook: New growth dependent on new productivity ...
19. Coal consumption and economic growth in China
International Nuclear Information System (INIS)
Li, Raymond; Leung, Guy C.K.
2012-01-01
The aim of this paper is to re-examine the relationship between coal consumption and real GDP of China with the use of panel data. This paper applies modern panel data techniques to help shed light on the importance of the heterogeneity among different regions within China. Empirical analyses are conducted for the full panel as well as three subgroups of the panel. The empirical results show that coal consumption and GDP are both I(1) and cointegrated in all regional groupings. Heterogeneity is found in the GDP equation of the full panel. The regional causality tests reveal that the coal consumption–GDP relationship is bidirectional in the Coastal and Central regions whereas causality is unidirectional from GDP to coal consumption in the Western region. Thus, energy conservation measures will not adversely affect the economic growth of the Western region but such measures will likely encumber the economy of the Coastal and Central regions, where most of the coal intensive industries are concentrated. - Highlights: ► We investigate the relationship between coal consumption and GDP in China. ► Panel data are used to account for the potential heterogeneity across different regions. ► Bidirectional causality is found in the Eastern and Central regions. ► Unidirectional causality from GDP to coal consumption is found in the Western region.
20. Exchange-rate regimes and economic growth: An empirical evaluation
OpenAIRE
Simón Sosvilla-Rivero; María del Carmen Ramos-Herrera
2014-01-01
Based on a dataset of 123 economies, this paper empirically investigates the relation between exchange-rate regimes and economic growth. We find that growth performance is best under intermediate exchange rate regimes, while the smallest growth rates are associated with flexible exchange rates. Nevertheless, this conclusion is tempered when we analyze the countries by income level: even though countries that adopt intermediate exchange-rate regimes are characterized by higher economic growth,...
1. BANKING SECTOR DEVELOPMENT AND ECONOMIC GROWTH INPALESTINE; 1995-2014
Directory of Open Access Journals (Sweden)
Gaber H. Abugamea
2016-07-01
Full Text Available This study uses both OLS regression estimation and Granger Causality test toinvestigate the relationship between the banking sector development andeconomic growth in Palestine over the period 1995-2014.OLS results show asignificant impact of banking size with a negative sign, insignificant impact ofcredit lending with a marginal one for lag credit andinsignificant impact ofefficiency on economic growth, respectively.Granger Causality testresultsshowone way causality runningfrom banking size to(GDPeconomic growthandfrom banking efficiency to(GDP per capitaeconomic growth one. Overall resultsreveals a weak nexus between banking sector development and economic growth.In specific, it recommends more improving in banking lending policy to beeffective in promoting economic growth.
2. Bubble nucleation and growth in very strong cosmological phase transitions
Energy Technology Data Exchange (ETDEWEB)
Mégevand, Ariel, E-mail: [email protected]; Ramírez, Santiago
2017-06-15
Strongly first-order phase transitions, i.e., those with a large order parameter, are characterized by a considerable supercooling and high velocities of phase transition fronts. A very strong phase transition may have important cosmological consequences due to the departures from equilibrium caused in the plasma. In general, there is a limit to the strength, since the metastability of the old phase may prevent the transition to complete. Near this limit, the bubble nucleation rate achieves a maximum and thus departs from the widely assumed behavior in which it grows exponentially with time. We study the dynamics of this kind of phase transitions. We show that in some cases a gaussian approximation for the nucleation rate is more suitable, and in such a case we solve analytically the evolution of the phase transition. We compare the gaussian and exponential approximations with realistic cases and we determine their ranges of validity. We also discuss the implications for cosmic remnants such as gravitational waves.
3. GROWTH ECONOMICS AND DEVELOPMENT ECONOMICS: WHAT SHOULD DEVELOPMENT ECONOMISTS LEARN (IF ANYTHING) FROM THE NEW GROWTH THEORY?
OpenAIRE
Ruttan, Vernon W.
1998-01-01
Since their emergence as a distinct fields of inquiry in the early post World War II period there has been an uneasy relationship between growth economics and development economics. The emergence of a richer new growth economics' has opened up the possibilities of a more fruitful dialogue between the two subdisciplines. In spite of recent advances, particularly with respect to the human capital, and understanding of differences in growth rates and income levels across countries remains elusiv...
4. Does globalization contribute to economic growth in developing ...
African Journals Online (AJOL)
This paper examines empirically whether or not globalization contributes to economic growth in developing countries, drawing empirical lessons from Nigeria. The globalization – growth link, is anchored on Husain Schematic representation, Solow model, and the new growth (endogenous growth) theory. The paper adopts ...
5. Economic growth of the United States: perspective and prospective. [Monograph
Energy Technology Data Exchange (ETDEWEB)
Fabricant, S
1979-01-01
A post-World War II analysis of the potential for US economic expansion projects a continuation of the basic social and economic expectations and international relations and of the upward trend of labor input, labor productivity, and national output. How economic growth of the future will differ as a result of global changes in population and resources is examined in the context of other national objectives. The rapid increase in labor productivity during the postwar period was taken in the form of income rather than leisure. This led to a growth of goods and real per capita income as well as higher standards of living, education, and economic stability. The implications for future growth indicate the need to slow the growth of the national product in line with the rate of population growth. The improved welfare of the people should be the overall goal of which economic growth is one component. 23 tables. (DCK)
6. Islam and Economic Growth in Malaysia
National Research Council Canada - National Science Library
bin
2003-01-01
.... The teachings of Islam, however, prescribe democratic governance and free-market economics. While Muslims, as a whole, have tremendous economics potential, many Muslims are among the world's poorest and least educated...
7. When economic growth is less than exponential
DEFF Research Database (Denmark)
Groth, Christian; Koch, Karl-Josef; Steger, Thomas
2010-01-01
This paper argues that growth theory needs a more general notion of "regularity" than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set...
8. When Economic Growth is Less than Exponential
DEFF Research Database (Denmark)
Groth, Christian; Koch, Karl-Josef; Steger, Thomas M.
This paper argues that growth theory needs a more general notion of "regularity" than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set...
9. Employment, Economic Growth and Labor Market Performance: The Case of Turkey
OpenAIRE
Alparslan AKÇORAOĞLU
2010-01-01
The fundamental aim of this paper is to explore the empirical relationship between employment and economic growth in Turkey over the period 1995Q1-2007Q4 by using modern time series techniques. The employment growth performance is a concern for Turkey as its employment rate is well below any European Union (EU) member country. Some authors have argued that the rates of employment growth in Turkey have remained low over the same period despite relatively strong economic growth. The results of ...
10. Export and Economic Growth Nexus in the GCC Countries: A panel Data Approach
Directory of Open Access Journals (Sweden)
2017-12-01
Full Text Available The export and economic growth nexus, which is called Balassa’s Export-Led Growth Hypothesis (ELGH in the literature, is still an unstill issue in both the theoretical and empirical literature. In the present study, the effect of export on economic growth in oil exporting developing countries, namely, Bahrain, Saudi Arabia, Qatar, Kuwait, UAE, and Oman in the 1990–2014 period was tested based on three models, pooled ordinary least squares (POLS, fixed effects model (FEM, and random effects model (REM via panel data analysis . The findings revealed strong support for the “export-led growth” hypothesis. In addition, our results show that apart from growth in the labor force, investments in capital formation are necessary for economic growth. According to the obtained results, the ability to adopt technological changes in order to increase efficiency, and sustain economic development is also important.
11. Business regulation and economic growth in the Western Balkan countries
Directory of Open Access Journals (Sweden)
Engjell PERE
2013-06-01
Full Text Available Actually economic policies in many countries aimed to stimulate their economic growth, particularly after negative impact of the global economic crisis. In this regards, fiscal regulation are an important aspect of those policies, that can promote or obstacle the economic growth in general. In this point of view this paper aims to analyze the system of administration rules in different Western Balkans Countries, (which includes Albania, Bosnia & Herzegovina, Croatia, Kosovo, Macedonia (FYROM, Montenegro and Serbia. Moreover, a special attention is given investigation of the regulation and administrative facilitation aspects of doing business in the above-mentioned countries, whether this system stimulates, or not, the development of private business and economic growth.The paper is divided into three main sections. The first part provides a retrospective of economic growth in the Western Balkan countries and the dependence of this growth on global economic development. The second part proceeds with the investigations of the impact of administrative regulation on economic growth. The third part, based on an econometric model, will analyze the correlation between economic growth and elaborated indicators which present the level of business administrative regulation system. Furthermore, this last section discusses the results and concludes. In this analysis, the paper is based substantially on the data base of "Doing Business 2013" (World Bank.
12. Problems of social and economic growth in the Kyrgyz Republic
Directory of Open Access Journals (Sweden)
Guseva Valentina Ivanovna
2016-04-01
Full Text Available In the article author explores the indirect influence of non-economic factors on the growth dynamics of the volume of GDP, including shows the effect of social problems on economic growth. It is proved that the existence of social problems have a negative impact on the pace of the economic dynamics of the country, due to the mutual dependence of key economic and non-economic factors of growth. On the one hand, the level of income of the population affects the purchasing power, which leads to the increase of the acceleration in economic growth. On the other hand, high levels of poverty and a deepening income inequality dictate political and social instability in society, which negatively affects the dynamics of economic growth. It was revealed that the feature of economic growth in the transitional economy is the negative impact of inflation and unemployment rates of economic dynamics, despite the fact that in most Western models, they are not considered as limiting growth factors.
13. Energy consumption, carbon emissions and economic growth nexus in Bangladesh: Cointegration and dynamic causality analysis
International Nuclear Information System (INIS)
2012-01-01
The paper investigates the possible existence of dynamic causality between energy consumption, electricity consumption, carbon emissions and economic growth in Bangladesh. First, we have tested cointegration relationships using the Johansen bi-variate cointegration model. This is complemented with an analysis of an auto-regressive distributed lag model to examine the results' robustness. Then, the Granger short-run, the long-run and strong causality are tested with a vector error correction modelling framework. The results indicate that uni-directional causality exists from energy consumption to economic growth both in the short and the long-run while a bi-directional long-run causality exists between electricity consumption and economic growth but no causal relationship exists in short-run. The strong causality results indicate bi-directional causality for both the cases. A uni-directional causality runs from energy consumption to CO 2 emission for the short-run but feedback causality exists in the long-run. CO 2 Granger causes economic growth both in the short and in the long-run. An important policy implication is that energy (electricity as well) can be considered as an important factor for the economic growth in Bangladesh. Moreover, as higher energy consumption also means higher pollution in the long-run, policy makers should stimulate alternative energy sources for meeting up the increasing energy demand. - Highlights: ► Dynamic causality among energy and electricity consumption, CO 2 and economic growth. ► Uni-directional causality exists from energy consumption to economic growth. ► Bi-directional causality exists between electricity consumption and economic growth. ► Feedback causality exists between CO 2 emission to energy consumption. ► CO 2 Granger causes economic growth both in the short and in the long-run.
14. Analysis of Fiji’s Export and Its Impact on Economic Growth
Directory of Open Access Journals (Sweden)
Shivneil Kumar Raj
2017-05-01
Full Text Available Exports are vital for Fiji’s economy as it contributes significantly to its gross domestic product (GDP and economic growth. The export data over the years show very slow growth and is gradually increasing. Fiji’s GDP data show that GDP is gradually increasing. Thus, Fiji’s economic growth is also increasing at a steady rate. This study aims to measure the relationship between exports and economic growth in Fiji. A regression analysis on data collected for Fiji from 2000-2015 shows that there is a strong positive relationship between exports and economic growth. Thus, when exports increase, economic growth also increases. Potential sectors that can be further developed to boost Fiji’s exports are sugar, garment, tourism and agriculture. The government should restrict imports through import quotas, tariffs and embargoes and give subsidies and tax incentives to potential export sectors to boost domestic production and increase exports. The government’s motive is to increase export incentives and promote Fiji made products both locally and overseas. Thus, this leads to an increase in exports, improves the trade balance and economic growth. This research article was undertaken to carry out research to investigate the link between Fiji’s export and economic growth and highlight ways and potential sectors to increase Fiji’s export and reduce imports.
15. ANALYSIS OF THE ECONOMIC GROWTH TRENDS IN ROMANIA BETWEEN 2010-2012
Directory of Open Access Journals (Sweden)
Daniela Mihaela NEAMȚU
2014-06-01
Full Text Available The question: "Why some countries are richer than others?" is a crucial problem that many economists have proposed to answer. Firstly, it should be noted the fact that the economic development is a quantitative and qualitative concept with a much broader area than growth. It is good that we have economic growth and stability but it is not enough to have economic development. Why? While economic growth is measured by a small number of indicators, among which the most important is the growth rate of GDP, the economic growth implies a long-term dynamic equilibrium, a sustainable growth trajectory based on optimal use of all available resources, the continued development of innovative potential and human capital and the development of strong institutions in order to support economic growth. This study aims, by keeping the interdependence of the investigated aspects, to analyze and describe the following dimensions: GDP per capita and the average productivity per hour, the most important issues that have led to changes of GDP, where Romania is classified from the growth point of view. The study includes the results of research, statistical series and arguments about the evolution of GDP based on National Institute of Statistics and Economic Studies and the Romanian National Bank over the last three years. Finally, the paper proposes a series of lines of action for further sustainable development of our country and reducing the disparities with the EU average.
16. The Impact of Education Investment on Sri Lankan Economic Growth
Science.gov (United States)
Ganegodage, K. Renuka; Rambaldi, Alicia N.
2011-01-01
We evaluate the contribution of investment on education to Sri Lanka's economic growth during the period 1959-2008. Physical capital, economic policy changes and the ethnic war are also evaluated due to their substantial importance. This study uses a framework encompassing both the neoclassical and endogenous growth model. The impact of education…
17. Using Wmatrix to Explore Discourse of Economic Growth
Science.gov (United States)
Hu, Chunyu
2015-01-01
Growth is a concept of particular interest for economic discourse. This paper sets out to explore a small corpus of economic growth, which consists of articles from "The Economist". The corpus software used in this study is a web-based tool Wmatrix, an automatic tagging software able to assign semantic field (domain) tags, and to permit…
18. Nuclear energy consumption and economic growth in nine developed countries
International Nuclear Information System (INIS)
Wolde-Rufael, Yemane; Menyah, Kojo
2010-01-01
This article attempts to test the causal relationship between nuclear energy consumption and real GDP for nine developed countries for the period 1971-2005 by including capital and labour as additional variables. Using a modified version of the Granger causality test developed by Toda and Yamamoto (1995), we found a unidirectional causality running from nuclear energy consumption to economic growth in Japan, Netherlands and Switzerland; the opposite uni-directional causality running from economic growth to nuclear energy consumption in Canada and Sweden; and a bi-directional causality running between economic growth and nuclear energy consumption in France, Spain, the United Kingdom and the United States. In Spain, the United Kingdom and the USA, increases in nuclear energy consumption caused increases in economic growth implying that conservation measures taken that reduce nuclear energy consumption may negatively affect economic growth. In France, Japan, Netherlands and Switzerland increases in nuclear energy consumption caused decreases in economic growth, suggesting that energy conservation measure taken that reduce nuclear energy consumption may help to mitigate the adverse effects of nuclear energy consumption on economic growth. In Canada and Sweden energy conservation measures affecting nuclear energy consumption may not harm economic growth.
19. Promoting Debates on Economic Growth and Poverty Reduction in ...
International Development Research Centre (IDRC) Digital Library (Canada)
Promoting Debates on Economic Growth and Poverty Reduction in Eastern Africa through Strengthening the Links between Research and the Media. Policy researchers have a key role to play in insuring that economic growth and poverty reduction plans are responsive to the needs and interests of poor people. They can ...
20. From entrepreneurship to economic growth: a three stage approach
NARCIS (Netherlands)
van Hemert, P.P.
2008-01-01
Over time, different economic theories have supported the idea that entrepreneurship and innovation are essential for spurring economic growth. One question, however, remains unanswered, namely, why some regions in different parts of the world manage to enter into a cycle of growth and development
1. From entrepreneurship to economic growth, a three stage approach
NARCIS (Netherlands)
van Hemert, P.P.
2007-01-01
Over time, different economic theories have supported the idea that entrepreneurship and innovation are essential for spurring economic growth. One question, however, remains unanswered, namely, why some regions in different parts of the world manage to enter into a cycle of growth and development
2. Funding of pensions and economic growth : are they really related?
NARCIS (Netherlands)
Zandberg, Eelco; Spierdijk, Laura
We examine whether changes in the degree of pension funding affect economic growth. Our sample consists of 54 countries, Organization for Economic Co-operation and Development (OECD) as well as non-OECD, during 2001-10. We do not find any effect of changes in the degree of funding on growth in the
3. The Republic of Yemen - Economic Growth : Sources, Constraints and Potentials
OpenAIRE
World Bank
2002-01-01
High and sustained rate of economic growth in Yemen is a necesary, though not sufficient, condition for reduction of the high incidence of poverty and for raising the living standards of Yemeni citizens. Evidence in this report suggests that the main obstacle to rapid and sustained economic growth is the weak governance that characterizes Yemen in addition to the weaknesses in domestic sec...
4. Impact of Currency Devaluation on Economic Growth of Nigeria ...
African Journals Online (AJOL)
The primary aim of the study is to estimate the long run relationship between economic growth (RGDP) and currency devaluation. This study investigated the impact of currency devaluation on economic growth of Nigeria. This was achieved through a review of literature and a test of hypothesis. In order to generate the ...
5. The Services Sector and Economic Growth in Mauritius. A Bounds ...
African Journals Online (AJOL)
This paper examines the long run and short run impact of the services sector on economic growth in Mauritius. Using an augmented aggregate production function growth model, we apply the bounds testing approach to cointegration to assess the impact of different activities in the services sector on economic performance ...
6. Crisis in the habitat of the economic growth monster
DEFF Research Database (Denmark)
Urhammer, Emil
2014-01-01
This article is inspired by empirical philosophy and provides an analysis of economic growth as a monster that circulates within collectives. Using this approach, I illustrate how economic growth has participated in shaping institutions and language, thus having necessitated its own circulation...... to such an extent that it has become the most prioritised economic policy objective, whereas urgent issues regarding living conditions on Earth are either ignored or treated as secondary priorities. Further, I argue that noble attempts to contest economic growth contribute to the circulation of the monster...
7. Models of the Economic Growth and their Relevance
Directory of Open Access Journals (Sweden)
Nicolae MOROIANU
2012-06-01
Full Text Available Until few years ago, the economic growth was something perfect normal, part of an era marked by the transformation speed. Normality itself has been transformed and we currently are influenced by other rules, unknown yet, which should answer the question: “How do we return to the economic growth?” The economic growth and the models aiming to solve this problem concern the economic history even since its beginnings. In this paper we would like to find out what is the relevance that the well-known macroeconomic models still have and which might be their applicability level in a framework created by a black swan event type.
8. NIGERIA’S ECONOMIC GROWTH THROUGH TOURISM PROMOTION/SUSTAINABILITY
Directory of Open Access Journals (Sweden)
Victor N. ITUMO
2017-08-01
Full Text Available Nigeria is currently facing economic growth and development challenge. The economic challenge is occasioned by mono-cultural economic reliance on the single resource of crude oil export revenue as well as other internal and international effects that affect her economic drive for heightened growth and development. The Nigerian government had over the years searched for ways of diversifying its economy for greater growth and development especially given the various challenges in the economy, mainly the steep reduction in crude oil revenue arising from volatility of global oil price. This paper therefore uses the research methodology of case study to do a holistic assessment of the possibility of Nigeria diversifying into her tourism potentials for economic growth and development. This would be done equally by drawing relevant comparative analysis of other countries bringing economic benefits in Africa and across the globe.
9. Economic Growth as a Factor of Political Stability
Directory of Open Access Journals (Sweden)
Анна Олеговна Ярославцева
2015-12-01
Full Text Available The article analyzes actual problems of the impact of economic growth on the political stability of different state. The author shows that despite the undoubted correlation of the level of economic development and political stability, economic growth by itself is not a panacea for destabilization risks because of the effects of inflated expectations and transformations of social consciousness. The author argues that the impact of economic growth on political stability is largely ambivalent. On the basis of “Tocqueville's law” and the range of theories of “relative deprivation”, the author makes a conclusion about the principal limitations of predictive and interpretive capabilities of economic indicators (primarily economic growth for the analysis of political stability.
10. Road infrastructure, spatial spillover and county economic growth
Science.gov (United States)
Hu, Zhenhua; Luo, Shuang
2017-09-01
This paper analyzes the spatial spillover effect of road infrastructure on the economic growth of poverty-stricken counties, based on the spatial Durbin model, by using the panel data of 37 poor counties in Hunan province from 2006 to 2015. The results showed that there is a significant spatial dependence of economic growth in Poor Counties. Road infrastructure has a positive impact on economic growth, and the results will be overestimated without considering spatial factors. Considering the spatial factors, the road infrastructure will promote the economic growth of the surrounding areas through the spillover effect, but the spillover effect is restricted by the distance factor. Capital investment is the biggest factor of economic growth in poor counties, followed by urbanization, labor force and regional openness.
11. Economic Growth and the Environment. An empirical analysis
Energy Technology Data Exchange (ETDEWEB)
De Bruyn, S.M.
1999-12-21
A number of economists have claimed that economic growth benefits environmental quality as it raises political support and financial means for environmental policy measures. Since the early 1990s this view has increasingly been supported by empirical evidence that has challenged the traditional belief held by environmentalists that economic growth degrades the environment. This study investigates the relationship between economic growth and environmental quality and elaborates the question whether economic growth can be combined with a reduced demand for natural resources. Various hypotheses on this relationship are described and empirically tested for a number of indicators of environmental pressure. The outcome of the tests advocates the use of alternative models for estimation that alter conclusions about the relationship between economic growth and the environment and give insight into the driving forces of emission reduction in developed economies. refs.
12. What Drives Economic Growth in Some CEE Countries?
Directory of Open Access Journals (Sweden)
Simionescu Mihaela
2018-03-01
Full Text Available Considering the potential factors that might generate economic growth, a target for any economy, this paper identified some determinants of economic growth in the countries from Central and Eastern Europe (CEE countries that are member states of the European Union. The foreign direct investment was the most important determinant of economic growth in most of the countries (Bulgaria, Slovenia, Estonia, Hungary, Romania, Poland, Latvia, Lithuania in the period 2003-2016, according to Bayesian bridge regressions. The indicators related to the level and the quality of labour resources proved to be insignificant in explaining the economic growth in these countries. Moreover, in Croatia, Estonia, Latvia, Lithuania, and Poland, the government expenditure on education had a negative effect on economic growth.
13. Energy consumption, political regime and economic growth in sub-Saharan Africa
International Nuclear Information System (INIS)
Adams, Samuel; Klobodu, Edem Kwame Mensah; Opoku, Eric Evans Osei
2016-01-01
In this paper, we examine the relationship between energy consumption and economic growth, and how democracy moderates this relationship using panel data of 16 sub-Saharan African (SSA) countries for the period 1971–2013. Employing a panel vector autoregressive model (PVAR) in a generalized method of moments (GMM) framework, the findings support the feedback hypothesis for energy consumption and growth. Second, the interaction variable (energy consumption and democracy) is positively and significantly related to economic growth, supporting the view that democracy moderates the energy consumption and growth nexus. Further, the results provide strong evidence of a uni-directional relationship from trade openness to energy consumption. Additionally, impulse responses and variance decompositions also confirm positive feedback relationships between energy consumption and economic growth, energy prices and economic growth. - Highlights: •Feedback exists between energy consumption and economic growth. •Democracy moderates the energy consumption and growth nexus. •positive feedback between energy prices and economic growth. •Uni-directional relationship from openness to energy consumption.
14. Economic Growth and Development in the Undergraduate Curriculum
Science.gov (United States)
Acemoglu, Daron
2013-01-01
A central theme of this article is that economics instructors should spend more time teaching about economic growth and development at the undergraduate level because the topic is of interest to students, is less abstract than other macroeconomic topics, and is the focus of exciting research in economics. Facts and data can be presented to…
15. Economic growth and technological change : an evolutionary interpretation
NARCIS (Netherlands)
Verspagen, B.
2000-01-01
The aim of this paper is to apply insights from evolutionary economic theory to the question of what can explain recent trends in economic growth, with emphasis on the role of technological change. Obviously, a basic question that precedes this question is "what is evolutionary economic theory"? The
16. Financial development and economic growth nexus in Russia
Directory of Open Access Journals (Sweden)
Shigeki Ono
2017-09-01
Full Text Available This paper examines the finance-growth nexus in Russia with the vector autoregression model, taking oil prices and foreign exchange rates into account. The analyzed period is from 1999 through 2008 (Subperiod 1 and from 2009 through 2014 (Subperiod 2. The results for Subperiod 1 suggest that there is causality from economic growth to money supply and bank lending, which implies demand-following responses. The results for Subperiod 2 show that economic growth Granger causes bank lending while there is no causality from money supply to economic growth, which could be related to the dramatic decrease in the amount of intervention in foreign exchange markets.
17. ANALYSIS OF FACTORS WHICH AFFECTING THE ECONOMIC GROWTH
Directory of Open Access Journals (Sweden)
Suparna Wijaya
2017-03-01
Full Text Available High economic growth and sustainable process are main conditions for sustainability of economic country development. They are also become measures of the success of the country's economy. Factors which tested in this study are economic and non-economic factors which impacting economic development. This study has a goal to explain the factors that influence on macroeconomic Indonesia. It used linear regression modeling approach. The analysis result showed that Tax Amnesty, Exchange Rate, Inflation, and interest rate, they jointly can bring effect which amounted to 77.6% on economic growth whereas the remaining 22.4% is the influenced by other variables which not observed in this study. Keywords: tax amnesty, exchange rates, inflation, SBI and economic growth
18. Nation Building as a Determinent of Economic Growth
Science.gov (United States)
2010-05-18
Consortium for Political and Social Reserch (2007). Mankiw , N. Gregory, David Romer, and David N. Weil. “A Contribution to the Empirics of Economic Growth...Determinent of Economic Growth 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6 . AUTHOR(S) 5d. PROJECT NUMBER Creasey. Ellyn Ann 5e. TASK NUMBER 51...J ss istance and econom ic aid impact the development process. The primary resu lts suggest a 1% increase in spending on nation building result s
19. The Political Economy of Recent Economic Growth in India
OpenAIRE
Raghbendra Jha
2004-01-01
The political economy of India’s economic growth is an issue of abiding interest. Higher and sustained economic growth has, all over the world, been the surest and most time tested means of raising living standards and reducing poverty. Further, given that it is a functioning democracy, economic policy in India can often be dictated by political expediency as political parties indulge in competitive populism in the face of improvements in social indicators such as literacy, infant mortality a...
20. Human Capital, Population Growth and Economic Development: Beyond Correlations
OpenAIRE
Rosenzweig, Mark R.
1987-01-01
Empirical evidence on three assertions commonly-made by population policy advocates about the relationships among population growth, human capital formation and economic development is discussed and evaluated in the light of economic-biological models of household behavior and of its relevance to population policy. The three assertions are that (a) population growth and human capital investments jointly reflect and respond to changes in the economic environment, (b) larger families directly i...
1. Law, Economic Growth and Human Development: Evidence from Africa
OpenAIRE
Asongu Simplice
2011-01-01
This paper cuts adrift the mainstream approach to the legal-origins debate on the law-growth nexus by integrating both overall economic and human components in our understanding of how regulation quality and the rule of law lie at the heart of economic and inequality adjusted human developments. Findings summarily reveal that legal-origin does not explain economic growth and human development beyond the mechanisms of law. Our results support the current consensus that, English common-law coun...
2. Does the internet generate economic growth, international trade, or both?
OpenAIRE
Meijers, Huub
2012-01-01
Recent cross country panel data studies find a positive impact of internet use on economic growth and a positive impact of internet use on trade. The present study challenges the first finding by showing that internet use does not explain economic growth directly in a fully specified growth model. In particular openness to international trade variables seems to be highly correlated with internet use and the findings in the literature that internet use causes trade is confirmed here, suggestin...
3. Malaysia Economic Monitor, December 2016 : The Quest for Productivity Growth
OpenAIRE
World Bank Group
2016-01-01
Malaysia’s economic growth has slowed down but remains resilient to external headwinds. The economic growth rate slowed from 5 percent in 2015 to 4.2 percent, year on year, in the first three quarters of 2016. Private consumption growth slowed down due to a softening labor market and households’ ongoing adjustment to a context of fiscal consolidation. Public investment in infrastructure is...
4. Urban population and economic growth: South Asia perspective
Directory of Open Access Journals (Sweden)
Sandip Sarker
2016-07-01
Full Text Available Previously economic growth was generally discussed in terms of foreign direct investment (FDI, educational growth, savings, investments, inflation as well as trade openness of a nation. Very recently it has been identified that population is one of the major determinants of economic growth of a nation. In the recent years, the study of urbanization has gained a matter of concern in developing countries as it has been recognized as part of a larger process of economic development which is affecting developing countries. South Asian countries are one of the emerging economics and growing at a faster rate over the past few years. At the same time, population of South Asia is growing at a significant rate. Therefore the study has attempted to identify the causal relationship between urban population and economic growth in South Asia using a panel data analysis. The study makes use of the Augmented Dickey-Fuller (ADF and Phillips-Perron (PP, Pesaran as well as Fisher methods for panel unit root test. The panel Pedroni cointegration test suggests that there is long run relationship between the variables. The further panel Vector Error Correction Model (VECM suggests that there is long run causality running from urban population growth to economic growth in South Asia. The study concludes that the growth of urban population can have significant impact on economic growth in South Asia in the long run.
5. Economic growth and change in southeast Alaska.
Science.gov (United States)
Rhonda Mazza
2004-01-01
This report focuses on economic trends since the 1970s in rural southeast Alaska. These trends are compared with those in the Nation and in nonmetropolitan areas of the country to determine the extent to which the economy in rural southeast Alaska is affected by regional activity and by larger market forces. Many of the economic changes occurring in rural southeast...
6. Rethinking Economics and Education: Exponential Growth and Post-Growth Strategies
Science.gov (United States)
Irwin, Ruth
2017-01-01
Education is increasingly vocational and structured to serve the ongoing exponential increase in economic growth. Climate change is an outcome of these same economic values and praxes. Attempts to shift these values and our approach to technology are continually absorbed and overcome by the pressing motif of economic growth. In this article, Ruth…
7. Economic growth and intangible capitals: Europe versus Asia
Directory of Open Access Journals (Sweden)
Navarro José-Luis Alfaro
2014-01-01
Full Text Available At present, the international growth model includes important restrictions about the consideration of GDP as a unique tool for measurement. In this sense, taking into consideration the wealth of a country, we must add intangibles such as human development, country image, employment conditions, environmental, innovation, public sector efficiency, and synergies to the variable production, which is defined as national intellectual capital. In this paper, we use a mathematical model of intellectual capital to determine, in monetary terms, the intangible elements that have a greater impact on long-term economic development in European and Asian countries. We have the main limitation of available information and we provide objective results using statistical method. By identifying these components, countries will be able to redirect their policies toward achieving sustainable long-term growth. The results show that the long-term growth of both continents are strongly dependent on the skills of their human resources, but register differences in structural factors such as trade, innovation, or environment.
8. Strong persistent growth differences govern individual performance and population dynamics in a tropical forest understorey palm
NARCIS (Netherlands)
Jansen, M.; Zuidema, P.A.; Anten, N.P.R.; Martínez-Ramos, M.
2012-01-01
1. Persistent variation in growth rate between individual plants can have strong effects on population dynamics as fast growers reach the reproductive size at an earlier age and thus potentially contribute more to population growth than slow growers. In tropical forests, such persistent growth
9. MEASURING ECONOMIC GROWTH FROM OUTER SPACE
Science.gov (United States)
Henderson, J. Vernon; Storeygard, Adam; Weil, David N.
2013-01-01
GDP growth is often measured poorly for countries and rarely measured at all for cities or subnational regions. We propose a readily available proxy: satellite data on lights at night. We develop a statistical framework that uses lights growth to augment existing income growth measures, under the assumption that measurement error in using observed light as an indicator of income is uncorrelated with measurement error in national income accounts. For countries with good national income accounts data, information on growth of lights is of marginal value in estimating the true growth rate of income, while for countries with the worst national income accounts, the optimal estimate of true income growth is a composite with roughly equal weights. Among poor-data countries, our new estimate of average annual growth differs by as much as 3 percentage points from official data. Lights data also allow for measurement of income growth in sub- and supranational regions. As an application, we examine growth in Sub Saharan African regions over the last 17 years. We find that real incomes in non-coastal areas have grown faster by 1/3 of an annual percentage point than coastal areas; non-malarial areas have grown faster than malarial ones by 1/3 to 2/3 annual percent points; and primate city regions have grown no faster than hinterland areas. Such applications point toward a research program in which “empirical growth” need no longer be synonymous with “national income accounts.” PMID:25067841
10. Measuring Economic Growth in New Zealand
OpenAIRE
Peter Mawson
2002-01-01
This paper examines New Zealand’s ranking in the OECD based on real GDP per capita. The fall in ranking experienced by New Zealand implies that real GDP per capita growth in New Zealand has been relatively poor in comparison to other OECD countries. The paper examines the history of New Zealand’s growth rate and explores the differences between various techniques for measuring average growth rates. The approaches are all shown to be variants of the average annual growth rate but differ in ter...
11. Life Insurance Contribution, Insurance Development and Economic Growth in China
Directory of Open Access Journals (Sweden)
Wang Ying
2017-07-01
Full Text Available Under L-type economy, remodelling the growth power in the medium and long term is essential. The insurance industry during the 13th Five-year Plan period has been given a heavy expectation on promoting economic quality and upgrading economic efficiency, so it will try to accelerate its innovation and development process which serves national needs, market demand and people's requirements. Referring to the previous researches of Solow and Zhang and measuring Capital Stock and Total Factor Productivity independently, the paper analyses the inherent correlation between insurance (including life insurance and non-life insurance and economic growth, reveals the contribution law of the insurance development in economic growth in the short and long term from both economic scale and quality respectively. It also shows enlightenments on policy decision for insurance industry, thus helps economic stability under the downturn periods.
12. Financial Development Following Economic Growth: The Chinese Case
Directory of Open Access Journals (Sweden)
Chan il Park
2003-06-01
Full Text Available The purpose of this paper is to investigate the relationship between financial development and economic growth based on Chinese experiences during the period of 1979~2000. This study places more emphasis on the causality running from economic growth to financThe purpose of this paper is to investigate the relationship between financial development and economic growth based on Chinese experiences during the period of 1979~2000. This study places more emphasis on the causality running from economic growth to financial development contrary to the mainstream view, which asserts that the well-functioning financial systems exert a large positive impact on economic growth via two channels- capital accumulation and technological innovations. The reverse causality is postulated by considering two factors in developments of the country's financial system. Firstly, this paper argues that the rapid accumulation of financial assets and the remarkable expansion of the financial system during the examined period are due primarily to income rises and changes in industrial structures rather than inefficient financial reforms. Secondly, it is recognized in this study that various financial reform measures undertaken by the state since 1994 are emerged endogenously in response to Chinese financial disorders and macroeconomic imbalances built up during the 1979~93 period. This line of thinking is not following the mainstream view in which financial reforms are regarded as policy variables (or exogenous variables in promoting economic growth. These two factors imply that the causality may run from economic growth to financial development at least in China.
13. Women's economic empowerment and inclusive growth: labour ...
International Development Research Centre (IDRC) Digital Library (Canada)
Deyanira Carvajal
IDRC commissioned Professor Naila Kabeer to review existing research on women's economic ..... common theme but there are also some important differences. ...... women's entry into the labour market, qualitative research suggests that part ...
14. Four Centuries of British Economic Growth
DEFF Research Database (Denmark)
Madsen, Jakob B.; Ang, James B.; Banerjee, Rajabrata
2010-01-01
Using long historical data for Britain over the period 1620–2006, this paper seeks to explain the importance of innovative activity, population growth and other factors in inducing the transition from the Malthusian trap to the post-Malthusian growth regime. Furthermore, the paper tests the ability...
15. The Biology and Economics of Coral Growth
NARCIS (Netherlands)
Osinga, R.; Schutter, M.; Griffioen, B.; Wijffels, R.H.; Verreth, J.A.J.; Shafit, S.; Henard, S.; Taruffi, M.; Gili, C.; Lavorano, S.
2011-01-01
To protect natural coral reefs, it is of utmost importance to understand how the growth of the main reef-building organisms-the zooxanthellate scleractinian corals-is controlled. Understanding coral growth is also relevant for coral aquaculture, which is a rapidly developing business. This review
16. The Effect of Foreign Direct Investment in Economic Growth from the Perspective of Nonlinear Dynamics
Directory of Open Access Journals (Sweden)
Ch. K. Volos
2015-09-01
Full Text Available In today’s globalized economy one of the most crucial factors for the economic growth of a country, especially of a developing country, is the foreign direct investment, not only because of the transfer of capital but also of technology. In this work, the effect of foreign direct investments in a county’s economic growth by using tools of nonlinear dynamics is studied. As a model of the economic growth of a country, a well-known nonlinear discrete-time dynamical system, the Logistic map, is used. The system under study consists of two countries with a strong economic relationship. The source country of foreign direct investments is an industrialized, economically powerful and technologically advanced country that makes significant investments in the host country, which is a developing country and strong dependent from the source country. Simulation results of system’s behavior and especially the bifurcation diagrams reveal the strong connection between the countries of the proposed system and the effect of foreign direct investments in the economic growth of the host country.
17. The South African tax mix and economic growth
Directory of Open Access Journals (Sweden)
AH de Wet
2014-10-01
Full Text Available The research reported in this paper suggests that government fiscal policy can influence economic growth through alterations in the tax mix and the overall size of government spending. The authors estimate the impact on economic growth of changes in fiscal policy via government expenditure, direct taxation and indirect taxation. The results show that economic growth is negatively affected by increases in the size of government, as reflected in its expenditures and direct tax revenues, although significant indirect tax effects are not found.
18. Review of capital investment in economic growth cycle
Science.gov (United States)
Shaffie, Siti Salihah; Jaaman, Saiful Hafizah; Mohamad, Daud
2016-11-01
The study of linkages of macroeconomics factors is prominent in order to understand how the economic cycle affects one another. These factors include interest rate, growth rate, saving and capital investment which are mutually correlated to stabilize the GDP. Part of this study, it will look upon the impact of investment which emphasize the efficiency of capital investment to the economic growth. Capital investment is one investment appraisal that gives impact to the economic growth. It is a long term investment and involve with large amount of capital to incorporate the development of private and public capital investment.
19. Energy consumption and economic growth. Assessing the evidence from Greece
International Nuclear Information System (INIS)
Hondroyiannis, George; Lolos, Sarantis; Papapetrou, Evangelia
2002-01-01
This paper attempts to shed light into the empirical relationship between energy consumption and economic growth, for Greece (1960-1996) employing the vector error-correction model estimation. The vector specification includes energy consumption, real GDP and price developments, the latter taken to represent a measure of economic efficiency. The empirical evidence suggests that there is a long-run relationship between the three variables, supporting the endogeneity of energy consumption and real output. These findings have important policy implications, since the adoption of suitable structural policies aiming at improving economic efficiency can induce energy conservation without impeding economic growth
20. Natural gas facing the new energy disorders: opportunities and constraints of a waited economic growth
International Nuclear Information System (INIS)
Valais, M.
1991-01-01
This paper studies natural gas industry facing the new disorders on energy markets. Energy world-wide demand growth is the strong point of natural gas development. Natural gas supply is based on abundant resources, well geographically distributed, but more expensive. This paper describes international trade growth and economic constraints, the impact of economic growth reduction, Gulf crisis and USSR or East Europe disorders on natural gas market. In the last part, the influence of environmental policy, regulations and ecological anxiety are briefly approached. 1 fig., 3 tabs
1. Further evidence on the relationship between economic freedom and economic growth
NARCIS (Netherlands)
De Haan, J; Siermann, CLJ
Often it is maintained that economic freedom may further high levels of economic growth. Using various measures of economic freedom constructed by Scully and Slottje, the robustness of this relationship is examined. Both direct and indirect effects of lack of liberties are analysed. Our main
2. The Dynamic Relationship between Crime and Economic Growth in Nigeria
Directory of Open Access Journals (Sweden)
2017-03-01
Full Text Available Crime is a major impediment to economic growth and development in Nigeria despite measures taken to reduce it. There is, however, currently no major statistical analysis of how crime affects economic growth in that country. This study examines the link between crime and growth based on the theory of rational choice and empirical data. Exogenous and endogenous growth models are employed, and include deterrence variables. The period examined is 1970–2013 and estimation is done using the autoregressive distributed lag model. The results of our study show that crime affects economic growth at a 1% and 10% level of significance. In other words, crime imposes the costs of prosecution and punishment on the citizens and country, which influences the growth of the economy. Given our results, we suggest that police and the system of justice should be strengthened. Indeed, this may be necessary if the development target stated in Nigeria vision 20: 2020 is to be reached.
3. Economic growth and poverty alleviation in Africa - linking hard and soft economics
DEFF Research Database (Denmark)
2014-01-01
soft and hard economics, arguing that economic growth must be converted into social change that benefits poor for it to be described as development-oriented. It provides a direction for future research into issues of economic growth and poverty alleviation in Sub-Sahara Africa......This paper provides a quick glance at the dominant issues that have characterized the development economics debate during the past five decades. It is based on a review of a selection of literature that highlights the dominant perspectives in development economics. It draws a distinction between...
4. Economic Growth and the Rise of Political Extremism
OpenAIRE
Markus Bruckner; Hans Peter Gruner
2011-01-01
In many western democracies, political parties with extreme platforms challenge more moderate incumbents. This paper analyses the impact of economic growth on the support for extreme political platforms. We provide a theoretical argument in favor of growth effects (as opposed to level effects) on the support for extreme political parties and we empirically investigate the relationship between growth and extremist votes. Lower growth rates benefit right-wing and nationalist parties, but do not...
5. Causality analysis of diesel consumption and economic growth in Cameroon
International Nuclear Information System (INIS)
Tamba, Jean Gaston; Njomo, Donatien; Limanond, Thirayoot; Ntsafack, Borel
2012-01-01
This study examines the causal relationship between diesel consumption and economic growth in Cameroon by using a three-step modern time-series technique. Tests for unit roots, cointegration, and Granger-causality based on error correction model are employed on annual data covering the period 1975–2008. Empirical results of the study confirm the presence of a long-run equilibrium relationship between diesel consumption and economic growth. The error correction model shows that an estimated 1% increase in economic growth causes a rise in diesel consumption of 1.30% in the long-run. The overall results show that there exists bidirectional causality in the long-run relationship and no causality in the short-run relationship between diesel consumption and economic growth at the 5% level of significance. Thus, the energy policies in Cameroon should place priority on the discovery of new oil field and building capacity additions of the refinery to increase production of petroleum products, as this would propel the economic growth of the country. - Highlights: ► We examine the causal relationship between diesel consumption and GDP in Cameroon. ► we analyze the petroleum products sector in Cameroon. ► 1% increase in economic growth causes a rise in diesel consumption of 1.30%. ► The policy aimed at improving diesel supply have a positive impact on economics.
6. THE CONNECTION BETWEEN ECONOMIC GROWTH AND STOCK MARKETS
Directory of Open Access Journals (Sweden)
Andreea Maria PECE
2015-04-01
Full Text Available This paper examines the connection between economic growth and stock market performance in the case of an emerging economy, namely Romania, by using quarterly financial data, during the period 2000-2013. This topic is widely studied in the financial literature and seeks to provide an answer for the following questions: does economic growth influences the capital market, does capital market influences economic growth, or there is no connection between these variables. I have analyzed the long term relationship between economic growth and stock market for Romania, by applying Johansen cointegration test, Granger causality and Gregory Hansen cointegration test, which allows the presence of the structural breaks in the time series. The empirical results obtained highlighted that portfolio investments have a positive impact on economic growth and the GDP growth engages in turn, a long term positive capital markets return. The main conclusion of this study is that in the case of Romanian economy, is a bi-directional link between the economic growth and the capital market performance.
7. ECONOMIC GROWTH AND REGIONAL INEQUALITY IN ROMANIA
Directory of Open Access Journals (Sweden)
Marinela ISTRATE
2016-10-01
Full Text Available After the collapse of communism, Romania, just like other Central and East European countries, has experienced profound social and economic mutations, reflected in all activity sectors (from the transition to a market economy and democratic freedom-based society to the decreasing number of active and working population, increasing unemployment, workforce’s growing risk of poverty, rising vulnerability of certain socio-professional groups. Starting from these findings and using an appropriate methodology to identify regional convergences and disparities, the present paper is meant to perform a statistical and territorial analysis of the economic gaps recorded at the level of the Romanian counties (NUTS 3 level during the last two decades and a half. The conclusions converge towards the existence of an adjustment of the economic structures, both from the territorial and temporal perspective, while the issue of reducing regional gaps remains one of the main challenges of the future.
8. Investigating Causality Between Agricultural and Economic Growth in Iran
Directory of Open Access Journals (Sweden)
A. Falsafian
2010-10-01
Full Text Available Although rate of economic growth is not the only way to measure economic development, it is relatively more important than the other indices. Agriculture sector plays the main role on economic growth and sustainable development. In addition, it has significant impact on most social, political and economic issues by producing strategic food products for ever-increasing population. Therefore, the present study investigated causal relationship between agricultural and economic growth in Iran. To this end, the Granjer’s causality test was used after employing the Augmented Dicky-Fuller test to see if the variables under consideration are stationary. The result showed that there is a long learn feedback relationship between these variables and agricultural developments.
9. Economic Growth - Quality of Life Nexus in Ethiopia: Time Series ...
African Journals Online (AJOL)
Optiplex 7010 Pro
This study investigates the nexus between economic growth and quality of life ..... competitiveness of political participation, the openness and competitiveness ..... women contributes to minimal food expenditure in the urban areas in the LR.
10. Framework for Creating a Smart Growth Economic Development Strategy
Science.gov (United States)
This step-by-step guide can help small and mid-sized cities, particularly those that have limited population growth, areas of disinvestment, and/or a struggling economy, build a place-based economic development strategy.
11. Informal sector, business environment and economic growth: A ...
International Development Research Centre (IDRC) Digital Library (Canada)
2012-12-01
Informal sector, business environment and economic growth: A comparative analysis of West and Central Africa ... taxes, which undermines fair competition and puts formal enterprises at a disadvantage. ... Start Date. December 1, 2012 ...
12. Fuelling Economic Growth: The Role of Public–Private Sector ...
International Development Research Centre (IDRC) Digital Library (Canada)
2009-04-26
Apr 26, 2009 ... At the same time, however, traditional sources of research funding – from ... Fuelling Economic Growth: The Role of Public–Private Sector ... IDRC congratulates first cohort of Women in Climate Change Science Fellows.
13. Inclusive growth and development: An IDRC-World Economic Forum ...
International Development Research Centre (IDRC) Digital Library (Canada)
Advancing economic growth while achieving broad-based progress in living ... It will develop regional and global platforms whereby the private sector, local ... cooperation agreement to support joint research projects in December 2017.
14. Public procurement, governance and economic growth: some policy ...
African Journals Online (AJOL)
Public procurement, governance and economic growth: some policy ... Employing the Keynesian income-expenditure approach to measuring the Gross Domestic ... reduce wastage, enhance the effectiveness of government spending, ensure ...
15. Redefining prosperity : resource productivity, economic growth and sustainable development
OpenAIRE
Sustainable Development Commission
2003-01-01
This report seeks to stimulate debate on how we define prosperity and addresses the inadequacies of standard definitions of Gross Domestic Product and economic growth as yardsticks for well-being. Publisher PDF
16. A panel study of nuclear energy consumption and economic growth
International Nuclear Information System (INIS)
Apergis, Nicholas; Payne, James E.
2010-01-01
This study examines the relationship between nuclear energy consumption and economic growth for sixteen countries within a multivariate panel framework over the period 1980-2005. Pedroni's (1999, 2004) heterogeneous panel cointegration test reveals there is a long-run equilibrium relationship between real GDP, nuclear energy consumption, real gross fixed capital formation, and the labor force with the respective coefficients positive and statistically significant. The results of the panel vector error correction model finds bidirectional causality between nuclear energy consumption and economic growth in the short-run while unidirectional causality from nuclear energy consumption to economic growth in the long-run. Thus, the results provide support for the feedback hypothesis associated with the relationship between nuclear energy consumption and economic growth.
17. ARDL Approach to Trade Libralisation and Economic Growth in the ...
African Journals Online (AJOL)
Nneka Umera-Okeke
the long and short run impact of trade liberalization to economic growth suggested that ..... To ensure the goodness of fit of the model, diagnostic and stability tests are conducted. .... The results indicate the absence of any instability of the.
18. The impact of the British model on economic growth
Directory of Open Access Journals (Sweden)
Simon György Jr.
2007-01-01
Full Text Available The paper is searching for an answer to the question how the British model affected economic development in its mother country, the United Kingdom. The statistical analysis, models of mathematical economics and econometric investigation make it probable to conclude that there was a substantial difference in success between the Thatcherite and the Blairite economic policies; the latter proved more effective. It is particularly remarkable that the Blairite model, connecting privatization with a successful employment policy, reduced unemployment and social sensitivity, has not only speeded up economic growth but also improved economic equilibrium, curtailing, among others, the budget deficit.
19. Internationalisation and Economic Growth: The Portuguese Case
Science.gov (United States)
da Costa, Renato J. Lopes; António, Nélson J. Santos; Miguel, Maria Isabel
2017-01-01
Historically, a policy of enforcement in internationalisation processes is still seen by many as an approach to solve certain economic crises. However, Portugal's solution for this problem is part of a greater problem, namely trying to solve a European problem that has recently worsened and is largely uncontrolled. This paper aims to contribute,…
20. Teaching Economic Growth Theory with Data
Science.gov (United States)
Elmslie, Bruce T.; Tebaldi, Edinaldo
2010-01-01
Many instructors in subjects such as economics are frequently concerned with how to teach technical material to undergraduate students with limited mathematical backgrounds. One method that has proven successful for the authors is to connect theoretically sophisticated material with actual data. This enables students to see how the theory relates…
1. Building Regional Economic Growth and Innovation Capacity
Science.gov (United States)
Rafn, H. Jeffrey
2012-01-01
Like many states at the turn of the century, Wisconsin was faced with a multibillion-dollar deficit due to a sagging economy brought on by the dotcom bubble burst and the economic impact of the 9/11 terrorist attack on the World Trade Center. As the state legislature grappled with the budget crisis, blame was freely assigned. The state was at…
2. Growth and Women's Economic Empowerment: Can Political ...
International Development Research Centre (IDRC) Digital Library (Canada)
This research project will generate evidence on how women's political ... Kingdom's Department for International Development, The William and Flora Hewlett ... support 11 projects addressing barriers to women's economic empowerment and ... Call for new OWSD Fellowships for Early Career Women Scientists now open.
3. SOCIAL LIMITS OF THE ROMANIAN ECONOMICAL GROWTH
Directory of Open Access Journals (Sweden)
2009-05-01
Full Text Available The phenomena and processes from the economical life have evolved with intensity and different results, determining the necessity of knowing the way in which the national economy evolves, as well as its dynamic approach. The existence and the dynamics of
4. Financial Market Liberalization and Economic Growth
NARCIS (Netherlands)
G.A. Garita (Gus)
2008-01-01
textabstractThe literature has shown that it is hard to
find unambiguous evidence that financial openness yields an improvement in economic performance, particularly at the macro level. One of the major problems in empirical work is the bundling of
financial openness with a potential host of other
5. Economic growth and advertising expenditures in different media
NARCIS (Netherlands)
van der Wurff, R.; Bakker, P.; Picard, R.G.
2008-01-01
Newspaper advertising expenditures depend more strongly on economic development than advertising spent in other media. Gross domestic product (GDP), therefore, predicts ad spending better in countries where newspapers are an important advertising medium. GDP also predicts ad spending better in
6. Determinants of Economic Growth in Malaysia 1970-2010
OpenAIRE
Fauzi HUSSIN; Norazrul Mat ROS; Mohd Saifoul Zamzuri NOOR
2013-01-01
This paper investigates the determinants of economic growth in Malaysia. Trade openness, foreign direct investment, government development expenditure and gross fixed capital formation are used as indicators of economic growth. The study used time series data for the period 1970 to 2010. The Johansen and Juselius cointegration approach was applied to determine the long-run relationship between the variables. The study found that trade openness and foreign direct investment have significant bu...
7. Tax Revenue, Stock Market and Economic Growth of Pakistan
OpenAIRE
2014-01-01
The purpose of this paper is to examine the effects of capital market and fiscal policy influences in determining the nexus of economic growth in Pakistan from July 2003 to July 2012. The authors utilize ADF unit root test, Johansen Cointegration test, VECM test, Granger causality test and variance decomposition analysis to test the relationship among tax revenue, stock market and economic growth in Pakistan. Granger causality analysis is used to answer questions whether “Does tax revenue cau...
8. 136 Tax Revenue, Stock Market and Economic Growth of Pakistan
OpenAIRE
2014-01-01
The purpose of this paper is to examine the effects of capital market and fiscal policy influences in determining the nexus of economic growth in Pakistan from July 2003 to July 2012. The authors utilize ADF unit root test, Johansen Cointegration test, VECM test, Granger causality test and variance decomposition analysis to test the relationship among tax revenue, stock market and economic growth in Pakistan. Granger causality analysis is used to answer questions whether “Does ...
9. Joint determinants of fiscal policy, income inequality and economic growth
OpenAIRE
Leonel Muinelo-Gallo; Oriol Roca-Sagalés
2012-01-01
This paper analyses the relationship between income inequality and economic growth through fiscal policy. To this end, we present and estimate two systems of structural equiation with error components through which gross income inequality determines different fiscal policy outcomes, which subsequently affects the evolution of economic growth and net income inequality. The empirical results, obtained using an unbalanced panel data of 21 high-income OCDE countries during the period 1972-2006, s...
10. The Impact of Social Media on Economic Growth
OpenAIRE
Dell'Anno, Roberto; Rayna, Thierry; Solomon, O. Helen
2015-01-01
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. This article attempts to investigate the impact of social media (SM) on economic growth. Using information obtained from memberships to social networks, we find that SM has a negative and significant impact on economic growth. This provides evidence in favour of our hypothesis that SM increases the search costs for information and also increase...
11. Dynamic inter-relationship between trade, economic growth and tourism in Malaysia
OpenAIRE
Sarmidi, Tamat; Salleh, Norlida H
2010-01-01
This study aims to test a hypothesis that postulate a positive inter-relationship between international flows of tourist, trade and economic growth. Although tourism is one of the major components in the trade of services, and it has been certified by large number of literatures on the strong correlation between tourism industry and economic development, yet not much is known on the dynamic inter-relationship between these three variables. Closing-up this gaping hole, this study employs the c...
12. Determinants of Economic Growth in V4 Countries and Romania
Directory of Open Access Journals (Sweden)
Simionescu Mihaela
2017-03-01
Full Text Available The middle and long-term slowdown in growth dynamics could bring serious social and political problems for V4 countries (Czech Republic, Slovak Republic, Hungary, Poland and Romania. It would threaten reaching benefits from potential of convergence process with the developed countries of the European Union. As a result, the V4 economies and Romania should find solutions to achieving a sustainable growth that is associated with an improvement of their international competitiveness. This paper provides an empirical analysis of factors that might determine a stable economic growth in the five mentioned countries. The empirical analysis conducted for the period of 2003-2016 employed Bayesian generalized ridge regression. The main results indicated that the FDI promoted economic growth in all countries, except the Slovak Republic. Only in the Czech Republic, the expenditure on education generated economic growth, while the expenditure on R&D had positive effects in Romania, Hungary and the Czech Republic.
13. Information and communication technology use and economic growth.
Science.gov (United States)
2012-01-01
In recent years, progress in information and communication technology (ICT) has caused many structural changes such as reorganizing of economics, globalization, and trade extension, which leads to capital flows and enhancing information availability. Moreover, ICT plays a significant role in development of each economic sector, especially during liberalization process. Growth economists predict that economic growth is driven by investments in ICT. However, empirical studies on this issue have produced mixed results, regarding to different research methodology and geographical configuration of the study. This paper examines the impact of Information and Communication Technology (ICT) use on economic growth using the Generalized Method of Moments (GMM) estimator within the framework of a dynamic panel data approach and applies it to 159 countries over the period 2000 to 2009. The results indicate that there is a positive relationship between growth rate of real GDP per capita and ICT use index (as measured by the number of internet users, fixed broadband internet subscribers and the number of mobile subscription per 100 inhabitants). We also find that the effect of ICT use on economic growth is higher in high income group rather than other groups. This implies that if these countries seek to enhance their economic growth, they need to implement specific policies that facilitate ICT use.
14. Income taxes, public fiscal policy and economic growth
Directory of Open Access Journals (Sweden)
Tomasz Wołowiec
2014-12-01
Full Text Available The main goal of this article is to find the relationship between public fiscal policy and economic growth. The article consist of a few parts. The first is an introduction, which creates the background for the analysis in the following sections. It shows the main point of view on public fiscal policy especially in the case of personal income tax and creates a framework for the analysis of the relationship between taxation and economic growth. The second part focuses on the relations between central government decisions on taxation and its influence on savings, investments and economic growth. In this part we will find selected analyses of the impact of taxes on economic growth based on the examples of OECD countries. Finally, the last part of the work is a study on fiscal level and tax system structures and economic growth. In this part the authors checks two points of view on taxation. The first is that a low level tax burden is conducive to economic growth, and the second emphasizes negative consequences of decreasing budget tax revenues. The article shows both theoretical and empirical points of view on taxation and influence of government taxation decisions on the economy.
15. The dynamics of oil consumption and economic growth in Malaysia
International Nuclear Information System (INIS)
Park, Sun-Young; Yoo, Seung-Hoon
2014-01-01
This study attemps to investiagte the causal relationship between oil consumption and economic growth in Malaysia where oil consumption and real gross domestic product have been rapidly increased in recent years. To this end, the study employs annual data covering the period 1965–2011. Tests for unit roots, co-integration, and Granger-causality based on the error-correction models are presented. The overall results support the existence of bi-directional causality between oil consumption and economic growth in Malaysia. This means that an increase in oil consumption directly affect economic growth. Thus, in order not to make an adverse effect on economic growth, Malaysia should endeavor to overcome the constraints on oil consumption. Moreover, it appears that economic growth induces oil consumption. - Highlights: • We examine the causality between oil consumption and economic growth in Malaysia. • We employed the annual data covering the period 1965–2011. • We estimated error-correction models to test for the direction of causality. • We found that there is bi-directional causality between the two
16. Information and communication technology use and economic growth.
Directory of Open Access Journals (Sweden)
Full Text Available In recent years, progress in information and communication technology (ICT has caused many structural changes such as reorganizing of economics, globalization, and trade extension, which leads to capital flows and enhancing information availability. Moreover, ICT plays a significant role in development of each economic sector, especially during liberalization process. Growth economists predict that economic growth is driven by investments in ICT. However, empirical studies on this issue have produced mixed results, regarding to different research methodology and geographical configuration of the study. This paper examines the impact of Information and Communication Technology (ICT use on economic growth using the Generalized Method of Moments (GMM estimator within the framework of a dynamic panel data approach and applies it to 159 countries over the period 2000 to 2009. The results indicate that there is a positive relationship between growth rate of real GDP per capita and ICT use index (as measured by the number of internet users, fixed broadband internet subscribers and the number of mobile subscription per 100 inhabitants. We also find that the effect of ICT use on economic growth is higher in high income group rather than other groups. This implies that if these countries seek to enhance their economic growth, they need to implement specific policies that facilitate ICT use.
17. How Does Social Trust Affect Economic Growth?
DEFF Research Database (Denmark)
Bjørnskov, Christian
This paper connects two strands of the literature on social trust by estimating the effects of trust on growth through a set of potential transmission mechanisms directly. It does so by modelling the process using a three-stage least squares estimator on a sample of countries for which a full data...... set is available. The results indicate that trust affects schooling and the rule of law directly. These variables in turn affect the investment rate (schooling) and provide a direct effect (rule of law) on the growth rate. The paper closes with a short discussion of the relevance of the findings....
18. State Investment in Universities: Rethinking the Impact on Economic Growth
Science.gov (United States)
Schalin, Jay
2010-01-01
Does investing taxpayer money in higher education lead to major payoffs in economic growth? State legislators and policy makers say yes. They routinely advocate massive appropriations for university education and research, even in poor economic times, on the grounds that taxpayers will be rewarded many times over. The investment of federal funds…
19. Balance of Payments Constrained Economic Growth in Nigeria ...
African Journals Online (AJOL)
African Journal of Economic Review, Volume V, Issue II, July 2017 ... between economic growth and current account balance equilibrium. .... With these precedents, there is a need to analyze the degree to which balance of payments .... With this result, we can now investigate the long run relationship between our variables.
20. ECONOMIC GROWTH - AN ILLUSION? STUDY CASE:ROMANIA
Directory of Open Access Journals (Sweden)
Camelia MORARU
2013-12-01
Full Text Available Literature has devoted considerable attention to economic growth because it creates the premises for achieving major goals such as route out of poverty of underdeveloped countries or contribute to raising the standard of living in developed countries. Economic growth has become an “order of the day” term, propagated by various "players" of economic and social life, in this way gaining various interpretations and meanings. This paper presents the results of the measures adopatate in order to recover Romanian economic situation. The austerity measures adopted until recently not allowed, however, to create a favorable environment for growth, taking into consideration that it is almost impossible for an economy to grow when conditions are limiting. Fiscal policies have focused on reducing the budget deficit, which led on slaughtering economic growth. Given the uncertain economic context, FDI was hardly drew into our country, their value last year has been insignificant. We can even say that the previous ended year was one economically, because our country did not recognize the road to the economic recovery.
1. The impact of microfinance institution in economic growth of a ...
African Journals Online (AJOL)
The findings of the study show that microfinance loans have a significant positive impact on the short run economic performance in Nigeria. Microfinance loans enhanced consumption per capita in short run with an impressive coefficient, although these banks' loans do not have a significant impact on economic growth in ...
2. Economic Growth, Structural Change and Productive Employment Linkages in India
DEFF Research Database (Denmark)
2018-01-01
This article presents a quantitative analysis of growth, structural change and employment linkages at the aggregate level and by sector under the state- and market-led regimes in India. The underlying objectives are: (a) to understand how economic liberalization has affected the economic and labour...... intervention to broad base structural change for generating productive employment, which is at the core of poverty reduction....
3. Health and economic growth in South East, Nigeria | Umezinwa ...
African Journals Online (AJOL)
African Research Review ... In the South eastern states of Nigeria, health cannot be said to be making any significant impact in economic growth. ... There will be a meaningful economic improvement if ever there is a combined proactive engagement in healthcare delivery by the state governments and the citizens.
4. How Strategic Entrepreneurship and the Institutional Context Drive Economic Growth
DEFF Research Database (Denmark)
Bjørnskov, Christian; Foss, Nicolai Juul
2013-01-01
The economics of growth has shown that countries grow by better allocating whatever resources are at their disposal and by introducing productivity-enhancing innovations. Strategic entrepreneurship plays a key role in this process by searching for, combining, trying out, etc., new resource......, and the Fraser Institute's economic freedom data. Copyright © 2013 Strategic Management Society....
5. Business Planning and the Economic Growth of Small and Medium ...
African Journals Online (AJOL)
The purpose of this study was to determine the relevance of business planning the economic growth of Small and Medium Scale Enterprises (SMEs) and their ability to attract investors and loans, in the face of dwindling economic returns in Nigeria. A five point likert-type questionnaire was utilized in gathering data from 450 ...
6. Economic openness and economic growth: A cointegration analysis for ASEAN-5 countries
Directory of Open Access Journals (Sweden)
Klimis Vogiatzoglou
2016-11-01
Full Text Available The paper considers three channels of economic openness, namely FDI, imports, and exports, and examines their short-run and long-run effects on the economic growth in the five founding member countries of the Association of Southeast Asian Nations (ASEAN over the period from 1980 to 2014. Besides the impact on the economic growth, the authors analyze all possible causal interrelationships to discern patterns and directions of causality among FDI, imports, exports, and GDP. The quantitative analysis, which is based on the vector error correction co-integration framework, is conducted separately for each country in order to assess their individual experiences and allow for a comparative view. Although the precise details differ across countries, the findings indicate that there is a long-run equilibrium relationship between economic openness and GDP in all ASEAN-5 economies. FDI, imports and exports have a significantly positive short-run and long-run impact on the economic growth. Our results also show that export-led growth is the most important economic growth factor in most countries, followed by FDI-led growth. Another crucial finding is the bi-directional causality between exports and FDI across the ASEAN-5 countries. This indicates the presence of direct and indirect effects on GDP and a self-reinforcing process of causality between those two variables, which strengthens their impact on the economic growth.
7. Foreign Direct Investment, Host Country Factors and Economic Growth
OpenAIRE
Edna Maeyen Solomon
2011-01-01
This paper analyses how the levels of economic development, human capital, financial development and the qualities of the economic and political environments in host countries simultaneously affects the impact of aggregate inflows of Foreign Direct Investment (FDI) on economic growth. Multiple interaction terms are employed between inward FDI and each of the host country factors mentioned above. The System GMM estimator is applied to a panel of 111 countries from 1981 to 2005. The results sho...
8. Financial Intermediation and Economic Growth of Jordan 1964-1988
OpenAIRE
Magableh, Ali H.
1995-01-01
Until recently, the economics and financial literature placed little attention on the role that financial intermediation can play in accelerating the rate of economic development in less Developed Countries (LDCs). This has been changed now, however, where some instrumental role has been emphasised for financial intermediation in the process of economic development and growth. It is argued that an expansion of the financial system, size and intermediation in LDCs tends to increase the level o...
9. Financial Sector Structure and Economic Growth
DEFF Research Database (Denmark)
Rapp, Marc Steffen
Economists consider a well-functioning financial sector to be of first order importance for a modern (capitalist) economy. However, in the aftermath of the financial crisis a debate about the future role of the financial sector emerged and many commentators have called into question whether...... the financial sector actually creates value for the wider society. This research, which is part of a broad research project “Nordic Finance and the Good Society”, aims to contribute to this debate by studying the role of the financial sector structure for economic development of an economy. Therefore......, it proceeds in five steps. First, it provides some reflections on the financial sector and the existing literature studying financial sector structure and its association with economic development. Second, it presents stylized firm-level evidence on capital structure choice and firm behavior. It is argued...
10. Size of government and economic growth: A nonlinear analysis
Directory of Open Access Journals (Sweden)
Herath Shanaka
2012-01-01
Full Text Available The new growth theory establishes, among other things, that government expenditure can manipulate the economic growth of a country. This study attempts to explain whether government expenditure increases or decreases economic growth in the context of Sri Lanka. Results obtained employing a productive output series and applying an analytical framework based on second degree polynomial regression are generally consistent with previous findings: government expenditure and economic growth are positively correlated; excessive government expenditure is negatively correlated with economic growth; and investment promotes growth. In a separate section, the article examines Armey’s idea of a quadratic curve that explains the level of government expenditure in an economy and the corresponding level of economic growth [Armey, D. (1995. The Freedom Revolution. Washington, D.C.: Regnery Publishing Co.]. The findings confirm the possibility of constructing the Armey curve for Sri Lanka, and it estimates the optimal level of government expenditure to be approximately 27%. This article adds to the literature indicating that the Armey curve is a reality not only for developed economies, but also for developing economies.
11. Economic analysis of crystal growth in space
Science.gov (United States)
Ulrich, D. R.; Chung, A. M.; Yan, C. S.; Mccreight, L. R.
1972-01-01
Many advanced electronic technologies and devices for the 1980's are based on sophisticated compound single crystals, i.e. ceramic oxides and compound semiconductors. Space processing of these electronic crystals with maximum perfection, purity, and size is suggested. No ecomonic or technical justification was found for the growth of silicon single crystals for solid state electronic devices in space.
12. Self-Serving Dictators and Economic Growth
NARCIS (Netherlands)
Haile, D.; Sadrieh, A.; Verbon, H.A.A.
2003-01-01
A new line of theoretical and empirical literature emphasizes the pivotal role of fair institutions for growth.We present a model, a laboratory experiment, and a simple cross-country regression supporting this view.We model an economy with an unequal distribution of property rights, in which
13. The Non-Linear Effect of Corporate Taxes on Economic Growth
Directory of Open Access Journals (Sweden)
2015-03-01
Full Text Available The paper deals with the problem of taxation and its potential impact on economic growth and presents some new empirical insights into this topic. The main aim of the paper is to verify an assumed nonlinear impact of corporate tax rates on economic growth. Based on the theory of public finance and taxation, we hypothesize that at relatively low tax rates it is possible that the impact of taxation on economic growth become slightly positive. On the other hand when the tax rates are higher a negative impact of taxation on economic growth could be expected. Despite the fact that the most of the existing studies find a negative linear relationship between these variables, we can also find strong support for a non-linear relationship from several theoretical models as well as some empirical studies. Based on panel data fixed-effects econometric models, we, as well, find empirical evidence for a non-linear relationship between nominal and effective corporate tax rates and economic growth. Our data consists of annual observations for the period 1999 to 2011 for EU Member States. Based on the results, we also estimated the optimal level of the corporate tax rate in terms of maximizing economic growth in the average of the EU countries.
14. Outward foreign direct investments and home country's economic growth
Science.gov (United States)
Ciesielska, Dorota; Kołtuniak, Marcin
2017-09-01
The study examines the time stability of the causality direction and cross-correlations between the home country's economic growth and pace of growth of its outward foreign direct investment (OFDI) stocks within the complex system of the Polish national economy. The research has been performed in order to verify, using both the time and frequency domains time series analyses, if economic agents' long term decisions on outward foreign direct investments, leading to cross-border value chains and production fragmentation processes, are of adaptive or predictive character. Consequently, the aim was to check if the home country's economic growth leads the internationalization processes of domestic enterprises, which stays in line with Dunning's Investment Development Path (IDP) paradigm, or if these complex processes, thanks to entrepreneurs' ability to formulate relevant rational expectations, precede the home country's economic growth, which would be supported with the introduction of the policy on reinforcing the internationalization processes of domestic enterprises. The presence of the unidirectional economic growth-led internationalization, consistent with the IDP concept's base assumptions, has been ascertained by the results of the short term Granger causality tests. Nevertheless, the results of the wavelet analyses, supported with the results of the econometric block exogeneity long term causality Wald tests, have revealed that in the long term the OFDI stocks' growth permanently precedes the home country's economic growth, which stays in the unequivocal contrast with the IDP paradigm's premises, as well as with the indicated above short term Granger causality tests' outcomes and indicates that economic agents' choices are not strictly of adaptive but also of predictive character, which influences the current state of knowledge on economic complex systems' characteristics. Such a result is of a great importance in the light of the existence of the significant
15. Subtle mechanisms of growth: technology and economic growth
Directory of Open Access Journals (Sweden)
Glauco Arbix
Full Text Available The article deals with obstacles faced by developing countries to reach economic development. Passivity in technological learning, low productivity in relation to developed economies, adoption of spurious competitive advantages and reproduction of technological delay are presented as challenges to overcome. It states that breaking the passive strategy is the only way for these countries to build a better future.
16. Population growth, economic security, and cultural change in wilderness counties
Science.gov (United States)
Paul A. Lorah
2000-01-01
A familiar version of the âjobs versus the environmentâ argument asserts that wilderness areas limit economic growth by locking up potentially productive natural resources. Analysis of the development paths of rural Western counties shows that this is unlikely: the presence of Wilderness is correlated with income, employment and population growth. Similarly, Wilderness...
17. Balance of Payments Constrained Economic Growth in Nigeria ...
African Journals Online (AJOL)
modified by Thirwall and Hussain (1982) on Nigeria's economic growth to ... Results signify cointegration between our variables, lending support to ... the fact that the factor inputs have inconclusive roles in the growth process in developing ... towards public sector expansion at the expense of the private sector as well as a ...
18. CONSIDERATIONS ON THE ROLE OF FINANCIAL MARKETS IN ECONOMIC GROWTH
Directory of Open Access Journals (Sweden)
Carmen ALBU
2014-06-01
Full Text Available Generally accepted in economic literature, the financial market has a positive impact on growth in a modern economy. Nevertheless, due to the global crises starting in 2008, a number of authors are questioning today about this assertion. Among them, there are authors which are attributing as initial impulse to the crisis an exaggerated expansion of financial market (and non-covered on the real side of economy. In this study, based on economic literature and empirical evidences, we are presentig few considerations regarding the development of financial market during last decades and its role on economic growth.
19. Economic Limits to Corporate Growth in America
Science.gov (United States)
2006-12-01
data ranges. Such simple models are certainly open to criticism , particularly that they do not incorporate factors likely to drive the growth...involved. This relationship stipulates higher expected returns for riskier endeavors. In the capital asset pricing model ( CAPM ), the relationship...premium associated with taking on risk levels different than that of the market. A model like the CAPM predicts that the only risk rewarded in the
20. PRIORITIZING ECONOMIC GROWTH: ENHANCING MACROECONOMIC POLICY CHOICE
OpenAIRE
2005-01-01
This paper spells out a logic for increasing macroeconomic policy space in order to prioritize the goals of growth, employment creation and poverty reduction. First, there is the need to create additional policy instruments so that a greater number of policy goals can be addressed. Frequently, real economy goals get partly crowded out by financial objectives because there are too few instruments for too many goals. Second, the calibrated use of policy tools by degrees of commitment, deploymen...
1. South Africa: poised for economic growth
Energy Technology Data Exchange (ETDEWEB)
Zuma, J. (African National Congress (South Africa))
1993-01-01
South Africa is now emerging from the period of Apartheid. Elections will be held soon, but the economic damage caused by Apartheid has to be rectified. Partly this will be through an industrial strategy, and the minerals industry will play its part. The coal mining industry provides a large proportion of South Africa's exports and 90% of electricity. It is also the basis of a synfuels industry. The coal industry will continue to be an important source of exports, either directly, or as the provider of power to energy intensive industries such as aluminium production.
2. CLUSTERS- SOURCES OF ECONOMIC GROWTH IN EUROPE
Directory of Open Access Journals (Sweden)
Constantin BORDEI
2016-05-01
Full Text Available Global competition has evolved from the competition between companies to the competition between regions. In this context, clusters play an important role as competences’ concentration poles. The cluster initiatives represent concentrated efforts to increase the wealth and competitiveness in a certain region including companies, local administration, research and training institutions. This paper proposes the analysis of the European clusters’ role in ensuring the regional development. Resulted conclusions emphasize both the positive results of clusters’ existence, as well as the fields where improvements can be made in order to increase the clusters’ impact on the economic development.
3. Economics of Future Growth in Photovoltaics Manufacturing
Energy Technology Data Exchange (ETDEWEB)
Basore, Paul A.; Chung, Donald; Buonassisi, Tonio
2015-06-14
The past decade's record of growth in the photovoltaics manufacturing industry indicates that global investment in manufacturing capacity for photovoltaic modules tends to increase in proportion to the size of the industry. The slope of this proportionality determines how fast the industry will grow in the future. Two key parameters determine this slope. One is the annual global investment in manufacturing capacity normalized to the manufacturing capacity for the previous year (capacity-normalized capital investment rate, CapIR, units $/W). The other is how much capital investment is required for each watt of annual manufacturing capacity, normalized to the service life of the assets (capacity-normalized capital demand rate, CapDR, units$/W). If these two parameters remain unchanged from the values they have held for the past few years, global manufacturing capacity will peak in the next few years and then decline. However, it only takes a small improvement in CapIR to ensure future growth in photovoltaics. Any accompanying improvement in CapDR will accelerate that growth.
4. Why is electricity consumption inconsistent with economic growth in China?
International Nuclear Information System (INIS)
Lin, Boqiang; Liu, Chang
2016-01-01
Studies have indicated that there exists a relatively stable and positive correlation between electricity consumption and economic growth and there should not be a large deviation between them. However, the deviation between electricity consumption and economic growth in China during the Asian Financial Crisis and Global Economic Crisis sparks intense debates. We attempt to explain the deviation from the perspective of inventory investment adjustment in the business cycle using the SVAR model in this paper. The results show that the effects of inventory investment adjustment shock and electricity consumption structure shock on the deviation are positive but tend to be negative for electricity efficiency shock. The results of historical decomposition of these shocks also show that the inventory investment adjustment shock is the main factor that influences the deviation during the Global Economic Crisis. Economic fluctuation in the short term can not change the economic development pattern and the characteristics of electricity demand. Once the economy returns to stable growth, the deviation between electricity consumption and economic growth will shrink and disappear soon. - Highlights: • We analyze the deviation between GDP and electricity consumption in business cycle. • The inventory investment adjustment mainly impacts the deviation in China. • Concentrated electricity consumption of heavy industry magnifies the deviation.
5. Towards a solidarity economy zakat Decrease poverty vs economic growth
Directory of Open Access Journals (Sweden)
Mébarek BOUBLAL
2015-02-01
Full Text Available Historically, inequalities in the distribution of goods between men existed. Different economic policies have been developed in order to solve not only the problem of inequality, but also that of unemployment. The statistics speak for themselves; despite efforts provided, no solution has been able to solve this twofold problem. Indeed, we must understand that today's economy is primarily responsible for capital growth; support social policy is the responsibility of the welfare state. Policies such as the single tax , or flat tax and the social economy, or non profit sector, have emerged but not able to reconcile the dilemma posed by the management of the social side with economic growth and to help grow the capital. Consideration of zakat as a social economic system, or zakat solidarity economy, provides an opening to a third way. This pathway is ale to support the reduction of inequalities in redistribution and unemployment, without jeopardizing economic growth.
6. Stock Market and Sustainable Economic Growth in Nigeria
Directory of Open Access Journals (Sweden)
Erasmus L Owusu
2016-11-01
Full Text Available This paper examines the relationship between stock market evolution and sustainable economic growth in Nigeria. The study employs Auto-Regressive Distributed Lag (ARDL-bounds testing approach and a combined stock market indicators index to examine the relationship. The paper finds that, in the long run, stock markets have no positive and at best mixed effect on economic growth in Nigeria. This finding supports the numerous past studies, which have reported negative/mixed or inconclusive results on the effects of stock markets on economic growth. The paper, therefore, concludes that, there is the need for increasing financial deepening and the removal of bottlenecks in the financial sectors of the economy by providing further public and institutional education on the value of stock markets for economic development.
7. Some Peculiarities of the Economic Growth in ECOWAS Countries
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Babacar NDIAYE
2017-12-01
Full Text Available This article seeks to determine some of the peculiarities of the economic growth in the countries from the Economic Community of West African States (ECOWAS. Thus, the study is based on the country approach and uses econometric regression tests. In fact, in the context of the determination of the real GDP per capita growth rate of the countries in this region during the period 1987-2014, the results obtained show that it is still weak and unstable. Moreover, the weak convergence that has only been observed beginning with 2008 feeds the hope that ECOWAS can truly improve its level of development despite the heterogeneous nature of the countries. In order to overcome these difficulties, improving the socio-economic performance through the growth rate of real GDP per capita represents, among others, a necessity in relation to economic policy decisions.
8. The Role of Agriculture on the Recent Brazilian Economic Growth
OpenAIRE
Spolador, Humberto Francisco Silva; Roe, Terry L.
2012-01-01
This paper investigates the contribution of the Brazilian agriculture to economic growth of the Brazilian economy. It draws upon the Global Trade Analysis Project (GTAP) data base, and other time series data to construct a multi-sector Ramsey model that shows the transition growth of the Brazilian agricultural sector and its effects on growth of the Brazilian economy, with particular emphasis given to the years 1994–2010.
9. The impact of remittances on economic growth: An econometric model
Directory of Open Access Journals (Sweden)
Dietmar Meyer
2017-05-01
In other words, the econometric analysis will be based on those six remittance receiving countries. The paper is then to review the empirical literature devoted to the impact of remittances on economic growth, in order, to identify empirically if there are significant relationships between remittances and growth in these countries. The results suggest that remittances have a positive impact on growth and that this impact increases at higher levels of remittances relative to GDP.
10. Capital Market Development: A Spur to Economic Growth in Nigeria
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Ismail O. Fasanya
2013-10-01
Full Text Available This paper examines the relationship between capital market development and Nigeria’s economic growth using data covering the range of 1981 to 2010 using a Johansen Cointegration technique to test for long run relationship among the variables under study. The empirical findings from the research work suggest that the capital market is an essential catalyst for economic growth and is on the average and beneficial to the economy. However, the high costs of raising capital and structural imbalances in the market as well as inconsistent government policies may distorts the speedy growth of the market and thus, limit its positive impact on the economy.
11. Electricity consumption and economic growth nexus in Bangladesh: Revisited evidences
Energy Technology Data Exchange (ETDEWEB)
Ahamad, Mazbahul Golam, E-mail: [email protected] [Research Division, Centre for Policy Dialogue (CPD), House: 40C, Road: 11, Dhanmondi, Dhaka 1209 (Bangladesh); Islam, A.K.M. Nazrul, E-mail: [email protected] [Research Division, Centre for Policy Dialogue (CPD), House: 40C, Road: 11, Dhanmondi, Dhaka 1209 (Bangladesh)
2011-10-15
In this paper, an attempt is being made to examine the causal relationship between per capita electricity consumption and per capita GDP of Bangladesh using the vector error correction specified Granger causality test to search their short-run, long-run and joint causal relationships for the period of 1971-2008. Empirical findings reveal that there is a short-run unidirectional causal flow running from per capita electricity consumption to per capita GDP without feedback. The presence of a positive short-run causality explains that an increase in electricity consumption directly affects economic activity in Bangladesh. Likewise, results from joint causality exhibit the same as in short-run. By contrast, long-run results show a bi-directional causality running from electricity consumption to economic growth with feedback. These findings can provide essential policy insights to design immediate and long-term growth prospect for Bangladesh keeping in mind its present planned growth strategy and dismal power and energy sector. - Highlights: > Short-run causality running from electricity consumption to economic growth. > Positive SR causality explains electricity generation directly affects economic growth. > For long run, causality runs from electricity consumption to economic growth with feedback. > Joint causality implies the same as in short-run.
12. Electricity consumption and economic growth nexus in Bangladesh: Revisited evidences
International Nuclear Information System (INIS)
Ahamad, Mazbahul Golam; Islam, A.K.M. Nazrul
2011-01-01
In this paper, an attempt is being made to examine the causal relationship between per capita electricity consumption and per capita GDP of Bangladesh using the vector error correction specified Granger causality test to search their short-run, long-run and joint causal relationships for the period of 1971-2008. Empirical findings reveal that there is a short-run unidirectional causal flow running from per capita electricity consumption to per capita GDP without feedback. The presence of a positive short-run causality explains that an increase in electricity consumption directly affects economic activity in Bangladesh. Likewise, results from joint causality exhibit the same as in short-run. By contrast, long-run results show a bi-directional causality running from electricity consumption to economic growth with feedback. These findings can provide essential policy insights to design immediate and long-term growth prospect for Bangladesh keeping in mind its present planned growth strategy and dismal power and energy sector. - Highlights: → Short-run causality running from electricity consumption to economic growth. → Positive SR causality explains electricity generation directly affects economic growth. → For long run, causality runs from electricity consumption to economic growth with feedback. → Joint causality implies the same as in short-run.
13. Economic growth and military expenditure linkages: a panel data analysis
Directory of Open Access Journals (Sweden)
Ahmed Shahid
2015-12-01
Full Text Available This paper has made an attempt to examine relationship between military expenditure and economic growth using 56 country panel data spanning over 1995—2011. Panel fixed effect model has been estimated for all 56 countries and sub-groups classified on the basis of World Bank income criteria. The results of this study indicate a positive effect of military expenditure on economic growth but this positive effect is negligible compared to the alternative uses of scare resources on non-military expenditure. Thus, the effect of military expenditure on economic growth is very low compared to the effect of expenditure on capital formation, hence military expenditure as a sub-optimal means of increasing economic growth compared to alternative uses of government spending on formation of fixed capital. This study raises an important argument of huge opportunity cost of military expenditure. The present study concludes that the boosting of economic growth through higher military expenditure is neither effective nor efficient way of achieving higher growth in the economy.
14. An Attempt to Assess the Quantitative Impact of Institutions on Economic Growth and Economic Development
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Próchniak Mariusz
2014-10-01
Full Text Available This study aims at assessing to what extent institutional environment is responsible for worldwide differences in economic growth and economic development. To answer this question, we use an innovative approach based on a new concept of the institutions-augmented Solow model which is then estimated empirically using regression equations. The analysis covers 180 countries during the 1993-2012 period. The empirical analysis confirms a large positive impact of the quality of institutional environment on the level of economic development. The positive link has been evidenced for all five institutional indicators: two indices of economic freedom (Heritage Foundation and Fraser Institute, the governance indicator (World Bank, the democracy index (Freedom House, and the EBRD transition indicator for post-socialist countries. Differences in physical capital, human capital, and institutional environment explain about 70-75% of the worldwide differences in economic development. The institutions-augmented Solow model, however, performs slightly poorer in explaining differences in the rates of economic growth: only one institutional variable (index of economic freedom has a statistically significant impact on economic growth. In terms of originality, this paper extends the theoretical analysis of the Solow model by including institutions, on the one hand, and shows a comprehensive empirical analysis of the impact of various institutional indicators on both the level of development and the pace of economic growth, on the other. The results bring important policy implications.
15. Strain selection, biomass to biofuel conversion, and resource colocation have strong impacts on the economic performance of algae cultivation sites
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Erik R. Venteris
2014-09-01
Full Text Available Decisions involving strain selection, biomass to biofuel technology, and the location of cultivation facilities can strongly influence the economic viability of an algae-based biofuel enterprise. We summarize our past results in a new analysis to explore the relative economic impact of these design choices. Our growth model is used to predict average biomass production for two saline strains (Nannocloropsis salina, Arthrospira sp., one fresh to brackish strain (Chlorella sp., DOE strain 1412, and one freshwater strain (order Sphaeropleales. Biomass to biofuel conversion is compared between lipid extraction (LE and hydrothermal liquefaction (HTL technologies. National-scale models of water, CO2 (as flue gas, land acquisition, site leveling, construction of connecting roads, and transport of HTL oil to existing refineries are used in conjunction with estimates of fuel value (from HTL to prioritize and select from 88,692 unit farms (UF, 405 ha in pond area, a number sufficient to produce 136E+9 L yr-1 of renewable diesel (36 billion gallons yr-1. Strain selection and choice of conversion technology have large economic impacts, with differences between combinations of strains and biomass to biofuel technologies being up to $10 million dollars yr-1 UF-1. Results based on the most productive strain, HTL-based fuel conversion, and resource costs show that the economic potential between geographic locations within the selection can differ by up to$4 million yr-1 UF-1, with 1.8 BGY of production possible from the most cost-effective sites. The local spatial variability in site rank is extreme, with very high and low sites within 10s of km of each other. Colocation with flue gas sources has a strong influence on rank, but the most costly resource component varies from site to site. The highest rank UFs are located predominantly in Florida and Texas, but most states south of 37°N latitude contain promising locations.
16. Impacts of Seaport Investment on the Economic Growth
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Tahar Ammar Jouili
2016-08-01
Full Text Available The aim of this paper is to estimate the impact of seaports investment on the economic growth. Seaports are seen by many governments as an important factor in the strengthening of the economies. During the last two decades, the Tunisian succeeding governments have been allocating a great amount of money to develop seaport infrastructures. However, the Tunisian economy witnessed fluctuations in the economic growth rates and decrease in the rate of employment during the same period of time. This study used an econometric model by employing the Cobb-Douglas production function. The sample was composed of Tunisia's economic sectors (manufacturing, services and agriculture over the period 1983-2011. The results of the study show that the public investment in seaport infrastructures has apositive influence on Tunisian economic growth. The study also revealed that the biggest beneficiary from the seaport investment infrastructure is the service sector.This paper aims to estimate the impact of seaports investment on the economic growth. The seaports are seen by many governments as an important factor in the strengthening of the economies. During the last two decades, the Tunisian succeeding governments were allocating a great amount of money to develop seaports' infrastructures. However, the Tunisian economy witnessed fluctuating in the economic growth rates and decreased in the rate of employment during the same period of time. This study used an econometric model by employing the Cobb-Douglas production function. The sample composed of Tunisia's economic sectors (manufacturing, services and agriculture over the period 1983-2011. The results of the study show that the public investment in seaports' infrastructures has a positive influence on Tunisian economic growth. The study also revealed that the biggest beneficiary from the seaports investment infrastructure is the services sector.
17. Energy, Economic Growth and Environmental Sustainability: Five Propositions
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Steven Sorrell
2010-06-01
Full Text Available This paper advances five linked and controversial propositions that have both deep historical roots and urgent contemporary relevance. These are: (a the rebound effects from energy efficiency improvements are significant and limit the potential for decoupling energy consumption from economic growth; (b the contribution of energy to productivity improvements and economic growth has been greatly underestimated; (c the pursuit of improved efficiency needs to be complemented by an ethic of sufficiency; (d sustainability is incompatible with continued economic growth in rich countries; and (e a zero-growth economy is incompatible with a fractional reserve banking system. These propositions run counter to conventional wisdom and each highlights either a "blind spot" or "taboo subject" that deserves closer scrutiny. While accepting one proposition reinforces the case for accepting the next, the former is neither necessary nor sufficient for the latter.
18. Insurance Market Activity and Economic Growth: Evidence from Nigeria
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Philip Chimobi Omoke
2012-04-01
Full Text Available The focus of this study is to empirically assess insurance market activities in Nigeria withthe view to determining its impact on economic growth. The period of study was 1970- 2008, thestudy made use of insurance density measures (premium per capita as a measure for insurancemarket activity and real GDP for economic growth. It also employed control variables such asinflation and savings rate as other determinants ofgrowth. The Johansen cointegration and vectorerror correction approach was used to estimate therelationship between the variables. All thevariables used were stationary at first differenceand the result showed a long term relationshipexisting among the variables. The hallmark findingof this study is that the insurance sector did notreveal any positively and significant affect on economic growth in Nigeria within the period of study.The result shows a low insurance market activity inNigeria and that Nigerians have not fully embracethe insurance industry despite its importance to the growth of theeconomy.
19. Back to oil: Indonesia economic growth after Asian financial crisis
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Heru Iswahyudi
2016-04-01
Full Text Available This paper examines the growth experience of Indonesia in the years before and after the Asian financial crisis. Particular attention is paid to the relationship between economic growth and petroleum sector’s total factor productivity (TFP. It finds the possibility that post-crisis Indonesian economic growth has ‘recoupled’ with petroleum sector’s TFP – fluctuations in petroleum TFP is directly correlated with fluctuations in economic growth. Further, although keeping Indonesia’s petroleum sector open to fair competition should be the prime policy, the fact regarding resource nationalism might need to be taken into account in designing the policy to develop the productivity of Indonesia’s petroleum sector.
20. Growth Versus Government Management Improvement During Economic Downturn
Science.gov (United States)
Podobnik, Boris; Baaquie, Belal E.; Bishop, Steven; Njavro, Djuro; Li, Baowen
2013-04-01
In estimating how economic growth depends on various inputs, economists commonly use long periods of data encompassing both main extremes to fluctuations in the economy: recession and expansion. Here we focus on recession years because during expansion even countries with bad economic policies may experience large growth. Specifically, we study how growth depends on the proportion of public-sector workforce, p and competitiveness, quantified by the Global Competitiveness Index, GCI. For the 2008-2011 economic downturn and for 57 countries, we find that the growth rate of GDP per capita, g, decreases with p, and increases with ΔGCI. Further, more competitive countries attract more foreign direct investments per capita, I, than less competitive countries, where I ~ GCIα. We propose a production function, divided into the private and public sectors, where GDP depends on market capitalization, the public (private)-sector workforce, and competitiveness level, used to quantify the public sector efficiency.
1. CURRENT ACCOUNT DEFICIT AND ECONOMIC GROWTH IN ARMENIA
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Arus Tunian
2015-07-01
Full Text Available The article is devoted to the study of the problem of economic growth in Armenia. It is identified the nature of the balance of payments of the country, indicating a net debtor position, which leads to inherent deterioration of the international investment position. A small open economy of Armenia moves to a new phase of development, in the frame of the integration processes within the Customs Union and the Eurasian Economic Union of Russia, Belarus and Kazakhstan. One of the main characteristics of the Armenian economy vulnerability remains a negative balance in foreign trade, which continues to grow, despite the export growth. Economic growth is provided, as before, mostly due to the sale of raw materials - non-ferrous metals and metal ores, both in the primary as well as in the previous preprocessing. Estimating the econometric VAR models revealed that the negative current account impacts on GDP growth negatively.
2. Do Corruption and Social Trust affect Economic Growth? A Review
DEFF Research Database (Denmark)
Serritzlew, Søren; Sønderskov, Kim Mannemar; Svendsen, Gert Tinggaard
2014-01-01
Two separate literatures suggest that corruption and social trust, respectively, are related to economic growth, although the strengths of the relationships, and the direction of causality, are still debated. In this paper, we review these literatures and evaluate the evidence for causal effects...... of corruption and trust on economic growth, and discuss how corruption and trust are interrelated. The reviews show that absence of corruption and high levels of social trust foster economic growth. The literatures also indicate that corruption has a causal effect on social trust, while the opposite effect...... is more uncertain. In the conclusion, we offer the suggestion that fighting corruption may yield a “double dividend”, as reduced corruption is likely to have both direct and indirect effects on growth....
3. Strong regional links between socio-economic background factors and disability and mortality in Oslo, Norway
International Nuclear Information System (INIS)
Rognerud, Marit Aase; Krueger, Oystein; Gjertsen, Finn; Thelle, Dag Steinar
1998-01-01
Study objective: To study geographical differences in mortality and disability and sosio-economic status in Oslo, Norway. Setting: A total of 25 local authority districts within the city of Oslo. Design: Analysis of age adjusted mortality rates aged 0-74 in the period 1991-1994, and cross sectional data on disability pensioners aged 50-66 and socio-economic indicators (low education, single parenthood, unemployment, high income) in 1994. Main outcome measures: The levels of correlation between the health outcomes (mortality and disability) and sosio-economic exposure variables. Main results: The geographical patterns of mortality and disability display substantial similarities and show strong linear correlation with area measures of socio-economic deprivation. The ratios between the highest and lowest area mortality rates were 3.3 for men and 2.1 for women, while the high-low ratios of disability were 7.0 for men and 3.8 for women. For women deprivation measures are better correlated with disability than mortality. While disability and mortality display similar correlations with deprivation measures for men. Conclusions: The social gradients in health are substantial in Oslo. Further ecological analysis of cause specific morbidity and mortality and the distribution of risk factors ought to be done to identify problem areas suitable for interventions. However, to understand the mechanisms and the relative importance of each etiological factor, studies based on individual data have to be performed
4. Unstable periodic orbits and chaotic economic growth
International Nuclear Information System (INIS)
Ishiyama, K.; Saiki, Y.
2005-01-01
We numerically find many unstable periodic solutions embedded in a chaotic attractor in a macroeconomic growth cycle model of two countries with different fiscal policies, and we focus on a special type of the unstable periodic solutions. It is confirmed that chaotic behavior represented by the model is qualitatively and quantitatively related to the unstable periodic solutions. We point out that the structure of a chaotic solution is dissolved into a class of finite unstable periodic solutions picked out among a large number of periodic solutions. In this context it is essential for the unstable periodic solutions to be embedded in the chaotic attractor
5. Remittances, financial development and economic growth: Empirical evidence from Lesotho
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Athenia Bongani Sibindi
2014-11-01
Full Text Available Increasingly remittances now constitute a great source of foreign currency inflows for many developing countries. In some instances remittances have outpaced the growth of foreign direct investment (FDI. Amongst others, remittances can be used as a vehicle of savings mobilisation as well as fostering the supply of credit by providing liquidity to the market. In this article we investigate the causal relationship between the remittances, financial development and economic growth in Lesotho for the period 1975 to 2010. We make use of per capita remittances, real per capita broad money supply and real per capita growth domestic product as the proxies for remittances, financial development and economic growth respectively. We then test for cointegration amongst the variables by applying the Johansen procedure and then test for Granger causality based on the vector error correction model (VECM. Our results confirm the existence of at least one cointegrating relationship and also indicate that the direction of causality runs from remittances to the economy without feedback. The results also suggest that financial development Granger causes economic growth without feedback which is consistent with ‘supply-leading’ growth hypothesis. The results also confirm a causal relationship running from financial development to remittances without feedback. The results also lend credence to the “complementarity’ hypothesis in that, remittances complement rather than substitute financial development in bringing about economic growth.
6. Electricity Consumption, Carbon Emissions and Economic Growth in Nigeria
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Godwin Effiong Akpan
2012-01-01
Full Text Available This paper applies a Multivariate Vector Error Correction (VECM framework to examine the long run and causal relationship between electricity consumption, carbon emissions and economic growth in Nigeria. Using annual time series data for 1970 to 2008, findings show that in the long run, economic growth is associated with increase carbon emissions, while an increase in electricity consumption leads to an increase in carbon emissions. These imply that Nigeria’s growth process is pollution intensive, while the negative relationship between electricity consumption (or positive relationship between electricity consumption and emissions in Nigeria is a clear indication that electricity consumption in the country has intensified carbon emissions. No support was obtained for the hypothesized environmental Kuznets curve (EKC. Granger-causality results confirm a unidirectional causality running from economic growth to carbon emissions, indicating that carbon emissions reduction policies could be pursued without reducing economic growth in Nigeria. No causality was found between electricity and growth, in either way, which further lends credence to the crisis in the Nigerian electricity sector. Overall, the paper submits that efficient planning and increased investment in electricity infrastructure development may be the crucial missing variable in the obtained neutrality hypothesis between electricity and growth.
7. A critical realist perspective on decoupling negative environmental impacts from housing sector growth and economic growth
DEFF Research Database (Denmark)
Xue, Jin
2012-01-01
The question that motivates this article has been a matter of dispute: Is it possible to combine perpetual economic growth and longterm environmental sustainability based on the premise that economic growth can be fully decoupled from negative environmental impacts? The article addresses...... this question from the position of critical realism. An empirical study focusing on the housing sector is conducted, indicating that housing stock growth and economic growth have been, at best, weakly decoupled from environmental impacts. In the long run, it seems implausible that the degree of decoupling can...... be increased at a rate sufficient to compensate for continual growth in the volume of housing stock. A further elaboration of the topic at an ontological level leads to the conclusion that continual economic growth and long-term environmental sustainability can hardly be combined....
8. Tax Evasion and Economic Growth in an Endogenous Growth Model
OpenAIRE
加藤, 秀弥; KATO, Hideya
2004-01-01
This paper presents an endogenous growth model with tax evasion where government expenditures affect production. An individual evades a tax so as to maximize his or her utility, the tax authority controls the detection probability to maximize net tax revenue, and the government chooses the income tax rate to maximize individuals’ utility. The main conclusions are as follows. First, the optical income tax rate with tax evasion is higher than that without tax evasion. Second, the rise in a ...
9. Health, "illth," and economic growth: medicine, environment, and economics at the crossroads.
Science.gov (United States)
Egger, Garry
2009-07-01
Economic growth has been the single biggest contributor to population health since the Industrial Revolution. The growth paradigm, by definition, is dynamic, implying similar diminishing returns on investment at both the macro- and the micro-economic levels. Changes in patterns of health in developing countries, from predominantly microbial-related infectious diseases to lifestyle-related chronic diseases (e.g., obesity, type 2 diabetes) beyond a point of economic growth described as the epidemiologic transition, suggest the start of certain declining benefits from further investment in the growth model. These changes are reflected in slowing improvements in some health indices (e.g., mortality, infant mortality) and deterioration in others (e.g., disability-associated life years, obesity, chronic diseases). Adverse environmental consequences, such as climate change from economic development, are also related to disease outcomes through the development of inflammatory processes due to an immune reaction to new environmental and lifestyle-related inducers. Both increases in chronic disease and climate change can be seen as growth problems with a similar economic cause and potential economic and public health-rather than personal health-solutions. Some common approaches for dealing with both are discussed, with a plea for greater involvement by health scientists in the economic and environmental debates in order to deal effectively with issues like obesity and chronic disease.
10. Energy consumption, pollutant emissions and economic growth in South Africa
Energy Technology Data Exchange (ETDEWEB)
Menyah, Kojo [London Metropolitan Business School, London Metropolitan University (United Kingdom); Wolde-Rufael, Yemane [Independent Researcher (United Kingdom)
2010-11-15
This paper examines the long-run and the causal relationship between economic growth, pollutant emissions and energy consumption for South Africa for the period 1965-2006 in a multivariate framework which includes labour and capital as additional variables. Using the bound test approach to cointegration, we found a short-run as well as a long-run relationship among the variables with a positive and a statistically significant relationship between pollutant emissions and economic growth. Further, applying a modified version of the Granger causality test we also found a unidirectional causality running from pollutant emissions to economic growth; from energy consumption to economic growth and from energy consumption to CO{sub 2} emissions all without a feedback. The econometric evidence suggests that South Africa has to sacrifice economic growth or reduce its energy consumption per unit of output or both in order to reduce pollutant emissions. In the long-run however, it is possible to meet the energy needs of the country and at the same time reduce CO{sub 2} emissions by developing energy alternatives to coal, the main source of CO{sub 2} emissions. However, the econometric results upon which the policy suggestions are made should be interpreted with care, as they may not be sufficiently robust enough to categorically warrant the choice of an unpalatable policy option by South Africa. (author)
11. The economic growth enigma: Capital, labour and useful energy?
International Nuclear Information System (INIS)
Ayres, Robert; Voudouris, Vlasios
2014-01-01
We show that the application of flexible semi-parametric statistical techniques enables significant improvements in model fitting of macroeconomic models. As applied to the explanation of the past economic growth (since 1900) in US, UK and Japan, the new results demonstrate quite conclusively the non-linear relationships between capital, labour and useful energy with economic growth. They also indicate that output elasticities of capital, labour and useful energy are extremely variable over time. We suggest that these results confirm the economic intuition that growth since the industrial revolution has been driven largely by declining energy costs due to the discovery and exploitation of relatively inexpensive fossil fuel resources. Implications for the 21st century, which are also discussed briefly by exploring the implications of an ACEGES-based scenario of oil production, are as follows: (a) the provision of adequate and affordable quantities of useful energy as a pre-condition for economic growth and (b) the design of energy systems as ‘technology incubators’ for a prosperous 21st century. - Highlights: • Economic growth needs three factors of production. • We propose a semi-parametric generalised production function. • Exploitation of inexpensive fossil fuel resources has profound policy implications
12. FDI in Tourism Sector and Economic Growth in Sumatra Utara
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Parhimpunan Simatupang
2014-09-01
Full Text Available Globalization and neo liberal policies such as liberalization and privatization have generated a significant growth for FDI and considered an important source for capital and foreign currency, capable of spurring economic growth in developing countries. One sector that received particular attention, due to its significant contributions towards economic development, especially in Indonesia, is tourism. Tourism investments in Indonesia are mainly focused on the development of fully-integrated resort sites that help boost the construction of tourist facilities such as hotels and the development of the surrounding environment through social and cultural aspects. The total contribution of travel and tourism to GDP was IDR736.3 billion or 8.9% of GDP in 2012. Foreign direct tourism investments grew by 210% between 2011 and 2012, or at an annual compound average growth rate of 38% between 2006 and 2012. While the implications are at national level, not much could be gathered on the local perspectives. This paper intends to explore the implication of FDI in tourism sector towards economic growth in one of tourism attraction provinces in Indonesia—Sumatra Utara. Specifically, which economic factors contributed towards FDI inflows and their impacts on economic growth in Sumatra Utara.
13. THE TERTIARY CIVILIZATION – CONCEPT OF THE ECONOMIC GROWTH
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Gabriela Liliana CIOBAN
2014-06-01
Full Text Available Providing services has become the most important sector of the economy and the main dynamic factor of the economic competition, within the developed countries economies. In such economies, the sector of economies has assimilated the workforce issued in the other sector, when this over plus of labor force represented simultaneously the cause of its expansion. The services have had a double part: they contribute on both the material entertainment of the labor force, as well as on maintaining the reestablishment of people’s health, to their physical and intellectual recovery, to the development of the individual, as regards the cultural and scientific points of view, and implicitly, to the growth of the living standards. For the time being, one can characterize the economies of the developed countries, as well as of many other countries in progress of development, as services oriented economies; the development and diversification of services has been determined by the need of satisfying diversified social needs. In this way, the part of services aims on becoming proportional to their contribution within the process of economic growth. One can definitely say that between services and the economic growth, a double conditioning takes place, meaning: on one hand, the development of services appears as a consequence of the economic growth, and on the other hand, it grows up the economic growth, thus contributing on diversifying the production and on improving the level of training or qualification of the labor force.
14. Poverty and Economic Growth in Swaziland: An Empirical Investigation
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Angelique G. Nindi
2015-03-01
Full Text Available This paper examines the causal relationship between poverty reduction and economic growth in Swaziland during the period 1980–2011. Unlike some of the previous studies, the current study uses the newly developed ARDL-bounds testing approach to co-integration, and the ECM-based Granger causality method to examine this linkage. The study also incorporates financial development as a third variable affecting both poverty reduction and economic growth – thereby leading to a trivariate model. The results of this study show that economic growth does not Granger cause poverty reduction in Swaziland – either in the short run or in the long run. Instead, the study finds a causal flow from poverty reduction to economic growth in the short run. These findings, however, are not surprising, given the high level of income inequality in Swaziland. Studies have shown that when the level of income inequality is too high, economic growth alone may not necessarily lead to poverty reduction.
15. Convergence and economic growth in Mexico
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Alejandro Bautista-Díaz
2000-01-01
Full Text Available Recientemente, se ha puesto mucha atención en lo escrito sobre crecimiento económico, el fenómeno de convergencia condicional o la tendencia de las economías regionales con niveles bajos de ingreso a un crecimiento rápido, como condicional en su tasa de acumulación de factores. El estudio utiliza teorías neoclásicas de crecimiento estandarizadas, para obtener la aproximación empírica de la hipótesis de convergencia sobre el capital humano entre los 31 estados y el Distrito Federal en México, utilizando índices de educación. El estudio encuentra que la tasa anual de convergencia de capital humano per cápita en México oscila del 3.55 al 4.58 por ciento. También estima la convergencia de ingreso per cápita condicional en variables de capital humano.
16. China and India: Openness, Trade and Effects on Economic Growth
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Marelli, Enrico
2011-06-01
Full Text Available The purpose of this paper is to analyse the economic growth of China and India in terms of their integration in the global economy. We begin with a discussion of some stylized facts concerning their recent economic growth, the most significant institutional reforms, with particular reference to trade relations, and their impact on their economic development. We then propose a descriptive analysis of economic growth, opening up of the economies and trade specialisation, by comparing the features and trends of the two countries (by considering trade and foreign direct investment data. We have also estimated some econometric relations between economic growth and trade/openness, with the addition of control variables (such as the gross fixed capital formation. We initially used a panel data model for the two countries, to be estimated with fixed effects; to test for reverse causality, we re-estimated the fixed effects model by 2SLS (with the inclusion of specific instrumental variables. The effect on economic growth (in terms of GDP per capita of our variables of interest - Openness and FDI - remains positive and statistically significant in all specifications, which confirms our findings even if we treat these variables as endogenous variables. The results prove the positive growth effects, for the two countries, of opening up and integrating in the world economy. Note that the robust growth of these two "giants" has contained the initial impact of the recent global crisis and is now sustaining the recovery of the entire world economy. Other policy relevant implications are discussed in the concluding section.
17. The Impact of Regional Disparities on Economic Growth
Directory of Open Access Journals (Sweden)
Henryk Gurgul
2011-01-01
Full Text Available The authors investigated how economic growth affects the disparity in the distribution of regional income in Poland and vice versa. The research was based on annual data covering the period 2000-2009. In general, the research was divided into two main parts. First, the authors examined the evolution of the level of spatial inequalities in income in Poland over the last decade using the concepts of sigma and beta convergence. Next the nature of causal dependences was investigated between this inequality and economic growth. It was found that Polish regions did not converge with respect to the distribution of income as total GDP grew. The second part of the research provided evidence to claim that this inequality caused growth. Moreover, the evidence was also found that growth affected regional inequality. Finally, the authors noticed that the effects of both these factors were positive. The results suggest that as a consequence of rapid economic growth, some regions in Poland seized new opportunities, while less developed regions were unable to keep up with the challenging requirements of a decade of fast economic growth. (original abstract
18. Determinants of Economic Growth: Empirical Evidence from Russian Regions
Directory of Open Access Journals (Sweden)
Svetlana Ledyaeva
2008-06-01
Full Text Available A modification of Barro and Sala-i-Martin empirical framework of growth model is specified to examine determinants of per capita growth in 74 Russian regions during period of 1996-2005. We utilize both panel and cross-sectional data. Results imply that in general regional growth in 1996-2005 is explained by the initial level of region's economic development, the 1998 financial crisis, domestic investments, and exports. Growth convergence between poor and rich regions in Russia was not found for the period studied.
19. The Dynamic Effects of Entrepreneurship on Regional Economic Growth
DEFF Research Database (Denmark)
Matejovsky, Lukas; Mohapatra, Sandeep; Steiner, Bodo
2014-01-01
This study explores the temporal pattern of income disparity for Canadian provinces in two estimation steps. First, an econometric growth regression model is applied to identify the impact of entrepreneurship on regional economic growth. The estimation results suggest that entrepreneurship......, measured in terms of the selfemployment rate, plays a pivotal role in determining regional development in Canada. Second, a dynamic vector autoregression (VAR) model is employed to predict the long-run regional growth effects that result from policy shocks affecting entrepreneurship. Compared to other...... growth drivers, entrepreneurship is found to have more pronounced and long-term stimulative effects on regional development for the period of 1987 to 2007...
20. Intelligent robotics can boost America's economic growth
Science.gov (United States)
Erickson, Jon D.
1994-01-01
A case is made for strategic investment in intelligent robotics as a part of the solution to the problem of improved global competitiveness for U.S. manufacturing, a critical industrial sector. Similar cases are made for strategic investments in intelligent robotics for field applications, construction, and service industries such as health care. The scope of the country's problems and needs is beyond the capability of the private sector alone, government alone, or academia alone to solve independently of the others. National cooperative programs in intelligent robotics are needed with the private sector supplying leadership direction and aerospace and non-aerospace industries conducting the development. Some necessary elements of such programs are outlined. The National Aeronautics and Space Administration (NASA) and the Lyndon B. Johnson Space Center (JSC) can be key players in such national cooperative programs in intelligent robotics for several reasons: (1) human space exploration missions require supervised intelligent robotics as enabling tools and, hence must develop supervised intelligent robotic systems; (2) intelligent robotic technology is being developed for space applications at JSC (but has a strong crosscutting or generic flavor) that is advancing the state of the art and is producing both skilled personnel and adaptable developmental infrastructure such as integrated testbeds; and (3) a NASA JSC Technology Investment Program in Robotics has been proposed based on commercial partnerships and collaborations for precompetitive, dual-use developments.
1. Energy and economic growth: Grounding our understanding in physical reality
International Nuclear Information System (INIS)
Ockwell, David G.
2008-01-01
This article attempts to summarise the complex, wide ranging and unresolved debate within the economics literature on the possibility of decoupling economic growth from energy use. It explores the difference between neo-classical and ecological economic worldviews and highlights how the ecological economic approach attempts to ground its analysis within the physical limits implied by the laws of thermodynamics. Once these laws are accounted for, the possibility of decoupling economic growth from energy use seems more limited than neo-classical economics implies. Analysis of empirical evidence also demonstrates that observed improvements in GDP/energy use ratios in the USA are better explained by shifts towards higher quality fuels than by improvements in the energy efficiency of technologies. This implies a need to focus on decarbonising energy supply. Furthermore, where energy-efficiency improvements are attempted, they must be considered within the context of a possible rebound effect, which implies that net economy-wide energy savings from energy-efficiency improvements may not be as large as the energy saved directly from the efficiency improvement itself. Both decarbonising energy supply and improving energy efficiency require the rapid development and deployment of new and existing low-carbon technologies. This review therefore concludes by briefly outlining areas of economic thought that have emerged as a result of engagement between economists and experts from other disciplines. They include ecological, evolutionary and institutional economics, all of which can make policy-relevant contributions to achieving a transition to a low-carbon economy
2. Energy consumption and economic growth in China: A reconciliation
International Nuclear Information System (INIS)
Talha Yalta, A.; Cakar, Hatice
2012-01-01
In conventional causality testing based on asymptotic distribution theory, there is a high risk of wrongly rejecting the true null of no causality especially when the sample size is as small as typically seen in the literature. In this study, we offer a formal diagnosis of the existing contradictory results on the causal relationship between energy consumption and real GDP. We also employ a time series oriented advanced data generation process to perform simulation based inference for the People's Republic of China. Our study covers the 1971–2007 period and considers five different aggregated and disaggregated energy consumption measures as well as three different lag orders in both a bivariate as well as a multivariate frameworks. Our maximum entropy bootstrap based analysis, which avoids pretest biases and is also robust to Type I errors, supports the neutrality hypothesis in 53 out of the total of 60 model estimations. The strong results show that coarse aggregate data has a limited potential to observe the complex causal linkages between energy consumption and economic growth. Future policy oriented research on this nexus requires more focused analyses based on sectoral and provincial data. - Highlights: ► Some of the contradictory findings on the energy–growth nexus are due to asymptotic testing under small samples. ► The bootstrap method can provide huge improvements upon the approximations of asymptotic theory. ► 53 out of a total of 60 models that we consider consistently support the neutrality hypothesis for China. ► Future policy oriented research on this nexus should aim toward detailed analyses using sectoral and provincial data.
3. Technical conditions for sustainable growth in economic theory. An analysis
International Nuclear Information System (INIS)
Granda C, Catalina
2008-01-01
Economic theory and its models point out returns to scale, substitution among productive factors and technological progress as conditions for sustainable growth. This work aims at a critical appraisal of these conditions, particularly the ones related to substitution between natural resources and manmade capital and technical change, by recognizing the inevitable physical scarcity of resources concomitant to the human actions in a world governed by hemodynamic restrictions. To do so, the role that the mentioned conditions play in the theories of economic growth with resources is analyzed, and its limitations and objections from a biophysical perspective are indicated as well. Finally, a brief consideration as to how inappropriate the theoretical representations of economic activities are to take account of growth in spite of resource exhaustion or degradation is carried out
4. FDI and Economic Growth in Central and Eastern Europe
Directory of Open Access Journals (Sweden)
Gheorghe H. Popescu
2014-11-01
Full Text Available This paper discusses the major trends in scholarship about the role of FDI and exports on economic growth, the effect of tax policies on FDI, the formation of the economic catch up of the Central and Eastern Europe (CEE region and the determinants of FDI inflows in CEE nations. I am specifically interested in how previous research investigated the influence of FDI on host country economic growth, the inward FDI stock as a percentage of GDP, the features and restrictions of fiscal schemes in CEE economies and the institutional soundness displayed in policies towards FDI. The analysis presented in this paper contributes to research on FDI as a mechanism in the transition to the market, the dissimilarities in the FDI-assisted development methods among the CEE nations, the impact of FDI inflows for productivity convergence in CEE and the current slowing of growth in emerging Europe.
5. Role of Strong versus Weak Networks in Small Business Growth in an Emerging Economy
Directory of Open Access Journals (Sweden)
M. Kamil Kozan
2014-02-01
Full Text Available The study tests whether strong rather than weak ties account for small business growth in Turkey. Data were collected by means of a questionnaire filled out by the owners of small firms operating in four cities. Growth is comprised of two main areas, production expansion and knowledge acquisition. Results show that strong ties are positively related to both types of growth. In contrast, loose ties have no effect on small business growth in either area. This finding is attributed to the influence of the collectivistic nature of the mainstream Turkish culture, where owners of small businesses are likely to rely on in-groups rather than out-groups for advice and for financial support. Implications of relative absence of weak ties for small business growth and innovation in emerging economies are discussed. The findings suggest that culture should be included as a contingency variable in future studies of network strength and growth relationship. The paper also discusses the possible moderating role of affective and cognition-based trust in the relation of strong and weak ties to small business growth.
6. One interpretation of the low economic growth in Mexico
OpenAIRE
Isaac, Sánchez Juárez
2011-01-01
Since 1982 the Mexican economy was characterized by the presence of low economic growth rates, this situation has caused a severe reduction in employment and thus the welfare of the Mexican population. Following a kaldorian’s framework of development we assume that the process of stagnation suffered by México, especially in recent years is explained by the lack of dynamism in the domestic manufacturing sector. The latter is attributed mainly to the current economic model, implemented in the l...
7. A theory of organized crime, corruption and economic growth
OpenAIRE
Rana, MP; Blackbourn, K; Neanidis, KC
2017-01-01
We develop a framework for studying the interactions between organized crime and corruption, together with the individual and combined effects of these phenomena on economic growth. Criminal organizations co-exist with law-abiding productive agents and potentially corrupt law enforcers. The crime syndicate obstructs the economic activities of agents through extortion, and may pay bribes to law enforcers in return for their compliance in this. We show how organized crime has a negative effect ...
8. A Theory of Organized Crime, Corruption and Economic Growth
OpenAIRE
Blackburn, Keith; Neanidis, Kyriakos; Rana, Maria Paola
2017-01-01
We develop a framework for studying the interactions between organized crime and corruption, together with the individual and combined e¤ects of these phenomena on economic growth. Criminal organizations co-exist with law-abiding productive agents and potentially corrupt law enforcers. The crime syndicate obstructs the economic activities of agents through extortion, and may pay bribes to law enforcers in return for their compliance in this. We show how organized crime has a negative e¤ect on...
9. ECONOMIC GROWTH AND TAXATION IN CENTRAL AND EASTERN EUROPE
Directory of Open Access Journals (Sweden)
Cristina BOROVINA (COJOCARU
2016-05-01
Full Text Available In the context of the economic crisis that started in the United States in 2007, economic growth has become of great importance for the countries affected by the crisis further to their confrontation with lower growth rates of GDP per capita. At national level, governments are searching for that mix of optimal economic policies that would revive economies on the upward and also sustainable trend. One of the key policies in this regard, especially for the countries in Central and Eastern Europe which intend to adopt the euro currency, is the tax policy. Its main instruments are taxes. In this paper, we pay special attention to these instruments and to the connection that they have with the economic growth. This paper is divided into three parts. The first part presents a few ideas related to the importance of taxes at national level, the second part is an analysis in terms of taxation of the Central and Eastern Europe countries, while the third part consists of a panel-type assessment of the relation between economic growth and taxation level.
10. Economic Growth of a Rapidly Developing Economy: Theoretical Formulation
Directory of Open Access Journals (Sweden)
Oleg Sergeyevich Sukharev
2016-06-01
Full Text Available The subject matter of the article is the description of economic growth. Modern economy is characterized by a high rate of changes. These changes are the limiting parameters of modern development, which requires a modification of the basic models of growth, the substantiation of the expediency and necessity of a rapid development strategy. In a simple mathematical form, the statement of the problem of economic growth in the “green economy” is examined, in which the costs of environmental measures are not considered a priori as hampering economic development (as it is common for a number of modern neoclassical and neo-Keynesian growth models. The methodological basis of the article are the econometric approach and modelling method. The article has a theoretical character. The main hypothesis supposes that the rapid development strategy cannot make an adequate development strategy under certain conditions, but may be acceptable in other its specific conditions. In this sense, the important growth conditions are the availability of resources, the effectiveness of institutions and the current economic structure, the technological effectiveness of economy, as well as the conditions of technological development (“green economy” and the path of such development. In the article, on the theoretical level of analysis, the substantiation of the adequacy of the rapid development strategy for an economic system is given, whose goal is to achieve the standard of living of the countryleader. Based on the assumptions introduced, the period for which the rapid development strategy might be implemented and the economic lag of the country might be reduced from the country-leader is determined. The conditions that ensure the impact of innovations on the rate of economic development are summarized. The introduced range of dependencies and relations can be useful for the elaboration of the theory of innovation development and for the formation of a new
11. Performance Agent Groups in the Promotion of Smart Economic Growth
Directory of Open Access Journals (Sweden)
Krūzmētra Maiga
2017-12-01
Full Text Available Any country is interested in economic growth regardless of its development level in any period; yet an increasingly important role in defining growth is played by the term ‘smart growth’. The EU development strategy until 2020 defines smart growth as a strategic objective. Smart growth does not take place automatically. It is affected both by the condition of the economic, social and natural environments and by subjective factors - the competence of performance agents. The present research distinguished three groups of rural space and regional performance agents: national institutions, local governments and communities of residents of the territories examined by the research. The research summarised the opinions of experts (Latvia n=171; Lithuania n=163 from the south-eastern part of Latvia and the north-eastern part of Lithuania with the purpose of assessing the contribution of the performance agent groups to the promotion of smart economic growth. The research aimed to identify the positive indications of the contribution made by each performance agent group as well as the largest problems affecting the promotion of smart economic growth in each country. Despite the fact that the sample groups were not representative (did not reflect the views of the entire population, the obtained survey data and the results of this analysis provided insight into the performance agents’ action ratings from the bottom-up position and allowed comparing the situations in Latvia and Lithuania. The research has become an urgent task in project No. 5.2.3 “Rural and Regional Development Processes and Opportunities in Latvia in the Context of Knowledge Economy” in National Research Programme 5.2. "Economic Transformation, Smart Growth, Governance and Legal Framework for the State and Society for Sustainable Development - a New Approach to the Creation of a Sustainable Learning Community: EKOSOC-LV”.
12. Economic Growth and CO2 Emissions in the European Union
International Nuclear Information System (INIS)
Bengochea-Morancho, A.; Martinez-Zarzoso, I.; Higon-Tamarit, F.
2001-01-01
This paper examines the relationship between economic growth and CO 2 emissions in the European Union. A panel data analysis for the period 1981 to 1995 is applied in order to estimate the relationship between Gross Domestic Product (GDP) growth and CO 2 emissions in ten selected European countries. The analysis shows important disparities between the most industrialised countries and the rest. The results do not seem to support a uniform policy to control emissions; they rather indicate that a reduction in emissions should be achieved by taking into account the specific economic situation and the industrial structure of each EU member state. 20 refs
13. Decoupling economic growth from CO2 emissions: A decomposition analysis of China's household energy consumption
Directory of Open Access Journals (Sweden)
Xiao-Wei Ma
2016-09-01
Full Text Available This paper analyzes Chinese household CO2 emissions in 1994–2012 based on the Logarithmic Mean Divisia Index (LMDI structure decomposition model, and discusses the relationship between household CO2 emissions and economic growth based on a decoupling indicator. The results show that in 1994–2012, household CO2 emissions grew in general and displayed an accelerated growth trend during the early 21st century. Economic growth leading to an increase in energy consumption is the main driving factor of CO2 emission growth (an increase of 1.078 Gt CO2 with cumulative contribution rate of 55.92%, while the decline in energy intensity is the main cause of CO2 emission growth inhibition (0.723 Gt CO2 emission reduction with cumulative contribution rate of 38.27%. Meanwhile, household CO2 emissions are in a weak state of decoupling in general. The change in CO2 emissions caused by population and economic growth shows a weak decoupling and expansive decoupling state, respectively. The CO2 emission change caused by energy intensity is in a state of strong decoupling, and the change caused by energy consumption structure fluctuates between a weak and a strong decoupling state.
14. Financial Intermediaries and Economic Growth: The Nigerian Evidence
Directory of Open Access Journals (Sweden)
Oba Efayena
2014-06-01
Full Text Available This study seeks to examine the role of financial intermediaries and to find out whether financial intermediaries impact on economic growth in Nigeria. The study adopts the Harrod-Domar growth model which states that economic growth will proceed at the rate which society can mobilize domestic savings resources coupled with the productivity of the investment. The study employed the use of secondary data for the period 1981 to 2011 which were sourced from the CBN statistical bulletin. Nigerian banks being the dominant financial intermediaries, loans credits and advances from banks were used as proxy for the independent variable. Gross domestic product (GDP was used as proxy for economic growth. Using the technique of correlation analysis in determining the association between loan credits and advances, and the GDP, the study reveals a relatively high positive correlation between financial intermediaries and economic growth in the Nigerian economy. The study recommends that Nigerian banks should lend higher proportion of their loanable funds to small and medium enterprises (SMEs and should invest in information technology and human capital.
15. US carbon emissions, technological progress and economic growth since 1870
International Nuclear Information System (INIS)
Huntington, H.G.
2005-01-01
The long-term US experience emphasises the importance of controlling for electrification and other major technology transformations when evaluating the growth of carbon emissions at different stages of development. Prior to World War I, carbon emissions grew faster than economic growth by 2.3% per year. As electricity use expanded and steam engines became much larger, carbon emissions began to grow slower than economic growth by 1.6% per year. Adjusting to this technological shift, an expanding economy continues to increase carbon emissions by about 9% for each 10% faster growth. There is little evidence of a decline in this elasticity as the income level rises. These results suggest that the USA today will need to find additional policies to curb carbon emissions if it wishes to prevent any further increase in its per capita emissions, and if its per capita economy grows by more than 1.8% per year. (Author)
16. End-of-the-year economic growth and time-varying expected returns
DEFF Research Database (Denmark)
Møller, Stig V.; Rangvid, Jesper
2015-01-01
We show that macroeconomic growth at the end of the year (fourth quarter or December) strongly influences expected returns on risky financial assets, whereas economic growth during the rest of the year does not. We find this pattern for many different asset classes, across different time periods......, and for US and international data. We also show that movements in the surplus consumption ratio of Campbell and Cochrane (1999) , a theoretically well-founded measure of time-varying risk aversion linked to macroeconomic growth, influence expected returns stronger during the fourth quarter than the other...
17. Geomagnetic and strong static magnetic field effects on growth and chlorophyll a fluorescence in Lemna minor.
Science.gov (United States)
Jan, Luka; Fefer, Dušan; Košmelj, Katarina; Gaberščik, Alenka; Jerman, Igor
2015-04-01
The geomagnetic field (GMF) varies over Earth's surface and changes over time, but it is generally not considered as a factor that could influence plant growth. The effects of reduced and enhanced GMFs and a strong static magnetic field on growth and chlorophyll a (Chl a) fluorescence of Lemna minor plants were investigated under controlled conditions. A standard 7 day test was conducted in extreme geomagnetic environments of 4 µT and 100 µT as well as in a strong static magnetic field environment of 150 mT. Specific growth rates as well as slow and fast Chl a fluorescence kinetics were measured after 7 days incubation. The results, compared to those of controls, showed that the reduced GMF significantly stimulated growth rate of the total frond area in the magnetically treated plants. However, the enhanced GMF pointed towards inhibition of growth rate in exposed plants in comparison to control, but the difference was not statistically significant. This trend was not observed in the case of treatments with strong static magnetic fields. Our measurements suggest that the efficiency of photosystem II is not affected by variations in GMF. In contrast, the strong static magnetic field seems to have the potential to increase initial Chl a fluorescence and energy dissipation in Lemna minor plants. © 2015 Wiley Periodicals, Inc.
18. The State Financial Policy as Instrument of Economic Growth
Directory of Open Access Journals (Sweden)
Mostitskaya Natalya А.
2017-12-01
Full Text Available The article is aimed at disclosing the essence and defining the role of the State financial policy as instrument of economic growth in the conditions of economic transformation. The main functions of the country’s financial policy were analyzed. The necessity of formation of institutional and methodological bases of the State financial mechanism with the purpose of strengthening of efficiency of structural changes of economy and social sphere has been substantiated. Directions of formation and implementation of the State financial policy on maintenance of socio-economic development of the country have been proposed.
19. Electricity consumption and economic growth in South Africa. A trivariate causality test
Energy Technology Data Exchange (ETDEWEB)
Odhiambo, Nicholas M. [Economics Department, University of South Africa (UNISA), P.O. Box 392, UNISA, 0003, Pretoria (South Africa)
2009-09-15
In this paper we examine the causal relationship between electricity consumption and economic growth in South Africa. We incorporate the employment rate as an intermittent variable in the bivariate model between electricity consumption and economic growth - thereby creating a simple trivariate causality framework. Our empirical results show that there is a distinct bidirectional causality between electricity consumption and economic growth in South Africa. In addition, the results show that employment in South Africa Granger-causes economic growth. The results apply irrespective of whether the causality is estimated in the short-run or in the long-run formulation. The study, therefore, recommends that policies geared towards the expansion of the electricity infrastructure should be intensified in South Africa in order to cope with the increasing demand exerted by the country's strong economic growth and rapid industrialisation programme. This will certainly enable the country to avoid unprecedented power outages similar to those experienced in the country in mid-January 2008. (author)
OpenAIRE
John Smithin
2014-01-01
1. Endogenous economic growth, EROI, and transition towards renewable energy
OpenAIRE
Victor Court; Pierre-André Jouvet; Frédéric Lantz
2015-01-01
Due to their initial lack of emphasis on energy and natural resources, exogenous and endogenous growth models have suffered the same critic regarding the limits to economic growth imposed by finite Earth resources. Thus, various optimal control models that incorporate energy or natural resources have been developed during the last decades. However, in all these models the importance of the Energy Return On Energy Investment (EROI) has never been raised. The EROI is the ratio of the quantity o...
2. Thermodynamics of long-run economic innovation and growth
OpenAIRE
Garrett, Timothy J.
2013-01-01
This article derives prognostic expressions for the evolution of globally aggregated economic wealth, productivity, inflation, technological change, innovation and growth. The approach is to treat civilization as an open, non-equilibrium thermodynamic system that dissipates energy and diffuses matter in order to sustain existing circulations and to further its material growth. Appealing to a prior result that established a fixed relationship between a very general representation of global eco...
3. THE RELATIONSHIP BETWEEN TOURIST RECEIPTS AND ECONOMIC GROWTH IN TUNISIA
OpenAIRE
Slim Mahfoudh*, Mohamed Ben Amar
2016-01-01
Considered as a global booming business, tourism contributes by 11% of the world GDP. In many developing countries, this sector has become a key source of growth and wealth that affects directly and indirectly sectors linked to it as well as others. According to the World Tourism Organization (2004) tourism doubled between 1995 and 2005 and it has become itself for some small and medium-sized countries the exporting sector by excellence! Contributing massively to the national economic growth ...
4. R&D Expenditures and Economic Growth Relationship in Turkey
OpenAIRE
Cuma BOZKURT
2015-01-01
In today's world, globalization has reached to such an extent that, investment in information and technology is inevitable to be integrated with global system and increase competitive power. Therefore, R&D investments are of high importance and priority for growth process of economy. This paper investigates the long-run relationship between R&D expenditure and economic growth using the Johansen co-integration and the vector error correction models. The research findings indicate that there is...
5. EFFECTS OF THE ECONOMIC FREEDOMS ON THE ECONOMIC GROWTH: EVIDENCE FROM THE EU AND COMCEC COUNTRIES (1996-2015
Directory of Open Access Journals (Sweden)
HALİL İBRAHİM AYDIN
2017-06-01
Full Text Available In this research, the effects of the economic freedoms on the economic growth for EU and COMCEC countries at different development/income level are econometrically analyzed via panel data analysis for the period of 1996- 2014 by being considered the improvement of economic growth theories for the key determinants of economic growth. From this aspect, it is aimed at this research that to evaluate the effects of the economic freedoms on the long termed economic growth performances and income level differences of EU and COMCEC countries which have different statuses in terms of economic freedoms and income level indicators. It is determined at the end of the study that the economic freedoms have a positive and statistically significant effect on the economic growth of EU countries in investigation period, on the other hand, these freedoms have not any effect on the economic growth of COMCEC countries. Moreover, the existence of a one-way causality relation operates from economic freedoms to the economic growth in EU countries is specified while there is any causality link found between these freedoms and the economic growth for the countries in COMCEC group. All these results indicate that also the economic freedoms besides the physical human capital accumulation, in other words, whether the EU and COMCEC countries have a market economy adopts outward-oriented liberal fiscal policies plays a major role in differentiating the income levels or the economic growth performances.
6. Strain selection, biomass to biofuel conversion, and resource colocation have strong impacts on the economic performance of algae cultivation sites
Energy Technology Data Exchange (ETDEWEB)
Venteris, Erik R.; Wigmosta, Mark S.; Coleman, Andre M.; Skaggs, Richard
2014-09-16
Decisions involving strain selection, biomass to biofuel technology, and the location of cultivation facilities can strongly influence the economic viability of an algae-based biofuel enterprise. In this contribution we summarize our past results in a new analysis to explore the relative economic impact of these design choices. We present strain-specific growth model results from two saline strains (Nannocloropsis salina, Arthrospira sp.), a fresh to brackish strain (Chlorella sp., DOE strain 1412), and a freshwater strain of the order Sphaeropleales. Biomass to biofuel conversion is compared between lipid extraction (LE) and hydrothermal liquefaction (HTL) technologies. National-scale models of water, CO2 (as flue gas), land acquisition, site leveling, construction of connecting roads, and transport of HTL oil to existing refineries are used in conjunction with estimates of fuel value (from HTL) to prioritize and select from 88,692 unit farms (UF, 405 ha in pond area), a number sufficient to produce 136E+9 L yr-1 of renewable diesel (36 billion gallons yr-1, BGY). Strain selection and choice of conversion technology have large economic impacts, with differences between combinations of strains and biomass to biofuel technologies being up to $10 million dollars yr-1 UF-1. Results based on the most productive species, HTL-based fuel conversion, and resource costs show that the economic potential between geographic locations within the selection can differ by up to$4 million yr-1 UF-1, with 2.0 BGY of production possible from the most cost-effective sites. The local spatial variability in site rank is extreme, with very high and low rank sites within 10s of km of each other. Colocation with flue gas sources has a strong influence on site rank, but the most costly resource component varies from site to site. The highest rank sites are located predominantly in Florida and Texas, but most states south of 37°N latitude contain promising locations. Keywords: algae
7. Economic growth and mortality: do social protection policies matter?
Science.gov (United States)
Bilal, Usama; Cooper, Richard; Abreu, Francis; Nau, Claudia; Franco, Manuel; Glass, Thomas A
2017-08-01
In the 20th century, periods of macroeconomic growth have been associated with increases in population mortality. Factors that cause or mitigate this association are not well understood. Evidence suggests that social policy may buffer the deleterious impact of economic growth. We sought to explore associations between changing unemployment (as a proxy for economic change) and trends in mortality over 30 years in the context of varying social protection expenditures. We model change in all-cause mortality in 21 OECD (Organization for Economic Cooperation and Development) countries from 1980 to 2010. Data from the Comparative Welfare States Data Set and the WHO Mortality Database were used. A decrease in the unemployment rate was used as a proxy for economic growth and age-adjusted mortality rates as the outcome. Social protection expenditure was measured as percentage of gross domestic product expended. A 1% decrease in unemployment (i.e. the proxy for economic growth) was associated with a 0.24% increase in the overall mortality rate (95% confidence interval: 0.07;0.42) in countries with no changes in social protection. Reductions in social protection expenditure strengthened this association between unemployment and mortality. The magnitude of the association was diminished over time. Our results are consistent with the hypothesis that social protection policies that accompany economic growth can mitigate its potential deleterious effects on health. Further research should identify specific policies that are most effective. © The Author 2017; all rights reserved. Published by Oxford University Press on behalf of the International Epidemiological Association
8. Carbon nanotube growth on nanozirconia under strong cathodic polarization in steam and carbon dioxide
DEFF Research Database (Denmark)
Tao, Youkun; Ebbesen, Sune Dalgaard; Zhang, Wei
2014-01-01
nanozirconia acting as a catalyst for the growth of carbon nanotubes (CNTs) during electrochemical conversion of carbon dioxide and water in a nickel-yttria- stabilized zirconia cermet under strong cathodic polarization. An electrocatalytic mechanism is proposed for the growth of the CNTs. ${{{\\rm {\\rm V......Growth of carbon nanotubes (CNTs) catalyzed by zirconia nanoparticles was observed in the Ni-yttria doped zirconia (YSZ) composite cathode of a solid oxide electrolysis cell (SOEC) at approximately 875 °C during co-electrolysis of CO2 and H2O to produce CO and H 2. CNT was observed to grow under... 9. Energy consumption and economic growth relationship: Evidence from panel data for low and middle income countries International Nuclear Information System (INIS) Ozturk, Ilhan; Aslan, Alper; Kalyoncu, Huseyin 2010-01-01 This paper uses the panel data of energy consumption (EC) and economic growth (GDP) for 51 countries from 1971 to 2005. These countries are divided into three groups: low income group, lower middle income group and upper middle income group countries. Firstly, a relationship between energy consumption and economic growth is investigated by employing panel cointegration method. Secondly, panel causality test is applied to investigate the way of causality between the energy consumption and economic growth. Finally, we test whether there is a strong or weak relationship between these variables by using method. The empirical results of this study are as follows: i) Energy consumption and GDP are cointegrated for all three income group countries. ii) The panel causality test results reveal that there is long-run Granger causality running from GDP to EC for low income countries and there is bidirectional causality between EC and GDP for middle income countries. iii) The estimated cointegration factor, β, is not close to 1. In other words, no strong relation is found between energy consumption and economic growth for all income groups considered in this study. The findings of this study have important policy implications and it shows that this issue still deserves further attention in future research. 10. Life insurance, financial development and economic growth in South Africa Directory of Open Access Journals (Sweden) Athenia Bongani Sibindi 2014-09-01 Full Text Available The life insurance sector may contribute to economic growth by its very mechanism of savings mobilisation and thereby performing an intermediation role in the economy. This ensures that capital is provided to deficient units who are in need of capital to finance their working capital requirements and invest in technology thereby resulting in an increase in output. In this way, it could be argued that life insurance development spurs financial development. In this article we investigate the causal relationship between the life insurance sector, financial development and economic growth in South Africa for the period 1990 to 2012. We make use of life insurance density as the proxy for life insurance development, real per capita growth domestic product as the proxy for economic growth and real broad money per capita as the proxy for financial development. We test for cointegration amongst the variables by applying the Johansen procedure and then proceed to test for Granger causality based on the vector error correction model (VECM. Our results confirm the existence of at least one cointegrating relationship amongst the variables. The results indicate that the direction of causality runs from the economy to the life insurance sector which is consistent with the “demand-following” insurance-growth hypothesis. There is also evidence of causality running from the economy to financial development which is consistent with the “demand following” finance-growth hypothesis. The results also reveal that life insurance complements economic growth in bringing about financial development further lending credence to the “complementarity” hypothesis 11. R.M. Solow Adjusted Model of Economic Growth Directory of Open Access Journals (Sweden) Ion Gh. Rosca 2007-05-01 Full Text Available Besides the models of M. Keynes, R.F. Harrod, E. Domar, D. Romer, Ramsey-Cass-Koopmans etc., the R.M. Solow model is part of the category which characterizes the economic growth. The paper proposes the study of the R.M. Solow adjusted model of economic growth, while the adjustment consisting in the model adaptation to the Romanian economic characteristics. The article is the first one from a three paper series dedicated to the macroeconomic modelling theme, using the R.M. Solow model, such as: “Measurement of the economic growth and extensions of the R.M. Solow adjusted model” and “Evolution scenarios at the Romanian economy level using the R.M. Solow adjusted model”. The analysis part of the model is based on the study of the equilibrium to the continuous case with some interpretations of the discreet one, by using the state diagram. The optimization problem at the economic level is also used; it is built up of a specified number of representative consumers and firms in order to reveal the interaction between these elements. 12. Effects of culture systems on growth and economic performance of ... African Journals Online (AJOL) The effect of culture system on growth and economics performance of Orechromis niloticus (Nile tilapia) in concrete tanks was investigated. Four outdoor concrete tanks measuring 2.5 x 2 m was used for the study for 24 weeks culture period. The culture systems included the use of algae only at the stocking rates of 4 ... 13. Educational Expansion, Economic Growth and Antisocial Behaviour: Evidence from England Science.gov (United States) Sabates, Ricardo 2010-01-01 This paper investigates the impact of the increase in post-compulsory schooling and economic growth on conviction rates for antisocial behaviour in England. I hypothesise that both educational and employment opportunities should lead to greater reductions in antisocial behaviour when they are combined than when they exist in isolation. I test this… 14. Bonding and Bridging Social Capital and Economic Growth NARCIS (Netherlands) Beugelsdijk, S.; Smulders, J.A. 2009-01-01 In this paper we develop a formal model of economic growth and two types of social capital. Following extant literature, we model social capital as participation in two types of social networks: first, closed networks of family and friends, and, second, open networks that bridge different 15. A Note on Entrepreneurship, Small Business and Economic Growth NARCIS (Netherlands) A.R. Thurik (Roy); A.R.M. Wennekers (Sander) 2001-01-01 textabstractThe aim of the present short paper is to show that since the 1970s the world has changed considerably, and that this change has had consequences for the current policy debate on the determinants of economic growth. Our paper deals with some aspects of the recent scientific literature on 16. Debt servicing and economic growth in Nigeria: an empirical ... African Journals Online (AJOL) In this study we reviewed and analyse the effect of external debt service payment practices on sustainable economic growth and development with particular emphasis on Nigeria. To achieve the objective of this research, we use debt payment to Multilateral Financial creditors, Paris club creditors, London club creditors, ... 17. Financial liberalization and economic growth : A meta-analysis NARCIS (Netherlands) Bumann, Silke; Hermes, Niels; Lensink, Robert This study provides a systematic analysis of the empirical literature on the relationship between financial liberalization and economic growth by conducting a meta-analysis, based on 441 t-statistics reported in 60 empirical studies. We focus on explaining the heterogeneity of results in our sample 18. Education in Thailand: When Economic Growth Is No Longer Enough Science.gov (United States) Michel, Sandrine 2015-01-01 After fifty years of almost continuous economic growth in Thailand, it is now possible to reevaluate the developmental process of the education system. Until now, the structural indicators of education development that have been mainly used are the level and pace of the increases in public expenditure on education, the effect of increasing… 19. The Easterlin Illusion: Economic growth does go with greater happiness NARCIS (Netherlands) R. Veenhoven (Ruut); F. Vergunst (Floris) 2014-01-01 markdownabstract__Abstract__ The 'Easterlin Paradox' holds that economic growth in nations does not buy greater happiness for the average citizen. This thesis was advanced in the 1970s on the basis of the then available data on happiness in nations. Later data have disproved most of the empirical 20. The causality between energy consumption and economic growth in Turkey International Nuclear Information System (INIS) Erdal, Guelistan; Erdal, Hilmi; Esenguen, Kemal 2008-01-01 This paper applies the causality test to examine the causal relationship between primary energy consumption (EC) and real Gross National Product (GNP) for Turkey during 1970-2006. We employ unit root tests, the augmented Dickey-Fuller (ADF) and the Philips-Perron (PP), Johansen cointegration test, and Pair-wise Granger causality test to examine relation between EC and GNP. Our empirical results indicate that the two series are found to be non-stationary. However, first differences of these series lead to stationarity. Further, the results indicate that EC and GNP are cointegrated and there is bidirectional causality running from EC to GNP and vice versa. This means that an increase in EC directly affects economic growth and that economic growth also stimulates further EC. This bidirectional causality relationship between EC and GNP determined for Turkey at 1970-2006 period is in accordance with the ones in literature reported for similar countries. Consequently, we conclude that energy is a limiting factor to economic growth in Turkey and, hence, shocks to energy supply will have a negative impact on economic growth 1. Modeling and forecasting mortality with economic growth : a multipopulation approach NARCIS (Netherlands) Boonen, T.J.; Li, H. 2017-01-01 Research on mortality modeling of multiple populations focuses mainly on extrapolating past mortality trends and summarizing these trends by one or more common latent factors. This article proposes a multipopulation stochastic mortality model that uses the explanatory power of economic growth. In 2. A mean-field game economic growth model KAUST Repository Gomes, Diogo A.; Lafleche, Laurent; Nurbekyan, Levon 2016-01-01 Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks 3. The balance of payment-constrained economic growth in Ethiopia ... African Journals Online (AJOL) The objective of this paper is to empirically test the validity of the simplified version of the balance of payment-constrained economic growth model for Ethiopia during the period 1971-20082. According to the model, economies only grow at a pace allowed by the constraints imposed by the requirement of balance of payment ... 4. An analysis of tourism contribution to economic growth in SADC ... African Journals Online (AJOL) The study how the tourism sector can be an engine of economic growth in SADC member countries. The paper found the contribution of tourism to GDP, employment, export receipts and investment is significant. Although this sector's contribution to the economy varies among SADC countries, the the study found that ... 5. THE CONDITIONS OF TRANSITION TO INNOVATIVE TYPE OF ECONOMIC GROWTH OpenAIRE D. E. Sorokin 2010-01-01 Article is devoted theoretical-methodological problems of transition of the Russian economy to innovative type of economic growth. Realization of the problems set forth above are possible only in case of a support of the Russian economy on the fifth technological way and its abilities to pass to the sixth technological way. 6. To what extent does banks' credit stimulate economic growth ... African Journals Online (AJOL) This study examines the extent to which banks' credit affects economic growth in Nigeria. The data used was collected from the Central Bank of Nigeria statistical bulletin for a period of 24 years from 1990 to 2013. We used credit to the private sector, credit to the public sector and inflation to proxy commercial bank credit ... 7. Models of Economic Growth and Development in the Context of ... African Journals Online (AJOL) The better-known models of economic growth such as the Lewis, Rostow,. Harrod-Domar ... produce highly educated populaces usually reap the benefits of such in terms of high per capita ..... The Russian revolution of 1917 led by Lenin proposed in theory a .... This was about government intervention into the economy to ... 8. Inequality, Credit Market Imperfection, Segmentation and Economic Growth NARCIS (Netherlands) Zhu, D. 2001-01-01 This paper investigates how initial inequality can causally affect economic growth when moral hazard problems exist in credit markets.Two regimes of the credit markets aiming at overcoming the moral hazard problems are analyzed.The formal one such as bank relies on intermediary between borrowers and 9. Do 'green' taxes work? Decoupling environmental pressures and economic growth DEFF Research Database (Denmark) Andersen, Mikael Skou 2005-01-01 This essay intends to shed light on whether environmental taxation can help to decouple environmental pressures from economic growth, a policy outcome widely desired and particularly pressing in the context of climate change where radical measures are needed to curb CO2 build up.... 10. Health and Economic Growth in South East, Nigeria African Journals Online (AJOL) info to be making any significant impact in economic growth. ... The south eastern geographical space of Nigeria is the country home of the. Igbo. .... However, if, for example, many workers in one sector are not regular to work .... private health care providers, is not only associated with welfare .... individuals and families apart. 11. The Role of Stock Market Development on Economic Growth in ... African Journals Online (AJOL) The method of analysis used is Ordinary Least Square (OLS) techniques. The study measures the relationship between stock market development indices and economic growth. The stock market capitalization ratio was used as a proxy for market size while value traded ratio and turnover ratio were used as proxy for market ... 12. Government expenditure, efficiency and economic growth: a panel ... African Journals Online (AJOL) Finally Generalized Methods of Moments (GMM) is applied to answer the two research questions. The results demonstrate that increasing government expenditure accelerates economic growth of low income countries in Sub Saharan Africa. However, when government expenditure is interacted with government efficiency ... 13. Regional technical innovation suitability and economic growth in China NARCIS (Netherlands) Zhou, Qing; Zhu, Dan; Brouwers-Ren, Liqin 2012-01-01 This paper aims to use quantitative method to analyse the suitability of regional technical innovation and further compare its influence to regional economic growth in China. Based on literature review, the authors develop an evaluation index system containing four aspects (namely, innovators, 14. Foreign direct investment and economic growth in developing ... African Journals Online (AJOL) It has been widely claimed that foreign direct investment (FDI) stimulates economic growth. In this study, an attempt is made to verify this for ten selected Sub-Saharan African (SSA) countries using data spanning from 2008 to 2013 obtained from world development indicators. Preliminary analysis conducted indicates that ... 15. Transportation and economic growth in Nigeria | Nwakeze | Journal ... African Journals Online (AJOL) This paper attempts to provide empirical evidence on the contribution of transport investment, congestion and traffic related accidents to economic growth in Nigeria. In this paper, transport investment is proxied by physical stock of road infrastructure while congestion is proxied by automobile density. Using the extended ... 16. Natural disasters and economic growth: A meta-analysis NARCIS (Netherlands) Klomp, J.G.; Valckx, K. 2014-01-01 Using more than 750 estimates, we perform a meta-regression analysis of studies examining the relationship between economic growth per capita and natural disasters. The studies considered are very different with respect to the type of disasters considered, the sample of countries and time periods 17. Disasters and development: natural disasters, credit constraints, and economic growth NARCIS (Netherlands) McDermott, T.K.J.; Barry, F.; Tol, R.S.J. 2014-01-01 Using a simple two-period model of the economy, we demonstrate the potential effects of natural disasters on economic growth over the medium to long term. In particular, we focus on the effect of such shocks on investment. We examine two polar cases: an economy in which agents have unconstrained 18. The electricity consumption and economic growth nexus: Evidence from Greece International Nuclear Information System (INIS) Polemis, Michael L.; Dagoumas, Athanasios S. 2013-01-01 This paper attempts to cast light into the relationship between electricity consumption and economic growth in Greece in a multivariate framework. For this purpose we used cointegration techniques and the vector error correction model in order to capture short-run and long-run dynamics over the sample period 1970–2011. The empirical results reveal that in the long-run electricity demand appears to be price inelastic and income elastic, while in the short-run the relevant elasticities are below unity. We also argue that the causal relationship between electricity consumption and economic growth in Greece is bi-directional. Our results strengthen the notion that Greece is an energy dependent country and well directed energy conservation policies could even boost economic growth. Furthermore, the implementation of renewable energy sources should provide significant benefits ensuring sufficient security of supply in the Greek energy system. This evidence can provide a new basis for discussion on the appropriate design and implementation of environmental and energy policies for Greece and other medium sized economies with similar characteristics. -- Highlights: •We examine the causality between electricity consumption and economic growth. •We used cointegration techniques to capture short-run and long-run dynamics. •The relationship between electricity consumption and GDP is bi-directional. •Residential energy switching in Greece is still limited. •The implementation of renewable energy sources should ensure security of supply 19. The current Russian model of social development, and economic growth Directory of Open Access Journals (Sweden) V V Paramonov 2016-12-01 Full Text Available Although the Article 7 of the Constitution of Russia adopted in 1993 defines the country as a social state, the contemporary social and economic situation is significantly different from this declaration. The author considers the current situation focusing on the foundations of the welfare state. The indicators of social inequality and stratification that allow to identify the country as a social state prove the widening gap between the rich and poor. In recent years, nothing has been done to achieve the more equitable distribution of income and national wealth, which led to the further growth of social inequality exceeding the global indices. The author believes that the high level of social inequality negatively affects the economic growth. Based on the studies of Russian scientists he concludes that equal distribution of income provides higher rates of economic growth and prosperity of the country. The modified theory of the factors of production explains this interconnection, and adds a few more factors, including such a specific resource as sales market, to three factors introduced by J.B. Say at the beginning of the XIX century. The huge social inequality and, consequently, a significant number of the poor deprive the country of such an important resource. To change the situation, the author proposes to return to the progressive tax scale and introduce the zero rate of income tax for the poorest groups in order to create prerequisites for the growth of consumer demand under the economic crisis. 20. Debt servicing and economic growth in Nigeria: An empirical ... African Journals Online (AJOL) In this study we reviewed and analyse the effect of external debt service payment practices on sustainable economic growth and development with particular emphasis on Nigeria. To achieve the objective of this research, we use debt payment to Multilateral Financial creditors, Paris club creditors, London club creditors ... 1. Foreign direct investment, financial development and economic growth NARCIS (Netherlands) Hermes, C.L.M.; Lensink, B.W. 2003-01-01 This article argues that the development of the financial system of the recipient country is an important precondition for FDI to have a positive impact on economic growth. A more developed financial system positively contributes to the process of technological diffusion associated with FDI. The 2. Decentralization and Economic Growth per capita in Europe NARCIS (Netherlands) Crucq, Pieter; Hemminga, Hendrik-Jan 2007-01-01 In this paper the relationship between decentralization and economic growth is investigated. The focus is on decentralization from the national government to the highest substate level in a country, which we define as regional decentralization. Section 2 discusses the different dimensions of 3. Harnessing the Gender Dividend to Boost Economic Growth in ... International Development Research Centre (IDRC) Digital Library (Canada) Taking advantage of the gender dividend to accelerate economic growth in ECOWAS. This project aims to analyze the gender dividend in West Africa. The gender dividend is the increase in national production per head attributable to more equality between women and men in the labour market. Declining birth rates can ... 4. Transport infrastructure and economic growth in Nigeria | Ighodaro ... African Journals Online (AJOL) The paper considered transport infrastructure and economic growth in Nigeria. Findings from the study show that in the three national development plans in Nigeria, road transportation system has been given more priority followed by water and air. It was found that the local government authority controls about 67% of the ... 5. Contribution of timber exports to economic growth in Nigeria: an ... African Journals Online (AJOL) The paper examined the contribution of timber exports to the economic growth in Nigeria, using an econometric approach. Augmented Dickey-Fuller (ADF) and Johansen Co-integration techniques were respectively used to test for unit root and examine the relationship between the variables used. In addition, Granger ... 6. road sector development and economic growth in ethiopia1 African Journals Online (AJOL) Eyerusalem Regarding community roads, both the management and accountancy .... previous years and its impact on overall and sectoral economic growth. Descriptive analysis is deployed to capture the link between the road transport sector and performance indicators, like rural accessibility, road density, road network, road financing ... 7. Foreign direct investment and economic growth in Nigeria: a ... African Journals Online (AJOL) The paper examines the causal relationship between foreign direct investment ( FDI) and economic growth, measured by the gross domestic product (GDP). Augumented Dickey-Fuller (ADF) test was used for the unit root test, Johansen Cointegration test was conducted to establish short and long run relationship between ... 8. Effects of culture systems on growth and economic performance of ... African Journals Online (AJOL) IFEOMA PIUS 2013-07-03 Jul 3, 2013 ... The effect of culture system on growth and economics performance of Orechromis niloticus ( ... from the Food and Agriculture Organization (FAO) stated ... in the reduction of the availability of natural fish food ..... lowest profit, while algae only had the lowest cost and ... Also, maximizing production in terms of. 9. Agricultural Trade and Economic Growth in East African Community ... African Journals Online (AJOL) East African Community states, as many other states in the region, depend largely on agricultural activities to boost their economic growth and create employment. Up to 80 per cent of the populace depends on agriculture directly and indirectly for food, employment and income, while about 40 million people in EAC suffer ... 10. Growth and Economic Opportunities for Women | Page 3 | IDRC ... International Development Research Centre (IDRC) Digital Library (Canada) Growth and Economic Opportunities for Women. Language English. a woman in her shop, Ghana. Photo credit: World Bank. Read more about Building the evidence to grow female entrepreneurship. Language English. Read more about Together We Can: Assessing the Impact of Women's Action Groups on Social Change ... 11. Growth Performance, Yields and Economic Benefits of Nile Tilapia ... African Journals Online (AJOL) fish culture integration in the growth, yields and economic benefits of fish and vegetables. Two 200 m2 earthen fishponds were stocked with Nile tilapia Oreochromis niloticus at 20,000 fish fingerlings per hectare. Pond A was fertilized with ... 12. Road Sector Development and Economic Growth in Ethiopia ... African Journals Online (AJOL) The study attempts to see the trends, stock of achievements, and impact of road network on economic growth in Ethiopia. To do so, descriptive and econometric analyses are utilized. From the descriptive analysis, the findings indicate that the stock of road network is by now growing at an encouraging pace. 13. QUALITY OF NATIONAL ECONOMIC GROWTH: FACTORS AND DETERMINANTS Directory of Open Access Journals (Sweden) Nikolaj I. Komkov 2015-01-01 Full Text Available The subject / topic: TThe theme of this article is very relevant in the light of changes in the global geo-economic structure and changing the role and place ofRussiain world economic and geopolitical relations. The article deals with the basic aspects of national economic growth, which slowed down in the last three years. The main reason for slowing national economic growth is associated with the depletion of the reserves of the traditional export-oriented development of the Russian economy, as well as problems with sluggish innovative transformation. In this paper, based on a systematic analysis of economic processes and the interpretation of analytical data, addresses the general theoretical and methodological aspects of the quality of economic development, as well as practical guidelines and recommendations related to sustainable national socio-economic development in the context of external constraints.The purpose / objectives: The aim of the article is to analyze the theoretical and methodological aspects of the quality of economic development of the Russian economy, which happened in the face of economic sanctions. Objectives of the article: justify practical directions and recommendations related to sustainable national socio-economic development in the context of external constraints, determine the prospects for the economy of theRussian Federationin the conditions of the introduction of sectoral sanctions by Western countries. Methodology:Methodological basis of this article are the comparative and economic-statistical methods of analysis.The Results: The study revealed that the harsh environment (sanctions, depreciation of the ruble, and others. Require surgical intervention and adjustments not only the current socio-economic plans, but also to take urgent measures to ensure the development prospects. The most important decision is the degree of support advanced scientific and technical programs and the creation of new domestic 14. U.S. Government Supports Low Emission Economic Growth Energy Technology Data Exchange (ETDEWEB) 2015-11-01 Countries around the world face the challenge of maintaining long-term sustainable economic growth and development under the threat of climate change. By identifying and pursuing a sustainable development pathway now, they are better positioned to reach their economic growth goals while addressing climate change impacts and lowering greenhouse gas (GHG) emissions. Low emission development strategies - development plans that promote sustainable social and economic development while reducing long-term GHG emissions - provide a pathway to preparing for a global low emission future. Partner country governments are working with the U.S. government through the Enhancing Capacity for Low Emission Development Strategies (EC-LEDS) program to further their national development objectives. 15. A note on inflation targeting and economic growth in Brazil Directory of Open Access Journals (Sweden) Gilberto Libânio 2010-03-01 Full Text Available This paper analyzes the relation between monetary policy and economic performance in Brazil during the period 1999-2006. In particular, it discusses the growth effects of the inflation targeting regime through its effects on aggregate demand. It is argued that monetary policy under IT reacts in a procyclical and asymmetric way to fluctuations in economic activity (too "tight" during recessions, not so "loose" during expansions. Such pattern may generate a downward bias in aggregate demand, with negative real effects on output growth and employment. Our results suggest that monetary policy has been procyclical and asymmetrical in Brazil under inflation targeting. The main economic policy implication of this study is that central banks should consider more seriously the real effects of monetary policy on output and employment. 16. ECONOMIC GROWTH AND ENVIRONMENTAL QUALITY INTURKEY: ARE THEY OPPOSITE CONCEPTS? Directory of Open Access Journals (Sweden) E.Yasemin Bozdağlıoğlu 2013-01-01 Full Text Available The growing interest in global environmental issues whose importance hasbeen steadily increasing and the demand for environmental quality and theirmutual relation with economic growthare closely related. Economic growth,while increasing the level ofnational income over time, brings with it concernsabout environmental quality.The purpose of this study is to examine therelationship between Turkey's economicgrowth (Gross Domestic Income-GDPand environmental quality. In this study,the Environmental Kuznet Hypothesis,which assumes a correlation between various indicators of environmentaldegradation and per capita income in examining the relationship, will be used.The Granger Causality Test and Cointegration Test methods will be used indetermining the relationship between thecourse of environmental degradation inthe first phase of economic growth and thedegree of environmental effect in theperiod between 1960 and 2011 (with annual data in Turkey. 17. ECONOMIC GROWTH, TRADE AND ENVIRONMENTAL ISSUES: TESTING ENVIRONMENTAL KUZNETS CURVE Directory of Open Access Journals (Sweden) Dedi Budiman Hakim 2013-04-01 Full Text Available ASEAN experiences a dynamic economic growth due to its liberalised markets. However concerns arise related to environmental issues resulting from the economic activities. It reflects tradeoffs between economic growth driven by trade and foreign direct investment (FDI, and environment. To investigate such a relation the Environmental Kuznets Curve was applied by regressing amount of carbon emission with gross domestic product (GDP, quadratic GDP, trade openness and FDI. The result reveals that amount of carbon emission is linearly and positively correlated with GDP per capita. It is predicted that as ASEAN economies grow, carbon emission increases. Trade openness is also found to contribute to carbon emission. Keywords: Kuznets curve, carbon emission, gross domestic product, trade, foreign direct investment JEL classification number: F15, F18 18. STIMULATION OF ECONOMIC GROWTH IN ROMANIA BETWEEN REALITY AND DESIDERATE Directory of Open Access Journals (Sweden) DOBROTĂ GABRIELA 2013-12-01 Full Text Available Fragility of economical environment subject to a dynamic process of globalization in recent decades has been demonstrated abundantly, year 2007 representing an important point in terms of triggering the accentuated macroeconomic imbalances. The propagation of the financial crisis in the economic environment is clearly reflected by the contraction of the global economy after a long period of growth, the emphasizing of budget deficits, reducing wages, increase of unemployment. Romania was significantly affected by the global economic crisis, amid a long line of inadequate policies. The orientation excessive economic development through consumption and the unfavorable ratio between income and productivity are issues that have contributed significantly to the decline of the Romanian economy. Inadequate measures taken have worsened the effects of crisis: reducing foreign investment, increasing of trade deficit, reduction of living standards, decreasing the number of SMEs, worsening the institutional weaknesses etc. In this paper, are addressed aspects which highlights the effects of economic policy measures promoted in Romania after the transition to market economy, on stages, specifying measures necessary to ensure the functionality of coordination mechanisms, in order to register determinant impulses of economic growth. 19. Interaction between Financial Intermediation Efficiency and Economic Growth Directory of Open Access Journals (Sweden) Milka Grbic 2016-12-01 Full Text Available Financial intermediaries have the key role in making a connection between savings and investments. Given the fact that an efficient transfer of savings into investments is made more difficult by transaction and information costs, financial intermediaries are specialized in minimizing the said costs per unit of invested capital. They are also trained to identify productive and innovative investment endeavors which contribute to the growth of real output. Real output growth is the basis for increasing the financial potential, which creates the basis for the development of financial intermediaries. In connection with that, apart from the analysis of the relevant factors making the process of the mobilization and transfer of savings more difficult, the theoretical models that put an emphasis on the relationship between the efficiency of financial intermediation and economic growth are discussed in the paper. The research results are indicative of the fact that the improvement in financial intermediaries’ business doing enables faster economic growth. Simultaneously, the growth of the economic activity increases the scope of the business operations conducted by financial intermediaries. Thanks to the effects of the economies of scale that contribute to a reduction in transaction and information costs, the efficiency of financial intermediations grows. 20. Natural resources endowment and economic growth: The West African Experience Directory of Open Access Journals (Sweden) Mohamed Jalloh 2013-06-01 Full Text Available This study aims at investigating the nexus between natural resource endowment and economic growth using a sample of West African countries. The study adopted a Barrow-type growth model to analyse the impact of natural resource wealth on economic growth. A dynamic panel estimation technique was employed using relevant data from West African Countries. The results from the panel regressions indicate that natural resource endowments have very minimal impact in terms of promoting economic growth in West Africa, more so in resource rich countries. In terms of relative effects, the results indicate that a 10% increase in natural resource export reduces growth in income per capita by approximately 0.4%. Part of the factors explaining this finding amongst others; include high corruption in the public sector as well as the frequency of civil conflicts in resource rich economies of West Africa. For the natural resources of the region to fully benefit its citizens, these countries require , urgently, to improve management of natural resource export revenues and to apply effective policy measures to eradicate/ mitigate incidences of rampant corruption in the public sector. 1. The role of intangible assets in the regional economic growth Directory of Open Access Journals (Sweden) Jordi Suriñach 2011-01-01 Full Text Available This paper is the summary of the IAREG (Intangible Assets and RegionalEconomic Growth European project, which analyzed the role of intangibleassets (IA on regional economic growth. We focused on some of the most relevantintangible assets, for which statistical information is available and where the consortiumhad more expertise. Consequently, in this paper we put special attentionin four big factors: knowledge capital, human capital, social capital and entrepreneurshipcapital. Additional to the main characteristics of each of these IA (relatedwith their measurement and their effects on regional economic growth, we alsoanalyzed the ensemble effects of these IA over the location of firms. For each asset,we describe its main characteristics, the indicators for its measuring and its limitations,as well as the main results associated to its impact on regional growth. Wemust outline that in order to improve the analysis of the effects of the IA in regionaleconomic growth it is necessary to develop more and better databases. We presentsome thoughts in this respect, based on our research experience. Finally, we givesome policy implications and recommendations. 2. Energy consumption and economic growth revisited in African countries Energy Technology Data Exchange (ETDEWEB) Eggoh, Jude C., E-mail: [email protected] [Laboratoire d' Economie d' Orleans (LEO), Universite d' Orleans, Rue de Blois, BP: 6739, 45067 Orleans Cedex 2 (France); Bangake, Chrysost [Laboratoire d' Economie d' Orleans (LEO), Universite d' Orleans, Rue de Blois, BP: 6739, 45067 Orleans Cedex 2 (France); Universite d' Artois and Laboratoire EQUIPPE, Lille 1, FSES, 59655 Villeneuve d' Ascq Cedex (France); Rault, Christophe [Laboratoire d' Economie d' Orleans (LEO), Universite d' Orleans, Rue de Blois, BP: 6739, 45067 Orleans Cedex 2 (France); Toulouse Business School (France) 2011-11-15 The aim of this paper is to provide new empirical evidence on the relationship between energy consumption and economic growth for 21 African countries over the period from 1970 to 2006, using recently developed panel cointegration and causality tests. The countries are divided into two groups: net energy importers and net energy exporters. It is found that there exists a long-run equilibrium relationship between energy consumption, real GDP, prices, labor and capital for each group of countries as well as for the whole set of countries. This result is robust to possible cross-country dependence and still holds when allowing for multiple endogenous structural breaks, which can differ among countries. Furthermore, we find that decreasing energy consumption decreases growth and vice versa, and that increasing energy consumption increases growth, and vice versa, and that this applies for both energy exporters and importers. Finally, there is a marked difference in the cointegration relationship when country groups are considered. - Highlights: > We assess the energy consumption and economic growth nexus in 21 African countries. > There exists a long-run relationship between energy consumption and economic growth. > This result is robust to cross-country dependence and for structural breaks. > Our findings finally support the feedback hypothesis of bidirectional causality. 3. A reconsideration of effect of energy scarcity on economic growth International Nuclear Information System (INIS) Uri, N.D. 1995-01-01 This analysis is concerned with the effect of energy scarcity on economic growth in the U.S. After defining the notion of scarcity and introducing measures of scarcity (unit costs and relative energy price), changes in the trend in resource scarcity for NG, bituminous coal, anthracite coal, and crude oil over the most recent three decades are investigated. Each of the energy resources became a significantly scarcer resource during the decade of the 1970s in the Malthusian Stock Scarcity and Malthusian Flow Scarcity sense. Unit costs exhibit a similar change for NG and crude oil but not for bituminous and anthracite coals. The situation reversed itself during the 1980s. NG, bituminous and anthracite coals, and crude oil all became significantly less scarce resources during the decade of the 1980s than they had been during the 1970s, i.e. the increase in scarcity as measured by relative energy prices observed during the decade of the 1970s was not reversed completely during the 1980s for NG and crude oil demonstrate similar patterns. Given that change has taken place, it has implications for future economic growth to the extent resource scarcity and economic growth are interrelated. To see whether this is a relevant concern, subsequent to the examination of changing resource scarcity trends, an objective effort is made to identify a long run equilibrium relationship between energy scarcity and economic growth. Relying on cointegration techniques, only for crude oil is there a suggestion that resource scarcity has affected economic growth in the U.S. over the period 1889-1992. (author) 4. Economic Growth and Budget Constraints: EU Countries Panel Data Analysis Directory of Open Access Journals (Sweden) Zimčík Petr 2016-06-01 Full Text Available The aim of this paper is to identify the impacts of different taxes and expenditures on economic growth. The research is focused on 20 selected European Union Member States. These countries are equally divided into four groups based on their average tax burden as presented in the World Tax Index. A comparison of fiscal attributes among these groups is important for the analysis. Annual government finance data from the years 1995 to 2012 are used for an empirical study. The indicators observed are real GDP change, the composition and volume of total government expenditures, tax quotas of individual taxes and total budget balance. These indicators are used within an endogenous growth model together with capital stock and an approximation of human capital. A panel regression with fixed effects is used as an analytic tool. The main results are that an increase in social contributions, property, production and personal income tax quotas has an adverse effect on economic growth. 5. Energy expenditure, economic growth, and the minimum EROI of society International Nuclear Information System (INIS) Fizaine, Florian; Court, Victor 2016-01-01 We estimate energy expenditure for the US and world economies from 1850 to 2012. Periods of high energy expenditure relative to GDP (from 1850 to 1945), or spikes (1973–74 and 1978–79) are associated with low economic growth rates, and periods of low or falling energy expenditure are associated with high and rising economic growth rates (e.g. 1945–1973). Over the period 1960–2010 for which we have continuous year-to-year data for control variables (capital formation, population, and unemployment rate) we estimate that, statistically, in order to enjoy positive growth, the US economy cannot afford to spend more than 11% of its GDP on energy. Given the current energy intensity of the US economy, this translates in a minimum societal EROI of approximately 11:1 (or a maximum tolerable average price of energy of twice the current level). Granger tests consistently reveal a one way causality running from the level of energy expenditure (as a fraction of GDP) to economic growth in the US between 1960 and 2010. A coherent economic policy should be founded on improving net energy efficiency. This would yield a “double dividend”: increased societal EROI (through decreased energy intensity of capital investment), and decreased sensitivity to energy price volatility. - Highlights: •We estimate energy expenditures as a fraction of GDP for the US, the world (1850–2012), and the UK (1300–2008). •Statistically speaking, the US economy cannot afford to allocate more than 11% of its GDP to energy expenditures in order to have a positive growth rate. •This corresponds to a maximum tolerable average price of energy of twice the current level. •In the same way, US growth is only possible if its primary energy system has at least a minimum EROI of approximately 11:1. 6. Influence of the Budgetary Decentralization on the Economic Growth of Regions of Ukraine: Statistical Estimation Directory of Open Access Journals (Sweden) Voznyak Halyna V. 2017-06-01 Full Text Available The aim of the article is to define, determine and analyze the interrelationships between the budgetary decentralization and the economic growth of regions of Ukraine under conditions of reforming the power and financial resources. A statistical estimation of the influence of the budgetary decentralization on the economic growth of regions of Ukraine for 2015-2016 is carried out. The application of the panel data modeling allowed to build econometric models that made it possible to determine the ambiguous nature of the budgetary decentralization and identify key factors of its influence. It is shown that in terms of the income and expenditures the budgetary decentralization is positively associated with the economic growth of regions of Ukraine during the chosen time range of the study. The dynamic growth of the own revenues of local budgets is not a catalyst for the economic development of the regions. A strong negative effect of transfers on the dependent variable is confirmed. Among the variables included in the model and additionally characterizing the budgetary decentralization, the single tax and subsidies for the socio-economic development of individual territories attract attention. As a result of the study, the author justifies the need to minimize the transfer dependence of the regions at a simultaneous increasing of their own revenue base with local taxes and fees serving as a reliable basis for a long-term planning and development. 7. Oil Price Volatility and Economic Growth in Nigeria: a Vector Auto-Regression (VAR Approach Directory of Open Access Journals (Sweden) Edesiri Godsday Okoro 2014-02-01 Full Text Available The study examined oil price volatility and economic growth in Nigeria linking oil price volatility, crude oil prices, oil revenue and Gross Domestic Product. Using quarterly data sourced from the Central Bank of Nigeria (CBN Statistical Bulletin and World Bank Indicators (various issues spanning 1980-2010, a non‐linear model of oil price volatility and economic growth was estimated using the VAR technique. The study revealed that oil price volatility has significantly influenced the level of economic growth in Nigeria although; the result additionally indicated a negative relationship between the oil price volatility and the level of economic growth. Furthermore, the result also showed that the Nigerian economy survived on crude oil, to such extent that the country‘s budget is tied to particular price of crude oil. This is not a good sign for a developing economy, more so that the country relies almost entirely on revenue of the oil sector as a source of foreign exchange earnings. This therefore portends some dangers for the economic survival of Nigeria. It was recommended amongst others that there should be a strong need for policy makers to focus on policy that will strengthen/stabilize the economy with specific focus on alternative sources of government revenue. Finally, there should be reduction in monetization of crude oil receipts (fiscal discipline, aggressive saving of proceeds from oil booms in future in order to withstand vicissitudes of oil price volatility in future. 8. THE SUCCESS OF EMERGING CAPITAL MARKETS IN DETERMINING ECONOMIC GROWTH Directory of Open Access Journals (Sweden) Ion POHOAŢĂ 2014-06-01 Full Text Available Capital markets are regarded as “the barometer” of economic activity at the national level, but among emerging markets, the position of this segment in the economy is far from ideal. The answers that we try to offer are concerning the contribution of capital markets to the economic welfare of nations in transition from Central and Eastern Europe, using Granger causality tests. Our findings highlight that in this geographical area, the relation between capital markets and economic growth is a bidirectional one. However, although both the establishment of stock exchanges and their liberalization represented governments’ strategy of economic development, their objective was not fully achieved. Institutional transformations are required in order to attract foreign investors. 9. Historic, economic and geographic approach to the relations between economic growth and oil prices International Nuclear Information System (INIS) Girard, C. 1992-01-01 This paper attempts to analyze the complex relations between energy prices and economic growth. In part 1, the history of the last 30 years is used to analyze the consequences of energy price variations on world economic growth. In part 2, two interpretation schemes are described successively. One has to do with the international oil market, and the other concerns the impact of oil shocks on national economies. In part 3, an approach by type of country leads to conclusions respectively for the industrialized countries, for the developing countries and for the newly industrialized countries. 1 fig 10. Strain Selection, Biomass to Biofuel Conversion, and Resource Colocation have Strong Impacts on the Economic Performance of Algae Cultivation Sites Energy Technology Data Exchange (ETDEWEB) Venteris, Erik R., E-mail: [email protected]; Wigmosta, Mark S.; Coleman, Andre M.; Skaggs, Richard L. [Pacific Northwest National Laboratory, Richland, WA (United States) 2014-09-16 Decisions involving strain selection, biomass to biofuel technology, and the location of cultivation facilities can strongly influence the economic viability of an algae-based biofuel enterprise. We summarize our past results in a new analysis to explore the relative economic impact of these design choices. Our growth model is used to predict average biomass production for two saline strains (Nannochloropsis salina and Arthrospira sp.), one fresh to brackish strain (Chlorella sp., DOE strain 1412), and one freshwater strain (order Sphaeropleales). Biomass to biofuel conversion is compared between lipid extraction and hydrothermal liquefaction (HTL) technologies. National-scale models of water, CO{sub 2} (as flue gas), land acquisition, site leveling, construction of connecting roads, and transport of HTL oil to existing refineries are used in conjunction with estimates of fuel value (from HTL) to prioritize and select from 88,692 unit farms (UF, 405 ha in pond area), a number sufficient to produce 136E + 9 L year{sup −1} of renewable diesel [36 billion gallons year{sup −1} (BGY)]. Strain selection and choice of conversion technology have large economic impacts, with differences between combinations of strains and biomass to biofuel technologies being up to$10 million year{sup −1} UF{sup −1}. Results based on the most productive strain, HTL-based fuel conversion, and resource costs show that the economic potential between geographic locations within the selection can differ by up to 4 million year{sup −1} UF{sup −1}, with 1.8 BGY of production possible from the most cost-effective sites. The local spatial variability in site rank is extreme, with very high and low sites within 10 kms of each other. Colocation with flue gas sources has a strong influence on rank, but the most costly resource component varies from site to site. The highest rank UFs are located predominantly in Florida and Texas, but most states south of 37°N latitude contain promising
11. THE INFLUENCE OF COMMUNITY FINANCIAL INSTRUMENTS ON THE ECONOMIC GROWTH
Directory of Open Access Journals (Sweden)
ANCA SIMINA POPESCU
2015-12-01
Full Text Available The absorption of structural and cohesion funds for the period 2007-2013 was relatively low, several reasons were identified by the European Union and the European Commission and had several gaps in legislative terms and in terms of management. Financial and economic crisis that started in 2008, dramatically altered the socio-economic context for cohesion policy programs. The economic downturn also triggered a sharp deterioration in the business climate and consumer confidence, investment (gross fixed capital formation decreased from 21% of GDP in 2008 to 18% in 2012, exports of goods and services and investment direct foreign having the same negative trend. Absorption capacity non-reimbursable financial resources is a variable with a direct and very strong link in ensuring economic and social cohesition with resources available from European funds.
12. Modeling economic growth fuelled by science and technology
Directory of Open Access Journals (Sweden)
Leonardo Costa Ribeiro
2010-06-01
Full Text Available This paper suggests a simulation model to investigate how science and technology fuel economic growth. This model is built upon a synthesis of technological capabilities represented by national innovation systems. This paper gathers data of papers and patents for 183 countries between 1999 and 2003, as well as GDP and population for 2003. These data show a strong correlation between science, technology and income. Three simulation exercises are performed. Feeding our algorithm with data for population, patents and scientific papers, we obtain the world income distribution. These results support our conjecture on the role of science and technology as sources of the wealth of nations.Este artigo propõe um modelo de simulação para investigar a contribuição da ciência e da tecnologia para o crescimento econômico. O ponto de partida são os sistemas nacionais de inovação, um conceito que sintetiza a capacitação tecnológica das nações. Desta forma, o modelo pode preservar simplicidade e parcimônia. Os dados coletados (patentes, artigos e PIB e população, para 183 países indicam uma forte correlação entre ciência, tecnologia e renda. Três exercícios com simulações são realizados para diversos momentos do tempo, mostrando a progressiva aderência do modelo a essas variáveis tecnológicas.
13. Burkina Faso - Promoting Growth, Competitiveness and Diversification : Country Economic Memorandum, Volume 3. Enhancing Growth Factors
OpenAIRE
World Bank
2010-01-01
The main conclusion of Country Economic Memorandum is that the previous model of extensive growth has now exhausted its potential and must be renewed. Given the existing population dynamics, low environmental tolerance due to its Sahelian climate and competition forces imposed due to its open economy, Burkina Faso is heavily investing in growth based on increased productivity to overcome i...
14. Environmental Disaster and Economic Change: Do tropical cyclones have permanent effects on economic growth and structure?
Science.gov (United States)
Jina, A.; von der Goltz, J.; Hsiang, S. M.
2011-12-01
Natural disasters have important, often devastating, effects upon economic growth and well-being. Due to this, disasters have become an active area of recent research and policy attention. However, much of this research has been narrowly focused, relying on anecdotal evidence and aggregated data to support conclusions about disaster impacts in the short-term. Employing a new global data set of tropical cyclone exposure from 1960 to 2008, we investigate in greater detail whether permanent changes in economic performance and structure can result from these extreme events in some cases. Our macro-economic analyses use the World Development Indicator dataset and have shown promising results: there are dramatic long-term economic transformations associated with tropical cyclones across a number of countries and industries. This effect is most clearly seen in Small Island Developing States (SIDS) and some countries in Latin America, where negative changes in long-term growth trends are observed in the years following a large tropical cyclone. In many economies with a high exposure to tropical cyclone damage, there are noticeable structural changes within the economy. The impacts of disasters might be expressed through various economic and social channels, through direct loss of lives and infrastructure damage; for instance, the destruction of infrastructure such as ports may damage export opportunities where replacement capital is not readily available. These structural changes may have far-reaching implications for economic growth and welfare. Larger nations subjected to the impacts of tropical cyclones are thought to be able to relocate economically important activities that are damaged by cyclones, and so long-term trend changes are not observed, even for events that cause a large immediate decrease in national productivity. By investigating in a more rigorous fashion the hypothesis that the environment triggers these permanent economic changes, our work has
15. SUSTAINABILITY OF ECONOMIC GROWTH AND INEQUALITY IN INCOMES DISTRIBUTION
Directory of Open Access Journals (Sweden)
Bogdan Ion Boldea
2012-07-01
Full Text Available The problem of inequality in incomes distribution is a present one, much discussed. Economic growth is considered an essential force to reduce the level of poverty by increasing the labor demand and finally the wages within the economy. But the extent to which poverty is reduced as a result of economic growth depends mostly on the initial inequalities in income and on how the distribution of income changes with economic growth. A lot of researches are focused on studying the evolution of inequality in incomes distribution and others have attempted to explore the relationship between income inequality and economic growth. There are also studies which try to identify the main factors which have impact on inequality in incomes distribution. The objective of this study is to put in discussion another possible factor that affects the variability on inequality of incomes distribution – economic growth variability. As background research, until now, we did not find any studies which are investigating this possible relation between inequality of incomes distribution and economic growth variability. To provide some empirical evidences for a positive impact of social output volatility on inequality of incomes’ distribution we are involving a small sample of 27 developing countries for an observation time span between 1995 and 2006. The values of the Gini coefficient reported in World Income Inequality Database are used as dependent variable. As a first step in testing our research hypothesis, we are involving a static panel data model with pooled ordinary least squares (OLS, fixed effects (FE and random effects (RE estimators. The F statistics tests the null hypothesis of same specific effects for all countries. If we accept the null hypothesis, we could use the OLS estimator. The Hausman test can decide which model is better: random effects (RE versus fixed effects (FE. The FE model was selected because it avoids the inconsistency due to
16. Driving Economic Growth: Higher Education--A Core Strategic Asset to the UK. Higher Education in Focus: Driving Economic Growth
Science.gov (United States)
Universities UK, 2011
2011-01-01
This publication highlights the critical role UK universities will continue to play in reviving and sustaining economic growth across the country. Using a range of visual data and statistics, it highlights that the UK's future success depends on developing innovation and the knowledge economy in what is an increasingly competitive global…
17. The contribution of foreign direct investment to clean energy use, carbon emissions and economic growth
International Nuclear Information System (INIS)
Lee, Jung Wan
2013-01-01
The paper investigates the contributions of foreign direct investment (FDI) net inflows to clean energy use, carbon emissions, and economic growth. The paper employs cointegration tests to examine a long-run equilibrium relationship among the variables and fixed effects models to examine the magnitude of FDI contributions to the other variables. The paper analyzes panel data of 19 nations of the G20 from 1971 to 2009. The test results indicate that FDI has played an important role in economic growth for the G20 whereas it limits its impact on an increase in CO 2 emissions in the economies. The research finds no compelling evidence of FDI link with clean energy use. Given the results, the paper discusses FDI's potential role in achieving green growth goals. - Highlights: ► FDI inflows strongly lead to economic growth in the G20. ► FDI inflows lead to an increase in energy use in the G20. ► FDI inflows are in no relation to CO 2 emissions in the G20. ► FDI inflows are in no relation to clean energy use in the G20. ► Economic growth is in negative relation to CO 2 emissions in the G20
18. Temperature and rainfall strongly drive temporal growth variation in Asian tropical forest trees.
Science.gov (United States)
Vlam, Mart; Baker, Patrick J; Bunyavejchewin, Sarayudh; Zuidema, Pieter A
2014-04-01
Climate change effects on growth rates of tropical trees may lead to alterations in carbon cycling of carbon-rich tropical forests. However, climate sensitivity of broad-leaved lowland tropical trees is poorly understood. Dendrochronology (tree-ring analysis) provides a powerful tool to study the relationship between tropical tree growth and annual climate variability. We aimed to establish climate-growth relationships for five annual-ring forming tree species, using ring-width data from 459 canopy and understory trees from a seasonal tropical forest in western Thailand. Based on 183/459 trees, chronologies with total lengths between 29 and 62 years were produced for four out of five species. Bootstrapped correlation analysis revealed that climate-growth responses were similar among these four species. Growth was significantly negatively correlated with current-year maximum and minimum temperatures, and positively correlated with dry-season precipitation levels. Negative correlations between growth and temperature may be attributed to a positive relationship between temperature and autotrophic respiration rates. The positive relationship between growth and dry-season precipitation levels likely reflects the strong water demand during leaf flush. Mixed-effect models yielded results that were consistent across species: a negative effect of current wet-season maximum temperatures on growth, but also additive positive effects of, for example, prior dry-season maximum temperatures. Our analyses showed that annual growth variability in tropical trees is determined by a combination of both temperature and precipitation variability. With rising temperature, the predominantly negative relationship between temperature and growth may imply decreasing growth rates of tropical trees as a result of global warming.
19. Pressurized Martian-Like Pure CO2 Atmosphere Supports Strong Growth of Cyanobacteria, and Causes Significant Changes in their Metabolism
Science.gov (United States)
Murukesan, Gayathri; Leino, Hannu; Mäenpää, Pirkko; Ståhle, Kurt; Raksajit, Wuttinun; Lehto, Harry J.; Allahverdiyeva-Rinne, Yagut; Lehto, Kirsi
2016-03-01
Surviving of crews during future missions to Mars will depend on reliable and adequate supplies of essential life support materials, i.e. oxygen, food, clean water, and fuel. The most economical and sustainable (and in long term, the only viable) way to provide these supplies on Martian bases is via bio-regenerative systems, by using local resources to drive oxygenic photosynthesis. Selected cyanobacteria, grown in adequately protective containment could serve as pioneer species to produce life sustaining substrates for higher organisms. The very high (95.3 %) CO2 content in Martian atmosphere would provide an abundant carbon source for photo-assimilation, but nitrogen would be a strongly limiting substrate for bio-assimilation in this environment, and would need to be supplemented by nitrogen fertilizing. The very high supply of carbon, with rate-limiting supply of nitrogen strongly affects the growth and the metabolic pathways of the photosynthetic organisms. Here we show that modified, Martian-like atmospheric composition (nearly 100 % CO2) under various low pressure conditions (starting from 50 mbar to maintain liquid water, up to 200 mbars) supports strong cellular growth. Under high CO2 / low N2 ratio the filamentous cyanobacteria produce significant amount of H2 during light due to differentiation of high amount of heterocysts.
20. The impact and determinants of the energy paradigm on economic growth in European Union.
Science.gov (United States)
Andrei, Jean Vasile; Mieila, Mihai; Panait, Mirela
2017-01-01
Contemporary economies are strongly reliant on energy and analyzing the determining factors that trigger the changes in energy paradigm and their impact upon economic growth is a topical research subject. Our contention is that energy paradigm plays a major role in achieving the sustainable development of contemporary economies. In order to prove this the panel data methodology of research was employed, namely four panel unit root tests (LLC, IPS, F-ADF and F-PP) aiming to reveal the connections and relevance among 17 variables denoting energy influence on economic development. Moreover, it was introduced a specific indicator to express energy consumption per capita. Our findings extend the classical approach of the changes in energy paradigm and their impact upon economic growth and offer a comprehensive analysis which surpasses the practices and policy decisions in the field.
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http://math.stackexchange.com/questions/31724/additive-functors-and-zero-homomorphisms
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# Additive functors and zero homomorphisms
The question:
Let $F:\mbox{Ab} \to \mbox{Ab}$ be an additive functor; if $f$ is a zero homomorphism, then so is $F(f)$; if $A$ is the zero group, then so is $F(A)$.
This boils down to showing that, for an additive functor $F(0)=0$. Obviously this is true, but my category theory is very basic, and I can't quite yet get a handle on what is allowed.
Is it simply just the case that
$$F(f+g)=F(f)+f(g) \implies F(0) = F(f+(-f))=F(f)+F(-f)=F(f)-F(f)=0?$$
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You would need to show that $F(-f) = -F(f)$. – Arturo Magidin Apr 8 '11 at 13:15
By definition an additive functor induces homomorphisms on the hom-groups, that is $$\begin{array}{c} \mbox{Hom}_{\mathbb Z}(A,B) \to \mbox{Hom}_{\mathbb Z}(FA,FB)\\ f \mapsto F(f) \end{array}$$ is an homomorphism. And well, homomorphisms preserve the neutral element.
Notice that $\mbox{Hom}_{\mathbb Z}(A,B)$ is a group with the point-wise operation inherited from $\mathbb Z$. Therefore the neutral element is the $0$ morphism
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http://math.stackexchange.com/questions/545157/example-of-field-extension-with-specific-galois-group
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# Example of field extension with specific galois group
So I want to find examples of $K/L$ field extensions with $G(K/L)=\mathbb{Z}/n$ and $A_n$.
For the first case I just take $\mathbb{F}_{p^n}$ over $\mathbb{F}_p$. I am just looking for an example for the $A_n$ case, I will prove that indeed the provided example works.
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A generic example is $K(t_1,\ldots,t_n) / K(s_1, \ldots, s_n, \sqrt{\Delta})$ where $K$ is a field with $\text{char}(K) \neq 2$; $\{t_1, \ldots, t_n\}$ is an algebraically independent set over $K$; $s_1, \ldots, s_n$ are the elementary symmetric polynomials in the indeterminates $t_1, \ldots, t_n$ (ie, such that $f = (X-t_1) \ldots (X-t_n) = X^n + \sum_{j=1}^{n-1} (-1)^j s_j X^{n-j}$); and $\displaystyle \Delta = \prod_{1 \leq i < j \leq n} (t_i - t_j)^2$. ($\Delta$ is called the discrimiminant of the polynomial $f$.)
For concrete examples where $L = \mathbb{Q}$ and $K$ is the splitting field of a polynomial $f \in \mathbb{Z}[X]$ of degree $n$, see the examples here.
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https://nrich.maths.org/12555/solution
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### Some(?) of the Parts
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
### Triangle Midpoints
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
### Fermat's Poser
Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
# Octagonal Ratio
##### Age 14 to 16 Short Challenge Level:
Dividing the octagon into rectangles and triangles
By drawing some extra lines you get this picture:
The red and green triangles are right-angled isosceles triangles with a hypotenuse equal to the side length of the octagon.
The blue and yellow triangles are also right-angled isoseles triangles, and as the central square's length is the same as the side lenght of the octagon, these triangles are congruent to the red and green triangles.
There is one rectangle and two triangles shaded in each of the four colours, so the four shaded areas are equal. Therefore the ratio of the shaded to unshaded parts of the original octagon is $1:3$.
Using the centre of the octagon
AE divides the octagon in half.
The green triangle is $\frac{1}{8}$ of the total area of the octagon.
Triangle ABE has the same base and twice the height, so twice the area, so is $\frac{1}{4}$ of the total area of the octagon.
So Trapezium BCDE is $\frac{1}{4}$ of the total area.
So the ratio is $1:3$.
Finding areas of shapes
We can label the side length as $1$ since we are looking for ratios between areas, so it doesn't matter how big the octagon is. Three helpful shapes are drawn in. Finding their areas will enable us to find the areas of the shaded and unshaded parts of the octagon.
The area of the red triangle is $\frac{1}{2}\times x\times x=\frac{1}{2}x^2.$ Applying Pythagoras' Theorem to the red triangle gives $x^2+x^2=1,$ so $x^2$ must be $\frac{1}{2},$ so $\frac{1}{2}x^2$ must be $\frac{1}{4}.$ So the area of the red triangle is $\frac{1}{4}.$
The area of the yellow rectangle is $1\times x=x.$ Since $x^2=\frac{1}{2},$ $x=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt2}.$ So the area of the yellow rectangle is $\frac{1}{\sqrt2}.$
The area of the blue square is $1$.
So the area of the shaded part of the octagon is $\frac{1}{4}+\frac{1}{\sqrt2}+\frac{1}{4}=\frac{1}{2}+\frac{1}{\sqrt2}$
And the area of the unshaded part of the octagon is $\frac{1}{\sqrt2}+1+\frac{1}{\sqrt2}+\frac{1}{4}+\frac{1}{\sqrt2}+\frac{1}{4}=1\frac{1}{2}+\frac{1}{\sqrt2},$ which is the same as $3\times\left(\frac{1}{2}+\frac{1}{\sqrt2}\right),$ which is $3$ times the shaded area.
So the ratio of the shaded area to the unshaded area is $1:3.$
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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https://hal.archives-ouvertes.fr/hal-01860113
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# Optimal Multirate Sampling in Symbolic Models for Incrementally Stable Switched Systems
Abstract : Methods for computing approximately bisimilar symbolic models for incrementally stable switched systems are often based on discretization of time and space, where the value of time and space sampling parameters must be carefully chosen in order to achieve a desired precision. These approaches can result in symbolic models that have a very large number of transitions, especially when the time sampling, and thus the space sampling parameters are small. In this paper, we present an approach to the computation of symbolic models for switched systems with dwell-time constraints using multirate time sampling, where the period of symbolic transitions is a multiple of the control (i.e. switching) period. We show that all the multirate symbolic models, resulting from the proposed construction, are approximately bisimilar to the original incrementally stable switched system with the precision depending on the sampling parameters, and the sampling factor between transition and control periods. The main contribution of the paper is the explicit determination of the optimal sampling factor, which minimizes the number of transitions in the class of proposed symbolic models for a prescribed precision. Interestingly, we prove that this optimal sampling factor is mainly determined by the state space dimension and the number of modes of the switched system. Finally, an illustration of the proposed approach is shown on an example, which shows the benefit of multirate symbolic models in reducing the computational cost of abstraction-based controller synthesis.
Keywords :
Type de document :
Article dans une revue
Automatica, Elsevier, 2018, 98, pp.58-65. 〈10.1016/j.automatica.2018.09.005〉
Littérature citée [29 références]
https://hal.archives-ouvertes.fr/hal-01860113
Soumis le : jeudi 23 août 2018 - 02:50:06
Dernière modification le : lundi 26 novembre 2018 - 16:57:47
Document(s) archivé(s) le : samedi 24 novembre 2018 - 12:42:13
### Fichier
v2.pdf
Fichiers produits par l'(les) auteur(s)
### Citation
Adnane Saoud, Antoine Girard. Optimal Multirate Sampling in Symbolic Models for Incrementally Stable Switched Systems. Automatica, Elsevier, 2018, 98, pp.58-65. 〈10.1016/j.automatica.2018.09.005〉. 〈hal-01860113〉
### Métriques
Consultations de la notice
## 150
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https://www.techwhiff.com/issue/find-the-mass-of-a-water-balloon-that-was-thrown-at--312311
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# Find the mass of a water balloon that was thrown at Bookie with a force of 42 N and an acceleration of 3.99 m/s2.
1 answer
###### Question:
Find the mass of a water balloon that was thrown at Bookie with a force of 42 N and an acceleration of 3.99 m/s2.
## Answers
1 answer
### Someone help me ASAP!!!
Someone help me ASAP!!!...
1 answer
### A radioactive substance decays exponentially. A scientist begins with 190 milligrams of a radioactive substance. After 33 hours, 95 mg of the substance remains. How many milligrams will remain after 51 hours? mg Give your answer accurate to at least one decimal place. Submit Question Jump to Answer
A radioactive substance decays exponentially. A scientist begins with 190 milligrams of a radioactive substance. After 33 hours, 95 mg of the substance remains. How many milligrams will remain after 51 hours? mg Give your answer accurate to at least one decimal place. Submit Question Jump to Answer...
2 answers
### What factors led to an economic crisis in 1997?
What factors led to an economic crisis in 1997?...
1 answer
### What do the differences between the points (as shown on the graph) represent? Please answer
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1 answer
### Y and x have a proportional relationship and y=9 when x=2 what is the value of y when x=3
y and x have a proportional relationship and y=9 when x=2 what is the value of y when x=3...
1 answer
### When a number is decreased by 10% of itself, the result is 54. What is the number? a) Write an equation to modèl the problem. Use x to represent the number. Answer: b) Solve the equation to find the number: Answer:
When a number is decreased by 10% of itself, the result is 54. What is the number? a) Write an equation to modèl the problem. Use x to represent the number. Answer: b) Solve the equation to find the number: Answer:...
1 answer
### An entrepreneur who is eager to learn something new is very _______________.(a) Loyal(b) Persistent(c) Interested(d) Goal setting
An entrepreneur who is eager to learn something new is very _______________.(a) Loyal(b) Persistent(c) Interested(d) Goal setting...
1 answer
### How does the statue contrast with the exhibit at the Art Institute?
How does the statue contrast with the exhibit at the Art Institute?...
1 answer
### Three-quarters of a number is 15. Work out four-fifths of the number.
Three-quarters of a number is 15. Work out four-fifths of the number....
2 answers
### Who was the first female president in the whole globe
Who was the first female president in the whole globe...
1 answer
### There are 42 girls and 56 boys who want to play a game. Each team will have both boys and girls on it. The ratio of boy to girls has to be the same for each team. Everyone must participate in the game. What is the greatest number of teams that can be formed?
There are 42 girls and 56 boys who want to play a game. Each team will have both boys and girls on it. The ratio of boy to girls has to be the same for each team. Everyone must participate in the game. What is the greatest number of teams that can be formed?...
1 answer
### −4(6) + 10 Evaluate the expression
−4(6) + 10 Evaluate the expression...
1 answer
### What 3 major reformers in the field of womens' rights.
What 3 major reformers in the field of womens' rights....
1 answer
### Barriers of trade for Ancient China need 3 answers pls.
Barriers of trade for Ancient China need 3 answers pls....
1 answer
### Prove that (a-b) x (a+b)=2a x b is true. (a and b are vectors)
Prove that (a-b) x (a+b)=2a x b is true. (a and b are vectors)...
1 answer
### Will our sun ever undergo a white dwarf supernova explosion? Why or why not?
Will our sun ever undergo a white dwarf supernova explosion? Why or why not?...
2 answers
### Algernon. [Raising his hat.] You are my little cousin Cecily, I’m sure. Cecily. You are under some strange mistake. I am not little. In fact, I believe I am more than usually tall for my age. –The Importance of Being Earnest, Oscar Wilde The pun in this passage relies on which two definitions of the word little? “narrow” “younger” “unimportant” “brief” “small in size”
Algernon. [Raising his hat.] You are my little cousin Cecily, I’m sure. Cecily. You are under some strange mistake. I am not little. In fact, I believe I am more than usually tall for my age. –The Importance of Being Earnest, Oscar Wilde The pun in this passage relies on which two definitions...
1 answer
### Which of the following is true?Justin is married with one child. He works 40 hours each week at a rate of $16 per hour. His wife began working part time after their daughter was born, but still contributes about$350 to the cash inflow each month. Their monthly cash outflow is generally about $3,000. They have a balance of$2,000 in their saving
Which of the following is true?Justin is married with one child. He works 40 hours each week at a rate of $16 per hour. His wife began working part time after their daughter was born, but still contributes about$350 to the cash inflow each month. Their monthly cash outflow is generally about \$3,000...
2 answers
### Another name for large beautiful movie theaters in the 1920s
Another name for large beautiful movie theaters in the 1920s...
-- 0.010003--
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http://www.r-bloggers.com/author/aschinchon/page/2/
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# Blog Archives
## A Simple Interactive Map Of US Prisons With Leaflet
September 8, 2015
By
The love of one’s country is a splendid thing. But why should love stop at the border? (Pablo Casals, Spanish cellist) Some time ago, I discovered Enigma, an amazing open platform that unifies billions of records from thousands of government sources to make the world of public data universally accessible and useful. This is the … Continue reading...
## The World We Live In #5: Calories And Kilograms
August 19, 2015
By
I enjoy doing new tunes; it gives me a little bit to perk up, to pay a little bit more attention (Earl Scruggs, American musician) I recently finished reading The Signal and the Noise, a book by Nate Silver, creator of the also famous FiveThirtyEight blog. The book is a very good reading for all … Continue reading...
## Going Bananas #2: A Needle In A Haystack
August 3, 2015
By
Now I’m gonna tell my momma that I’m a traveller, I’m gonna follow the sun (The Sun, Parov Stelar) Inspired by this book I read recently, I decided to do this experiment. The idea is comparing how easy is to find sequences of numbers inside Pi, e, Golden Ratio (Phi) and a randomly generated number. … Continue reading...
## The Moon And The Sun
July 8, 2015
By
Do not swear by the moon, for she changes constantly. Then your love would also change (William Shakespeare, Romeo and Juliet) The sun is a big point ant the moon is a cardioid: Here you have the code. It is a simple example of how to use ggplot:
## Trigonometric Pattern Design
July 1, 2015
By
$Trigonometric Pattern Design$
Triangles are my favorite shape, three points where two lines meet (Tessellate, Alt-J) Inspired by recurrence plots and by the Gauss error function, I have done the following plots. The first one represents the recurrence plot of where distance between points is measured by Gauss error function: This one is the same for And this … Continue reading...
## The 2D-Harmonograph In Shiny
June 23, 2015
By
If you wish to make an apple pie from scratch, you must first invent the universe (Carl Sagan) I like Shiny and I can’t stop converting into apps some of my previous experiments: today is the turn of the harmonograph. This is a simple application since you only can press a button to generate a random harmonograph-simulated … Continue reading...
## Shiny Wool Skeins
June 15, 2015
By
Chaos is not a pit: chaos is a ladder (Littlefinger in Game of Thrones) Some time ago I wrote this post to show how my colleague Vu Anh translated into Shiny one of my experiments, opening my eyes to an amazing new world. I am very proud to present you the first Shiny experiment entirely … Continue reading...
## Simple Data Science To Maximize Return On Lottery Investment
June 1, 2015
By
Every finite game has an equilibrium point (John Nash, Non-Cooperative Games, 1950) I read recently this amazing book, where I discovered that we (humans) are not capable of generating random sequences of numbers by ourselves when we play lottery. John Haigh demonstrates this fact analyzing a sample of 282 raffles of 6/49 UK Lotto. Once … Continue reading...
## Bertrand or (The Importance of Defining Problems Properly)
May 13, 2015
By
We better keep an eye on this one: she is tricky (Michael Banks, talking about Mary Poppins) Professor Bertrand teaches Simulation and someday, ask his students: Given a circumference, what is the probability that a chord chosen at random is longer than a side of the equilateral triangle inscribed in the circle? Since they must reach the … Continue reading...
## Odd Connections Inside The NASDAQ-100
May 8, 2015
By
Distinguishing the signal from the noise requires both scientific knowledge and self-knowledge (Nate Silver, author of The Signal and the Noise) Analyzing the evolution of NASDAQ-100 stock prices can discover some interesting couples of companies which share a strong common trend despite of belonging to very different sectors. The NASDAQ-100 is made up of 107 … Continue reading...
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https://planetmath.org/AFiniteIntegralDomainIsAField
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# a finite integral domain is a field
A finite integral domain is a field.
Proof:
Let $R$ be a finite integral domain. Let $a$ be nonzero element of $R$.
Define a function $\varphi\colon R\rightarrow R$ by $\varphi(r)=ar$.
Suppose $\varphi(r)=\varphi(s)$ for some $r,s\in R$. Then $ar=as$, which implies $a(r-s)=0$. Since $a\neq 0$ and $R$ is a cancellation ring, we have $r-s=0$. So $r=s$, and hence $\varphi$ is injective.
Since $R$ is finite and $\varphi$ is injective, by the pigeonhole principle we see that $\varphi$ is also surjective. Thus there exists some $b\in R$ such that $\varphi(b)=ab=1_{R}$, and thus $a$ is a unit.
Thus $R$ is a finite division ring. Since it is commutative, it is also a field.
Note:
A more general result is that an Artinian integral domain is a field.
Title a finite integral domain is a field AFiniteIntegralDomainIsAField 2013-03-22 12:50:02 2013-03-22 12:50:02 yark (2760) yark (2760) 11 yark (2760) Theorem msc 13G05 FiniteRingHasNoProperOverrings
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http://mail-archives.apache.org/mod_mbox/commons-dev/201212.mbox/%[email protected]%3E
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# commons-dev mailing list archives
##### Site index · List index
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From Konstantin Berlin <[email protected]>
Subject Re: [Math] Old to new API ("MultivariateDifferentiable(Vector)Function")
Date Sat, 01 Dec 2012 00:42:11 GMT
Hi,
Now that I have some time, let me try to make my case clearly. First I want to say that this
is not some attack on the automatic-differentation package. I love automatic-differentation
and symbolic packages. I personally cannot compute a derivative without a computer for the
life of me. And I am also glad we are finally starting to agree on something :)
This discussion is about figuring out how an incorrect framework and storage affects the performance
of an optimization. That is why I am so worried.
So lets start with the basics. A Newton method must compute a descent step by solving a linear
equation
H*p = -g, (1)
where H is the Hessian, g is the gradient, and p is the desired descent step. What I am about
to say also holds for non-linear least squares method, where Hessian is approximated using
the Jacobian as
H \approx J^T*J+\lambda I.
Now, if you are not solving a simple optimization problem that you keep giving examples for,
you can easily have a Hessian be a very large matrix,
like 1000x1000 or larger. Now, you better hope that you are storing H using your linear algebra
framework, otherwise eq. (1) computation is going to take a while.
This is actually a very active area of research, and that is why having sparse linear algebra
(aren't you removing this? ;) ) and iterative solvers is important to a lot of people.
What you are proposing as good OO style is that if someone has a function that they want to
optimize, they need to take what is probably already a RealMatrix or [][], and create 1000x1000
DerivativeStructure objects, that,
within the next 10 lines in the optimizer, are going to be converted back to a RealMatrix?
Not only have you just fragmented your heap space, but your garbage collector
is going crazy, and you are wasting an incredible amount of memory. Now imagine if your Jacobian
is actually very simple to compute but large, then this whole conversion back and forth actually
takes much longer than the function evaluation.
So, why exactly are you insisting on taking this performance penalty? You claim that the optimizer
can work better if it gets a DerivativeStructure, why? Where is the fact that you are holding
a DerivativeStructure come into effect for a Newton method? Can you provide any literature
in that regard? The classical optimization bottleneck, if not the actual function evaluation,
is eq. (1). The optimization methodology is build on top of years of research in computational
linear algebra concepts, and does not care how the matrices are actually computed. Efficient
memory usage and speed is critical here because in Newton optimizations eq. (1) is evaluated
thousands of times. The goal of the Jacobian is not to store derivatives it is to store a
matrix of numbers that allows you to quadratically approximate your target function.
You guys are focusing on people using finite differences and trying to optimize a newton method
to use finite differences. This is not what the main purpose of a newton method is. If you
want a method that dynamically adjusts finite differences step size, you should switch to
BOBYQA, which was designed for this case.
Derivatives can be computed by a computer using a symbolic toolbox a priori (something that
I was referring to when I accidentally said auto-differenation). They can also be efficiently
simplified by that toolbox before being pasted back into you program. Auto-diff could also
be an important tool for people if their problem is simple or they are not concerned with
optimal efficiency . This can easily be handled by a wrapper and has nothing to do with Newton
optimization. If you want to talk about proper OO design and internal simplification then
you should focus on being able to pass a linear solver into your optimization method. This
way you allow people to use iterative and sparse solvers when needed. If you are concerned
about people getting derivatives wrong, you can do what MATLAB does, which is to add an option
to check the derivatives using finite differences when debugging.
This brings me to my second issue. There are important problems where computation of the derivatives
combined with the actual function evaluation is *significantly* faster than computing each
alone. I am not clear why I am hitting such resistance with this. For example, you are doing
some sort of a simulation, which can be trivially adjusted in the end to give a derivative
or a function value. A very real example of this is a Fast Multipole Method, which takes time
to compute a series expansion of the function, but the resulting series expansion can be analytically
differentiated.
What I suggested as function interfaces was just an initial quick suggestion that I would
be happy for anyone to change in a way that everyone feels positive about. I just don't want
my second issue to be ignored like a non-issue.
Konstantin
On Nov 30, 2012, at 5:15 PM, Gilles Sadowski <[email protected]> wrote:
>>>
>>> I don't know if people are confused about auto-differentation, I
>>> think most people working in numerical analysis are very well aware
>>> of what it does. The issue here is that it is a completely separate
>>> subject from optimizations. In a proper OO design you would not mix
>>> the two together. Computation of the derivatives is a separate
>>> component from optimization. Optimization only assumes that you can
>>> compute one, it shouldn't care or force you two compute one in a
>>> specific way. That's bad design. Everyone component should only have
>>> necessary and sufficient requirements for use. Automatic
>>> differentiation is not necessary for optimization so it should not
>>> exist in the interface.
>>
>> You are right.
>>
>>>
>>> I would like to add, that if my function is simple enough, I am very
>>> capable of running autdiff package a priori myself. The real need for
>>> finite-difference is when you cannot analytically compute the
>>> derivative. Though I think having a wrapper function around autdiff
>>> package is a nice tool to help developers quickly write code, if they
>>> prefer to have quicker development time but slightly slower code.
>>
>>>
>>> If someone can explain to me why auto-diff package should be directly
>>> forced or even be provided as alternative into optimization package
>>> when a simple wrapper function can do this task while maintaining
>>> much cleaner OO design, please tell me.
>>
>> You just found the reason and explained it by yourself: it was bad
>> design and I am the one to blame for this. I was (and still am) stupid.
>
> I'm not convinced that it was bad design. Maybe I'm completely off now:
> I thought that the purpose was internal simplification. I don't think
> that it can be inherently wrong to store any sort of derivatives (be it
> gradient or Jacobian) into a structure aimed at storing... partial
> derivatives (i.e. "DerivativeStructure").
>
> Please let me know whether the problem is more in-depth than what I
> described previously (allowing the current way to provide the gradient
> and Jacobian).
>
> I would nevertheless have suggested to delete the method
> MultivariateFunction partialDerivative(int k);
> from "DifferentiableMultivariateFunction".
>
>>
>> So I suggest we disconnect differentiation from optimization, but in a
>> way that would let users decide how they provide the differentials. This
>> means I would not like to reintroduce the former interfaces.
>>
>> What about having the optimize() methods taking two arguments function,
>> a MultivariateFunction for the value and a MultivariateVectorFunction
>> for the gradient? It would be up to the user to select how they compute
>> each function. They could use direct coding, they could use a finite
>> differences wrapper around the first function to implement the second,
>
>
>
>> they could use our differentiation framework and put one wrapper to
>> extract the value and another one to extract the gradient.
>
> That would also be a nice example of usage of the differentiation
> framework.
>
>> What do you think?
>
> Yes. Now I got it (I think). IIUC, we could even introduce the new interface
> before 3.1, and deprecated old the older ones (as you wanted to do anyways,
> IIRC).
>
> I'll give it a try in the next days. OK?
>
>
> Gilles
>
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https://pos.sissa.it/291/142/
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# PoS(CKM2016)142
Prospects for time-dependent mixing and CP-violation measurements at Belle II
A. Schwartz, On behalf of the BELLE II collaboration
Contribution: pdf
Abstract
The Belle II experiment is under construction at the KEK laboratory in Japan. Belle II will study $e^+e^-$ collisions at or near the $\Upsilon(4S)$ resonance with the goal of collecting 50 ab$^{-1}$ of data, which is a large increase over that recorded by the Belle and BaBar experiments. This data will provide a large sample of charm meson decays. In this report we present the expected sensitivity of Belle II for measuring time-dependent mixing and $CP$ violation in the $D^0$-$\overline{D}{}^0$ system. We focus on measurements of
$D^0\rightarrow K^+\pi^-$, $D^0\rightarrow K^+\pi^-\pi^0$, and $D^0\rightarrow K^0_S\pi^+\pi^-$ decays.
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http://www-math.umd.edu/gcal_rss.php?seminar_key=LOGIC&year=2017&html
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### Logic Archives for Academic Year 2017
#### Organizational meeting
When: Tue, August 30, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Organizational meeting () -
#### Structure and enumeration theorems in hereditary properties of L-structures
When: Tue, September 6, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Caroline Terry (UMCP) -
Abstract: The study of structure and enumeration for hereditary graph properties has been a major area of research in extremal combinatorics. Over the years such results have been extended to many combinatorial structures other than graphs. This line of research has developed an informal strategy for how to prove these results in various settings. In this talk we formalize this strategy. In particular, we generalize certain definitions, tools, and theorems which appear commonly in approximate structure and enumeration theorems in extremal combinatorics. Our results apply to classes of finite L-structures which are closed under isomorphism and model-theoretic substructure, where L is any finite relational language with maximum arity at least two.
#### Large scale geometry of automorphism groups
When: Tue, September 13, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Christian Rosendal (University of Illiniois, Chicago and UMCP) -
Abstract: We present a framework for investigating the large scale geometry or geometric group theory of automorphism groups of countable first order structures, which extends he geometric theory of countable discrete and locally compact groups. Within this framework, we show how the geometric structure of automorphism groups is reflected in model theoretical properties of the underlying first order structure.
#### Asymptotic dimension in generic models of amalgamation classes
When: Tue, October 4, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Cameron Hill (Wesleyan University) -
Abstract: Given an amalgamation class K of finite structures, one recovers a generic model M, and if M has the finite sub-model property, one can ask about how Hrushovski-style pseudo-finite dimensions interact with the theory of M. In this talk, I will discuss how some discrete mathematical properties of K — namely, having a 0,1-law or having a Ramsey-lift — can be seen to govern this interaction. I will also discuss how these observations may suggest approaches to settling the question of the pseudo-finiteness of the Henson graph.
#### Fields with bells, whistles, and an automorphism
When: Tue, October 11, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Alice Medvedev (City College, CUNY)
#### On tame expansions of the group of integers
When: Tue, October 18, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Gabriel Conant (University of Notre Dame) - https://www3.nd.edu/~gconant/
Abstract: We discuss some recent work concerning expansions of the group Z of integers, which are tame with respect to model theoretic dividing lines such as stability and dp-rank. Our focus is on the ordered group of integers (also called Presburger arithmetic), which is a well-known example of a dp-minimal expansion of Z. It was asked by Aschenbrenner et. al. whether every dp-minimal expansion of Z is a reduct of Presburger. We present a result in the opposite direction: there are no intermediate structures strictly between the group of integers and Presburger arithmetic. The proof of this result uses Cluckers' cell decomposition for Presburger sets, as well as work of Kadets on the geometry of convex polyhedra.
#### On Collapses of Generalized Indiscernibles.
When: Tue, October 25, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Vincent Guingona (Towson University) -
Abstract: I discuss the characterization of various model theoretic dividing lines via the collapse of generalized indiscernibles. For example, S. Shelah showed that a theory is stable if and only if all order indiscernibles are set indiscernible and L. Scow showed that a theory has NIP if and only if all ordered graph indiscernibles are order indiscernible. I give other similar characterizations for dp-rank and rosiness. Finally, I explore means of framing all of these results in a general context. This work is joint with C. Hill and L. Scow.
#### Visceral Theories
When: Tue, November 1, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Alfred Dolich (CUNY) -
Abstract: We consider theories T expanding that of densely ordered Abelian groups with the property that for any model M of T and any definable subset X of M if X is infinite then X has non-empty interior. We call such theories visceral. Visceral theories arise naturally when considering dp-minimal theories. We show that in many ways visceral theories behave much like weakly o-minimal theories in that definable functions are piecewise continuous and definable sets admit a weak form of cell decomposition. Yet crucially, in a visceral theory there does not appear to be any form of local monotonicity for definable functions.
#### Application of Ramsey-type results to the decoding in the automorphism group of PA
When: Tue, November 8, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Ermek Nurkhaidarov (Penn State -- Mont Alto) -
#### Straw into gold: Turning forcing arguments into ZFC proofs
When: Tue, November 15, 2016 - 3:30pm
Where: Kirwan Hall 1311
#### A Tale of Two (or One) Liouville Closures...
When: Tue, November 22, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Allen Gehret (University of Illinois, Urbana-Champaign) -
Abstract: $H$-fields are ordered differential fields which serve as an abstract generalization of both Hardy fields (ordered differential fields of germs of real-valued functions at $+\infty$) and transseries (ordered valued differential fields such as $\mathbb{T}$ and $\mathbb{T}_{\log}$). A \emph{Liouville closure} of an $H$-field $K$ is a minimal real-closed $H$-field extension of $K$ that is closed under integration and exponential integration. In 2002, Lou van den Dries and Matthias Aschenbrenner proved that every $H$-field $K$ has exactly one, or exactly two, Liouville closures, up to isomorphism over $K$. Recently (in arxiv.org/abs/1608.00997), I was able to determine the precise dividing line of this dichotomy. It involves a technical property of $H$-fields called $\lambda$-freeness. In this talk, I will review the 2002 result of van den Dries and Aschenbrenner and discuss my recent contribution.
#### n-simple theories
When: Tue, November 29, 2016 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Alexei Kolesnikov (Towson University) -
#### Organizational meeting
When: Tue, January 31, 2017 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Organizational meeting () -
#### Compact, metrizable structures and classification theory
When: Tue, February 7, 2017 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Christian Rosendal (UIC and UMCP) -
#### Generalized Indiscernibles and Dividing Lines
When: Tue, February 14, 2017 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Vincent Guingona (Towson University) -
#### Keisler's order need not be linear
When: Tue, February 21, 2017 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Douglas Ulrich (UMCP) -
#### Analogues of the Shelah-Spencer graphs
When: Tue, March 7, 2017 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Danul Gunatilleka (UMCP) -
#### Model theory for functional analysis
When: Tue, March 28, 2017 - 3:30pm
Where: Kirwan Hall 1311
Speaker: David Sherman (University of Virginia) -
Abstract: Historically, model theory has not had much influence on functional analysis. One reason is that the ultrapowers appropriate for analysis do not quite have the same model theoretic significance as their classical counterparts. An elegant recent solution -- not the first -- is to switch to a logic in which truth values are drawn from the interval [0,1]. This "continuous model theory" is natural for analysts and has opened up a flurry of interaction between the two fields. I will try to explain what this approach is, where it came from, and what kinds of things happen when model theorists start playing with Banach spaces, C*-algebras, etc.
#### The subgroup structure of Thompson's group F
When: Tue, April 4, 2017 - 3:30pm
Where: Kirwan Hall 1311
Speaker: Justin Moore (Cornell University) -
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https://cob.silverchair.com/dev/article/132/3/429/43070/Transcriptional-program-controlled-by-the-floral
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Floral organs, whose identity is determined by specific combinations of homeotic genes, originate from a group of undifferentiated cells called the floral meristem. In Arabidopsis, the homeotic gene AGAMOUS(AG) terminates meristem activity and promotes development of stamens and carpels. To understand the program of gene expression activated by AG, we followed genome-wide expression during early stamen and carpel development. The AG target genes included most genes for which mutant screens revealed a function downstream of AG. Novel targets were validated by in situ hybridisation and binding to AG in vitro and in vivo. Transcription factors formed a large fraction of AG targets, suggesting that during early organogenesis, much of the genetic program is concerned with elaborating gene expression patterns. The results also suggest that AG and other homeotic proteins with which it interacts (SEPALLATA3, APETALA3,PISTILLATA) are coordinately regulated in a positive-feedback loop to maintain their own expression, and that AG activates biosynthesis of gibberellin, which has been proposed to promote the shift from meristem identity to differentiation.
The genetic control of floral organ identity is one of the most remarkable examples of how regulatory genes determine plant structure (reviewed by Ferrario et al., 2004; Zik and Irish, 2003a). A flower starts its development as a group of undifferentiated cells (the floral meristem), which arises on the flank of the shoot apical meristem. The floral meristem gives rise to organ primordia, which develop into each of the four types of floral organs: sepals, petals, stamens and carpels. The identity of these organs is specified by homeotic genes, most of which encode MADS-domain transcription factors. The homeotic genes are expressed in different but partially overlapping domains in the floral meristem, and the specific combination of homeotic genes active in each organ primordium directs the development of its organ type. These partially overlapping expression domains are set up by genes that are active in the meristem, but subsequently the expression and function of the homeotic genes is maintained throughout organ development.
The molecular basis for the combinatorial action of homeotic genes may be that in each case, the corresponding proteins are assembled into a different protein complex. For example, stamen development requires combination of the homeotic genes AGAMOUS (AG), APETALA3(AP3), PISTILLATA (PI) and at least one of the SEPALLATA (SEP1, SEP2 and SEP3) genes, whereas carpel development occurs when AG and SEP are expressed, but not AP3/PI (Bowman and Meyerowitz, 1991; Honma and Goto, 2001; Jack et al.,1992; Krizek and Meyerowitz,1996; Pelaz et al.,2000; Yanofsky et al.,1990). Based on protein-protein interactions in yeast and on co-immunoprecipitation, it has been proposed that stamen development is directed by a protein complex in which SEP3 bridges the interaction between AG and the AP3/PI heterodimer; similarly, the direct interaction between SEP3 and AG in yeast and suggests that these two proteins associate to control carpel development (Honma and Goto,2001).
Presumably each of the complexes containing homeotic proteins selects a different set of downstream target genes that participate in the development of a specific organ type, although the exact composition of these complexes in vivo, and how they select different target genes, remains unknown(Jack, 2001). To understand how the activity of homeotic genes is combined and translated into the patterns of cell division and differentiation that actually shape the floral organs, it is necessary to identify these downstream targets. However, very little is known about the genes that function downstream of the floral homeotic genes.
Genetic analysis has revealed some intermediate regulatory genes that control specific aspects of floral organ development. For example, AG activates SPOROCYTELESS (SPL), which controls sporogenesis in both stamens and carpels (Ito et al.,2004). SUPERMAN (SUP) controls cell proliferation in stamen and carpel primordia and its expression depends on AG, AP3 and PI (Sakai et al., 2000; Sakai et al.,1995). The SHATTERPROOF genes (SHP1 and SHP2) are required in the carpel margins for differentiation of the dehiscence zone, where later the fruit splits open to release the seeds(Liljegren et al., 2000). SPATULA (SPT) controls cell differentiation at the carpel margins and in the transmitting tract (the tissue that guides the growth of pollen tubes towards the ovules) (Bowman and Smyth, 1999; Heisler et al., 2001), and CRABS CLAW (CRC) participates in directing the development of tissues derived from the abaxial side of the carpel primordium (e.g. the outer epidermis)(Eshed et al., 1999).
A more comprehensive view of gene expression in floral organs came from transcript profiling experiments comparing wild type and homeotic mutants(Wellmer et al., 2004; Zik and Irish, 2003b). These experiments revealed hundreds of genes that are preferentially expressed in different organs, but these were mostly expressed at late stages of development and were probably only indirectly dependent on the floral homeotic genes (Wellmer et al., 2004). To fully understand the program of gene expression controlled by the floral homeotic genes, it is necessary to know how it unfolds from organ initiation to maturity. Here, we report the results of a global analysis of the program of gene expression triggered by AG, from the onset of organogenesis to early stages of reproductive organ development.
### Plant material
Plants were grown on a mix of vermiculite:soil:sand at 18°C with 16-hour light/8-hour dark cycles. All mutants (ag-3, ap1-1, ap1-1 cal-1 and ag-3 ap1-1) and AGGR were in a Lerbackground, which was used as the wild type.
Dexamethasone (Sigma, stock solution 10 mM in ethanol) was used at a final concentration of 10 μM in Silwet L-77 0.015%, applied directly on the inflorescence tips; for mock treatments, the solution contained the same amount of ethanol (0.1%) and Silwet L-77. After treatment, RNA was extracted from inflorescence apices and stored at -70°C until activation of AGGR was confirmed (2 weeks later).
### Scanning electron microscopy (SEM)
Plants were fixed in 2.5% glutaraldehyde in phosphate-buffered saline (PBS)at 4°C overnight, dehydrated in an ethanol series, critical-point dried in liquid CO2, sputter-coated with gold palladium, analysed and photographed with a Philips XL 30 FEG SEM.
### RNA isolation
Total RNA was extracted using TRI reagent (Sigma) according to the manufacturer's instructions. For array hybridisation, the RNA was cleaned up with RNeasy columns (Qiagen) and precipitated to increase final concentration.
### Array hybridisation and analysis of expression data
Gene Chip arrays were hybridised as in the manufacturer's protocol(Affymetrix). To calculate P-values for increase or decrease in expression, the Wilcoxon signed-rank test(Hubbell et al., 2002; Liu et al., 2002) was applied to each pair of chips after normalisation across all probe sets, using Micro Array Suite 5.0 (Affymetrix). To calculate fold differences in expression, raw expression levels were imported from Micro Array Suite 5.0 into Gene Spring 5.1 (Silicon Genetics) and normalised first to the fiftieth percentile of each chip, then across all chips before further analysis.
### Reverse transcription-PCR (RT-PCR)
Total RNA (2 μg) was treated with RNase-free DNase, and first strand cDNA was synthesised using oligo(dT) primer (Invitrogen) and Superscript RT(Invitrogen). Aliquots of the cDNA were used as template for PCR with gene specific primers (see Table S3 in supplementary material).
### In situ hybridisation
RNA was hybridised in situ (Fobert et al., 1996), using digoxigenin-labelled probes transcribed with T7 polymerase from linearised plasmid (pGEM-T easy, Promega) containing 3′cDNA fragments. Colour detection was performed with BCIP/NBT according to the manufacturer's instructions (Boehringer).
### Production of recombinant AG protein
To produce AG protein, the AG ORF was PCR-amplified from pCIT1516 vector(Yanofsky et al., 1990) and cloned into pRSET-A (Invitrogen). BL21(DE3) pLysE cells were transformed with the construct, and His-AG proteins were expressed under the control of the T7 promoter. To prepare recombinant His-AG, inclusion bodies were purified using the BugBuster HT Protein Extraction Reagent (Novagen), according to the manufacturer's instructions, dissolved in dialysis buffer (20 mM Tris, 100 mM KCl, 1 mM EDTA, 1 mM DTT, 1 mM PMSF, 12% glycerol, pH 8.0) containing 6M urea,dialysed overnight against the same buffer without urea and stored at-20°C.
### Electrophoretic mobility shift assays (EMSA)
Probes were made from complementary oligonucleotides (see Table S3 in supplementary material), annealed in 20 mM Tris (pH 8.0), 50 mM NaCl, 1 mM EDTA, labelled with 32P by filling in with DNA polymerase I (Klenow fragment), and gel-purified prior to use. DNA-binding assays and gel electrophoresis were essentially as described previously(Riechmann et al., 1996).
### Chromatin immunoprecipitation (ChIP)
The procedure was adapted from Ito et al. and Wang et al.(Ito et al., 1997; Wang et al., 2002). Inflorescence tissue (∼1 g) of Col-0 plants was fixed with 1% formaldehyde in MC buffer [10 mM sodium phosphate (pH 7.0), 50 mM NaCl, 0.1 M sucrose) for 1 hour under vacuum. Fixation was stopped with 0.125 M glycine, followed by three washes with MC. The tissue was ground in liquid nitrogen, the powder was suspended in M1 buffer [10 mM sodium phosphate (pH 7.0), 0.1 M NaCl, 1 M 2-methyl 2,4-pentanediol, 10 mM β-mercaptoethanol, Complete™Protease Inhibitor Cocktail (Roche Diagnostics GmbH, Mannhein, Germany)], the slurry was filtrated through 55 μm mesh and centrifuged at 1000 g for 10 minutes. Subsequent steps were at 4°C unless indicated otherwise. Filtration and centrifugation were repeated twice, then the pellet was washed five times with M2 buffer (M1 buffer with 10 mM MgCl2, 0.5% Triton X-100) and once with M3 buffer (M1 without 2-methyl 2,4-pentanediol). The nuclear pellet was resuspended in 1 ml Sonic buffer [10 mM sodium phosphate (pH 7.0), 0.1 M NaCl, 0.5% Sarkosyl, 10 mM EDTA, Complete™ Protease Inhibitor Cocktail (Roche Diagnostics GmbH), 1 mM PMSF]. Chromatin was solubilised on ice with a probe sonicator (MSE,Soniprep 150) by 25 cycles of 15-second pulses of half maximal power with 30 seconds cooling time between pulses. After sonication, the suspension was centrifuged (microcentrifuge, top speed) for 5 minutes and the supernatant was mixed with one volume of IP buffer [50 mM Hepes (pH 7.5), 150 mM KCl, 5 mM MgCl2, 10 μM ZnSO4, 1% Triton X-100, 0.05% SDS]. The solubilised chromatin was pre-adsorbed overnight with 7.5 μl antiserum against CLAVATA3 (CLV3) (sc-12598, Santa Cruz Biotechnology, Santa Cruz, CA) (used as AG-negative serum due to the lack of pre-immune serum). After centrifugation, the supernatant was mixed with 40 μl of protein G-Sepharose [Sigma, 50% slurry in 10 mM Tris (pH 7.5), 150 mM NaCl] and incubated on a rotating wheel for 1 hour. After centrifuging, the supernatant was equally divided over two tubes with 2.5 μl AG antiserum(sc-12697, Santa Cruz Biotechnology) or 2.5 μl CLV3 serum(control). After 1 hour on a rotating wheel and centrifugation, the supernatant was mixed with 20 μl protein G-Sepharose (Sigma) before incubation for another hour on the rotating wheel. The protein G-Sepharose beads were washed five times with 1 ml IP buffer for 10 minutes at room temperature. Elution with 0.1 M glycine, 0.5 M NaCl, 0.05% Tween-20 (pH 2.8)was as described (Wang et al.,2002). The eluate was treated with 1 μl RNase A (10 mg/ml) and proteinase K (to final of 0.5 mg/ml). After overnight incubation, a second aliquot of proteinase K was added and incubated at 65°C for 6 hours. After phenol/cloroform, then chloroform extraction, DNA was precipitated with 2.5 volumes of ethanol, one-tenth volume 3M NaAc (pH 5.4) and 1 μl glycogen,and resuspended in 10 μl of 10 mM Tris (pH 8.0).
ChIP PCR was performed to reveal if a specific DNA fragment was enriched in the immunoprecipitated DNA sample compared with the pre-immune DNA sample. Primers were designed around the consensus AG binding sites and control primers were made for regions lacking the consensus AG binding site. Template ChIP DNA was diluted, amplified for 35 to 40 cycles (see Fig. 5), and analysed on a 1.5%agarose gel, followed by scanning with a Molecular Imager FX-PRO Plus (Bio-Rad Laboratories, Hercules, CA). The primer sequences were (5′ to 3′):
Fig. 5.
AG binds to candidate target genes. (A) Binding sites identified by sequence analysis. m' is a mutated version of the binding site in AP3, used as a negative control. Next to each numbered binding site, the corresponding gene and sequence are shown, with mismatches to the consensus AG binding site TT(A/T/G)CC(A/T)6GG(A/T/C)AA(Shiraishi et al., 1993)marked in boldface. The white boxes represent sequences upstream of the start codon (except for AG, where the reference point is the 5′splice site of the second intron), with vertical lines indicating the position of the AG binding sites. The horizontal bars above some of the binding sites indicate the fragment amplified in the ChIP experiment (C). (B) Binding to AG in vitro, shown by electrophoretic mobility shift assays (EMSA). The probes contained the binding sites numbered in A. Each probe was incubated with extract from bacteria induced to express AG (+) or an empty expression vector(-). In all experiments, the same amount of labelled probe was used and a lane with probe 2 (not shown) was included to adjust the exposure to comparable levels. (C) Binding to AG in vivo, shown by ChIP. Numbers correspond to the binding sites shown in A; in each panel, PCR amplification (35 cycles) of sequences containing the binding site (black bars in A) is compared in immunoprecipitates obtained with antiserum against AG (+) or CLV3 (-). In the last panel on the left, the fourth exon of EIF4A1 was used as a negative control lacking AG binding sequences: with 35 cycles (not shown), no band was seen; with 40 cycles (panel), similar levels of contaminating template were amplified. The results shown were replicated in two fully independent ChIP experiments.
Fig. 5.
AG binds to candidate target genes. (A) Binding sites identified by sequence analysis. m' is a mutated version of the binding site in AP3, used as a negative control. Next to each numbered binding site, the corresponding gene and sequence are shown, with mismatches to the consensus AG binding site TT(A/T/G)CC(A/T)6GG(A/T/C)AA(Shiraishi et al., 1993)marked in boldface. The white boxes represent sequences upstream of the start codon (except for AG, where the reference point is the 5′splice site of the second intron), with vertical lines indicating the position of the AG binding sites. The horizontal bars above some of the binding sites indicate the fragment amplified in the ChIP experiment (C). (B) Binding to AG in vitro, shown by electrophoretic mobility shift assays (EMSA). The probes contained the binding sites numbered in A. Each probe was incubated with extract from bacteria induced to express AG (+) or an empty expression vector(-). In all experiments, the same amount of labelled probe was used and a lane with probe 2 (not shown) was included to adjust the exposure to comparable levels. (C) Binding to AG in vivo, shown by ChIP. Numbers correspond to the binding sites shown in A; in each panel, PCR amplification (35 cycles) of sequences containing the binding site (black bars in A) is compared in immunoprecipitates obtained with antiserum against AG (+) or CLV3 (-). In the last panel on the left, the fourth exon of EIF4A1 was used as a negative control lacking AG binding sequences: with 35 cycles (not shown), no band was seen; with 40 cycles (panel), similar levels of contaminating template were amplified. The results shown were replicated in two fully independent ChIP experiments.
CRC, TGGATGCATGAATAATGGGTAG and CGTGGACTAGAAATAATGAGACGA;
AP3, CGGAGCTCCGTTAATAAATTGACG and TTTGGTGGAGAGGACAAGAGA;
AP3 exon 7, AACATGTTTTGGTGAATTAGGAA and GCACCAGCAAACCTTTTAGC;
GA4, TTGTCCCTTTATATACGCATTAATCA and GAGACCAAGAGGAGGCAAAA;
AG, TGGTCTGCCTTCTACGATCC and CAACAACCCATTAACACATTGG;
SEP3, CGGCCATATCCACTTTTACG and TTTTTGGGATAATTTTACTTTCCAC; and
EIF4A1 control, TCTTGGTGAAGCGTGATGAG and GCTGAGTTGGGAGATCGAAG.
### Activation of AG in cal-1, ap1-1 plants induced synchronised stamen and carpel primordia
To follow changes in gene expression after stamen and carpel initiation, we generated plants with AG under external control. Plants were transformed with a construct in which the 35S promoter directed a fusion between AG and part of the rat glucocorticoid receptor (GR), as reported previously(Ito et al., 2004); for simplicity, we will refer to the 35S:AG-GR construct as AGGR. In the loss-of-function ag-3 mutants, AGGRrescued development of stamens and carpels only when the plants were treated daily with the steroid dexamethasone (DEX), confirming that the AG-GR fusion could replace AG function (Fig. 1A-D).
Fig. 1.
Steroid-inducible stamen and carpel development. (A,B) ag-3, AGGRinflorescences, mock treated (A) or treated with dexamethasone (DEX; B). (C,D)Close-up view of flowers from the plants shown in A,B; while the mock-treated plant shows an indeterminate number of sepals and petals (C), DEX treatment has induced stamen (st) and carpel (ca) development (D). (E,F) cal-1,ap1-1, AGGR inflorescences, two weeks after mock treatment (E) or treatment with DEX (F). Note the mass of meristems in E (similar to those shown at high magnification in G) compared with the mature stamens and carpels in F. (G-I) Scanning electron micrographs of cal-1, ap1-1, AGGRinflorescences 1 day (G), 3 days (H) and 7 days (I) after DEX treatment. The arrows in H indicate meristems that are beginning to produce organ primordia;in I, developing stamens (st) and carpels (ca) are morphologically identifiable. Scale bars: 5 mm in A,B; 1 mm in C-F; 100 μm in G-I.
Fig. 1.
Steroid-inducible stamen and carpel development. (A,B) ag-3, AGGRinflorescences, mock treated (A) or treated with dexamethasone (DEX; B). (C,D)Close-up view of flowers from the plants shown in A,B; while the mock-treated plant shows an indeterminate number of sepals and petals (C), DEX treatment has induced stamen (st) and carpel (ca) development (D). (E,F) cal-1,ap1-1, AGGR inflorescences, two weeks after mock treatment (E) or treatment with DEX (F). Note the mass of meristems in E (similar to those shown at high magnification in G) compared with the mature stamens and carpels in F. (G-I) Scanning electron micrographs of cal-1, ap1-1, AGGRinflorescences 1 day (G), 3 days (H) and 7 days (I) after DEX treatment. The arrows in H indicate meristems that are beginning to produce organ primordia;in I, developing stamens (st) and carpels (ca) are morphologically identifiable. Scale bars: 5 mm in A,B; 1 mm in C-F; 100 μm in G-I.
To focus on early organogenesis, AGGR was combined with the ap1-1 and cal-1 mutations. AP1 and CAL act redundantly to specify floral meristem identity. The double mutant accumulates indeterminate lateral meristems that fail to initiate floral organs(Kempin et al., 1995)(Fig. 1E,G), although the defect can become less severe late in development, allowing flowers to form(Ferrandiz et al., 2000). Expression of AG under the 35S promoter in ap1-1, cal-1 plants restored robust stamen and carpel development(Mizukami and Ma, 1997). In AGGR, ap1-1, cal-1 plants, DEX treatment induced stamen and carpel formation, whereas mock-treated controls remained meristematic(Fig. 1E,F). A single DEX treatment was sufficient for full stamen and carpel development, which followed a time course comparable to wild-type development(Smyth et al., 1990)(Fig. 1F). However, in AGGR, ap1-1, cal-1 plants that were also homozygous for the ag-3 mutation, organ development required daily DEX treatments (not shown), implying that a single DEX treatment initiated stamen and carpel development that was subsequently sustained by the endogenous AG.Thus, although an artificial construct was used to trigger organogenesis,subsequent development was controlled by the endogenous gene, followed the normal time course and yielded fully functional organs.
In plants treated in parallel with solution lacking DEX, organogenesis was not seen, whereas the frequency of DEX-induced organogenesis after a single DEX treatment ranged from between 30% and 100% of plants in different experiments. Individual DEX-treated plants showed an all-or-nothing response(i.e. either robust organ induction in all treated inflorescence apices, or no induction). AGGR was still expressed in plants that failed to initiate organs in response to DEX (not shown), so transgene silencing was unlikely to be the cause of the variable organ induction. The all-or-nothing response suggested that organ induction was a bistable switch (see Discussion).
### Global analysis of gene expression during AG-induced organogenesis
To screen for genes whose expression changed in ap1-1, cal-1meristems after AG activation, we used the Arabidopsis ATH1 high-density oligonucleotide array (Affymetrix). Three time points were chosen after a single DEX treatment of 35S::AG-GR, cal-1, ap1-1 meristems:one day, when no morphological changes were visible, three days, when the earliest signs of organ primordia were seen, and seven days, when stamen and carpel primordia were recognisable (Fig. 1G-I). To ensure that the samples came from plants in which organogenesis had been induced, a few treated meristems were left on each plant and organ development was checked after two weeks. For each time point,two independent samples with AGGR activated were compared with two mock-treated controls, giving four possible combinations of treatment versus control. Genes up- or downregulated were defined independently for each time point as those with a statistically significant change in all four treatment/control pairs (Wilcoxon signed-rank test, P<0.05)(Hubbell et al., 2002; Liu et al., 2002) and a mean change of at least twofold.
Using these filtering criteria, 149 of the 22,810 genes represented on the array were upregulated in at least one of the three time points(Fig. 2A, and Tables S1 and S2 in supplementary material). Based on their predicted molecular function, the majority of these genes fell into three classes: unknown function (50),DNA-binding proteins (38) and metabolic enzymes (30)(Fig. 2C). The set of upregulated genes contained most of the known genes with a specific role in stamen and/or carpel development, including AG itself(Yanofsky et al., 1990), AP3 (Jack et al.,1992), PI (Goto and Meyerowitz, 1994), SEP1, SEP2 and SEP3(Pelaz et al., 2000), SUP (Sakai et al.,1995), CRC (Bowman and Smyth, 1999) and SHP1, SHP2(Liljegren et al., 2000). JAGGED (JAG) (Dinneny et al., 2004; Ohno et al.,2004), which controls the development of leaves and floral organs,was also activated, in addition to four (At2g01520, At3g04960, At4g21590,At5g57720) out of ten uncharacterised genes whose expression correlated with that of floral homeotic genes during floral induction(Schmid et al., 2003). Thus our array experiment independently detected many of the genes expected to function downstream of AG, based on previous genetic and array-based experiments.
Fig. 2.
Summary of changes in gene expression after AGGR activation. (A,B) Venn diagrams showing the number of genes significantly activated (A) or repressed(B), 1, 3 or 7 days after DEX treatment. The grey area contains the 12 genes chosen for more detailed analysis because their activation was sustained during the time course. (C) Predicted functions of the proteins encoded by the genes shown in A. The ratio between the number of genes and the area of the coloured sections is the same across the diagrams for 1, 3 and 7 days after AGGR activation.
Fig. 2.
Summary of changes in gene expression after AGGR activation. (A,B) Venn diagrams showing the number of genes significantly activated (A) or repressed(B), 1, 3 or 7 days after DEX treatment. The grey area contains the 12 genes chosen for more detailed analysis because their activation was sustained during the time course. (C) Predicted functions of the proteins encoded by the genes shown in A. The ratio between the number of genes and the area of the coloured sections is the same across the diagrams for 1, 3 and 7 days after AGGR activation.
The set of downregulated genes was smaller (16 on day 1, 9 on day 3, 43 on day 7; Fig. 2B, and Tables S1 and S2 in supplementary material) and included only one gene with a well-known role in floral development. UFO is expressed in meristems, functions upstream of the floral homeotic genes to set the pattern of AP3expression and is only expressed at the earliest stages of reproductive organ development (Ingram et al.,1995; Lee et al.,1997; Levin and Meyerowitz,1995). Accordingly, UFO appeared among the genes that were repressed at day 7 of organ development.
A set of 1453 genes expressed mostly at relatively late stages in specific floral organs has been identified by comparing the transcripts in wild-type and homeotic mutant flowers (Wellmer et al., 2004). The overlap between these genes and our list of AG-regulated genes is relatively small (20 of the 149 AG-activated genes and six of the AG-repressed genes; see Tables S1 and S2 in supplementary material), suggesting that the transcriptional program in early organogenesis is distinct from that in late organs.
### Genes that showed sustained activation are expressed in wild-type carpel and stamen development
To confirm independently of the array data that we have identified genes controlled by AG, we focused on genes that were activated at multiple time points after AG induction. A set of twelve genes were upregulated on day 1 or 3 and then remained activated until day 7(Fig. 3A). This set includes four well-known regulators of stamen or carpel development (AP3, CRC, AG,SEP3), and two genes implicated in the biosynthesis of the growth regulator, gibberellin: GA4 encodes an enzyme that catalyses the production of bioactive gibberellin(William et al., 2004; Williams et al., 1998) and ATH1 encodes a homeodomain protein proposed to regulate gibberellin biosynthetic genes (Garcia-Martinez and Gil, 2001). The remaining six genes encode a B3 domain protein(At3g17010), a zinc-finger protein (At1g13400) related to SUP, a homologue (At3g11000) of a protein implicated in somatic embryogenesis in carrot (Schrader et al.,1997), a predicted bifunctional nuclease (At4g21590), a WD-domain protein (At1g47610) and a protein (At1g02190) similar to CER1, which is involved in the synthesis of epicuticular wax and in pollen development(Aarts et al., 1995).
Fig. 3.
Expression levels of selected genes after AGGR activation. (A) Expression detected on the oligonucleotide array. M1 to M7 and D1 to D7 indicate 1, 3 and 7 days after mock treatment and DEX treatment, respectively. The coloured rectangles show normalised mean expression according to the colour scale on the left; the levels are shown only when the difference between mock and DEX treatment was statistically significant. The 12 genes in the grey box showed sustained activation and correspond to the grey area in Fig. 2A. Additional genes with previously characterised roles in stamen or carpel development and with significant activation at day 7 only are also shown. (B) Activation of the 12 genes in the grey box in Fig. 2A, confirmed by RT-PCR (in the case of AG, the primers used did not amplify AGGR). M1-7 and D1-7 are as described in A; APT1(adenosine phosphotransferase) was used as a constitutive control.
Fig. 3.
Expression levels of selected genes after AGGR activation. (A) Expression detected on the oligonucleotide array. M1 to M7 and D1 to D7 indicate 1, 3 and 7 days after mock treatment and DEX treatment, respectively. The coloured rectangles show normalised mean expression according to the colour scale on the left; the levels are shown only when the difference between mock and DEX treatment was statistically significant. The 12 genes in the grey box showed sustained activation and correspond to the grey area in Fig. 2A. Additional genes with previously characterised roles in stamen or carpel development and with significant activation at day 7 only are also shown. (B) Activation of the 12 genes in the grey box in Fig. 2A, confirmed by RT-PCR (in the case of AG, the primers used did not amplify AGGR). M1-7 and D1-7 are as described in A; APT1(adenosine phosphotransferase) was used as a constitutive control.
Activation of all 12 genes in cal-1, ap1-1, AGGR plants was verified by RT-PCR using a new set of RNA samples collected 1, 3 and 7 days after treatment (Fig. 3B). Genes controlled by AG should also be active during stamen or carpel development in wild-type flowers. This has already been shown for AP3, AG,SEP3 and CRC; for other genes in the set, expression was analysed by RNA in situ hybridisation (Fig. 4). At4g21590 was expressed in the centre of the floral meristem,in a pattern similar to that of AG, and continued to be expressed at later stages of stamen development (Fig. 4A,B). At3g17010 and At1g13400 were expressed in emerging stamen primordia and later in part of the developing carpels; expression of At3g17010, but not At1g13400, remained high in the sporogenous tissue of stamens and in the carpel ovary (Fig. 4C-E). Both genes implicated in gibberellin biosynthesis were expressed at very low levels in developing stamens: ATH1 expression was seen in the early organs, while GA4 was only detectable in the stamen filaments (Fig. 4F-H). Expression of At3g11000, At1g47610 and At1g02190 was below detection levels by in situ hybridisation. In all in situ hybridisation experiments, sense control probes showed only uniform background signal (not shown).
Fig. 4.
RNA in situ hybridisation of selected genes during wild-type floral development. (A,B) At4g21590. The arrows show expression in the centre of a stage 3 bud (A), and later in developing stamens (B). (C) At1g13400. Arrows indicate expression in emerging stamen primordia (st), and in the placental region in early carpels (ca). (D,E) At3g17010. Expression in emerging stamen primordia (st) is indicated in D; arrows in E indicate expression in the sporogenous tissue of stamens (st) and in the placental region of carpels(ca). (F) Expression of GA4 in stamen filaments (arrow). (G,H) Expression of ATH1 in developing stamens (st). For better contrast, the sections in A, B, G and H were photographed in aqueous medium, before the tissues were permanently mounted.
Fig. 4.
RNA in situ hybridisation of selected genes during wild-type floral development. (A,B) At4g21590. The arrows show expression in the centre of a stage 3 bud (A), and later in developing stamens (B). (C) At1g13400. Arrows indicate expression in emerging stamen primordia (st), and in the placental region in early carpels (ca). (D,E) At3g17010. Expression in emerging stamen primordia (st) is indicated in D; arrows in E indicate expression in the sporogenous tissue of stamens (st) and in the placental region of carpels(ca). (F) Expression of GA4 in stamen filaments (arrow). (G,H) Expression of ATH1 in developing stamens (st). For better contrast, the sections in A, B, G and H were photographed in aqueous medium, before the tissues were permanently mounted.
### Binding to AG in vitro and in vivo
We next tested whether the 12 genes in the `core' set contained AG binding sites. We scanned sequences upstream of the start codon for the CArG box bound by AG in vitro, TT(A/T/G)CC(A/T)6GG(A/T/C)AA(Shiraishi et al., 1993),accepting a maximum of two nucleotide mismatches, except when the mismatches eliminated either the CC or GG sequences flanking the A/T core. This level of stringency was calibrated using the well-characterised CArG boxes present in the AP3 promoter and in the second intron of AG(Hill et al., 1998; Hong et al., 2003; Tilly et al., 1998). Of the remaining 10 genes, eight had at least one CArG box match within 3 kb upstream of the start codon (Fig. 5A);in all cases, binding to AG was confirmed in vitro(Fig. 5B).
One caveat of detecting AG binding sites is that the frequency of CArG boxes in Arabidopsis genes is high: our search criteria detected at least one match in 49% of 27,186 upstream 3 kb sequences(www.arabidopsis.org/cgi-bin/patmatch/nph-patmatch.pl). The likelihood of finding a match in eight out of ten genes, however, is relatively low (4.8%, assuming binomial distribution and 49% likelihood for any single gene). Thus our subset of 12 genes was enriched for AG binding sites. A comparable enrichment was not seen for the complete set of AG-activated or repressed genes (matches were found in the upstream 3 kb sequences for 61% of the upregulated genes and 56% of downregulated genes),possibly because the complete set includes indirect AG targets.
Another caveat of the in vitro binding results is that multiple MADS domain proteins recognise similar sequences in vitro(Riechmann et al., 1996), so the CArG boxes might be targeted in vivo by MADS domain proteins other than AG. To confirm binding to AG in vivo, we used chromatin immunoprecipitation(ChIP) for a subset of genes of particular interest: AG, AP3, SEP3and CRC (which suggested that AG activated itself and most of the other regulators of stamen and carpel identity); and GA4(which suggested that another role of AG is to promote gibberellin biosynthesis). Fragments of these genes containing the in vitro-detected AG binding sites were enriched in immunoprecipitates obtained with antibodies against AG, but not with an unrelated antibody(Fig. 5C). By contrast,fragments that lacked AG binding sequences, such exon 4 of EIF4A1(Fig. 5C) and exon 7 of AP3 (not shown), were detected to the same background levels with both antibodies. Thus AG interacted in vivo with predicted regulatory sequences of AG, AP3, CRC, SEP3 and GA4.
### AG and AP1 maintain AP3 expression during organogenesis
The activation of AP3 by AG was not predicted by previous genetic and molecular analysis, particularly because AP3 is expressed normally in ag mutants (Jack et al.,1992) (Fig. 6B). This, however, could be due to redundant activation by AP1(Lamb et al., 2002; Ng and Yanofsky, 2001), which is normally repressed by AG in the centre of the floral bud(Gustafson-Brown et al., 1994)and could take over AP3 activation in the innermost organs of ag mutant flowers. To test this idea, we compared AP3expression in the ag-3 mutant, in the ap1-1 mutant and in the double mutant (Fig. 6). In the ag-3 mutant, stamens and carpels are replaced by additional whorls of sepals and petals (Yanofsky et al., 1990) (Fig. 6A). As expected, AP3 expression was readily detected in stage 3 buds and persisted throughout the development of both normal and ectopic petals of the ag-3 mutant(Jack et al., 1992)(Fig. 6B). In the ap1-1 mutant, petals are mostly absent and sepals are replaced by leaf-like organs that often subtend ectopic flowers(Mandel et al., 1992)(Fig. 6C). In this mutant, AP3 expression was normal in stage 3 and continued throughout stamen development (Fig. 6D). Like ag-3, the ag3-3, ap1-1 double mutant flower produced an indeterminate number of organs, which were leaf-like and subtended secondary flowers (Fig. 6E), similar to the first whorl organs of ap1-1. In the double mutant, early AP3 expression showed the normal pattern in both the primary and secondary flowers, while expression in later organ development was abolished(Fig. 6F).
Fig. 6.
Maintenance of AP3 expression requires either AG or AP1. (A,C,E)Top view of inflorescence in ag-3 (A), ap1-1 (C), and in the ag-3, ap1-1 double mutant (E). (B,D,F) RNA in situ hybridisation with the AP3 probe hybridised to longitudinal sections through the inflorescence apex of ag-3 (B), ap1-1 (D), and the ag-3, ap1-1double mutant (F). Arrows point at stage 3 buds, where AP3 expression is initiated, and arrowheads indicate later expression during petal (B) and stamen (D) development. The sections of the three genotypes were hybridised in parallel on the same slides, to allow comparison of the expression levels. Scale bars: 1 mm in A,C,E.
Fig. 6.
Maintenance of AP3 expression requires either AG or AP1. (A,C,E)Top view of inflorescence in ag-3 (A), ap1-1 (C), and in the ag-3, ap1-1 double mutant (E). (B,D,F) RNA in situ hybridisation with the AP3 probe hybridised to longitudinal sections through the inflorescence apex of ag-3 (B), ap1-1 (D), and the ag-3, ap1-1double mutant (F). Arrows point at stage 3 buds, where AP3 expression is initiated, and arrowheads indicate later expression during petal (B) and stamen (D) development. The sections of the three genotypes were hybridised in parallel on the same slides, to allow comparison of the expression levels. Scale bars: 1 mm in A,C,E.
We conclude that early AP3 expression did not require AGor AP1, and was probably due to activation by other regulatory genes,such as LEAFY in combination with UFO(Lamb et al., 2002; Parcy et al., 1998). Maintenance of AP3 expression in later stages of floral development,however, required either AG or AP1.
### Regulators of floral organ identity function in an auto-regulatory module
Positive auto-regulatory loops are a common device to stabilise expression patterns that arise from transient inputs during development(Davidson et al., 2002). Our results suggest that AG, AP3, PI and SEP3 are part of such an auto-regulatory loop: in ap1-1, cal-1 plants, transient AG activation was sufficient to trigger self-maintaining stamen and carpel development, during which AG, AP3, PI and SEP3 were activated; in addition, AG interacted directly with the AG, AP3 and SEP3 genes in vitro and in vivo.
Previously, auto-regulation of floral homeotic genes was known only for AP3 and PI, and their orthologues in snapdragon, DEF/GLO. In early buds, these genes are activated independently of each other, and, where they overlap, a positive-feedback loop is established that maintains their expression during petal and stamen development (Jack et al.,1994; Schwarz-Sommer et al.,1992). Activation of AP3 by AP3/PI is likely to be direct, whereas activation of PI requires an intermediate protein synthesis step (Honma and Goto,2000). In the case of AP3, the auto-regulatory loop is required only in stamens: AP3 expression is still maintained in the sepal-like organs that replace petals in the pi-1 mutant(Jack et al., 1992). This is an important point, because it shows that AP3 expression can be uncoupled from the organ identity directed by AP3/PI, and therefore the absence of AP3 expression in the developing organs of ag-3, ap1-1 double mutants was not a trivial consequence of the fact that these organs were neither petals nor stamens. The requirement of AG to maintain AP3 expression when this role cannot be fulfilled by AP1 supported the idea that AG also participates in AP3/PI regulation.
The co-ordinated regulation of AG, AP3, PI and SEP3 would be expected if, as proposed by recent models, these proteins function together in the same protein complexes (Honma and Goto, 2001; Jack,2001). In particular, if the predicted protein complexes are correct, the AP3/PI auto-regulatory loop should also require either AG or AP1 (which has also been proposed to form a complex with AP3/PI and SEP during petal development)(Honma and Goto, 2001). Our results confirmed this prediction.
However, if AG can only function when complexed with other MADS-domain proteins, then initiation of organogenesis by AGGR must have relied on partner proteins already present in the cal-1, ap1-1 meristems. One possibility is that a low level of AG-independent expression of SEP,AP3 and PI genes provided the required partners. This initial expression could be controlled by the same mechanism that activates these genes independently of each other in early wild-type buds. The need to establish a regulatory loop to amplify initially limiting levels of its partners may be the reason why a single activation of AGGR in cal-1, ap1-1 meristems resulted either in no response, or in robust organogenesis in an apparently random fashion.
In addition to AP3, CRC was strongly activated by AG. This was not expected because of the genetic evidence that CRC can function in the absence of AG. In the ag-1, ap2-2, pi-1triple mutant, in spite of the loss of AG function, the floral organs develop several carpelloid features, such as stigmatic cells and ectopic ovules. In this background, loss of CRC function caused a clear reduction of these carpelloid features, showing that CRC does not require AG to direct carpel development(Alvarez and Smyth, 1999). Our results suggest that although independently activated, CRC expression is reinforced by AG. Previous genetic results suggest that this reinforcement may be mutual: loss of CRC weakens AGfunction, causing the heterozygous ag-1/AG plants, which normally have a wild-type phenotype, to show a partial ag loss-of-function phenotype (Alvarez and Smyth,1999). It remains to be tested whether this occurs because CRC also activates AG, participating in the auto-regulatory loop.
We also saw that, at least in the cal-1, ap1-1 backgound, AG activated its own transcription. This could be inferred independently of the array experiments, from the fact that the endogenous AG was required for organogenesis in cal-1, ap1-1 plants after transient activation of AGGR, and was supported by the chromatin immunoprecipitation results. One difficulty with the idea that AG auto-regulates, however, is that AG is still expressed in the inner organs of ag-1 mutant flowers(Gustafson-Brown et al.,1994). Thus if AG activates itself during normal development, this activity must be redundant. As discussed above, if CRC participates in the AG regulatory loop, then CRC activity might account for the continued AG expression in ag flowers.
Combined with the published data, our results suggest a model for how AG and other floral organ identity genes are coordinately regulated(Fig. 7). In stamen development, AG, AP3, SEP3 and PI are initially expressed independently of each other. Where their expression overlaps, the predicted AG/SEP3/AP3/PI MADS protein complex (Honma and Goto,2001; Jack, 2001)maintains and amplifies their expression. In carpel development, the predicted AG/SEP3 complex may establish a similar feedback loop, which also reinforces CRC expression.
Fig. 7.
Model for the co-ordinated regulation of floral organ identity regulators.(A) In stamen development, AG, AP3, PI and SEP3 are initially activated independently (grey arrows)(Ferrario et al., 2004; Zik and Irish, 2003a). LFY is responsible for the initial activation of AG, whereas early activation of AP3/PI occurs in areas of the meristem that express both LFY and UFO (Parcy et al.,1998). The AG, AP3, PI and SEP3 proteins (circles) function together in a complex to promote stamen development(Honma and Goto, 2001), and to amplify and maintain their own expression. Solid black arrows indicate direct interactions supported by ChIP; feedback activation of PI may be indirect(dashed arrow) (Honma and Goto,2000). (B) The protein complex proposed to control carpel development contains AG and SEP3 (Honma and Goto, 2001). As in A, the initially independent expression of AG and SEP3 is maintained by a positive-feedback loop. In addition, CRC expression is reinforced, although CRC expression can promote carpel development independently of AG (indicated by the parallel grey arrow)(Alvarez and Smyth, 1999). As in A, interactions supported by ChIP are indicated by solid black arrows. The possibility that CRC might also promote AG activity is indicated by the dashed arrow with a question mark.
Fig. 7.
Model for the co-ordinated regulation of floral organ identity regulators.(A) In stamen development, AG, AP3, PI and SEP3 are initially activated independently (grey arrows)(Ferrario et al., 2004; Zik and Irish, 2003a). LFY is responsible for the initial activation of AG, whereas early activation of AP3/PI occurs in areas of the meristem that express both LFY and UFO (Parcy et al.,1998). The AG, AP3, PI and SEP3 proteins (circles) function together in a complex to promote stamen development(Honma and Goto, 2001), and to amplify and maintain their own expression. Solid black arrows indicate direct interactions supported by ChIP; feedback activation of PI may be indirect(dashed arrow) (Honma and Goto,2000). (B) The protein complex proposed to control carpel development contains AG and SEP3 (Honma and Goto, 2001). As in A, the initially independent expression of AG and SEP3 is maintained by a positive-feedback loop. In addition, CRC expression is reinforced, although CRC expression can promote carpel development independently of AG (indicated by the parallel grey arrow)(Alvarez and Smyth, 1999). As in A, interactions supported by ChIP are indicated by solid black arrows. The possibility that CRC might also promote AG activity is indicated by the dashed arrow with a question mark.
### Interaction between AG and gibberellin
A link between gibberellin and homeotic genes has been shown previously via regulation of LEAFY (LFY), which activates homeotic genes in the early stages of floral development(Blazquez et al., 1998). More recently, gibberellin has been reported to activate floral homeotic genes at later stages of development, when LFY is no longer active(Yu et al., 2004). Our results suggest that the reverse is also true, that is, homeotic genes positively regulate the gibberellin pathway. GA4 is part of a small family of genes that encode GA3-β-hydroxylases, which catalyse the last step in the biosynthesis of gibberellin and have a regulatory role in the pathway(Hedden and Phillips, 2000; Itoh et al., 1999; Talon et al., 1990), so GA4 activation suggested that AG induced gibberellin biosynthesis during organogenesis.
Activation of GA4 by AG may be another branch of the homeotic gene autoregulatory loop. There may be, however, additional functions for gibberellin in floral organogenesis. Another gibberellin biosynthetic gene, encoding GA20-oxidase, is repressed by genes that maintain undifferentiated cells in the meristem, and activated in the leaf primordia that emerge from the meristem (Hay et al.,2002; Sakamoto et al.,2001). This suggests that gibberellin may have a more general role in the transition from meristem identity to organogenesis. This idea seems inconsistent with the fact that organ emergence is normal in gibberellin-deficient mutants, both during the vegetative phase and in flowers(the floral defects in ga1-3 become visible only at later stages of development) (Goto and Pharis,1999; Wilson et al.,1992). However, even severe mutants such as ga1-3, still produce low levels of gibberellin (Hedden and Phillips, 2000), which might be sufficient for the proposed functions in early organ development. Although it is not clear what these functions might be, the known role of gibberellin in controlling cell growth and division (Yang et al.,1996) suggests that it might play a role in the localised changes in growth that drive the emergence of organ primordia from the meristem. If this is true in the floral organ primordia, then gibberellin could be part of the link between homeotic genes and the cellular behaviour that shapes floral organs.
### Global view of gene expression in stamen and carpel primordia
From the predicted protein functions of the 149 genes that were upregulated by AG, two prominent features emerged (Fig. 2). First, genes expected to function in transcriptional control were over-represented (26%), compared with their total frequency in the genome(5.9%) (Riechmann and Ratcliffe,2000). The fraction of regulatory genes increased over the time course from 13% (day 1) to 28% (day 3) to 34% (day 7). This contrasts with more mature organs, where the frequency of regulatory genes was 5.5%, similar to their representation in the genome(Wellmer et al., 2004), and suggests that up to 7 days after organ initiation much of the program of gene expression downstream of AG was concerned with refining patterns of gene expression. Complex cascades of transcription factors, as seen in early development of Drosophila and sea urchin, also cause delayed responses to initial inputs and have been proposed to function as timing devices during development (Rosenfeld and Alon, 2003).
Second, of the 36 predicted DNA-binding proteins that were upregulated at day 7, 53% belonged to two transcription factor families (10 B3 domain, PFAM profile PF02362, and 9 MADS domain, PF00319). MADS domain proteins play a prominent role in floral development and the diversification of this family correlates with the evolution of plant reproductive structures(Theissen et al., 2000). Our data suggests that the B3 domain family has undergone a comparable diversification of roles in reproductive development.
Developmental genetics has identified many regulatory genes whose expression determines where and when a specific structure or organ develops. The problem of understanding how regulatory gene expression is translated into complex multicellular structures is universal, and has led to a number of attempts to describe the gene expression programs controlled by these regulators (Furlong et al.,2001; Livesey et al.,2000; Michaut et al.,2003). Like other global descriptions of changes in gene expression during development, however, our view of gene expression under AG has two limitations. First, it is unlikely to be complete, because we cannot guarantee that genes with very low or localised expression were not missed,and because of the difficulties associated with detecting downregulation if it occurs only in a subset of the cells. Second, the set of genes controlled by AG probably cannot be organised within a single network of interactions,because they may represent the overlap of multiple programs of gene expression that run in parallel in different regions and cell types of organ primordia.
In spite of these limitations, the list of genes controlled by AG will provide a basis for the functional analysis of intermediate regulators of early organogenesis, and will provide target promoters that are needed to test current models for the molecular basis of how homeotic genes act combinatorially.
We thank James Hadfield (JIC) for help with the Affymetrix chip experiments and John Walshaw (JIC) for bioinformatics help. C.G.-M. was funded by a Marie-Curie fellowship (QLK5-CT-2001-52), M.M.R.C. received a fellowship from the FCT, Portugal (SFRH/BPD/3604/2000), S.d.F. was supported by the Netherlands Proteomics Centre (NPC) and R.S. received a grant from the Biotechnology and Biological Sciences Research Council (BBS/B/04234).
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http://dosamobile.com/Rationing/
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# When too little is as good as nothing at all
When too little is as good as nothing at all
We study the problem of rationing a divisible good among a group of people. Each person’s preferences are characterized by an ideal amount that he would prefer to receive and a minimum quantity that he will accept: any amount less than this threshold is just as good as receiving nothing at all. Any amount beyond his ideal quantity has no effect on his welfare.
We search for Pareto-efficient, strategy-proof, and envy-free rules. The definitions of these axioms carry through from the more commonly studied problem without disposability or acceptance thresholds. However, these are not compatible in the model that we study. We adapt the equal-division lower bound axiom and propose another fairness axiom called awardee-envy-freeness. Unfortunately, these are also incompatible with strategy-proofness. We characterize all of the the Pareto-efficient rules that satisfy these two properties. We also characterize all Pareto-efficient, strategy-proof, and non-bossy rules.
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http://en.wikipedia.org/wiki/Dense_graph
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# Dense graph
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges. The opposite, a graph with only a few edges, is a sparse graph. The distinction between sparse and dense graphs is rather vague, and depends on the context.
For undirected simple graphs, the graph density is defined as:
$D = \frac{2|E|}{|V|\,(|V|-1)}$
The maximum number of edges is ½ |V| (|V|−1), so the maximal density is 1 (for complete graphs) and the minimal density is 0 (Coleman & Moré 1983).
## Upper density
Upper density is an extension of the concept of graph density defined above from finite graphs to infinite graphs. Intuitively, an infinite graph has arbitrarily large finite subgraphs with any density less than its upper density, and does not have arbitrarily large finite subgraphs with density greater than its upper density. Formally, the upper density of a graph G is the infimum of the values α such that the finite subgraphs of G with density α have a bounded number of vertices. It can be shown using the Erdős–Stone theorem that the upper density can only be 1 or one of the superparticular ratios 0, 1/2, 2/3, 3/4, 4/5, ... n/(n + 1), ... (see, e.g., Diestel, p. 189).
## Sparse and tight graphs
Lee & Streinu (2008) and Streinu & Theran (2009) define a graph as being (k,l)-sparse if every nonempty subgraph with n vertices has at most kn − l edges, and (k,l)-tight if it is (k,l)-sparse and has exactly kn − l edges. Thus trees are exactly the (1,1)-tight graphs, forests are exactly the (1,1)-sparse graphs, and graphs with arboricity k are exactly the (k,k)-sparse graphs. Pseudoforests are exactly the (1,0)-sparse graphs, and the Laman graphs arising in rigidity theory are exactly the (2,3)-tight graphs.
Other graph families not characterized by their sparsity can also be described in this way. For instance the facts that any planar graph with n vertices has at most 3n - 6 edges, and that any subgraph of a planar graph is planar, together imply that the planar graphs are (3,6)-sparse. However, not every (3,6)-sparse graph is planar. Similarly, outerplanar graphs are (2,3)-sparse and planar bipartite graphs are (2,4)-sparse.
Streinu and Theran show that testing (k,l)-sparsity may be performed in polynomial time when k and l are integers and 0 ≤ l < 2k.
## Sparse and dense classes of graphs
Ossona de Mendez & Nešetřil (2010) considered that the sparsity/density dichotomy makes it necessary to consider infinite graph classes instead of single graph instances. They defined somewhere dense graph classes as those classes of graphs for which there exists a threshold t such that every complete graph appears as a t-subdivision in a subgraph of a graph in the class. To the contrary, if such a threshold does not exist, the class is nowhere dense. Properties of the nowhere dense vs somewhere dense dichotomy are discussed in Ossona de Mendez & Nešetřil (2012).
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https://www.targetmathematics.com/2020/06/g10-chap4-domain-and-range-of-function-exercise-4-3-solutions.html
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# Domain and Range of a Function - Exercise (4.3) :Solutions
#### How to Determine the Domain of a Function
When the domain of a function is not specified, then assume that it is the set of all possible real numbers for which the function makes sense.
ပေးထားသော function တစ်ခုအတွက် domain သတ်မှတ်ပေးထားခြင်း မရှိလျှင် function ၏ သတ်မှတ်ချက်ကို ပြေလည်စေသော အစုဝင်အားလုံးပါသည် ကိန်းစစ်အစုသည် အဆိုပါ function ၏ domain ဖြစ်သည်ဟု မှတ်ယူရမည်။
#### Equality of Functions
Two functions $f$ and $g$ are equal (and we write $f=g$) if and only if
1. $f$ and $g$ have the same domain, and
2. $f(c)$ = $g(c)$ for each element $c$ in the domain.
Function နှစ်ခု $f$ နှင့် $g$ ၏ domain များတူညီကြပြီး domain ထဲရှိ အစုဝင် $c$ တိုင်းအတွက် $f(c)= g(c)$ [$c$ ၏ image တူညီလျှင်] ဖြစ်လျှင် $f$ နှင့် $g$ သည် တူညီသော function များ ဖြစ်ကြသည်။
1. Determine whether each relation is a function or not. If it is a function, state the domain and range.
Show/Hide Solution
$\begin{array}{ll} \text{(a)} & \text{The relation}\ R\ \text{is a function.}\\\\ & \text{dom}\ (R ) = \{-1, 0, 1\}\\\\ & \text{ran}\ (R) = \{0, 1\}\\\\ \text{(b)} & \text{The relation}\ R\ \text{is not a function.}\\\\ \text{(c)} & \text{The relation}\ R\ \text{is not a function.} \end{array}$
2. Consider the following relations. Determine whether each relation is a function or not. If it is a function, write down the domain and range.
$\begin{array}{l} \text{(a)}\ \ \{(1,3),(2,5),(3,7),(4,9)\} \\\\ \text{(b)}\ \ \{(-2,5),(-1,3),(0,1),(-1,1)\}\\\\ \text{(c)}\ \ \{(1,3),(2,3),(3,2),(2,1)\} \\\\ \text{(d)}\ \ \{(2,4),(3,6),(4,6),(7,14)\} \\\\ \text{(e)}\ \ \{(0,0),(1,1),(3,3),(4,4)\} \\\\ \text{(f)}\ \ \{(2, a),(4, c),(5, a),(4, e)\} \end{array}$
Show/Hide Solution
$\begin{array}{l}\text{(a)}\;\;\{(1,3),(2,5),(3,7),(4,9)\}\\\ \ \ \ \ \text{The given relation is a function because }\\\ \ \ \ \ \text{each element of domain is related}\\\ \ \ \ \ \text{to exactly one element}\text{.}\\\ \ \ \ \ \text{Domain}=\{1,\ 2,\ 3,\ 4\}\\\ \ \ \ \ \text{Range}=\{3,\ 5,\ 7,\ 9\}\\\\\text{(b)}\;\;\{(-2,5),(-1,3),(0,1),(-1,1)\}\\\ \ \ \ \ \text{The given relation is not}\ \text{a function}\ \text{because }\\\ \ \ \ \ \text{the element }-\text{1 of domain is related to two}\\\ \ \ \ \ \text{elements 3 and 1}\text{.}\\\\\text{(c)}\;\;\{(1,3),(2,3),(3,2),(2,1)\}\\\ \ \ \ \ \text{The given relation is not}\ \text{a function}\ \text{because }\\\ \ \ \ \ \text{the element }2\text{ of domain is related to two}\\\ \ \ \ \ \text{elements 3 and 1}\text{.}\\\\\text{(d)}\;\;\{(2,4),(3,6),(4,6),(7,14)\}\\\ \ \ \ \ \text{The given relation is a function because }\\\ \ \ \ \ \text{each element of domain is related}\\\ \ \ \ \ \text{to exactly one element}\text{.}\\\ \ \ \ \ \text{Domain}=\{2,\ 3,\ 4,\ 7\}\\\ \ \ \ \ \text{Range}=\{4,\ 6,\ 14\}\\\\\text{(e)}\;\;\{(0,0),(1,1),(3,3),(4,4)\}\\\ \ \ \ \ \text{The given relation is a function because }\\\ \ \ \ \ \text{each element of domain is related}\\\ \ \ \ \ \text{to exactly one element}\text{.}\\\ \ \ \ \ \text{Domain}=\{0,\ 1,\ 3,\ 4\}\\\ \ \ \ \ \text{Range}=\{0,\ 1,\ 3,\ 4\}\\\\\text{(f)}\;\;\{(2,a),(4,c),(5,a),(4,e)\}\\\ \ \ \ \ \text{The given relation is not}\ \text{a function}\ \text{because }\\\ \ \ \ \ \text{the element }4\text{ of domain is related to two}\\\ \ \ \ \ \text{elements }c\text{ and }e\text{.}\end{array}$
3. Let $f$ be a function from $\mathbb{R} \rightarrow \mathbb{R}$. Which of the following statements are true?
(a) If $f(x)=5-x,$ the image of -3 under $f$ is 8.
(b) If $f(x)=x^{2}+9,$ the image of -3 under $f$ is zero.
(c) If $f(x)=3 x+4,$ then $f(a)=a$ implies that $a=-2$.
(d) If $f(x)=x+3,$ there is only one value $a \in \mathbb{R}$ such that $f(a)=0$.
(e) If $f(x)=x^{2}-1,$ then there are exactly two values $a \in \mathbb{R}$ such that $f(a)=0$.
Show/Hide Solution
$\begin{array}{l}\ \ \ \ \ \ \ \ f:\mathbb{R}\to \mathbb{R}\\\\\text{(a)}\ \ f(x)=5-x\\\ \ \ \ \ f(-3)=5-(-3)=8\\\ \ \ \ \ \therefore \ \text{ The statements is true}\text{.}\\\\\text{(b)}\ \ f(x)={{x}^{2}}+9\\\ \ \ \ \ f(-3)={{(-3)}^{2}}+9=18\\\ \ \ \ \ \therefore \ \text{ The statements is false}\text{.}\\\\\text{(c)}\ \ f(x)=3x+4\\\ \ \ \ \ f(a)=a\\\ \ \ \ \ 3a+4=a\\\ \ \ \ \ 2a=-4\\\ \ \ \ \ a=-2\\\ \ \ \ \ \therefore \ \text{ The statements is true}\text{.}\\\\\text{(d)}\ \ f(x)=x+3\\\ \ \ \ \ f(a)=0\\\ \ \ \ \ a+3=0\\\ \ \ \ \ a=-3\\\ \ \ \ \ \therefore \ \text{ The statements is true}\text{.}\\\\\text{(e)}\ \ f(x)={{x}^{2}}-1\\\ \ \ \ \ f(a)=0\\\ \ \ \ \ {{a}^{2}}-1=0\\\ \ \ \ \ {{a}^{2}}=1\\\ \ \ \ \ a=\pm 1\\\ \ \ \ \ \therefore \ \text{ The statements is true}\text{.}\end{array}$
4. Illustrate the function $f: x \mapsto x+2$ with an arrow diagram for the domain $\{3,5,7,9,10\} .$ Write down the range of $f$.
Show/Hide Solution
$\begin{array}{l}\ \ \ f:x\mapsto x+2\\\\\ \ \ \therefore \ f(x)=x+2\\\\\ \ \ \operatorname{dom}(f)=\{3,5,7,9,10\}\\\\\ \ \ f(3)=3+2=5\\\\\ \ \ f(5)=5+2=7\\\\\ \ \ f(7)=7+2=9\\\\\ \ \ f(9)=9+2=11\\\\\ \ \ f(10)=10+2=12\\\\\ \ \ \operatorname{ran}(f)=\{5,7,9,11,12\}\end{array}$
5. Let the domain of function $h: x \mapsto 0$ be $\{2,4,6,7\} .$ What is the range of $h ?$ Draw an arrow diagram for $h$.
Show/Hide Solution
$\begin{array}{l}h:x\mapsto 0\\\\\operatorname{dom}(h)=\{2,4,6,7\}\\\\\therefore \ \ h:2\mapsto 0\\\\\ \ \ h:4\mapsto 0\\\\\ \ \ h:6\mapsto 0\\\\\ \ \ h:7\mapsto 0\\\\\operatorname{ran}(h)=\{0\}\end{array}$
6. Let the domain of function $f: x \mapsto 3 x$ be the set of natural numbers less than $5 .$ State the domain and range.
Show/Hide Solution
$\begin{array}{l} f:x\mapsto 3x\\\\ \operatorname{dom}(f)=\text{the set of natural numbers less}\ \text{than 5}\text{.}\\\\ \operatorname{dom}(f)=\{1,\ 2,\ 3,\ 4\}\\\\ f:1\mapsto 3(1)=3\\f:2\mapsto 3(2)=6\\\\ f:3\mapsto 3(3)=9\\f:4\mapsto 3(4)=12\\\\ \operatorname{ran}(f)=\{3,\ 6,\ 9,\ 12\}\ end{array}$
7. Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be given by
(a) $g(x)=3-4 x$ .Find $g(1), \quad g(3), \quad g(-2), \quad g(x+3), \quad g\left(\displaystyle \frac{1}{2}\right).$
(b) $g(x)=2 x-5 .$ Find $g(3), g\left(\displaystyle\frac{1}{2}\right), g(0), g(-4), g(4) .$ If $g(a)=99,$ find $a$.
(c) $g(x)=\displaystyle\frac{x+5}{2} .$ Find the images of $3,0,-3 .$ Find $x$ if $g(x)=0$.
(d) $g(x)=3 x-1 .$ Find $x$ such that $g(x)=20$.
Show/Hide Solution
$\begin{array}{ll} \text{(a)} & g(x) = 3-4x\\ & g(1) = 3-4(1) = -1\\ & g(3) = 3-4(3) = -9\\ & g(-2) = 3-4(-2) = 11\\ & g(x+3) = & 3-4(x+3) = -4x-9\\ & g \left({\displaystyle\frac{1}{2}} \right) = 3- 4\left(\displaystyle\frac{1}{2}\right) = 1\\\\ \text{(b)} & g(x) = 2x-5\\ & g(3) = 2(3)-5 = 1\\ & g \left(\displaystyle\frac{1}{2}\right) = 2 \left(\displaystyle\frac{1}{2}\right)-5 = -4\\ & g(0) = 2(0)-5 = -5\\ & g(-4) = 2(-4)-5 = -13\\ & g(4) = 2(4)-5 = 3\\\\ & g(x) = 0\\ & 2x-5 = 0\\ & x = \displaystyle\frac{5}{2}\\\\ \text{(c)} & g(x) = \displaystyle\frac{x+5}{2}\\ & g(3) = \displaystyle\frac{3+5}{2} = 4\\ & g(0) = \displaystyle\frac{0+5}{2} = \displaystyle\frac{5}{2}\\ & g(-3) = \displaystyle\frac{-3+5}{2} = 1\\\\ \text{(d)} & g(x) = 3x-1\\ & g(x) = 20\\ & 3x-1 = 20\\ & x = 7 \end{array}$
8. A function $f$ from $A$ to $A$, where $A$ is the set of positive integers, is given by $f(x)=$ the sum of all possible divisors of $x$.
For example $f(6)=1+2+3+6=12$
(a) Find the values of $f(2), f(5), f(13), f(18)$.
(b) Show that $f(14)=f(15)$ and $f(3) \cdot f(5)=f(15)$.
Show/Hide Solution
$\begin{array}{l}f(x)=\text{the sum of all possible divisors of }x\\\\f(2)=1+2=3\\\\f(5)=1+5=6\\\\f(13)=1+13=14\\\\f(15)=1+3+5+15=24\\\\f(14)=1+2+7+14=24\\\\\therefore \ f(15)=f(14)\\\\f(3)=1+3=4\\\\f(3)\cdot f(5)=4\times 6=24\\\\\therefore \ f(3)\cdot f(5)=f(15)\end{array}$
9. Let $A=$ the set of positive integers greater than 3 and $B=$ the set of all positive integers. Let $d: A \rightarrow B$ be a function given by $d(n)=\frac{1}{2} n(n-3)$ the number of diagonals of a polygon of $n$ sides.
(a) Find $d(6), d(8), d(10), d(12)$.
(b) How many diagonals will a polygon of 20 sides have?
Show/Hide Solution
$\begin{array}{l}\text{(a)}\ \ \ \ A=\text{ the set of positive integers greater than 3}\\\\\ \ \ \ \ \ \ A=\{4,\ 5,\ 6,\ ...\}\\\\\ \ \ \ \ \ \ B=\text{ the set of positive all integers }\\\\\ \ \ \ \ \ \ B=\{1,\ 2,\ 3,\ ...\}\\\\\ \ \ \ \ \ \ d:A\to B\ \\\\\ \ \ \ \ \ d(n)=\displaystyle \frac{1}{2}n(n-3)\\\\\ \ \ \ \ \ d(6)=\displaystyle \frac{1}{2}\cdot 6\cdot (6-3)=9\\\\\ \ \ \ \ \ d(8)=\displaystyle \frac{1}{2}\cdot 8\cdot (8-3)=20\\\\\ \ \ \ \ \ d(10)=\displaystyle \frac{1}{2}\cdot 10\cdot (10-3)=35\\\\\ \ \ \ \ \ d(12)=\displaystyle \frac{1}{2}\cdot 12\cdot (12-3)=54\\\\\text{(b)}\ \ \ d(20)=\displaystyle \frac{1}{2}\cdot 20\cdot (20-3)=170\end{array}$
10. Determine whether $f$ and $g$ are equal functions or not. Give reason:
(a) $f(x)=x^{2}+2,\ g(x)=(x+2)^{2}$.
(b) $f(x)=x^{2},\ g(x)=|x|^{2}$.
(c) $f(x)=\displaystyle\frac{x^{2}-1}{x+1},\ g(x)=x-1$.
(d) $f(x)=\displaystyle\frac{x+2}{x^{2}-4},\ g(x)=\frac{1}{x-2}$.
Show/Hide Solution
$\begin{array}{l} \text{(a)}\ \ f(x)={{x}^{2}}+2,\;g(x)={{(x+2)}^{2}}\\ \ \ \ \ \ \operatorname{dom}(f)=\mathbb{R},\ \operatorname{dom}(g)=\mathbb{R}\\ \,\,\,\ \ \ f(1)={{1}^{2}}+2=3\\\ \ \ \ \ g(1)={{(1+2)}^{2}}=9\\ \ \ \ \ \ \therefore \ \operatorname{ran}(f)\ne \operatorname{ran}(g)\\ \ \ \ \ \ \therefore \ f\ne g\\\\ \text{(b)}\ \ f(x)={{x}^{2}},\;g(x)=|x{{|}^{2}}\\ \ \ \ \ \ \operatorname{dom}(f)=\mathbb{R},\ \operatorname{dom}(g)=\mathbb{R}\\ \,\,\,\ \ \ \operatorname{ran}(f)=\{x\ |\ x\ge 0,\ x\in \mathbb{R}\}\\ \,\,\,\ \ \ \operatorname{ran}(g)=\{x\ |\ x\ge 0,\ x\in \mathbb{R}\}\\ \ \ \ \ \ \therefore \ \operatorname{dom}(f)=\operatorname{dom}(g)\ \ \text{and }\operatorname{ran}(f)=\operatorname{ran}(g)\\ \ \ \ \ \ \therefore \ f=g\\\\ \text{(c)}\ \ f(x)=\displaystyle \frac{{{{x}^{2}}-1}}{{x+1}},\;g(x)=x-1\\ \ \ \ \ f(x)\ \text{exists only when }x+1\ne 0,\ \text{i}\text{.e,}\ x\ne -1\\ \ \ \ \ \ \operatorname{dom}(f)=\mathbb{R}\smallsetminus \{-1\},\ \operatorname{dom}(g)=\mathbb{R}\\ \ \ \ \ \ \therefore \ \operatorname{dom}(f)\ne \operatorname{dom}(g)\\ \ \ \ \ \ \therefore \ f\ne g\\\\ \text{(d)}\ \ f(x)=\displaystyle \frac{{x+2}}{{{{x}^{2}}-4}},\;g(x)=\displaystyle \frac{1}{{x-2}}\\ \ \ \ \ \ f(x)\ \text{exists only when }\\ \,\ \ \ \ {{x}^{2}}-4\ne 0\\ \ \ \ \ \ {{x}^{2}}\ne 4\\ \ \ \ \ \ \therefore x\ne \pm \ 2\\ \ \ \ \ \ \therefore \ \ \operatorname{dom}(f)=\mathbb{R}\smallsetminus \{\pm \ 2\}\\ \ \ \ \ \ g(x)\ \text{exists only when }\\ \,\ \ \ \ x-2\ne 0\\\ \ \ \ \ x\ne 2\\ \ \ \ \ \ \therefore \ \operatorname{dom}(g)=\mathbb{R}\smallsetminus \{2\}\\ \ \ \ \ \ \therefore \ \operatorname{dom}(f)\ne \operatorname{dom}(g)\\ \ \ \ \ \ \therefore \ f\ne g\end{array}$
11. State the domain of the following functions.
(a) $f(x)=\sqrt{x-2}$.
(b) $f(x)=\displaystyle\frac{1}{2 x-1}$.
(c) $f(x)=\displaystyle\frac{4}{x-3}$.
(d) $f(x)=\displaystyle\frac{2}{x^{2}-1}$.
Show/Hide Solution
$\begin{array}{l}\text{(a)}\ \ f(x)=\sqrt{{x-2}}\\\ \ \ \ \ f(x)\ \text{exists only when}\\\ \ \ \ \ x-2\ge 0\\\ \ \ \ \ \text{i}\text{.e}\text{.,}\ \ x\ge 2\\\ \ \ \ \ \therefore \ \ \operatorname{dom}(f)=\{x\ |\ x\ge 2,\ x\in \mathbb{R}\}\\\\\text{(b)}\ \ f(x)=\displaystyle \frac{1}{{2x-1}}\\\ \ \ \ \ f(x)\ \text{exists only when}\\\ \ \ \ \ 2x-1\ne 0\\\ \ \ \ \ \text{i}\text{.e}\text{.,}\ \ x\ne \displaystyle \frac{1}{2}\\\ \ \ \ \ \therefore \ \ \operatorname{dom}(f)=\{x\ |\ x\ne \displaystyle \frac{1}{2},\ x\in \mathbb{R}\}\\\\\text{(c)}\ \ f(x)=\displaystyle \frac{4}{{x-3}}\\\ \ \ \ \ f(x)\ \text{exists only when}\\\ \ \ \ \ x-3\ne 0\\\ \ \ \ \ \text{i}\text{.e}\text{.,}\ \ x\ne 3\\\ \ \ \ \ \therefore \ \ \operatorname{dom}(f)=\{x\ |\ x\ne 3,\ x\in \mathbb{R}\}\\\\\text{(d)}\ \ f(x)=\displaystyle \frac{2}{{{{x}^{2}}-1}}\\\ \ \ \ \ f(x)\ \text{exists only when }\\\,\ \ \ \ {{x}^{2}}-1\ne 0\\\ \ \ \ \ \text{i}\text{.e}\text{.,}\ {{x}^{2}}\ne 1\\\ \ \ \ \ \therefore x\ne \pm \ 1\\\ \ \ \ \ \therefore \ \ \operatorname{dom}(f)=\{x\ |\ x\ne \pm \ 1,\ x\in \mathbb{R}\}\end{array}$
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https://worldwidescience.org/topicpages/i/inverting+membrane+scintillator.html
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Sample records for inverting membrane scintillator
1. Inverted-conical light guide for crosstalk reduction in tightly-packed scintillator matrix and MAPMT assembly
DEFF Research Database (Denmark)
Chang, Y.-Y.; Chen, P.; Huang, J.-J.
2015-01-01
and explained it as a consequence of the total reflection produced by the photocathode. The result indicated that the crosstalk mechanism could be a common case in most of the contact-assembled scintillation detectors. The concept of the Inverted-Conical light guide was to suppress the total reflection......In this paper we present the Inverted-Conical light guide designed for optical crosstalk reduction in the scintillator-MAPMT assemblies. The research was motivated by the 30% crosstalk observed in UFFO X-ray telescope, UBAT, during the preliminary calibration with MAPMTs of 64 2.88 × 2.88 mm2...... by contracting the incident angle of the scintillation. We optimized the design in the simulation and fabricated a test sample. The test sample reduced 52% crosstalk with a loss of 6% signal yield. The idea of the Inverted-Conical light guide can be adapted by scintillation detectors multi-pixel, imaging...
2. Pore-Filled Scintillating Membrane as Sensing Matrix for α-Emitting Actinides.
Science.gov (United States)
Chavan, Vivek; Agarwal, Chhavi; Pandey, A K
2016-04-05
Pore-filled membranes with scintillating properties have been synthesized for sensing α-emitting radionuclides. The membranes have been prepared by in situ UV-initiator-induced polymerization of monomer bis[2-(methacryloxy)ethyl] phosphate in pores of the host membranes, poly(propylene) and poly(ethersulfone). The polymerization has been carried out in the presence of scintillating molecules, 2,5-diphenyloxazole. These scintillating molecules are physically trapped in the thus formed microgel in the membrane. Much higher α-scintillation efficiency has been obtained for the (241)Am-loaded poly(ethersulfone)-based grafted membrane compared to poly(propylene)-based membrane. This was attributed to the aromatic backbone of the poly(ethersulfone) membrane. The scintillation response of poly(ethersulfone)-based membranes has been found to be linear over the range of (241)Am activity studied. The pore-filled scintillating membranes have been found to be selective toward Pu(4+) ions at higher HNO3 concentration compared to Am(3+). The analytical performance of the pore-filled scintillating membranes has been evaluated. The membranes have been found to be stable and reusable. The scintillating membrane with optimized composition has been applied for quantification of Pu in a soil sample.
3. Development and Performance of a Thin Membrane Scintillator Containment Vessel for a Solar Neutrino Detector
Science.gov (United States)
Vogelaar, R. B.; Benziger, J. B.; Calaprice, F. P.; Chen, M.; Darnton, N.; Johnson, M.; Loeser, F.
1996-10-01
The Borexino solar neutrino experiment will detect neutrino-electron scattering interactions in a large mass (300 tons) of an organic solvent-based liquid scintillator. Requirements for the scintillator containment vessel include optical clarity, chemical resistance to the scintillator, ultra-low radioactivity and mechanical strength. These requirements are met in a thin membrane design utilizing a nylon copolymer C38F, manufactured by the Miles-Mobay Corporation. For the Borexino Counting Test Facility, a 2 meter diameter nylon sphere was constructed and used. Its performance will be discussed and the status of the development of an 8.5 meter diameter sphere for the Borexino detector will be presented.
4. INVERTED INTERNAL LIMITING MEMBRANE FLAP TECHNIQUE FOR MACULAR HOLE SURGERY WITHOUT EXTRA MANIPULATION OF THE FLAP.
Science.gov (United States)
Casini, Giamberto; Mura, Marco; Figus, Michele; Loiudice, Pasquale; Peiretti, Enrico; De Cillà, Stefano; Fuentes, Taiusha; Nasini, Francesco
2017-11-01
To determine whether surgical manipulation steps of the internal limiting membrane (ILM) flap, such as ILM trimmed, ILM tuck inside the hole, ILM massage, are mandatory to obtain satisfactory outcomes for the repair of large stage IV idiopathic macular hole using the inverted ILM flap technique. In this interventional comparative prospective single-masked study, 81 eyes were randomized into 2 treatments groups. In Group 1 (41 eyes), the classic inverted ILM flap technique was performed. In Group 2 (40 eyes), a modified procedure was used: after ILM peeling, no extra flap manipulation was performed. The macular hole was covered by the inverted ILM flap because of the air pressure at the time of the fluid-air exchange. At 12 months, macular hole closure was observed in 40 eyes (97.6%) in Group 1 and in 39 eyes in Group 2 (97.5%). U-shape closure rate, ellipsoid zone defects, and external limiting membrane defects were similar in both groups. The results indicate no statistical difference in anatomical and functional success between both groups. The macular hole closure rate, improved visual acuity, and no extra complications indicate noninferiority of the modified inverted ILM technique. Internal limiting membrane finishing, tucking, and massage may not be required to obtain surgical success.
5. Interaction between plasticized polyvinyl chloride waterproofing membrane and extruded polystyrene board, in the inverted flat roof
Directory of Open Access Journals (Sweden)
Pedrosa, A.
2014-12-01
Full Text Available The inverted flat roof is a constructive system widely used in flat roof construction. In this constructive solution, the insulation is placed over the waterproofing material as a protection. It is believed that this solution provides a longer life cycle; given the fact that it limits the thermal variation the waterproofing material bears up to the end of its life cycle. Consequently, the result will be providing a longer life to the waterproofing membrane. This constructive solution always incorporates polymers or other materials with a thermoplastic addition in their composition. Some polymers show interactions between them that can affect their integrity, and, at the same time, the bulk of the polymeric materials are incompatible. The extruded polystyrene board is always present in the inverted flat roof, and although it is an unbeatable product for this use, it presents incompatibilities and interactions with other materials, and these can affect their properties and therefore the durability of them.La cubierta plana invertida es un sistema constructivo muy utilizado en las cubiertas planas. En esta solución constructiva, el aislamiento se coloca sobre el material impermeabilizante a modo de protección. Se cree que esta solución proporciona un ciclo de vida más largo; dado que se limita la variación térmica de la impermeabilización hasta el final de su ciclo de vida. En consecuencia, el resultado proporciona una vida más larga a la membrana impermeable. Esta solución constructiva siempre incorpora polímeros u otros materiales con adición termoplástica en su composición. Algunos polímeros muestran interacciones entre ellos que pueden afectar a su integridad, además, la mayor parte de los materiales poliméricos son incompatibles. La plancha de poliestireno extrusionado está siempre presente en la cubierta plana invertida, y aunque es un producto inmejorable para este uso, presenta incompatibilidades e interacciones con otros
6. [Observation of single-layered inverted internal limiting membrane flap technique for macular hole with retinal detachment in high myopia].
Science.gov (United States)
Xu, C Z; Wu, J H; He, J W; Feng, C
2017-05-11
Objective: To compare the outcome of pars plana vitrectomy (PPV) with a single-layered inverted internal limiting membrane (ILM) flap versus PPV with ILM peeling for the treatment of macular hole associated retinal detachment (MHRD) in high myopia. Methods: In a retrospective cohort study, PPV with 2 kinds of adjuvant surgical procedures were used in 35 moderately high myopia eyes with MHRD. These eyes were divided into 2 groups: group 1 (17 eyes) receiving PPV and ILM peeling and group 2 (18 eyes) receiving PPV with a single-layered inverted ILM flap. Anatomical reattachment of the retina, macular hole closure, and best-corrected visual acuity (BCVA) were measured at 6 months after surgery. Results: The retina was successfully reattached in all cases. The difference of the retinal reattachment rate between the two groups was not statistically significant (Fisher's exact test, P= 1.000). The rate of macular hole closure was 47.1% in group 1 (8 eyes) and 88.9% in group 2 (16 eyes). The difference of the macular hole closure rate between the two groups was statistically significant (Fisher's exact test, P= 0.012). Significant improvement in logarithm of minimal angle of resolution (logMAR) BCVA was achieved in both groups. There was no difference in the initial, final, or improved logMAR BCVA in the 2 groups. Conclusion: Single-layered inverted ILM flap technique effectively helps close the macular hole in moderately high myopia with MHRD. This may prevent the possible redetachment from the macular hole. (Chin J Ophthalmol, 2017, 53: 338 - 343) .
7. MACULAR HOLE CLOSURE OVER RESIDUAL SUBRETINAL FLUID BY AN INVERTED INTERNAL LIMITING MEMBRANE FLAP TECHNIQUE IN PATIENTS WITH MACULAR HOLE RETINAL DETACHMENT IN HIGH MYOPIA.
Science.gov (United States)
Okuda, Tetsuhiko; Higashide, Tomomi; Kobayashi, Koh; Ikuno, Yasushi; Sugiyama, Kazuhisa
2016-01-01
To describe the closure of a macular hole over residual subretinal fluid in patients with macular hole retinal detachment in high myopia who had been treated using an inverted internal limiting membrane flap technique. Three patients with macular hole retinal detachment in high myopia underwent pars plana vitrectomy using the inverted internal limiting membrane flap technique. One patient received a silicone oil injection, and the other two patients received a long-acting gas injection at the end of the surgery. After surgery, spectral domain ocular coherence tomography examination was performed. In the patient with the silicone oil injection, spectral domain optical coherence tomography revealed that the macular hole was sealed with an inverted internal limiting membrane flap in the presence of subretinal fluid 1 day after surgery. The inner retinal layers gradually regained a more physiologic configuration over the residual subretinal fluid. In all patients, macular holes were completely closed over the subretinal fluid, which was gradually absorbed. Using the inverted internal limiting membrane flap technique, macular holes were closed over residual subretinal fluid in patients with macular hole retinal detachment. The results indicate that reattachment of the retina may not be necessary for closure of macular holes.
8. Combined FDTD-Monte Carlo analysis and a novel design for ZnO scintillator rods in polycarbonate membrane for X-ray imaging
Energy Technology Data Exchange (ETDEWEB)
Mohammadian-Behbahani, Mohammad-Reza [Department of Energy Engineering and Physics, Amir-Kabir University of Technology (Tehran Polytechnic), Tehran (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), Tehran (Iran, Islamic Republic of); Saramad, Shahyar, E-mail: [email protected] [Department of Energy Engineering and Physics, Amir-Kabir University of Technology (Tehran Polytechnic), Tehran (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), Tehran (Iran, Islamic Republic of); Mohammadi, Mohammad [Department of Electrical Engineering, Amir-Kabir University of Technology (Tehran Polytechnic), Tehran (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), Tehran (Iran, Islamic Republic of)
2017-05-01
A combination of Finite Difference Time Domain (FDTD) and Monte Carlo (MC) methods is proposed for simulation and analysis of ZnO microscintillators grown in polycarbonate membrane. A planar 10 keV X-ray source irradiating the detector is simulated by MC method, which provides the amount of absorbed X-ray energy in the assembly. The transport of generated UV scintillation light and its propagation in the detector was studied by the FDTD method. Detector responses to different probable scintillation sites and under different energies of X-ray source from 10 to 25 keV are reported. Finally, the tapered geometry for the scintillators is proposed, which shows enhanced spatial resolution in comparison to cylindrical geometry for imaging applications.
9. Inverted sugar syrup attained from sucrose hydrolysis using a membrane reactor
Directory of Open Access Journals (Sweden)
Ester Junko Tomotani
2010-09-01
Full Text Available Invertase, whether adsorbed on styrene-divinylbenzene copolymers or otherwise, was used for continuous sucrose hydrolysis using a cell-type membrane reactor (CTMR, coupled with an ultra (UF-100kDa, or a microfiltration (MF- pore diameter of 5 µm membrane. In all tests, the pH (5.5, temperature (30 ºC, reaction volume (10 mL and agitation (100 rpm were set constant; whereas, variable parameters were: feeding rate (0.4, 0.8 and 1.6 h-1, inlet sucrose concentration (2.5, 6.5, 50 and 100 mM and enzyme/resin ratio (1.64 mg or 3.28 mg of protein per 25, 50 or 100 mg of resin. The best result (yield of 100%, steady-state duration over 20h and specific reaction rate over 243 x 10-3 mmol/h.mE was obtained when insoluble invertase (1.64 mg protein/100 mg resin was used to convert 50 mM or 100 mM of sucrose solution at 0.4 h-1 using a UF-CTMR.Invertase, na forma adsorvida ou não em copolímeros de estireno-divinilbenzeno, foi usada para a hidrólise contínua de sacarose utilizando um reator com membrana (RM, acoplado a uma membrana de ultrafiltração (UF-100kDa, ou de microfiltração (MF - um diâmetro de poro de 5µm. Em todos os testes, o pH (5,5, a temperatura (30ºC, o volume reacional (10mL e a agitação (100 rpm foram mantidas constantes; os parâmetros variados foram: a vazão de alimentação (0,4; 0,8 e 1,6 h-1, a concentração de sacarose alimentada (2,5; 6,5; 50 e 100 mM e a relação enzima/resina (1,64 mg ou 3,28 mg de proteína por 25, 50 ou 100 mg de resina. O melhor resultado (um rendimento de 100%, um período de estado estacionário acima de 20h e uma taxa de reação específica maior de 243 x 10-3 mmol/h.mE foi obtido quando a invertase insolúvel (1,64 mg de proteína/100 de mg resina foi usado para converter 50 mM ou 100 mM de solução de sacarose a 0,4 h-1 usando UF-RM.
10. Photonic crystal scintillators and methods of manufacture
Science.gov (United States)
Torres, Ricardo D.; Sexton, Lindsay T.; Fuentes, Roderick E.; Cortes-Concepcion, Jose
2015-08-11
Photonic crystal scintillators and their methods of manufacture are provided. Exemplary methods of manufacture include using a highly-ordered porous anodic alumina membrane as a pattern transfer mask for either the etching of underlying material or for the deposition of additional material onto the surface of a scintillator. Exemplary detectors utilizing such photonic crystal scintillators are also provided.
11. Na+,HCO3--cotransport is functionally upregulated during human breast carcinogenesis and required for the inverted pH gradient across the plasma membrane
DEFF Research Database (Denmark)
Lee, Soojung; Mele, Marco; Vahl, Pernille
2015-01-01
Metabolic and biochemical changes during breast carcinogenesis enhance cellular acid production. Extrusion of the acid load from the cancer cells raises intracellular pH, while it decreases extracellular pH creating an inverted pH gradient across the plasma membrane compared to normal cells....... Intracellular pH was measured by fluorescence microscopy, while protein expression was investigated by immunofluorescence imaging and immunoblotting. We found that cellular net acid extrusion increased during human breast carcinogenesis due to enhanced Na(+),HCO3 (-)-cotransport, which created an alkaline shift...... (~0.3 units of magnitude) in steady-state intracellular pH of human primary breast carcinomas compared to normal breast tissue. Na(+)/H(+)-exchange activity and steady-state intracellular pH in the absence of CO2/HCO3 (-) were practically unaffected by breast carcinogenesis. These effects were evident...
12. Scintillation Counters
Science.gov (United States)
Bell, Zane W.
Scintillators find wide use in radiation detection as the detecting medium for gamma/X-rays, and charged and neutral particles. Since the first notice in 1895 by Roentgen of the production of light by X-rays on a barium platinocyanide screen, and Thomas Edison's work over the following 2 years resulting in the discovery of calcium tungstate as a superior fluoroscopy screen, much research and experimentation have been undertaken to discover and elucidate the properties of new scintillators. Scintillators with high density and high atomic number are prized for the detection of gamma rays above 1 MeV; lower atomic number, lower-density materials find use for detecting beta particles and heavy charged particles; hydrogenous scintillators find use in fast-neutron detection; and boron-, lithium-, and gadolinium-containing scintillators are used for slow-neutron detection. This chapter provides the practitioner with an overview of the general characteristics of scintillators, including the variation of probability of interaction with density and atomic number, the characteristics of the light pulse, a list and characteristics of commonly available scintillators and their approximate cost, and recommendations regarding the choice of material for a few specific applications. This chapter does not pretend to present an exhaustive list of scintillators and applications.
13. [Inverted nipples].
Science.gov (United States)
Saltvig, Iselin; Sjøstrand, Helle; Oldenburg, Mette Holmqvist; Matzen, Steen Henrik
2016-10-17
Inverted nipples is an anatomical variation which can be uni- or bilateral, congenital or acquired. The degree of inversion can vary from slight to severe. Treatment can be surgical or non-surgical and should depend on the degree of functional problems. Non-surgical treatment can be beneficial, does not risk affecting sensibility, spares the lactiferous ducts, and therefore does not risk any interference with breast-feeding. Surgical options should only be considered when non-surgical treatment is insufficient.
14. Lipoplexes formed from sugar-based gemini surfactants undergo a lamellar-to-micellar phase transition at acidic pH. Evidence for a non-inverted membrane-destabilizing hexagonal phase of lipoplexes.
Science.gov (United States)
Wasungu, Luc; Stuart, Marc C A; Scarzello, Marco; Engberts, Jan B F N; Hoekstra, Dick
2006-10-01
The present study aims at a better understanding of the mechanism of transfection mediated by two sugar-based gemini surfactants GS1 and GS2. Previously, these gemini surfactants have been shown to be efficient gene vectors for transfection both in vitro and in vivo. Here, using Nile Red, a solvatochromic fluorescent probe, we investigated the phase behavior of these gemini surfactants in complexes with plasmid DNA, so-called lipoplexes. We found that these lipoplexes undergo a lamellar-to-non-inverted micellar phase transition upon decreasing the pH from neutral to mildly acidic. This normal (non-inverted) phase at acidic pH is confirmed by the colloidal stability of the lipoplexes as shown by turbidity measurements. We therefore propose a normal hexagonal phase, H(I), for the gemini surfactant lipoplexes at acidic endosomal pH. Thus, we suggest that besides an inverted hexagonal (H(II)) phase as reported for several transfection-potent cationic lipid systems, another type of non-inverted non-bilayer structure, different from H(II), may destabilize the endosomal membrane, necessary for cytosolic DNA delivery and ultimately, cellular transfection.
15. Scintillating fibres
International Nuclear Information System (INIS)
Nahnhauer, R.
1990-01-01
In the search for new detector techniques, scintillating fibre technology has already gained a firm foothold, and is a strong contender for the extreme experimental conditions of tomorrow's machines. Organized by a group from the Institute of High Energy Physics, Berlin-Zeuthen, a workshop held from 3-5 September in the nearby village of Blossin brought together experts from East and West, and from science and industry
16. Plastic scintillation dosimetry: Optimal selection of scintillating fibers and scintillators
International Nuclear Information System (INIS)
Archambault, Louis; Arsenault, Jean; Gingras, Luc; Sam Beddar, A.; Roy, Rene; Beaulieu, Luc
2005-01-01
Scintillation dosimetry is a promising avenue for evaluating dose patterns delivered by intensity-modulated radiation therapy plans or for the small fields involved in stereotactic radiosurgery. However, the increase in signal has been the goal for many authors. In this paper, a comparison is made between plastic scintillating fibers and plastic scintillator. The collection of scintillation light was measured experimentally for four commercial models of scintillating fibers (BCF-12, BCF-60, SCSF-78, SCSF-3HF) and two models of plastic scintillators (BC-400, BC-408). The emission spectra of all six scintillators were obtained by using an optical spectrum analyzer and they were compared with theoretical behavior. For scintillation in the blue region, the signal intensity of a singly clad scintillating fiber (BCF-12) was 120% of that of the plastic scintillator (BC-400). For the multiclad fiber (SCSF-78), the signal reached 144% of that of the plastic scintillator. The intensity of the green scintillating fibers was lower than that of the plastic scintillator: 47% for the singly clad fiber (BCF-60) and 77% for the multiclad fiber (SCSF-3HF). The collected light was studied as a function of the scintillator length and radius for a cylindrical probe. We found that symmetric detectors with nearly the same spatial resolution in each direction (2 mm in diameter by 3 mm in length) could be made with a signal equivalent to those of the more commonly used asymmetric scintillators. With augmentation of the signal-to-noise ratio in consideration, this paper presents a series of comparisons that should provide insight into selection of a scintillator type and volume for development of a medical dosimeter
17. Liquid scintillation solution
International Nuclear Information System (INIS)
Long, E.C.
1977-01-01
A liquid scintillation solution is described which includes (1) a scintillation solvent (toluene and xylene), (2) a primary scintillation solute (PPO and Butyl PBD), (3) a secondary scintillation solute (POPOP and Dimethyl POPOP), (4) a plurality of substantially different surfactants and (5) a filter dissolving and/or transparentizing agent. 8 claims
18. Inorganic scintillating materials and scintillation detectors.
Science.gov (United States)
Yanagida, Takayuki
2018-01-01
Scintillation materials and detectors that are used in many applications, such as medical imaging, security, oil-logging, high energy physics and non-destructive inspection, are reviewed. The fundamental physics understood today is explained, and common scintillators and scintillation detectors are introduced. The properties explained here are light yield, energy non-proportionality, emission wavelength, energy resolution, decay time, effective atomic number and timing resolution. For further understanding, the emission mechanisms of scintillator materials are also introduced. Furthermore, unresolved problems in scintillation phenomenon are considered, and my recent interpretations are discussed. These topics include positive hysteresis, the co-doping of non-luminescent ions, the introduction of an aimed impurity phase, the excitation density effect and the complementary relationship between scintillators and storage phosphors.
19. Inverted base pavements: construction and performance
KAUST Repository
2017-05-11
Inverted base pavements involve a well-compacted granular aggregate base built between a thin asphalt concrete layer and a cement-treated base. Inverted base pavements can be constructed using conventional equipment and procedures but require proper quality control. This study reviews the extensive South African experience and case histories in the USA. Accumulating evidence suggests that inverted base pavements are a viable alternative and can outperform conventional pavements at a lower cost. Inverted base pavements rely on the complementary interaction between layers. The cement-treated base provides a stiff foundation for efficient compaction and constrains the deformation of the stress-sensitive granular aggregate base. The thin asphalt surface layer deforms as a membrane and develops low tensile stress. Additional large-scale field tests should be conducted to assess the performance of inverted base pavement designs in a wide range of conditions relevant to the USA.
20. Liquid scintillation solution
International Nuclear Information System (INIS)
Long, E.C.
1976-01-01
The invention deals with a liquid scintillation solution which contains 1) a scintillation solvent (toluol), 2) a primary scintillation solute (PPO), 3) a secondary scintillation solute (dimethyl POPOP), 4) several surfactants (iso-octyl-phenol polyethoxy-ethanol and sodium di-hexyl sulfosuccinate) essentially different from one another and 5) a filter resolution and/or transparent-making agent (cyclic ether, especially tetrahydrofuran). (HP) [de
1. Scintillation response of organic and inorganic scintillators
CERN Document Server
1999-01-01
A method to evaluate the scintillation response of organic and inorganic scintillators to different heavy ionizing particles is suggested. A function describing the rate of the energy consumed as fluorescence emission is derived, i.e., the differential response with respect to time. This function is then integrated for each ion and scintillator (anthracene, stilbene and CsI(Tl)) to determine scintillation response. The resulting scintillation responses are compared to the previously reported measured responses. Agreement to within 2.5% is observed when these data are normalized to each other. In addition, conclusions regarding the quenching parameter kB dependence on the type of the particle and the computed values of kB for certain ions are included. (author)
2. Scintillator Design Via Codoping
Science.gov (United States)
Melcher, C. L.; Koschan, M.; Zhuravleva, M.; Wu, Y.; Rothfuss, H.; Meng, F.; Tyagi, M.; Donnald, S.; Yang, K.; Hayward, J. P.; Eriksson, L.
Scintillation materials that lack intrinsic luminescence centers must be doped with optically active ions in order to provide luminescent centers that radiatively de-excite as the final step of the scintillation process. Codoping, on the other hand, can be defined as the incorporation of additional specific impurity species usually for the purpose of modifying the scintillation properties, mechanical properties, or the crystal growth behavior. In recent years codoping has become an increasingly popular approach for engineering scintillators with optimal performance for targeted applications. This report reviews several successful examples and its effect on specific properties.
3. Capture, isolation and electrochemical detection of industrially-relevant engineered aerosol nanoparticles using poly (amic) acid, phase-inverted, nano-membranes
International Nuclear Information System (INIS)
Okello, Veronica A.; Gass, Samuel; Pyrgiotakis, Georgios; Du, Nian; Lake, Andrew; Kariuki, Victor; Sotiriou, Georgios A.; Addolorato, Jessica; Demokritou, Philip; Sadik, Omowunmi A.
2014-01-01
Graphical abstract: - Highlights: • Exposure level assessment of aerosol nanoparticles reported using Harvard's VENGES. • Device equipped with pi-conjugated conducting PAA membrane filters/sensor arrays. • PAA membrane motifs used to capture, isolate and detect the nanoparticles. • Manipulating the PAA delocalized π electron enabled electrocatalytic detection. • Fe 2 O 3 , ZnO and TiO 2 quantified using impedance spectroscopy and cyclic voltammetry. - Abstract: Workplace exposure to engineered nanoparticles (ENPs) is a potential health and environmental hazard. This paper reports a novel approach for tracking hazardous airborne ENPs by applying online poly (amic) acid membranes (PAA) with offline electrochemical detection. Test aerosol (Fe 2 O 3 , TiO 2 and ZnO) nanoparticles were produced using the Harvard (Versatile Engineered Generation System) VENGES system. The particle morphology, size and elemental composition were determined using SEM, XRD and EDS. The PAA membrane electrodes used to capture the airborne ENPs were either stand-alone or with electron-beam gold-coated paper substrates. Cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) were used to conceptually illustrate that exposure levels of industry-relevant classes of airborne nanoparticles could be captured and electrochemically detected at PAA membranes filter electrodes. CV parameters showed that PAA catalyzed the reduction of Fe 2 O 3 to Fe 2+ with a size-dependent shift in reduction potential (E 0 ). Using the proportionality of peak current to concentration, the amount of Fe 2 O 3 was found to be 4.15 × 10 −17 mol/cm 3 PAA electrodes. Using EIS, the maximum phase angle (Φ max ) and the interfacial charge transfer resistance (R ct ) increased significantly using 100 μg and 1000 μg of TiO 2 and ZnO respectively. The observed increase in Φ max and R ct at increasing concentration is consistent with the addition of an insulating layer of material on the
4. Anticoincidence scintillation counter
CERN Multimedia
CERN PhotoLab
1966-01-01
This anticoincidence scintillation counter will be mounted in a hydrogen target vessel to be used in a measurement of the .beta. parameter in the .LAMBDA0. decay. The geometry of the counter optimizes light collection in the central part where a scintillation disk of variable thickness can be fitted.
5. Gas proportional scintillation counter
International Nuclear Information System (INIS)
Iguchi, Tetsuo; Nakazawa, Masaharu; Sekiguchi, Akira
1980-01-01
As the trial in the first stage of utilizing recoil helium for the measurement of 2 - 14 MeV neutron spectra in the simulated blanket for a nuclear fusion reactor, the He-Xe system gas proportional scintillation counter (GPSC) has been manufactured for trial, giving consideration to the advantages of gas scintillators and further to improve the energy resolution. In GPSC, delayed secondary scintillation pulses are produced, and its amplitude gives the energy resolution the adverse effect. Thus, in order to improve the energy resolution, it is desirable to realize such geometry of proportional counters that the electric field in the vicinity of center wire is sufficiently intense to induce the secondary excitation or ionization. The counters of such construction are called GPSC, in which the actual energy resolution can be improved according to the secondary scintillation pulses without losing the fast primary scintillation pulses useful for fast coincidence technique. The experimental results and the consideration on them are described. As compared with proportional counters, GPSC can give large output pulses even at low voltage, improve the energy resolution greatly as compared with ordinary gas scintillators, and measure the time data by the primary scintillation and the energy data based on the secondary scintillation simultaneously. However, it is likely to be affected by gas impurities more than proportional counters, and inferior in the reproducibility and stability of measurement. (Wakatsuki, Y.)
6. Plastic Organic Scintillator Chemistry
Science.gov (United States)
Brightwell, C. R.; Temanson, E. S.; Febbraro, M. T.
2017-09-01
Due to their high light output, quick decay time, affordability, durability and ability to be molded, plastic organic scintillators are increasingly becoming a more viable method of particle detection. Since the plastic is composed entirely of single molecular chains with repeating units, scintillating properties remain stable despite changes in experimental conditions. Different scintillating plastics can be modified and tailored to suit specific experiments depending on a variety of requirements such as light output, scintillating wavelength, and PMT compatibility. The synthesis chemistry of a recent but well-known scintillating polyester, polyethylene naphthalate (PEN) will be presented to demonstrate how plastic organic scintillators can be modified for different particle detection experiments. PEN has been successfully synthesized at ORNL, and procedures are currently being investigated to modify PEN using different reactants and catalysts. The goal is to achieve a transparent scintillating plastic with an incorporated wavelength shifter in the chain that scintillates with a wavelength around 440 nm. The status of this project will be presented. This research is supported by the U. S. Department of Energy Office of Science.
7. Next Generation Inverter
Energy Technology Data Exchange (ETDEWEB)
Zhao, Zilai [General Motors LLC, Detroit, MI (United States); Gough, Charles [General Motors LLC, Detroit, MI (United States)
2016-04-22
The goal of this Cooperative Agreement was the development of a Next Generation Inverter for General Motors’ electrified vehicles, including battery electric vehicles, range extended electric vehicles, plug-in hybrid electric vehicles and hybrid electric vehicles. The inverter is a critical electronics component that converts battery power (DC) to and from the electric power for the motor (AC).
8. Y-source inverter
DEFF Research Database (Denmark)
Siwakoti, Yam P.; Town, Graham; Loh, Poh Chiang
2014-01-01
This paper introduces a new 3-phase Y-source inverter whose gain is presently not matched by classical impedance-network-based inverters operating at the same duty ratio. The proposed network uses a tightly coupled transformer with three windings. By squeezing the shoot-through range while keeping...
9. Modular inverter system
Science.gov (United States)
Ma, Mingyao; Hu, Haibing; Kutkut, Nasser; Batarseh, Issa; Shen, John; , Bkayrat, Raed
2017-08-01
A system connected to an AC power grid having an AC phase signal includes an inverter module including a first inverter coupled to a DC voltage, actuated based on the AC phase signal. The first inverter provides a first voltage signal having predetermined harmonic components. A second inverter includes second switch elements coupled to the DC voltage and actuated by a second set of control signals phase delayed with respect to the first control signals. A transformer module has first and second primary windings coupled to the first and second inverters. The transformer module further includes a secondary winding coupled to first primary winding, the second primary winding, and the AC power grid. The secondary winding is configured to provide a secondary output voltage to the AC power grid by combining the first voltage signal and the second voltage signal such that the predetermined harmonic components are substantially cancelled.
10. Ionospheric scintillation observations
International Nuclear Information System (INIS)
Kakane, V.C.K.
1982-12-01
Ionospheric scintillation observations made at Legon, Ghana (5.63 deg. N, 0.19 deg. E, dip angle 8.50) during the year 1979 are reported for two geostationary satellites, Marisat and Sirio, transmitting at 257 MHz and 136 MHz, respectively. The night-time scintillation showed a single peak around 2200-3000 hours local time (GMT). Seasonally, Marisat showed a fast decay of scintillation for the months April-June and June-September from around midnight whilst it persisted for the other months January-March and October-December. (author)
11. Polarized scintillator targets
Science.gov (United States)
van den Brandt, B.; Bunyatova, E. I.; Hautle, P.; Konter, J. A.; Mango, S.
2000-05-01
The hydrogen nuclei in an organic scintillator have been polarized to more than 80% and the deuterons in its fully deuterated version to 24%. The scintillator, doped with TEMPO, has been polarized dynamically in a field of 2.5 T in a vertical dilution refrigerator in which a plastic lightguide transports the scintillation light from the sample in the mixing chamber to a photomultiplier outside the cryostat. Sizeable solid samples with acceptable optical properties and light output have been prepared and successfully operated as "live" polarized targets in nuclear physics experiments.
12. Polarized scintillator targets
Energy Technology Data Exchange (ETDEWEB)
Brandt, B. van den E-mail: [email protected]; Bunyatova, E.I.; Hautle, P.; Konter, J.A.; Mango, S
2000-05-21
The hydrogen nuclei in an organic scintillator have been polarized to more than 80% and the deuterons in its fully deuterated version to 24%. The scintillator, doped with TEMPO, has been polarized dynamically in a field of 2.5 T in a vertical dilution refrigerator in which a plastic lightguide transports the scintillation light from the sample in the mixing chamber to a photomultiplier outside the cryostat. Sizeable solid samples with acceptable optical properties and light output have been prepared and successfully operated as 'live' polarized targets in nuclear physics experiments.
Science.gov (United States)
Su, Gui-Jia
2003-06-10
A multilevel DC link inverter and method for improving torque response and current regulation in permanent magnet motors and switched reluctance motors having a low inductance includes a plurality of voltage controlled cells connected in series for applying a resulting dc voltage comprised of one or more incremental dc voltages. The cells are provided with switches for increasing the resulting applied dc voltage as speed and back EMF increase, while limiting the voltage that is applied to the commutation switches to perform PWM or dc voltage stepping functions, so as to limit current ripple in the stator windings below an acceptable level, typically 5%. Several embodiments are disclosed including inverters using IGBT's, inverters using thyristors. All of the inverters are operable in both motoring and regenerating modes.
14. Reliable inverter systems
Science.gov (United States)
Nagano, S.
1979-01-01
Base driver with common-load-current feedback protects paralleled inverter systems from open or short circuits. Circuit eliminates total system oscillation that can occur in conventional inverters because of open circuit in primary transformer winding. Common feedback signal produced by functioning modules forces operating frequency of failed module to coincide with clock drive so module resumes normal operating frequency in spite of open circuit.
15. Phosphor scintillator structure
International Nuclear Information System (INIS)
Cusano, D.A.; Prener, J.S.
1980-01-01
A method of fabricating scintillators is described in which the phosphor is distributed within the structure in such a way as to enhance the escape of the visible wavelength radiation that would otherwise be dissipated within the scintillator body. Two embodiments of the present invention are disclosed: one in which the phosphor is distributed in a layered structure and another in which the phosphor is dispersed throughout a transparent matrix. (U.K.)
16. New heavy plastic scintillators
International Nuclear Information System (INIS)
Britvich, G.I.; Vasil'chenko, V.G.; Lapshin, V.G.; Solov'ev, A.S.
2000-01-01
The possibility of manufacturing through the quenching method new transparent heavy scintillators on the basis of polystyrene with the light yield of approximately 32% from anthracene by general concentration of metalloorganic additions of approximately 17% by weight is shown. Doping of plastic scintillators through a set of various metalloorganic additives makes it possible to achieve more efficient and homogeneous by energy absorption of soft γ-quanta therein [ru
17. Fast-scintillator measurements
International Nuclear Information System (INIS)
Graves, W.R.; Slaughter, D.R.; Lerche, R.A.
1985-01-01
The authors are investigating scintillators because their fast timing properties may be applied to the development of neutron diagnostics. Measuring the history of a target burn by direct observation of DT neutrons requires a time resolution of 20 ps. An instrument designed to measure the plasma ion temperature by neutron time of flight, when the flight path is less than or equal to 1m, requires a detector system with resolution of 60 to 100 ps. Fast plastic scintillators like NE111, BC-422, and SG180 typically have decay constants of about 1400 ps. With quenching, the decay constant can be decreased to about 700 ps - still to slow for the instruments that they would like to build. One yet-unexploited property of fast scintillators is their rise time. In 1984, they began experiments designed to measure scintillator rise times. For our application - the measurement of target burn histories - they are especially concerned with the temporal width of the sample excitation pulse, the temporal resolution of our measurement system, and the need to characterize the excitation pulse and the scintillator output simultaneously. Application of plastic scintillators to a neutron streak camera is described
18. Scintillating properties of frozen new liquid scintillators
CERN Document Server
Britvich, G I; Golovkin, S V; Martellotti, G; Medvedkov, A M; Penso, G; Soloviev, A S; Vasilchenko, V G
1999-01-01
The light emission from scintillators which are liquid at room temperature was studied in the interval between $+20$~$^{\\circ}$C and $-120$~$^{\\circ}$C, where the phase transition from liquid to solid takes place. The light yield measured at $-120$~$^{\\circ}$C is about twice as much as that observed at $+20$~$^{\\circ}$C. By cooling the scintillator from $+20$~$^{\\circ}$C to $-120$~$^{\\circ}$C and then heating it from $-120$~$^{\\circ}$C to $+20$~$^{\\circ}$C, the light yield varies in steps at well defined temperatures, which are different for the cooling and heating processes. These hysteresis phenomena appear to be related to the solvent rather than to the dopant. The decay time of scintillation light was measured at $+20$~$^{\\circ}$C and $-120$~$^{\\circ}$C. Whilst at room temperature most of the light is emitted with a decay time of 6--8 ns, at $-120$~$^{\\circ}$C a slower component, with a decay time of 25--35 ns, becomes important.
19. Resonant snubber inverter
Science.gov (United States)
Lai, J.S.; Young, R.W. Sr.; Chen, D.; Scudiere, M.B.; Ott, G.W. Jr.; White, C.P.; McKeever, J.W.
1997-06-24
A resonant, snubber-based, soft switching, inverter circuit achieves lossless switching during dc-to-ac power conversion and power conditioning with minimum component count and size. Current is supplied to the resonant snubber branches solely by the main inverter switches. Component count and size are reduced by use of a single semiconductor switch in the resonant snubber branches. Component count is also reduced by maximizing the use of stray capacitances of the main switches as parallel resonant capacitors. Resonance charging and discharging of the parallel capacitances allows lossless, zero voltage switching. In one embodiment, circuit component size and count are minimized while achieving lossless, zero voltage switching within a three-phase inverter. 14 figs.
20. Resonant snubber inverter
Science.gov (United States)
Lai, Jih-Sheng; Young, Sr., Robert W.; Chen, Daoshen; Scudiere, Matthew B.; Ott, Jr., George W.; White, Clifford P.; McKeever, John W.
1997-01-01
A resonant, snubber-based, soft switching, inverter circuit achieves lossless switching during dc-to-ac power conversion and power conditioning with minimum component count and size. Current is supplied to the resonant snubber branches solely by the main inverter switches. Component count and size are reduced by use of a single semiconductor switch in the resonant snubber branches. Component count is also reduced by maximizing the use of stray capacitances of the main switches as parallel resonant capacitors. Resonance charging and discharging of the parallel capacitances allows lossless, zero voltage switching. In one embodiment, circuit component size and count are minimized while achieving lossless, zero voltage switching within a three-phase inverter.
1. SEEPAGE/INVERT INTERACTIONS
International Nuclear Information System (INIS)
P.S. Domski
2000-01-01
As directed by a written development plan (CRWMS M andO 1999a), a conceptual model for water entering the drift and reacting with the invert materials is to be developed. The purpose of this conceptual model is to assist Performance Assessment Operations (PAO) and its Engineered Barrier Performance Department in modeling the geochemical environment within a repository drift, thus allowing PAO to provide a more detailed and complete in-drift geochemical model abstraction, and to answer the key technical issues (KTI) raised in the NRC Issue Resolution Status Report (IRSR) for the Evolution of the Near-Field Environment (NFE), Revision 2 (NRC 1999). This AMR also seeks to: (1) Develop a logical conceptual model for physical/chemical interactions between seepage and the invert materials; (2) screen potential processes and reactions that may occur between seepage and invert to evaluate the potential consequences of the interactions; and (3) outline how seepage/invert processes may be quantified. This document provides the conceptual framework for screening out insignificant processes and for identifying and evaluating those seepage/invert interactions that have the potential to be important to subsequent PAO analyses including the Engineered Barrier System (EBS) physical and chemical model abstraction effort. This model has been developed to serve as a basis for the in-drift geochemical analyses performed by PAO. Additionally, the concepts discussed within this report may also apply to certain near and far-field geochemical processes and may have conceptual application within the unsaturated zone (UZ) and saturated zone (SZ) transport modeling efforts. The seepage/invert interactions will not directly affect any principal factors
2. Inorganic liquid scintillator
International Nuclear Information System (INIS)
Pavlicek, Z.; Barta, C.; Jursova, L.
1986-01-01
An inorganic liquid scintillator is designed which contains 1 to 30 wt.% of an inorganic molecular compound as the basic active component; the compound contains a cation with an atomic number higher than 47 and a halogen anion. The basic inorganic component is dissolved in water or in an organic solvent in form of non-dissociated molecules or self-complexes in which the bond is preserved between the cation and anion components. The light yield from these scintillators ranges between 70 and 150% of the light yield of a standard organic scintillator based on toluene. They are advantageous in that that they allow to increase the water content in the sample to up to 100%. (M.D.)
3. Response of ultrafast scintillators
International Nuclear Information System (INIS)
Cheng, J.C.; Lerche, R.A.; Tirsell, K.G.; Tripp, G.R.
1976-01-01
Measurements of the properties of subnanosecond, quenched NE111 plastic scintillators with various concentrations of acetophenone and benzophenone are presented. These quenching agents have been found to very significantly decrease the NE111 decay time. Measurements are made using UV and laser produced x-ray radiations. The scintillations are detected using a visible streak camera with 10 ps resolution. The paper will include measurements of: (1) 10-90 percent rise time, (2) FWHM, (3) decay time, (4) relative scintillator efficiencies, (5) amplitudes vs. time measurements of the long decay component. All temporal measurements are obtained from a gold cathode ultrafast x-ray streak camera, and the detailed x-ray energy spectrum above 1 keV is also measured using an array of x-ray PIN diodes equipped with the appropriate K-edge filters. Details of the experimental measurements are discussed and anticipated applications are included
4. Response of ultrafast scintillators
International Nuclear Information System (INIS)
Cheng, J.C.; Lerche, R.A.; Tripp, G.R.; Coleman, L.W.
1976-09-01
Measurements of the properties of subnanosecond, quenched NE111 plastic scintillators with various concentrations of acetophenone and benzophenone are presented. These quenching agents have been found to very significantly decrease the NE111 decay time. Measurements are made using UV and laser produced x-ray radiations. The scintillations are detected using a visible streak camera with 10 ps resolution. Measurements of: (1) 10-90 percent rise time, (2) FWHM, (3) decay time, (4) relative scintillator efficiencies, and (5) amplitudes vs. time measurements of the long decay component are presented. All temporal measurements are obtained from a gold cathode ultrafast x-ray streak camera, and the detailed x-ray energy spectrum above 1 keV is also measured using an array of x-ray PIN diodes equipped with the appropriate K-edge filters. Details of the experimental measurements are discussed and anticipated applications are included
5. Microfluidic Scintillation Detectors
CERN Multimedia
Microfluidic scintillation detectors are devices of recent introduction for the detection of high energy particles, developed within the EP-DT group at CERN. Most of the interest for such technology comes from the use of liquid scintillators, which entails the possibility of changing the active material in the detector, leading to an increased radiation resistance. This feature, together with the high spatial resolution and low thickness deriving from the microfabrication techniques used to manufacture such devices, is desirable not only in instrumentation for high energy physics experiments but also in medical detectors such as beam monitors for hadron therapy.
6. Polarized Scintillating Targets at Psi
Science.gov (United States)
van den Brandt, B.; Bunyatova, E. I.; Hautle, P.; Konter, J. A.; Mango, S.
2001-02-01
Scintillating polarized targets are now routinely available: blocks of 18×18×5 mm scintillating organic polymer, doped with TEMPO, polarized dynamically in a field of 2.5 T in a vertical 3He-4He dilution refrigerator. A 19 mm diameter plastic lightguide transports the scintillation light from the sample in the mixing chamber to a photomultiplier outside the cryostat.
7. Liquid scintillation, counting, and compositions
International Nuclear Information System (INIS)
Sena, E.A.; Tolbert, B.M.; Sutula, C.L.
1975-01-01
The emissions of radioactive isotopes in both aqueous and organic samples can be measured by liquid scintillation counting in micellar systems. The micellar systems are made up of scintillation solvent, scintillation solute and a mixture of surfactants, preferably at least one of which is relatively oil-soluble water-insoluble and another which is relatively water-soluble oil-insoluble
8. Energy-Saving Inverter
Science.gov (United States)
Rippel, W. E.; Edwards, D. B.
1984-01-01
Commutation by field-effect transistor allows more efficient operation. High voltage field-effect transistor (FET) controls silicon controlled rectifiers (SCR's). Circuit requires only one capacitor and one inductor in commutation circuit: simpler, more efficient, and more economical than conventional inverters. Adaptable to dc-to-dc converters.
9. Scintillation properties of acrylate based plastic scintillator by photoploymerization method
Energy Technology Data Exchange (ETDEWEB)
Kim, Sung Hwan [Dept. of Radiological Science, Cheongju University, Cheongju (Korea, Republic of); Lee, Joo Il [Dept. of of Radiology, Daegu Health College, Daegu (Korea, Republic of)
2016-12-15
In this study, we prepared and characterized a acrylate based UV-curable plastic scintillator. It was used co-polymers TMPTA, DHPA and Ultima GoldTM LLT organic scintillator. The emission spectrum of the plastic scintillator was located in the range of 380⁓520 nm, peaking at 423 nm. And the scintillator is more than 50% transparent in the range of 400⁓ 800 nm. The emission spectrum is well match to the quantum efficiency of photo-multiplier tube and the fast decay time of the scintillation is 12 ns, approximately. This scintillation material provides the possibility of combining 3D printing technology, and then the applications of the plastic scintillator may be expected in human dosimetry etc.
10. Inverter communications using output signal
Science.gov (United States)
Chapman, Patrick L.
2017-02-07
Technologies for communicating information from an inverter configured for the conversion of direct current (DC) power generated from an alternative source to alternating current (AC) power are disclosed. The technologies include determining information to be transmitted from the inverter over a power line cable connected to the inverter and controlling the operation of an output converter of the inverter as a function of the information to be transmitted to cause the output converter to generate an output waveform having the information modulated thereon.
11. Uranium-scintillator device
International Nuclear Information System (INIS)
Smith, S.D.
1979-01-01
The calorimeter subgroup of the 1977 ISABELLE Summer Workshop strongly recommended investigation of the uranium-scintillator device because of its several attractive features: (1) increased resolution for hadronic energy, (2) fast time response, (3) high density (i.e., 16 cm of calorimeter per interaction length), and, in comparison with uranium--liquid argon detectors, (4) ease of construction, (5) simple electronics, and (6) lower cost. The AFM group at the CERN ISR became interested in such a calorimeter for substantially the same reasons, and in the fall of 1977 carried out tests on a uranium-scintillator (U-Sc) calorimeter with the same uranium plates used in their 1974 studies of the uranium--liquid argon (U-LA) calorimeter. The chief disadvantage of the scintillator test was that the uranium plates were too small to fully contain the hadronic showers. However, since the scintillator and liquid argon tests were made with the plates, direct comparison of the two types of devices could be made
12. Inverting the Linear Algebra Classroom
Science.gov (United States)
Talbert, Robert
2014-01-01
The inverted classroom is a course design model in which students' initial contact with new information takes place outside of class meetings, and students spend class time on high-level sense-making activities. The inverted classroom model is so called because it inverts or "flips" the usual classroom design where typically class…
13. Quasi-Y-source inverter
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Loh, Poh Chiang
2015-01-01
This paper introduces a new inverter topology called a “quasi-Y-source inverter”. The proposed inverter inherits all the advantages of the original Y-source inverter. In addition, the new topology draws continuous current from the source which is required for many renewable sources. It also has dc...
14. Milliwatt dc/dc Inverter
Science.gov (United States)
Mclyman, C. W.
1983-01-01
Compact dc/dc inverter uses single integrated-circuit package containing six inverter gates that generate and amplify 100-kHz square-wave switching signal. Square-wave switching inverts 10-volt local power to isolated voltage at another desired level. Relatively high operating frequency reduces size of filter capacitors required, resulting in small package unit.
15. Performance of molded plastic scintillators
International Nuclear Information System (INIS)
Gen, N.S.; Leman, V.E.; Solomonov, V.M.
1989-01-01
The performance of molded plastic scintillators is studied. The plastic scintillators studied were formed by transfer molding and intrusion from a scintillation composition consisting of polystyrene and a standard system of luminescent additives: 2 mass % of paraterphenyl + 0.06 mass % 1,4-di-/2-[5-phenyloxazoyly]/benzene and a plasticizer. The combined effect of mechanical load and temperature was studied. The effect of radiation on molded plastic scintillators was studied using gamma radiation from a 60 Co source. The studies show that the main operating characteristics of molded plastic scintillators are on a par with those of polymerized plastic scintillators. At the same time, molded plastic scintillators are superior in thermal stability at temperatures below the glass transition temperature and with respect to their working temperature range
16. Inverter ratio failure detector
Science.gov (United States)
Wagner, A. P.; Ebersole, T. J.; Andrews, R. E. (Inventor)
1974-01-01
A failure detector which detects the failure of a dc to ac inverter is disclosed. The inverter under failureless conditions is characterized by a known linear relationship of its input and output voltages and by a known linear relationship of its input and output currents. The detector includes circuitry which is responsive to the detector's input and output voltages and which provides a failure-indicating signal only when the monitored output voltage is less by a selected factor, than the expected output voltage for the monitored input voltage, based on the known voltages' relationship. Similarly, the detector includes circuitry which is responsive to the input and output currents and provides a failure-indicating signal only when the input current exceeds by a selected factor the expected input current for the monitored output current based on the known currents' relationship.
17. DETECTORS: scintillating fibres
International Nuclear Information System (INIS)
Anon.
1994-01-01
In the continual search for improved detection techniques, new materials are continually proving profitable. A good example is scintillating plastic fibres - tiny transparent threads sometimes finer than a human hair which transmit light. The narrowness and flexibility of these fibres was a major breakthrough for endoscopy - non-invasive techniques for viewing the otherwise inaccessible in surgery or machine inspection. In a more sophisticated form, these fibres find ready application in communications technology, where the goal is to transmit information rather than electrical power, replacing conventional and unwieldy current-carrying wire conductors. In particle physics, fibres have long been used to take the tiny scintillations produced when high energy particles hit fluorescent materials and 'conduct' them to photosensitive detectors some distance away
International Nuclear Information System (INIS)
Lucas, H.F. Jr.
1977-01-01
Radon counting chambers which utilize the alpha-scintillation properties of silver activated zinc sulfide are simple to construct, have a high efficiency, and, with proper design, may be relatively insensitive to variations in the pressure or purity of the counter filling. Chambers which were constructed from glass, metal, or plastic in a wide variety of shapes and sizes were evaluated for the accuracy and the precision of the radon counting. The principles affecting the alpha-scintillation radon counting chamber design and an analytic system suitable for a large scale study of the 222 Rn and 226 Ra content of either air or other environmental samples are described. Particular note is taken of those factors which affect the accuracy and the precision of the method for monitoring radioactivity around uranium mines
19. Scintillator detector array
International Nuclear Information System (INIS)
Cusano, D.A.; Dibianca, F.A.
1981-01-01
This patent application relates to a scintillator detector array for use in computerized tomography and comprises a housing including a plurality of chambers, the said housing having a front wall transmissive to x-rays and side walls opaque to x-rays, such as of tungsten and tantalum, a liquid scintillation medium including a soluble fluor, the solvent for the fluor being disposed in the chambers. The solvent comprises either an intrinsically high Z solvent or a solvent which has dissolved therein a high Z compound e.g. iodo or bromonaphthalene; or toluene, xylene or trimethylbenzene with a lead or tin alkyl dissolved therein. Also disposed about the chambers are a plurality of photoelectric devices. (author)
20. Modular scintillation camera
International Nuclear Information System (INIS)
Barrett, H. H.
1985-01-01
Improved optical coupling modules to be used in coded-aperture-type radiographic imaging systems. In a first system, a rotating slit coded-aperture is employed between the radioactive object and the module. The module consists of one pair of side-by-side photomultipliers receiving light rays from a scintillation crystal exposed to the object via the coded-aperture. The light rays are guided to the photomultipliers by a mask having a central transverse transparent window, or by a cylindrical lens, the mask or lens being mounted in a light-conveying quartz block assembly providing internal reflections at opposite faces of the assembly. This generates output signals from the photomultipliers which can be utilized to compute one-dimensional coordinate values for restoring the image of the radioactive object on a display screen. In another form of optical coupling module, usable with other types of coded-apertures, four square photomultipliers form a substantially square block and receive light rays from scintillations from a scintillation crystal exposed to the radioactive object via the coded-aperture. The light rays are guided to the photomultipliers by a square mask or a centrally transparent square lens configuration mounted in a light-conveying assembly formed by internally reflecting quartz blocks, the optical rays being directed to the respective photomultipliers so as to generate resultant output signals which can be utilized to compute image coordinate values for two-dimensional representation of the radioactive object being examined
1. Embedded EZ-Source Inverters
DEFF Research Database (Denmark)
Chiang Loh, Poh; Gao, Feng; Blaabjerg, Frede
2010-01-01
Z-source inverters are recent topological options proposed for buck–boost energy conversion with a number of possible voltage- and current-type circuitries already reported in the literature. Comparing them, a common feature noted is their inclusion of an LC impedance network, placed between the dc...... input source and inverter bridge. This impedance network allows the output end of a voltage-type Z-source inverter to be shorted for voltage boosting without causing a large current flow and the terminal current of a current-type inverter to be interrupted for current boosting without introducing...... overvoltage oscillations to the system. Therefore, Z-source inverters are, in effect, safer and less complex and can be implemented using only passive elements with no additional active semiconductor needed. Believing in the prospects of Z-source inverters, this paper contributes by introducing a new family...
2. Embedded EZ-Source Inverters
DEFF Research Database (Denmark)
Blaabjerg, Frede; Loh, Poh Chiang; Gao, F.
2008-01-01
Z-source inverters are recent topological options proposed for buck-boost energy conversion with a number of possible voltage and current-type circuitries already reported in the literature. Comparing them, a common feature noted is their inclusion of a LC impedance network, placed between the dc...... input source and inverter bridge. This impedance network allows the output end of a voltage-type Z-source inverter to be shorted for voltage-boosting without causing a large current flow, and the terminal current of a current-type inverter to be interrupted for current boosting without introducing over......-voltage oscillations to the system. Therefore, Z-source inverters are in effect safer and less complex, and can be implemented using only passive elements with no additional active semiconductor needed. Believing in the prospects of Z-source inverters, this paper contributes by introducing a new family of embedded EZ-source...
DEFF Research Database (Denmark)
Anthon, Alexander
and preferably low complexity leads to new research demands. This is especially true in the field of low cost residential PV inverters where efficiencies are used as major selling arguments. Traditional converter topologies equipped with conventional Silicon based semiconductors to date reach their limitations......, a replacement of only two switching devices per phase leg can greatly reduce the semiconductor losses. The Hybrid-NPC converter can be seen as an attractive and cost competitive alternative to the Silicon Carbide based converter, also allowing to overcome the major drawbacks with the conventional Silicon IGBT...
4. Gas cooled traction drive inverter
Science.gov (United States)
2013-10-08
The present invention provides a modular circuit card configuration for distributing heat among a plurality of circuit cards. Each circuit card includes a housing adapted to dissipate heat in response to gas flow over the housing. In one aspect, a gas-cooled inverter includes a plurality of inverter circuit cards, and a plurality of circuit card housings, each of which encloses one of the plurality of inverter cards.
5. Γ-Z-Source Inverters
DEFF Research Database (Denmark)
Loh, Poh Chiang; Li, Ding; Blaabjerg, Frede
2013-01-01
Voltage-type Γ-Z-source inverters are proposed in this letter. They use a unique Γ-shaped impedance network for boosting their output voltage in addition to their usual voltage-buck behavior. Comparing them with other topologies, the proposed inverters use lesser components and a coupled transfor......Voltage-type Γ-Z-source inverters are proposed in this letter. They use a unique Γ-shaped impedance network for boosting their output voltage in addition to their usual voltage-buck behavior. Comparing them with other topologies, the proposed inverters use lesser components and a coupled...
6. Scintillating fiber detector
CERN Document Server
Vozak, Matous
2016-01-01
NA61 is one of the physics experiments at CERN dedicated to study hadron states coming from interactions of SPS beams with various targets. To determine the position of a secondary beam, three proportional chambers are placed along the beamline. However, these chambers tend to have slow response. In order to obtain more precise time information, use of another detector is being considered. Fast response and compact size is making scintillation fiber (SciFi) with silicon photomultiplier (Si-PM) read out a good candidate. This report is focused on analysing data from SciFi collected in a test beam at the beginning of July 2016.
7. Scintillating-fibre calorimetry
International Nuclear Information System (INIS)
Livan, M.; Vercesi, V.; Wigmans, R.
1995-01-01
In the past decade, calorimetry based on scintillating plastic fibres as active elements was developed from a conceptual idea to a mature detector technology, which is nowadays widely applied in particle physics experiments. This development and the performance characteristics of representative calorimeters, both for the detection of electromagnetic and hadronic showers, are reviewed. We also discuss new information on shower development processes in dense matter and its application to calorimetric principles that has emerged from some very thorough studies that were performed in the framework of this development. (orig.)
8. Hybrid scintillators for neutron discrimination
Science.gov (United States)
Feng, Patrick L; Cordaro, Joseph G; Anstey, Mitchell R; Morales, Alfredo M
2015-05-12
A composition capable of producing a unique scintillation response to neutrons and gamma rays, comprising (i) at least one surfactant; (ii) a polar hydrogen-bonding solvent; and (iii) at least one luminophore. A method including combining at least one surfactant, a polar hydrogen-bonding solvent and at least one luminophore in a scintillation cell under vacuum or an inert atmosphere.
9. Laser Beam Scintillation with Applications
CERN Document Server
Andrews, Larry C; Young, Cynthia
2001-01-01
Renewed interest in laser communication systems has sparked development of useful new analytic models. This book discusses optical scintillation and its impact on system performance in free-space optical communication and laser radar applications, with a detailed look at propagation phenomena and the role of scintillation on system behavior. Intended for practicing engineers, scientists, and students.
10. Liquid scintillation in medical diagnosis
International Nuclear Information System (INIS)
Painter, K.
1976-01-01
With the tremendous increase in the application of radioassay, particularly radioimmunoassay, in the clinical laboratory liquid scintillation counting became an indispensable tool in diagnostic medicine. Few publications, however, have concerned themselves with problem areas which occur with the method in the clinical laboratory. The purpose of this presentation is to summarize our experiences with the liquid scintillation technique in the clinical situation
11. Thermal degradation of plastic scintillators
International Nuclear Information System (INIS)
Andreeshchev, E.A.; Kilin, S.F.; Kushakevich, Yu.P.; Rozman, I.M.; Shoniya, V.M.
1982-01-01
The methods for investigations of thermal degradation of plastic scintillators (PS) in air at 120 deg C are described and the results of studies are presented. It is shown that at the elevated temperature under conditions of free access of air a decrease in the luminescence yield and reduction in scintillation duration is observed. In the near-surface layer of scintillators a quenching of molecular excited states and absorption of luminescence are observed. No restoration of the scintillation properties in scintillators treated with heat has been observed. A conclusion is drawn that the PS thermal stability could be improved either by the use of a reflector or larger sizes of PS, or by shifting the luminescence spectrum to the long-wave region
12. Simplified High-Power Inverter
Science.gov (United States)
Edwards, D. B.; Rippel, W. E.
1984-01-01
Solid-state inverter simplified by use of single gate-turnoff device (GTO) to commutate multiple silicon controlled rectifiers (SCR's). By eliminating conventional commutation circuitry, GTO reduces cost, size and weight. GTO commutation applicable to inverters of greater than 1-kilowatt capacity. Applications include emergency power, load leveling, drives for traction and stationary polyphase motors, and photovoltaic-power conditioning.
13. (SPWM) Voltage Source Inverter (VSI)
African Journals Online (AJOL)
The quest to achieve less-distorted dc-ac power conversion has resulted in the proliferation of many multilevel inverter configurations. This paper presents an experimental report of a simplified topology for single-phase, SPWM, three-level voltage source inverter wit R-L load. To keep the power circuit component count to a ...
14. Analisis Harmonisa Inverter PWM Satu Fasa
OpenAIRE
Rejeki Simanjorang
2008-01-01
Pada tesis ini dianalisis harmonisa inverter PWM satu fasa. Inverter PWM satu fasa yang akan ditinjau adalah inverter satu fasa jembatan penuh (konvensional) dan inverter komposit. Analisis difokuskan pada penentuan pola penyaklaran yang optimum agar pembangkitan harmonisa dan switching losses inverter rendah. Untuk menentukan pola penyaklaran optimum maka dilakukan analisis yang berbasis pada rangkaian ekivalen harmonisa inverter satu fasa. Dengan menggunakan pola penyaklaran optimum, kedua ...
15. Scintillators and other particle optical detectors
International Nuclear Information System (INIS)
Chipaux, R.
2011-01-01
The author reports and comments his researcher career in the field of particle optical detectors. He addresses the cases of organic scintillators (scintillating fibers, liquid scintillators), inorganic scintillators (crystals for electromagnetic calorimetry, crystals for solar neutrino spectroscopy), and Cherenkov Effect detectors. He also reports his works on Cd Te detectors and their modelling
16. Scintillating plate calorimeter optical design
International Nuclear Information System (INIS)
McNeil, R.; Fazely, A.; Gunasingha, R.; Imlay, R.; Lim, J.
1990-01-01
A major technical challenge facing the builder of a general purpose detector for the SSC is to achieve an optimum design for the calorimeter. Because of its fast response and good energy resolution, scintillating plate sampling calorimeters should be considered as a possible technology option. The work of the Scintillating Plate Calorimeter Collaboration is focused on compensating plate calorimeters. Based on experimental and simulation studies, it is expected that a sampling calorimeter with alternating layers of high-Z absorber (Pb, W, DU, etc.) and plastic scintillator can be made compensating (e/h = 1.00) by suitable choice of the ratio of absorber/scintillator thickness. Two conceptual designs have been pursued by this subsystem collaboration. One is based on lead as the absorber, with read/out of the scintillator plates via wavelength shifter fibers. The other design is based on depleted uranium as the absorber with wavelength shifter (WLS) plate readout. Progress on designs for the optical readout of a compensating scintillator plate calorimeter are presented. These designs include readout of the scintillator plates via wavelength shifter plates or fiber readout. Results from radiation damage studies of the optical components are presented
17. Transformerless PV inverters. Final report
Energy Technology Data Exchange (ETDEWEB)
Borup, U.
2009-12-15
Since the start of the project the market for grid connected PV inverters have developed further. When the project started three - phase inverter were only available in high power systems. The technology developed within this project will enable three phase technology also to be implemented in string inverters for system down to 10 kW. We expect this to be very attractive due to the increased demand for symmetrical feed-in to the grid. The project relevance is therefore high and the sector continues to develop very much driven by technology. Especially the inverter technology is getting a lot of focus. The inverter systems are expected to take a much larger role in supporting the electrical grid in the future. The technology platform developed within the project is prepared to be extended with these utility functionalities. The main results of the project were: 1) A new technology concept for transformer-less inverters has been demonstrated with a number of prototypes. 2) Efficiency above 97,7% has been proven. 3) Efficiency and Maximum power point tracking has been optimized to ensure that almost all energy produced of the panels is transferred to the grid. 4) The platform is developed with a very fast control board, which enables extended functionality as demanding grid supporting functions in the future. Details about cost price and details about the control loop implementation is excluded from the report due to the competitive situation for Danfoss Solar Inverters A/S. (LN)
18. Sub-nanosecond plastic scintillators
International Nuclear Information System (INIS)
Lyons, P.B.; Caldwell, S.E.; Hocker, L.P.; Crandall, D.G.; Zagarino, P.A.; Cheng, J.; Tirsell, G.; Hurlbut, C.R.
1976-01-01
Quenched plastic scintillators have been developed that yield much faster short decay components and greatly reduced long decay components compared to conventional plastic scintillators. The plastics are produced through the addition of selected quench agents to NE111 plastic scintillator that result in reduced total light output. Eight different agents have been studied. Benzophenone and piperidine are two of the most effective quench agents. Data are presented both for short and long decay components. The plastics are expected to make significant contributions in areas of plasma diagnostics
19. Sub-nanosecond plastic scintillators
International Nuclear Information System (INIS)
Lyons, P.B.; Caldwell, S.E.; Hocker, L.P.; Crandall, D.G.; Zagarino, P.A.; Cheng, J.; Tirsell, G.; Hurlbut, C.R.
1977-01-01
Quenched plastic scintillators have been developed that yield much faster short decay components and greatly reduced long decay components compared to conventional plastic scintillators. The plastics are produced through the addition of selected quench agents to NE111 plastic scintillator that result in reduced total light output. Eight different agents have been studied. Benzophenone and piperidine are two of the most effective quench agents. Data are presented both for short and long decay components. The plastics are expected to make significant contributions in areas of plasma diagnostics
20. Scintillation counter, segmented shield
International Nuclear Information System (INIS)
Olson, R.E.; Thumim, A.D.
1975-01-01
A scintillation counter, particularly for counting gamma ray photons, includes a massive lead radiation shield surrounding a sample-receiving zone. The shield is disassembleable into a plurality of segments to allow facile installation and removal of a photomultiplier tube assembly, the segments being so constructed as to prevent straight-line access of external radiation through the shield into radiation-responsive areas. Provisions are made for accurately aligning the photomultiplier tube with respect to one or more sample-transmitting bores extending through the shield to the sample receiving zone. A sample elevator, used in transporting samples into the zone, is designed to provide a maximum gamma-receiving aspect to maximize the gamma detecting efficiency. (U.S.)
1. Encapsulated scintillation detector
International Nuclear Information System (INIS)
Toepke, I.L.
1982-01-01
A scintillation detector crystal is encapsulated in a hermetically sealed housing having a glass window. The window may be mounted in a ring by a compression seal formed during cooling of the ring and window after heating. The window may be chemically bonded to the ring with or without a compression seal. The ring is welded to the housing along thin weld flanges to reduce the amount of weld heat which must be applied. A thin section is provided to resist the flow of welding heat to the seal between the ring and the window thereby forming a thermal barrier. The thin section may be provided by a groove cut partially through the wall of the ring. A layer of PTFE between the tubular body and the crystal minimizes friction created by thermal expansion. Spring washers urge the crystal towards the window. (author)
2. Properties of scintillator solutes
International Nuclear Information System (INIS)
Fluornoy, J.M.
1998-06-01
This special report summarizes measurements of the spectroscopic and other properties of the solutes that were used in the preparation of several new liquid scintillators developed at EG and G/Energy Measurements/Santa Barbara Operations (the precursor to Bechtel Nevada/Special Technologies Laboratory) on the radiation-to-light converter program. The data on the individual compounds are presented in a form similar to that used by Prof. Isadore Berlman in his classic handbook of fluorescence spectra. The temporal properties and relative efficiencies of the new scintillators are presented in Table 1, and the efficiencies as a function of wavelength are presented graphically in Figure 1. In addition, there is a descriptive glossary of the abbreviations used herein. Figure 2 illustrates the basic structures of some of the compounds and of the four solvents reported in this summary. The emission spectra generally exhibit more structure than the absorption spectra, with the result that the peak emission wavelength for a given compound may lie several nm away from the wavelength, λ avg , at the geometric center of the emission spectrum. Therefore, the author has chosen to list absorption peaks, λ max , and emission λ avg values in Figures 3--30, as being most illustrative of the differences between the compounds. The compounds, BHTP, BTPB, ADBT, and DPTPB were all developed on this program. P-terphenyl, PBD, and TPB are commercially available blue emitters. C-480 and the other longer-wavelength emitters are laser dyes available commercially from Exciton Corporation. 1 ref., 30 figs
3. Temperature dependence of plastic scintillators
Science.gov (United States)
Peralta, L.
2018-03-01
Plastic scintillator detectors have been studied as dosimeters, since they provide a cost-effective alternative to conventional ionization chambers. Several articles have reported undesired response dependencies on beam energy and temperature, which provides the motivation to determine appropriate correction factors. In this work, we studied the light yield temperature dependency of four plastic scintillators, BCF-10, BCF-60, BC-404, RP-200A and two clear fibers, BCF-98 and SK-80. Measurements were made using a 50 kVp X-ray beam to produce the scintillation and/or radioluminescence signal. The 0 to 40 °C temperature range was scanned for each scintillator, and temperature coefficients were obtained.
4. Nanowire NMOS Logic Inverter Characterization.
Science.gov (United States)
Hashim, Yasir
2016-06-01
This study is the first to demonstrate characteristics optimization of nanowire N-Channel Metal Oxide Semiconductor (NW-MOS) logic inverter. Noise margins and inflection voltage of transfer characteristics are used as limiting factors in this optimization. A computer-based model used to produce static characteristics of NW-NMOS logic inverter. In this research two circuit configuration of NW-NMOS inverter was studied, in first NW-NMOS circuit, the noise margin for (low input-high output) condition was very low. For second NMOS circuit gives excellent noise margins, and results indicate that optimization depends on applied voltage to the inverter. Increasing gate to source voltage with (2/1) nanowires ratio results better noise margins. Increasing of applied DC load transistor voltage tends to increasing in decreasing noise margins; decreasing this voltage will improve noise margins significantly.
5. Inverter Ground Fault Overvoltage Testing
Energy Technology Data Exchange (ETDEWEB)
Hoke, Andy [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Nelson, Austin [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Chakraborty, Sudipta [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Chebahtah, Justin [SolarCity Corporation, San Mateo, CA (United States); Wang, Trudie [SolarCity Corporation, San Mateo, CA (United States); McCarty, Michael [SolarCity Corporation, San Mateo, CA (United States)
2015-08-12
This report describes testing conducted at NREL to determine the duration and magnitude of transient overvoltages created by several commercial PV inverters during ground fault conditions. For this work, a test plan developed by the Forum on Inverter Grid Integration Issues (FIGII) has been implemented in a custom test setup at NREL. Load rejection overvoltage test results were reported previously in a separate technical report.
6. Invertibility in L-Topological Spaces
Directory of Open Access Journals (Sweden)
Anjaly Jose
2014-03-01
Full Text Available In this paper, we extend the concept of invertibility to L-topological spaces and delineate its properties. Then, we study further completely invertible L-topological spaces and introduce two types of invertible L-topologies based on the inverting maps, studying their sums, subspaces and simple extensions.
7. Extruded plastic scintillator including inorganic powders
Science.gov (United States)
Bross, Alan D.; Mellott, Kerry L.; Pla-Dalmau, Anna
2006-06-27
A method for producing a plastic scintillator is disclosed. A plurality of nano-sized particles and one or more dopants can be combined with a plastic material for the formation of a plastic scintillator thereof. The nano-sized particles, the dopant and the plastic material can be combined within the dry inert atmosphere of an extruder to produce a reaction that results in the formation of a plastic scintillator thereof and the deposition of energy within the plastic scintillator, such that the plastic scintillator produces light signifying the detection of a radiative element. The nano-sized particles can be treated with an inert gas prior to processing the nano-sized particles, the dopant and the plastic material utilizing the extruder. The plastic scintillator can be a neutron-sensitive scintillator, x-ray sensitive scintillator and/or a scintillator for the detection of minimum ionizing particles.
8. Cherenkov and scintillation light separation in organic liquid scintillators
International Nuclear Information System (INIS)
Caravaca, J.; Descamps, F.B.; Land, B.J.; Orebi Gann, G.D.; Yeh, M.
2017-01-01
The CHErenkov/Scintillation Separation experiment (CHESS) has been used to demonstrate the separation of Cherenkov and scintillation light in both linear alkylbenzene (LAB) and LAB with 2 g/L of PPO as a fluor (LAB/PPO). This is the first successful demonstration of Cherenkov light detection from the more challenging LAB/PPO cocktail and improves on previous results for LAB. A time resolution of 338 ± 12 ps FWHM results in an efficiency for identifying Cherenkov photons in LAB/PPO of 70 ± 3% and 63 ± 8% for time- and charge-based separation, respectively, with scintillation contamination of 36 ± 5% and 38 ± 4. LAB/PPO data is consistent with a rise time of τ r = 0.72 ± 0.33 ns. (orig.)
9. Cherenkov and scintillation light separation in organic liquid scintillators
Science.gov (United States)
Caravaca, J.; Descamps, F. B.; Land, B. J.; Yeh, M.; Orebi Gann, G. D.
2017-12-01
The CHErenkov/Scintillation Separation experiment (CHESS) has been used to demonstrate the separation of Cherenkov and scintillation light in both linear alkylbenzene (LAB) and LAB with 2 g/L of PPO as a fluor (LAB/PPO). This is the first successful demonstration of Cherenkov light detection from the more challenging LAB/PPO cocktail and improves on previous results for LAB. A time resolution of 338± 12 ps FWHM results in an efficiency for identifying Cherenkov photons in LAB/PPO of 70 ± 3 % and 63± 8% for time- and charge-based separation, respectively, with scintillation contamination of 36± 5% and 38± 4%. LAB/PPO data is consistent with a rise time of τ _r=0.72± 0.33 ns.
10. Scintillation of artificial satellite radio waves
International Nuclear Information System (INIS)
Ryuguji, Osamu
1974-01-01
Scintillation is generally explained. Specifically, phase scintillation, amplitude scintillation, and scintillation index are described. The relationship between Spread-F and scintillation shown in the figures of the results observed at Huancayo in Peru is illustrated. The comparison between the scintillation occurrence frequency in case of Early Bird satellite and the change in fsub(o)Esub(S) observation value at Fort Bervoir is illustrated. The marked correlation between geomagnetic activity Ksub(p) and the scintillation of ATS-3 at Narrsarssuaq is shown. In order to facilitate the understanding of scintillation, scintillation profile, that is the dependence on geographical conditions, reception frequency, angle to elevation, time and season must be made clear. Attention has been directed to the movement of scintillation boundary between latitude zones in north- south direction according to time and season, as shown in the observation of Explorer-22 at Oulu. Scintillation region expanded in proportion to geomagnetic activity as shown in the observation of Transit-4A and Explorer-22 at Sagamore Hill and ATS-3 at Thule. In the mid-latitude as Japan, there is no substantial trouble caused by scintillation. But, in the case of establishing world wide satellite net work, scintillation occurrence and its effect must be taken into consideration. The names of research institutes and researchers in the world are listed. (Iwakiri, K.)
11. Molecular origins of scintillation in organic scintillators (Conference Presentation)
Science.gov (United States)
Feng, Patrick; Mengesha, Wondwosen; Myllenbeck, Nicholas
2016-09-01
Organic-based scintillators are indispensable materials for radiation detection owing to their high sensitivity to fast neutrons, low cost, and tailorable properties. There has been a recent resurgence of interest in organic scintillators due to exciting discoveries related to neutron discrimination and gamma-ray spectroscopy, which represent capabilities previously thought not possible in these materials. I will discuss our development of crystalline and polymer-based scintillators for these applications. Structure-property relationships related to intermolecular interactions and host-guest electronic exchange will be discussed in the context of energy-transfer pathways relevant to scintillation. An emphasis will be placed on the rational design of these materials, as guided by first principles and DFT calculations. Two related topics will be discussed: 1) Incorporation of organometallic triplet-harvesting additives to plastic scintillator matrices to confer a 'two-state' (singlet and triplet) luminescence signature to different types of ionizing radiation. This approach relies upon energetic and spatial overlap between the donor and acceptor excited states for efficient electronic exchange. Key considerations also include synthetic modification of the luminescence spectra and kinetics, as well as the addition of secondary additives to increase the recombination efficiency. 2) Design of organotin-containing plastic scintillators as a route towards gamma-ray spectroscopy. Organometallic compounds were selected on the basis of distance-dependent quenching relationships, phase compatibility with the polymer matrix, and the gamma-ray cross sections. This approach is guided by molecular modeling and radiation transport modeling to achieve the highest possible detection sensitivity luminescence intensity.
12. Accelerating development of advanced inverters :
Energy Technology Data Exchange (ETDEWEB)
Neely, Jason C.; Gonzalez, Sigifredo; Ropp, Michael; Schutz, Dustin
2013-11-01
The high penetration of utility interconnected photovoltaic (PV) systems is causing heightened concern over the effect that variable renewable generation will have on the electrical power system (EPS). These concerns have initiated the need to amend the utility interconnection standard to allow advanced inverter control functionalities that provide: (1) reactive power control for voltage support, (2) real power control for frequency support and (3) better tolerance of grid disturbances. These capabilities are aimed at minimizing the negative impact distributed PV systems may have on EPS voltage and frequency. Unfortunately, these advanced control functions may interfere with island detection schemes, and further development of advanced inverter functions requires a study of the effect of advanced functions on the efficacy of antiislanding schemes employed in industry. This report summarizes the analytical, simulation and experimental work to study interactions between advanced inverter functions and anti-islanding schemes being employed in distributed PV systems.
13. Ionospheric precursors to scintillation activity
Directory of Open Access Journals (Sweden)
Paul S.J. Spencer
2014-03-01
Full Text Available Ionospheric scintillation is the rapid fluctuation of both phase and amplitude of trans-ionospheric radio waves due to small scale electron density irregularities in the ionosphere. Prediction of the occurrence of scintillation at L band frequencies is needed to mitigate the disruption of space-based communication and navigation systems. The purpose of this paper is to present a method of using tomographic inversions of the ionospheric electron density obtained from ground-based GPS data to infer the location and strength of the post-sunset plasma drift vortex. This vortex is related to the pre-reversal enhancement in the eastwards electric field which has been correlated to the subsequent occurrence of scintillation.
Science.gov (United States)
Stephens, Donald R.
2015-01-01
CommLargo, Inc., has developed a scintillation-hardened Global Positioning System (GPS) receiver that improves reliability for low-orbit missions and complies with NASA's Space Telecommunications Radio System (STRS) architecture standards. A software-defined radio (SDR) implementation allows a single hardware element to function as either a conventional radio or as a GPS receiver, providing backup and redundancy for platforms such as the International Space Station (ISS) and high-value remote sensing platforms. The innovation's flexible SDR implementation reduces cost, weight, and power requirements. Scintillation hardening improves mission reliability and variability. In Phase I, CommLargo refactored an open-source GPS software package with Kalman filter-based tracking loops to improve performance during scintillation and also demonstrated improved navigation during a geomagnetic storm. In Phase II, the company generated a new field-programmable gate array (FPGA)-based GPS waveform to demonstrate on NASA's Space Communication and Navigation (SCaN) test bed.
15. Unitary scintillation detector and system
Science.gov (United States)
McElhaney, S.A.; Chiles, M.M.
1994-05-31
The invention is a unitary alpha, beta, and gamma scintillation detector and system for sensing the presence of alpha, beta, and gamma radiations selectively or simultaneously. The scintillators are mounted in a light-tight housing provided with an entrance window for admitting alpha, beta, and gamma radiation and excluding ambient light from the housing. Light pulses from each scintillator have different decay constants that are converted by a photosensitive device into corresponding differently shaped electrical pulses. A pulse discrimination system identifies the electrical pulses by their respective pulse shapes which are determined by decay time. The identified electrical pulses are counted in separate channel analyzers to indicate the respective levels of sensed alpha, beta, and gamma radiations. 10 figs.
16. Nanophosphor composite scintillator with a liquid matrix
Science.gov (United States)
McKigney, Edward Allen; Burrell, Anthony Keiran; Bennett, Bryan L.; Cooke, David Wayne; Ott, Kevin Curtis; Bacrania, Minesh Kantilal; Del Sesto, Rico Emilio; Gilbertson, Robert David; Muenchausen, Ross Edward; McCleskey, Thomas Mark
2010-03-16
An improved nanophosphor scintillator liquid comprises nanophosphor particles in a liquid matrix. The nanophosphor particles are optionally surface modified with an organic ligand. The surface modified nanophosphor particle is essentially surface charge neutral, thereby preventing agglomeration of the nanophosphor particles during dispersion in a liquid scintillator matrix. The improved nanophosphor scintillator liquid may be used in any conventional liquid scintillator application, including in a radiation detector.
17. Inverter design for high frequency power distribution
Science.gov (United States)
King, R. J.
1985-01-01
A class of simple resonantly commutated inverters are investigated for use in a high power (100 KW - 1000 KW) high frequency (10 KHz - 20 KHz) AC power distribution system. The Mapham inverter is found to provide a unique combination of large thyristor turn-off angle and good utilization factor, much better than an alternate 'current-fed' inverter. The effects of loading the Mapham inverter entirely with rectifier loads are investigated by simulation and with an experimental 3 KW 20 KHz inverter. This inverter is found to be well suited to a power system with heavy rectifier loading.
18. Development of scintillating fiber tracker
International Nuclear Information System (INIS)
Ishikawa, Shuzo; Kawai, Toshihide; Kozaki, Tetsuo
1995-01-01
In order to use thin scintillating fiber (diameter 500 micron) as a particle tracking detector, we have developed a method to construct precise multi-layer scintillating fiber sheets. We have also developed dedicated machines for this purpose. This paper presents the details of the method and the machines. Using these machines, we have produced fiber sheets for CERN WA95/CHORUS, which intend to detect a neutrino oscillation in the νμ-ντ channel using Hybrid Emulsion Set-up. Fiber Trackers are used as a vertex detector which support the neutrino event location in the nuclear emulsion target. (author)
19. Hygroscopicity Evaluation of Halide Scintillators
Energy Technology Data Exchange (ETDEWEB)
Zhuravleva, M [The University of Tennessee; Stand, L [The University of Tennessee; Wei, H [The University of Tennessee; Hobbs, C. L. [University of Tennessee, Knoxville (UTK); Boatner, Lynn A [ORNL; Ramey, Joanne Oxendine [ORNL; Burger, Arnold [Fisk University, Nashville; Rowe, E [Fisk University, Nashville; Bhattacharya, P. [Fisk University, Nashville; Tupitsyn, E [Fisk University, Nashville; Melcher, Charles L [University of Tennessee, Knoxville (UTK)
2014-01-01
A collaborative study of relative hygroscopicity of anhydrous halide scintillators grown at various laboratories is presented. We have developed a technique to evaluate moisture sensitivity of both raw materials and grown crystals, in which the moisture absorption rate is measured using a gravimetric analysis. Degradation of the scintillation performance was investigated by recording gamma-ray spectra and monitoring the photopeak position, count rate and energy resolution. The accompanying physical degradation of the samples exposed to ambient atmosphere was photographically recorded as well. The results were compared with ben
20. Magnetic fields and scintillator performance
International Nuclear Information System (INIS)
Green, D.; Ronzhin, A.; Hagopian, V.
1995-06-01
Experimental data have shown that the light output of a scintillator depends on the magnitude of the externally applied magnetic fields, and that this variation can affect the calorimeter calibration and possibly resolution. The goal of the measurements presented here is to study the light yield of scintillators in high magnetic fields in conditions that are similar to those anticipated for the LHC CMS detector. Two independent measurements were performed, the first at Fermilab and the second at the National High Magnetic Field Laboratory at Florida State University
1. Composite scintillators for detection of ionizing radiation
Science.gov (United States)
Dai, Sheng [Knoxville, TN; Stephan, Andrew Curtis [Knoxville, TN; Brown, Suree S [Knoxville, TN; Wallace, Steven A [Knoxville, TN; Rondinone, Adam J [Knoxville, TN
2010-12-28
Applicant's present invention is a composite scintillator having enhanced transparency for detecting ionizing radiation comprising a material having optical transparency wherein said material comprises nano-sized objects having a size in at least one dimension that is less than the wavelength of light emitted by the composite scintillator wherein the composite scintillator is designed to have selected properties suitable for a particular application.
2. Time resolution research in liquid scintillating detection
International Nuclear Information System (INIS)
He Hongkun; Shi Haoshan
2006-01-01
The signal processing design method is introduced into liquid scintillating detection system design. By analyzing the signal of liquid scintillating detection, improving time resolution is propitious to upgrade efficiency of detecting. The scheme of realization and satisfactory experiment data is demonstrated. Besides other types of liquid scintillating detection is the same, just using more high speed data signal processing techniques and elements. (authors)
3. Thin Scintillating Polarized Targets for Spin Physics
Science.gov (United States)
van den Brandt, B.; Bunyatova, E. I.; Hautle, P.; Konter, J. A.
2003-07-01
At PSI polarized scintillating targets are available since 1996. Proton polarizations of more than 80%, and deuteron polarizations of 25% in polystyrene-based scintillators can be reached under optimum conditions in a vertical dilution refrigerator with optical access, suited for nuclear and particle physics experiments. New preparation procedures allow to provide very thin polarizable scintillating targets and widen the spectrum of conceivable experiments.
4. Pulse Shape Discrimination with EJ299 scintillators
Science.gov (United States)
Muoio, A.; Cappuzzello, F.; Carbone, D.; Cavallaro, M.; Lanzalone, G.; Pappalardo, A.; Santagati, G.; Trifirò, A.; Tudisco, S.
2018-02-01
Recently a new generation plastic scintillator PPO have been developed. They promise excellent performances in terms of neutron/gamma discrimination. In this work we will present the activity made at INFN-LNS on the plastic scintillator EJ299 in comparison with the most traditional liquid scintillator EJ301 used in several nuclear physics experiments.
5. Advanced Modular Inverter Technology Development
Energy Technology Data Exchange (ETDEWEB)
2006-02-04
Electric and hybrid-electric vehicle systems require an inverter to convert the direct current (DC) output of the energy generation/storage system (engine, fuel cells, or batteries) to the alternating current (AC) that vehicle propulsion motors use. Vehicle support systems, such as lights and air conditioning, also use the inverter AC output. Distributed energy systems require an inverter to provide the high quality AC output that energy system customers demand. Today's inverters are expensive due to the cost of the power electronics components, and system designers must also tailor the inverter for individual applications. Thus, the benefits of mass production are not available, resulting in high initial procurement costs as well as high inverter maintenance and repair costs. Electricore, Inc. (www.electricore.org) a public good 501 (c) (3) not-for-profit advanced technology development consortium assembled a highly qualified team consisting of AeroVironment Inc. (www.aerovironment.com) and Delphi Automotive Systems LLC (Delphi), (www.delphi.com), as equal tiered technical leads, to develop an advanced, modular construction, inverter packaging technology that will offer a 30% cost reduction over conventional designs adding to the development of energy conversion technologies for crosscutting applications in the building, industry, transportation, and utility sectors. The proposed inverter allows for a reduction of weight and size of power electronics in the above-mentioned sectors and is scalable over the range of 15 to 500kW. The main objective of this program was to optimize existing AeroVironment inverter technology to improve power density, reliability and producibility as well as develop new topology to reduce line filter size. The newly developed inverter design will be used in automotive and distribution generation applications. In the first part of this program the high-density power stages were redesigned, optimized and fabricated. One of the main
6. Complex oxide scintillators: material defects and scintillation performace
Czech Academy of Sciences Publication Activity Database
Nikl, Martin; Laguta, Valentyn; Vedda, A.
2008-01-01
Roč. 245, č. 9 (2008), 1701-1722 ISSN 0370-1972 R&D Projects: GA AV ČR IAA100100810 Institutional research plan: CEZ:AV0Z10100521 Keywords : scintillator * structural defects * impurities * trapping states * electron paramagnetic resonance * thermoluminescence Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.166, year: 2008
7. Invertible extensions and growth conditions
Czech Academy of Sciences Publication Activity Database
2004-01-01
Roč. 339, - (2004), s. 21-26 ISSN 1631-073X R&D Projects: GA ČR GA201/03/0041; GA AV ČR KSK1019101 Institutional research plan: CEZ:AV0Z1019905 Keywords : invertible extensions * growth conditions Subject RIV: BA - General Mathematics Impact factor: 0.284, year: 2004
8. Inverting an Introductory Statistics Classroom
Science.gov (United States)
Kraut, Gertrud L.
2015-01-01
The inverted classroom allows more in-class time for inquiry-based learning and for working through more advanced problem-solving activities than does the traditional lecture class. The skills acquired in this learning environment offer benefits far beyond the statistics classroom. This paper discusses four ways that can make the inverted…
9. Overload protection system for power inverter
Science.gov (United States)
Nagano, S. (Inventor)
1977-01-01
An overload protection system for a power inverter utilized a first circuit for monitoring current to the load from the power inverter to detect an overload and a control circuit to shut off the power inverter, when an overload condition was detected. At the same time, a monitoring current inverter was turned on to deliver current to the load at a very low power level. A second circuit monitored current to the load, from the monitoring current inverter, to hold the power inverter off through the control circuit, until the overload condition was cleared so that the control circuit may be deactivated in order for the power inverter to be restored after the monitoring current inverter is turned off completely.
10. Fast plastic scintillator SPS-B18
International Nuclear Information System (INIS)
Andreeshchev, E.A.; Avetisyan, V.S.; Veronyan, S.M.
1988-01-01
The test results of fast response of SPS-B18 scintillators with 25 mm diameter and height are presented. The scintillators are made by thermal polymerization of solution by two luminescent additions in highly refined styrene. As a first luminescent addition n-terphenyl with 3.5 % concentration is used. The scintillator fast response is obtained by introduction of the second luminescent addition, which atoms (halogen atoms) have small excited state lifetime. The use of the effect of intramolecular quenching of the luminescent addition permits to make a plastic scintillator having scintillation pulse duration at halfheight of 0.15 ns
11. Physics of lead tungstate scintillators
Czech Academy of Sciences Publication Activity Database
Laguta, Valentyn; Nikl, Martin; Zazubovich, S.
2008-01-01
Roč. 55, č. 3 (2008), s. 1275-1282 ISSN 0018-9499 Institutional research plan: CEZ:AV0Z10100521 Keywords : scintillator * PbWO 4 * luminiscence * photothermal defect creation Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.518, year: 2008
12. Inverter for Installations with Intermittent Electricity Production
OpenAIRE
Ermuraki Iu.; Berzan V.
2016-01-01
A new architecture of the inverter used in the convertion of electric energy generated by renewable energy sources is studied in this paper. The distinctive features of this inverter is the special block which compensates pulsing of the current with double frequency, characteristic for these inverters. The switching of electronic keys is realized using the method TCM In this block, like in the inverter, which assures the switching at the voltages near to zero (ZVC). The proposed algorithm of ...
13. Improved Performance via the Inverted Classroom
Science.gov (United States)
Weinstein, Randy D.
2015-01-01
This study examined student performance in an inverted thermodynamics course (lectures provided by video outside of class) compared to a traditional lecture class. Students in the inverted class performed better on their exams. Students in the bottom third of the inverted course showed the greatest improvement. These bottom third students had a C…
14. 21 CFR 184.1859 - Invert sugar.
Science.gov (United States)
2010-04-01
... 21 Food and Drugs 3 2010-04-01 2009-04-01 true Invert sugar. 184.1859 Section 184.1859 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) FOOD FOR HUMAN... Substances Affirmed as GRAS § 184.1859 Invert sugar. (a) Invert sugar (CAS Reg. No. 8013-17-0) is an aqueous...
15. Γ-source Neutral Point Clamped Inverter
DEFF Research Database (Denmark)
Mo, Wei; Loh, Poh Chiang; Blaabjerg, Frede
Transformer based Z-source inverters are recently proposed to achieve promising buck-boost capability. They have improved higher buck-boost capability, smaller size and less components count over Z-source inverters. On the other hand, neutral point clamped inverters have less switching stress...
16. Multilevel Inverter by Cascading Industrial VSI
DEFF Research Database (Denmark)
Teodorescu, Remus; Blaabjerg, Frede; Pedersen, John Kim
2002-01-01
-source inverter that uses three IGBT triphase inverter modules along with an output transformer to obtain a 3 p.u. multilevel output voltage is introduced. The system yields in high-quality multistep voltage with up to 4 levels and low dv/dt, balanced operation of the inverter modules, each supplying a third...
17. Scintillators for positron emission tomography
International Nuclear Information System (INIS)
Moses, W.W.; Derenzo, S.E.
1995-09-01
Like most applications that utilize scintillators for gamma detection, Positron Emission Tomography (PET) desires materials with high light output, short decay time, and excellent stopping power that are also inexpensive, mechanically rugged, and chemically inert. Realizing that this ''ultimate'' scintillator may not exist, this paper evaluates the relative importance of these qualities and describes their impact on the imaging performance of PET. The most important PET scintillator quality is the ability to absorb 511 keV photons in a small volume, which affects the spatial resolution of the camera. The dominant factor is a short attenuation length (≤ 1.5 cm is required), although a high photoelectric fraction is also important (> 30% is desired). The next most important quality is a short decay time, which affects both the dead time and the coincidence timing resolution. Detection rates for single 511 keV photons can be extremely high, so decay times ≤ 500 ns are essential to avoid dead time losses. In addition, positron annihilations are identified by time coincidence so ≤5 ns fwhm coincidence pair timing resolution is required to identify events with narrow coincidence windows, reducing contamination due to accidental coincidences. Current trends in PET cameras are toward septaless, ''fully-3D'' cameras, which have significantly higher count rates than conventional 2-D cameras and so place higher demands on scintillator decay time. Light output affects energy resolution, and thus the ability of the camera to identify and reject events where the initial 511 keV photon has undergone Compton scatter in the patient. The scatter to true event fraction is much higher in fully-3D cameras than in 2-D cameras, so future PET cameras would benefit from scintillators with a 511 keV energy resolution < 10--12% fwhm
18. Energy resolution of scintillation detectors
Energy Technology Data Exchange (ETDEWEB)
Moszyński, M., E-mail: [email protected]; Syntfeld-Każuch, A.; Swiderski, L.; Grodzicka, M.; Iwanowska, J.; Sibczyński, P.; Szczęśniak, T.
2016-01-01
According to current knowledge, the non-proportionality of the light yield of scintillators appears to be a fundamental limitation of energy resolution. A good energy resolution is of great importance for most applications of scintillation detectors. Thus, its limitations are discussed below; which arise from the non-proportional response of scintillators to gamma rays and electrons, being of crucial importance to the intrinsic energy resolution of crystals. The important influence of Landau fluctuations and the scattering of secondary electrons (δ-rays) on intrinsic resolution is pointed out here. The study on undoped NaI and CsI at liquid nitrogen temperature with a light readout by avalanche photodiodes strongly suggests that the non-proportionality of many crystals is not their intrinsic property and may be improved by selective co-doping. Finally, several observations that have been collected in the last 15 years on the influence of the slow components of light pulses on energy resolution suggest that more complex processes are taking place in the scintillators. This was observed with CsI(Tl), CsI(Na), ZnSe(Te), and undoped NaI at liquid nitrogen temperature and, finally, for NaI(Tl) at temperatures reduced below 0 °C. A common conclusion of these observations is that the highest energy resolution, and particularly intrinsic resolution measured with the scintillators, characterized by two or more components of the light pulse decay, is obtainable when the spectrometry equipment integrates the whole light of the components. In contrast, the slow components observed in many other crystals degrade the intrinsic resolution. In the limiting case, afterglow could also be considered as a very slow component that spoils the energy resolution. The aim of this work is to summarize all of the above observations by looking for their origin.
19. Fault-tolerant three-level inverter
Science.gov (United States)
Edwards, John; Xu, Longya; Bhargava, Brij B.
2006-12-05
A method for driving a neutral point clamped three-level inverter is provided. In one exemplary embodiment, DC current is received at a neutral point-clamped three-level inverter. The inverter has a plurality of nodes including first, second and third output nodes. The inverter also has a plurality of switches. Faults are checked for in the inverter and predetermined switches are automatically activated responsive to a detected fault such that three-phase electrical power is provided at the output nodes.
20. Neutral Point Clamped Npc Type Multilevel Inverter
Directory of Open Access Journals (Sweden)
2015-08-01
Full Text Available Concept of the multilevel inverter is same as the other inverter which is to converts Direct current DC to Alternating current AC .The inverted current can be at any vital voltage and frequency with the use of pertinent transformers switching and control circuits. From the source like batteries solar panel wind turbine or fuel cell the inverter will convert the DC electricity to AC electricity. In this modern technology Power electronics is very important where it used in a great variety of product. With the high potential in high power for industry multilevel inverter will become most popular for so many applications.
1. Integrated Inverter And Battery Charger
Science.gov (United States)
Rippel, Wally E.
1988-01-01
Circuit combines functions of dc-to-ac inversion (for driving ac motor in battery-powered vehicle) and ac-to-dc conversion (for charging battery from ac line when vehicle not in use). Automatically adapts to either mode. Design of integrated inverter/charger eliminates need for duplicate components, saves space, reduces weight and cost of vehicle. Advantages in other applications : load-leveling systems, standby ac power systems, and uninterruptible power supplies.
2. Effective switching frequency multiplier inverter
Science.gov (United States)
Su, Gui-Jia; Peng, Fang Z.
2007-08-07
A switching frequency multiplier inverter for low inductance machines that uses parallel connection of switches and each switch is independently controlled according to a pulse width modulation scheme. The effective switching frequency is multiplied by the number of switches connected in parallel while each individual switch operates within its limit of switching frequency. This technique can also be used for other power converters such as DC/DC, AC/DC converters.
3. A helical scintillating fiber hodoscope
CERN Document Server
Altmeier, M; Bisplinghoff, J; Bissel, T; Bollmann, R; Busch, M; Büsser, K; Colberg, T; Demiroers, L; Diehl, O; Dohrmann, F; Engelhardt, H P; Eversheim, P D; Felden, O; Gebel, R; Glende, M; Greiff, J; Gross, A; Gross-Hardt, R; Hinterberger, F; Jahn, R; Jeske, M; Jonas, E; Krause, H; Lahr, U; Langkau, R; Lindemann, T; Lindlein, J; Maier, R; Maschuw, R; Mayer-Kuckuck, T; Meinerzhagen, A; Naehle, O; Pfuff, M; Prasuhn, D; Rohdjess, H; Rosendaal, D; Von Rossen, P; Sanz, B; Schirm, N; Schulz-Rojahn, M; Schwarz, V; Scobel, W; Thomas, S; Trelle, H J; Weise, E; Wellinghausen, A; Wiedmann, W; Woller, K; Ziegler, R
1999-01-01
A novel scintillating fiber hodoscope in helically cylindric geometry has been developed for detection of low multiplicity events of fast protons and other light charged particles in the internal target experiment EDDA at the Cooler Synchrotron COSY. The hodoscope consists of 640 scintillating fibers (2.5 mm diameter), arranged in four layers surrounding the COSY beam pipe. The fibers are helically wound in opposing directions and read out individually using 16-channel photomultipliers connected to a modified commercial encoding system. The detector covers an angular range of 9 deg. <= THETA<=72 deg. and 0 deg. <=phi (cursive,open) Greek<=360 deg. in the lab frame. The detector length is 590 mm, the inner diameter 161 mm. Geometry and granularity of the hodoscope afford a position resolution of about 1.3 mm. The detector design took into consideration a maximum of reliability and a minimum of maintenance. An LED array may be used for monitoring purposes. (author)
4. LHCb Upgrade: Scintillating Fibre Tracker
International Nuclear Information System (INIS)
Tobin, Mark
2016-01-01
The LHCb detector will be upgraded during the Long Shutdown 2 (LS2) of the LHC in order to cope with higher instantaneous luminosities and to read out the data at 40 MHz using a trigger-less read-out system. All front-end electronics will be replaced and several sub-detectors must be redesigned to cope with higher occupancy. The current tracking detectors downstream of the LHCb dipole magnet will be replaced by the Scintillating Fibre (SciFi) Tracker. The SciFi Tracker will use scintillating fibres read out by Silicon Photomultipliers (SiPMs). State-of-the-art multi-channel SiPM arrays are being developed to read out the fibres and a custom ASIC will be used to digitise the signals from the SiPMs. The evolution of the design since the Technical Design Report in 2014 and the latest R & D results are presented.
5. Studies of novel plastic scintillators
International Nuclear Information System (INIS)
McInally, I.D.
1979-08-01
The general aim of this study was to synthesize fluorescent compounds which are capable of polymerisation, to prepare polymers and co-polymers from these compounds and to study the photophysical properties of these materials. In this way it is hoped to produce plastic scintillators exhibiting improved energy transfer efficiency. Materials studied included POS(2-phenyl-5-(p vinyl) phenyloxazole) vinyl naphthalene, methyl anthracene terminated poly vinyl toluene) and derivatives of BuPBD. (author)
6. Buried plastic scintillator muon telescope
Science.gov (United States)
Sanchez, F.; Medina-Tanco, G.A.; D'Olivo, J.C.; Paic, G.; Patino Salazar, M.E.; Nahmad-Achar, E.; Valdes Galicia, J.F.; Sandoval, A.; Alfaro Molina, R.; Salazar Ibarguen, H.; Diozcora Vargas Trevino, M.A.; Vergara Limon, S.; Villasenor, L.M.
Muon telescopes can have several applications, ranging from astrophysical to solar-terrestrial interaction studies, and fundamental particle physics. We show the design parameters, characterization and end-to-end simulations of a detector composed by a set of three parallel dual-layer scintillator planes, buried at fix depths ranging from 0.30 m to 3 m. Each layer is 4 m2 and is composed by 50 rectangular pixels of 4cm x 2 m, oriented at a 90 deg angle with respect to its companion layer. The scintillators are MINOS extruded polystyrene strips with two Bicron wavelength shifting fibers mounted on machined grooves. Scintillation light is collected by multi-anode PMTs of 64 pixels, accommodating two fibers per pixel. The front-end electronics has a time resolution of 7.5 nsec. Any strip signal above threshold opens a GPS-tagged 2 micro-seconds data collection window. All data, including signal and background, are saved to hard disk. Separation of extensive air shower signals from secondary cosmic-ray background muons and electrons is done offline using the GPS-tagged threefold coincidence signal from surface water cerenkov detectors located nearby in a triangular array. Cosmic-ray showers above 6 PeV are selected. The data acquisition system is designed to keep both, background and signals from extensive air showers for a detailed offline data.
7. Multi element high resolution scintillator structure
International Nuclear Information System (INIS)
Cusano, D.A.
1980-01-01
A gamma camera scintillator structure, suitable for detecting high energy gamma photons which, in a single scintillator camera, would require a comparatively thick scintillator crystal, so resulting in unacceptable dispersion of light photons, comprises a collimator array of a high Z material with elongated, parallel wall channels with the scintillator material being disposed in one end of the channels so as to form an integrated collimator/scintillator structure. The collimator channel walls are preferably coated with light reflective material and further light reflective surfaces being translucent to gamma photons, may be provided in each channel. The scintillators may be single crystals or preferably comprise a phosphor dispersed in a thermosetting translucent matrix as disclosed in GB2012800A. The light detectors of the assembled camera may be photomultiplier tubes charge coupled devices or charge injection devices. (author)
8. A Review of Ionospheric Scintillation Models.
Science.gov (United States)
This is a general review of the existing climatological models of ionospheric radio scintillation for high and equatorial latitudes. Trans-ionospheric communication of radio waves from transmitter to user is affected by the ionosphere which is highly variable and dynamic in both time and space. Scintillation is the term given to irregular amplitude and phase fluctuations of the received signals and related to the electron density irregularities in the ionosphere. Key sources of ionospheric irregularities are plasma instabilities; every irregularities model is based on the theory of radio wave propagation in random media. It is important to understand scintillation phenomena and the approach of different theories. Therefore, we have briefly discussed the theories that are used to interpret ionospheric scintillation data. The global morphology of ionospheric scintillation is also discussed briefly. The most important (in our opinion) analytical and physical models of scintillation are reviewed here.
9. Morphology of auroral zone radio wave scintillation
International Nuclear Information System (INIS)
Rino, C.L.; Matthews, S.J.
1980-01-01
This paper describes the morphology of midnight sector and morning sector auroral zone scintillation observations made over a two-year period using the Wideband satelite, which is in a sun-synchronous, low-altitude orbit. No definitive seasonal variation was found. The nighttime data showed the highest scintillation ocurrence levels, but significant amounts of morning scintillation were observed. For the most part the scintillation activity followed the general pattern of local magnetic activity. The most prominent feature in the nightime data is a localized amplitude and phase scintillation enhancement at the point where the propagation vector lies within an L shell. A geometrical effect due to a dynamic slab of sheetlike structures in the F region is hypothesized as the source of his enhancement. The data have been sorted by magnetic activity, proximity to local midnight, and season. The general features of the data are in agreement with the accepted morphology of auroral zone scintillation
10. Monte Carlo model of light transport in scintillating fibers and large scintillators
International Nuclear Information System (INIS)
Chakarova, R.
1995-01-01
A Monte Carlo model is developed which simulates the light transport in a scintillator surrounded by a transparent layer with different surface properties. The model is applied to analyse the light collection properties of scintillating fibers and a large scintillator wrapped in aluminium foil. The influence of the fiber interface characteristics on the light yield is investigated in detail. Light output results as well as time distributions are obtained for the large scintillator case. 15 refs, 16 figs
11. Scintillation properties of quantum-dot doped styrene based plastic scintillators
International Nuclear Information System (INIS)
Park, J.M.; Kim, H.J.; Hwang, Y.S.; Kim, D.H.; Park, H.W.
2014-01-01
We fabricated quantum-dot doped plastic scintillators in order to control the emission wavelength. We studied the characterization of the quantum-dots (CdSe/ZnS) and PPO (2, 5-diphenyloxazole) doped styrene based plastic scintillators. PPO is usually used as a dopant to enhance the scintillation properties of organic scintillators with a maximum emission wavelength of 380 nm. In order to study the scintillation properties of the quantum-dots doped plastic scintillators, the samples were irradiated with X-ray, photon, and 45 MeV proton beams. We observed that only PPO doped plastic scintillators shows a luminescence peak around 380 nm. However, both the quantum-dots and PPO doped plastic scintillators shows luminescence peaks around 380 nm and 520 nm. Addition of quantum-dots had shifted the luminescence spectrum from 380 nm (PPO) toward the region of 520 nm (Quantum-dots). Emissions with wavelength controllable plastic scintillators can be matched to various kinds of photosensors such as photomultiplier tubes, photo-diodes, avalanche photo-diodes, and CCDs, etc. Also quantum-dots doped plastic scintillator, which is irradiated 45 MeV proton beams, shows that the light yield of quantum-dots doped plastic scintillator is increases as quantum-dots doping concentration increases at 520 nm. And also the plastic scintillators were irradiated with Cs-137 γ-ray for measuring fluorescence decay time. -- Highlights: • Quantum-dot doped plastic scintillator is grown by the thermal polymerization method. • Quantum-dot doped plastic scintillators can control the emission wavelength to match with photo-sensor. • Quantum-dots and PPO doped plastic scintillators emitted luminescence peaks around 380 nm and 520 nm. • We observed the energy transfer from PPO to quantum-dot in the quantum-dot doped plastic scintillator
12. High-symmetry organic scintillator systems
Science.gov (United States)
Feng, Patrick L.
2018-02-06
An ionizing radiation detector or scintillator system includes a scintillating material comprising an organic crystalline compound selected to generate photons in response to the passage of ionizing radiation. The organic compound has a crystalline symmetry of higher order than monoclinic, for example an orthorhombic, trigonal, tetragonal, hexagonal, or cubic symmetry. A photodetector is optically coupled to the scintillating material, and configured to generate electronic signals having pulse shapes based on the photons generated in the scintillating material. A discriminator is coupled to the photon detector, and configured to discriminate between neutrons and gamma rays in the ionizing radiation based on the pulse shapes of the output signals.
13. Design of Fluorescent Compounds for Scintillation Detection
Energy Technology Data Exchange (ETDEWEB)
Pla-Dalmau, Anna [Northern Illinois U.
1990-01-01
Plastic scintillation detectors for high energy physics applications require the development of new fluorescent compounds to meet the demands set by the future generation of particle accelerators such as the Superconducting Supercollider (SSe). Plastic scintillators are commonly based on a polymer matrix doped with two fluorescent compounds: the primary dopant and the wavelength shifter. Their main characteristics are fast response time and high quantum efficiency. The exposure to larger radiation doses and demands for larger light output questions their survivability in the future experiments. A new type of plastic scintillator - intrinsic scintillator - has been suggested. It uses a single dopant as primary and wavelength shifter, and should be less susceptible to radiation damage....
14. Waveshifters and Scintillators for Ionizing Radiation Detection
Energy Technology Data Exchange (ETDEWEB)
B.Baumgaugh; J.Bishop; D.Karmgard; J.Marchant; M.McKenna; R.Ruchti; M.Vigneault; L.Hernandez; C.Hurlbut
2007-12-11
Scintillation and waveshifter materials have been developed for the detection of ionizing radiation in an STTR program between Ludlum Measurements, Inc. and the University of Notre Dame. Several new waveshifter materials have been developed which are comparable in efficiency and faster in fluorescence decay than the standard material Y11 (K27) used in particle physics for several decades. Additionally, new scintillation materials useful for fiber tracking have been developed which have been compared to 3HF. Lastly, work was done on developing liquid scintillators and paint-on scintillators and waveshifters for high radiation environments.
15. High-symmetry organic scintillator systems
Energy Technology Data Exchange (ETDEWEB)
Feng, Patrick L.
2018-03-13
An ionizing radiation detector or scintillator system includes a scintillating material comprising an organic crystalline compound selected to generate photons in response to the passage of ionizing radiation. The organic compound has a crystalline symmetry of higher order than monoclinic, for example an orthorhombic, trigonal, tetragonal, hexagonal, or cubic symmetry. A photodetector is optically coupled to the scintillating material, and configured to generate electronic signals having pulse shapes based on the photons generated in the scintillating material. A discriminator is coupled to the photon detector, and configured to discriminate between neutrons and gamma rays in the ionizing radiation based on the pulse shapes of the output signals.
16. Designing an optimally proportional inorganic scintillator
Energy Technology Data Exchange (ETDEWEB)
Singh, Jai, E-mail: [email protected] [School of Engineering and IT, B-Purple-12, Faculty of EHSE, Charles Darwin University, NT 0909 (Australia); Koblov, Alexander [School of Engineering and IT, B-Purple-12, Faculty of EHSE, Charles Darwin University, NT 0909 (Australia)
2012-09-01
The nonproportionality observed in the light yield of inorganic scintillators is studied theoretically as a function of the rates of bimolecular and Auger quenching processes occurring within the electron track initiated by a gamma- or X-ray photon incident on a scintillator. Assuming a cylindrical track, the influence of the track radius and concentration of excitations created within the track on the scintillator light yield is also studied. Analysing the calculated light yield a guideline for inventing an optimally proportional scintillator with optimal energy resolution is presented.
DEFF Research Database (Denmark)
Li, Ding; Chiang Loh, Poh; Zhu, Miao
2013-01-01
Inverters with high-output voltage gain usually face the problem of high-input current flowing through their components. The problem might further be exaggerated if the inverters use high-frequency magnetic devices like transformers or coupled inductors. Leakage inductances of these devices must...... strictly be small to prevent overvoltages caused by switching of their winding currents. To avoid these related problems, cascaded trans-Z-source inverters are proposed. They use multiple magnetic cells in an alternately cascading pattern rather than a single magnetic cell with large turns ratio....... Simulation and experimental results have shown that the multicell inverters can produce the same high-voltage gain, while keeping currents and voltages of the components low. The inverters can also step down their output voltages like a traditional voltage-source inverter without compromising waveform...
18. Inverter design for four-wire microgrids
OpenAIRE
Heredero Peris, Daniel; Pagès Giménez, Marc; Montesinos Miracle, Daniel
2015-01-01
This paper presents a PQ four quadrant four-wire three-phase inverter for microgrids integration. The inverter is based in two full-bridge IGBT modules connected in a three-phase configuration plus a threephase parallelized neutral branch. This topology is galvanically isolated through a single-phase transformer bank. The converter operates as a non-ideal voltage-controlled voltage source inverter under AC droop strategy with hot-swap capability based on a dynamic virtual impedance.
19. Photodetectors for scintillator proportionality measurement
Energy Technology Data Exchange (ETDEWEB)
Moses, William W. [Lawrence Berkeley National Laboratory (United States)], E-mail: [email protected]; Choong, Woon-Seng [Lawrence Berkeley National Laboratory (United States); Hull, Giulia; Payne, Steve; Cherepy, Nerine; Valentine, John D. [Lawrence Livermore National Laboratory (United States)
2009-10-21
We evaluate photodetectors for use in a Compton Coincidence apparatus designed for measuring scintillator proportionality. There are many requirements placed on the photodetector in these systems, including active area, linearity, and the ability to accurately measure low light levels (which implies high quantum efficiency and high signal-to-noise ratio). Through a combination of measurement and Monte Carlo simulation, we evaluate a number of potential photodetectors, especially photomultiplier tubes and hybrid photodetectors. Of these, we find that the most promising devices available are photomultiplier tubes with high ({approx}50%) quantum efficiency, although hybrid photodetectors with high quantum efficiency would be preferable.
20. Scintillating fibre tracking neutron detector
International Nuclear Information System (INIS)
Karlsson, Joakim.
1995-04-01
A detector for measurements of collimated fluxes of neutrons in the energy range 2-20 MeV is proposed. It utilizes (n.p) elastic scattering in scintillating optical fibres placed in successive orthogonal layers perpendicular to the neutron flux. A test module has been designed, constructed and tested with respect to separation of neutron and gamma events. The pulse height measurements show the feasibility to discriminate between neutron, gamma and background events. Application to measurements of fusion neutrons is considered. 18 refs, 22 figs, 4 tabs
1. New shaper of scintillation signals
International Nuclear Information System (INIS)
Brovchenko, V.G.
2001-01-01
Summation of the exponential shape pulse (abrupt front, exponential fall-off) with the pulse, proportional to its integral (the integration time constant is equal to the exponent fall-off constant), results in the pulse, the apex whereof is horizontal (parallel to the base line). Such a pulse is suitable for registration through standard analog-to-digital converters of the consecutive binary approximation, The described scheme is accomplished for verification of the basic principle of the shaper action. The parameters of the scheme are approximated to those ones, necessary for processing scintillation signals NaI(Tl) [ru
2. Quantum Dots in Liquid Scintillator
Science.gov (United States)
Gooding, Diana
2017-09-01
Quantum dots are semiconducting crystals with dimensions on the order of nanometers. Due to quantum confinement, their size gives rise to optical properties that resemble those of single atoms, rather than bulk material. One of these is their absorption of light shorter than a characteristic wavelength and reemission in a narrow peak around that wavelength. This unique photoluminescence makes quantum dots ideal wavelength shifters. Moreover, their chemistry provides a straight-forward method to suspend heavy elements in organic scintillators. The NuDot collaboration has been pursuing a variety of new quantum dots, and a review of the current results will be presented.
3. Supernova Neutrino Detection With Liquid Scintillators
Energy Technology Data Exchange (ETDEWEB)
Ianni, Aldo, E-mail: [email protected] [I.N.F.N. Gran Sasso Laboratory, S.S. 17bis, 67100, Assergi (Italy)
2011-08-10
Core collapse supernovae are a remarkable source of neutrinos. These neutrinos can also be detected by means of massive liquid scintillators located underground. Observations of supernova neutrinos can shed light on the explosion mechanism and on neutrino properties. In this paper we review the detection channels for neutrinos in liquid scintillators. We consider present and future experiments for supernova neutrino searches.
4. Ionospheric Scintillation Activity Over Ilorin, Nigeria
Science.gov (United States)
2018-02-01
Scintillation of radio waves in the L-band frequency is a regular occurrence at the equatorial and auroral regions at night most especially during high solar activity periods. Scintillation is caused by plasma density irregularities, and this could cause loss of lock of Global Navigation Satellite System (GNSS) signals leading to impairment of the applications that rely on this system. A study on the occurrence of scintillation activity over Ilorin (latitude = 8.48°N, longitude = 4.67°W, and geomagnetic latitude = 1.89°S), Nigeria was done using S4 index data from NovAtel GPStation-2 receiver (2009-2012) and NovAtel GPStation-6 receiver (August 2013 to December 2016) which are both located at this station. The solar maximum period of the solar cycle 24 is located well within the period of this investigation; hence, this study provides opportunity to see the occurrence pattern of scintillation during different seasons as well as the pattern from low solar activity to solar maximum. The results obtained showed that scintillation occurs between 21:00 LT and 04:00 LT at the peak of the occurrence in 2014. The time window of occurrence decreases with decrease in solar activity. Similarly, scintillation activity was observed to be more regular during high solar activity and it has two peaks of occurrence in March and October. A solar activity trend was observed in scintillation occurrence; scintillation activity increases with increase in the level of solar activity.
5. Present development of scintillator counters in France
International Nuclear Information System (INIS)
Koechlin, Y.; Koch, L.; Lansiart, A.
1958-01-01
For a number of years photomultipliers and scintillators have been produced on an industrial scale in France. The AEC has accepted the task of testing their performance, and advising the industry in consequence. This combined effort has resulted in the wide range of photomultipliers and scintillators summarised in the following paper. (author) [fr
6. New Organic Scintillators for Neutron Detection
Science.gov (United States)
2016-03-01
New Organic Scintillators for Neutron Detection Distribution Statement A. Approved for public release; distribution is unlimited. March...Title: New Organic Scintillators for Neutron Detection I. Abstract In this project, Radiation Monitoring Devices (RMD) proposes to develop novel...boron containing organic single crystal detectors for neutron detection as an alternative for 3He based detectors that will fulfill the needs of the
7. Current status on plastic scintillators modifications
Energy Technology Data Exchange (ETDEWEB)
Hamel, Matthieu; Bertrand, Guillaume H.V.; Carrel, Frederick; Coulon, Romain; Dumazert, Jonathan; Montbarbon, Eva; Sguerra, Fabien [CEA, LIST, Laboratoire Capteurs and Architectures electroniques, 91191 Gif-sur-Yvette cedex, (France)
2015-07-01
Recent developments of plastic scintillators are reviewed, from 2000 to March 2015. All examples are distributed into the main purpose, i.e. the nature of the radionuclide provided with the scope of detection of various radiation particles. The main characteristics of these newly created scintillators and their detection properties are given. (authors)
8. Mounting LHCb hadron calorimeter scintillating tiles
CERN Multimedia
Maximilien Brice
2004-01-01
Scintillating tiles are carefully mounted in the hadronic calorimeter for the LHCb detector. These calorimeters measure the energy of particles that interact via the strong force, called hadrons. The detectors are made in a sandwich-like structure where these scintillator tiles are placed between metal sheets.
9. Infrared scintillation of Yb(10%): YAG crystal
NARCIS (Netherlands)
Antonini, P; Belogurov, S.; Bressi, G; Carugno, G.; Iannuzzi, D
2002-01-01
Ytterbium-doped yttrium aluminum garnets (Yb:YAG) are known as IR laser crystals. Previously, we have shown that they are also fast scintillators in the near UV region. In this work we report on the measurements of I R scintillation properties of Yb(10%):YAG crystal. It emits at room temperature at
10. Some possible improvements in scintillation calorimeters
International Nuclear Information System (INIS)
Lorenz, E.
1985-03-01
Two ideas for improvements of scintillation calorimeters will be presented: a) improved readout of scintillating, totally active electromagnetic calorimeters with combinations of silicon photodiodes and fluorescent panel collectors, b) use of time structure analysis on calorimetry, both for higher rate applications and improved resolution for hadron calorimeters. (orig.)
11. Plastic scintillator with small pulse duration
International Nuclear Information System (INIS)
Andreeshchev, E.A.; Kilin, S.F.; Kovyrzina, K.A.; Kushakevich, Yu.P.; Rozman, I.M.; Shoniya, V.M.
1983-01-01
Characteristics of plastic scintillators with small pulse duration are analysed. For manufacturing the latter two methods of quencher introduction are applied: into the scintillator composition and the molecule of luminescent addition. The second method turned to be more effective. The pulse duration < 0.5 nc is attained
12. Status of timing with plastic scintillation detectors
International Nuclear Information System (INIS)
Moszynski, M.; Bengtson, B.
1979-01-01
Timing properties of scintillators and photomultipliers as well as theoretical and experimental studies of time resolution of scintillation counters are reviewed. Predictions of the theory of the scintillation pulse generation processes are compared with the data on the light pulse shape from small samples, in which the light pulse shape depends only on the composition of the scintillator. For larger samples the influence of the light collection process and the self-absorption process on the light pulse shape are discussed. The data on rise times, fwhm's, decay times and light yield of several commercial scintillators used in timing are collected. The next part of the paper deals with the properties of photomultipliers. The sources of time uncertainties in photomultipliers as a spread of the initial velocity of photoelectrons, emission of photoelectrons under different angles and from different points at the photocathode, the time spread and the gain dispersion introduced by electron photomultiplier are reviewed. The experimental data on the time jitter, single electron response and photoelectron yield of some fast photomultipliers are collected. As the time resolution of the timing systems with scintillation counters depends also on time pick-off units, a short presentation of the timing methods is given. The discussion of timing theories is followed by a review of experimental studies of the time resolution of scintillation counters. The paper is ended by an analysis of prospects on further progress of the subnanosecond timing with scintillation counters. (Auth.)
13. Performance and characteristics of a new scintillator
CERN Document Server
Czirr, J B; MacGillivray, R R; Seddon, P J
1999-01-01
A new class of scintillators for neutron imaging, based upon lithium gadolinium borate, is described. These scintillators offer the ability to tailor their response to the neutron spectrum by varying the relative absorption of neutrons by the key constituents (lithium, gadolinium and boron). The isotopic compositions of each constituent can be varied in order to change the spectral response.
14. Detector construction for a scintillation camera
International Nuclear Information System (INIS)
Ashe, J.B.
1977-01-01
An improved transducer construction for a scintillation camera in which a light conducting element is equipped with a layer of moisture impervious material is described. A scintillation crystal is thereafter positioned in optical communication with the moisture impervious layer and the remaining surfaces of the scintillation crystal are encompassed by a moisture shield. Affixing the moisture impervious layer to the light conducting element prior to attachment of the scintillation crystal reduces the requirement for mechanical strength in the moisture impervious layer and thereby allows a layer of reduced thickness to be utilized. Preferably, photodetectors are also positioned in optical communication with the light conducting element prior to positioning the scintillation crystal in contact with the impervious layer. 13 claims, 4 figures
15. Development of scintillation materials for PET scanners
CERN Document Server
Korzhik, Mikhail; Annenkov, Alexander N; Borissevitch, Andrei; Dossovitski, Alexei; Missevitch, Oleg; Lecoq, Paul
2007-01-01
The growing demand on PET methodology for a variety of applications ranging from clinical use to fundamental studies triggers research and development of PET scanners providing better spatial resolution and sensitivity. These efforts are primarily focused on the development of advanced PET detector solutions and on the developments of new scintillation materials as well. However Lu containing scintillation materials introduced in the last century such as LSO, LYSO, LuAP, LuYAP crystals still remain the best PET species in spite of the recent developments of bright, fast but relatively low density lanthanum bromide scintillators. At the same time Lu based materials have several drawbacks which are high temperature of crystallization and relatively high cost compared to alkali-halide scintillation materials. Here we describe recent results in the development of new scintillation materials for PET application.
16. Inorganic-organic rubbery scintillators
CERN Document Server
Gektin, A V; Pogorelova, N; Neicheva, S; Sysoeva, E; Gavrilyuk, V
2002-01-01
Spectral-kinetic luminescence properties of films, containing homogeneously dispersed scintillation particles of CsI, CsI:Tl, CsI:Na, and NaI:Tl in optically transparent organosiloxane matrix, are presented. Material is flexible and rubbery and in consequence the detectors of convenient shapes can be produced. It is found that luminescence spectra of the received films are identical whereas decay times are much shorter compared to the same ones of the corresponding single crystals. Layers with pure CsI demonstrate only the fast UV emission (307 nm, 10 ns) without blue microsecond afterglow typical for crystals. The films containing NaI:Tl are non-hygroscopic and preserve scintillation properties for a long time in humid atmosphere unlike single crystals. Organosiloxane layers with CsI:Tl particles provide high light output with good energy resolution for sup 5 sup 5 Fe, sup 1 sup 0 sup 9 Cd, sup 2 sup 4 sup 1 Am sources, and are capable of detecting both X-rays and alpha-, beta-particles.
17. Explosion-proof scintillation counter
International Nuclear Information System (INIS)
Opitts, P.; Borkert, R.
1979-01-01
It is noted that measuring devices used in the research works conducted with the help of radioactive isotopes on the chemical industry installations dangerous from the point of view of explosions, especially on the installations of the petrochemistry industry, must not limit the exploitation safety of these installations. The said especially concerns with the Geiger-Mueller type counters and scintillation detectors, located immediately in the places of measurements on the installations and supplied by high voltage power supply. It has been shown that electronic circuits for the detector's signals processing and obtaining working voltages can be located out of the explosive dangerous premices, for example, in the car trailer. Description is given of the device, with the help of which explosion safety is provided for the serially produced scintillation counter with forced ventilation (counter of the VA-S-50 type). Due to this device application, the exploitation parameters of the counter do not go down and there is no need for any changes in its design. Description is given of the device for external power supply and control of the counter which can swich off the power supply in the case of an accident, dangerous from the point of view of violation of the explosion safety conditions. The device is described for providing service to 10 measuring chanels, mounted on the car trailer [ru
18. Improvements in ANIS and inverted sputter sources
NARCIS (Netherlands)
Zwol, N.A. van; Vermeer, A.; Strasters, B.A.
1984-01-01
In this article two sputter sources, i.e. an ANIS and an inverted sputter source are described. The ANIS has been changed into a SNICS-like configuration and measurements of the output current for different sputter target geometries are presented. In the inverted sputter source an immersion lens was
19. Leakage current measurement in transformerless PV inverters
DEFF Research Database (Denmark)
Kerekes, Tamas; Sera, Dezso; Mathe, Laszlo
2012-01-01
Photovoltaic (PV) installations have seen a huge increase during the last couple of years. Transformerless PV inverters are gaining more share of the total inverter market, due to their high conversion efficiency, small weight and size. Nevertheless safety should have an important role in case...... of these tranformerless systems, due to the missing galvanic isolation. Leakage and fault current measurement is a key issue for these inverter topologies to be able to comply with the required safety standards. This article presents the test results of two different current measurement sensors that were suggested...... to be used in commercial PV inverters for the measurement of leakage and fault ground currents. The German VDE0126–1–1 standard gives the limit for fault and leakage ground currents and all grid connected PV inverters have to comply with these limits and disconnect from the grid in case of a fault....
20. New liquid scintillators for detectors based on capillary fibers
International Nuclear Information System (INIS)
Vasil'chenko, V.G.; Golovkin, S.V.; Zimin, K.V.
1997-01-01
Results of investigations of luminescent and optical characteristics of liquid scintillators intended for using in track detectors and calorimeters are presented. The scintillation efficiency of the vacuumed scintillators is by 22-32% higher than in air. Capillaries filled by liquid scintillators are compared with plastic fibers. 19 refs
1. Estimation of Fano factor in inorganic scintillators
International Nuclear Information System (INIS)
Bora, Vaibhav; Barrett, Harrison H.; Fastje, David; Clarkson, Eric; Furenlid, Lars; Bousselham, Abdelkader; Shah, Kanai S.; Glodo, Jarek
2016-01-01
The Fano factor of an integer-valued random variable is defined as the ratio of its variance to its mean. Correlation between the outputs of two photomultiplier tubes on opposite faces of a scintillation crystal was used to estimate the Fano factor of photoelectrons and scintillation photons. Correlations between the integrals of the detector outputs were used to estimate the photoelectron and photon Fano factor for YAP:Ce, SrI 2 :Eu and CsI:Na scintillator crystals. At 662 keV, SrI 2 :Eu was found to be sub-Poisson, while CsI:Na and YAP:Ce were found to be super-Poisson. An experiment setup inspired from the Hanbury Brown and Twiss experiment was used to measure the correlations as a function of time between the outputs of two photomultiplier tubes looking at the same scintillation event. A model of the scintillation and the detection processes was used to generate simulated detector outputs as a function of time for different values of Fano factor. The simulated outputs from the model for different Fano factors was compared to the experimentally measured detector outputs to estimate the Fano factor of the scintillation photons for YAP:Ce, LaBr 3 :Ce scintillator crystals. At 662 keV, LaBr 3 :Ce was found to be sub-Poisson, while YAP:Ce was found to be close to Poisson.
2. Low background techniques in liquid scintillator detectors
Science.gov (United States)
Miramonti, Lino
2017-10-01
Many neutrino physics experiments use organic liquid scintillators, which present a unique advantage: enormous masses (in the order of tens ktons) with very low radioactive background can be reached by assembling a detector with organic liquid scintillators. Thanks to the very fast decay rate, it is possible to localize the event in space and time and discriminate it from the background signals. Furthermore, organic liquid scintillators are very efficient in alfa/beta discrimination and offer the possibility to dissolve solvents in the chemical compounds to enhance the signal.
3. Measurement of light emission in scintillation vials
International Nuclear Information System (INIS)
Duran Ramiro, M. Teresa; Garcia-Torano, Eduardo
2005-01-01
The efficiency and energy resolution of liquid scintillation counting (LSC) systems are strongly dependent on the optical characteristics of scintillators, vials, and reflectors. This article presents the results of measurements of the light-emission profile of scintillation vials. Two measurement techniques, autoradiographs and direct measurements with a photomultiplier tube, have been used to obtain light-emission distribution for standard vials of glass, etched glass and polyethylene. Results obtained with both techniques are in good agreement. For the first time, the effect of the meniscus in terms of light contribution has been numerically estimated. These results can help design LSC systems that are more efficient in terms of light collection
4. Advanced plastic scintillators for fast neutron discrimination
Energy Technology Data Exchange (ETDEWEB)
Feng, Patrick L [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Anstey, Mitchell [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Doty, F. Patrick [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Mengesha, Wondwosen [Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2014-09-01
The present work addresses the need for solid-state, fast neutron discriminating scintillators that possess higher light yields and faster decay kinetics than existing organic scintillators. These respective attributes are of critical importance for improving the gamma-rejection capabilities and increasing the neutron discrimination performance under high-rate conditions. Two key applications that will benefit from these improvements include large-volume passive detection scenarios as well as active interrogation search for special nuclear materials. Molecular design principles were employed throughout this work, resulting in synthetically tailored materials that possess the targeted scintillation properties.
5. Scintillation of rare earth doped fluoride nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Jacobsohn, L. G.; McPherson, C. L.; Sprinkle, K. B.; Ballato, J. [Center for Optical Materials Science and Engineering Technologies (COMSET), and School of Materials Science and Engineering, Clemson University, Clemson, South Carolina 29634 (United States); Yukihara, E. G. [Physics Department, Oklahoma State University, Stillwater, Oklahoma 74078-3072 (United States); DeVol, T. A. [Department of Environmental Engineering and Earth Sciences, Clemson University, Clemson, South Carolina 29634-0905 (United States)
2011-09-12
The scintillation response of rare earth (RE) doped core/undoped (multi-)shell fluoride nanoparticles was investigated under x-ray and alpha particle irradiation. A significant enhancement of the scintillation response was observed with increasing shells due: (i) to the passivation of surface quenching defects together with the activation of the REs on the surface of the core nanoparticle after the growth of a shell, and (ii) to the increase of the volume of the nanoparticles. These results are expected to reflect a general aspect of the scintillation process in nanoparticles, and to impact radiation sensing technologies that make use of nanoparticles.
6. Scintillation camera with second order resolution
International Nuclear Information System (INIS)
Muehllehner, G.
1976-01-01
A scintillation camera for use in radioisotope imaging to determine the concentration of radionuclides in a two-dimensional area is described in which means is provided for second order positional resolution. The phototubes, which normally provide only a single order of resolution, are modified to provide second order positional resolution of radiation within an object positioned for viewing by the scintillation camera. The phototubes are modified in that multiple anodes are provided to receive signals from the photocathode in a manner such that each anode is particularly responsive to photoemissions from a limited portion of the photocathode. Resolution of radioactive events appearing as an output of this scintillation camera is thereby improved
7. POLARIS: Portable Liquid Argon Imaging Scintillator
Science.gov (United States)
Jia, Yanyu; Kovacs, Benjamin; Kamp, Nicholas; Aidala, Christine; Polaris Team
2017-09-01
Liquefied noble gas detectors have become widely used in nuclear and particle physics, in particular for detecting neutrinos and in dark matter searches. However, their potential for neutron detection in low-energy nuclear physics has not yet been realized. The University of Michigan has been constructing a hybrid scintillating time projection chamber for detection of neutrons in the 200 keV 10 MeV range. The scintillation material is argon, and various dopants to improve detector efficiency are being explored. With collection of both scintillation light and ionization charge, improved energy resolution for neutrons is expected compared to existing measurement techniques.
8. Scintillation particle detection based on microfluidics
CERN Document Server
Mapelli, A; Renaud, P; Gorini, B; Trivino, N Vico; Jiguet, S; Vandelli, W; Haguenauer, M
2010-01-01
A novel type of particle detector based on scintillation, with precise spatial resolution and high radiation hardness, is being studied. It consists of a single microfluidic channel filled with a liquid scintillator and is designed to define an array of scintillating waveguides each independently coupled to a photodetector. Prototype detectors built using an SU-8 epoxy resin have been tested with electrons from a radioactive source. The experimental results show a light yield compatible with the theoretical expectations and confirm the validity of the approach. (C) 2010 Elsevier B.V. All rights reserved.
9. Scintillation counter: photomultiplier tube alignment
International Nuclear Information System (INIS)
Olson, R.E.
1975-01-01
A scintillation counter, particularly for counting gamma ray photons, includes a massive lead radiation shield surrounding a sample-receiving zone. The shield is disassembleable into a plurality of segments to allow facile installation and removal of a photomultiplier tube assembly, the segments being so constructed as to prevent straight-line access of external radiation through the shield into the sample receiving zone. Provisions are made for accurately aligning the photomultiplier tube with respect to one or more sample-transmitting bores extending through the shield to the sample receiving zone. A sample elevator, used in transporting samples into the zone, is designed to provide a maximum gamma-receiving aspect to maximize the gamma detecting efficiency. (auth)
10. Scintillation counter, maximum gamma aspect
International Nuclear Information System (INIS)
Thumim, A.D.
1975-01-01
A scintillation counter, particularly for counting gamma ray photons, includes a massive lead radiation shield surrounding a sample-receiving zone. The shield is disassembleable into a plurality of segments to allow facile installation and removal of a photomultiplier tube assembly, the segments being so constructed as to prevent straight-line access of external radiation through the shield into radiation-responsive areas. Provisions are made for accurately aligning the photomultiplier tube with respect to one or more sample-transmitting bores extending through the shield to the sample receiving zone. A sample elevator, used in transporting samples into the zone, is designed to provide a maximum gamma-receiving aspect to maximize the gamma detecting efficiency. (U.S.)
11. Static Characteristics of the Ferroelectric Transistor Inverter
Science.gov (United States)
Mitchell, Cody; Laws, crystal; MacLeond, Todd C.; Ho, Fat D.
2010-01-01
The inverter is one of the most fundamental building blocks of digital logic, and it can be used as the foundation for understanding more complex logic gates and circuits. This paper presents the characteristics of an inverter circuit using a ferroelectric field-effect transistor. The voltage transfer characteristics are analyzed with respect to varying parameters such as supply voltage, input voltage, and load resistance. The effects of the ferroelectric layer between the gate and semiconductor are examined, and comparisons are made between the inverters using ferroelectric transistors and those using traditional MOSFETs.
12. Switching Characteristics of Ferroelectric Transistor Inverters
Science.gov (United States)
Laws, Crystal; Mitchell, Coey; MacLeod, Todd C.; Ho, Fat D.
2010-01-01
This paper presents the switching characteristics of an inverter circuit using a ferroelectric field effect transistor, FeFET. The propagation delay time characteristics, phl and plh are presented along with the output voltage rise and fall times, rise and fall. The propagation delay is the time-delay between the V50% transitions of the input and output voltages. The rise and fall times are the times required for the output voltages to transition between the voltage levels V10% and V90%. Comparisons are made between the MOSFET inverter and the ferroelectric transistor inverter.
13. GEM scintillation readout with avalanche photodiodes
CERN Document Server
Conceição, A S; Fernandes, L M P; Monteiro, C M B; Coelho, L C C; Azevedo, C D R; Veloso, J F C A; Lopesac, J A M; dos Santosa, J M F
2007-01-01
The use of the scintillation produced in the charge avalanches in GEM holes as signal amplification and readout is investigated for xenon. A VUV-sensitive avalanche photodiode has been used as photosensor. Detector gains of about 4 × 104 are achieved in scintillation readout mode, for GEM voltages of 490 V and for a photosensor gain of 150. Those gains are more than one order of magnitude larger than what is obtained using charge readout. In addition, the energy resolutions achieved with the scintillation readout are lower than those achieved with charge readout. The GEM scintillation yield in xenon was measured as a function of GEM voltage, presenting values that are about a half of those achieved for the charge yield, and reach about 730 photons per primary electron at GEM voltages of 490 V.
14. High-efficiency organic glass scintillators
Science.gov (United States)
Feng, Patrick L.; Carlson, Joseph S.
2017-12-19
A new family of neutron/gamma discriminating scintillators is disclosed that comprises stable organic glasses that may be melt-cast into transparent monoliths. These materials have been shown to provide light yields greater than solution-grown trans-stilbene crystals and efficient PSD capabilities when combined with 0.01 to 0.05% by weight of the total composition of a wavelength-shifting fluorophore. Photoluminescence measurements reveal fluorescence quantum yields that are 2 to 5 times greater than conventional plastic or liquid scintillator matrices, which accounts for the superior light yield of these glasses. The unique combination of high scintillation light-yields, efficient neutron/gamma PSD, and straightforward scale-up via melt-casting distinguishes the developed organic glasses from existing scintillators.
15. Cementation of radioactive liquid scintillator waste simulate
International Nuclear Information System (INIS)
Bayoumi, T.A.
2010-01-01
Liquid scintillation counting is an important analytical tool with extensive applications in medicine and basic applied research and used in quantification of □ -particles, weak □ and x-rays. The generated spent liquid scintillator radioactive waste should be limited and controlled to protect man and his environment. In this study, the radioactive spent liquid scintillator waste simulate (SLS) was immobilized in cement matrix using a surfactant in order to facilitate and increase the amount of SLS incorporated into the cementitious materials. Mechanical properties of the final cement waste form were acceptable for blocks containing up to 20% SLS in presence of surfactant. X-ray diffraction, IR analysis and scanning electron microscope proved that the hydration of cement materials is not significantly affected by organic scintillator waste. Therefore, the cement matrix could be recommended for solidification of SLS for the acceptable mechanical, physical and chemical characterizations reached.
16. Inverted CERN School of Computing
CERN Document Server
IT Department
2011-01-01
The 5th edition of the Inverted CERN School of Computing (iCSC, “Where students turn into teachers”) will take place next Thursday and Friday (3 and 4 of March) at CERN, Building 31 - IT Amphitheatre - Third Floor. Attendance is free and open to everyone. The programme is designed so that you can attend the lectures that interest you. This year highlights: Cloud Computing, Software Engineering, Cryptography Registration is not mandatory, but will allow you to obtain a copy of the full booklet (first registered, first served). Programme overview: Thursday 3 March 2011 10:00 - 10:15 Introduction School opening 10:15 - 11:10 Lecture 1 Virtualization: what it is, how it works – Luigi Gallerani 11:20 - 12:15 Lecture 2 Server Virtualization at work – Carlos Garcia Fernandez 14:00 - 14:55 Lecture 3 Unweaving Clouds: Principles and Practice – Belmiro Moreira 15:30 - 16:25 Lecture 4 Understanding Cryptography: From Caesar to Public-Key – Nicola...
17. Liquid scintillators for optical fiber applications
International Nuclear Information System (INIS)
Franks, L.A.; Lutz, S.S.
1982-01-01
A multicomponent liquid scintillator solution for use as a radiation-to-light converter in conjunction with a fiber optic transmission system. The scintillator includes a quantity of 1, 2 , 4, 5, 3H, 6H, 1 OH, tetrahydro-8-trifluoromethyl (1) benzopyrano (9, 9a, 1-gh) quinolizin-10-one (Coumarin) as a solute in a fluor solvent such as benzyl alcohol or pseudocumene. The use of bibuq as an additional or primary solute is also disclosed
18. Composition for use in scintillator systems
International Nuclear Information System (INIS)
Tarkkanen, V.
1976-01-01
A liquid scintillation counting composition of the type comprising an aromatic hydrocarbon solvent, an ethoxylated alkyl phenol surfactant, and a scintillation solute, containing a small amount of a substituted ethoxylated carboxylate acid and/or a tertiary amine salt or a quaternary ammonium salt of such acid is described. The free acid reduces chemiluminescence upon the addition of an alkaline sample to the composition, while the tertiary amine or quaternary ammonium salt enhances the water miscibility of the composition
19. Real-time volumetric scintillation dosimetry
Science.gov (United States)
Beddar, S.
2015-01-01
The goal of this brief review is to review the current status of real-time 3D scintillation dosimetry and what has been done so far in this area. The basic concept is to use a large volume of a scintillator material (liquid or solid) to measure or image the dose distributions from external radiation therapy (RT) beams in three dimensions. In this configuration, the scintillator material fulfills the dual role of being the detector and the phantom material in which the measurements are being performed. In this case, dose perturbations caused by the introduction of a detector within a phantom will not be at issue. All the detector configurations that have been conceived to date used a Charge-Coupled Device (CCD) camera to measure the light produced within the scintillator. In order to accurately measure the scintillation light, one must correct for various optical artefacts that arise as the light propagates from the scintillating centers through the optical chain to the CCD chip. Quenching, defined in its simplest form as a nonlinear response to high-linear energy transfer (LET) charged particles, is one of the disadvantages when such systems are used to measure the absorbed dose from high-LET particles such protons. However, correction methods that restore the linear dose response through the whole proton range have been proven to be effective for both liquid and plastic scintillators. Volumetric scintillation dosimetry has the potential to provide fast, high-resolution and accurate 3D imaging of RT dose distributions. Further research is warranted to optimize the necessary image reconstruction methods and optical corrections needed to achieve its full potential.
20. Elastic scintillation materials based on polyorganosiloxane
International Nuclear Information System (INIS)
Grinev, B.V.; Andryushchenko, L.A.; Shershukov, V.M.; Ulanenko, K.B.; Minakova, R.A.; Sevastjanova, I.V.
1994-01-01
The developed elastic scintillators based on polymethyl-phenylsiloxane rubber are characterized by an elevated light output and a low toxicity. The increase of their light output is achieved by raising the content of phenyl chains, varying the chemical structure of luminescent additions and using isopropylnaphthalene. This high-boiling solvent introduced into the scintillation siloxane compositions is confined within siloxane matrix after the hardening of the rubber
1. Scintillation response of nuclear particle detectors
International Nuclear Information System (INIS)
Michaelian, K.; Menchaca-Rocha, A.; Belmont-Moreno, E.
1995-01-01
We derive simple algebraic expressions for the ion-induced light output response of most of the popular scintillation detectors used in nuclear and particle physics. The analytical calculation is based on a model for the energy deposition by secondary electrons scattered along the track of the ion, and the subsequent energy transport to luminescence centers. Predictions are compared with published experimental data for various scintillating materials over a wide range of incident ions and energies. ((orig.))
2. Spectrometric characteristics of polystyrene scintillation films
CERN Document Server
Astvatsaturov, A R; Gavalyan, V B; Gavalyan, V G
1999-01-01
The spectrometric characteristics of five types of polystyrene scintillation films with thicknesses of 10, 30, 50 and 80 mu m and of analogous 250 mu m thick plates irradiated with sup 2 sup 3 sup 9 Pu, sup 2 sup 3 sup 8 Pu and sup 2 sup 2 sup 6 Ra sources of alpha-particles have been studied. The prospects of utilization of scintillation films as radiators for detection of heavy charged particles and measurement of their energy was experimentally shown.
3. A new technique for infrared scintillation measurements
OpenAIRE
Chiossi, F.; Brylew, K.; Borghesani, A. F.; Braggio, C.; Carugno, G.; Drozdowski, W.; Guarise, M.
2016-01-01
We propose a new technique to measure the infrared scintillation light yield of rare earth (RE) doped crystals by comparing it to near UV-visible scintillation of a calibrated Pr:(Lu$_{0.75}$Y$_{0.25}$)$_{3}$Al$_5$O$_{12}$ sample. As an example, we apply this technique to provide the light yield in visible and infrared range up to \\SI{1700}{nm} of this crystal.
4. A new technique for infrared scintillation measurements
Energy Technology Data Exchange (ETDEWEB)
Chiossi, F., E-mail: [email protected] [Dip. di Fisica e Astronomia and INFN, University of Padua, Via F. Marzolo 8, I-35131 Padova (Italy); Brylew, K. [Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun (Poland); Borghesani, A.F. [CNISM Unit and Dip. di Fisica e Astronomia, University of Padua, Via F. Marzolo 8, I-35131 Padova (Italy); Braggio, C.; Carugno, G. [Dip. di Fisica e Astronomia and INFN, University of Padua, Via F. Marzolo 8, I-35131 Padova (Italy); Drozdowski, W. [Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun (Poland); Guarise, M. [Dip. di Fisica e Astronomia and INFN, University of Padua, Via F. Marzolo 8, I-35131 Padova (Italy)
2017-05-21
We propose a new technique to measure the infrared scintillation light yield of rare earth doped crystals by comparing it to near UV–visible scintillation of a calibrated Pr:(Lu{sub 0.75}Y{sub 0.25}){sub 3}Al{sub 5}O{sub 12} sample. As an example, we apply this technique to provide the light yield in visible and infrared range up to 1700 nm of this crystal.
5. New Developments in Scintillators for Security Applications
Science.gov (United States)
Glodo, Jarek; Wang, Yimin; Shawgo, Ryan; Brecher, Charles; Hawrami, Rastgo H.; Tower, Joshua; Shah, Kanai S.
Radiation is an important part of security space: It is detected either passively in search of special nuclear materials or actively to monitor or interrogate objects of interest. Systems relying on radiation require adequate detectors. The most common radiation detectors are based on scintillating materials that convert hard (gamma, x-ray or neutron) radiation into visible light registered by a photodetector. The last decade has seen development of new materials driven by various security applications. This included the search for He-3 replacement technologies, which resulted in development of neutron sensing scintillators such as Ce-doped Cs2LiYCl6 (CLYC) or more recently Cs2LiLa(Br,Cl)6 (CLLBC). Since they are also good gamma-ray scintillators, they have also penetrated the detection market for passive dual-mode (gamma and neutron) detection systems, replacing scintillators such as NaI(Tl) or CsI(Tl) and competing with LaBr3(Ce). High-energy Non-Intrusive Inspection is another area where active research is being pursued in order to replace existing scintillator choices such as CdWO4, which is commonly used in simple radiography, and PbWO4, which is being studied for spectroscopic alternatives to radiography. For radiography, in particular, new ceramic scintillators such as Ce-doped GLuGAG (garnet) are considered, and for spectroscopy, Yb doped Lu2O3. In this paper we provide a short overview of these technologies.
6. Survey meter using novel inorganic scintillators
International Nuclear Information System (INIS)
Yoshikawa, Akira; Fukuda, Kentaro; Kawaguchi, Noriaki; Kamada, Kei; Fujimoto, Yutaka; Yokota, Yuui; Kurosawa, Shunsuke; Yanagida, Takayuki
2012-01-01
Single crystal scintillator materials are widely used for detection of high-energy photons and particles. There is continuous demand for new scintillator materials with higher performance because of increasing number of medical, industrial, security and other applications. This article presents the recent development of three novel inorganic scintillators; Pr-doped Lu 3 Al 5 O 12 (Pr:LuAG), Ce doped Gd 3 (Al, Ga) 5 O 12 (Ce:GAGG) and Ce or Eu-doped 6 LiCaAlF 6 (Ce:LiCAF, Eu:LiCAF). Pr:LuAG shows very interesting scintillation properties including very fast decay time, high light yield and excellent energy resolution. Taking the advantage of these properties, positron emission mammography (PEM) equipped with Pr:LuAG were developed. Ce:GAGG shows very high light yield, which is much higher than that of Ce:LYSO. Survey meter using Ce:GAGG is developed using this scintillator. Ce:LiCAF and Eu:LiCAF were developed for neutron detection. The advantage and disadvantage are discussed comparing with halide scintillators. Eu-doped LiCAF indicated five times higher light yield than that of existing Li-glass. It is expected to be used as the alternative of 3 He. (author)
7. Cascaded impedance networks for NPC inverter
DEFF Research Database (Denmark)
Li, Ding; Gao, Feng; Loh, Poh Chiang
2010-01-01
Multilevel inverters are getting more and more attracted because they have better output waveform quality and lower semiconductor voltage stress. The Z-source NPC is a kind of single stage multilevel inverter which has the ability of voltage boost. But the boost capability is relatively low when...... they are subject to the renewable sources. To date, three distinct types of impedance networks can be summarized for implementing a hybrid source impedance network, which can in principle be combined and cascaded before connected to a NPC inverter by proposed two ways. The resulting cascaded impedance network NPC...... would have a higher output voltage gain. It is anticipated that it would help the formed inverters find applications in photovoltaic and other renewable systems, where a high voltage gain is usually requested. Experimental testing has already been conducted and verifies the theory....
8. Integrated Inverter For Driving Multiple Electric Machines
Science.gov (United States)
Su, Gui-Jia [Knoxville, TN; Hsu, John S [Oak Ridge, TN
2006-04-04
An electric machine drive (50) has a plurality of inverters (50a, 50b) for controlling respective electric machines (57, 62), which may include a three-phase main traction machine (57) and two-phase accessory machines (62) in a hybrid or electric vehicle. The drive (50) has a common control section (53, 54) for controlling the plurality of inverters (50a, 50b) with only one microelectronic processor (54) for controlling the plurality of inverters (50a, 50b), only one gate driver circuit (53) for controlling conduction of semiconductor switches (S1-S10) in the plurality of inverters (50a, 50b), and also includes a common dc bus (70), a common dc bus filtering capacitor (C1) and a common dc bus voltage sensor (67). The electric machines (57, 62) may be synchronous machines, induction machines, or PM machines and may be operated in a motoring mode or a generating mode.
9. Performance analysis of new type grid-tied inverter-Aalborg Inverter
DEFF Research Database (Denmark)
Wu, Weimin; Wang, Zhen; Ji, Junhao
2014-01-01
Aalborg Inverter is a grid-tied DC/AC inverter. In order to optimize the design, its power losses are analyzed in detail, combined with a description of the single-phase operating principle and the modulation strategy. A 2 kW / 220 V experimental prototype is constructed to verify the theoretical...... analysis. It is concluded that a minimize inductance in the power loop does help the inverter to achieve the high efficiency with the good dynamic performance....
10. Improvements in ANIS and inverted sputter sources
Science.gov (United States)
Strasters, B. A.; Vermeer, A.; van Zwol, N. A.
1984-02-01
In this article two sputter sources, i.e. an ANIS and an inverted sputter source are described. The ANIS has been changed into a SNICS-like configuration and measurements of the output current for different sputter target geometries are presented. In the inverted sputter source an immersion lens was placed between the ionizer and the sputter target. This source is provided with a modified revolving target head with eight targets.
11. Inverted mesiodens--a case report.
Science.gov (United States)
Nikhil, S; Vineeta; Gupta, P
1999-09-01
A nine and a half years old female school child was examined in a during routine dental examination. The patient had swelling over maxillary midline area just near the labial frenum. Both the central incisors were in position. Radiographic examination revealed presence of an inverted supernumerary tooth between the roots of the central incisors. Surgical extraction of the supernumerary was planned. A unique case of inverted (upside down) mesiodens is presented.
12. Automatic load sharing in inverter modules
Science.gov (United States)
Nagano, S.
1979-01-01
Active feedback loads transistor equally with little power loss. Circuit is suitable for balancing modular inverters in spacecraft, computer power supplies, solar-electric power generators, and electric vehicles. Current-balancing circuit senses differences between collector current for power transistor and average value of load currents for all power transistors. Principle is effective not only in fixed duty-cycle inverters but also in converters operating at variable duty cycles.
13. Base drive for paralleled inverter systems
Science.gov (United States)
Nagano, S. (Inventor)
1980-01-01
In a paralleled inverter system, a positive feedback current derived from the total current from all of the modules of the inverter system is applied to the base drive of each of the power transistors of all modules, thereby to provide all modules protection against open or short circuit faults occurring in any of the modules, and force equal current sharing among the modules during turn on of the power transistors.
14. Conference on Engineering of Scintillation Materials and Radiation Technologies
CERN Document Server
Gektin, Alexander
2017-01-01
This volume provides a broad overview of the latest achievements in scintillator development, from theory to applications, and aiming for a deeper understanding of fundamental processes, as well as the discovery and availability of components for the production of new generations of scintillation materials. It includes papers on the microtheory of scintillation and the initial phase of luminescence development, applications of the various materials, and development and characterization of ionizing radiation detection equipment. The book also touches upon the increased demand for cryogenic scintillators, the renaissance of garnet materials for scintillator applications, nano-structuring in scintillator development, development and applications for security, and exploration of hydrocarbons and ecological monitoring.
15. Role of hot electron transport in scintillators: A theoretical study
Energy Technology Data Exchange (ETDEWEB)
Huang, Huihui [SZU-NUS Collaborative Innovation Center for Optoelectronic Science and Technology, Key Lab. of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen Univ. (China); Li, Qi [Physical Sciences Division, IBM TJ Watson Research Center, Yorktown Heights, NY (United States); Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL (United States); Lu, Xinfu; Williams, R.T. [Department of Physics, Wake Forest University, Winston Salem, NC (United States); Qian, Yiyang [College of Engineering and Applied Science, Nanjing University (China); Wu, Yuntao [Scintillation Materials Research Center, University of Tennessee, Knoxville, TN (United States)
2016-10-15
Despite recent intensive study on scintillators, several fundamental questions on scintillator properties are still unknown. In this work, we use ab-initio calculations to determine the energy dependent group velocity of the hot electrons from the electronic structures of several typical scintillators. Based on the calculated group velocities and optical phonon frequencies, a Monte-Carlo simulation of hot electron transport in scintillators is carried out to calculate the thermalization time and diffusion range in selected scintillators. Our simulations provide physical insights on a recent trend of improved proportionality and light yield from mixed halide scintillators. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
16. Scintillation Detectors for Charged Particles and Photons
CERN Document Server
Lecoq, P
2011-01-01
Scintillation Detectors for Charged Particles and Photons in 'Charged Particle Detectors - Particle Detectors and Detector Systems', part of 'Landolt-Börnstein - Group I Elementary Particles, Nuclei and Atoms: Numerical Data and Functional Relationships in Science and Technology, Volume 21B1: Detectors for Particles and Radiation. Part 1: Principles and Methods'. This document is part of Part 1 'Principles and Methods' of Subvolume B 'Detectors for Particles and Radiation' of Volume 21 'Elementary Particles' of Landolt-Börnstein - Group I 'Elementary Particles, Nuclei and Atoms'. It contains the Subsection '3.1.1 Scintillation Detectors for Charged Particles and Photons' of Section '3.1 Charged Particle Detectors' of Chapter '3 Particle Detectors and Detector Systems' with the content: 3.1.1 Scintillation Detectors for Charged Particles and Photons 3.1.1.1 Basic detector principles and scintillator requirements 3.1.1.1.1 Interaction of ionizing radiation with scintillator material 3.1.1.1.2 Important scint...
17. Inverter for Installations with Intermittent Electricity Production
Directory of Open Access Journals (Sweden)
Ermuraki Iu.
2016-04-01
Full Text Available A new architecture of the inverter used in the convertion of electric energy generated by renewable energy sources is studied in this paper. The distinctive features of this inverter is the special block which compensates pulsing of the current with double frequency, characteristic for these inverters. The switching of electronic keys is realized using the method TCM In this block, like in the inverter, which assures the switching at the voltages near to zero (ZVC. The proposed algorithm of controlling the electronic keys permits to increase the work frequency up to hundreds of kHz. Electronic keys operate at variable frequency, which changes during the work cycle both slowly and by jump. The assurance of admissible heat regime is performed using forced cooling air flux and by convection. The increase of releasing process of the heat is assured by original construction of radiators which forms the turbulent mode of cooling air flux. These changes of the architecture of the inverter have allowed the minimization of mass, sizes and price indicators. It has been manufactured a functional laboratory sample with output power of 2kW the voltage of direct current of 450V or 48 V and output alternating voltage of 230V, with sizes 175mmX35mmX30mm.
18. Radiation imaging with a new scintillator and a CMOS camera
Czech Academy of Sciences Publication Activity Database
Kurosawa, S.; Shoji, Y.; Pejchal, Jan; Yokota, Y.; Yoshikawa, A.
2015-01-01
Roč. 9, Jul (2015), C07015 ISSN 1748-0221 Institutional support: RVO:68378271 Keywords : scintillators * scintillation and light emission processes * image processin Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 1.310, year: 2015
19. Addressable inverter matrix for process and device characterization
Science.gov (United States)
Buehler, M. G.; Sayah, H. R.
1985-01-01
The addressable inverter matrix consists of 222 inverters each accessible with the aid of a shift register. The structure has proven useful in characterizing the variability of inverter transfer curves and in diagnosing processing faults. For good 3-micron CMOS bulk inverters investigated, the percent standard deviation of the inverter threshold voltage was less than one percent and the inverter gain (the slope of the inverter transfer curve at the inverter threshold vltage) was less than 3 percent. The average noise margin for the inverters was near 2 volts for a power supply voltage of 5 volts. The specific faults studied included undersize pull-down transistor widths and various open contacts in the matrix.
20. Current trends in scintillator detectors and materials
International Nuclear Information System (INIS)
Moses, William W.
2001-01-01
The last decade has seen a renaissance in inorganic scintillator development for gamma ray detection. Lead tungstate (PbWO4) has been developed for high energy physics experiments, and possesses exceptionally high density and radiation hardness, albeit with low luminous efficiency. Lutetium orthosilicate or LSO (Lu2SiO5:Ce) possesses a unique combination of high luminous efficiency, high density, and reasonably short decay time, and is now incorporated in commercial positron emission tomography (PET) cameras. There have been advances in understanding the fundamental mechanisms that limit energy resolution, and several recently discovered materials (such as LaBr3:Ce) possess energy resolution that approaches that of direct solid state detectors. Finally, there are indications that a neglected class of scintillator materials that exhibit near band-edge fluorescence could provide scintillators with sub-nanosecond decay times and high luminescent efficiency
1. Current trends in scintillator detectors and materials
CERN Document Server
Moses, W W
2002-01-01
The last decade has seen a renaissance in inorganic scintillator development for gamma ray detection. Lead tungstate (PbWO sub 4) has been developed for high-energy physics experiments, and possesses exceptionally high density and radiation hardness, albeit with low luminous efficiency. Lutetium orthosilicate or LSO (Lu sub 2 SiO sub 5 :Ce) possesses a unique combination of high luminous efficiency, high density, and reasonably short decay time, and is now incorporated in commercial positron emission tomography cameras. There have been advances in understanding the fundamental mechanisms that limit energy resolution, and several recently discovered materials (such as LaBr sub 3 :Ce) possess energy resolution that approaches that of direct solid state detectors. Finally, there are indications that a neglected class of scintillator materials that exhibit near band-edge fluorescence could provide scintillators with sub-nanosecond decay times and high luminescent efficiency.
2. Development of 300 g scintillating calorimeters
International Nuclear Information System (INIS)
Frank, T.; Bruckmayer, M.; Cozzini, C.; Di Stefano, P.; Hauff, D.; Proebst, F.; Seidel, W.; Angloher, G.; Schmidt, J.
2002-01-01
The sensitivity for WIMP detection can be improved by an ability to efficiently discriminate the γ and β backgrounds from the nuclear recoil signals. The CRESST phase II detectors will achieve this discrimination by means of simultaneous measurement of phonons and scintillation light. We report on the development of a 300 g detector module consisting of two separate calorimeters fitted with tungsten phase transition thermometers. A 300 g CaWO 4 crystal serves as the target material in which a recoiling WIMP creates both phonons and scintillation light. Phonons are detected by a thermometer on the CaWO 4 crystal. A second smaller detector in close proximity detects the scintillation light. Measurements with this setup will be presented
3. Current trends in scintillator detectors and materials
International Nuclear Information System (INIS)
Moses, W.W.
2002-01-01
The last decade has seen a renaissance in inorganic scintillator development for gamma ray detection. Lead tungstate (PbWO 4 ) has been developed for high-energy physics experiments, and possesses exceptionally high density and radiation hardness, albeit with low luminous efficiency. Lutetium orthosilicate or LSO (Lu 2 SiO 5 :Ce) possesses a unique combination of high luminous efficiency, high density, and reasonably short decay time, and is now incorporated in commercial positron emission tomography cameras. There have been advances in understanding the fundamental mechanisms that limit energy resolution, and several recently discovered materials (such as LaBr 3 :Ce) possess energy resolution that approaches that of direct solid state detectors. Finally, there are indications that a neglected class of scintillator materials that exhibit near band-edge fluorescence could provide scintillators with sub-nanosecond decay times and high luminescent efficiency
4. Determination of light yield from weak scintillations
International Nuclear Information System (INIS)
Mandzhukov, I.G.; Mandzhukova, B.V.
1987-01-01
Simulation of amplitude distribution of weak scintillation pulses by Puasson distribution is suggestd, if average number of photoelectrons collected on the first dinode of the photomultiplier is of the order of 1. The method permits to determine scintillation yield even in those cases, when the photomultiplier does not have a maximum in monoelectron pulse distribution. Scintillation yields of some aqueous solutions of sodium salicylate and aromatic solvents (benzene, toluene, xylol) at inner α-particle irradiation are determined. It is observed from the given results that efficiency of 239 Pu α-particle detection for aqueous solutions of sodium salicylate with 10% concentration is rather high; it makes up 0.94. They may appear useful for applied problems, paticularly, for measuring α-radiation
5. Microfluidic Scintillation Detectors for High Energy Physics
CERN Document Server
Maoddi, Pietro; Mapelli, Alessandro; CERN
This thesis deals with the development and study of microfluidic scintillation detectors, a technology of recent introduction for the detection of high energy particles. Most of the interest for such devices comes from the use of a liquid scintillator, which entails the possibility of changing the active material in the detector, leading to increased radiation resistance. A first part of the thesis focuses on the work performed in terms of design and modelling studies of novel prototype devices, hinting to new possibilities and applications. In this framework, the simulations performed to validate selected designs and the main technological choices made in view of their fabrication are addressed. The second part of this thesis deals with the microfabrication of several prototype devices. Two different materials were studied for the manufacturing of microfluidic scintillation detectors, namely the SU-8 photosensitive epoxy and monocrystalline silicon. For what concerns the former, an original fabrication appro...
6. Scintillation counting: an extrapolation into the future
International Nuclear Information System (INIS)
Ross, H.H.
1983-01-01
Progress in scintillation counting is intimately related to advances in a variety of other disciplines such as photochemistry, photophysics, and instrumentation. And while there is steady progress in the understanding of luminescent phenomena, there is a virtual explosion in the application of semiconductor technology to detectors, counting systems, and data processing. The exponential growth of this technology has had, and will continue to have, a profound effect on the art of scintillation spectroscopy. This paper will review key events in technology that have had an impact on the development of scintillation science (solid and liquid) and will attempt to extrapolate future directions based on existing and projected capability in associated fields. Along the way there have been occasional pitfalls and several false starts; these too will be discussed as a reminder that if you want the future to be different than the past, study the past
7. Scintillation γ spectrography. Physical principles. Apparatus. Operation
International Nuclear Information System (INIS)
Julliot, C.
1960-01-01
The scintillation detector forms the main part of the instrument used, the electronic unit presenting the results produced. After a brief description of the process of γ photon absorption in the material, the particular case of NaI (T1), the scintillator used, is examined. The intensity of the scintillation caused by γ ray absorption and the characteristics of the photomultiplier play a determining part in the energy resolution of the instrument. For the γ recording spectrograph, we show to what extent the technique for using the electronic unit can modify the results. A detailed description is given of the activity measurement of a γ-emitting radioelement by the spectrographic method. (author) [fr
8. Collimated trans-axial tomographic scintillation camera
International Nuclear Information System (INIS)
1980-01-01
The objects of this invention are first to reduce the time required to obtain statistically significant data in trans-axial tomographic radioisotope scanning using a scintillation camera. Secondly, to provide a scintillation camera system to increase the rate of acceptance of radioactive events to contribute to the positional information obtainable from a known radiation source without sacrificing spatial resolution. Thirdly to reduce the scanning time without loss of image clarity. The system described comprises a scintillation camera detector, means for moving this in orbit about a cranial-caudal axis relative to a patient and a collimator having septa defining apertures such that gamma rays perpendicular to the axis are admitted with high spatial resolution, parallel to the axis with low resolution. The septa may be made of strips of lead. Detailed descriptions are given. (U.K.)
9. Radiocarbon dating methods using benzene liquid scintillation
International Nuclear Information System (INIS)
Togashi, Shigeko; Matsumoto, Eiji
1983-01-01
The radiocarbon dating method using benzene liquid scintillation is reported in detail. The results of measurement of NBS oxalic acid agree with the recommended value, indicating that isotopic fractionation during benzene synthesis can be negligible. Ten samples which have been already measured by gas counter are dated by benzene liquid scintillation. There is no significant difference in age for the same sample between benzene liquid scintillation and gas counters. It is shown that quenching has to be corrected for the young sample. Memory effect in stainless steel reaction vessel can be removed by using an exchangeable inner vessel and by baking it in the air. Using this method, the oldest age that can be measured with 2.3 g carbon is 40,000 years B.P. (author)
10. Optics study of liquid scintillation counting systems
International Nuclear Information System (INIS)
Duran Ramiro, M. T.; Garcia-Torano, E.
2005-01-01
Optics is a key issue in the development of any liquid scintillation counting (LSC) system. Light emission in the scintillating solution, transmission through the vial and reflector design are some aspects that need to be considered in detail. This paper describes measurements and calculations carried out to optimise these factors for the design of a new family of LSC counters. Measurements of the light distribution emitted by a scintillation vial were done by autoradiographs of cylindrical vials made of various materials and results were compared to those obtained by direct measurements of the light distribution made by scanning the vial with a photomultiplier tube. Calculations were also carried out to study the light transmission in the vial and the optimal design of the reflector for a system with one photomultiplier tube. (Author)
11. Time resolution measurements with an improved discriminator and conical scintillators
International Nuclear Information System (INIS)
McGervey, J.D.; Vogel, J.; Sen, P.; Knox, C.
1977-01-01
A new constant fraction discriminator with improved stability and walk characteristics is described. The discriminator was used with RCA C31024 photomultiplier tubes to test scintillators of conical and cylindrical shapes. Conical scintillators of 2.54 cm base diameter, 1.0 cm top diameter, and 2.54 cm height gave a fwhm of 155 ps for 60 Co gamma rays; larger conical scintillators gave an improvement of 10-15% in fwhm over cylindrical scintillators of equal volume. (Auth.)
12. Power inverter implementing phase skipping control
Science.gov (United States)
2016-10-18
A power inverter includes a DC/AC inverter having first, second and third phase circuitry coupled to receive power from a power source. A controller is coupled to a driver for each of the first, second and third phase circuitry (control input drivers). The controller includes an associated memory storing a phase skipping control algorithm, wherein the controller is coupled to receive updating information including a power level generated by the power source. The drivers are coupled to control inputs of the first, second and third phase circuitry, where the drivers are configured for receiving phase skipping control signals from the controller and outputting mode selection signals configured to dynamically select an operating mode for the DC/AC inverter from a Normal Control operation and a Phase Skipping Control operation which have different power injection patterns through the first, second and third phase circuitry depending upon the power level.
13. Radiological follow-up of inverted papilloma
Energy Technology Data Exchange (ETDEWEB)
Petit, P.; Vivarrat-Perrin, L.; Champsaur, P.; Juhan, V.; Chagnaud, C.; Vidal, V.; Gaubert, J.Y.; Bartoli, J.M.; Moulin, G. [Department of Radiology, Groupe Hospitalier de la Timone, Centre Hospitalier et Universitaire de Marseille, F-13385 Marseille Cedex 5 (France); Dessi, P.; Zanaret, M. [Department of Head and Neck Surgery, Groupe Hospitalier de la Timone, Centre Hospitalier et Universitaire de Marseille, F-13385 Marseille Cedex 5 (France)
2000-07-01
The aim of this study was to describe cross-sectional imaging features of recurrent papilloma of the nasal fossa and paranasal sinuses and to evaluate the role of MR and CT in the postoperative follow-up of this lesion. Magnetic resonance imaging and CT of ten patients who presented recurrence of inverted papilloma were reviewed and correlated to initial imaging, endoscopy, and surgical reports. Imaging patterns of recurrent inverted papilloma are identical to those of initial tumors and recurrence location is closely related to the site of the former lesion. Magnetic resonance is more efficient than CT for the diagnosis and evaluation of extensions. Magnetic resonance supplies the deficiencies of endoscopy in case of extensions to the frontal sinus or the lateral recess of the antrum, especially if mucosal hyperplasia or sinusitis is associated. Magnetic resonance imaging is the first imaging modality to perform in the follow-up after removal of inverted papilloma. (orig.)
14. An SCR inverter for electric vehicles
Science.gov (United States)
Latos, T.; Bosack, D.; Ehrlich, R.; Jahns, T.; Mezera, J.; Thimmesch, D.
1980-01-01
An inverter for an electric vehicle propulsion application has been designed and constructed to excite a polyphase induction motor from a fixed propulsion battery source. The inverter, rated at 35kW peak power, is fully regenerative and permits vehicle operation in both the forward and reverse directions. Thyristors are employed as the power switching devices arranged in a dc bus commutated topology. This paper describes the major role the controller plays in generating the motor excitation voltage and frequency to deliver performance similar to dc systems. Motoring efficiency test data for the controller are presented. It is concluded that an SCR inverter in conjunction with an ac induction motor is a viable alternative to present dc vehicle propulsion systems on the basis of performance and size criteria.
15. Inorganic Scintillation Crystals for Neutron Detection
International Nuclear Information System (INIS)
Costa-Pereira, Maria-da-Conceicao; Filho, Tufic-Madi; Nahuel-Cardenas, Jose-Patricio
2013-06-01
Inorganic scintillators play an important role in the detection and spectroscopy of gamma and X-rays, as well as in neutrons and charged particles. For a variety of applications, new inorganic scintillation materials are being studied. New scintillation detector applications arise continuously and, consequently, the interest in the introduction of new fast scintillators becomes relevant. Scintillation crystals based on cesium iodide (CsI) have relatively low hygroscope, easy handling and low cost, features that favor their use as radiation detectors. In this work, lithium and bromine doped CsI crystals were grown using the vertical Bridgman technique. In this technique, the charge is maintained at high temperature for 10 h for the material melting and complete reaction. The temperature gradient 21 deg. C/cm and 1 mm/h descending velocity are chosen as technique parameters. After growth is finished, the furnace is cooled at a rate of 20 deg. C/h to room temperature. The concentration of the lithium doping element (Li) studied was 10 -3 M and the concentration of the bromine was 10 -2 M. Analyses were carried out to evaluate the scintillators developed concerning the neutron from the AmBe source, with energy range of 1 MeV to 12 MeV. Lithium can capture neutrons without gamma-ray emission, thus, reducing the back-ground. The neutron detection reaction is 6 Li(n, α) 3 H with a thermal neutron cross section of 940 barns. In this paper, it was investigated the feasibility of the CsI:Li and CsI:Br crystals as neutron detectors for monitoring, due to the fact that in our work environment there are two nuclear research reactors and calibration systems. (authors)
16. Luminescence and scintillation properties of rare-earth-doped LuF.sub.3./sub. scintillation crystals
Czech Academy of Sciences Publication Activity Database
Pejchal, Jan; Fukuda, K.; Kurosawa, S.; Yokota, Y.; Yoshikawa, A.
2015-01-01
Roč. 41, Mar SI (2015), s. 58-62 ISSN 0925- 3467 Institutional support: RVO:68378271 Keywords : lutetium fluoride * scintillator * scintillator * VUV luminescence Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.183, year: 2015
17. Near-infrared scintillation of liquid argon
Energy Technology Data Exchange (ETDEWEB)
Alexander, T. [Fermilab; Escobar, C. O. [Campinas State U.; Lippincott, W. H. [Fermilab; Rubinov, P. [Fermilab
2016-03-03
Since the 1970s it has been known that noble gases scintillate in the near infrared (NIR) region of the spectrum (0.7 $\\mu$m < $\\lambda$; < 1.5$\\mu$m). More controversial has been the question of the NIR light yield for condensed noble gases. We first present the motivation for using the NIR scintillation in liquid argon detectors, then briefly review early as well as more recent efforts and finally show encouraging preliminary results of a test performed at Fermilab.
18. Fluorescence quenching of plastic scintillators in oxygen
Science.gov (United States)
Horstmann, D.; Holm, U.
1993-01-01
The plastic scintillators SCSN-38, SCSN-81T, 3HF in polystyrene and a PMMA based Polivar scintillator show a loss in light yield when operated in air or oxygen. Both the fluorescence of the base material polystyrene or the PMMA admixture naphtalene as well as that of the dyes is reduced. The quenching ratio is proportional to the partial pressure of the surrounding oxygen. The maximum overall quenching amounts to 11.1% for SCSN-38 in one atmosphere of oxygen when excited with light of 262 nm.
19. Fluorescence quenching of plastic scintillators in oxygen
International Nuclear Information System (INIS)
Horstmann, D.; Holm, U.
1992-01-01
The plastic scintillators SCSN-38, SCSN-81T, 3HF in polystyrene and a PMMA based Polivar scintillator show a loss in light yield when operated in air or oxygen. Both the fluorescence of the base material polystyrene or the PMMA admixture naphtalene as well as that of the dyes is reduced. The quenching ratio is proportional to the partial pressure of the surrounding oxygen. The maximum overall quenching amounts to 11.1 % for SCSN-38 in one atmosphere of oxygen when excited with light of 262 nm. (Author)
20. Full-absorption scintillation spectrometer for neutrons
International Nuclear Information System (INIS)
Dzhelepov, V.P.; Filchenkov, V.V.; Konin, A.D.; Rudenko, A.I.; Solovieva, G.M.; Zinov, V.G.
1988-01-01
A full-absorption scintillation spectrometer for neutrons (volume of scintillator = 24 l) has been developed and employed in investigations of muon catalysed processes. Its application allows: (a) Considerably increasing the rate of accummulation of events; (b) efficiently using muon catalysis multiplicity for fuller and more reliable determination of its parameters; (c) significantly reducing uncertainty in the calculated and experimentally found values of neutron detection efficiency. The device combines good spectrometric properties for neutron energies E n = 1-6 MeV and reliable n-γ separation (the degree of separation for a Pu-Be source 3 starting from an electron energy of 50 keV). (orig.)
1. Plastic scintillators modifications for a selective radiation detection
Energy Technology Data Exchange (ETDEWEB)
Hamel, Matthieu; Bertrand, Guillaume H.V.; Carrel, Frederick; Coulon, Romain; Dumazert, Jonathan; Montbarbon, Eva; Sguerra, Fabien [CEA, LIST, Laboratoire Capteurs and Architectures electroniques, 91191 Gif-sur-Yvette cedex (France)
2015-07-01
Recent developments of plastic scintillators are reviewed, from January 2000 to June 2015. All examples are distributed into the main application, i.e. how the plastic scintillator was modified to enhance the detection towards a given radiation particle. The main characteristics of these newly created scintillators and their detection properties are given. (authors)
2. Upconverting nanoparticles for optimizing scintillator based detection systems
Science.gov (United States)
Kross, Brian; McKisson, John E; McKisson, John; Weisenberger, Andrew; Xi, Wenze; Zom, Carl
2013-09-17
An upconverting device for a scintillation detection system is provided. The detection system comprises a scintillator material, a sensor, a light transmission path between the scintillator material and the sensor, and a plurality of upconverting nanoparticles particles positioned in the light transmission path.
3. Smart Inverters for Utility and Industry Applications
DEFF Research Database (Denmark)
Xue, Yaosuo; Guerrero, Josep M.
2015-01-01
Smart inverters are emerging with increasing renewable energy and smart grid development. While the recent work reviewed mostly focuses on defining standardized control functionalities and smart grid communication protocols, we take a holistic approach in this paper and propose a holon-type smart...... inverter concept, which features autonomous, adaptive, cooperative and plug-and-play functions. Self-awareness is also continually driven by power electronics inherently. These features can be favorable in a complex environment with more and more small-scale power electronics-based devices, and can reduce...
4. Asymmetrical transformer-based embedded Z-source inverters
DEFF Research Database (Denmark)
Wei, Mo; Loh, Poh Chiang; Blaabjerg, Frede
2013-01-01
Z-source inverters are inverters with buck-boost capability that traditional inverters cannot match. Despite this ability, present Z-source topologies are burdened by some limitations such as chopping input current, high-voltage stress and poor spectral performance at high gain. To improve...... their performances, a number of asymmetrical transformer-based embedded Z-source inverters are proposed. Through theoretical derivation and experiments, the proposed inverters have been shown to draw a smooth input current and produce a high gain by varying the transformer turns ratio n. The range of variation for n...... depends on the inverter topology chosen, which in turn depends on the application under consideration....
5. Characteristics Comparison of High-Frequency Multi-Level Inverter Connected with Filter Inverters
Science.gov (United States)
Iwaya, Kazuki; Noguchi, Toshihiko
This paper presents characteristics comparison of a high-frequency multi-level inverter connected with small capacity filter inverters. In general, PWM inverters require a low-pass filter in order to reduce switching harmonics. However, in the high-frequency systems such as class D power amplifiers, the cut-off frequency of the low-pass filter must set at high frequency. Thus, harmonic distortion of the output voltage harmfully enlarges. Increasing the number of output voltage levels is effective to reduce the harmonic distortion of the output voltage and the low-pass filter size. The proposed systems consist of a 5-level inverter and several cascade-connected low-voltage full bridge inverters without any external DC power sources for filtering the output voltage. The 5-level inverter generates a stepwise waveform with 5-level voltage, and the low voltage filter inverter superimposes harmonic components to compensate for the voltage waveform distortion. Therefore, the proposed system can reduce its total switching loss and can increase the number of the output voltage levels. In this paper, effectiveness of the proposed systems is verified through several experiments.
6. Robust GPS carrier tracking under ionospheric scintillation
Science.gov (United States)
Susi, M.; Andreotti, M.; Aquino, M. H.; Dodson, A.
2013-12-01
7. Live Imaging of Shoot Meristems on an Inverted Confocal Microscope Using an Objective Lens Inverter Attachment.
Science.gov (United States)
Nimchuk, Zachary L; Perdue, Tony D
2017-01-01
Live imaging of above ground meristems can lead to new insights in plant development not possible from static imaging of fixed tissue. The use of an upright confocal microscope offers several technical and biological advantages for live imaging floral or shoot meristems. However, many departments and core facilities possess only inverted confocal microscopes and lack the funding for an additional upright confocal microscope. Here we show that imaging of living apical meristems can be performed on existing inverted confocal microscopes with the use of an affordable and detachable InverterScope accessory.
8. High voltage series resonant inverter ion engine screen supply. [SCR series resonant inverter for space applications
Science.gov (United States)
Biess, J. J.; Inouye, L. Y.; Shank, J. H.
1974-01-01
A high-voltage, high-power LC series resonant inverter using SCRs has been developed for an Ion Engine Power Processor. The inverter operates within 200-400Vdc with a maximum output power of 2.5kW. The inverter control logic, the screen supply electrical and mechanical characteristics, the efficiency and losses in power components, regulation on the dual feedback principle, the SCR waveforms and the component weight are analyzed. Efficiency of 90.5% and weight density of 4.1kg/kW are obtained.
9. The SNO+ Scintillator Purification Plant and Projected Sensitivity to Solar Neutrinos in the Pure Scintillator Phase
Science.gov (United States)
Pershing, Teal; SNO+ Collaboration
2016-03-01
The SNO+ detector is a neutrino and neutrinoless double-beta decay experiment utilizing the renovated SNO detector. In the second phase of operation, the SNO+ detector will contain 780 tons of organic liquid scintillator composed of 2 g/L 2,5-diphenyloxazole (PPO) in linear alkylbenzene (LAB). In this phase, SNO+ will strive to detect solar neutrinos in the sub-MeV range, including CNO production neutrinos and pp production neutrinos. To achieve the necessary detector sensitivity, a four-part scintillator purification plant has been constructed in SNOLAB for the removal of ionic and radioactive impurities. We present an overview of the SNO+ scintillator purification plant stages, including distillation, water extraction, gas stripping, and metal scavenger columns. We also give the projected SNO+ sensitivities to various solar-produced neutrinos based on the scintillator plant's projected purification efficiency.
10. Scintillator device using a combined organic-inorganic scintillator as dose ratemeter
International Nuclear Information System (INIS)
Kolb, W.; Lauterbach, U.
1974-01-01
The dose ratemeter independent of energy in the energy region 17 keV to 3 MeV consists of an organic and an inorganic scintillator. The organic scintillation material of an anthracene monocrystal is surrounded by ZnS surface coating. The coating thickness of the inorganic scintillator ZnS is measured in such a manner for gamma and X-radiation below 100 keV that the light produced due to the incident radiation compensates for the decrease of light produced in the organic scintillator. The whole energy and dose rate region of interest for radiation protection can thus be measured with a detector volume of 135 cm 3 . (DG) [de
11. General considerations for SSC scintillator calorimeters (For the scintillator general subgroup)
International Nuclear Information System (INIS)
Nodulman, L.
1989-01-01
The Scintillator Calorimetry group divided into three subgroups: a conventional uranium and plate design ala ZEUS, fiber design, and a group on general considerations. The considerations of the third group are reported here on geometrical and technical issues. 1 fig
12. Temperature dependence of scintillation properties of bright oxide scintillators for well-logging
Czech Academy of Sciences Publication Activity Database
Yanagida, T.; Fujimoto, Y.; Kurosawa, S.; Kamada, K.; Takahashi, H.; Fukazawa, Y.; Nikl, Martin; Chani, V.
2013-01-01
Roč. 52, č. 7 (2013), "076401-1"-"076401-6" ISSN 0021-4922 Institutional support: RVO:68378271 Keywords : scintillator * high temperature * light yield Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.057, year: 2013
13. Modification of Karasawa tropospheric scintillation model for Malaysia climate
Science.gov (United States)
Yee, C. C.; Mandeep, J. S.; Islam, M. T.
2013-09-01
Tropospheric scintillation is the rapid fluctuation and degradation of satellite signals due to changes in refractive index of atmosphere. This phenomenon tends to affect signals more strongly at frequencies above 10 GHz. This paper introduces a new scintillation prediction model created by modifying the existing Karasawa model. The proposed model is compared with currently existing model using scintillation data collected in Parit Buntar, Malaysia. The proposed model can simultaneously predict scintillation intensity of both fade and enhancement scintillation with an error rate below 5 %.
14. Inverted Pedagogy in Second Semester Calculus
Science.gov (United States)
Kennedy, Ellie; Beaudrie, Brian; Ernst, Dana C.; St. Laurent, Roy
2015-01-01
This study investigates the effects of applying an inverted classroom model in a second-semester calculus course at a large regional university in the southwest during the Spring of 2013. The sample consisted of four class sections with the same instructor, with a total of 173 students; two class sections were in the experimental group, whereas…
15. Inverting the Transition-to-Proof Classroom
Science.gov (United States)
Talbert, Robert
2015-01-01
In this paper, we examine the benefits of employing an inverted or "flipped" class design in a Transition-to-Proof course for second-year mathematics majors. The issues concomitant with such courses, particularly student acquisition of "sociomathematical norms" and self-regulated learning strategies, are discussed along with…
16. MPPT algorithm for voltage controlled PV inverters
DEFF Research Database (Denmark)
Kerekes, Tamas; Teodorescu, Remus; Liserre, Marco
2008-01-01
This paper presents a novel concept for an MPPT that can be used in case of a voltage controlled grid connected PV inverters. In case of single-phase systems, the 100 Hz ripple in the AC power is also present on the DC side. Depending on the DC link capacitor, this power fluctuation can be used...
17. The Internet and the Inverted Classroom.
Science.gov (United States)
Lage, Maureen J.; Platt, Glenn
2000-01-01
Describes a Web site that is for an undergraduate principles of microeconomics course and a main component of "The Inverted Classroom" in which lectures take place outside of class. Explains that the Web site is divided into four sections: (1) the classroom; (2) the desk; (3) the coffee shop; and (4) the library. (CMK)
18. Solar Power Station Output Inverter Control Design
Directory of Open Access Journals (Sweden)
J. Bauer
2011-04-01
Full Text Available The photovoltaic applications spreads in these days fast, therefore they also undergo great development. Because the amount of the energy obtained from the panel depends on the surrounding conditions, as intensity of the sun exposure or the temperature of the solar array, the converter must be connected to the panel output. The Solar system equipped with inverter can supply small loads like notebooks, mobile chargers etc. in the places where the supplying network is not present. Or the system can be used as a generator and it shall deliver energy to the supply network. Each type of the application has different requirements on the converter and its control algorithm. But for all of them the one thing is common – the maximal efficiency. The paper focuses on design and simulation of the low power inverter that acts as output part of the whole converter. In the paper the design of the control algorithm of the inverter for both types of inverter application – for islanding mode and for operation on the supply grid – is discussed. Attention is also paid to the design of the output filter that should reduce negative side effects of the converter on the supply network.
19. Subintegrality, invertible modules and Laurent polynomial extensions
Indian Acad. Sci. (Math. Sci.) Vol. 125, No. 2, May 2015, pp. 149–160. c Indian Academy of Sciences. Subintegrality, invertible modules and Laurent polynomial extensions. VIVEK SADHU. Department of Mathematics ...... comments which have improved the exposition. Further, he would like to thank CSIR,. India for financial ...
20. Two-Stage Series-Resonant Inverter
Science.gov (United States)
Stuart, Thomas A.
1994-01-01
Two-stage inverter includes variable-frequency, voltage-regulating first stage and fixed-frequency second stage. Lightweight circuit provides regulated power and is invulnerable to output short circuits. Does not require large capacitor across ac bus, like parallel resonant designs. Particularly suitable for use in ac-power-distribution system of aircraft.
1. Inverter Matrix for the Clementine Mission
Science.gov (United States)
Buehler, M. G.; Blaes, B. R.; Tardio, G.; Soli, G. A.
1994-01-01
An inverter matrix test circuit was designed for the Clementine space mission and is built into the RRELAX (Radiation and Reliability Assurance Experiment). The objective is to develop a circuit that will allow the evaluation of the CMOS FETs using a lean data set in the noisy spacecraft environment.
2. Pulse width modulation inverter with battery charger
Science.gov (United States)
Slicker, James M. (Inventor)
1985-01-01
An inverter is connected between a source of DC power and a three-phase AC induction motor, and a microprocessor-based circuit controls the inverter using pulse width modulation techniques. In the disclosed method of pulse width modulation, both edges of each pulse of a carrier pulse train are equally modulated by a time proportional to sin .theta., where .theta. is the angular displacement of the pulse center at the motor stator frequency from a fixed reference point on the carrier waveform. The carrier waveform frequency is a multiple of the motor stator frequency. The modulated pulse train is then applied to each of the motor phase inputs with respective phase shifts of 120.degree. at the stator frequency. Switching control commands for electronic switches in the inverter are stored in a random access memory (RAM) and the locations of the RAM are successively read out in a cyclic manner, each bit of a given RAM location controlling a respective phase input of the motor. The DC power source preferably comprises rechargeable batteries and all but one of the electronic switches in the inverter can be disabled, the remaining electronic switch being part of a flyback DC-DC converter circuit for recharging the battery.
3. The invertible double of elliptic operators
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Lesch, Matthias; Zhu, Chaofeng
We construct a canonical invertible double for general first order elliptic differential operators over smooth compact manifolds with boundary and derive a natural formula for the Calderon projector which yields a generalization of the famous Cobordism Theorem. Assuming symmetric principal symbol...
4. Neutron spectrometer using NE218 liquid scintillator
International Nuclear Information System (INIS)
Dance, J.B.; Francois, P.E.
1976-01-01
A neutron spectrometer has been constructed using NE218 liquid scintillator. Discrimination against electron-gamma events was obtained usng a charge-comparison pulse shape discrimination system. The resolution obtained was about 0.25 MeV F.W.H.M. at 2.0 MeV
5. Progress in studying scintillator proportionality: Phenomenological model
Energy Technology Data Exchange (ETDEWEB)
Bizarri, Gregory; Cherepy, Nerine; Choong, Woon-Seng; Hull, Giulia; Moses, William; Payne, Sephen; Singh, Jai; Valentine, John; Vasilev, Andrey; Williams, Richard
2009-04-30
We present a model to describe the origin of non-proportional dependence of scintillator light yield on the energy of an ionizing particle. The non-proportionality is discussed in terms of energy relaxation channels and their linear and non-linear dependences on the deposited energy. In this approach, the scintillation response is described as a function of the deposited energy deposition and the kinetic rates of each relaxation channel. This mathematical framework allows both a qualitative interpretation and a quantitative fitting representation of scintillation non-proportionality response as function of kinetic rates. This method was successfully applied to thallium doped sodium iodide measured with SLYNCI, a new facility using the Compton coincidence technique. Finally, attention is given to the physical meaning of the dominant relaxation channels, and to the potential causes responsible for the scintillation non-proportionality. We find that thallium doped sodium iodide behaves as if non-proportionality is due to competition between radiative recombinations and non-radiative Auger processes.
6. Improved light yield of lead tungstate scintillators
CERN Document Server
Annenkov, A N; Hofstäetter, A; Korzhik, M V; Ligun, V; Lecoq, P; Missevitch, O V; Novotny, R; Peigneux, J P
2000-01-01
The application at medium and low energies of lead tungstate scintillators, so far optimized for the ECAL calorimeter of CMS for the future LHC, is strongly limited by their poor light yield. Suitable dopants like molybdenum and terbium can help to overcome this problem. Concepts, results, advantages and drawbacks of this approach are discussed. (11 refs).
7. An improved model of equatorial scintillation
Science.gov (United States)
Secan, J. A.; Bussey, R. M.; Fremouw, E. J.; Basu, Sa.
1995-05-01
One of the main limitations of the modeling work that went into the equatorial section of the Wideband ionospheric scintillation model (WBMOD) was that the data set used in the modeling was limited to two stations near the dip equator (Ancon, Peru, and Kwajalein Island, in the North Pacific Ocean) at two fixed local times (nominally 1000 and 2200). Over the past year this section of the WBMOD model has been replaced by a model developed using data from three additional stations (Ascension Island, in the South Atlantic Ocean, Huancayo, Peru, and Manila, Phillipines; data collected under the auspices of the USAF Phillips Laboratory Geophysics Directorate) which provide a greater diversity in both latitude and longitude, as well as cover the entire day. The new model includes variations with latitude, local time, longitude, season, solar epoch, and geomagnetic activity levels. The way in which the irregularity strength parameter CkL is modeled has also been changed. The new model provides the variation of the full probability distribution function (PDF) of log (CkL) rather than simply the average of log (CkL). This permits the user to specify a threshold on scintillation level, and the model will calculate the percent of the time that scintillation will exceed that level in the user-specified scenario. It will also permit calculation of scintillation levels at a user-specified percentile. A final improvement to the WBMOD model is the implementation of a new theory for calculating S4 on a two-way channel.
8. High resolution scintillation detector with semiconductor readout
Science.gov (United States)
Levin, Craig S.; Hoffman, Edward J.
2000-01-01
A novel high resolution scintillation detector array for use in radiation imaging such as high resolution Positron Emission Tomography (PET) which comprises one or more parallelepiped crystals with at least one long surface of each crystal being in intimate contact with a semiconductor photodetector such that photons generated within each crystal by gamma radiation passing therethrough is detected by the photodetector paired therewith.
9. Neutron energy response measurement of scintillation detectors
International Nuclear Information System (INIS)
Yang Hongqiong; Peng Taiping; Yang Jianlun; Tang Zhengyuan; Yang Gaozhao; Li Linbo; Hu Mengchun; Wang Zhentong; Zhang Jianhua; Li Zhongbao; Wang Lizong
2004-01-01
Neutron sensitivities of detectors composed of plastic scintillator ST401, ST1422, ST1423 and phyotomultiplier tube in primary energy range of fission neutron are calibrated by direct current. The energy response curve of the detectors is obtained in this experiment. The experimental result has been compared with the theoretical calculation and they are in agreement within measuring uncertainty. (authors)
10. Thallium bromide photodetectors for scintillation detection
CERN Document Server
Hitomi, K; Shoji, T; Hiratate, Y; Ishibashi, H; Ishii, M
2000-01-01
A wide bandgap compound semiconductor, TlBr, has been investigated as a blue sensitive photodetector material for scintillation detection. The TlBr photodetectors have been fabricated from the TlBr crystals grown by the TMZ method using materials purified by many pass zone refining. The performance of the photodetectors has been evaluated by measuring their leakage current, quantum efficiency, spatial uniformity, direct X-ray detection and scintillation detection characteristics. The photodetectors have shown high quantum efficiency for the blue wavelength region and high spatial uniformity for their optical response. In addition, good direct X-ray detection characteristics with an energy resolution of 4.5 keV FWHM for 22 keV X-rays from a sup 1 sup 0 sup 9 Cd radioactive source have been obtained. Detection of blue scintillation from GSO and LSO scintillators irradiated with a sup 2 sup 2 Na radioactive source has been done successfully by using the photodetectors at room temperature. A clear full-energy pea...
11. Infrared scintillation in gases, liquids and crystals
NARCIS (Netherlands)
Belogurov, S.; Bressi, G; Carugno, G.; Conti, E; Iannuzzi, D; Meneguzzo, AT
2000-01-01
We report about experimental evidences of infrared scintillation in gaseous, liquid and crystal samples. We firstly studied noble gases at room temperature and near atmospheric pressure in the wavelength range between 0.7 and 1.81 mum. Ar gas emits infrared photons when irradiated by a proton beam.
12. A multidetector scintillation camera with 254 channels
DEFF Research Database (Denmark)
Sveinsdottir, E; Larsen, B; Rommer, P
1977-01-01
A computer-based scintillation camera has been designed for both dynamic and static radionuclide studies. The detecting head has 254 independent sodium iodide crystals, each with a photomultiplier and amplifier. In dynamic measurements simultaneous events can be recorded, and 1 million total coun...
13. Basic processes and scintillator and semiconductor detectors
International Nuclear Information System (INIS)
Bourgeois, C.
1994-01-01
In the following course, the interaction of heavy charged particles, electrons and Γ with matter is represented. Two types of detectors are studied, organic and inorganic scintillators and semiconductors. The signal formation is analysed. (author). 13 refs., 48 figs., 5 tabs
14. Light pulse shapes from plastic scintillators
International Nuclear Information System (INIS)
Moszynski, M.; Bengtson, B.
1977-01-01
A detailed study of the light pulse shape from the binary NE 111 and the ternary Pilot U, Naton 136, KL 236, NE 102A, NE 104 and NE 110 plastic scintillators was performed by the single photon method using XP 1021 and C 31024 photomultipliers. The analysis of the shape of the light pulses determined experimentally for several samples of different dimensions gave the following conclusions. The original light pulse shape from the binary NE 111 scintillator, as measured with a 5 mm thick polished sample is described analytically by the convolution integral of a Gaussian and an exponential function. The Gaussian function may reflect a deexcitation of several higher levels of the solvent molecules excited by nuclear particles preceding an intermolecular energy transfer in the scintillator. It may introduce a rather important limitation of the speed of plastic scintillators as the standard deviation of the Gaussian function is equal to 0.2 ns. The light pulse shape from the ternary plastics is described by the convolution integral of a Gaussian and two exponential functions. The Gaussian function presents the rate of energy transfer from nuclear particles to the primary solute as in the binary plastics. The exponential functions describe the energy transfer from the primary solute to the wavelength shifter and the final emission of the light. (Auth.)
15. A multidetector scintillation camera with 254 channels
DEFF Research Database (Denmark)
Sveinsdottir, E; Larsen, B; Rommer, P
1977-01-01
A computer-based scintillation camera has been designed for both dynamic and static radionuclide studies. The detecting head has 254 independent sodium iodide crystals, each with a photomultiplier and amplifier. In dynamic measurements simultaneous events can be recorded, and 1 million total counts...
16. Scintillating fibre (SciFi) tracker
CERN Multimedia
Caraban Gonzalez, Noemi
2017-01-01
128 modules – containing 11 000 km of scintillating fibres – will make up the new SciFi tracker, which will replace the outer and inner trackers of the LHCb detector as part of the experiment’s major upgrade during Long Shutdown 2 (LS2)
17. System and method of liquid scintillation counting
International Nuclear Information System (INIS)
Rapkin, E.
1977-01-01
A method of liquid scintillation counting utilizing a combustion step to overcome quenching effects comprises novel features of automatic sequential introduction of samples into a combustion zone and automatic sequential collection and delivery of combustion products into a counting zone. 37 claims, 13 figures
18. Large area scintillators for massive neutrino detectors
CERN Document Server
Bonesini, M
2003-01-01
A technique based on extruded scintillators for the active elements of large mass neutrino detectors is described in this paper. The robustness of the technique, pioneered by the Minos Collaboration, is demonstrated by the good results obtained on a six months timescale research and development done for the 1216 proposal at CERN.
19. Fluorescent compounds for plastic scintillation applications
Energy Technology Data Exchange (ETDEWEB)
Pla-Dalmau, A.; Bross, A.D.
1994-04-01
Several 2-(2{prime}-hydroxyphenyl)benzothiazole, -benzoxazole, and -benzimidazole derivatives have been prepared. Transmittance, fluorescence, light yield, and decay time characteristics of these compounds have been studied in a polystyrene matrix and evaluated for use in plastic scintillation detectors. Radiation damage studies utilizing a {sup 60}C source have also been performed.
20. Experimental evidence of infrared scintillation in crystals
CERN Document Server
Belogurov, S; Carugno, Giovanni; Conti, E; Iannuzzi, D; Meneguzzo, Anna Teresa
2000-01-01
We present experimental results on infrared emission induced by protons in some solid-state samples. Infrared scintillation occurs in many crystals, with different yield values and time-response behaviours. A rough measurement of the emission wavelength of CsI(Tl) is also reported.
1. FPGA Based Compensation Method for Correcting Distortion in Voltage Inverters
National Research Council Canada - National Science Library
Williamson, Kenya D
2007-01-01
...) voltage source inverters. Blanking time distortion is caused by the delay inserted to prevent the short circuit that would occur if the two transistors in the same inverter leg are both on at the same time...
2. Inverter Anti-Islanding with Advanced Grid Support in Single- and Multi-Inverter Islands
Energy Technology Data Exchange (ETDEWEB)
Hoke, Andy
2016-08-16
As PV and other DER systems are connected to the grid at increased penetration levels, island detection may become more challenging for two reasons: 1. In islands containing many DERs, active inverter-based anti-islanding methods may have more difficulty detecting islands because each individual inverter's efforts to detect the island may be interfered with by the other inverters in the island. 2. The increasing numbers of DERs are leading to new requirements that DERs ride through grid disturbances and even actively try to regulate grid voltage and frequency back towards nominal operating conditions. These new grid support requirements may directly or indirectly interfere with anti-islanding controls. This report describes a series of tests designed to examine the impacts of both grid support functions and multi-inverter islands on anti-islanding effectiveness.
3. Systematic study of particle quenching in organic scintillators
International Nuclear Information System (INIS)
Santiago, L.M.; Bagán, H.; Tarancón, A.; Rauret, G.; Garcia, J.F.
2013-01-01
Among the different factors that affect measurements by organic scintillators, the majority of attention has been focused on those related to the scintillator (i.e., ionization, chemical, color and optical quenching), and less attention has been paid to the loss of energy before the particle (i.e., alpha or beta) arrives at the scintillator (i.e., particle quenching). This study evaluates the effect of particle quenching in different scintillation methods (i.e., using two plastic scintillation microspheres (PSm1 and PSm2), liquid scintillator and gel scintillator) by measuring solutions that contain increasing concentrations of NaCl, BaCl 2 and glycerin. The results show the importance of particle quenching in PSm measurements because detection efficiency decreases with increasing concentrations of the quenching component, although the spectrum position and external standard parameter remain constant. The results have shown evidence of particle quenching, although at a lower magnitude, in the liquid scintillation or gel scintillation measurements. Moreover, the use of two PSm with different diameters and salty compound that alters the equilibrium of the liquid and gel emulsions also exemplified the importance of the transmission of optical photons through different scintillation media (i.e., optical quenching). Improvement and deterioration of the optical conditions on the scintillation media is manifested as a movement of the spectrum to higher and lower energies, respectively. The results obtained with PSm were confirmed by Monte Carlo simulation.
4. Systematic study of particle quenching in organic scintillators
Science.gov (United States)
Santiago, L. M.; Bagán, H.; Tarancón, A.; Rauret, G.; Garcia, J. F.
2013-01-01
Among the different factors that affect measurements by organic scintillators, the majority of attention has been focused on those related to the scintillator (i.e., ionization, chemical, color and optical quenching), and less attention has been paid to the loss of energy before the particle (i.e., alpha or beta) arrives at the scintillator (i.e., particle quenching). This study evaluates the effect of particle quenching in different scintillation methods (i.e., using two plastic scintillation microspheres (PSm1 and PSm2), liquid scintillator and gel scintillator) by measuring solutions that contain increasing concentrations of NaCl, BaCl2 and glycerin. The results show the importance of particle quenching in PSm measurements because detection efficiency decreases with increasing concentrations of the quenching component, although the spectrum position and external standard parameter remain constant. The results have shown evidence of particle quenching, although at a lower magnitude, in the liquid scintillation or gel scintillation measurements. Moreover, the use of two PSm with different diameters and salty compound that alters the equilibrium of the liquid and gel emulsions also exemplified the importance of the transmission of optical photons through different scintillation media (i.e., optical quenching). Improvement and deterioration of the optical conditions on the scintillation media is manifested as a movement of the spectrum to higher and lower energies, respectively. The results obtained with PSm were confirmed by Monte Carlo simulation.
5. Non-Carbon Dyes For Platic Scintillators- Report
Energy Technology Data Exchange (ETDEWEB)
Teprovich, J. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Colon-Mercado, H. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Gaillard, J. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Sexton, L. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Washington, A. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Ward, P. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Velten, J. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)
2015-10-19
Scintillation based detectors are desirable for many radiation detection applications (portal and border monitoring, safeguards verification, contamination detection and monitoring). The development of next generation scintillators will require improved detection sensitivity for weak gamma ray sources, and fast and thermal neutron quantification. Radiation detection of gamma and neutron sources can be accomplished with organic scintillators, however, the single crystals are difficult to grow for large area detectors and subject to cracking. Alternatives to single crystal organic scintillators are plastic scintillators (PS) which offer the ability to be shaped and scaled up to produce large sized detectors. PS is also more robust than the typical organic scintillator and are ideally suited for deployment in harsh real-world environments. PS contain a mixture of dyes to down-convert incident radiation into visible light that can be detected by a PMT. This project will evaluate the potential use of nano-carbon dyes in plastic scintillators.
6. Efficient/reliable dc-to-dc inverter circuit
Science.gov (United States)
Pasciutti, E. R.
1970-01-01
Feedback loop, which contains an inductor in series with a saturable reactor, is added to a standard inverter circuit to permit the inverter power transistors to be switched in a controlled and efficient manner. This inverter is applicable where the power source has either high or low impedance properties.
7. Do pregnant women know how to correct inverted nipples ...
African Journals Online (AJOL)
Inverted nipples occur in an estimated 9 to 10 percent of women globally, contributing to the number of women who are not exclusively breastfeeding their infants. Women with inverted nipples may want to breastfeed, but infants may be unable to latch to the breast. Inverted nipples can be corrected, but it is unclear if women ...
8. Pulsewidth-modulated 2-source neutral-point-clamped inverter
DEFF Research Database (Denmark)
Blaabjerg, Frede; Loh, Poh Chang; Gao, Feng
2007-01-01
This paper presents the careful integration of a newly proposed Z-source topological concept to the basic neutral-point-clamped (NPC) inverter topology for designing a three-level inverter with both voltage-buck and voltage-boost capabilities. The designed Z-source NPC inverter uses two unique X-...
9. Mobile Inverted Constructivism: Education of Interaction Technology in Social Media
Science.gov (United States)
Chai, Jia-Xiang; Fan, Kuo-Kuang
2016-01-01
The combination of social media and invert teaching is a new path to inverting interation technology education and reconstructing the curriculum of context. In this paper, based on the theory of constructivism learning, a model named Mobile Inverted Constructivism (MIC) is provided. Moreover, in view of the functional quality of social media in…
10. Power Inverter Topologies for Photovoltaic Modules - A Review
DEFF Research Database (Denmark)
Kjær, Søren Bækhøj; Pedersen, John Kim; Blaabjerg, Frede
2002-01-01
This review-paper focuses on the latest development of inverters for photovoltaic AC-Modules. The power range for these inverters is usually within 90 Watt to 500 Watt, which covers the most commercial photovoltaic-modules. Self-commutated inverters have replaced the grid-commutated ones. The same...
11. Diode-Assisted Buck-Boost Current Source Inverters
DEFF Research Database (Denmark)
Gao, F.; Cai, Liang; Loh, P.C.
2007-01-01
This paper presents a couple of novel current source inverters (CSIs) with the enhanced current buckboost capability. With the unique diode-inductor network added between current source inverter circuitry and current boost elements, the proposed buck-boost current source inverters demonstrate...
12. A single phase photovoltaic inverter control for grid connected system
during light load condition the excess energy generated from the PV inverter is fed to the grid and; during an overload condition or in case of unfavorable atmospheric conditions the load demand is met by both PV inverter and the grid. In order to synchronize the PV inverter with the grid a dual transport delay based phase ...
13. Online Variable Topology-Type Photovoltaic Grid-Connected Inverter
DEFF Research Database (Denmark)
Wu, Fengjiang; Sun, Bo; Duan, Jiandong
2015-01-01
and H-bridge inverter under the conditions of variable output voltage and power of the PV array. It is proved that, compared with the H-bridge inverter, the operation range of the cascaded inverter is wider, whereas the total loss is larger. Furthermore, a novel online variable topology-type grid...
14. DC-to-AC inverter ratio failure detector
Science.gov (United States)
Ebersole, T. J.; Andrews, R. E.
1975-01-01
Failure detection technique is based upon input-output ratios, which is independent of inverter loading. Since inverter has fixed relationship between V-in/V-out and I-in/I-out, failure detection criteria are based on this ratio, which is simply inverter transformer turns ratio, K, equal to primary turns divided by secondary turns.
15. A scintillating bolometer array for double beta decay studies: The LUCIFER experiment
Energy Technology Data Exchange (ETDEWEB)
Gironi, L., E-mail: [email protected] [Università degli Studi di Milano-Bicocca, Milano (Italy); INFN – Sezione di Milano-Bicocca, Milano (Italy)
2016-07-11
The main goal of the LUCIFER experiment is to study the neutrinoless double beta decay, a rare process allowed if neutrinos are Majorana particles. Although aiming at a discovery, in the case of insufficient sensitivity the LUCIFER technique will be the demonstrator for a higher mass experiment able to probe the entire inverted hierarchy region of the neutrino mass. In order to achieve this challenging result, high resolution detectors with active background discrimination capability are required. This very interesting possibility can be largely fulfilled by scintillating bolometers thanks to the simultaneous read-out of heat and light emitted by the interactions in the detector or by pulse shape analysis. - Highlights: • The LUCIFER technique will be the demonstrator for a higher mass experiment. • Scintillating bolometers allow high energy resolution and background discrimination. • The first choice for the LUCIFER tower are ZnSe crystals. • The LUCIFER setup will consist of an array of 30 individual single module detectors. • An array of ZnMoO4 crystals allowed the bolometric observation of the 2vDBD of {sup 100}Mo.
16. Stochastic p-Bits for Invertible Logic
Directory of Open Access Journals (Sweden)
Kerem Yunus Camsari
2017-07-01
Full Text Available Conventional semiconductor-based logic and nanomagnet-based memory devices are built out of stable, deterministic units such as standard metal-oxide semiconductor transistors, or nanomagnets with energy barriers in excess of ≈40–60 kT. In this paper, we show that unstable, stochastic units, which we call “p-bits,” can be interconnected to create robust correlations that implement precise Boolean functions with impressive accuracy, comparable to standard digital circuits. At the same time, they are invertible, a unique property that is absent in standard digital circuits. When operated in the direct mode, the input is clamped, and the network provides the correct output. In the inverted mode, the output is clamped, and the network fluctuates among all possible inputs that are consistent with that output. First, we present a detailed implementation of an invertible gate to bring out the key role of a single three-terminal transistorlike building block to enable the construction of correlated p-bit networks. The results for this specific, CMOS-assisted nanomagnet-based hardware implementation agree well with those from a universal model for p-bits, showing that p-bits need not be magnet based: any three-terminal tunable random bit generator should be suitable. We present a general algorithm for designing a Boltzmann machine (BM with a symmetric connection matrix [J] (J_{ij}=J_{ji} that implements a given truth table with p-bits. The [J] matrices are relatively sparse with a few unique weights for convenient hardware implementation. We then show how BM full adders can be interconnected in a partially directed manner (J_{ij}≠J_{ji} to implement large logic operations such as 32-bit binary addition. Hundreds of stochastic p-bits get precisely correlated such that the correct answer out of 2^{33} (≈8×10^{9} possibilities can be extracted by looking at the statistical mode or majority vote of a number of time samples. With perfect
17. Stochastic p -Bits for Invertible Logic
Science.gov (United States)
Camsari, Kerem Yunus; Faria, Rafatul; Sutton, Brian M.; Datta, Supriyo
2017-07-01
Conventional semiconductor-based logic and nanomagnet-based memory devices are built out of stable, deterministic units such as standard metal-oxide semiconductor transistors, or nanomagnets with energy barriers in excess of ≈40 - 60 kT . In this paper, we show that unstable, stochastic units, which we call "p -bits," can be interconnected to create robust correlations that implement precise Boolean functions with impressive accuracy, comparable to standard digital circuits. At the same time, they are invertible, a unique property that is absent in standard digital circuits. When operated in the direct mode, the input is clamped, and the network provides the correct output. In the inverted mode, the output is clamped, and the network fluctuates among all possible inputs that are consistent with that output. First, we present a detailed implementation of an invertible gate to bring out the key role of a single three-terminal transistorlike building block to enable the construction of correlated p -bit networks. The results for this specific, CMOS-assisted nanomagnet-based hardware implementation agree well with those from a universal model for p -bits, showing that p -bits need not be magnet based: any three-terminal tunable random bit generator should be suitable. We present a general algorithm for designing a Boltzmann machine (BM) with a symmetric connection matrix [J ] (Ji j=Jj i) that implements a given truth table with p -bits. The [J ] matrices are relatively sparse with a few unique weights for convenient hardware implementation. We then show how BM full adders can be interconnected in a partially directed manner (Ji j≠Jj i) to implement large logic operations such as 32-bit binary addition. Hundreds of stochastic p -bits get precisely correlated such that the correct answer out of 233 (≈8 ×1 09) possibilities can be extracted by looking at the statistical mode or majority vote of a number of time samples. With perfect directivity (Jj i=0 ) a small
18. Transistor Clamped Five-Level Inverter using Non-Inverting Double Reference Single Carrier PWM Technique for photovoltaic applications
DEFF Research Database (Denmark)
2017-01-01
supplies or capacitor banks. To design the proposed five level inverter five numbers of power control switches and eight diodes are required. The proposed inverter circuitry is investigated by using Non-Inverting Double Reference Single Carrier PWM (NIDRSC PWM) Technique in terms of harmonics content...
19. Nonproportionality of Scintillator Detectors: Theory and Experiment
Energy Technology Data Exchange (ETDEWEB)
Payne, Stephen; Cherepy, Nerine; Hull, Giulia; Valentine, John; Moses, William; Choong, Woon-Seng
2009-08-17
On the basis of nonproportionality data obtained for several scintillators, we have developed a theory to describe the carrier dynamics to fit the light yield versus electron energy. The theory of Onsager was adapted to explain how the carriers form excitons or sequentially arrive at the activators to promote the ion to an excited state, and the theory of Birks was employed to allow for exciton-exciton annihilation. We then developed a second theory to deduce the degradation in resolution that results from nonproportionality by evoking Landau fluctuations, which are essentially variations in the deposited energy density that occur as the high energy electron travels along its trajectory. In general there is good agreement with the data, in terms of fitting the nonproportionality curves and reproducing the literature values of nonproportionality's contribution to the scintillator resolution. With the resurgence of interest in developing scintillator detectors that have good energy resolution, an improved understanding of nonproportionality has become a crucial matter since it presents the fundamental limit to the achievable resolution. In order to hasten an improved understanding of scintillator nonproportionality, we have constructed an instrument referred to as SLYNCI (Scintillator Light Yield Nonproportionality Compton Instrument). This is a second-generation instrument to the original device developed by Valentine and coworkers, wherein several new principles of operation have served to increase the data rate by an order of magnitude as discussed in detail in References. In the present article, the focus is on a theory to describe the measured electron response, which is the light yield as a function of the electron energy. To do this, we account for transport of carriers and excitons, in terms of how they transfer their energy to the activators with competition from nonradiative decay pathways. This work builds on the original work of Murray and coworkers
20. A Transformer-less Single Phase Inverter For photovoltaic Systems
DEFF Research Database (Denmark)
Mostaan, Ali; Alizadeh, Ebrahim; Qu, Ying
2017-01-01
A single phase transformer-less inverter is introduced in this paper. The negative polarities of the input voltage and output terminal have common ground. Therefore, the leakage current problem that is common in PV systems is eliminated naturally. In addition, the proposed inverter has fewer...... components compared with its counterparts and only one switch conducts during the active states which enhance the inverter efficiency. The proposed inverter is analyzed in details and compared with some existing topologies. The performance of the proposed inverter is validated using the simulation results....
1. Mid-latitude ionospheric scintillation anomaly in the Far East
Directory of Open Access Journals (Sweden)
L. A. Hajkowicz
2003-02-01
Full Text Available A long-term (over 3 years study has been undertaken to obtain a comprehensive evaluation of VHF ionospheric scintillation morphology in East Asia (at Kokobunji in Japan, using amplitude records from Transit satellites. It is now evident that summer day and night scintillation enhancement in this mid-latitude region is a long-term evidence of a well-known Asian ionospheric disturbance anomaly. The scintillation activity is particularly strong during summer nights (21:00–24:00 LT and on occasion, all satellite passes recorded on consecutive days are associated with pronounced scintillation activity. A second sub-maximum is observed in the summer pre-noon period (09:00–12:00 LT. The scintillation regions extend latitudinally for a distance of 400–600 km in the F-region and 100–200 km in the E-region, mostly equatorwards of Kokobunji. For comparison similar scintillation data obtained for one year at the same longitudinal sector but in southern mid-latitudes (Brisbane in Australia were compared with the simultaneous northern scintillation data. The scintillation activity at Brisbane was much less pronounced in the southern summer but was of the same low level during other seasons as that for Kokobunji. This consistent scintillation anomaly, as yet, has not been included in the global scintillation models, which are essential for radio-satellite communications.Key words. Ionosphere (mid-latitude ionosphere; ionospheric irregularities
2. Mid-latitude ionospheric scintillation anomaly in the Far East
Directory of Open Access Journals (Sweden)
L. A. Hajkowicz
Full Text Available A long-term (over 3 years study has been undertaken to obtain a comprehensive evaluation of VHF ionospheric scintillation morphology in East Asia (at Kokobunji in Japan, using amplitude records from Transit satellites. It is now evident that summer day and night scintillation enhancement in this mid-latitude region is a long-term evidence of a well-known Asian ionospheric disturbance anomaly. The scintillation activity is particularly strong during summer nights (21:00–24:00 LT and on occasion, all satellite passes recorded on consecutive days are associated with pronounced scintillation activity. A second sub-maximum is observed in the summer pre-noon period (09:00–12:00 LT. The scintillation regions extend latitudinally for a distance of 400–600 km in the F-region and 100–200 km in the E-region, mostly equatorwards of Kokobunji. For comparison similar scintillation data obtained for one year at the same longitudinal sector but in southern mid-latitudes (Brisbane in Australia were compared with the simultaneous northern scintillation data. The scintillation activity at Brisbane was much less pronounced in the southern summer but was of the same low level during other seasons as that for Kokobunji. This consistent scintillation anomaly, as yet, has not been included in the global scintillation models, which are essential for radio-satellite communications.
Key words. Ionosphere (mid-latitude ionosphere; ionospheric irregularities
3. Advanced Control of Wheeled Inverted Pendulum Systems
CERN Document Server
Li, Zhijun; Fan, Liping
2013-01-01
Advanced Control of Wheeled Inverted Pendulum Systems is an orderly presentation of recent ideas for overcoming the complications inherent in the control of wheeled inverted pendulum (WIP) systems, in the presence of uncertain dynamics, nonholonomic kinematic constraints as well as underactuated configurations. The text leads the reader in a theoretical exploration of problems in kinematics，dynamics modeling, advanced control design techniques,and trajectory generation for WIPs. An important concern is how to deal with various uncertainties associated with the nominal model, WIPs being characterized by unstable balance and unmodelled dynamics and being subject to time-varying external disturbances for which accurate models are hard to come by. The book is self-contained, supplying the reader with everything from mathematical preliminaries and the basic Lagrange-Euler-based derivation of dynamics equations to various advanced motion control and force control approaches as well as trajectory generation met...
4. Micro-inverter solar panel mounting
Science.gov (United States)
Morris, John; Gilchrist, Phillip Charles
2016-02-02
Processes, systems, devices, and articles of manufacture are provided. Each may include adapting micro-inverters initially configured for frame-mounting to mounting on a frameless solar panel. This securement may include using an adaptive clamp or several adaptive clamps secured to a micro-inverter or its components, and using compressive forces applied directly to the solar panel to secure the adaptive clamp and the components to the solar panel. The clamps can also include compressive spacers and safeties for managing the compressive forces exerted on the solar panels. Friction zones may also be used for managing slipping between the clamp and the solar panel during or after installation. Adjustments to the clamps may be carried out through various means and by changing the physical size of the clamps themselves.
5. Design of High Efficient MPPT Solar Inverter
Directory of Open Access Journals (Sweden)
Sunitha K. A.
2017-01-01
Full Text Available This work aims to design a High Efficient Maximum Power Point Tracking (MPPT Solar Inverter. A boost converter is designed in the system to boost the power from the photovoltaic panel. By this experimental setup a room consisting of 500 Watts load (eight fluorescent tubes is completely controlled. It is aimed to decrease the maintenance cost. A microcontroller is introduced for tracking the P&O (Perturb and Observe algorithm used for tracking the maximum power point. The duty cycle for the operation of the boost convertor is optimally adjusted by using MPPT controller. There is a MPPT charge controller to charge the battery as well as fed to inverter which runs the load. Both the P&O scheme with the fixed variation for the reference current and the intelligent MPPT algorithm were able to identify the global Maximum power point, however the performance of the MPPT algorithm was better.
6. Design And Implementation Of Cost Effective Inverter
Directory of Open Access Journals (Sweden)
Niaz Morshedul Haque
2017-10-01
Full Text Available This paper deals with the design and construct of a 100 Watt 220 Volt and 50 Hz Inverter. The system is designed without any microcontroller and it has a cost-effective design architecture. The elementary purpose of this device is to transmute 12 V DC to 220 V AC. Snubber technology is used to diminish the reverse potential transients and excessive heat of transformer winding and transistor switches. Switching pulse generated by NE 555 timer circuit and comparator circuit was used to take signal strength input from its rear as well as from both sides for triggering the MOSFET switches. Another switch is used to invert pulse between two switching circuitries. A 5 volts regulator IC 7805 was used to supply fixed 5V for biasing the switching and amplifying circuitry.
7. Electronic Document Management Using Inverted Files System
Directory of Open Access Journals (Sweden)
Suhartono Derwin
2014-03-01
Full Text Available The amount of documents increases so fast. Those documents exist not only in a paper based but also in an electronic based. It can be seen from the data sample taken by the SpringerLink publisher in 2010, which showed an increase in the number of digital document collections from 2003 to mid of 2010. Then, how to manage them well becomes an important need. This paper describes a new method in managing documents called as inverted files system. Related with the electronic based document, the inverted files system will closely used in term of its usage to document so that it can be searched over the Internet using the Search Engine. It can improve document search mechanism and document save mechanism.
8. Electron Cloud with Inverted Beam Screens
CERN Document Server
Maury Cuna, H
2011-01-01
We report the results of computer simulations studying the effect of wrongly oriented LHC beam screens on the local electron-cloud heat load and density. At 3.5 or 7-TeV energy and for maximum secondary emission-yield values below 1.5, with the inverted sawtooth orientation about ten times higher heat load is expected than for the standard orientation, and the wrongly oriented sawtooth chambers could lead to a local heat-load bottleneck during the process of surface conditioning at 25-ns bunch spacing. The available cooling margin can be significantly increased by correcting the sawtooth orientations at least for two dipole magnets in LHC arc cells 26 and 32 R3, in order that there be no half-cell cooling loop containing more than one inverted screen.
9. Electron Cloud with Inverted Beam Screens
CERN Document Server
Maury Cuna, H; CERN. Geneva. ATS Department
2011-01-01
We report the results of computer simulations studying the effect of wrongly oriented LHC beam screens on the local electron-cloud heat load and density. At 3.5 or 7-TeV energy and for maximum secondary emission-yield values below 1.5, with the inverted sawtooth orientation about ten times higher heat load is expected than for the standard orientation, and the wrongly oriented sawtooth chambers could lead to a local heatload bottleneck during the process of surface conditioning at 25-ns bunch spacing. The available cooling margin can be significantly increased by correcting the sawtooth orientations at least for two dipole magnets in LHC arc cells 26 and 32 R3, in order that there be no half-cell cooling loop containing more than one inverted screen.
10. Stability Analysis Method of Parallel Inverter
OpenAIRE
Li, Jun; Chen, Jie; Xue, Yaru; Qiu, Ruichang; Liu, Zhigang
2017-01-01
In order to further provide theoretical support for the stability of an auxiliary inverter parallel system, a new model which covers most of control parameters needs to be established. However, the ability of the small-signal model established by the traditional method is extremely limited, so this paper proposes a new small-signal modeling method for the parallel system. The new small-signal model not only can analyze the influence of the droop parameters on the system performance, but also ...
11. Development of High-Resolution Scintillator Systems
International Nuclear Information System (INIS)
Larry A. Franks; Warnick J. Kernan
2007-01-01
Mercuric iodide (HgI2) is a well known material for the direct detection of gamma-rays; however, the largest volume achievable is limited by the thickness of the detector which needs to be a small fraction of the average trapping length for electrons. We report results of using HgI2 crystals to fabricate photocells used in the readout of scintillators. The optical spectral response and efficiency of these photocells were measured and will be reported. Nuclear response from an HgI2 photocell that was optically matched to a cerium-activated scintillator is presented and discussed. Further improvements can be expected by optimizing the transparent contact technology
12. Development of High-Resolution Scintillator Systems
Energy Technology Data Exchange (ETDEWEB)
Larry A. Franks; Warnick J. Kernan
2007-09-01
Mercuric iodide (HgI2) is a well known material for the direct detection of gamma-rays; however, the largest volume achievable is limited by the thickness of the detector which needs to be a small fraction of the average trapping length for electrons. We report results of using HgI2 crystals to fabricate photocells used in the readout of scintillators. The optical spectral response and efficiency of these photocells were measured and will be reported. Nuclear response from an HgI2 photocell that was optically matched to a cerium-activated scintillator is presented and discussed. Further improvements can be expected by optimizing the transparent contact technology.
13. Liquid scintillation alpha particle spectrometry. Progress report
International Nuclear Information System (INIS)
Bell, L.L.; Hakooz, S.A.; Johnson, L.O.; Nieschmidt, E.B.; Meikrantz, D.H.
1979-12-01
Objective to develop a technique whereby Pu may be put into solution, extracted by solvent extraction into a suitable extractive scintillant and subsequently counted. Presented here are results of attempts to separate beta and alpha activities through pulse shape discrimination. A qualitative discussion is given which yields alpha particle peak widths, resolution and response. The detection efficiency for alpha particles in a liquid scintillant is 100%. Present detection sensitivities of the equipment being used are: 4.5 x 10 -6 μCi (100 s), 1.2 x 10 -6 μCi (1000 s), and 4.0 x 10 -7 μCi (10,000 s) at the 3 sigma level. The detectability of a particular alpha-emitting species is strongly dependent upon the population of other species. The ability to discriminate depends upon the system resolution. 14 figures, 2 tables
14. Scintillation detectors of Alborz-I experiment
International Nuclear Information System (INIS)
Pezeshkian, Yousef; Bahmanabadi, Mahmud; Abbasian Motlagh, Mehdi; Rezaie, Masume
2015-01-01
A new air shower experiment of the Alborz Observatory, Alborz-I, located at the Sharif University of Technology, Iran, will be constructed in near future. An area of about 30×40 m 2 will be covered by 20 plastic scintillation detectors (each with an area of 50×50 cm 2 ). A series of experiments have been performed to optimize the height of light enclosures of the detectors for this array and the results have been compared to an extended code simulation of these detectors. Operational parameters of the detector obtained by this code are cross checked by the Geant4 simulation. There is a good agreement between the extended-code and Geant4 simulations. We also present further discussions on the detector characteristics, which can be applicable for all scintillation detectors with a similar configuration
15. Central Tracking Detector Based on Scintillating Fibres
CERN Multimedia
2002-01-01
Scintillating fibres form a reasonable compromise for central tracking detectors in terms of price, resolution, response time, occupancy and heat production. \\\\ \\\\ New fluorescents with large Stokes shifts have been produced, capable of working without wavelength shifters. Coherent multibundles have been developed to achieve high packing fractions. Small segments of tracker shell have been assembled and beam tests have confirmed expectations on spatial resolution. An opto-electronic delay line has been designed to delay the track patterns and enable coincidences with a first level trigger. Replacement of the conventional phosphor screen anode with a Si pixel chip is achieved. This tube is called ISPA-tube and has already been operated in beam tests with a scintillating fibres tracker. \\\\ \\\\ The aim of the proposal is to improve hit densities for small diameter fibres by increasing the fraction of trapped light, by reducing absorption and reflection losses, by reflecting light at the free fibre end, and by inc...
16. Multifrequency techniques for studying interplanetary scintillations
International Nuclear Information System (INIS)
Woo, R.
1975-01-01
Rytov's approximation or the method of smooth perturbations is utilized to derive the temporal frequency spectra of the amplitude and phase fluctuations of multifrequency plane and spherical waves propagating in the interplanetary medium and solar corona. It is shown that multifrequency observations of interplanetary scintillations using either compact radio stars or spacecraft radio signals are desirable because the correlation of the multifrequency waves yields additional independent measurements of the solar wind and turbulence. Measurements of phase fluctuations are also desirable because, unlike amplitude fluctuations, they provide information on the full range of scale sizes for the electron density fluctuations. It is shown that a coherent dual-frequency radio system is particularly useful in making such measurements. In addition to providing a means for interpreting observations of multifrequency interplanetary scintillations, the analysis is also essential for estimating the effects of solar corona turbulence on the communications and navigation of a spacecraft whose line-of-sight path passes close to the Sun
17. Background characterization in a liquid scintillation spectrometer
International Nuclear Information System (INIS)
Rodriguez Barquero, L.; Los Arcos, J.M.; Jimenez de Mingo, A.
1995-01-01
An alternate procedure for background count rate estimation in a liquid scintillation spectrometer is presented, which does not require to measure a blank with similar composition, volume and quench, to the problem sample. The procedure is based on a double linear parameterization which was obtained from a systematic study of the background observed with glass vials, in three different windows, 0 - 20 KeV, 0 - 800 KeV and 0 - 2 MeV, for volume between 2 and 20 mi of three commercial scintillators, Hisafe II, Ultima-Gold and Instagel, and quenching degree in the interval equivalent to 50% - 3% tritium efficiency. This procedure was tested with standard samples of 3H, and led to average discrepancies less than 10% for activity ≥0,6 Bq, against conventional methods for which the discrepancies are twice on average. (Author) 10 refs
18. Background characterization in a liquid scintillation spectrometer
International Nuclear Information System (INIS)
Rodriguez Barquero, L.; Los arcos, J.M.; Jimenez de Mingo, A.
1995-01-01
An alternate procedure for background count rate estimation in a liquid scintillation spectrometer is presented, which does not require to measure a blank with similar composition, volume and quench, to the problem sample. The procedure is based on a double linear parameterization which was obtained from a systematic study of the background observed with glass vials, in three different windows, 0-20 KeV, 0-800 KeV and 0-2 MeV, for volume between 2 and 20 ml of three commercial scintillators, Hisafe II, Ultima-gold and Instagel, and quenching degree in the interval equivalent to 50%-3% tritium efficiency. This procedure was tested with standard samples of ''3 H, and led to average discrepancies less than 10% for activity => 0,6 Bq, against conventional methods for which the discrepancies are twice on average
19. Calibration of the neutron scintillation counter threshold
International Nuclear Information System (INIS)
Noga, V.I.; Ranyuk, Yu.N.; Telegin, Yu.N.
1978-01-01
A method for calibrating the threshold of a neutron counter in the form of a 10x10x40 cm plastic scintillator is described. The method is based on the evaluation of the Compton boundary of γ-spectrum from the discrimination curve of counter loading. The results of calibration using 60 Co and 24 Na γ-sources are given. In order to eValuate the Compton edge rapidly, linear extrapolation of the linear part of the discrimination curve towards its intersection with the X axis is recommended. Special measurements have shown that the calibration results do not practically depend on the distance between the cathode of a photomultiplier and the place where collimated γ-radiation of the calibration source reaches the scintillator
20. A study of scintillation beta microprobes
Science.gov (United States)
Woody, C. L.; Stoll, S. P.; Schlyer, D. J.; Gerasimov, M.; Vaska, P.; Shokouhi, S.; Volkow, N.; Fowler, J. S.; Dewey, S. L.
2002-10-01
Several types of scintillation microprobes have recently been developed to directly measure positron activity from radiotracers in live animals. These probes consist of either a small lutetium oxyorthosilicate (LSO) crystal or plastic scintillator coupled to an optical fiber that is read out with a photomultiplier tube operated in a single photon counting mode. In this paper, a comparison is made between the two types of probes in terms of their sensitivity to both positrons and gammas. It was found that LSO offers very high sensitivity to positrons due to its high density and light output, and allows the construction of very small probes for certain applications. The LSO probe can also provide effective discrimination between positrons and gammas, and provide better localization of positron decays, using pulse height discrimination. Results are also given on the use of the microprobe on live laboratory animals.
1. Scintillating Optical Fiber Imagers for biology
International Nuclear Information System (INIS)
Mastrippolito, R.
1990-01-01
S.O.F.I (Scintillating Optical Fiber Imager) is a detector developed to replace the autoradiographic films used in molecular biology for the location of radiolabelled ( 32 P) DNA molecules in blotting experiments. It analyses samples on a 25 x 25 cm 2 square area still 25 times faster than autoradiographic films, with a 1.75 and 3 mm resolution for two orthogonal directions. This device performs numerised images with a dynamic upper than 100 which allows the direct quantitation of the analysed samples. First, this thesis describes the S.O.F.I. development (Scintillating Optical Fibers, coding of these fibers and specific electronic for the treatment of the Multi-Anode Photo-Multiplier signals) and experiments made in collaboration with molecular biology laboratories. In a second place, we prove the feasibility of an automatic DNA sequencer issued from S.O.F.I [fr
2. FET commutated current-FED inverter
Science.gov (United States)
Rippel, Wally E. (Inventor); Edwards, Dean B. (Inventor)
1983-01-01
A shunt switch comprised of a field-effect transistor (Q.sub.1) is employed to commutate a current-fed inverter (10) using thyristors (SCR1, SCR2) or bijunction transistors (Q.sub.2, Q.sub.3) in a full bridge (1, 2, 3, 4) or half bridge (5, 6) and transformer (T.sub.1) configuration. In the case of thyristors, a tapped inverter (12) is employed to couple the inverter to a dc source to back bias the thyristors during commutation. Alternatively, a commutation power supply (20) may be employed for that purpse. Diodes (D.sub.1, D.sub.2) in series with some voltage dropping element (resistor R.sub.12 or resistors R.sub.1, R.sub.2 or Zener diodes D.sub.4, D.sub.5) are connected in parallel with the thyristors in the half bridge and transformer configuration to assure sharing the back bias voltage. A clamp circuit comprised of a winding (18) negatively coupled to the inductor and a diode (D.sub.3) return stored energy from the inductor to the power supply for efficient operation with buck or boost mode.
3. Stability Analysis Method of Parallel Inverter
Directory of Open Access Journals (Sweden)
Jun Li
2017-01-01
Full Text Available In order to further provide theoretical support for the stability of an auxiliary inverter parallel system, a new model which covers most of control parameters needs to be established. However, the ability of the small-signal model established by the traditional method is extremely limited, so this paper proposes a new small-signal modeling method for the parallel system. The new small-signal model not only can analyze the influence of the droop parameters on the system performance, but also can analyze the influence of the output impedance of the inverter, the unbalanced and nonlinear loads, and the power calculation method and cut-off frequency of the low-pass filter on the system performance and stability. Based on this method, this paper carries out a comprehensive analysis on the performance of a parallel inverter system. And the correctness of the modeling method and analysis process of the system performance and stability are verified by the consistency of the simulation and experimental results.
4. Improved Neutron Scintillators Based on Nanomaterials
International Nuclear Information System (INIS)
Friesel, Dennis
2008-01-01
The development work conducted in this SBIR has so far not supported the premise that using nano-particles in LiFZnS:Ag foils improves their transparency to 420 (or other frequency) light. This conclusion is based solely on the light absorption properties of LiFZnS foils fabricated from nano- and from micro-particles. Furthermore, even for the case of the Gd 2 O 3 foils, the transmission of 420 nm light gained by using nano-particles all but disappears as the foil thickness is increased beyond about 0.2 mm, a practical scintillator thickness. This was not immediately apparent from the preliminary study since no foils thicker than about 0.04 mm were produced. Initially it was believed that the failure to see an improvement by using nano-particles for the LiFZnS foils was caused by the clumping of the particles in Toluene due to the polarity of the ZnS particles. However, we found, much to our surprise, that nano-particle ZnS alone in polystyrene, and in Epoxy, had worse light transmission properties than the micro-particle foils for equivalent thickness and density foils. The neutron detection measurements, while disappointing, are attributable to our inability to procure or fabricate Bulk Doped ZnS nanoparticles. The cause for the failure of nano-particles to improve the scintillation light, and hence improved neutron detection efficiency, is a fundamental one of light scattering within the scintillator. A consequence of PartTec's documentation of this is that several concepts for the fabrication of improved 6 LiFZnS scintillators were formulated that will be the subject of a future SBIR submission.
5. Prompt angle measurements with large aperture scintillators
International Nuclear Information System (INIS)
Schneid, E.J.
1976-01-01
A technique is described for the measurement of particle trajectory angle through a pair of scintillator tiles. Signal processing provides an analog signal proportional to the tangent of the angle between the particle trajectory and the axis normal to the pair of tiles. This signal is readily available for use in fast decision logic if required: i.e., sorting energy loss signals from the tiles according to geometrical factors or restricting the events to be analyzed on the basis of incident direction
6. Improved Neutron Scintillators Based on Nanomaterials
Energy Technology Data Exchange (ETDEWEB)
Dennis Friesel, PhD
2008-06-30
The development work conducted in this SBIR has so far not supported the premise that using nano-particles in LiFZnS:Ag foils improves their transparency to 420 (or other frequency) light. This conclusion is based solely on the light absorption properties of LiFZnS foils fabricated from nano- and from micro-particles. Furthermore, even for the case of the Gd{sub 2}O{sub 3} foils, the transmission of 420 nm light gained by using nano-particles all but disappears as the foil thickness is increased beyond about 0.2 mm, a practical scintillator thickness. This was not immediately apparent from the preliminary study since no foils thicker than about 0.04 mm were produced. Initially it was believed that the failure to see an improvement by using nano-particles for the LiFZnS foils was caused by the clumping of the particles in Toluene due to the polarity of the ZnS particles. However, we found, much to our surprise, that nano-particle ZnS alone in polystyrene, and in Epoxy, had worse light transmission properties than the micro-particle foils for equivalent thickness and density foils. The neutron detection measurements, while disappointing, are attributable to our inability to procure or fabricate Bulk Doped ZnS nanoparticles. The cause for the failure of nano-particles to improve the scintillation light, and hence improved neutron detection efficiency, is a fundamental one of light scattering within the scintillator. A consequence of PartTec's documentation of this is that several concepts for the fabrication of improved {sup 6}LiFZnS scintillators were formulated that will be the subject of a future SBIR submission.
7. Interaction probability value calculi for some scintillators
International Nuclear Information System (INIS)
Garcia-Torano Martinez, E.; Grau Malonda, A.
1989-01-01
Interaction probabilities for 17 gamma-ray energies between 1 and 1.000 KeV have been computed and tabulated. The tables may be applied to the case of cylindrical vials with radius 1,25 cm and volumes 5, 10 and 15 ml. Toluene, Toluene/Alcohol, Dioxane-Naftalen, PCS, INSTAGEL and HISAFE II scintillators are considered. Graphical results for 10 ml are also given. (Author) 11 refs
8. Development of a reference liquid scintillation cocktail
CSIR Research Space (South Africa)
Van Wyn Gaardt, WM
2006-02-01
Full Text Available for Ionizing Radiation CCRI(II). The system will be maintained at the International Bureau of Weights and Measures (BIPM), France. The system requires a non-commercial reference liquid scintillation cocktail, the development of which is described here. A... Committee for Ionizing Radiation (CCRI(II)) of the International Committee of Weights and Measures (CIPM) enables laboratories to do this by organising comparisons of the activity measurements of a given radionuclide solution. Alternatively...
9. Nanophosphor composite scintillators comprising a polymer matrix
Science.gov (United States)
Muenchausen, Ross Edward; Mckigney, Edward Allen; Gilbertson, Robert David
2010-11-16
An improved nanophosphor composite comprises surface modified nanophosphor particles in a solid matrix. The nanophosphor particle surface is modified with an organic ligand, or by covalently bonding a polymeric or polymeric precursor material. The surface modified nanophosphor particle is essentially charge neutral, thereby preventing agglomeration of the nanophosphor particles during formation of the composite material. The improved nanophosphor composite may be used in any conventional scintillator application, including in a radiation detector.
10. Scintillator materials-achievements, opportunities, and puzzles
Czech Academy of Sciences Publication Activity Database
Nikl, Martin; Mihóková, Eva; Pejchal, Jan; Vedda, A.; Fasoli, M.; Fontana, I.; Laguta, Valentyn; Babin, V.; Nejezchleb, K.; Yoshikawa, A.; Ogino, H.; Ren, G.
2008-01-01
Roč. 55, č. 3 (2008), s. 1035-1045 ISSN 0018-9499 R&D Projects: GA MŠk ME 903; GA MŠk ME 953; GA ČR GA202/05/2471; GA AV ČR 1QS100100506 Institutional research plan: CEZ:AV0Z10100521 Keywords : scintillator * Ce 3+ and Pr 3+ doped * traps * complex oxide Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.518, year: 2008
11. New scintillating crystals for PET scanners
CERN Document Server
Lecoq, P
2002-01-01
Systematic R&D on basic mechanism in inorganic scintillators, initiated by the Crystal Clear Collaboration at CERN 10 years ago, has contributed not to a small amount, to the development of new materials for a new generation of medical imaging devices with increased resolution and sensitivity. The first important requirement for a scintillator to be used in medical imaging devices is the stopping power for the given energy range of X and gamma rays to be considered, and more precisely the conversion efficiency. A high light yield is also mandatory to improve the energy resolution, which is essentially limited by the photostatistics and the electronic noise at these energies. A short scintillation decay time allows to reduce the dead time and therefore to increase the limiting counting rate. When all these requirements are fulfilled the sensitivity and image contrast are increased for a given patient dose, or the dose can be reduced. Examples of new materials under development by the Crystal Clear Collabor...
CERN Document Server
Bell, Z W; Maya, L; Sloop, F V J
2003-01-01
Silicone rubber received attention as an alternative to polyvinyltoluene in applications in which the scintillator is exposed to high doses because of the increased resistance of the rubber to the formation of blue-absorbing color centers. Work by Bowen, et al., and Harmon, et al., demonstrated their properties under gamma/x-ray irradiation, and Bell, et al. have shown their response to thermal neutrons. This last work, however, provided an example of a silicone in which both the boron and the scintillator were contained in the rubber as solutes, a formulation which led to the precipitation of solids and sublimation of the boron component. In the present work we describe a scintillator in which the boron is chemically bonded to the siloxane and so avoids the problem of precipitation and loss of boron to sublimation. Material containing up to 18% boron, by weight, was prepared, mounted on photomultipliers, and exposed to both neutron and gamma fluxes. Pulse height spectra showing the neutron and photon respons...
13. Liquid-scintillation alpha-detection techniques
International Nuclear Information System (INIS)
McKlveen, J.W.; McDowell, W.J.
1983-01-01
Accurate, quantitative determinations of alpha-emitting nuclides by conventional plate-counting methods are difficult because of sample self-absorption problems in counting and because of non-reproducible losses in conventional sample separation methods. Liquid scintillation alpha spectrometry offers an attractive with no sample self-absorption or geometry problems and with 100% counting efficiency. Sample preparation may include extraction of the alpha emitter of interest by a specific organic-phase-soluble compound directly into the liquid scintillation counting medium. Detection electronics use energy and pulse-shape discrimination to yield alpha spectra without beta and gamma background interference. Specific procedures have been developed for gross alpha, uranium, plutonium, thorium, and polonium assay. Possibilities for a large number of other applications exist. Accuracy and reproducibility are typically in the 1% range. Backgrounds on the order of 0.01 cpm are readily achievable. The paper will present an overview of liquid scintillation alpha counting techniques and some of the results achieved for specific applications
14. Composition for use in scintillator systems
International Nuclear Information System (INIS)
Tarkkanen, V.
1976-01-01
Reference is made to compositions for liquid scintillation counting of aqueous radioactive samples. A composition is described that reduces chemiluminescence on the addition of an alkaline material. Many common sample materials, for example body fluids, are inherently alkaline, whilst samples such as animal tissues are often dissolved in alkaline media. Another problem is water miscibility, and the object is to provide a scintillation counting composition that, when mixed with an aqueous sample, produces a single phase low viscosity mixture over a wide range of water contents and temperatures. The composition described includes a major amount of an aromatic hydrocarbon solvent, a minor amount of an ethoxylated alkyl phenol surfactant, a scintillation solute, an amount of a substituted ethoxylated carboxylic acid sufficient to reduce chemiluminescence, and an amount of a tertiary amine salt or a quaternary ammonium salt of the substituted ethoxylated carboxylic acid sufficient to enhance the water miscibility. The hydrocarbon solvent and the surfactant may be pre-treated with a reactive solid metal hydride to remove peroxides, and then subsequently pre-treated with SO 2 . Examples of the use of the composition are given. (U.K)
Energy Technology Data Exchange (ETDEWEB)
Bell, Z.W.; Maya, L.; Brown, G.M.; Sloop, F.V.Jr
2003-05-12
Silicone rubber received attention as an alternative to polyvinyltoluene in applications in which the scintillator is exposed to high doses because of the increased resistance of the rubber to the formation of blue-absorbing color centers. Work by Bowen, et al., and Harmon, et al., demonstrated their properties under gamma/x-ray irradiation, and Bell, et al. have shown their response to thermal neutrons. This last work, however, provided an example of a silicone in which both the boron and the scintillator were contained in the rubber as solutes, a formulation which led to the precipitation of solids and sublimation of the boron component. In the present work we describe a scintillator in which the boron is chemically bonded to the siloxane and so avoids the problem of precipitation and loss of boron to sublimation. Material containing up to 18% boron, by weight, was prepared, mounted on photomultipliers, and exposed to both neutron and gamma fluxes. Pulse height spectra showing the neutron and photon response were obtained, and although the light output was found to be much poorer than from samples in which boron was dissolved, the higher boron concentrations enabled essentially 100% neutron absorption in only a few millimeters' thickness of rubber.
16. Scintillation counter with MRS APD light readout
International Nuclear Information System (INIS)
Akindinov, A.; Bondarenko, G.; Golovin, V.; Grigoriev, E.; Grishuk, Yu.; Mal'kevich, D.; Martemiyanov, A.; Ryabinin, M.; Smirnitskiy, A.; Voloshin, K.
2005-01-01
START, a high-efficiency and low-noise scintillation detector for ionizing particles, was developed for the purpose of creating a high-granular system for triggering cosmic muons. Scintillation light in START is detected by MRS APDs (Avalanche Photo-Diodes with Metal-Resistance-Semiconductor Structure), operated in the Geiger mode, which have 1mm 2 sensitive areas. START is assembled from a 15x15x1cm 3 scintillating plastic plate, two MRS APDs and two pieces of wavelength-shifting optical fiber stacked in circular coils inside the plastic. The front-end electronic card is mounted directly on the detector. Tests with START have confirmed its operational consistency, over 99% efficiency of MIP registration and good homogeneity. START demonstrates a low intrinsic noise of about 10 -2 Hz. If these detectors are to be mass-produced, the cost of a mosaic array of STARTs is estimated at a moderate level of 2-3kUSD/m 2
17. Temperature quenching in LAB based liquid scintillator
Science.gov (United States)
Sörensen, A.; Hans, S.; Junghans, A. R.; Krosigk, B. v.; Kögler, T.; Lozza, V.; Wagner, A.; Yeh, M.; Zuber, K.
2018-01-01
The effect of temperature changes on the light output of LAB based liquid scintillator is investigated in a range from -5 to 30°C with α -particles and electrons in a small scale setup. Two PMTs observe the scintillator liquid inside a cylindrically shaped aluminum cuvette that is heated or cooled and the temperature dependent PMT sensitivity is monitored and corrected. The α -emitting isotopes in dissolved radon gas and in natural Samarium (bound to a LAB solution) excite the liquid scintillator mixtures and changes in light output with temperature variation are observed by fitting light output spectra. Furthermore, also changes in light output by compton electrons, which are generated from external calibration γ -ray sources, is analysed with varying temperature. Assuming a linear behaviour, a combined negative temperature coefficient of {(-0.29 ± 0.01)}{ %/°}C is found. Considering hints for a particle type dependency, electrons show {(-0.17 ± 0.02)}{ %/°}C, whereas the temperature dependency seems stronger for α -particles, with {(-0.35 ± 0.03)}{ %/°}C. Due to a high sampling rate, a pulse shape analysis can be performed and shows an enhanced slow decay component at lower temperatures, pointing to reduced non-radiative triplet state de-excitations.
18. Neutron scintillators using wavelength shifting fibers
International Nuclear Information System (INIS)
Hutchinson, D.P.; Miller, V.C.; Ramsey, J.A.
1995-01-01
A proposed design for an optically-based, one-dimension scintillation detector to replace the gas-filled position-sensitive proportional counter currently used for a wide-angle neutron detector (WAND) at the high-Flux Isotope Reactor (HFIR) at the Oak Ridge National Laboratory (ORNL) is presented. The scintillator, consisting of a mixture of 6 LiF and ZnS(Ag) powders in an epoxy binder, is coupled to an array of wavelength shifting optical fibers which provide position resolution. The wide-angle neutron detector is designed to cover a 120 degree arc with a 75 cm radius of curvature. The final detector design provides for 600 optical fibers coupled to the scintillator screen with an angular resolution of 0.2 degrees. Each individual pixel of the detector will be capable of operating at count rates exceeding 1 MHz. Results are presented from the measurement of neutron conversion efficiencies for several screen compositions, gamma-ray sensitivity, and spatial resolution of a 16 element one-dimensional array prototype
19. B-Loaded Plastic Scintillator on the Base of Polystyrene
CERN Document Server
Brudanin, V B; Nemchenok, I B; Smolnikov, A A
2000-01-01
A method to produce polystyrene-based plastic scintillators with boron concentration from 0.38 to 5.0% of boron have been developed. o-Carborane was used as B-containing additive. The results of investigations of the optical, spectral and scintillation characteristics are presented and discussed. It is shown that 5% B-loaded scintillator has a light output as much as 70% relative to the unloaded one. High efficiency for thermal neutron registration achieved for produced samples makes it possible to use such scintillators in complex neutron high sensitive spectrometers. Measured level of radioactive contamination in this scintillation materials is good enough for using the B-loaded scintillators in the proposed large scale neutrino experiments.
20. Characteristics of plastic scintillators fabricated by a polymerization reaction
Energy Technology Data Exchange (ETDEWEB)
Lee, Cheol Ho; Son, Jaebum; Kim, Tae Hoon; Kim, Yong Kyun [Dept. of Nuclear Engineering, Hanyang University, Seoul (Korea, Republic of)
2017-04-15
Three plastic scintillators of 4.5 cm diameter and 2.5-cm length were fabricated for comparison with commercial plastic scintillators using polymerization of the styrene monomer 2.5-diphenyloxazole (PPO) and 1,4-bis benzene (POPOP). Their maximum emission wavelengths were determined at 426.06 nm, 426.06 nm, and 425.00 nm with a standard error of 0.2% using a Varian spectrophotometer (Agilent, Santa Clara, CA, USA). Compton edge spectra were measured using three gamma ray sources [i.e., cesium 137 ({sup 137}Cs), sodium 22 ({sup 22}Na), and cobalt 60 ({sup 60}Co)]. Energy was calibrated by analyzing the Compton edge spectra. The fabricated scintillators possessed more than 99.7% energy linearity. Light output was comparable to that of the BC-408 scintillator (Saint-Gobain, Paris, France). The fabricated scintillators showed a light output of approximately 59–64% of that of the BC-408 scintillator.
1. The Expansion of RPE Atrophy after the Inverted ILM Flap Technique for a Chronic Large Macular Hole
Directory of Open Access Journals (Sweden)
Hisanori Imai
2014-03-01
Full Text Available Purpose: To report a case of the expansion of submacular retinal pigment epithelium (RPE atrophy after using the inverted internal limiting membrane (ILM flap technique for a persisting, large, stage IV macular hole (MH. Case Report: A 79-year-old woman presented with a chronic large MH that remained open despite pars plana vitrectomy (PPV. The surgery was performed twice for the MH closure 14 years earlier. ILM peeling was not performed during the previous surgeries. The best-corrected visual acuity (BCVA with the Landolt ring chart was 0.08 at her visit. The minimum MH diameter was 1,240 μm. Inverted ILM flap technique with 20% SF6 gas tamponade was performed for the MH closure. For the inverted ILM flap technique, 25-gauge PPV and ILM staining with indocyanine green were used. The ILM was peeled off for 2 disc diameters around the MH, but the ILM was not removed completely. The ILM was then inverted and covered the MH. Results: One month after surgery, the MH was closed, accompanied by glial cell proliferation spreading from the inverted ILM flap (as reported before. On the other hand, the area of the submacular RPE atrophy, which was already observed 1 week after surgery, gradually increased in size. BCVA improved to 0.3 six months after the surgery. Conclusions: The inverted ILM flap technique may be promising even for persisting large MH which were not closed in previous surgeries, but long-term observation is needed because the detailed behavior of the inverted ILM and the Müller cells after surgery is not yet known.
2. Membrane dynamics
DEFF Research Database (Denmark)
Bendix, Pól Martin
2015-01-01
Current topics include membrane-protein interactions with regard to membrane deformation or curvature sensing by BAR domains. Also, we study the dynamics of membrane tubes of both cells and simple model membrane tubes. Finally, we study membrane phase behavior which has important implications...
3. A Scintillator Purification System for the Borexino Solar Neutrino Detector
OpenAIRE
Benziger, J.; Cadonati, L.; Calaprice, F.; Chen, M.; Corsi, A.; Dalnoki-Veress, F.; Fernholz, R.; Ford, R.; Galbiati, C.; Goretti, A.; Harding, E.; Ianni, Aldo; Ianni, Andrea; Kidner, S.; Leung, M.
2007-01-01
Purification of the 278 tons of liquid scintillator and 889 tons of buffer shielding for the Borexino solar neutrino detector was performed with a system that combined distillation, water extraction, gas stripping and filtration. The purification of the scintillator achieved unprecedented low backgrounds for the large scale liquid scintillation detector. This paper describes the principles of operation, design, construction and commissioning of the purification system, and reviews the require...
4. Progress in Scintillating Polarized Targets for Spin Physics
Science.gov (United States)
van den Brandt, B.; Hautle, P.; Konter, J. A.; Bunyatova, E. I.
2003-06-01
At PSI polarized scintillating targets have been operated in several particle physics experiments over extended periods of time. They proved to be very robust and reliable. Proton polarizations of more than 80%, and deuteron polarizations of 25% in fully deuterated polystyrene based scintillator have been reached in a vertical dilution refrigerator with optical access. New choices of materials and preparation procedures show potential for an improvement of the scintillation and polarization properties.
5. Paraffin scintillator for radioassay of solid support samples
International Nuclear Information System (INIS)
Fujii, Haruo; Takiue, Makoto
1989-01-01
A new paraffin scintillator used for solid support sample counting has been proposed, and its composition and various characteristics are described. The solid support sample treated with this scintillator can be easily handled because of rigid sample conditions. This technique provides great advantages such as the elimination of a large volume of scintillator and little radioactive waste material by using an economical polyethylene bag instead of the conventional counting vial. (author)
6. Structural Origins of Scintillation: Metal Organic Frameworks as a Nanolaboratory
Science.gov (United States)
2016-06-01
discrimination (PSD), for which the prompt component of the scintillation response is quenched for high specific energy loss (dE/dX) particles such as protons...for neutron discrimination (LDRD, $250k/year, FY10) - MOF-based scintillators (NA-22, ~600k / year, FY10-FY12) - Triplet-Harvesting doped plastic ...Structural Origins of Scintillation : Metal Organic Frameworks as a Nanolaboratory Distribution Statement A. Approved for public release 7. Liquid emulsion scintillators which solidify for facile disposal International Nuclear Information System (INIS) O'Brien, R.E.; Krieger, J.K. 1981-01-01 A liquid organic scintillation cocktail is described which counts solutions of radiolabelled compounds containing up to ten % by volume of water with high efficiency and is readily polymerizable to a solid for easy disposal. The cocktail comprises a polymerizable organic solvent, a solubilizing agent, an intermediate solvent, and an organic scintillator. A method of disposing of liquid organic scintillation cocktail waste and a kit useful for practising the method are also described. (U.K.) 8. Growth and scintillation properties of gadolinium and yttrium orthovanadate crystals International Nuclear Information System (INIS) Voloshina, O.V.; Baumer, V.N.; Bondar, V.G.; Kurtsev, D.A.; Gorbacheva, T.E.; Zenya, I.M.; Zhukov, A.V.; Sidletskiy, O.Ts. 2012-01-01 Aiming to explore the possibility of using the undoped rare-earth orthovanadates as scintillation materials, we developed the procedure for growth of gadolinium (GdVO 4 ) and yttrium (YVO 4 ) orthovanadate single crystals by Czochralski method, and determined the optimal conditions of their after-growth annealing. Optical, luminescent, and scintillation properties of YVO 4 and GdVO 4 were discussed versus known literature data. Scintillation characteristics of GdVO 4 were determined for the first time. 9. Comparing the aerodynamic forces produced by dragonfly forewings during inverted and non-inverted flight Science.gov (United States) Shumway, Nathan; Gabryszuk, Mateusz; Laurence, Stuart 2017-11-01 Experiments were conducted with live dragonflies to determine their wing kinematics during free flight. The motion of one forewing in two different tests, one where the dragonfly is inverted, is described using piecewise functions and simulated using the OVERTURNS Reynolds-averaged Navier-Stokes solver that has been used in previous work to determine trim conditions for a fruit fly model. For the inverted dragonfly the upstrokes were significantly longer than the downstrokes, pitching amplitude is lower than that for the right-side up flight and the flap amplitude is larger. Simulations of dragonfly kinematics of a single forewing are presented to determine how the forces differ for a dragonfly flying inverted and a dragonfly flying right-side up. This work was supported by the United States Army Research Laboratory's Micro Autonomous Systems and Technology Collaborative Technology Alliance Project MCE-16-17 1.2. 10. Ionospheric scintillation observations over Kenyan region - Preliminary results Science.gov (United States) Olwendo, O. J.; Xiao, Yu; Ming, Ou 2016-11-01 Ionospheric scintillation refers to the rapid fluctuations in the amplitude and phase of a satellite signal as it passes through small-scale plasma density irregularities in the ionosphere. By analyzing ionospheric scintillation observation datasets from satellite signals such as GPS signals we can study the morphology of ionospheric bubbles. At low latitudes, the diurnal behavior of scintillation is driven by the formation of large-scale equatorial density depletions which form one to two hours after sunset via the Rayleigh-Taylor instability mechanism near the magnetic equator. In this work we present ionospheric scintillation activity over Kenya using data derived from a newly installed scintillation monitor developed by CRIRP at Pwani University (39.78°E, 3.24°S) during the period August to December, 2014. The results reveal the scintillation activity mainly occurs from post-sunset to post-midnight hours, and ceases around 04:00 LT. We also found that the ionospheric scintillation tends to appear at the southwest and northwest of the station. These locations coincide with the southern part of the Equatorial Ionization Anomaly crest over Kenya region. The occurrence of post-midnight L-band scintillation events which are not linked to pre-midnight scintillation observations raises fundamental question on the mechanism and source of electric fields driving the plasma depletion under conditions of very low background electron density. 11. Large-scale liquid scintillation detectors for solar neutrinos Energy Technology Data Exchange (ETDEWEB) Benziger, Jay B.; Calaprice, Frank P. [Princeton University Princeton, Princeton, NJ (United States) 2016-04-15 Large-scale liquid scintillation detectors are capable of providing spectral yields of the low energy solar neutrinos. These detectors require > 100 tons of liquid scintillator with high optical and radiopurity. In this paper requirements for low-energy neutrino detection by liquid scintillation are specified and the procedures to achieve low backgrounds in large-scale liquid scintillation detectors for solar neutrinos are reviewed. The designs, operations and achievements of Borexino, KamLAND and SNO+ in measuring the low-energy solar neutrino fluxes are reviewed. (orig.) 12. Lanthanide doped strontium-barium cesium halide scintillators Science.gov (United States) Bizarri, Gregory; Bourret-Courchesne, Edith; Derenzo, Stephen E.; Borade, Ramesh B.; Gundiah, Gautam; Yan, Zewu; Hanrahan, Stephen M.; Chaudhry, Anurag; Canning, Andrew 2015-06-09 The present invention provides for a composition comprising an inorganic scintillator comprising an optionally lanthanide-doped strontium-barium, optionally cesium, halide, useful for detecting nuclear material. 13. Cesium hafnium chloride scintillator coupled with an avalanche photodiode photodetector Czech Academy of Sciences Publication Activity Database Kurosawa, S.; Kodama, S.; Yokota, Y.; Horiai, T.; Yamaji, A.; Shoji, Y.; Král, Robert; Pejchal, Jan; Ohashi, Y.; Kamada, K.; Nikl, Martin; Yoshikawa, A. 2017-01-01 Roč. 12, Feb (2017), s. 1-8, č. článku C02042. ISSN 1748-0221 Grant - others:AV ČR(CZ) JSPS-17-18 Program:Bilaterální spolupráce Institutional support: RVO:68378271 Keywords : gamma detectors * scintillators and scintillating fibres * scintillators * scintillation and light emission processes Subject RIV: BM - Solid Matter Physics ; Magnetism OBOR OECD: Condensed matter physics (including formerly solid state physics, supercond.) Impact factor: 1.220, year: 2016 14. Liquid-helium scintillation detection with germanium photodiodes International Nuclear Information System (INIS) Luke, P.N.; Haller, E.E.; Steiner, H.M. 1982-05-01 Special high-purity germanium photodiodes have been developed for the direct detection of vacuum ultraviolet scintillations in liquid helium. The photodiodes are immersed in the liquid helium, and scintillations are detected through one of the bare sides of the photodiodes. Test results with scintillation photons produced by 5.3-MeV α particles are presented. The use of these photodiodes as liquid-helium scintillation detectors may offer substantial improvements over the alternate detection method requiring the use of wavelength shifters and photomultiplier tubes 15. Study on determination of 90Sr by liquid scintillation spectrometry International Nuclear Information System (INIS) Zhai Xiufang; Li Weiping; Tian Mei; Zou Ronghu 2012-01-01 Both of Liquid scintillation counting and Cerenkov counting can be used to determinate 90 Sr in samples by Liquid scintillation spectrometry. In this work, effects of scintillation vials wit-h different material, Liquid scintillation cocktails, sample volume, Strontium carrier, pH, quenching (chemical quenching and color quenching)are studied, and both counting methods are compared. For Liquid scintillation counting. The results show that the best appropriate volume ratio of sample and liquid scintillation cocktail is 8:12 for OPTIPHASE HISAFE-3 and OPTIPHASE HISAFE-2, stability of solution decreased when sample load exceeds the maximum load for both Liquid scintillation cocktails, and OPTIPHASE HISAFE-3 also show superior performance for high saline solution. The type of scintillation vial haven't clear influence on the MDA of 90 Sr. Chemical quenching and color quenching can decrease the counting efficiency. For Cerenkov counting, the lowest MDA is obtained when polyethylene plastic vial is used and sample volume is 20 ml. Color quenching decreases the counting efficiency, while there isn't chemical quenching for Cerenkov counting. The MDA of 90 Sr is 1.19 and 1.00 Bq/L for Liquid scintillation counting and Cerenkov counting with the optimal labeling condition. (authors) 16. Plastic scintillator response to relativistic Ne, Ar, Fe IONS Science.gov (United States) Salamon, M. H.; Ahlen, S. P. 1982-04-01 The response to relativistic (0-600 MeV/amu) Ne, Ar, and Fe ions and to cosmic ray muons of four widely used commercial plastic scintillators, NE110, Pilot Y, Pilot F, and Pilot B, is discussed. Fitted expressions for scintillation efficiency for each scintillator and charge are given, and these are compared with the predictions of both the Voltz model and a modification of the Birks model. Resolution measurements demonstrate the relative roles of the halo and quenched core in heavy ion response, and point to a novel use for plastic scintillators. 17. Radiation converter scintillator screen and its manufacturing process International Nuclear Information System (INIS) Delattre, D.; Rougeot, H.; Tassin, C. 1984-01-01 The present invention concerns scintillating screens receiving X or gamma radiation and converting it in luminous photons. The screen comprises a needle structure scintillating material. Its concave surface is quite smooth. The screen is obtained by evaporation on a frame having a perfectly smooth convex surface; the constituting material has a thermal dilatation coefficient different from the scintillating material one. After evaporation, the scintillating screen is set apart from the frame by simple heating. It is used for radiological image intensifier tubes and scintigraphy tubes [fr 18. Scintillation response of Ce-doped or intrinsic scintillating crystals in the range up to 1 MeV Czech Academy of Sciences Publication Activity Database Mareš, Jiří A.; Beitlerová, Alena; Nikl, Martin; Solovieva, Natalia; D´Ambrosio, C.; Blažek, K.; Malý, P.; Nejezchleb, K.; De Notaristefani, F. 2004-01-01 Roč. 38, - (2004), s. 353-357 ISSN 1350-4487 R&D Projects: GA MŠk(CZ) ME 462 Grant - others:NATO SfP (XX) 973510 Institutional research plan: CEZ:AV0Z1010914 Keywords : scintillation * Ce-doped scintillators * photoelectron and light yields * intrinsic and extrinsic scintillators Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.664, year: 2004 19. Design of inverters for the PHOTONERGY project Energy Technology Data Exchange (ETDEWEB) NONE 2003-08-01 The PHOTONERGY project (the former SolcelleInverter project) was initiated on the 1st of September 2001, with a state-of-the-art analysis, which concluded into specifications. Based on this 23 topologies were analyzed in for efficiencies. The results from this analysis was five candidates which all showed a somewhat good efficiency. These five topologies were in further investigated by means of an initial design-iteration and simulations. Two different solutions were picked up in due to their high efficiency and low cost. 1. The standard full-bridge phase shifted DC/DC converter together with a standard DC/AC inverter, 2. A modified version of the novel Shimizu topology. A patent is pending on this modified version. These two inverters are in this document developed and made ready for prototyping. This includes design and selection of reactive- and switching-components, e.g. filter- and bulk-capacitors, low- and high-frequency inductors, high frequency transformers, MOSFETs and diodes. The design of auxiliary circuits is also included, e.g. gate drivers for the MOSFETs, measuring circuits for the grid-current and -voltage, PV-module-current and voltage, protection circuits, hardware near controllers and finally a switch mode power supply. However, the design of the various controllers, except the hardware near PV-current controller for the full bridge phase shifted converter, is not documented in this report but will come later on. This includes all controllers, e.g. maximum power point tracking for the PV-module, utility grid current controller, DC-link voltage controller, phase locked loops, and detection of islanding operation. All of these control loops are to be implemented in a micro-controller. (au) 20. An overview of inverted colloidal crystal systems for tissue engineering. Science.gov (United States) João, Carlos Filipe C; Vasconcelos, Joana Marta; Silva, Jorge Carvalho; Borges, João Paulo 2014-10-01 Scaffolding is at the heart of tissue engineering but the number of techniques available for turning biomaterials into scaffolds displaying the features required for a tissue engineering application is somewhat limited. Inverted colloidal crystals (ICCs) are inverse replicas of an ordered array of monodisperse colloidal particles, which organize themselves in packed long-range crystals. The literature on ICC systems has grown enormously in the past 20 years, driven by the need to find organized macroporous structures. Although replicating the structure of packed colloidal crystals (CCs) into solid structures has produced a wide range of advanced materials (e.g., photonic crystals, catalysts, and membranes) only in recent years have ICCs been evaluated as devices for medical/pharmaceutical and tissue engineering applications. The geometry, size, pore density, and interconnectivity are features of the scaffold that strongly affect the cell environment with consequences on cell adhesion, proliferation, and differentiation. ICC scaffolds are highly geometrically ordered structures with increased porosity and connectivity, which enhances oxygen and nutrient diffusion, providing optimum cellular development. In comparison to other types of scaffolds, ICCs have three major unique features: the isotropic three-dimensional environment, comprising highly uniform and size-controllable pores, and the presence of windows connecting adjacent pores. Thus far, this is the only technique that guarantees these features with a long-range order, between a few nanometers and thousands of micrometers. In this review, we present the current development status of ICC scaffolds for tissue engineering applications. 1. Multilayer control for inverters in parallel operation without signal interconnection DEFF Research Database (Denmark) Hua, Ming; Hu, Haibing; Xing, Yan 2011-01-01 A multilayer control is proposed for inverters with wireless parallel operation in this paper. The control is embedded in every inverter respectively and consists of three layers. The first layer is based on an improved droop method, which shares the active and reactive power in each module...... by adjusting the phase and amplitude of the output voltage respectively. The second layer is to compensate the droop voltage caused by the droop control and thus improve the load regulation performance of the inverter. The third layer limits the phase deviation between the inverter and the shared ac bus...... in order to ensure all the paralleled inverters keeping in phase. The operational principle and implementation are analyzed in details. A prototype, configured by two paralleled inverters, is set up. Experimental results verify the validity of the proposed control.... 2. The mirror map for invertible LG models OpenAIRE Kreuzer, M 1994-01-01 Calculating the (a,c) ring of the maximal phase orbifold for `invertible' Landau--Ginzburg models, we show that the Berglund--H"ubsch construction works for all potentials of the relevant type. The map that sends a monomial in the original model to a twisted state in the orbifold representation of the mirror is constructed explicitly. Via this map, the OP selection rules of the chiral ring exactly correspond to the twist selection rules for the orbifold. This shows that we indeed arrive at th... 3. On the invertibility of elementary operators OpenAIRE Boudi, Nadia; Bračič, Janko 2013-01-01 Let$\\mathscr{X}$be a complex Banach space and$\\mathcal{L}(\\mathscr{X})$be the algebra of all bounded linear operators on$\\mathscr{X}$. For a given elementary operator$\\Phi$of length$2$on$\\mathcal{L}(\\mathscr{X})$, we determine necessary and sufficient conditions for the existence of a solution of the equation${\\rm X} \\Phi=0$in the algebra of all elementary operators on$\\mathcal{L}(\\mathscr{X}). Our approach allows us to characterize some invertible elementary operators of length... 4. Magnetically Coupled Impedance-Source Inverters DEFF Research Database (Denmark) Loh, Poh Chiang; Blaabjerg, Frede 2013-01-01 input-to-output gain and the presence of an impedance network. The former means a high dc-link voltage, which can stress the semiconductor switches unnecessarily. The latter leads to increases in cost and size, which similarly are undesirable. To lessen these concerns, an interesting approach is to use...... magnetically coupled transformers or inductors to raise the gain and modulation ratio simultaneously, while reducing the number of passive components needed. A study of the approach is now presented to show how various existing magnetically coupled inverters can be derived by applying a generic methodology... 5. Using Inverted Indices for Accelerating LINGO Calculations DEFF Research Database (Denmark) Kristensen, Thomas Greve; Nielsen, Jesper; Pedersen, Christian Nørgaard Storm 2011-01-01 queries. The previous best method for rapidly calculating the LINGOsim similarity matrix required specialised hardware to yield a significant speedup over existing methods. By representing LINGO multisets in the verbose representation and using inverted indices it is possible to calculate LINGOsim......The ever growing size of chemical data bases calls for the development of novel methods for representing and comparing molecules. One such method called LINGO is based on fragmenting the SMILES string representation of molecules. Comparison of molecules can then be performed by calculating... 6. Nonlinear Feedback Control of the Rotary Inverted Pendulum Science.gov (United States) 2017-06-01 pendulum include wheeled mobile robots, which can be useful for personal mobility . C. PRIOR WORK There are nonlinear control techniques that have...results. Among the applications of the inverted pendulum is a two wheeled robot. One mobile inverted pendulum robot was created by Grasser, D’Arrigo... pendulum which could shift the weight of the load to keep the pendulum straight up when on a slope [10]. The work in mobile inverted pendulums can 7. Hawaiian Electric Advanced Inverter Test Plan - Result Summary Energy Technology Data Exchange (ETDEWEB) Hoke, Anderson; Nelson, Austin; Prabakar, Kumaraguru; Nagarajan, Adarsh 2016-10-14 This presentation is intended to share the results of lab testing of five PV inverters with the Hawaiian Electric Companies and other stakeholders and interested parties. The tests included baseline testing of advanced inverter grid support functions, as well as distribution circuit-level tests to examine the impact of the PV inverters on simulated distribution feeders using power hardware-in-the-loop (PHIL) techniques. hardware-in-the-loop (PHIL) techniques. 8. VHF Scintillation in an Artificially Heated Ionosphere Science.gov (United States) Suszcynsky, D. M.; Layne, J.; Light, M. E.; Pigue, M. J.; Rivera, L. 2017-12-01 As part of an ongoing project to characterize very-high-frequency (VHF) radio wave propagation through structured ionospheres, Los Alamos National Laboratory has been conducting a set of experiments to measure the scintillation effects of VHF transmissions under a variety of ionospheric conditions. Previous work (see 2015 Fall AGU poster by D. Suszcynsky et al.) measured the S4 index and ionospheric coherence bandwidth in the 32 - 44 MHz frequency range under naturally scintillated conditions in the equatorial region at Kwajalein Atoll during three separate campaigns centered on the 2014 and 2015 equinoxes. In this paper, we will present preliminary results from the February and September, 2017 High Altitude Auroral Research Project (HAARP) Experimental Campaigns where we are attempting to make these measurements under more controlled conditions using the HAARP ionospheric heater in a twisted-beam mode. Two types of measurements are made by transmitting VHF signals through the heated ionospheric volume to the Radio Frequency Propagation (RFProp) satellite experiment. The S4 scintillation index is determined by measuring the power fluctuations of a 135-MHz continuous wave signal and the ionospheric coherence bandwidth is simultaneously determined by measuring the delay spread of a frequency-modulated continuous wave (FMCW) signal in the 130 - 140 MHz frequency range. Additionally, a spatial Fourier transform of the CW time series is used to calculate the irregularity spectral density function. Finally, the temporal evolution of the time series is used to characterize spread-Doppler clutter effects arising from preferential ray paths to the satellite due to refraction off of isolated density irregularities. All results are compared to theory and scaled for comparison to the 32 - 44 MHz Kwajalein measurements. 9. Integral inverter/battery charger for use in electric vehicles Science.gov (United States) Thimmesch, D. 1983-01-01 The design and test results of a thyristor based inverter/charger are discussed. A battery charger is included integral to the inverter by using a subset of the inverter power circuit components. The resulting charger provides electrical isolation between the vehicle propulsion battery and ac line and is capable of charging a 25 kWh propulsion battery in 8 hours from a 220 volt ac line. The integral charger employs the inverter commutation components at a resonant ac/dc isolated converter rated at 3.6 kW. Charger efficiency and power factor at an output power of 3.6 kW are 86% and 95% respectively. The inverter, when operated with a matching polyphase ac induction motor and nominal 132 volt propulsion battery, can provide a peak shaft power of 34 kW (45 ph) during motoring operation and 45 kW (60 hp) during regeneration. Thyristors are employed for the inverter power switching devices and are arranged in an input-commutated topology. This configuration requires only two thyristors to commutate the six main inverter thyristors. Inverter efficiency during motoring operation at motor shaft speeds above 450 rad/sec (4300 rpm) is 92-94% for output power levels above 11 KW (15 hp). The combined ac inverter/charger package weighs 47 kg (103 lbs). 10. A new Zero Voltage Switching three-level NPC inverter DEFF Research Database (Denmark) He, Ning; Chen, Yenan; Xu, Dehong 2015-01-01 A novel Zero Voltage Switching (ZVS) three-level NPC inverter topology using a new ZVS Space Vector Modulation (SVM) scheme is proposed. A detailed operation analysis of ZVS three-level NPC inverter is given. The ZVS condition of the proposed ZVS inverter is derived and it can be achieved of all...... switches in the proposed inverter, which include both the main switches and the auxiliary switches. The design of resonant circuits parameters is also provided. Finally the proposed circuit and ZVS SVM scheme are verified by experimental results and demonstrate a superior performance.... 11. Advanced DC/AC inverters applications in renewable energy CERN Document Server Luo, Fang Lin 2013-01-01 DC/AC inversion technology is of vital importance for industrial applications, including electrical vehicles and renewable energy systems, which require a large number of inverters. In recent years, inversion technology has developed rapidly, with new topologies improving the power factor and increasing power efficiency. Proposing many novel approaches, Advanced DC/AC Inverters: Applications in Renewable Energy describes advanced DC/AC inverters that can be used for renewable energy systems. The book introduces more than 100 topologies of advanced inverters originally developed by the authors, 12. Optimized Pulse Width Modulation for transformerless active-NPC inverters DEFF Research Database (Denmark) Achilladelis, Nikolaos; Koutroulis, Eftichios; Blaabjerg, Frede 2014-01-01 The transformerless DC/AC inverter topologies are employed in Photovoltaic systems in order to improve the power conversion efficiency, power density and cost. The Active-Neutral Point Clamped (Active-NPC) transformerless inverters have the advantage of achieving better thermal balance among...... their power semiconductors. In this paper, a new modulation technique is proposed for optimally controlling the power switches employed in transformerless Active-NPC inverters. The design results demonstrate that compared to the existing PWM strategies, using the proposed method results in lower total power...... losses and significantly better distribution of the power losses among the semiconductors of the Active-NPC inverter.... 13. Experience with uranium-scintillator calorimetry International Nuclear Information System (INIS) Hasell, D.K.; Frisken, W.R. 1990-01-01 The ZEUS experiment on HERA will employ depleted uranium-scintillator calorimetry. Extensive studies have been made to optimize the calorimeter design. Test results and design aspects are discussed with a view to energy resolution, uniformity of response, mechanical assembly and calibration and monitoring. The energy resolution of four prototype calorimeter modules has been measured as 18%/v√E for electrons from 1 to 75 GeV and 35%/√E for pions from 1 to 100 GeV with an e/h ratio equal to one 14. Scintillating ribbon x-ray detector International Nuclear Information System (INIS) Kinchen, B.E.; Rogers, A. 1995-01-01 A patent in the early 1970's by Aerojet Corporation in Sacramento, CA put forth the idea of using an array of scintillating fibers for x-ray detection and imaging. In about 1975, Pratt and Whitney Aircraft in East Hartford, CT designed and manufactured an imaging system based on the patent. The device was 1.75 in thick in the direction of the x-ray beam and about 4 in. by 4 in. square. The device was used with a 8 MeV x-ray source to image and measure internal clearances within operating aircraft, gas turbines engines. There are significant advantages of fiber optic detectors in x-ray detection. However, the advantages are often outweighed by the disadvantages. Two of the advantages of scintillating fiber optic x-ray detectors are: (1) high limiting spatial frequency -- between 20 and 25 lp/mm; and (2) excellent x-ray stopping power -- they can be made thick and retain spatial resolution. In traditional fiber optic detectors the x-rays are oriented parallel to the long axis of the fiber. For the scintillating ribbon x-ray sensor, the x-rays are oriented normal to the fiber long axis. This ribbon sensor technique has a number of advantages over the two current radiographic techniques digital x-radiography and x-ray film: The main advantage the ribbon has is size and shape. It can be as thin as 0.05 in., virtually any width or length, and flexible. Once positioned in a given location, 20 to 100 square inches of the object being inspected can be imaged with a single x-ray beam sweep. It is clear that conventional digital cameras do not lend themselves to placement between walls of aircraft structures or similar items requiring x-ray inspections. A prototype scintillating ribbon x-ray sensor has been fabricated and tested by Synergistic Detector Designs. Images were acquired on corrosion test panels of aluminum fabricated by Iowa State University 15. AA, beam stopper with scintillator screen CERN Multimedia CERN PhotoLab 1980-01-01 An insertable steel-plate beam stopper was located after nearly a full turn downstream of the injection point. It was fitted with a scintillator screen, a thin plate of Cr-doped alumina, imprinted with a grid and reference points. The screen was illuminated through a window and observed with a highly sensitive TV camera plus image intensifier. This allowed observation of beam position and size of a proton test beam and of the beam from the target, which consisted not only of antiprotons but contained as well electrons, pions and muons of the same momentum. 16. Collimator trans-axial tomographic scintillation camera International Nuclear Information System (INIS) Jaszczak, R.J. 1977-01-01 A collimator is provided for a scintillation camera system in which a detector precesses in an orbit about a patient. The collimator is designed to have high resolution and lower sensitivity with respect to radiation traveling in paths laying wholly within planes perpendicular to the cranial-caudal axis of the patient. The collimator has high sensitivity and lower resolution to radiation traveling in other planes. Variances in resolution and sensitivity are achieved by altering the length, spacing or thickness of the septa of the collimator 17. Scintillating Fibre Calorimetry at the LHC CERN Multimedia 2002-01-01 Good electromagnetic and hadronic calorimetry will play a central role in an LHC detector. The lead/scintillating fibre calorimeter technique provides a fast signal response well matched to the LHC rate requirements. It can be made to give equal response for electrons and hadrons (compensation) with good electromagnetic and hadronic energy resolutions.\\\\ \\\\ The aim of this R&D proposal is to study in detail the aspects that are relevant for application of this type of calorimeter in an LHC environment, including its integration in a larger system of detectors, e.g.~projective geometry, radiation hardness, light detection, calibration and stability monitoring, electron/hadron separation..... 18. Marine radioactivity measurements with liquid scintillation spectrometers International Nuclear Information System (INIS) Liong Wee Kwong, L.; Povinec, P.P. 1999-01-01 Liquid Scintillation Spectrometry (LSS) has now become the most widespread method for quantitative analytical measurement of low levels of β-emitting radionuclides like 3 H and 14 C. The high efficiency resulting from the latest development in LSS makes this technique not only appropriate but also enables direct measurement in environmental samples without excessive preparation. The introduction of several new cocktails based on solvents with a high flashpoint containing surfactants and having a high degree of aqueous sample compatibility has also contributed to the simplification of procedures 19. Recent advances in gas scintillation proportional counters International Nuclear Information System (INIS) Palmer, H.E. 1975-01-01 Various geometrical configurations for gas scintillation proportional counters have been investigated in order to determine which is best for use in a large volume, high efficiency counter for measuring low energy gamma and x-rays. A xenon filled counter having a rod anode inside a cylindrical cathode appears to provide the best configuration for providing a uniform field and the best resolution over the total volume of the counter. The details of construction and operating characteristics of various shaped counters are described. (U.S.) 20. Quality control of liquid scintillation counters International Nuclear Information System (INIS) Jaubert, F.; Tartes, I.; Cassette, P. 2006-01-01 Liquid scintillation counting (LSC) is widely used at LNHB for primary standardization of radionuclides (TDCR method), for secondary calibration and also for source stability studies or radioactive purity measurements. A total of five LSC counters are used for these purposes: two locally developed 3-photodetector counters for the implementation of the TDCR method, two Wallac 1414 counters and one Wallac 1220 Quantulus counter. The quality of the LSC measurements relies on the correct operation of these counters and their traceability to the frequency and time units 1. Fundamental limits of scintillation detector timing precision International Nuclear Information System (INIS) Derenzo, Stephen E; Choong, Woon-Seng; Moses, William W 2014-01-01 In this paper we review the primary factors that affect the timing precision of a scintillation detector. Monte Carlo calculations were performed to explore the dependence of the timing precision on the number of photoelectrons, the scintillator decay and rise times, the depth of interaction uncertainty, the time dispersion of the optical photons (modeled as an exponential decay), the photodetector rise time and transit time jitter, the leading-edge trigger level, and electronic noise. The Monte Carlo code was used to estimate the practical limits on the timing precision for an energy deposition of 511 keV in 3 mm × 3 mm × 30 mm Lu 2 SiO 5 :Ce and LaBr 3 :Ce crystals. The calculated timing precisions are consistent with the best experimental literature values. We then calculated the timing precision for 820 cases that sampled scintillator rise times from 0 to 1.0 ns, photon dispersion times from 0 to 0.2 ns, photodetector time jitters from 0 to 0.5 ns fwhm, and A from 10 to 10 000 photoelectrons per ns decay time. Since the timing precision R was found to depend on A −1/2 more than any other factor, we tabulated the parameter B, where R = BA −1/2 . An empirical analytical formula was found that fit the tabulated values of B with an rms deviation of 2.2% of the value of B. The theoretical lower bound of the timing precision was calculated for the example of 0.5 ns rise time, 0.1 ns photon dispersion, and 0.2 ns fwhm photodetector time jitter. The lower bound was at most 15% lower than leading-edge timing discrimination for A from 10 to 10 000 photoelectrons ns −1 . A timing precision of 8 ps fwhm should be possible for an energy deposition of 511 keV using currently available photodetectors if a theoretically possible scintillator were developed that could produce 10 000 photoelectrons ns −1 . (paper) 2. Random wave fields and scintillated beams CSIR Research Space (South Africa) Roux, FS 2009-01-01 Full Text Available morphologies the circulation values fluctuates, but differs significantly for two topological charges. CSIR National Laser Centre – p.17/29 Forces annihilation To get rid of optical vortices in strongly scintillated optical beams, the idea is to force a vortex... dipole to annihilate sooner by introducing a special phase function. u t Gaussian beam Vortex trajectory t Dipole annihilation u Phase function for forced annihilation CSIR National Laser Centre – p.18/29 Annihilation in Gaussian beam Using our knowledge... 3. Inverted papillomas of the paranasal sinuses and the nasal cavity: DNA indices and HPV infection. Science.gov (United States) Bernauer, H S; Welkoborsky, H J; Tilling, A; Amedee, R G; Mann, W J 1997-01-01 Inverted papillomas are rare tumors of the nasal cavity and paranasal sinuses. These tumors are commonly regarded as benign lesions; nevertheless, malignant transformation occurs in up to 13% of cases. In the present retrospective study, specimens from 21 patients with inverted papillomas of the paranasal sinuses and the nasal cavity were investigated in order to analyze the distribution of genetic imbalance and to classify chromosomal aneuploidy in these tumors as a predictor for their biological behavior. Currently, human papilloma viruses (HPVs) are accepted as tumor-inducing and -promoting agents involved in benign and malignant tumors of mucosal tissues in the upper aerodigestive tract. To date more than 80 HPV types have been identified by differences in the nucleotide sequences. Several types (e.g., HPV16, HPV18) are associated with an increased risk for developing cancer. Other types (e.g., HPV6/11) are identified more frequently in benign lesions of stratified mucous membranes. We detected HPV genomes by universal and specific primer polymerase chain reaction. Using degenerated primers derived from the L1 major envelope gene, an amplification of HPV DNA fragments of the correct size was observed in 7 of 21 cases. In one specimen, where an inverted papilloma associated with a squamous cell carcinoma was histologically confirmed, HPV18-specific primers detected the HPV18 genome. The tumors in which an amplification of HPV DNA fragments were observed showed the highest proliferation scores along with the highest rate of aneuploid cells detected by quantitative DNA analysis. 4. Scintillator's sensitivity calibration method in synchrotron radiation facility International Nuclear Information System (INIS) He Xiao'an; Du Huabing; Li Chaoguang; Yi Rongqing; Xiao Tiqiao 2012-01-01 Researches on scintillator's sensitivity method has been carried out recently in Shanghai synchrotron radiation facility. By some experimental researches in light source and detector's linearity, it built a new method for calibrating scintillator's sensitivity. Finally, calibration results were acquired by theory simulation of experimental data which were in accordance with radioactive source methods results, and the new method improved the data accuracy. (authors) 5. Optimization of light collection from crystal scintillators for cryogenic experiments International Nuclear Information System (INIS) Mokina, V.M.; Danevich, F.A.; Kobychev, V.V.; Kraus, H.; Mikhailik, V.B.; Nagornaya, L.L. 2012-01-01 Cryogenic scintillation bolometers are a promising technique to search for dark matter and neutrinoless double decay. Improvement of light collection and energy resolution are important requirements in such experiments. Energy resolutions and relative pulse amplitudes of scintillation detectors using ZnWO 4 scintillation crystals of different shapes (cylinder 20x20 mm and hexagonal prism with diagonal 20 mm and height 20 mm), reflector materials and shapes, optical contact and surface properties (polished and diffused) were measured. The crystal scintillator of hexagonal shape shows the better energy resolution and pulse amplitude. The best energy resolution (FWHM = 9.3 % for 662 keV γ quanta of 137 Cs) was obtained with a hexagonal scintillator with all surfaces diffuse, in optical contact with a PMT and surrounded by a reflector (3M) of size 26x25 mm. In the geometry w ithout optical contact r epresenting the conditions of light collection for a cryogenic scintillating bolometer the best energy resolution and relative pulse amplitude was obtained for a hexagonal shape scintillator with diffuse side and polished face surfaces, surrounded by a reflector with a gap between the scintillator and the reflector 6. Systematic studies of small scintillators for new sampling calorimeter Indian Academy of Sciences (India) mirror film, teflon, white paint, black tape, gold, aluminum and white paint+teflon. The pulse height dependence on position, length and thickness of the 3M reflective mirror film and teflon wrapped scintillators are measured. Results show that the 3M radiant mirror film-wrapped scintillator has the greatest light yield with an ... 7. Systematic studies of small scintillators for new sampling calorimeter Indian Academy of Sciences (India) A new sampling calorimeter using very thin scintillators and the multi-pixel photon counter (MPPC) has been proposed to produce better position resolution for the international linear collider (ILC) experiment. As part of this R & D study, small plastic scintillators of different sizes, thickness and wrapping reflectors are ... 8. Some history of liquid scintillator development at Los Alamos International Nuclear Information System (INIS) Ott, D.G. 1979-01-01 The early developments in liquid scintillation counting made at Los Alamos Scientific Laboratory are reviewed. Most of the work was under the direction of F.N. Hayes and included counter development and applications as well as synthesis and chemistry of liquid scintillators 9. Microprocessor-based single particle calibration of scintillation counter Science.gov (United States) Mazumdar, G. K. D.; Pathak, K. M. 1985-01-01 A microprocessor-base set-up is fabricated and tested for the single particle calibration of the plastic scintillator. The single particle response of the scintillator is digitized by an A/D converter, and a 8085 A based microprocessor stores the pulse heights. The digitized information is printed. Facilities for CRT display and cassette storing and recalling are also made available. 10. Influence of propagation technology on radiation stability of polystyren scintillators International Nuclear Information System (INIS) Senchishin, V.G.; Khlapova, N.P.; Borisenko, A.Yu.; Lebedev, V.N. 1999-01-01 In this work was studied the radiation hardness of polystyrene-based scintillators produced by injection molding technology and by polymerization in glass cast. The influence of crosslinking and low molecular filler on the radiation resistance was described. It was shown that the radiation resistance of scintillator depends on the viscosity properties of its polymer basis 11. Scintillator quenching effects observed in the AMS-1 TOF data International Nuclear Information System (INIS) Esquivel, O.; Reyes, T.; Menchaca-Rocha, A. 2001-01-01 An analytical expression for the light output response of plastic scintillators as a function of the energy and the z identity of the incident ion is proposed. The effect of the δ rays is considered in the calculation of the scintillation efficiency 12. Non-Proportionality of Organic Scintillators and BGO Science.gov (United States) Nassalski, A.; Moszy¿ski, M.; Syntfeld-Ka¿uch, A.; ¿widerski, ¿.; Szcze¿¿niak, T. 2008-06-01 According to the present knowledge the non-proportionality of the light yield of scintillators appears to be the fundamental limitation of energy resolution. Thus, the understanding of its origin is of the great importance for a development of new scintillators with enhanced energy resolution. In this respect, the non-proportional response of the typical organic scintillators was studied in comparison to that of a BGO crystal. The studies covered tests of BC408 plastic, BC501A liquid scintillator and anthracene organic crystal. The measurements showed a much larger range of energies presenting non-proportional response compared to that known for inorganic scintillators. In the case of anthracene the non-proportionality covers energy range up to about 500 keV, while for the BC408 plastic and BC501A liquid scintillators, it is above 4 MeV energy lost by gamma quanta. The observed effect can be related to a strong quenching of the light for charged particles in organic scintillators, which is much larger than that observed in inorganic scintillators. 13. How to quench light attenuation in plastic scintillators CERN Document Server Gabriele, S A; Massam, Thomas; Zichichi, A 1972-01-01 The problem of light attenuation in plastic scintillators is well known and has existed since their invention. The authors show how the problem has been investigated and overcome via a study of the effect of the chemical concentration of the scintillator components on the light output pattern. (1 refs). 14. Scintillator quenching effects observed in the AMS-1 TOF data Science.gov (United States) Esquivel, O.; Reyes, T.; Menchaca-Rocha, A. 2001-05-01 An analytical expression for the light output response of plastic scintillators as a function of the energy and the z identity of the incident ion is proposed. The effect of the δ rays is considered in the calculation of the scintillation efficiency. . 15. Systematic studies of small scintillators for new sampling calorimeter Indian Academy of Sciences (India) The wrapped scintillator that gives the best light yield is determined by comparing the measured pulse height of each 10 × 40 × 2 mm strip scintillator covered with 3M reflective mirror film, teflon, white paint, black tape, gold, aluminum and white paint+teflon. The pulse height dependence on position, length and thickness of ... 16. A study of GPS ionospheric scintillations observed at Guilin Science.gov (United States) Zou, Yuhua; Wang, Dongli 2009-12-01 The occurrence of strong ionospheric scintillations with S4>=0.2 was studied using global positioning system (GPS) measurements at Guilin (25.29°N, 110.33°E; geomagnetic: 15.04°N, 181.98°E), a station located near the northern crest of equatorial anomaly in China. The results are presented for data collected from January 2007 to December 2008. The results show that amplitude scintillations occurred only during the first five months of the considered years. Nighttime amplitude scintillations, observed mainly in the south of Guilin, always occurred with phase scintillations, total electron content (TEC) depletions, and Rate Of change of TEC (ROT) fluctuations. However, TEC depletions and ROT fluctuations were weak during daytime amplitude scintillations, and daytime amplitude scintillations usually occurred in most of the azimuth directions. GPS scintillation/TEC observations recorded at Guilin and signal-to-noise-ratio measurements obtained from GPS-COSMIC radio occultation indicate that nighttime and daytime scintillations are very likely caused by ionospheric F region irregularities and sporadic E, respectively. 17. Inverted face processing in body dysmorphic disorder. Science.gov (United States) Feusner, Jamie D; Moller, Hayley; Altstein, Lily; Sugar, Catherine; Bookheimer, Susan; Yoon, Joanne; Hembacher, Emily 2010-11-01 Individuals with body dysmorphic disorder (BDD) are preoccupied with perceived defects in appearance. Preliminary evidence suggests abnormalities in global and local visual information processing. The objective of this study was to compare global and local processing in BDD subjects and healthy controls by testing the face inversion effect, in which inverted (upside-down) faces are recognized more slowly and less accurately relative to upright faces. Eighteen medication-free subjects with BDD and 17 matched, healthy controls performed a recognition task with sets of upright and inverted faces on a computer screen that were either presented for short duration (500 ms) or long duration (5000 ms). Response time and accuracy rates were analyzed using linear and logistic mixed effects models, respectively. Results indicated that the inversion effect for response time was smaller in BDD subjects than controls during the long duration stimuli, but was not significantly different during the short duration stimuli. Inversion effect on accuracy rates did not differ significantly between groups during either of the two durations. Lesser inversion effect in BDD subjects may be due to greater detail-oriented and piecemeal processing for long duration stimuli. Similar results between groups for short duration stimuli suggest that they may be normally engaging configural and holistic processing for brief presentations. Abnormal visual information processing in BDD may contribute to distorted perception of appearance; this may not be limited to their own faces, but to others' faces as well. Copyright © 2010 Elsevier Ltd. All rights reserved. 18. INVERTING ORTHOTOPIC ILEOCYSTOPLASTY FOR SHORT MESENTERY Directory of Open Access Journals (Sweden) V. A. Perepechay 2010-01-01 Full Text Available During orthotopic ileocystoplasty, the short mesentery causes an increase in the risk of incompetence of anastomosis of the reservoir with the urethra. Inverting orthotopic ileocystoplasty ensures a free reservoir pull-through into the small pelvis and eliminates tissue tension in the anastomosis. The proposed procedure differs from the Studer operation in that the reservoir is sutured lengthwise, after which it is inverted between the mesenteric leaves. The posterior reservoir wall is anteverted and freely brought out into the small pelvis. This reduces the distance to the urethral stump by 3-4 cm. This procedure was used in 19 patients to be operated on. There were no cases of reservoir or reservoir-urethral anastomotic incompetence. The mean neocystic capacity was 110, 350, and 490 ml 0, 3, and 12 months, respectively, after urethral catheter removal. The maximum reservoir pressure does not exceed 40 (mean 30 cm H2O. Daytime urinary retention was 94.7%; nocturnal urinary retention during forced nocturnal miction was 79%. The obtained functional results compare well with those achieved during the similar procedures. 19. INVERTING ORTHOTOPIC ILEOCYSTOPLASTY FOR SHORT MESENTERY Directory of Open Access Journals (Sweden) V. A. Perepechay 2014-07-01 Full Text Available During orthotopic ileocystoplasty, the short mesentery causes an increase in the risk of incompetence of anastomosis of the reservoir with the urethra. Inverting orthotopic ileocystoplasty ensures a free reservoir pull-through into the small pelvis and eliminates tissue tension in the anastomosis. The proposed procedure differs from the Studer operation in that the reservoir is sutured lengthwise, after which it is inverted between the mesenteric leaves. The posterior reservoir wall is anteverted and freely brought out into the small pelvis. This reduces the distance to the urethral stump by 3-4 cm. This procedure was used in 19 patients to be operated on. There were no cases of reservoir or reservoir-urethral anastomotic incompetence. The mean neocystic capacity was 110, 350, and 490 ml 0, 3, and 12 months, respectively, after urethral catheter removal. The maximum reservoir pressure does not exceed 40 (mean 30 cm H2O. Daytime urinary retention was 94.7%; nocturnal urinary retention during forced nocturnal miction was 79%. The obtained functional results compare well with those achieved during the similar procedures. 20. Inverting dedevelopment: geometric singularity theory in embryology Science.gov (United States) Bookstein, Fred L.; Smith, Bradley R. 2000-10-01 The diffeomorphism model so useful in the biomathematics of normal morphological variability and disease is inappropriate for applications in embryogenesis, where whole coordinate patches are created out of single points. For this application we need a suitable algebra for the creation of something from nothing in a carefully organized geometry: a formalism for parameterizing discrete nondifferentiabilities of invertible functions on Rk, kGTR 1. One easy way to begin is via the inverse of the development map - call it the dedevelopment map, the deformation backwards in time. Extrapolated, this map will inevitably have singularities at which its derivative is zero. When the dedevelopment map is inverted to face forward in time, the singularities become appropriately isolated infinities of derivative. We have recently introduced growth visualizations via extrapolations to the isolated singularities at which only one directional derivative is zero. Maps inverse to these create new coordinate patches directionally rather than radically. The most generic singularity that suits this purpose is the crease f(x,y) equals (x,x2y+y3), which has already been applied in morphometrics for the description of focal morphogenetic phenomena. We apply it to embryogenesis in the form of its analytic inverse, and demonstrate its power using a priceless new data set of mouse embryos imaged in 3D by micro-MR with voxels smaller than 100micrometers 3.
1. Membrane fusion
DEFF Research Database (Denmark)
Bendix, Pól Martin
2015-01-01
At Stanford University, Boxer lab, I worked on membrane fusion of small unilamellar lipid vesicles to flat membranes tethered to glass surfaces. This geometry closely resembles biological systems in which liposomes fuse to plasma membranes. The fusion mechanism was studied using DNA zippering...... between complementary strands linked to the two apposing membranes closely mimicking the zippering mechanism of SNARE fusion complexes....
2. Biobased Membrane
NARCIS (Netherlands)
Koenders, E.A.B.; Zlopasa, J.; Picken, S.J.
2015-01-01
The present invention is in the field of a composition for forming a bio-compatible membrane applicable to building material, such as concrete, cement, etc., to a meth od of applying said composition for forming a bio-compatible membrane, a biocompatible membrane, use of said membrane for various
3. Analysis of Ionospheric Scintillation Characteristics in Sub-Antarctica Region with GNSS Data at Macquarie Island.
Science.gov (United States)
Guo, Kai; Liu, Yang; Zhao, Yan; Wang, Jinling
2017-01-12
Ionospheric scintillation has a great impact on radio propagation and electronic system performance, thus is extensively studied currently. The influence of scintillation on Global Navigation Satellite System (GNSS) is particularly evident, making GNSS an effective medium to study characteristics of scintillation. Ionospheric scintillation varies greatly in relation with temporal and spatial distribution. In this paper, both temporal and spatial characteristics of scintillation are investigated based on Macquarie Island's GNSS scintillation data collected from 2011 to 2015. Experiments demonstrate that occurrence rates of amplitude scintillation have a close relationship with solar activity, while phase scintillation is more likely to be generated by geomagnetic activity. In addition, scintillation distribution behaviors related to elevation and azimuth angles are statistically analyzed for both amplitude and phase scintillation. The proposed work is valuable for a deeper understanding of theoretical mechanisms of ionospheric scintillation in this region, and provides a reference for GNSS applications in certain regions around sub-Antarctica.
4. The Scintillating Grid Illusion is Enhanced by Binocular Viewing
Directory of Open Access Journals (Sweden)
2012-12-01
Full Text Available The scintillating grid illusion is an intriguing stimulus consisting of a grey grid on a black background, with white discs at the grid intersections. Most viewers perceive illusory “scintillating” black discs within the physical white discs, especially at non-fixated locations. Here, we report for the first time that this scintillation percept is stronger when the stimulus is viewed binocularly than when it is presented to only one eye. Further experiments indicate that this is not simply because two monocular percepts combine linearly, but involves a specifically cyclopean contribution (Schrauf & Spillmann, 2000. However, the scintillation percept does not depend on the absolute disparity of the stimulus relative to the screen. In an intriguing twist, although the basic illusion shows more scintillation when viewed binocularly, when the illusion is weakened by shifting the discs away from the grid intersections, scintillation becomes stronger with monocular viewing.
5. Development of a double scintillator fast neutron spectrometer
International Nuclear Information System (INIS)
Shirakata, Keisho; Iijima, Tsutomu; Cho, Mann.
1976-03-01
A double scintillator fast neutron spectrometer based on the time-of-flight measurement between two plastic scintillators has been developed for spectrum measurement in FCA cores and other fast systems. Neutrons extracted from a fast system are scattered by the 1st scintillator and the 2nd scintillator detects the scattered neutrons. By measuring the time-of-flight between the two scintillators, the neutron spectrum is determined. The method is essentially differential, and a complicated unfolding process is not required. The results of its application indicate excellence of the method over other methods in the energy range above several hundreds keV. Design and characteristics of the spectrometer, application, analysis of the measured data are described in detail. (auth.)
6. Neutron-gamma discrimination of boron loaded plastic scintillator
International Nuclear Information System (INIS)
Wang Dong; He Bin; Zhang Quanhu; Wu Chuangxin; Luo Zhonghui
2010-01-01
Boron loaded plastic scintillator could detect both fast neutrons thanks to hydrogen and thermal neutrons thanks to 10B. Both reactions have large cross sections, and results in high detection efficiency of incident neutrons. However, similar with other organic scintillators, boron loaded plastic scintillator is sensitive to gamma rays and neutrons. So gamma rays must be rejected from neutrons using their different behavior in the scintillator. In the present research zero crossing method was used to test neutron-gamma discrimination of BC454 boron loaded plastic scintillator. There are three Gaussian peaks in the time spectrum, they are corresponding to gamma rays, fast neutrons and flow neutrons respectively. Conclusion could be made that BC454 could clear discriminate slow neutrons and gamma, but the discrimination performance turns poor as the neutrons' energy becomes larger. (authors)
7. Scintillating fiber detector development for the SSC: Annual progress report
International Nuclear Information System (INIS)
Ruchti, R.C.
1989-01-01
During the past year, considerable effort has been applied to the development of scintillating fiber detectors in several areas: new scintillation liquids and studies of their fluorescence properties; new fluorescent dyes based on non-intramolecular proton transfer; new dyes based on intramolecular proton transfer; incorporation of these new dyes in plastic (polystyrene) and liquid scintillation solutions; development of small cross section glass capillaries for the containment of liquid scintillators; studies of waveguide characteristics; studies of image intensifier phosphor screen characteristics; initial steps to form a collaboration to study and develop appropriate new properties of the Solid State Photomultiplier; construction of a new laboratory at Notre Dame to enhance our capabilities for further measurements and studies; and organization of and execution of a Workshop on Scintillating Fiber Detector Development for the SSC, held at Fermilab, November 14--16, 1988
8. Optimization of light collection from crystal scintillators for cryogenic experiments
Energy Technology Data Exchange (ETDEWEB)
Danevich, F.A., E-mail: [email protected] [Institute for Nuclear Research, MSP 03680, Kyiv (Ukraine); Kobychev, R.V. [Institute for Nuclear Research, MSP 03680, Kyiv (Ukraine); National Technical University of Ukraine “Kyiv Polytechnic Institute”, 03056 Kyiv (Ukraine); Kobychev, V.V. [Institute for Nuclear Research, MSP 03680, Kyiv (Ukraine); Kyungpook National University, Daegu 702-701 (Korea, Republic of); Kraus, H. [Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH (United Kingdom); Mikhailik, V.B. [Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH (United Kingdom); Diamond Light Source, Harwell Science Campus, Didcot, OX11 0DE (United Kingdom); Mokina, V.M. [Institute for Nuclear Research, MSP 03680, Kyiv (Ukraine)
2014-04-21
High light collection efficiency is an important requirement in any application of scintillation detectors. The purpose of this study is to investigate the possibility for improving this parameter in cryogenic scintillation bolometers, which can be considered as promising detectors in experiments investigating neutrinoless double beta decay and dark matter. Energy resolutions and relative pulse amplitudes of scintillation detectors using ZnWO{sub 4} scintillation crystals of different shapes (cylinder ∅ 20×20 mm and hexagonal prism with diagonal 20 mm and height 20 mm), reflector materials and shapes, optical contact and surface properties (polished and diffused) were measured at room temperature. Propagation of optical photons in these experimental conditions was simulated using Geant4 and ZEMAX codes. The results of the simulations are found to be in good agreement with each other and with direct measurements of the crystals. This could be applied to optimize the geometry of scintillation detectors used in the cryogenic experiments.
9. Regional Arctic observations of TEC gradients and scintillations
DEFF Research Database (Denmark)
Durgonics, Tibor; Høeg, Per; von Benzon, Hans-Henrik
2015-01-01
near-real time observations of the stateand variations of the high-latitude ionosphere. This data can be employed to obtain relevant geophysical variablesand statistics. In our study GPS-derived total electron content (TEC) measurements have been complemented with amplitudescintillation indices (S4......), and phase scintillation indices (σϕ) The investigation of relations of these geophysical variables can lead to possible new ways to study the underlying processes and to build tools for monitoring and predicting Arctic TEC and scintillation large-scale patterns. A number of specific ionosphere events...... will be presented and the underlying geophysical process will be identified and described. Especially results where large-scale gradients in the regional TEC are compared with the growth of scintillations.The statistics of the scintillations will be investigated, with emphasis on how well the scintillations follow...
10. Aalborg Inverter - A New Type of “Buck in Buck, Boost in Boost” Grid-Tied Inverter
DEFF Research Database (Denmark)
Wu, Weimin; Ji, Junhao; Blaabjerg, Frede
2015-01-01
This paper presents a new family of high efficiency dc/ac grid-tied inverter with a wide variation of input dc voltage. It is a “boost in boost, buck in buck” inverter, meaning that only one power stage works at high frequency in order to achieve minimum switching loss. The minimum voltage drop...... is larger than the magnitude of the ac voltage, it is a voltage-source inverter, and on the contrary it is current-source inverter in the other mode. A 220 V/50 Hz/ 2000 W prototype has been constructed. Simulations and experiments show that it has a good control and system performance....
11. Decontamination and modification of liquid scintillators
International Nuclear Information System (INIS)
Sachan, S.R.; Soman, S.D.
1980-01-01
New techniques of decontaminating and recycling used radioactive liquid scintillators (LS) are discussed. Aromatic LS Tritel spiked with tritiated water was decontaminated with NaOH; single extraction gave a decontamination factor of about 90% and 3-4 extractions decontaminated the LS to background level. The counting efficiency of the decontaminated LS was about 88% of the fresh LS. A modification of hydrophobic toluene LS for use with aqueous samples is also described. The water holding capacity (WHC) of modified toluene/alcohol LS decreased while the counting efficiency increased with increasing concentration of toluene in LS; an optimum working range of around 50% toluene concentration was selected. The decontamination of used modified LS was achieved by a single washing with an excess amount of water. The counting efficiency of decontaminated LS was about 92% of the fresh LS. This recycling of used liquid scintillators after decontamination will not only save expenditure on LS but also help waste disposal problems as the radioactivity is contained in aqueous phase with reduced volume. (UK)
Energy Technology Data Exchange (ETDEWEB)
Atac, M. (Univ. of California, Los Angeles, CA (United States) Fermi National Accelerator Lab., Batavia, IL (United States)); Buchanan, C.; Chrisman, D.; Cline, D.; Kolonko, J.; Kubic, J.; Park, J. (Univ. of California, Los Angeles, CA (United States)); Baumbaugh, A.; Binkley, M.; Bross, A.D.; Finley, D.; Elias, J.; Foster, G.W.; Kephart, R.; Kephart, R.; Kim, C.; Park, H.; Pla-Dalmau, A.; Rivetta, C.; Tkaczyk, S.; Wagner, R. (Fermi National Accelerator Lab., Batavia, IL (United States)); Chung, M.; Goldberg, H.; Jeskik, R.; Margulies, S.; Mendez, H.; Solomon, J.; Vaca, F. (Univ. of Illinois, Chicago, IL (United States)); Kelley, C. (Massachusetts College of Pharmacy and Allied Health Sciences, Boston, MA (United States)); Baumbaugh, B.; Bishop, J.; Biswas, N.; Cason, N.; Jacques, J.; Kehoe, R.; Kelly, M.; Kenney, V.; LoSecco, J.; Ruchti, R.; Shephard, W.; Warchol, J.; Wayne, M.; Marchant, J.; Mountain, R.J. (Univ. of Notre Dame, IN (United States)); Davis, D.; Vandergriff, D. (O
1993-08-01
13. Collimator trans-axial tomographic scintillation camera
International Nuclear Information System (INIS)
Jaszczak, Ronald J.
1979-01-01
14. Semiconductor scintillator detector for gamma radiation
International Nuclear Information System (INIS)
Laan, F.T.V. der; Borges, V.; Zabadal, J.R.S.
2015-01-01
Nowadays the devices employed to evaluate individual radiation exposition are based on dosimetric films and thermoluminescent crystals, whose measurements must be processed in specific transductors. Hence, these devices carry out indirect measurements. Although a new generation of detectors based on semiconductors which are employed in EPD's (Electronic Personal Dosemeters) being yet available, it high producing costs and large dimensions prevents the application in personal dosimetry. Recent research works reports the development of new detection devices based on photovoltaic PIN diodes, which were successfully employed for detecting and monitoring exposition to X rays. In this work, we step forward by coupling a 2mm anthracene scintillator NE1, which converts the high energy radiation in visible light, generating a Strong signal which allows dispensing the use of photomultipliers. A low gain high performance amplifier and a digital acquisition device are employed to measure instantaneous and cumulative doses for energies ranging from X rays to Gamma radiation up to 2 MeV. One of the most important features of the PIN diode relies in the fact that it can be employed as a detector for ionization radiation, since it requires a small energy amount for releasing electrons. Since the photodiode does not amplify the corresponding photon current, it must be coupled to a low gain amplifier. Therefore, the new sensor works as a scintillator coupled with a photodiode PIN. Preliminary experiments are being performed with this sensor, showing good results for a wide range of energy spectrum. (author)
15. Distributed imaging for liquid scintillation detectors
Science.gov (United States)
Dalmasson, J.; Gratta, G.; Jamil, A.; Kravitz, S.; Malek, M.; Wells, K.; Bentley, J.; Steven, S.; Su, J.
2018-03-01
We discuss a novel paradigm in the optical readout of scintillation radiation detectors. In one common configuration, such detectors are homogeneous and the scintillation light is collected and recorded by external photodetectors. It is usually assumed that imaging in such a photon-starved and large-emittance regime is not possible. Here we show that the appropriate optics, matched with highly segmented photodetector coverage and dedicated reconstruction software, can be used to produce images of the radiation-induced events. In particular, such a "distributed imaging" system can discriminate between events produced as a single cluster and those resulting from more delocalized energy depositions. This is crucial in discriminating many common backgrounds at MeV energies. With the use of simulation, we demonstrate the performance of a detector augmented with a practical, if preliminary, set of optics. Finally, we remark that this new technique lends itself to be adapted to different detector sizes and briefly discuss the implications for a number of common applications in science and technology.
16. Buried plastic scintillator muon telescope (BATATA)
International Nuclear Information System (INIS)
Alfaro, R.; De Donato, C.; D'Olivo, J.C.; Guzman, A.; Medina-Tanco, G.; Moreno Barbosa, E.; Paic, G.; Patino Salazar, E.; Salazar Ibarguen, H.; Sanchez, F.A.; Supanitsky, A.D.; Valdes-Galicia, J.F.; Vargas Trevino, A.D.; Vergara Limon, S.; Villasenor, L.M.
2010-01-01
Muon telescopes have multiple applications in the area of cosmic ray research. We are currently building such a detector with the objective of comparing the ground penetration of muon vs. electron-gamma signals originated in cosmic ray showers. The detector is composed by a set of three parallel dual-layer scintillator planes, buried at fixed depths ranging from 120 to 600g/cm 2 . Each layer is 4m 2 and is composed by 49 rectangular strips of 4cmx2m, oriented at a 90 0 angle with respect to its companion layer, which gives an xy-coincidence pixel of 4x4cm 2 . The scintillators are MINOS extruded polystyrene strips, with an embedded Bicron BC92 wavelength shifting (WLS) fibers, of 1.5 mm in diameter. Light is collected by Hamamatsu H7546B multi-anode PMTs of 64 pixels. The front-end (FE) electronics works in counting mode and signals are transmitted to the surface DAQ stage using low-voltage differential signaling (LVDS). Any strip signal above threshold opens a GPS-tagged 2μs data collection window. Data, including signal and background, are acquired by a system of FPGA (Spartan 2E) boards and a single-board computer (TS7800).
17. Data process of liquid scintillation counting
International Nuclear Information System (INIS)
Ishikawa, Hiroaki; Kuwajima, Susumu.
1975-01-01
The use of liquid scintillation counting system has been significantly spread because automatic sample changers and printers have recently come to be incorporated. However, the system will be systematized completely if automatic data processing and the sample preparation of radioactive materials to be measured are realized. Dry or wet oxidation method is applied to the sample preparation when radioactive materials are hard to dissolve into scintillator solution. Since these several years, the automatic sample combustion system, in which the dry oxidation is automated, has been rapidly spread and serves greatly to labor saving. Since the printers generally indicate only counted number, data processing system has been developed, and speeded up calculating process, which automatically corrects quenching of samples for obtaining the final radioactivity required. The data processing system is roughly divided into on-line and off-line systems according to whether computers are connected directly or indirectly, while its hardware is classified to input, calculating and output devices. Also, the calculation to determine sample activity by external standard method is explained. (Wakatsuki, Y.)
18. Multifrequency techniques for studying interplanetary scintillations
Science.gov (United States)
Woo, R.
1975-01-01
Rytov's approximation, or the method of smooth perturbations, is utilized to derive the temporal frequency spectra of the amplitude and phase fluctuations of multifrequency plane and spherical waves propagating in the interplanetary medium and solar corona. It is shown that multifrequency observations of interplanetary scintillations using either compact radio stars of spacecraft radio signals are desirable because the correlation of the multifrequency waves yields additional independent measurements of the solar wind and turbulence. Measurements of phase fluctuations are also desirable because, unlike amplitude fluctuations, they provide information on the full range of scale sizes for the electron-density fluctuations. It is also shown that a coherent dual-frequency radio system is particularly useful in making such measurements. In addition to providing a means for interpreting observations of multifrequency interplanetary scintillations, the present analysis is essential for estimating the effects of solar corona turbulence on the communications and navigation of a spacecraft whose line-of-sight path passes close to the sun.
19. Lanthanum halide scintillators: Properties and applications
International Nuclear Information System (INIS)
Iltis, Alain; Mayhugh, M.R.; Menge, P.; Rozsa, C.M.; Selles, O.; Solovyev, V.
2006-01-01
BrilLanCe[reg]-350 and BrilLanCe[reg]-380, Saint-Gobain Crystals' trade-names for LaCl 3 :Ce and LaBr 3 :Ce are being brought to market under exclusive license to Delft and Bern Universities. We are reporting the properties of crystals produced with commercially viable processes and find they match others' observations. These scintillators are bright (60,000 photons/MeV for LaBr 3 :Ce) and have very linear response, a combination that leads to very good energy resolution ( 3 :Ce). The materials also have fast scintillation decay times ( 3 :Ce). These excellent properties are retained at high temperature with only moderate light loss ( 138 and Ac 227 , the latter having been substantially reduced in recent processing. BrilLanCe[reg]-350 is now available in detectors up to 51 mm diameter while 38 mm diameter is available for BrilLanCe[reg]-380. Larger sizes are expected
20. Search for missing baryons through scintillation
International Nuclear Information System (INIS)
Habibi, F.
2011-06-01
Cool molecular hydrogen H 2 may be the ultimate possible constituent to the Milky-Way missing baryon. We describe a new way to search for such transparent matter in the Galactic disc and halo, through the diffractive and refractive effects on the light of background stars. By simulating the phase delay induced by a turbulent medium, we computed the corresponding illumination pattern on the earth for an extended source and a given passband. We show that in favorable cases, the light of a background star can be subjected to stochastic fluctuations of the order of a few percent at a characteristic time scale of a few minutes. We have searched for scintillation induced by molecular gas in visible dark nebulae as well as by hypothetical halo clumpuscules of cool molecular hydrogen (H 2 -He) during two nights, using the NTT telescope and the IR SOFI detector. Amongst a few thousands of monitored stars, we found one light-curve that is compatible with a strong scintillation effect through a turbulent structure in the B68 nebula. Because no candidate were found toward the SMC (Small Magellan Cloud), we are able to establish upper limits on the contribution of gas clumpuscules to the Galactic halo mass. We show that the short time-scale monitoring of a few 10 6 star*hour in the visible band with a >4 m telescope and a fast readout camera should allow one to interestingly quantify or constrain the contribution of turbulent molecular gas to the Galactic halo. (author)
1. Inverting adherent cells for visualizing ECM interactions at the basal cell side
International Nuclear Information System (INIS)
Gudzenko, Tetyana; Franz, Clemens M.
2013-01-01
Interactions with the extracellular matrix (ECM) govern a wide range of cellular functions, including survival, migration and invasion. However, in adherent cells these interactions occur primarily on the basal cell side, making them inaccessible to high-resolution, surface-scanning imaging techniques such as atomic force microscopy (AFM) or scanning electron microscopy (SEM). Here we describe a fast and reliable method for inverting adherent cells, exposing the basal cell membrane for direct analysis by AFM or SEM in combination with fluorescence microscopy. Cells including their matrix adhesion sites remain intact during the inversion process and are transferred together with the complete array of basally associated ECM proteins. Molecular features of ECM proteins, such as the characteristic 67 nm collagen D-periodicity, are well preserved after inversion. To demonstrate the versatility of the method, we compared basal interactions of fibroblasts with fibrillar collagen I and fibronectin matrices. While fibroblasts remodel the fibronectin layer exclusively from above, they actively invade even thin collagen layers by contacting individual collagen nanofibrils both basally and apically through a network of cellular extensions. Cell–matrix entanglement coincides with enhanced cell spreading and flattening, indicating that nanoscale ECM interactions govern macroscopic changes in cell morphology. The presented cell inversion technique can thus provide novel insight into nanoscale cell–matrix interactions at the basal cell side. - Highlights: ► We present a novel method for inverting adherent cells to expose the basal cell side. ► Basal cell sides can be imaged at high resolution by AFM and SEM. ► Cells can be inverted together with the underlying extracellular matrix. ► AFM images of inverted cells provide a nanoscale look at basal cell–ECM interactions
2. Sine-wave three phase resonance inverter for operation of ...
African Journals Online (AJOL)
naeema
conventional and simple solution to this requirement are in the following [8]. Using conventional H-bridge inverter beside of a step-up transformer. Using a renewable energy source with sufficiently large output voltage, which may be realized by a string of series connected modules followed by an H-bridge inverter [12], [13].
3. Human Mobile Inverted Pendulum Transporter - a Mechatronic System Case Study
DEFF Research Database (Denmark)
Bech, Michael Møller; Hansen, Anders Hedegaard; Pedersen, Henrik C.
2011-01-01
, which nevertheless illustrates the potentials of unifying classical engineering technologies (mechanics, electronics, control systems) with modern high-efficient inverter-fed permanent magnet AC motors and the latest MEMS sensor technology. A full-scale fully operational prototype of a two-wheel mobile...... inverted pendulum has been built based on the presented design....
4. Modified impedance source inverter for power conditioning system
... generalized discussion and design of impedance network elements are presented. Comparison with the classical impedance source inverter is presented. Using simulation, analytical results are presented that ensure stability. The proposed voltage type inverter has reduced inrush current at startup, less capacitor voltage ...
5. Multiple-load series resonant inverter for induction cooking ...
P Sharath Kumar
In addition, it can achieve efficient and stable zero voltage switching operation in the whole load range. The proposed control scheme is simulated and experimentally verified with two-load inverter configuration. Keywords. Induction cooking; multiple load; series resonant inverter; ZVS; pulse density modulation control. 1.
6. Requirements of inverted roofs with a drainage layer
DEFF Research Database (Denmark)
Leimer, Hans-Peter; Rode, Carsten; Künzel, Hartwig
2005-01-01
This contribution illustrates the application of the standard EN ISO 6946 regarding the heat loss of an inverted roof for different regions of Europe. An addendum to the standard (EN ISO 6946:1996/A1, 2003) introduces a correction to the thermal transmittance of inverted roofs due to rain water f...
7. Power system services provided by inverter connected distributed energy resources
DEFF Research Database (Denmark)
For the last few years there has been a significant increase of DER units in Denmark, of those units more and more are connected to the power system using inverters. These inverter connected units have the potential to support the electrical power system with various power system services. One...
8. Three-phase inverter for small high speed motors
Science.gov (United States)
Mccormick, John A.; Valenzuela, Javier A.
1991-01-01
A high-frequency three-phase inverter is being developed to drive a miniature centrifugal compressor which is a key component in a long-life space-borne cryocooler. The inverter is a unique transformer-coupled design, tailored to the low-voltage high-current characteristic of the compressor's induction motor. The design and performance demonstration of a breadboard model of the inverter are described. The cryocooler uses a reverse-Brayton cycle with turbomachines to provide 5 watt of cooling at 70 K. The design target for input power to the compressor motor is 175 watts. Line-to-neutral phase voltage waveforms to be supplied by the inverter have an amplitude of 15 volt-rms at a frequency of 8 kHz. DC power at 28 volt is supplied to the inverter. The breadboard inverter was tested with a preliminary development model of the compressor. It drove the compressor over a range of operating conditions encompassing frequencies of 5 to 9 kHz at powers of 56 to 437 watt. Inverter efficiencies, calculated from experimentally verified loss models, ranged from 89 to 95 percent over the tests. The design target on efficiency is 90 percent. The inverter was demonstrated to supply starting current adequate to overcome the starting friction of the compressor's self-acting gas bearings by a safe margin.
9. Three Phase Soft Commutation Auxilary Resonant Pole Inverter
OpenAIRE
2006-01-01
This paper covers the circuit modification of the power part of the inverter with auxiliary resonant poles utilising configuration of switches realised with routinely produced IGBT modules. Covered is also the control optimisation which goal is the minimisation of switching of the auxiliary resonant pole. Presented results were gained on a prototype of an inverter laboratory sample.
10. Trans-Z-source Neutral Point Clamped inverter
DEFF Research Database (Denmark)
Mo, W.; Loh, P. C.; Li, D.
2012-01-01
for buck-boost energy conversion with all the favourable advantages of multi-level switching retained. This paper presents three-level trans-Z-source Neutral Point Clamped (NPC) inverter topology, which achieves both the advantages of trans-Z-source and three-level NPC inverter configuration. With proper...
11. Five-level Z-source diode-clamped inverter
DEFF Research Database (Denmark)
Gao, F.; Loh, Poh Chiang; Blaabjerg, Frede
2010-01-01
This study proposes a five-level Z-source diode-clamped inverter designed with two intermediate Z-source networks connected between the dc input sources and rear-end inverter circuitry. By partially shorting the Z-source networks, new operating states not previously reported for two-level Z...
12. Improving generalized inverted index lock wait times
Science.gov (United States)
Borodin, A.; Mirvoda, S.; Porshnev, S.; Ponomareva, O.
2018-01-01
Concurrent operations on tree like data structures is a cornerstone of any database system. Concurrent operations intended for improving read\\write performance and usually implemented via some way of locking. Deadlock-free methods of concurrency control are known as tree locking protocols. These protocols provide basic operations(verbs) and algorithm (ways of operation invocations) for applying it to any tree-like data structure. These algorithms operate on data, managed by storage engine which are very different among RDBMS implementations. In this paper, we discuss tree locking protocol implementation for General inverted index (Gin) applied to multiversion concurrency control (MVCC) storage engine inside PostgreSQL RDBMS. After that we introduce improvements to locking protocol and provide usage statistics about evaluation of our improvement in very high load environment in one of the world’s largest IT company.
13. Modifications to Battery chargers and inverters Units
International Nuclear Information System (INIS)
Raison, Florent
2015-01-01
Over-exceeding the seismic specifications of the nuclear industry has always been the top priority of AEG Power Solutions. Since the Forsmark event, and especially since the Fukushima Daichi accident, utilities have reviewed their specifications. As a consequence, safety related battery chargers and inverters have to withstand higher acceleration levels. Simulation, design and test procedures are key drivers of the battery charger and inverter industry. Forces analysis through simulation is the first step of the product design process. The CAD drawings of our equipment, including the mechanical frame of the cabinet and the internal components, are used for the simulation of vibration. In the frame of 10 Hz, most new specifications show higher values, with higher constraints on our equipment. Our nuclear product range has been adapted to these new requirements. PCBs (Printed Circuit Boards), as key components in charge of the regulation and monitoring of the load, are first separately tested during the design phase, as a specific component. They are subjected to the following tests: Critical load analysis, Thermal imaging, Climatic test, Vibration and shock test. Then the complete equipment will follow a complete test program, including: Type test, EMC test, Seismic test, Aging test. Technology is key in achieving goals in terms of robustness and reliability of battery chargers and inverters. AEG Power Solutions renewed its entire range of products in 2011-2013 and made relevant choices. By updating its complete range of nuclear products, AEG Power Solutions is now offering a new range of solutions to the nuclear industry which minimize the risk of component obsolescence, in case of product replacement on existing nuclear power plants, or of new construction. In order to increase the product reliability and to facilitate the qualification programs of the products, the decision was made to offer 100% analogue technology (Software free). The different regulation and
14. Motion Analysis Based on Invertible Rapid Transform
Directory of Open Access Journals (Sweden)
J. Turan
1999-06-01
Full Text Available This paper presents the results of a study on the use of invertible rapid transform (IRT for the motion estimation in a sequence of images. Motion estimation algorithms based on the analysis of the matrix of states (produced in the IRT calculation are described. The new method was used experimentally to estimate crowd and traffic motion from the image data sequences captured at railway stations and at high ways in large cities. The motion vectors may be used to devise a polar plot (showing velocity magnitude and direction for moving objects where the dominant motion tendency can be seen. The experimental results of comparison of the new motion estimation methods with other well known block matching methods (full search, 2D-log, method based on conventional (cross correlation (CC function or phase correlation (PC function for application of crowd motion estimation are also presented.
15. On Invertible Sampling and Adaptive Security
DEFF Research Database (Denmark)
Ishai, Yuval; Kumarasubramanian, Abishek; Orlandi, Claudio
2011-01-01
Secure multiparty computation (MPC) is one of the most general and well studied problems in cryptography. We focus on MPC protocols that are required to be secure even when the adversary can adaptively corrupt parties during the protocol, and under the assumption that honest parties cannot reliably...... erase their secrets prior to corruption. Previous feasibility results for adaptively secure MPC in this setting applied either to deterministic functionalities or to randomized functionalities which satisfy a certain technical requirement. The question whether adaptive security is possible for all...... functionalities was left open. We provide the first convincing evidence that the answer to this question is negative, namely that some (randomized) functionalities cannot be realized with adaptive security. We obtain this result by studying the following related invertible sampling problem: given an efficient...
16. Scalar field cosmologies with inverted potentials
International Nuclear Information System (INIS)
Boisseau, B.; Giacomini, H.; Polarski, D.
2015-01-01
Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities arising at the limit of physical viability of the model in the Jordan frame (JF) are either of the Big Bang or of the Big Crunch type in the EF. As a result we obtain integrable scalar field cosmological models in general relativity (GR) with inverted double-well potentials unbounded from below which possess solutions regular in the future, tending to a de Sitter space, and starting with a Big Bang. The existence of the two fixed points for the field dynamics at late times found earlier in the JF becomes transparent in the EF
17. Scalar field cosmologies with inverted potentials
Energy Technology Data Exchange (ETDEWEB)
Boisseau, B.; Giacomini, H. [Université de Tours, Laboratoire de Mathématiques et Physique Théorique, CNRS/UMR 7350, 37200 Tours (France); Polarski, D., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Université Montpellier and CNRS, Laboratoire Charles Coulomb, UMR 5221, F-34095 Montpellier (France)
2015-10-01
Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities arising at the limit of physical viability of the model in the Jordan frame (JF) are either of the Big Bang or of the Big Crunch type in the EF. As a result we obtain integrable scalar field cosmological models in general relativity (GR) with inverted double-well potentials unbounded from below which possess solutions regular in the future, tending to a de Sitter space, and starting with a Big Bang. The existence of the two fixed points for the field dynamics at late times found earlier in the JF becomes transparent in the EF.
18. Analytical modeling of inverted annular film boiling
International Nuclear Information System (INIS)
1987-01-01
By employing a two-fluid formulation similar to the one used in the most recent LWR accident analysis codes, a model for the Inverted Annular Film Boiling region is developed. The conservation equations, together with appropriate closure relations are solved numerically. Successful comparisons are made between model predictions and heat transfer coefficient distributions measured in a series of single-tube reflooding experiments. Generally, the model predicts correctly the dependence of the heat transfer coefficient on liquid subcooling and flow rate; for some cases, however, heat transfer is still under-predicted, and an enhancement of the heat exchange from the liquid-vapour interface to the bulk of the liquid is required. The importance of the initial conditions at the quench front is also discussed. (orig.)
19. Analytical modeling of inverted annular film boiling
International Nuclear Information System (INIS)
1985-01-01
By employing a two-fluid formulation similar to the one used in the most recent LWR accident analysis codes, a model for the Inverted Annular Film Boiling region is developed. The conservation equations, together with appropriate constitutive relations are solved numerically and successful comparisons are made between model predictions and heat transfer coefficient distributions measured in a series of single-tube reflooding experiments. The model predicts generally correctly the dependence of the heat transfer coefficient on liquid subcooling and flow rate, through, for some cases, heat transfer is still under-predicted, and an enhancement of the heat exchange from the liquid-vapour interface to the bulk of the liquid is required
20. On Stability of Voltage Source Inverters in Weak Grids
DEFF Research Database (Denmark)
2018-01-01
of circuit and control parameters on the stability of voltage source inverters are studied using a small-signal state-space model in the synchronously rotating dq-frame of reference. The full order state-space model developed in this work is directly extracted from Pulse-Width Modulation (PWM) switching......As the number of inverters increases in the power grid, the stability of grid-tied inverters becomes an important concern for the power industry. In particular, a weak grid can lead to voltage fluctuations at the inverter terminals and consequently cause inverter instability. In this paper, impacts...... pattern, and enables the stability analysis of concurrent variations in the three-phase circuit and control parameters. This paper demonstrates that the full-order model of a grid-tied PQ-controlled VSI can be significantly reduced to a second-order model, preserving the overall system stability in case...
1. Transistorized PWM inverter-induction motor drive system
Science.gov (United States)
Peak, S. C.; Plunkett, A. B.
1982-01-01
This paper describes the development of a transistorized PWM inverter-induction motor traction drive system. A vehicle performance analysis was performed to establish the vehicle tractive effort-speed requirements. These requirements were then converted into a set of inverter and motor specifications. The inverter was a transistorized three-phase bridge using General Electric power Darlington transistors. The description of the design and development of this inverter is the principal object of this paper. The high-speed induction motor is a design which is optimized for use with an inverter power source. The primary feedback control is a torque angle control with voltage and torque outer loop controls. A current-controlled PWM technique is used to control the motor voltage. The drive has a constant torque output with PWM operation to base motor speed and a constant horsepower output with square wave operation to maximum speed. The drive system was dynamometer tested and the results are presented.
2. Evaluation of a high power inverter for potential space applications
Science.gov (United States)
Guynes, B. V.; Lanier, J. R., Jr.
1976-01-01
The ADM-006 inverter discussed utilizes a unique method of using power switching circuits to produce three-phase low harmonic content voltages without any significant filtering. This method is referred to as the power center approach to inverter design and is explained briefly. The results are presented of tests performed by MSFC to evaluate inverter performance, especially when required to provide power to nonlinear loads such as half or full wave rectified loads with capacitive filtering. Test preocedures and results are described. These tests show that the power center inverter essentially met or exceeded all of claims excluding voltage regulation (3.9 percent versus specified 3.3 percent) and would be a good candidate for high power inverter applications such as may be found on Space Station, Spacelab, etc.
3. Optimal Design of Modern Transformerless PV Inverter Topologies
DEFF Research Database (Denmark)
Saridakis, Stefanos; Koutroulis, Eftichios; Blaabjerg, Frede
2013-01-01
The design optimization of H5, H6, neutral point clamped, active-neutral point clamped, and conergy-NPC transformerless photovoltaic (PV) inverters is presented in this paper. The components reliability in terms of the corresponding malfunctions, affecting the PV inverter maintenance cost during...... the operational lifetime period of the PV installation, is also considered in the optimization process. According to the results of the proposed design method, different optimal values of the PV inverter design variables are derived for each PV inverter topology and installation site. The H5, H6, neutral point...... clamped, active-neutral point clamped and conergy-NPC PV inverters designed using the proposed optimization process feature lower levelized cost of generated electricity and lifetime cost, longer mean time between failures and inject more PV-generated energy into the electric grid than their nonoptimized...
Science.gov (United States)
Alsidawi, Said; Muth, James; Wilkin, James
2011-11-15
Takotsubo Cardiomyopathy (TTC), also known as stress-induced cardiomyopathy, was initially described in Japan in 1990. Both illicit and prescription drugs have added to the growing list of insulting stressors. We describe an interesting case of atypical TTC triggered by adderall overdose. A 19-year-old female was brought to the Emergency Department after ingesting 30 Adderall tablets. She was complaining of pressure like chest pain and shortness of breath. Her cardiac enzymes were elevated but the electrocardiogram was unremarkable. Echocardiography identified an ejection fraction (EF) of 25-30% with severe hypokinesis of the base and a preserved apex. Cardiac angiography demonstrated normal coronary arteries with an EF of 35%, hyperkinetic apex and akinetic base consistent with the diagnosis of inverted-TTC. Her symptoms resolved in 24 hrs. Repeat echocardiogram performed 3 days later showed an EF of 60% with no regional wall motion abnormalities. TTC can be identified as a rapid development of severe and reversible left ventricular dysfunction extending beyond the territory of a single epicardial coronary artery in the absence of coronary artery disease or pheochromocytoma. Clinical presentation can be challenging and very hard to distinguish from acute myocardial infarction. Medication induced-TTC has been reported. In our case, the patient overdosed on Adderall which is a sympathomimetic medication. Cardiac imaging identified wall motion abnormalities consistent with inverted type TTC. Restoration of left ventricular function within days confirms the diagnosis of TTC. In conclusion, this case offers an interesting insight into the pathophysiology of TTC. Copyright © 2011 Wiley Periodicals, Inc.
5. Scintillation densimeter for liquids and an isotopic conveyor weighers with plastic scintillator
International Nuclear Information System (INIS)
Makhaj, B.; Antonyak, V.; Plyater, Z.
1979-01-01
The method is described of the weighted material's mass measuring according to the results of the conveyor momentary load measurement derived from the attenuation of radiation in the transmission geometry, conveyor belt velocity measurement and digital processing of the signals from the measurement of the bouth values. In the measuring gage there are located: the point type gamma source of cesium-137 with 4 mCi capacity, the scintillation detector with plastic cylindric scintillator of 5 cm in diameter and with the length approximately equal to the width of the conveyor belt and also the tachometer-generator. The conveyor weighers described is intended for use with conveyor having belt; from 60 to 180 cm wide. The results are given of industrial exploitation of the instrument [ru
6. Scintillation properties of transparent ceramic and single crystalline Nd:YAG scintillators
International Nuclear Information System (INIS)
Yanagida, Takayuki; Kamada, Kei; Fujimoto, Yutaka; Yokota, Yuui; Yoshikawa, Akira; Yagi, Hideki; Yanagitani, Takagimi
2011-01-01
Nd 0.1, 1.1, 2, 4, and 6 mol% doped YAG transparent ceramics are manufactured by the sintering method and their scintillation properties are compared with those of single crystalline Nd 1 mol% doped YAG grown by the micro-pulling down method. They show ∼80% transmittance at wavelengths longer than 300 nm and strong emission lines due to Nd 3+ 4f-4f emission in their radio-luminescence spectra. Among them, the single crystalline sample shows the highest light yield of 11,000 ph/MeV under γ-ray excitation and the second highest one is from Nd 1.1 mol% doped transparent ceramic, which shows 6000 ph/MeV. In these scintillators, dominant decay time constant is around 2-3 μs due to Nd 3+ 4f-4f transitions.
7. Scintillation properties of transparent ceramic and single crystalline Nd:YAG scintillators
Energy Technology Data Exchange (ETDEWEB)
Yanagida, Takayuki, E-mail: [email protected] [Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan); Kamada, Kei; Fujimoto, Yutaka; Yokota, Yuui [Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan); Yoshikawa, Akira [Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan); New Industry Creation Hatchery Center (NICHe), Tohoku University, 6-6-10 Aoba, Aramaki, Aoba-ku, Sendai 980-8579 (Japan); Yagi, Hideki; Yanagitani, Takagimi [Konoshima Chemical Co., Ltd., 80 Kouda, Takuma, Mitoyo-gun, Kagawa 769-1103 (Japan)
2011-03-01
Nd 0.1, 1.1, 2, 4, and 6 mol% doped YAG transparent ceramics are manufactured by the sintering method and their scintillation properties are compared with those of single crystalline Nd 1 mol% doped YAG grown by the micro-pulling down method. They show {approx}80% transmittance at wavelengths longer than 300 nm and strong emission lines due to Nd{sup 3+} 4f-4f emission in their radio-luminescence spectra. Among them, the single crystalline sample shows the highest light yield of 11,000 ph/MeV under {gamma}-ray excitation and the second highest one is from Nd 1.1 mol% doped transparent ceramic, which shows 6000 ph/MeV. In these scintillators, dominant decay time constant is around 2-3 {mu}s due to Nd{sup 3+} 4f-4f transitions.
8. Field-Aligned GPS Scintillation: Multisensor Data Fusion
Science.gov (United States)
Mrak, Sebastijan; Semeter, Joshua; Hirsch, Michael; Starr, Gregory; Hampton, Don; Varney, Roger H.; Reimer, Ashton S.; Swoboda, John; Erickson, Philip J.; Lind, Frank; Coster, Anthea J.; Pankratius, Victor
2018-01-01
The Mahali Global Positioning System (GPS) array (9 receivers, 15-30 km baseline distance) in central Alaska has probed auroral structures in a field-aligned direction during a geomagnetic substorm on 7 October 2015. We present results from a collaborative study of GPS phase scintillation, optical emission brightness, and ionospheric density perturbations, by virtue of data fusion procedure from the Mahali GPS array, all-sky imager (ASI), and the Poker Flat Incoherent Scatter Radar (PFISR). First, we present observations in a traditional way using colocated GPS-ASI sensors, giving us a principal pattern of the phase scintillation with respect to auroral brightness, free of any mapping ambiguities. Next, we use an assumption that the plasma irregularities are located at an altitude of 120 km, we map the optical data to this altitude, and we extend the GPS-ASI study over the entire field of view of the GPS receiver array. We obtain a repeatable and persuasive pattern, revealing that GPS phase scintillation is clustered at the auroral edges. Moreover, investigation of the colinear ISR observations supports the altitude assumption of scintillation producing irregularities, and PFISR-derived electric field estimates suggest that the source for irregularities is gradient drift instability. The phase scintillation was observed on all GPS receivers, phase scintillation exceeded once cycle during several electrojet intensifications, and several events lasted for more than a minute. Finally, phase scintillation was observed during all surge events, independent of the particular auroral morphology.
9. Attenuation of GPS scintillation in Brazil due to magnetic storms
Science.gov (United States)
Bonelli, E.
2008-09-01
Amplitude scintillations in satellite signals can cause errors in communications, because of signal fading, but can be very useful for scientists trying to improve their understanding of the physics of the ionosphere. Usually, magnetic storms are expected to affect the ionosphere in such way as to increase ionospheric irregularities responsible for scintillations. To help change the view of scientists and engineers, in this respect, we show that amplitude scintillation on GPS signals show dramatic decrease during selected magnetic storms, at Brazilian GPS stations. These stations are located on magnetic latitudes that go from equatorial (São Luís) to low-latitude (São José dos Campos and Cachoeira Paulista) so that a region of several thousand kilometers is represented by the data. We present 4 months of data chosen from 2003 to 2005 to represent the strongest storms during each scintillation season. Although there is lack of data for some days from the different stations, it is possible to see, especially for the Halloween Storm (October 2003), that scintillations are attenuated in this wide range of latitudes. During magnetically calm periods scintillations are strong, in this region, from August to March, during solar maxima. Although the data are clear about the attenuation of scintillations during greater magnetic storms, it is not possible to easily conclude which physical mechanism was responsible for this phenomenon, even with the aid of more detailed data like Dst and AE.
10. Cerium doped lanthanum halides: fast scintillators for medical imaging
International Nuclear Information System (INIS)
Selles, O.
2006-12-01
This work is dedicated to two recently discovered scintillating crystals: cerium doped lanthanum halides (LaCl 3 :Ce 3+ and LaBr 3 :Ce 3+ ).These scintillators exhibit interesting properties for gamma detection, more particularly in the field of medical imaging: a short decay time, a high light yield and an excellent energy resolution. The strong hygroscopicity of these materials requires adapting the usual experimental methods for determining physico-chemical properties. Once determined, these can be used for the development of the industrial manufacturing process of the crystals. A proper comprehension of the scintillation mechanism and of the effect of defects within the material lead to new possible ways for optimizing the scintillator performance. Therefore, different techniques are used (EPR, radioluminescence, laser excitation, thermally stimulated luminescence). Alongside Ce 3+ ions, self-trapped excitons are involved in the scintillation mechanism. Their nature and their role are detailed. The knowledge of the different processes involved in the scintillation mechanism leads to the prediction of the effect of temperature and doping level on the performance of the scintillator. A mechanism is proposed to explain the thermally stimulated luminescence processes that cause slow components in the light emission and a loss of light yield. Eventually the study of afterglow reveals a charge transfer to deep traps involved in the high temperature thermally stimulated luminescence. (author)
11. Comparative photoluminescence study of crystalline and nanostructured scintillators
Science.gov (United States)
McKinney, George; McDonald, Warren; Tzolov, Marian
2014-03-01
Scintillators are widely used for conversion of high energy radiation/particles to visible light which can be either directly observed or further converted to electrical signal in photomultipliers or solid state detectors. We compare the light emission properties of traditional crystalline scintillators with nanostructured films created in our laboratory with the potential for use as scintillators. We have studied zinc oxide (ZnO) nanowires, zinc tungstate (ZnWO4) thin films, commercially available crystals of ZnO, ZnWO4 and commercial scintillators of yttrium aluminum garnet (YAG) and yttrium aluminum perovskite (YAP). We will present the photoluminescence emission spectra, the intensity dependence of the emission, and the photoluminescence excitation spectra. We have found that the emission spectrum of zinc oxide nanowires becomes very intense at high excitation intensities and becomes comparable with the emission from the commercial scintillators. The excitation spectra indicate the presence of subgap electronic states in the nanostructured samples and in the commercial scintillators. This study contributes to our effort of creating electron detectors for scanning electron microscopy using nanostructured scintillators.
12. Study of the correlation of scintillation decay and emission wavelength
International Nuclear Information System (INIS)
Yanagida, Takayuki; Fujimoto, Yutaka; Yamaji, Akihiro; Kawaguchi, Noriaki; Kamada, Kei; Totsuka, Daisuke; Fukuda, Kentaro; Yamanoi, Kohei; Nishi, Ryosuke; Kurosawa, Shunsuke; Shimizu, Toshihiko; Sarukura, Nobuhiko
2013-01-01
In photoluminescence which directly excites the emission center of phosphor material is known to have a correlation between the emission wavelength and the decay time based on quantum mechanics. In scintillation phenomenon, host lattice of the material is first excited by ionizing radiation and then the excitation energy is transferred to emission centers. For the first time, we investigated the correlation between the scintillation decay and the emission wavelength by using pulse X-ray equipped streak camera system which could observe time and wavelength resolved scintillation phenomenon. Investigated materials were Ce 3+ , Pr 3+ and Nd 3+ doped oxides and fluorides which all showed 5d-4f transition based emission. As a result, we obtained the relation that τ (scintillation decay time) was proportional to the λ 2.15 (emission wavelength). -- Highlights: ► The correlation between emission wavelength and scintillation decay time is investigated. ► Photoluminescence decay times are also evaluated and compared with scintillation decay times. ► It is proved the relaxation process in emission center is dominant even in scintillation decay
13. Scintillation detectors as self organized critical systems?
International Nuclear Information System (INIS)
Kalinka, G.; Elekes, Z.; Fueloep, Zs.; Saito, A.
2004-01-01
Complete text of publication follows. Recently we have constructed a 312 element scintillation detector (SD) system for nuclear physics experiments. Both manufacture and the quality test were carried out under well controlled conditions. One of the main issues during manufacture was the uniformity of performance of the elements. Performance is determined by the signal amplitude delivered (a product of light creation, collection and detection) and the resolution (dispersion of amplitude). It is the mean and the standard deviation of these two parameters, which can be used to characterize the quality of the detector system. More careful analysis of the amplitude and resolution data, taken with 5.5 MeV particles, in addition, reveals fundamental features of scintillation detectors. Those, familiar with electrical noises, easily recognize from the time order series of data (Fig.a,b) the presence of 1/f α or flicker noise. This can be confirmed by Fourier analysis, which provides the spectral density distribution of the fluctuations, resulting in α = 1.85 ± 0.05 for amplitude and resolution alike (Fig.c). For resolution, however, at higher frequencies there is a transition to white noise. It is well known that 1/f α noise has been observed in several systems having temporal, spatial or spatiotemporal degrees of freedom. Earlier examples are electric current in conductors, rotation of Earth, flow of rivers, heartbeat, stock exchange price indices, etc., recent ones are DNA sequence, human cognition, prime numbers, dynamic images, etc., and now scintillation detectors. Despite extensive research, no universal theory for this ubiquitous phenomenon yet exists. One successful explanation, self organized criticality (SOC), seems, however to fit to our case. Systems, with SOC are characterised by strong interdependence between their constituents. This dynamics results in collective behavior which cannot be understood by studying individual constituents in isolation. They
14. An Optimal Current Controller Design for a Grid Connected Inverter to Improve Power Quality and Test Commercial PV Inverters
Directory of Open Access Journals (Sweden)
2017-01-01
Full Text Available Grid connected inverters play a crucial role in generating energy to be fed to the grid. A filter is commonly used to suppress the switching frequency harmonics produced by the inverter, this being passive, and either an L- or LCL-filter. The latter is smaller in size compared to the L-filter. But choosing the optimal values of the LCL-filter is challenging due to resonance, which can affect stability. This paper presents a simple inverter controller design with an L-filter. The control topology is simple and applied easily using traditional control theory. Fast Fourier Transform analysis is used to compare different grid connected inverter control topologies. The modelled grid connected inverter with the proposed controller complies with the IEEE-1547 standard, and total harmonic distortion of the output current of the modelled inverter has been just 0.25% with an improved output waveform. Experimental work on a commercial PV inverter is then presented, including the effect of strong and weak grid connection. Inverter effects on the resistive load connected at the point of common coupling are presented. Results show that the voltage and current of resistive load, when the grid is interrupted, are increased, which may cause failure or damage for connecting appliances.
15. An Optimal Current Controller Design for a Grid Connected Inverter to Improve Power Quality and Test Commercial PV Inverters.
Science.gov (United States)
Algaddafi, Ali; Altuwayjiri, Saud A; Ahmed, Oday A; Daho, Ibrahim
2017-01-01
Grid connected inverters play a crucial role in generating energy to be fed to the grid. A filter is commonly used to suppress the switching frequency harmonics produced by the inverter, this being passive, and either an L- or LCL-filter. The latter is smaller in size compared to the L-filter. But choosing the optimal values of the LCL-filter is challenging due to resonance, which can affect stability. This paper presents a simple inverter controller design with an L-filter. The control topology is simple and applied easily using traditional control theory. Fast Fourier Transform analysis is used to compare different grid connected inverter control topologies. The modelled grid connected inverter with the proposed controller complies with the IEEE-1547 standard, and total harmonic distortion of the output current of the modelled inverter has been just 0.25% with an improved output waveform. Experimental work on a commercial PV inverter is then presented, including the effect of strong and weak grid connection. Inverter effects on the resistive load connected at the point of common coupling are presented. Results show that the voltage and current of resistive load, when the grid is interrupted, are increased, which may cause failure or damage for connecting appliances.
16. An Optimal Current Controller Design for a Grid Connected Inverter to Improve Power Quality and Test Commercial PV Inverters
Science.gov (United States)
Altuwayjiri, Saud A.; Ahmed, Oday A.; Daho, Ibrahim
2017-01-01
Grid connected inverters play a crucial role in generating energy to be fed to the grid. A filter is commonly used to suppress the switching frequency harmonics produced by the inverter, this being passive, and either an L- or LCL-filter. The latter is smaller in size compared to the L-filter. But choosing the optimal values of the LCL-filter is challenging due to resonance, which can affect stability. This paper presents a simple inverter controller design with an L-filter. The control topology is simple and applied easily using traditional control theory. Fast Fourier Transform analysis is used to compare different grid connected inverter control topologies. The modelled grid connected inverter with the proposed controller complies with the IEEE-1547 standard, and total harmonic distortion of the output current of the modelled inverter has been just 0.25% with an improved output waveform. Experimental work on a commercial PV inverter is then presented, including the effect of strong and weak grid connection. Inverter effects on the resistive load connected at the point of common coupling are presented. Results show that the voltage and current of resistive load, when the grid is interrupted, are increased, which may cause failure or damage for connecting appliances. PMID:28540362
17. Surface preparation and coupling in plastic scintillator dosimetry
International Nuclear Information System (INIS)
Ayotte, Guylaine; Archambault, Louis; Gingras, Luc; Lacroix, Frederic; Beddar, A. Sam; Beaulieu, Luc
2006-01-01
One way to improve the performance of scintillation dosimeters is to increase the light-collection efficiency at the coupling interfaces of the detector system. We performed a detailed study of surface preparation of scintillating fibers and their coupling with clear optical fibers to minimize light loss and increase the amount of light collected. We analyzed fiber-surface polishing with aluminum oxide sheets, coating fibers with magnesium oxide, and the use of eight different coupling agents (air, three optical gels, an optical curing agent, ultraviolet light, cyanoacrylate glue, and acetone). We prepared 10 scintillating fiber and clear optical fiber light guide samples to test different coupling methods. To test the coupling, we first cut both the scintillating fiber and the clear optical fiber. Then, we cleaned and polished both ends of both fibers. Finally, we coupled the scintillating fiber with the clear optical fiber in either a polyethylene jacket or a V-grooved support depending on the coupling agent used. To produce more light, we used an ultraviolet lamp to stimulate scintillation. A typical series of similar couplings showed a standard deviation in light-collection efficiency of 10%. This can be explained by differences in the surface preparation quality and alignment of the scintillating fiber with the clear optical fiber. Absence of surface polishing reduced the light collection by approximately 40%, and application of magnesium oxide on the proximal end of the scintillating fiber increased the amount of light collected from the optical fiber by approximately 39%. Of the coupling agents, we obtained the best results using one of the optical gels. Because a large amount of the light produced inside a scintillator is usually lost, better light-collection efficiency will result in improved sensitivity
18. Monte Carlo simulation of electron thermalization in scintillator materials: Implications for scintillator nonproportionality
Science.gov (United States)
Prange, Micah P.; Xie, YuLong; Campbell, Luke W.; Gao, Fei; Kerisit, Sebastien
2017-12-01
The lack of reliable quantitative estimates of the length and time scales associated with hot electron thermalization after a gamma-ray induced energy cascade obscures the interplay of various microscopic processes controlling scintillator performance and hampers the search for improved detector materials. We apply a detailed microscopic kinetic Monte Carlo model of the creation and subsequent thermalization of hot electrons produced by gamma irradiation of six important scintillating crystals to determine the spatial extent of the cloud of excitations produced by gamma rays and the time required for the cloud to thermalize with the host lattice. The main ingredients of the model are ensembles of microscopic track structures produced upon gamma excitation (including the energy distribution of the excited carriers), numerical estimates of electron-phonon scattering rates, and a calculated particle dispersion to relate the speed and energy of excited carriers. All these ingredients are based on first-principles density functional theory calculations of the electronic and phonon band structures of the materials. The details of the Monte Carlo model are presented along with the results for thermalization time and distance distributions. These results are discussed in light of previous work. It is found that among the studied materials, calculated thermalization distances are positively correlated with measured nonproportionality. In the important class of halide scintillators, the particle dispersion is found to be more influential than the largest phonon energy in determining the thermalization distance.
19. Monte Carlo simulation of electron thermalization in scintillator materials: Implications for scintillator nonproportionality
Energy Technology Data Exchange (ETDEWEB)
Prange, Micah P. [Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, USA; Xie, YuLong [Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, USA; Campbell, Luke W. [National Security Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, USA; Gao, Fei [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109, USA; Kerisit, Sebastien [Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, USA
2017-12-21
The lack of reliable quantitative estimates of the length and time scales associated with hot electron thermalization after a gamma-ray induced energy cascade obscures the interplay of various microscopic processes controlling scintillator performance and hampers the search for improved detector materials. We apply a detailed microscopic kinetic Monte Carlo model of the creation and subsequent thermalization of hot electrons produced by gamma irradiation of six important scintillating crystals to determine the spatial extent of the cloud of excitations produced by gamma rays and the time required for the cloud to thermalize with the host lattice. The main ingredients of the model are ensembles of microscopic track structures produced upon gamma excitation (including the energy distribution of the excited carriers), numerical estimates of electron-phonon scattering rates, and a calculated particle dispersion to relate the speed and energy of excited carriers. All these ingredients are based on first-principles density functional theory calculations of the electronic and phonon band structures of the materials. Details of the Monte Carlo model are presented along with results for thermalization time and distance distributions. These results are discussed in light of previous work. It is found that among the studied materials, calculated thermalization distances are positively correlated with measured nonproportionality. In the important class of halide scintillators, the particle dispersion is found to be more influential than the largest phonon energy in determining the thermalization distance.
20. Scintillation properties of N2 and CF4 and performances of a scintillating ionization chamber
Science.gov (United States)
Lehaut, G.; Salvador, S.; Fontbonne, J.-M.; Lecolley, F.-R.; Perronnel, J.; Vandamme, Ch.
2015-10-01
In this work, we studied the emission yields, decay times and coincidence resolving times (CRT) of two gases, nitrogen (N2) and tetrafluoromethane (CF4), used for particle detection in the context of fission products measurement. The set-up was made of an ionization chamber and two photomultiplier tubes (PMTs) placed front-to-front on each side of the active zone of the chamber. Using the photomultiplier tubes, the number of photoelectrons (phe) converted at the photocathodes from the scintillation processes in each gas was quantified and the scintillation time spectra were recorded. A scintillation emission yield of 24 phe MeV-1 with a decay time of τd = 2.5 ns in N2, and 225 phe MeV-1 with τd = 6.2 ns for CF4, has been measured. With our set-up, the coincidence resolving time (σ values) between the two PMTs have been measured using alpha particles at 1.4 ns and 0.34 ns for N2 and CF4, respectively.
1. Assessment of nylon 6, 6 nanofibre membrane for microalgae harvesting
Science.gov (United States)
Azizo, Amar Shafrin; Wirzal, Mohd Dzul Hakim; Bilad, Muhammad Roil; Yusoff, Abdull Rahim Mohd
2017-10-01
Pressure driven membrane processes have been proven suitable for the separation of microorganisms in many of biotechnical applications. In this paper, we report the preparation and characterization of a novel nylon 6, 6 nanofibers membranes and applied it for filtration of Chlorella vulgaris broth. Its performance is compared with a phase inverted polyvinylidene fluoride (PVDF) membrane, an established membrane material for this application. The tests on the filterability of both membranes and their harvesting efficiency were conducted. Results show that nanofiber membrane is more hydrophilic (contact angle of zero), and has 45% higher surface pore size and 20% surface pore population that contribute significantly into its higher clean water permeability (of 1018 and 493 l/m2hbar for nanofiber and PVDF membranes respectively). Filterability results show that nanofiber membrane has superior advantages over the phase inverted one: 2-5 times higher in productivity while maintaining similar rejection of 92%. Those results were consistent for three independent filterability tests. This finding confirms the potential application of nanofiber membrane. However, further development with respect to improving its mechanical strength and its ability to be assembled into a membrane module should be critical to serve its promise in this particular application.
2. Experimental Evaluation of PV Inverter Anti-Islanding with Grid Support Functions in Multi-Inverter Island Scenarios
Energy Technology Data Exchange (ETDEWEB)
Hoke, Anderson [National Renewable Energy Lab. (NREL), Golden, CO (United States); Nelson, Austin [National Renewable Energy Lab. (NREL), Golden, CO (United States); Miller, Brian [National Renewable Energy Lab. (NREL), Golden, CO (United States); Chakraborty, Sudipta [National Renewable Energy Lab. (NREL), Golden, CO (United States); Bell, Frances [SolarCity, San Mateo, CA (United States); McCarty, Michael [SolarCity, San Mateo, CA (United States)
2016-07-01
As PV and other DER systems are connected to the grid at increased penetration levels, island detection may become more challenging for two reasons: 1.) In islands containing many DERs, active inverter-based anti-islanding methods may have more difficulty detecting islands because each individual inverter's efforts to detect the island may be interfered with by the other inverters in the island. 2.) The increasing numbers of DERs are leading to new requirements that DERs ride through grid disturbances and even actively try to regulate grid voltage and frequency back towards nominal operating conditions. These new grid support requirements may directly or indirectly interfere with anti-islanding controls. This report describes a series of tests designed to examine the impacts of both grid support functions and multi-inverter islands on anti-islanding effectiveness. Crucially, the multi-inverter anti-islanding tests described in this report examine scenarios with multiple inverters connected to multiple different points on the grid. While this so-called 'solar subdivision' scenario has been examined to some extent through simulation, this is the first known work to test it using hardware inverters. This was accomplished through the use of power hardware-in-the-loop (PHIL) simulation, which allows the hardware inverters to be connected to a real-time transient simulation of an electric power system that can be easily reconfigured to test various distribution circuit scenarios. The anti-islanding test design was a modified version of the unintentional islanding test in IEEE Standard 1547.1, which creates a balanced, resonant island with the intent of creating a highly challenging condition for island detection. Three common, commercially available single-phase PV inverters from three different manufacturers were tested. The first part of this work examined each inverter individually using a series of pure hardware resistive-inductive-capacitive (RLC
3. Membranous nephropathy
Science.gov (United States)
... check for hepatitis B, hepatitis C, and syphilis Complement levels Cryoglobulin test Treatment The goal of treatment ... not as helpful for people with membranous nephropathy. Medicines used treat membranous nephropathy include: Angiotensin-converting enzyme ( ...
4. Scintillation trigger system of the liquid argon neutrino detector
International Nuclear Information System (INIS)
Belikov, S.V.; Gurzhiev, S.N.; Gutnikov, Yu.E.; Denisov, A.G.; Kochetkov, V.I.; Matveev, M.Yu.; Mel'nikov, E.A.; Usachev, A.P.
1994-01-01
This paper presents the organization of the Scintillation Trigger System (STS) for the Liquid Argon Neutrino Detector of the Tagged Neutrino Facility. STS is aimed at the effective registration of the needed neutrino interaction type and production of a fast trigger signal with high time resolution. The fast analysis system of analog signal from the trigger scintillation planes for rejection of the trigger signals from background processes is described. Real scintillation trigger planes characteristics obtained on the basis of the presented data acquisition system are shown. 10 refs., 12 figs., 3 tabs
5. Neutron detector using lithiated glass-scintillating particle composite
Science.gov (United States)
Wallace, Steven [Knoxville, TN; Stephan, Andrew C [Knoxville, TX; Dai, Sheng [Knoxville, TN; Im, Hee-Jung [Knoxville, TN
2009-09-01
A neutron detector composed of a matrix of scintillating particles imbedded in a lithiated glass is disclosed. The neutron detector detects the neutrons by absorbing the neutron in the lithium-6 isotope which has been enriched from the natural isotopic ratio to a commercial ninety five percent. The utility of the detector is optimized by suitably selecting scintillating particle sizes in the range of the alpha and the triton. Nominal particle sizes are in the range of five to twenty five microns depending upon the specific scintillating particle selected.
6. Ionization and scintillation of nuclear recoils in gaseous xenon
Energy Technology Data Exchange (ETDEWEB)
Renner, J., E-mail: [email protected] [Lawrence Berkeley National Laboratory (LBNL), 1 Cyclotron Road, Berkeley, CA 94720 (United States); Department of Physics, University of California, Berkeley, CA 94720 (United States); Gehman, V.M.; Goldschmidt, A.; Matis, H.S.; Miller, T.; Nakajima, Y.; Nygren, D.; Oliveira, C.A.B.; Shuman, D. [Lawrence Berkeley National Laboratory (LBNL), 1 Cyclotron Road, Berkeley, CA 94720 (United States); Álvarez, V. [Instituto de Física Corpuscular (IFIC), CSIC & Universitat de València, Calle Catedrático José Beltrán, 2, 46980 Paterna, Valencia (Spain); Borges, F.I.G. [Departamento de Fisica, Universidade de Coimbra, Rua Larga, 3004-516 Coimbra (Portugal); Cárcel, S. [Instituto de Física Corpuscular (IFIC), CSIC & Universitat de València, Calle Catedrático José Beltrán, 2, 46980 Paterna, Valencia (Spain); Castel, J.; Cebrián, S. [Laboratorio de Física Nuclear y Astropartículas, Universidad de Zaragoza, Calle Pedro Cerbuna 12, 50009 Zaragoza (Spain); Cervera, A. [Instituto de Física Corpuscular (IFIC), CSIC & Universitat de València, Calle Catedrático José Beltrán, 2, 46980 Paterna, Valencia (Spain); Conde, C.A.N. [Departamento de Fisica, Universidade de Coimbra, Rua Larga, 3004-516 Coimbra (Portugal); and others
2015-09-01
Ionization and scintillation produced by nuclear recoils in gaseous xenon at approximately 14 bar have been simultaneously observed in an electroluminescent time projection chamber. Neutrons from radioisotope α-Be neutron sources were used to induce xenon nuclear recoils, and the observed recoil spectra were compared to a detailed Monte Carlo employing estimated ionization and scintillation yields for nuclear recoils. The ability to discriminate between electronic and nuclear recoils using the ratio of ionization to primary scintillation is demonstrated. These results encourage further investigation on the use of xenon in the gas phase as a detector medium in dark matter direct detection experiments.
7. Design and Prototyping of a High Granularity Scintillator Calorimeter
International Nuclear Information System (INIS)
Zutshi, Vishnu
2016-01-01
A novel approach for constructing fine-granularity scintillator calorimeters, based on the concept of an Integrated Readout Layer (IRL) was developed. The IRL consists of a printed circuit board inside the detector which supports the directly-coupled scintillator tiles, connects to the surface-mount SiPMs and carries the necessary front-end electronics and signal/bias traces. Prototype IRLs using this concept were designed, prototyped and successfully exposed to test beams. Concepts and implementations of an IRL carried out with funds associated with this contract promise to result in the next generation of scintillator calorimeters.
8. CsI(Tl) infrared scintillation light yield and spectrum
CERN Document Server
Belogurov, S; Carugno, Giovanni; Conti, E; Iannuzzi, D; Meneguzzo, Anna Teresa
2000-01-01
Infrared emission from CsI(Tl) excited by approx 70 keV electrons was detected with an InGaAs PIN photodiode. Some parameters of infrared scintillation were studied. The emission spectrum is located between 1.55 and 1.70 mu m with a maximum at 1.60 mu m. The light yield of infrared scintillation is (4.9+-0.3)x10 sup 3 photons/MeV. Infrared scintillation caused by 3 MeV alpha-particles is detected as well.
9. Design and Prototyping of a High Granularity Scintillator Calorimeter
Energy Technology Data Exchange (ETDEWEB)
Zutshi, Vishnu [Northern Illinois Univ., DeKalb, IL (United States). Dept. of Physics
2016-03-27
A novel approach for constructing fine-granularity scintillator calorimeters, based on the concept of an Integrated Readout Layer (IRL) was developed. The IRL consists of a printed circuit board inside the detector which supports the directly-coupled scintillator tiles, connects to the surface-mount SiPMs and carries the necessary front-end electronics and signal/bias traces. Prototype IRLs using this concept were designed, prototyped and successfully exposed to test beams. Concepts and implementations of an IRL carried out with funds associated with this contract promise to result in the next generation of scintillator calorimeters.
10. Method for measuring multiple scattering corrections between liquid scintillators
Energy Technology Data Exchange (ETDEWEB)
Verbeke, J.M., E-mail: [email protected]; Glenn, A.M., E-mail: [email protected]; Keefer, G.J., E-mail: [email protected]; Wurtz, R.E., E-mail: [email protected]
2016-07-21
A time-of-flight method is proposed to experimentally quantify the fractions of neutrons scattering between scintillators. An array of scintillators is characterized in terms of crosstalk with this method by measuring a californium source, for different neutron energy thresholds. The spectral information recorded by the scintillators can be used to estimate the fractions of neutrons multiple scattering. With the help of a correction to Feynman's point model theory to account for multiple scattering, these fractions can in turn improve the mass reconstruction of fissile materials under investigation.
11. Modelling of an IR scintillation counter
CERN Document Server
Fraga, M M F; Policarpo, Armando
2000-01-01
A systematic study of the excitation and de-excitation mechanisms in ternary gas mixtures Ar+CO sub 2 +N sub 2 is presented regarding the possibility of developing a proportional scintillation counter based on the detection of the infrared molecular emissions associated with the lowest vibrational states of molecules. The use of visible or near-infrared photons (lambda<1 mu m) for applications like imaging and quality control of microstructure detectors has been reported. In view of these applications we analyse the processes leading to near-infrared emissions in pure argon and give an estimation of the number of photons emitted per electron, at several pressures, as a function of the charge gain.
12. Collimated trans-axial tomographic scintillation camera
International Nuclear Information System (INIS)
1980-01-01
The principal problem in trans-axial tomographic radioisotope scanning is the length of time required to obtain meaningful data. Patient movement and radioisotope migration during the scanning period can cause distortion of the image. The object of this invention is to reduce the scanning time without degrading the images obtained. A system is described in which a scintillation camera detector is moved to an orbit about the cranial-caudal axis relative to the patient. A collimator is used in which lead septa are arranged so as to admit gamma rays travelling perpendicular to this axis with high spatial resolution and those travelling in the direction of the axis with low spatial resolution, thus increasing the rate of acceptance of radioactive events to contribute to the positional information obtainable without sacrificing spatial resolution. (author)
13. A readout system for plastic scintillating fibers
Science.gov (United States)
Akbari, H.; Bao, J.; Chien, C.-Y.; Fenker, H.; Fitzgerald, R.; Fisher, P.; Glaubman, M.; Grimes, A.; Hofer, H.; Horvath, I.; Kaplan, D.; Lanius, K.; Leedom, I.; Macdermott, M.; Mnich, J.; Newman, D.; Orndorff, J.; Pevsner, A.; Reucroft, S.; Rose, J.; Spangler, J.; Spartiotis, C.; Tonisch, F.; Viertel, G.; Waldmeier, S.; Zehnder, L.
1991-05-01
A readout system for plastic scintillating fibers has been developed using a multi-anode microchannel photomultiplier tube operated in a 5 kG magnetic field and the CMOS MX4 microplexer chip. The microchannel photomultiplier tube with an anode array of 10×10 is coupled to an array of fibers using a precise alignment procedure. Each readout unit is capable of sampling signals from 100 fibers simultaneously and multiplexing the analog signals serially with rates of up to 5 MHz. The analog signals are subsequently digitized and subtracted from the pedestals previously stored using a specially designed analog to digital VME module. Such a readout system has many applications in high energy physics, solid state physics, and other fields where a large number of fibers must be read out in short times and at relatively high rates.
14. Elevator mechanism and method for scintillation detectors
International Nuclear Information System (INIS)
Frank, E.
1975-01-01
An elevator mechanism and method for raising and lowering radioactive samples through a shielded vertical counting chamber in a benchtop scintillation detector is described. The elevator mechanism adds little or nothing to the height of the detector by using an elongated flexible member such as a metal tape secured to the bottom of the elevator platform and extending downwardly through the counting chamber and its bottom shielding, where the tape is bent laterally for connection to a drive means. In the particular embodiment illustrated, the tape is bent laterally below the bottom shielding for the counting chamber, and then upwardly along or through one side of the shielding to a reel at the top of the shielding. The tape is wound onto the reel, and the reel is driven by a reversible motor which winds and unwinds the tape on the reel to raise and lower the elevator platform
15. Liquid xenon/krypton scintillation calorimeter
International Nuclear Information System (INIS)
Akimov, D.Yu.; Bolozdynya, A.I.; Brastilov, A.D.
1994-01-01
A scintillating LXe/LKr electromagnetic calorimeter has been built at the ITEP and tested at the BATES (MIT) accelerator. The detector consists of PMT matrix and 45 light collecting cells made of aluminized 50 microns Mylar partially covered with p-terphenyl as a wavelength-shifter. Each pyramidal cell has (2.1 x 2.1) x 40 x (4.15 x 4.15) cm dimensions and is viewed by FEU-85 glass-window photomultiplier. The detector has been exposed at 106-348 MeV electron beam. The energy resolution σ E /E ≅ 5% √ E at 100 - 350 MeV range in LXe, the coordinate resolution τ x ≅ 0.7 cm, the time resolution for single cell ≅ 0.6 ns have been obtained. Possible ways to improve energy resolution are discussed. 8 refs., 15 figs
16. Quench determination in liquid scintillation counting systems
International Nuclear Information System (INIS)
Anon.
1978-01-01
A method and apparatus for measuring the degree of quench in a liquid scintillation sample by irradiating the sample with a standard source, such as a cesium-137 gamma source, to produce a Compton scattered electron distribution exhibiting a Compton edge configuration as the leading edge are described. For increasing the quench levels in the sample, the Compton edge shifts to lower pulse height values and the extent of this shift is indicative of the degree of quench. To measure the degree of quench, a unique point on the Compton edge, namely the point at which the second derivative of the edge is zero (i.e. the inflection point), is measured for the quenched sample and the pulse height value corresponding to the inflection point is determined. The pulse height value is compared with the pulse height value determined for a calibration standard in a similar manner, the difference in pulse height values indicating the degree of quench
17. Spectroscopic neutron detection using composite scintillators
Science.gov (United States)
Jovanovic, I.; Foster, A.; Kukharev, V.; Mayer, M.; Meddeb, A.; Nattress, J.; Ounaies, Z.; Trivelpiece, C.
2016-09-01
Shielded special nuclear material (SNM), especially highly enriched uranium, is exceptionally difficult to detect without the use of active interrogation (AI). We are investigating the potential use of low-dose active interrogation to realize simultaneous high-contrast imaging and photofission of SNM using energetic gamma-rays produced by low-energy nuclear reactions, such as 11B(d,nγ)12C and 12C(p,p‧)12C. Neutrons produced via fission are one reliable signature of the presence of SNM and are usually identified by their unique timing characteristics, such as the delayed neutron die-away. Fast neutron spectroscopy may provide additional useful discriminating characteristics for SNM detection. Spectroscopic measurements can be conducted by recoil-based or thermalization and capture-gated detectors; the latter may offer unique advantages since they facilitate low-statistics and event-by-event neutron energy measurements without spectrum unfolding. We describe the results of the development and characterization of a new type of capture-gated spectroscopic neutron detector based on a composite of scintillating polyvinyltoluene and lithium-doped scintillating glass in the form of millimeter-thick rods. The detector achieves >108 neutron-gamma discrimination resulting from its geometric properties and material selection. The design facilitates simultaneous pulse shape and pulse height discrimination, despite the fact that no materials intrinsically capable of pulse shape discrimination have been used to construct the detector. Accurate single-event measurements of neutron energy may be possible even when the energy is relatively low, such as with delayed fission neutrons. Simulation and preliminary measurements using the new composite detector are described, including those conducted using radioisotope sources and the low-dose active interrogation system based on low-energy nuclear reactions.
18. Production of the Large-area Plastic Scintillator for Beta-ray Detection using Epoxy Resin
Energy Technology Data Exchange (ETDEWEB)
Nam, Jong Soo; Choi, Yong Seok; Hong, Sang Bum; Seo, Bum Kyung; Moon, Jei Kwon; Choi, Jong Won [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2016-10-15
In this study, we prepared a plastic scintillator whose manufacturing process is simple and can be freely shaped. A thin plate of the plastic scintillator was manufactured using epoxy resin as a polymer. The plastic scintillator was made by mixing epoxy resin and organic scintillators under various conditions. The optimal mixture ratio to prepare the plastic scintillator was derived from the above results. Using the derived results, we made the large-area plastic scintillator which can quickly measure the contamination site and evaluated characteristics of the large-area plastic scintillator in the laboratory. A thin plate of a plastic scintillator with a simple preparation process can be freely shaped using epoxy resin and organic scintillators such as PPO and POPOP. PPO emits scintillation of light in the ultraviolet range, and POPOP is a wave shifter for moving the wavelength responsible for the PMT. The mixture ratio of PPO and POPOP was determined using their emission spectra. The optimal weight percentage of PPO and POPOP in an organic scintillator was determined to be 0.2 wt%:0.01 wt%. Based on the above results, the large-area plastic scintillator of the window size of a typical pancake-type αβ surface contamination counter was prepared. We want to evaluate the characteristics of the large-area plastic scintillator. However, there were the difficulties in evaluating characteristics of the large-area plastic scintillator. The cross-sectional area of the large-area plastic scintillator is significantly different to PMT.
19. Membrane Biophysics
CERN Document Server
2013-01-01
Physics, mathematics and chemistry all play a vital role in understanding the true nature and functioning of biological membranes, key elements of living processes. Besides simple spectroscopic observations and electrical measurements of membranes we address in this book the phenomena of coexistence and independent existence of different membrane components using various theoretical approaches. This treatment will be helpful for readers who want to understand biological processes by applying both simple observations and fundamental scientific analysis. It provides a deep understanding of the causes and effects of processes inside membranes, and will thus eventually open new doors for high-level pharmaceutical approaches towards fighting membrane- and cell-related diseases.
20. Recent developments in plastic scintillators with pulse shape discrimination
Science.gov (United States)
Zaitseva, N. P.; Glenn, A. M.; Mabe, A. N.; Carman, M. L.; Hurlbut, C. R.; Inman, J. W.; Payne, S. A.
2018-05-01
The paper reports results of studies conducted to improve scintillation performance of plastic scintillators capable of neutron/gamma pulse-shape discrimination (PSD). Compositional modifications made with the polymer matrix improved physical stability, allowing for increased loads of the primary dye that, in combination with selected secondary dyes, provided enhanced PSD especially important for the lower energy ranges. Additional measurements were made with a newly-introduced PSD plastic EJ-276, that replaces the first commercially produced EJ-299. Comparative studies conducted with the new materials and EJ-309 liquids at large scale (up to 10 cm) show that current plastics may provide scintillation and PSD performance sufficient for the replacement of liquid scintillators. Comparison to stilbene single crystals compliments the information about the status of the solid-state materials recently developed for fast neutron detection applications.
1. Proton damage measurements of rare earth oxide scintillators
International Nuclear Information System (INIS)
Hollerman, W.A.; Fisher, J.H.; Shelby, G.A.; Holland, L.R.; Jenkins, G.M.
1990-01-01
This paper reports on the development of a measurement technique to determine the degradation in light output under exposure to 3 MeV protons. The rare earth oxide scintillators included Gd 2 O 2 S doped with Pr, Tb, and Eu; Y 2 O 2 S doped with Tb and Eu; Y 3 Al 5 O 12 (YAG) doped with Ce; and ZnS doped with Ag. Four scintillator samples were painted on a rotable water cooled turret used to measure the proton beam current with thermocouples for temperature monitoring. The data acquisition and storage system consists of an ACRO module interfaced to a Macintosh SE/30 computer running LabVIEW software. Results indicate that the YAG doped with Ce scintillator coating withstood a proton dose an order of magnitude larger than that tolerated by the other phosphor compounds. This fact has significant implications for the use of this material for experimental scintillator applications
2. Photonic Crystals: Enhancing the Light Output of Scintillation Based Detectors
CERN Document Server
Knapitsch, Arno Richard
A scintillator is a material which emits light when excited by ionizing radiation. Such materials are used in a diverse range of applications; From high energy particle physics experiments, X-ray security, to nuclear cameras or positron emission tomography. Future high-energy physics (HEP) experiments as well as next generation medical imaging applications are more and more pushing towards better scintillation characteristics. One of the problems in heavy scintillating materials is related to their high index of refraction. As a consequence, most of the scintillation light produced in the bulk material is trapped inside the crystal due to total internal reflection. The same problem also occurs with light emitting diodes (LEDs) and has for a long time been considered as a limiting factor for their overall efficiency. Recent developments in the area of nanophotonics were showing now that those limitations can be overcome by introducing a photonic crystal (PhC) slab at the outcoupling surface of the substrate. P...
3. Inorganic scintillators for detector systems physical principles and crystal engineering
CERN Document Server
Lecoq, Paul; Korzhik, Mikhail
2017-01-01
This second edition features new chapters highlighting advances in our understanding of the behavior and properties of scintillators, and the discovery of new families of materials with light yield and excellent energy resolution very close to the theoretical limit. The book focuses on the discovery of next-generation scintillation materials and on a deeper understanding of fundamental processes. Such novel materials with high light yield as well as significant advances in crystal engineering offer exciting new perspectives. Most promising is the application of scintillators for precise time tagging of events, at the level of 100 ps or higher, heralding a new era in medical applications and particle physics. Since the discovery of the Higgs Boson with a clear signature in the lead tungstate scintillating blocks of the CMS Electromagnetic Calorimeter detector, the current trend in particle physics is toward very high luminosity colliders, in which timing performance will ultimately be essential to mitigating...
4. Scintillation effects on radio wave propagation through solar corona
Science.gov (United States)
Ho, C. M.; Sue, M. K.; Bedrossian, A.; Sniffin, R. W.
2002-01-01
When RF waves pass through the solar corona and solar wind regions close to the Sun, strong scintillation effects appear at their amplitude, frequency and phase, especially in the regions very close to the Sun (less than 4 solar radius).
5. Energy response and reaction losses in plastic scintillators
International Nuclear Information System (INIS)
Papandreou, Z.; Lolos, G.J.; Huber, G.M.; Cormier, J.C.; Naqvi, S.I.H.; Mathie, E.L.; Jones, G.; Trelle, R.P.; Alanoglu, X.; Orfanakos, S.
1987-12-01
The energy dependence of the scintillation response (light output) of plastic scintillator BC400 has been investigated for protons in the energy region of 60 to 220 MeV. In this region the scintillation exhibits a linear response, as well as a noticeable difference in the light output between stopping and passing-through (transmission) protons. A comparison between our results and theoretical calculations is presented. Losses due to edge effects have been separated from losses due to the bona-fide reaction of protons in the scintillator with the aid of Multi-Wire Proportional Chamber (MWPC) trajectory information. The number of events associated with reaction losses was found to range from 10% to 25% of the total number of events, depending on the incident proton kinetic energy. (Author) (12 refs., tab., 2 figs.)
6. A sensitivity analysis approach to optical parameters of scintillation detectors
International Nuclear Information System (INIS)
Ghal-Eh, N.; Koohi-Fayegh, R.
2008-01-01
In this study, an extended version of the Monte Carlo light transport code, PHOTRACK, has been used for a sensitivity analysis to estimate the importance of different wavelength-dependent parameters in the modelling of light collection process in scintillators
7. Mechanical deformation effect on CsI(Tl) scintillators efficiency
International Nuclear Information System (INIS)
Gayshan, V.; Boyarintsev, A.; Gektin, A.; Zosim, D.
2003-01-01
Due to the technological limitations in scintillation crystal growth and machining afterwards, crystals always contain certain internal defects and nonuniform distribution of intrinsic stresses. This work is directed to study the effect of CsI(Tl) mechanical deformation on their scintillation efficiency. It is shown that light output changes depend on the type of deformation (shock, steady deformation) and crystallographic orientation of specimen. The value of the phenomenon reaches up to 20% of the CsI(Tl) light output. Stress relaxation is the reason for the scintillator light output recovery. For CsI(Tl) scintillator mechanical deformation effects on light output will significantly decrease in the first 7-10 days after application of the stress and might completely disappear within 30-40 days
8. High-density scintillating glasses for a proton imaging detector
Science.gov (United States)
Tillman, I. J.; Dettmann, M. A.; Herrig, V.; Thune, Z. L.; Zieser, A. J.; Michalek, S. F.; Been, M. O.; Martinez-Szewczyk, M. M.; Koster, H. J.; Wilkinson, C. J.; Kielty, M. W.; Jacobsohn, L. G.; Akgun, U.
2017-06-01
High-density scintillating glasses are proposed for a novel proton-imaging device that can improve the accuracy of the hadron therapy. High-density scintillating glasses are needed to build a cost effective, compact calorimeter that can be attached to a gantry. This report summarizes the study on Europium, Terbium, and Cerium-doped scintillating glasses that were developed containing heavy elements such as Lanthanum, Gadolinium, and Tungsten. The density of the samples reach up to 5.9 g/cm3, and their 300-600 nm emission overlaps perfectly with the peak cathode sensitivity of the commercial photo detectors. The developed glasses do not require any special quenching and can be poured easily, which makes them a good candidate for production in various geometries. Here, the glass making conditions, preliminary tests on optical and physical properties of these scintillating, high-density, oxide glasses developed for a novel medical imaging application are reported.
9. Scintillation Particle Detectors Based on Plastic Optical Fibres and Microfluidics
CERN Document Server
Mapelli, Alessandro; Renaud, Philippe
2011-01-01
This thesis presents the design, development, and experimental validation of two types of scintillation particle detectors with high spatial resolution. The first one is based on the well established scintillating fibre technology. It will complement the ATLAS (A Toroidal Large ApparatuS) detector at the CERN Large Hadron Collider (LHC). The second detector consists in a microfabricated device used to demonstrate the principle of operation of a novel type of scintillation detector based on microfluidics. The first part of the thesis presents the work performed on a scintillating fibre tracking system for the ATLAS experiment. It will measure the trajectory of protons elastically scattered at very small angles to determine the absolute luminosity of the CERN LHC collider at the ATLAS interaction point. The luminosity of an accelerator characterizes its performance. It is a process-independent parameter that is completely determined by the properties of the colliding beams and it relates the cross section of a ...
10. Inorganic Scintillators for Detector Systems Physical Principles and Crystal Engineering
CERN Document Server
AUTHOR|(CDS)2068219; Gektin, Alexander; Korzhik, Mikhail; Pédrini, Christian
2006-01-01
The development of new scintillators as components of modern detector systems is increasingly defined by the end user's needs. This book provides an introduction to this emerging topic at the interface of physics and materials sciences, with emphasis on bulk inorganic scintillators. After surveying the end user's needs in a vast range of applications, ranging from astrophysics to industrial R & D, the authors move on to review scintillating mechanisms and the properties of the most important materials used. A chapter on crystal engineering and examples of recent developments in the field of high-energy physics and medical imaging introduce the reader to the practical aspects. This book will benefit researchers and scientists working in academic and industrial R & D related to the development of scintillators.
11. Multilayer Scintillation Detector for Nuclear Physics Monitoring of Space Weather
Science.gov (United States)
Batischev, A. G.; Aleksandrin, S. Yu.; Gurov, Yu. B.; Koldashov, S. V.; Lapushkin, S. V.; Mayorov, A. G.
The physical characteristics of the multilayer scintillation spectrometer (MSS) for identification and energy measurement of cosmic electrons, positrons and nuclei are considered in this paper. This spectrometer is made on the basis of several plastic scintillator plates with various thick viewed by photomultipliers. Two upper layers are strips of orthogonal scintillators. The nuclei energy measurement range is 3 - 100 MeV/nucleon. Spectrometer is planning for space weather monitoring and investigation of solar-magnetospheric and geophysics effects on satellite. MSS time resolution is about 1 microsecond and it can measure the time profiles of fast processes in the Earth's magnetosphere. Spectrometer experimental characteristics were estimated by means of computer simulation. The ionization loss fluctuations, ion charge exchange during pass through detector and, especially, scintillation quenching effect (Bircs effect) were taken into account in calculations.
12. Set of counts by scintillations for atmospheric samplings
International Nuclear Information System (INIS)
Appriou, D.; Doury, A.
1962-01-01
The author reports the development of a scintillation-based counting assembly with the following characteristics: a photo-multiplier with a wide photo-cathode, a thin plastic scintillator for the counting of beta + alpha (and possibility of mounting an alpha scintillator), a relatively small own motion with respect to activities to be counted, a weakly varying efficiency. The authors discuss the counting objective, present equipment tests (counter, proportional amplifier and pre-amplifier, input drawer). They describe the apparatus operation, discuss the selection of scintillators, report the study of the own movement (electron-based background noise, total background noise, background noise reduction), discuss counts (influence of the external source, sensitivity to alpha radiations, counting homogeneity, minimum detectable activity) and efficiencies
13. Use of pliable bags in liquid scintillation counting
International Nuclear Information System (INIS)
Simonnet, G.; Jacquet, M.A.; Sharif, A.; Engler, R.
1981-01-01
Pliable plastic bags have been used to replace glass or plastic vials for liquid scintillation counting. The two major advantages of this method are the lower cost of the plastic bags and the fact that, per sample, the radioactive waste is significantly reduced. The following parameters have been checked: the impermeability of the bags to various scintillator mixtures and the fact that neither the irregular shape of the bags nor their position in the counting chamber had any effect on the results of the counting. The latter was also constant with time, at least over a period of 10 days. The technique has been used to count the radioactivity of 3 H-DNA precipitates prepared from bacteria and lymphocytes and deposited on filters impregnated with only 200 μl scintillator. It is a method that can be applied to the counting of any samples deposited on filters and insoluble in scintillator. (author)
14. Search of new scintillation materials for nuclear medicine application
CERN Document Server
Korzhik, M V
2000-01-01
Oxide crystals have a great potential to develop new advanced scintillation materials which are dense, fast, and bright. This combination of parameters, when combined to affordable price, gives a prospect for materials to be applied in nuclear medicine devices. Some of them have been developed for the last two decades along the line of rear-earth (RE) garnet (RE/sub 3/Al/sub 5/O/sub 12/) oxiorthosilicate (RE/sub 2/SiO/sub 5/) and perovskite (REAlO/sub 3/) crystals doped with Ce ions. Among recently developed oxide materials the lead tungstate scintillator (PWO) becomes the most used scintillation material in high energy physics experiments due to its application in CMS and ALICE experiments at LHC. In this paper we discuss scintillation properties of some new heavy compounds doped with Ce as well as light yield improvement of PWO crystals to apply them in low energy physics and nuclear medicine. (18 refs).
15. Final LDRD report : advanced plastic scintillators for neutron detection.
Energy Technology Data Exchange (ETDEWEB)
Vance, Andrew L.; Mascarenhas, Nicholas; O' Bryan, Greg; Mrowka, Stanley
2010-09-01
This report summarizes the results of a one-year, feasibility-scale LDRD project that was conducted with the goal of developing new plastic scintillators capable of pulse shape discrimination (PSD) for neutron detection. Copolymers composed of matrix materials such as poly(methyl methacrylate) (PMMA) and blocks containing trans-stilbene (tSB) as the scintillator component were prepared and tested for gamma/neutron response. Block copolymer synthesis utilizing tSBMA proved unsuccessful so random copolymers containing up to 30% tSB were prepared. These copolymers were found to function as scintillators upon exposure to gamma radiation; however, they did not exhibit PSD when exposed to a neutron source. This project, while falling short of its ultimate goal, demonstrated the possible utility of single-component, undoped plastics as scintillators for applications that do not require PSD.
16. Liquid scintillation cocktails comparison for tritium contamination measurements
International Nuclear Information System (INIS)
Bazzarri, S.; Belloni, P.
1996-01-01
Liquid scintillation counting is one of the most used techniques for the measurements of tritium contamination. Until few years ago a problem related to this kind of measurement was the potential toxicity of the liquid cocktails used to produce the required scintillation. Some new products that guarantee an almost negligible impact on the environment and that are no longer toxic for the operators are now available. Some of this new scintillation cocktail are suitable to be used for tritium measurement. Due to the great benefit from the health point of view of these new materials a test of their scintillation performance has been done at the ENEA centers to select the product having the best characteristics for tritium measurement. (author)
17. Comparison of the methods for determination of scintillation light yield
CERN Document Server
Sysoeva, E; Zelenskaya, O
2002-01-01
One of the most important characteristics of scintillators is the light yield. It depends not only on the properties of scintillators, but also on the conditions of measurements. Even for widely used crystals, such as alkali halide scintillators NaI(Tl) and CsI(Tl), light yield data, obtained by various authors, are different. Therefore, it is very important to choose the convenient method of the light yield measurements. In the present work, methods for the determination of the physical light yield, based on measurements of pulse amplitude, single-electron pulses and intrinsic photomultiplier resolution are discussed. These methods have been used for the measurements of light yield of alkali halide crystals and oxide scintillators. Repeatability and reproducibility of results were determined. All these methods are rather complicated in use, not for measurements, but for further data processing. Besides that, they demand a precise determination of photoreceiver's parameters, as well as determination of light ...
18. Large liquid-scintillator trackers for neutrino experiments
CERN Document Server
Benussi, L; D'Ambrosio, N; Déclais, Y; Dupraz, J P; Fabre, Jean-Paul; Fanti, V; Forton, E; Frekers, D; Frenkel, A; Girerd, C; Golovkin, S V; Grégoire, G; Harrison, K; Jonkmans, G; Jonsson, P; Katsanevas, S; Kreslo, I; Marteau, J; Martellotti, G; Martínez, S; Medvedkov, A M; Moret, G; Niwa, K; Novikov, V; Van Beek, G; Penso, G; Vasilchenko, V G; Vuilleumier, J L; Wilquet, G; Zucchelli, P; Kreslo, I E
2002-01-01
Results are given on tests of large particle trackers for the detection of neutrino interactions in long-baseline experiments. Module prototypes have been assembled using TiO$_2$-doped polycarbonate panels. These were subdivided into cells of $\\sim 1$~cm$^2$ cross section and 6~m length, filled with liquid scintillator. A wavelength-shifting fibre inserted in each cell captured a part of the scintillation light emitted when a cell was traversed by an ionizing particle. Two different fibre-readout systems have been tested: an optoelectronic chain comprising an image intensifier and an Electron Bombarded CCD (EBCCD); and a hybrid photodiode~(HPD). New, low-cost liquid scintillators have been investigated for applications in large underground detectors. Testbeam studies have been performed using a commercially available liquid scintillator. The number of detected photoelectrons for minimum-ionizing particles crossing a module at different distances from the fibre readout end was 6 to 12 with the EBCCD chain and ...
19. Is radical surgery of an inverted papilloma of the maxillary sinus obsolete? a case report
Directory of Open Access Journals (Sweden)
Vedat Yildirim
2016-12-01
Full Text Available Abstract Background Sinonasal inverted papilloma is a locally aggressive tumor arising from the Schneiderian membrane which lines the nasal cavity and paranasal sinuses. Aggressive surgical approaches, such as lateral rhinotomy, were used until recently for complete removal of the inverted papilloma. Currently, endoscopic resection is the gold standard in the treatment of inverted papilloma. However, there are situations that justify an open approach. For example there are studies that report a higher postoperative recurrence rate after endonasal endoscopic resection, particularly in the treatment of recurrent diseases. While endoscopic resection performed by an experienced surgeon is definitely a minimally invasive therapy, an open approach is not necessarily associated with functional and aesthetic disadvantages. This case report describes the treatment of inverted papilloma by an open approach. This has been described before but the new gold standard of endoscopic resection has to be taken into account before any treatment decision is made nowadays. Case presentation Contrast-enhanced magnetic resonance imaging of the head and neck area was indicated in a 72-year-old white German man who presented with suspected squamous cell carcinoma of his lower lip. Magnetic resonance imaging additionally revealed a 3×2 cm2 polycyclic arranged mucosal thickening with cystic and solid contrast affine shares at the antral laterocaudal area of his right maxillary sinus, extending from his right lateral nasal wall to his maxillary sinus floor. He received antral polypectomy with medial maxillectomy via a unilateral LeFort I osteotomy approach. His pterygoid plate was preserved. A histological examination demonstrated a tumor composed of hyperplastic squamous epithelium protruding into the stroma (surface epithelial cells grew downward into the underlying supportive tissue, thus producing a grossly convoluted cerebriform appearance. Two weeks later, the
20. Electric machine and current source inverter drive system
Science.gov (United States)
Hsu, John S
2014-06-24
A drive system includes an electric machine and a current source inverter (CSI). This integration of an electric machine and an inverter uses the machine's field excitation coil for not only flux generation in the machine but also for the CSI inductor. This integration of the two technologies, namely the U machine motor and the CSI, opens a new chapter for the component function integration instead of the traditional integration by simply placing separate machine and inverter components in the same housing. Elimination of the CSI inductor adds to the CSI volumetric reduction of the capacitors and the elimination of PMs for the motor further improve the drive system cost, weight, and volume.
1. Intelligence Controller for STATCOM Using Cascaded Multilevel Inverter
Directory of Open Access Journals (Sweden)
C. C. Asir Rajan
2010-01-01
Full Text Available This paper presents a special gating pattern swapping technique for cascaded multilevel inverter, which is used for STATCOM.By using this technique besides minimizing the harmonic level, the inverter unit fundamental output voltages areequalized. Therefore, all the inverter units in each phase leg can equally share the exchanged active and reactive powerwith the utility grid. This greatly helps the dc-link voltages balancing control. PI Control is employed for improving performance.Fuzzy control is employed to the system for enhancing transient stability. The performance is analyzed usingdigital simulation.
2. Asymmetrical and symmetrical embedded Z-source inverters
DEFF Research Database (Denmark)
Gao, F.; Loh, P.C.; Li, D.
2011-01-01
This study presents two types of embedded Z-source inverters with each type further divided into asymmetrical and symmetrical realisations. Being different from their traditional counterparts, the presented inverters have their dc sources inserted within their X-shaped impedance networks so...... ends, which indirectly translates to a lowering of overall system cost. These noted advantages are indeed appropriate for applications like photovoltaic and fuel cell energy harnessing, and have already been confirmed in simulation and experimentally using a laboratory-implemented inverter prototype....
3. Flash Welding Control by Use of PWM Inverter Power Supply
Science.gov (United States)
Nagura, Kouki; Sato, Yukihiko; Yamamura, Naoki; Ishida, Muneaki
The flash welding is characterized by the high quality, the high production efficiency and the large sectional area welding, and is used to weld rails and hot coils in shop welding mainly. In order to realize high accuracy and high response control of flash welding, the inverter technology has been applied to flash welding in this study. In this paper, a method of process control combined with inverter flash control and mechanical control is proposed. Experiment results of the proposed process control combined with inverter flash control and mechanical control are presented.
4. Component-Minimized Buck-Boost Voltage Source Inverters
DEFF Research Database (Denmark)
Gao, F.; Loh, P.C.; Blaabjerg, Frede
2007-01-01
. In order to form a distinct neutral potential in the corresponding voltage boost circuitry for correct B4 inverter operation, necessary modifications are derived step by step. The resulted dc networks with symmetrical placement of passive components allow complete charging and equal energy distribution...... semiconductors. Besides the advantage of reduced active components, buck-boost B4 inverters use a little more passive components when compared with buck-boost B6 inverters, which would allow a selectable tradeoff in practice. Moreover, analysis for discontinuous conduction mode of inductor current reveals...
5. Power Inverter Topologies for Photovoltaic Modules - A Review
DEFF Research Database (Denmark)
Kjær, Søren Bækhøj; Pedersen, John Kim; Blaabjerg, Frede
2002-01-01
This review-paper focuses on the latest development of inverters for photovoltaic AC-Modules. The power range for these inverters is usually within 90 Watt to 500 Watt, which covers the most commercial photovoltaic-modules. Self-commutated inverters have replaced the grid-commutated ones. The same...... is true for the bulky low-frequency transformers versus the high-frequency transformers, which are used to adapt the voltage level. The AC-Module provides a modular design and a flexible behaviour in various grid conditions. It hereby opens the market for photovoltaic-power for everyone at a low cost due...
6. Discontinuous interleaving of parallel inverters for efficiency improvement
DEFF Research Database (Denmark)
2017-01-01
Interleaved switching of parallel inverters has previously been proposed for efficiency/size improvements of grid connected three-phase inverters. This paper proposes a novel interleaving method which practically eliminates insulated gate bipolar transistor (IGBT) turn-on losses and drastically...... reduces diode reverse recovery losses. The reduction in switching losses are obtained by interleaving two parallel inverter branches so that only one branch conducts the load current at a time. By placing saturable inductors between the parallel branches, soft switching may be obtained, and thereby...
7. Closed-loop waveform control of boost inverter
DEFF Research Database (Denmark)
Zhu, Guo Rong; Xiao, Cheng Yuan; Wang, Haoran
2016-01-01
The input current of single-phase inverter typically has an AC ripple component at twice the output frequency, which causes a reduction in both the operating lifetime of its DC source and the efficiency of the system. In this paper, the closed-loop performance of a proposed waveform control method...... to eliminate such a ripple current in boost inverter is investigated. The small-signal stability and the dynamic characteristic of the inverter system for input voltage or wide range load variations under the closed-loop waveform control method are studied. It is validated that with the closedloop waveform...
8. Ground Fault Overvoltage With Inverter-Interfaced Distributed Energy Resources
Energy Technology Data Exchange (ETDEWEB)
Ropp, Michael; Hoke, Anderson; Chakraborty, Sudipta; Schutz, Dustin; Mouw, Chris; Nelson, Austin; McCarty, Michael; Wang, Trudie; Sorenson, Adam
2017-04-01
Ground Fault Overvoltage can occur in situations in which a four-wire distribution circuit is energized by an ungrounded voltage source during a single phase to ground fault. The phenomenon is well-documented with ungrounded synchronous machines, but there is considerable discussion about whether inverters cause this phenomenon, and consequently whether inverters require effective grounding. This paper examines the overvoltages that can be supported by inverters during single phase to ground faults via theory, simulation and experiment, identifies the relevant physical mechanisms, quantifies expected levels of overvoltage, and makes recommendations for optimal mitigation.
9. A PWM transistor inverter for an ac electric vehicle drive
Science.gov (United States)
Slicker, J. M.
1981-01-01
A prototype system consisting of closely integrated motor, inverter, and transaxle has been built in order to demonstrate the feasibility of a three-phase ac transistorized inverter for electric vehicle applications. The microprocessor-controlled inverter employs monolithic power transistors to drive an oil-cooled, three-phase induction traction motor at a peak output power of 30 kW from a 144 V battery pack. Transistor safe switching requirements are discussed, and a circuit is presented for recovering trapped snubber inductor energy at transistor turn-off.
10. LCCT-derived three-level three-phase inverters
DEFF Research Database (Denmark)
Shults, Tatiana; Husev, Oleksandr; Blaabjerg, Frede
2017-01-01
Solutions for a family of the novel three-level neutral-point-clamped (NPC) inductor-capacitor-capacitor-transformer (LCCT)-derived three-phase inverters are described and compared. Component design guidelines and steady state analysis, current and voltage waveforms are given. The authors......' simulation results confirm the theoretical predictions. It was found that an asymmetrical three-level NPC LCCT-derived inverter with a single diode in the impedance source network is the most promising solution. Experimental results for an asymmetrical three-level NPC LCCT-derived inverter with a single...
11. An iterative method to invert the LTSn matrix
Energy Technology Data Exchange (ETDEWEB)
Cardona, A.V.; Vilhena, M.T. de [UFRGS, Porto Alegre (Brazil)
1996-12-31
Recently Vilhena and Barichello proposed the LTSn method to solve, analytically, the Discrete Ordinates Problem (Sn problem) in transport theory. The main feature of this method consist in the application of the Laplace transform to the set of Sn equations and solve the resulting algebraic system for the transport flux. Barichello solve the linear system containing the parameter s applying the definition of matrix invertion exploiting the structure of the LTSn matrix. In this work, it is proposed a new scheme to invert the LTSn matrix, decomposing it in blocks and recursively inverting this blocks.
12. Detection of {sup 8}B solar neutrinos in liquid scintillators
Energy Technology Data Exchange (ETDEWEB)
Ianni, A [Laboratori Nazionali del Gran Sasso and INFN, I-67010 Assergi (Italy); Montanino, D [Dipartimento di Fisica, Universita' di Lecce and INFN, I-73100 Lecce (Italy); Villante, F L [Dipartimento di Fisica, Universita di Ferrara and INFN, I-44100 Ferrara (Italy)
2006-05-15
We show that liquid organic scintillator detectors (e. g., KamLAND and Borexino) can measure the {sup 8}B solar neutrino flux by means of the {nu}{sub e} charged current interaction with the {sup 13}C nuclei naturally contained in the scintillators. The neutrino events can be identified by exploiting the time and space coincidence with the subsequent decay of the produced {sup 13}N nuclei.
13. Development of water radiocontamination monitor using a plastic scintillator detector
International Nuclear Information System (INIS)
1990-01-01
An alpha, beta and gamma radiation water monitor was developed using a plastic scintillator detector with a sensitivity level of 15 bplastic scintillator detector with a sensitivity level of 15 Bq.L -1 and a counting efficiency of 25% for 131 I. It was proposed to be used in the radiation monitoring program of the research reactor swimming-pool of Sao Paulo. A simplified design and some properties of this monitor are presented. (author) [pt
14. Scintillator for radiation detection and process for producing the same
International Nuclear Information System (INIS)
Ishii, M.; Akiyama, S.; Ishibashi, H.
1985-01-01
A scintillator for radiation detection obtained by coating a light reflective material in a thickness of 50 to 150 μm by a screen printing method on the surface of a solid scintillator material substrate is excellent in uniformity, dimensional accuracy with high light output. When the light reflective material layer is covered with a synthetic resin film, adhesive strength of the light reflective material layer to the substrate is increased remarkably
15. Multiple event 2D image intensifier scintillation detector
International Nuclear Information System (INIS)
Thieberger, P.; Wegner, H.E.; Lee, R.C.
1981-01-01
An image intensifier scintillation detector has been developed for the simultaneous detection of multiple light or heavy ions down to very low energies. The relative X-Y positions of each ion are read out by digitization of a television image of the light amplified scintillations. The maximum data rate is limited by the present television scan speed to 15 multiple events per second and to about one event second by the microcomputer presently used to store and process the data. (orig.)
16. Performance studies of scintillating ceramic samples exposed to ionizing radiation
CERN Document Server
Dissertori, G; Nessi-Tedaldi, F; Wallny, R
2014-01-01
Scintillating ceramics are a promising, new development for various applications in science and industry. Their application in calorimetry for particle physics experiments is expected to involve an exposure to high levels of ionizing radiation. In this paper, changes in performance have been measured for scintillating ceramic samples of different composition after exposure to penetrating ionizing radiation up to a dose of 38 kGy. 2012 IEEE Nuclear Science Symposium Conference Record
17. Simulation study of liquid scintillator based 4π neutron detector
International Nuclear Information System (INIS)
Banerjee, K.; Kundu, S.; Bhattacharya, C.; Dey, A.; Bhattacharya, S.
2004-01-01
Neutron multiplicity detectors play an important role in deciphering the complexities of intermediate energy nucleus-nucleus reactions. Several neutron multiplicity detectors are in operation. As part of the super conducting cyclotron utilization project, it has been planned to make one liquid scintillator based neutron multiplicity detector at VECC, Kolkata. Here reported are initial results of the simulation study of the characteristics of a large liquid scintillator based neutron multiplicity detector
18. Liquid scintillators and composites in fast neutron detection
Science.gov (United States)
Iwanowska, J.; Swiderski, L.; Moszynski, M.
2012-04-01
Helium-3 world crisis requires a development of new methods of neutron detection to replace commonly used 3He proportional counters. One of the option is application of liquid scintillators widely used in detection of fast neutrons, mostly in physics experiments, especially in applications where large volumes are required. Moreover, recently studied 10B loaded liquid scintillators cover detection of neutrons down to thermal energy. The several years' studies of liquid scintillators in our laboratory, brought us a knowledge about their efficiency to neutron detection, gamma sensitivity, etc. We have also tested composite scintillators, which are an alternative to organic single crystals, used in the 70's last century. In the report, we will present the results of the study of several liquid scintillators, also 10B loaded, as well as high flashpoint ones. We also show the neutron detection properties of some samples of composite scintillators. Composites are based on small grains of p-terphenyl or stilbene, introduced into a polymer matrix, which acts as a diffuser. The composite is encapsulated in a housing made of organic glass. P-terphenyl and stilbene are organic scintillators, which were commonly used in the seventies last century. They are characterized by good neutron/gamma discrimination properties. The present studies covers neutron/gamma discrimination by the zero-crossing method, a comparison of detection efficiency of liquid scintillators to 3He detectors and methods to reduce their gamma-ray sensitivity. In conclusion, a detection system, based on several small liquid cells of 2'' × 2'', is preferred, with pulse shape discrimination circuit equipped with the pile-up rejection circuit (PUR), as well as lead and tin shielding.
19. Research to Operations of Ionospheric Scintillation Detection and Forecasting
Science.gov (United States)
Jones, J.; Scro, K.; Payne, D.; Ruhge, R.; Erickson, B.; Andorka, S.; Ludwig, C.; Karmann, J.; Ebelhar, D.
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http://maps.thefullwiki.org/Coriolis_effect
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# Coriolis effect: Map
### Map showing all locations mentioned on Wikipedia article:
In physics, the Coriolis effect is an apparent deflection of moving objects when they are viewed from a rotating reference frame.
Newton's laws of motion govern the motion of an object in an inertial frame of reference. When transforming Newton's laws to a rotating frame of reference, the Coriolis force appears, along with the centrifugal force. If the rotation speed of the frame is not constant, the Euler force will also appear. All three forces are proportional to the mass of the object. The Coriolis force is proportional to the speed of rotation and the centrifugal force is proportional to its square. The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object's speed in the rotating frame. The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame.
These three additional forces are termed either inertial forces, fictitious forces or pseudo forces. These names are used in a technical sense, to mean simply that these forces vanish in an inertial frame of reference.
The mathematical expression for the Coriolis force appeared in an 1835 paper by a French scientist Gaspard-Gustave Coriolis in connection with hydrodynamics, and also in the tidal equations of Pierre-Simon Laplace in 1778. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.
Perhaps the most commonly encountered rotating reference frame is the Earth. Moving objects on the surface of the Earth experience a Coriolis force, and appear to veer to the right in the northern hemisphere, and to the left in the southern. Exactly on the equator, motion east or west, remains (precariously) along the line of the equator. Initial motion of a pendulum in any other direction will lead to a motion in a loop. Movements of air in the atmosphere and water in the ocean are notable examples of this behavior: rather than flowing directly from areas of high pressure to low pressure, as they would on a non-rotating planet, winds and currents tend to flow to the right of this direction north of the equator, and to the left of this direction south of the equator. This effect is responsible for the rotation of large cyclones (see Coriolis effects in meteorology).
## History
Gaspard-Gustave Coriolis published a paper in 1835 on the energy yield of machines with rotating parts, such as waterwheels. This paper considered the supplementary forces that are detected in a rotating frame of reference. Coriolis divided these supplementary forces into two categories. The second category contained a force that arises from the cross product of the angular velocity of a coordinate system and the projection of a particle's velocity into a plane perpendicular to the system's axis of rotation. Coriolis referred to this force as the "compound centrifugal force" due to its analogies with the centrifugal force already considered in category one. By the early 20th century the effect was known as the "acceleration of Coriolis." By 1919 it was referred by to as "Coriolis' force" and by 1920 as "Coriolis force".
In 1856, William Ferrel proposed the existence of a circulation cell in the mid-latitudes with air being deflected by the Coriolis force to create the prevailing westerly winds.
Understanding the kinematics of how exactly the rotation of the Earth affects airflow was partial at first. Late in the 19th century, the full extent of the large scale interaction of pressure gradient force and deflecting force that in the end causes air masses to move along isobars was understood.
## Formula
In non-vector terms: at a given rate of rotation of the observer, the magnitude of the Coriolis acceleration of the object is proportional to the velocity of the object and also to the sine of the angle between the direction of movement of the object and the axis of rotation.
The vector formula for the magnitude and direction of the Coriolis acceleration is
\boldsymbol{ a}_C = -2 \, \boldsymbol{ \Omega \times v}
where (here and below) v is the velocity of the particle in the rotating system, and Ω is the angular velocity vector which has magnitude equal to the rotation rate ω and is directed along the axis of rotation of the rotating reference frame, and the × symbol represents the cross product operator.
The equation may be multiplied by the mass of the relevant object to produce the Coriolis force:
\boldsymbol{ F}_C = -2 \, m \, \boldsymbol{\Omega \times v}.
See fictitious force for a derivation.
The Coriolis effect is the behavior added by the Coriolis acceleration. The formula implies that the Coriolis acceleration is perpendicular both to the direction of the velocity of the moving mass and to the frame's rotation axis. So in particular:
• if the velocity is parallel to the rotation axis, the Coriolis acceleration is zero.
• if the velocity is straight inward to the axis, the acceleration is in the direction of local rotation.
• if the velocity is straight outward from the axis, the acceleration is against the direction of local rotation.
• if the velocity is in the direction of local rotation, the acceleration is outward from the axis.
• if the velocity is against the direction of local rotation, the acceleration is inward to the axis.
The vector cross product can be evaluated as the determinant of a matrix:
\boldsymbol{\Omega \times v} = \begin{vmatrix} \boldsymbol{i}&\boldsymbol{j}&\boldsymbol{k} \\ \Omega_x & \Omega_y & \Omega_z \\ v_x & v_y & v_z \end{vmatrix}\ = \begin{pmatrix} \Omega_y v_z - \Omega_z v_y \\ \Omega_z v_x - \Omega_x v_z \\ \Omega_x v_y - \Omega_y v_x \end{pmatrix}\ ,
where the vectors i, j, k are unit vectors in the x, y and z directions.
## Causes
The Coriolis effect exists only when using a rotating reference frame. In the rotating frame it behaves exactly like a real force (that is to say, it causes acceleration and has real effects). However, Coriolis force is a consequence of inertia, and is not attributable to an identifiable originating body, as is the case for electromagnetic or nuclear forces, for example. From an analytical viewpoint, to use Newton's second law in a rotating system, Coriolis force is mathematically necessary, but it disappears in a non-accelerating, inertial frame of reference. For a mathematical formulation see Mathematical derivation of fictitious forces.
A denizen of a rotating frame, such as an astronaut in a rotating space station, very probably will find the interpretation of everyday life in terms of the Coriolis force accords more simply with intuition and experience than a cerebral reinterpretation of events from an inertial standpoint. For example, nausea due to an experienced push may be more instinctively explained by Coriolis force than by the law of inertia. See also Coriolis effect . In meteorology, a rotating frame (the Earth) with its Coriolis force proves a more natural framework for explanation of air movements than a hypothetical, non-rotating, inertial frame without Coriolis forces. In long-range gunnery, sight corrections for the Earth's rotation are based upon Coriolis force. These examples are described in more detail below.
The acceleration entering the Coriolis force arises from two sources of change in velocity that result from rotation: the first is the change of the velocity of an object in time. The same velocity (in an inertial frame of reference where the normal laws of physics apply) will be seen as different velocities at different times in a rotating frame of reference. The apparent acceleration is proportional to the angular velocity of the reference frame (the rate at which the coordinate axes change direction), and to the component of velocity of the object in a plane perpendicular to the axis of rotation. This gives a term -\boldsymbol\Omega\times\boldsymbol v.The minus sign arises from the traditional definition of the cross product (right hand rule), and from the sign convention for angular velocity vectors.
The second is the change of velocity in space. Different positions in a rotating frame of reference have different velocities (as seen from an inertial frame of reference). In order for an object to move in a straight line it must therefore be accelerated so that its velocity changes from point to point by the same amount as the velocities of the frame of reference. The effect is proportional to the angular velocity (which determines the relative speed of two different points in the rotating frame of reference), and to the component of the velocity of the object in a plane perpendicular to the axis of rotation (which determines how quickly it moves between those points). This also gives a term -\boldsymbol\Omega\times\boldsymbol v.
## Length scales and the Rossby number
The time, space and velocity scales are important in determining the importance of the Coriolis effect. Whether rotation is important in a system can be determined by its Rossby number, which is the ratio of the velocity, U, of a system to the product of the Coriolis parameter,f, and the length scale, L, of the motion:
Ro = \frac{U}{fL}.
The Rossby number is the ratio of inertial to Coriolis forces. A small Rossby number signifies a system which is strongly affected by Coriolis forces, and a large Rossby number signifies a system in which inertial forces dominate. For example, in tornadoes, the Rossby number is large, in low-pressure systems it is low and in oceanic systems it is of the order of unity. As a result, in tornadoes the Coriolis force is negligible, and balance is between pressure and centrifugal forces. In low-pressure systems, centrifugal force is negligible and balance is between Coriolis and pressure forces. In the oceans all three forces are comparable.
An atmospheric system moving at U = 10 m/s occupying a spatial distance of L = 1000 km, has a Rossby number of approximately 0.1.A man playing catch may throw the ball at U = 30 m/s in a garden of length L = 50 m. The Rossby number in this case would be about = 6000.Needless to say, one does not worry about which hemisphere one is in when playing catch in the garden. However, an unguided missile obeys exactly the same physics as a baseball, but may travel far enough and be in the air long enough to notice the effect of Coriolis. Long-range shells in the Northern Hemisphere landed close to, but to the right of, where they were aimed until this was noted. (Those fired in the southern hemisphere landed to the left.) In fact, it was this effect that first got the attention of Coriolis himself.
## Applied to Earth
### Rotating sphere
Consider a location with latitude \varphi on a sphere that is rotating around the north-south axis. A local coordinate system is set up with the x axis horizontally due east, the y axis horizontally due north and the z axis vertically upwards.The rotation vector, velocity of movement and Coriolis acceleration expressed in this local coordinate system (listing components in the order East (e), North (n) and Upward (u)) are:
\boldsymbol{ \Omega} = \omega \begin{pmatrix} 0 \\ \cos \varphi \\ \sin \varphi \end{pmatrix}\ , \boldsymbol{ v} = \begin{pmatrix} v_e \\ v_n \\ v_u \end{pmatrix}\ ,
\boldsymbol{ a}_C =-2\boldsymbol{\Omega \times v}= 2\,\omega\, \begin{pmatrix} v_n \sin \varphi-v_u \cos \varphi \\ -v_e \sin \varphi \\ v_e \cos\varphi\end{pmatrix}\ .
When considering atmospheric or oceanic dynamics, the vertical velocity is small and the vertical component of the Coriolis acceleration is small compared to gravity. For such cases, only the horizontal (East and North) components matter. The restriction of the above to the horizontal plane is (setting vu=0):
\boldsymbol{ v} = \begin{pmatrix} v_e \\ v_n\end{pmatrix}\ , \boldsymbol{ a}_c = \begin{pmatrix} v_n \\ -v_e\end{pmatrix}\ f\ ,
where f = 2 \omega \sin \varphi \, is called the Coriolis parameter.
By setting vn = 0, it can be seen immediately that (for positive \varphi and \omega\,) a movement due east results in an acceleration due south. Similarly, setting , it is seen that a movement due north results in an acceleration due east. In general, observed horizontally, looking along the direction of the movement causing the acceleration, the acceleration always is turned 90° to the right and of the same size regardless of the horizontal orientation. That is:
As a different case, consider equatorial motion setting φ = 0°. In this case, Ω is parallel to the North or n-axis, and:
\boldsymbol{ \Omega} = \omega \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}\ , \boldsymbol{ v} = \begin{pmatrix} v_e \\ v_n \\ v_u \end{pmatrix}\ , \boldsymbol{ a}_C =-2\boldsymbol{\Omega \times v}= 2\,\omega\, \begin{pmatrix}-v_u \\0 \\ v_e \end{pmatrix}\ .
Accordingly, an eastward motion (that is, in the same direction as the rotation of the sphere) provides an upward acceleration known as the Eötvös effect, and an upward motion produces an acceleration due west.
### The Sun and distant stars
The motion of the Sun as seen from Earth is dominated by the Coriolis and centrifugal forces. For ease of explanation consider the situation of a distant star (with mass m) located over the equator, at position \boldsymbol r, perpendicular to the rotation vector \boldsymbol \Omega so \boldsymbol{\Omega \cdot r} = 0. It is observed to rotate in the opposite direction as the Earth's rotation once a day, making its velocity \boldsymbol v = -\boldsymbol \Omega \times \boldsymbol r. The fictitious force consisting of Coriolis and centrifugal forces is:
\boldsymbol {F_f} = -2 \, m \, \boldsymbol{\Omega \times v} - m \, \boldsymbol{\Omega \times { (\Omega \times r)}}
: = +2 \, m \, \boldsymbol{\Omega \times (\Omega \times r)} - m \, \boldsymbol{\Omega \times {(\Omega \times r)}}
: = m \, \boldsymbol{\Omega \times (\Omega \times r)}
: = m \, (\boldsymbol{\Omega (\Omega \cdot r) - r (\Omega \cdot \Omega))}
: = - m \, \Omega^2 \, \boldsymbol r
This can be recognised as the centripetal force that will keep the star in a circular movement around the observer.
The general situation for a star, not above the equator is more complicated. Just as for air flows on Earth's surface, on the northern hemisphere a star's trajectory will be deflected to the right. After rising at a certain angle, it will bend to the right, culminate and start setting.
### Meteorology
Figure 14: Schematic representation of inertial circles of air masses in the absence of other forces, calculated for a wind speed of approximately 50 to 70 m/s.
Note that the rotation is exactly opposite of that normally experienced with air masses in weather systems around depressions.
Perhaps the most important instance of the Coriolis effect is in the large-scale dynamics of the oceans and the atmosphere. In meteorology and ocean science, it is convenient to use a rotating frame of reference where the Earth is stationary. The fictitious centrifugal and Coriolis forces must then be introduced. Their relative importance is determined by the Rossby number. Tornadoes have a high Rossby number, so Coriolis forces are unimportant, and are not discussed here. As discussed next, low-pressure areas are phenomena where Coriolis forces are significant.
#### Flow around a low-pressure area
If a low-pressure area forms in the atmosphere, air will tend to flow in towards it, but will be deflected perpendicular to its velocity by the Coriolis acceleration. A system of equilibrium can then establish itself creating circular movement, or a cyclonic flow. Because the Rossby number is low, the force balance is largely between the pressure gradient force acting towards the low-pressure area and the Coriolis force acting away from the center of the low pressure.
Instead of flowing down the gradient, large scale motions in the atmosphere and ocean tend to occur perpendicular to the pressure gradient. This is known as geostrophic flow. On a non-rotating planet fluid would flow along the straightest possible line, quickly eliminating pressure gradients. Note that the geostrophic balance is thus very different from the case of "inertial motions" (see below) which explains why mid-latitude cyclones are larger by an order of magnitude than inertial circle flow would be.
This pattern of deflection, and the direction of movement, is called Buys-Ballot's law. In the atmosphere, the pattern of flow is called a cyclone. In the Northern Hemisphere the direction of movement around a low-pressure area is counterclockwise. In the Southern Hemisphere, the direction of movement is clockwise because the rotational dynamics is a mirror image there. At high altitudes, outward-spreading air rotates in the opposite direction. Cyclones rarely form along the equator due to the weak Coriolis effect present in this region.
#### Inertial circles
An air or water mass moving with speed v\, subject only to the Coriolis force travels in a circular trajectory called an 'inertial circle'. Since the force is directed at right angles to the motion of the particle, it will move with a constant speed, and perform a complete circle with frequency f. The magnitude of the Coriolis force also determines the radius of this circle:
R=v/f\,.
On the Earth, a typical mid-latitude value for f is 10−4 s−1; hence for a typical atmospheric speed of 10 m/s the radius is 100 km, with a period of about 14 hours. In the ocean, where a typical speed is closer to 10 cm/s, the radius of an inertial circle is 1 km. These inertial circles are clockwise in the northern hemisphere (where trajectories are bent to the right) and anti-clockwise in the southern hemisphere.
If the rotating system is a parabolic turntable, then f is constant and the trajectories are exact circles. On a rotating planet, f varies with latitude and the paths of particles do not form exact circles. Since the parameter f varies as the sine of the latitude, the radius of the oscillations associated with a given speed are smallest at the poles (latitude = ±90°), and increase toward the equator.
#### Other terrestrial effects
The Coriolis effect strongly affects the large-scale oceanic and atmospheric circulation, leading to the formation of robust features like jet streams and western boundary currents. Such features are in geostrophic balance, meaning that the Coriolis and pressure gradient forces balance each other. Coriolis acceleration is also responsible for the propagation of many types of waves in the ocean and atmosphere, including Rossby waves and Kelvin waves. It is also instrumental in the so-called Ekman dynamics in the ocean, and in the establishment of the large-scale ocean flow pattern called the Sverdrup balance.
### Eötvös effect
The practical impact of the Coriolis effect is mostly caused by the horizontal acceleration component produced by horizontal motion.
There are other components of the Coriolis effect. Eastward-traveling objects will be deflected upwards (feel lighter), while westward-traveling objects will be deflected downwards (feel heavier). This is known as the Eötvös effect. This aspect of the Coriolis effect is greatest near the equator. The force produced by this effect is similar to the horizontal component, but the much larger vertical forces due to gravity and pressure mean that it is generally unimportant dynamically.
In addition, objects traveling upwards or downwards will be deflected to the west or east respectively. This effect is also the greatest near the equator. Since vertical movement is usually of limited extent and duration, the size of the effect is smaller and requires precise instruments to detect.
### Draining in bathtubs and toilets
Coriolis rotation can conceivably play a role on scales as small as a bathtub. It is a commonly held myth that the every-day rotation of a bathtub or toilet vortex is due to whether one is in the northern or southern hemisphere. An article in Nature, by Ascher Shapiro, describes an experiment in which all other forces to the system are removed by filling a 6 ft. tank with water and allowing it to settle for 24 hrs (to remove any internal velocity), in a room where the temperature has stabilized (temperature differences in the room can introduce forces inside the fluid). The drain plug is then very slowly removed, and tiny pieces of floating wood are used to observe rotation. During the first 12 to 15 mins, no rotation is observed. Then, a vortex appears and consistently begins to rotate in a counter-clockwise direction (the experiment was performed in the Northern hemisphere, in Boston, MA). This is repeated and the results averaged to make sure the effect is real. The Coriolis effect does indeed play a role in vortex rotation for draining liquids that have come to rest for a long time. ["Bath-Tub Vortex", Nature. Dec 15th, 1962. Vol 195, No. 4859, p. 1080-1081]
In reality, this experiment shows that the Coriolis effect is a few orders of magnitude smaller than various random influences on drain direction, such as the geometry of the container and the direction in which water was initially added to it. In the above experiment, if the water settles for 2 hrs or less (instead of 24), then the vortex can be seen to rotate in either direction. Most toilets flush in only one direction, because the toilet water flows into the bowl at an angle. If water shot into the basin from the opposite direction, the water would spin in the opposite direction.
The idea that toilets and bathtubs drain differently in the Northern and Southern Hemispheres has been popularized by several television programs, including The Simpsons episode "Bart vs. Australia" and the The X-Files episode "Die Hand Die Verletzt." Several science broadcasts and publications, including at least one college-level physics textbook, have also stated this. Some sources that incorrectly attribute draining direction to the Coriolis force also get the direction wrong, claiming that water would turn clockwise into drains in the Northern Hemisphere.
The Rossby number can also tell us about the bathtub. If the length scale of the tub is about L = 1 m, and the water moves towards the drain at about U = 60 cm/s, then the Rossby number is about 6 000.Thus, the bathtub is, in terms of scales, much like a game of catch, and rotation is unlikely to be important.
### Ballistic missiles and satellites
Ballistic missiles and satellites appear to follow curved paths when plotted on common world maps mainly because the earth is spherical and the shortest distance between two points on the Earth's surface (called a great circle) is usually not a straight line on those maps. Every two-dimensional (flat) map necessarily distorts the Earth's curved (three-dimensional) surface in some way. Typically (as in the commonly used Mercator projection, for example), this distortion increases with proximity to the poles. In the northern hemisphere for example, a ballistic missile fired toward a distant target using the shortest possible route (a great circle) will appear on such maps to follow a path north of the straight line from target to destination, and then curve back toward the equator. This occurs because the latitudes, which are projected as straight horizontal lines on most world maps, are in fact circles on the surface of a sphere, which get smaller as they get closer to the pole. Being simply a consequence of the sphericity of the Earth, this would be true even if the Earth didn't rotate. The Coriolis effect is of course also present, but its effect on the plotted path is much smaller.
The Coriolis effects became important in external ballistics for calculating the trajectories of very long-range artillery shells. The most famous historical example was the Paris gun, used by the Germans during World War I to bombard Paris from a range of about .
## Special cases
### Cannon on turntable
Figure 6: Coriolis acceleration, centrifugal acceleration and net acceleration vectors at three selected points on the trajectory as seen on the turntable.
Figure 1 is an animation of the classic illustration of Coriolis force. Another visualization of the Coriolis and centrifugal forces is this animation clip. Figure 3 is a graphical version.
Here is a question: given the radius of the turntable R, the rate of angular rotation ω, and the speed of the cannonball (assumed constant) v, what is the correct angle θ to aim so as to hit the target at the edge of the turntable?
The inertial frame of reference provides one way to handle the question: calculate the time to interception, which is tf = R / v . Then, the turntable revolves an angle ω tf in this time. If the cannon is pointed an angle θ = ω tf = ω R / v, then the cannonball arrives at the periphery at position number 3 at the same time as the target.
No discussion of Coriolis force can arrive at this solution as simply, so the reason to treat this problem is to demonstrate Coriolis formalism in an easily visualized situation.
The trajectory in the inertial frame (denoted A) is a straight line radial path at angle θ. The position of the cannonball in ( x, y ) coordinates at time t is:
\mathbf{r}_A (t) = vt\ \left( \cos (\theta ),\right.\left. {\color{white}..}\ \sin (\theta )\right) \ .
In the turntable frame (denoted B), the x- y axes rotate at angular rate ω, so the trajectory becomes:
\mathbf{r}_B (t) = vt\ \left( \cos ( \theta - \omega t),\right.\left. {\color{white}..} \sin ( \theta - \omega t)\right) \ ,
and three examples of this result are plotted in Figure 4.
To determine the components of acceleration, a general expression is used from the article fictitious force:\mathbf{a}_{B} =\mathbf{a}_A - 2 \boldsymbol\Omega \times \mathbf{v}_{B} - \boldsymbol\Omega \times (\boldsymbol\Omega \times \mathbf{r}_B ) - \frac{d \boldsymbol\Omega}{dt} \times \mathbf{r}_B \ ,in which the term in Ω × vB is the Coriolis acceleration and the term in Ω × ( Ω × rB) is the centrifugal acceleration. The results are (let α = θ − ωt):
\boldsymbol{\Omega} \mathbf{\times r_B} = \begin{vmatrix} \boldsymbol{i}&\boldsymbol{j}&\boldsymbol{k} \\ 0 & 0 & \omega \\ v t \cos \alpha & vt \sin \alpha & 0 \end{vmatrix}\ = \omega t v \left(-\sin\alpha, \cos\alpha\right )\ ,
\boldsymbol{\Omega \ \times} \left( \boldsymbol{\Omega} \mathbf{\times r_B}\right) = \begin{vmatrix} \boldsymbol{i}&\boldsymbol{j}&\boldsymbol{k} \\ 0 & 0 & \omega \\ -\omega t v \sin\alpha & \omega t v \cos\alpha & 0 \end{vmatrix}\ \ ,
producing a centrifugal acceleration:
\mathbf{a_{\mathrm{Cfgl}}} = \omega^2 v t \left(\cos\alpha, \sin\alpha\right )=\omega^2 \mathbf{r_B}(t) \ .
Also:
\mathbf{v_B} = \frac{d\mathbf{r_B}(t)}{dt}=(v \cos \alpha + \omega t \ v \sin \alpha, \ v \sin \alpha -\omega t \ v \cos \alpha ,\ 0)\ \ ,
\boldsymbol{\Omega} \mathbf{\times v_B} = \begin{vmatrix}\! \boldsymbol{i}& \! \boldsymbol{j}& \! \boldsymbol{k} \\ 0 & 0 & \omega \\v \cos \alpha\quad &v \sin \alpha\quad &\quad \\ \; + \omega t \ v \sin \alpha & \; -\omega t \ v \cos \alpha & 0
\end{vmatrix}\ \ , producing a Coriolis acceleration:
\mathbf{a_{\mathrm{Cor}}} = -2\left[ -\omega v \left( \sin\alpha - \omega t \cos\alpha\right),\right.\left. {\color{white}...}\ \omega v \left(\cos\alpha + \omega t \sin \alpha \right) \right]\
:=2\omega v \left(\sin\alpha,\ - \cos\alpha \right) -2\omega^2 \mathbf{r_B}(t) \ .
Figure 5 and Figure 6 show these accelerations for a particular example.
It is seen that the Coriolis acceleration not only cancels the centrifugal acceleration, but together they provide a net "centripetal", radially inward component of acceleration (that is, directed toward the center of rotation):
\mathbf{a_{\mathrm{Cptl}}} = -\omega^2 \mathbf{r_B}(t) \ ,
and an additional component of acceleration perpendicular to rB (t):
\mathbf{a_{C\perp}} = 2\omega v \left(\sin\alpha,\ -\cos\alpha \right) \ .
The "centripetal" component of acceleration resembles that for circular motion at radius rB, while the perpendicular component is velocity dependent, increasing with the radial velocity v and directed to the right of the velocity. The situation could be described as a circular motion combined with an "apparent Coriolis acceleration" of 2ωv. However, this is a rough labeling: a careful designation of the true centripetal force refers to a local reference frame that employs the directions normal and tangential to the path, not coordinates referred to the axis of rotation.
These results also can be obtained directly by two time differentiations of rB (t). Agreement of the two approaches demonstrates that one could start from the general expression for fictitious acceleration above and derive the trajectories of Figure 4. However, working from the acceleration to the trajectory is more complicated than the reverse procedure used here, which, of course, is made possible in this example by knowing the answer in advance.
As a result of this analysis an important point appears: all the fictitious accelerations must be included to obtain the correct trajectory. In particular, besides the Coriolis acceleration, the centrifugal force plays an essential role. It is easy to get the impression from verbal discussions of the cannonball problem, which are focussed on displaying the Coriolis effect particularly, that the Coriolis force is the only factor that must be considered; emphatically, that is not so. A turntable for which the Coriolis force is the only factor is the parabolic turntable. A somewhat more complex situation is the idealized example of flight routes over long distances, where the centrifugal force of the path and aeronautical lift are countered by gravitational attraction.
### Tossed ball on a rotating carousel
Figure 7 illustrates a ball tossed from 12:00 o'clock toward the center of a counterclockwise rotating carousel. On the left, the ball is seen by a stationary observer above the carousel, and the ball travels in a straight line to the center, while the ball-thrower rotates counterclockwise with the carousel. On the right the ball is seen by an observer rotating with the carousel, so the ball-thrower appears to stay at 12:00 o'clock. The figure shows how the trajectory of the ball as seen by the rotating observer can be constructed.
On the left, two arrows locate the ball relative to the ball-thrower. One of these arrows is from the thrower to the center of the carousel (providing the ball-thrower's line of sight), and the other points from the center of the carousel to the ball.(This arrow gets shorter as the ball approaches the center.) A shifted version of the two arrows is shown dotted.
On the right is shown this same dotted pair of arrows, but now the pair are rigidly rotated so the arrow corresponding to the line of sight of the ball-thrower toward the center of the carousel is aligned with 12:00 o'clock. The other arrow of the pair locates the ball relative to the center of the carousel, providing the position of the ball as seen by the rotating observer. By following this procedure for several positions, the trajectory in the rotating frame of reference is established as shown by the curved path in the right-hand panel.
The ball travels in the air, and there is no net force upon it. To the stationary observer the ball follows a straight-line path, so there is no problem squaring this trajectory with zero net force. However, the rotating observer sees a curved path. Kinematics insists that a force (pushing to the right of the instantaneous direction of travel for a counterclockwise rotation) must be present to cause this curvature, so the rotating observer is forced to invoke a combination of centrifugal and Coriolis forces to provide the net force required to cause the curved trajectory.
### Bounced ball
Figure 8 describes a more complex situation where the tossed ball on a turntable bounces off the edge of the carousel and then returns to the tosser, who catches the ball. The effect of Coriolis force on its trajectory is shown again as seen by two observers: an observer (referred to as the "camera") that rotates with the carousel, and an inertial observer. Figure 8 shows a bird's-eye view based upon the same ball speed on forward and return paths. Within each circle, plotted dots show the same time points. In the left panel, from the camera's viewpoint at the center of rotation, the tosser (smiley face) and the rail both are at fixed locations, and the ball makes a very considerable arc on its travel toward the rail, and takes a more direct route on the way back. From the ball tosser's viewpoint, the ball seems to return more quickly than it went (because the tosser is rotating toward the ball on the return flight).
On the carousel, instead of tossing the ball straight at a rail to bounce back, the tosser must throw the ball toward the right of the target and the ball then seems to the camera to bear continuously to the left of its direction of travel to hit the rail (left because the carousel is turning clockwise). The ball appears to bear to the left from direction of travel on both inward and return trajectories. The curved path demands this observer to recognize a leftward net force on the ball. (This force is "fictitious" because it disappears for a stationary observer, as is discussed shortly.) For some angles of launch, a path has portions where the trajectory is approximately radial, and Coriolis force is primarily responsible for the apparent deflection of the ball (centrifugal force is radial from the center of rotation, and causes little deflection on these segments). When a path curves away from radial, however, centrifugal force contributes significantly to deflection.
The ball's path through the air is straight when viewed by observers standing on the ground (right panel). In the right panel (stationary observer), the ball tosser (smiley face) is at 12 o'clock and the rail the ball bounces from is at position one (1). From the inertial viewer's standpoint, positions one (1), two (2), three (3) are occupied in sequence. At position 2 the ball strikes the rail, and at position 3 the ball returns to the tosser. Straight-line paths are followed because the ball is in free flight, so this observer requires that no net force is applied.
A video clip of the tossed ball and other experiments are found at youtube: coriolis effect (2-11), University of Illinois WW2010 Project (some clips repeat only a fraction of a full rotation), and youtube.
## Visualization of the Coriolis effect
Figure 9: A fluid assuming a parabolic shape as it is rotating
To demonstrate the Coriolis effect, a parabolic turntable can be used. On a flat turntable, the inertia of a co-rotating object would force it off the edge. But if the surface of the turntable has the correct parabolic bowl shape (see Figure 9) and is rotated at the correct rate, the force components shown in Figure 10 are arranged so the component of gravity tangential to the bowl surface will exactly equal the centripetal force necessary to keep the object rotating at its velocity and radius of curvature (assuming no friction). (See banked turn.) This carefully contoured surface allows the Coriolis force to be displayed in isolation.
Discs cut from cylinders of dry ice can be used as pucks, moving around almost frictionlessly over the surface of the parabolic turntable, allowing effects of Coriolis on dynamic phenomena to show themselves. To get a view of the motions as seen from the reference frame rotating with the turntable, a video camera is attached to the turntable so as to co-rotate with the turntable, with results as shown in Figure 11. In the left panel of Figure 11, which is the viewpoint of a stationary observer, the gravitational force in the inertial frame pulling the object toward the center (bottom ) of the dish is proportional to the distance of the object from the center. A centripetal force of this form causes the elliptical motion. In the right panel, which shows the viewpoint of the rotating frame, the inward gravitational force in the rotating frame (the same force as in the inertial frame) is balanced by the outward centrifugal force (present only in the rotating frame). With these two forces balanced, in the rotating frame the only unbalanced force is Coriolis (also present only in the rotating frame), and the motion is an inertial circle. Analysis and observation of circular motion in the rotating frame is a simplification compared to analysis or observation of elliptical motion in the inertial frame.
Because this reference frame rotates several times a minute, rather than only once a day like the Earth, the Coriolis acceleration produced is many times larger, and so easier to observe on small time and spatial scales, than is the Coriolis acceleration caused by the rotation of the Earth.
In a manner of speaking, the Earth is analogous to such a turntable. The rotation has caused the planet to settle on a spheroid shape, such that the normal force, the gravitational force and the centrifugal force exactly balance each other on a "horizontal" surface. (See equatorial bulge.)
The Coriolis effect caused by the rotation of the Earth can be seen indirectly through the motion of a Foucault pendulum.
## Coriolis effects in other areas
### Coriolis flow meter
Figure 11: Object moving frictionlessly over the surface of a very shallow parabolic dish.
The object has been released in such a way that it follows an ellipse-shaped trajectory.
Left: The inertial point of view.
Right: The co-rotating point of view.
A practical application of the Coriolis effect is the mass flow meter, an instrument that measures the mass flow rate and density of a fluid flowing through a tube. The operating principle, introduced in 1977 by Micro Motion Inc., involves inducing a vibration of the tube through which the fluid passes. The vibration, though it is not completely circular, provides the rotating reference frame which gives rise to the Coriolis effect. While specific methods vary according to the design of the flow meter, sensors monitor and analyze changes in frequency, phase shift, and amplitude of the vibrating flow tubes. The changes observed represent the mass flow rate and density of the fluid.
### Molecular physics
In polyatomic molecules, the molecule motion can be described by a rigid body rotation and internal vibration of atoms about their equilibrium position. As a result of the vibrations of the atoms, the atoms are in motion relative to the rotating coordinate system of the molecule. Coriolis effects will therefore be present and will cause the atoms to move in a direction perpendicular to the original oscillations. This leads to a mixing in molecular spectra between the rotational and vibrational levels.
### Insect flight
Flies (Diptera) and moths (Lepidoptera) utilize the Coriolis effect when flying: their halteres, or antennae in the case of moths, oscillate rapidly and are used as vibrational gyroscopes. See Coriolis effect in insect stability. In this context, the Coriolis effect has nothing to do with the rotation of the Earth.
## References
1. Dugas, René and J. R. Maddox (1988). A History of Mechanics. Courier Dover Publications: pg 374. ISBN 0486656322
2. Retrieved on 2009-01-01.
3. MIT essays by James F. Price, Woods Hole Oceanographic Institution (2006). See in particular §4.3 in the Coriolis lecture
4. The claim is made that in the Falklands in WW I, the British failed to correct their sights for the southern hemisphere, and so missed their targets. . For set up of the calculations, see
5. Cloud Spirals and Outflow in Tropical Storm Katrina from Earth Observatory (NASA)
6. (Vorticity, Part 1)
7. Knew? The No-Spin Zone"from Berkeley Science Review (PDF)
8. "Flush Bosh"fromsnopes.com
9. "X-Files coriolis error leaves viewers wondering" from Skeptical Inquirer
10. "Bad Coriolis" from Penn State College of Earth and Mineral Sciences
11. "Bad Coriolis" from Penn State College of Earth and Mineral Sciences
12. Here the description "radially inward" means "toward the axis of rotation". That direction is not toward the center of curvature of the path, however, which is the direction of the true centripetal force. Hence, the quotation marks on "centripetal".
13. When a container of fluid is rotating on a turntable, the surface of the fluid naturally assumes the correct parabolic shape. This fact may be exploited to make a parabolic turntable by using a fluid that sets after several hours, such as a synthetic resin. For a video of the Coriolis effect on such a parabolic surface, see Geophysical fluid dynamics lab demonstration John Marshall, Massachusetts Institute of Technology.
14. For a java applet of the Coriolis effect on such a parabolic surface, see Brian Fiedler School of Meteorology at the University of Oklahoma.
15. "Antennae as Gyroscopes", Science, Vol. 315, 9 Feb 2007, p. 771
16. Halteres for the micromechanical flying insect (Wu, W.C.; Wood, R.J.; Fearing, R.S.) Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA; This paper appears in: Robotics and Automation, 2002. Proceedings. ICRA '02. IEEE International Conference on Publication Date: 2002 Volume: 1, On page(s): 60- 65 vol.1 ISBN 0-7803-7272-7 Date Published in Issue: 2002-08-07 00:46:34.0
### Further reading: physics and meteorology
• Coriolis, G.G., 1832: Mémoire sur le principe des forces vives dans les mouvements relatifs des machines. Journal de l'école Polytechnique, Vol 13, 268–302.
( Original article [in French], PDF-file, 1.6 MB, scanned images of complete pages.)
• Coriolis, G.G., 1835: Mémoire sur les équations du mouvement relatif des systèmes de corps. Journal de l'école Polytechnique, Vol 15, 142–154
( Original article [in French] PDF-file, 400 KB, scanned images of complete pages.)
• Gill, AE Atmosphere-Ocean dynamics, Academic Press, 1982.
• Durran, D. R., 1993: Is the Coriolis force really responsible for the inertial oscillation?, Bull. Amer. Meteor. Soc., 74, 2179–2184; Corrigenda. Bulletin of the American Meteorological Society, 75, 261
• Grattan-Guinness, I., Ed., 1994: Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Vols. I and II. Routledge, 1840 pp.
1997: The Fontana History of the Mathematical Sciences. Fontana, 817 pp. 710 pp.
• Khrgian, A., 1970: Meteorology — A Historical Survey. Vol. 1. Keter Press, 387 pp.
• Kuhn, T. S., 1977: Energy conservation as an example of simultaneous discovery. The Essential Tension, Selected Studies in Scientific Tradition and Change, University of Chicago Press, 66–104.
• Kutzbach, G., 1979: The Thermal Theory of Cyclones. A History of Meteorological Thought in the Nineteenth Century. Amer. Meteor. Soc., 254 pp.
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https://www.aimsciences.org/article/doi/10.3934/amc.2009.3.235
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# American Institute of Mathematical Sciences
August 2009, 3(3): 235-250. doi: 10.3934/amc.2009.3.235
## A review of the available construction methods for Golomb rulers
1 UCD CASL, University College Dublin, Belfield, Dublin 4, Ireland
Received January 2009 Revised July 2009 Published August 2009
We collect the main construction methods for Golomb rulers available in the literature along with their proofs. In particular, we demonstrate that the Bose-Chowla method yields Golomb rulers that appear as the main diagonal of a special subfamily of Golomb Costas arrays. We also show that Golomb rulers can be composed to yield longer Golomb rulers.
Citation: Konstantinos Drakakis. A review of the available construction methods for Golomb rulers. Advances in Mathematics of Communications, 2009, 3 (3) : 235-250. doi: 10.3934/amc.2009.3.235
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2019 Impact Factor: 0.734
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https://www.physicsforums.com/threads/rotational-work-and-a-hamster.49867/
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# Homework Help: Rotational Work and a Hamster!
1. Oct 26, 2004
### Hughey85
After getting a drink of water, a hamster jumps onto an exercise wheel for a run. A few seconds later the hamster is running in place with a speed of 0.8 m/s. Find the work done by the hamster to get the exercise wheel moving, assuming it is a hoop of radius 0.10 m and mass 5.9 g.
I'm not sure how to solve this one. I think you use
Work=(torque) x (delta theta)
Torque = rF
but, after that, i'm not sure what theta would be. Am I even using the right set of equations? Thanks for all the help!
2. Oct 27, 2004
### Tide
All you need to do is compare the rotational energy before and after! That will equal the amount of work the hamster did. The rotational energy is half the product the moment of inertia and the square of the angular velocity.
Thanks to ehild for catching my missing 1/2!
Last edited: Oct 27, 2004
3. Oct 27, 2004
### ehild
half of this...
$$E_{rot}=\frac{1}{2}I\omega^2$$
ehild
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http://www.petermc.net/blog/category/maths/
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Jucys-Murphy elements and induction
This post concerns the representation theory of the symmetric group over the complex numbers. Recall that the irreducible representations of the symmetric group are indexed by partitions of . Let be the irreducible representation indexed by . I want to say some words about the theorem that the decomposition of the induced module is given by the decomposition into eigenspaces under the action of the Jucys-Murphy element.
First, the relevant Jucys-Murphy element is
The way it acts on is not as an element of but by This is well-defined since commutes with .
What this action defines is a natural transformation from the functor to itself. The induction functor is (bi)-adjoint to the restriction functor and this natural transformation is even simpler to construct on the adjoint side. Recall that if and are adjoint functors, then there is an isomorphism
Here refers to the natural transformations from to itself, and the map in this isomorphism is given by pre- and post-composition by the unit and counit of the adjunction.
And the way that yields a natural transformation from to itself is very simple, it’s just by its usual action as an element of . If you transport this natural transformation to a natural transformation of the induction functor via the method I just mentioned, then you get the formula mentioned above.
Now given a pair of adjoint functors and , a natural transformation from to (and hence from to ) and a complex number , we can define a functor by
and similarly for (this requires some linearity assumptions, but they’re satisfied here. Also you could take generalised eigenspaces if you wanted to, but in our application there is no difference).
When you do this, the functors and are adjoint:
Proof: Both and are the -eigenspace of the action of on .
Now apply this to our situation. We also use the following standard fact about the action of the Jucys-Murphy element (as developed e.g. in the Vershik-Okounkov approach):
Consider the decomposition
Then the Jucys-Murphy element acts by the scalar on , where is the content of the box added to to get .
Now translating this statement via the above yoga onto the adjoint side, we get
In the decomposition
the Jucys-Murphy element acts by the scalar on , where is the content of the box added to to get .
Singularities of Schubert varieties within a right cell
Martina Lanini and I recently posted our preprint Singularities of Schubert varieties within a right cell to the arXiv. In it, we show that every singularity which appears in a type A Schubert variety appears between two permutations lying in the same right cell. This shows that any behaviour controlled by the singularities of Schubert varieties manifests itself within a Specht module. Some exmples are discussed.
The work was conducted during our recent visit to the thematic trimester program on representation theory at the Institut Henri Poincaré in Paris. I spent an enjoyable first month there before returning to Australia. Originally I was scheduled to be on a plane right now to return to Paris for the end of the program, but alas this is no longer possible. Oh well.
We’re hiring
The University of Melbourne maths department is hiring. All our ads can be found on mathjobs.
In pure maths, we have a continuing position in analysis. Applications should be submitted by the earlier deadline of 25 October to ensure full consideration.
There are also other positions available in applied and statistics, as well as a temporary position open to all areas.
Sydney Mathematical Research Institute International Visitor Program
There is a new (established in the last couple of years) mathematical institute based at the University of Sydney. I want to call attention to a visitor program they run, for mathematical visits to Australia.
They fund research visits of at least one month’s duration. At least two weeks must be spent at the University of Sydney, but the rest can be taken anywhere in Australia.
Funding rounds for these research visits happen periodically. Currently there is one open for visits within the period April-December 2020, with applications closing on 28 July.
Anyone interested should check out the research intstitute’s webpage.
Latex in WordPress
To activate Latex support in this blog, I have now activated the QuickLatex plugin. This has solved the problems with vertical alignment of mathematics that previously plagued this blog (only in new posts using QuickLatex, the back catalogue has not been converted).
The plugin webpage linked above shows its usage (for both posts and comments), allowing Latex to be typed natively once the word “latexpage” in square parentheses appears (so no inserting of the word “latex” after a dollar symbol anymore).
The binary tetrahedral group as a p-adic Galois group.
Let be the binary tetrahedral group. This group appears as the double cover of the group of rotations of the tetrahedron (under ), as a group of units in an appropriate -form of the quaternion group, or as .
Consider a local field of residue characteristic . Now consider the Galois group of a finite Galois extension. It has a large pro- part, together with two cyclic parts corresponding to the tamely ramified part and the unramified part. This structure alone shows that cannot be such a group unless .
Alternatively, every 2-dimensional irreducible representation of the Galois group of a local field of odd residue characteristic is induced, and has no index two subgroups, so again cannot occur as a Galois group when is odd.
So what about when is even? By considering the fixed field of a Sylow-2-subgroup, we see that if appears as a Galois group, then it is the Galois closure of a degree 8 extension.
Now the degree 8 extensions of are finite and number and have all been computed, together with their Galois groups. They can be found at this online database. A quick examination shows that our binary tetrahedral group does not appear.
But it does appear as an inertia group. So is not a Galois group over , but is a Galois group over the unramified quadratic extension of .
An exceptional isomorphism
We will construct the exceptional isomorphism $S_6\cong Sp_4(\mathbb{F}_2)$.
The group $S_6$ acts on $\mathbb{F}_2^6$ preserving the usual pairing $\langle e_i,e_j\rangle=\delta_{ij}$ where the $e_i$ are the usual basis vectors.
There is an invariant line $L$, the span of $\sum_i e_i$ and an invariant hyperplane $H=\{\sum_i a_ie_i|\sum_i a_i=0\}$. Let $V=H/L$. $S_6$ acts on $V$.
Since $L$ is the radical of the pairing $\langle \cdot,\cdot\rangle$ on $H$, the pairing $\langle \cdot,\cdot\rangle$ descends to a non-degenerate bilinear pairing on $V$. As it is symmetric and we are in characteristic 2, it is automatically skew-symmetric.
The $S_6$-action preserves this pairing, hence we get our desired homomorphism from $S_6$ to $Sp_4(\mathbb{F}_2)$.
To check injectivity, it suffices to show that $(12)$ is not in the kernel, since we know all normal subgroups of $S_6$. Surjectivity then follows by a counting argument, so we get our desired isomorphism.
Simon Marais Problem Competition 2017
A couple of weeks ago, there was the inaugural Simon Marais Mathematics Competition, a new maths competition for undergraduate students living in the time zones between New Zealand and India inclusive.
The students’ scripts have not yet been marked. As a member of the problem committee, I will be especially interested to see how they did. The questions and solutions can be found on the Simon Marais website. There will be a greater variety of solutions posted some time in November after the scripts have been marked. I will currently permit myself a few brief comments on the problems.
I actually came up with B1, which surprised me! The idea here was to specifically come up with an easy problem. One day I was leafing through some old Olympiad material, and on a sheet of preparatory problems for a maths camp from when I was a student, I saw a problem about classifying configurations of 4 points in the plane such that the sum of the distances from each point to the other points was the same. I wondered to myself what happened in three dimensions and the problem was born.
Problem A4 is expected to be very hard and has an interesting solution which I found and wrote up here. This is similar to an approach to the fundamental theorem of algebra which I believe goes back to Gauss and which I may discuss here if I have time.
As a member of the problem committee, I am always looking out for problem submissions for future competitions and welcome anybody who has what they think might be a suitable problem to submit it (which can be directly to me, or the chair of the committee, via email).
The medians of a triangle are concurrent
In case anyone reading this does not know, a median is a line connecting a vertex of a triangle to the midpoint of the opposite edge. The theorem is that the three medians of a triangle are concurrent (i.e. they meet in a single point). Here are four proofs.
Proof 1: (Transformation geometry)
Let E and F be the midpoints as shown and let BE and CF intersect at G. Consider the dilation about A with factor 2. It sends E to C, F to B and G to Q (this is the definition of Q). Then EG and CQ are parallel, as are FG and BQ. Thus BGCQ is a parallellogram and the diagonals of a parallelogram bisect each other QED.
Proof 2: (Vectors. Efficient and boring). Write ${\bf a}$, ${\bf b}$ and ${\bf c}$ for A, B and C respectively. Let G be $({\bf a}+{\bf b}+{\bf c})/3$. It is easy then to check that the midpoint D of AB is $({\bf a}+{\bf b})/2$ and that A, D and G are concurrent.
Proof 3: (Why not just prove Ceva’s Theorem)
Ceva’s Theorem states that in the situation shown, AD, BE and CF are concurrent if and only if
$\displaystyle \frac{BD}{DC}\frac{CE}{EA}\frac{AF}{FB}=1.$
To prove this, note that in the case of concurrence
$\displaystyle \frac{BD}{DC}=\frac{|ABG|}{|ACG|}.$
The rest of the proof is routine.
Proof 4: (my favourite) WLOG the triangle is equilateral. Now the statement is obvious (e.g. by symmetry).
Perhaps some elaboration should be made to the WLOG. An affine transformation of $\mathbb{R}^2$ is a map of the form ${\bf{v}}\mapsto A{\bf{v}}+{\bf{b}}$ where $A$ is an invertible matrix and ${\bf{b}}$ is a vector. The affine transformations act transitively on the set of (nondegenerate) triangles and the property of having concurrent medians is clearly invariant under these transformations.
Acknowledgements: Thanks to Inna Lukyanenko for the first proof and tikz files, and to pdftoppm for converting the .pdf output to .png.
A different proof of the fundamental theorem of arithmetic
The fundamental theorem of arithmetic states that every integer can be uniquely written as a product of primes (i.e. $\mathbb{Z}$ is a unique factorisation domain).
The usual proof proceeds through the Euclidean algorithm. Yesterday at lunch I was surprised to learn (thanks to Ole Warnaar) of a different proof bypassing the Euclidean algorithm which I reproduce below. Its primary attraction is its cuteness, as it provides a weaker result than the usual proof (i.e. doesn’t prove that $\mathbb{Z}$ is a Euclidean domain, or even a principal ideal domain).
Suppose that $n=p_1^{a_1}p_2^{a_2}\cdots p_k^{a_k}$ where $p_1,p_2,\ldots,p_k$ are distinct primes. Consider the finite cyclic group $C_n$. It has a composition series where the group $C_{p_i}$ appears $a_i$ times as a simple subquotient (and no other simple factors appear). Therefore by the Jordan-Holder theorem, the primes $p_i$ together with their multiplicities $a_i$ are unique. QED.
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http://www.physicsforums.com/showpost.php?p=188932&postcount=30
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View Single Post
mikie1, The answer to your question may be somewhere in this thread. If not: The definition of the definite integral as the limit of an infinite sum, is just that, a definition. So it's true by definition. And yes, you have to accept it. But I suspect that what you really meant to ask is whether this has been proven: Given a function, continuous on a closed interval [a,b], the difference between the values of the anti-derivative at a and b is the same as the definite integral of the function on the interval [a,b]. This is the fundamental theorem of calculus, and yes, like all theorems, it's been proven. If you didn't see the proof when you first learned integral calculus, either you were asleep or your teacher should be fired!
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http://home.wlu.edu/~levys/kalman_tutorial/kalman_18.html
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# The Extended Kalman Filter: An Interactive Tutorial for Non-Experts
### Part 18: Computing the Derivative
If you've made it this far, you are in a very good position to understand the Extended Kalman Filter. There are just two more things to consider:
1. How to compute the first derivative from an actual signal, without knowing its underlying function.
2. How to generalize our single-valued nonlinear state/observation model to the multi-valued systems we've been considering.
To answer the first question, we note that the first derivative of a function is defined as the limit of the difference between successive values of that function, divided by the timestep, as the timestep approaches zero: $f'(x) = \lim_{\Delta x \to 0} \frac{f(x+\Delta x) - f(x)}{\Delta x}$ If you don't understand that equation, don't worry: just think about subtracting successive differences of a signal $y$ to approximate its first derivative: $\frac{(y_{k+1} - y_k)} {timestep}$ Indeed, as the demo below shows, this finite difference formula is often a very good approximation to the first derivative. The demo allows you to choose among the same three functions as on the previous page (shown in the interval [0,1]), but this time you can select between the derivative and finite difference:
$f(x) = e^{2x}$ $f(x) = 10 log_{10}(x)$ $f(x) = 10 e^{-x/10}$ Derivative Finite difference
If one signal (like sensor value $z_k$) is a function of another signal (like state $x_k$), we can divide successive differences of the first signal by successive differences of the second signal: $\frac{z_{k+1} - z_k}{x_{k+1}-x_k}$
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http://math.stackexchange.com/questions/30523/is-it-possible-to-collude-in-a-perfect-information-game
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# Is it possible to collude in a perfect information game?
Is it possible to collude in a perfect information game?
Exercise 10-7 from book "Algorithms And Networking For Computer Games" - Jouni Smed, Harri Hakonen, p 225
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Yes, consider the following situation: Suppose we have two companies $A$ and $B$ that produce oranges. Company $A$ chooses some amount $q_A$ of oranges to produce. Given this information, company $B$ chooses $q_B$ of oranges to produce. The goal of both companies is to maximize their profits. We know that the total quantity is $Q = q_A+ q_B$ and the demand is $f(Q)$. So it is possible for both companies to jointly maximize their profits.
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Yes but you can't collude with your partner in chess. Am I miss something? – user8985 Apr 2 '11 at 22:48
You can collude against other players - in the answer here, the companies are colluding against their customers. In chess, players can collude but typically won't want to because there are no other opponents. Imagine, though, if you are playing a chess match where you both need a draw to progress in a tournament, it's likely you will play for stalemate (to both players' advantage). – Ronald Apr 8 '12 at 11:30
@Ronald: What you in fact do is play into a boring position and agree a draw. This is a common form of collusion in chess tournaments. – Chris Eagle Nov 26 '12 at 12:27
Collusion is one of the major problems with games with more than 2 players: the players that are losing can join forces to bring down the leader. This often becomes more a matter of politics than mathematics, and is therefore difficult to analyse.
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An extensive form is a complete desription of the strategic environment faces. So players have exactly the options available that the game tree presents. In some cases, one might think about some background story in which one can interpret some moves as "colluding", but such an interpretation lies outside game theory.
Edit: It seems the book considers "colluding" as players in a computer game cheating by not following the explicit rules. In a perfect information game, players cannot cheat by exchanging information. In a generic finite game of perfec information, super-rational players can't collude by the usual backward-induction logic. In infite games, they might be able to coordinate by pre-play communication.
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http://math.stackexchange.com/questions/286866/showing-a-vector-field-is-tangent-to-the-2-sphere/286946
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# Showing a vector field is tangent to the 2-sphere
How would I go about showing that the vector field $X = x\frac{\partial}{\partial y} - y\frac{\partial}{\partial x}$ is tangent to the unit sphere in $\mathbb{R}^3$? I can see it pictorially but I'm not sure what would be required to actually prove it.
(This isn't homework! I understand the definitions of vector field as either a derivation of $C^\infty(M)$ or as a section of the tangent bundle $TM$, but I don't know how to compute anything about it so I'm trying to work through some examples.)
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To be absolutely precise, we need a definition of "field tangent to a submanifold". Without being absolutely precise, I'd be happy with showing that $Xf=0$ on $M$ where $f$ is a defining equation of $M=\{f=0\}$ – user53153 Jan 25 '13 at 19:07
Your comment pretty much solves the problem. For your function $f$ is the standard equation for the sphere, $f=x^2+y^2+z^2-R^2$. Just directly apply the derivatives and show that it is zero. – F. Solis Jan 25 '13 at 19:13
@5PM Ok, so $Xf = 2xy-2yx =0$ everywhere on the sphere. This might be obvious, but why does $Xf$ being zero suffice? – Anna Jan 25 '13 at 19:16
Tangent vectors are the infinitesimal versions of flows. A flow maps a space into itself with $t$ as a parameter, say, $x'=F(x,t)$. We can look at the change in a function as we move: $df/dt=df(x'(t))/dt=df(F(x,t))/dt=Xf$, with the last equality being pretty much the definition of the tangent vector. To say that $X$ is tangent means that the flow it generates stays within the submanifold. If your function is constant in the submanifold the flow induces a change of zero. Further, in this case our function is not zero outside it, so that if the vector was not tangent, we would get $Xf\neq=0$. – F. Solis Jan 25 '13 at 19:55
Here's how to make the argument from the comments a little more rigorous from basic properties of tangent bundles. Let $i: S^2 \to \mathbb R^3$ be the inclusion. For every $x \in S^2$ this induces an injection $i_* T_xS^2 \to T_x \mathbb R^3$. Then asking if a vector field $X$ on $\mathbb R^3$ is tangent to $S^2$ is the same as asking if for all $x \in S^2, X_x \in i_* T_x S^2$. Now consider the map $f: \mathbb R^3 \to \mathbb R, (x,y,z) \mapsto x^2 + y^2 + z^2$. Now $f \circ i : S^2 \to \mathbb R$ is constant so that $f_* \circ i_* = 0$. In other words, $i_* TS^2 \subset \ker f_*$. Since $f_* \ne 0$ on $S^2$, by dimensionality reasons we must have that $i_* TS^2 = \ker f_*$. Finally, a vector field is in $\ker f_*$ is equivalent to $Xf = 0$ since $Xf = df(X) = f_* X$.
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The unit sphere in $\Bbb R^3$ is nice in the sense that its tangent spaces admit a simple interpretation: If $r \in S^2$, then $$T_r S^2 = \{v \in \Bbb R^3 : r \cdot v = 0 \}.$$ Now we can make the identification $$x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x} \leftrightarrow (-y, x, 0) \in \Bbb R^3.$$ Now for any $r = (x,y,z) \in S^2$, we have $$(x, y,z) \cdot (-y, x,0) = -xy + xy + 0= 0 \implies (-y, x, 0) \in T_r S^2.$$ This holds for all points $r \in S^2$, so $x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x}$ is a vector field on $S^2$.
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Since we're explicitly considering an embedding, you can use the concept of a vector manifold to attack this problem. There are many benefits to doing so: in particular, you can use geometric (clifford) algebra to analyze the problem.
What Henry has done is clever: he's using the normal to the surface to characterize it, which is something you can always do in $\mathbb R^3$, but not something you can do generally. For instance, if your manifold $M$ has $\dim M = 2$ in $\mathbb R^4$, you can't construct a vector normal to it.
Geometric algebra allows you to characterize an orientable manifold by its pseudoscalar. This is what I will do here.
The unit sphere can be characterized by two angles $\theta, \phi$. We assign each point a vector in $\mathbb R^3$, which is obvious by the embedding. Let these vectors be $r$ (so that $r^2$, the second component of this vector, is $y$ as usual). We can then take, at any $r$, partial derivatives with respect to our angular coordinates to characterize tangent vectors.
\begin{align*}e_\theta &= \frac{\partial x}{\partial \theta} = \cos \theta \cos \phi e_1+ \cos \theta \sin \phi e_2 - \sin \theta e_3 \\ e_\phi &= \frac{\partial x}{\partial \phi} = \sin \theta (-\sin \phi e_1 + \cos \phi e_2)\end{align*}
For this problem, it helps to rewrite the variables back in terms of $x, y, z$.
\begin{align*}e_\theta &= \frac{zx}{\sqrt{x^2 + y^2}} e_x+ \frac{zy}{\sqrt{x^2+y^2}}e_y - \sqrt{x^2+y^2} e_z \\ e_\phi &= - y e_x + x e_y\end{align*}
We can now characterize the surface by its pseudoscalar $i$, which is formed by a wedge product of the tangent vectors.
$$i = e_\theta \wedge e_\phi = \sqrt{x^2 + y^2} (z e_{xy} + y e_{zx} + x e_{xy})$$
The pseudoscalar represents, for a surface, an area element. It is a function of position, as you can see. Because it has orientation, the pseudoscalar itself can tell you about the orientation of a manifold (indeed, if you were to get that the pseuscalar is multivalued, you would rightly conclude that the manifold is non-orientable). The pseudoscalar is used to perform projections under the geometric product. If a vector field lies entirely in the tangent space, then its wedge product with the pseudoscalar should be zero. We can see that this is indeed the case.
$$i \wedge X \propto (z e_{xy} + y e_{zx} + x e_{yz}) \wedge (x e_y - y e_x) = yx e_{zxy} - xy e_{yzx} = (yx -xy) e_{xyz} = 0$$
This approach is a bit more complicated for $\mathbb R^3$ than the standard approach, and the clifford algebra aspects of it may take some getting used to, but it's a powerful formalism when you have access to an embedding, and we could've just as easily used it for a 2-dimensional surface in $\mathbb R^4$ with almost no change in approach.
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https://www.ams.org//publicoutreach/students/mathgame/jmm2014
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# The 2014 National Who Wants to Be a Mathematician at the Joint Mathematics Meetings in Baltimore
It has a been a wonderful experience participating in the Joint Mathematics Meetings through the [Who Wants to Be a Mathematician] math contest. I am very grateful that you invited us here to compete. This is a great contest and it was a lot of fun. Thank you!
Thank you very much for the invitation to the national contest. My son enjoyed very much the Who Wants to Be a Mathematician contest. He met old friends and made new friends. The contestants are smart and the games are so fun.
It is great that the AMS is able to conduct this competition which values and encourages mathematical talent. While sports are usually celebrated, it is wonderful that students interested in mathematics can also be encouraged. I sincerely hope that many more students gain the opportunity to participate in this competition.
Vivek Miglani, a junior from Marjory Stoneman Douglas High School in Florida, won the 2014 national Who Wants to Be a Mathematician, taking home US$5,000 and a TI-Nspire CX for himself, and$5,000 for the math department at his school. Here's Vivek just after his victory:
Vivek was joined in the finals by Jesse Zhang of Fairview High School (CO), who took second, and Tahsin Saffat of Westview High School (OR). Jesse won $3,000 for himself and the Fairview math department, as well as a TI-Nspire CX, while Tahsin won$1,000 for himself and the Westview math department, as well as a copy of Maple 17, published by the game's technology sponsor, Maplesoft.
Videos of the games, of the awards ceremony and of Tim Chartier's (Davidson College) pre-finals mime performance, "The Infinite Rope" are below. We'll have more videos soon. Below are slideshows of the games and the awards ceremony afterwards, as well as a description of the game and more photos.
Created with flickr slideshow.
(The first Championsip Bowl picture and the individual photos of the contestants--except we somehow missed getting one of Clark--were taken by AMS Public Awareness Officer Annette Emerson. The remaining images were taken by Sandy Huffaker, as are the next six photos below.)
Left to right: Patrick Guo (Westwood HS, TX), Tahsin Saffat (Westview HS, OR), Jesse Zhang (Fairview HS, CO), Shyam Narayanan (Blue Valley West HS, KS), Clark Lyons (High Technology HS, NJ), Emily Mu (Illinois Mathematics and Science Academy), Sammy Luo (North Carolina School of Science and Mathematics), Dennis Zhao (Montgomery Blair HS, MD), Kevin Sun (Phillips Exeter Academy, NH), and Vivek Miglani (Marjory Stoneman Douglas HS, FL)
Videos of the games (photos and descriptions of the games follow):
In the first semifinal, Jesse and Tahsin were tied for first at the halfway point. Patrick answered question five correctly to move into a three-way tie for the top spot, and the three remained tied after question six. Shyam, Jesse, and Tahsin answered the next question correctly which put Shyam in third and Jesse and Tahsin back into a tie by themselves for first. Four of the five contestants answered question eight correctly (a question concerning the arithmetic and geometric mean), so the positions of the contestants were unchanged and Jesse and Tahsin qualified for the finals. This semifinal featured a video by Judith Grabiner (Pitzer College), winner of the 2014 Beckenback Book Prize from the MAA, explaining some of the work and questions of David Hilbert.
Game two, which was even tighter than game one, also featured a video, this one by Jean-Marie de Koninck (Université de Laval) about normal numbers. Sammy held the lead at the halfway point. Before that, on question three, Vivek forgot to signal in, even though he thought he had signaled in. The judges huddled and since they were convinced that he did know the answer to the question, awarded him the points. Vivek moved ahead after question five, one about matrix multiplication, which only he and Dennis answered correctly. Vivek held that lead until question seven, at which point Clark moved into first. But on the last question, Sammy and Vivek answered correctly which put Vivek in the finals.
Tim Chartier then captivated the audience with his mime performance, "The Infinite Rope." Here's video of some of his performance:
Vivek dominated in the finals (left to right: Jesse, Vivek, and Tahsin), answering early and correctly on a majority of the questions. Even mathematicians are surprised by how much the national Who Wants to Be a Mathematician contestants know and they were even more surprised by how quickly Vivek could determine the right answers in the finals. Jesse finished second, which broke the game one tie between him and Tahsin. Vivek won $5,000 for himself and a matching amount for the math department at his school--both from the AMS--and a TI-Nspire CX from Texas Instruments. Jesse also won a TI-Nspire, as well as$3,000 for himself and his school's math department. More prizes are listed after the pictures and slideshow.
Videos of the awards ceremony:
Below is a slideshow of the post-game awards ceremony and luncheon (all but the last photo by Sandy Huffaker.)
Created with flickr slideshow.
Here are all the prizes and cash won by the contestants in the 2014 national Who Wants to Be a Mathematician. For each cash prize, a matching amount is awarded to the math department of the student's school
• TI-Nspire CX graphing caclulator from Texas Instruments and $5000 from the AMS: Vivek Miglani, Marjory Stoneman Douglas High School (FL) • TI-Nspire CX graphing calculator from Texas Instruments and$3000 from the AMS: Jesse Zhang, Fairview High School (CO)
• Maple 17 from Maplesoft and $1000 from the AMS: Tahsin Saffat, Westview High School (OR) and Sammy Luo, North Carolina School of Science and Mathematics • Calculus with Early Transcendentals by Anton, Bivens and Davis from John Wiley and Sons and$1000 from the AMS: Shyam Narayanan, Blue Valley West High School (KS), and Kevin Sun, Phillips Exeter Academy (NH)
• What's Happening in the Mathematical Sciences and $500 from the AMS: Patrick Guo,Westwood HS (TX), and Clark Lyons, High Technology High School (NJ) • Five-Minute Mathematics and$500 from the AMS: Emily Mu, Illinois Mathematics and Science Academy, and Dennis Zhao, Montgomery Blair High School (MD)
Vivek and his principal Ty Thompson, receiving the \$5,000 check from the AMS for the Marjory Stoneman Douglas High School math department. Shyam Narayanan (middle) with principal Brett Potts (left) and teacher Theresa Grospitch (right), with the check for the Blue Valley West High School Math Club.
Thanks very much to our sponsors: Maplesoft, the Who Wants to Be a Mathematician technology sponsor, Texas Instruments, and John Wiley and Sons. Thanks also to our judges: Bill Butterworth (also Who Wants to Be a Mathematician co-creator), DePaul University, Caren Diefenderfer, Hollins University, Bernie Madison, University of Arkansas, Ivelisse Rubio, University of Puerto Rico-Rio Piedras, and Katherine Socha, Math for America; and to our performers: Tim Chartier (live), Davidson College, Judith Grabiner, Pitzer College, and Jean-Marie De Koninck, Université de Laval. Thanks as well to Thomas Dick, Oregon State University, and Carl Yerger, Davidson College, for yeoman-like work behind the scenes.
|
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http://mathhelpforum.com/pre-calculus/162201-find-zeros-function-print.html
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# Find the zeros of this function
• November 5th 2010, 12:22 PM
aa751
Find the zeros of this function
y=x^2/275
I am not sure if it have any but please comment if it doesnt .
• November 5th 2010, 12:32 PM
pickslides
The best way to go here is simply make y=0 and solve for x.
i.e. $\displaystyle 0 = \frac{x^2}{275} \implies 275\times 0 = x^2 \implies 0=x^2 \implies \sqrt{0} = x \implies x= 0$
For a better unstanding ask yourself, what does the factor of $\frac{1}{275}$ have on the function of $y = x^2$ . Do the two functions have the same zeros?
• November 5th 2010, 12:52 PM
aa751
I thought so to0 , i set the equation to 0 and got x=0 I just hoped I was wrong lol Cuase i Needed the zeros for integration=/ I was trying to find a volume of a darn barrel. lol
• November 5th 2010, 10:17 PM
CaptainBlack
Quote:
Originally Posted by aa751
I thought so to0 , i set the equation to 0 and got x=0 I just hoped I was wrong lol Cuase i Needed the zeros for integration=/ I was trying to find a volume of a darn barrel. lol
Try posting the original question.
CB
|
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https://dltw.wordpress.com/category/geeky/computer-scienceprogramming/
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## Manacher Algorithm
This post tries to explain the idea behind Manacher’s algorithm. It is written mainly for my own future reference so it might lack some clarity. I might improve upon it in the future when I have the time.
## Introduction
Manacher’s algorithm is a O(N) solution for finding the longest palindromic substring of a given string.
A palindrome is a sequence of symbols or elements that reads the same forward or reversed.
It is a dynamic programming problem. We let $dp[i]$ be the longest palindrome length for the palindrome that is centered at character i. We use a bottom up approach and fill the table dp. After that we find the maximum value in dp and retrieve the substring.
## The transformation (preprocessing)
A clever trick to avoid splitting cases for odd and even as well as boundary checks is to transform the given string into one with delimiters added in between each character.
$abacabb \mapsto \#a\#b\#a\#c\#a\#b\#b\#$
This will help us easily identify our palindrome because in our transformed string, the longest palindrome must start and end on a delimiter, and this maps nicely back to the index of the original string, providing an easy way to extract the substring. For example, to extract the palindrome bb, we note that it is a palindrome about index 12, and the left and right limits are 10 and 14 respectively. Dividing it by 2 gives us the indices of the original string, 5 and 7. And we can extract the substring by using s.substring(5,7).
## The crux
The crux of the algorithm is noting that after calculating some $dp[k]$, we can save calculations of $dp[n]$ for $k < n \le k + dp[k]$.
To see why. Let us denote the indices of left limit of the palindrome as L, right limit as R, and the center as C. Let T be the transformed string. Then let $C = T[k], L = T[k-m], R = T[k+m]$ where $m$ is the range on either side of the palindrome centered at C.
Suppose we are now calculating $dp[i]$ where i is between C and R. There are two cases for this palindrome that is centered at i. Either it extends past R or it doesn’t. Suppose it doesn’t extend past R. Then by looking at the reflected point about C, that is dp[2C – i], we know that the palindrome centered at that point must not extend past L either. Therefore, $dp[i] = dp[2C-i]$. In the other case, the palindrome extends beyond R so we have to manually calculate the length of this palindrome centered at i. However, we can speed up this calculation by noting that since this extends past R, it’s length must be at least R-i, so we can start comparing characters after that distance.
This translate into code by setting dp[i] = min(dp[2C-i], R-i) and then updating dp[i] by trying to extend the palindrome.
## Functional programming languages
When I first came across the functional paradigm, I thought that it sounded very cool and hip because other paradigms were too mainstream.
But when asked in several occasions to explain it, I found difficulty in conveying the essence of what it means to be a functional language. So I have decided to sit down and examine this issue.
While mainly emphasized in academia (standard ml, haskell), there have been many uses in the real world. Jane Street uses OCaml, some financial institutions use q. Many non-functional languages even support functional paradigm. In C++11 for instance, lambdas are introduced.
So what is a functional language? Firstly, a functional language is mostly pure. That is, given the same input, the function will always return the same output. This is similar to the mathematical definition of a function. Other forms of programming paradigm sometimes use function to mean a subroutine – jumping out of sequential execution to execute a block of code – and this may not be pure because the block might have some side effects such as modifying a global variable. Such pureness can lead to optimisations such as running code in parallel and memoization, which are attractive now that Moore’s law is arguably no longer true and people are looking at other ways to improve performance.
Secondly, a functional language will most likely have first class functions which means that functions are treated as values which can be returned by a function or passed around (to other functions). This is supported in most scripting languages like javascript, python, etc. Personally, I think this is a sensible way programme. Compare
`for (int i = 0; i < Thing.length; i++) {doStuff(i)}`
with
`Thing.forEach(doStuff)`
However, this comes at a cost because extra indirection is needed to treat functions as values.
I am not a big advocate of functional languages, but I think that a functional paradigm is inherently very elegant and neat (also readable) and this should be encouraged if it is the most natural way to write code for a use case.
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https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-3-section-3-1-exponential-functions-exercise-set-page-449/45
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## Precalculus (6th Edition) Blitzer
See graph; asymptote as $y=1$ Domain: $(-\infty,\infty)$ and range: $(1,\infty)$
Step 1. Start from the original function $f(x)=e^x$ shown as the green curve in the figure. Step 2. To obtain the new curve of $h(x)=e^{2x}+1$, shrink the original horizontally by a factor of 2, then shift the result vertically 1 unit up to get the red curve as shown. Step 3. We can identify the new asymptote as $y=1$ Step 4. We can determine the domain as $(-\infty,\infty)$ and range as $(1,\infty)$
|
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https://shelah.logic.at/papers/370/
|
# Sh:370
• Shelah, S., & Soukup, L. (1994). On the number of nonisomorphic subgraphs. Israel J. Math., 86(1-3), 349–371.
• Abstract:
Let \mathcal K be the family of graphs on \omega_1 without cliques or independent subsets of size \omega_1. We prove that:
1) it is consistent with CH that every G\in{\mathcal K} has 2^{\omega_1} many pairwise non-isomorphic subgraphs,
2) the following proposition holds in L: (*) there is a G\in{\mathcal K} such that for each partition (A,B) of \omega_1 either G\cong G[A] or G\cong G[B],
3) the failure of (*) is consistent with ZFC.
• Version 1994-08-30_10 (25p) published version (23p)
Bib entry
@article{Sh:370,
author = {Shelah, Saharon and Soukup, Lajos},
title = {{On the number of nonisomorphic subgraphs}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {86},
number = {1-3},
year = {1994},
pages = {349--371},
issn = {0021-2172},
mrnumber = {1276143},
mrclass = {03E35 (03E75 05C30)},
doi = {10.1007/BF02773686},
note = {\href{https://arxiv.org/abs/math/9401210}{arXiv: math/9401210}},
arxiv_number = {math/9401210}
}
|
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https://bookdown.dongzhuoer.com/hadley/ggplot2-book/new-themes.html
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## 20.1 New themes
Themes are probably the easiest form of extensions as they only require you to write code you would normally write when creating plots with ggplot2. While it is possible to build up a new theme from the ground it is usually easier and less error-prone to modify an existing theme. This is done in ggplot2 as well as can be seen by looking at e.g. theme_minimal():
print(theme_minimal)
#> function (base_size = 11, base_family = "", base_line_size = base_size/22,
#> base_rect_size = base_size/22)
#> {
#> theme_bw(base_size = base_size, base_family = base_family,
#> base_line_size = base_line_size, base_rect_size = base_rect_size) %+replace%
#> theme(axis.ticks = element_blank(), legend.background = element_blank(),
#> legend.key = element_blank(), panel.background = element_blank(),
#> panel.border = element_blank(), strip.background = element_blank(),
#> plot.background = element_blank(), complete = TRUE)
#> }
#> <bytecode: 0x558485562f08>
#> <environment: namespace:ggplot2>
here the base is theme_bw() and the theme then replaces certain parts of it with its own style using the exported %+replace% operator. As can be seen, the code doesn’t look much different to the code you normally write when styling a plot. While not adviced, it is also possible to create a theme without modifying an existing one. The general approach is to simply use the theme() function while setting complete = TRUE. It is important to make sure that at least all theme elements that do not inherit from other elements have been defined when using this approach. See e.g. theme_gray() for an example of this.
When writing new themes it is a good idea to provide a few parameters to the user for defining overarching aspects of the theme. One important such aspect is sizing of text and lines but other aspects could be e.g. key and accent colours of the theme.
Maybe something about creating new theme elements?
|
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|
https://www.arxiv-vanity.com/papers/gr-qc/0611024/
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# Planck-Scale Modified Dispersion Relations and Finsler Geometry
F. Girelli1, S. Liberati2, L. Sindoni3 SISSA, Via Beirut 2-4, 34014 Trieste, Italy and INFN, Sezione di Trieste
11
22
33
###### Abstract
A common feature of all Quantum Gravity (QG) phenomenology approaches is to consider a modification of the mass shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such approaches is therefore usually set up in the cotangent bundle (phase space). However it was recently proposed that this phenomenology could be associated with an energy dependent geometry that has been coined “rainbow metric”. We show here that the latter actually corresponds to a Finsler geometry, the natural generalization of Riemannian geometry. We provide in this way a new and rigorous framework to study the geometrical structure possibly arising in the semiclassical regime of QG. We further investigate the symmetries in this new context and discuss their role in alternative scenarios like Lorentz violation in emergent spacetimes or Deformed Special Relativity-like models.
###### pacs:
03.30.+p, 04.60.-m,11.30.Cp
## I Introduction
The quest for a quantum theory of gravity (QG) has nowadays a long standing record that stretches for several decades in the past. While this research has lead to great achievements in theoretical physics the final answer still remains hidden to us. In particular the lack of observational and experimental tests has been a constant problem in the development of QG models. Fortunately in the last decades the improved sensitivity of our experiments and observations has lead to unexpected opportunities to tests sub-Planckian consequences of several QG scenarios. Among these opportunities let us remember deviations from Newton’s law at very short distances Hoyle:2004cw ; Hoyle:2000cv , Planck-scale fuzziness of spacetime Amelino-Camelia:1999gg , possible production in TeV-scale QG scenarios of mini-black holes at colliders Dimopoulos:2001hw or in cosmic rays Anchordoqui:2001cg , QG induced violations of discrete symmetries of the Standard Model Ellis:1995xd ; Kostelecky:2005mj as well as spacetime symmetries Garay:1994en . This broad field of research goes under the general name of quantum gravity phenomenology.
It should not come as a surprise that a preeminent role in this field of research has been played by possible tests of QG scenarios proposing departures from Lorentz invariance (LI) at energies approaching the Planck scale (for an extensive review see e.g. Mattingly:2005re ). While LI is deeply rooted both in quantum field theory as well as in General Relativity, still it is strictly linked to the idea that spacetime would have the same continuous structure at any energy scale: large boosts naturally uncover the structure of spacetime at arbitrary small scales and it is unclear how this could be conciliated with the existence of a fundamental scale for the quantum gravitational phenomena, i.e. the Planck scale.
Departures from standard Lorentz invariance have nowadays been proposed within several QG scenarios. A succinct list includes: arguments based on string field theory tensor VEVs KS89 , cosmologically varying moduli scenarios Damour:1994zq , spacetime foam models Amelino-Camelia:1997gz , semiclassical spin-network calculations in Loop QG Gambini:1998it ; loopqg , as well as non-commutative geometry studies Hayakawa ; Mocioiu:2000ip ; Carroll:2001ws ; Anisimov:2001zc and some brane-world scenarios Burgess:2002tb . Albeit none of the above cited calculations can be considered at the moment a conclusive evidence that departures from Lorentz invariance are generic in QG models, they can indeed be considered a robust hint that Lorentz violations could be a theoretical possibility in most of the scenarios we are envisaging for QG. Moreover they generally agree in predicting departures from LI in the form of modified dispersion relations (MDR) for elementary particles of the form
E2 = m2+p2+D(p,μ,M) (1) = m2+p2+∞∑n=1αn(μ,M)pn,
where , are dimensional coefficients, is some particle physics mass scale, and is the scale associated to the new physics responsible for the correction to the dispersion relation (which is typically taken to be the Planck mass: GeV).
While it is not the scope of the present paper to explain how constraints can be cast on such MDR (see e.g. Jacobson:2005bg ) it is interesting to note that these are generally requiring to choose a well defined dynamical framework. While the most stringent constraints have been so far obtained considering the MDR as a by-product of an effective field theory with Planck suppressed Lorentz violating operators Jacobson:2005bg , there is an alternative point of view that tries to preserve the relativity principle and extend it to the case in which there are two (the speed of light and the Planck energy) invariant scales in place of a single one (the speed of light). This proposal goes under the name of Doubly or Deformed Special Relativity (DSR) Amelino-Camelia:2000mn . Unfortunately while on the one hand we have precise formulations of DSR in momentum space on the other hand, the implementation of DSR in spacetime is a more subtle subject and it is a theme of intense debate at present time Amelino-Camelia:2000mn ; Magueijo:2001cr ; Magueijo:2002am ; Judes:2002bw ; Kimberly:2003hp . This is a crucial point as it is clear that no DSR proposal could be really competitive with Lorentz violation scenarios, lacking a concrete understanding of the spacetime symmetries associated with this deformed Lorentz symmetry and their possible geometrical interpretation.
In this direction, a very well studied scenario for the spacetime realization of DSR is non-commutative geometry (see e.g. Amelino-Camelia:2000mn ; Kowalski-Glikman:2002jr ). While some promising results linking DSR to some special form of spacetime non-commutativity have been found in 2+1 dimensions Freidel:2003sp , we are still lacking a consistent physical picture in 3+1 dimensions. Moreover attempts to develop a quantum field theory associated with different forms of non-commutativity, a much needed step in order to be able to effectively cast phenomenological constraints, led to highly non-trivial quantum field theories (possibly with problematic features as the IR/UV-mixing Minwalla:1999px ; Matusis:2000jf ; Amelino-Camelia:2002au ).
Our investigation here will be based on different assumptions: we shall not presume any manifold non-commutativity but show instead that MDRs of the sort shown in (1) can be interpreted as due to a different form of departure from standard spacetime structure: its pseudo-Riemaniann geometry. In doing this we shall not assume neither that such departures from the standard spacetime structure are due to UV Lorentz violations or to DSR.
Attempts to reconstruct a spacetime structure starting from a MDR have been already made in the existent literature (see e.g. Kimberly:2003hp ). Interestingly the key feature of the corresponding spacetime is to be described by an energy dependent metric, called a rainbow metric Magueijo:2002xx . This is a natural concept from the QG point of view and arose in different contexts like spacetime foam Ellis:1999uh , the Renormalization Group (RG) applied to gravity Girelli:2006sc or as a consequence of averaging over QG fluctuations Aloisio:2005qt . Perhaps even more intriguing is the fact that we have concrete realization of rainbow geometries in the so called analogue models of gravity where phonons at high energy show exactly MDR like (1) as a consequence of the energy dependence of the effective geometry induced by the condensed matter background structure (see e.g. Barcelo:2005fc ).
However the rainbow metric idea proposed in Magueijo:2002xx still lacks a rigorous formulation since it involves a metric defined on the tangent bundle, while depending on a quantity associated to the cotangent bundle (i.e. the energy)444Note that the aforementioned examples of effective rainbow metrics do not have this problem since the energy scale is either associated to an external quantity (momentum exchange between the string and the topological defect) in the case of the string Liouville theory, or the theory is defined only in the cotangent space in the RG approach Girelli:2006sc .. Henceforth the aim of the present paper will consist in defining the geometry associated to a MDR in a mathematically rigorous way.
In searching for a geometrical structure leading to dispersion relations of the form (1) it is clear that we will be forced to abandon the safe harbor of Riemannian geometry as they certainly cannot accommodate any energy dependence555Remarkably the same intuition has been used 35 years ago to bypass the GZK cutoff Kirzhnits:1972sg . Unfortunately the authors have only considered a very restricted set of modified dispersion relations (i.e. homogeneous of degree two in momentum) which was erroneously supposed to lead to new physics at high energy.. In this sense it can be illuminating to look again at the situations appearing in analogue models. In fact there it can be showed that departures from exact LI at low energies can be naturally described via the considerations of the so called Finsler geometries Barcelo:2001cp ; Weinfurtner:2006wt . Finsler structures are the most studied generalizations of Riemannian geometry and are defined starting from norms on the tangent bundle instead than from inner products baochernshen .
In what follows we shall further investigate this possibility and show that indeed any MDR of the kind (1) can be seen as describing the propagation of a particle on a Finsler geometry. In this sense we prove that any rainbow metric is indeed a Finsler metric. While we cannot show that this definitely hints towards a deformed symmetry scenarios (with respect to a Lorentz violation one) we hope that this will help further developments by providing a well posed and consistent framework within which one can hope to set up a proper quantum field theory (as needed to cast constraints).
The plan of the paper will be the following: after a first section devoted to Finsler geometries, we shall deal directly with the way one can reconstruct a Finsler structure from a MDR. We shall then consider the symmetries associated to this new structures making a distinction between those relevant only on the manifold and those defined on the whole (co)tangent bundle. Finally we shall discuss the relevance of our results highlighting some possible developments of our investigation.
## Ii Finsler Geometry
Let us start with a brief review of the basic notions relevant for Finsler geometries. (Further material can be found, for example, in baochernshen ; rund .) Finsler geometry is a generalization of Riemannian geometry: instead of defining an inner product structure over the tangent bundle, we define a norm . This norm will be a real function of a spacetime point and of a tangent vector , such that it satisfies the usual norm properties namely
• if ,
• .
From the norm squared we can define the so called Finsler metric:
gμν(x,v)=12∂2F2∂vμ∂vν, (2)
which we require to be continuous and non-degenerate. Using Euler’s theorem666If is a homogenous function of degree , then . on homogeneous functions, it can be shown that (2) is equivalent to
F(x,v)=√gμν(x,v)vμvν. (3)
This shows that is a homogeneous function of degree zero of the vector . Also, since by definition is non degenerate, it admits an inverse such that .
Given the above definition a few comments are in order. First of all it is clear that Riemannian geometry can now be seen as the special case of Finsler geometry in which is given by an inner product (i.e. when does not depend on ). It is also important to stress that the Finsler metric defined in (2) is defined in the Euclidean signature, that is when is positive definite. The extension to the pseudo-finslerian case, although not always obvious, can be done in many situations (see e.g. the appendix of Weinfurtner:2006wt ).
Finally, since the Finsler metric is homogenous of degree zero, it cannot be defined on the zero section of the tangent bundle. Finsler geometry is therefore usually defined over the slit-tangent bundle, which is simply the tangent bundle minus the zero section baochernshen :
˘TM=⋃x∈M(TxM∖{0}). (4)
This is only a mathematical subtlety, since smooth curves are defined to have non-vanishing tangent vector, and we will never encounter explicitly this problem in our discussion.
We have given in the definition of a Finsler norm the condition of homogeneity, , according to the usual postulates regarding norms over vector spaces. However there are situations in which it is good to have an asymmetry with respect to the inversion . In this case, we restrict the homogeneity condition to the so called positive homogeneity condition: . Notice that this provides an extension of the usual definition of norms over vector spaces.
While in Riemannian geometry the inverse metric was directly inducing a scalar product between forms, to do the same thing in Finsler geometry one must use some caution. The duality between vectors and forms which is used in Riemannian geometry is given by the formula:
ωμ(v)=gμν(x)vν. (5)
Due to the fact that the metric tensor is represented by a non degenerate matrix, we can invert this relation to express a vector in terms of its dual form
vμ(ω)=gμν(x)ων. (6)
Therefore, given the scalar product between vectors we can naturally induce a scalar product between forms exploiting this duality. More precisely, we put:
⟨ω1,ω2⟩forms≡⟨v(ω1),v(ω2)⟩vectors. (7)
We have to extend this formalism to the case of Finsler metrics since we want to deal with the four momentum of a particle, which is more easily treated as a form.
We define the dual form to a vector by the equation:
ωμ=gμν(x,v)vν. (8)
In terms of the norm this relation can be written as:
ω(v)μ=12∂F2(x,v)∂vμ. (9)
It is important to note that, if is a non degenerate Finsler metric, then the map just defined between forms and vectors is invertible. We can exploit this inverse mapping to define the norm of a form given the norm of a vector:
G(x,ω)=F(x,v(ω)). (10)
The tensor obtained from this norm plays the same role of the inverse metric tensor in Riemannian geometry, and it is simply given by
hμν(x,ω)=12∂2G2(x,ω)∂ωμ∂ων. (11)
We can connect this tensor to the inverse metric just using the definition of .
hμν(x,ω)=gμν(x,v(ω)). (12)
The above derivation concludes our formal definition of the Finsler geometries and shows that these geometrical structures define a proper working framework which can be used indifferently either in the tangent bundle or in the cotangent bundle. However, in order to complete our treatment of Finsler geometries, a brief discussion about the treatment of curvature in these spaces is due.
The theory of curvature of Finsler spaces is more involved than the case of Riemannian geometry. Nevertheless it is worth to give some key ideas for understanding the possibilities given by this kind of structure to describe new gravitational physics. If one considers the case of a position dependent Finsler norm , and looks at the geodesic equation, one obtains:
¨xμ+Γμνρ(x,˙x)˙xν˙xρ=0, (13)
where the Christoffel’s symbols contain derivatives of the metric only in the coordinates, while keeping an explicit dependence on the velocity (See the appendix for an explicit derivation of and further discussion). Without going into mathematical details, we can hence say that not only the metric structure of the theory is velocity dependent, but also curvature effects, like tidal forces, can have modifications due to the nonlinear nature of the connection.
We define the Finsler metric to be “flat” when there exists a global coordinate system in which the connection coefficients vanish. Given that the connection contain derivatives of the metric only with respect to the coordinates, the above definition is equivalent to the statement that the “flat” Finsler metric is globally independent on the coordinates. Note however, that such metric will still be velocity dependent so it will not be the trivial Minkowski one.
The above discussion shows that the concept of Finsler structure allows to treat rigorously the idea of velocity/momentum dependent metric. Consequently, we can fit into this scheme the idea that there is a microscopic structure of spacetime which cannot be described by ordinary (pseudo-)Riemannian geometry. Notice, however, that the extension we are considering is still metric, i.e. we are not introducing non-metric structures as in metric-affine theories of gravity Hehl:1976kj ; Hehl:1994ue ; Sotiriou:2006qn .
## Iii Modified dispersion relations and Finsler norms
A particle moving in a Finsler manifold is described by the action:
I=m∫baF(x,˙x)dτ, (14)
where the norm can in principle also depend on several parameters like for example the mass of the particle and the Planck scale.
Action (14) is simply the straightforward generalization to Finsler geometry of the standard action for the free relativistic particle
I=m∫ba√gμν(x)˙xμ˙xνdτ, (15)
and as such allows to recover Eq. (13) as the Euler–Lagrange equation and to define the canonical momentum
pμ=m∂F∂˙xμ=mgμν(x,˙x)˙xνF, (16)
which satisfies the generalized mass-shell condition
hμν(x,p)pμpν = m2gμν(x,˙x)gμρ(x,˙x)˙xρgνσ(x,˙x)˙xσgαβ(x,˙x)˙xα˙xβ (17) = m2.
It is important to note that, due to the homogeneity of the norm in its vector argument, the action (14) is reparametrization invariant. If instead we have a positively homogenous norm, the action will then be only invariant under time “Orientation Preserving” (OP) reparametrizations. This more general set of actions will be called OP reparametrization invariant.
We now want to show that for any MDR of the form (1) it is possible to introduce a (OP) reparametrization invariant action whose Lagrangian can be identified with a (positively homogenous) Finsler norm. Also, given that we are interested in modifications of Special Relativity, we shall consider from now on the case of a “flat” Finsler norm . Let us stress that we will always assume through all the paper that coordinates and momenta satisfy the canonical Poisson bracket .
Let us start noticing that the assumed reparametrization invariance of the action implies that the Hamiltonian is identically zero. Consequently in order to implement a given mass-shell condition (like for example (1)) we have to introduce a Lagrange multiplier so that the action becomes
I=∫(˙xμpμ−λ(M(p)−m2))dτ. (18)
Note that the reparametrization invariance of this action implies that should hold.
To find out what is the connection between the action (18) and a Finsler geometry we have to pass to the Lagrangian formalism. To do this we use one of the Hamilton’s equations:
˙xμ=λ∂M∂pμ. (19)
In the case in which this relation is invertible we can express as a function of and , hence obtaining an action of the form:
I=∫L(˙x,λ)dτ. (20)
We can eliminate from this action just using the equation of motion obtained from varying the action with respect to this parameter so that .
So, in the end, we derive a Lagrangian which is a function only of and that is homogeneous of degree one, consequently it can be identified with a Finsler norm.
L(˙x,λ(˙x))=mF(˙x). (21)
Note however that if the action is only OP reparametrization invariant and the Lagrangian is a positively homogeneous Finsler norm.
To make this discussion clearer, let us consider the simple example of a MDR for a particle moving in two dimensions
M(p0,p1)=p20−p21−αMp31, (22)
where is a dimensionless quantity. The corresponding action is given by777In the following we will use the notation .
I=∫(˙tp0+˙xp1−λ(M−m2))dτ. (23)
Clearly this action is only OP reparametrization invariant, since the mass shell condition is not invariant under time inversion.
Let us consider the Legendre transform to the Lagrangian formalism. We obtain:
˙x = λ{x,M}=λ(−2p1−3αMp21), (24) ˙t = 2λp0. (25)
Performing the Legendre transformation, we find that the Lagrangian describing the motion of the particle is given by:
L=14˙t2−˙x2λ−18αM˙x3λ2+λm2+O(α2). (26)
The equation of motion obtained varying in the above Lagrangian is rather difficult to solve but we can find an approximate solution for by requiring that so that for any momenta well below the Planck scale we can safely keep only the order corrections. This procedure gives the following (approximate) solution:
λ(˙x)≈√˙t2−˙x22m−α2M˙x3˙t2−˙x2. (27)
Using this relation we obtain the particle Lagrangian:
L(˙x,λ(˙x))=m√˙t2−˙x2−αm22M˙x3˙t2−˙x2, (28)
which allows us to identify the Finsler norm
Fm(˙x)=√˙t2−˙x2−αm2M˙x3˙t2−˙x2. (29)
One can easily check that, as expected, this line element is a positively homogeneous Finsler norm. When we recover the Lagrangian for the relativistic particle.
In the case of more general mass shell functions , these passages can be more involved due to algebraic complications, but the final result must be the same: if the action describing the propagation of a particle is (OP) reparametrization invariant then, whatever is the mass-shell condition888The massless case should be treated with care, since the relation between the multiplier and the mass might not have a smooth limit for . In general one cannot expect then, to be able to remove the multiplier from the action (at least in the way we did in the massive case). However, this is a problem as well in the case of the massless particle in Special Relativity, where one cannot eliminate from the action since this parameter is undetermined by the equations of motion. On the other hand, determining the trajectories of the massless particle with a modified dispersion relation can be done in the same way as in Special Relativity., the trajectories followed by this particle are the geodesics of a particular, possibly particle dependent, (positively homogenous) Finsler metric, given by the procedure just described.
A final comment concerns the fact that even assuming a universal coefficient in (22) still the MDR corresponds to a Finsler norm which is mass dependent: particles with different masses see different Finsler structures. This is consistent with the fact that Finsler norms have no scale embedded in them (by homogeneity), while in general modified dispersion relations can contain several energy scales at which different physical effects are turned on.
If on the contrary the mass shell condition involves a single universal metric homogeneous of degree zero in momentum
M(p)=gμν(p)pμpν, (30)
then different particles with different masses propagate over the same Finsler structure which is given by the Legendre transform of such a metric in tangent space. It has to be noticed however that in this case the homogeneity of the metric plus its uniqueness999These are precisely the assumptions of Kirzhnits:1972sg . imply that there is no interesting phenomenology associated to the MDR. If instead one allows for a particle dependence of the metric in (30) — but still preserving homogeneity in momentum — then one would recover (in the limit ) dispersion relations of the kind for which a rich new phenomenology and consequently constraints are expected (as for example Coleman:1998ti ).
## Iv Symmetries
The effect of modifying the special relativistic dispersion relation is twofold: on one side we have a modification in the relation between energy, momentum and mass. On the other, we have a modification of the symmetry group of the the system, and correspondingly a modification in the associated Noether charges.
In order to give a physical meaning to our mathematical formalism we have to give precise definitions of physical observables, and in particular of conserved charges. For particles moving along geodesics of pseudo-Riemannian manifolds we can use Killing vector fields to generate conserved quantities
Q=ξμ(x)˙xνgμν(x), (31)
where is a Killing vector field for the metric and is an affine parametrization of the geodesic. For example, the energy of a particle can be defined as the projection of the speed along the direction of the Killing vector field associated to time translations.
It is clear that we need to provide a definition of Killing vector field of a Finsler metric. This can be done rund (although we shall not give here the mathematical derivation for sake of conciseness) just by applying the definition of Lie derivative to the Finsler metric tensor, taking into account that there is a contribution to the derivative coming from the dependence of the metric on the tangent vector on which it is evaluated.
As we have discussed in the previous section, the natural way of describing the motion of particles with modified dispersion relation is Finsler geometry, which can be formulated in an elegant way in the (co)tangent bundle. Therefore, when considering the issue of symmetries, we have to consider all the transformations on the (co)tangent bundle which leave invariant the Finsler metric. As a consequence, the diffeomorphisms of the manifold are only a special case for these symmetries.
For Killing vector fields which generate these manifold diffeomorphisms, we have the Killing equations:
gρμ(x,˙x)∂νξρ+gνρ(x,˙x)∂μξρ+2Cρμν(x,˙x)∂ξρ∂xσ˙xσ+∂gμν∂xρξρ=0, (32)
where we have defined the Cartan tensor:
Cμνρ=12∂gμν(x,˙x)∂˙xρ. (33)
This equation is obtained exactly as the Killing equation in Riemannian geometry, just considering the Lie derivative of the metric tensor. Using equation (32), it is now easy to show that if is a Killing vector field, the associated Noether charge can be written as
Q=ξμ(x)˙xνgμν(x,˙x). (34)
In this way we can provide a consistent definition of energy and momentum relating them to the Noether charges.
In particular, for the specific case of flat Finsler geometries (i.e. a metric tensor depending only on the velocity and not on the position), we see that spacetime translations are symmetries of the system and hence one can apply equation (34) to this special case. Therefore the conserved quantities associated to spacetime translations are:
E=g0μ(˙x)˙xμ,Pi=giμ(˙x)˙xμ. (35)
On shell, using an affine parameter for the geodesic and modulo a mass rescaling, these quantities coincide with the canonical momenta appearing in the action (18), or, equivalently, in the action (14) given that
pμ=m∂F∂˙x=mFgμν(˙x)˙xν, (36)
and that, in the case of an affine parametrization, F is constant along a geodesic. Hence, taking into account normalizations, the energy momentum co-vector obtained using Noether’s theorem obeys the mass shell condition appearing in (18). Therefore the momenta appearing in the MDR are really the physical momenta associated to spacetime translations, so that .
This discussion shows how we can treat the case of diffeomorphisms of the manifold with the same language used in Riemannian geometry. However, as we have stressed, these are only a subset of the transformations of the full tangent bundle. To show that there are other transformations which are relevant, we now pass to the discussion of the Lorentz group and its action for the case of a modified dispersion relation. Since using Killing vector fields can be difficult, we will describe the symmetries of a MDR using the Hamiltonian formalism. The infinitesimal generators of the symmetry group obey the equation
{G,M(p)}=0.
By construction the translation generators given by leave invariant the MDR
{pμ,M(p)}=0.
This is consistent with the fact that the system described by the action (14) is invariant under translations. On the other hand the usual Lorentz generators are not commuting anymore with the MDR
{Jμν,M(p)}≠0.
In particular, there could be a situation in which while the generators of rotations are conserved, the generators of boosts do not commute with the MDR.
With respect to the fate of the Lorentz group, one could adopt two different points of view. The first one consists in considering the MDR as a manifestation of a symmetry breaking mechanism which destroys the original Lorentz symmetry, reducing it to a smaller group. This could be related to the fact that the underlying theory, as in the case of analogue models Barcelo:2005fc , might not have the Lorentz group as fundamental symmetry group, this latter appearing only as an approximate symmetry in the low energy regime, leading to our geometric description of spacetime in terms of a pseudo-Riemannian manifold.
The alternative point of view is to look for a deformed action of the Lorentz group, i.e. a representation of the Lorentz group acting on the whole phase space i.e. mixing configuration and momentum space. In this case it is therefore necessary to deform the Lorentz generators, for example adding extra terms
Jμν→Jμν=Jμν+αiCiμν(x,p,M), (37)
where are functions on phase space to be determined by the equations
{Jμν,M(p)}=0, (38) {Jμν,Jρσ}=ημσJρν+ηνρJσμ+ημρJνσ+ηνσJμρ.
Here the are the components of the Minkowski metric, which are the structure constants of the Lorentz group, while our physical metric tensor is given by the Finsler metric tensor obtained from the norm. The action of the deformed Lorentz infinitesimal generators on phase space coordinates is given by
{xβ,Jμν}={xβ,Jμν}+αi∂∂pβCiμν(x,p,M)=xμδβν−xνδβμ+αi∂∂pβCiμν(x,p,M), (39) {pβ,Jμν}={pβ,Jμν}−αi∂∂xβCiμν(x,p,M)=−pμδβν+pνδβμ−αi∂∂xβCiμν(x,p,M). (40)
This should be compared with the special relativistic counterpart. In the case of Minkowski spacetime, the Lorentz group acts on the position and on momenta separately. They do not mix. In the general Finsler case we expect a mixing, because the functions can be very complicated and not just of the form . This means that in certain cases we can expect to find a representation of the Lorentz group acting on the phase space in such a complicated way. Making the Legendre transformation we can translate this statement by saying that a symmetry transformation for a Finsler line element can be a map acting on the tangent bundle. This map, in general, is not the lift to the tangent bundle of a symmetry acting only on the manifold as in Riemannian geometry. This is expected in Finsler geometry since, in some sense, it is the geometry of the tangent bundle lagrangegeom .
It should be noted that the deformation of the Lorentz group implies in general non canonical commutation relations between boost and momenta, affecting therefore the definition of the Poincaré group. One should check with care the consequences of this fact in the context of particle physics, in which the role of the Poincaré group is crucial in determining the vacuum state and the classification of particles.
On the other hand, one could try to complete this deformed Lorentz group with deformed momenta in such a way to recover the usual Poincaré group. To establish which of these groups is the physical one, the deformed Poincaré group or the remnant from the breaking of the Lorentz group, we would have to do, as usual, quantum field theory tests by looking at processes which are able to discriminate between the two scenarios.
It is important to recall that, while the action of the symmetry group is unique in phase space, given a specific MDR, the realization in the tangent bundle of this group is particle dependent, due to the explicit mass dependence of the Finsler metric. Therefore we cannot give in the tangent bundle a unique, absolute, spacetime representation of the deformed Lorentz group.
## V Conclusion
To summarize, we have showed that the notion of Finsler metric is the geometric structure encoding the notion of rainbow metric. More precisely we showed how a metric in the cotangent space constructed from a MDR is related to a (positively homogenous) Finsler norm in tangent space, the key point of the analysis being the time (OP) reparametrization invariance.
The Finsler metric arising from the MDR is then particle dependent: each particle of different mass will see a different Finsler metric. We could have expected this from the intuition behind the rainbow metric: in the cotangent space, the metric is dependent on the momentum of the particle, so that in the tangent space, the metric should depend both on velocity and mass. A metric depending on velocity is a Finsler metric, a rainbow metric is then naturally a mass dependent Finsler metric. Note that as a direct consequence, in the case of many particles we obtain a multi Finsler metric structure. This is similar to the construction that appears in the Coleman-Glashow analysis Coleman:1998ti .
The discussion made in this paper shows that there could be a regime in which the standard geometrical description breaks down in a serious way. Not only we have to pass from Riemannian geometry to Finsler geometry, but we have that each particle sees a different geometrical structure depending on its mass, making the notion of “the spacetime geometry” or even of “tangent bundle geometry” completely meaningless.
This should be compared with the case of analogue models for gravity. There, the concept of a Lorentzian spacetime geometry is a low-energy, emergent one, while the true underlying spacetime theory is completely different. The fact that the notion of spacetime geometry is shaking as it stands is just a manifestation of something deep: the MDR are a consequence of the fact that we are probing the microstructure of spacetime, which of course could be non-geometric.
However, there could be other ways in which a geometric description could be preserved. In fact there are good reasons to think that behind the Standard Model there is a unified field theory (GUT) of gauge interactions. In these theories, fermions are organized in multiplets within which they share the same features. Originally they are massless, acquiring a mass only via a Higgs mechanism at suitable energies. If we postulate, as it seems reasonable, that all fermions are massless when we start probing quantum gravity effects, then it makes sense to speak about a geometry (at least in the tangent bundle), since they all have the same MDR in this limit.
Clearly the low energy regime brings into the game the details of the pattern of the various symmetry breakings, leading to deviations from a single geometrical picture. Nevertheless, it is also true that at low energies quantum gravity effects are presumably subdominant, so that the Lorentzian spacetime geometry becomes, to a very good degree of approximation, the appropriate description for the stage of the Standard Model dynamics.
Alternatively one can remove the mass dependence from (29) by just substituting by a new dimensionless coefficient and assuming it to be universal (i.e. particle independent). In this case compatibility with observations would however require hinting that it would have to be a small ratio of some particle physics mass/energy scale, , and, presumably, the Planck one: . Let us notice however that in our example (22) the above cited rescaling would lead to a dispersion relation with a LIV term . This implies that, at least for the case of electrons with a cubic term in the MDR, this new energy scale would have to be smaller than the electron mass in order to be compatible with current constraints (if EFT can be applied then the best constraints for the dimensionless coefficient of the term range nowadays between and , see e.g. Jacobson:2005bg ). It is tantalizing that such line of reasoning seems to suggest that should be identified with some sort of IR fundamental scale for gravitational physics complementary to the UV one represented by the Planck mass.
The study of symmetries associated to the Finsler metric showed that there are two possibilities. We can have broken Lorentz symmetries if we consider that a symmetry transformation should be (as usual) a transformation that lives separately in the manifold and in the (co)tangent space. If we relax this, that is allow for symmetry transformation mixing (co)tangent space and manifold, then the Lorentz symmetries are still present. They are then called deformed. This construction arises for example in Deformed Special Relativity (e.g. in the bicrossproduct basis or DSR1 Majid:1994cy ). From the geometrical perspective this is a change of paradigm: the fundamental object is not the manifold anymore but the full tangent bundle. This point of view is consistent with the DSR intuition: when trying to implement some universal momentum scale, we are led to unify the notion of spacetime with momentum just as in Special Relativity one unifies space and time by introducing a universal speed. Once again this picture is still consistent with the rainbow metric since to have full information about a system in this framework, we need to know both its position and momentum.
In this sense the Finsler structure seems to be the natural framework for a geometric interpretation of DSR. The fact that DSR structures involve usually non trivial symplectic forms does not contradict this. Indeed it is always possible to make a Darboux transformation to obtain a trivial symplectic form Girelli:2005dc and perform there our analysis. Alternatively brute force calculations can also be made as in Ghosh:2006cb . Note en passant that the Darboux transformation implies in general that the new configuration coordinates should be function of both the old configuration and momentum variables, so that on the geometric point of view we are really living on the full tangent bundle.
In conclusion, this new geometric point of view provides a new angle of attack to deal with some of the problems met in the context of Lorentz violations or deformed symmetries as in DSR. For example it might provide new insights for the construction of Effective Field Theory in these contexts: something necessary to make meaningful experimental predictions. The proposed framework provides also a concrete mathematical set up to describe the QG corrections to the notion of uniformly accelerated observer, horizons… These are exciting questions that we leave for further studies.
###### Acknowledgements.
SL and LS wish to thank S. Sonego and M. Visser for illuminating discussions.
## Appendix A Geodesic equation
Let us consider in detail the geodesic equation for Finsler manifolds. We start from the action (14), with the most general case of position dependent Finsler norm. The Euler–Lagrange equations of motion reduce to:
ddτ[1F(gμν˙xν+12∂gαβ∂˙xμ˙xα˙xβ)]−121F∂gαβ∂xμ˙xα˙xβ=0. (41)
If we introduce the Cartan tensor
Cμνρ=14∂3∂˙xμ∂˙xν∂˙xρF2=12∂∂˙xμgνρ, (42)
we see that, due to the zero degree of homogeneity of the metric tensor, as a consequence of Euler’s theorem on homogeneous functions:
zdfdz=nf(z)⟺f(az)=anf(z), (43)
applied to the case we obtain:
Cμνρ(x,˙x)˙xμ=Cμνρ(x,˙x)˙xν=Cμνρ(x,˙x)˙xρ=0. (44)
The Cartan tensor is a useful tensorial quantity which can describe the non-Riemannian curvature of the Finsler metric tensor, being non-vanishing even in what we call the “flat” case. As a consequence of (44), we obtain that the geodesic equation, in the affine parametrization, becomes
¨xμ+Γμνρ(x,˙x)˙xν˙xρ=0, (45)
where these generalization of the Christoffel’s coefficients to the case of Finsler structures are given by the usual expression:
Γμνρ(x,˙x)=12gμσ(x,˙x)[−∂σgνρ(x,˙x)+∂νgρσ(x,˙x)+∂ρgσν(x,˙x)]. (46)
We note that these coefficients depend on the velocity as well, and in a non-linear way. This means that to treat the theory of curvature in Finsler space we have to use the language of non-linear connections, for which we refer to the literature rund ; baochernshen ; lagrangegeom .
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http://en.wikipedia.org/wiki/Quantum_mutual_information
|
# Quantum mutual information
In quantum information theory, quantum mutual information, or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state. It is the quantum mechanical analog of Shannon mutual information.
## Motivation
For simplicity, it will be assumed that all objects in the article are finite-dimensional.
The definition of quantum mutual entropy is motivated by the classical case. For a probability distribution of two variables p(x, y), the two marginal distributions are
$p(x) = \sum_{y} p(x,y)\; , \; p(y) = \sum_{x} p(x,y).$
The classical mutual information I(X, Y) is defined by
$\;I(X,Y) = S(p(x)) + S(p(y)) - S(p(x,y))$
where S(q) denotes the Shannon entropy of the probability distribution q.
One can calculate directly
$\; S(p(x)) + S(p(y))$
$\; = -(\sum_x p_x \log p(x) + \sum_y p_y \log p(y))$
$\; = -(\sum_x \; ( \sum_{y'} p(x,y') \log \sum_{y'} p(x,y') ) + \sum_y ( \sum_{x'} p(x',y) \log \sum_{x'} p(x',y)))$
$\; = -(\sum_{x,y} p(x,y) (\log \sum_{y'} p(x,y') + \log \sum_{x'} p(x',y)))$
$\; = -\sum_{x,y} p(x,y) \log p(x) p(y) .$
So the mutual information is
$I(X,Y) = \sum_{x,y} p(x,y) \log \frac{p(x,y)}{p(x) p(y)}.$
But this is precisely the relative entropy between p(x, y) and p(x)p(y). In other words, if we assume the two variables x and y to be uncorrelated, mutual information is the discrepancy in uncertainty resulting from this (possibly erroneous) assumption.
It follows from the property of relative entropy that I(X,Y) ≥ 0 and equality holds if and only if p(x, y) = p(x)p(y).
## Definition
The quantum mechanical counterpart of classical probability distributions are density matrices.
Consider a composite quantum system whose state space is the tensor product
$H = H_A \otimes H_B.$
Let ρAB be a density matrix acting on H. The von Neumann entropy of ρ, which is the quantum mechanical analogy of the Shannon entropy, is given by
$S(\rho^{AB}) = - \operatorname{Tr} \rho^{AB} \log \rho^{AB}.$
For a probability distribution p(x,y), the marginal distributions are obtained by integrating away the variables x or y. The corresponding operation for density matrices is the partial trace. So one can assign to ρ a state on the subsystem A by
$\rho^A = \operatorname{Tr}_B \; \rho^{AB}$
where TrB is partial trace with respect to system B. This is the reduced state of ρAB on system A. The reduced von Neumann entropy of ρAB with respect to system A is
$\;S(\rho^A).$
S(ρB) is defined in the same way.
Technical Note: In mathematical language, passing from the classical to quantum setting can be described as follows. The algebra of observables of a physical system is a C*-algebra and states are unital linear functionals on the algebra. Classical systems are described by commutative C*-algebras, therefore classical states are probability measures. Quantum mechanical systems have non-commutative observable algebras. In concrete considerations, quantum states are density operators. If the probability measure μ is a state on classical composite system consisting of two subsystem A and B, we project μ onto the system A to obtain the reduced state. As stated above, the quantum analog of this is the partial trace operation, which can be viewed as projection onto a tensor component. End of note
It can now be seen that the appropriate definition of quantum mutual information should be
$\; I(\rho^{AB}) = S(\rho^A) + S(\rho^B) - S(\rho^{AB}).$
Quantum mutual information can be interpreted the same way as in the classical case: it can be shown that
$I(\rho^{AB}) = S(\rho^{AB} \| \rho^A \otimes \rho^B)$
where $S(\cdot \| \cdot)$ denotes quantum relative entropy.
|
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https://sites.cs.ucsb.edu/~emre/cs32/hw/12.html
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# Homework 12: Dynamic Dispatch and Polymorphism
Due: 5/18 2pm
Name & Perm #:
Homework buddy (leave blank if you worked alone):
## 1. (10 pts)
In the lectures, I mentioned dynamic dispatch is a form of polymorphism, and that some object-oriented programming resources mistakenly conflate the two.
1. (4 pts) What is dynamic dispatch? Why is it "dynamic"? Explain briefly.
2. (4 pts) What is the purpose of polymorphism? How does it differ from dynamic dispatch? Polymorphism is more general than dynamic dispatch, explain how it is more general.
## 2.
On page 868 in PS, in Display 15.12, line 17, there is a use of the overloaded operator < on two objects, one of type Sale and another of type DiscountSale. The definition of that operator appears on lines 25 - 28 of Display 15.10 on p. 866. On line 27, there is an invocation of first.bill() and an invocation of second.bill().
1. (2 pts) For first.bill() in the case of the invocation in Display 15.12 line 17, where is the definition of the member function bill() that is invoked? Give the name of the class whose bill() function is invoked.
2. (2 pts) For second.bill() in the case of the invocation in Display 15.12 line 17, where is the definition of the member function bill() that is invoked? Give the name of the class whose bill() function is invoked.
3. (2 pts) The bill() member function is special in that the exact definition of the function used depends on what type of object it is invoked on–whether it is an instance of Sale or DiscountSale, which may not be known until run-time. What is the C++ keyword that is used in the definition of bill() that signals this so called dynamic dispatch of the member function?
## 3. (8 pts)
Assume we have a base class (e.g. Person) and derived class (e.g. Student), and there is some function such as toString() that is defined in both the base class and the dervied class.
For example, suppose that:
• for Person, toString returns the person's name, e.g. Chris Gaucho
• for Student, toString returns the person's name and their perm number in parentheses. e.g. Chris Gaucho (1234567).
We say that toString() is overridding in the derived class. However, in PS (15.3), Savitch makes a distinction between the two cases, one that is properly called overriding and another that should really be called redefinition. Most of the cases we've seen so far are really just redefinition. What is different, according to Savitch, in the case where this should be called overriding? Hint: the override keyword covered in class is relevant here.
## 4.
Given the following class definitions (you may assume all necessary libraries have already been included):
class A {
public:
~A() { cout << "A::~A()" << endl; }
void f1() { cout << "A::f1()" << endl; }
virtual void f2() { cout << "A::f2()" << endl; }
};
class B : public A {
public:
virtual ~B() { cout << "B::~B()" << endl; }
virtual void f1() { cout << "B::f1()" << endl; }
void f2() { cout << "B::f2()" << endl; }
virtual void f3() = 0;
};
class C : public B {
public:
~C() { cout << "C::~C()" << endl; }
void f1() { cout << "C::f1()" << endl; }
virtual void f3() { cout << "C::f3()" << endl; }
};
1. (6 pts) What will the output be if we ran the following code (be sure to include destructors' output):
void f1() { C c1; A a1 = c1; a1.f1(); a1.f2(); }
int main() { f1(); }
2. (6 pts) What will the output be if we ran the following code (be sure to include destructors' output):
void f2() { B* b1 = new C(); b1->f1(); b1->f2(); b1->f3(); delete b1; }
int main() { f2(); }
Author: Instructor: Mehmet Emre
Created: CS 32 Spring '22
The material for this class is based on Prof. Richert Wang's material for CS 32
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https://www.openfluids.engineer/2017/05/07/osx-split-l2tp-vpn/
|
# OSX Split L2TP VPN
I recently had to configure a L2TP VPN into my office network that, for a simple network, is trivial in OSX as there is a GUI in the Network pane of System Preferences. However, we run a mix of both publicly routable and private IPv4 subnets and I really wanted to run with split tunnelling through my relatively fast HFC home network connection. There are certainly references from Google, e.g. [1, 2], on how to set this up, as well as some debate [3] as whether it is possible to accomplish this server side. Irrespective: I have no control of the VPN concentrator so this is all done client side and, as I spend most of my life in a terminal, this seemed the way to go.
The general process is:
1. Use the OSX GUI to create a split tunnel VPN
3. Add two supporting AppleScript scriptlets
4. Modify sudo privileges (if desired)
5. Test and relax
The key really here is that the bash scripts act as controllers to execute the AppleScripts, which start and stop the VPN respectively, and then modify the routing table.
## IP Ranges
For this example assume the following:
1. The VPN allocates a private IPv4 address in the 10.0.0.0/24 range
2. I have a publicly routable IPv4 address at 172.0.0.1/24 but its behind my VPN concentrator
3. I have a private 192.168.240.0/24 subnet also behind my VPN concentrator
## GUI Install
There’s really good online guides for this so I’m not going to go through this again.
## Bash Scripts
For ease of execution, these two bash scripts should be installed somewhere on your path. I use ~/bin, which is in my path.
launch-vpn:
#!/bin/bash
# set -o noexec
# set -o verbose
# set -o xtrace
set -o nounset
# Simple script to launch the VPN.
# It is better to do this as the L2TP does not allow for split tunnelling,
# easily that is, so I can execute the commands here. This does assume that
# there is no overlap in the IP ranges, for example if you are at home on
# 192.168.1.0/24 then work cannot be the same.
#
#
# Need to ad to sudo via: sudo visudo
#
# Dr Peter Brady &lt;[email protected]&gt;
# 2017-05-07
# Step 1: AppleScript VPN
sudo /sbin/route -nq add 172.0.0.1/24 -interface ppp0
sudo /sbin/route -nq add 192.168.240.0/24 -interface ppp0
disconnect-vpn:
#!/bin/bash
# set -o noexec
# set -o verbose
# set -o xtrace
set -o nounset
# Simple script to close the VPN.
# It is better to do this as the L2TP does not allow for split tunnelling,
# easily that is, so I can execute the commands here. This does assume that
# there is no overlap in the IP ranges, for example if you are at home on
# 192.168.1.0/24 then work cannot be the same.
#
#
# Need to ad to sudo via: sudo visudo
#
# Dr Peter Brady &lt;[email protected]&gt;
# 2017-05-07
sudo /sbin/route -nq delete 172.0.0.1/24 -interface ppp0
sudo /sbin/route -nq delete 192.168.240.0/24 -interface ppp0
# Step 2: AppleScript VPN
## AppleScript
These scripts were inspired by a discussion and example over on superuser.com where I could adapt the bash functions described to the following.
esi-connect.scpt:
-- Inspired by:
-- https://superuser.com/questions/358513/start-configured-vpn-from-command-line-osx
tell application "System Events"
tell current location of network preferences
set VPN to service "MyVPN"
if exists VPN then connect VPN
repeat while (current configuration of VPN is not connected)
delay 1
end repeat
end tell
end tell
esi-disconnect.scpt:
-- Inspired by:
-- https://superuser.com/questions/358513/start-configured-vpn-from-command-line-osx
tell application "System Events"
tell current location of network preferences
set VPN to service "Pacific ESI"
if exists VPN then disconnect VPN
end tell
end tell
return
## Modify sudo Permissions
Finally, because I’m lazy and this is my personal laptop, I modified my sudo file via
speleo:~ pbrady\$ sudo visudo
username ALL= NOPASSWD: /sbin/route
This allows me to run the route commands without adding a password for the sudo.
|
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|
http://www.ck12.org/book/CK-12-Calculus/section/1.2/
|
<meta http-equiv="refresh" content="1; url=/nojavascript/"> Relations and Functions | CK-12 Foundation
# 1.2: Relations and Functions
Created by: CK-12
## Learning Objectives
A student will be able to:
• Identify functions from various relationships.
• Review function notation.
• Determine domains and ranges of particular functions.
• Identify key properties of some basic functions.
• Sketch graphs of basic functions.
• Sketch variations of basic functions using transformations.
• Compose functions.
## Introduction
In our last lesson we examined a variety of mathematical equations that expressed mathematical relationships. In this lesson we will focus on a particular class of relationships called functions, and examine their key properties. We will then review how to sketch graphs of some basic functions that we will revisit later in this class. Finally, we will examine a way to combine functions that will be important as we develop the key concepts of calculus.
Let’s begin our discussion by reviewing four types of equations we examined in our last lesson.
Example 1:
$y = x^2$
$y = 2x + 3$
$x^2 + y^2 = 4$
$y = x^3 - 9x$
Of these, the circle has a quality that the other graphs do not share. Do you know what it is?
Solution:
The circle’s graph includes points where a particular $x-$value has two points associated with it; for example, the points $(1,\sqrt{3})$ and $(1,-\sqrt{3})$ are both solutions to the equation $x^2 + y^2 = 4.$ For each of the other relationships, a particular $x-$value has exactly one $y-$value associated with it.
The relationships that satisfy the condition that for each $x-$value there is a unique $y-$value are called functions. Note that we could have determined whether the relationship satisfied this condition by a graphical test, the vertical line test. Recall the relationships of the circle, which is not a function. Let’s compare it with the parabola, which is a function.
If we draw vertical lines through the graphs as indicated, we see that the condition of a particular $x-$value having exactly one $y-$value associated with it is equivalent to having at most one point of intersection with any vertical line. The lines on the circle intersect the graph in more than one point, while the lines drawn on the parabola intersect the graph in exactly one point. So this vertical line test is a quick and easy way to check whether or not a graph describes a function.
We want to examine properties of functions such as function notation, their domain and range (the sets of $x$ and $y$ values that define the function), graph sketching techniques, how we can combine functions to get new functions, and also survey some of the basic functions that we will deal with throughout the rest of this book.
Let’s start with the notation we use to describe functions. Consider the example of the linear function $y = 2x + 3.$ We could also describe the function using the symbol $f(x)$ and read as "$f$ of $x$" to indicate the $y-$value of the function for a particular $x-$value. In particular, for this function we would write $f(x) = 2x + 3$ and indicate the value of the function at a particular value, say $x = 4$ as $f(4)$ and find its value as follows: $f(4) = 2(4) + 3 = 11.$ This statement corresponds to the solution $(4, 11)$ as a point on the graph of the function. It is read, "$f$ of $4$ is $11$."
We can now begin to discuss the properties of functions, starting with the domain and the range of a function. The domain refers to the set of $x-$values that are inputs in the function, while the range refers to the set of $y-$values that the function takes on. Recall our examples of functions:
Linear Function $g(x) = 2x + 3$
Quadratic Function $f(x) = x^2$
Polynomial Function $p(x) = x^3 - 9x$
We first note that we could insert any real number for an $x-$value and a well-defined $y-$value would come out. Hence each function has the set of all real numbers as a domain and we indicate this in interval form as $D: (-\infty,\infty)$. Likewise we see that our graphs could extend up in a positive direction and down in a negative direction without end in either direction. Hence we see that the set of $y-$values, or the range, is the set of all real numbers $R: (-\infty,\infty).$
Example 2:
Determine the domain and range of the function.
$f(x) = 1/(x^2 - 4).$
Solution:
We note that the condition for each $y-$value is a fraction that includes an $x$ term in the denominator. In deciding what set of $x-$values we can use, we need to exclude those values that make the denominator equal to $0.$ Why? (Answer: division by $0$ is not defined for real numbers.) Hence the set of all permissible $x-$values, is all real numbers except for the numbers $(2, -2),$ which yield division by zero. So on our graph we will not see any points that correspond to these $x-$values. It is more difficult to find the range, so let’s find it by using the graphing calculator to produce the graph.
From the graph, we see that every $y \neq 0$ value in $(-\infty,\infty)$ (or "All real numbers") is represented; hence the range of the function is $\{-\infty, 0\} \cup \{0, \infty\}.$ This is because a fraction with a non-zero numerator never equals zero.
Eight Basic Functions
We now present some basic functions that we will work with throughout the course. We will provide a list of eight basic functions with their graphs and domains and ranges. We will then show some techniques that you can use to graph variations of these functions.
Linear
$f(x) = x$
Domain $=$ All reals
Range $=$ All reals
$f(x) = x^2$
Domain $=$ All reals
Range $= \left \{ y \ge 0 \right \}$
Cube (Polynomial)
$f(x)=x^3$
Domain $=$ All reals
Range $=$ All reals
Square Root
$f(x) = \sqrt{x}$
Domain $=\left \{ x \ge 0 \right \}$
Range $= \left \{ y \ge 0 \right \}$
Absolute Value
$f(x) = |x|$
Domain $=$ All reals
Range $=\left \{ y \ge 0 \right \}$
Reciprocal
$f(x) = 1/x$
Domain $=\left \{ x \neq 0 \right \}$
Range $=\left \{ y \neq 0 \right \}$
Sine
$f(x) = \sin x$
Domain $=$ All reals
Range $= \left \{ -1 \le y \le 1 \right \}$
Cosine
$f(x) = \cos x$
Domain $=$ All reals
Range $= \left \{ -1 \le y \le 1 \right \}$
Graphing by Transformations
Once we have the basic functions and each graph in our memory, we can easily sketch variations of these. In general, if we have $f(x),$ and $c$ is some constant value, then the graph of $f(x - c)$ is just the graph of $f(x)$ shifted $c\;\mathrm{units}$ to the right. Similarly, the graph of $f(x + c)$ is just the graph of $f(x)$ shifted $c\;\mathrm{units}$ to the left.
Example 3:
$f(x) = x^2$
$f(x) = (x - 2)^2$
In addition, we can shift graphs up and down. In general, if we have $f(x),$ and $c$ is some constant value, then the graph of $f(x)+ c$ is just the graph of $f(x)$ shifted $c\;\mathrm{units}$ up on the $y-$axis. Similarly, the graph of $f(x)-c$ is just the graph of $f(x)$ shifted $c\;\mathrm{units}$ down on the $y-$axis.
Example 4:
$f(x) = \sqrt{x}$
$f(x) = \sqrt{x} + 3$
We can also flip graphs in the $x-$axis by multiplying by a negative coefficient.
$f(x) = x^2$
$f(x) = - x^2$
Finally, we can combine these transformations into a single example as follows.
Example 5:
$f(x) = -(x-2)^2 + 3.$ The graph will be generated by taking $f(x) = x^2,$ flipping in the $y-$axis, and moving it two units to the right and up three units.
Function Composition
The last topic for this lesson involves a way to combine functions called function composition. Composition of functions enables us to consider the effects of one function followed by another. Our last example of graphing by transformations provides a nice illustration. We can think of the final graph as the effect of taking the following steps:
$x \rightarrow -(x-2)^2 \rightarrow -(x-2)^2 + 3$
We can think of it as the application of two functions. First, $g(x)$ takes $x$ to $-(x-2)^2$ and then we apply a second function, $f(x)$ to those $y-$values, with the second function adding $+3$ to each output. We would write the functions as
$f(g(x)) = -(x -2)^2+3$ where $g(x) = -(x -2)^2$ and $f(x)= x + 3.$ We call this operation the composing of $f$ with $g$ and use notation $f \circ g.$ Note that in this example, $f \circ g \neq g \circ f.$ Verify this fact by computing $g \circ f$ right now. (Note: this fact can be verified algebraically, by showing that the expressions $f \circ g$ and $g \circ f$ differ, or by showing that the different function decompositions are not equal for a specific value.)
## Lesson Summary
1. Learned to identify functions from various relationships.
2. Reviewed the use of function notation.
3. Determined domains and ranges of particular functions.
4. Identified key properties of basic functions.
5. Sketched graphs of basic functions.
6. Sketched variations of basic functions using transformations.
7. Learned to compose functions.
## Review Questions
In problems 1 - 2, determine if the relationship is a function. If it is a function, give the domain and range of the function.
In problems 3 - 5, determine the domain and range of the function and sketch the graph if no graph is provided.
1. $f(x)= \frac {3x^2}{x^2 - 1}$
2. $y = \sqrt{-x + 3}$
3. $f(x) = |2x -3|-2$
In problems 6 - 8, sketch the graph using transformations of the graphs of basic functions.
1. $f(x) = -(x + 2)^2 + 5$
2. $f(x) = -\frac {1}{x - 2} +3$
3. $y = -\sqrt {-x - 2} +3$
4. Find the composites, $f \circ g$ and $g \circ f$ for the following functions. $f(x) = -3x + 2, g(x)=\sqrt{x}$
5. Find the composites, $f \circ g$ and $g \circ f$ for the following functions. $f(x) = x^2, g(x) = \sqrt {x}$
## Date Created:
Feb 23, 2012
Dec 03, 2014
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https://study.com/academy/answer/a-company-has-a-policy-investigate-all-variances-exceeding-3-000-or-15-of-the-budgeted-cost-there-is-a-variance-of-2-000-in-repair-and-maintenance-costs-of-12-000-what-does-the-company-do-i.html
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# A company has a policy - "investigate all variances exceeding $3,000 or 15% of the budgeted... ## Question: A company has a policy - "investigate all variances exceeding$3,000 or 15% of the budgeted cost."
There is a variance of $2,000 in repair and maintenance costs of$12,000. What does the company do in the given situation?
a) It should be ignored as it is less than $3,000. b) It should be investigated as all variances are equally important. c) It deserves more attention as it is more than 15% of the total repair cost. d) It should be considered an in-control occurrence. ## Variances in Budgets: Variances in budgets are the differences between the actual results and the expected results according to the budget. Management should decide on a policy of how to react to variances. ## Answer and Explanation: 1 Become a Study.com member to unlock this answer! Let us consider the alternatives: a) It should be ignored as it is less than$3,000. No, while it is less than \$3,000, it is more than 15% of the...
Variances in Budgets: Definition, Calculations & Analysis
from
Chapter 9 / Lesson 16
8.4K
Calculating variances is one component of budgeting and accounting in business. Understand the definition of variances in budgets, and examine how variances are calculated and analyzed.
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https://plainmath.net/advanced-physics/100588-a-transverse-sinusoidal-wave
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2023-01-01
A transverse sinusoidal wave moves along a string in the positive x - direction at a speed of 10 cms−1. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap - shot of the wave. The velocity of point P when its displacement is 5 cm is...
Armeebildzku
Expert
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http://link.springer.com/article/10.1007%2Fs11120-005-1002-9
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Photosynthesis Research
, Volume 83, Issue 3, pp 329–333
# Cyanobacterial Photosystem I lacks specificity in its interaction with cytochrome c6 electron donors
• Manuel Hervás
• Antonio Díaz-Quintana
• Cheryl A. Kerfeld
• David W. Krogmann
• Miguel A. De la Rosa
• José A. Navarro
Regular paper
DOI: 10.1007/s11120-005-1002-9
Hervás, M., Díaz-Quintana, A., Kerfeld, C.A. et al. Photosynth Res (2005) 83: 329. doi:10.1007/s11120-005-1002-9
## Abstract
In cyanobacteria, plastocyanin and cytochrome c6, the alternate donor proteins to Photosystem I, can be acidic, neutral or basic; the role of electrostatics in their interaction with photosystem I varies accordingly. In order to elucidate whether these changes in the electron donors’ properties correlate with complementary changes in the docking site of the corresponding photosystem, we have investigated the kinetics of reactions between three cytochrome c6 with isoelectric points of 5.6, 7.0 and 9.0, with Photosystem I particles from the same three genera of cyanobacteria which provided the cytochromes. The model systems compared here thus sample the full range of charge properties observed in cytochromes c6: acidic, basic and neutral. The rate constants and dependence on ionic strength for photosystem I reduction were distinctive for each cytochrome c6, but independent of Photosystem I. We conclude that the specific structural features of each cytochrome c6 dictate their different kinetic behaviours, whereas the three photosystems are relatively indiscriminate in docking with the electron donors.
### Keywords:
Arthrospiracytochrome c6laser flash photolysisNostocPhotosystem ISynechocystis
### Abbreviations
Cyt c6
cytochrome c6
k2
second order rate constant
kobs
observed pseudo first-order rate constant
PS I
Photosystem I
## Authors and Affiliations
• Manuel Hervás
• 1
• Antonio Díaz-Quintana
• 1
• Cheryl A. Kerfeld
• 2
• David W. Krogmann
• 3
• Miguel A. De la Rosa
• 1
• José A. Navarro
• 1
1. 1.Instituto de Bioquímica Vegetal y Fotosíntesis, Centro de Investigaciones Científicas Isla de la CartujaUniversidad de Sevilla y CSICSevillaSpain
2. 2.Molecular Biology InstituteUCLALos AngelesUSA
3. 3.Department of BiochemistryPurdue UniversityWest LafayetteUSA
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https://web2.0calc.com/questions/magick-of-the-quadratic
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+0
+14
1227
8
+163
Hear ye, hear ye! To all peoples of this land and beyond:
This be a demonstration of the Magick of the Quadratic.
The Equation:
$$a x^2\; +\; b x\; +\; c\; =\; 0$$
The Factored Form:
$$f(x)\; =\; (x\; +\; a)\;(x\; +\; b)$$
The Formula:
$$x\; =\; \frac {-b\; \pm\; \sqrt {b^2\; -\; 4ac}}{2a}$$
This hath no words, only the icons used by the magicians and sorcerers of math magick. Though I looketh deep into the crystal sphere for this knowledge, the creator of this wonder remaineth unknown.
If ye wish to observe without the distractions that cluttereth the crystal sphere, here be the coordinates to its quintessence in the aether.
http://i.imgur.com/o9hMoIG.gif
Presented here,
In service to Her Majesty
M-1
Jul 1, 2014
#8
+163
+19
Aye, Sir Cphill, this hath the sound of great power, I shall investigate in this inst. this not(quadratic) magick of which ye speak.
Doeth not the Magick of the Quadratic findeth the Zeros?
For now, there be no less than three kittys that needeth my attention. Appeared suddenly they did, not sure from thither they come.
M-1
Jul 1, 2014
#1
+114940
+8
Like WOW!
(Message given) info: enter a more detailed answer..
Like WOW again.
I had to stop laughing long enough to write this!
Err I mean....
----------------------------
The Queen is most impressed Chiurgeon Tud.
It doth indeed appear that thou art not only a fine surgeon but a gifted conjerer as well.
I trust this is not Black magick that you show us here. I did see a black cat on this morn.
A worry it is - indeed, Sir, it is a worry!
Lady Guinevere, Queen of all Camelot.
Jul 1, 2014
#2
+163
+8
If Her Majesty see a black cat, it bringeth thee good fortune, and to the cat a destiny of charm.
M-1
Jul 1, 2014
#3
+114940
+11
Thank you Sir. I see thee be generous with thou phalanges too. (thumbs up)
In kind I shall reward thee. The cat shall curl upon my lap and together we be warmed and charmed.
Jul 1, 2014
#4
+163
+5
For sure, the Kitty be no less than 3 times charmed, my Lady.
M-1
Jul 1, 2014
#5
+114940
+10
I see, I see, but in truth she be not more than 3 times charmed.
Still charmed she is - undeniably the truth this be!
Jul 1, 2014
#6
+163
+5
Aye! But the power of Majesty maketh that which be less than, now be greater than.
M-1
Jul 1, 2014
#7
+121048
+11
Thou magic is powerful Morgan Tud, but it hath produced not a single zero......!!!! Twas more crafty when thou employed "not(0)" to obtain like answers as found by thy Humble Servant with the employ of that magical digit. A true trick of conjuring on thy part!!! Thus....thou may find that "not(quadratic)" be of more power and produce results that edge on - or, possibly, even duplicate - those produced by the equally powerful "quadratic! "
For Thou Consideration.......
Sir CPhill
Jul 1, 2014
#8
+163
+19
Aye, Sir Cphill, this hath the sound of great power, I shall investigate in this inst. this not(quadratic) magick of which ye speak.
Doeth not the Magick of the Quadratic findeth the Zeros?
For now, there be no less than three kittys that needeth my attention. Appeared suddenly they did, not sure from thither they come.
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http://physics.stackexchange.com/questions/28029/toda-equations-and-surface-operator?answertab=oldest
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# Toda equations and surface operator
I would like to know the reason why the equation (14) in the paper by Yamada is called the Toda equation. $$\left[\frac12\sum_{i=1}^N\left(y_i\frac{\partial}{\partial y_i}-y_{i+1}\frac{\partial}{\partial y_{i+1}} \right)^2+\sum_{i=1}^N u_iy_i\frac{\partial}{\partial y_i}+{\rm const}\sum_{i=1}^N y_i\right]Z=0.$$
This equation was obtained by taking the decoupling limit of the equation (12) which is the equation conformal blocks in $SL(N)$ WZNW theory satisfy.
1. Does a certain correlation function in Toda conformal field theory satisfy the equation (14)? If so, there should be a realization of a full surface operator by M2-branes in the context of the AGT relation.
2. What kind of correlation functions in Toda conformal field theory satisfy the equation (14)?
3. Is there any good reference which explains the Toda equations?
-
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https://flixprint.com/product-category/wallpapers/by-room/living-room/
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###### 200,85 \$
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https://worldwidescience.org/topicpages/p/phosphorus-31+nmr+downfield.html
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#### Sample records for phosphorus-31 nmr downfield
1. Phosphorus-31 NMR analysis of gold plating baths
Energy Technology Data Exchange (ETDEWEB)
Smith, R.E.
1992-03-01
This report describes the nuclear magnetic resonance (NMR) analysis of gold plating baths in the Micro-Miniature Electronic Assembly department of Allied-Signal Inc., Kansas City Division (KCD). The baths were analyzed for phosphorylated components. In freshly prepared gold plating baths in this department the principle compound observed is aminotrimethyl-phosphonate, or ATMP. As the bath is used in production, the ATMP breaks down; and new compounds, aminodimethylphosphonate (ADMP), aminomonomethylphosphonate, (AMMP), and inorganic phosphate (H{sub 2}PO{sub 4}{sup {minus}}), are formed. The NMR method has been used for almost three years to monitor the concentrations of the ATMP and breakdown products. In a previous report, results from January through October 1988 were reported. In this report, results from November 1988 through January 1991 are given.
2. Monitoring of the insecticide trichlorfon by phosphorus-31 nuclear magnetic resonance (31P NMR) spectroscopy
International Nuclear Information System (INIS)
Talebpour, Zahra; Ghassempour, Alireza; Zendehzaban, Mehdi; Bijanzadeh, Hamid Reza; Mirjalili, Mohammad Hossein
2006-01-01
Trichlorfon is an organophosphorus insecticide, which is extensively being used for protection of fruit crops. Trichlorfon is a thermal labile compound, which cannot be easily determined by gas chromatography (GC) and has no suitable group for sensitive detection by high performance liquid chromatography (HPLC). In this study, a 31 P nuclear magnetic resonance ( 31 P NMR) has been described for monitoring of trichlorfon without any separation step. The quantitative works of 31 P NMR spectroscopy has been performed in the presence of an internal standard (hexamethylphosphoramide). Limit of detection (LOD) for this method has been found to be 55 mg L -1 , without any sample preparation, and the linear working range was 150-5500 mg L -1 . Relative standard deviation (R.S.D.%) of the method for three replicates within and between days was obtained ≤9%. The average recovery efficiency was approximately 99-112%. This method was applied for monitoring trichlorfon in a commercial insecticide sample and tomato sample
3. Phosphorus-31 NMR (nuclear magnetic resonance) analysis of gold plating baths
Energy Technology Data Exchange (ETDEWEB)
Smith, R.E.
1990-01-01
This report describes the nuclear magnetic resonance (NMR) analysis of the gold plating baths in the Micro-Miniature Electronic Assembly department of Allied-Signal Inc., Kansas City Division (KCD). The baths were analyzed for phosphorylated components. In freshly prepared gold plating baths, a 50-percent aqueous solution of aminotrimethylphosphonate (ATMP) is the principal compound observed. As the bath is used in production, the ATMP breaks down and new materials (phosphate, ADMP, and AMMP) are identified. The NMR method was used to monitor the concentrations of the ATMP and breakdown products for a nine-month period. The 225-liter bath had plated approximately 100 square feet of gold during the nine-month period. These results can be used to predict the performance of baths as they are used in production. The accuracy of the analysis is 96 percent for ATMP and 92 percent for phosphate. The precision (relative standard deviation) is 5.2 percent for ATMP and 4.5 percent for phosphate. 1 ref., 5 figs., 2 tabs.
4. Phosphorus-31, 15N, and 13C NMR of glyphosate: Comparison of pH titrations to the herbicidal dead-end complex with 5-enolpyruvoylshikimate-3-phosphate synthase
International Nuclear Information System (INIS)
Castellino, S.; Leo, G.C.; Sammons, R.D.; Sikorski, J.A.
1989-01-01
The herbicidal dead-end ternary complex (E S3P Glyph ) of glyphosate [N-(phosphonomethyl)glycine] with 5-enolpyruvoylshikimate-3-phosphate synthase (EPSPS) and the substrate shikimate 3-phosphate (S3P) has been characterized by 31 P, 15 N, and 13 C NMR. The NMR spectra of EPSPS-bound glyphosate show unique chemical shifts (δ) for each of the three nuclei. By 31 P NMR, glyphosate in the dead-end complex is a distinct species 3.5 ppm downfield from free glyphosate. The 13 C signal of glyphosate in the dead-end complex is shifted 4 ppm downfield from that of free glyphosate. The 15 N signal for glyphosate (99%) in the dead-end complex is 5 ppm further downfield than that of any free zwitterionic species and 10 ppm downfield from that of the average free species at pH 10.1. The structures of each ionic state of glyphosate are modeled with force field calculations by using MacroModel. A correlation is made for the 31 P δ and the C-P-O bond angle, and the 13 C and 15 N δ values are postulated to be related to C-C-O and C-N-C bond angles, respectively. The downfield 31 P chemical shift perturbation for S3P in the EPSPS binary complex is consistent with ionization of the 3-phosphate of S3P upon binding. Comparison with the S3P 31 P δ vs pH titration curve specifies predominantly the dianion of the 3-phosphate in the E S3P binary complex, while the E S3P Glyph complex indicates net protonation at the 3-phosphate. Chemical shift perturbations of this latter type may be explained by changes in the O-P-O bond angle
5. Phosphorus-31 NMR magnetization transfer measurements of metabolic reaction rates in the rat heart and kidney in vivo
International Nuclear Information System (INIS)
Koretsky, A.P.
1984-01-01
31 P NMR is a unique tool to study bioenergetics in living cells. The application of magnetization transfer techniques to the measurement of steady-state enzyme reaction rates provides a new approach to understanding the regulation of high energy phosphate metabolism. This dissertation is concerned with the measurement of the rates of ATP synthesis in the rat kidney and of the creatine kinase catalyzed reaction in the rat heart in situ. The theoretical considerations of applying magnetization transfer techniques to intact organs are discussed with emphasis on the problems associated with multiple exchange reactions and compartmentation of reactants. Experimental measurements of the ATP synthesis rate were compared to whole kidney oxygen consumption and Na + reabsorption rates to derive ATP/O values. The problems associated with ATP synthesis rate measurements in kidney, e.g. the heterogeneity of the inorganic phosphate resonance, are discussed and experiments to overcome these problems proposed. In heart, the forward rate through creatine kinase was measured to be larger than the reverse rate. To account for the difference in forward and reverse rates a model is proposed based on the compartmentation of a small pool of ATP
6. Mechanism of adenylate kinase. Demonstration of a functional relationship between aspartate 93 and Mg2+ by site-directed mutagenesis and proton, phosphorus-31, and magnesium-25 NMR
International Nuclear Information System (INIS)
Yan, Honggao; Tsai, Mingdaw
1991-01-01
Earlier magnetic resonance studies suggested no direct interaction between Mg 2+ ions and adenylate kinase (AK) in the AK·MgATP (adenosine 5'-triphosphate) complex. However, recent NMR studies concluded that the carboxylate of aspartate 119 accepts a hydrogen bond from a water ligand of the bound Mg 2+ ion in the muscle AK · MgATP complex. On the other hand, in the 2.6-angstrom crystal structure of the yeast AK·MgAP 5 A [P 1 , P 5 -bis(5'-adenosyl)pentaphosphate] complex, the Mg 2+ ion is in proximity to aspartate 93. Substitution of Asp-93 with alanine resulted in no change in dissociation constants, 4-fold increases in K m , and a 650-fold decrease in k cat . Notable changes have been observed in the chemical shifts of the aromatic protons of histidine 36 and a few other aromatic residues. However, the results of detailed analyses of the free enzymes and the AK·MgAP 5 A complexes by one- and two-dimensional NMR suggested that the changes are due to localized perturbations. Thus it is concluded that Asp-93 stabilizes the transition state by ca. 3.9 kcal/mol. Other results raised the question of whether Mg 2+ could bind to D93A·nucleotide complexes, which was then probed by 25 MgNMR. The results suggest that Mg 2+ does bind to the D93A·AP 5 A complex, but possibly only weakly
7. Studies concerning the interaction between local anesthetics and lipid membrane by phosphorus-31, deuterium and proton NMR; Estudo da interacao entre anestesicos locais e membranas lipidicas por ressonancia magnetica de fosforo ({sup 31} P), deuterio ({sup 2} H) e proton ({sup 1} H)
Energy Technology Data Exchange (ETDEWEB)
Paula, Eneida de [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Dept. de Bioquimica; Jarrell, Harold C. [National Research Council of Canada, Ottawa, ON (Canada). Inst. for Biological Sciences; Schreier, Shirley [Sao Paulo Univ., SP (Brazil). Inst. de Quimica
1993-12-31
Local anesthetics block the conduction of nervous stimulus by impeding the entrance of sodium ion and the consequently depolarization of the nervous membrane. The action mechanism of local anesthetics, however, is not fully understood yet. In the present work the interaction between local anesthetics and membranes are studied by the perspective of lipid phase perturbation using NMR to elucidate the mechanism. Results are presented and discussed 5 refs., 1 fig., 1 tab.
8. First NMR observation of 47Ti and 49Ti in cyclopentadienyl complexes
International Nuclear Information System (INIS)
Dormond, A.; Fauconet, M.; Leblanc, J.C.; Moise, C.
1984-01-01
47 Ti and 49 Ti NMR spectra of some mono and biscyclopentadienyl complexes are reported for the first time. The resonances span a relatively large range: electron donating substituents on the cyclopentadienyl ring cause an unexpected downfield shift. (author)
9. Phosphorus-31 magnetic resonance spectroscopy of experimentally induced arthritis in rats
International Nuclear Information System (INIS)
Blatter, D.D.
1987-01-01
Phosphorus-31 magnetic resonance spectroscopy (MRS) of the hind paws of rats was performed at 1.5 Tesla before and during the course of an experimentally-induced inflammatory arthritis. Arthritis was induced by daily subcutaneous administration of 6-sulfanilamidoindazole, an antibacterial sulfa known to produce an acute, self-limited arthritis and periarthritis in the hind paws of rats. Phosphorus-31 spectra obtained after the development of clinical arthritis showed a significant (p 31 P MRS may permit evaluation of the severity of an inflammatory arthritis with greater accuracy than the bony changes definable by plain roentgenograms. (orig.)
10. Phosphorus-31 spectroscopic imaging of the human liver
International Nuclear Information System (INIS)
Biran, M.; Raffard, G.; Canioni, P.; Kien, P.
1993-01-01
During the last decade, progresses in the field of nuclear magnetic resonance spectroscopy (M.R.S.), have allowed the metabolic studies of complex biological systems. Since the coming out of whole body magnets, clinical applications are possible; they utilize magnetic field gradients coupled with selective pulse sequences. Study of the phosphorylated metabolism of human liver can be performed with sequences as ISIS, FROGS or 1D-CSI. But they present some disadvantages (for instance contamination by phosphocreatine from muscle). In the present work, we have studied the human liver in vivo by 31 P spectroscopic imaging. Several spectra could be acquired with only one acquisition. This study has needed the building of radiofrequency coils (surface coils), specially designed for liver observation (15 cm diameter 31 P coil and 19 cm diameter proton coil, both transmitter and receiver coils). Preliminary studies have been done on a phantom followed by in vivo measurements on healthy subject livers. We have obtained localized 31 P N.M.R. spectra corresponding to different voxels within the hepatic tissue. The conditions of acquisition of spectra and the problems related to the saturation of phosphorylated metabolite signals (in particular phosphodiesters) are discussed. (author). 5 figs., 15 refs
11. NMR
International Nuclear Information System (INIS)
Kneeland, J.B.; Lee, B.C.P.; Whalen, J.P.; Knowles, R.J.R.; Cahill, P.T.
1984-01-01
Although still quite new, NMR imaging has already emerged as a safe, noninvasive, painless, and effective diagnostic modality requiring no ionizing radiation. Also, NMR appears already to have established itself as the method of choice for the examination of the brain spinal cord (excluding herniated disks). Another area in which NMR excels is in the examination of the pelvis. The use of surface coils offers the promise of visualizing structures with resolution unobtainable by any other means. In addition, NMR, with its superb visualization of vascular structures and potential ability to measure flow, may soon revolutionize the diagnosis of cardiovascular disease. Finally, NMR, through biochemically and physiologically based T/sub 1/ and T/sub 2/ indices or through spectroscopy, may provide a means of monitoring therapeutic response so as to permit tailoring of treatment to the individual patient. In short, NMR is today probably at the same stage as the x-ray was in Roentgen's day
12. Phosphorus-31 nuclear magnetic resonance studies of wild-type and glycolytic pathway mutants of Saccharomyces cerevisiae.
Science.gov (United States)
Navon, G; Shulman, R G; Yamane, T; Eccleshall, T R; Lam, K B; Baronofsky, J J; Marmur, J
1979-10-16
High-resolution phosphorus-31 nuclear magnetic resonance (31P NMR) spectra of wild-type and mutant strains of Saccharomyces cerevisiae were observed at a frequency of 145.7 MHz. Levels of various phosphorus metabolites were investigated upon addition of glucose under both aerobic and anaerobic conditions. Three mutant strains were isolated and their biochemical defects characterized: pfk lacked phosphofructokinase activity; pgi lacked phosphoglucose isomerase activity; and cif had no glucose catabolite repression of the fructose bisphosphatase activity. Each mutant strain was found to accumulate characteristic sugar phosphates when glucose was added to the cell suspension. In the case of the phosphofructokinase deficient mutant, the appearance of a pentose shunt metabolite was observed. 31P NMR peak assignments were made by a pH titration of the acid extract of the cells. Separate signals for terminal, penultimate, and central phosphorus atoms in intracellular polyphosphates allowed the estimation of their average molecular weight. Signals for glycero(3)phosphochline, glycero(3)phosphoserine, and glycero(3) phosphoethanolamine as well as three types of nucleotide diphosphate sugars could be observed. The intracellular pH in resting and anaerobic cells was in the range 6.5--6.8 and the level of adenosine 5'-triphosphate (ATP) low. Upon introduction of oxygen, the ATP level increased considerably and the intracellular pH reached a value of pH 7.2--7.3, irrespective of the external medium pH, indicating active proton transport in these cells. A new peak representing the inorganic phosphate of one of the cellular organelles, whose pH differed from the cytoplasmic pH, could be detected under appropriate conditions.
13. Deuterium and phosphorus-31 nuclear magnetic resonance study of the interaction of melittin with dimyristoylphosphatidylcholine bilayers and the effects of contaminating phospholipase A2
International Nuclear Information System (INIS)
Dempsey, C.E.; Watts, A.
1987-01-01
The interaction of bee venom melittin with dimyristoylphosphatidylcholine (DMPC) selectively deuteriated in the choline head group has been studied by deuterium and phosphorus-31 nuclear magnetic resonance (NMR) spectroscopy. The action of residual phospholipase A 2 in melittin samples resulted in mixtures of DMPC and its hydrolytic products that underwent reversible transitions at temperatures between 30 and 35 0 C from extended bilayers to micellar particles which gave narrow single-line deuterium and phosphorus-31 NMR spectra. Similar transitions were observed in DMPC-myristoyllysophosphatidylcholine (lysoPC)-myristic acid mixtures containing melittin but not in melittin-free mixtures, indicating that melittin is able to stabilize extended bilayers containing DMPC and its hydrolytic products in the liquid-crystalline phase. Melittin, free of phospholipase A 2 activity, and at 3-5 mol % relative to DMPC, induced reversible transitions between extended bilayers and micellar particles on passing through the liquid-crystalline to gel phase transition temperature of the lipid, effects similar to those observed in melittin-acyl chain deuteriated dipalmitoylphosphatidylcholine (DPPC) mixtures. LysoPC at concentrations of 20 mol % or greater relative to DMPC induced transitions between extended bilayers and micellar particles with characteristics similar to those induced by melittin. It is proposed that these melittin- and lysoPC-induced transitions share similar mechanisms. The effects of melittin on the quadrupole splittings and T 1 relaxation times of head-group-deuteriated DMPC in the liquid-crystalline phase share features similar to the effects of metal ions on DPPC head groups, indicating that the conformational properties of the choline head group in PC bilayers may be affected by melittin and by metal ions in a similar manner
14. Deuterium and phosphorus-31 nuclear magnetic resonance study of the interaction of melittin with dimyristoylphosphatidylcholine bilayers and the effects of contaminating phospholipase A/sub 2/
Energy Technology Data Exchange (ETDEWEB)
Dempsey, C.E.; Watts, A.
1987-09-08
The interaction of bee venom melittin with dimyristoylphosphatidylcholine (DMPC) selectively deuteriated in the choline head group has been studied by deuterium and phosphorus-31 nuclear magnetic resonance (NMR) spectroscopy. The action of residual phospholipase A/sub 2/ in melittin samples resulted in mixtures of DMPC and its hydrolytic products that underwent reversible transitions at temperatures between 30 and 35/sup 0/C from extended bilayers to micellar particles which gave narrow single-line deuterium and phosphorus-31 NMR spectra. Similar transitions were observed in DMPC-myristoyllysophosphatidylcholine (lysoPC)-myristic acid mixtures containing melittin but not in melittin-free mixtures, indicating that melittin is able to stabilize extended bilayers containing DMPC and its hydrolytic products in the liquid-crystalline phase. Melittin, free of phospholipase A/sub 2/ activity, and at 3-5 mol % relative to DMPC, induced reversible transitions between extended bilayers and micellar particles on passing through the liquid-crystalline to gel phase transition temperature of the lipid, effects similar to those observed in melittin-acyl chain deuteriated dipalmitoylphosphatidylcholine (DPPC) mixtures. LysoPC at concentrations of 20 mol % or greater relative to DMPC induced transitions between extended bilayers and micellar particles with characteristics similar to those induced by melittin. It is proposed that these melittin- and lysoPC-induced transitions share similar mechanisms. The effects of melittin on the quadrupole splittings and T/sub 1/ relaxation times of head-group-deuteriated DMPC in the liquid-crystalline phase share features similar to the effects of metal ions on DPPC head groups, indicating that the conformational properties of the choline head group in PC bilayers may be affected by melittin and by metal ions in a similar manner.
15. Cyclohexanecarbonitriles: Assigning Configurations at Quaternary Centers From 13C NMR CN Chemical Shifts.1
Science.gov (United States)
Wei, Guoqing
2009-01-01
13C NMR chemical shifts of the nitrile carbon in cyclohexanecarbonitriles directly correlate with the configuration of the quaternary, nitrile-bearing stereocenter. Comparing 13C NMR chemical shifts for over 200 cyclohexanecarbonitriles reveals that equatorially oriented nitriles resonate 3.3 ppm downfield, on average, from their axial counterparts. Pairs of axial/equatorial diastereomers varying only at the nitrile-bearing carbon consistently exhibit downfield shifts of δ 0.4–7.2 for the equatorial nitrile carbon, even in angularly substituted decalins and hydrindanes. PMID:19348434
16. A sex-specific metabolite identified in a marine invertebrate utilizing phosphorus-31 nuclear magnetic resonance.
Directory of Open Access Journals (Sweden)
Robert A Kleps
Full Text Available Hormone level differences are generally accepted as the primary cause for sexual dimorphism in animal and human development. Levels of low molecular weight metabolites also differ between men and women in circulating amino acids, lipids and carbohydrates and within brain tissue. While investigating the metabolism of blue crab tissues using Phosphorus-31 Nuclear Magnetic Resonance, we discovered that only the male blue crab (Callinectes sapidus contained a phosphorus compound with a chemical shift well separated from the expected phosphate compounds. Spectra obtained from male gills were readily differentiated from female gill spectra. Analysis from six years of data from male and female crabs documented that the sex-specificity of this metabolite was normal for this species. Microscopic analysis of male and female gills found no differences in their gill anatomy or the presence of parasites or bacteria that might produce this phosphorus compound. Analysis of a rare gynandromorph blue crab (laterally, half male and half female proved that this sex-specificity was an intrinsic biochemical process and was not caused by any variations in the diet or habitat of male versus female crabs. The existence of a sex-specific metabolite is a previously unrecognized, but potentially significant biochemical phenomenon. An entire enzyme system has been synthesized and activated only in one sex. Unless blue crabs are a unique species, sex-specific metabolites are likely to be present in other animals. Would the presence or absence of a sex-specific metabolite affect an animal's development, anatomy and biochemistry?
17. The study of human organs by phosphorus-31 topical magnetic resonance spectroscopy
International Nuclear Information System (INIS)
Oberhaensli, R.D.; Galloway, G.J.; Hilton-Jones, David; Bore, P.J.; Styles, Peter; Rajagopalan, Bheeshma; Taylor, D.J.; Radda, G.K.
1987-01-01
The potential clinical use of topical magnetic resonance spectroscopy (volume selection by static magnetic field gradients) was tested in 50 studies in volunteers. Topical magnetic resonance spectroscopy (MRS) was shown to be a straightforward method for localising 31 P spectra of brain and liver. However, the spherical shape and fixed position of the selected volume posed serious limitations to the study of heart and transplanted kidney by topical MRS. Phosphorus-31 spectra of approx. 30 cm -3 of brain or liver could be obtained in 8 min. Ratios of metabolite concentrations could be determined with a coefficient of variation ranging from 10% to 30%. The ratios of phosphocreatine/ATP and inorganic phosphate/ATP in brain were 1.8 and 0.3, respectively. The ratio of inorganic phosphate/ATP in liver was 0.9. Intracellular pH was 7.03 in brain and 7.24 in liver. The T 1 relaxation times of phosphocreatine, inorganic phosphate and γ-ATP in brain were 4.8 s, 2.5 s and 1.0 s, respectively. (author)
18. Phosphorus-31 and proton magnetic resonance spectroscopy of the medial temporal region in schizophrenic patients
International Nuclear Information System (INIS)
1996-01-01
Phosphorus-31 magnetic resonance spectroscopy (MRS) was performed 22 schizophrenic patients and in 22 healthy volunteers. Psychiatric symptoms were estimated on the Brief Psychiatric Rating Scale (BPRS), the Scale for the Assessment of Negative Symptoms (SANS) and the Scale for the Assessment of Positive Symptoms (SAPS). The spectra were quantified for phosphomonoesters (PME), inorganic orthophosphate (Pi), phosphodiesters (PDE), phosphocreatine (Pcr) and the γ, α and β phosphates of 5'-adenosine triphosphate (ATP) by peak area measurements. Proton MRS was performed in 15 schizophrenic patients and in 15 healthy volunteers. Psychiatric symptoms were estimated on the Positive and Negative Syndrome Scale (PANSS) and the SANS. The spectra of N-acetylates (NA), choline-containing compounds (Cho) and creatine-phosphocreatine (Cr) were quantified. The patients showed an increase in the % PDE and a decrease in the % β-ATP in the left temporal region. Positive correlations were found between the % PDE and the subscale of positive symptoms on the BPRS and the total score of SAPS. The % β-ATP correlated negatively with the total score on SAPS. The NA/Cho and NA/Cr ratios were significantly lower in patients than in normal subjects. The Cho/Cr ratio was higher in the patient group. The age at onset of illness correlated positively with the NA/Cho and NA/Cr ratios. No significant correlations were observed between the ratios of metabolites and the scores of PANSS and SANS. There were no significant associations between the mole percentages and the ratios and the daily doses of neuroleptics and anticholinergics. These findings suggest that the disturbed membrane phospholipid and high-energy phosphate metabolism in the left medial temporal region may be one of the pathophysiologies of neuroleptic-resistant positive symptoms in schizophrenia and these abnormalities may be related to neuronal loss and/or neuronal dysfunction in this region. (H.O.)
19. Effects of mutation on the downfield proton nuclear magnetic resonance spectrum of the 5S RNA of Escherichia coli
International Nuclear Information System (INIS)
Gewirth, D.T.; Moore, P.B.
1987-01-01
The imino proton spectra of several mutants of the 5S RNA of Escherichia coli are compared with that of the wild type. Three of the variants discussed are point mutations, and the fourth is a deletion mutant lacking bases 11-69 of the parent sequence, all obtained by site-directed mutagenesis techniques. The spectroscopic effects of mutation are limited in all cases, and the differences between normal and mutant spectra can be used to make or confirm the assignments of resonances. Several new assignments in the 5S spectrum are reported. Spectroscopic differences due to sequence differences permit the products of single genes within the 5S gene family to be distinguished and their fates followed by NMR
20. Phosphorus-31 nuclear magnetic resonance spectroscopic study of the canine pancreas: applications to acute alcoholic pancreatitis
International Nuclear Information System (INIS)
Janes, N.; Clemens, J.A.; Glickson, J.D.; Cameron, J.L.
1988-01-01
The first nuclear magnetic resonance spectroscopic study of the canine pancreas is described. Both in-vivo, ex-vivo protocols and NMR observables are discussed. The stability of the ex-vivo preparation based on the NMR observables is established for at least four hours. The spectra obtained from the in-vivo and ex-vivo preparations exhibited similar metabolite ratios, further validating the model. Metabolite levels were unchanged by a 50% increase in perfusion rate. Only trace amounts of phosphocreatine were observed either in the intact gland or in extracts. Acute alcoholic pancreatitis was mimicked by free fatty acid infusion. Injury resulted in hyperamylasemia, edema (weight gain), increased hematocrit and perfusion pressure, and depressed levels of high energy phosphates
1. Phosphorus-31 MRI of bones using quadratic echo line-narrowing
Science.gov (United States)
Frey, Merideth; Barrett, Sean; Insogna, Karl; Vanhouten, Joshua
2012-02-01
There is a great need to probe the internal composition of bone on the sub-0.1 mm length scale, both to study normal features and to look for signs of disease. Despite the obvious importance of the mineral fraction to the biomechanical properties of skeletal tissue, few non-destructive techniques are available to evaluate changes in its chemical structure and functional microarchitecture on the interior of bones. MRI would be an excellent candidate, but bone is a particularly challenging tissue to study given the relatively low water density and wider linewidths of its solid components. Recent fundamental research in quantum computing gave rise to a new NMR pulse sequence - the quadratic echo - that can be used to narrow the broad NMR spectrum of solids. This offers a new route to do high spatial resolution, 3D ^31P MRI of bone that complements conventional MRI and x-ray based techniques to study bone physiology and structure. We have used our pulse sequence to do 3D ^31P MRI of ex vivo bones with a spatial resolution of (sub-450 μm)^3, limited only by the specifications of a conventional 4 Tesla liquid-state MRI system. We will describe our plans to push this technique towards the factor of 1000 increase in spatial resolution imposed by fundamental limits.
2. Study of the muscular metabolism using Phosphorus 31 Magnetic Resonance Spectroscopy (31P-MRS) in normal subjects
International Nuclear Information System (INIS)
Batista, T.S.; Salmon, C.E.G.; Santos, A.C.
2008-01-01
Phosphorus 31 Magnetic Resonance Spectroscopy ( 31 P-MRS) is a powerful technique for evaluating human muscular metabolism. Some reports indicated the behavior of phosphorylated metabolites (PCr, ADP and Pi) and other indirect parameters (intracellular pH and [Mg 2+ ]) in muscles at rest and after an exercise load. The aim of this work is a quantitative study of the phosphorylated metabolite levels in the calf muscle of normal subjects at rest and post-exercise, in order to create a normal control database. 31 P spectra of seven volunteers were acquired in both conditions. Firstly, different quantification methodologies were evaluated to use the more reliable. The P Cr metabolite was the more stable at rest and it had mono-exponential behavior after exercise. The Pi was the more sensible indicator of the physical activities. The time constants of the recuperation process are report for all the evaluated metabolites and parameters. Finally, the temporal behavior of phospho monoesters was quantified. (author)
3. Transport and phosphorylation of choline in higher plant cells. Phosphorus-31 nuclear magnetic resonance studies
Energy Technology Data Exchange (ETDEWEB)
Bligny, R.; Foray, M.F.; Roby, C.; Douce, R.
1989-03-25
When sycamore cells were suspended in basal medium containing choline, the latter was taken up by the cells very rapidly. A facilitated diffusion system appertained at low concentrations of choline and exhibited Michaelis-Menten kinetics. At higher choline concentrations simple diffusion appeared to be the principal mode of uptake. Addition of choline to the perfusate of compressed sycamore cells monitored by /sup 31/P NMR spectroscopy resulted in a dramatic accumulation of P-choline in the cytoplasmic compartment containing choline kinase and not in the vacuole. The total accumulation of P-choline over a 10-h period exhibited Michaelis-Menten kinetics. During this period, in the absence of Pi in the perfusion medium there was a marked depletion of glucose-6-P, and the cytoplasmic Pi resonance disappeared almost completely. When a threshold of cytoplasmic Pi was attained, the phosphorylation of choline was sustained by the continuous release of Pi from the vacuole although at a much lower rate. However, when 100 microM inorganic phosphate was present in the perfusion medium, externally added Pi was preferentially used to sustain P-choline synthesis. It is clear, therefore, that cytosolic choline kinase associated with a carrier-mediated transport system for choline uptake appeared as effective systems for continuously trapping cytoplasmic Pi including vacuolar Pi entering the cytoplasm.
4. Organic phosphorus fractionation in wetland soil profiles by chemical extraction and phosphorus-31 nuclear magnetic resonance spectroscopy
International Nuclear Information System (INIS)
Li, Min; Zhang, Jing; Wang, Guangqian; Yang, Haijun; Whelan, Michael J.; White, Sue M.
2013-01-01
Highlights: ► Chemical sequential extraction and 31 P NMR spectroscopy were used for organic P analysis. ► Organic P includes orthophosphate, monoester and diester phosphate and pyrophosphate. ► Highly resistant organic P and monoester phosphate were the dominant organic P. ► HCl pretreatment can remove most inorganic P and increase organic P recovery rate. ► A comprehensive organic P chemical sequential fractionation approach was proposed. - Abstract: Organic P (OP) plays an important role in soil P cycling and is a potential P source for wetland plants. In this study, a modified chemical sequential fractionation method and 31 P nuclear magnetic resonance spectroscopy ( 31 P NMR) of NaOH–EDTA extracts were used to examine the distribution of organic P fractions and compounds in soil profiles of the Beijing Yeyahu Wetland, China. The influence of acid treatment prior to NaOH–EDTA extraction on 31 P NMR spectra was also investigated. Results show that highly resistant OP was the major class of organic P. The rank order of organic P fractions was highly resistant OP (on average accounting for 68.5% of total OP) > moderately resistant OP (15.8%m of total OP) > moderately labile OP (11.4% of total OP) > labile OP (4.3% of total OP). Most of the organic P fractions decreased with soil depth due to the accumulation of plant residues in surface soils and the deposition and diagenesis of soils. Moderately (r = 0.586, p < 0.01) and highly (r = 0.741, p < 0.01) resistant OP fractions were positively correlated with soil organic matter. Phosphorus compounds including orthophosphate (23–74.6% of total P in spectra), monoester phosphate (18.6–76%), diester phosphate (nil-7.8%) and pyrophosphate (nil-6.7%) were characterized using 31 P NMR. Monoester-P was the dominant soil organic P compound identified. The proportion of monoester-P increased significantly in NaOH–EDTA extracts with HCl pretreatment and it was confirmed by chemical analysis. Therefore, it
5. Absolute concentration determination of phosphorus metabolites in the Langendorff-perfused rabbit heart by phosphorus-31 nuclear magnetic resonance
International Nuclear Information System (INIS)
Gard, J.K.
1984-01-01
The concentrations of mobile high energy phosphorus metabolites and intracellular pH of Langendorff-perfused rabbit heart have been determined under control and reduced flow conditions. Absolute concentration determination was accomplished by Lorentzian lineshape analysis after development of hexachlorocyclotriphosphazene as an external intensity standard. Hearts were demonstrated to be biochemically and physiologically competent during control perfusion periods and compromised during reduced flow conditions by independent hemodynamic and metabolic measurements coincident with the NMR experiment. Reduction in perfusate flow from 20 mL/min to 5.0 mL/min (25% flow) or 2.5 mL/min (12.5% flow) demonstrated a fall in phosphocreatine and adenosine triphosphate concentrations, a rise in cytosolic inorganic phosphate concentrations, and drops in pH. Subsequent recovery upon reflow was observed. The derived values for the free concentration of ADP were very close to the reported values of the Michaelis constant for respiratory stimulation, implicating a regulatory role for this molecule in cellular respiration. Strong evidence that the creating kinase reaction was in equilibrium in the 25% flow study was seen. The NMR observable correlated closely with myocardial performance and biochemical indices of metabolic function, and supported the use of phosphocreatine as an indicator of current metabolic integrity
6. Differentiation between healthy thyroid remnants and tumor tissue after radioiodine therapy in patients with differentiated thyroid carcinoma using in-vitro phosphorus-31 magnetic resonance spectroscopy
International Nuclear Information System (INIS)
Moka, D.; Dietlein, M.; Schicha, H.; Raffelt, K.; Hahn, J.
2002-01-01
Full text: In many tumors, tumor growth and spread is triggered by changes in cell membrane metabolism, which can lead to systemic alterations in levels of phospholipids. The aim of this study was to differentiate between healthy remnants of thyroid tissue and residual/recurrent tumor tissue or metastases in patients with thyroid carcinoma by measurement of plasma levels of various phospholipids. Phospholipid concentrations was measured by in-vitro phosphorus-31-magnetic resonance spectroscopy ( 31 P-MRS) in blood samples from 30 patients with thyroid cancer, who had been rendered hypothyroid in preparation for diagnostic/therapeutic administration of iodine-131. All patients were already thyroidectomized. 131 I-whole-body scintigraphy and measurements of thyroglobulin values in a 2-year-follow-up were used to distinguish between patients in remission, patients with only healthy thyroid remnants and patients with cancerous thyroid tissue and/or metastases. Significantly lower blood plasma levels of systemic sphingomyelin (0.33±0.06 vs. 0.46±0.03 (controls) mmol/l; p 31 P-MRS can be used to differentiate between the presence of tumor tissue, healthy remnants of thyroid tissue not requiring further treatment and remission in patients with thyroid cancer. In future, therefore, plasma 31 P-MRS could be developed as an additional diagnostic tool for the follow-up of differentiated thyroid cancer. (author)
7. Phosphorus forms and chemistry in the soil profile under long-term conservation tillage: a phosphorus-31 nuclear magnetic resonance study.
Science.gov (United States)
Cade-Menun, Barbara J; Carter, Martin R; James, Dean C; Liu, Corey W
2010-01-01
In many regions, conservation tillage has replaced conventional tilling practices to reduce soil erosion, improve water conservation, and increase soil organic matter. However, tillage can have marked effects on soil properties, specifically nutrient redistribution or stratification in the soil profile. The objective of this research was to examine soil phosphorus (P) forms and concentrations in a long-term study comparing conservation tillage (direct drilling, "No Till") and conventional tillage (moldboard plowing to 20 cm depth, "Till") established on a fine sandy loam (Orthic Humo-Ferric Podzol) in Prince Edward Island, Canada. No significant differences in total carbon (C), total nitrogen (N), total P, or total organic P concentrations were detected between the tillage systems at any depth in the 0- to 60-cm depth range analyzed. However, analysis with phosphorus-31 nuclear magnetic resonance spectroscopy showed differences in P forms in the plow layer. In particular, the concentration of orthophosphate was significantly higher under No Till than Till at 5 to 10 cm, but the reverse was true at 10 to 20 cm. Mehlich 3-extractable P was also significantly higher in No Till at 5 to 10 cm and significantly higher in Till at 20 to 30 cm. This P stratification appears to be caused by a lack of mixing of applied fertilizer in No Till because the same trends were observed for pH and Mehlich 3-extractable Ca (significantly higher in the Till treatment at 20 to 30 cm), reflecting mixing of applied lime. The P saturation ratio was significantly higher under No Till at 0 to 5 cm and exceeded the recommended limits, suggesting that P stratification under No Till had increased the potential for P loss in runoff from these sites.
8. Recent trends on NMR imaging in UK and USA
Energy Technology Data Exchange (ETDEWEB)
Endo, Masahiro [National Inst. of Radiological Sciences, Chiba (Japan)
1981-12-01
The development of nuclear magnetic resonance (NMR) by major research centers and manufacturers is reviewed. The spin warp method is used at Aberdeen University, and the T1 images of esophageal cancer and hepatic metastasis obtained by this method are shown. The Moore group at Nottingham University developed an instrument to scan the head region, and it produces spatial resolution comparable to x-ray computed tomography. The transverse image of the thorax obtained by the QED-80 developed by FONAR (U.S.A.) is shown. It uses field focusing NMR, and can measure spin density, T1, T2 and NMR spectrum, but its precision is slightly lowered because fewer proton spins are activated. These methods all measure the proton distribution in vivo, but with the TMR developed by Oxford Research Co. (U.K.) high resolution spectra of phosphorus 31 compounds can be obtained. The NMR spectra obtained for the phosphorus compounds in the muscle is shown. The rate of the phosphorus compounds such as ATP, ADP creatine phosphate and inorganic phosphate are markedly changed by exercise or depending on the blood flow.
9. Development of Selective Excitation Methods in Nuclear Magnetic Resonance: Investigation of Hemoglobin Oxygenation in Erythrocytes Using Proton and Phosphorus -31 Nuclear Magnetic Resonance
Science.gov (United States)
Fetler, Bayard Keith
1993-01-01
Nuclear magnetic resonance (NMR) offers a potential method for making measurements of the percent oxygenation of hemoglobin (Hb) in living tissue non-invasively. As a demonstration of the feasibility of such measurements, we measured the percent oxygenation of Hb in red blood cells (erythrocytes) using resonances in the proton-NMR (^1H-NMR) spectrum which are characteristic of oxyhemoglobin (oxy-Hb) and deoxyhemoglobin (deoxy-Hb), and are due to the unique magnetic properties of these molecules. To perform these measurements, we developed a new NMR method of selectively exciting signals in a region of interest with uniform phase and amplitude, while suppressing the signal of the water resonance. With this method, we are able to make exact calculations distinguishing between uniform phase excitation produced at large flip-angles using the non-linear properties of the Bloch equations, and uniform phase excitation produced at small flip-angles using asymmetric pulse excitation functions. We measured the percent oxygenation of three characteristic ^1H-NMR resonances of Hb: two from deoxy-Hb, originating from the N_delta H protons of histidine residue F8, which occur at different frequencies for the alpha and beta chains of Hb; and one from oxy-Hb, originating from the gamma_2 -CH_3 protons of valine residue E11. We performed experiments both on fresh erythrocytes and on erythrocytes depleted of 2,3-diphosphoglycerate (2,3-DPG), and found that oxygen is more tightly bound to Hb in the former case. In both fresh and 2,3-DPG-depleted samples, we found that: (i) from the deoxy-Hb marker resonances, there is a small but significant difference in the oxygen saturation between the alpha and beta chains; (ii) the decrease in the areas of the deoxy-Hb marker resonances correlates well with the increase in the percent oxygenation of Hb as measured optically; (iii) the area of the oxy-Hb marker resonance may be up to ~15% less than the optically measured Hb saturation. We are
10. NMR studies of myocardial energy metabolism and ionic homeostasis during ischemia and reperfusion
International Nuclear Information System (INIS)
Kirkels, J.H.
1989-01-01
In this study several aspects of myocardial energy metabolism and ionic homeostasis during ischemia and reperfusion were investigated in isolated perfused rat hearts, regionally ischemic rabbit hearts, and ex vivo human donor hearts during long term hypothermic cardioplegia. Phosphorus-31 nuclear magnetic resonance ( 31 P NMR) spectroscopy was used as a powerful tool to non-destructively follow the time course in changes in intracellular high-energy phosphates, (creatine phosphate and ATP), inorganic phosphate, and pH. In addition, changes in intracellular free magnesium were followed during ischemia and reperfusion. Sodium-23 ( 23 Na) NMR spectroscopy was used to study intracellular sodium during ischemia and reperfusion and during calcium-free perfusion. (author). 495 refs.; 33 figs.; 11 tabs
11. NMR imaging
International Nuclear Information System (INIS)
Andrew, E.R.
1983-01-01
Since hydrogen is the most abundant element in all living organisms, proton NMR lends itself well as a method of investigation in biology and medicine. NMR imaging has some special advantages as a diagnostic tool: no ionizing radiation is used, it is noninvasive; it provides a safer means of imaging than the use of x-rays, gamma rays, positrons, or heavy ions. In contrast with ultrasound, the radiation penetrates the bony structures without attenuation. In additional to morphological information, NMR imaging provides additional diagnostic insights through relaxation parameters, which are not available from other imaging methods. In the decade since the first primitive NMR images were obtained, the quality of images now obtained approaches those from CT x-ray scanners. Prototype instruments are being constructed for clinical evaluation and the first whole-body scanners are beginning to appear on the market at costs comparable to CT scanners. Primary differences in equipment for conventional NMR and NMR imaging are the much larger aperture magnets that are required for the examination of human subjects and the addition of coils to generate field gradients and facilities for manipulating the gradients. Early results from clinical trials in many parts of the world are encouraging, and in a few years, the usefuleness of this modality of medical imaging to the medical profession in diagnosis and treatment of disease will be defined. 10 figures
12. Peptides containing internal residues of pyroglutamic acid: proton NMR characteristics
International Nuclear Information System (INIS)
Khan, S.A.
1986-01-01
The proton NMR characteristics of internal pyroglutamic acid (Glp; 5-oxoproline) residues in seven tripeptides of the general structure Boc-Xxx-Glp-Yyy-NH 2 were studied. In general, the chemical shifts of several diagnostic protons moved downfield on going from the Glu-containing peptides (Boc-Xxx-Glu-Yyy-NH 2 ) to the corresponding Glp-containing peptides. The C-2 proton of the Xxx residue was shifted by about 1.1 ppm. The N-2 proton of the Yyy residue was shifted by about 0.5 ppm. The C-2 proton of the Glx residue itself was shifted by about 0.5 ppm. One of the Glx C-3 protons was also shifted by about 0.5 ppm, but the other remained essentially unchanged. Finally, the Glx C-4 protons were shifted by about 0.3 ppm. Internal Glu residues are readily converted chemically into internal Glp residues. This conversion also occurs as a side reaction during HP cleavage of the protecting group from Glu(OBzl) residues. The spontaneous fragmentation of serum proteins C3, C4 and λ 2 -macroglobulin under denaturing conditions is probably due to regioselective hydrolysis of an internal Glp residue formed in each of these proteins upon denaturation. These proton NMR characteristics may be useful in establishing the presence of internal Glp residues in synthetic and natural peptides
13. Compact NMR
Energy Technology Data Exchange (ETDEWEB)
Bluemich, Bernhard; Haber-Pohlmeier, Sabina; Zia, Wasif [RWTH Aachen Univ. (Germany). Inst. fuer Technische und Makromolekulare Chemie (ITMC)
2014-06-01
Nuclear Magnetic Resonance (NMR) spectroscopy is the most popular method for chemists to analyze molecular structures, while Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool for medical doctors that provides high-contrast images of biological tissue. In both applications, the sample (or patient) is positioned inside a large, superconducting magnet to magnetize the atomic nuclei. Interrogating radio-frequency pulses result in frequency spectra that provide the chemist with molecular information, the medical doctor with anatomic images, and materials scientist with NMR relaxation parameters. Recent advances in magnet technology have led to a variety of small permanent magnets to allow compact and low-cost instruments. The goal of this book is to provide an introduction to the practical use of compact NMR at a level nearly as basic as the operation of a smart phone.
14. NMR imaging
International Nuclear Information System (INIS)
Ouchi, Toshihiro; Steiner, R.E.
1984-01-01
Three epidermoid and two dermoid tumours, pathologically proven, were examined by NMR and CT scans. Although most brain tumours have a low signal with a long T 1 , a dermoid cyst and one of the two components of the other dermoid tumour had a high signal and therefore a short T 1 . All three epidermoid tumours had a low signal and a long T 1 . Because of the high level contrast between some of the tumours and cerebrospinal fluid, NMR is helpful to detect the lesion. Neither of the liquid fluid levels in the tumour cysts or floating fat in the subarachnoid space was recognized in one patients, but the fine leakage of the content from the epidermoid cyst into the lateral ventricle was detected on a saturation recovery 1000 image in one case. (author)
15. 31P-NMR differentiation between intracellular phosphate pools in Cosmarium (chlorophyta)
International Nuclear Information System (INIS)
Elgavish, A.; Elgavish, G.A.
1980-01-01
31 P nuclear magnetic resonance (NMR) spectroscopy of intact Cosmarium sp. cells is presented as a suitable tool for the differentiation of intracellular accumulation pools of polyphosphates. The cold trichloroacetic acid (TCA) insoluble fraction is shown to contain most of the total cellular phosphate in the phosphate rich Cosmarium cells. Moreover, evidence from a 31 P-NMR study and electron microscopic observations of cold TCA treated Cosmarium cells indicate that this fraction consists mostly of polyphosphates which seem to retain the native morphological structure observed in the untreated cells. The determination of orthophosphate in the hot water extract of Cosmarium cells did not measure the polyphosphate pools. Determination of total phosphorus content in the hot water extract rendered a value three times higher than the frequently used orthophosphate determination procedure. However, as revealed by the 31 P-NMR spectra and the chemical analyses of the extract and of the treated cells, even total phosphorus in the extract measured only 30% of the total cellular phosphorus. 31 P-NMR enabled the unequivocal chemical identification of the major phosphate compounds in the hot water extract (Surplus P) as orthophosphate and polyphosphates of about 10 phosphate units chainlength. More than 70% of the accumulation pool of polyphosphates was still in the cells after extraction. However, the electron microscopy study revealed that the native granular structure of polyphosphates had been destroyed by the hot water extraction procedure
16. NMR spectroscopy
International Nuclear Information System (INIS)
Gruenert, J.
1989-01-01
The book reviews the applications of NMR-spectroscopy in medicine and biology. The first chapter of about 40 pages summarizes the history of development and explains the chemical and physical fundamentals of this new and non-invasive method in an easily comprehensible manner. The other chapters summarize diagnostic results obtained with this method in organs and tissues, so that the reader will find a systematic overview of the available findings obtained in the various organ systems. It must be noted, however, that ongoing research work and new insight quite naturally will necessitate corrections to be done, as is the case here with some biochemical interpretations which would need adjustment to latest research results. NMR-spectroscopy is able to measure very fine energy differences on the molecular level, and thus offers insight into metabolic processes, with the advantage that there is no need of applying ionizing radiation in order to qualitatively or quantitatively analyse the metabolic processes in the various organ systems. (orig./DG) With 40 figs., 4 tabs [de
17. 1H NMR spectra of vertebrate [2Fe-2S] ferredoxins. Hyperfine resonances suggest different electron delocalization patterns from plant ferredoxins
International Nuclear Information System (INIS)
Skjeldal, L.; Markley, J.L.; Coghlan, V.M.; Vickery, L.E.
1991-01-01
The authors report the observation of paramagnetically shifted (hyperfine) proton resonances from vertebrate mitochondrial [2Fe-2S] ferredoxins. The hyperfine signals of human, bovine, and chick [2Fe-2S] ferredoxins are described and compared with those of Anabena 7120 vegetative ferredoxin, a plant-type [2Fe-2S] ferredoxin studied previously. The hyperfine resonances of the three vertebrate ferredoxins were very similar to one another both in the oxidized state and in the reduced state, and slow (on the NMR scale) electron self-exchange was observed in partially reduced samples. For the oxidized vertebrate ferredoxins, hyperfine signals were observed downfield of the diamagnetic envelope from +13 to +50 ppm, and the general pattern of peaks and their anti-Curie temperature dependence are similar to those observed for the oxidized plant-type ferredoxins. For the reduced vertebrate ferredoxins, hyperfine signals were observed for the oxidized plant-type ferredoxins. For the reduced vertebrate ferredoxins, hyperfine signals were observed both upfield (-2 to -18 ppm) and downfield (+15 to +45 ppm), and all were found to exhibit Curie-type temperature dependence. These results indicate that the contact-shifted resonances in the reduced vertebrate ferredoxins detect different spin magnetization from those in the reduced plant ferredoxins and suggest that plant and vertebrate ferredoxins have fundamentally different patterns of electron delocalization in the reduced [2Fe-2S] center
18. Exploring the structure-activity relations of N-carbethoxyphthalimide by combining FTIR, FT-Raman and NMR spectroscopy with DFT electronic structure method.
Science.gov (United States)
Arjunan, V; Govindaraja, S Thillai; Ravindran, P; Mohan, S
2014-01-01
The complete vibrational assignment and analysis of N-carbethoxyphthalimide were carried out using the experimental FTIR and FT-Raman data in the range 4000-450 and 4000-100 cm(-1), respectively along with quantum chemical studies of the compound using DFT-B3LYP gradient calculations employing the 6-31G**, 6-311++G** and cc-pVDZ basis sets. The 1H (400 MHz; CDCl3) and 13C (100 MHz;CDCl3) nuclear magnetic resonance (NMR) spectra were also recorded. Due to the partial ionic nature of the carbonyl group, the carbon atoms C1 and C3 in NCEP show downfield effect and the corresponding observed chemical shift of both are observed at 163.76 ppm and the carbon atom C16 in the carbethoxy group also give signal in the downfield at 148.45 ppm. The active sites are determined by molecular electrostatic potential. The possible electronic transitions are determined by HOMO and LUMO orbital shapes and their energies. The structure-chemical reactivity relations of the compound were determined through chemical potential, global hardness, global softness, electronegativity, electrophilicity and local reactivity descriptors by conceptual DFT methods. Copyright © 2013 Elsevier B.V. All rights reserved.
19. 1H NMR spectrum of the native human insulin monomer. Evidence for conformational differences between the monomer and aggregated forms.
Science.gov (United States)
Roy, M; Lee, R W; Brange, J; Dunn, M F
1990-04-05
The effects of high dilution on the 1H Fourier transform NMR spectrum of native human insulin at pH* 8.0 and 9.3 have been examined at 500 MHz resolution. The dependence of the spectrum on concentration and comparison with the spectrum of a biologically highly potent monomeric insulin mutant (SerB9----Asp) establish that at 36 microM (pH* 9.3) or 18 microM (pH* 8) and no added buffer or salts, human insulin is monomeric. Under these conditions of dilution, ionic strength, and pH*, human insulin and the SerB9----Asp mutant exhibit nearly identical 1H NMR spectra. At higher concentrations (i.e. greater than 36 microM to 0.91 mM), native human insulin dimerizes, and this aggregation causes a change in insulin conformation. Although there are many changes in the spectrum, the TyrB26 ring H3,5 proton signals located at 6.63 ppm and the methyl signal located at 0.105 ppm (characteristics of monomeric insulin) are particularly distinct signatures of the conformation change that accompanies dimerization. Magnetization transfer experiments show that the 0.105 ppm methyl signal shifts downfield to a new position at 0.45 ppm. We conclude that the 0.105 ppm methyl signal is due to a conformation in which a Leu methyl group is centered over and in van der Waals contact with the ring of an aromatic side chain. Dimerization causes a conformation change that alters this interaction, thereby causing the downfield shift. Nuclear Overhauser studies indicate that the methyl group involved is located within a cluster of aromatic side chains and that the closest ring-methyl group interaction is with the ring of PheB24.
20. Conformational Change in the Mechanism of Inclusion of Ketoprofen in β-Cyclodextrin: NMR Spectroscopy, Ab Initio Calculations, Molecular Dynamics Simulations, and Photoreactivity.
Science.gov (United States)
Guzzo, T; Mandaliti, W; Nepravishta, R; Aramini, A; Bodo, E; Daidone, I; Allegretti, M; Topai, A; Paci, M
2016-10-11
Inclusion of drugs in cyclodextrins (CDs) is a recognized tool for modifying several properties such as solubility, stability, bioavailability, and so on. The photoreactive behavior of the β-CD/ketoprofen (KP) complex upon UV exposure showed a significant increase in photodecarboxylation, whereas the secondary degradation products by hydroxylation of the benzophenone moiety were inhibited. The results may account for an improvement of KP photophysical properties upon inclusion, thus better fostering its topical use. To correlate the structural details of the inclusion with these results, an NMR spectroscopic study of KP upon inclusion in β-CD was performed. Effects of the magnetically anisotropic centers of KP, changing their orientations upon inclusion and giving chemical shift variations, were specifically correlated with the results of the molecular dynamic simulations and ab initio calculations. In the large variety of papers focusing on the structural analysis of β-CD complexes, this work represents one of the few examples in which a detailed analysis of these simultaneous upfield-downfield NMR shifts of the same aromatic molecule upon inclusion is reported. Interestingly, the results demonstrate that the observed upfield and downfield shifts upon inclusion are not related to any direct magnetic role of β-CD. The conformational change of KP upon the inclusion process consists of a slight reduction in the angle between the two phenyl rings and in a remarkable reduction in the mobility of the carboxyl group, the latter being one of the main contributions to the NMR resonance shifts. These structural details help in understanding the features of the inclusion complex and, eventually, the driving force for its formation.
1. Forms and Lability of Phosphorus in Algae and Aquatic Macrophytes Characterized by Solution 31P NMR Coupled with Enzymatic Hydrolysis
Science.gov (United States)
Feng, Weiying; Zhu, Yuanrong; Wu, Fengchang; He, Zhongqi; Zhang, Chen; Giesy, John P.
2016-11-01
Solution Phosphorus-31 nuclear magnetic resonance (31P NMR) spectroscopy coupled with enzymatic hydrolysis (EH) with commercially available phosphatases was used to characterize phosphorus (P) compounds in extracts of the dominant aquatic macrophytes and algae in a eutrophic lake. Total extractable organic P (Po) concentrations ranged from 504 to 1643 mg kg-1 and 2318 to 8395 mg kg-1 for aquatic macrophytes and algae, respectively. Using 31P NMR spectroscopy, 11 Po species were detected in the mono- and diester region. Additionally, orthophosphate, pyrophosphate and phosphonates were also detected. Using EH, phytate-like P was identified as the prevalent class of enzyme-labile Po, followed by labile monoester- and diester-P. Comparison of the NMR and EH data indicated that the distribution pattern of major P forms in the samples determined by the two methods was similar (r = 0.712, p < 0.05). Additional 31P NMR spectroscopic analysis of extracts following EH showed significant decreases in the monoester and pyrophosphate regions, with a corresponding increase in the orthophosphate signal, as compared to unhydrolyzed extracts. Based on these quantity and hydrolysis data, we proposed that recycling of Po in vegetative biomass residues is an important mechanism for long-term self-regulation of available P for algal blooming in eutrophic lakes.
2. NMR of lignins
Science.gov (United States)
John Ralph; Larry L. Landucci
2010-01-01
This chapter will consider the basic aspects and findings of several forms of NMR spectroscopy, including separate discussions of proton, carbon, heteronuclear, and multidimensional NMR. Enhanced focus will be on 13C NMR, because of its qualitative and quantitative importance, followed by NMRâs contributions to our understanding of lignin...
3. Analysis of monoglycerides, diglycerides, sterols, and free fatty acids in coconut (Cocos nucifera L.) oil by 31P NMR spectroscopy.
Science.gov (United States)
Dayrit, Fabian M; Buenafe, Olivia Erin M; Chainani, Edward T; de Vera, Ian Mitchelle S
2008-07-23
Phosphorus-31 nuclear magnetic resonance spectroscopy ( (31)P NMR) was used to differentiate virgin coconut oil (VCO) from refined, bleached, deodorized coconut oil (RCO). Monoglycerides (MGs), diglycerides (DGs), sterols, and free fatty acids (FFAs) in VCO and RCO were converted into dioxaphospholane derivatives and analyzed by (31)P NMR. On the average, 1-MG was found to be higher in VCO (0.027%) than RCO (0.019%). 2-MG was not detected in any of the samples down to a detection limit of 0.014%. On the average, total DGs were lower in VCO (1.55%) than RCO (4.10%). When plotted in terms of the ratio [1,2-DG/total DGs] versus total DGs, VCO and RCO samples grouped separately. Total sterols were higher in VCO (0.096%) compared with RCO (0.032%), and the FFA content was 8 times higher in VCO than RCO (0.127% vs 0.015%). FFA determination by (31)P NMR and titration gave comparable results. Principal components analysis shows that the 1,2-DG, 1,3-DG, and FFAs are the most important parameters for differentiating VCO from RCO.
4. NMR-CT scanner
International Nuclear Information System (INIS)
Kose, Katsumi; Sato, Kozo; Sugimoto, Hiroshi; Sato, Masataka.
1983-01-01
A brief explanation is made on the imaging methods for a practical diagnostic NMR-CT scanner : A whole-body NMR-CT scanner utilizing a resistive magnet has been developed by Toshiba in cooperation with the Institute for Solid State Physics, the University of Tokyo. Typical NMR-CT images of volunteers and patients obtained in the clinical experiments using this device are presented. Detailed specifications are also shown about the practical NMR-CTs which are to be put on the market after obtaining the government approval. (author)
5. NMR imaging and pharmaceutical sciences
International Nuclear Information System (INIS)
Beall, P.T.; Good, W.R.
1986-01-01
Described is the technique of NMR-imaging in diagnostic medicine. Proton and phosphorus NMR in diagnosis of abnormal tissue pathology. Discussed is the value of NMR to the pharmaceutical sciences. NMR may play an important role in monitoring the response of tissues to drugs, determining the localization of drugs, performing real time pharmacokinetics and testing the use of NMR contrast pharmaceuticals
6. Lectures on pulsed NMR
International Nuclear Information System (INIS)
Pines, A.
1988-08-01
These lectures discuss some recent developments in pulsed NMR, emphasizing fundamental principles with selected illustrative applications. Major topics covered include multiple-quantum spectroscopy, spin decoupling, the interaction of spins with a quantized field, adiabatic rapid passage, spin temperature and statistics of cross-polarization, coherent averaging, and zero field NMR. 32 refs., 56 figs
7. Lectures on pulsed NMR
International Nuclear Information System (INIS)
Pines, A.
1986-09-01
These lectures discuss some recent developments in pulsed NMR, emphasizing fundamental principles with selected illustrative applications. Major topics covered include multiple-quantum spectroscopy, spin decoupling, the interaction of spins with a quantized field, adiabatic rapid passage, spin temperature and statistics of cross-polarization, coherent averaging, and zero field NMR. 55 figs
8. Conformation and Complexation of Tannins: NMR Spectra and Molecular Search Modeling of Flavan-3-ols
Science.gov (United States)
Richard W. Hemingway; Fred L. Tohiason; G. Wayne McGraw; Jan P. Steynberg
1996-01-01
Studies offlavan-3-01sin their biologically significant phenolic form show that both H-6 and C-6 resonances are downfield from H-8 and C-8. Therefore, assignments for the H atoms of the A-ring are inverse to those commonly reported. By contrast, in the methyl ether and methyl ether acetate derivatives, both H-8 and C-8 are downfield from H-6 and C-6 and assignments...
9. Interaction of the Saccharomyces cerevisiae α-factor with phospholipid vesicles as revealed by proton and phosphorus NMR
International Nuclear Information System (INIS)
Jelicks, L.A.; Broido, M.S.; Becker, J.M.; Naider, F.R.
1989-01-01
Proton and phosphorus-31 nuclear magnetic resonance ( 1 H and 31 P NMR) studies of the interaction between a tridecapeptide pheromone, the α-factor of Saccharomyces cerevisiae, and sonicated lipid vesicles are reported. 31 P NMR studies demonstrate that there is interaction of the peptide with the phosphorus headgroups, and quasielastic light scattering (QLS) studies indicate that lipid vesicles increase in size upon addition of peptide. Previous solution (aqueous and DMSO) studies from this laboratory indicate that α-factor is highly flexible with only one long-lived identifiable structural feature, a type II β-turn spanning the central portion of the peptide. Two-dimensional (2D) 1 H nuclear Overhauser effect spectroscopy (NOESY) studies demonstrate a marked ordering of the peptide upon interaction with lipid, suggesting a compact N-terminus, in addition to a stabilized β-turn. In contrast to these results in both solution and lipid environment, Wakamatsu et al. proposed a lipid environment conformation, on the basis of one-dimensional transferred NOE studies in D 2 O, which does not include the β-turn
10. Human calf muscular metabolism study with a home-made ergometer using 31P NMR spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Peynsaert, J; Achten, E; Claeys, E [Ghent University Hospital (Belgium); Rousseaux, M [Ghent University Hospital (Belgium). Dept. of Sport Medicine
1995-12-01
Phosphorus-31 NMR measurements were performed to examine the variations in the concentration of phosphate metabolites in calf muscle during exercise. Therefore, volunteers, installed in the supine position, were asked to push repetitively on the pedal of a home-made ergometer. The produced work and the changes in phosphorus containing metabolites were measured continuously. Correlations were made between the inorganic phosphate/phosphocreatine ratio and the cumulative work and between the intracellular pH and the cumulative work. The exercise protocol could be changed interactively with respect to the imposed initial pressure, the maximum pressure, the pressure increase per level and the time a certain level was held. The whole experiment could be graphically followed on-line. In the first stadium, the in vitro reproducibility of the ergometer was tested for different protocols. These tests revealed that, though the deviation in produced work was markedly the highest at high working pressures, the relative error never exceeded 3%. Consequently, the ex vitro reproducibility of the data was examined with the equipment placed in the scanner. Generally, same conclusions could be derived. In a next stage, the work will be synchronized with the biochemical data. Extreme precautions will be taken to examine each volunteer every time under the same physical and psychological conditions.
11. Human calf muscular metabolism study with a home-made ergometer using 31P NMR spectroscopy
International Nuclear Information System (INIS)
Peynsaert, J.; Achten, E.; Claeys, E. . Dept. of Magnetic Resonance; Rousseaux, M.
1995-01-01
Phosphorus-31 NMR measurements were performed to examine the variations in the concentration of phosphate metabolites in calf muscle during exercise. Therefore, volunteers, installed in the supine position, were asked to push repetitively on the pedal of a home-made ergometer. The produced work and the changes in phosphorus containing metabolites were measured continuously. Correlations were made between the inorganic phosphate/phosphocreatine ratio and the cumulative work and between the intracellular pH and the cumulative work. The exercise protocol could be changed interactively with respect to the imposed initial pressure, the maximum pressure, the pressure increase per level and the time a certain level was held. The whole experiment could be graphically followed on-line. In the first stadium, the in vitro reproducibility of the ergometer was tested for different protocols. These tests revealed that, though the deviation in produced work was markedly the highest at high working pressures, the relative error never exceeded 3%. Consequently, the ex vitro reproducibility of the data was examined with the equipment placed in the scanner. Generally, same conclusions could be derived. In a next stage, the work will be synchronized with the biochemical data. Extreme precautions will be taken to examine each volunteer every time under the same physical and psychological conditions
12. Functional studies using NMR
International Nuclear Information System (INIS)
McCready, V.R.; Leach, M.O.; Sutton; Ell, P.
1986-01-01
The object of this book is to discuss and evaluate an area of Nuclear Magnetic Resonance which to date has been less emphasized than it might be, namely the use of NMR for functional studies. The book commences with a discussion of the areas in which the NMR techniques might be needed due to deficiencies in other techniques. The physics of NMR especially relating to functional measurement are then explained. Technical factors in producing functional images are discussed and the use of paramagnetic substances for carrying out flow studies are detailed. Particular attention is paid to specific studies in the various organs. The book ends with a survey of imaging in each organ and the relation of NMR images to other techniques such as ultrasound, nuclear medicine and X-rays
13. Functional studies using NMR
International Nuclear Information System (INIS)
McCready, V.R.; Leach, M.; Ell, P.J.
1987-01-01
This volume is based on a series of lectures delivered at a one-day teaching symposium on functional and metabolic aspects of NMR measurements held at the Middlesex Hospital Medical School on 1st September 1985 as a part of the European Nuclear Medicine Society Congress. Currently the major emphasis in medical NMR in vivo is on its potential to image and display abnormalities in conventional radiological images, providing increased contrast between normal and abnormal tissue, improved definition of vasculature, and possibly an increased potential for differential diagnosis. Although these areas are undeniably of major importance, it is probable that NMR will continue to complement conventional measurement methods. The major potential benefits to be derived from in vivo NMR measurements are likely to arise from its use as an instrument for functional and metabolic studies in both clinical research and in the everyday management of patients. It is to this area that this volume is directed
14. NMR of unfolded proteins
Unknown
2005-01-03
Jan 3, 2005 ... covering all the systems, so far discovered.5,7,8,12. With the increasing ... Structural investigations on proteins by NMR are, currently ... rapid analysis of unfolded proteins. ...... and hence help in design of drugs against them.
15. Theory of NMR probe design
International Nuclear Information System (INIS)
Schnall, M.D.
1988-01-01
The NMR probe is the intrinsic part of the NMR system which allows transmission of a stimulus to a sample and the reception of a resulting signal from a sample. NMR probes are used in both imaging and spectroscopy. Optimal probe design is important to the production of adequate signal/moise. It is important for anyone using NMR techniques to understand how NMR probes work and how to optimize probe design
16. Microprocessorized NMR measurement
International Nuclear Information System (INIS)
Rijllart, A.
1984-01-01
An MC68000 CAMAC microprocessor system for fast and accurate NMR signal measurement will be presented. A stand-alone CAMAC microprocessor system (MC68000 STAC) with a special purpose interface sweeps a digital frequency synthesizer and digitizes the NMR signal with a 16-bit ADC of 17 μs conversion time. It averages the NMR signal data over many sweeps and then transfers it through CAMAC to a computer for calculation of the signal parameters. The computer has full software control over the timing and sweep settings of this signal averager, and thus allows optimization of noise suppression. Several of these processor systems can be installed in the same crate for parallel processing, and the flexibility of the STAC also allows easy adaptation to other applications such as transient recording or phase-sensitive detection. (orig.)
17. Fourier transform NMR
International Nuclear Information System (INIS)
Hallenga, K.
1991-01-01
This paper discusses the concept of Fourier transformation one of the many precious legacies of the French mathematician Jean Baptiste Joseph Fourier, essential for understanding the link between continuous-wave (CW) and Fourier transform (FT) NMR. Although in modern FT NMR the methods used to obtain a frequency spectrum from the time-domain signal may vary greatly, from the efficient Cooley-Tukey algorithm to very elaborate iterative least-square methods based other maximum entropy method or on linear prediction, the principles for Fourier transformation are unchanged and give invaluable insight into the interconnection of many pairs of physical entities called Fourier pairs
18. International symposium on NMR spectroscopy
International Nuclear Information System (INIS)
The publication consists of 32 papers and presentations from the field of NMR spectroscopy applications submitted to the International Symposium on NMR Spectroscopy held at Smolenice between 29 Sep and 3 Oct, 1980. (B.S.)
19. Single-sided NMR
CERN Document Server
Casanova, Federico; Blümich, Bernhard
2011-01-01
Single-Sided NMR describes the design of the first functioning single-sided tomograph, the related measurement methods, and a number of applications. One of the key advantages to this method is the speed at which the images are obtained.
20. Autonomous driving in NMR.
Science.gov (United States)
Perez, Manuel
2017-01-01
The automatic analysis of NMR data has been a much-desired endeavour for the last six decades, as it is the case with any other analytical technique. This need for automation has only grown as advances in hardware; pulse sequences and automation have opened new research areas to NMR and increased the throughput of data. Full automatic analysis is a worthy, albeit hard, challenge, but in a world of artificial intelligence, instant communication and big data, it seems that this particular fight is happening with only one technique at a time (let this be NMR, MS, IR, UV or any other), when the reality of most laboratories is that there are several types of analytical instrumentation present. Data aggregation, verification and elucidation by using complementary techniques (e.g. MS and NMR) is a desirable outcome to pursue, although a time-consuming one if performed manually; hence, the use of automation to perform the heavy lifting for users is required to make the approach attractive for scientists. Many of the decisions and workflows that could be implemented under automation will depend on the two-way communication with databases that understand analytical data, because it is desirable not only to query these databases but also to grow them in as much of an automatic manner as possible. How these databases are designed, set up and the data inside classified will determine what workflows can be implemented. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
1. NMR for chemists and biologists
CERN Document Server
Carbajo, Rodrigo J
2013-01-01
This book offers a concise introduction to the field of nuclear magnetic resonance or NMR. It presents the basic foundations of NMR in a non-mathematical way and provides an overview of both recent and important biological applications of NMR.
2. Ab Initio Calculations of 31P NMR Chemical Shielding Anisotropy Tensors in Phosphates: Variations Due to Ring Formation
Directory of Open Access Journals (Sweden)
Todd M. Alam
2002-08-01
Full Text Available Abstract: Ring formation in phosphate systems is expected to influence both the magnitude and orientation of the phosphorus (31P nuclear magnetic resonance (NMR chemical shielding anisotropy (CSA tensor. Ab initio calculations of the 31P CSA tensor in both cyclic and acyclic phosphate clusters were performed as a function of the number of phosphate tetrahedral in the system. The calculation of the 31P CSA tensors employed the GAUSSIAN 98 implementation of the gauge-including atomic orbital (GIAO method at the Hartree-Fock (HF level. It is shown that both the 31P CSA tensor anisotropy, and the isotropic chemical shielding can be used for the identification of cyclic phosphates. The differences between the 31P CSA tensor in acyclic and cyclic phosphate systems become less pronounced with increasing number of phosphate groups within the ring. The orientation of the principal components for the 31P CSA tensor shows some variation due to cyclization, most notably with the smaller, highly strained ring systems.
3. NMR, water and plants
International Nuclear Information System (INIS)
As, H. van.
1982-01-01
This thesis describes the application of a non-destructive pulsed proton NMR method mainly to measure water transport in the xylem vessels of plant stems and in some model systems. The results are equally well applicable to liquid flow in other biological objects than plants, e.g. flow of blood and other body fluids in human and animals. The method is based on a pulse sequence of equidistant π pulses in combination with a linear magnetic field gradient. (Auth.)
4. Magic Angle Spinning NMR Metabolomics
Energy Technology Data Exchange (ETDEWEB)
Zhi Hu, Jian
2016-01-01
Nuclear Magnetic Resonance (NMR) spectroscopy is a non-destructive, quantitative, reproducible, untargeted and unbiased method that requires no or minimal sample preparation, and is one of the leading analytical tools for metabonomics research [1-3]. The easy quantification and the no need of prior knowledge about compounds present in a sample associated with NMR are advantageous over other techniques [1,4]. 1H NMR is especially attractive because protons are present in virtually all metabolites and its NMR sensitivity is high, enabling the simultaneous identification and monitoring of a wide range of low molecular weight metabolites.
5. NMR in clinical practice
International Nuclear Information System (INIS)
Smith, F.W.
1987-01-01
The development of NMR for clinical use has been complicated by a number of controversies, the largest of these being the question of what is the optimum field strength for proton imaging. Many workers believe that diagnostically useful images can only be produced at high field strength (i.e. 0.5 - 2.0 T), where in fact diagnostically useful images are made using field strengths of as low as 0.02 T. Because the method is more complex than X-ray CT, which relies on the measurement of only one parameter, tissue density, many new users have difficulty in selecting the correct imaging pulse sequence to provide the most useful image for diagnosis. NMR imaging pulse sequence may be selected to produce images of the proton density, T/sub 1/ or T/sub 2/ signals, or combinations of them. When this facility is used, images which are T/sub 1/ or T/sub 2/ weighted can be selected. Inversion-recovery sequences are more appropriate for imaging the abdomen where by selecting a short TR interval the signal from subcutaneous fat, which is the major cause of image artefact in abdominal imaging, is suppressed thereby improving image quality. The use of surface receiver coils, which are applied closely to the area of the body being examined is becoming more widespread and is of particular value when examining the orbits, facial structures, neck, breast, spine and limbs. The use of these coils together with a discussion of patient selection for NMR imaging, image interpretation and data storage follow
6. NMR spectroscopy and drug development
International Nuclear Information System (INIS)
Craik, D.; Munro, S.
1990-01-01
The use of nuclear magnetic resonance (NMR) spectroscopy for structural and conformational studies on drug molecules, the three-dimensional investigation of proteins structure and their interactions with ligands are discussed. In-vivo NMR studies of the effects of drugs on metabolism in perfused organs and whole animals are also briefly presented. 5 refs., ills
7. NMR in pulsed magnetic field
KAUST Repository
Abou-Hamad, Edy; Bontemps, P.; Rikken, Geert L J A
2011-01-01
Nuclear magnetic resonance (NMR) experiments in pulsed magnetic fields up to 30.4 T focused on 1H and 93Nb nuclei are reported. Here we discuss the advantage and limitation of pulsed field NMR and why this technique is able to become a promising research tool. © 2011 Elsevier Inc. All Rights Reserved.
8. NMR imaging of osteoarticular pathology
International Nuclear Information System (INIS)
Frocrain, L.; Duvauferrier, R.; Gagey, N.
1987-01-01
NMR imaging is assuming an increasingly important role in the diagnosis of osteo-articular disorders. Semiological descriptions of the mean pathological disorders of the locomotor system are presented. Some investigation strategies are proposed to compare NMR imaging with other imaging techniques in various pathological states [fr
9. Nuclear magnetic resonance (NMR) tomography
International Nuclear Information System (INIS)
Skalpe, I.O.
1984-01-01
A brief survey of the working principle of the NMR technique in diagnostical medicine is given. Its clinical usefulness for locating tumors, diagnosing various other diseases, such as some mental illnesses and multiple sclerosis, and its possibilities for studying biochemical processes in vivo are mentioned. The price of NMR image scanners and the problems of the strong magnetic field around the machines are mentioned
10. NMR imaging studies of coal
Energy Technology Data Exchange (ETDEWEB)
Ma, Z.R.; Zhang, P.Z.; Ding, G.L.; Li, L.Y.; Ye, C.H. [University of Science and Technology, Beijing (China). Dept. of Chemistry
1996-06-01
The permeation transportation and swelling behavior of solvents into coal are investigated by NMR imaging using pyridine-d{sub 5} and acetone-d{sub 6}. Images of coal swollen with deuterated solvents illuminate proton distributions of mobile phases within the coal macromolecular networks. More information about the chemical and physical structure of coal can be obtained using NMR imaging techniques.
11. NMR in pulsed magnetic field
KAUST Repository
2011-09-01
Nuclear magnetic resonance (NMR) experiments in pulsed magnetic fields up to 30.4 T focused on 1H and 93Nb nuclei are reported. Here we discuss the advantage and limitation of pulsed field NMR and why this technique is able to become a promising research tool. © 2011 Elsevier Inc. All Rights Reserved.
12. Structural Biology: Practical NMR Applications
CERN Document Server
Teng, Quincy
2005-01-01
This textbook begins with an overview of NMR development and applications in biological systems. It describes recent developments in instrument hardware and methodology. Chapters highlight the scope and limitation of NMR methods. While detailed math and quantum mechanics dealing with NMR theory have been addressed in several well-known NMR volumes, chapter two of this volume illustrates the fundamental principles and concepts of NMR spectroscopy in a more descriptive manner. Topics such as instrument setup, data acquisition, and data processing using a variety of offline software are discussed. Chapters further discuss several routine stategies for preparing samples, especially for macromolecules and complexes. The target market for such a volume includes researchers in the field of biochemistry, chemistry, structural biology and biophysics.
13. Fundamentals of Protein NMR Spectroscopy
CERN Document Server
Rule, Gordon S
2006-01-01
NMR spectroscopy has proven to be a powerful technique to study the structure and dynamics of biological macromolecules. Fundamentals of Protein NMR Spectroscopy is a comprehensive textbook that guides the reader from a basic understanding of the phenomenological properties of magnetic resonance to the application and interpretation of modern multi-dimensional NMR experiments on 15N/13C-labeled proteins. Beginning with elementary quantum mechanics, a set of practical rules is presented and used to describe many commonly employed multi-dimensional, multi-nuclear NMR pulse sequences. A modular analysis of NMR pulse sequence building blocks also provides a basis for understanding and developing novel pulse programs. This text not only covers topics from chemical shift assignment to protein structure refinement, as well as the analysis of protein dynamics and chemical kinetics, but also provides a practical guide to many aspects of modern spectrometer hardware, sample preparation, experimental set-up, and data pr...
14. Two dimensional solid state NMR
International Nuclear Information System (INIS)
Kentgens, A.P.M.
1987-01-01
This thesis illustrates, by discussing some existing and newly developed 2D solid state experiments, that two-dimensional NMR of solids is a useful and important extension of NMR techniques. Chapter 1 gives an overview of spin interactions and averaging techniques important in solid state NMR. As 2D NMR is already an established technique in solutions, only the basics of two dimensional NMR are presented in chapter 2, with an emphasis on the aspects important for solid spectra. The following chapters discuss the theoretical background and applications of specific 2D solid state experiments. An application of 2D-J resolved NMR, analogous to J-resolved spectroscopy in solutions, to natural rubber is given in chapter 3. In chapter 4 the anisotropic chemical shift is mapped out against the heteronuclear dipolar interaction to obtain information about the orientation of the shielding tensor in poly-(oxymethylene). Chapter 5 concentrates on the study of super-slow molecular motions in polymers using a variant of the 2D exchange experiment developed by us. Finally chapter 6 discusses a new experiment, 2D nutation NMR, which makes it possible to study the quadrupole interaction of half-integer spins. 230 refs.; 48 figs.; 8 tabs
15. nmr spectroscopic study and dft calculations of giao nmr shieldings
African Journals Online (AJOL)
Preferred Customer
3Department of Physics, Arts and Science Faculty, Dumlupinar University, Kütahya, ... 1H, 13C NMR chemical shifts and 1JCH coupling constants of .... then estimated using the corresponding TMS shieldings calculated in advance at the same.
16. Two-dimensional 1H and 31P NMR spectra and restrained molecular dynamics structure of an extrahelical adenosine tridecamer oligodeoxyribonucleotide duplex
International Nuclear Information System (INIS)
Nikonowicz, E.; Roongta, V.; Jones, C.R.; Gorenstein, D.G.
1989-01-01
Assignment of the 1H and 31P NMR spectra of an extrahelical adenosine tridecamer oligodeoxyribonucleotide duplex, d(CGCAGAATTCGCG)2, has been made by two-dimensional 1H-1H and heteronuclear 31P-1H correlated spectroscopy. The downfield 31P resonance previously noted by Patel et al. (1982) has been assigned by both 17O labeling of the phosphate as well as a pure absorption phase constant-time heteronuclear 31P-1H correlated spectrum and has been associated with the phosphate on the 3' side of the extrahelical adenosine. JH3'-P coupling constants for each of the phosphates of the tridecamer were obtained from the 1H-31P J-resolved selective proton-flip 2D spectrum. By use of a modified Karplus relationship the C4-C3'-O3-P torsional angles (epsilon) were obtained. There exists a good linear correlation between 31P chemical shifts and the epsilon torsional angle. The 31P chemical shifts and epsilon torsional angles follow the general observation that the more internal the phosphate is located within the oligonucleotide sequence, the more upfield the 31P resonance occurs. Because the extrahelical adenosine significantly distorts the deoxyribose phosphate backbone conformation even several bases distant from the extrahelical adenosine, 31P chemical shifts show complex site- and sequence-specific variations. Modeling and NOESY distance-restrained energy minimization and restrained molecular dynamics suggest that the extrahelical adenosine stacks into the duplex. However, a minor conformation is also observed in the 1H NMR, which could be associated with a structure in which the extrahelical adenosine loops out into solution
17. NMR-based milk metabolomics
DEFF Research Database (Denmark)
Sundekilde, Ulrik; Larsen, Lotte Bach; Bertram, Hanne Christine S.
2013-01-01
and processing capabilities of bovine milk is closely associated to milk composition. Metabolomics is ideal in the study of the low-molecular-weight compounds in milk, and this review focuses on the recent nuclear magnetic resonance (NMR)-based metabolomics trends in milk research, including applications linking...... compounds. Furthermore, metabolomics applications elucidating how the differential regulated genes affects milk composition are also reported. This review will highlight the recent advances in NMR-based metabolomics on milk, as well as give a brief summary of when NMR spectroscopy can be useful for gaining...
18. Annual reports on NMR spectroscopy
CERN Document Server
Webb, Graham A; McCarthy, M J
1995-01-01
Over recent years, no other technique has grown to such importance as that of NMR spectroscopy. It is used in all branches of science where precise structural determination is required and where the nature of interactions and reactions in solution is being studied. Annual Reports on NMR Spectroscopy has established itself as a means for the specialist and non-specialist alike to become familiar with new applications of the technique in all branches of chemistry, including biochemistry, and pharmaceutics. This volume focuses on theoretical aspects of NMR nuclear shielding and on applications of
19. β-NMR sample optimization
CERN Document Server
Zakoucka, Eva
2013-01-01
During my summer student programme I was working on sample optimization for a new β-NMR project at the ISOLDE facility. The β-NMR technique is well-established in solid-state physics and just recently it is being introduced for applications in biochemistry and life sciences. The β-NMR collaboration will be applying for beam time to the INTC committee in September for three nuclei: Cu, Zn and Mg. Sample optimization for Mg was already performed last year during the summer student programme. Therefore sample optimization for Cu and Zn had to be completed as well for the project proposal. My part in the project was to perform thorough literature research on techniques studying Cu and Zn complexes in native conditions, search for relevant binding candidates for Cu and Zn applicable for ß-NMR and eventually evaluate selected binding candidates using UV-VIS spectrometry.
20. NMR Studies of Polymer Nanocomposites
National Research Council Canada - National Science Library
Greenbaum, Steve
2001-01-01
.... The primary tool is pulsed field gradient NMR. A static field gradient method was developed which makes possible variable pressure diffusion measurement, and the application to the important fuel cell membrane NAFION constitute the first results...
1. Integrative NMR for biomolecular research
International Nuclear Information System (INIS)
Lee, Woonghee; Cornilescu, Gabriel; Dashti, Hesam; Eghbalnia, Hamid R.; Tonelli, Marco; Westler, William M.; Butcher, Samuel E.; Henzler-Wildman, Katherine A.; Markley, John L.
2016-01-01
NMR spectroscopy is a powerful technique for determining structural and functional features of biomolecules in physiological solution as well as for observing their intermolecular interactions in real-time. However, complex steps associated with its practice have made the approach daunting for non-specialists. We introduce an NMR platform that makes biomolecular NMR spectroscopy much more accessible by integrating tools, databases, web services, and video tutorials that can be launched by simple installation of NMRFAM software packages or using a cross-platform virtual machine that can be run on any standard laptop or desktop computer. The software package can be downloaded freely from the NMRFAM software download page ( http://pine.nmrfam.wisc.edu/download-packages.html http://pine.nmrfam.wisc.edu/download_packages.html ), and detailed instructions are available from the Integrative NMR Video Tutorial page ( http://pine.nmrfam.wisc.edu/integrative.html http://pine.nmrfam.wisc.edu/integrative.html ).
2. Integrative NMR for biomolecular research
Energy Technology Data Exchange (ETDEWEB)
Lee, Woonghee, E-mail: [email protected]; Cornilescu, Gabriel; Dashti, Hesam; Eghbalnia, Hamid R.; Tonelli, Marco; Westler, William M.; Butcher, Samuel E.; Henzler-Wildman, Katherine A.; Markley, John L., E-mail: [email protected] [University of Wisconsin-Madison, National Magnetic Resonance Facility at Madison and Biochemistry Department (United States)
2016-04-15
NMR spectroscopy is a powerful technique for determining structural and functional features of biomolecules in physiological solution as well as for observing their intermolecular interactions in real-time. However, complex steps associated with its practice have made the approach daunting for non-specialists. We introduce an NMR platform that makes biomolecular NMR spectroscopy much more accessible by integrating tools, databases, web services, and video tutorials that can be launched by simple installation of NMRFAM software packages or using a cross-platform virtual machine that can be run on any standard laptop or desktop computer. The software package can be downloaded freely from the NMRFAM software download page ( http://pine.nmrfam.wisc.edu/download-packages.html http://pine.nmrfam.wisc.edu/download{sub p}ackages.html ), and detailed instructions are available from the Integrative NMR Video Tutorial page ( http://pine.nmrfam.wisc.edu/integrative.html http://pine.nmrfam.wisc.edu/integrative.html ).
3. Interpretations of NMR images
International Nuclear Information System (INIS)
Shi, J.Z.; McFarland, W.D.; Chen, S.S.; Sadhu, V.K.
1986-01-01
Two color display schemes are generally considered in medical images: pseudo-color and color composite. Psuedo-color technique maps the intensity means of a single monochrome image into a three dimensional color space, the gray level is thus replaced by the assigned color. Such a psuedo-color assignment is somewhat arbitrary but may be advantageous if the monochrome image is composed of simple intensity patterns. A good example of psuedo-color application is in nuclear medicine: The change of gray levels can be simply determined and the isocounts from two regions with different surroundings can be readily recognized. However, the use of psuedo-color in CT or MR imaging is controversial because it does not give additional information and may exaggerate insignificant gray scale differences. The color composite technique maps three parametric image data into a three dimensional color space, and thus three monochrome images are merged to form a single color image. The color composite technique increases the number of ways information can be displayed and provides both quantitative and qualitative data about the object or event represented. This paper describes the application of color composite in NMR images
4. NMR characterization of thin films
Science.gov (United States)
Gerald II, Rex E.; Klingler, Robert J.; Rathke, Jerome W.; Diaz, Rocio; Vukovic, Lela
2010-06-15
A method, apparatus, and system for characterizing thin film materials. The method, apparatus, and system includes a container for receiving a starting material, applying a gravitational force, a magnetic force, and an electric force or combinations thereof to at least the starting material, forming a thin film material, sensing an NMR signal from the thin film material and analyzing the NMR signal to characterize the thin film of material.
5. NMR imaging of cerebral infarction
International Nuclear Information System (INIS)
Takusagawa, Yoshihiko; Yamaoka, Naoki; Doi, Kazuaki; Okada, Keisei
1987-01-01
One hundred and five patients with cerebral infarction were studied by nuclear magnetic resonance (NMR) CT (resistive type of magnet with strength of 0.1 tesla) and X-ray CT. Pulse sequences used saturation recovery (Tr = 600 mSec), Inversion recovery (Tr = 500 mSec, Td = 300 mSec) and spin echo (Tr = 1500 mSec, Te = 40, 80, 120, 160 mSec). Fifteen cases were examined by NMR-CT within 24 hours from onset. Proton NMR imaging could not detect cerebral ischemia as early as 2 hours after onset, but except could detect the lesions in Se image the area of cerebral infarct 3 hours after onset. After 5 hours from onset image changes in SE were evident and corresponded to the area of cerebral infarct, but image changes in IR could not fully delineate the infarcted area. NMR images of 41 year-old woman with cerebral embolism by MCA trunck occlusion associated with mitral stenosis were presented, and NMR-CT was examined 10 hours, 9th and 43th days after episode of MCA occlusion. Sixty patents (64 times) with lacunar infarction were studied by NMR-CT and X-ray CT. The inversion recovery images were used mainly for detection of lesions and comparison with X-ray CT. In 160 lesions which were detected by NMR-CT or X-ray CT, could 156 lesions be detected by NMR-CT and 78 lesions by X-ray CT. Inversion recovery images were more useful for detection of lacunes than X-ray CT. Calculated T1 and T2 values prolonged with time course from onset. (author)
6. Optical pumping and xenon NMR
International Nuclear Information System (INIS)
Raftery, M.D.
1991-11-01
Nuclear Magnetic Resonance (NMR) spectroscopy of xenon has become an important tool for investigating a wide variety of materials, especially those with high surface area. The sensitivity of its chemical shift to environment, and its chemical inertness and adsorption properties make xenon a particularly useful NMR probe. This work discusses the application of optical pumping to enhance the sensitivity of xenon NMR experiments, thereby allowing them to be used in the study of systems with lower surface area. A novel method of optically-pumping 129 Xe in low magnetic field below an NMR spectrometer and subsequent transfer of the gas to high magnetic field is described. NMR studies of the highly polarized gas adsorbed onto powdered samples with low to moderate surface areas are now possible. For instance, NMR studies of optically-pumped xenon adsorbed onto polyacrylic acid show that xenon has a large interaction with the surface. By modeling the low temperature data in terms of a sticking probability and the gas phase xenon-xenon interaction, the diffusion coefficient for xenon at the surface of the polymer is determined. The sensitivity enhancement afforded by optical pumping also allows the NMR observation of xenon thin films frozen onto the inner surfaces of different sample cells. The geometry of the thin films results in interesting line shapes that are due to the bulk magnetic susceptibility of xenon. Experiments are also described that combine optical pumping with optical detection for high sensitivity in low magnetic field to observe the quadrupoler evolution of 131 Xe spins at the surface of the pumping cells. In cells with macroscopic asymmetry, a residual quadrupolar interaction causes a splitting in the 131 Xe NMR frequencies in bare Pyrex glass cells and cells with added hydrogen
7. NMR characterization of thin films
Science.gov (United States)
Gerald, II, Rex E.; Klingler, Robert J.; Rathke, Jerome W.; Diaz, Rocio; Vukovic, Lela
2008-11-25
A method, apparatus, and system for characterizing thin film materials. The method, apparatus, and system includes a container for receiving a starting material, applying a gravitational force, a magnetic force, and an electric force or combinations thereof to at least the starting material, forming a thin film material, sensing an NMR signal from the thin film material and analyzing the NMR signal to characterize the thin film of material.
8. Medical applications of NMR imaging and NMR spectroscopy with stable isotopes. Summary
Energy Technology Data Exchange (ETDEWEB)
Matwiyoff, N.A.
1983-01-01
The current status of NMR imaging and NMR spectroscopy are summarized. For the most part examples from the March 1983 Puerto Rico symposium are used to illustrate the utility of NMR in medicine. 18 refs., 5 figs.
9. Medical applications of NMR imaging and NMR spectroscopy with stable isotopes. Summary
International Nuclear Information System (INIS)
Matwiyoff, N.A.
1983-01-01
The current status of NMR imaging and NMR spectroscopy are summarized. For the most part examples from the March 1983 Puerto Rico symposium are used to illustrate the utility of NMR in medicine. 18 refs., 5 figs
10. Carbon-13 NMR of flavinoids
International Nuclear Information System (INIS)
Agrawal, P.K.
1989-01-01
The present book has been written with the objective of introducing the organic chemists with the conceptual and experimental basis required for interpretation of 13 C NMR spectra of a flavonoid and to a discussion of general usefulness of the technique in solving flavonoid structural problem. After a brief general introduction to the essential aspects of flavonoids and 13 C NMR spectroscopy, considerable emphasis has been placed in chapter 2 on the various experimental methods and the interpretation of spectral details which enable individual resonance lines to be associated with the appropriate carbons in a molecule. The whole bulk of the literature, published on 13 C NMR of flavonoids in the major journals upto 1986 alongwith some recent references of 1987 has been classified in several categories such as: flavonoids, isflavonoids, other flavonoids, flavonoid glycosides, chalconoids and flavanoids. Each category constitutes a chapter. Finally the last chapter is devoted largely to a discussion for the differentiation of various categories and subcategories of flavonoids and for the establishment of aromatic substitution pattern in these compounds. It should be emphasized that the book is a data book and only concerned with the actual analysis of 13 C NMR spectra, thus a reasonable familiarity with basic instrumentation of 13 C NMR and general pattern of nuclear chemical shifts has been assumed. (author). refs.; figs.; tabs
11. NMR investigation of coal extracts
Energy Technology Data Exchange (ETDEWEB)
Lang, I; Sebor, G [Ceskoslovenska Akademie Ved, Prague. Hornicky Ustav; Sebor, G Jr; Hajek, M; Mostecky, J [Vysoka Skola Chemicko-Technologicka, Prague (Czechoslovakia)
1978-07-01
Proton NMR spectroscopy was used for the evaluation of 10% coal extract solutions in deuterated pyridine. Four types of Czechoslovak coal were analyzed. Agreement was found between the aromaticity of coal extracts calculated from /sup 1/H NMR data using Brown's method and Ladner's and Williams' method and the characterization of an average molecule of the coal extract by the number of non-bridge carbon atoms of aromatic rings, by the overall number of aromatic ring carbon atoms and the number of aromatic rings, determined by the Williams and Ferris methods. The methods for calculating carbon distribution from /sup 1/H NMR data, however, contain some constants theoretically estimated or experimentally found using the method which still remain to be verified.
12. Two-dimensional NMR spectrometry
International Nuclear Information System (INIS)
Farrar, T.C.
1987-01-01
This article is the second in a two-part series. In part one (ANALYTICAL CHEMISTRY, May 15) the authors discussed one-dimensional nuclear magnetic resonance (NMR) spectra and some relatively advanced nuclear spin gymnastics experiments that provide a capability for selective sensitivity enhancements. In this article and overview and some applications of two-dimensional NMR experiments are presented. These powerful experiments are important complements to the one-dimensional experiments. As in the more sophisticated one-dimensional experiments, the two-dimensional experiments involve three distinct time periods: a preparation period, t 0 ; an evolution period, t 1 ; and a detection period, t 2
13. Solid state NMR of materials
Energy Technology Data Exchange (ETDEWEB)
Taylor, Sharon A; Ferguson, David B; Haw, James F [Texas A and M Univ., College Station, TX (United States). Dept. of Chemistry
1994-12-31
In situ NMR experiments are studied, including probe of several structures such as the structures of the organic adsorbates, Broensted acid sites, other nuclei associated with active sites, and other framework sites. The authors report that in the absence of high concentrations of paramagnetic sites or metal particles, high resolution MAS spectra are relatively easy to obtain and interpret. It is also concluded that NMR can measure spatial distributions and rates of diffusion; and are able to characterize equilibrium structures and the frequencies and amplitudes of molecular motion
14. Push-through Direction Injectin NMR Automation
Science.gov (United States)
Nuclear magnetic resonance (NMR) and mass spectrometry (MS) are the two major spectroscopic techniques successfully used in metabolomics studies. The non-invasive, quantitative and reproducible characteristics make NMR spectroscopy an excellent technique for detection of endogeno...
15. Fourier transform n.m.r. spectroscopy
International Nuclear Information System (INIS)
Shaw, D.
1976-01-01
This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques
16. NMR investigations of molecular dynamics
Science.gov (United States)
Palmer, Arthur
2011-03-01
NMR spectroscopy is a powerful experimental approach for characterizing protein conformational dynamics on multiple time scales. The insights obtained from NMR studies are complemented and by molecular dynamics (MD) simulations, which provide full atomistic details of protein dynamics. Homologous mesophilic (E. coli) and thermophilic (T. thermophilus) ribonuclease H (RNase H) enzymes serve to illustrate how changes in protein sequence and structure that affect conformational dynamic processes can be monitored and characterized by joint analysis of NMR spectroscopy and MD simulations. A Gly residue inserted within a putative hinge between helices B and C is conserved among thermophilic RNases H, but absent in mesophilic RNases H. Experimental spin relaxation measurements show that the dynamic properties of T. thermophilus RNase H are recapitulated in E. coli RNase H by insertion of a Gly residue between helices B and C. Additional specific intramolecular interactions that modulate backbone and sidechain dynamical properties of the Gly-rich loop and of the conserved Trp residue flanking the Gly insertion site have been identified using MD simulations and subsequently confirmed by NMR spin relaxation measurements. These results emphasize the importance of hydrogen bonds and local steric interactions in restricting conformational fluctuations, and the absence of such interactions in allowing conformational adaptation to substrate binding.
17. PSYCHE Pure Shift NMR Spectroscopy.
Science.gov (United States)
Foroozandeh, Mohammadali; Morris, Gareth; Nilsson, Mathias
2018-03-13
Broadband homodecoupling techniques in NMR, also known as "pure shift" methods, aim to enhance spectral resolution by suppressing the effects of homonuclear coupling interactions to turn multiplet signals into singlets. Such techniques typically work by selecting a subset of "active" nuclear spins to observe, and selectively inverting the remaining, "passive", spins to reverse the effects of coupling. Pure Shift Yielded by Chirp Excitation (PSYCHE) is one such method; it is relatively recent, but has already been successfully implemented in a range of different NMR experiments. Paradoxically, PSYCHE is one of the trickiest of pure shift NMR techniques to understand but one of the easiest to use. Here we offer some insights into theoretical and practical aspects of the method, and into the effects and importance of the experimental parameters. Some recent improvements that enhance the spectral purity of PSYCHE spectra will be presented, and some experimental frameworks including examples in 1D and 2D NMR spectroscopy, for the implementation of PSYCHE will be introduced. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
18. High resolution NMR theory and chemical applications
CERN Document Server
Becker, Edwin D
1999-01-01
High Resolution NMR provides a broad treatment of the principles and theory of nuclear magnetic resonance (NMR) as it is used in the chemical sciences. It is written at an "intermediate" level, with mathematics used to augment, rather than replace, clear verbal descriptions of the phenomena. The book is intended to allow a graduate student, advanced undergraduate, or researcher to understand NMR at a fundamental level, and to see illustrations of the applications of NMR to the determination of the structure of small organic molecules and macromolecules, including proteins. Emphasis is on the study of NMR in liquids, but the treatment also includes high resolution NMR in the solid state and the principles of NMR imaging and localized spectroscopy. Careful attention is given to developing and interrelating four approaches - steady state energy levels, the rotating vector picture, the density matrix, and the product operator formalism. The presentation is based on the assumption that the reader has an acquaintan...
19. PVT Degradation Studies: NMR Analysis
Energy Technology Data Exchange (ETDEWEB)
Cho, Herman M. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Kouzes, Richard T. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2017-06-06
Under certain environmental conditions, polyvinyl toluene (PVT) plastic scintillator has been observed to undergo internal fogging. Nuclear magnetic resonance spectroscopy has been used to elucidate the state of water inside the PVT. The deuterium NMR results show that water absorbed by PVT under warm, humid conditions enters several distinct environments, and when the PVT is transferred from incubation to ambient temperature and humidity the water is lost on a time scale of a few hours from these samples. Most of the deuterium NMR peaks can be assigned to bulk liquid water, but almost 35% of the detected signal intensity is contained in a resonance that resembles spectra of water contained in nanometer-scale pores in mesoporous carbon.
20. NMR imaging of human atherosclerosis
International Nuclear Information System (INIS)
Toussaint, J.F.
1995-01-01
Diagnosis and prognosis of atherosclerosis can no longer be evaluated with morphological parameters only. A description of atherosclerotic plaque composition is necessary to study the mechanisms of plaque rupture, which depends on collagenous cap and lipid core thicknesses. NMR, as a biochemical imaging technique, allows visualization of these components using T1 contrast (mobile lipids), T2 contrast (cap vs. core), spin density (calcifications), diffusion imaging, 1H and 13C spectroscopy. Today, these imaging sequences allow to study in vitro the effects of interventional techniques such as angioplasty or atherectomy. Clinical investigations begin, which will attempt to develop in vivo microscopy and test the ability of NMR to predict plaque rupture. (author). 13 refs., 7 figs
1. High resolution NMR in zeolites
Energy Technology Data Exchange (ETDEWEB)
Diaz, Anix [INTEVEP, Filial de Petroleos de Venezuela, SA, Caracas (Venezuela). Dept. de Analisis y Evalucion
1992-12-31
In this work {sup 29} Si and {sup 27} Al NMR spectroscopy was used to study various types of zeolites. The corresponding spectra were used to measure the Si/Al ratios, to follow chemical modifications induced by acid and hydrothermal treatments, to determine non-equivalent crystallographic sites in highly dealuminated mordenites, and to detect modifications of faujasites due to the insertion of titanium atoms in the lattice. (author) 7 refs., 7 figs., 2 tabs.
2. High resolution NMR in zeolites
International Nuclear Information System (INIS)
Diaz, Anix
1991-01-01
In this work 29 Si and 27 Al NMR spectroscopy was used to study various types of zeolites. The corresponding spectra were used to measure the Si/Al ratios, to follow chemical modifications induced by acid and hydrothermal treatments, to determine non-equivalent crystallographic sites in highly dealuminated mordenites, and to detect modifications of faujasites due to the insertion of titanium atoms in the lattice. (author)
3. Advanced NMR technology for bioscience and biotechnology
Energy Technology Data Exchange (ETDEWEB)
Hammel, P.C.; Hernandez, G.; Trewhella, J.; Unkefer, C.J. [Los Alamos National Lab., NM (US); Boumenthal, D.K. [Univ. of Utah, Salt Lake City, UT (US); Kennedy, M.A. [Pacific Northwest National Lab., Richland, WA (US); Moore, G.J. [Wayne State Univ., Detroit, MI (US)
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). NMR plays critical roles in bioscience and biotechnology in both imaging and structure determination. NMR is limited, however, by the inherent low sensitivity of the NMR experiment and the demands for spectral resolution required to study biomolecules. The authors addressed both of these issues by working on the development of NMR force microscopy for molecular imaging, and high field NMR with isotope labeling to overcome limitations in the size of biomolecules that can be studied using NMR. A novel rf coil design for NMR force microscopy was developed that increases the limits of sensitivity in magnetic resonance detection for imaging, and the authors demonstrated sub-surface spatial imaging capabilities. The authors also made advances in the miniaturization of two critical NMR force microscope components. They completed high field NMR and isotope labeling studies of a muscle protein complex which is responsible for regulating muscle contraction and is too large for study using conventional NMR approaches.
4. Solid-state NMR of inorganic semiconductors.
Science.gov (United States)
Yesinowski, James P
2012-01-01
Studies of inorganic semiconductors by solid-state NMR vary widely in terms of the nature of the samples investigated, the techniques employed to observe the NMR signal, and the types of information obtained. Compared with the NMR of diamagnetic non-semiconducting substances, important differences often result from the presence of electron or hole carriers that are the hallmark of semiconductors, and whose theoretical interpretation can be involved. This review aims to provide a broad perspective on the topic for the non-expert by providing: (1) a basic introduction to semiconductor physical concepts relevant to NMR, including common crystal structures and the various methods of making samples; (2) discussions of the NMR spin Hamiltonian, details of some of the NMR techniques and strategies used to make measurements and theoretically predict NMR parameters, and examples of how each of the terms in the Hamiltonian has provided useful information in bulk semiconductors; (3) a discussion of the additional considerations needed to interpret the NMR of nanoscale semiconductors, with selected examples. The area of semiconductor NMR is being revitalized by this interest in nanoscale semiconductors, the great improvements in NMR detection sensitivity and resolution that have occurred, and the current interest in optical pumping and spintronics-related studies. Promising directions for future research will be noted throughout.
5. Teaching NMR spectra analysis with nmr.cheminfo.org.
Science.gov (United States)
Patiny, Luc; Bolaños, Alejandro; Castillo, Andrés M; Bernal, Andrés; Wist, Julien
2018-06-01
Teaching spectra analysis and structure elucidation requires students to get trained on real problems. This involves solving exercises of increasing complexity and when necessary using computational tools. Although desktop software packages exist for this purpose, nmr.cheminfo.org platform offers students an online alternative. It provides a set of exercises and tools to help solving them. Only a small number of exercises are currently available, but contributors are invited to submit new ones and suggest new types of problems. Copyright © 2018 John Wiley & Sons, Ltd.
CERN Document Server
2014-01-01
Dealing with the basics, theory and applications of dynamic pulsed-field-gradient NMR NMR (PFG NMR), this book describes the essential theory behind diffusion in heterogeneous media that can be combined with NMR measurements to extract important information of the system being investigated. This information could be the surface to volume ratio, droplet size distribution in emulsions, brine profiles, fat content in food stuff, permeability/connectivity in porous materials and medical applications currently being developed. Besides theory and applications it will provide the readers with background knowledge on the experimental set-ups, and most important, deal with the pitfalls that are numerously present in work with PFG-NMR. How to analyze the NMR data and some important basic knowledge on the hardware will be explained, too.
7. An Inversion Recovery NMR Kinetics Experiment
OpenAIRE
Williams, Travis J.; Kershaw, Allan D.; Li, Vincent; Wu, Xinping
2011-01-01
A convenient laboratory experiment is described in which NMR magnetization transfer by inversion recovery is used to measure the kinetics and thermochemistry of amide bond rotation. The experiment utilizes Varian spectrometers with the VNMRJ 2.3 software, but can be easily adapted to any NMR platform. The procedures and sample data sets in this article will enable instructors to use inversion recovery as a laboratory activity in applied NMR classes and provide research students with a conveni...
8. NMR in structure-based drug design.
Science.gov (United States)
Carneiro, Marta G; Ab, Eiso; Theisgen, Stephan; Siegal, Gregg
2017-11-08
NMR spectroscopy is a powerful technique that can provide valuable structural information for drug discovery endeavors. Here, we discuss the strengths (and limitations) of NMR applications to structure-based drug discovery, highlighting the different levels of resolution and throughput obtainable. Additionally, the emerging field of paramagnetic NMR in drug discovery and recent developments in approaches to speed up and automate protein-observed NMR data collection and analysis are discussed. © 2017 The Author(s). Published by Portland Press Limited on behalf of the Biochemical Society.
9. NMR spectroscopy using liquid crystal solvents
CERN Document Server
Emsley, JW
2013-01-01
NMR Spectroscopy using Liquid Crystal Solvents covers the importance of using a liquid crystal solvent in NMR to derive nuclear dipolar spin-spin coupling constants. This book is composed of ten chapters, and begins with a brief description of the features and benefits of liquid crystal in NMR spectroscopic analysis. The succeeding chapters deal with the mode of operation of nuclear spin Hamiltonian for partially oriented molecules and the analysis of NMR spectra of partially oriented molecules, as well as the determination of rigid molecule structure. These topics are followed by discussions
10. Solution NMR structure determination of proteins revisited
International Nuclear Information System (INIS)
Billeter, Martin; Wagner, Gerhard; Wuethrich, Kurt
2008-01-01
This 'Perspective' bears on the present state of protein structure determination by NMR in solution. The focus is on a comparison of the infrastructure available for NMR structure determination when compared to protein crystal structure determination by X-ray diffraction. The main conclusion emerges that the unique potential of NMR to generate high resolution data also on dynamics, interactions and conformational equilibria has contributed to a lack of standard procedures for structure determination which would be readily amenable to improved efficiency by automation. To spark renewed discussion on the topic of NMR structure determination of proteins, procedural steps with high potential for improvement are identified
11. NMR studies of isotopically labeled RNA
Energy Technology Data Exchange (ETDEWEB)
Pardi, A. [Univ. of Colorado, Boulder, CO (United States)
1994-12-01
In summary, the ability to generate NMR quantities of {sup 15}N and {sup 13}C-labeled RNAs has led to the development of heteronuclear multi-dimensional NMR techniques for simplifying the resonance assignment and structure determination of RNAs. These methods for synthesizing isotopically labeled RNAs are only several years old, and thus there are still relatively few applications of heteronuclear multi-dimensional NMR techniques to RNA. However, given the critical role that RNAs play in cellular function, one can expect to see an increasing number of NMR structural studies of biologically active RNAs.
12. Ligand-receptor Interactions by NMR Spectroscopy
Directory of Open Access Journals (Sweden)
Novak. P.
2008-04-01
Full Text Available Today NMR spectroscopy is a method of choice for elucidation of interactions between biomolecules and the potential ligands. Knowledge on these interactions is an essential prerequisite for the rational drug design. The most important contribution of NMR to drug design a few years ago was the 3D structure determination of proteins. Besides delivering the 3D structures of the free proteins as a raw material for the modeling studies on ligand binding, NMR can directly yield valuable experimental data on the biologically important protein-ligand complexes. In addition to X-ray diffraction, NMR spectroscopy can provide information on the internal protein dynamics ordynamics of intermolecular interactions. Changes in NMR parameters allow us to detect ("SAR by NMR" and quantitatively determine binding affinities (titration, diffusion NMR experiments, etc. of potential ligands. Also, it is possible to determine the binding site and conformations of ligands, receptors and receptor-ligand complexes with the help of NMR methods such as tr-NOESY. Epitopes or functional groups responsible for binding of ligands to the receptor can be identified by employing STD or WaterLOGSY experiments. In this review are described some of the most frequent NMR methods for the characterization of the interactions between biomolecules and ligands, together with their advantages and disadvantages.
13. NMR characterization of pituitary tumors
International Nuclear Information System (INIS)
Osbakken, M.; Gonzales, J.; Page, R.
1984-01-01
Twelve patients (5 male, 7 female, mean age 37.9 +- 20) with pituitary tumors were extensively evaluated with NMR imaging using a 1.5K gauss resistive magnet. Saturation recovery (SR), inversion recovery (IR) and spin echo (SE) pulse sequences were used for qualitative characterization of the lesions. T/sub 1/ calculations were also performed for brain and pituitary. Tumor histology and endocrine status were correlated with NMR data. All tumors were large with suprasellar extension (6 with prolactin secretion, 6 without). Pituitary T/sub 1/'s ranged from .2 to .64, the mean T/sub 1/ being longer than that of brain (Brain = .4 +- .04; Pit = .48 +- .14). 3 patients with histological evidence of homogeneous adenomas had long T/sub 1/'s (0.58 +- .05). 3 patients with evidence of recent or old hemorhage into the pituitary had much shorter T/sub 1/'s (0.29 +- .12). There was no relationship between prolactin secretion and T/sub 1/. Qualitative T/sub 1/ and T/sub 2/ information can be obtained by using a combination of SR, IR, and SE images. Using this method in the patients, homogeneous adenomas had similar T/sub 1/'s and longer T/sub 2/'s compared to the brain, while patients with bleeds had shorter T/sub 1/'s and T/sub 2/'s. Image T/sub 1/ characteristics correlated well with the calculated T/sub 1/ values. The range of T/sub 1/ (and potentially T/sub 2/) values which occur in apparently similar lesions are most likely due to anatomical and pathophysiological variations in these lesions. It may be ultimately possible to separate different types of pathological processes based on NMR image T/sub 1/ and T/sub 2/ characteristics after careful comparative studies of NMR and histological data are completed. The combination of calculated T/sub 1/ and T/sub 2/ with image T/sub 1/ and T/sub 2/ information may also be useful in further characterization of lesions
14. Short recovery time NMR probe
International Nuclear Information System (INIS)
Ramia, M.E.; Martin, C.A.; Jeandrevin, S.
2011-01-01
A NMR probe for low frequency and short recovery time is presented in this work. The probe contains the tuning circuit, diode expanders and quarter wavelength networks to protect the receiver from both the amplifier noise and the coil ringing following the transmitter power pulse. It also possesses a coil damper which is activated by of non active components. The probe performance shows a recovery time of about of 15μs a sensitive Q factor reduction and an increase of the signal to noise ratio of about 68% during the reception at a work frequency of 2 MHz. (author)
15. Performance of the WeNMR CS-Rosetta3 web server in CASD-NMR
NARCIS (Netherlands)
Van Der Schot, Gijs; Bonvin, Alexandre M J J
We present here the performance of the WeNMR CS-Rosetta3 web server in CASD-NMR, the critical assessment of automated structure determination by NMR. The CS-Rosetta server uses only chemical shifts for structure prediction, in combination, when available, with a post-scoring procedure based on
16. 1H-NMR urinalysis
International Nuclear Information System (INIS)
Yamamoto, Hideaki; Yamaguchi, Shuichi
1988-01-01
In an effort to examine the usefulness of 1 H-nuclear magnetic resonance (NMR) urinalysis in the diagnosis of congenital metabolic disorders, 70 kinds of urinary metabolites were analysed in relation to the diagnosis of inborn errors of amino acid and organic acid disorders. Homogated decoupling (HMG) method failed to analyze six metabolites within the undetectable range. When non-decoupling method (NON), in which the materials are dissolved in dimethyl sulfoxide, was used, the identification of signals became possible. The combination of HMG and NON methods was, therefore, considered to identify all of the metabolites. When the urine samples, which were obtained from patients with hyperglycerolemia, hyperornithinemia, glutaric acidemia type II, or glycerol kinase deficiency, were analysed by using both HMG and NON methods, abnormally increased urinary metabolites were detected. 1 H-NMR urinalysis, if used in the combination of HMG and NON methods, may allow simultanenous screening of inborn errors of metabolism of amino acid and organic acid disorders. (Namekawa, K.)
17. Early history of NMR at Los Alamos
International Nuclear Information System (INIS)
Jackson, J.A.
1985-11-01
Nuclear magnetic resonance (NMR) spectroscopy has developed into an important research tool in chemistry. More recently, NMR imaging and in vivo spectroscopy promise to produce a revolution in medicine and biochemistry. Early experiments at Los Alamos led to DOE programs involving stable isotopes of importance to biology and to medicine. These events are briefly recounted. 2 refs
18. Characterization of natural bentonite by NMR
International Nuclear Information System (INIS)
Leite, Sidnei Q.M.; Dieguez, Lidia C.; Menezes, Sonia M.C.; San Gil, Rosane A.S.
1993-01-01
Solid state NMR as well as several other instrumental chemical analysis techniques were used in order to characterize two natural occurring bentonite. The methodology is described. The NMR spectra, together with the other used techniques suggest that the observed differences are due to iron inclusions in tetrahedral and octahedral sites
19. Using Cloud Storage for NMR Data Distribution
Science.gov (United States)
Soulsby, David
2012-01-01
An approach using Google Groups as method for distributing student-acquired NMR data has been implemented. We describe how to configure NMR spectrometer software so that data is uploaded to a laboratory section specific Google Group, thereby removing bottlenecks associated with printing and processing at the spectrometer workstation. Outside of…
20. Quartz Crystal Temperature Sensor for MAS NMR
Science.gov (United States)
Simon, Gerald
1997-10-01
Quartz crystal temperature sensors (QCTS) were tested for the first time as wireless thermometers in NMR MAS rotors utilizing the NMR RF technique itself for exiting and receiving electro-mechanical quartz resonances. This new tool in MAS NMR has a high sensitivity, linearity, and precision. When compared to the frequently used calibration of the variable temperature in the NMR system by a solid state NMR chemical shift thermometer (CST), such as lead nitrate, QCTS shows a number of advantages. It is an inert thermometer in close contact with solid samples operating parallel to the NMR experiment. QCTS can be manufactured for any frequency to be near a NMR frequency of interest (typically 1 to 2 MHz below or above). Due to the strong response of the crystal, signal detection is possible without changing the tuning of the MAS probe. The NMR signal is not influenced due to the relative sharp crystal resonance, restricted excitation by finite pulses, high probeQvalues, and commonly used audio filters. The quadratic dependence of the temperature increase on spinning speed is the same for the QCTS and for the CST lead nitrate and is discussed in terms of frictional heat in accordance with the literature about lead nitrate and with the results of a simple rotor speed jump experiment with differently radial located lead nitrate in the rotor.
1. NMR studies of the structure of glasses
International Nuclear Information System (INIS)
Bray, P.J.; Gravina, S.J.; Stallworth, P.E.; Szu, S.P.; Jianhui Zhong
1988-01-01
Earlier continuous wave (CW) NMR studies of chemical bonding and structure in glasses are summarized. Examples are given of this use of the quadrupolar interaction and chemical shift to obtain structural information. New NMR data and analyses are presented for alkali borate and gallate glasses. Extensions to other elements (e.g. molybdenum, lanthanum) are suggested. 44 refs. (author)
2. An Inversion Recovery NMR Kinetics Experiment
Science.gov (United States)
Williams, Travis J.; Kershaw, Allan D.; Li, Vincent; Wu, Xinping
2011-01-01
A convenient laboratory experiment is described in which NMR magnetization transfer by inversion recovery is used to measure the kinetics and thermochemistry of amide bond rotation. The experiment utilizes Varian spectrometers with the VNMRJ 2.3 software, but can be easily adapted to any NMR platform. The procedures and sample data sets in this…
3. Selective sensitivity enhancement in FT-NMR
International Nuclear Information System (INIS)
Farrar, T.C.
1987-01-01
In this article the basic two-spin nuclear magnetic resonance (NMR) experiment and the new sensitivity enhancement experiments are reviewed. In part two of this two-part series an overview of two-dimensional NMR experiments will be presented. Part two will appear in the June 1 issue of Analytical Chemistry
4. 2D NMR studies of biomolecules
International Nuclear Information System (INIS)
Lamerichs, R.M.J.N.
1989-01-01
The work described in this thesis comprises two related subjects. The first part describes methods to derive high-resolution structures of proteins in solution using two-dimensional (2-D) NMR. The second part describes 2-D NMR studies on the interaction between proteins and DNA. (author). 261 refs.; 52 figs.; 23 tabs
5. Synthesis and NMR Elucidation of Novel Pentacycloundecane ...
African Journals Online (AJOL)
Herein we report the synthesis and NMR elucidation of five novel pentacycloundecane (PCU)-derived short peptides as potential HIV protease inhibitors. 1H and 13C spectral analysis show major overlapping of methine resonance of the PCU 'cage' thereby making it extremely difficult to assign the NMR signals. Attachment ...
6. Development and applications of quantitative NMR spectroscopy
International Nuclear Information System (INIS)
Yamazaki, Taichi
2016-01-01
Recently, quantitative NMR spectroscopy has attracted attention as an analytical method which can easily secure traceability to SI unit system, and discussions about its accuracy and inaccuracy are also started. This paper focuses on the literatures on the advancement of quantitative NMR spectroscopy reported between 2009 and 2016, and introduces both NMR measurement conditions and actual analysis cases in quantitative NMR. The quantitative NMR spectroscopy using an internal reference method enables accurate quantitative analysis with a quick and versatile way in general, and it is possible to obtain the precision sufficiently applicable to the evaluation of pure substances and standard solutions. Since the external reference method can easily prevent contamination to samples and the collection of samples, there are many reported cases related to the quantitative analysis of biologically related samples and highly scarce natural products in which NMR spectra are complicated. In the precision of quantitative NMR spectroscopy, the internal reference method is superior. As the quantitative NMR spectroscopy widely spreads, discussions are also progressing on how to utilize this analytical method as the official methods in various countries around the world. In Japan, this method is listed in the Pharmacopoeia and Japanese Standard of Food Additives, and it is also used as the official method for purity evaluation. In the future, this method will be expected to spread as the general-purpose analysis method that can ensure traceability to SI unit system. (A.O.)
7. NMR imaging of soft tissue tumors
International Nuclear Information System (INIS)
Laval-Jeantet, M.; Tobolsk, F.; Delepine, N.; Delepine, G.; Roger, B.; Cabanis, E.A.
1986-01-01
Preliminary findings on NMR imaging of 30 soft tissue tumors demonstrated the indispensable value of this examination (particularly when a surface antenna is used) for preoperative investigation and diagnosis of tumoral recurrence when compared with other radiologic techniques. The possible potential of NMR imaging for characterization of tissues, apart from lipoma or liposarcoma, cannot be evaluated at the present time [fr
8. Carbon-13 NMR spectroscopy of biological systems
CERN Document Server
Beckmann, Nicolau
1995-01-01
This book is intended to provide an in-depth understanding of 13C NMR as a tool in biological research. 13C NMR has provided unique information concerning complex biological systems, from proteins and nucleic acids to animals and humans. The subjects addressed include multidimensional heteronuclear techniques for structural studies of molecules in the liquid and solid states, the investigation of interactions in model membranes, the elucidation of metabolic pathwaysin vitro and in vivo on animals, and noninvasive metabolic studies performed on humans. The book is a unique mix of NMR methods and biological applications which makes it a convenient reference for those interested in research in this interdisciplinary area of physics, chemistry, biology, and medicine.Key Features* An interdisciplinary text with emphasis on both 13C NMR methodology and the relevant biological and biomedical issues* State-of-the-art 13C NMR techniques are described; Whenever possible, their advantages over other approaches are empha...
9. Hepatic lipid profiling of deer mice fed ethanol using 1H and 31P NMR spectroscopy: A dose-dependent subchronic study
International Nuclear Information System (INIS)
Fernando, Harshica; Bhopale, Kamlesh K.; Boor, Paul J.; Ansari, G.A. Shakeel; Kaphalia, Bhupendra S.
2012-01-01
10. An introduction to biological NMR spectroscopy
International Nuclear Information System (INIS)
Marion, Dominique
2013-01-01
NMR spectroscopy is a powerful tool for biologists interested in the structure, dynamics, and interactions of biological macromolecules. This review aims at presenting in an accessible manner the requirements and limitations of this technique. As an introduction, the history of NMR will highlight how the method evolved from physics to chemistry and finally to biology over several decades. We then introduce the NMR spectral parameters used in structural biology, namely the chemical shift, the J-coupling, nuclear Overhauser effects, and residual dipolar couplings. Resonance assignment, the required step for any further NMR study, bears a resemblance to jigsaw puzzle strategy. The NMR spectral parameters are then converted into angle and distances and used as input using restrained molecular dynamics to compute a bundle of structures. When interpreting a NMR-derived structure, the biologist has to judge its quality on the basis of the statistics provided. When the 3D structure is a priori known by other means, the molecular interaction with a partner can be mapped by NMR: information on the binding interface as well as on kinetic and thermodynamic constants can be gathered. NMR is suitable to monitor, over a wide range of frequencies, protein fluctuations that play a crucial role in their biological function. In the last section of this review, intrinsically disordered proteins, which have escaped the attention of classical structural biology, are discussed in the perspective of NMR, one of the rare available techniques able to describe structural ensembles. This Tutorial is part of the International Proteomics Tutorial Programme (IPTP 16 MCP). (authors)
11. NMR imaging of the brain: initial impressions
International Nuclear Information System (INIS)
Spencer, D.H.; Bydder, G.M.
1983-01-01
An NMR imaging system designed and built by Thorn-EMI Ltd was installed at Hammersmith Hospital in March 1981. In the first year of operation 180 patients and 40 volunteers have had cranial examinations and initial impressions bases on this experience are presented. Patients with a wide variety of neurological diseases have been studied to provide a basis for diagnostic interpretation, to define distinctive features, and to evaluate different types of scanning sequences. NMR imaging appears to be of considerable value in neurological diagnosis and has a number of advantages over CT. The detailed evaluation of NMR imaging will require much more work but the initial results are very promising
12. Oriented solid-state NMR spectrosocpy
DEFF Research Database (Denmark)
Bertelsen, Kresten
This thesis is concerned with driving forward oriented solid-state NMR spectroscopy as a viable technique for studying peptides in membrane bilayers. I will show that structural heterogeneity is an intrinsic part of the peptide/lipid system and that NMR can be used to characterize static...... and dynamic structural features of the peptides and its local surroundings. In fact one need to take into account the dynamical features of the system in order to correctly predict the structure from oriented solid-state NMR spectra. ...
13. NMR reaction monitoring in flow synthesis
Directory of Open Access Journals (Sweden)
M. Victoria Gomez
2017-02-01
Full Text Available Recent advances in the use of flow chemistry with in-line and on-line analysis by NMR are presented. The use of macro- and microreactors, coupled with standard and custom made NMR probes involving microcoils, incorporated into high resolution and benchtop NMR instruments is reviewed. Some recent selected applications have been collected, including synthetic applications, the determination of the kinetic and thermodynamic parameters and reaction optimization, even in single experiments and on the μL scale. Finally, software that allows automatic reaction monitoring and optimization is discussed.
14. NMR reaction monitoring in flow synthesis.
Science.gov (United States)
Gomez, M Victoria; de la Hoz, Antonio
2017-01-01
Recent advances in the use of flow chemistry with in-line and on-line analysis by NMR are presented. The use of macro- and microreactors, coupled with standard and custom made NMR probes involving microcoils, incorporated into high resolution and benchtop NMR instruments is reviewed. Some recent selected applications have been collected, including synthetic applications, the determination of the kinetic and thermodynamic parameters and reaction optimization, even in single experiments and on the μL scale. Finally, software that allows automatic reaction monitoring and optimization is discussed.
15. Introduction to some basic aspects of NMR
International Nuclear Information System (INIS)
Goldman, M.
1992-01-01
The principal interactions are reviewed that are experienced by nuclear spins making magnetic resonance feasible and which disturb it in a way that gives access to the properties of bulk matter. The interactions leading to NMR include Zeeman interaction, dipole-dipole interactions, and exchange interactions. Spin-lattice relaxation relevant to NMR is revisited next. It is followed by an overview of spin temperature. Finally, the care of periodic Hamiltonian is discussed in detail as another contribution to NMR. (R.P.) 48 refs., 12 figs
16. NMR study of LaPb2
International Nuclear Information System (INIS)
Ueda, K.; Kohara, T.; Yamada, Y.
1995-01-01
La and Pb NMR signals were observed in LaPb 2 with a superconducting transition temperature of about 7 K. The width of the Pb NMR spectrum with an asymmetric line shape was rather narrower than those of Er-, Gd- and Ho-Pb 2 . The spin-lattice relaxation time of Pb nuclei was twice longer than that of Pb metal. La NMR spectrum had satellites due to the electric quadrupole interaction. These results show that each local environment at La or Pb site in LaPb 2 compound is uniquely determined, compared with those in randomly substituted alloys. ((orig.))
17. Graphical programming for pulse automated NMR experiments
International Nuclear Information System (INIS)
Belmonte, S.B.; Oliveira, I.S.; Guimaraes, A.P.
1999-01-01
We describe a software program designed to control a broadband pulse Nuclear Magnetic Resonance (NMR) spectrometer used in zero-field NMR studies of magnetic metals. The software is written in the graphical language LabVIEW. This type of programming allows modifications and the inclusion of new routines to be easily made by the non-specialist, without changing the basic structure of the program. The program corrects for differences in the gain of the two acquisition channels [U (phase) and V (quadrature)], and automatic baseline subtraction. We present examples of measurements of NMR spectra, spin-echo decay (T 2 ), and quadrupolar oscillations, performed in magnetic intermetallic compounds. (author)
18. The characterisation of polymers using pulsed NMR
International Nuclear Information System (INIS)
Charlesby, A.
1983-01-01
Broad line pulsed NMR is applied to obtain information on radiation-induced polymer changes and other aspects of polymer science based on the interpretation of spin-spin relaxation curves. Calculations are made to determine the molecular weight, the crosslink density of simple, low molecular weight, flexible polymers. For higher molecular weight polymers, a conclusion can be drawn on the concentrations of entangled and crosslinked units by means of pulsed NMR. Some typical applications of the technique are illustrated by the examples of polyethylenes, rubbers, filled polymeric systems and aqueous polyethylene oxide solutions. The morphology of polymers can be followed by pulsed NMR. (V.N.)
19. MAS NMR of HIV-1 protein assemblies
Science.gov (United States)
Suiter, Christopher L.; Quinn, Caitlin M.; Lu, Manman; Hou, Guangjin; Zhang, Huilan; Polenova, Tatyana
2015-04-01
The negative global impact of the AIDS pandemic is well known. In this perspective article, the utility of magic angle spinning (MAS) NMR spectroscopy to answer pressing questions related to the structure and dynamics of HIV-1 protein assemblies is examined. In recent years, MAS NMR has undergone major technological developments enabling studies of large viral assemblies. We discuss some of these evolving methods and technologies and provide a perspective on the current state of MAS NMR as applied to the investigations into structure and dynamics of HIV-1 assemblies of CA capsid protein and of Gag maturation intermediates.
20. NMR data-driven structure determination using NMR-I-TASSER in the CASD-NMR experiment
Energy Technology Data Exchange (ETDEWEB)
Jang, Richard [Huazhong University of Science and Technology, School of Software Engineering (China); Wang, Yan [Huazhong University of Science and Technology, School of Life Science and Technology (China); Xue, Zhidong, E-mail: [email protected] [Huazhong University of Science and Technology, School of Software Engineering (China); Zhang, Yang, E-mail: [email protected] [University of Michigan, Department of Computational Medicine and Bioinformatics (United States)
2015-08-15
NMR-I-TASSER, an adaption of the I-TASSER algorithm combining NMR data for protein structure determination, recently joined the second round of the CASD-NMR experiment. Unlike many molecular dynamics-based methods, NMR-I-TASSER takes a molecular replacement-like approach to the problem by first threading the target through the PDB to identify structural templates which are then used for iterative NOE assignments and fragment structure assembly refinements. The employment of multiple templates allows NMR-I-TASSER to sample different topologies while convergence to a single structure is not required. Retroactive and blind tests of the CASD-NMR targets from Rounds 1 and 2 demonstrate that even without using NOE peak lists I-TASSER can generate correct structure topology with 15 of 20 targets having a TM-score above 0.5. With the addition of NOE-based distance restraints, NMR-I-TASSER significantly improved the I-TASSER models with all models having the TM-score above 0.5. The average RMSD was reduced from 5.29 to 2.14 Å in Round 1 and 3.18 to 1.71 Å in Round 2. There is no obvious difference in the modeling results with using raw and refined peak lists, indicating robustness of the pipeline to the NOE assignment errors. Overall, despite the low-resolution modeling the current NMR-I-TASSER pipeline provides a coarse-grained structure folding approach complementary to traditional molecular dynamics simulations, which can produce fast near-native frameworks for atomic-level structural refinement.
1. NMR mechanisms in gel dosimetry
International Nuclear Information System (INIS)
Schreiner, L J
2009-01-01
Nuclear magnetic resonance was critical to the development of gel dosimetry, as it established the potential for three dimensional dosimetry with chemical dosimeter systems through magnetic resonance imaging [1]. In the last two decades MRI has served as the gold standard for imaging, while NMR relaxometry has played an important role in the development and understanding of the behaviour of new gel dosimetry systems. Therefore, an appreciation of the relaxation mechanisms determining the NMR behaviour of irradiated gel dosimeters is important for a full comprehension of a considerable component of the literature on gel dosimetry. A number of excellent papers have presented this important theory, this brief review will highlight some of the salient points made previously [1-5]. The spin relaxation of gel dosimeters (which determines the dose dependence in most conventional MR imaging) is determined principally by the protons on water molecules in the system. These water protons exist in different environments, or groups (see Figure 1): on bulk water, on water hydrating the chemical species that are being modified under irradiation, and on water hydrating the gel matrix used to spatially stabilize the dosimeter (e.g., gelatin, agarose, etc). The spin relaxation depends on the inherent relaxation rate of each spin group, that is, on the relaxation rate which would be observed for the specific group if it were isolated. Also, the different water environments are not isolated from each other, and the observed relaxation rate also depends on the rate of exchange of magnetization between the groups, and on the fraction of protons in each group. In fact, the water exchanges quickly between the environments, so that relaxation is in what is usually termed the fast exchange regime. In the limit of fast exchange, the relaxation of the water protons is well characterized by a single exponential and hence by a single apparent relaxation rate. In irradiated gel dosimeters this
2. Structural investigations of substituted indolizine derivatives by NMR studies
International Nuclear Information System (INIS)
Furdui, Bianca; Dinica, Rodica; Demeunynck, Martine; Druta, Ioan
2008-01-01
Owing to the increasing importance of indolizine heterocycles in the field of biology and pharmacology we have synthesized and investigated the obtained heterocycles by NMR techniques. In order to investigate the substituent effects on the spectroscopic properties, a series of indolizine derivatives were studied by 1 H-NMR, 13 C-NMR and 2D NMR (GCOSY, GHMBC and GHMQC spectra). (authors)
3. NMR in the SPINE Structural Proteomics project.
Science.gov (United States)
Ab, E; Atkinson, A R; Banci, L; Bertini, I; Ciofi-Baffoni, S; Brunner, K; Diercks, T; Dötsch, V; Engelke, F; Folkers, G E; Griesinger, C; Gronwald, W; Günther, U; Habeck, M; de Jong, R N; Kalbitzer, H R; Kieffer, B; Leeflang, B R; Loss, S; Luchinat, C; Marquardsen, T; Moskau, D; Neidig, K P; Nilges, M; Piccioli, M; Pierattelli, R; Rieping, W; Schippmann, T; Schwalbe, H; Travé, G; Trenner, J; Wöhnert, J; Zweckstetter, M; Kaptein, R
2006-10-01
This paper describes the developments, role and contributions of the NMR spectroscopy groups in the Structural Proteomics In Europe (SPINE) consortium. Focusing on the development of high-throughput (HTP) pipelines for NMR structure determinations of proteins, all aspects from sample preparation, data acquisition, data processing, data analysis to structure determination have been improved with respect to sensitivity, automation, speed, robustness and validation. Specific highlights are protonless (13)C-direct detection methods and inferential structure determinations (ISD). In addition to technological improvements, these methods have been applied to deliver over 60 NMR structures of proteins, among which are five that failed to crystallize. The inclusion of NMR spectroscopy in structural proteomics pipelines improves the success rate for protein structure determinations.
4. NMR study of Albemoschus esculentus characterization
International Nuclear Information System (INIS)
Bathista, A.L.B.S; Silva, E.O.; Nogueira, Jose de S.; Tavares, M.I.B.
2001-01-01
The investigation of the main compounds presented in the Albemoschus esculentus has been carried out employing nuclear magnetic resonance spectroscopy (NMR), using solution and solid state NMR when it one was necessary. The evaluation of NMR data allowed us to characterize the main type of components presented in this kind of sample. It was necessary to use a total information from solid state NMR and also the solution response. From these information we could get that four main components were presented in this sample. One in the shell, that is cellulose, another one between the shell and seeds that is a polysaccharide and in the seed two components were found one is a starch and the second one is an oil, a triacylglycerol. These components are responsible by its physical chemistry properties. (author)
5. Bayesian Peak Picking for NMR Spectra
KAUST Repository
Cheng, Yichen
2014-02-01
Protein structure determination is a very important topic in structural genomics, which helps people to understand varieties of biological functions such as protein-protein interactions, protein–DNA interactions and so on. Nowadays, nuclear magnetic resonance (NMR) has often been used to determine the three-dimensional structures of protein in vivo. This study aims to automate the peak picking step, the most important and tricky step in NMR structure determination. We propose to model the NMR spectrum by a mixture of bivariate Gaussian densities and use the stochastic approximation Monte Carlo algorithm as the computational tool to solve the problem. Under the Bayesian framework, the peak picking problem is casted as a variable selection problem. The proposed method can automatically distinguish true peaks from false ones without preprocessing the data. To the best of our knowledge, this is the first effort in the literature that tackles the peak picking problem for NMR spectrum data using Bayesian method.
6. NMR and optical studies of piezoelectric polymers
International Nuclear Information System (INIS)
Schmidt, V.H.; Tuthill, G.F.
1993-01-01
Progress is reported in several areas dealing with piezoelectric (electroactive) polymers (mostly vinylidene fluoride, trifluoroethylene, copolymers, PVF 2 ) and liquid crystals. Optical studies, neutron scattering, NMR, thermal, theory and modeling were done
7. High resolution NMR theory and chemical applications
CERN Document Server
Becker, Edwin D
2012-01-01
High Resolution NMR: Theory and Chemical Applications discusses the principles and theory of nuclear magnetic resonance and how this concept is used in the chemical sciences. This book is written at an intermediate level, with mathematics used to augment verbal descriptions of the phenomena. This text pays attention to developing and interrelating four approaches - the steady state energy levels, the rotating vector picture, the density matrix, and the product operator formalism. The style of this book is based on the assumption that the reader has an acquaintance with the general principles of quantum mechanics, but no extensive background in quantum theory or proficiency in mathematics is required. This book begins with a description of the basic physics, together with a brief account of the historical development of the field. It looks at the study of NMR in liquids, including high resolution NMR in the solid state and the principles of NMR imaging and localized spectroscopy. This book is intended to assis...
8. NMR studies of cerebral metabolism in vivo
International Nuclear Information System (INIS)
Prichard, J.W.
1986-01-01
The nature and extent of the potential synergism between PET and NMR methods is not yet well appreciated in the biomedical community. The long-range interest of medical neurobiology will be well served by efforts of PET and NMR scientists to follow each others' work so that opportunities for productive interchange can be efficiently exploited. Appreciation of the synergism by the rest of the biomedical community will follow naturally. PET is said by the people doing it to be still in its infancy, for they are more concerned with advancing their discipline than with admiring its already impressive achievements. On the scale of the same developmental metaphor, many NMR methods for studying the living human brain are still in utero. The best way to provide the reader a sense of the current status and future course of NMR research in medical neurobiology is by discussion of published in vivo studies. Such a discussion, adapted from another article is what follows
9. Development of Two-Dimensional NMR
Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 11. Development of Two-Dimensional NMR: Strucure Determination of Biomolecules in Solution. Anil Kumar. General Article Volume 20 Issue 11 November 2015 pp 995-1002 ...
10. NMR spectroscopy of coal pyrolysis products
Energy Technology Data Exchange (ETDEWEB)
Polonov, V.M.; Kalabin, G.A.; Kushnarev, D.F.; Shevchenko, G.G.
1985-12-01
The authors consider the scope for using H 1 and C 13 NMR spectroscopy to describe the products from coal pyrolysis and hydrogenization. The accuracy of the structural information provided by the best NMR methods is also considered. The stuctural parameters derived from H 1 and C 13 NMR spectra are presented. Results demonstrate the high accuracy and sensitivity of the structural information provided by H 1 AND C 13 NMR spectra for coal products. There are substantial structural differences between the soluble products from medium-temperature coking of Cheremkhov coal and high-speed pyrolysis of Kan-Acha coal, and also differences in behavior during hydrogenation. These differences are related to the structure of the organic matter in the initial coal and to differences in the pyrolysis mechanisms.
11. NMR study of hydride systems
International Nuclear Information System (INIS)
Peretz, M.
1980-02-01
The hydrides of thorium (ThH 2 , Th 4 H 15 and Th 4 D 15 ) and the intermetallic compound system (Zr(Vsub(1-x)Cosub(x)) 2 and its hydrides were investigated using the nuclear magnetic resonance (NMR) technique. From the results for the thorium hydride samples it was concluded that the density of states at the Fermi level n(Esub(f)) is higher in Th 4 H 15 than in ThH 2 ; there is an indirect reaction between the protons and the d electrons belonging to the Th atoms in Th 4 H 15 ; n(E) has a sharp structure near Esub(f). It was also found that the hydrogen diffusion mechanism changes with temperature. From the results for the intermetallic compound system conclusions were drawn concerning variations in the electronic structure, which explain the behavior of the system. In hydrogen diffusion studies in several samples it was found that Co atoms slow the diffusion rate. Quadrupole spectra obtained at low temperatures show that the H atoms preferably occupy tetrahedral sites formed by three V atoms and one Z atom. (H.K.)
12. Frontiers of NMR in Molecular Biology
Energy Technology Data Exchange (ETDEWEB)
NONE
1999-08-25
NMR spectroscopy is expanding the horizons of structural biology by determining the structures and describing the dynamics of blobular proteins in aqueous solution, as well as other classes of proteins including membrane proteins and the polypeptides that form the aggregates diagnostic of prion and amyloid diseases. Significant results are also emerging on DNA and RNA oligomers and their complexes with proteins. This meeting focused attention on key structural questions emanating from molecular biology and how NMR spectroscopy can be used to answer them.
13. NMR studies of multiphase flows II
Energy Technology Data Exchange (ETDEWEB)
Altobelli, S.A.; Caprihan, A.; Fukushima, E. [Lovelace Institutes, Albuquerque, NM (United States)] [and others
1995-12-31
NMR techniques for measurements of spatial distribution of material phase, velocity and velocity fluctuation are being developed and refined. Versions of these techniques which provide time average liquid fraction and fluid phase velocity have been applied to several concentrated suspension systems which will not be discussed extensively here. Technical developments required to further extend the use of NMR to the multi-phase flow arena and to provide measurements of previously unobtainable parameters are the focus of this report.
14. observed by high pressure NMR and NQR
Akogun, Hyogo 678-1297, Japan. ∗. Email: [email protected] tech.ac.jp. Abstract. NMR and NQR studies on two interesting systems (URu2Si2, CeTIn5) were performed under high pressure. (1) URu2Si2: In the pressure range 3.0 to 8.3 kbar, we have observed new 29Si. NMR signals arising from the antiferromagnetic ...
15. NMRbox: A Resource for Biomolecular NMR Computation.
Science.gov (United States)
Maciejewski, Mark W; Schuyler, Adam D; Gryk, Michael R; Moraru, Ion I; Romero, Pedro R; Ulrich, Eldon L; Eghbalnia, Hamid R; Livny, Miron; Delaglio, Frank; Hoch, Jeffrey C
2017-04-25
16. A microscale protein NMR sample screening pipeline
Energy Technology Data Exchange (ETDEWEB)
Rossi, Paolo; Swapna, G. V. T.; Huang, Yuanpeng J.; Aramini, James M. [State University of New Jersey, Center for Advanced Biotechnology and Medicine, Department of Molecular Biology and Biochemistry, Rutgers (United States); Anklin, Clemens [Bruker Biospin Corporation (United States); Conover, Kenith; Hamilton, Keith; Xiao, Rong; Acton, Thomas B.; Ertekin, Asli; Everett, John K.; Montelione, Gaetano T., E-mail: [email protected] [State University of New Jersey, Center for Advanced Biotechnology and Medicine, Department of Molecular Biology and Biochemistry, Rutgers (United States)
2010-01-15
As part of efforts to develop improved methods for NMR protein sample preparation and structure determination, the Northeast Structural Genomics Consortium (NESG) has implemented an NMR screening pipeline for protein target selection, construct optimization, and buffer optimization, incorporating efficient microscale NMR screening of proteins using a micro-cryoprobe. The process is feasible because the newest generation probe requires only small amounts of protein, typically 30-200 {mu}g in 8-35 {mu}l volume. Extensive automation has been made possible by the combination of database tools, mechanization of key process steps, and the use of a micro-cryoprobe that gives excellent data while requiring little optimization and manual setup. In this perspective, we describe the overall process used by the NESG for screening NMR samples as part of a sample optimization process, assessing optimal construct design and solution conditions, as well as for determining protein rotational correlation times in order to assess protein oligomerization states. Database infrastructure has been developed to allow for flexible implementation of new screening protocols and harvesting of the resulting output. The NESG micro NMR screening pipeline has also been used for detergent screening of membrane proteins. Descriptions of the individual steps in the NESG NMR sample design, production, and screening pipeline are presented in the format of a standard operating procedure.
17. O-17 NMR measurement of water
International Nuclear Information System (INIS)
1990-01-01
Recently, attention has been paid to the various treatment of water and the utilization of water by magnetic treatment, electric field treatment and so on. It has been said that by these treatments, the change in the properties of water arises. The state of this treated water cannot be explained by the properties of water from conventional physical and chemical standpoints. In addition, the method of measurement of whether the change arose or not is not yet determined. It is necessary to establish the method of measurement for the basic state of water. In this study, O-17 NMR which observes the state of water directly at molecular or atomic level was investigated as the method of measuring water. The measurement of O-17 NMR was carried out with a JNR 90Q FT NMR of Fourier transformation type of JEOL Ltd. The experimental method and the results are reported. The result of measurement of the O-17 NMR spectrum for distilled ion exchange water is shown. It is know that it has very wide line width as compared with the NMR spectra of protons and C-13. The relative sensitivity of O-17 observation is about 1/100,000 of that of protons. As to the information on the state of water obtained by O-17 NMR, there are chemical shift and line width. As temperature rose, the line width showed decrease, which seemed to be related to the decrease of hydrogen combination. (K.I.)
18. Basics of spectroscopic instruments. Hardware of NMR spectrometer
International Nuclear Information System (INIS)
Sato, Hajime
2009-01-01
NMR is a powerful tool for structure analysis of small molecules, natural products, biological macromolecules, synthesized polymers, samples from material science and so on. Magnetic Resonance Imaging (MRI) is applicable to plants and animals Because most of NMR experiments can be done by an automation mode, one can forget hardware of NMR spectrometers. It would be good to understand features and performance of NMR spectrometers. Here I present hardware of a modern NMR spectrometer which is fully equipped with digital technology. (author)
19. 33S NMR cryogenic probe for taurine detection
Science.gov (United States)
Hobo, Fumio; Takahashi, Masato; Maeda, Hideaki
2009-03-01
With the goal of a S33 nuclear magnetic resonance (NMR) probe applicable to in vivo NMR on taurine-biological samples, we have developed the S33 NMR cryogenic probe, which is applicable to taurine solutions. The NMR sensitivity gain relative to a conventional broadband probe is as large as 3.5. This work suggests that improvements in the preamplifier could allow NMR measurements on 100 μM taurine solutions, which is the level of sensitivity necessary for biological samples.
20. Petrophysical properties of greensand as predicted from NMR measurements
DEFF Research Database (Denmark)
Hossain, Zakir; Grattoni, Carlos A.; Solymar, Mikael
2011-01-01
ABSTRACT: Nuclear magnetic resonance (NMR) is a useful tool in reservoir evaluation. The objective of this study is to predict petrophysical properties from NMR T2 distributions. A series of laboratory experiments including core analysis, capillary pressure measurements, NMR T2 measurements...... with macro-pores. Permeability may be predicted from NMR by using Kozeny's equation when surface relaxivity is known. Capillary pressure drainage curves may be predicted from NMR T2 distribution when pore size distribution within a sample is homogeneous....
1. Continuous Flow 1H and 13C NMR Spectroscopy in Microfluidic Stripline NMR Chips
NARCIS (Netherlands)
Oosthoek-de Vries, Anna Jo; Bart, Jacob; Tiggelaar, Roald M.; Janssen, Johannes W.G.; van Bentum, Jan (P.J.M.); Gardeniers, Han J.G.E.; Kentgens, Arno P.M.
2017-01-01
Microfluidic stripline NMR technology not only allows for NMR experiments to be performed on small sample volumes in the submicroliter range, but also experiments can easily be performed in continuous flow because of the stripline's favorable geometry. In this study we demonstrate the possibility of
2. Performance of the WeNMR CS-Rosetta3 web server in CASD-NMR.
Science.gov (United States)
van der Schot, Gijs; Bonvin, Alexandre M J J
2015-08-01
We present here the performance of the WeNMR CS-Rosetta3 web server in CASD-NMR, the critical assessment of automated structure determination by NMR. The CS-Rosetta server uses only chemical shifts for structure prediction, in combination, when available, with a post-scoring procedure based on unassigned NOE lists (Huang et al. in J Am Chem Soc 127:1665-1674, 2005b, doi: 10.1021/ja047109h). We compare the original submissions using a previous version of the server based on Rosetta version 2.6 with recalculated targets using the new R3FP fragment picker for fragment selection and implementing a new annotation of prediction reliability (van der Schot et al. in J Biomol NMR 57:27-35, 2013, doi: 10.1007/s10858-013-9762-6), both implemented in the CS-Rosetta3 WeNMR server. In this second round of CASD-NMR, the WeNMR CS-Rosetta server has demonstrated a much better performance than in the first round since only converged targets were submitted. Further, recalculation of all CASD-NMR targets using the new version of the server demonstrates that our new annotation of prediction quality is giving reliable results. Predictions annotated as weak are often found to provide useful models, but only for a fraction of the sequence, and should therefore only be used with caution.
3. Use of NMR and NMR Prediction Software to Identify Components in Red Bull Energy Drinks
Science.gov (United States)
Simpson, Andre J.; Shirzadi, Azadeh; Burrow, Timothy E.; Dicks, Andrew P.; Lefebvre, Brent; Corrin, Tricia
2009-01-01
A laboratory experiment designed as part of an upper-level undergraduate analytical chemistry course is described. Students investigate two popular soft drinks (Red Bull Energy Drink and sugar-free Red Bull Energy Drink) by NMR spectroscopy. With assistance of modern NMR prediction software they identify and quantify major components in each…
4. New methods for the correction of 31P NMR spectra in in vivo NMR spectroscopy
International Nuclear Information System (INIS)
Starcuk, Z.; Bartusek, K.; Starcuk, Z. jr.
1994-01-01
The new methods for the correction of 31 P NMR spectra in vivo NMR spectroscopy have been performed. A method for the baseline correction of the spectra which represents a combination of time-domain and frequency-domain has been discussed.The method is very fast and efficient for minimization of base line artifacts of biological tissues impact
5. HPLC-NMR revisited: Using time-slice HPLC-SPE-NMR with database assisted dereplication
DEFF Research Database (Denmark)
Johansen, Kenneth; Wubshet, Sileshi Gizachew; Nyberg, Nils
2013-01-01
Time based trapping of chromatographically separated compounds on to solid-phase extraction cartridges (SPE) and subsequent elution to NMR-tubes was done to emulate the function of HPLC–NMR for dereplication purposes. Sufficient mass sensitivity was obtained by the use of a state-of-the-art HPLC......–SPE–NMR-system with a cryogenically cooled probe head, designed for 1.7 mm NMR-tubes. The resulting 1H NMR spectra (600 MHz) were evaluated against a database of previously acquired and prepared spectra. The in-house developed matching algorithm, based on partitioning of the spectra and allowing for changes in the chemical shifts......, is described and the code included as Supplementary Information. Two mixtures of natural products was used to test the approach; one extract of Carthamus oxyacantha (wild safflower) containing an array of spiro compounds and one extract of the endophytic fungus Penicillum namyslowski containing griseofulvin...
6. NMR techniques in the study of cardiovascular structure and functions
International Nuclear Information System (INIS)
Osbakken, M.; Haselgrove, J.
1987-01-01
The chapter titles of this book are: Introduction to NMR Techniques;Theory of NMR Probe Design;Overview of Magnetic Resonance Imaging to Study the Cardiovascular System;Vascular Anatomy and Physiology Studied with NMR Techniques;Assessment of Myocardial Ischemia and Infarction by Nuclear Magnetic Resonance Imaging;The Use of MRI in Congenital Heart Disease;Cardiomyopathies and Myocarditis Studied with NMR Techniques;Determination of Myocardial Mechanical Function with Magnetic Resonance Imaging Techniques;Determination of Flow Using NMR Techniques;The Use of Contrast Agents in Cardiac MRI;Can Cardiovascular Disease Be Effectively Evaluated with NMR Spectroscopy? NMR Studies of ATP Synthesis Reactions in the Isolated Heart;Studies of Intermediary Metabolism in the Heart by 13C NMR Spectroscopy;23Na and 39K NMR Spectroscopic Studies of the Intact Beating Heart;and Evaluation of Skeletal Muscle Metabolism in Patients with Congestive Heart Failure Using Phosphorus Nuclear Magnetic Resonance
7. High resolution NMR spectroscopy of synthetic polymers in bulk
International Nuclear Information System (INIS)
Komorski, R.A.
1986-01-01
The contents of this book are: Overview of high-resolution NMR of solid polymers; High-resolution NMR of glassy amorphous polymers; Carbon-13 solid-state NMR of semicrystalline polymers; Conformational analysis of polymers of solid-state NMR; High-resolution NMR studies of oriented polymers; High-resolution solid-state NMR of protons in polymers; and Deuterium NMR of solid polymers. This work brings together the various approaches for high-resolution NMR studies of bulk polymers into one volume. Heavy emphasis is, of course, given to 13C NMR studies both above and below Tg. Standard high-power pulse and wide-line techniques are not covered
8. The Oxidation of Rhenium(III) by Dioxygen in the Presence of Tri ...
African Journals Online (AJOL)
NICO
Both compounds were characterized by 1H NMR and infrared spectroscopy, and ... Microanalyses were obtained on a Carlo Erba EA 1108 elemental .... Spectral Characterization ... of this signal so far downfield indicates the existence of the.
9. Nuclear magnetic resonance (NMR): principles and applications
International Nuclear Information System (INIS)
Quibilan, E.I.
The basis for the phenomenon of nuclear magnetic resonance (NMR) is the ability of certain nuclei possessing both intrinsic angular momentum or ''spin'' I and magnetic moment to absorb electromagnetic energy in the radio frequency range. In principle, there are approximately 200 nuclei which may be investigated using the NMR technique. The NMR spectrum consists of intensity peaks along an axis calibrated in terms of the steady magnetic field or the frequency of the radiofrequency electromagnetic radiation. Analysis of the number, spacing, position and intensity of the lines in an NMR spectrum consists of intensity peaks along an axis calibrated in terms of the steady magnetic field or the frequency of the radiofrequency electromagnetic radiation. Analysis of the number, spacing, position and intensity of the lines in an NMR spectrum provides a variety of qualitative and quantitative analytical applications. The most obvious applications consist of the measurements of nuclear properties, such as spin number and nuclear magnetic moment. In liquids, the fine structure of resonance spectra provides a tool for chemical identification and molecular structure analysis. Other applications include the measurements of self-diffusion coefficients, magnetic fields and field homogeneity, inter-nuclear distances, and, in some cases, the water content of biological materials. (author)
10. Understanding Chemistry and Unique NMR Characters of Novel Amide and Ester Leflunomide Analogues
Directory of Open Access Journals (Sweden)
Morkos A. Henen
2017-12-01
Full Text Available A series of diverse substituted 5-methyl-isoxazole-4-carboxylic acid amides, imide and esters in which the benzene ring is mono or disubstituted was prepared. Spectroscopic and conformational examination was investigated and a new insight involving steric interference and interesting downfield deviation due to additional diamagnetic anisotropic effect of the amidic carbonyl group and the methine protons in 2,6-diisopropyl-aryl derivative (2 as conformationaly restricted analogues Leflunomide was discussed. Individual substituent electronic effects through π resonance of p-substituents and most stable conformation of compound (2 are discussed.
11. NMR Phase Noise in Bitter Magnets
Science.gov (United States)
Sigmund, E. E.; Calder, E. S.; Thomas, G. W.; Mitrović, V. F.; Bachman, H. N.; Halperin, W. P.; Kuhns, P. L.; Reyes, A. P.
2001-02-01
We have studied the temporal instability of a high field resistive Bitter magnet through nuclear magnetic resonance (NMR). This instability leads to transverse spin decoherence in repeated and accumulated NMR experiments as is normally performed during signal averaging. We demonstrate this effect via Hahn echo and Carr-Purcell-Meiboom-Gill (CPMG) transverse relaxation experiments in a 23-T resistive magnet. Quantitative analysis was found to be consistent with separate measurements of the magnetic field frequency fluctuation spectrum, as well as with independent NMR experiments performed in a magnetic field with a controlled instability. Finally, the CPMG sequence with short pulse delays is shown to be successful in recovering the intrinsic spin-spin relaxation even in the presence of magnetic field temporal instability.
12. Remote tuning of NMR probe circuits.
Science.gov (United States)
Kodibagkar, V D; Conradi, M S
2000-05-01
There are many circumstances in which the probe tuning adjustments cannot be located near the rf NMR coil. These may occur in high-temperature NMR, low-temperature NMR, and in the use of magnets with small diameter access bores. We address here circuitry for connecting a fixed-tuned probe circuit by a transmission line to a remotely located tuning network. In particular, the bandwidth over which the probe may be remotely tuned while keeping the losses in the transmission line acceptably low is considered. The results show that for all resonant circuit geometries (series, parallel, series-parallel), overcoupling of the line to the tuned circuit is key to obtaining a large tuning bandwidth. At equivalent extents of overcoupling, all resonant circuit geometries have nearly equal remote tuning bandwidths. Particularly for the case of low-loss transmission line, the tuning bandwidth can be many times the tuned circuit's bandwidth, f(o)/Q. Copyright 2000 Academic Press.
13. Deuterium NMR, induced and intrinsic cholesteric lyomesophases
International Nuclear Information System (INIS)
Alcantara, M.R.
1982-01-01
Induced and intrinsic cholesteric lyotropic mesophases were studied. Induced cholesteric lyomesophases based on potassium laurate (KL) system, with small amounts of cholesterol added, were studied by deuterium NMR and by polarizing microscopy. Order profiles obtained from deuterium NMR of KL perdenderated chains in both induced cholesteric and normal mesophases were compared. The intrinsic cholesteric lyotropic mesophases were based on the amphiphile potassium N-lauroyl serinate (KLNS) in the resolved levo form. The study of the type I intrinsic cholesteric mesophase was made by optical microscopy under polarized light and the type II intrinsic cholesteric lyomesophase was characterized by deuterium NMR. The new texture was explained by the use of the theory of disclinations developed for thermotropic liquid crystals, specially for cholesteric type. (M.J.C.) [pt
14. Determination of solid fat content by NMR
International Nuclear Information System (INIS)
Kawada, Tsukasa; Kato, Chihiro; Suzuki, Kazuaki
1984-01-01
To establish a standard method for determing solid fat content, the NMR method was tested at six laboratories and the results were examined for collaboration. Two types of instruments, pulse NMR and wide-line NMR were used. Standard deviation in results at six laboratories was less than 1.5 for the step wise method, but more than 1.5 for the rapid method. The standard deviation in results at a single laboratory was much less than either of these cases. No significant difference could be observed in the values obtained using both instruments. Solid fat content values measured for a mixture of fully hydrogenated rapeseed and rapeseed oil agreed well with the percentage of solid by weight. (author)
15. Muscular pathology: echographic and NMR imaging aspects
International Nuclear Information System (INIS)
Pascal-Suisse, P.; Beaurain, P.; Mougniot, C.
1995-01-01
A comparison of echographic techniques and NMR imaging has been done for the diagnosis of muscular trauma and tumor pathologies. In traumatic pathology, the echographic analysis allows to determine the complete assessment of recent muscular injuries. NMR imaging can be used in granuloma or fibrous callosity appreciation and for the analysis of deep injury (muscles and muscles-tendon junctions) and of muscular aponeurosis. Echography must be used together with color coding Doppler technique in the diagnosis of tumor pathology and for the study of slow fluxes. The recently available energy Doppler technique seems to be powerful in the study of vascularization of small expansive formations, but their extension to adjacent bone or tissue can only be appreciated using NMR imaging. (J.S.)
16. Contact replacement for NMR resonance assignment.
Science.gov (United States)
Xiong, Fei; Pandurangan, Gopal; Bailey-Kellogg, Chris
2008-07-01
Complementing its traditional role in structural studies of proteins, nuclear magnetic resonance (NMR) spectroscopy is playing an increasingly important role in functional studies. NMR dynamics experiments characterize motions involved in target recognition, ligand binding, etc., while NMR chemical shift perturbation experiments identify and localize protein-protein and protein-ligand interactions. The key bottleneck in these studies is to determine the backbone resonance assignment, which allows spectral peaks to be mapped to specific atoms. This article develops a novel approach to address that bottleneck, exploiting an available X-ray structure or homology model to assign the entire backbone from a set of relatively fast and cheap NMR experiments. We formulate contact replacement for resonance assignment as the problem of computing correspondences between a contact graph representing the structure and an NMR graph representing the data; the NMR graph is a significantly corrupted, ambiguous version of the contact graph. We first show that by combining connectivity and amino acid type information, and exploiting the random structure of the noise, one can provably determine unique correspondences in polynomial time with high probability, even in the presence of significant noise (a constant number of noisy edges per vertex). We then detail an efficient randomized algorithm and show that, over a variety of experimental and synthetic datasets, it is robust to typical levels of structural variation (1-2 AA), noise (250-600%) and missings (10-40%). Our algorithm achieves very good overall assignment accuracy, above 80% in alpha-helices, 70% in beta-sheets and 60% in loop regions. Our contact replacement algorithm is implemented in platform-independent Python code. The software can be freely obtained for academic use by request from the authors.
17. Prediction of peak overlap in NMR spectra
International Nuclear Information System (INIS)
Hefke, Frederik; Schmucki, Roland; Güntert, Peter
2013-01-01
Peak overlap is one of the major factors complicating the analysis of biomolecular NMR spectra. We present a general method for predicting the extent of peak overlap in multidimensional NMR spectra and its validation using both, experimental data sets and Monte Carlo simulation. The method is based on knowledge of the magnetization transfer pathways of the NMR experiments and chemical shift statistics from the Biological Magnetic Resonance Data Bank. Assuming a normal distribution with characteristic mean value and standard deviation for the chemical shift of each observable atom, an analytic expression was derived for the expected overlap probability of the cross peaks. The analytical approach was verified to agree with the average peak overlap in a large number of individual peak lists simulated using the same chemical shift statistics. The method was applied to eight proteins, including an intrinsically disordered one, for which the prediction results could be compared with the actual overlap based on the experimentally measured chemical shifts. The extent of overlap predicted using only statistical chemical shift information was in good agreement with the overlap that was observed when the measured shifts were used in the virtual spectrum, except for the intrinsically disordered protein. Since the spectral complexity of a protein NMR spectrum is a crucial factor for protein structure determination, analytical overlap prediction can be used to identify potentially difficult proteins before conducting NMR experiments. Overlap predictions can be tailored to particular classes of proteins by preparing statistics from corresponding protein databases. The method is also suitable for optimizing recording parameters and labeling schemes for NMR experiments and improving the reliability of automated spectra analysis and protein structure determination.
18. Applications of NMR spectroscopy to xenobiotic metabolism
International Nuclear Information System (INIS)
Harris, T.M.
1989-01-01
Recent years have seen high field NMR spectrometers become commonplace in research laboratories. At the same time, major advances in methodology for structural analysis have occurred, particularly notable among these being the development of two-dimensional spectroscopic techniques. Many applications have been made of NMR spectroscopy in the study of xenobiotic metabolic processes. This deals with two specific applications which have been made in the author's laboratory and involve mechanistic studies of the reactions of the carcinogens ethylene dibromide and aflatoxin with DNA
19. Tritiation methods and tritium NMR spectroscopy
International Nuclear Information System (INIS)
Jaiswal, D.K.; Morimoto, H.; Salijoughian, M.; Williams, P.G.
1991-09-01
We have used a simple process for the production of highly tritiated water and characterized the product species by 1 H and 3 H NMR spectroscopy. The water is readily manipulated and used in subsequent reactions either as T 2 O, CH 3 COOT or CF 3 COOT. Development of tritiated diimide has progressed to the point where cis-hydrogenated products at 1-20 Ci/mmole S.A. are possible. Tri-n-butyl tin tritide has been produced at >95% tritium content and well characterized by multinuclear NMR techniques. 27 refs., 3 figs
20. Applications of NMR in biological metabolic research
International Nuclear Information System (INIS)
Nie Jiarui; Li Xiuqin; He Chunjian
1989-01-01
The nuclear magnetic resonance has become a powerful means of studying biological metabolism in non-invasive and non-destructive way. Being used to study the metabolic processes of living system in normal physiological conditions as well as in molecular level, the method is better than other conventional approaches. Using important parameters such as NMR-chemical shifts, longitudinal relaxation time and transverse relaxation time, it is possible to probe the metabolic processes as well as conformation, concentration, transportation and distribution of reacting and resulting substances. The NMR spectroscopy of 1 H, 31 P and 13 C nuclei has already been widely used in metabolic researches
1. Deuteron NMR and modelling in solid polymers
International Nuclear Information System (INIS)
Hirschinger, J.
1992-01-01
Deuteron NMR techniques are described and some recent applications to the study of rotational motions in solid polymers are reviewed. The information content and the domain of applicability of each technique are presented. Ultra-slow motions are studied in real time without any motional model consideration. For very fast motions, computer molecular dynamics simulations are shown to complement the NMR results. Experimental examples deal with the chain motion in the crystalline α-phase of poly(vinylidenefluoride) and nylon 6,6
2. Programmable pulse series generator for NMR relaxometer
International Nuclear Information System (INIS)
Stolbunov, R.N.; Chichikov, S.A.; Lundin, A.G.
2005-01-01
Paper describes a pulse series generator for NMR relaxometer. The operation mode is set on the basis of the PC program by the PCI bus in the internal memory. The design is based on two Altera Company MAX7000S and Cyclone family microcircuits using the Qartus II 4.0 software. The basic parameters are as follows: pulse minimum length - 50 ns, time resolution - 10 ns, pulse maximum number - 1024, number of controlled output channels - 8. The designed device as a part of the NMR hardware-software system enables to record, to process and to store the experiment results in the form of electronic document [ru
3. NMR relaxation times of natural rubber latex
International Nuclear Information System (INIS)
Harun, S.; Aziz, H.; Basir, Z.
1994-01-01
NMR relaxation times T sub 1 and T sub 2 of natural rubber latex have been measured at 25 degree C on a pulsed NMR spectrometer. The work focuses on the variation of the relaxation times with the amount of water content from 0% to 50%. The water content was adjusted by centrifuging and removing a certain amount of water from the sample. The data were analysed using a biexponential fitting procedure which yields simultaneously either T sub 1a and T sub 1b or T sub 2a and T sub 2b. The amount of solid was compared with the known amount of dry rubber content
4. Recommendations of the wwPDB NMR Validation Task Force
Science.gov (United States)
Montelione, Gaetano T.; Nilges, Michael; Bax, Ad; Güntert, Peter; Herrmann, Torsten; Richardson, Jane S.; Schwieters, Charles; Vranken, Wim F.; Vuister, Geerten W.; Wishart, David S.; Berman, Helen M.; Kleywegt, Gerard J.; Markley, John L.
2013-01-01
As methods for analysis of biomolecular structure and dynamics using nuclear magnetic resonance spectroscopy (NMR) continue to advance, the resulting 3D structures, chemical shifts, and other NMR data are broadly impacting biology, chemistry, and medicine. Structure model assessment is a critical area of NMR methods development, and is an essential component of the process of making these structures accessible and useful to the wider scientific community. For these reasons, the Worldwide Protein Data Bank (wwPDB) has convened an NMR Validation Task Force (NMR-VTF) to work with the wwPDB partners in developing metrics and policies for biomolecular NMR data harvesting, structure representation, and structure quality assessment. This paper summarizes the recommendations of the NMR-VTF, and lays the groundwork for future work in developing standards and metrics for biomolecular NMR structure quality assessment. PMID:24010715
5. Structural properties of carbon nanotubes derived from 13C NMR
KAUST Repository
Abou-Hamad, E.; Babaa, M.-R.; Bouhrara, M.; Kim, Y.; Saih, Y.; Dennler, S.; Mauri, F.; Basset, Jean-Marie; Goze-Bac, C.; Wå gberg, T.
2011-01-01
We present a detailed experimental and theoretical study on how structural properties of carbon nanotubes can be derived from 13C NMR investigations. Magic angle spinning solid state NMR experiments have been performed on single- and multiwalled
6. nmrML: A Community Supported Open Data Standard for the Description, Storage, and Exchange of NMR Data.
Science.gov (United States)
Schober, Daniel; Jacob, Daniel; Wilson, Michael; Cruz, Joseph A; Marcu, Ana; Grant, Jason R; Moing, Annick; Deborde, Catherine; de Figueiredo, Luis F; Haug, Kenneth; Rocca-Serra, Philippe; Easton, John; Ebbels, Timothy M D; Hao, Jie; Ludwig, Christian; Günther, Ulrich L; Rosato, Antonio; Klein, Matthias S; Lewis, Ian A; Luchinat, Claudio; Jones, Andrew R; Grauslys, Arturas; Larralde, Martin; Yokochi, Masashi; Kobayashi, Naohiro; Porzel, Andrea; Griffin, Julian L; Viant, Mark R; Wishart, David S; Steinbeck, Christoph; Salek, Reza M; Neumann, Steffen
2018-01-02
NMR is a widely used analytical technique with a growing number of repositories available. As a result, demands for a vendor-agnostic, open data format for long-term archiving of NMR data have emerged with the aim to ease and encourage sharing, comparison, and reuse of NMR data. Here we present nmrML, an open XML-based exchange and storage format for NMR spectral data. The nmrML format is intended to be fully compatible with existing NMR data for chemical, biochemical, and metabolomics experiments. nmrML can capture raw NMR data, spectral data acquisition parameters, and where available spectral metadata, such as chemical structures associated with spectral assignments. The nmrML format is compatible with pure-compound NMR data for reference spectral libraries as well as NMR data from complex biomixtures, i.e., metabolomics experiments. To facilitate format conversions, we provide nmrML converters for Bruker, JEOL and Agilent/Varian vendor formats. In addition, easy-to-use Web-based spectral viewing, processing, and spectral assignment tools that read and write nmrML have been developed. Software libraries and Web services for data validation are available for tool developers and end-users. The nmrML format has already been adopted for capturing and disseminating NMR data for small molecules by several open source data processing tools and metabolomics reference spectral libraries, e.g., serving as storage format for the MetaboLights data repository. The nmrML open access data standard has been endorsed by the Metabolomics Standards Initiative (MSI), and we here encourage user participation and feedback to increase usability and make it a successful standard.
7. Software Library for Bruker TopSpin NMR Data Files
Energy Technology Data Exchange (ETDEWEB)
2016-10-14
A software library for parsing and manipulating frequency-domain data files that have been processed using the Bruker TopSpin NMR software package. In the context of NMR, the term "processed" indicates that the end-user of the Bruker TopSpin NMR software package has (a) Fourier transformed the raw, time-domain data (the Free Induction Decay) into the frequency-domain and (b) has extracted the list of NMR peaks.
8. NMR imaging of the cardiovascular system
International Nuclear Information System (INIS)
Canby, R.C.; Evanochko, W.T.; Pohost, G.M.
1986-01-01
Proton nuclear magnetic resonance (NMR) imaging permits high-resolution tomographic and three-dimensional images of the human body to be obtained without exposure to ionizing radiation. Such imaging not only yields anatomic resolution comparable to X-ray examinations but also provides a potential means to discriminate between healthy tissue and diseased tissue. This potential is based on certain NMR properties known as relaxation times, which determine, in part, the signal intensity in an image. These properties are related to such factors as the sizes and concentrations of proteins and mobile lipids and the compartmentalization of the protons of water. Although NMR imaging (also called magnetic resonance imaging, MRI) is becoming widely available for clinical use, application to the cardiovascular system, though promising, remains primarily a research tool. Gated proton NMR imaging can generate cardiac images with excellent morphologic detail and contrast; however, its ultimate importance as a cardiovascular diagnostic modality will depend on the development of several unique applications. These applications are discussed in this paper
9. NMR imaging of the musculoskeletal system
International Nuclear Information System (INIS)
Naegele, M.; Lienemann, A.; Hahn, D.
1988-01-01
NMR imaging now allows in vivo imaging of soft tissue hitherto undetectable by non-invasive means. This opens up excellent perspectives with regard to the diagnosis and therapy of various diseases in the field of traumatology and oncology, of which examples are discussed in this paper. (orig.) [de
10. Fourier transform zero field NMR and NQR
International Nuclear Information System (INIS)
Zax, D.B.
1985-01-01
In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive, or the information contained in the dipole-dipole couplings is more important. In these cases, Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subject of this thesis. Chapter I presents the quantum mechanical background and notational formalism for what follows. Chapter II gives a brief review of high resolution magnetic resonance methods, with particular emphasis on techniques applicable to dipole-dipole and quadrupolar couplings. Level crossings between spin-1/2 and quadrupolar spins during demagnetization transfer polarization from high to low λ nuclei. This is the basis of very high sensitivity zero field NQR measurements by field cycling. Chapter III provides a formal presentation of the high resolution Fourier transform zero field NMR method. Theoretical signal functions are calculated for common spin systems, and examples of typical spectra are presented. Chapters IV and V review the experimental progress in zero field NMR of dipole-dipole coupled spin-1/2 nuclei and for quadrupolar spin systems. Variations of the simple experiment describe in earlier chapters that use pulsed dc fields are presented in Chapter VI
11. NMR analog of Bell's inequalities violation test
International Nuclear Information System (INIS)
Souza, A M; Oliveira, I S; Sarthour, R S; Magalhaes, A; Teles, J; Azevedo, E R de; Bonagamba, T J
2008-01-01
In this paper, we present an analog of Bell's inequalities violation test for N qubits to be performed in a nuclear magnetic resonance (NMR) quantum computer. This can be used to simulate or predict the results for different Bell's inequality tests, with distinct configurations and a larger number of qubits. To demonstrate our scheme, we implemented a simulation of the violation of the Clauser, Horne, Shimony and Holt (CHSH) inequality using a two-qubit NMR system and compared the results to those of a photon experiment. The experimental results are well described by the quantum mechanics theory and a local realistic hidden variables model (LRHVM) that was specifically developed for NMR. That is why we refer to this experiment as a simulation of Bell's inequality violation. Our result shows explicitly how the two theories can be compatible with each other due to the detection loophole. In the last part of this work, we discuss the possibility of testing some fundamental features of quantum mechanics using NMR with highly polarized spins, where a strong discrepancy between quantum mechanics and hidden variables models can be expected
12. NMR Analysis of Some Pentacycloundecanedione Derivatives
African Journals Online (AJOL)
NJD
Although many authors have commented on the difficulty of ... coming these former difficulties. Cookson's dione 19,10 .... and 2.58 ppm) is the common factor and the positions of H-2. (2.94 ppm) .... Owing to advances in NMR technology, the.
13. Proton NMR imaging in experimental ischemic infarction
International Nuclear Information System (INIS)
Buonanno, F.S.; Pykett, I.L.; Brady, T.J.; Vielma, J.; Burt, C.T.; Goldman, M.R.; Hinshaw, W.S.; Pohost, G.M.; Kistler, J.P.
1983-01-01
Proton nuclear magnetic resonance (NMR) images depict the distribution and concentration of mobile protons modified by the relaxation times T1 and T2. Using the steady-state-free-precession (SSFP) technique, serial coronal images were obtained sequentially over time in laboratory animals with experimental ischemic infarction. Image changes were evident as early as 2 hours after carotid artery ligation, and corresponded to areas of ischemic infarction noted pathologically. Resulting SSFP images in experimental stroke are contrasted to inversion-recovery NMR images in an illustrative patient with established cerebral infarction. Bulk T1 and T2 measurements were made in vitro in three groups of gerbils: normal, those with clinical evidence of infarction, and those clinically normal after carotid ligature. Infarcted hemispheres had significantly prolonged T1 and T2 (1.47 +/- .12 sec, 76.0 +/- 9.0 msec, respectively) when compared to the contralateral hemisphere (T1 . 1.28 +/- .05 sec, T2 . 58.7 +/- 3.9 msec) or to the other two groups. These data suggest that changes in NMR parameters occur and can be detected by NMR imaging as early as two hours after carotid artery ligation
14. Hyperpolarized NMR Probes for Biological Assays
Directory of Open Access Journals (Sweden)
Sebastian Meier
2014-01-01
Full Text Available During the last decade, the development of nuclear spin polarization enhanced (hyperpolarized molecular probes has opened up new opportunities for studying the inner workings of living cells in real time. The hyperpolarized probes are produced ex situ, introduced into biological systems and detected with high sensitivity and contrast against background signals using high resolution NMR spectroscopy. A variety of natural, derivatized and designed hyperpolarized probes has emerged for diverse biological studies including assays of intracellular reaction progression, pathway kinetics, probe uptake and export, pH, redox state, reactive oxygen species, ion concentrations, drug efficacy or oncogenic signaling. These probes are readily used directly under natural conditions in biofluids and are often directly developed and optimized for cellular assays, thus leaving little doubt about their specificity and utility under biologically relevant conditions. Hyperpolarized molecular probes for biological NMR spectroscopy enable the unbiased detection of complex processes by virtue of the high spectral resolution, structural specificity and quantifiability of NMR signals. Here, we provide a survey of strategies used for the selection, design and use of hyperpolarized NMR probes in biological assays, and describe current limitations and developments.
15. Structural Studies of Biological Solids Using NMR
Science.gov (United States)
Ramamoorthy, Ayyalusamy
2011-03-01
High-resolution structure and dynamics of biological molecules are important in understanding their function. While studies have been successful in solving the structures of water-soluble biomolecules, it has been proven difficult to determine the structures of membrane proteins and fibril systems. Recent studies have shown that solid-state NMR is a promising technique and could be highly valuable in studying such non-crystalline and non-soluble biosystems. I will present strategies to study the structures of such challenging systems and also about the applications of solid-state NMR to study the modes of membrane-peptide interactions for a better assessment of the prospects of antimicrobial peptides as substitutes to antibiotics in the control of human disease. Our studies on the mechanism of membrane disruption by LL-37 (a human antimicrobial peptide), analogs of the naturally occurring antimicrobial peptide magainin2 extracted from the skin of the African frog Xenopus Laevis, and pardaxin will be presented. Solid-state NMR experiments were used to determine the secondary structure, dynamics and topology of these peptides in lipid bilayers. Similarities and difference in the cell-lysing mechanism, and their dependence on the membrane composition, of these peptides will be discussed. Atomic-level resolution NMR structures of amyloidogenic proteins revealing the misfolding pathway and early intermediates that play key roles in amyloid toxicity will also be presented.
16. Synthesis and NMR elucidation of novel pentacycloundecane ...
African Journals Online (AJOL)
NICO
SYNTHESIS AND NMR ELUCIDATION OF NOVEL. PENTACYCLOUNDECANE DERIVED PEPTIDES. Rajshekhar Karpoormath, a. Oluseye K. Onajole, a. Thavendran Govender, b. Glenn E. M. Maguire, a and Hendrik G. Kruger a* a. School of Chemistry, University of KwaZulu-Natal, Durban 4001, South Africa b. School of ...
17. The bar coil for NMR tomograph
International Nuclear Information System (INIS)
Bogorodzki, P.; Piatkowski, A.; Wasielewski, J.
1995-01-01
The bar coil (bi-planar) for the NMR tomograph, designed for medical diagnostics, has been described. The tests of coil shown that it generates good homogenous magnetic field in a big volume what results in improving of the signal-to-noise ratio
18. NMR characterization of polymers: Review and update
Science.gov (United States)
NMR spectroscopy is a major technique for the characterization and analysis of polymers. A large number of methodologies have been developed in both the liquid and the solid state, and the literature has grown considerably (1-5). The field now covers a broad spectrum of activities, including polym...
19. Some exercises in quantitative NMR imaging
International Nuclear Information System (INIS)
Bakker, C.J.G.
1985-01-01
The articles represented in this thesis result from a series of investigations that evaluate the potential of NMR imaging as a quantitative research tool. In the first article the possible use of proton spin-lattice relaxation time T 1 in tissue characterization, tumor recognition and monitoring tissue response to radiotherapy is explored. The next article addresses the question whether water proton spin-lattice relaxation curves of biological tissues are adequately described by a single time constant T 1 , and analyzes the implications of multi-exponentiality for quantitative NMR imaging. In the third article the use of NMR imaging as a quantitative research tool is discussed on the basis of phantom experiments. The fourth article describes a method which enables unambiguous retrieval of sign information in a set of magnetic resonance images of the inversion recovery type. The next article shows how this method can be adapted to allow accurate calculation of T 1 pictures on a pixel-by-pixel basis. The sixth article, finally, describes a simulation procedure which enables a straightforward determination of NMR imaging pulse sequence parameters for optimal tissue contrast. (orig.)
20. Structures of Biomolecules by NMR Spectroscopy
an edge over the X-ray method as it can be used to study biomolecules ... currently as an Associate. Professor. ... Such a wealth of data is made available to the NMR ... important step towards structural characterization of a biomolecule. Box 1.
1. NMR blood vessel imaging method and apparatus
International Nuclear Information System (INIS)
Riederer, S.J.
1988-01-01
A high speed method of forming computed images of blood vessels based on measurements of characteristics of a body is described comprising the steps of: subjecting a predetermined body area containing blood vessels of interest to, successively, applications of a short repetition time (TR) NMR pulse sequence during the period of high blood velocity and then to corresponding applications during the period of low blood velocity for successive heart beat cycles; weighting the collected imaging data from each application of the NMR pulse sequence according to whether the data was acquired during the period of high blood velocity or a period of low blood velocity of the corresponding heart beat cycle; accumulating weighted imaging data from a plurality of NMR pulse sequences corresponding to high blood velocity periods and from a plurality of NMR pulse sequences corresponding to low blood velocity periods; subtracting the weighted imaging data corresponding to each specific phase encoding acquired during the high blood velocity periods from the weighted imaging data for the same phase encoding corresponding to low blood velocity periods in order to compute blood vessel imaging data; and forming an image of the blood vessels of interest from the blood vessel imaging data
2. Recent Advances in Targeted and Untargeted Metabolomics by NMR and MS/NMR Methods
Energy Technology Data Exchange (ETDEWEB)
Bingol, Kerem
2018-04-18
Metabolomics has made significant progress in multiple fronts in the last 18 months. This minireview aimed to give an overview of these advancements in the light of their contribution to targeted and untargeted metabolomics. New computational approaches have emerged to overcome manual absolute quantitation step of metabolites in 1D 1H NMR spectra. This provides more consistency between inter-laboratory comparisons. Integration of 2D NMR metabolomics databases under a unified web server allowed very accurate identification of the metabolites that have been catalogued in these databases. For the remaining uncatalogued and unknown metabolites, new cheminformatics approaches have been developed by combining NMR and mass spectrometry. These hybrid NMR/MS approaches accelerated the identification of unknowns in untargeted studies, and now they are allowing to profile ever larger number of metabolites in application studies.
3. Solid-state NMR spectroscopy on complex biomolecules
NARCIS (Netherlands)
Renault, M.A.M.; Cukkemane, A.A.; Baldus, M.
2010-01-01
Biomolecular applications of NMR spectroscopy are often merely associated with soluble molecules or magnetic resonance imaging. However, since the late 1970s, solid-state NMR (ssNMR) spectroscopy has demonstrated its ability to provide atomic-level insight into complex biomolecular systems ranging
4. Polymeric proanthocyanidins 13C NMR studies of procyanidins
Science.gov (United States)
Lawrence J. Porter; Roger H. Newman; Lai Yeap Foo; Herbert Wong; Richard W. Hemingway
1982-01-01
Proanthocyanidin polymers have been shown to consist entirely of flavan-3-ol units by a combination of techniques including 13C n.m.r. spectroscopy. The 13C n.m.r. spectra of the polymers and related molecules are now considered in more detail. Prior to this study UC n.m.r. data has been published of procyanidins and...
5. Performance of the WeNMR CS-Rosetta3 web server in CASD-NMR
Energy Technology Data Exchange (ETDEWEB)
Schot, Gijs van der [Uppsala University, Laboratory of Molecular Biophysics, Department of Cell and Molecular Biology (Sweden); Bonvin, Alexandre M. J. J., E-mail: [email protected] [Utrecht University, Faculty of Science – Chemistry, Bijvoet Center for Biomolecular Research (Netherlands)
2015-08-15
We present here the performance of the WeNMR CS-Rosetta3 web server in CASD-NMR, the critical assessment of automated structure determination by NMR. The CS-Rosetta server uses only chemical shifts for structure prediction, in combination, when available, with a post-scoring procedure based on unassigned NOE lists (Huang et al. in J Am Chem Soc 127:1665–1674, 2005b, doi: 10.1021/ja047109h 10.1021/ja047109h ). We compare the original submissions using a previous version of the server based on Rosetta version 2.6 with recalculated targets using the new R3FP fragment picker for fragment selection and implementing a new annotation of prediction reliability (van der Schot et al. in J Biomol NMR 57:27–35, 2013, doi: 10.1007/s10858-013-9762-6 10.1007/s10858-013-9762-6 ), both implemented in the CS-Rosetta3 WeNMR server. In this second round of CASD-NMR, the WeNMR CS-Rosetta server has demonstrated a much better performance than in the first round since only converged targets were submitted. Further, recalculation of all CASD-NMR targets using the new version of the server demonstrates that our new annotation of prediction quality is giving reliable results. Predictions annotated as weak are often found to provide useful models, but only for a fraction of the sequence, and should therefore only be used with caution.
6. Performance of the WeNMR CS-Rosetta3 web server in CASD-NMR
International Nuclear Information System (INIS)
Schot, Gijs van der; Bonvin, Alexandre M. J. J.
2015-01-01
We present here the performance of the WeNMR CS-Rosetta3 web server in CASD-NMR, the critical assessment of automated structure determination by NMR. The CS-Rosetta server uses only chemical shifts for structure prediction, in combination, when available, with a post-scoring procedure based on unassigned NOE lists (Huang et al. in J Am Chem Soc 127:1665–1674, 2005b, doi: 10.1021/ja047109h 10.1021/ja047109h ). We compare the original submissions using a previous version of the server based on Rosetta version 2.6 with recalculated targets using the new R3FP fragment picker for fragment selection and implementing a new annotation of prediction reliability (van der Schot et al. in J Biomol NMR 57:27–35, 2013, doi: 10.1007/s10858-013-9762-6 10.1007/s10858-013-9762-6 ), both implemented in the CS-Rosetta3 WeNMR server. In this second round of CASD-NMR, the WeNMR CS-Rosetta server has demonstrated a much better performance than in the first round since only converged targets were submitted. Further, recalculation of all CASD-NMR targets using the new version of the server demonstrates that our new annotation of prediction quality is giving reliable results. Predictions annotated as weak are often found to provide useful models, but only for a fraction of the sequence, and should therefore only be used with caution
7. First NMR Experiments in the Hybrid, 40T and beyond: A challenge to traditional NMR instrumentation
Science.gov (United States)
Reyes, Arneil P.
2001-03-01
The recent commissioning of the continuous 45T hybrid magnet at NHMFL has opened new horizon for science but carried with it new challenges that forced NMR spectroscopists to reevaluate the traditional approach to NMR instrumentation. Very recently, a world record frequency at 1.5GHz has been achieved, signaling the new era of NMR probe designs that may someday blur the distinction between the classic NMR and millimeter-wave spectroscopies. No longer can we ignore stray capacitances and exposed leads in the terrain where every millimeter of cable counts. The challenge brought about by ever increasing fields and consequently, frequency, requirements has stimulated ingenuity among scientists. This is eased by accelerated growth in RF communications and computing technologies that made available advanced devices with more speed, power, bandwidth, noise immunity, flexibility, and complexity in small space at very low costs. Utilization of these devices have been paramount consideration in cutting-edge designs at NHMFL for Condensed Matter NMR and will be described in this talk. I will also discuss a number of first >33T NMR experiments to date utilizing the strength of the field to expose, as well as to induce occurrence of, new physical phenomena in condensed matter and which resulted in better understanding of the physics of materials. This work has been a result of continuing collaboration with P. L Kuhns, W. G. Moulton, W. P. Halperin (NU), and W. G. Clark (UCLA). The NHMFL is supported through the National Science Foundation and the State of Florida.
8. Direct 13C NMR Detection in HPLC Hyphenation Mode
DEFF Research Database (Denmark)
Wubshet, Sileshi Gizachew; Johansen, Kenneth; Nyberg, Nils
2012-01-01
Solid phase extraction (SPE) was introduced as a crucial step in the HPLC-SPE-NMR technique to enable online analyte enrichment from which proton-detected NMR experiments on submicrogram amounts from complex mixtures were possible. However, the significance of direct-detected (13)C NMR experiments...... application of HPLC-SPE-NMR analysis using direct-detected (13)C NMR spectra. HPLC column loading, accumulative SPE trappings, and the effect of different elution solvents were evaluated and optimized. A column loading of approximately 600 mug of a prefractionated triterpenoid mixture, six trappings...
9. Use of NMR as an online sensor in industrial processes
International Nuclear Information System (INIS)
2012-01-01
Nuclear magnetic resonance (NMR) is one of the most versatile analytical techniques for chemical, biochemical and medical applications. Despite this great success, NMR is seldom used as a tool in industrial applications. The first application of NMR in flowing samples was published in 1951. However, only in the last ten years Flow NMR has gained momentum and new and potential applications have been proposed. In this review we present the historical evolution of flow or online NMR spectroscopy and imaging, and current developments for use in the automation of industrial processes. (author)
10. Solid-state NMR basic principles and practice
CERN Document Server
Apperley, David C; Hodgkinson, Paul
2014-01-01
Nuclear Magnetic Resonance (NMR) has proved to be a uniquely powerful and versatile tool for analyzing and characterizing chemicals and materials of all kinds. This book focuses on the latest developments and applications for "solid-state" NMR, which has found new uses from archaeology to crystallography to biomaterials and pharmaceutical science research. The book will provide materials engineers, analytical chemists, and physicists, in and out of lab, a survey of the techniques and the essential tools of solid-state NMR, together with a practical guide on applications. In this concise introduction to the growing field of solid-state nuclear magnetic resonance spectroscopy The reader will find: * Basic NMR concepts for solids, including guidance on the spin-1/2 nuclei concept * Coverage of the quantum mechanics aspects of solid state NMR and an introduction to the concept of quadrupolar nuclei * An understanding relaxation, exchange and quantitation in NMR * An analysis and interpretation of NMR data, with e...
11. NMR shielding calculations across the periodic table: diamagnetic uranium compounds. 2. Ligand and metal NMR.
Science.gov (United States)
Schreckenbach, Georg
2002-12-16
In this and a previous article (J. Phys. Chem. A 2000, 104, 8244), the range of application for relativistic density functional theory (DFT) is extended to the calculation of nuclear magnetic resonance (NMR) shieldings and chemical shifts in diamagnetic actinide compounds. Two relativistic DFT methods are used, ZORA ("zeroth-order regular approximation") and the quasirelativistic (QR) method. In the given second paper, NMR shieldings and chemical shifts are calculated and discussed for a wide range of compounds. The molecules studied comprise uranyl complexes, [UO(2)L(n)](+/-)(q); UF(6); inorganic UF(6) derivatives, UF(6-n)Cl(n), n = 0-6; and organometallic UF(6) derivatives, UF(6-n)(OCH(3))(n), n = 0-5. Uranyl complexes include [UO(2)F(4)](2-), [UO(2)Cl(4)](2-), [UO(2)(OH)(4)](2-), [UO(2)(CO(3))(3)](4-), and [UO(2)(H(2)O)(5)](2+). For the ligand NMR, moderate (e.g., (19)F NMR chemical shifts in UF(6-n)Cl(n)) to excellent agreement [e.g., (19)F chemical shift tensor in UF(6) or (1)H NMR in UF(6-n)(OCH(3))(n)] has been found between theory and experiment. The methods have been used to calculate the experimentally unknown (235)U NMR chemical shifts. A large chemical shift range of at least 21,000 ppm has been predicted for the (235)U nucleus. ZORA spin-orbit appears to be the most accurate method for predicting actinide metal chemical shifts. Trends in the (235)U NMR chemical shifts of UF(6-n)L(n) molecules are analyzed and explained in terms of the calculated electronic structure. It is argued that the energy separation and interaction between occupied and virtual orbitals with f-character are the determining factors.
12. DNA oligonucleotide conformations: high resolution NMR studies
International Nuclear Information System (INIS)
Mellema, J.-R.
1984-01-01
The present work describes a DNA double-helix model, which is well comparable with the models derived from fibre-diffraction studies. The model has a mononucleotide repeat with torsion angles in accordance with average geometries as derived from 1 H NMR studies. Special attention was paid to reduce the number of short H-H nonbonding contacts, which are abundantly present in the 'classical' fibre-diffraction models. Chapter 3 describes the first complete assignment of a 1 H NMR spectrum of a DNA tetramer, d(TAAT). Preliminary conformational data derived from the spectral parameters recorded at 27 0 C are given. A more detailed analysis employing temperature-dependence studies is given in Chapter 4. (Auth.)
13. Some nitrogen-14 NMR studies in solids
Energy Technology Data Exchange (ETDEWEB)
Pratum, T.K.
1983-11-01
The first order quadrupolar perturbation of the /sup 14/N NMR spectrum yields information regarding the static and dynamic properties of the surrounding electronic environment. Signal to noise problems caused by long /sup 14/N longitudinal relaxation times (T/sub 1/) and small equilibrium polarizations are reduced by rotating frame cross polarization (CP) experiments between /sup 14/N and /sup 1/H. Using quadrupolar echo and CP techniques, the /sup 14/N quadrupolar coupling constants (e/sup 2/qQ/h) and asymmetry parameters (eta) have been obtained for a variety of tetraalkylammonium compounds by observation of their quadrupolar powder patterns at various temperatures. For choline chloride and iodide the /sup 14/N NMR powder patterns exhibit the effects of anisotropic molecular motion, while choline bromide spectra show no such effects.
14. Fully automated system for pulsed NMR measurements
International Nuclear Information System (INIS)
Cantor, D.M.
1977-01-01
A system is described which places many of the complex, tedious operations for pulsed NMR experiments under computer control. It automatically optimizes the experiment parameters of pulse length and phase, and precision, accuracy, and measurement speed are improved. The hardware interface between the computer and the NMR instrument is described. Design features, justification of the choices made between alternative design strategies, and details of the implementation of design goals are presented. Software features common to all the available experiments are discussed. Optimization of pulse lengths and phases is performed via a sequential search technique called Uniplex. Measurements of the spin-lattice and spin-spin relaxation times and of diffusion constants are automatic. Options for expansion of the system are explored along with some of the limitations of the system
15. Exploring the limits to spatially resolved NMR
Energy Technology Data Exchange (ETDEWEB)
Gaedke, Achim; Nestle, Nikolaus [TU Darmstadt, Institute of Condensed Matter Physics (Germany)
2010-07-01
Recent advances in MRI have demonstrated resolutions down to 1 {mu}m. Magnetic resonance force microscopy has the potential to reach sensitivity for single nuclear spins. Given these numbers, in vivo imaging of single cells or even biomacromolecules may seem possible. However, for in vivo applications, there are fundamental differences in the contrast mechanisms compared to MRI at macroscopic scales as the length scale of of molecular self-diffusion exceeds that of the spatial resolution on the NMR time scale. Those effects - which are fundamentally different from the echo attenuation in field gradient NMR - even may lead to general limitations on the spatial resolution achievable in aqueous systems with high water content. In our contribution, we explore those effects on a model system in a high-resolution stray-field imaging setup. In addition to experimental results, simulations based on the Bloch-Torrey equation are presented.
16. Recent topics in NMR imaging and MRI
International Nuclear Information System (INIS)
Watanabe, Tokuko
2002-01-01
NMR and NMR imaging (MRI) are finding increasing use not only in the clinical and medical fields, but also in material, physicochemical, biological, geological, industrial and environmental applications. This short review is limited to two topics: new techniques and pulse sequences and their application to non-clinical fields that may have clinical application; and new trends in MR contrast agents. The former topic addresses pulse sequence and data analysis; dynamics such as diffusion, flow, velocity and velocimetry; chemometrics; pharmacological agents; and chemotherapy; the latter topic addresses contrast agents (CA) sensitive to biochemical activity; CA based on water exchange; molecular interactions and stability of CA; characteristics of emerging CA; superparamagnetic CA; and macromolecular CA. (author)
17. Some nitrogen-14 NMR studies in solids
International Nuclear Information System (INIS)
Pratum, T.K.
1983-11-01
The first order quadrupolar perturbation of the 14 N NMR spectrum yields information regarding the static and dynamic properties of the surrounding electronic environment. Signal to noise problems caused by long 14 N longitudinal relaxation times (T 1 ) and small equilibrium polarizations are reduced by rotating frame cross polarization (CP) experiments between 14 N and 1 H. Using quadrupolar echo and CP techniques, the 14 N quadrupolar coupling constants (e 2 qQ/h) and asymmetry parameters (eta) have been obtained for a variety of tetraalkylammonium compounds by observation of their quadrupolar powder patterns at various temperatures. For choline chloride and iodide the 14 N NMR powder patterns exhibit the effects of anisotropic molecular motion, while choline bromide spectra show no such effects
18. NMR dispersion measurement of dynamic nuclear polarization
International Nuclear Information System (INIS)
Davies, K.; Cox, S.F.J.
1978-01-01
The feasibility of monitoring dynamic nuclear polarization from the NMR dispersive susceptibility is examined. Two prototype instruments are tested in a polarized proton target using organic target material. The more promising employs a tunnel diode oscillator, inside the target cavity, and should provide a precise polarization measurement working at a frequency far enough from the main resonance for the disturbance of the measured polarization to be negligible. Other existing methods for measuring target polarization are briefly reviewed. (author)
19. Structure of high-resolution NMR spectra
CERN Document Server
Corio, PL
2012-01-01
Structure of High-Resolution NMR Spectra provides the principles, theories, and mathematical and physical concepts of high-resolution nuclear magnetic resonance spectra.The book presents the elementary theory of magnetic resonance; the quantum mechanical theory of angular momentum; the general theory of steady state spectra; and multiple quantum transitions, double resonance and spin echo experiments.Physicists, chemists, and researchers will find the book a valuable reference text.
20. NMR of 1,2-dioxiquinolines
International Nuclear Information System (INIS)
Figueroa Villar, Jose Daniel; Santos, N.L. dos
1993-01-01
Several derivates of quinoline are known for presenting pharmacological activity as antibiotics and anti-parasites, from which an important group are the antibiotics for the treatment of malaria and infections of the urinary tract. This work presents the structures and the NMR spectra of three new derivates of quinoline. These compounds are being tested as possible antibiotics for the treatment of urinary infections caused by Escherichia coli which are extremely resistant to other types of antibiotics
1. 31-P NMR spectroscopy in radiotherapy
International Nuclear Information System (INIS)
Kiricuta, I.C.; Schmitt, W.G.H.; Beyer, H.K.
1987-01-01
Results suggest 31-P NMR spectroscopy to allow a discrimination between good and bad blood supply to the tumour owing to different metabolic behaviour and to furnish important information on tumour response to radiotherapy just a few hours after the application of a relatively low dose. Spectroscopy showed the radiation-sensitive tumour cells to behave relatively uniformly after radiotherapy suggesting this behaviour to be interpreted as therapeutical effectiveness. (orig./SHA) [de
2. 3D Reconstruction of NMR Images
Directory of Open Access Journals (Sweden)
Peter Izak
2007-01-01
Full Text Available This paper introduces experiment of 3D reconstruction NMR images scanned from magnetic resonance device. There are described methods which can be used for 3D reconstruction magnetic resonance images in biomedical application. The main idea is based on marching cubes algorithm. For this task was chosen sophistication method by program Vision Assistant, which is a part of program LabVIEW.
3. Characterization of functional polymers by NMR
International Nuclear Information System (INIS)
Neto, Oscar H.S. A.S.; San Gil, Rosane A.S.; Nakayama, T.; Costa Neto, Claudio
1993-01-01
Several synthetic polymers are used in the chemical analysis of complexes mixtures aiming to extract certain specific functional groups for further identification. This work describes the utilization of NMR in the characterization of one of the above mentioned compounds which will be used as reagent for the synthesis of another compound of the same type, which will be further used in the chemical analysis of alcohols and phenols. The methodology is described. The results are described and discussed
4. NMR characteristics of rat mammary tumors
International Nuclear Information System (INIS)
Osbakken, M.; Kreider, J.; Taczanowsky, P.
1984-01-01
12 rats were injected intradermally with 13762A rat mammary adenocarcinoma (1 x 10/sup 6/ cells). 3 rats died before completion of the study and 2 rat had tumor regression; the first 3 were excluded from data analysis. NMR imaging with a 1.5K gauss resistive magnet at 2, 3, 4, and 5 weeks after injection demonstrated increasing tumor mass. Saturation recovery (SR), inversion recovery (IR), and spin echo (SE) pulse sequence images and T/sub 1/ calculation were done for tumor characterization. (Tumor size was too small to identify at 2 weeks.) 3 rats were sacrificed after the last 3 imaging periods for histological studies, done to distinguish solid tumor mass from necrosis. Planimetry of tumor areas showed that as tumors grew in size, the ratio of necrotic area to area of solid tumor increased (week 3 = .3 +- .11; week 4 = .45 +- .07; week 5 = .51 +- 05); simultaneous calculated T/sub 1/ values also increased (week 3 = .35 +- .15; week 4 = .45 +- .06; week 5 = .42 +- 03). Qualitative NMR image T/sub 1/ values also increased as evidenced by progression of SR and IR tumor image intensity from very bright compared to the rest of the body at week 3 to less intense than other structures at week 5. These findings indicate that change in T/sub 1/ may be secondary to the pathophysiological change in the tumor (the increasing in necrosis, associated with increased free water). Thus, the range of T/sub 1/ values obtained in tumors in this study (and in previous studies) may be due to change in tumor physiology and anatomy. Careful correlation of histological with NMR data may allow ultimate use of NMR relaxation characteristics for determination of the physiological state of tumors
5. The examination of cardiac metabolism of patients with hypercholesterolemia by phosphorus-31 magnetic resonance spectroscopy
International Nuclear Information System (INIS)
Martinek, M.
2001-07-01
Objectives: we decided to investigate weather alterations in high energy phosphates occur in the myocardium of persons with hypercholesterolemia. Background: myocardial high energy phosphates have been shown to be reduced in various diseases of the heart such as coronary artery disease, heart failure and dilated cardiomyopathy. The latest studies on hypercholesterolemia show direct effects of high serum cholesterol on heart muscle cells, so do studies on statins. Methods: in the present study 32 male patients (mean age 48) with hypercholesterolemia and 27 male healthy volunteers (mean age 44,5) as age matched controls were included. The patients were divided into a statin-treated (n = 17) and an untreated subgroup (n = 15). Using a 1,5 Tesla whole-body magnetic resonance scanner (Siemens, Germany) phosphor-31 magnetic resonance spectroscopic imaging (31P MRSI) of the heart was performed in all subjects. The 31P MRSI slab (slab thickness = 40 mm, field of view = 320 mm, matrix 32 x 32, TR = 323 ms, TE 3 ms) contained the left anterior ventricular wall (region of interest = 32 ml). The measurement was triggered on electrocardiography. The ratios of phosphocreatinine (PCr) to β-adenosine-triphosphate (β-ATP) were calculated. Results: the myocardium of untreated patients with hypercholesterolemia shows significantly decreased ratios of PCr/β-ATP compared with patients treated with statins (2,09 vs. 2,45). When comparing the untreated group with healthy persons there was a trend to significance for a difference of the groups (2,09 vs. 2,34). Conclusion: with this study we demonstrate the first time alterations of high energy phosphates in the myocardium of persons with hypercholesterolemia and the beneficial effects of statins on these parameters. (author)
6. Altered phospholipid metabolism in schizophrenia: a phosphorus 31 nuclear magnetic resonance spectroscopy study.
Science.gov (United States)
Weber-Fahr, Wolfgang; Englisch, Susanne; Esser, Andrea; Tunc-Skarka, Nuran; Meyer-Lindenberg, Andreas; Ende, Gabriele; Zink, Mathias
2013-12-30
Phospholipid (PL) metabolism is investigated by in vivo 31P magnetic resonance spectroscopy (MRS). Inconsistent alterations of phosphocholine (PC), phosphoethanolamine (PE), glycerophosphocholine (GPC) and glycerophosphoethanolamine (GPE) have been described in schizophrenia, which might be overcome by specific editing techniques. The selective refocused insensitive nuclei-enhanced polarization transfer (RINEPT) technique was applied in a cross-sectional study involving 11 schizophrenia spectrum disorder patients (SZP) on stable antipsychotic monotherapy and 15 matched control subjects. Metabolite signals were found to be modulated by cerebrospinal fluid (CSF) content and gray matter/brain matter ratio. Corrected metabolite concentrations of PC, GPC and PE differed between patients and controls in both subcortical and cortical regions, whereas antipsychotic medication exerted only small effects. Significant correlations were found between the severity of clinical symptoms and the assessed signals. In particular, psychotic symptoms correlated with PC levels in the cerebral cortex, depression with PC levels in the cerebellum and executive functioning with GPC in the insular and temporal cortices. In conclusion, after controlling for age and tissue composition, this investigation revealed alterations of metabolite levels in SZP and correlations with clinical properties. RINEPT 31P MRS should also be applied to at-risk-mental-state patients as well as drug-naïve and chronically treated schizophrenic patients in order to enhance the understanding of longitudinal alterations of PL metabolism in schizophrenia. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
7. 43Ca NMR in solid state
Science.gov (United States)
Bellot, P.-V.; Trokiner, A.; Zhdanov, Yu.; Yakubovskii, A.
1998-02-01
In this paper we show that 43Ca is a suitable NMR probe to study the properties of high-Tc superconducting oxides. In the normal state, we report the temperature and doping dependencies of the spin susceptibility measured by 43Ca NMR. In the superconducting state and more exactly in the mixed state, by analysing 43Ca NMR linewidth, we have studied the magnetic induction distribution due to the presence of vortices and deduced λ, the penetration depth. Dans cet article, on montre que l'isotope 43 du calcium est une bonne sonde RMN pour l'étude des propriétés des oxydes supraconducteurs à haute température. Dans l'état normal, par la détermination du déplacement de la raie, en fonction de la température, on accède à la variation thermique de la susceptibilité de spin. Dans l'état supraconducteur et plus particulièrement dans l'état mixte, la largeur de raie RMN permet d'étudier la distribution d'induction magnétique due à la présence des vortex et de déterminer λ, la longueur de pénétration.
8. Automatic maximum entropy spectral reconstruction in NMR
International Nuclear Information System (INIS)
Mobli, Mehdi; Maciejewski, Mark W.; Gryk, Michael R.; Hoch, Jeffrey C.
2007-01-01
Developments in superconducting magnets, cryogenic probes, isotope labeling strategies, and sophisticated pulse sequences together have enabled the application, in principle, of high-resolution NMR spectroscopy to biomolecular systems approaching 1 megadalton. In practice, however, conventional approaches to NMR that utilize the fast Fourier transform, which require data collected at uniform time intervals, result in prohibitively lengthy data collection times in order to achieve the full resolution afforded by high field magnets. A variety of approaches that involve nonuniform sampling have been proposed, each utilizing a non-Fourier method of spectrum analysis. A very general non-Fourier method that is capable of utilizing data collected using any of the proposed nonuniform sampling strategies is maximum entropy reconstruction. A limiting factor in the adoption of maximum entropy reconstruction in NMR has been the need to specify non-intuitive parameters. Here we describe a fully automated system for maximum entropy reconstruction that requires no user-specified parameters. A web-accessible script generator provides the user interface to the system
9. Phosphorus NMR of isolated perfused morris hepatomas
International Nuclear Information System (INIS)
Graham, R.A.; Meyer, R.A.; Brown, T.R.; Sauer, L.A.
1986-01-01
The authors are developing techniques for the study of perfused solid tumors by NMR. Tissue-isolated solid hepatomas were grown to 1-2 cm diameter as described previously. The arterial supply was isolated and the tumors perfused (0.5 - 1.0 ml/min) in vitro at 25 C with a 15% suspension of red blood cells in Krebs-Henseliet solution. 31 P-NMR spectra were acquired at 162 MHz in a specially-designed NMR probe using a solenoidal coil. Intracellular pH (monitored from the chemical shift of inorganic phosphate) and ATP levels were stable for up to 6 hrs during perfusion. During 30 min of global ischemia, ATP decreased by 75% and pH fell from 7.0 to 6.7. These changes were reversed by 1 hr reperfusion. In addition to ATP and phosphate, the spectra included a large resonance due to phosphomonoesters, as well as peaks consistent with glycerylphosphocholine, glyceryl-phosphoethanolamine, phosphocreatine, NAD, and UDPG. However, the most novel feature of the spectra was the presence of an unidentified peak in the phosphonate region (+ 16.9 ppm). The peak was not present in spectra of muscle, liver, brain, kidney, or fat tissues excised from the same animals. They are presently attempting to identify the compound that gives rise to this peak and to establish its metabolic origin
10. Solid state NMR study of cumbaru flour
International Nuclear Information System (INIS)
Nogueira, Jose S.; Bathista, Andre L.B.S.; Silva, Emerson O.; Priante Filho, Nicolau; Tavares, Maria I.B.
2001-01-01
The polysaccharide obtained by seed of Dipteryx alata Vog, has been characterised by 13 C solid state, using the basic routine techniques, like MAS and CPMAS and by the proton spin-lattice relaxation time in the rotating frame parameter (T 1 H ρ). Knowing that the chemical structure and molecular dynamic are extremely necessary route to obtain information on the polysaccharides, this work contributes to the classification of the seed containing in the cumbaru fruit to get response on its application. To obtain the initial responses for our purposes some solid state NMR techniques were chosen. The CPMAS 13 C NMR spectrum of the polysaccharide was investigated to know if it has some crystallinity. The MAS 13 C NMR spectrum showed the presence of domains with distinct molecular mobility, because these domains will differ basically in the distribution size and chain packing. The variable contact time experiment was used to analyse the distribution form of 13 C decays, which give us more information about sample heterogeneity. The T 1 H ρHr values were obtained from the variable contact time and by delayed contact time experiment, because these parameter indicate the order of polysaccharides. From the values of this parameter, we found that this polysaccharide is completely non-ordered. (author)
11. NMR measurement of bitumen at different temperatures.
Science.gov (United States)
Yang, Zheng; Hirasaki, George J
2008-06-01
Heavy oil (bitumen) is characterized by its high viscosity and density, which is a major obstacle to both well logging and recovery. Due to the lost information of T2 relaxation time shorter than echo spacing (TE) and interference of water signal, estimation of heavy oil properties from NMR T2 measurements is usually problematic. In this work, a new method has been developed to overcome the echo spacing restriction of NMR spectrometer during the application to heavy oil (bitumen). A FID measurement supplemented the start of CPMG. Constrained by its initial magnetization (M0) estimated from the FID and assuming log normal distribution for bitumen, the corrected T2 relaxation time of bitumen sample can be obtained from the interpretation of CPMG data. This new method successfully overcomes the TE restriction of the NMR spectrometer and is nearly independent on the TE applied in the measurement. This method was applied to the measurement at elevated temperatures (8-90 degrees C). Due to the significant signal-loss within the dead time of FID, the directly extrapolated M0 of bitumen at relatively lower temperatures (viscosity, the extrapolated M0 of bitumen at over 60 degrees C can be reasonably assumed to be the real value. In this manner, based on the extrapolation at higher temperatures (> or = 60 degrees C), the M0 value of bitumen at lower temperatures (index (HI), fluid content and viscosity were evaluated by using corrected T2.
12. Rhodopsin-lipid interactions studied by NMR.
Science.gov (United States)
Soubias, Olivier; Gawrisch, Klaus
2013-01-01
The biophysical properties of the lipid matrix are known to influence function of integral membrane proteins. We report on a sample preparation method for reconstitution of membrane proteins which uses porous anodic aluminum oxide (AAO) filters with 200-nm-wide pores of high density. The substrate permits formation of tubular, single membranes that line the inner surface of pores. One square centimeter of filter with a thickness of 60μm yields on the order of 500cm(2) of solid-supported single bilayer surface, sufficient for NMR studies. The tubular bilayers are free of detergent, fully hydrated, and accessible for ligands from one side of the membrane. The use of AAO filters greatly improves reproducibility of the reconstitution process such that the influence of protein on lipid order parameters can be studied with high resolution. As an example, results for the G protein-coupled receptor of class A, bovine rhodopsin, are shown. By (2)H NMR order parameter measurements, it is detected that rhodopsin insertion elastically deforms membranes near the protein. Furthermore, by (1)H saturation-transfer NMR under conditions of magic angle spinning, we demonstrate detection of preferences in interactions of rhodopsin with particular lipid species. It is assumed that function of integral membrane proteins depends on both protein-induced elastic deformations of the lipid matrix and preferences for interaction of the protein with particular lipid species in the first layer of lipids surrounding the protein. Copyright © 2013 Elsevier Inc. All rights reserved.
13. Principles of high resolution NMR in solids
CERN Document Server
Mehring, Michael
1983-01-01
The field of Nuclear Magnetic Resonance (NMR) has developed at a fascinating pace during the last decade. It always has been an extremely valuable tool to the organic chemist by supplying molecular "finger print" spectra at the atomic level. Unfortunately the high resolution achievable in liquid solutions could not be obtained in solids and physicists and physical chemists had to live with unresolved lines open to a wealth of curve fitting procedures and a vast amount of speculations. High resolution NMR in solids seemed to be a paradoxon. Broad structure less lines are usually encountered when dealing with NMR in solids. Only with the recent advent of mUltiple pulse, magic angle, cross-polarization, two-dimen sional and multiple-quantum spectroscopy and other techniques during the last decade it became possible to resolve finer details of nuclear spin interactions in solids. I have felt that graduate students, researchers and others beginning to get involved with these techniques needed a book which trea...
14. Nuclear magnetic resonance apparatus having semitoroidal RF coil for use in topical NMR and NMR imaging
International Nuclear Information System (INIS)
Fukushima, E.; Assink, R.A.; Roeder, S.B.W.; Gibson, A.A.V.
1984-01-01
An improved nuclear magnetic resonance (NMR) apparatus for use in topical magnetic resonance (TMR) spectroscopy and other remote sensing NMR applications includes a semitoroidal radio frequency (rf) coil. The semitoroidal rf coil produces an effective alternating magnetic field at a distance from the poles of the coil, to enable NMR measurements to be taken from selected regions inside an object, particularly human and other living subjects. The semitoroidal rf coil is relatively insensitive to magnetic interference from metallic objects located behind the coil, thereby rendering the coil particularly suited for use in both conventional and superconducting NMR magnets. The semitoroidal NMR coil can be constructed so that it emits little or no excess rf electric field associated with the rf magnetic field, thus avoiding adverse effects due to dielectric heating of the sample or to any other electric field interactions. The coil may be combined with a like orthogonal coil and suitably driven to provide a circularly polarised field; or it may be used in conjunction with a concentrically nested smaller semitoroidal coil to move the maximum field further from the coil assembly. (author)
15. CcpNmr AnalysisAssign: a flexible platform for integrated NMR analysis
Energy Technology Data Exchange (ETDEWEB)
Skinner, Simon P.; Fogh, Rasmus H. [University of Leicester, Department of Molecular and Cell Biology, Leicester Institute for Structural- and Chemical Biology (United Kingdom); Boucher, Wayne [University of Cambridge, Department of Biochemistry (United Kingdom); Ragan, Timothy J.; Mureddu, Luca G.; Vuister, Geerten W., E-mail: [email protected] [University of Leicester, Department of Molecular and Cell Biology, Leicester Institute for Structural- and Chemical Biology (United Kingdom)
2016-10-15
NMR spectroscopy is an indispensably powerful technique for the analysis of biomolecules under ambient conditions, both for structural- and functional studies. However, in practice the complexity of the technique has often frustrated its application by non-specialists. In this paper, we present CcpNmr version-3, the latest software release from the Collaborative Computational Project for NMR, for all aspects of NMR data analysis, including liquid- and solid-state NMR data. This software has been designed to be simple, functional and flexible, and aims to ensure that routine tasks can be performed in a straightforward manner. We have designed the software according to modern software engineering principles and leveraged the capabilities of modern graphics libraries to simplify a variety of data analysis tasks. We describe the process of backbone assignment as an example of the flexibility and simplicity of implementing workflows, as well as the toolkit used to create the necessary graphics for this workflow. The package can be downloaded from www.ccpn.ac.uk/v3-software/downloads http://www.ccpn.ac.uk/v3-software/downloads and is freely available to all non-profit organisations.
16. CcpNmr AnalysisAssign: a flexible platform for integrated NMR analysis
International Nuclear Information System (INIS)
Skinner, Simon P.; Fogh, Rasmus H.; Boucher, Wayne; Ragan, Timothy J.; Mureddu, Luca G.; Vuister, Geerten W.
2016-01-01
NMR spectroscopy is an indispensably powerful technique for the analysis of biomolecules under ambient conditions, both for structural- and functional studies. However, in practice the complexity of the technique has often frustrated its application by non-specialists. In this paper, we present CcpNmr version-3, the latest software release from the Collaborative Computational Project for NMR, for all aspects of NMR data analysis, including liquid- and solid-state NMR data. This software has been designed to be simple, functional and flexible, and aims to ensure that routine tasks can be performed in a straightforward manner. We have designed the software according to modern software engineering principles and leveraged the capabilities of modern graphics libraries to simplify a variety of data analysis tasks. We describe the process of backbone assignment as an example of the flexibility and simplicity of implementing workflows, as well as the toolkit used to create the necessary graphics for this workflow. The package can be downloaded from www.ccpn.ac.uk/v3-software/downloads http://www.ccpn.ac.uk/v3-software/downloads and is freely available to all non-profit organisations.
17. Guiding automated NMR structure determination using a global optimization metric, the NMR DP score
Energy Technology Data Exchange (ETDEWEB)
Huang, Yuanpeng Janet, E-mail: [email protected]; Mao, Binchen; Xu, Fei; Montelione, Gaetano T., E-mail: [email protected] [Rutgers, The State University of New Jersey, Department of Molecular Biology and Biochemistry, Center for Advanced Biotechnology and Medicine, and Northeast Structural Genomics Consortium (United States)
2015-08-15
ASDP is an automated NMR NOE assignment program. It uses a distinct bottom-up topology-constrained network anchoring approach for NOE interpretation, with 2D, 3D and/or 4D NOESY peak lists and resonance assignments as input, and generates unambiguous NOE constraints for iterative structure calculations. ASDP is designed to function interactively with various structure determination programs that use distance restraints to generate molecular models. In the CASD–NMR project, ASDP was tested and further developed using blinded NMR data, including resonance assignments, either raw or manually-curated (refined) NOESY peak list data, and in some cases {sup 15}N–{sup 1}H residual dipolar coupling data. In these blinded tests, in which the reference structure was not available until after structures were generated, the fully-automated ASDP program performed very well on all targets using both the raw and refined NOESY peak list data. Improvements of ASDP relative to its predecessor program for automated NOESY peak assignments, AutoStructure, were driven by challenges provided by these CASD–NMR data. These algorithmic improvements include (1) using a global metric of structural accuracy, the discriminating power score, for guiding model selection during the iterative NOE interpretation process, and (2) identifying incorrect NOESY cross peak assignments caused by errors in the NMR resonance assignment list. These improvements provide a more robust automated NOESY analysis program, ASDP, with the unique capability of being utilized with alternative structure generation and refinement programs including CYANA, CNS, and/or Rosetta.
18. Application of the Fenske-Hall molecular orbital method to the calculation of 11B NMR chemical shifts. Antipodal substituent effects in deltahedral clusters
International Nuclear Information System (INIS)
Fehlner, T.P.; Czech, P.T.; Fenske, R.F.
1990-01-01
Utilizing Fenske-Hall wave functions and eigenvalues combined with the Ramsey sum over states (SOS) approximation, it is demonstrated that the sign and magnitude of the paramagnetic contribution to the shielding correlates well with the observed 11 B chemical shifts of a substantial variety of boron- and metal-containing compounds. Analysis of the molecular orbital (MO) contributions in the SOS approximation leads to an explanation of the large downfield shifts associated with metal-rich metallaboranes. A similar analysis demonstrates the importance of selected cluster occupied and unoccupied MO's in explaining both exo-cage substituent effects in which the antipodal boron resonance is shifted upfield and endo-cage substituent effects (interchange of isolobal fragments within the cage framework) in which the antipodal boron resonance is shifted downfield. Exo- and endo-cage substitution perturbs these MO's in an understandable fashion, leading to an internally consistent explanation of the observed chemical shift changes. 36 refs., 8 figs., 4 tabs
19. Knowns and unknowns in metabolomics identified by multidimensional NMR and hybrid MS/NMR methods
Energy Technology Data Exchange (ETDEWEB)
Bingol, Kerem; Brüschweiler, Rafael
2017-02-01
Metabolomics continues to make rapid progress through the development of new and better methods and their applications to gain insight into the metabolism of a wide range of different biological systems from a systems biology perspective. Customization of NMR databases and search tools allows the faster and more accurate identification of known metabolites, whereas the identification of unknowns, without a need for extensive purification, requires new strategies to integrate NMR with mass spectrometry, cheminformatics, and computational methods. For some applications, the use of covalent and non-covalent attachments in the form of labeled tags or nanoparticles can significantly reduce the complexity of these tasks.
20. Direct Comparison of 19F qNMR and 1H qNMR by Characterizing Atorvastatin Calcium Content
Directory of Open Access Journals (Sweden)
Yang Liu
2016-01-01
Full Text Available Quantitative nuclear magnetic resonance (qNMR is a powerful tool in measuring drug content because of its high speed, sensitivity, and precision. Most of the reports were based on proton qNMR (1H qNMR and only a few fluorine qNMR (19F qNMR were reported. No research has been conducted to directly compare the advantage and disadvantage between these two methods. In the present study, both 19F and 1H qNMR were performed to characterize the content of atorvastatin calcium with the same internal standard. Linearity, precision, and results from two methods were compared. Results showed that 19F qNMR has similar precision and sensitivity to 1H qNMR. Both methods generate similar results compared to mass balance method. Major advantage from 19F qNMR is that the analyte signal is with less or no interference from impurities. 19F qNMR is an excellent approach to quantify fluorine-containing analytes.
1. Isotope labeling for NMR studies of macromolecular structure and interactions
International Nuclear Information System (INIS)
Wright, P.E.
1994-01-01
Implementation of biosynthetic methods for uniform or specific isotope labeling of proteins, coupled with the recent development of powerful heteronuclear multidimensional NMR methods, has led to a dramatic increase in the size and complexity of macromolecular systems that are now amenable to NMR structural analysis. In recent years, a new technology has emerged that combines uniform 13 C, 15 N labeling with heteronuclear multidimensional NMR methods to allow NMR structural studies of systems approaching 25 to 30 kDa in molecular weight. In addition, with the introduction of specific 13 C and 15 N labels into ligands, meaningful NMR studies of complexes of even higher molecular weight have become feasible. These advances usher in a new era in which the earlier, rather stringent molecular weight limitations have been greatly surpassed and NMR can begin to address many central biological problems that involve macromolecular structure, dynamics, and interactions
2. 13C-NMR assignment, structure, and dynamics of deoxyoligonucleotides
International Nuclear Information System (INIS)
Zanatta, N.; Borer, P.N.; Levy, G.C.
1986-01-01
The unique spectral properties of 13 C-NMR for studying nucleic acids and some of the important features of 13 C-NMR in oligonucleotide studies are demostrated. The main difficulty in studying oligonucleotides by 13 C-NMR and recent improvements in NMR instrumentation and advances in oligonucleotide synthesis are presented. The high resolution 13 C-NMR spectra, T 1 relaxation times and NOEs were measured for duplex of the self-complementary oligo-DNAs: d(CG) 3 and d(GGTATACC) are studied. The target of this study is to developed a systematic 13 C-NMR spectral assignment and to investigate the structure and dynamics of these two sequences by this techniques. (M.J.C.) [pt
3. A primer to nutritional metabolomics by NMR spectroscopy and chemometrics
DEFF Research Database (Denmark)
Savorani, Francesco; Rasmussen, Morten Arendt; Mikkelsen, Mette Skau
2013-01-01
This paper outlines the advantages and disadvantages of using high throughput NMR metabolomics for nutritional studies with emphasis on the workflow and data analytical methods for generation of new knowledge. The paper describes one-by-one the major research activities in the interdisciplinary...... metabolomics platform and highlights the opportunities that NMR spectra can provide in future nutrition studies. Three areas are emphasized: (1) NMR as an unbiased and non-destructive platform for providing an overview of the metabolome under investigation, (2) NMR for providing versatile information and data...... structures for multivariate pattern recognition methods and (3) NMR for providing a unique fingerprint of the lipoprotein status of the subject. For the first time in history, by combining NMR spectroscopy and chemometrics we are able to perform inductive nutritional research as a complement to the deductive...
4. Isotope labeling for NMR studies of macromolecular structure and interactions
Energy Technology Data Exchange (ETDEWEB)
Wright, P.E. [Scripps Research Institute, La Jolla, CA (United States)
1994-12-01
Implementation of biosynthetic methods for uniform or specific isotope labeling of proteins, coupled with the recent development of powerful heteronuclear multidimensional NMR methods, has led to a dramatic increase in the size and complexity of macromolecular systems that are now amenable to NMR structural analysis. In recent years, a new technology has emerged that combines uniform {sup 13}C, {sup 15}N labeling with heteronuclear multidimensional NMR methods to allow NMR structural studies of systems approaching 25 to 30 kDa in molecular weight. In addition, with the introduction of specific {sup 13}C and {sup 15}N labels into ligands, meaningful NMR studies of complexes of even higher molecular weight have become feasible. These advances usher in a new era in which the earlier, rather stringent molecular weight limitations have been greatly surpassed and NMR can begin to address many central biological problems that involve macromolecular structure, dynamics, and interactions.
5. NMR examinations of the facial skeleton. Pt. 1
International Nuclear Information System (INIS)
Grodd, W.; Lenz, M.; Baumann, R.; Schroth, G.
1984-01-01
The resolution of NMR and CT was compared using axial sections of the normal anatomic structures of the facial skeleton. Is was shown that NMR was superior in differentiating muscles, tonsils, mucosa, lymph nodes and blood vessels. The demonstration of bone and its differentiation from air-containing spaces is often difficult. Metallic, non-ferromagnetic dental fillings, which cause serious artefacts on CT, do not after NMR. (orig.) [de
6. NMR as a probe metabolic disorders in disease and treatment
Energy Technology Data Exchange (ETDEWEB)
Yushmanov, Victor E [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Chemical Physics
1994-12-31
The effects of malignant tumors, chemical and physical factors (toxic agents, ionizing radiation) as well as of their treatment on tissue metabolism were studied by NMR imaging. The importance of NMR is highlighted since it enables to a better understanding of molecular mechanisms of diseases and therapeutic interventions, in addition to the analysis of metabolic disorders in human beings. Combined with the studies of experimental animal pathologies, may constitute a base for new types of NMR-diagnosis in vivo 10 refs.
7. Fluid-Rock Characterization and Interactions in NMR Well Logging
Energy Technology Data Exchange (ETDEWEB)
Hirasaki, George J.; Mohanty, Kishore K.
2003-02-10
The objective of this project was to characterize the fluid properties and fluid-rock interactions that are needed for formation evaluation by NMR well logging. The advances made in the understanding of NMR fluid properties are summarized in a chapter written for an AAPG book on NMR well logging. This includes live oils, viscous oils, natural gas mixtures, and the relation between relaxation time and diffusivity.
8. NMR-Fragment Based Virtual Screening: A Brief Overview.
Science.gov (United States)
Singh, Meenakshi; Tam, Benjamin; Akabayov, Barak
2018-01-25
Fragment-based drug discovery (FBDD) using NMR has become a central approach over the last twenty years for development of small molecule inhibitors against biological macromolecules, to control a variety of cellular processes. Yet, several considerations should be taken into account for obtaining a therapeutically relevant agent. In this review, we aim to list the considerations that make NMR fragment screening a successful process for yielding potent inhibitors. Factors that may govern the competence of NMR in fragment based drug discovery are discussed, as well as later steps that involve optimization of hits obtained by NMR-FBDD.
9. Optimization and practical implementation of ultrafast 2D NMR experiments
Energy Technology Data Exchange (ETDEWEB)
Queiroz Junior, Luiz H. K., E-mail: [email protected] [Universidade Federal de Sao Carlos (UFSC), SP (Brazil). Departamento de Quimica; Universidade Federal de Goias (UFGO), Goiania, GO (Brazil). Inst. de Quimica; Ferreira, Antonio G. [Universidade Federal de Sao Carlos (UFSC), SP (Brazil). Departamento de Quimica; Giraudeau, Patrick [Universite de Nantes (France). CNRS, Chimie et Interdisciplinarite: Synthese, Analyse, Modelisation
2013-09-01
Ultrafast 2D NMR is a powerful methodology that allows recording of a 2D NMR spectrum in a fraction of second. However, due to the numerous non-conventional parameters involved in this methodology its implementation is no trivial task. Here, an optimized experimental protocol is carefully described to ensure efficient implementation of ultrafast NMR. The ultrafast spectra resulting from this implementation are presented based on the example of two widely used 2D NMR experiments, COSY and HSQC, obtained in 0.2 s and 41 s, respectively. (author)
10. Straightforward and complete deposition of NMR data to the PDBe
International Nuclear Information System (INIS)
Penkett, Christopher J.; Ginkel, Glen van; Velankar, Sameer; Swaminathan, Jawahar; Ulrich, Eldon L.; Mading, Steve; Stevens, Tim J.; Fogh, Rasmus H.; Gutmanas, Aleksandras; Kleywegt, Gerard J.; Henrick, Kim; Vranken, Wim F.
2010-01-01
We present a suite of software for the complete and easy deposition of NMR data to the PDB and BMRB. This suite uses the CCPN framework and introduces a freely downloadable, graphical desktop application called CcpNmr Entry Completion Interface (ECI) for the secure editing of experimental information and associated datasets through the lifetime of an NMR project. CCPN projects can be created within the CcpNmr Analysis software or by importing existing NMR data files using the CcpNmr FormatConverter. After further data entry and checking with the ECI, the project can then be rapidly deposited to the PDBe using AutoDep, or exported as a complete deposition NMR-STAR file. In full CCPN projects created with ECI, it is straightforward to select chemical shift lists, restraint data sets, structural ensembles and all relevant associated experimental collection details, which all are or will become mandatory when depositing to the PDB. Instructions and download information for the ECI are available from the PDBe web site at http://www.ebi.ac.uk/pdbe/nmr/deposition/eci.htmlhttp://www.ebi.ac.uk/pdbe/nmr/deposition/eci.html.
11. NMR-Fragment Based Virtual Screening: A Brief Overview
Directory of Open Access Journals (Sweden)
Meenakshi Singh
2018-01-01
Full Text Available Fragment-based drug discovery (FBDD using NMR has become a central approach over the last twenty years for development of small molecule inhibitors against biological macromolecules, to control a variety of cellular processes. Yet, several considerations should be taken into account for obtaining a therapeutically relevant agent. In this review, we aim to list the considerations that make NMR fragment screening a successful process for yielding potent inhibitors. Factors that may govern the competence of NMR in fragment based drug discovery are discussed, as well as later steps that involve optimization of hits obtained by NMR-FBDD.
12. NMR characteristics of low-grade glioma. Comparison with CT
Energy Technology Data Exchange (ETDEWEB)
Asato, Reinin; Tokuriki, Yasuhiko; Nakano, Yoshihisa; Itoh, Harumi; Torizuka, Kanji; Ueda, Tohru; Yamashita, Junkoh; Handa, Hajime
1985-08-01
Sixteen low-grade gliomas were evaluated both with nuclear magnetic resonance (NMR) imaging and with computed tomography (CT). In 13 cases (81%), the NMR images were much better in tissue contrast than the contrast-enhanced CT images. The tumors were shown as well-circumscribed oval lesions in the NMR, though they appeared as ill-defined, irregular, low-attenuation areas in the CT. The extent of the lesion, which was supposed to represent the active tumor tissue, was greater in the NMR than in the CT, because NMR tissue parameters (T/sub 1/, T/sub 2/) are more sensitive to pathological changes in brain tissue than is the X-ray attenuation coefficient. Though, in an optic glioma and a brain-stem astrocytoma, the CT with contrast enhancement displayed the contour of the mass as well as did NMR, it was inferior to the NMR in showing the cephalocaudal extension of the tumors. Calcification does not give a proton NMR signal under the present measuring conditions; thus the calcified cystic wall of a hypothalamic astrocytoma was displayed only in the CT images. In conclusion, the NMR imaging was apparently superior to contrast-enhanced CT in demonstrating the lesions due to low-grade glioma.
13. NMR studies of spin dynamics in cuprates
International Nuclear Information System (INIS)
Takigawa, M.; Mitzi, D.B.
1994-01-01
The authors report recent NMR results in cuprates. The oxygen Knight shift and the Cu nuclear spin-lattice relaxation rate in Bi 2.1 Sr 1.94 Ca 0.88 Cu 2.07 O 8+σ single crystals revealed a gapless superconducting state, which can be most naturally explained by a d-wave pairing state and the intrinsic disorder in this material. The Cu nuclear spin-spin relaxation rate in underdoped YBa 2 Cu 3 O 6.63 shows distinct temperature dependence from the spin-lattice relaxation rate, providing direct evidence for a pseudo spin-gap near the antiferromagnetic wave vector
14. NMR studies of spin dynamics in cuprates
Science.gov (United States)
Takigawa, M.; Mitzi, D. B.
1994-04-01
We report recent NMR results in cuprates. The oxygen Knight shift and the Cu nuclear spin-lattice relaxation rate in Bi2.1Sr1.94Ca0.88Cu2.07O8+δ single crystals revealed a gapless superconducting state, which can be most naturally explained by a d-wave pairing state and the intrinsic disorder in this material. The Cu nuclear spin-spin relaxation rate in underdoped YBa2Cu3O6.63 shows distinct temperature dependence from the spin-lattice relaxation rate, providing direct evidence for a pseudo spin-gap near the antiferromagnetic wave vector.
15. NMR-tomography of the heart
International Nuclear Information System (INIS)
Weikl, A.; Bachmann, K.
1987-01-01
The NMR-tomography as a non-invasive imaging process is examined regarding to the value to answer clinical issues. This method allows an evaluation of qualitative, quantitative, morphological and functional parameters. The diagnostic use on the heart shows early myocardial changes, thrombosis, changes in the dynamics of the left ventricle (EDV, ESV, EF), the quantitative wall movement and the blood flow in a shunt defect. The placed value of echocardiography, myocardial scintigraphy and coronary angiography in the diagnosis of acquired valvular heart disease, myocardial perfusion and coronary heart disease is not lowered by the above mentioned method. (orig.) [de
16. NMR-tomography of the heart
Energy Technology Data Exchange (ETDEWEB)
Weikl, A.; Bachmann, K.
1987-04-03
The NMR-tomography as a non-invasive imaging process is examined regarding to the value to answer clinical issues. This method allows an evaluation of qualitative, quantitative, morphological and functional parameters. The diagnostic use on the heart shows early myocardial changes, thrombosis, changes in the dynamics of the left ventricle (EDV, ESV, EF), the quantitative wall movement and the blood flow in a shunt defect. The placed value of echocardiography, myocardial scintigraphy and coronary angiography in the diagnosis of acquired valvular heart disease, myocardial perfusion and coronary heart disease is not lowered by the above mentioned method.
17. Structural study of pyrones by NMR
International Nuclear Information System (INIS)
Mandarino, D.G.
1985-01-01
Extracts of two species of Aniba, designed Aniba-SA (light petroleum extract) and Aniba-SB (benzene extract), afforded by chromatographic fraccionation some compounds. The isolated compounds were identified using spectrometric data and C 13 -NMR coupled and decompled spectra of pyrones were registered. Measurement of the heteronuclear residual coupling by irradiation proton frequency off-resonance was used for distinguish C-5, C-7 and C-8 carbons of the pyrones SB-1, SB-3, SB-4 and SB-5. (M.J.C.) [pt
18. Touch NMR: An NMR Data Processing Application for the iPad
Science.gov (United States)
Li, Qiyue; Chen, Zhiwei; Yan, Zhiping; Wang, Cheng; Chen, Zhong
2014-01-01
Nuclear magnetic resonance (NMR) spectroscopy has become one of the most powerful technologies to aid research in numerous scientific disciplines. With the development of consumer electronics, mobile devices have played increasingly important roles in our daily life. However, there is currently no application available for mobile devices able to…
19. Extracting protein dynamics information from overlapped NMR signals using relaxation dispersion difference NMR spectroscopy.
Science.gov (United States)
Konuma, Tsuyoshi; Harada, Erisa; Sugase, Kenji
2015-12-01
Protein dynamics plays important roles in many biological events, such as ligand binding and enzyme reactions. NMR is mostly used for investigating such protein dynamics in a site-specific manner. Recently, NMR has been actively applied to large proteins and intrinsically disordered proteins, which are attractive research targets. However, signal overlap, which is often observed for such proteins, hampers accurate analysis of NMR data. In this study, we have developed a new methodology called relaxation dispersion difference that can extract conformational exchange parameters from overlapped NMR signals measured using relaxation dispersion spectroscopy. In relaxation dispersion measurements, the signal intensities of fluctuating residues vary according to the Carr-Purcell-Meiboon-Gill pulsing interval, whereas those of non-fluctuating residues are constant. Therefore, subtraction of each relaxation dispersion spectrum from that with the highest signal intensities, measured at the shortest pulsing interval, leaves only the signals of the fluctuating residues. This is the principle of the relaxation dispersion difference method. This new method enabled us to extract exchange parameters from overlapped signals of heme oxygenase-1, which is a relatively large protein. The results indicate that the structural flexibility of a kink in the heme-binding site is important for efficient heme binding. Relaxation dispersion difference requires neither selectively labeled samples nor modification of pulse programs; thus it will have wide applications in protein dynamics analysis.
20. Extracting protein dynamics information from overlapped NMR signals using relaxation dispersion difference NMR spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Konuma, Tsuyoshi [Icahn School of Medicine at Mount Sinai, Department of Structural and Chemical Biology (United States); Harada, Erisa [Suntory Foundation for Life Sciences, Bioorganic Research Institute (Japan); Sugase, Kenji, E-mail: [email protected], E-mail: [email protected] [Kyoto University, Department of Molecular Engineering, Graduate School of Engineering (Japan)
2015-12-15
Protein dynamics plays important roles in many biological events, such as ligand binding and enzyme reactions. NMR is mostly used for investigating such protein dynamics in a site-specific manner. Recently, NMR has been actively applied to large proteins and intrinsically disordered proteins, which are attractive research targets. However, signal overlap, which is often observed for such proteins, hampers accurate analysis of NMR data. In this study, we have developed a new methodology called relaxation dispersion difference that can extract conformational exchange parameters from overlapped NMR signals measured using relaxation dispersion spectroscopy. In relaxation dispersion measurements, the signal intensities of fluctuating residues vary according to the Carr-Purcell-Meiboon-Gill pulsing interval, whereas those of non-fluctuating residues are constant. Therefore, subtraction of each relaxation dispersion spectrum from that with the highest signal intensities, measured at the shortest pulsing interval, leaves only the signals of the fluctuating residues. This is the principle of the relaxation dispersion difference method. This new method enabled us to extract exchange parameters from overlapped signals of heme oxygenase-1, which is a relatively large protein. The results indicate that the structural flexibility of a kink in the heme-binding site is important for efficient heme binding. Relaxation dispersion difference requires neither selectively labeled samples nor modification of pulse programs; thus it will have wide applications in protein dynamics analysis.
1. Proton NMR studies on Megaphaera elsdenii flavodoxin : structure elucidation by 2D-NMR and implications
NARCIS (Netherlands)
Mierlo, van C.
1990-01-01
1H NMR techniques have been applied for a thorough study of the uncrystallizable Megasphaera elsdenii flavodoxin in its three redox states. The aim of the research project described in this thesis was to obtain answers regarding questions
2. Crystallographic and dynamic aspects of solid-state NMR calibration compounds: towards ab initio NMR crystallography
DEFF Research Database (Denmark)
Li, Xiaozhou; Tapmeyer, Lukas; Bolte, Michael
2016-01-01
The excellent results of dispersion-corrected density functional theory (DFT-D) calculations for static systems have been well established over the past decade. The introduction of dynamics into DFT-D calculations is a target, especially for the field of molecular NMR crystallography. Four 13C ss...
3. In vivo NMR spectroscopy of ripening avocado
International Nuclear Information System (INIS)
Bennett, A.B.; Smith, G.M.; Nichols, B.
1987-01-01
Ripening of avocado fruit is associated with a dramatic increase in respiration. Previous studies have indicated that the increase in respiration is brought about by activation of the glycolytic reaction catalyzing the conversion of fructose-6-phosphate to fructose 1,6-bisphosphate. The authors reinvestigated the proposed role of glycolytic regulation in the respiratory increase using in vivo 31 P nuclear magnetic resonance (NMR) spectroscopy using an external surface coil and analysis of phosphofructokinase (PFK), phosphofructophosphotransferase (PFP), and fructose 2,6-bisphosphate (fru 2,6-P 2 ) levels in ripening avocado fruit. In vivo 31 P NMR spectroscopy revealed large increases in ATP levels accompanying the increase in respiration. Both glycolytic enzymes, PFK and PFP, were present in avocado fruit, with the latter activity being highly stimulated by fru 2,6-P 2 . Fructose 2,6-bisphosphate levels increased approximately 90% at the onset of ripening, indicating that the respiratory increase in ripening avocado may be regulated by the activation of PFP brought about by an increase in fru 2,6-P 2
4. The D0 solenoid NMR magnetometer
International Nuclear Information System (INIS)
Sten Uldall Hansen; Terry Kiper; Tom Regan; John Lofgren
2002-01-01
A field monitoring system for the 2 Tesla Solenoid of the D0 detector is described. It is comprised of a very small NMR probe cabled to a DSP based signal processing board. The design magnetic field range is from 1.0 to 2.2 Tesla, corresponding to an RF frequency range of 42.57 to 93.67 MHz. The desired an accuracy is one part in 10 5 . To minimize material in the interaction region of the D0 detector, the overall thickness of the NMR probe is 4 mm, including its mounting plate, and its width is 10 mm. To minimize cable mass, 4mm diameter IMR-100A cables are used for transmitting the RF signals from a nearby patch panel 25 meters to each of four probes mounted within the bore of the solenoid. RG213U cables 45 meters long are used to send the RF from the movable counting house to the patch panel. With this setup, the detector signal voltage at the moving counting room is in the range of 250-400 mV
5. System of liquid thermostatic control for jet experiments on NMR
International Nuclear Information System (INIS)
Selivanov, S.I.; Bogatkin, R.A.; Ershov, B.A.
1983-01-01
The system of liquid thermostating of a sensor of NMR spectrometer, used as a registering device in the method of continuous and interrupting stream, is described. Such method of thermostating permits to make kinetic measurements in the temperature range from -40 to +60 deg C with the accuracy +-0.1 deg C and removes the necessity for applying secondary temperature NMR standards
6. NMR-Metabolic Methodology in the Study of GM Foods
Science.gov (United States)
The 1H NMR methodology used in the study of genetically modified (GM) foodstuff is discussed. The study of transgenic lettuce (Lactuca sativa cv "Luxor") over-expressing the KNAT1 gene from Arabidopsis is presented as a novel study-case. The 1H NMR metabolic profiling was carried out. Twenty-two wat...
7. Rapid prediction of multi-dimensional NMR data sets
International Nuclear Information System (INIS)
Gradmann, Sabine; Ader, Christian; Heinrich, Ines; Nand, Deepak; Dittmann, Marc; Cukkemane, Abhishek; Dijk, Marc van; Bonvin, Alexandre M. J. J.; Engelhard, Martin; Baldus, Marc
2012-01-01
We present a computational environment for Fast Analysis of multidimensional NMR DAta Sets (FANDAS) that allows assembling multidimensional data sets from a variety of input parameters and facilitates comparing and modifying such “in silico” data sets during the various stages of the NMR data analysis. The input parameters can vary from (partial) NMR assignments directly obtained from experiments to values retrieved from in silico prediction programs. The resulting predicted data sets enable a rapid evaluation of sample labeling in light of spectral resolution and structural content, using standard NMR software such as Sparky. In addition, direct comparison to experimental data sets can be used to validate NMR assignments, distinguish different molecular components, refine structural models or other parameters derived from NMR data. The method is demonstrated in the context of solid-state NMR data obtained for the cyclic nucleotide binding domain of a bacterial cyclic nucleotide-gated channel and on membrane-embedded sensory rhodopsin II. FANDAS is freely available as web portal under WeNMR (http://www.wenmr.eu/services/FANDAShttp://www.wenmr.eu/services/FANDAS).
8. Two-dimensional NMR spectroscopy. Applications for chemists and biochemists
International Nuclear Information System (INIS)
Croasmun, W.R.; Carlson, R.M.K.
1987-01-01
Two-dimensional nuclear magnetic resonance spectroscopy (2-D NMR) has become a very powerful class of experiments (in the hands of an adept scientist) with broad adaptability to new situations. It is the product of a happy marriage between modern pulse FT-NMR technology, with its large memory and high-speed computers, and the physicists and chemists who love to manipulate spin systems. Basic 2-D experiments are now a standard capability of modern NMR spectrometers, and this timely book intends to make 2-D NMR users of those who are familiar with normal 1-D NMR. The 2-D NMR goal is correlation of the lines of the observed NMR spectrum with other properties of the system. This book deals with applications to high-resolution spectrum analysis, utilizing either coupling between the NMR-active nuclei or chemical exchange to perform the correlation. The coupling can be scalar (through bonds) or direct through space (within 5 A). The coupling may be homonuclear (between like nuclei) or heteronuclear
9. Rapid prediction of multi-dimensional NMR data sets
Energy Technology Data Exchange (ETDEWEB)
Gradmann, Sabine; Ader, Christian [Utrecht University, Faculty of Science, Bijvoet Center for Biomolecular Research (Netherlands); Heinrich, Ines [Max Planck Institute for Molecular Physiology, Department of Physical Biochemistry (Germany); Nand, Deepak [Utrecht University, Faculty of Science, Bijvoet Center for Biomolecular Research (Netherlands); Dittmann, Marc [Max Planck Institute for Molecular Physiology, Department of Physical Biochemistry (Germany); Cukkemane, Abhishek; Dijk, Marc van; Bonvin, Alexandre M. J. J. [Utrecht University, Faculty of Science, Bijvoet Center for Biomolecular Research (Netherlands); Engelhard, Martin [Max Planck Institute for Molecular Physiology, Department of Physical Biochemistry (Germany); Baldus, Marc, E-mail: [email protected] [Utrecht University, Faculty of Science, Bijvoet Center for Biomolecular Research (Netherlands)
2012-12-15
We present a computational environment for Fast Analysis of multidimensional NMR DAta Sets (FANDAS) that allows assembling multidimensional data sets from a variety of input parameters and facilitates comparing and modifying such 'in silico' data sets during the various stages of the NMR data analysis. The input parameters can vary from (partial) NMR assignments directly obtained from experiments to values retrieved from in silico prediction programs. The resulting predicted data sets enable a rapid evaluation of sample labeling in light of spectral resolution and structural content, using standard NMR software such as Sparky. In addition, direct comparison to experimental data sets can be used to validate NMR assignments, distinguish different molecular components, refine structural models or other parameters derived from NMR data. The method is demonstrated in the context of solid-state NMR data obtained for the cyclic nucleotide binding domain of a bacterial cyclic nucleotide-gated channel and on membrane-embedded sensory rhodopsin II. FANDAS is freely available as web portal under WeNMR (http://www.wenmr.eu/services/FANDAShttp://www.wenmr.eu/services/FANDAS).
10. Improved Baseline in 29Si NMR Spectra of Water Glasses
Czech Academy of Sciences Publication Activity Database
Schraml, Jan; Sandor, P.; Korec, S.; Krump, M.; Foller, B.
2013-01-01
Roč. 51, č. 7 (2013), s. 403-406 ISSN 0749-1581 Grant - others:GA MPO(CZ) FR-TI1/335; GA MŠk(CZ) LM2011020 Institutional support: RVO:67985858 Keywords : NMR * 29Si NMR * acoustic ringing Subject RIV: JI - Composite Materials Impact factor: 1.559, year: 2013
11. Fluid-Rock Characterization and Interactions in NMR Well Logging
Energy Technology Data Exchange (ETDEWEB)
George J. Hirasaki; Kishore K. Mohanty
2005-09-05
The objective of this report is to characterize the fluid properties and fluid-rock interactions that are needed for formation evaluation by NMR well logging. The advances made in the understanding of NMR fluid properties are summarized in a chapter written for an AAPG book on NMR well logging. This includes live oils, viscous oils, natural gas mixtures, and the relation between relaxation time and diffusivity. Oil based drilling fluids can have an adverse effect on NMR well logging if it alters the wettability of the formation. The effect of various surfactants on wettability and surface relaxivity are evaluated for silica sand. The relation between the relaxation time and diffusivity distinguishes the response of brine, oil, and gas in a NMR well log. A new NMR pulse sequence in the presence of a field gradient and a new inversion technique enables the T{sub 2} and diffusivity distributions to be displayed as a two-dimensional map. The objectives of pore morphology and rock characterization are to identify vug connectivity by using X-ray CT scan, and to improve NMR permeability correlation. Improved estimation of permeability from NMR response is possible by using estimated tortuosity as a parameter to interpolate between two existing permeability models.
12. Solution NMR Spectroscopy in Target-Based Drug Discovery.
Science.gov (United States)
Li, Yan; Kang, Congbao
2017-08-23
Solution NMR spectroscopy is a powerful tool to study protein structures and dynamics under physiological conditions. This technique is particularly useful in target-based drug discovery projects as it provides protein-ligand binding information in solution. Accumulated studies have shown that NMR will play more and more important roles in multiple steps of the drug discovery process. In a fragment-based drug discovery process, ligand-observed and protein-observed NMR spectroscopy can be applied to screen fragments with low binding affinities. The screened fragments can be further optimized into drug-like molecules. In combination with other biophysical techniques, NMR will guide structure-based drug discovery. In this review, we describe the possible roles of NMR spectroscopy in drug discovery. We also illustrate the challenges encountered in the drug discovery process. We include several examples demonstrating the roles of NMR in target-based drug discoveries such as hit identification, ranking ligand binding affinities, and mapping the ligand binding site. We also speculate the possible roles of NMR in target engagement based on recent processes in in-cell NMR spectroscopy.
13. SPE-NMR metabolite sub-profiling of urine
NARCIS (Netherlands)
Jacobs, D.M.; Spiesser, L.; Garnier, M.; Roo, de N.; Dorsten, van F.; Hollebrands, B.; Velzen, van E.; Draijer, R.; Duynhoven, van J.P.M.
2012-01-01
NMR-based metabolite profiling of urine is a fast and reproducible method for detection of numerous metabolites with diverse chemical properties. However, signal overlap in the (1)H NMR profiles of human urine may hamper quantification and identification of metabolites. Therefore, a new method has
14. Crystallographically-based analysis of the NMR spectra of maghemite
International Nuclear Information System (INIS)
Spiers, K.M.; Cashion, J.D.
2012-01-01
All possible iron environments with respect to nearest neighbour vacancies in vacancy-ordered and vacancy-disordered maghemite have been evaluated and used as the foundation for a crystallographically-based analysis of the published NMR spectra of maghemite. The spectral components have been assigned to particular configurations and excellent agreement obtained in comparing predicted spectra with published spectra taken in applied magnetic fields. The broadness of the published NMR lines has been explained by calculations of the magnetic dipole fields at the various iron sites and consideration of the supertransferred hyperfine fields. - Highlights: ► Analysis of 57 Fe NMR of maghemite based on vacancy ordering and nearest neighbour vacancies. ► Assignment of NMR spectral components based on crystallographic analysis of unique iron sites. ► Strong agreement between predicted spectra and published spectra taken in applied magnetic fields. ► Maghemite NMR spectral broadening due to various iron sites and supertransferred hyperfine field.
15. NMR and the surgery of tumours at the craniocervical junction
International Nuclear Information System (INIS)
Ahyai, A.; Matsumara, A.; Rittmeyer, K.
1987-01-01
The diagnosis of tumors in the posterior fossa and at the craniocervical junction has always been problematic. In this region of the brain a clear visualization of the exact extent and relations of a space-occupying lesion is indispensable in assessing whether it is operable. Even though a tumor with its perifocal edema can be detected by CT, NMR opens new perspectives for the neurosurgeon. The authors present these cases in 3 groups. Group 1 comprises patients for whom NMR results contra-indicated operation. Group II consists of patients who would probably not have been operated on prior to the use of NMR. Group III includes patients who would probably not have been operated on prior to the use of NMR (e.g arachnoid cysts, Dandy-Walker malformations, etc); the excellent multi-dimensional imaging by NMR rendered the advisability of operation questionable, so that improved diagnostics may have spared the patients unnecessary operations
16. $\\beta$-NMR of copper isotopes in ionic liquids
CERN Multimedia
We propose to test the feasibility of spin-polarization and $\\beta$-NMR studies on several short-lived copper isotopes, $^{58}$ Cu, $^{74}$Cu and $^{75}$Cu in crystals and liquids. The motivation is given by biological studies of Cu with $\\beta$-NMR in liquid samples, since Cu is present in a large number of enzymes involved in electron transfer and activation of oxygen. The technique is based on spin-polarization via optical pumping in the new VITO beamline. We will use the existing lasers, NMR magnet and NMR chambers and we will prepare a new optical pumping system. The studies will be devoted to tests of achieved $\\beta$-asymmetry in solid hosts, the behaviour of asymmetry when increasing vacuum, and finally NMR scans in ionic liquids. The achieved spin polarization will be also relevant for the plans to measure with high precision the magnetic moments of neutron-rich Cu isotopes.
17. Dynamics of solutions and fluid mixtures by NMR
International Nuclear Information System (INIS)
Delpuech, J.J.
1994-01-01
After a short introduction to NMR spectroscopy, with a special emphasis on dynamical aspects, an overview on two fundamental aspects of molecular dynamics, NMR relaxation and its relationship with molecular reorientation, and magnetization transfer phenomena induced by molecular rate processes (dynamic NMR) is presented, followed by specific mechanisms of relaxation encountered in paramagnetic systems or with quadrupolar nuclei. Application fields are then reviewed: solvent exchange on metal ions with a variable pressure NMR approach, applications of field gradients in NMR, aggregation phenomena and micro-heterogeneity in surfactant solutions, polymers and biopolymers in the liquid state, liquid-like molecules in rigid matrices and in soft matter (swollen polymers and gels, fluids in and on inorganic materials, food)
18. Value of NMR logging for heavy oil characterization
Energy Technology Data Exchange (ETDEWEB)
Chen, S.; Chen, J.; Georgi, D. [Baker Hughes, Calgary, AB (Canada); Sun, B. [Chevron Energy Technology Co., Calgary, AB (Canada)
2008-07-01
Non-conventional, heavy oil fields are becoming increasingly important to the security of energy supplies and are becoming economically profitable to produce. Heavy oil reservoirs are difficult to evaluate since they are typically shallow and the connate waters are very fresh. Other heavy oil reservoirs are oil-wet where the resistivities are not indicative of saturation. Nuclear magnetic resonance (NMR) detects molecular level interactions. As such, it responds distinctively to different hydrocarbon molecules, thereby opening a new avenue for constituent analysis. This feature makes NMR a more powerful technique than bulk oil density or viscosity measurements for characterizing oils, and is the basis for detecting gas in heavy oil fields. NMR logging, which measures fluid in pore space directly, is capable of separating oil from water. It is possible to discern movable from bound water by analyzing NMR logs. The oil viscosity can be also quantified from NMR logs, NMR relaxation time and diffusivity estimates. The unique challenges for heavy oil reservoir characterization for the NMR technique were discussed with reference to the extra-fast decay of the NMR signal in response to extra-heavy oil/tars, and the lack of sensitivity in measuring very slow diffusion of heavy oil molecules. This paper presented various methods for analyzing heavy oil reservoirs in different viscosity ranges. Heavy oil fields in Venezuela, Kazakhstan, Canada, Alaska and the Middle East were analyzed using different data interpretation approaches based on the reservoir formation characteristics and the heavy oil type. NMR direct fluid typing was adequate for clean sands and carbonate reservoirs while integrated approaches were used to interpret extra heavy oils and tars. It was concluded that NMR logs can provide quantitative measures for heavy oil saturation, identify sweet spots or tar streaks, and quantify heavy oil viscosity within reasonable accuracy. 14 refs., 16 figs.
19. Investigation of zeolites by solid state quadrapole NMR
International Nuclear Information System (INIS)
Janssen, R.
1990-01-01
The subject of this thesis is the NMR investigation of zeolites. The nature and properties of zeolites are discussed. Some of the basic priniples of NMR techniques on quadrupole nuclei are presented. A special technique, namely a two-dimensional nutation experiment is discussed in detail. The theory of the nutation experiment for quadrupole spin species with spin quantum number 3/2 as well as 5/2 is presented. For both spin spcies the theoretical spectra are compared with experimental results. It is also shown that the nutation expeirment can be performed with several pulse schemes. It is shown how phase-sensitive pure-absorption nutation spectra can be obtained and an NMR-probe is presented that is capable of performing NMR experiments at high (up to 500 degree C) temperatures. The two-dimensional nutation NMR technique has been applied to sodium cations in zeolite NaA. For this purpose a numbre of zeolite samples were prepared that contained different amounts of water. With the aid of nutation NMR the hydration of the zeolite can be studied and conclusions can be drawn about the symmetry of the surrounding of the sodium cations. With the aid of an extension of the nutation NMR experiment: Rotary Echo Nutation NMR, it is shown that in zeolite NaA, in various stages of hydration, the sodium cations or water molecules are mobile. Proof is given by means of high-temperature 23 Na-NMR that dehydrates zeolite NaA undergoes a phase transition at ca. 120 degree C. In a high-temperature NMR investigation of zeolite ZSM-5 it is shown that the sodium ions start to execute motions when the temperature is increased. (author). 198 refs.; 72 figs.; 6 tabs
20. Variations of NMR signals by hyperpolarization and ultrasound; Variation von NMR-Signalen durch Hyperpolarisation und Ultraschall
Energy Technology Data Exchange (ETDEWEB)
Engelbertz, A.
2006-07-01
In this thesis it is described how p-NMR can be applied to metals with verlo low hydrogen concentrations and how a combination of ultrasound and NMR can lead to an improvement of the measureing method. As examples measurements on H{sub 2}O and ethanol are described. (HSI)
1. Automated protein structure calculation from NMR data
International Nuclear Information System (INIS)
Williamson, Mike P.; Craven, C. Jeremy
2009-01-01
Current software is almost at the stage to permit completely automatic structure determination of small proteins of <15 kDa, from NMR spectra to structure validation with minimal user interaction. This goal is welcome, as it makes structure calculation more objective and therefore more easily validated, without any loss in the quality of the structures generated. Moreover, it releases expert spectroscopists to carry out research that cannot be automated. It should not take much further effort to extend automation to ca 20 kDa. However, there are technological barriers to further automation, of which the biggest are identified as: routines for peak picking; adoption and sharing of a common framework for structure calculation, including the assembly of an automated and trusted package for structure validation; and sample preparation, particularly for larger proteins. These barriers should be the main target for development of methodology for protein structure determination, particularly by structural genomics consortia
2. High Magnetic Field Vortex Microscopy by NMR
Science.gov (United States)
Mitrović, V. F.; Sigmund, E. E.; Bachman, H. N.; Halperin, W. P.; Reyes, A. P.; Kuhns, P.; Moulton, W. G.
2001-03-01
At low temperatures the ^17O NMR spectrum of HTS exhibits a characteristic vortex lattice line shape. Measurements of spin-lattice relaxation rate, T_1-1, across the vortex spectrum represent a probe of low-energy quasiparticle excitations as a function of distance from the vortex core. We report ^17O(2,3) T_1-1 measurements of YBa_2Cu_3O7 at low temperatures in magnetic fields up to 37 T. We find that the rate increases on approaching the vortex core. In the vortex core region at 37 T we observe an additional increase in the relaxation rate. The temperature dependence of the rate will also be discussed. Work at Northwestern University is supported by the NSF (DMR 91-20000) through the Science and Technology Center for Superconductivity.
3. INFOS: spectrum fitting software for NMR analysis
Energy Technology Data Exchange (ETDEWEB)
Smith, Albert A., E-mail: [email protected] [ETH Zürich, Physical Chemistry (Switzerland)
2017-02-15
Software for fitting of NMR spectra in MATLAB is presented. Spectra are fitted in the frequency domain, using Fourier transformed lineshapes, which are derived using the experimental acquisition and processing parameters. This yields more accurate fits compared to common fitting methods that use Lorentzian or Gaussian functions. Furthermore, a very time-efficient algorithm for calculating and fitting spectra has been developed. The software also performs initial peak picking, followed by subsequent fitting and refinement of the peak list, by iteratively adding and removing peaks to improve the overall fit. Estimation of error on fitting parameters is performed using a Monte-Carlo approach. Many fitting options allow the software to be flexible enough for a wide array of applications, while still being straightforward to set up with minimal user input.
4. NMR Measurements of Granular Flow and Compaction
Science.gov (United States)
Fukushima, Eiichi
1998-03-01
Nuclear magnetic resonance (NMR) can be used to measure statistical distributions of granular flow velocity and fluctuations of velocity, as well as spatial distributions of particulate concentration, flow velocity, its fluctuations, and other parameters that may be derived from these. All measurements have been of protons in liquid-containing particles such as mustard seeds or pharmaceutical pills. Our favorite geometry has been the slowly rotating partially filled rotating drum with granular flow taking place along the free surface of the particles. All the above-mentioned parameters have been studied as well as a spatial distribution of particulate diffusion coefficients, energy dissipation due to collisions, as well as segregation of non-uniform mixtures of granular material. Finally, we describe some motions of granular material under periodic vibrations.
5. NMR spectroscopy: a tool for conformational analysis
International Nuclear Information System (INIS)
Tormena, Claudio F.; Cormanich, Rodrigo A.; Rittner, Roberto; Freitas, Matheus P.
2011-01-01
The present review deals with the application of NMR data to the conformational analysis of simple organic compounds, together with other experimental methods like infrared spectroscopy and with theoretical calculations. Each sub-section describes the results for a group of compounds which belong to a given organic function like ketones, esters, etc. Studies of a single compound, even of special relevance, were excluded since the main goal of this review is to compare the results for a given function, where different substituents were used or small structural changes were introduced in the substrate, in an attempt to disclose their effects in the conformational equilibrium. Moreover, the huge amount of data available in the literature, on this research field, imposed some limitations which will be detailed in the Introduction, but it can be reminded in advance that these limitations include mostly the period when these results were published. (author)
6. ImatraNMR: Novel software for batch integration and analysis of quantitative NMR spectra
Science.gov (United States)
Mäkelä, A. V.; Heikkilä, O.; Kilpeläinen, I.; Heikkinen, S.
2011-08-01
Quantitative NMR spectroscopy is a useful and important tool for analysis of various mixtures. Recently, in addition of traditional quantitative 1D 1H and 13C NMR methods, a variety of pulse sequences aimed for quantitative or semiquantitative analysis have been developed. To obtain actual usable results from quantitative spectra, they must be processed and analyzed with suitable software. Currently, there are many processing packages available from spectrometer manufacturers and third party developers, and most of them are capable of analyzing and integration of quantitative spectra. However, they are mainly aimed for processing single or few spectra, and are slow and difficult to use when large numbers of spectra and signals are being analyzed, even when using pre-saved integration areas or custom scripting features. In this article, we present a novel software, ImatraNMR, designed for batch analysis of quantitative spectra. In addition to capability of analyzing large number of spectra, it provides results in text and CSV formats, allowing further data-analysis using spreadsheet programs or general analysis programs, such as Matlab. The software is written with Java, and thus it should run in any platform capable of providing Java Runtime Environment version 1.6 or newer, however, currently it has only been tested with Windows and Linux (Ubuntu 10.04). The software is free for non-commercial use, and is provided with source code upon request.
7. NMR study of hyper-polarized 129Xe and applications to liquid-phase NMR experiments
International Nuclear Information System (INIS)
Marion, D.
2008-07-01
In liquid samples where both nuclear polarization and spin density are strong, the magnetization dynamics, which can be analysed by NMR (nuclear magnetic resonance) methods, is deeply influenced by the internal couplings induced by local dipolar fields. The present thesis describes some of the many consequences associated to the presence in the sample of concentrated xenon hyper-polarized by an optical pumping process. First, we deal with the induced modifications in frequency and line width of the proton and xenon spectra, then we present the results of SPIDER, a coherent polarization transfer experiment designed to enhance the polarization of protons, in order to increase their NMR signal level. A third part is dedicated to the description of the apparition of repeated chaotic maser emissions by un unstable xenon magnetization coupled to the detection coil tuned at the xenon Larmor frequency (here 138 MHz). In the last part, we present a new method allowing a better tuning of any NMR detection probe and resulting in sensible gains in terms of sensitivity and signal shaping. Finally, we conclude with a partial questioning of the classical relaxation theory in the specific field of highly polarized and concentrated spin systems in a liquid phase. (author)
8. Can NMR solve some significant challenges in metabolomics?
Science.gov (United States)
Gowda, G.A. Nagana; Raftery, Daniel
2015-01-01
The field of metabolomics continues to witness rapid growth driven by fundamental studies, methods development, and applications in a number of disciplines that include biomedical science, plant and nutrition sciences, drug development, energy and environmental sciences, toxicology, etc. NMR spectroscopy is one of the two most widely used analytical platforms in the metabolomics field, along with mass spectrometry (MS). NMR's excellent reproducibility and quantitative accuracy, its ability to identify structures of unknown metabolites, its capacity to generate metabolite profiles using intact biospecimens with no need for separation, and its capabilities for tracing metabolic pathways using isotope labeled substrates offer unique strengths for metabolomics applications. However, NMR's limited sensitivity and resolution continue to pose a major challenge and have restricted both the number and the quantitative accuracy of metabolites analyzed by NMR. Further, the analysis of highly complex biological samples has increased the demand for new methods with improved detection, better unknown identification, and more accurate quantitation of larger numbers of metabolites. Recent efforts have contributed significant improvements in these areas, and have thereby enhanced the pool of routinely quantifiable metabolites. Additionally, efforts focused on combining NMR and MS promise opportunities to exploit the combined strength of the two analytical platforms for direct comparison of the metabolite data, unknown identification and reliable biomarker discovery that continue to challenge the metabolomics field. This article presents our perspectives on the emerging trends in NMR-based metabolomics and NMR's continuing role in the field with an emphasis on recent and ongoing research from our laboratory. PMID:26476597
9. Can NMR solve some significant challenges in metabolomics?
Science.gov (United States)
Nagana Gowda, G. A.; Raftery, Daniel
2015-11-01
The field of metabolomics continues to witness rapid growth driven by fundamental studies, methods development, and applications in a number of disciplines that include biomedical science, plant and nutrition sciences, drug development, energy and environmental sciences, toxicology, etc. NMR spectroscopy is one of the two most widely used analytical platforms in the metabolomics field, along with mass spectrometry (MS). NMR's excellent reproducibility and quantitative accuracy, its ability to identify structures of unknown metabolites, its capacity to generate metabolite profiles using intact bio-specimens with no need for separation, and its capabilities for tracing metabolic pathways using isotope labeled substrates offer unique strengths for metabolomics applications. However, NMR's limited sensitivity and resolution continue to pose a major challenge and have restricted both the number and the quantitative accuracy of metabolites analyzed by NMR. Further, the analysis of highly complex biological samples has increased the demand for new methods with improved detection, better unknown identification, and more accurate quantitation of larger numbers of metabolites. Recent efforts have contributed significant improvements in these areas, and have thereby enhanced the pool of routinely quantifiable metabolites. Additionally, efforts focused on combining NMR and MS promise opportunities to exploit the combined strength of the two analytical platforms for direct comparison of the metabolite data, unknown identification and reliable biomarker discovery that continue to challenge the metabolomics field. This article presents our perspectives on the emerging trends in NMR-based metabolomics and NMR's continuing role in the field with an emphasis on recent and ongoing research from our laboratory.
10. Molecular dynamics simulations on PGLa using NMR orientational constraints
Energy Technology Data Exchange (ETDEWEB)
Sternberg, Ulrich, E-mail: [email protected]; Witter, Raiker [Tallinn University of Technology, Technomedicum (Estonia)
2015-11-15
NMR data obtained by solid state NMR from anisotropic samples are used as orientational constraints in molecular dynamics simulations for determining the structure and dynamics of the PGLa peptide within a membrane environment. For the simulation the recently developed molecular dynamics with orientational constraints technique (MDOC) is used. This method introduces orientation dependent pseudo-forces into the COSMOS-NMR force field. Acting during a molecular dynamics simulation these forces drive molecular rotations, re-orientations and folding in such a way that the motional time-averages of the tensorial NMR properties are consistent with the experimentally measured NMR parameters. This MDOC strategy does not depend on the initial choice of atomic coordinates, and is in principle suitable for any flexible and mobile kind of molecule; and it is of course possible to account for flexible parts of peptides or their side-chains. MDOC has been applied to the antimicrobial peptide PGLa and a related dimer model. With these simulations it was possible to reproduce most NMR parameters within the experimental error bounds. The alignment, conformation and order parameters of the membrane-bound molecule and its dimer were directly derived with MDOC from the NMR data. Furthermore, this new approach yielded for the first time the distribution of segmental orientations with respect to the membrane and the order parameter tensors of the dimer systems. It was demonstrated the deuterium splittings measured at the peptide to lipid ratio of 1/50 are consistent with a membrane spanning orientation of the peptide.
11. Molecular dynamics computer simulations based on NMR data
International Nuclear Information System (INIS)
Vlieg, J. de.
1989-01-01
In the work described in this thesis atom-atom distance information obtained from two-dimensional cuclear magnetic resonance is combined with molecular dynamics simulaitons. The simulation is used to improve the accuracy of a structure model constructed on the basis of NMR data. During the MD refinement the crude NMR structure is simultaneously optimized with respect to the atomic interaction function and to the set of atom-atom distances or other NMR information. This means that insufficient experimental data is completed with theoretical knowledge and the combination will lead to more reliable structures than would be obtained from one technique alone. (author). 191 refs.; 17 figs.; 12 schemes; 22 tabs
12. Moessbauer and NMR study of novel Tin(IV)-lactames
Energy Technology Data Exchange (ETDEWEB)
Kuzmann, Erno; Szalay, Roland; Homonnay, Zoltan, E-mail: [email protected]; Nagy, Sandor [Eoetvoes Lorand University, Institute of Chemistry (Hungary)
2012-03-15
N-tributylstannylated 2-pyrrolidinone was reacted with tributyltin triflate in different molar ratios and the complex formation monitored using {sup 1}H-NMR, {sup 13}C-NMR and {sup 119}Sn Moessbauer spectroscopy. Comparing the carbon NMR and tin Moessbauer results, a reaction scheme is suggested for the complexation which assumes the formation of a simultaneously O- and N-tributylstannylated pyrrolidinone cation. The formation of the only O-stannylated pyrrolidinone is also assumed to account for the non-constant Moessbauer parameters of the two tin environments in the distannylated pyrrolidinone cation when the ratio of tributyltin triflate is increased in the reaction.
13. NMR imaging of bladder tumors in males. Preliminary clinical experience
International Nuclear Information System (INIS)
Sigal, R.; Rein, A.J.J.T.; Atlan, H.; Lanir, A.; Kedar, S.; Segal, S.
1985-01-01
Nuclear magnetic resonance (NMR) of the normal and pathologic bladder was performed in 10 male subjects: 5 normal volunteers, 4 with bladder primary carcinoma, 1 with bladder metastasis. All scanning was done using a superconductive magnet operating at 0.5 T. Spin echo was used as pulse sequence. The diagnosis was confirmed in all cases by NMR imaging. The ability of the technique to provide images in axial, sagital and coronal planes allowed a precise assessment of the morphology and the size of the tumors. The lack of hazards and the quality of images may promote NMR imaging to a prominent role in the diagnosis of human bladder cancer [fr
14. NMR and domain wall mobility in intermetallic compounds
International Nuclear Information System (INIS)
Guimaraes, A.P.; Sampaio, L.C.; Cunha, S.F.; Alves, K.M.B.
1991-01-01
The technique of pulsed NMR can be used to study the distribution of hyperfine fields in a magnetic matrix. The dynamics of the domain walls are relevant to the generation of NMR signals. In the present study on the (R x Y 1-x ) Fe 2 intermetallic compounds, the reduction in the signals is associated to increased propagation fields. This indicates that a smaller domain wall mobility is at the origin of these effects. NMR spectra in this system show the importance of direct and indirect (i.e., mediated by Fe atoms) terms in the transferred hyperfine field. (author)
15. NMR studies of metallic tin confined within porous matrices
International Nuclear Information System (INIS)
Charnaya, E. V.; Tien, Cheng; Lee, M. K.; Kumzerov, Yu. A.
2007-01-01
119 Sn NMR studies were carried out for metallic tin confined within synthetic opal and porous glass. Tin was embedded into nanoporous matrices in the melted state under pressure. The Knight shift for liquid confined tin was found to decrease with decreasing pore size. Correlations between NMR line shapes, Knight shift, and pore filling were observed. The melting and freezing phase transitions of tin under confinement were studied through temperature dependences of NMR signals upon warming and cooling. Melting of tin within the opal matrix agreed well with the liquid skin model suggested for small isolated particles. The influence of the pore filling on the melting process was shown
16. Study on the Effects of Oligo chitosan and Bioliquifert on Two Rice Mutants, NMR 151 and NMR 152
International Nuclear Information System (INIS)
Shakinah Salleh; Faiz Ahmad; Sobri Hussein
2016-01-01
Nuclear Malaysia has successfully developed two new rice mutants namely NMR 151 and NMR 152. In addition, Nuclear Malaysia has also successfully developed Oligo chitosan and liquid bio fertilizer (Bioliquifert). Oligo chitosan acts as elicitor that has been proven to be very effective in controlling disease infections and improving yield productivity. Bioliquifert on the other hand is a mixture of microbes containing major nutrient-providing microorganisms. The objective of this study is to observe the effects of Oligo chitosan and Bioliquifert on rice mutants, NMR 151 and NMR 152. The treatment was applied on 14 day old seedlings of MR 219, NMR 151 and NMR 152 sowed in 20 cm pots containing silty clay from the paddy soil of Tanjung Karang, Selangor. The seedlings were then placed in the greenhouse at Nuclear Malaysia until it reaches 110 days old. Study was conducted in a Complete Randomized Design (CRD) with 3 replications was used and each replication consisted of three plants. All treatments received compound and single dressing fertilizer as recommended by National Rice Production Package except for Treatment 2 and 3, in which Treatment 2 received Oligo chitosan and Bioliquifert while Treatment 3 only received Bioliquifert. Results on plant height, number of tiller and plant fresh weight are not significantly different for all cultivar except for seed dry weight of NMR 152 and MR 219. (author)
17. Force field refinement from NMR scalar couplings
Energy Technology Data Exchange (ETDEWEB)
Huang Jing [Department of Chemistry, University of Basel, Klingelbergstrasse 80, 4056 Basel (Switzerland); Meuwly, Markus, E-mail: [email protected] [Department of Chemistry, University of Basel, Klingelbergstrasse 80, 4056 Basel (Switzerland)
2012-03-02
Graphical abstract: We show that two classes of H-bonds are sufficient to quantitatively describe scalar NMR coupling constants in small proteins. Highlights: Black-Right-Pointing-Pointer We present force field refinements based on explicit MD simulations using scalar couplings across hydrogen bonds. Black-Right-Pointing-Pointer This leads to {sup h3}J{sub NC{sup }{sup P}{sup r}{sup i}{sup m}{sup e}} couplings to within 0.03 Hz at best compared to experiment. Black-Right-Pointing-Pointer A classification of H-bonds according to secondary structure is not sufficiently robust. Black-Right-Pointing-Pointer Grouping H-bonds into two classes and reparametrization yields an RMSD of 0.07 Hz. Black-Right-Pointing-Pointer This is an improvement of 50. - Abstract: NMR observables contain valuable information about the protein dynamics sampling a high-dimensional potential energy surface. Depending on the observable, the dynamics is sensitive to different time-windows. Scalar coupling constants {sup h3}J{sub NC{sup }{sup P}{sup r}{sup i}{sup m}{sup e}} reflect the pico- to nanosecond motions associated with the intermolecular hydrogen bond network. Including an explicit H-bond in the molecular mechanics with proton transfer (MMPT) potential allows us to reproduce experimentally determined {sup h3}J{sub NC{sup }{sup P}{sup r}{sup i}{sup m}{sup e}} couplings to within 0.02 Hz at best for ubiquitin and protein G. This is based on taking account of the chemically changing environment by grouping the H-bonds into up to seven classes. However, grouping them into two classes already reduces the RMSD between computed and observed {sup h3}J{sub NC{sup }{sup P}{sup r}{sup i}{sup m}{sup e}} couplings by almost 50%. Thus, using ensemble-averaged data with two classes of H-bonds leads to substantially improved scalar couplings from simulations with accurate force fields.
18. 13C-NMR of diterpenes with pimarane skeleton
International Nuclear Information System (INIS)
Garcez, W.S.; Pereira, A.L.; Silva Queiroz, P.P. da; Silva, R.S. da; Valente, L.M.M.; Peixoto, E.M.; Cunha Pinto, A. da
1981-01-01
The effect of substituent groups on the chemical shift of carbons using nuclear magnetic resonance spectra of carbon 13 ( 13 C-NMR) is discussed. Diterpenes having pimarane skeleton, isolated from plants of Velloziaceae family are analysed. (ARHC) [pt
19. Isotope labeling strategies for NMR studies of RNA
International Nuclear Information System (INIS)
Lu, Kun; Miyazaki, Yasuyuki; Summers, Michael F.
2010-01-01
The known biological functions of RNA have expanded in recent years and now include gene regulation, maintenance of sub-cellular structure, and catalysis, in addition to propagation of genetic information. As for proteins, RNA function is tightly correlated with structure. Unlike proteins, structural information for larger, biologically functional RNAs is relatively limited. NMR signal degeneracy, relaxation problems, and a paucity of long-range 1 H- 1 H dipolar contacts have limited the utility of traditional NMR approaches. Selective isotope labeling, including nucleotide-specific and segmental labeling strategies, may provide the best opportunities for obtaining structural information by NMR. Here we review methods that have been developed for preparing and purifying isotopically labeled RNAs, as well as NMR strategies that have been employed for signal assignment and structure determination.
20. NMR - from basic physics to images of the human body
International Nuclear Information System (INIS)
Richards, Rex.
1985-01-01
Nuclear magnetic resonance (NMR) is a remarkable phenomenon which involves the exchange of very weak radio frequency radiation between atomic nuclei and a sensitive detecting apparatus. It was originally regarded as a rather esoteric effect of great theoretical interest, but has since proved to have an amazing range of applications over many scientific disciplines, including nuclear physics, solid state physics, all branches of chemistry, biochemistry, physiology and most recently in medical diagnosis. In this Discourse the principles of NMR and trace briefly the history of its applications are examined and illustrated. Headings are: early history; nuclear resonance; relaxation time; the chemical shift; spin-spin coupling (NMR spectra); chemical shifts in biological tissue; NMR imaging; conclusions. (author)
1. Cell signaling, post-translational protein modifications and NMR spectroscopy
International Nuclear Information System (INIS)
Theillet, Francois-Xavier; Smet-Nocca, Caroline; Liokatis, Stamatios; Thongwichian, Rossukon; Kosten, Jonas; Yoon, Mi-Kyung; Kriwacki, Richard W.; Landrieu, Isabelle; Lippens, Guy; Selenko, Philipp
2012-01-01
Post-translationally modified proteins make up the majority of the proteome and establish, to a large part, the impressive level of functional diversity in higher, multi-cellular organisms. Most eukaryotic post-translational protein modifications (PTMs) denote reversible, covalent additions of small chemical entities such as phosphate-, acyl-, alkyl- and glycosyl-groups onto selected subsets of modifiable amino acids. In turn, these modifications induce highly specific changes in the chemical environments of individual protein residues, which are readily detected by high-resolution NMR spectroscopy. In the following, we provide a concise compendium of NMR characteristics of the main types of eukaryotic PTMs: serine, threonine, tyrosine and histidine phosphorylation, lysine acetylation, lysine and arginine methylation, and serine, threonine O-glycosylation. We further delineate the previously uncharacterized NMR properties of lysine propionylation, butyrylation, succinylation, malonylation and crotonylation, which, altogether, define an initial reference frame for comprehensive PTM studies by high-resolution NMR spectroscopy.
2. EPR and NMR detection of transient radicals and reaction products
International Nuclear Information System (INIS)
Trifunac, A.D.
1981-01-01
Magnetic resonance methods in radiation chemistry are illustrated. The most recent developments in pulsed EPR and NMR studies in pulse radiolysis are outlined with emphasis on the study of transient radicals and their reaction products. 12 figures
3. Applications of NMR to studies of tissue metabolism
International Nuclear Information System (INIS)
Avison, M.J.; Hetherington, H.P.; Shulman, R.G.
1986-01-01
From its beginnings as a tool for the elucidation of biochemical pathways and bioenergetic status in unicellular organisms, the field of NMR studie in vivo has grown to encompass not only the study of isolated perfused organs, but also the study of various aspects of the biochemistry, physiology, and pathophysiology of these same organs in the intact animal. In recent years several groups have begun to extend the techniques developed in animals to the study of clinically relevant conditions in humans. A comprehensive review of all areas of NMR studies in vivo would be either unacceptably long or very superficial. For this reason the authors have restricted this review to studies published since 1980, except where an earlier study is particularly relevant to the topic under discussion. Furthermore, they have concentrated on areas that have been extending the scope of NMR in vivo. One specific omission is review of NMR studies of tumors, since a comprehensive review has recently appeared
4. International NMR-based Environmental Metabolomics Intercomparison Exercise
Science.gov (United States)
Several fundamental requirements must be met so that NMR-based metabolomics and the related technique of metabonomics can be formally adopted into environmental monitoring and chemical risk assessment. Here we report an intercomparison exercise which has evaluated the effectivene...
5. NMR methods for the investigation of structure and transport
Energy Technology Data Exchange (ETDEWEB)
Hardy, Edme H. [Karlsruher Institut fuer Technologie (KIT), Karlsruhe (Germany). Inst. fuer Mechanische Verfahrenstechnik und Mechanik
2012-07-01
Extensive derivations of required fundamental relations for readers with engineering background New applications based on MRI, PGSE-NMR, and low-field NMR New concepts in quantitative data evaluation and image analysis Methods of nuclear magnetic resonance (NMR) are increasingly applied in engineering sciences. The book summarizes research in the field of chemical and process engineering performed at the Karlsruhe Institute of Technology (KIT). Fundamentals of the methods are exposed for readers with an engineering background. Applications cover the fields of mechanical process engineering (filtration, solid-liquid separation, powder mixing, rheometry), chemical process engineering (trickle-bed reactor, ceramic sponges), bioprocess engineering (biofilm growth), and food process engineering (microwave heating, emulsions). Magnetic Resonance Imaging (MRI) as well as low-field NMR are covered with notes on hardware. Emphasis is placed on quantitative data analysis and image processing. (orig.)
6. NMR methods for the investigation of structure and transport
International Nuclear Information System (INIS)
Hardy, Edme H.
2012-01-01
Extensive derivations of required fundamental relations for readers with engineering background New applications based on MRI, PGSE-NMR, and low-field NMR New concepts in quantitative data evaluation and image analysis Methods of nuclear magnetic resonance (NMR) are increasingly applied in engineering sciences. The book summarizes research in the field of chemical and process engineering performed at the Karlsruhe Institute of Technology (KIT). Fundamentals of the methods are exposed for readers with an engineering background. Applications cover the fields of mechanical process engineering (filtration, solid-liquid separation, powder mixing, rheometry), chemical process engineering (trickle-bed reactor, ceramic sponges), bioprocess engineering (biofilm growth), and food process engineering (microwave heating, emulsions). Magnetic Resonance Imaging (MRI) as well as low-field NMR are covered with notes on hardware. Emphasis is placed on quantitative data analysis and image processing. (orig.)
7. Structure of Coordination Complexes: The Synergy between NMR ...
African Journals Online (AJOL)
NICO
determined by density functional theory (DFT) methods and the application of the Boltzmann equation, are in ... single crystals suitable for crystallography can be obtained, ...... NMR analysis of bonding in transition metal olefin complexes.
8. Simultaneous acquisition of three NMR spectra in a single ...
Simultaneous acquisition of three NMR spectra in a single experiment ... set, which is based on a combination of different fast data acquisition techniques such as G-matrix ..... The sign and intensity of the CHn resonance depends on the delay.
9. Applications of high resolution 3H NMR spectroscopy
International Nuclear Information System (INIS)
Williams, P.G.
1987-10-01
The advantages of tritium as an NMR nucleus are pointed out. Examples of its use are given, including labelled toluene, hydrogenation of β-methylstyrene, and maltose and its binding proteins. 7 refs., 2 figs
10. Studies on supramolecular gel formation using DOSY NMR
Czech Academy of Sciences Publication Activity Database
Nonappa, N.; Šaman, David; Kolehmainen, E.
2015-01-01
Roč. 53, č. 4 (2015), s. 256-260 ISSN 0749-1581 Institutional support: RVO:61388963 Keywords : DOSY * VT NMR * gel * diffusion coefficients Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.226, year: 2015
11. [Rapid analysis of suppositories by quantitative 1H NMR spectroscopy].
Science.gov (United States)
Abramovich, R A; Kovaleva, S A; Goriainov, S V; Vorob'ev, A N; Kalabin, G A
2012-01-01
Rapid analysis of suppositories with ibuprofen and arbidol by quantitative 1H NMR spectroscopy was performed. Optimal conditions for the analysis were developed. The results are useful for design of rapid methods for quality control of suppositories with different components
12. Determination of moisture in fiber reinforced composites using pulsed NMR
International Nuclear Information System (INIS)
Matzkanin, G.A.
1982-01-01
Nuclear magnetic resonance (NMR) signals from hydrogen atoms in two organic matrix composite systems subjected to environmental conditioning at 51.6 C (125 F) and 95% relative humidity were examined. The composites were 8 ply, + or - 45 deg laminates fabricated from SP 250 resin/S2 glass fiber and Reliabond 9350 resin/Kevlar 49 fiber. Free induction decay NMR signals from the composite specimens consisted of a large amplitude, fast decaying component associated with hydrogen in rigid polymer molecules and a lower amplitude, slower decaying component associated with hydrogen in the mobile absorbed moisture molecules. The absorbed moisture NMR signals consists of distinct multiple components which were attributed to moisture in various states of molecular binding. Particularly complex free induction decay signals were observed from Kevlar composite as well as from Kevlar fiber. Good correlation was obtained between the NMR signal amplitude and the dry weight moisture percentage for both composite systems. Results of destructive tensile tests were examined
13. 1H NMR visibility of mammalian glycogen in solution
International Nuclear Information System (INIS)
Zang, L.H.; Rothman, D.L.; Shulman, R.G.
1990-01-01
High-resolution 1 H NMR spectra of rabbit liver glycogen in 2 H 2 O were obtained at 500 MHz, and several resonances were assigned by comparison with the chemical shifts of α-linked diglucose molecules. The NMR relaxation times T 1 and T 2 of glycogen in 2 H 2 O were determined to be 1.1 and 0.029 s, respectively. The measured natural linewidth of the carbon-1 proton is in excellent agreement with that calculated from T 2 . The visibility measurements made by digesting glycogen and comparing glucose and glycogen signal intensities demonstrate that in spite of the very high molecular weight, all of the proton nuclei in glycogen contribute to the NMR spectrum. The result is not unexpected, since 100% NMR visibility was previously observed from the carbon nuclei of glycogen, due to the rapid intramolecular motions
14. Artificial intelligence in NMR imaging and image processing
International Nuclear Information System (INIS)
Kuhn, M.H.
1988-01-01
NMR tomography offers a wealth of information and data acquisition variants. Artificial intelligence is able to efficiently support the selection of measuring parameters and the evaluation of results. (orig.) [de
15. Structural biology by NMR: structure, dynamics, and interactions.
Directory of Open Access Journals (Sweden)
Phineus R L Markwick
2008-09-01
Full Text Available The function of bio-macromolecules is determined by both their 3D structure and conformational dynamics. These molecules are inherently flexible systems displaying a broad range of dynamics on time-scales from picoseconds to seconds. Nuclear Magnetic Resonance (NMR spectroscopy has emerged as the method of choice for studying both protein structure and dynamics in solution. Typically, NMR experiments are sensitive both to structural features and to dynamics, and hence the measured data contain information on both. Despite major progress in both experimental approaches and computational methods, obtaining a consistent view of structure and dynamics from experimental NMR data remains a challenge. Molecular dynamics simulations have emerged as an indispensable tool in the analysis of NMR data.
16. (S)Pinning down protein interactions by NMR
DEFF Research Database (Denmark)
Teilum, Kaare; Kunze, Micha Ben Achim; Erlendsson, Simon
2017-01-01
Protein molecules are highly diverse communication platforms and their interaction repertoire stretches from atoms over small molecules such as sugars and lipids to macromolecules. An important route to understanding molecular communication is to quantitatively describe their interactions...... all types of protein reactions, which can span orders of magnitudes in affinities, reaction rates and lifetimes of states. As the more versatile technique, solution NMR spectroscopy offers a remarkable catalogue of methods that can be successfully applied to the quantitative as well as qualitative...... descriptions of protein interactions. In this review we provide an easy-access approach to NMR for the non-NMR specialist and describe how and when solution state NMR spectroscopy is the method of choice for addressing protein ligand interaction. We describe very briefly the theoretical background...
17. Quantification of aluminium-27 NMR spectra of high-surface-area oxides
International Nuclear Information System (INIS)
Pearson, R.M.; Schramm, C.M.
1990-01-01
This paper discusses the quantitation of 27 Al NMR spectra. It is showns that the so called 'invisible' aluminium atoms seen by recent workers are completely consistent with known continuous wave NMR studies of the 27 Al NMR spectra of high surface area aluminium oxides. The use of pulsed NMR techniques further complicate the quantitative measurement of 27 Al NMR spectra, especially when high resolution NMR spectrometers are used for this purpose. Methods are described which allow both the estimation of aluminium not seen by continuous wave techniques and the amounts of the NMR spectra lost in pulsed work. (author). 24 refs.; 6 figs.; 1 tab
18. NMR and MS Methods for Metabolomics.
Science.gov (United States)
Amberg, Alexander; Riefke, Björn; Schlotterbeck, Götz; Ross, Alfred; Senn, Hans; Dieterle, Frank; Keck, Matthias
2017-01-01
Metabolomics, also often referred as "metabolic profiling," is the systematic profiling of metabolites in biofluids or tissues of organisms and their temporal changes. In the last decade, metabolomics has become more and more popular in drug development, molecular medicine, and other biotechnology fields, since it profiles directly the phenotype and changes thereof in contrast to other "-omics" technologies. The increasing popularity of metabolomics has been possible only due to the enormous development in the technology and bioinformatics fields. In particular, the analytical technologies supporting metabolomics, i.e., NMR, UPLC-MS, and GC-MS, have evolved into sensitive and highly reproducible platforms allowing the determination of hundreds of metabolites in parallel. This chapter describes the best practices of metabolomics as seen today. All important steps of metabolic profiling in drug development and molecular medicine are described in great detail, starting from sample preparation to determining the measurement details of all analytical platforms, and finally to discussing the corresponding specific steps of data analysis.
19. NMR and MS methods for metabonomics.
Science.gov (United States)
Dieterle, Frank; Riefke, Björn; Schlotterbeck, Götz; Ross, Alfred; Senn, Hans; Amberg, Alexander
2011-01-01
Metabonomics, also often referred to as "metabolomics" or "metabolic profiling," is the systematic profiling of metabolites in bio-fluids or tissues of organisms and their temporal changes. In the last decade, metabonomics has become increasingly popular in drug development, molecular medicine, and other biotechnology fields, since it profiles directly the phenotype and changes thereof in contrast to other "-omics" technologies. The increasing popularity of metabonomics has been possible only due to the enormous development in the technology and bioinformatics fields. In particular, the analytical technologies supporting metabonomics, i.e., NMR, LC-MS, UPLC-MS, and GC-MS have evolved into sensitive and highly reproducible platforms allowing the determination of hundreds of metabolites in parallel. This chapter describes the best practices of metabonomics as seen today. All important steps of metabolic profiling in drug development and molecular medicine are described in great detail, starting from sample preparation, to determining the measurement details of all analytical platforms, and finally, to discussing the corresponding specific steps of data analysis.
20. Quantitative NMR measurements on core samples
International Nuclear Information System (INIS)
Olsen, Dan
1997-01-01
Within the frame of an EFP-95 project NMR methods for porosity determination in 2D, and for fluid saturation determination in 1D and 2D have been developed. The three methods have been developed and tested on cleaned core samples of chalk from the Danish North Sea. The main restriction for the use of the methods is the inherently short T2 relaxation constants of rock samples. Referring to measurements conducted at 200 MHz, the 2D porosity determination method is applicable to sample material with T2 relaxation constants down to 5 ms. The 1D fluid saturation determination method is applicable to sample material with T2 relaxation constants down to 3 ms, while the 2D fluid saturation determination method is applicable to material with T2 relaxation constants down to 8 ms. In the case of the 2D methods these constraints as a minimum enables work on the majority of chalk samples of Maastrichtian age. The 1D fluid saturation determination method in addition is applicable to at least some chalk samples of Danian and pre-Maastrichtian age. The spatial resolution of the 2D porosity determination method, the 1D fluid saturation methods, and the 2D fluid saturation method is respectively 0.8 mm, 0.8 mm and 2 mm. Reproducibility of pixel values is for all three methods 2%- points. (au)
1. NMR-CT image and symbol phantoms
International Nuclear Information System (INIS)
Hongo, Syozo; Yamaguchi, Hiroshi; Takeshita, Hiroshi
1990-01-01
We have developed Japanese phantoms in two procedures. One is described as a mathematical expression. Another is 'symbol phantoms' in 3 dimensional picture-elements, each of which symbolize an organ name. The concept and the algorithm of the symbol phantom enables us to make a phantom for a individual in terms of all his transversal section images. We got 85 transversal section images of head and trunk parts, and those of 40 legs parts by using NMR-CT. We have made the individual phantom for computation of organ doses. The transversal section images were not so clear to identify all organs needed to dose estimation that we had to do hand-editing the shapes of organs with viewing a typical section images: we could not yet make symbol phantom in a automatic editing. Symbols were coded to be visual cords as ASCII characters. After we got the symbol phantom of the first stage, we can edit it easily using a word-processor. Symbol phantom could describe more freely the shape of organs than mathematical phantom. Symbol phantom has several advantages to be an individual phantom, but the only difficult point is how to determine its end-point as a reference man when we apply the method to build the reference man. (author)
2. Proton NMR relaxation in hydrous melts
International Nuclear Information System (INIS)
Braunstein, J.; Bacarella, A.L.; Benjamin, B.M.; Brown, L.L.; Girard, C.
1976-01-01
Pulse and continuous wave NMR measurements are reported for protons in hydrous melts of calcium nitrate at temperatures between -4 and 120 0 C. Although measured in different temperature ranges, spin-lattice (T 1 ) and spin-spin (T 2 ) relaxation times appear to be nearly equal to each other and proportional to the self-diffusion coefficients of solute metal cations such as Cd 2+ . At temperatures near 50 0 C, mean Arrhenius coefficients Δ H/sub T 1 / (kcal/mol) are 7.9, 7.3, and 4.8, respectively, for melts containing 2.8, 4.0, and 8.0 moles of water per mole of calcium nitrate, compared to 4.6 kcal/mol for pure water. Temperature dependence of T 1 and T 2 in Ca(NO 3 ) 2 -2.8 H 2 O between -4 and 120 0 C are non-Arrhenius and can be represented by a Fulcher-type equation with a ''zero mobility temperature'' (T 0 ) of 225 0 K, close to the value of T 0 for solute diffusion, electrical conductance and viscosity. Resolution of the relaxation rates into correlation times for intramolecular (rotational) and intermolecular (translational) diffusional motion is discussed in terms of the Bloembergen-Purcell-Pound and more recent models for dipolar relaxation
3. A multinuclear static NMR study of geopolymerisation
Energy Technology Data Exchange (ETDEWEB)
Favier, Aurélie, E-mail: [email protected] [Univ Paris-Est, IFSTTAR, Materials Department, 14-20 bd Newton, F-77447 Marne la Vallée Cedex 2 (France); Habert, Guillaume [Institute for Construction and Infrastructure Management, ETH Zurich, CH-8093 Zurich (Switzerland); Roussel, Nicolas [Univ Paris-Est, IFSTTAR, Materials Department, 14-20 bd Newton, F-77447 Marne la Vallée Cedex 2 (France); D' Espinose de Lacaillerie, Jean-Baptiste [Ecole Supérieure de Physique et de Chimie Indusrtrielles de la Ville de Paris (ESPCI), ParisTech, PSL Research University, Soft Matter Sciences and Engineering Laboratory SIMM, CNRS UMR 7615, 10 rue Vauquelin, F-75005 Paris (France)
2015-09-15
Geopolymers are inorganic binders obtained by alkali activation of aluminosilicates. While the structure of geopolymers is now well understood, the details of the geopolymerisation reaction and their impact on the rheology of the paste remain uncertain. In this work, we follow the elastic properties of a paste made with metakaolin and sodium silicate solution. After the first sharp increase of elastic modulus occurring a few hundred of seconds after mixing and related to the heterogeneous formation of an alumina–silicate gel with a molar ratio Si/Al < 4 located at the grains boundaries, we focus on the progressive increase in elastic modulus on a period of few hours during the setting of the geopolymer. In this study, we combine the study of rheological properties of the paste with {sup 23}Na, {sup 27}Al and {sup 29}Si static NMR measurement in order to better understand the origin of this second increase in elastic modulus. Our results show that, after a few hours, Al and Na evolution in the liquid phase are concomitant. This suggests the precipitation of an aluminosilicate phase where Al is in tetrahedral position and Na compensates the charge. Furthermore, Si speciation confirms this result and allows us to identify the precipitation of a product, which has a chemical composition close to the final composition of geopolymer. This study provides strong evidence for a heterogeneous formation of an aluminosilicate glass directly from the first gel and the silicate solution without the need for a reorganisation of Gel 1 into Gel 2.
4. Fluid-Rock Characterization and Interactions in NMR Well Logging
Energy Technology Data Exchange (ETDEWEB)
Hirasaki, George J.; Mohanty, Kishore K.
2003-02-10
The objective of this project was to characterize the fluid properties and fluid-rock interactions which are needed for formation evaluation by NMR well logging. NMR well logging is finding wide use in formation evaluation. The formation parameters commonly estimated were porosity, permeability, and capillary bound water. Special cases include estimation of oil viscosity, residual oil saturation, location of oil/water contact, and interpretation on whether the hydrocarbon is oil or gas.
5. Chemical shifts of oxygen-17 NMR in polyoxotungstates
International Nuclear Information System (INIS)
Kazanskij, L.P.; Fedotov, M.A.; Spitsyn, V.I.
1977-01-01
17 O NMR spectra of aqueous solutions containing paratungstate BH 2 W 12 O 42 10- and metatungstate H 2 W 12 O 40 6- anions have been measured. On the basis of the obtained data a scale of chemical shifts for oxygen atoms connected by various bonds with tungsten atoms is suggested. The obtained data are compared with the Raman spectra of crystalline salts and their aqueous solutions. Chemical shifts of 17 O NMR spectra have been also measured in other heteropolyanions
6. Flow units from integrated WFT and NMR data
Energy Technology Data Exchange (ETDEWEB)
Kasap, E.; Altunbay, M.; Georgi, D.
1997-08-01
Reliable and continuous permeability profiles are vital as both hard and soft data required for delineating reservoir architecture. They can improve the vertical resolution of seismic data, well-to-well stratigraphic correlations, and kriging between the well locations. In conditional simulations, permeability profiles are imposed as the conditioning data. Variograms, covariance functions and other geostatistical indicators are more reliable when based on good quality permeability data. Nuclear Magnetic Resonance (NMR) logging and Wireline Formation Tests (WFT) separately generate a wealth of information, and their synthesis extends the value of this information further by providing continuous and accurate permeability profiles without increasing the cost. NMR and WFT data present a unique combination because WFTs provide discrete, in situ permeability based on fluid-flow, whilst NMR responds to the fluids in the pore space and yields effective porosity, pore-size distribution, bound and moveable fluid saturations, and permeability. The NMR permeability is derived from the T{sub 2}-distribution data. Several equations have been proposed to transform T{sub 2} data to permeability. Regardless of the transform model used, the NMR-derived permeabilities depend on interpretation parameters that may be rock specific. The objective of this study is to integrate WFT permeabilities with NMR-derived, T{sub 2} distribution-based permeabilities and thereby arrive at core quality, continuously measured permeability profiles. We outlined the procedures to integrate NMR and WFT data and applied the procedure to a field case. Finally, this study advocates the use of hydraulic unit concepts to extend the WFT-NMR derived, core quality permeabilities to uncored intervals or uncored wells.
7. Modeling Ne-21 NMR parameters for carbon nanosystems
Czech Academy of Sciences Publication Activity Database
Kupka, T.; Nieradka, M.; Kaminský, Jakub; Stobinski, L.
2013-01-01
Roč. 51, č. 10 (2013), s. 676-681 ISSN 0749-1581 R&D Projects: GA ČR GAP208/11/0105; GA MŠk(CZ) LH11033 Grant - others:AV ČR(CZ) M200551205 Institutional support: RVO:61388963 Keywords : Ne-21 NMR * GIAO NMR * molecular modeling * carbon nanostructures Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.559, year: 2013
8. Solid-state NMR studies of nucleic acid components
Czech Academy of Sciences Publication Activity Database
Dračínský, Martin; Hodgkinson, P.
2015-01-01
Roč. 5, č. 16 (2015), s. 12300-12310 ISSN 2046-2069 R&D Projects: GA ČR GA13-24880S Institutional support: RVO:61388963 Keywords : NMR spectroscopy * nucleic acid s * solid-state NMR Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 3.289, year: 2015 http://pubs.rsc.org/en/content/articlepdf/2015/ra/c4ra14404j
9. Fast mapping of global protein folding states by multivariate NMR:
DEFF Research Database (Denmark)
Malmendal, Anders; Underhaug, Jarl; Otzen, Daniel
2010-01-01
To obtain insight into the functions of proteins and their specific roles, it is important to establish efficient procedures for exploring the states that encapsulate their conformational space. Global Protein folding State mapping by multivariate NMR (GPS NMR) is a powerful high-throughput method......-lactalbumin in the presence of the anionic surfactant sodium dodecyl sulfate, SDS, and compare these with other surfactants, acid, denaturants and heat....
10. Solid state NMR of spin-1/2 nuclei
International Nuclear Information System (INIS)
Wind, R.A.
1991-01-01
The detection of nuclear magnetic resonance by Bloch et al. and Purcell and co-workers in 1946 has led to the development of one of the most powerful spectroscopic techniques known today. The reason is that, besides the applied external magnetic field, a nuclear spin also experiences extra local magnetic fields, which are due to surrounding electron clouds (the chemical shift) and other spins. These local fields differ for nuclei located at chemically different positions in a molecule. The result is that an NMR spectrum often consists of several lines, which can be considered to be a fingerprint of the material under investigation an can assist the clarifying its molecular structure. NMR has been especially successful in liquids and liquid like materials, where fast molecular tumblings average out the anisotropies in the local fields, resulting in well-resolved NMR spectra. This paper reports that initially the development of solid-state NMR was less dramatic. Originally, for reasons of sensitivity, attention was focused mainly on 1 H NMR. The result is that the NMR spectrum usually consists of single, broad, featureless line, which, except for special cases such as more or less isolated spin pairs or methyl groups, does not provide much information
11. ECG gated NMR-CT for cardiovascular diseases
International Nuclear Information System (INIS)
Nishikawa, J.; Machida, K.; Iio, M.; Yoshimoto, N.; Sugimoto, T.; Kawaguchi, H.; Mano, H.
1984-01-01
The authors applied NMR-CT to cardiac study with ECG gated technique to evaluate the left ventricular (LV) function and compared it with cardiovascular nuclear medicine study (NM). The NMR-CT machine has resistive air-core magnet with 0.15 Tesla. The saturation recovery image or inversion recovery image were obtained as 256 x 256 matrix and 15 mm in thickness. The study population was ten patients who were evaluated both by NMR image and by NM performed within one week interval. The heart muscle was able to be visualized without any contrast material nor radioisotopes in inversion recovery images, whereas saturation recovery images failed to separate heart muscle from blood pool. The wall motions of LV in both methods were well correlated except for inferior wall. The values of ejection fraction in NMR image were moderately low, but two modalities showed satisfactory correlation (r=0.85). The region of myocardial infarction was revealed as wall thinning and/or wall motion abnormality. It is still preliminary to draw a conclusion, however, it can be said that in the evaluation of LV function, method by NMR might be of equal value to those of NM. It can be certain that eventually gated NMR-CT will become more effective method for various aspects of cardiovascular evaluation
12. Protein folding on the ribosome studied using NMR spectroscopy
Science.gov (United States)
Waudby, Christopher A.; Launay, Hélène; Cabrita, Lisa D.; Christodoulou, John
2013-01-01
NMR spectroscopy is a powerful tool for the investigation of protein folding and misfolding, providing a characterization of molecular structure, dynamics and exchange processes, across a very wide range of timescales and with near atomic resolution. In recent years NMR methods have also been developed to study protein folding as it might occur within the cell, in a de novo manner, by observing the folding of nascent polypeptides in the process of emerging from the ribosome during synthesis. Despite the 2.3 MDa molecular weight of the bacterial 70S ribosome, many nascent polypeptides, and some ribosomal proteins, have sufficient local flexibility that sharp resonances may be observed in solution-state NMR spectra. In providing information on dynamic regions of the structure, NMR spectroscopy is therefore highly complementary to alternative methods such as X-ray crystallography and cryo-electron microscopy, which have successfully characterized the rigid core of the ribosome particle. However, the low working concentrations and limited sample stability associated with ribosome–nascent chain complexes means that such studies still present significant technical challenges to the NMR spectroscopist. This review will discuss the progress that has been made in this area, surveying all NMR studies that have been published to date, and with a particular focus on strategies for improving experimental sensitivity. PMID:24083462
13. Development of 19F-NMR chemical shift detection of DNA B-Z equilibrium using 19F-NMR.
Science.gov (United States)
Nakamura, S; Yang, H; Hirata, C; Kersaudy, F; Fujimoto, K
2017-06-28
Various DNA conformational changes are in correlation with biological events. In particular, DNA B-Z equilibrium showed a high correlation with translation and transcription. In this study, we developed a DNA probe containing 5-trifluoromethylcytidine or 5-trifluoromethylthymidine to detect DNA B-Z equilibrium using 19 F-NMR. Its probe enabled the quantitative detection of B-, Z-, and ss-DNA based on 19 F-NMR chemical shift change.
14. Catalyst surface characterized by high magnetic field NMR; Kojiba NMR ni yoru shokubai hyomen no kansatsu
Energy Technology Data Exchange (ETDEWEB)
Sato, S. [Chiba University, Chiba (Japan). Faculty of Engineering
1997-08-01
This paper introduces studies performed by the authors on observation of surface of solid catalysts by means of solid NMR measurement using the high-speed MAS technology which uses a high magnetic field device. In the studies, a device with 14.1T (resonant frequency of proton at 600 MHz) was used to conduct CP-MAS NMR measurement on {sup 29}Si to identify bonding of silica carrier in a fixed aluminum chloride catalyst. As a result, it was verified that the surface structure of aluminum chloride species deposited on the silica carrier turns to a structure in which AlCl2 species of a monomeric substance is bonded with a surface hydroxyl group and fixed in four- or five-orientation. When adjusted at low temperatures, an Al2Cl5 structure is formed, which is fixed as a dimeric substance with AlCl3 oriented in the AlCl2 species. It is conceived that the Al2Cl5 species has higher electrophilicity than the AlCl2 species as a result of AlCl3 oriented in AlCl2, whereas the hydroxyl group on the silica surface oriented with the Al2Cl5 species dissociates, discharging protons, thus showing strong acidity. 18 refs., 8 figs., 2 tabs.
15. Whole-core analysis by 13C NMR
International Nuclear Information System (INIS)
Vinegar, H.J.; Tutunjian, P.N.; Edelstein, W.A.; Roemer, P.B.
1991-01-01
This paper reports on a whole-core nuclear magnetic resonance (NMR) system that was used to obtain natural abundance 13 C spectra. The system enables rapid, nondestructive measurements of bulk volume of movable oil, aliphatic/aromatic ratio, oil viscosity, and organic vs. carbonate carbon. 13 C NMR can be used in cores where the 1 H NMR spectrum is too broad to resolve oil and water resonances separately. A 5 1/4-in. 13 C/ 1 H NMR coil was installed on a General Electric (GE) CSI-2T NMR imager/spectrometer. With a 4-in.-OD whole core, good 13 C signal/noise ratio (SNR) is obtained within minutes, while 1 H spectra are obtained in seconds. NMR measurements have been made of the 13 C and 1 H density of crude oils with a wide range of API gravities. For light- and medium-gravity oils, the 13 C and 1 H signal per unit volume is constant within about 3.5%. For heavy crudes, the 13 C and 1 H density measured by NMR is reduced by the shortening of spin-spin relaxation time. 13 C and 1 H NMR spin-lattice relaxation times were measured on a suite of Cannon viscosity standards, crude oils (4 to 60 degrees API), and alkanes (C 5 through C 16 ) with viscosities at 77 degrees F ranging from 0.5 cp to 2.5 x 10 7 cp. The 13 C and 1 H relaxation times show a similar correlation with viscosity from which oil viscosity can be estimated accurately for viscosities up to 100 cp. The 13 C surface relaxation rate for oils on water-wet rocks is very low. Nonproton decoupled 13 C NMR is shown to be insensitive to kerogen; thus, 13 C NMR measures only the movable hydrocarbon content of the cores. In carbonates, the 13 C spectrum also contains a carbonate powder pattern useful in quantifying inorganic carbon and distinguishing organic from carbonate carbon
16. NMR-CT in muscular disorders
International Nuclear Information System (INIS)
Matsumura, Kiichiro; Nakano, Imaharu; Fukuda, Nobuo; Ikehira, Hiroo; Tateno, Yukio.
1987-01-01
Proton NMR-CT (magnetic field strength 0.1 Tesla, resonant frequency 4.5 MHz) was performed in 10 normal females and 19 Duchenne muscular dystrophy (DMD) carriers. The mean age was 39 ± 12 years for the normal females and 42 ± 6 years for the DMD carriers. In DMD carriers, there were 4 definite, 4 probable, and 11 possible carriers. T 1 (spin-lattice relaxation time) image was obtained for a slice at the buttock, mid-thigh and calf levels respectively. T 1 values were measured for the medial portion of the gluteus maximus, the vastus lateralis of the quadriceps femoris, and the gastrocnemius. The bound water fraction (BWF) was calculated from Fullerton's equation based on the fast proton diffusion model. The following results were obtained: (1) In normal females, muscle T 1 value was highest in the gastrocnemius and lowest in the gluteus maximus. (2) In DMD carriers, T 1 values of the gluteus maximus and quadriceps femoris were significantly higher than those of the normal females. There was, however, no significant difference in T 1 value of the gastrocnemius between DMD carriers and normal females. (3) In DMD carriers, BWFs of the gluteus maximus and quadriceps femoris were significantly lower than those of the normal females. (4) In DMD carriers, no significant correlation was observed between the muscle T 1 values and the serum creatine phosphokinase values. Increased tissue water content in the lower parts of the body due to gravity is considered to be the primary cause of the high T 1 value in the gastrocnemius of normal females. The presence of the degenerating muscle fibers are presumed responsible for the high T 1 value and low BWF in the proximal muscles of DMD carriers. (author)
17. Accessible surface area from NMR chemical shifts
Energy Technology Data Exchange (ETDEWEB)
Hafsa, Noor E.; Arndt, David; Wishart, David S., E-mail: [email protected] [University of Alberta, Department of Computing Science (Canada)
2015-07-15
Accessible surface area (ASA) is the surface area of an atom, amino acid or biomolecule that is exposed to solvent. The calculation of a molecule’s ASA requires three-dimensional coordinate data and the use of a “rolling ball” algorithm to both define and calculate the ASA. For polymers such as proteins, the ASA for individual amino acids is closely related to the hydrophobicity of the amino acid as well as its local secondary and tertiary structure. For proteins, ASA is a structural descriptor that can often be as informative as secondary structure. Consequently there has been considerable effort over the past two decades to try to predict ASA from protein sequence data and to use ASA information (derived from chemical modification studies) as a structure constraint. Recently it has become evident that protein chemical shifts are also sensitive to ASA. Given the potential utility of ASA estimates as structural constraints for NMR we decided to explore this relationship further. Using machine learning techniques (specifically a boosted tree regression model) we developed an algorithm called “ShiftASA” that combines chemical-shift and sequence derived features to accurately estimate per-residue fractional ASA values of water-soluble proteins. This method showed a correlation coefficient between predicted and experimental values of 0.79 when evaluated on a set of 65 independent test proteins, which was an 8.2 % improvement over the next best performing (sequence-only) method. On a separate test set of 92 proteins, ShiftASA reported a mean correlation coefficient of 0.82, which was 12.3 % better than the next best performing method. ShiftASA is available as a web server ( http://shiftasa.wishartlab.com http://shiftasa.wishartlab.com ) for submitting input queries for fractional ASA calculation.
18. NMR-CT in muscular disorders
International Nuclear Information System (INIS)
Matsumura, Kiichiro; Nakano, Imaharu; Ikehira, Hiroo; Fukuda, Nobuo; Tateno, Yukio.
1986-01-01
Proton NMR-CT (magnetic field strength 0.1 Tesla, resonant frequency 4.5 MHz) was performed in 15 normal (NC) and 20 Duchenne muscular dystrophy (DMD) males. The age ranged from 3 to 47 years for the NC males, and 1 to 14 years for the DMD males. In the DMD group there were one subclinical stage, 4 stage 1, 6 stage 2, 4 stage 3, and 5 stage 5 or higher patients. T 1 (longitudinal relaxation) images were obtained for three slices at the buttock, midthigh, and calf levels. The T 1 values were measured for the medial portion of the gluteus maximus, the vastus lateralis of the quadriceps femoris, the adductors, the sartorius, the gracilis, and the gastrocnemius muscles. Bound water fraction (BWF) was calculated from Fullerton's equation based on the fast diffusion model. The following results were obtained: (1) In the NC group, muscle T 1 values declined gradually with maturation under the age of 10, and became constant beyond that. The average T 1 value was 280 ms for the age group between 3 and 6 years, 270 ms for 7 and 10 years, and 260 ms for those older than 10 years. (2) Muscle BWF increased with maturation in the NC group. (3) In the DMD group, T 1 values were initially higher than normal (300 ms), declined rapidly with the progress of the disease, and reached the same low level as the subcutaneous fat (190 ms). (4) This decrease of T 1 value in DMD was not uniform for all muscles, being most prominent in the gluteus maximus and least so in the sartorius and gracilis. (5) In the early stages of DMD, the BWF was lower than normal. (J.P.N.)
19. Timing and related artifacts in multidimensional NMR
International Nuclear Information System (INIS)
Marion, Dominique
2012-01-01
The information content of multidimensional NMR spectra is limited by the presence of several kinds of artifacts that originate from incorrect timing of evolution periods. The objective of this review is to provide tools for successful implementation of published pulse sequences, in which timing and pulse compensations are often implicit. We will analyze the constraints set by the use of Fourier transformation, the spin precession during rectangular or shaped pulses, the Bloch-Siegert effects due to pulse on other spins and the delay introduced by the filters for the acquisition dimension. A frequency dependent phase correction or an incorrect scaling of the first data point leads to baseline offsets or curvature due to the properties of the Fourier transform. Because any r.f. pulse has a finite length, chemical shift is always active during excitation, flip-back, inversion, and refocusing pulses. Rectangular or selective shaped pulses can be split into three periods: an ideal rotation surrounded by two chemical shift evolution periods, which should be subtracted from the adjacent delays to avoid linear phase correction. Bloch-Siegert effects originate from irradiation at frequencies near those observed in the spectrum and can lead to phase or frequency shifts. They can be minimized by simultaneous irradiation on both sides of the observed spins. In terms of timing, the very end of the pulse sequence the acquisition behaves differently since the data are filtered by either analog or digital means. This additional delay is filter and spectrometer specific and should be tuned to minimize the required phase correction. Combined together, all these adjustments lead to perfectly phased spectra with flat baseline and no peak shifts or distortion. (author)
20. Accurate, fully-automated NMR spectral profiling for metabolomics.
Directory of Open Access Journals (Sweden)
Siamak Ravanbakhsh
Full Text Available Many diseases cause significant changes to the concentrations of small molecules (a.k.a. metabolites that appear in a person's biofluids, which means such diseases can often be readily detected from a person's "metabolic profile"-i.e., the list of concentrations of those metabolites. This information can be extracted from a biofluids Nuclear Magnetic Resonance (NMR spectrum. However, due to its complexity, NMR spectral profiling has remained manual, resulting in slow, expensive and error-prone procedures that have hindered clinical and industrial adoption of metabolomics via NMR. This paper presents a system, BAYESIL, which can quickly, accurately, and autonomously produce a person's metabolic profile. Given a 1D 1H NMR spectrum of a complex biofluid (specifically serum or cerebrospinal fluid, BAYESIL can automatically determine the metabolic profile. This requires first performing several spectral processing steps, then matching the resulting spectrum against a reference compound library, which contains the "signatures" of each relevant metabolite. BAYESIL views spectral matching as an inference problem within a probabilistic graphical model that rapidly approximates the most probable metabolic profile. Our extensive studies on a diverse set of complex mixtures including real biological samples (serum and CSF, defined mixtures and realistic computer generated spectra; involving > 50 compounds, show that BAYESIL can autonomously find the concentration of NMR-detectable metabolites accurately (~ 90% correct identification and ~ 10% quantification error, in less than 5 minutes on a single CPU. These results demonstrate that BAYESIL is the first fully-automatic publicly-accessible system that provides quantitative NMR spectral profiling effectively-with an accuracy on these biofluids that meets or exceeds the performance of trained experts. We anticipate this tool will usher in high-throughput metabolomics and enable a wealth of new applications of
1. Comparing pharmacophore models derived from crystallography and NMR ensembles
Science.gov (United States)
Ghanakota, Phani; Carlson, Heather A.
2017-11-01
NMR and X-ray crystallography are the two most widely used methods for determining protein structures. Our previous study examining NMR versus X-Ray sources of protein conformations showed improved performance with NMR structures when used in our Multiple Protein Structures (MPS) method for receptor-based pharmacophores (Damm, Carlson, J Am Chem Soc 129:8225-8235, 2007). However, that work was based on a single test case, HIV-1 protease, because of the rich data available for that system. New data for more systems are available now, which calls for further examination of the effect of different sources of protein conformations. The MPS technique was applied to Growth factor receptor bound protein 2 (Grb2), Src SH2 homology domain (Src-SH2), FK506-binding protein 1A (FKBP12), and Peroxisome proliferator-activated receptor-γ (PPAR-γ). Pharmacophore models from both crystal and NMR ensembles were able to discriminate between high-affinity, low-affinity, and decoy molecules. As we found in our original study, NMR models showed optimal performance when all elements were used. The crystal models had more pharmacophore elements compared to their NMR counterparts. The crystal-based models exhibited optimum performance only when pharmacophore elements were dropped. This supports our assertion that the higher flexibility in NMR ensembles helps focus the models on the most essential interactions with the protein. Our studies suggest that the "extra" pharmacophore elements seen at the periphery in X-ray models arise as a result of decreased protein flexibility and make very little contribution to model performance.
2. Can NMR solve some significant challenges in metabolomics?
Science.gov (United States)
Nagana Gowda, G A; Raftery, Daniel
2015-11-01
The field of metabolomics continues to witness rapid growth driven by fundamental studies, methods development, and applications in a number of disciplines that include biomedical science, plant and nutrition sciences, drug development, energy and environmental sciences, toxicology, etc. NMR spectroscopy is one of the two most widely used analytical platforms in the metabolomics field, along with mass spectrometry (MS). NMR's excellent reproducibility and quantitative accuracy, its ability to identify structures of unknown metabolites, its capacity to generate metabolite profiles using intact bio-specimens with no need for separation, and its capabilities for tracing metabolic pathways using isotope labeled substrates offer unique strengths for metabolomics applications. However, NMR's limited sensitivity and resolution continue to pose a major challenge and have restricted both the number and the quantitative accuracy of metabolites analyzed by NMR. Further, the analysis of highly complex biological samples has increased the demand for new methods with improved detection, better unknown identification, and more accurate quantitation of larger numbers of metabolites. Recent efforts have contributed significant improvements in these areas, and have thereby enhanced the pool of routinely quantifiable metabolites. Additionally, efforts focused on combining NMR and MS promise opportunities to exploit the combined strength of the two analytical platforms for direct comparison of the metabolite data, unknown identification and reliable biomarker discovery that continue to challenge the metabolomics field. This article presents our perspectives on the emerging trends in NMR-based metabolomics and NMR's continuing role in the field with an emphasis on recent and ongoing research from our laboratory. Copyright © 2015 Elsevier Inc. All rights reserved.
3. 1H-NMR, 1H-NMR T2-edited, and 2D-NMR in bipolar disorder metabolic profiling.
Science.gov (United States)
Sethi, Sumit; Pedrini, Mariana; Rizzo, Lucas B; Zeni-Graiff, Maiara; Mas, Caroline Dal; Cassinelli, Ana Cláudia; Noto, Mariane N; Asevedo, Elson; Cordeiro, Quirino; Pontes, João G M; Brasil, Antonio J M; Lacerda, Acioly; Hayashi, Mirian A F; Poppi, Ronei; Tasic, Ljubica; Brietzke, Elisa
2017-12-01
The objective of this study was to identify molecular alterations in the human blood serum related to bipolar disorder, using nuclear magnetic resonance (NMR) spectroscopy and chemometrics. Metabolomic profiling, employing 1 H-NMR, 1 H-NMR T 2 -edited, and 2D-NMR spectroscopy and chemometrics of human blood serum samples from patients with bipolar disorder (n = 26) compared with healthy volunteers (n = 50) was performed. The investigated groups presented distinct metabolic profiles, in which the main differential metabolites found in the serum sample of bipolar disorder patients compared with those from controls were lipids, lipid metabolism-related molecules (choline, myo-inositol), and some amino acids (N-acetyl-L-phenyl alanine, N-acetyl-L-aspartyl-L-glutamic acid, L-glutamine). In addition, amygdalin, α-ketoglutaric acid, and lipoamide, among other compounds, were also present or were significantly altered in the serum of bipolar disorder patients. The data presented herein suggest that some of these metabolites differentially distributed between the groups studied may be directly related to the bipolar disorder pathophysiology. The strategy employed here showed significant potential for exploring pathophysiological features and molecular pathways involved in bipolar disorder. Thus, our findings may contribute to pave the way for future studies aiming at identifying important potential biomarkers for bipolar disorder diagnosis or progression follow-up.
4. Quantitative analysis of protein-ligand interactions by NMR.
Science.gov (United States)
Furukawa, Ayako; Konuma, Tsuyoshi; Yanaka, Saeko; Sugase, Kenji
2016-08-01
Protein-ligand interactions have been commonly studied through static structures of the protein-ligand complex. Recently, however, there has been increasing interest in investigating the dynamics of protein-ligand interactions both for fundamental understanding of the underlying mechanisms and for drug development. NMR is a versatile and powerful tool, especially because it provides site-specific quantitative information. NMR has widely been used to determine the dissociation constant (KD), in particular, for relatively weak interactions. The simplest NMR method is a chemical-shift titration experiment, in which the chemical-shift changes of a protein in response to ligand titration are measured. There are other quantitative NMR methods, but they mostly apply only to interactions in the fast-exchange regime. These methods derive the dissociation constant from population-averaged NMR quantities of the free and bound states of a protein or ligand. In contrast, the recent advent of new relaxation-based experiments, including R2 relaxation dispersion and ZZ-exchange, has enabled us to obtain kinetic information on protein-ligand interactions in the intermediate- and slow-exchange regimes. Based on R2 dispersion or ZZ-exchange, methods that can determine the association rate, kon, dissociation rate, koff, and KD have been developed. In these approaches, R2 dispersion or ZZ-exchange curves are measured for multiple samples with different protein and/or ligand concentration ratios, and the relaxation data are fitted to theoretical kinetic models. It is critical to choose an appropriate kinetic model, such as the two- or three-state exchange model, to derive the correct kinetic information. The R2 dispersion and ZZ-exchange methods are suitable for the analysis of protein-ligand interactions with a micromolar or sub-micromolar dissociation constant but not for very weak interactions, which are typical in very fast exchange. This contrasts with the NMR methods that are used
5. NMR studies of echinomycin bisintercalation complexes with d(A1-C2-G3-T4) and d(T1-C2-G3-A4) duplexes in aqueous solution: sequence-dependent formation of Hoogsteen A1 x T4 and Watson-Crick T1 x A4 base pairs flanking the bisintercalation site
International Nuclear Information System (INIS)
Gao, X.; Patel, D.J.
1988-01-01
The authors report on two-dimensional proton NMR studies of echinomycin complexes with the self-complementary d(A1-C2-G3-Tr) and d(T1-C2-G3-A4) duplexes in aqueous solution. The exchangeable and nonexchangeable antibiotic and nucleic acid protons in the 1 echinomycin per tetranucleotide duplex complexes have been assigned from analyses of scalar coupling and distance connectivities in two-dimensional data sets records in H 2 O and D 2 O solution. An analysis of the intermolecular NOE patterns for both complexes combined with large upfield imino proton and large downfield phosphorus complexation chemical shift changes demonstrates that the two quinoxaline chromophores of echinomycin bisintercalate into the minor groove surrounding the dC-dG step of each tetranucleotide duplex. Further, the quinoxaline rings selectively stack between A1 and C2 bases in the d(ACGT) complex and between T1 and C2 bases in the d(TCGA) complex. The intermolecular NOE patterns and the base and sugar proton chemical shifts for residues C2 and G3 are virtually identical for the d(ACGT) and d(TCGA) complexes. A large set of intermolecular contacts established from nuclear Overhauser effects (NOEs) between antibiotic and nucleic acid protons in the echinomycin-tetranucleotide complexes in solution are consistent with corresponding contacts reported for echinomycin-oligonucleotide complexes in the crystalline state. The authors demonstrate that the G x G base pairs adopt Watson-Crick pairing in both d(ACGT) and d(TCGA) complexes in solution. By contrast, the A1 x T4 base pairs adopt Hoogsteen pairing for the echinomycin-d(A1-C2-G3-Tr) complex while the T1 x A4 base pairs adopt Watson-Crick pairing for the echinomycin-d(T1-C2-G3-A4) complex in aqueous solution. These results emphasize the role of sequence in discriminating between Watson-Crick and Hoogsteen pairs at base pairs flanking the echinomycin bisintercalation site in solution
6. NMR Characterization of Flavanone Naringenin 7-O-Glycoside Diastereomer
Directory of Open Access Journals (Sweden)
SUN Li-juan
2017-12-01
Full Text Available To discriminate R and S flavanone glycoside using NMR, the mixture of R and S naringenin 7-O-glycoside was first isolated from Gleditsia sinensis. 1H and 13C NMR data of the mixture were recorded with 1H NMR, 13C NMR, 1H-1H COSY, 1H-13C HSQC and 1H-13C HMBC in DMSO-d6 solution. The two diastereomers were then separated with chiral chromatographic isolation, with their absolute configurations determined by circular dichroism. To avoid the disturbance of protons from glucose residues to dihydroflavonoid, 1H NMR spectra were acquired for pure R and S naringenin 7-O-glycoside and their mixture in CD3CN. The two diastereomers showed the largest proton chemical shift differences at the end group of glucose residue (H-1" with a chemical shift difference of 9.4 Hz. The OH-5 proton showed a chemical shift difference of 5.8 Hz. The chemical shift of the three protons on ring C were all influenced by configuration.
7. Chirp echo Fourier transform EPR-detected NMR.
Science.gov (United States)
Wili, Nino; Jeschke, Gunnar
2018-04-01
A new ultra-wide band (UWB) pulse EPR method is introduced for observing all nuclear frequencies of a paramagnetic center in a single shot. It is based on burning spectral holes with a high turning angle (HTA) pulse that excites forbidden transitions and subsequent detection of the hole pattern by a chirp echo. We term this method Chirp Echo Epr SpectroscopY (CHEESY)-detected NMR. The approach is a revival of FT EPR-detected NMR. It yields similar spectra and the same type of information as electron-electron double resonance (ELDOR)-detected NMR, but with a multiplex advantage. We apply CHEESY-detected NMR in Q band to nitroxides and correlate the hyperfine spectrum to the EPR spectrum by varying the frequency of the HTA pulse. Furthermore, a selective π pulse before the HTA pulse allows for detecting hyperfine sublevel correlations between transitions of one nucleus and for elucidating the coupling regime, the same information as revealed by the HYSCORE experiment. This is demonstrated on hexaaquamanganese(II). We expect that CHEESY-detected NMR is generally applicable to disordered systems and that our results further motivate the development of EPR spectrometers capable of coherent UWB excitation and detection, especially at higher fields and frequencies. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.
8. Selected topics in solution-phase biomolecular NMR spectroscopy
Science.gov (United States)
Kay, Lewis E.; Frydman, Lucio
2017-05-01
Solution bio-NMR spectroscopy continues to enjoy a preeminent role as an important tool in elucidating the structure and dynamics of a range of important biomolecules and in relating these to function. Equally impressive is how NMR continues to 'reinvent' itself through the efforts of many brilliant practitioners who ask increasingly demanding and increasingly biologically relevant questions. The ability to manipulate spin Hamiltonians - almost at will - to dissect the information of interest contributes to the success of the endeavor and ensures that the NMR technology will be well poised to contribute to as yet unknown frontiers in the future. As a tribute to the versatility of solution NMR in biomolecular studies and to the continued rapid advances in the field we present a Virtual Special Issue (VSI) that includes over 40 articles on various aspects of solution-state biomolecular NMR that have been published in the Journal of Magnetic Resonance in the past 7 years. These, in total, help celebrate the achievements of this vibrant field.
9. Development of a superconducting bulk magnet for NMR and MRI.
Science.gov (United States)
Nakamura, Takashi; Tamada, Daiki; Yanagi, Yousuke; Itoh, Yoshitaka; Nemoto, Takahiro; Utumi, Hiroaki; Kose, Katsumi
2015-10-01
A superconducting bulk magnet composed of six vertically stacked annular single-domain c-axis-oriented Eu-Ba-Cu-O crystals was energized to 4.74 T using a conventional superconducting magnet for high-resolution NMR spectroscopy. Shim coils, gradient coils, and radio frequency coils for high resolution NMR and MRI were installed in the 23 mm-diameter room-temperature bore of the bulk magnet. A 6.9 ppm peak-to-peak homogeneous region suitable for MRI was achieved in the central cylindrical region (6.2 mm diameter, 9.1 mm length) of the bulk magnet by using a single layer shim coil. A 21 Hz spectral resolution that can be used for high resolution NMR spectroscopy was obtained in the central cylindrical region (1.3 mm diameter, 4 mm length) of the bulk magnet by using a multichannel shim coil. A clear 3D MR image dataset of a chemically fixed mouse fetus with (50 μm)(3) voxel resolution was obtained in 5.5 h. We therefore concluded that the cryogen-free superconducting bulk magnet developed in this study is useful for high-resolution desktop NMR, MRI and mobile NMR device. Copyright © 2015 Elsevier Inc. All rights reserved.
10. Experimental solid state NMR of gas hydrates : problems and solutions
Energy Technology Data Exchange (ETDEWEB)
Moudrakovski, I.; Lu, H.; Ripmeester, J. [National Research Council of Canada, Ottawa, ON (Canada). Steacie Inst. for Molecular Sciences; Kumar, R.; Susilo, R. [British Columbia Univ., Vancouver, BC (Canada). Dept. of Chemical and Biological Engineering; Luzi, M. [GeoForschungsZentrum Potsdam, Potsdam (Germany)
2008-07-01
Solid State NMR is a suitable spectroscopic technique for hydrate research for several reasons, including its capability to distinguish between different structural types of hydrates, its quantitative nature and potential for both in-situ and time resolved experiments. This study illustrated the applications of solid state NMR for compositional and structural studies of clathrate hydrates, with particular emphasis on experimental techniques and potential ways to overcome technical difficulties. In order to use the method to its full capacity, some instrumental developments are needed to adapt it to the specific experimental requirements of hydrate studies, such as very low temperatures and high pressures. This presentation discussed the quantification of the Carbon-13 spectra with examples from natural and synthetic hydrates prepared from multi-component mixtures of hydrocarbons. The main approach used for the first two examples was Carbon-13 NMR with Magic Angle Spinning (MAS) at -100 degrees C. The detailed characterization of mixed hydrogen hydrates required low temperature hydrogen MAS. The quantification problems encountered during these experiments were also discussed. The purpose of these recent experimental developments was to prompt wider application of Solid State NMR in hydrate research. NMR proved to be a viable method for analyzing the composition and structure of multi-component mixed gas hydrates; characterizing natural gas hydrates; and, evaluating the formation conditions and properties of mixed hydrogen hydrates. The limitations of the method were highlighted and sensible choices of experimental conditions and techniques that ensure accurate results were discussed. 34 refs., 10 figs.
11. Condensed Matter NMR under Extreme Conditions: Challenges and Opportunities
Science.gov (United States)
Reyes, Arneil
2006-11-01
Advances in resistive magnet and power supply technology have made available extremely high magnetic fields suitable for condensed matter broadline NMR experiments. This capability expands the available phase space for investigating a wide variety of materials using magnetic resonance; utilizing the strength of the field to expose or induce new physical phenomena resulting in better understanding of the physics. Continuous fields up to 45T in NHMFL Hybrid magnet have brought new challenges in designing NMR instrumentation. Field strengths and sample space limitations put constraints on RF pulse power, tuning range, bandwidth, and temperature control. The inclusion of other capabilities, including high pressure, optics, and sample rotation requires intricate probe design and construction, while extremely low milliKelvin temperatures are desired in order to explore energy scales where thermal fluctuations are suppressed. Optimization of these devices has been of paramount consideration in NHMFL Condensed Matter NMR user program. Science achieved at high fields, the new initiatives to develop resistively-detected NMR in 2D electron gas and similar systems, and the current new generation Series-Connected Hybrid magnets for NMR work will be discussed. The NHMFL is supported by the National Science Foundation and the State of Florida.
12. In situ viscosity of oil sands using low field NMR
International Nuclear Information System (INIS)
Bryan, J.; Moon, D.; Kantzas, A.
2005-01-01
In heavy oil and bitumen reservoirs, oil viscosity is a vital piece of information that will have great bearing on the chosen EOR scheme and the recovery expected. Prediction of in situ viscosity with a logging tool would he very beneficial in reservoir characterization and exploitation design. Low field NMR is a technology that has shown great potential as a tool for characterizing hydrocarbon properties in heavy oil and bitumen reservoirs. An oil viscosity correlation has previously been developed that is capable of providing order of magnitude viscosity estimates for a wide range of oils taken from various fields in Alberta. This paper presents tuning procedures to improve the NMR predictions for different viscosity ranges, and extends the NMR viscosity model to in situ heavy oil in unconsolidated sands. The results of this work show that the NMR oil peak can be de-convoluted from the in situ signals of the oil and water, and the bulk viscosity correlation that was developed for bulk oils can he applied to predict the in situ oil viscosity. These results can be translated to an NMR logging tool algorithm, allowing for in situ measurements of oil viscosity at the proper reservoir conditions. (author)
13. The NMR Probe of High-T$_{c}$ Materials
CERN Document Server
Walstedt, Russell E
2008-01-01
The NMR probe has yielded a vast array of data for the high-Tc materials, corresponding to different compounds, ionic sites, and nuclear species, as well as to a wide variety of experimental conditions. Over the twenty years, since the discovery of superconducting cuprates, ongoing analysis and discussion of cuprate NMR data have resulted in a wealth of important insights into the physics of these exotic systems. The aims of this monograph are threefold. First, it reviews NMR methodology as it has been applied to the cuprate studies. This is addressed to NMR practitioners and to physics laypersons alike. Next, it presents a review of cuprate NMR measurements and the wide variety of phenomena which they represent. The third phase is to recount the theoretical model calculations and other proposals which have been put forward to account for these data. Parts two and three are presented in parallel, as there are many aspects to both topics, each with its own interesting history. There is, even twenty years on, a...
14. Chirp echo Fourier transform EPR-detected NMR
Science.gov (United States)
Wili, Nino; Jeschke, Gunnar
2018-04-01
A new ultra-wide band (UWB) pulse EPR method is introduced for observing all nuclear frequencies of a paramagnetic center in a single shot. It is based on burning spectral holes with a high turning angle (HTA) pulse that excites forbidden transitions and subsequent detection of the hole pattern by a chirp echo. We term this method Chirp Echo Epr SpectroscopY (CHEESY)-detected NMR. The approach is a revival of FT EPR-detected NMR. It yields similar spectra and the same type of information as electron-electron double resonance (ELDOR)-detected NMR, but with a multiplex advantage. We apply CHEESY-detected NMR in Q band to nitroxides and correlate the hyperfine spectrum to the EPR spectrum by varying the frequency of the HTA pulse. Furthermore, a selective π pulse before the HTA pulse allows for detecting hyperfine sublevel correlations between transitions of one nucleus and for elucidating the coupling regime, the same information as revealed by the HYSCORE experiment. This is demonstrated on hexaaquamanganese(II). We expect that CHEESY-detected NMR is generally applicable to disordered systems and that our results further motivate the development of EPR spectrometers capable of coherent UWB excitation and detection, especially at higher fields and frequencies.
15. Application of Solution NMR Spectroscopy to Study Protein Dynamics
Directory of Open Access Journals (Sweden)
Christoph Göbl
2012-03-01
Full Text Available Recent advances in spectroscopic methods allow the identification of minute fluctuations in a protein structure. These dynamic properties have been identified as keys to some biological processes. The consequences of this structural flexibility can be far‑reaching and they add a new dimension to the structure-function relationship of biomolecules. Nuclear Magnetic Resonance (NMR spectroscopy allows the study of structure as well as dynamics of biomolecules in a very broad range of timescales at atomic level. A number of new NMR methods have been developed recently to allow the measurements of time scales and spatial fluctuations, which in turn provide the thermodynamics associated with the biological processes. Since NMR parameters reflect ensemble measurements, structural ensemble approaches in analyzing NMR data have also been developed. These new methods in some instances can even highlight previously hidden conformational features of the biomolecules. In this review we describe several solution NMR methods to study protein dynamics and discuss their impact on important biological processes.
16. Time domain NMR evaluation of poly(vinyl alcohol) xerogels
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, Elton Jorge da Rocha; Cavalcante, Maxwell de Paula; Tavares, Maria Ines Bruno, E-mail: [email protected] [Universidade Federal do Rio de Janeiro (IMA/UFRJ), Rio de Janeiro, RJ (Brazil). Centro de Tecnologia. Instituto de Macromoleculas Professora Eloisa Mano
2016-05-15
Poly(vinyl alcohol) (PVA)-based chemically cross-linked xerogels, both neat and loaded with nanoparticulate hydrophilic silica (SiO{sub 2}), were obtained and characterized mainly through time domain NMR experiments (TD-NMR). Fourier-transform infrared (FT-IR) and wide angle X-ray diffraction (WAXD) analyses were employed as secondary methods. TD-NMR, through the interpretation of the spin-lattice relaxation constant values and related information, showed both cross-linking and nanoparticle influences on PVA matrix. SiO{sub 2} does not interact chemically with the PVA chains, but has effect on its molecular mobility, as investigated via TD-NMR. Apparent energy of activation, spin-lattice time constant and size of spin domains in the sample have almost linear dependence with the degree of cross-linking of the PVA and are affected by the addition of SiO{sub 2}. These three parameters were derived from a single set of TD-NMR experiments, which demonstrates the versatility of the technique for characterization of inorganic-organic hybrid xerogels, an important class of materials. (author)
17. The GNAT: A new tool for processing NMR data.
Science.gov (United States)
Castañar, Laura; Poggetto, Guilherme Dal; Colbourne, Adam A; Morris, Gareth A; Nilsson, Mathias
2018-06-01
The GNAT (General NMR Analysis Toolbox) is a free and open-source software package for processing, visualising, and analysing NMR data. It supersedes the popular DOSY Toolbox, which has a narrower focus on diffusion NMR. Data import of most common formats from the major NMR platforms is supported, as well as a GNAT generic format. Key basic processing of NMR data (e.g., Fourier transformation, baseline correction, and phasing) is catered for within the program, as well as more advanced techniques (e.g., reference deconvolution and pure shift FID reconstruction). Analysis tools include DOSY and SCORE for diffusion data, ROSY T 1 /T 2 estimation for relaxation data, and PARAFAC for multilinear analysis. The GNAT is written for the MATLAB® language and comes with a user-friendly graphical user interface. The standard version is intended to run with a MATLAB installation, but completely free-standing compiled versions for Windows, Mac, and Linux are also freely available. © 2018 The Authors Magnetic Resonance in Chemistry Published by John Wiley & Sons Ltd.
18. Novel NMR tools to study structure and dynamics of biomembranes.
Science.gov (United States)
Gawrisch, Klaus; Eldho, Nadukkudy V; Polozov, Ivan V
2002-06-01
Nuclear magnetic resonance (NMR) studies on biomembranes have benefited greatly from introduction of magic angle spinning (MAS) NMR techniques. Improvements in MAS probe technology, combined with the higher magnetic field strength of modern instruments, enables almost liquid-like resolution of lipid resonances. The cross-relaxation rates measured by nuclear Overhauser enhancement spectroscopy (NOESY) provide new insights into conformation and dynamics of lipids with atomic-scale resolution. The data reflect the tremendous motional disorder in the lipid matrix. Transfer of magnetization by spin diffusion along the proton network of lipids is of secondary relevance, even at a long NOESY mixing time of 300 ms. MAS experiments with re-coupling of anisotropic interactions, like the 13C-(1)H dipolar couplings, benefit from the excellent resolution of 13C shifts that enables assignment of the couplings to specific carbon atoms. The traditional 2H NMR experiments on deuterated lipids have higher sensitivity when conducted on oriented samples at higher magnetic field strength. A very large number of NMR parameters from lipid bilayers is now accessible, providing information about conformation and dynamics for every lipid segment. The NMR methods have the sensitivity and resolution to study lipid-protein interaction, lateral lipid organization, and the location of solvents and drugs in the lipid matrix.
19. High resolution deuterium NMR studies of bacterial metabolism
Energy Technology Data Exchange (ETDEWEB)
Aguayo, J.B.; Gamcsik, M.P.; Dick, J.D.
1988-12-25
High resolution deuterium NMR spectra were obtained from suspensions of five bacterial strains: Escherichia coli, Clostridium perfringens, Klebsiella pneumoniae, Proteus mirabilis, and Staphylococcus aureus. Deuterium-labeled D-glucose at C-1, C-2, and C-6 was used to monitor dynamically anaerobic metabolism. The flux of glucose through the various bacterial metabolic pathways could be determined by following the disappearance of glucose and the appearance of the major end products in the 2H NMR spectrum. The presence of both labeled and unlabeled metabolites could be detected using 1H NMR spectroscopy since the proton resonances in the labeled species are shifted upfield due to an isotopic chemical shift effect. The 1H-1H scalar coupling observed in both the 2H and 1H NMR spectra was used to assign definitively the resonances of labeled species. An increase in the intensity of natural abundance deuterium signal of water can be used to monitor pathways in which a deuteron is lost from the labeled metabolite. The steps in which label loss can occur are outlined, and the influence these processes have on the ability of 2H NMR spectroscopy to monitor metabolism are assessed.
20. High resolution deuterium NMR studies of bacterial metabolism
International Nuclear Information System (INIS)
Aguayo, J.B.; Gamcsik, M.P.; Dick, J.D.
1988-01-01
High resolution deuterium NMR spectra were obtained from suspensions of five bacterial strains: Escherichia coli, Clostridium perfringens, Klebsiella pneumoniae, Proteus mirabilis, and Staphylococcus aureus. Deuterium-labeled D-glucose at C-1, C-2, and C-6 was used to monitor dynamically anaerobic metabolism. The flux of glucose through the various bacterial metabolic pathways could be determined by following the disappearance of glucose and the appearance of the major end products in the 2H NMR spectrum. The presence of both labeled and unlabeled metabolites could be detected using 1H NMR spectroscopy since the proton resonances in the labeled species are shifted upfield due to an isotopic chemical shift effect. The 1H-1H scalar coupling observed in both the 2H and 1H NMR spectra was used to assign definitively the resonances of labeled species. An increase in the intensity of natural abundance deuterium signal of water can be used to monitor pathways in which a deuteron is lost from the labeled metabolite. The steps in which label loss can occur are outlined, and the influence these processes have on the ability of 2H NMR spectroscopy to monitor metabolism are assessed
1. Unified integration intervals for the structural characterization of oil, coal or fractions there of by 1h NMR and 13c NMR
International Nuclear Information System (INIS)
Avella, Eliseo; Fierro, Ricardo
2010-01-01
Based on an analysis of publications reported between 1972 and 2006, it became clear that there are inaccuracies in the limits of the ranges of integration that the authors assigned to signals in nuclear magnetic resonance (NMR) to the structural characterization of petroleum, coals and their derived fractions, from their hydrogen (1H NMR) and carbon (13C NMR) spectra. Consequently, consolidated limits were determined for the integration of 1H NMR spectra and 13C NMR of these samples using a statistical treatment applied to the limits of integration intervals already published. With these unified limits, correlation NMR charts were developed that are useful for the allocation of the integral at such intervals, and at smaller intervals defined in terms of the intersection between different assignments. Also raised equations needed to establish the integral attributable to specific fragments in an attempt to make a more accurate structural characterization from NMR spectra of oil, coal or fractions derived.
2. Experimental demonstration of quantum contextuality on an NMR qutrit
Energy Technology Data Exchange (ETDEWEB)
Dogra, Shruti; Dorai, Kavita, E-mail: [email protected]; Arvind
2016-05-20
We experimentally test quantum contextuality of a single qutrit using NMR. The contextuality inequalities based on nine observables developed by Kurzynski et al. are first reformulated in terms of traceless observables which can be measured in an NMR experiment. These inequalities reveal the contextuality of almost all single-qutrit states. We demonstrate the violation of the inequality on four different initial states of a spin-1 deuterium nucleus oriented in a liquid crystal matrix, and follow the violation as the states evolve in time. We also describe and experimentally perform a single-shot test of contextuality for a subclass of qutrit states whose density matrix is diagonal in the energy basis. - Highlights: • A contextuality inequality for a single qutrit was designed using traceless observables. • The violation of the inequality was experimentally demonstrated using NMR. • A single-shot test was experimentally performed for a subclass of diagonal qutrit states.
3. 129 Xe-NMR of carbon black filled elastomers
International Nuclear Information System (INIS)
Sperling-Ischinsky, K.; Veeman, W.S.
1999-01-01
It is shown that 129 Xe-NMR is a powerful tool to investigate carbon black and carbon black filled elastomers. For the carbon black material itself the 129 Xe chemical shift of xenon adsorbed at the surface of carbon black aggregates yields information about the relative average pore size of the carbon black aggregates. The experimental 129 Xe-NMR results of carbon black filled ethylene-propylene-diene (EPDM) can be explained when it is assumed that the xenon atoms in the bound EPDM fraction exchange rapidly on the NMR time scale between a state where they are adsorbed on the carbon black surface and a state in which they are absorbed in the EPDM layer. This would imply that the carbon black aggregates are not completely covered with EPDM chains. (author)
4. A fragment separator at LBL for beta-NMR experiment
International Nuclear Information System (INIS)
Matsuta, K.; Ozawa, A.; Nojiri, Y.; Minamisono, T.; Fukuda, M.; Kitagawa, A.; Ohtsubo, T.; Momota, S.; Fukuda, S.; Matsuo, Y.; Takechi, H.; Minami, I.; Sugimoto, K.; Tanihata, I.; Omata, K.; Alonso, J.R.; Krebs, G.F.; Symons, T.J.M.
1992-03-01
The Beam 44 fragment separator was built at the Bevalac of LBL for NMR studies of beta emitting nuclei. 37 K, 39 Ca, and 43 Ti fragments originating from 40 Ca and 46 Ti primary beams were separated by the separator for NMR studies on these nuclei. Nuclear spin polarization was created in 39 Ca and 43 Ti using the tilted foil technique (TFT), and the magnetic moment of 43 Ti was deduced. Fragment polarization was measured for 37 K and 39 Ca emitted to finite deflection angles. The Beam 44 fragment separator in combination with a proper polarization technique, such as TFT or fragment polarization, has been very effective for such NMR studies
5. Experimental demonstration of quantum contextuality on an NMR qutrit
International Nuclear Information System (INIS)
Dogra, Shruti; Dorai, Kavita; Arvind
2016-01-01
We experimentally test quantum contextuality of a single qutrit using NMR. The contextuality inequalities based on nine observables developed by Kurzynski et al. are first reformulated in terms of traceless observables which can be measured in an NMR experiment. These inequalities reveal the contextuality of almost all single-qutrit states. We demonstrate the violation of the inequality on four different initial states of a spin-1 deuterium nucleus oriented in a liquid crystal matrix, and follow the violation as the states evolve in time. We also describe and experimentally perform a single-shot test of contextuality for a subclass of qutrit states whose density matrix is diagonal in the energy basis. - Highlights: • A contextuality inequality for a single qutrit was designed using traceless observables. • The violation of the inequality was experimentally demonstrated using NMR. • A single-shot test was experimentally performed for a subclass of diagonal qutrit states.
6. NMRFx Processor: a cross-platform NMR data processing program
International Nuclear Information System (INIS)
Norris, Michael; Fetler, Bayard; Marchant, Jan; Johnson, Bruce A.
2016-01-01
NMRFx Processor is a new program for the processing of NMR data. Written in the Java programming language, NMRFx Processor is a cross-platform application and runs on Linux, Mac OS X and Windows operating systems. The application can be run in both a graphical user interface (GUI) mode and from the command line. Processing scripts are written in the Python programming language and executed so that the low-level Java commands are automatically run in parallel on computers with multiple cores or CPUs. Processing scripts can be generated automatically from the parameters of NMR experiments or interactively constructed in the GUI. A wide variety of processing operations are provided, including methods for processing of non-uniformly sampled datasets using iterative soft thresholding. The interactive GUI also enables the use of the program as an educational tool for teaching basic and advanced techniques in NMR data analysis.
7. Ligand screening by saturation-transfer difference (STD) NMR spectroscopy.
Energy Technology Data Exchange (ETDEWEB)
Krishnan, V V
2005-04-26
NMR based methods to screen for high-affinity ligands have become an indispensable tool for designing rationalized drugs, as these offer a combination of good experimental design of the screening process and data interpretation methods, which together provide unprecedented information on the complex nature of protein-ligand interactions. These methods rely on measuring direct changes in the spectral parameters, that are often simpler than the complex experimental procedures used to study structure and dynamics of proteins. The goal of this review article is to provide the basic details of NMR based ligand-screening methods, with particular focus on the saturation transfer difference (STD) experiment. In addition, we provide an overview of other NMR experimental methods and a practical guide on how to go about designing and implementing them.
8. 11B nutation NMR study of powdered borosilicates
International Nuclear Information System (INIS)
Woo, Ae Ja; Yang, Kyung Hwa; Han, Duk Young
1998-01-01
In this work, we applied the 1D 11 B nutation NMR method for the analysis of the local structural environments in powdered borosilicates (SiO 2 -B 2 O 3 ). Spin dynamics during a rf irradiation for spin I=3/2 was analytically calculated with a density matrix formalism. Spectral simulation programs were written in MATLAB on a PC. Two borosilicates prepared by the sol-gel process at different stabilization temperature were used for the 1D 11 B nutation NMR experiment. The 11 B NMR parameters, quadrupole coupling constants (e 2 qQ/h) and asymmetry parameters (η), for each borosilicate were extracted from the nonlinear least-squares fitting. The effects of heat treatments on the local structures of boron sites in borosilicates were discussed
9. Automated high-resolution NMR with a sample changer
International Nuclear Information System (INIS)
Wade, C.G.; Johnson, R.D.; Philson, S.B.; Strouse, J.; McEnroe, F.J.
1989-01-01
Within the past two years, it has become possible to obtain high-resolution NMR spectra using automated commercial instrumentation. Software control of all spectrometer functions has reduced most of the tedious manual operations to typing a few computer commands or even making selections from a menu. Addition of an automatic sample changer is the next natural step in improving efficiency and sample throughput; it has a significant (and even unexpected) impact on how NMR laboratories are run and how it is taught. Such an instrument makes even sophisticated experiments routine, so that people with no previous exposure to NMR can run these experiments after a training session of an hour or less. This A/C Interface examines the impact of such instrumentation on both the academic and the industrial laboratory
10. Variable-temperature NMR and conformational analysis of Oenothein B
International Nuclear Information System (INIS)
Santos, Suzana C.; Carvalho, Ariadne G.; Fortes, Gilmara A.C.; Ferri, Pedro H.; Oliveira, Anselmo E. de
2014-01-01
Oenothein B is a dimeric hydrolyzable tannin with a wide range of biological activities, such as antitumour, anti-inflammatory and antiviral. Its nuclear magnetic resonance (NMR) at room temperature show duplications and broadening of signals. Experiments of 1D and 2D NMR at lower temperatures were useful for the complete NMR assignments of all hydrogens and carbons. The 3D structure of the most stable conformer was determined for the first time by nuclear Overhauser effect spectroscopy (NOESY) experiment (-20 deg C) and density functional theory (DFT)(B3LYP/6-31G)/ polarizable continuum model (PCM) quantum chemical calculations. The favoured conformation showed a highly compacted geometry and a lack of symmetry, in which the two valoneoyl groups showed distinct conformational parameters and stabilities. (author)
11. Variable-temperature NMR and conformational analysis of Oenothein B
Energy Technology Data Exchange (ETDEWEB)
Santos, Suzana C.; Carvalho, Ariadne G.; Fortes, Gilmara A.C.; Ferri, Pedro H.; Oliveira, Anselmo E. de, [Universidade Federal de Goias (UFGO), Goiania, GO (Brazil). Instituto de Quimica
2014-02-15
Oenothein B is a dimeric hydrolyzable tannin with a wide range of biological activities, such as antitumour, anti-inflammatory and antiviral. Its nuclear magnetic resonance (NMR) at room temperature show duplications and broadening of signals. Experiments of 1D and 2D NMR at lower temperatures were useful for the complete NMR assignments of all hydrogens and carbons. The 3D structure of the most stable conformer was determined for the first time by nuclear Overhauser effect spectroscopy (NOESY) experiment (-20 deg C) and density functional theory (DFT)(B3LYP/6-31G)/ polarizable continuum model (PCM) quantum chemical calculations. The favoured conformation showed a highly compacted geometry and a lack of symmetry, in which the two valoneoyl groups showed distinct conformational parameters and stabilities. (author)
12. Canopy Dynamics in Nanoscale Ionic Materials Probed by NMR
Science.gov (United States)
Mirau, Peter
2013-03-01
Nanoscale ionic materials (NIMs) are hybrids prepared from ionically functionalized nanoparticles (NP) neutralized by oligomeric polymer counter-ions. NIMs are designed to behave as liquids under ambient conditions in the absence of solvent and have no volatile organic content, making them useful for a number of applications. We have used NMR relaxation and pulse-field gradient NMR to probe local and collective canopy dynamics in NIMs based on silica nanoparticles (NP), fullerols and proteins in order to understand the relationship between the core and canopy structure and the bulk properties. The NMR studies show that the canopy dynamics depend on the degree of neutralization, the canopy radius of gyration and molecular crowding at the ionically modified NP surface. The viscosity in NIMs can be directly controlled with the addition of ions that enhance the exchange rate for polymers at the NP surface. These results show that NIMs for many applications can be prepared by controlling the dynamics of the NP interface.
13. NMRFx Processor: a cross-platform NMR data processing program
Energy Technology Data Exchange (ETDEWEB)
Norris, Michael; Fetler, Bayard [One Moon Scientific, Inc. (United States); Marchant, Jan [University of Maryland Baltimore County, Howard Hughes Medical Institute (United States); Johnson, Bruce A., E-mail: [email protected] [One Moon Scientific, Inc. (United States)
2016-08-15
NMRFx Processor is a new program for the processing of NMR data. Written in the Java programming language, NMRFx Processor is a cross-platform application and runs on Linux, Mac OS X and Windows operating systems. The application can be run in both a graphical user interface (GUI) mode and from the command line. Processing scripts are written in the Python programming language and executed so that the low-level Java commands are automatically run in parallel on computers with multiple cores or CPUs. Processing scripts can be generated automatically from the parameters of NMR experiments or interactively constructed in the GUI. A wide variety of processing operations are provided, including methods for processing of non-uniformly sampled datasets using iterative soft thresholding. The interactive GUI also enables the use of the program as an educational tool for teaching basic and advanced techniques in NMR data analysis.
14. Achieving High Accuracy in Calculations of NMR Parameters
DEFF Research Database (Denmark)
Faber, Rasmus
quantum chemical methods have been developed, the calculation of NMR parameters with quantitative accuracy is far from trivial. In this thesis I address some of the issues that makes accurate calculation of NMR parameters so challenging, with the main focus on SSCCs. High accuracy quantum chemical......, but no programs were available to perform such calculations. As part of this thesis the CFOUR program has therefore been extended to allow the calculation of SSCCs using the CC3 method. CC3 calculations of SSCCs have then been performed for several molecules, including some difficult cases. These results show...... vibrations must be included. The calculation of vibrational corrections to NMR parameters has been reviewed as part of this thesis. A study of the basis set convergence of vibrational corrections to nuclear shielding constants has also been performed. The basis set error in vibrational correction...
15. NMR imaging of cell phone radiation absorption in brain tissue
Science.gov (United States)
Gultekin, David H.; Moeller, Lothar
2013-01-01
A method is described for measuring absorbed electromagnetic energy radiated from cell phone antennae into ex vivo brain tissue. NMR images the 3D thermal dynamics inside ex vivo bovine brain tissue and equivalent gel under exposure to power and irradiation time-varying radio frequency (RF) fields. The absorbed RF energy in brain tissue converts into Joule heat and affects the nuclear magnetic shielding and the Larmor precession. The resultant temperature increase is measured by the resonance frequency shift of hydrogen protons in brain tissue. This proposed application of NMR thermometry offers sufficient spatial and temporal resolution to characterize the hot spots from absorbed cell phone radiation in aqueous media and biological tissues. Specific absorption rate measurements averaged over 1 mg and 10 s in the brain tissue cover the total absorption volume. Reference measurements with fiber optic temperature sensors confirm the accuracy of the NMR thermometry. PMID:23248293
16. The installation of a commercial resistive NMR imager
International Nuclear Information System (INIS)
Smith, M.A.; Best, J.J.K.; Douglas, R.H.B.; Kean, D.M.
1984-01-01
It has been demonstrated that a relatively low-cost resistive NMR imager can be installed in a normal hospital environment without many major or expensive modifications. The magnet can be adjusted to give adequate uniformity and there is sufficient RF shielding to give good quality clinical images. The fringe field of the magnet of this system, which operates at the lowest field strength of any commercial NMR imager, does not present a problem to imaging unit staff. The long term reliability and detailed specifications with regard to image quality have yet to be determined. These will be determined whilst the imager is being used for clinical studies as part of the national clinical evaluation of NMR imaging supported by the Medical Research Council. (author)
17. Advances in solid-state NMR of cellulose.
Science.gov (United States)
Foston, Marcus
2014-06-01
Nuclear magnetic resonance (NMR) spectroscopy is a well-established analytical and enabling technology in biofuel research. Over the past few decades, lignocellulosic biomass and its conversion to supplement or displace non-renewable feedstocks has attracted increasing interest. The application of solid-state NMR spectroscopy has long been seen as an important tool in the study of cellulose and lignocellulose structure, biosynthesis, and deconstruction, especially considering the limited number of effective solvent systems and the significance of plant cell wall three-dimensional microstructure and component interaction to conversion yield and rate profiles. This article reviews common and recent applications of solid-state NMR spectroscopy methods that provide insight into the structural and dynamic processes of cellulose that control bulk properties and biofuel conversion. Copyright © 2014 Elsevier Ltd. All rights reserved.
18. Optimization and automation of quantitative NMR data extraction.
Science.gov (United States)
Bernstein, Michael A; Sýkora, Stan; Peng, Chen; Barba, Agustín; Cobas, Carlos
2013-06-18
NMR is routinely used to quantitate chemical species. The necessary experimental procedures to acquire quantitative data are well-known, but relatively little attention has been applied to data processing and analysis. We describe here a robust expert system that can be used to automatically choose the best signals in a sample for overall concentration determination and determine analyte concentration using all accepted methods. The algorithm is based on the complete deconvolution of the spectrum which makes it tolerant of cases where signals are very close to one another and includes robust methods for the automatic classification of NMR resonances and molecule-to-spectrum multiplets assignments. With the functionality in place and optimized, it is then a relatively simple matter to apply the same workflow to data in a fully automatic way. The procedure is desirable for both its inherent performance and applicability to NMR data acquired for very large sample sets.
19. Introduction to quantum calculation methods in high resolution NMR
International Nuclear Information System (INIS)
Goldman, M.
1996-01-01
New techniques as for instance the polarization transfer, the coherence with several quanta and the double Fourier transformation have appeared fifteen years ago. These techniques constitute a considerable advance in NMR. Indeed, they allow to study more complex molecules than it was before possible. But with these advances, the classical description of the NMR is not enough to understand precisely the physical phenomena induced by these methods. It is then necessary to resort to quantum calculation methods. The aim of this work is to present these calculation methods. After some recalls of quantum mechanics, the author describes the NMR with the density matrix, reviews the main methods of double Fourier transformation and then gives the principle of the relaxation times calculation. (O.M.)
20. De novo protein structure determination using sparse NMR data
International Nuclear Information System (INIS)
Bowers, Peter M.; Strauss, Charlie E.M.; Baker, David
2000-01-01
We describe a method for generating moderate to high-resolution protein structures using limited NMR data combined with the ab initio protein structure prediction method Rosetta. Peptide fragments are selected from proteins of known structure based on sequence similarity and consistency with chemical shift and NOE data. Models are built from these fragments by minimizing an energy function that favors hydrophobic burial, strand pairing, and satisfaction of NOE constraints. Models generated using this procedure with ∼1 NOE constraint per residue are in some cases closer to the corresponding X-ray structures than the published NMR solution structures. The method requires only the sparse constraints available during initial stages of NMR structure determination, and thus holds promise for increasing the speed with which protein solution structures can be determined
1. NMR-Metabolic Methodology in the Study of GM Foods
Directory of Open Access Journals (Sweden)
Irene D’Amico
2010-01-01
Full Text Available The 1H-NMR methodology used in the study of genetically modified (GM foods is discussed. Transgenic lettuce (Lactuca sativa cv "Luxor" over-expressing the Arabidopsis KNAT1 gene is presented as a case study. Twenty-two water-soluble metabolites (amino acids, organic acids, sugars present in leaves of conventional and GM lettuce were monitored by NMR and quantified at two developmental stages. The NMR spectra did not reveal any difference in metabolite composition between the GM lettuce and the wild type counterpart. Statistical analyses of metabolite variables highlighted metabolism variation as a function of leaf development as well as the transgene. A main effect of the transgene was in altering sugar metabolism.
2. Thermometry of hot spot using NMR for hyperthermia
International Nuclear Information System (INIS)
Amemiya, Yoshifumi; Kamimura, Yoshitsugu
1983-01-01
Lately noticed hyperthermia in cancer therapy requires non-invasive measurement of the temperature at the warmed site in the deep portion of human body. Nuclear magnetic relaxation time of NMR is also usable for cancer diagnosis. For coordination of these two techniques, it was judged suitable to measure temperature by NMR so that cancer diagnosis and treatment and evaluation of therapeutic effect might be incorporated into one system. This report dealt with concrete procedures of measuring the temperature of deep portions by NMR. Computations revealed that the coefficient of temperature of the thermal equilibrium magnetization was useful, that magnetic field focusing was the most effective imaging technique and that temperature rise in areas about 2 cm in radius could be measured without large errors. (Chiba, N.)
3. Combined chemometric analysis of (1)H NMR, (13)C NMR and stable isotope data to differentiate organic and conventional milk.
Science.gov (United States)
Erich, Sarah; Schill, Sandra; Annweiler, Eva; Waiblinger, Hans-Ulrich; Kuballa, Thomas; Lachenmeier, Dirk W; Monakhova, Yulia B
2015-12-01
The increased sales of organically produced food create a strong need for analytical methods, which could authenticate organic and conventional products. Combined chemometric analysis of (1)H NMR-, (13)C NMR-spectroscopy data, stable-isotope data (IRMS) and α-linolenic acid content (gas chromatography) was used to differentiate organic and conventional milk. In total 85 raw, pasteurized and ultra-heat treated (UHT) milk samples (52 organic and 33 conventional) were collected between August 2013 and May 2014. The carbon isotope ratios of milk protein and milk fat as well as the α-linolenic acid content of these samples were determined. Additionally, the milk fat was analyzed by (1)H and (13)C NMR spectroscopy. The chemometric analysis of combined data (IRMS, GC, NMR) resulted in more precise authentication of German raw and retail milk with a considerably increased classification rate of 95% compared to 81% for NMR and 90% for IRMS using linear discriminate analysis. Copyright © 2015 Elsevier Ltd. All rights reserved.
4. Quantum theory of NMR adiabatic pulses and their applications
International Nuclear Information System (INIS)
Ke, Y.
1993-01-01
5. Structural properties of carbon nanotubes derived from 13C NMR
KAUST Repository
2011-10-10
We present a detailed experimental and theoretical study on how structural properties of carbon nanotubes can be derived from 13C NMR investigations. Magic angle spinning solid state NMR experiments have been performed on single- and multiwalled carbon nanotubes with diameters in the range from 0.7 to 100 nm and with number of walls from 1 to 90. We provide models on how diameter and the number of nanotube walls influence NMR linewidth and line position. Both models are supported by theoretical calculations. Increasing the diameter D, from the smallest investigated nanotube, which in our study corresponds to the inner nanotube of a double-walled tube to the largest studied diameter, corresponding to large multiwalled nanotubes, leads to a 23.5 ppm diamagnetic shift of the isotropic NMR line position δ. We show that the isotropic line follows the relation δ = 18.3/D + 102.5 ppm, where D is the diameter of the tube and NMR line position δ is relative to tetramethylsilane. The relation asymptotically tends to approach the line position expected in graphene. A characteristic broadening of the line shape is observed with the increasing number of walls. This feature can be rationalized by an isotropic shift distribution originating from different diamagnetic shielding of the encapsulated nanotubes together with a heterogeneity of the samples. Based on our results, NMR is shown to be a nondestructive spectroscopic method that can be used as a complementary method to, for example, transmission electron microscopy to obtain structural information for carbon nanotubes, especially bulk samples.
6. MetAssimulo:Simulation of Realistic NMR Metabolic Profiles
Directory of Open Access Journals (Sweden)
De Iorio Maria
2010-10-01
Full Text Available Abstract Background Probing the complex fusion of genetic and environmental interactions, metabolic profiling (or metabolomics/metabonomics, the study of small molecules involved in metabolic reactions, is a rapidly expanding 'omics' field. A major technique for capturing metabolite data is 1H-NMR spectroscopy and this yields highly complex profiles that require sophisticated statistical analysis methods. However, experimental data is difficult to control and expensive to obtain. Thus data simulation is a productive route to aid algorithm development. Results MetAssimulo is a MATLAB-based package that has been developed to simulate 1H-NMR spectra of complex mixtures such as metabolic profiles. Drawing data from a metabolite standard spectral database in conjunction with concentration information input by the user or constructed automatically from the Human Metabolome Database, MetAssimulo is able to create realistic metabolic profiles containing large numbers of metabolites with a range of user-defined properties. Current features include the simulation of two groups ('case' and 'control' specified by means and standard deviations of concentrations for each metabolite. The software enables addition of spectral noise with a realistic autocorrelation structure at user controllable levels. A crucial feature of the algorithm is its ability to simulate both intra- and inter-metabolite correlations, the analysis of which is fundamental to many techniques in the field. Further, MetAssimulo is able to simulate shifts in NMR peak positions that result from matrix effects such as pH differences which are often observed in metabolic NMR spectra and pose serious challenges for statistical algorithms. Conclusions No other software is currently able to simulate NMR metabolic profiles with such complexity and flexibility. This paper describes the algorithm behind MetAssimulo and demonstrates how it can be used to simulate realistic NMR metabolic profiles with
7. NMR of geophysical drill cores with a mobile Halbach scanner
International Nuclear Information System (INIS)
Talnishnikh, E.
2007-01-01
This thesis is devoted to a mobile NMR with an improved Halbach scanner. This is a lightweight tube-shaped magnet with sensitive volume larger and a homogeneity of the magnetic field higher than the previous prototype version. The improved Halbach scanner is used for analysis of water-saturated drill cores and plugs with diameters up to 60 mm. To provide the analysis, the standard 1D technique with the CPMG sequence as well as 2D correlation experiments were successfully applied and adapted to study properties of fluid-saturated sediments. Afterwards the Halbach scanner was calibrated to fast non-destructive measurements of porosity, relaxation time distributions, and estimation of permeability. These properties can be calculated directly from the NMR data using the developed methodology. Any independent measurements of these properties with other methods are not needed. One of the main results of this work is the development of a new NMR on-line core scanner for measurements of porosity in long cylindrical and semi cylindrical drill cores. Also dedicated software was written to operate the NMR on-line core scanner. The physical background of this work is the study of the diffusion influence on transverse relaxation. The diffusion effect in the presence of internal gradients in porous media was probed by 1D and 2D experiments. The transverse relaxation time distributions obtained from 1D and from 2D experiments are comparable but different in fine details. Two new methodologies were developed based on the results of this study. First is the methodology quantifying the influence of diffusion in the internal gradients of water-saturated sediments on transverse relaxation from 2D correlation experiments. The second one is the correction of the permeability estimation from the NMR data taking in account the influence of the diffusion. Furthermore, PFG NMR technique was used to study restricted diffusion in the same kind of samples. Preliminary results are reported
8. NMR of geophysical drill cores with a mobile Halbach scanner
Energy Technology Data Exchange (ETDEWEB)
Talnishnikh, E.
2007-08-21
This thesis is devoted to a mobile NMR with an improved Halbach scanner. This is a lightweight tube-shaped magnet with sensitive volume larger and a homogeneity of the magnetic field higher than the previous prototype version. The improved Halbach scanner is used for analysis of water-saturated drill cores and plugs with diameters up to 60 mm. To provide the analysis, the standard 1D technique with the CPMG sequence as well as 2D correlation experiments were successfully applied and adapted to study properties of fluid-saturated sediments. Afterwards the Halbach scanner was calibrated to fast non-destructive measurements of porosity, relaxation time distributions, and estimation of permeability. These properties can be calculated directly from the NMR data using the developed methodology. Any independent measurements of these properties with other methods are not needed. One of the main results of this work is the development of a new NMR on-line core scanner for measurements of porosity in long cylindrical and semi cylindrical drill cores. Also dedicated software was written to operate the NMR on-line core scanner. The physical background of this work is the study of the diffusion influence on transverse relaxation. The diffusion effect in the presence of internal gradients in porous media was probed by 1D and 2D experiments. The transverse relaxation time distributions obtained from 1D and from 2D experiments are comparable but different in fine details. Two new methodologies were developed based on the results of this study. First is the methodology quantifying the influence of diffusion in the internal gradients of water-saturated sediments on transverse relaxation from 2D correlation experiments. The second one is the correction of the permeability estimation from the NMR data taking in account the influence of the diffusion. Furthermore, PFG NMR technique was used to study restricted diffusion in the same kind of samples. Preliminary results are reported
9. Open H-shaped permanent magnet structure for NMR imaging
International Nuclear Information System (INIS)
Nguyen, V.; Delamare, J.; Yonnet, J.P.
1996-01-01
Since NMR imaging at low field is now technically possible, permanent magnets can replace resistive coils or superconducting magnets. This paper reviews most of NMR structures that provide an uniform field using only permanent magnets. We propose a new open H-shaped structure that is simple to manufacture. This structure has been calculated thanks to an optimization program and a calculation method we presente here. It enables to determine with a good accuracy the field created by passive systems composed by permanent magnets and ferromagnetic materials. (author)
10. Biosynthetic origin of acetic acid using SNIF-NMR
International Nuclear Information System (INIS)
Boffo, Elisangela Fabiana; Ferreira, Antonio Gilberto
2006-01-01
The main purpose of this work is to describe the use of the technique Site-Specific Natural Isotopic Fractionation of hydrogen (SNIF-NMR), using 2 H and 1 H NMR spectroscopy, to investigate the biosynthetic origin of acetic acid in commercial samples of Brazilian vinegar. This method is based on the deuterium to hydrogen ratio at a specific position (methyl group) of acetic acid obtained by fermentation, through different biosynthetic mechanisms, which result in different isotopic ratios. We measured the isotopic ratio of vinegars obtained through C 3 , C 4 , and CAM biosynthetic mechanisms, blends of C 3 and C 4 (agrins) and synthetic acetic acid. (author)
11. Selected topics from recent NMR studies of organolithium compounds
Directory of Open Access Journals (Sweden)
Günther Harald
1999-01-01
Full Text Available After a short introduction to NMR spectroscopy of alkali and alkaline earth metals the review concentrates on NMR investigations of organolithium compounds. The isotopic fingerprint method, which rests on deuterium-induced isotope shifts for 6Li resonances, is introduced and exemplified with applications from the aggregation behavior of cyclopropyllithium systems and mixed aggregate formation between methyllithium and lithium salts. In the following chapter, one- and two-dimensional pulse experiments, both for homo- and for heteronuclear spin systems are discussed. Finally, the structural aspects associated with benzyllithium are outlined and the formation of polylithium systems by lithium reduction of biphenylenes is described.
12. Handbook of proton-NMR spectra and data index
CERN Document Server
Asahi Research Center Co, Ltd
2013-01-01
Handbook of Proton-NMR Spectra and Data: Index to Volumes 1-10 compiles four types of indexes used in charting the proton-NMR spectral database -Chemical Name Index, Molecular Formula Index, Substructure Index, and Chemical Shift Index. The Chemical Name Index compiles all chemical names in alphabetical order, followed by a spectrum number. When the desired organic compound cannot be found in the Chemical Name Index or its nomenclature is unclear, it becomes necessary to look for a compound by means of its molecular formula, hence the Molecular Formula Index. A unique notation system for repre
13. Signal restoration for NMR imaging using time-dependent gradients
International Nuclear Information System (INIS)
Frahm, J.; Haenicke, W.
1984-01-01
NMR imaging experiments that employ linear but time-dependent gradients for encoding spatial information in the time-domain signals result in distorted images when treated with conventional image reconstruction techniques. It is shown here that the phase and amplitude distortions can be entirely removed if the timeshape of the gradient is known. The method proposed is of great theoretical and experimental simplicity. It consists of a retransformation of the measured time-domain signal and corresponds to synchronisation of the signal sampling with the time-development of the gradient field strength. The procedure complements other treatments of periodically oscillating gradients in NMR imaging. (author)
14. NMR of mercury in porous coal and silica gel
International Nuclear Information System (INIS)
Kasperovich, V.S.; Charnaya, E.V.; Tien, C.; Wur, C.S.
2003-01-01
Temperature dependences of the integral intensity and NMR signals Knight shift in 199 Hg nuclei are measured for liquid and solid mercury introduced into the porous coal and silica gel. The decrease in the crystallization completion temperature and small temperature hysteresis (from 4 up to 9 K) between melting and crystallization are identified. Mercury melting temperature in pores coincided with melting temperature of the bulk mercury. NMR signal from crystalline mercury under conditions of limited geometry was observed for the first time. It is ascertained that Knight shift for mercury in the pores both in liquid and crystalline phases is lesser than for the bulk mercury [ru
15. NMR structural studies of peptides and proteins in membranes
Energy Technology Data Exchange (ETDEWEB)
Opella, S J [Pennsylvania Univ., Philadelphia, PA (United States). Dept. of Chemistry
1994-12-31
The use of NMR methodology in structural studies is described as applicable to larger proteins, considering that the majority of membrane proteins is constructed from a limited repertoire of structural and dynamic elements. The membrane associated domains of these proteins are made up of long hydrophobic membrane spanning helices, shorter amphipathic bridging helices in the plane of the bilayer, connecting loops with varying degrees of mobility, and mobile N- and C- terminal sections. NMR studies have been successful in identifying all of these elements and their orientations relative to each other and the membrane bilayer 19 refs., 9 figs.
16. Probing Spin Crossover in a Solution by Paramagnetic NMR Spectroscopy.
Science.gov (United States)
Pavlov, Alexander A; Denisov, Gleb L; Kiskin, Mikhail A; Nelyubina, Yulia V; Novikov, Valentin V
2017-12-18
Spin transitions in spin-crossover compounds are now routinely studied in the solid state by magnetometry; however, only a few methods exist for studies in solution. The currently used Evans method, which relies on NMR spectroscopy to measure the magnetic susceptibility, requires the availability of a very pure sample of the paramagnetic compound and its exact concentration. To overcome these limitations, we propose an alternative NMR-based technique for evaluating spin-state populations by only using the chemical shifts of a spin-crossover compound; those can be routinely obtained for a solution that contains unknown impurities and paramagnetic admixtures or is contaminated otherwise.
17. NMR analysis of silk for the interpretation of ancient history
International Nuclear Information System (INIS)
Chujo, Riichiro
1998-01-01
The aim of this paper is the characterization of archaeological silk with the aid of nuclear magnetic resonance (NMR). In this paper the nucleus is confined to 13C as a stable isotope carbon which is the most basic element in organic compounds. Among the stable carbon isotopes 12C is the most abundant but it has no magnetic moment and the natural abundance of 13C is only 1.108% and this isotope is frequently used in NMR due to its non-zero magnetic moment
18. Computer compensation for NMR quantitative analysis of trace components
International Nuclear Information System (INIS)
Nakayama, T.; Fujiwara, Y.
1981-01-01
A computer program has been written that determines trace components and separates overlapping components in multicomponent NMR spectra. This program uses the Lorentzian curve as a theoretical curve of NMR spectra. The coefficients of the Lorentzian are determined by the method of least squares. Systematic errors such as baseline/phase distortion are compensated and random errors are smoothed by taking moving averages, so that there processes contribute substantially to decreasing the accumulation time of spectral data. The accuracy of quantitative analysis of trace components has been improved by two significant figures. This program was applied to determining the abundance of 13C and the saponification degree of PVA
19. 31P Solid-state MAS NMR spectra
International Nuclear Information System (INIS)
Grobet, P.J.; Geerts, H.; Martens, J.A.; Jacobs, P.A.
1989-01-01
The structures of the silicoaluminiophosphates MCM-1 and MCM9 were characterized by 27 Al and 31 P MAS NMR. The structural identity of MCM-1 and its silicon-free homologue AlPO 4 -H 3 is demonstrated. The presence of a structural mixture in MCM-9 is confirmed. 31 P MAS NMR spectra of MCM-9 could be interpreted as a superposition of spectra of VPI-5, AlPO 4 -H 3 and SAPO-11 phases. (author). 12 refs.; 3 figs.; 1 tab
20. Hyperpolarized Xenon Nuclear Magnetic Resonance (NMR of Building Stone Materials
Directory of Open Access Journals (Sweden)
Michele Mauri
2012-09-01
Full Text Available We have investigated several building stone materials, including minerals and rocks, using continuous flow hyperpolarized xenon (CF-HP NMR spectroscopy to probe the surface composition and porosity. Chemical shift and line width values are consistent with petrographic information. Rare upfield shifts were measured and attributed to the presence of transition metal cations on the surface. The evolution of freshly cleaved rocks exposed to the atmosphere was also characterized. The CF-HP 129Xe NMR technique is non-destructive and it could complement currently used techniques, like porosimetry and microscopy, providing additional information on the chemical nature of the rock surface and its evolution.
1. Study of molecular movements in some organic crystals by NMR
International Nuclear Information System (INIS)
Alexandre, M.
1971-01-01
After a discussion on molecular crystals (generalities, movements within molecular solids, study of movements, complexes by charge transfer) and some specific ones (molecular complexes of trinitrobenzene or TNB), this research thesis reports the use of nuclear magnetic resonance (NMR) to study molecular movements: generalities on broadband NMR, spin relaxation and strong field network, observation of the absorption signal and measurement of the second moment. The last part reports and discusses experimental results obtained on TNB-naphthalene, on TNB-azulene, on TNB-benzothiophene, and on TNB-indole
2. 1H-NMR/13C-NMR studies of branched structures in PVC obtained at atmospheric pressure
International Nuclear Information System (INIS)
Braun, D.; Holzer, G.; Hjertberg, T.
1981-01-01
The 1 H-NMR-spectra of raw poly (vinyl cloride) obtained at atmospheric pressure (U-PVC) have revealed the presence of high concentrations of branches. The content of labile chlorine was determined by reaction with phenole in order to estimate the branch points with tertiary chlorine. The branch length of reductively dehalogenated U-PVC by 13 C-NMR analysis have provided evidence for both short chain branches including chloromethyl groups and 2.4-dichloro-n-butyl groups and long chain branching. For a number of U-polymers the total amount of branching ranges from 7.5 to 13.5/1000 C. The 13 C-NMR measurements point to a ratio of methyl/butyl branches of 1:1 and short chains/long chains of 6:1. (orig.)
3. NMR spectroscopy applied to the eye: Drugs and metabolic studies
Energy Technology Data Exchange (ETDEWEB)
Saether, Oddbjoern
2005-07-01
NMR spectroscopy has been extensively applied in biomedical research during the last decades. It has proved to be an analytical tool of great value. From being mainly used in chemistry, technological developments have expanded the application of NMR spectroscopy to a great wealth of disciplines. With this method, biochemical information can be obtained by analysing tissue extracts. Moreover, NMR spectroscopy is increasingly employed for pharmacokinetic studies and analysis of biofluids. Technological progress has provided increased sensitivity and resolution in the spectra, which enable even more of the complexity of biological samples to be elucidated. With the implementation of high-resolution magic angle spinning (HR-MAS) NMR spectroscopy in biomedicine, intact tissue samples or biopsies can be investigated. Thus, NMR spectroscopy has an ever-increasing impact in metabolic screening of human samples and in animal models, and methods are also increasingly realised in vivo. The present work, NMR spectroscopy applied to eye research, consists of two main parts. Firstly, the feasibility to monitor fluorinated ophthalmic drugs directly in the eye was assessed. Secondly, HR-MAS H1 NMR spectroscopy was applied for metabolic profiling of the anterior eye segment, specifically to analyse metabolic changes in intact corneal and lenticular samples after cataractogenic insults. This work included metabonomics with the application of pattern recognition methods to analyse HR-MAS spectra of eye tissues. Optimisation strategies were explored for F19 NMR detection of fluorinated drugs in a phantom eye. S/N gains in F19 NMR spectroscopy were achieved by implementing time-share H1 decoupling at 2.35 T. The method is advantageous for compounds displaying broad spectral coupling patterns, though detection of drugs at concentrations encountered in the anterior eye segment after topical application was not feasible. Higher magnetic fields and technological improvements could enable
4. NMR spectroscopy applied to the eye: Drugs and metabolic studies
International Nuclear Information System (INIS)
Saether, Oddbjoern
2005-01-01
NMR spectroscopy has been extensively applied in biomedical research during the last decades. It has proved to be an analytical tool of great value. From being mainly used in chemistry, technological developments have expanded the application of NMR spectroscopy to a great wealth of disciplines. With this method, biochemical information can be obtained by analysing tissue extracts. Moreover, NMR spectroscopy is increasingly employed for pharmacokinetic studies and analysis of biofluids. Technological progress has provided increased sensitivity and resolution in the spectra, which enable even more of the complexity of biological samples to be elucidated. With the implementation of high-resolution magic angle spinning (HR-MAS) NMR spectroscopy in biomedicine, intact tissue samples or biopsies can be investigated. Thus, NMR spectroscopy has an ever-increasing impact in metabolic screening of human samples and in animal models, and methods are also increasingly realised in vivo. The present work, NMR spectroscopy applied to eye research, consists of two main parts. Firstly, the feasibility to monitor fluorinated ophthalmic drugs directly in the eye was assessed. Secondly, HR-MAS H1 NMR spectroscopy was applied for metabolic profiling of the anterior eye segment, specifically to analyse metabolic changes in intact corneal and lenticular samples after cataractogenic insults. This work included metabonomics with the application of pattern recognition methods to analyse HR-MAS spectra of eye tissues. Optimisation strategies were explored for F19 NMR detection of fluorinated drugs in a phantom eye. S/N gains in F19 NMR spectroscopy were achieved by implementing time-share H1 decoupling at 2.35 T. The method is advantageous for compounds displaying broad spectral coupling patterns, though detection of drugs at concentrations encountered in the anterior eye segment after topical application was not feasible. Higher magnetic fields and technological improvements could enable
5. Adiabatic Low-Pass J Filters for Artifact Suppression in Heteronuclear NMR
DEFF Research Database (Denmark)
Meier, Sebastian; Benie, Andrew J; Duus, Jens Øllgaard
2009-01-01
NMR artifact purging: Modern NMR experiments depend on efficient coherence transfer pathways for their sensitivity and on suppression of undesired pathways leading to artifacts for their spectral clarity. A novel robust adiabatic element suppresses hard-to-get-at artifacts....
6. WaVPeak: Picking NMR peaks through wavelet-based smoothing and volume-based filtering
KAUST Repository
Liu, Zhi; Abbas, Ahmed; Jing, Bing-Yi; Gao, Xin
2012-01-01
Motivation: Nuclear magnetic resonance (NMR) has been widely used as a powerful tool to determine the 3D structures of proteins in vivo. However, the post-spectra processing stage of NMR structure determination usually involves a tremendous amount
7. TG/DTG, FT-ICR Mass Spectrometry, and NMR Spectroscopy Study of Heavy Fuel Oil
KAUST Repository
Elbaz, Ayman M.; Abdul Jameel, Abdul Gani; Hourani, Nadim; Emwas, Abdul-Hamid M.; Sarathy, Mani; Roberts, William L.
2015-01-01
infusion atmospheric pressure chemical ionization Fourier transform ion cyclotron resonance mass spectrometry (APCI-FTICR MS), high resolution 1H nuclear magnetic resonance (NMR), 13C NMR, and two-dimensional heteronuclear multiple bond correlation (HMBC
8. Cellular applications of 31P and 13C nuclear magnetic resonance
International Nuclear Information System (INIS)
Shulman, R.G.; Brown, T.R.; Ugurbil, K.; Ogawa, S.; Cohen, S.M.; den Hollander, J.A.
1979-01-01
High-resolution nuclear magnetic resonance (NMR) studies of cells and purified mitochondria are discussed to show the kind of information that can be obtained in vivo. In suspensions of Escherichia coli both phosphorus-31 and carbon-13 NMR studies of glycolysis of bioenergetics are presented. In rat liver cells the pathways of gluconeogenesis from carbon-13-labeled glycerol are followed by carbon-13 NMR. In the intact liver cells cytosolic and mitochondrial pH's were separately measured by phosphorus-31 NMR. In purified mitochondria the internal and external concentrations of inorganic phosphate, adenosine diphosphate, and adenosine triphosphate were determined by phosphorus-31 while the pH difference across the membrane was measured simultaneously
9. Relative Configuration of Natural Products Using NMR Chemical Shifts
Science.gov (United States)
By comparing calculated with experimental NMR chemical shifts, we were able to determine the relative configurations of three monoterpene diastereomers produced by the walkingstick Anisomorpha buprestoides. The combined RMSDs of both 1H and 13C quantum chemically calculated shifts were able to predi...
10. Conventions and nomenclature for double diffusion encoding NMR and MRI
DEFF Research Database (Denmark)
Shemesh, Noam; Jespersen, Sune N; Alexander, Daniel C
2015-01-01
, such as double diffusion encoding (DDE) NMR and MRI, may provide novel quantifiable metrics that are less easily inferred from conventional diffusion acquisitions. Despite the growing interest on the topic, the terminology for the pulse sequences, their parameters, and the metrics that can be derived from them...
11. Solid-State NMR Spectroscopy for the Physical Chemistry Laboratory
Science.gov (United States)
Kinnun, Jacob J.; Leftin, Avigdor; Brown, Michael F.
2013-01-01
Solid-state nuclear magnetic resonance (NMR) spectroscopy finds growing application to inorganic and organic materials, biological samples, polymers, proteins, and cellular membranes. However, this technique is often neither included in laboratory curricula nor typically covered in undergraduate courses. On the other hand, spectroscopy and…
12. NMR spectroscopy of muscle proteins; Spektroskopia MRJ bialek miesniowych
Energy Technology Data Exchange (ETDEWEB)
Slosarek, G. [Inst. Fizyki, Univ. A. Mickiewicza, Poznan (Poland)
1995-12-31
Author reviews various experimental techniques used for study of the structure of muscle proteins. Difficulties of application of NMR are described. Studies of the influence of Ca{sup 2+} on flexibility of actin polymer are presented. 11 refs, 3 figs.
13. Tritium NMR in the analysis of tritiated compounds
International Nuclear Information System (INIS)
Kaspersen, F.M.; Funke, C.W.; Vader, Jan; Wagenaars, G.N.
1993-01-01
An overview is given of the possibilities of 3 H NMR in the characterisation of 3 H-labelled compounds. This technique gives information on the identity of the tritiated compounds, the position of the tritium, the distribution of the label and even the radiochemical purity of the labelled products. (author)
14. Extraction of alkaloids for NMR-based profiling
DEFF Research Database (Denmark)
Yilmaz, Ali; Nyberg, Nils; Jaroszewski, Jerzy W.
2012-01-01
A museum collection of Cinchona cortex samples (n = 117), from the period 1850–1950, were extracted with a mixture of chloroform-d1, methanol-d4, water-d2, and perchloric acid in the ratios 5:5:1:1. The extracts were directly analyzed using 1H NMR spectroscopy (600 MHz) and the spectra evaluated...
15. NMR investigation of boron impurities in refined metallurgical grade silicon
Energy Technology Data Exchange (ETDEWEB)
Grafe, Hans-Joachim; Loeser, Wolfgang; Schmitz, Steffen; Sakaliyska, Miroslava [Leibniz Institute for Solid State and Materials Research (IFW), Dresden (Germany); Wurmehl, Sabine [Leibniz Institute for Solid State and Materials Research (IFW), Dresden (Germany); Institute for Solid State Physics, Technische Universitaet Dresden (Germany); Eisert, Stefan; Reichenbach, Birk; Mueller, Tim [Adensis GmbH, Dresden (Germany); Acker, Joerg; Rietig, Anja; Ducke, Jana [Department of Chemistry, Faculty for Natural Sciences, Brandenburg Technical University Cottbus-Senftenberg, Senftenberg (Germany)
2015-09-15
The nuclear magnetic resonance (NMR) method was applied for tracking boron impurities in the refining process of metallurgical grade (MG) silicon. From the NMR signal of the {sup 11}B isotope at an operating temperature 4.2 K, the boron concentration can be estimated down to the order of 1-10 wppm B. After melting and resolidification of MG-Si alloyed with Ca and Ti, a major fraction of B impurities remains in the Si solid solution as inferred from the characteristic NMR frequency. The alloying element Ti does not form substantial fractions of TiB{sub 2}. Acid leaching of crushed powders of MG-Si alloyed with Ca and Ti can diminish the initial impurity content of B suggesting its accumulation in the grain boundary phases. NMR signals of TiB{sub 2} at 4.2 K and room temperature (RT), and of poly-Si with different B doping at 4.2 K. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
16. NMR studies concerning base-base interactions in oligonucleotides
International Nuclear Information System (INIS)
Hoogen, Y.T. van den.
1988-01-01
Two main subjects are treated in the present thesis. The firsst part principally deals with the base-base interactions in single-stranded oligoribonucleotides. The second part presents NMR and model-building studies of DNA and RNA duplexes containing an unpaired base. (author). 242 refs.; 26 figs.; 24 tabs
17. 1H NMR spectroscopy-based interventional metabolic phenotyping
DEFF Research Database (Denmark)
Lauridsen, Michael B; Bliddal, Henning; Christensen, Robin
2010-01-01
1H NMR spectroscopy-based metabolic phenotyping was used to identify biomarkers in the plasma of patients with rheumatoid arthritis (RA). Forty-seven patients with RA (23 with active disease at baseline and 24 in remission) and 51 healthy subjects were evaluated during a one-year follow-up with a......1H NMR spectroscopy-based metabolic phenotyping was used to identify biomarkers in the plasma of patients with rheumatoid arthritis (RA). Forty-seven patients with RA (23 with active disease at baseline and 24 in remission) and 51 healthy subjects were evaluated during a one-year follow......-up with assessments of disease activity (DAS-28) and 1H NMR spectroscopy of plasma samples. Discriminant analysis provided evidence that the metabolic profiles predicted disease severity. Cholesterol, lactate, acetylated glycoprotein, and lipid signatures were found to be candidate biomarkers for disease severity.......0007). However, after 31 days of optimized therapy, the two patient groups were not significantly different (P=0.91). The metabolic profiles of both groups of RA patients were different from the healthy subjects. 1H NMR-based metabolic phenotyping of plasma samples in patients with RA is well suited...
18. 13C-NMR spectra and bonding situation in ketenimines
International Nuclear Information System (INIS)
Firl, J.; Runge, W.; Hartmann, W.; Utikal, H.P.
1975-01-01
13 C-NMR spectra of a series of substituted ketenimines are reported. The terminal carbon resonances are found at unusual high fields between delta 37 and 78, while the central carbon signals appear around delta 189 - 196. On the basis of these results, the bonding situation in ketenimines has been discussed. (auth.)
19. Quantitative 1D saturation profiles on chalk by NMR
DEFF Research Database (Denmark)
Olsen, Dan; Topp, Simon; Stensgaard, Anders
1996-01-01
Quantitative one-dimensional saturation profiles showing the distribution of water and oil in chalk core samples are calculated from NMR measurements utilizing a 1D CSI spectroscopy pulse sequence. Saturation profiles may be acquired under conditions of fluid flow through the sample. Results reveal...
20. Statistical models and NMR analysis of polymer microstructure
Science.gov (United States)
Statistical models can be used in conjunction with NMR spectroscopy to study polymer microstructure and polymerization mechanisms. Thus, Bernoullian, Markovian, and enantiomorphic-site models are well known. Many additional models have been formulated over the years for additional situations. Typica...
1. MULTIVARIATE CURVE RESOLUTION OF NMR SPECTROSCOPY METABONOMIC DATA
Science.gov (United States)
Sandia National Laboratories is working with the EPA to evaluate and develop mathematical tools for analysis of the collected NMR spectroscopy data. Initially, we have focused on the use of Multivariate Curve Resolution (MCR) also known as molecular factor analysis (MFA), a tech...
2. Nondestructive NMR technique for moisture determination in radioactive materials
International Nuclear Information System (INIS)
Aumeier, S.; Gerald, R.E. II; Growney, E.; Nunez, L.; Kaminski, M.
1998-01-01
This progress report focuses on experimental and computational studies used to evaluate nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) for detecting, quantifying, and monitoring hydrogen and other magnetically active nuclei ( 3 H, 3 He, 239 Pu, 241 Pu) in Spent nuclear fuels and packaging materials. The detection of moisture by using a toroid cavity NMR imager has been demonstrated in SiO 2 and UO 2 systems. The total moisture was quantified by means of 1 H NMR detection of H 2 O with a sensitivity of 100 ppm. In addition, an MRI technique that was used to determine the moisture distribution also enabled investigators to discriminate between bulk and stationary water sorbed on the particles. This imaging feature is unavailable in any other nondestructive assay (NDA) technique. Following the initial success of this program, the NMR detector volume was scaled up from the original design by a factor of 2000. The capacity of this detector exceeds the size specified by DOE-STD-3013-96
3. (Cicer arietinum L.) seeds during germination by NMR spectroscopy
African Journals Online (AJOL)
Experiments were conducted to characterize the changes in water status during imbibition by nuclear magnetic resonance (NMR) spectroscopy in chickpea seeds exposed to static magnetic fields of 100 mT for 1 h. Water uptake during seed germination showed three phases with rapid initial hydration phase I, followed by ...
4. Stable polyfluorinated cycloalkenyl cations and their NMR spectra
International Nuclear Information System (INIS)
Snegirev, V.F.; Galakhov, M.V.; Makarov, K.N.; Bakhmutov, V.I.
1986-01-01
New stable 1-methoxyperfluoro-2-ethylcyclobutenyl, 1-methoxyperfluoro-2-methylcyclo-pentenyl, and 1-methoxyperfluoro-2-ethylcyclohexenyl cations were obtained by the action of antimony pentafluoride on the corresponding olefins. The distribution of the charges in the investigated polyfluorinated cycloalkenyl cations was investigated by 13 C NMR method
5. Techniques and approaches to proton NMR imaging of the head
International Nuclear Information System (INIS)
Pykett, I.L.; Buonanno, F.S.; Brady, T.J.; Kistler, J.P.
1983-01-01
The next few years will undoubtedly see a refinement of proton imaging technology and a broader data base will indicate to what extent proton relaxation parameters are able to detect and characterize disease. In addition, it is likely that imaging of other nuclei (e.g. 31 P, 23 Na, 19 F) will become a reality, although it must be stated that due to their inherently lower sensitivity to NMR detection and/or lower physiological concentration, clinical images of nuclei other than 1 H will undoubtedly have a low spatial resolution and may require relatively long imaging times. Nonetheless, herein lies the exciting possibility of non-invasive metabolic or functional imaging. The realm of NMR contrast agents is just beginning to be explored, and developments in high-speed imaging indicate useful applications in cardiology. So whilst improvements in image quality can be expected, as was the case with X-ray CT, the application of NMR in medicine will diversify to yield information of a more specifically functional nature. This, together with the very low attendant biological risk, heralds a bright future for NMR in clinical diagnosis
6. Use of NMR in profiling of cocaine seizures
DEFF Research Database (Denmark)
Pagano, Bruno; Lauri, Ilaria; De Tito, Stefano
2013-01-01
Cocaine is the most widely used illicit drug, and its origin is always the focus of intense investigation aimed at identifying the trafficking routes. Since NMR represents a unique methodology for performing chemical identification and quantification, here it is proposed a strategy based on (1)H...... adding significant information in the process toward identification of the trafficking routes for this drug....
7. NMR determinations of molecular geometries in liquid crystal media
International Nuclear Information System (INIS)
Long, R.C.; Goldstein, J.H.
1983-01-01
The application of NMR spectroscopy in oriented media to the determination of molecular geometries is illustrated by results for three distinctly different molecules: naphthalene, ethylene oxide and spiropentane. The need for systematic application of vibrational corrections is emphasized and some of the effects associated with the different choices of solvent media are considered
8. New design on air-core resistive NMR imaging magnet
Energy Technology Data Exchange (ETDEWEB)
Chen, Yan; Mingwu, Fan; Yixin, Miao
1984-08-01
A new type of NMR imaging air-core resistive magnet is designed. Based on the BIM Magnetostatic calculation the resultant four equiradial coils structure with optimized shapes of cross section possesses a larger spherical working volume obviously, comparing with the common four-coils imaging magnet. The manufacturing tolerance is also calculated.
9. Two-dimensional NMR studies of allyl palladium complexes of ...
h3-Allyl complexes are intermediates in organic synthetic reactions such as allylic alkylation and amination. There is growing interest in understanding the structures of chiral h3-allyl intermediates as this would help to unravel the mechanism of enantioselective C–C bond forming reactions. Two-dimensional NMR study is a.
10. NMR - finding in a case of Morquio's syndrome with syncope
International Nuclear Information System (INIS)
Treig, T.; Huk, W.; Nusslein, B.
1987-01-01
Acute or chronic cervical myelopathies are well known neurological complications of mucopolysaccharidoses This paper deals with a case of a mild form of Morquio's disease which appeared with syncope. NMR-imaging of the cranio-spinal region demonstrated a high intensity echo in the medulla oblongata before and after spinal decompression
11. NMR study of thermoresponsive block copolymer in aqueous solution
Czech Academy of Sciences Publication Activity Database
Spěváček, Jiří; Konefal, Rafal; Čadová, Eva
2016-01-01
Roč. 217, č. 12 (2016), s. 1370-1375 ISSN 1022-1352 R&D Projects: GA ČR(CZ) GA15-13853S Institutional support: RVO:61389013 Keywords : aqueous solutions * NMR * NOESY Subject RIV: CD - Macromolecular Chemistry Impact factor: 2.500, year: 2016
12. An NMR Protonation Study of Metal Diethylenetriaminepentaacetic Acid Complexes.
Science.gov (United States)
Letkeman, Peter
1979-01-01
This experiment is suitable for an integrated laboratory course for senior chemistry majors. It introduces the student to a study of the relative basicity of different proton accepting sites. It serves as an opportunity to learn about nmr techniques and could extend to infrared, as well. (BB)
13. Advances in 27Al MAS NMR studies of geopolymers
Czech Academy of Sciences Publication Activity Database
Brus, Jiří; Abbrent, Sabina; Kobera, Libor; Urbanová, Martina; Cuba, P.
2016-01-01
Roč. 88, č. 2016 (2016), s. 79-147 ISSN 0066-4103 R&D Projects: GA ČR(CZ) GA13-24155S; GA MŠk(CZ) LO1507 Institutional support: RVO:61389013 Keywords : geopolymers * aluminosilicates * solid-state NMR Subject RIV: CD - Macromolecular Chemistry Impact factor: 2.600, year: 2016
14. Unraveling the meaning of chemical shifts in protein NMR.
Science.gov (United States)
Berjanskii, Mark V; Wishart, David S
2017-11-01
15. Neuroimaging (NMR) in the assessment of multiple sclerosis (MS)
International Nuclear Information System (INIS)
Gambi, D.; Uncini, A.
1990-01-01
Clinical well defined patients with MS have been submitted to series of controls of NMR investigations after an attack of the disease and during 12 months in order to organize a methodology useful to analyze patients in different periods or stages of the disease, when new lesions can develop. (author). 11 refs.; 2 figs.; 5 tabs
16. Pulsed zero field NMR of solids and liquid crystals
International Nuclear Information System (INIS)
Thayer, A.M.
1987-02-01
This work describes the development and applications to solids and liquid crystals of zero field nuclear magnetic resonance (NMR) experiments with pulsed dc magnetic fields. Zero field NMR experiments are one approach for obtaining high resolution spectra of amorphous and polycrystalline materials which normally (in high field) display broad featureless spectra. The behavior of the spin system can be coherently manipulated and probed in zero field with dc magnetic field pulses which are employed in a similar manner to radiofrequency pulses in high field NMR experiments. Nematic phases of liquid crystalline systems are studied in order to observe the effects of the removal of an applied magnetic field on sample alignment and molecular order parameters. In nematic phases with positive and negative magnetic susceptibility anisotropies, a comparison between the forms of the spin interactions in high and low fields is made. High resolution zero field NMR spectra of unaligned smectic samples are also obtained and reflect the symmetry of the liquid crystalline environment. These experiments are a sensitive measure of the motionally induced asymmetry in biaxial phases. Homonuclear and heteronuclear solute spin systems are compared in the nematic and smectic phases. Nonaxially symmetric dipolar couplings are reported for several systems. The effects of residual fields in the presence of a non-zero asymmetry parameter are discussed theoretically and presented experimentally. Computer programs for simulations of these and other experimental results are also reported. 179 refs., 75 figs
17. Numerical simulation of NQR/NMR: Applications in quantum computing.
Science.gov (United States)
Possa, Denimar; Gaudio, Anderson C; Freitas, Jair C C
2011-04-01
A numerical simulation program able to simulate nuclear quadrupole resonance (NQR) as well as nuclear magnetic resonance (NMR) experiments is presented, written using the Mathematica package, aiming especially applications in quantum computing. The program makes use of the interaction picture to compute the effect of the relevant nuclear spin interactions, without any assumption about the relative size of each interaction. This makes the program flexible and versatile, being useful in a wide range of experimental situations, going from NQR (at zero or under small applied magnetic field) to high-field NMR experiments. Some conditions specifically required for quantum computing applications are implemented in the program, such as the possibility of use of elliptically polarized radiofrequency and the inclusion of first- and second-order terms in the average Hamiltonian expansion. A number of examples dealing with simple NQR and quadrupole-perturbed NMR experiments are presented, along with the proposal of experiments to create quantum pseudopure states and logic gates using NQR. The program and the various application examples are freely available through the link http://www.profanderson.net/files/nmr_nqr.php. Copyright © 2011 Elsevier Inc. All rights reserved.
18. 235U NMR study of the itinerant antiferromagnet USb2
International Nuclear Information System (INIS)
Kato, Harukazu; Sakai, Hironori; Ikushima, Kenji; Kambe, Shinsaku; Tokunaga, Yo; Aoki, Dai; Haga, Yoshinori; O-bar nuki, Yoshichika; Yasuoka, Hiroshi; Walstedt, Russell E.
2005-01-01
We have succeeded in resolving a 235 U antiferromagnetic nuclear magnetic resonance (AFNMR) signal using 235 U-enriched samples of USb 2 . The uranium hyperfine field and coupling constant estimated for this compound are consistent with those from other experiments. This is the first reported observation of 235 U NMR in conducting host material
19. NMR spectroscopy in the optimization and evaluation of RAFT agents
NARCIS (Netherlands)
Klumperman, B.; McLeary, J.B.; van den Dungen, E.; Pound, G.
2007-01-01
The selection of a suitable mediating agent in Reversible Addition-Fragmentation Chain Transfer (RAFT) mediated polymerization is crucial to the degree of control that can be achieved. An overview of work from the Stellenbosch group is presented in which the use of NMR spectroscopy as a tool for
20. NMR metabolomics of thrips (Frankliniella occidentalis) resistance in Senecio hybrids.
Science.gov (United States)
Leiss, Kirsten A; Choi, Young H; Abdel-Farid, Ibrahim B; Verpoorte, Robert; Klinkhamer, Peter G L
2009-02-01
Western flower thrips (Frankliniella occidentalis) has become a key insect pest of agricultural and horticultural crops worldwide. Little is known about host plant resistance to thrips. In this study, we investigated thrips resistance in F (2) hybrids of Senecio jacobaea and Senecio aquaticus. We identified thrips-resistant hybrids applying three different bioassays. Subsequently, we compared the metabolomic profiles of these hybrids applying nuclear magnetic resonance spectroscopy (NMR). The new developments of NMR facilitate a wide range coverage of the metabolome. This makes NMR especially suitable if there is no a priori knowledge of the compounds related to herbivore resistance and allows a holistic approach analyzing different chemical compounds simultaneously. We show that the metabolomes of thrips-resistant and -susceptible hybrids differed considerably. Thrips-resistant hybrids contained higher amounts of the pyrrolizidine alkaloids (PA), jacobine, and jaconine, especially in younger leaves. Also, a flavanoid, kaempferol glucoside, accumulated in the resistant plants. Both PAs and kaempferol are known for their inhibitory effect on herbivores. In resistant and susceptible F (2) hybrids, young leaves showed less thrips damage than old leaves. Consistent with the optimal plant defense theory, young leaves contained increased levels of primary metabolites such as sucrose, raffinose, and stachyose, but also accumulated jacaranone as a secondary plant defense compound. Our results prove NMR as a promising tool to identify different metabolites involved in herbivore resistance. It constitutes a significant advance in the study of plant-insect relationships, providing key information on the implementation of herbivore resistance breeding strategies in plants.
1. Cation Hydration Constants by Proton NMR: A Physical Chemistry Experiment.
Science.gov (United States)
Smith, Robert L.; And Others
1988-01-01
Studies the polarization effect on water by cations and anions. Describes an experiment to illustrate the polarization effect of sodium, lithium, calcium, and strontium ions on the water molecule in the hydration spheres of the ions. Analysis is performed by proton NMR. (MVL)
2. Analysis of organophosphorus pesticides using FT-NMR
International Nuclear Information System (INIS)
Miyata, Yoshihiko; Takahashi, Yoshikazu; Ando, Hiroaki
1988-01-01
A rapid and highly selective method of the identification of 23 kinds of organophosphorus pesticides was develop by using 31 P FT-NMR with 1 H complete decoupling method. Chemical shifts referenced by 85 % H 3 PO 4 were within -4 to 100 ppm, and there was no overlapping among the organophosphorus pesticides used in this experiment. (author)
3. FT-IR, NMR SPECTROSCOPIC and QUANTUM MECHANICAL ...
African Journals Online (AJOL)
frequencies, potential energy distribution (PED) data, 1H and 13C NMR chemical shifts of Fc- .... Due to electronegative oxygen atom, C11 appears at the highest frequency field region. The most intense singlet appearing at 69.73 ppm arises.
4. Quantitative produced water analysis using mobile 1H NMR
International Nuclear Information System (INIS)
Wagner, Lisabeth; Fridjonsson, Einar O; May, Eric F; Stanwix, Paul L; Graham, Brendan F; Carroll, Matthew R J; Johns, Michael L; Kalli, Chris
2016-01-01
Measurement of oil contamination of produced water is required in the oil and gas industry to the (ppm) level prior to discharge in order to meet typical environmental legislative requirements. Here we present the use of compact, mobile 1 H nuclear magnetic resonance (NMR) spectroscopy, in combination with solid phase extraction (SPE), to meet this metrology need. The NMR hardware employed featured a sufficiently homogeneous magnetic field, such that chemical shift differences could be used to unambiguously differentiate, and hence quantitatively detect, the required oil and solvent NMR signals. A solvent system consisting of 1% v/v chloroform in tetrachloroethylene was deployed, this provided a comparable 1 H NMR signal intensity for the oil and the solvent (chloroform) and hence an internal reference 1 H signal from the chloroform resulting in the measurement being effectively self-calibrating. The measurement process was applied to water contaminated with hexane or crude oil over the range 1–30 ppm. The results were validated against known solubility limits as well as infrared analysis and gas chromatography. (paper)
5. Identification of Spinel Iron Oxide Nanoparticles by 57Fe NMR
Directory of Open Access Journals (Sweden)
SangGap Lee
2011-12-01
Full Text Available We have synthesized and studied monodisperse iron oxide nanoparticles of smaller than 10 nm to identify between the two spinel phases, magnetite and maghemite. It is shown that 57Fe NMR spectroscopy is a promising tool for distinguishing between the two phases.
6. Covariance NMR Processing and Analysis for Protein Assignment.
Science.gov (United States)
Harden, Bradley J; Frueh, Dominique P
2018-01-01
During NMR resonance assignment it is often necessary to relate nuclei to one another indirectly, through their common correlations to other nuclei. Covariance NMR has emerged as a powerful technique to correlate such nuclei without relying on error-prone peak peaking. However, false-positive artifacts in covariance spectra have impeded a general application to proteins. We recently introduced pre- and postprocessing steps to reduce the prevalence of artifacts in covariance spectra, allowing for the calculation of a variety of 4D covariance maps obtained from diverse combinations of pairs of 3D spectra, and we have employed them to assign backbone and sidechain resonances in two large and challenging proteins. In this chapter, we present a detailed protocol describing how to (1) properly prepare existing 3D spectra for covariance, (2) understand and apply our processing script, and (3) navigate and interpret the resulting 4D spectra. We also provide solutions to a number of errors that may occur when using our script, and we offer practical advice when assigning difficult signals. We believe such 4D spectra, and covariance NMR in general, can play an integral role in the assignment of NMR signals.
7. Dynamics in photosynthetic transient complexes studied by paramagnetic NMR spectroscopy
NARCIS (Netherlands)
Scanu, Sandra
2013-01-01
This PhD thesis focuses on fundamental aspects of protein-protein interactions. A multidisciplinary methodology for the detection and visualization of transient, lowly-populated encounter protein complexes is described. The new methodology combined paramagnetic NMR spectroscopy with computational
8. NMR study of structure of lanthanide complexes in solution
International Nuclear Information System (INIS)
Choppin, G.R.
1976-01-01
The diagnostic value PMR studies of diamagnetic lanthanide complexes to define the nature of the species in the lanthanide-pyruvate system is discussed. The use of NMR spectra of both diamagnetic and paramagnetic lanthanide complexes to obtain detailed structural information is reviewed
9. Hyperpolarized 129Xe as an NMR probe for functional studies
International Nuclear Information System (INIS)
Wolber, J.
2000-01-01
The nuclear spin polarization of 129 Xe can be enhanced by several orders of magnitude using optical pumping techniques, resulting in a dramatic enhancement of the 129 Xe Nuclear Magnetic Resonance (NMR) signal. The 'hyperpolarized' gas can be used for Magnetic Resonance Imaging (MRI) of the void spaces of the lungs after introduction of the gas into the respiratory system. Furthermore, the high solubility of xenon in blood and lipids suggests the use of 129 Xe NMR for studying blood flow, permeability, perfusion and blood volume. Hyperpolarized 129 Xe MRI has the potential of combining the high sensitivity and functional information of radioactive tracer studies with the high spatial and temporal resolution of MRI. The spin-lattice relaxation time T 1 of 129 Xe in blood determines the loss of polarization during transit from the lungs to the tissue of interest. A difference in the relaxation times of xenon in oxygenated and deoxygenated blood could be used as a contrast mechanism in functional Magnetic Resonance Imaging (fMRI). In this thesis, the hyperpolarized 129 Xe T 1 in human blood is measured in vitro as a function of blood oxygenation, and the relevant relaxation mechanisms are discussed. A new and unexpected finding is that the hyperpolarized 129 Xe NMR spectrum in blood is highly sensitive to blood oxygenation. Therefore, hyperpolarized 129 Xe NMR provides a powerful means of measuring blood oxygenation quantitatively and non-invasively. The interaction of xenon with hemoglobin is responsible for an oxygen-dependent shift of the 129 Xe NMR resonance of xenon in red blood cells. Injection delivery of hyperpolarized 129 Xe in solution could be a more efficient method of administrating the gas for functional NMR studies. For this purpose, suitable biocompatible carrier media have been studied. In particular, the use of perfluorocarbon emulsions, which are already in use as blood substitutes, as delivery media for hyperpolarized 129 Xe has been investigates
10. Solid-state NMR on complex biomolecules: novel methods and applications
NARCIS (Netherlands)
Nand, D.
2011-01-01
Solid-state NMR (ssNMR) represents a versatile technique in providing atomic-resolution information without the need for crystals or fast molecular motion required for X-ray crystallography and solution-state NMR, respectively. Recent past has witnessed the ability of this technique in providing
11. LC-NMR coupling technology: recent advancements and applications in natural products analysis
NARCIS (Netherlands)
Exarchou, V.; Krucker, M.; Beek, van T.A.; Vervoort, J.J.M.; Gerothanassis, I.P.; Albert, K.
2005-01-01
An overview of recent advances in nuclear magnetic resonance (NMR) coupled with separation technologies and their application in natural product analysis is given and discussed. The different modes of LC-NMR operation are described, as well as how technical improvements assist in establishing LC-NMR
12. 'In vivo' and high resolution spectroscopy in solids by NMR: an instrument for transgenic plants study
International Nuclear Information System (INIS)
Colnago, L.A.; Herrmann, P.S.P.; Bernardes Filho, R.
1995-01-01
This work has developed a study on transgenic plants using two different techniques of nuclear magnetic resonance, in vivo NMR and high resolution NMR. In order to understand the gene mutations and characterize the plants constituents, NMR spectral data were analysed and discussed, then the results were presented
13. Fourier transform and its application to 1D and 2D NMR
International Nuclear Information System (INIS)
Canet, D.
1988-01-01
In this review article, the following points are developed: Pulsed NMR and Fourier transform; Fourier transform and two-dimensional spectroscopy; Mathematical properties of Fourier transform; Fourier transform of a sine function- one dimensional NMR; Fourier transform of a product of sine functions - two-dimensional NMR; Data manipulations in the time domain; Numerical Fourier transform [fr
14. An NMR database for simulations of membrane dynamics.
Science.gov (United States)
Leftin, Avigdor; Brown, Michael F
2011-03-01
Computational methods are powerful in capturing the results of experimental studies in terms of force fields that both explain and predict biological structures. Validation of molecular simulations requires comparison with experimental data to test and confirm computational predictions. Here we report a comprehensive database of NMR results for membrane phospholipids with interpretations intended to be accessible by non-NMR specialists. Experimental ¹³C-¹H and ²H NMR segmental order parameters (S(CH) or S(CD)) and spin-lattice (Zeeman) relaxation times (T(1Z)) are summarized in convenient tabular form for various saturated, unsaturated, and biological membrane phospholipids. Segmental order parameters give direct information about bilayer structural properties, including the area per lipid and volumetric hydrocarbon thickness. In addition, relaxation rates provide complementary information about molecular dynamics. Particular attention is paid to the magnetic field dependence (frequency dispersion) of the NMR relaxation rates in terms of various simplified power laws. Model-free reduction of the T(1Z) studies in terms of a power-law formalism shows that the relaxation rates for saturated phosphatidylcholines follow a single frequency-dispersive trend within the MHz regime. We show how analytical models can guide the continued development of atomistic and coarse-grained force fields. Our interpretation suggests that lipid diffusion and collective order fluctuations are implicitly governed by the viscoelastic nature of the liquid-crystalline ensemble. Collective bilayer excitations are emergent over mesoscopic length scales that fall between the molecular and bilayer dimensions, and are important for lipid organization and lipid-protein interactions. Future conceptual advances and theoretical reductions will foster understanding of biomembrane structural dynamics through a synergy of NMR measurements and molecular simulations. Copyright © 2010 Elsevier B.V. All
15. NMR metabolomics for assessment of exercise effects with mouse biofluids
Energy Technology Data Exchange (ETDEWEB)
Le Moyec, Laurence; Mille-Hamard, Laurence; Breuneval, Carole; Petot, Helene; Billat, Veronique L. [Universite Evry Val d' Essonne, UBIAE INSERM U902, Evry Cedex (France); Triba, Mohamed N. [Universite Paris 13, CSPBAT UMR 7244, Bobigny (France)
2012-08-15
Exercise modulates the metabolome in urine or blood as demonstrated previously for humans and animal models. Using nuclear magnetic resonance (NMR) metabolomics, the present study compares the metabolic consequences of an exhaustive exercise at peak velocity (Vp) and at critical velocity (Vc) on mice. Since small-volume samples (blood and urine) were collected, dilution was necessary to acquire NMR spectra. Consequently, specific processing methods were applied before statistical analysis. According to the type of exercise (control group, Vp group and Vc group), 26 male mice were divided into three groups. Mice were sacrificed 2 h after the end of exercise, and urine and blood samples were drawn from each mouse. Proton NMR spectra were acquired with urine and deproteinized blood. The NMR data were aligned with the icoshift method and normalised using the probabilistic quotient method. Finally, data were analysed with the orthogonal projection of latent-structure analysis. The spectra obtained with deproteinized blood can neither discriminate the control mice from exercised mice nor discriminate according to the duration of the exercise. With urine samples, a significant statistical model can be estimated when comparing the control mice to both groups, Vc and Vp. The best model is obtained according to the exercise duration with all mice. Taking into account the spectral regions having the highest correlations, the discriminant metabolites are allantoin, inosine and branched-chain amino acids. In conclusion, metabolomic profiles assessed with NMR are highly dependent on the exercise. These results show that urine samples are more informative than blood samples and that the duration of the exercise is a more important parameter to influence the metabolomic status than the exercise velocity. (orig.)
16. NMR studies of macroscopic and microscopic properties of liquid crystals
International Nuclear Information System (INIS)
Hughes, J.R.
1998-03-01
The work presented is concerned with studies of orientational order in liquid crystals and the behaviour of certain mesophases. The experimental technique used in common with all the work is deuterium NMR spectroscopy. Much of the work involves studies of the orientational order of deuteriated solute molecules dissolved in liquid crystal solvents. Chapter 1 gives an introduction to liquid crystals followed by a quantitative description of orientational order. Deuterium NMR in liquid crystals is described and an outline of the molecular field theory behind the orientational order of a rigid, biaxial solute in a uniaxial mesophase is given. In Chapter 2 a novel type of mesophase induction is studied using NMR, where a solute induces up to two extra phases in a discotic mesogen depending on its concentration. The purpose of this work is to try to gain an understanding into the mechanism of the phase induction involved. Chapter 3 is concerned primarily with the macroscopic behaviour of the nematic phase formed by a semi-rigid main-chain polymer in solution. Of particular interest is the study of the reorientation of the monodomain, once the director has been rotated with respect to the magnetic field of the NMR spectrometer. A mesogen which has been claimed to exhibit a biaxial nematic phase is studied in Chapter 4, in order to determine the symmetry of the phase using NMR. Finally, Chapter 5 deals with the differing behaviour of a liquid crystal monomer and its dimer dissolved in common nematic solvents in order to determine whether this agrees with molecular field theory. (author)
17. A global analysis of NMR distance constraints from the PDB
International Nuclear Information System (INIS)
Vranken, Wim
2007-01-01
Information obtained from Nuclear Magnetic Resonance (NMR) experiments is encoded as a set of constraint lists when calculating three-dimensional structures for a protein. With the amount of constraint data from the world wide Protein Data Bank (wwPDB) that is now available, it is possible to do a global, large-scale analysis using only information from the constraints, without taking the coordinate information into account. This article describes such an analysis of distance constraints from NOE data based on a set of 1834 NMR PDB entries containing 1909 protein chains. In order to best represent the quality and extent of the data that is currently deposited at the wwPDB, only the original data as deposited by the authors was used, and no attempt was made to 'clean up' and further interpret this information. Because the constraint lists provide a single set of data, and not an ensemble of structural solutions, they are easier to analyse and provide a reduced form of structural information that is relevant for NMR analysis only. The online resource resulting from this analysis makes it possible to check, for example, how often a particular contact occurs when assigning NOESY spectra, or to find out whether a particular sequence fragment is likely to be difficult to assign. In this respect it formalises information that scientists with experience in spectrum analysis are aware of but cannot necessarily quantify. The analysis described here illustrates the importance of depositing constraints (and all other possible NMR derived information) along with the structure coordinates, as this type of information can greatly assist the NMR community
18. C-13 NMR spectroscopy of plasma reduces interference of hypertriglyceridemia in the H-1 NMR detection of malignancy
International Nuclear Information System (INIS)
Fossell, E.T.; Hall, F.M.; McDonagh, J.
1991-01-01
The authors have previously described the application of water-suppressed proton nuclear magnetic resonance (H-1 NMR) spectroscopy of plasma for detection of malignancy. Subsequently, hypertriglyceridemia has been identified as a source of false positive results. Here is described a confirmatory, adjunctive technique -analysis of the carbon-13 (C-13) NMR spectrum of plasma- which also identifies the presence of malignancy but is not sensitive to the plasma triglyceride level. Blinded plasma samples from 480 normal donors and 208 patients scheduled for breast biopsy were analyzed by water-suppressed H-1 and C-13 NMR spectroscopy. Triglyceride levels were also measured. Among the normal donors, there were 38 individuals with hypertriglyceridemia of whom 18 had results consistent with malignancy by H-1 NMR spectroscopy. However, the C-13 technique reduced the apparent H-1 false positive rate from 7.0 to 0.6 percent. Similarly, in the breast biopsy cohort, C-13 reduced the false positive rate from 2.8 to 0.9 percent. Furthermore, the accuracy of the combined H-1/C-13 test in this blinded study was greater than 96 percent in 208 patients studied. (author). 27 refs.; 5 figs.; 4 tabs
19. A First Laboratory Utilizing NMR for Undergraduate Education: Characterization of Edible Fats and Oils by Quantitative [superscript 13]C NMR
Science.gov (United States)
Fry, Charles G.; Hofstetter, Heike; Bowman, Matthew D.
2017-01-01
Quantitative [superscript 13]C NMR provides a straightforward method of analyzing edible oils in undergraduate chemistry laboratories. [superscript 13]C spectra are relatively easy to understand, and are much simpler to analyze and workup than corresponding [superscript 1]H spectra. Average chain length, degree of saturation, and average…
20. 1H NMR spectra dataset and solid-state NMR data of cowpea (Vigna unguiculata)
DEFF Research Database (Denmark)
Alves Filho, Elenilson G.; Silva, Lorena M. A.; Teofilo, Elizita M.
2017-01-01
In this article the NMR data from chemical shifts, coupling constants, and structures of all the characterized compounds were provided, beyond a complementary PCA evaluation for the corresponding manuscript (E.G. Alves Filho, L.M.A. Silva, E.M. Teofilo, F.H. Larsen, E.S. de Brito, 2017) [3]. In a...
1. Proton NMR studies of functionalized nanoparticles in aqueous environments
Science.gov (United States)
Tataurova, Yulia Nikolaevna
Nanoscience is an emerging field that can provide potential routes towards addressing critical issues such as clean and sustainable energy, environmental remediation and human health. Specifically, porous nanomaterials, such as zeolites and mesoporous silica, are found in a wide range of applications including catalysis, drug delivery, imaging, environmental protection, and sensing. The characterization of the physical and chemical properties of nanocrystalline materials is essential to the realization of these innovative applications. The great advantage of porous nanocrystals is their increased external surface area that can control their biological, chemical and catalytic activities. Specific functional groups synthesized on the surface of nanoparticles are able to absorb heavy metals from the solution or target disease cells, such as cancer cells. In these studies, three main issues related to functionalized nanomaterials will be addressed through the application of nuclear magnetic resonance (NMR) techniques including: 1) surface composition and structure of functionalized nanocrystalline particles; 2) chemical properties of the guest molecules on the surface of nanomaterials, and 3) adsorption and reactivity of surface bound functional groups. Nuclear magnetic resonance (NMR) is one of the major spectroscopic techniques available for the characterization of molecular structure and conformational dynamics with atomic level detail. This thesis deals with the application of 1H solution state NMR to porous nanomaterial in an aqueous environment. Understanding the aqueous phase behavior of functionalized nanomaterials is a key factor in the design and development of safe nanomaterials because their interactions with living systems are always mediated through the aqueous phase. This is often due to a lack of fundamental knowledge in interfacial chemical and physical phenomena that occur on the surface of nanoparticles. The use of solution NMR spectroscopy results
2. 19F labelled dextrans and antibodies as NMR imaging and spectroscopy agents
International Nuclear Information System (INIS)
Antich, P.P.; Kulkarni, P.V.
1993-01-01
A method is described of NMR imaging or spectroscopy, comprising the steps of administering to a living subject a 19 F labelled NMR agent, the NMR agent comprising (a) a transport polymer selected from the group consisting of dextran polymers and amino dextrans, having a molecular weight between approximately 100 d and 500 kd, and antibodies and fragments thereof, and (b) a 19F-containing sensor moiety selected from the group consisting of fluorinated alkyls, fluorinated acetates, fluoroaniline, and fluoroalkyl phosphonates, in an amount effective to provide a detectable NMR signal; and then detecting the 19 F NMR signal produced
3. Basicity determination for neutral phosphorus organic extragents by NMR 31P-method in two-phase systems, and quantitative interrelations of acido-basic extractive properties
International Nuclear Information System (INIS)
Laskorin, B.N.; Yakshin, V.V.; Meshcheryakov, N.M.; Yagodin, V.G.
1988-01-01
Consideration is given to the method for determination of basicity of neutral organophosphorus compounds of XGZP=0 type (X, G, Z=C 4 H 9 , C 8 H 17 , C 6 H 5 ). The method is based on change of chemical shift of phosphorus-31 nuclei in two-phase extraction system depending on acidity function H O , H A , H PO . It is shown that the method can be used for evaluation and forecasting of phosphine oxide ability in the processes of UO 2 SO 4 solvent extraction from aqueous solutions of sulfuric acid
4. Recent advances in solid state NMR and its application to ceramics
International Nuclear Information System (INIS)
Maekawa, Hideki
2006-01-01
The basic principles of solid state NMR are explained. Four application examples contained amorphous glass, determination of defects of oxide crystal, nano particle and ionic materials. The structure of inorganic glass is measured by 29 Si, 11 B, 31 P and 23 Na NMR and Magic Angle Spinning NMR (MAS-NMR), chemical species near hydrogen by Cross-Polarization Magic Angle Spinning (CP/MAS) method, and hydrogen by Combined Rotation And Multiple Pulse Spectroscopy (CRAMPS) and MAS-NMR. Hydrous and anhydrous silicate glass with condensed 17 O was measured by 17 O Multi Quantum Magic Angle Spinning (MQ/MAS). 27 Al in slags was analyzed by 27 Al 5Q-MAS. 89 Y NMR spectrum of YSZ (Yttria Stabilization Zirconia, Y 2 O 3 -ZrO 2 ) was explained. The ion transfer phenomena in the electrolyte are observed directly by the solid state NMR. (S.Y.)
5. Development of a micro flow-through cell for high field NMR spectroscopy.
Energy Technology Data Exchange (ETDEWEB)
Alam, Todd Michael; McIntyre, Sarah K.
2011-05-01
A highly transportable micro flow-through detection cell for nuclear magnetic resonance (NMR) spectroscopy has been designed, fabricated and tested. This flow-through cell allows for the direct coupling between liquid chromatography (LC) and gel permeation chromatography (GPC) resulting in the possibility of hyphenated LC-NMR and GPC-NMR. The advantage of the present flow cell design is that it is independent and unconnected to the detection probe electronics, is compatible with existing commercial high resolution NMR probes, and as such can be easily implemented at any NMR facility. Two different volumes were fabricated corresponding to between {approx}3.8 and 10 {micro}L detection volume. Examples of the performance of the cell on different NMR instruments, and using different NMR detection probes were demonstrated.
6. Classical and quantum molecular dynamics in NMR spectra
CERN Document Server
Szymański, Sławomir
2018-01-01
The book provides a detailed account of how condensed-phase molecular dynamics are reflected in the line shapes of NMR spectra. The theories establishing connections between random, time-dependent molecular processes and lineshape effects are exposed in depth. Special emphasis is placed on the theoretical aspects, involving in particular intermolecular processes in solution, and molecular symmetry issues. The Liouville super-operator formalism is briefly introduced and used wherever it is beneficial for the transparency of presentation. The proposed formal descriptions of the discussed problems are sufficiently detailed to be implemented on a computer. Practical applications of the theory in solid- and liquid-phase studies are illustrated with appropriate experimental examples, exposing the potential of the lineshape method in elucidating molecular dynamics NMR-observable molecular phenomena where quantization of the spatial nuclear degrees of freedom is crucial are addressed in the last part of the book. As ...
7. NMR imaging: A 'chemical' microscope for coal analysis
International Nuclear Information System (INIS)
French, D.C.; Dieckman, S.L.; Gopalsami, N.; Botto, R.E.
1991-01-01
This paper presents a new three-dimensional (3-D) nuclear magnetic resonance (NMR) imaging technique for spatially mapping proton distributions in whole coals and solvent-swollen coal samples. The technique is based on a 3-D back-projection protocol for data acquisition, and a reconstruction technique based on 3-D Radon transform inversion. In principle, the 3-D methodology provides higher spatial resolution of solid materials than is possible with conventional slice-selection protocols. The applicability of 3-D NMR imaging has been demonstrated by mapping the maceral phases in Utah Blind Canyon (APCS number-sign 6) coal and the distribution of mobile phases in Utah coal swollen with deuterated and protic pyridine. 7 refs., 5 figs
8. Structure and Dynamic Properties of Membrane Proteins using NMR
DEFF Research Database (Denmark)
Rösner, Heike; Kragelund, Birthe
2012-01-01
conformational changes. Their structural and functional decoding is challenging and has imposed demanding experimental development. Solution nuclear magnetic resonance (NMR) spectroscopy is one of the techniques providing the capacity to make a significant difference in the deciphering of the membrane protein...... structure-function paradigm. The method has evolved dramatically during the last decade resulting in a plethora of new experiments leading to a significant increase in the scientific repertoire for studying membrane proteins. Besides solving the three-dimensional structures using state-of-the-art approaches......-populated states, this review seeks to introduce the vast possibilities solution NMR can offer to the study of membrane protein structure-function analyses with special focus on applicability. © 2012 American Physiological Society. Compr Physiol 2:1491-1539, 2012....
9. Some new insights into biology and medicine through NMR spectroscopy
International Nuclear Information System (INIS)
1990-01-01
The contributions to biology and medicine by NMR spectroscopy in vivo require careful definition of the problems that are studied. Temporal and spatial resolution of the biochemical information obtained are the key to success, although the latter is limited owing to low sensitivity and small concentrations of the metabolites studied. Using 31 P NMR investigations in four areas are described. Control of energetics by ADP in normal and diseased muscle is shown to be important. Enzyme catalysed fluxes are obtained for creatine kinase and ATP synthase in muscle and in the human brain enzyme activity maps are derived. The measurements on the ionic environment and fluxes for H + , Na + and K + (Rb + ) give us new information about the role of ions in cell proliferation (e.g. in cancer) and hypertension. Molecular architecture of phospholipids in vivo is readily observed and is perturbed in the brain in chronic head injury and demyelination. (author)
10. Recombinant Kinase Production and Fragment Screening by NMR Spectroscopy.
Science.gov (United States)
Han, Byeonggu; Ahn, Hee-Chul
2016-01-01
During the past decade fragment-based drug discovery (FBDD) has rapidly evolved and several drugs or drug candidates developed by FBDD approach are clinically in use or in clinical trials. For example, vemurafenib, a V600E mutated BRAF inhibitor, was developed by utilizing FBDD approach and approved by FDA in 2011. In FBDD, screening of fragments is the starting step for identification of hits and lead generation. Fragment screening usually relies on biophysical techniques by which the protein-bound small molecules can be detected. NMR spectroscopy has been extensively used to study the molecular interaction between the protein and the ligand, and has many advantages in fragment screening over other biophysical techniques. This chapter describes the practical aspects of fragment screening by saturation transfer difference NMR.
11. $^{31}$Mg $\\beta$-NMR applied in chemistry and biochemistry
CERN Multimedia
Magnesium ions, Mg$^{2+}$, are essential in biological systems, taking part in practically all phosphate chemistry, in photosynthesis as an integral component of chlorophyll, and they are regulated via transport through selective membrane proteins. Nonetheless, the function of magnesium ions in biochemistry is difficult to characterize, as it is practically invisible to current experimental techniques. With this proposal we aim to advance the use of $^{31}$Mg $\\beta$-NMR to liquid samples, building on the experience from the successful Letter of Intent INTC-I-088 “$\\beta$-NMR as a novel technique for biological applications”. Initially a series of experiments will be conducted aiming to characterize the coordination chemistry of Mg$^{2+}$ in ionic liquids (ILs), demonstrating that it is possible within the lifetime of the radioisotope to achieve binding of Mg$^{2+}$ to a molecule dissolved in the IL. ILs are chosen as they display a very low vapor pressure, and are thus straightforwardly compatible with t...
12. Development and Investigation of NMR tools for chiral compound identification
Energy Technology Data Exchange (ETDEWEB)
Alam, Todd Michael [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Electronic, Optical and Nano Materials; Lansdon, Rick [Oak Ridge Inst. for Science and Education (ORISE), Oak Ridge, TN (United States)
2014-09-01
The goal behind the assigned summer project was to investigate the ability of nuclear magnetic resonance spectroscopy (NMR) to identify enantiomers of select chiral organo-fluorophosphates (OFPs) compounds which are analogs of chemical warfare agents (CWAs, e.g. Sarin). This involved investigations utilizing chiral solvating agents (CSAs) and characterizing the binding phenomena with cyclodextrins. The resolution of OFPs enantiomers using NMR would be useful for research into toxicodynamics and toxicokinetics in biological systems due to the widely differing properties of the CWA enantiomers [1]. The optimization of decontamination abilities in the case of a CWA events, with this method’s potential rapidity and robustness, as well as the development of models correlating chiral compounds with CSAs for optimal resolution are all rational benefits of this research.
13. NMR and rotational angles in solution conformation of polypeptides
Science.gov (United States)
Bystrov, V. F.
1985-01-01
Professor San-Ichiro Mizushima and Professor Yonezo Morino's classical contributions provided unique means and firm basis for understanding of conformational states and internal rotation in polypeptide molecules. Now the NMR spectroscopy is the best choice to study molecular conformation, mechanism of action and structure-functional relationships of peptide and proteins in solution under conditions approaching those of their physiological environments. Crucial details of spatial structure and interactions of these molecules in solution are revealed by using proton-proton and carbon-proton vicinal coupling constants, proton nuclear Overhauser effect and spectral perturbation techniques. The results of NMR conformational analysis are presented for valinomycin "bracelet", gramicidin A double helices, honey-bee neurotoxin apamin, scorpion insectotoxins and snake neurotoxins of long and short types.
14. Peakr: simulating solid-state NMR spectra of proteins
International Nuclear Information System (INIS)
Schneider, Robert; Odronitz, Florian; Hammesfahr, Bjorn; Hellkamp, Marcel; Kollmar, Martin
2013-01-01
When analyzing solid-state nuclear magnetic resonance (NMR) spectra of proteins, assignment of resonances to nuclei and derivation of restraints for 3D structure calculations are challenging and time-consuming processes. Simulated spectra that have been calculated based on, for example, chemical shift predictions and structural models can be of considerable help. Existing solutions are typically limited in the type of experiment they can consider and difficult to adapt to different settings. Here, we present Peakr, a software to simulate solid-state NMR spectra of proteins. It can generate simulated spectra based on numerous common types of internuclear correlations relevant for assignment and structure elucidation, can compare simulated and experimental spectra and produces lists and visualizations useful for analyzing measured spectra. Compared with other solutions, it is fast, versatile and user friendly. (authors)
15. Quali- and quantitative analysis of commercial coffee by NMR
International Nuclear Information System (INIS)
Tavares, Leila Aley; Ferreira, Antonio Gilberto
2006-01-01
Coffee is one of the beverages most widely consumed in the world and the 'cafezinho' is normally prepared from a blend of roasted powder of two species, Coffea arabica and Coffea canephora. Each one exhibits differences in their taste and in the chemical composition, especially in the caffeine percentage. There are several procedures proposed in the literature for caffeine determination in different samples like soft drinks, coffee, medicines, etc but most of them need a sample workup which involves at least one step of purification. This work describes the quantitative analysis of caffeine using 1 H NMR and the identification of the major components in commercial coffee samples using 1D and 2D NMR techniques without any sample pre-treatment. (author)
16. Broad line NMR study of modified polypropylene fibres
International Nuclear Information System (INIS)
Olcak, D.; Sevcovic, L.; Mucha, L.
1999-01-01
Study of drawn fibres prepared from an isostatic polypropylene modified by an ethylene aminoalkylacrylate copolymer has been done using the broad line of 1 H NMR. NMR spectra were measured on the set of fibres prepared with a draw ratio λ from 1 to 5.5 at two temperatures, one of them corresponding to the onset of segmental motion and the other one is the minddle of the temperature interval as determined by decrease of the second moment M 2 . Decomposition of the spectra into elementary components related to the amorphous, intermediate and crystalline regions of partially crystalline polymers has been made. The drawing of the fibres was found to enhance the chain mobility in the amorphous region and to restrain the molecular motion in the intermediate region. Such behaviour well supports conclusions predicted in the earlier study based on the spin-lattice relaxation time T 1 and dynamic mechanical data treated using the WLF theory. (Authors)
17. NMR structural studies of oligosaccharides and other natural products
DEFF Research Database (Denmark)
Kjærulff, Louise
produce secondary metabolites for signaling and competing against other organisms, and these molecules are important in drug discovery due to their inherent biological activities. From a marine Photobacterium (P. halotolerans) we isolated the solonamides and the ngercheumicins, two families of cyclic...... through the nJCH correlation, this experiment has exciting applications for configurational assignment of e.g. carbohydrates and for residual dipolar couplings. Identification of known molecules and discovery of novel molecules are other important applications of NMR spectroscopy. Bacteria and fungi....... fijiensis, was also investigated for production of novel secondary metabolites, and a new pyranonigrin (E) was isolated and structure elucidated by NMR spectroscopy along with JBIR-74 and decumbenone A, two known metabolites previously isolated from Aspergillus and Penicillium species. Oligosaccharides...
18. NMR of water in biological systems. I.-theoretical considerations
International Nuclear Information System (INIS)
Villa, M.; Borghi, L.; De Ambrosis, A.; Aldrovandi, S.
1983-01-01
A simple relationship has been thought to exist between the dynamics of water in heterogeneous (liquid-solid) systems and NMR response. This relationship is usually expressed by the Bloembergen-Purcell-Puond (BPP) equations for relaxation and the phase model. However, a requirement for the use of the BPP theory is that motions take place in an isotropic, infinite and three-dimensional space. It is shown that the mere presence of solid surfaces causes the appearance of solid-like features in the NMR response of the liquid even if its dynamics is directly affected by the surfaces. Some of these ''topological'' or ''indirect'' surface effects are of the same kind as the low-dimensionality effects. Their order of magnitude is estimated for simple geometries and by treating the liquid motion in a hydrodynamic approximation. Comparison with the experiment is carried on in a companion paper
19. The fluorescence properties and NMR analysis of protopine and allocryptopine
International Nuclear Information System (INIS)
Kubala, Martin; Vacek, Jan; Popa, Igor; Janovska, Marika; Kosina, Pavel; Ulrichova, Jitka; Travnicek, Zdenek; Simanek, Vilim
2011-01-01
The fluorescence properties of protopine and allocryptopine in aqueous and organic environments are described for the first time. The fluorescence of alkaloids and their pH-dependent interconversion to cationic forms (transannular interaction) were studied using steady-state and time-resolved fluorescence techniques. For the analysis of tricyclic base and cis/trans tetracyclic cations of the alkaloids, NMR and X-ray crystallography were used. - Highlights: → We describe fundamental fluorescence characteristics of alkaloids protopine and allocryptopine. → We analyzed the pH-dependent transitions and cis/trans isomerization. → These two alkaloids can be better distinguished by their fluorescence decay characteristics. → The fluorescence parameters are related to the NMR and crystallographic structural data.
20. Protein structure estimation from NMR data by matrix completion.
Science.gov (United States)
Li, Zhicheng; Li, Yang; Lei, Qiang; Zhao, Qing
2017-09-01
Knowledge of protein structures is very important to understand their corresponding physical and chemical properties. Nuclear Magnetic Resonance (NMR) spectroscopy is one of the main methods to measure protein structure. In this paper, we propose a two-stage approach to calculate the structure of a protein from a highly incomplete distance matrix, where most data are obtained from NMR. We first randomly "guess" a small part of unobservable distances by utilizing the triangle inequality, which is crucial for the second stage. Then we use matrix completion to calculate the protein structure from the obtained incomplete distance matrix. We apply the accelerated proximal gradient algorithm to solve the corresponding optimization problem. Furthermore, the recovery error of our method is analyzed, and its efficiency is demonstrated by several practical examples.
1. High Resolution NMR Studies of Encapsulated Proteins In Liquid Ethane
Science.gov (United States)
Peterson, Ronald W.; Lefebvre, Brian G.; Wand, A. Joshua
2005-01-01
Many of the difficulties presented by large, aggregation-prone, and membrane proteins to modern solution NMR spectroscopy can be alleviated by actively seeking to increase the effective rate of molecular reorientation. An emerging approach involves encapsulating the protein of interest within the protective shell of a reverse micelle, and dissolving the resulting particle in a low viscosity fluid, such as the short chain alkanes. Here we present the encapsulation of proteins with high structural fidelity within reverse micelles dissolved in liquid ethane. The addition of appropriate co-surfactants can significantly reduce the pressure required for successful encapsulation. At these reduced pressures, the viscosity of the ethane solution is low enough to provide sufficiently rapid molecular reorientation to significantly lengthen the spin-spin NMR relaxation times of the encapsulated protein. PMID:16028922
2. Two approaches to 3D reconstruction in NMR zeugmatography
International Nuclear Information System (INIS)
Marr, R.B.; Chen, C.N.; Lauterbur, P.C.
1980-01-01
In nuclear magnetic resonance (NMR) zeugmatography, the primary data pertain to integrals of the unknown nuclear spin density f(x,y,z) over planes instead of lines in R 3 . Two natural approaches to reconstructing f from such data are: (1) By numerical implementation of the inverse Radon transform in three dimensions (the direct approach), and (2) by application, in two successive stages, of existing well-known algorithms for inverting the two-dimensional Radon transform (the two-stage approach). These two approaches are discussed and compared, both from a theoretical standpoint and through computer results obtained with real NMR data. For the cases studied to date the two methods appear to produce qualitatively similar results
3. Study of β-NMR for Liquid Biological Samples
CERN Document Server
Beattie, Caitlin
2017-01-01
β-NMR is an exotic form of NMR spectroscopy that allows for the characterization of matter based on the anisotropic β-decay of radioactive probe nuclei. This has been shown to be an effective spectroscopic technique for many different compounds, but its use for liquid biological samples is relatively unexplored. The work at the VITO line of ISOLDE seeks to employ this technique to study such samples. Currently, preparations are being made for an experiment to characterize DNA G-quadruplexes and their interactions with stabilizing cations. More specifically, the work in which I engaged as a summer student focused on the experiment’s liquid handling system and the stability of the relevant biological samples under vacuum.
4. Double rotation NMR studies of zeolites and aluminophosphate molecular sieves
Energy Technology Data Exchange (ETDEWEB)
Jelinek, Raz [Univ. of California, Berkeley, CA (United States)
1993-07-01
Goal is to study the organization and structures of guest atoms and molecules and their reactions on internal surfaces within pores of zeolites and aluminophosphate molecular sieves. 27Al and 23Na double rotation NMR (DOR) is used since it removes the anisotropic broadening in NMR spectra of quadrupolar nuclei, thus increasing resolution. This work concentrates on probing aluminum framework atoms in aluminophosphate molecular sieves and sodium extra framework cations in porous aluminosilicates. In aluminophosphates, ordering and electronic environments of the framework 27Al nuclei are modified upon adsorption of water molecules within the channels; a relation is sought between the sieve channel topology and the organization of adsorbed water, as well as the interaction between the Al nuclei and the water molecules. Extra framework Na+ cations are directly involved in adsorption processes and reactions in zeolite cavities.
5. Conformational, vibrational, NMR and DFT studies of N-methylacetanilide.
Science.gov (United States)
Arjunan, V; Santhanam, R; Rani, T; Rosi, H; Mohan, S
2013-03-01
A detailed conformational, vibrational, NMR and DFT studies of N-methylacetanilide have been carried out. In DFT, B3LYP method have been used with 6-31G(**), 6-311++G(**) and cc-pVTZ basis sets. The vibrational frequencies were calculated resulting in IR and Raman frequencies together with intensities and Raman depolarisation ratios. The dipole moment derivatives were computed analytically. Owing to the complexity of the molecule, the potential energy distributions of the vibrational modes of the compound are also calculated. Isoelectronic molecular electrostatic potential surface (MEP) and electron density surface were examined. (1)H and (13)C NMR isotropic chemical shifts were calculated and the assignments made are compared with the experimental values. The energies of important MO's of the compound were also determined from TD-DFT method. Copyright © 2012 Elsevier B.V. All rights reserved.
6. Antiferro multipolar ordering and it's identification by NMR experiment
International Nuclear Information System (INIS)
Sakai, Osamu; Shiina, Ryousuke; Kikuchi, Jun; Takigawa, Masashi
2008-01-01
The antiferro-ordering of multipolar moments often plays important roles in the low temperature phase transition of f-electron systems. The splitting of NMR spectra, which is analyzed in terms of the invariant hyperfine coupling between the nuclear spin and the multipolar moments of magnetic ions, gives important information about the multipolar ordering. Experimental and theoretical studies on CeB 6 and NpO 2 are presented as typical examples. The study on the low temperature phase of PrFe 4 P 12 , whose nature has been controversial, are reviewed. It was concluded that it has an antiferro order with the order-parameter characterized by the identity representation of the point group. The large anisotropy of NMR splitting in the magnetic field direction dependence suggests important roles of moments with higher ranks in PrFe 4 P 12 . (author)
7. NMR structure of the HIV-1 reverse transcriptase thumb subdomain
Energy Technology Data Exchange (ETDEWEB)
Sharaf, Naima G. [University of Pittsburgh, School of Medicine, Department of Structural Biology and Pittsburgh Center for HIV Protein Interactions (United States); Brereton, Andrew E. [Oregon State University, Department of Biochemistry and Biophysics, 2011 Ag & Life Sciences Bldg (United States); Byeon, In-Ja L. [University of Pittsburgh, School of Medicine, Department of Structural Biology and Pittsburgh Center for HIV Protein Interactions (United States); Andrew Karplus, P. [Oregon State University, Department of Biochemistry and Biophysics, 2011 Ag & Life Sciences Bldg (United States); Gronenborn, Angela M., E-mail: [email protected] [University of Pittsburgh, School of Medicine, Department of Structural Biology and Pittsburgh Center for HIV Protein Interactions (United States)
2016-12-15
The solution NMR structure of the isolated thumb subdomain of HIV-1 reverse transcriptase (RT) has been determined. A detailed comparison of the current structure with dozens of the highest resolution crystal structures of this domain in the context of the full-length enzyme reveals that the overall structures are very similar, with only two regions exhibiting local conformational differences. The C-terminal capping pattern of the αH helix is subtly different, and the loop connecting the αI and αJ helices in the p51 chain of the full-length p51/p66 heterodimeric RT differs from our NMR structure due to unique packing interactions in mature RT. Overall, our data show that the thumb subdomain folds independently and essentially the same in isolation as in its natural structural context.
8. NMR studies of defects created by irradiation in metals
International Nuclear Information System (INIS)
Minier, M.; Minier, C.
1983-06-01
Nuclear Magnetic Resonance has been rarely used to study point defects created by irradiation in metals. Information obtained in this field using N.M.R. are shown. Some results are also described: characterization of migrating defects in electron irradiated copper; mobility of the complex interstitial-impurity in Al with 150 ppm of chromium; interstitial structure in irradiated aluminum and autodiffusion in metals [fr
9. NMR methods for the investigation of structure and transport
CERN Document Server
Hardy, Edme H
2011-01-01
Methods of nuclear magnetic resonance (NMR) are increasingly applied in engineering sciences. The book summarizes research in the field of chemical and process engineering performed at the Karlsruhe Institute of Technology (KIT). Fundamentals of the methods are exposed for readers with an engineering background. Applications cover the fields of mechanical process engineering (filtration, solid-liquid separation, powder mixing, rheometry), chemical process engineering (trickle-bed reactor, ceramic sponges), bioprocess engineering (biofilm growth), and food process engineering (microwave heating
10. Development of a computer-based pulsed NMR thermometer
International Nuclear Information System (INIS)
Hobeika, Alexandre; Haard, T.M.; Hoskinson, E.M.; Packard, R.E.
2003-01-01
We have designed a fully computer-controlled pulsed NMR system, using the National Instruments PCI-6115 data acquisition board. We use it for millikelvin thermometry and have developed a special control program, written in LabVIEW, for this purpose. It can perform measurements of temperature via the susceptibility or the τ 1 dependence. This system requires little hardware, which makes it very versatile, easily reproducible and customizable
11. Inverse problem for in vivo NMR spatial localization
Energy Technology Data Exchange (ETDEWEB)
Hasenfeld, A.C.
1985-11-01
The basic physical problem of NMR spatial localization is considered. To study diseased sites, one must solve the problem of adequately localizing the NMR signal. We formulate this as an inverse problem. As the NMR Bloch equations determine the motion of nuclear spins in applied magnetic fields, a theoretical study is undertaken to answer the question of how to design magnetic field configurations to achieve these localized excited spin populations. Because of physical constraints in the production of the relevant radiofrequency fields, the problem factors into a temporal one and a spatial one. We formulate the temporal problem as a nonlinear transformation, called the Bloch Transform, from the rf input to the magnetization response. In trying to invert this transformation, both linear (for the Fourier Transform) and nonlinear (for the Bloch Transform) modes of radiofrequency excitation are constructed. The spatial problem is essentially a statics problem for the Maxwell equations of electromagnetism, as the wavelengths of the radiation considered are on the order of ten meters, and so propagation effects are negligible. In the general case, analytic solutions are unavailable, and so the methods of computer simulation are used to map the rf field spatial profiles. Numerical experiments are also performed to verify the theoretical analysis, and experimental confirmation of the theory is carried out on the 0.5 Tesla IBM/Oxford Imaging Spectrometer at the LBL NMR Medical Imaging Facility. While no explicit inverse is constructed to ''solve'' this problem, the combined theoretical/numerical analysis is validated experimentally, justifying the approximations made. 56 refs., 31 figs.
12. 14N NMR of amminecobalt(III) compounds
DEFF Research Database (Denmark)
Kofod, Pauli
2003-01-01
Directly detected ammine 14N NMR chemical shifts of 20 amminecobalt(III) compounds are reported. The coordination shifts, δCS = δcoord − δfree, are in all cases negative and range from −4.4 ppm for the trans ammine ligand in [Co(NH3)5(CH3)]2+ to −73.6 ppm for the trans ammine ligand in [Co(NH3)5(F...
13. Metabolomic NMR fingerprinting: an exploratory and predictive tool
OpenAIRE
Lauri, Ilaria
2014-01-01
Metabolomics is the comprehensive assessment of low molecular weight organic metabolites within biological system. The identification and characterization of several chemical species, or metabolic fingerprinting, is an emergent approach in metabolomics field that provides a valuable “snapshot” of metabolic profiles. This approach is finding an increasing number of applications in many areas including cancer research, drug discovery and food science. The combined use of NMR spectroscopy, data ...
14. NMR clinical imaging and spectroscopy: Its impact on nuclear medicine
International Nuclear Information System (INIS)
1990-01-01
This is a collection of four papers describing aspects of past and future use of nuclear magnetic resonance as a clinical diagnostic tool. The four papers are entitled (1) What Does NMR Offer that Nuclear Medicine Does Not? by Jerry W. Froelich, (2) Oncological Imaging: Now, Future and Impact Jerry W. Froelich, (3) Magnetic Resonance Spectroscopy/Spectroscopic Imaging and Nuclear Medicine: Past, Present and Future by H. Cecil Charles, and (4) MR Cardiology: Now, Future and Impact by Robert J. Herfkens
15. Application of NMR circuit for superconducting magnet using signal averaging
International Nuclear Information System (INIS)
Yamada, R.; Ishimoto, H.; Shea, M.F.; Schmidt, E.E.; Borer, K.
1977-01-01
An NMR circuit was used to measure the absolute field values of Fermilab Energy Doubler magnets up to 44 kG. A signal averaging method to improve the S/N ratio was implemented by means of a Tektronix Digital Processing Oscilloscope, followed by the development of an inexpensive microprocessor based system contained in a NIM module. Some of the data obtained from measuring two superconducting dipole magnets are presented
16. Computer software for linear and nonlinear regression in organic NMR
International Nuclear Information System (INIS)
Canto, Eduardo Leite do; Rittner, Roberto
1991-01-01
Calculation involving two variable linear regressions, require specific procedures generally not familiar to chemist. For attending the necessity of fast and efficient handling of NMR data, a self explained and Pc portable software has been developed, which allows user to produce and use diskette recorded tables, containing chemical shift or any other substituent physical-chemical measurements and constants (σ T , σ o R , E s , ...)
17. [Derivative spectrophotometric and NMR spectroscopic study in pharmaceutical science].
Science.gov (United States)
Kitamura, Keisuke
2007-10-01
This review starts with an introduction of derivative spectrophotometry followed by a description on the construction of a personal computer-assisted derivative spectrophotometric (DS) system. An acquisition system for inputting digitalized absorption spectra into personal computers and a BASIC program for calculating derivative spectra were developed. Then, applications of the system to drug analyses that are difficult with traditional absorption methods are described. Following this, studies on the interactions of drugs with biological macromolecules by the DS and NMR methods were discussed. An (1)H NMR study elucidated that the small unilamellar vesicle (SUV) has a single membrane made of a phosphatidylcholine bilayer, and that chlorpromazine interacts with both the outer and inner layers. (13)C NMR revealed a reduction of the dissociation constants of phenothiazine drugs due to their interaction with SUV. The partition coefficients of phenothiazine, benzodiazepine and steroid drugs in an SUV-water system and the effects of cholesterol or amino lipids content on these partition coefficients were examined by the DS method. The binding constants of phenothiazine drugs to bovine serum albumin (BSA) and the influence of Na(+), K(+), Cl(-), Br(-), and I(-) on these binding constants were determined by DS. It was found that I(-), Br(-), Cl(-) reduce the binding constants in this order, and that Na(+) and K(+) have no effect. A (19)F NMR study revealed that triflupromazine binds to BSA and human serum albumin in two regions including Site II with different populations, and that a nonsteroidal anti-inflammatory drug, niflumic acid, binds Sites Ia and Ib.
18. 3D Reconstruction of NMR Images by LabVIEW
Directory of Open Access Journals (Sweden)
Peter IZAK
2007-01-01
Full Text Available This paper introduces the experiment of 3D reconstruction NMR images via virtual instrumentation - LabVIEW. The main idea is based on marching cubes algorithm and image processing implemented by module of Vision assistant. The two dimensional images shot by the magnetic resonance device provide information about the surface properties of human body. There is implemented algorithm which can be used for 3D reconstruction of magnetic resonance images in biomedical application.
19. Efficient Modeling of NMR Parameters in Carbon Nanosystems
Czech Academy of Sciences Publication Activity Database
Kupka, T.; Stachów, M.; Chelmecka, E.; Pasterny, K.; Stobinska, M.; Stobinski, L.; Kaminský, Jakub
2013-01-01
Roč. 9, č. 9 (2013), s. 4275-4286 ISSN 1549-9618 R&D Projects: GA MŠk(CZ) LH11033; GA ČR GAP208/11/0105 Grant - others:AV ČR(CZ) M200551205 Institutional support: RVO:61388963 Keywords : 13C NMR * zigzag SWCNT * DFT Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 5.310, year: 2013
20. Spin coherence transfer in chemical transformations monitoredNMR
Energy Technology Data Exchange (ETDEWEB)
Anwar, Sabieh M.; Hilty, Christian; Chu, Chester; Bouchard,Louis-S.; Pierce, Kimberly L.; Pines, Alexander
2006-07-31
We demonstrate the use of micro-scale nuclear magneticresonance (NMR) for studying the transfer of spin coherence innon-equilibrium chemical processes, using spatially separated NMRencoding and detection coils. As an example, we provide the map ofchemical shift correlations for the amino acid alanine as it transitionsfrom the zwitterionic to the anionic form. Our method is unique in thesense that it allows us to track the chemical migration of encodednuclear spins during the course of chemical transformations.
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https://waseda.pure.elsevier.com/ja/publications/associations-of-neighbourhood-walkability-indices-with-weight-gai
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# Associations of neighbourhood walkability indices with weight gain
Mohammad Javad Koohsari*, Koichiro Oka, Ai Shibata, Yung Liao, Tomoya Hanibuchi, Neville Owen, Takemi Sugiyama
*この研究の対応する著者
8 被引用数 (Scopus)
## 抄録
Background: Inconsistent associations of neighbourhood walkability with adults' body weight have been reported. Most studies examining the relationships of walkability and adiposity are cross-sectional in design. We examined the longitudinal relationships of two walkability indices - conventional walkability and space syntax walkability, and their individual components, with weight change among adults over four years. Methods: Data were from the Physical Activity in Localities and Community study in Adelaide, Australia. In 2003-2004, 2650 adults living in 154 Census Collection Districts (CCDs) returned baseline questionnaires; in 2007-2008, the follow-up survey was completed by 1098. Participants reported their weight at baseline and at follow-up. Neighbourhood walkability indices were calculated using geographic information systems and space syntax software. Linear marginal models using generalized estimating equations with robust standard errors were fitted to examine associations of the two walkability indices and their individual components with the weight at follow-up, adjusting for baseline weight, socio-demographic variables, and spatial clustering at the level of CCD. Results: The overall mean weight gain over four years was 1.5 kg. The two walkability indices were closely correlated (r = 0.76, p < 0.01). No significant associations were found between the overall neighbourhood walkability indices and weight change. Among walkability components, there was a marginally significant negative association between space syntax measure of street integration and weight change: one standard deviation increment in street integration was associated with 0.31 kg less weight gain (p = 0.09). Conclusions: Using a prospective study design and a novel space-syntax based measure of walkability, we were not able to identify relationships between neighbourhood walkability with weight gain. This is consistent with other inconclusive findings on the built environment and obesity. Research on the built environment and adults' weight gain may need to consider not just local environments but also a larger scale environment within a city or workplace environment in order to capture multiple behaviours relevant to weight gain.
本文言語 English 33 International Journal of Behavioral Nutrition and Physical Activity 15 1 https://doi.org/10.1186/s12966-018-0668-2 Published - 2018 4 3
## ASJC Scopus subject areas
• 医学（その他）
• 理学療法、スポーツ療法とリハビリテーション
• 栄養および糖尿病
## フィンガープリント
「Associations of neighbourhood walkability indices with weight gain」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。
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https://www.physicsforums.com/threads/integrating-a-curious-function.548098/
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# Homework Help: Integrating a curious function
1. Nov 7, 2011
### zip37
1. The problem statement, all variables and given/known data
I'm having some trouble trying to integrate the following function
2. Relevant equations
$\int([x/(logx)]dx)$
3. The attempt at a solution
I have tried integration by parts but I get stuck with harder integrals. What I'd like to know is that this function could be integrated or not. :) I've tried using Wolfram Alpha for this particular case but my math level is way below the explanations given there.
2. Nov 7, 2011
### Ray Vickson
Do you mean that the integrand is $f(x) = x/ \log(x)$ or do you mean $f(x) = [x/ \log(x)]$, where $[\cdots]$ is the "greatest-integer function"? If you mean the former, Maple expresses the result in terms of the non-elementary function Ei (the exponential integral): $$\mbox{Ei}(y) = P\int_{-\infty}^y \frac{e^t}{t} dt,$$
with P denoting the principal value integral.
RGV
3. Nov 7, 2011
### zip37
Yes, I meant the former, the integrand is x/logx.
Thank you for the information! I'm looking up a bit in other websites what this Ei function is in more detail.
4. Nov 7, 2011
### Matterwave
Are you integrating that through the whole real line? In that case you really do have a principal value integral because you are moving through a pole in the integrand.
5. Nov 8, 2011
### kmacinto
Integration by parts is the way I would go.
Try both functions for u. Ya got a 50% chance that your 1st choice is the correct one :)
6. Nov 8, 2011
### Ray Vickson
Integration by parts in NOT the way to go.
Your second comment makes no sense: the OP is 100% sure of what he/she means. Anyway, the second form f(x)= [x/log(x)] (where [] = greatest-integer function) will not have an analytically expressible integral---think about why not.
RGV
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https://study.com/academy/answer/evaluate-the-following-indefinite-integral-int-x-plus-9-4-dx.html
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# Evaluate the following indefinite integral \int (x+9)^{-4} dx
## Question:
Evaluate the following indefinite integral {eq}\int (x+9)^{-4} dx {/eq}
## Indefinite Integral in Calculus:
Indefinite integration is used to find out the antiderivative of a function.
The integrand is given with its derivative, so we'll solve this problem by using a process of substitution and it will turn the integrand into a function that is easier to integrate.
To integrate power functions we use the integration power rule {eq}\displaystyle \int x^n dx= \dfrac{x^{n+1}}{n+1}+C. {/eq}
We are given:
{eq}\displaystyle \int (x+9)^{-4} dx {/eq}
Apply u-substitution {eq}u = x+9 \rightarrow \ du = \ dx {/eq}
{eq}= \displaystyle \int u^{-4} \ du {/eq}
Apply integral power rule:
{eq}= \displaystyle \dfrac{u^{-4+1}}{-4+1}+C {/eq}
{eq}= \displaystyle \dfrac{u^{-3}}{-3}+C {/eq}
{eq}= \displaystyle - \dfrac{1}{3u^3}+C {/eq}
Substitute back {eq}u = x+9 {/eq}
{eq}= \displaystyle - \dfrac{1}{3 (x+9)^3}+C {/eq}
Therefore the solution is:
{eq}{\boxed{ \displaystyle \int (x+9)^{-4} dx =- \dfrac{1}{3 (x+9)^3}+C}} {/eq}
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https://github.polettix.it/ETOOBUSY/2020/04/09/autobiographical-numbers-constraints-basic/
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TL;DR
Remember last post about Autobiographical numbers? Here we will take a look at the constraints - horribly laid out, but effective (although maybe not very efficient).
So… the constraints. I coded a few of them, let’s start from a very basic one - although pretty effective on its own terms. If you want to try the code below, you can find it in autobiographical-numbers (the code itself is in stage 1).
# The code
1 sub constraint_basic ($status) { # little pruning, mostly checking 2 my$solution = $status->{solution}; 3 my %count_for; 4 my %is_exact = map {$_ => 1 } 0 .. $#$solution;
5 for my $i (0 ..$#$solution) { 6 my$slot = $solution->[$i];
7 my @candidates = keys $slot->%*; 8 die "no candidate for$i" unless @candidates;
9 my $exact = @candidates == 1; 10 for my$candidate (@candidates) {
11 $count_for{$candidate}++;
12 $is_exact{$candidate} = 0 unless $exact; 13 } 14 } ## end for my$i (0 .. $#$solution)
15 my $changes = 0; 16 for my$i (0 .. $#$solution) {
17 my $amount =$count_for{$i} // 0; 18 my$slot = $solution->[$i];
19 if ($is_exact{$i}) {
20 die "invalid amount if $i" unless exists$slot->{$amount}; 21 if (scalar keys$slot->%* > 1) { # prune
22 $slot->%* = ($amount => 1);
23 $changes++; 24 } 25 } 26 else { 27 for my$needed (keys $slot->%*) { 28 if ($needed > $amount) { 29 delete$slot->{$needed}; # this can't be fulfilled 30$changes++;
31 }
32 }
33 die "no valid candidate for $i" unless scalar keys$slot->%*;
34 }
35 } ## end for my $i (0 ..$#$solution) 36 return$changes;
37 } ## end sub constraint_basic ($status) The first loop (lines 5 to 14) counts the number of available slots where a specific amount can appear, collecting it in hash %count_for. Additionally, it also tracks whether the specific amount appears exactly in all those slots, i.e. if it’s the only candidate remained in there. The following loop (lines 16 to 35) does the constraints check and possibly pruning, keeping track of the number of changes on the way (so that the constraint function can signal whether pruning happened or not via return). Every slot is checked (line 16); the amount associated is the count of possible slots where it might appear (line 17). If the count associated to this slot is exact (i.e. it appeared as the only candidate in all slots where it was present), then we have to make an exact check. Hence we throw an exception in case this amount is not among the possibilities for this slot (line 20) or, if present, we make sure to mark it as the only possibility (lines 21 to 24, which avoid doing this operation over and over). If the count is not exact, then $amount represents the maximum number of times that the specific value of the slot (i.e. $i) can appear overall. For this reason, we can rule out all possibilities that would require more than $amount (lines 28 to 32). After this pruning, we must have some residual candidate for the slot, otherwise this cannot be a solution (line 33).
# How does it go?
I daresay that it goes pretty well - enough to solve the puzzle for the YouTube video in a bunch of milliseconds:
\$ time ./run.sh 01-basic/ 10
solution => [6,2,1,0,0,0,1,0,0,0]
real 0m0.084s
user 0m0.068s
sys 0m0.008s
# So long…
Curious about the whole series? Here it is:
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=42&t=38199&p=128993
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## tetrahedral
$sp, sp^{2}, sp^{3}, dsp^{3}, d^{2}sp^{3}$
davidryan3f
Posts: 63
Joined: Fri Sep 28, 2018 12:23 am
### tetrahedral
can someone explain to me why tetrahedral is sp3 hybridization?
404536963
Posts: 29
Joined: Fri Feb 02, 2018 3:02 am
### Re: tetrahedral
Tetrahedral is an atom that has 4 bonds. This means that the 2s orbital and the 2p orbital hybridize to form sp3. To determine a molecule's hybridization, just count the number of bonds/lone pairs on the central atom (1 bond= s, 2 bond= sp, 3 bond= p2, 4 bond= sp3, 5 bond= sp3d, 6 bond= sp3d2, etc.)
Elias Omar 1G
Posts: 52
Joined: Fri Sep 28, 2018 12:17 am
### Re: tetrahedral
The type of hyrbrid orbital is named after the number of p orbitals that are needed for the central atom to have the right amount of bonds. An sp3 hybrid orbital is 1 s orbital and the three p orbitals of the same energy level (sp2 would be one s orbital and 2 p orbitals). because the central atom bonds with 4 other atoms in a tetrahedral arrangement, all four sp3 orbitals are needed to hold valence electrons.
Xingzheng Sun 2K
Posts: 62
Joined: Fri Sep 28, 2018 12:29 am
### Re: tetrahedral
The tetrahedral shape has 4 bonds, which in order 1, 2, 3, 4 bonds form s, sp, sp2 and sp3 hybridization.
Ricardo Martin 1J
Posts: 63
Joined: Fri Sep 28, 2018 12:15 am
### Re: tetrahedral
4 areas of electron density equals sp3 hybridization.
Anmol_cheema_2F
Posts: 60
Joined: Fri Sep 28, 2018 12:26 am
### Re: tetrahedral
Since there are four areas of electron density, it is sp3.
2=sp 3=sp2 4=sp3 5=sp3d 6=sp3d2
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https://link.springer.com/article/10.1007%2Fs00371-018-1494-x
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The Visual Computer
, Volume 34, Issue 9, pp 1243–1254
# Is gender encoded in the smile? A computational framework for the analysis of the smile driven dynamic face for gender recognition
• Hassan Ugail
Open Access
Original Article
## Abstract
Automatic gender classification has become a topic of great interest to the visual computing research community in recent times. This is due to the fact that computer-based automatic gender recognition has multiple applications including, but not limited to, face perception, age, ethnicity, identity analysis, video surveillance and smart human computer interaction. In this paper, we discuss a machine learning approach for efficient identification of gender purely from the dynamics of a person’s smile. Thus, we show that the complex dynamics of a smile on someone’s face bear much relation to the person’s gender. To do this, we first formulate a computational framework that captures the dynamic characteristics of a smile. Our dynamic framework measures changes in the face during a smile using a set of spatial features on the overall face, the area of the mouth, the geometric flow around prominent parts of the face and a set of intrinsic features based on the dynamic geometry of the face. This enables us to extract 210 distinct dynamic smile parameters which form as the contributing features for machine learning. For machine classification, we have utilised both the Support Vector Machine and the k-Nearest Neighbour algorithms. To verify the accuracy of our approach, we have tested our algorithms on two databases, namely the CK+ and the MUG, consisting of a total of 109 subjects. As a result, using the k-NN algorithm, along with tenfold cross validation, for example, we achieve an accurate gender classification rate of over 85%. Hence, through the methodology we present here, we establish proof of the existence of strong indicators of gender dimorphism, purely in the dynamics of a person’s smile.
## Keywords
Smile dynamics Gender recognition Machine learning k-Nearest neighbour
## 1 Introduction
It is often said that the face is a window to the soul. Bearing a metaphor of this nature in mind, one might find it intriguing to understand, if any, how the physical, behavioural as well as emotional characteristics of a person could be decoded from the face itself. With the increasing deductive power of machine learning techniques, it is becoming plausible to address such questions through the development of appropriate computational frameworks.
Computational frameworks for human face analysis have recently found their way into great many application areas. These include computer vision, psychology, biometrics, security and even healthcare. The appealing, and the practical, nature of such face analysis techniques, are highlighted by the wealth of information it can provide in a non-invasive manner. Unsurprisingly, such applications have already found their way into furnishing useful telltale signs of an individual’s health status, identity, beauty and behaviour, all of which can be enhanced by the non-invasive information that leaks directly from the face, e.g. [1, 12, 27].
Additionally, computer-based analysis of the human face can provide strong and useful cues for personal attributes such as age, ethnicity and more appropriately gender, in the present context. Gender classification, in this sense, can, for example, aid as an advantageous biometric feature in order to improve the accuracy of determining an identity, especially in the presence of limited information on a subject. Recent research into gender classification has faced challenging hurdles, mainly due to the reliance of static data in the form of facial images. There are many inherent issues when looking for gender clues in appearance-based facial analysis. These include variability of lighting conditions, pose and occlusions. In this regard, in this work, we departed from such appearance-based analysis of facial images. Instead, we consider the analysis of the dynamic face, in particular, the dynamics of the smile, for clues of gender. This allows us to address the very intriguing question of whether a person’s sexual dimorphism is encoded in the dynamics of the smile itself.
Hence, this paper is concerned with the identification of gender from the dynamic behaviour of the face. Equally importantly, we seek to answer the crucial question of whether gender is encoded in the dynamics of a person’s smile. The case for such a computer-based investigation is fuelled by an array of cognitive physiological studies showing evidence of gender variances in facial expressions, e.g. [17, 22, 29]. We specifically focus on studying the smile as it is considered to be a rich, complex and sophisticated facial expression, formed through the synergistic action of emotions. According to Ekman [15], there are 18 different types of smile, each of them corresponds to a specific situation and reflects a different type of emotion. Moreover, various studies show that there are differences in smiles between males and females, i.e. females tend to bear more expressive smiles than males. Furthermore, recent research indicates that females express emotions more accurately in both spontaneous and posed situations, e.g. [7, 8].
Based on the findings from such psychological studies, we examine the intensity and the duration of a smile in the hope of finding a distinction between the two sexes. Hence, in this paper, we present an algorithm to measure gender solely based on the dynamics of the smile without resorting to appearance-based image analysis techniques. The dynamic framework we have developed for smile analysis has four key components. They are the spatial dynamics of the face based on geometric distances across the entire face, dynamic triangular areas of the mouth, the geometric flow across key areas of the face and statistically inspired intrinsic features which further analyse the spatial and area parameters. These purely dynamic features are then fed to a machine learning routine for classification, resulting in an algorithm for gender recognition.
This paper is structured as follows. In Sect. 2, we discuss some of the related work on gender classification from two different viewpoints, i,e. psychological and computational standpoints. In that Section, we specifically highlight the distinctiveness of our work in this area. Section 3 presents our proposed framework for identifying the 210 unique dynamic parameters for analysis of a smile. In Sect. 4, we then explain how we have utilised the computational framework we have developed to undertake analysis of smiles for gender classification. We then provide details of results we have obtained, and finally in Sect. 5, we conclude this paper.
## 2 Related work
In this Section, we discuss recent advances in face analysis for both smiles and gender classification. Research in these areas appears to be dominantly arising from psychological studies as well as computer aided analysis of both static and dynamic digital images.
In many psychological experiments, the use of facial electromyographic (EMG) is common, especially for studies relating to the analysis of the face. EMG is a diagnostic technique used for recording facial muscle activity by placing electrodes on the face [31]. Much work on face analysis have been undertaken using EMG. These include the study of facial reactions to auditory stimuli, gender differences in facial reactions to facial expressions and facial and emotional reactions to both genuine and induced smiles, e.g. [14, 30].
For example, in [13], it is reported that, based on the facial EMG activity, happy faces evoked increased zygomatic activity and the effects were more pronounced for females. Similarly, a number of other psychological studies show that females on average bear more expressive smiles. In fact, it has been documented that females smile more often than males in a variety of social contexts, e.g. [7, 10].
From a computational viewpoint, gender classification based on the analysis of the face can be divided into three main categories, namely geometric, appearance and methods comprising of a hybrid between geometric and appearance models. All these methods rely on some form of a technique for extracting features from facial images.
The geometric model relies on the spatial geometry derived from a set of facial landmarks for extracting the relevant facial features. These often include physical measurements such as the size of eyebrows, eyes, nose and the mouth. Furthermore, in the dynamic case, this model relies on measures based on the movement of the landmarks. For example, the work presented in [18] relies on the use of geometric features obtained from standard Canny edge detection. The result is a global feature set consisting of the inter ocular distance, the distance between the lips and the nose tip as well as the distance between the nose tip and the line joining the two eyes. The resulting classification was rather simple and was based on threshold values of Euclidean measures. In [19], a slightly more sophisticated model based on principle component analysis (PCA) was utilised while the classification was again based on Euclidean measures. It is claimed that they achieve an impressive gender recognition rate of 94% simply based on the geometric measures on still images.
The appearance model can also be referred to as template matching or using an exemplar of the object. Appearance models imply that objects look different under changes in lighting, colour, direction and can be at different scales. Furthermore, it describes the texture of the facial features. The work presented in [21, 26] utilises the Gabor function to extract the relevant texture from which facial features are derived. The Gabor function uses a set of wavelets with specific orientations and directions in order to represent a given texture. It is computationally intensive and so hardly applicable for real-time applications. A trick often employed to speed up the computations is to use PCA or local binary pattern (LBP) to minimise the number of features extracted. More sophisticated methods such as the use of convolutional neural networks for appearance-based gender recognition from facial images are also increasingly becoming popular, e.g. [5].
The hybrid model which takes advantage of both the appearance and geometric parameters uses a variety of techniques. The work presented in [33] makes use of a hybrid model consisting of active appearance model (AAM) and Haar wavelets for gender classification from faces. In their model, a total of 3403 geometric distances were chosen from which 10 significant features were extracted. They are then fed to an SVM classifier. The work described in [28] utilises case-based reasoning (CBR) whereby 8 geometric distances across the face along with 6 different facial feature ratios were used to train a hybrid of k-NN and Linear discriminant analysis (LDA) classifier. In [25], the use of discrete cosine transform (DCT) and LBP algorithms as appearance models and geometric distance features are described. Similarly, the work described in [24] divides the face into regions of interest to apply PCA and utilise SVM for classification.
It is entirely appropriate for us to place the work presented in this paper in the category of geometric models. However, the distinct difference between our work and the rest is that we concentrate purely on the dynamic facial features and more specifically the dynamics arising from the smile. The closest to our work in the present literature is the interesting piece of research in the area recently presented in [11] in which the use of smile for gender classification has been discussed. Their framework makes use of 49 facial landmarks produced by the cascade of linear regression, and they track them using sparse optical flow, which is used to measure 27 geometric distances across the face. For classification, they have used a pattern classifier on labelled data with an SVM. At a superficial level, it might appear that this work is rather similar to ours, though upon closer examination one would uncover distinct differences in that they have in fact utilised an appearance-based model along with smile dynamics to enhance the gender classification. On the other hand, as highlighted earlier, in our work, we resort to the pure dynamic features of the smile, and hence, we present an analysis framework to solely process the dynamics of the face for gender identification.
## 3 A computational framework for smile dynamics
It has been hypothesised and evidenced by various psychological experiments that there exist differences in smiles between the two genders. To verify this computationally and at the same time to develop a tool for gender classification solely based on the smiles, we propose a framework which can track the dynamic variations in the face from neutral to the peak of a smile. Our framework is based upon four key components. They are (1) the spatial features which are based on dynamic geometric distances on the overall face, (2) the changes that occur in the area of the mouth, (3) the geometric flow around prominent parts of the face and (4) a set of intrinsic features based on the dynamic geometry of the face. Note, all of the dynamic features described here are intuitive extensions of the relevant physical experimentations and are based on the reported literature on facial emotions, especially on the dynamics of the smile, eg. [8, 10].
Figure 1 presents a block diagram showing the key components of our framework for the analysis of the dynamics of a smile. The first step in our framework is to detect and track the face within a given video sequence. To do this, we have used a well-known Viola-Jones algorithm. It is based on Haar feature selection to create an integral image through the use of Adaboost training and cascade classifiers [32]. The ability of this algorithm to robustly detect faces under different lighting conditions is well established, and we have also demonstrated this in previous work [2].
The next step in our proposed framework involves automatic detection and tracking of a stable set of landmarks on the dynamic face. Automated Landmark detection is done using the CHEHRA model [6]. The algorithm has been trained to detect facial landmarks using in-the-wild datasets under various illumination, facial expressions and head poses. It is based on cascade linear regression for discriminative face alignment. This is done by applying Incremental Parallel Cascade of Linear Regression (iPar-CLR) method. The tests we have carried using the CHEHRA model appear to be acceptable though we noticed it is likely to suffer when it comes to real-time applications. The algorithm has been utilised to detect 49 landmarks on the face, marked as $$P_{1}\ldots P_{49}$$ as shown in Fig. 2b for the face shown in Fig. 2a. Note, in addition to the 49 landmarks which CHEHRA detects, we also include the centres of the eyes as two additional landmark points, as shown in Fig. 2b, marked as $$P_{50}$$ and $$P_{51}$$.
Table 1
Description of the geometric distances from which dynamic spatial parameters are derived
Distance
Description
Landmarks
$$d_{1}$$
Mouth corners
$$P_{32}$$ to $$P_{38}$$
$$d_{2}$$
Upper and lower lip
$$P_{45}$$ to $$P_{48}$$
$$d_{3}$$
Mouth to nose (left corners)
$$P_{32}$$ to $$P_{27}$$
$$d_{4}$$
Mouth to nose (right corners)
$$P_{38}$$ to $$P_{31}$$
$$d_{5}$$
Mouth to eye (left corners)
$$P_{32}$$ to $$P_{11}$$
$$d_{6}$$
Mouth to eye (right corners)
$$P_{38}$$ to $$P_{20}$$
### 3.1 Dynamics of the spatial parameters
Based on some of the positions of the 49 landmarks we obtain through the CHEHRA model, we identify 6 dynamic geometric Euclidean distances across the face which are utilised to compute our dynamic spatial parameters. Further details of these spatial parameters are given in Table 1. The general form of a given spatial parameter is,
\begin{aligned} \delta d_{i} = \frac{d_{i}}{N_{i}} + \sum _{n=1}^{t} \frac{d_{i}}{N_{i}} - \frac{d_{in}}{N_{in}}, \end{aligned}
(1)
where t is the total number of video frames corresponding to each $$\frac{1}{10}\hbox {th}$$ increment of the total time T for the smile, from neutral to the peak. Here $$N_{i}$$ is the length of the nose, for a given video frame, computed as the distance between $$P_{23}$$ and $$P_{26}$$. Thus, by dividing the spatial parameters by the length of the nose $$N_{i}$$, we normalise these parameters to the given dynamic facial image. It is noteworthy to point out that for a given smile, from neutral to the peak, we divide the time it takes into ten partitions and therefore for each of the $$d_{i}$$ we have 10 times $$d_{i}$$ parameters which are fed to the machine learning. Hence, in our dynamic smile framework, we have a total of 60 dynamic spatial parameters.
Figure 3 shows the variation of $$\delta d_{i}$$ across the 10 time partitions for a typical smile. As can be observed, there is a variation in each parameter as the smile proceeds from neutral to its peak.
### 3.2 Dynamic area parameters on the mouth
The second set of dynamic parameters concern the mouth. Here we compute the changes in the area of 22 triangular regions that occupy the total area of the mouth. This is shown in Fig. 4. Again these areas are computed using the corresponding landmarks obtained from the CHEHRA model. The general form of how the changes in the mouth area are computed is described as,
\begin{aligned} \bigtriangleup _\mathrm{area}^{i} = \sum _{n=1}^{22} \frac{\bigtriangleup _{i}}{\bigtriangleup N_{i}}, \end{aligned}
(2)
and,
\begin{aligned} \delta \bigtriangleup _{i} = \sum _{n=1}^{t} \bigtriangleup _\mathrm{area}^{i}, \end{aligned}
(3)
where t is the total number of video frames corresponding to each $$\frac{1}{10}\hbox {th}$$ increment of the total time T for the smile, from neutral to the peak. Here $$\bigtriangleup N_{i}$$ is the invariant triangle area determined by the landmarks defining the outer corners of the eyes and the tip of the nose, namely $$P_{11}$$,$$P_{20}$$ and $$P_{26}$$. Again we divide the total time of the smile, from neutral to peak, into ten partitions, and therefore we obtain 10 parameters from the $$\delta \bigtriangleup _{i}$$, though time, which are fed to the machine learning. Thus, in our dynamic smile framework, we have a total of 10 parameters which capture dynamics of the mouth.
For the purpose of illustration, in Fig. 5 we show the distribution of areas of the triangular regions, $$\bigtriangleup _{i}$$, across a typical smile.
### 3.3 Dynamic geometric flow parameters
The third component of our framework for smile dynamics is the computation of flow around the face during a smile. More specifically, we compute the flow around the mouth, cheeks and around the eyes. To do this, we have utilised the dense optical flow developed by Farnebäck [16]. It is a two-frame motion estimation algorithm in which quadratic polynomials are used to approximate the motion between two subsequent frames in order to approximate motion of neighbourhood pixels for both the frames. Using this algorithm, we are able to estimate the successive displacement of each of the landmarks during the smile.
Table 2
Description of how the optical flow parameters around the face are derived
Optical flow
Description
Landmarks/regions
$$\delta f_{1}$$
Mouth
Landmarks $$P_{32}$$ to $$P_{49}$$
$$\delta f_{2}$$
Left eye
$$f_{6}$$, $$f_{7}$$, $$f_{8}$$, $$f_{9}$$
$$\delta f_{3}$$
Right eye
$$f_{1}$$, $$f_{2}$$, $$f_{3}$$, $$f_{4}$$
$$\delta f_{4}$$
Left cheek
$$f_{10}$$
$$\delta f_{5}$$
Right cheek
$$f_{5}$$
Table 2 shows how the various landmarks and regions of the face are utilised to compute the optical flows around the face. The relevant facial regions and landmarks are given in Figs. 2b and 6 respectively. We also show the variations in the dynamic optical flows, $$\delta f_{i}$$, around the face for a typical smile in Fig. 7.
Note, the geometric flow, $$\delta f_{i}$$, for each of the regions is normalised upon computation by means of the corresponding flow around the invariant triangle area of the face determined by the landmarks defining the outer corners of the eyes and the tip of the nose, namely $$P_{11}$$,$$P_{20}$$ and $$P_{26}$$. Again, each of the geometric flow parameters $$\delta f_{i}$$ is computed across the 10 time interval through which the smile is measured, resulting in a total of 50 dynamic geometric flow parameters which are then fed to machine learning.
### 3.4 Intrinsic dynamic parameters
In addition to the spatial parameters, the area parameters and geometric flow parameters, we compute a family of intrinsic dynamic parameters on the face to further enhance the analysis of the dynamics of the smile. These intrinsic parameters are mainly based on the computation of the variations in the slopes and the growth rates of various features across the face. We identify these features as $$s_{1}$$, $$s_{2}$$, $$s_{3}$$ and $$s_{4}$$, details of which we describe as follows.
The first parameter family in this category relates to the computation of the overall slope variation around the mouth during a smile. To compute this, we use,
\begin{aligned} s_{1i} = \frac{ N\sum _{n=1}^{N} P_{ix}P_{iy} - \sum _{n=1}^{N} P_{ix} \sum _{n=1}^{N} P_{iy} }{\sum _{n=1}^{N} P_{ix}^2- \left( \sum _{n=1}^{N} P_{ix}\right) ^2}, \end{aligned}
(4)
where N is the number of video frames comprising the whole smile, from neutral to the peak, $$P_{ix}$$ and $$P_{iy}$$ are the Cartesian coordinate equivalents in the image space corresponding to the landmark point $$P_{i}$$. Hence, a total of 12 parameters are identified for the variations in slopes around mouth corresponding to the mouth landmarks $$P_{32}$$ to $$P_{43}$$.
Table 3
Parameter description for the computational framework for smile dynamics
Parameter
Description
Number of parameters
$$\delta d_{i}$$
Spatial—involving 6 geometric distances across the face
60
$$\delta \bigtriangleup _{i}$$
Mouth area—derived from the total area for the 22 parts of the mouth
10
$$\delta f_{i}$$
Geometric flow around the mouth, eyes and cheeks
50
$$s_{1i}$$
Slope measurements around mouth landmarks $$P_{32}$$ to $$P_{43}$$
12
$$s_{2i}$$
Growth rates of the spatial parameters and mouth areas
29
$$s_{3i}$$
Compound growth rates of the spatial parameters and mouth areas
29
$$s_{4i}$$
Gradient orientations for the mouth corners and the mouth area
20
The second family of parameters, $$s_{2}$$, in this category corresponds to the growth rates across smile corresponding to the spatial parameters as well as area parameters on the mouth. The growth rates arising from the spatial parameters are defined as,
\begin{aligned} s_{2i(\mathrm {spatial})} =\sum _{n=1}^{N} \frac{\delta d_{i}^{t} - \delta d_{i}^{t+1}}{\delta d_{i}^{t}}, \end{aligned}
(5)
and for the area parameters on the mouth are,
\begin{aligned} s_{2i(\mathrm {area})} =\sum _{n=1}^{N} \frac{\bigtriangleup _{i}^{t} - \bigtriangleup _{i}^{t+1}}{\bigtriangleup _{i}^{t}}, \end{aligned}
(6)
where N is identified as the total number of frames in the video sequence of the smile while t to $$t+1$$ defines two successive video frames. In addition to the growth rates $$s_{2i(\mathrm {area})}$$, for each of the 22 triangular regions of the mouth, we also compute the total growth rate for the mouth, by using Eq. (6) along with the 22 triangular mouth area information. This means we have a total of $$6+22+1 = 29$$ parameters of dynamic intrinsic type $$s_{2}$$.
The third family of parameters, $$s_{3}$$, in this category we have identified is for both spatial parameters across the face and area parameters in the mouth. These are defined as compound growth rates given as,
\begin{aligned} s_{3i(\mathrm {spatial})} = \left( \frac{\delta d_{i}^\mathrm{neutral}}{\delta d_{i}^\mathrm{peak}} \right) ^{1/N} -1, \end{aligned}
(7)
and,
\begin{aligned} s_{3i(\mathrm {area})} = \left( \frac{\bigtriangleup _{i}^\mathrm{neutral}}{\bigtriangleup _{i}^\mathrm{peak}} \right) ^{1/N} -1, \end{aligned}
(8)
where N, like previously, is the total number of frames in the video sequence of the smile. The compound growth rate is measured simply using the neutral and peak of the smile. Again, like previously, in addition to the compound growth rates $$s_{3i(\mathrm {area})}$$ we also compute the compound growth for the entire mouth by means of the utilising the total area of the mouth. This implies that we obtain a total of 29 parameters of dynamic intrinsic type $$s_{3}$$ too.
For the final family of parameters, $$s_{4}$$, in this category, we compute the gradient orientation of the mouth based on the two mouth corner landmarks $$P_{32}$$ and $$P_{38}$$ which provides us with a line m passing $$\delta d_{1}$$ at the neutral and the peak of the smile. We then use,
\begin{aligned} s_{4i} = \sum _{t=1}^{T} \delta d_{1}^t - m^t, \end{aligned}
(9)
to compute the rate of deviation of the mouth corners against the gradient m over the 10 time partitions where T is the total time from neutral to the peak of the smile. Similarly, we compute the gradient orientation of the mouth area based on the combined 22 triangular areas of the mouth between the neutral frame and the peak of the smile.
These parameters provide us with a sense of the smoothness of the smile and forms an additional $$10+10=20$$ parameters for machine learning.
Table 3 provides a summary and brief description of various parameters associated with our computational framework for smile dynamics.
## 4 Experiments
Once an appropriate framework for the analysis of the dynamics of the similes, as described above, is in place, we carried out a series of experiments to further analyse the pattern of smile and more importantly to look for clues of gender in the smile. For this purpose, we utilised two well-known datasets to carry out an initial set of experiments. We then utilised the same datasets to extract the parameters described in Table 3 and fed them to machine learning routines.
### 4.1 Datasets
We tested our approach on two main datasets namely, the CK+ [23] and the MUG [4] datasets. The CK+ dataset has a total of 83 subjects, consisting of 56 females and 27 males. The smile of each of the subjects went from the neutral expression to the peak of the smile. On the other hand, the MUG dataset contains a total of 26 subjects, consisting of 13 females and 13 males. The smile of each subject, in this case, went from the neutral expression through to the peak and finally returning to the neutral. Since our framework has been developed to analyse smiles from neutral to the peak, we modified the MUG dataset so as it only contained the relevant parts of the smile for each subject. In addition to this, for each smile, we also ensured that within the two datasets there contained an equal number of video frames. Thus, a total of 109 unique subjects were available to us for training and testing.
### 4.2 Initial experiments
Here we report an initial set of interesting experiments that we undertook to further understand the dynamics of smiles and to seek for clues of gender in smiles.
In our first experiment, we tried a rather brute force approach to identify the areas of the face that contain most information of the smile that relates to the gender. Figure 8 shows some results based on the changes in the areas of the mouth region for 54 subjects (27 females and 27 males) in the CK+ database for the peak of the smile. As can be observed, there appears to be no significant difference between genders when one considers this simple form of analysis.
Next, we considered a computation relating to the product value for the areas for the upper lip and lower lip using the $$\delta \bigtriangleup _{i}$$ given in Equation (2) throughout the smile expression. This was done by multiplying each feature value for the changes in the mouth areas from a given video frame by the corresponding values from the next frame, in order to obtain the product of the features (POF) through the smile expression, i.e.
\begin{aligned} \text{ POF }_{i} = \sum _{t=1}^{N} \bigtriangleup _{i}^{t}\bigtriangleup _{i}^{t+1}, \end{aligned}
(10)
where N is the number of video frames containing the smile expression from neutral to the peak.
Analysis of the POF data gave us some clues for gender difference between the smiles. Thus, by taking the average of each attribute, for both the genders, Fig. 9 shows the POF for the females and the males in the CK+ dataset and Fig. 10 shows the corresponding POF plots for the subjects in the MUG dataset. As can be inferred, from the average POF results shown in Figs. 9 and 10, there appears to be a distinguishable difference in the smile of the males and females in terms of the POF computations.
Furthermore, from a first glance at these results, one might infer that males have a more intense smile than females which directly conflicts with the various psychological studies. However, that is indeed not the case. In fact, we note that in this experiment we computed the POF for each triangular features whose values are always less than 1. Additionally, for normalisation, we divided the POF values with the invariant area of the eyes-nose triangle. The result is a very small number, less than 1. Since the product of smaller numbers is smaller too, the POF values for females are smaller than that for males. Hence, it indeed confirms the smiles of females expand more through time in comparison to males.
Though rather simple, using the above approach, we were able to classify the data, through the median POF value computed from the mouth triangular attributes. This lends us a 60% correct classification for gender. That, however, is just slightly above chance and hence would not be considered an acceptable method of classification. We then used all the features described in our computational framework for smile dynamics (Sect. 3) to train and test a machine learning classifier.
With this knowledge, we constructed a suitable machine learning approach for classification. Following the procedure described in the block diagram shown in Fig. 1, the following algorithmic form further elaborates the computational framework we have developed for the automatic analysis of smile dynamics.
### 4.3 Classification using machine learning
For our machine learning based classification, we have utilised two well-known classification algorithms namely, the support vector machine (SVM) and the k-nearest neighbour (KNN).
First, we tried to use PCA as a pre-step before applying SVM. The results indicated this approach yields a very low classification rate. This is probably due to the fact that PCA reduces the number of features, while at the same time eliminating some distinguishing features. Second, we used SVM on its own, without the PCA. We had a mild improvement in the classification rate of 69%.
Finally, we used the k-NN algorithm which is a nonparametric method used for classification and regression [3]. The output of k-NN algorithm is a class relationship. The object can be assigned a class by k nearest neighbours where k is a positive integer. We utilised all the 210 features described in Table 3 to train our classifier. Additionally, we used a tenfold cross validation scheme to validate our k-NN classifier. The results were tested on several distance functions namely, Euclidean, Cosine, Minkowsky and Correlation. In Table 4, we report the best results we have obtained using the k-NN classifier.
Table 4
Results using the k-NN classification
CK+
MUG
k-NN distance
Correlation
Cosine
k value
3
14
Classification
78%
86%
## 5 Conclusions
This paper is concerned with the identification of gender from the dynamic behaviour of the face. In this sense, we wanted to answer the crucial question of whether gender is encoded in the dynamics of a person’s smile. To do this, we have developed a computational framework which can analyse the dynamic variations of the face from the neutral pose to the peak of the smile. Our framework is based upon four key components. They are the spatial features which are based on dynamic geometric distances on the overall face, the changes that occur in the area of the mouth, the geometric flow around some of the prominent parts of the face and a set of intrinsic features based on the dynamic geometry of the face. This dynamic framework enables us to compute 210 unique features which can then be fed to a k-NN classifier for gender recognition.
We ran our experiments on a total of 109 subjects (69 females and 40 males) from two datasets, namely the CK+ and the MUG datasets. Firstly, our results do agree with that of various psychological studies, indicating that females are more expressive in their smiles. For example, this became evident to us by simply looking at the changes in the lip area during a smile in which the lip area of female subjects expands more in comparison with the male subjects. Further, and more importantly, using machine learning approaches, we can also classify gender from smiles. In particular, by means of the standard k-NN algorithm, we are able to obtain a classification rate of up to 86%, purely based on the dynamics of smiles.
We understand from the presently available literature that some of the recent work carried in gender classification can achieve over 90% recognition rates using hybrid models with a combination of geometric and appearance features which are both static and dynamic. This is particularly clear from the work presented in [11]. It is, however, noteworthy that our work is geared to study the gender classification rates purely based on the dynamics of a smile. In fact, some of the results reported in [11] indicate that using their chosen dynamic smile features they obtain a classification rate of 60%, whereas using the smile dynamics framework we have proposed, we are able to obtain a higher gender classification rate of over 75%. There is also an added advantage of using the dynamic features, as opposed to static images, for gender identification since it presents with the opportunity to infer gender from certain parts of the face such as the mouth and the eyes areas.
Going forward into the future, there are a number of directions in which this work can be further taken forward. It will be useful to see if it would be possible to enhance the classification rates using other correlation and sophisticated statistical analysis techniques. In this paper, we have only used simple machine classification techniques such as SVM and K-NN, since our prime aim here was to demonstrate the power of smile dynamics in gender identification. We believe the utilisation of sophisticated machine learning techniques will further improve the results. We also believe this will be the case if novel machine learning techniques such as convolutional neutral networks based deep learning (eg. [9, 20]) can be adopted to the problem at hand. However, having said that, we must also highlight the fact that such sophisticated machine learning techniques usually require sufficient and significant training data which, as far as smiles are concerned, are scarce at present.
In addition to this, the results could be further tested and validated on other datasets. One deficiency of this present study is that we did not look deeply into the gender variation between posed and spontaneous smiles. We believe our framework has merit in providing much room for such detailed analysis to seek gender differences between the two types of smiles. Additionally, aside from the expression of a smile, other basic emotional attributes such as surprise, fear, anger and disgust can be studied in detail to look for cues to enhance gender recognition from facial expressions in general. We believe the framework we have presented in this paper can easily be adapted to undertake such studies.
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https://www.sparrho.com/item/universal-scaling-effects-of-a-temperature-gradient-at-first-order-transitions/77fde4/
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# Universal scaling effects of a temperature gradient at first-order transitions.
Research paper by Claudio C Bonati, Massimo M D'Elia, Ettore E Vicari
Indexed on: 16 Jul '14Published on: 16 Jul '14Published in: Physical review. E, Statistical, nonlinear, and soft matter physics
#### Abstract
We study the effects of smooth inhomogeneities at first-order transitions. We show that a temperature gradient at a thermally driven first-order transition gives rise to nontrivial universal scaling behaviors with respect to the length scale l_{t} of the variation of the local temperature T_{x}. We propose a scaling ansatz to describe the crossover region at the surface where T_{x}=T_{c}, where the typical discontinuities of a first-order transition are smoothed out. The predictions of this scaling theory are checked, and get strongly supported, by numerical results for the two-dimensional (2D) Potts models, for a sufficiently large number of states to have first-order transitions. Comparing with analogous results at the 2D Ising transition, we note that the scaling behaviors induced by a smooth inhomogeneity appear quite similar in first-order and continuous transitions.
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https://forum.wilmott.com/viewtopic.php?f=15&t=97807&p=854449
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SERVING THE QUANTITATIVE FINANCE COMMUNITY
Collector
Posts: 4415
Joined: August 21st, 2001, 12:37 pm
### Re: "Unified Revolution" new book by Espen Haug
"For about hundred years, modern physics has not been able to build a bridge between quantum mechanics (QM) and gravity. However, a solution may be found here. We present our quantum gravity theory, which is rooted in indivisible particles where matter and gravity are related to collisions and can be described by collision-space-time. In this paper, we also show that we can formulate a quantum wave equation rooted in collision-space-time, which is equivalent to mass and energy.
Depuis une centaine d'années, la physique moderne n'a pas été en mesure de jeter un pont entre la mécanique quantique et la gravité. Cependant, une solution peut être trouvée ici. Nous présentons notre théorie de la gravité quantique, qui est enracinée dans des particules indivisibles où la matière et la gravité sont liées aux collisions et peuvent être décrites par l’espace-temps de collision. Dans cet article, nous montrons également que nous pouvons formuler une équation d'onde quantique enracinée dans l’espace-temps de collision, qui est équivalente à la masse et à l'énergie."
Standard physics contains two major mistakes that means they not can unify gravity with QM and not even properly with relativity theory.
1. They indirectly use two different mass definitions, without knowing so. In gravity they indirectly have incorporated the Planck scale into their mass by multiplying G with their kg mass M. The second mass in for example their weak field Newtonian gravity cancels out in anything directly observable. In all other areas off physics than gravity they use a different mass definition. This means it is impossible to unify the different areas of standard physics, without fixing this. (Actually if they have followed Newton's original formula and Newtons philosophy clearly pointed out in Principia and not fudged it with a G to get their incomplete kg mass to work in gravity they would possibly have solved it long time ago.
2. By using the de Broglie wave and the de Broglie momentum that are just mathematical derivatives of the real matter "wave", the Compton wave and the real momentum, adds to why standard physics not can get a consistent theory.
By fixing these two, viola and one can unify. We get a dramatically simplification of many formulas and concepts in modern physics, not at a cost. It is more compact and contains more information about the depth of reality!
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http://biomechanical.asmedigitalcollection.asme.org/article.aspx?articleid=1426207&journalid=114
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0
Technical Briefs
# Encapsulation of Living Cells in Small $(∼100 μm)$ Alginate Microcapsules by Electrostatic Spraying: A Parametric Study
[+] Author and Article Information
Wujie Zhang
Department of Mechanical Engineering and Biomedical Engineering Program, University of South Carolina, 300 Main Street, Columbia, SC 29208
Xiaoming He1
Department of Mechanical Engineering and Biomedical Engineering Program, University of South Carolina, 300 Main Street, Columbia, SC [email protected]
1
Corresponding author.
J Biomech Eng 131(7), 074515 (Jun 30, 2009) (6 pages) doi:10.1115/1.3153326 History: Received September 12, 2008; Revised May 07, 2009; Published June 30, 2009
## Abstract
A parametric study was performed to understand the effect of preparation parameters on size, morphology, and encapsulation efficiency (i.e., cells/microcapsule) of alginate microcapsules prepared using the electrostatic spray method. The preparation parameters studied include sodium alginate concentration, spray voltage, flow rate, and cell density. It was found that both the flow rate and spray voltage have a significant impact on microcapsule size while the microcapsule morphology is greatly influenced by both the sodium alginate concentration and spray voltage. To obtain small $(∼100 μm)$ cell-loaded microcapsules with good morphology (i.e., round in shape and uniform in size) and high encapsulation efficiency ($>5$ cells/microcapsule), the optimal ranges of spray voltage, flow rate, alginate concentration, and cell density are from 1.6–1.8 kV, 1.5–3 ml/h, >1.5% (w/v), and (3–5)$×$106 cells/ml, respectively. Under optimal preparation conditions, cells were found to survive the microencapsulation process well.
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## Figures
Figure 1
A sketch (not to scale) of the electrostatic spray device used for generating alginate microcapsules in this study
Figure 2
Microcapsule size as a function of sodium alginate concentration (a) and typical micrographs of the generated microcapsules with 2% (w/v) (b) and 1.5% (w/v) (c) alginate solutions in the absence of living cells: Spray voltage and flow rate are 2.0 kV and 5 ml/h, respectively. The error bar represents standard deviation. Scale bar: 100 μm.
Figure 3
Microcapsule size as a function of spray voltage (a) and typical micrographs of the generated microcapsules with 1.4 kV (b) and 1.6 kV (c) spray voltages in the absence of living cells: Alginate concentration and flow rate are 1.9% (w/v) and 5 ml/h, respectively. The error bar represents standard deviation. Scale bar: 100 μm.
Figure 4
Microcapsule size as a function of spray flow rate (a) and typical micrographs of the generated microcapsules with 1.5 ml/h (b) and 2.5 ml/h (c) flow rates in the absence of living cells: Alginate concentration and spray voltage are 1.9% (w/v) and 1.8 kV, respectively. The error bar represents standard deviation. Scale bar: 100 μm.
Figure 5
Microcapsules prepared under various conditions showing the effect of cell density in alginate solution on cell encapsulation efficiency: (a) 1×106cells/ml cell density, 2% (w/v) alginate solution, 1.6 kV spray voltage, and 1.5 ml/h flow rate; and (b) 3×106cells/ml cell density, 2% (w/v) alginate solution, 1.6 kV spray voltage, and 2 ml/h flow rate. Scale bar: 100 μm.
Figure 6
Typical images of microencapsulated cells (a) and calcein AM (green)/ethidium homodimer (EthD-1, red) staining of the cells in microcapsules (green for live cells and red for dead cells, visible in the online version only) (b). Scale bars: 100 μm.
Figure 7
Proliferation of cells collected post microencapsulation and liquefaction in 3 days together with typical micrographs (insets) of the cells cultured in a Petri dish in three different days
## Errata
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https://www.cs.utexas.edu/users/flame/laff/alaff/chapter11-overview.html
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## Subsection11.1.2Overview
• 11.1 Opening Remarks
• 11.1.1 Linking the Singular Value Decomposition to the Spectral Decomposition
• 11.1.2 Overview
• 11.1.3 What you will learn
• 11.2 Practical Computation of the Singular Value Decomposition
• 11.2.1 Computing the SVD from the Spectral Decomposition
• 11.2.2 A strategy for computing the SVD
• 11.2.3 Reduction to bidiagonal form
• 11.2.4 Implicitly shifted bidiagonal QR algorithm
• 11.3 Jacobi's Method
• 11.3.1 Jacobi rotation
• 11.3.2 Jacobi's method for computing the Spectral Decomposition
• 11.3.3 Jacobi's method for computing the Singular Value Decomposition
• 11.4 Enrichments
• 11.4.1 Casting the reduction to bidiagonal form in terms of matrix-matrix multiplication
• 11.4.2 Optimizing the bidiagonal QR algorithm
• 11.5 Wrap Up
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http://processalgebra.blogspot.co.il/2016/
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## Friday, December 23, 2016
### Mariangiola Dezani-Ciancaglini: 70, but still going strong
Mariangiola Dezani-Ciancaglini, one of the most influential Italian (theoretical) computer scientists, turned 70 yesterday. As witnessed by her DBLP entry, Mariangiola is still very active in research and is a prime example of a scientist who continues to challenge herself, to produce excellent work and to mentor young researchers at an age at which many are retired.
The purpose of this post is to celebrate Mariangiola's 70 birthday, hoping that some of the readers of this blog who are not familiar with her work will be tempted to read it and to spread it amongst their students.
Mariangiola Dezani has been one of the leading researchers in the foundations of programming languages and, in particular, of their type systems for about 40 years. She has offered seminal contributions to that field, introducing new type systems that deeply influenced theoretical developments and its practical applications.
In addition to her outstanding research activities, she has been a mentor and role model for young researchers, many of whom now have leading positions at high-class universities. Moreover, she has tirelessly supported female students and researchers in computer science at all stages of their career. She has turned the Department of Computer Science at the University of Turin, Italy, into a hotbed of research on the theory of programming languages. The group led by Simona Ronchi Della Rocca and her is one of the largest research teams in that field in the world, and is one of those with largest percentage of female researchers and students.
Mariangiola's research activity over the years has followed a path in which theoretical developments have been inspired by the evolution of programming languages: from lambda-calculus models in the 1980s, providing foundations for functional programming languages, to object orientation in the 1990s, to dynamic and distributed contexts with behavioural types for web services and session types since the year 2000.
Mariangiola's main scientific achievement in the first phase of her research career was the introduction of intersection type assignment systems, which were largely used as finitary descriptions of models of the lambda-calculus. Intersection types are one example of a theoretical concept developed by Mariangiola Dezani that has later had profound influence on the practice of programming languages. Indeed, their use in the typing discipline for a language has allowed compilers to generate more efficient code for different instantiations. In object-oriented languages, intersection types are employed, amongst other things, in expressing mixins (constructs that permit code reuse avoiding the ambiguities of multiple inheritance). They have also been advocated and are used for manipulating XML and semi-structured data in languages such as CDuce.
Since the year 2000, Mariangiola's research has been mainly devoted to the study of self-adapting types for ensuring safety and liveness of communication protocols also in presence of unexpected events. This work has offered seminal contributions to the study of session types and has led to practical applications whose impact will be felt for years to come. Mariangiola first proposed a formalisation of Java with session types, which was later applied to the design and implementation of SJ (Session Java). These contributions initiated a flurry of research activity aiming at applying session types to many real-world programming languages. She also first studied a theory of progress in the session types for the pi-calculus, whose core theory was later extended to multi-party session types. This formalism became the core of the current version of an open-source protocol description language, Scribble, which is developed at Red Hat and Imperial. This language is used in the multi-million-USD Ocean Observatory Initiative project, whose purpose is to build an infrastructure of sensors and other computing devices located on the ocean floor so that oceanographers to get data about the health of the marine ecosystem. This is an example of the effectiveness and practical impact of the deep and elegant theoretical work carried out by Mariangiola Dezani.
A belated happy 70th birthday, Mariangiola!
## Monday, December 05, 2016
### Great hiring opportunities for female researchers at the University of Groningen
Jorge A. Pérez asked me to post this very interesting opportunity for tenure-track positions at the University of Groningen, targeted to talented female researchers (see www.rug.nl/rff). Feel free to contact Jorge if you work in areas related to "Fundamental CS" (using the terminology in the call) and are interested in applying.
Rosalind Franklin Fellowships at the University of Groningen
The University of Groningen (The Netherlands) initiated the prestigious Rosalind Franklin Fellowship programme to promote the advancement of talented international researchers at the highest levels of the institution. The ambitious programme has been running since 2007 and has financed over 90 Fellows.
The Rosalind Franklin Fellowship programme is aimed at women in industry, academia or research institutes who have a PhD and would like a career as full professor in a European top research university. The Fellowship is only awarded to outstanding researchers. New Fellows are given:
• A tenure track position to work towards full professorship within a period of ten years;
• Budget for a PhD student to enable them to make a flying start.
Successful candidates will be expected to establish an independent, largely externally funded research programme in collaboration with colleagues at
our University and elsewhere.
The University of Groningen has 13 tenure track positions available in this programme, currently co-funded by the European Union.
Within these, the Faculty of Mathematics and Natural Sciences (FMNS) has five Rosalind Franklin Fellowships to offer, including positions on
• Fundamental Computer Science (Data Management, Theory of Computing, Algorithms, Networks, Security)
• Artificial Intelligence (logic, neuromorphic computing, cognitive modelling or robotics)
• Fundamental Mathematics (Algebra, Geometry, Analysis), Mathematical Data Analysis, Complex Systems
Ambitious female academics are invited to apply for these positions before February 1, 2017.
www.rug.nl/rff
- The applicants guide:
- The Johann Bernoulli Institute for Mathematics and Computer Science:
http://www.rug.nl/research/jbi/
### Martino Lupini receives the 2015 Sacks Prize of the Association for Symbolic Logic
The 2015 Sacks Prize of the Association for Symbolic Logic for the best doctoral dissertation in Logic will be shared by Omer Ben-Neria, University of California, Los Angeles, and Martino Lupini, California Institute of Technology. The prize citations can be found here and are also appended to this post for ease of reference. Congratulations to the prize recipients!
Omer Ben-Neria received his Ph.D. in 2015 from Tel Aviv University under the supervision of Moti Gitik.
Martino Lupini received his Ph.D. in 2015 from York University, Toronto under the supervision of Ilijas Farah. He received his bachelor degree at the University of Parma (under the supervision of Celestina Cotti Ferrero) and a master degree from the University of Pisa advised by Mauro Di Nasso with a thesis entitled Recurrence and Szemerédi’s Theorem.
Martino Lupini is the second Italian young researcher to receive this accolade; the first was Matteo Viale in 2006. The successes of young Italian logicians witness the quality of the research in logic in Italy. This is yet another vindication of the analysis of the European Commission on the quality of research in Italian universities, compared with the resources available to Italian researchers: "Strong public science base despite an overall underinvestment in research and innovation." The executive report on Italy also states "R&D investment has slightly increased in recent years but the gap with the EU average is still quite significant." I hope that Italy will devote more of its budget to supporting its universities and research in the future. A starved system cannot continue producing young researchers like Martino Lupini for much longer.
Prize citations
Ben-Neria received his Ph.D. in 2015 from Tel Aviv University under the supervision of Moti Gitik. In his thesis, The Possible Structure of the Mitchell Order, he proved the remarkable result that, under suitable large cardinal assumptions on the cardinal $\kappa$, every well-founded partial order of cardinality $\kappa$ can be realized as the Mitchell order of $\kappa$ in some forcing extension. The Prizes and Awards Committee noted that the proof is a tour de force combination of sophisticated forcing techniques with the methods of inner model theory.
Lupini received his Ph.D. in 2015 from York University, Toronto under the supervision of Ilijas Farah. His thesis, Operator Algebras and Abstract Classification, includes a beautiful result establishing a fundamental dichotomy in the classification problem for the automorphisms of a separable unital $C^*\/$-algebra up to unitary equivalence, as well as a proof that the Gurarij operator space is unique, homogeneous, and universal among separable 1-exact operator spaces. The Prizes and Awards Committee noted that his thesis exhibits a high level of originality, as well as technical sophistication, in a broad spectrum of areas of logic and operator algebras.
### Alonzo Church Award 2017: Call for Nominations
Gordon Plotkin asked me to post the call for nominations for the 2016 Alonzo Church Award for Outstanding Contributions to Logic and Computation. The first edition of the award was given to Rajeev Alur and David Dill for their invention of timed automata, see: http://eacsl.kahle.ch/church16.pdf. I strongly encourage members of the community to nominate their favourite paper(s) for this accolade. See the call for the rules regarding eligibility and on how to submit your nomination.
The 2017 Alonzo Church Award for Outstanding Contributions to Logic and Computation
Call for Nominations
Introduction
An annual award, called the Alonzo Church Award for Outstanding Contributions to Logic and Computation, was established in 2015 by the ACM Special Interest Group for Logic and Computation (SIGLOG), the European Association for Theoretical Computer Science (EATCS), the European Association for Computer Science Logic (EACSL), and the Kurt Gödel Society (KGS). The award is for an outstanding contribution represented by a paper or by a small group of papers published within the past 25 years. This time span allows the lasting impact and depth of the contribution to have been established. The award can be given to an individual, or to a group of individuals who have collaborated on the research. For the rules governing this award, see:
The 2016 Alonzo Church Award was given to Rajeev Alur and David Dill for their invention of timed automata, see: http://eacsl.kahle.ch/church16.pdf
Eligibility and Nominations
The contribution must have appeared in a paper or papers published within the past 25 years. Thus, for the 2017 award, the cut-off date is January 1, 1992. When a paper has appeared in a conference and then in a journal, the date of the journal publication will determine the cut-off date. In addition, the contribution must not yet have received recognition via a major award, such as the Turing Award, the Kanellakis Award, or the Gödel Prize. (The nominee(s) may have received such awards for other contributions.) While the contribution can consist of conference or journal papers, journal papers will be given a preference.
Nominations for the 2017 award are now being solicited. The nominating letter must summarise the contribution and make the case that it is fundamental and outstanding. The nominating letter can have multiple co-signers. Self-nominations are excluded. Nominations must include: a proposed citation (up to 25 words); a succinct (100-250 words) description of the contribution; and a detailed statement (not exceeding four pages) to justify the nomination. Nominations may also be accompanied by supporting letters and other evidence of worthiness.
Nominations are due by March 1, 2017, and should be submitted to [email protected].
Presentation of the Award
The 2017 award will be presented at the CSL conference, the annual meeting of the European Association for Computer Science Logic. The award will be accompanied by an invited lecture by the award winner, or by one of the award winners. The awardee(s) will receive a certificate and a cash prize of USD 2,000. If there are multiple awardees, this amount will be shared.
Award Committee
The 2017 Alonzo Church Award Committee consists of the following four members: Natarajan Shankar, Catuscia Palamidessi, Gordon Plotkin (chair), and Moshe Vardi.
## Monday, November 21, 2016
### Academic evaluation and hiring in Italy: The curious incident of Giovanni Sambin in the ASN 2016
Disclaimer: This post might contain imprecisions about the ASN, since I have never worked at an Italian university myself and I have never applied for the Italian ASN. I welcome corrections from whoever reads this post and has experience with this Italian evaluation exercise. Let me state at the outset that what I write pertains to fields such as computer science and mathematics. I do not know what is done in the humanities.
An Italian law dated 30 December 2010 specifies a procedure for academic hirings in Italy at the level of associate and full professor. According to that law, recruiting for those positions should be "based on scientific qualification criteria. A national commission evaluates and assesses the candidates scientific qualification." See this outdated web site, which should be compared with the one in Italian. Only candidates that have obtained the so-called Abilitazione Scientifica Nazionale (ASN, National Scientific Qualification) can then apply for a professor position at an Italian university, if and when such positions are advertised.
One can wonder why Italy uses this two-step system for academic hirings, whose need is not felt in any of the countries where I have worked so far. I guess that the first step is meant to filter out potential candidates who do not meet minimum requirements for being a professor at any of the 63 public universities in Italy.
According to the regulations a "national commission evaluates and assesses the candidates scientific qualification." In fact, there is one national commission for each of the many scientific areas considered in Italy. Many of these commissions have to examine hundreds of applications, and their members play the role of gatekeepers and paladins of quality in the Italian university system. I can only imagine how much work is needed to do a thoughtful job in one of those committees and how easy it is to make enemies regardless of how considerate one is in justifying one's opinions. The evaluation is partly based on bibliometric criteria, which are known beforehand, should simplify the work of the commissions and should give a look of objectivity to their decisions. However, as far as I know, the commissions can also base their decisions on a qualitative analysis of the applicants.
Given the crucial role played by the members of the evaluation committees, one would expect that their members are chosen by taking the candidates' scientific profile and experience carefully into account. As it turns out, however, the qualifications of candidates for the committee are evaluated using only the following three bibliometric criteria:
1. Number of publications in the period 2006-2016 (threshold 9);
2. Total number of citations in the period 2001-2015 (threshold 80);
3. H-index in the last 15 years (threshold 5).
In order to be eligible, one has to meet the thresholds in at least two of the above criteria. This might even seem reasonable. Note, however, that only publications indexed in Web of Science or Scopus count. In particular, journal papers published in outlets that are not indexed by Web of Science/Scopus are not taken into consideration (regardless of their content and impact) and conference papers don't count at all. Books and monographs don't count either, regardless of how influential they might be. Web of Science/Scopus are also used for calculating citations and the h-index. Again, this provides a smaller coverage than the one offered by Google Scholar, say.
By way of example, recently Giovanni Sambin, one of the most famous, currently active Italian logicians and an expert academic one would trust to lead a national evaluation committee for Mathematical Logic, was considered to be ineligible as an evaluator because he met only one of the above-mentioned criteria. His Google Scholar profile is here.
This kind of decisions makes me wonder whether there is an overemphasis on bibliometric evaluations in Italian academia. If experience over a long and distinguished academic career plays second fiddle to fairly arbitrary thresholds calculated using only Web of Science and Scopus, I wonder how reliable the decisions of the evaluation committees will be considered by Italian academics. Most importantly, having so many people spend a lot of time seeking the holy grail of the national qualification and small committees devote endless hours examining their qualifications looks like a huge waste of energy and resources. I cannot help but think that that energy and time would be best used for research, teaching and all the other tasks that make up our work.
## Tuesday, November 15, 2016
### Workshops at LICS 2017
The following six workshops will be co-located with LICS 2017 and will take place on Monday, 19 June 2017, on the premises of Reykjavik University:
• WiL: Women in Logic. Proposers: Valeria de Paiva, Amy Felty, Anna Ingolfsdottir, Ursula Martin
• LCC: Logic and Computational Complexity. Proposers: Norman Danner, Anuj Dawar, Isabel Oitavem, Heribert Vollmer
• LMW: Logic Mentoring Workshop. Proposers: Anupam Das, Valeria Vignudelli, Fabio Zanasi
• LA: Learning and Automata. Proposers: Borja Balle, Leonor Becerra-Bonache, Remi Eyraud
• LOLA: Syntax and Semantics of Low-Level Languages. Proposer: Matija Pretnar, Noam Zeilberger
• Metafinite model theory and definability and complexity of numeric graph parameters. Proposers: Andrew Goodall, Janos A. Makowsky, Elena V. Ravve.
More details on this workshops will be available from the conference web page in due course. I hope that you'll consider attending them and submitting excellent papers to the conference.
## Wednesday, November 09, 2016
### What makes a research institution excellent?
Some time ago I stumbled across the video of the panel discussion "IST Austria: On the Way to the Top: What Makes a Research Institution Excellent?". (There is also a much shorter, 11-minute version of the video here.) I watched the discussion with great interest, and found it inspirational and thought-provoking.
The panelists were Patrick Aebischer (president of EPFL until the end of 2016), Jonathan Dorfan (president of the Okinawa Institute of Science and Technology), Peter Gruss (former president of the Max-Planck-Gesellschaft from 2002 till 2014), Helga Nowotny (former President of the European Research Council), Rolf-Dieter Heuer (Director General of CERN from 2009 to 2015), Haim Harari (President, from 1988 to 2001, of the Weizmann Institute of Science) and Olaf Kübler (former president of ETH Zurich). It doesn't get much better than this, in terms of experience about the subject matter and, if you are interested in the topic or even just in hearing experienced academics discuss it, I'd encourage you to have a glass of your favourite beverage, relax and have a look. It is remarkable how much agreement there was in isolating the key ingredients leading to research excellence.
Here is my quarter-baked summary of some of the contributions, with apologies for not covering the whole discussion, possibly biased reporting and for any error I might have made.
Patrick Aebischer stated that Europe lacks super-brands such as Berkeley, CalTech, CMU, Harvard, MIT and Stanford. One needs elite universities to attract talents. The US attracts the best graduate students, the best young researchers with their tenure-track system and also people in high-ranking management positions. He also mentioned that to foster excellence, it is useful to have some competition between public and private universities. He said that integration of research and education is key to achieve excellence, as are attracting and keeping the best faculty, and giving early independence to young individuals.
In order to achieve excellence, funding must be significant. A flexible organizational structure is needed to be able to compete at the highest level.
In this era, one can rise fast, but one can also fall faster than before.
Peter Gruss started by asking a fundamental question: what makes creative research possible? In his words, it is amazing how easy the answer is and how difficult it is to achieve it: "Hire the most brilliant minds and give them everything they need to stay brilliant." That's it.
He referred to the work of the historian Rogers Hollingsworth who isolated the following ingredients for excellence in research institutions:
1. Excellence in research and leadership. On this point, Gruss said that is critical that one hires top people because top people hire people who are better than themselves. To get them, one has to do head hunting plus advertising. One should strike a good balance between tenured and non-tenured people to maintain flexibility.
2. Small research settings.
3. Small group size, but large context.
4. Multidisciplinary contacts. One has to install interfaces between different disciplines. (Examples: Have only one coffee room.)
5. Independence as early as possible. Give young people stability for a certain period of time to allow them to unfold their creativity. Coaching and mentoring of young researchers must be provided.
6. Core institutional and flexible funds. There should be a balance between high-trust and low-trust funding. When handing out high trust funding, an agency must trust the funded institution: Give them the money that you can afford and let them do what they want with it. Trust them to make the most of the received funding.
He also mentioned that a study in the US pointed out that 75% of citations in patents are to papers funded by public money. Of this 75% of papers most of them belong to the top10% of the papers cited within the scientific community. Hence one should invest in research, in fact, in top research. Hire the best without compromise. Put a lot of weight on top scientists.
Rolf-Dieter Heuer mentioned the importance of "taking society with you." One has to promote science in society.
For research, one needs to continuously develop a vision, which will drive innovation and technology, partnership with industry and feed back to research. Every excellent institution must keep this virtuous circle. One must think strategically and long term.
All staff needs to have intellectual challenges, including administrative staff. Excellence can be in individuals, but also in cooperation. Excellence must allow for failure, for some research that might fail. This is doing science at the edge. What one can guarantee is that the path will be fruitful.
Olaf Kuebler stated that the strategy to create a leading research institution is deceptively simple: "Search, appoint and retain world-leading scientists. All else will follow."
The reputation of a university is made by the people who leave the university students, graduate students, assistant professors etc.
He also stated that an excellent research institution must:
1. Make significant contributions to themes of global importance.
2. Identify and develop new themes of global importance.
3. Harmonize its portfolio with its funders.
Helga Nowotny said that being open towards the future is the key aspect of excellence. Invest in excellent young people, who are competent rebels and understand that scientific knowledge is always preliminary. One has to bear in mind that excellence is always a multi-dimensional concept.
One should provide the best possible working conditions. This involves
• a space component: space that makes it almost obligatory to run into each other and discuss, as ideas emerge by talking to each other, and
• a time component: give time for the unexpected, for the unforeseen, for serendipity.
Jonathan Dorfan mentioned that one should establish a setting that is conducive for inter-disciplinary research, where researchers from different fields can cooperate and exchange ideas.
Haim Harari closed the meeting with an articulate and thought-provoking short address. He started by pointing out what he considers to be key ingredients for an excellent research institution.
Funding must be versatile and come from many sources. Only if one is versatile one can have the right mix. Government funding leads inevitably to egalitarianism and democracy. However, science is not democratic. Still there has to be a balance between the power of the president and the faculty.
A research institution should be as international as possible and as national as possible. It should give something back to the taxpayers: education and touching society. Technology transfer is the other thing one return to society.
The Weizmann Institute put all the different subjects in the same campus, which leads to inter-disciplinary research that cannot be done by any single subject alone.
Harari also said that the excellence of a research institution should be evaluated according to three different measures:
1. its best ten people,
2. the average quality of its professors and
3. its worst professor.
The quality of the worst professor says what the threshold of the institution is for hiring and is a very important indicator of the standards of the research institute/university.
In Harari's opinion, the president of a research institute/university should regularly ask herself/himself: If I could fire some of my professors, how many would I fire?" If the number is a non-trivial fraction of the faculty, then the threshold of the institution is not high enough.
So, in your opinion, what makes a research institution excellent?
## Friday, October 21, 2016
### October issue of the Bulletin of the EATCS
The October 2016 issue of the EATCS Bulletin is now available online at http://bulletin.eatcs.org/index.php/beatcs/issue/view/22, featuring the following interesting columns
- "Chaining introduction with some computer science applications", by Jelani Nelson
- "The Weisfeiler-Lehman Procedure", by Vikraman Arvind
- "Approximation bounds for centrality maximization problems", by Gianlorenzo D’Angelo
- "Which Tasks of a Job are Susceptible to Computerization", by Philipp Brandes and Roger Wattenhofer
- "Demystifying coding for schools—what are we actually trying to teach", by Tim Bell
- "The 1966 International Congress of Mathematicians: A micro-memoir", by Yuri Gurevich
and much more. Lance Fortnow has also written a short introduction to his book
If you prefer the whole issue, you can download a pdf with the printed version of the bulletin from http://www.eatcs.org/images/bulletin/beatcs120.pdf
As usual, thanks to the support of the EATCS members, the EATCS Bulletin is published in open access form. Consider joining the association!
## Friday, October 07, 2016
### Ágnes Cseh receives one of the 2016 Klaus Tschira Awards for Achievements in Public Understanding of Science
It is fair to say that not many computer scientists try to present innovative research findings in a way that is accessible to an interested, but rather unspecialized, public. Even fewer succeed and the rewards for those who do are relatively minor. As a consequence, the number of essays and books about computer science that have a wide readership is substantially smaller than those about astronomy and physics, say. In my humble opinion, this is a pity, since many of intellectual achievements of computer science research deserve to be known by any intellectually curious layperson.
I was therefore happy to learn about the Klaus Tschira Award for Achievements in Public Understanding of Science. Since 2006, the Klaus Tschira Stiftung has looked for young scientists who can write a generally understandable article (8,000 to 9,000 words) in German about their research and the content of their PhD thesis. The prize is awarded in each of biology, chemistry, information technology, mathematics, neurosciences and physics as well as in closely related fields. The contributions are judged by a panel of experts on science and communication, which selects the winners based on scientific quality and on how well the scientific contribution is presented in a way that is amenable to public understanding. Yearly, up to six winners receive the award, which is endowed with prize money of 5,000 Euros. The prize-winning contributions are published in a supplementary issue of the popular science magazine bild der wissenschaft (German). Moreover, all competitors are off ered a participation in a two-day workshop for science communication.
The piece by Ágnes Cseh (a former postdoc of Magnús M. Halldórsson's at ICE-TCS, Reykjavík University) you can find here is the English translation of the German original that was selected as one of the prize-winning contributions for 2016. (It will appear in the October issue of the Bulletin of the EATCS.) It is based on Ágnes’ PhD thesis Complexity and algorithms in matching problems under preferences, which she defended in 2015 under the supervision of Martin Skutella at TU Berlin. I am sure that you will enjoy reading it as much as I did, regardless of whether you believe that algorithms can help us find stable marriages in real life.
## Thursday, October 06, 2016
### The calls for nominations for most of the EATCS-related awards are out
As usual, the EATCS has issued its calls for nominations for the 2017 edition of most of its awards with deadline 31 December 2016. You can find the calls on the EATCS web page, but I collect them below for ease of reference.
The calls for the Alonzo Church Prize and the Gödel Prize, which the EATCS awards jointly with other associations, will follow.
Let's make the job of the award committees difficult by nominating some of the many colleagues who would richly deserve the awards for these accolades!
## Friday, September 30, 2016
### CS@Aalborg University: Research evaluation 2011-2015
Every five years, the Department of Computer Science at Aalborg University undergoes a research evaluation. The purpose of this exercise is to provide the department with qualified and independent opinions on its "actual research topics, results, and performance, but also on strategic issues like funding, internal organization and synergies, possible new directions, collaboration with industry, internationalization, positioning IT as a key enabler in society, etc." So the overall aim is to improve the quality and impact of the research carried out within the department.
The evaluation committee for the period 2011-2015 consisted of Peter Apers (University of Twente, the Netherlands), Jan Gulliksen (KTH Royal Institute of Technology, Stockholm, Sweden), Chris Hankin (Institute for Security Science and Technology and Imperial College, UK), Heikki Mannila (Aalto University, President of the Academy of Finland, Finland) and Torben Bach Pedersen (Aalborg University, Denmark), who was the internal member and chair of the committee.
The report resulting from the latest such evaluation has recently been released and can be found here. The editors of the report were Manfred Jaeger, Jesper Kjeldskov, Hua Lu and Brian Nielsen. As a former editor of such a report in days long gone, I know that their job required a considerable use of time and effort.
So, what did the evaluation committee have to say? Quoting from its evaluation of the department as a whole,
"The Computer Science Department has two world-class groups and excellent staff in all groups. The Danish IT benchmarking exercise of 2014 shows that the Department is the best department in Denmark for number of refereed publications and BFI points per full-time faculty member. The Department is also top in a number of other metrics. During the review it was also reported that Aalborg Computer Science graduates are highly prized by industry. The Department thus deserves to be ranked even higher in the QS World University Rankings by Subject or the Academic Ranking of World University (ARWU \Shanghai") Subject ranking. The current rankings are to a large degree caused by the poor coverage of computer science publications in the commercial bibliometric indices used in these rankings (WoS, Scopus). Here, Google Scholar provides a much better coverage. However, the Department clearly has the potential to rise considerably in these rankings but will require support from the Faculty and University to achieve this."
The two world-class groups mentioned in the above quotation are the Database and Programming Technologies and the Distributed and Embedded Systems units. (The latter is now called Distributed, Embedded and Intelligent Systems unit as it now also includes researcers from what used to be the Machine Intelligence group.) Those two groups are led by the Danish computer scientists with the highest h-index, and have a truly impressive publication and grant-winning record.
You can find the committee's evaluations for each of the research groups in the report. Here I'll limit myself to mentioning an excerpt of what the committee wrote about the Distributed and Embedded Systems unit, where I had the pleasure to work for ten years.
"The Distributed and Embedded Systems group is a world-class group. It is involved in a broad range of activities from semantic foundations through tool development for verification and validation to real-world applications. The group is making excellent contributions across the whole spectrum of activity; this is internationally recognized by prestigious awards such as:
• The ERC Advanced Grant LASSO
• The 2013 CAV Award for Uppaal - the first time that this award has been granted to a non-US team
• The ranking of "Uppaal in a Nutshell" as the 9th most influential paper in Software Engineering since 1972
• Best paper awards, medals and other awards to Associate Professors
The h-index of Kim Guldstrand Larsen is outstanding and places him among the top echelon of researchers in this area; his h-index is higher than some Turing Award winners in cognate areas. It is also pleasing to note that some of the Associate Professors also have high h-indices for their career point. .....
The group has published well during the review period with 175 conference papers - 75% of which are in A and B venues - and 63 journals - 92% of which are in A and B venues. .....
The group has secured 37 new grants to a total value of DKK103.8M. ....
The major strength of the group is the people; not only the group leader but the strong group of more junior academic staff and an excellent group of support staff. The broad span from foundational work to applications is also unusual in such groups in other universities and is a considerable strength of DES. The profile and reach of the group is enhanced by its dissemination activities but also the engagement of senior staff in policy-related activities at national and European levels."
Of course there is still a lot of room for improvement, but this will require support from the university as a whole, high-profile new hires in the future and the development of the talent the department already boasts. However, the opinion of the evaluation committee clearly highlights the current strength of a CS department that, in my admittedly biased opinion, deserves to be better known worldwide.
## Thursday, September 29, 2016
### Zoltán Ésik (1951-2016): In Memoriam
The following obituary for Zoltán Ésik will appear in the October issue of the Bulletin of the EATCS and on the web page of Academia Europaea.
Zoltán Ésik (1951-2016)
In Memoriam
Luca Aceto and Anna Ingólfsdóttir
ICE-TCS, School of Computer Science, Reykjavik University
Our friend and colleague Zoltán Ésik passed away in Reykjavik, Iceland, on Wednesday, 25 May 2016. He was visiting us as he did with some regularity, compatibly with his many engagements throughout the world.
The day before his untimely death, Zoltán had delivered an ICE-TCS seminar entitled Equational Logic of Fixed Point Operations at Reykjavik University. At the start of his talk, he looked somewhat tired and out of breath. However, the more he was presenting a research topic that he loved and that has kept him busy for most of his research career, the more he seemed to be feeling at ease. After the talk, we spent some time making plans for mutual visits in the autumn of 2016 and we discussed some EATCS-related matters. His wife Zsuzsa and he were due to spend a few days travelling in the north of Iceland before their return to Szeged, but life had other ideas.
Zoltán was a scientist of the highest calibre and has left behind a large body of deep and seminal work that will keep researchers in theoretical computer science busy for a long time to come. The list of refereed publications available from his web site at
http://www.inf.u-szeged.hu/~ze/classified.pdf
includes two books, 32 edited volumes, 135 journal papers, four book chapters, 86 conference papers and seven papers in other edited volumes. However, impressive as they undoubtedly are, these numbers give only a very partial picture of Zoltán's scientific stature. Together with the late Stephen Bloom, Zoltán was the prime mover in the monumental development of Iteration Theories. As Stephen and Zoltán wrote in the preface of their massive book on the topic, which was published in 1993 by Springer:
Iteration plays a fundamental role in the theory of computation: for
example, in the theory of automata, in formal language theory, in the
study of formal power series, in the semantics of flowchart algorithms
and programming languages, and in circular data type definitions. It
is shown that in all structures that have been used as semantical
models, the equational properties of the fixed point operation are
captured by the axioms describing iteration theories. These structures
include ordered algebras, partial functions, relations, finitary and
infinitary regular languages, trees, synchronization trees, 2-categories,
and others.
It is truly remarkable that the equational laws satisfied by fixed point operations are essentially the same in a large number of structures used in computer science. Isolating those laws, and showing their applicability, has been one of the goals of Zoltán's scientific life and we trust that the members of our community will keep reading his work on iteration theories, which continued and went from strength to strength after Stephen and he published their 600-page research monograph in 1993. During his last talk in Reykjavik, we asked Zoltán whether he was planning to write a new edition of that book, and half-jokingly told him that it would probably be about 1,200 pages.
Zoltán's research output includes contributions to automata theory, category theory, concurrency theory, formal languages, fuzzy sets and fuzzy logic, graph theory, logic in computer science, logic programming, order theory, semiring theory and universal algebra, amongst others. The breadth of research areas to which he has contributed bears witness to his amazing mathematical powers and to his curiosity. Wherever he went and no matter how long he had travelled to get there, Zoltán's brain was always open.
Zoltán also contributed to the research community with his service work and received several awards. Here we will limit ourselves to mentioning that he was elected member of the Academy of Europe in 2010, was named Fellow of the EATCS in 2016, was a member of the council of the EATCS from 2003 to 2015, and of the Presburger Award Committee in 2015--2016. He represented the Hungarian theoretical computer science community in the International Federation for Information Processing (IFIP) as member of TC1 since 2000 and was one of the prime mover in the establishment of the IFIP WG 1.8, Working Group on Concurrency. He also received the Gy. Farkas Research Award and the K. Rényi Research Award of the János Bolyai Mathematical Society.
Zoltán's appetite for work was phenomenal, but he also liked to have fun, to spend time with friends eating good food and drinking excellent wine, and to travel. Indeed, Zoltán's lust for travel was amazing. We lost track of his visits to myriads of research institutions and universities all over the world. He attended conferences in the most remote locations and always made sure that he would reserve some time for enjoying the most beautiful and known sites. At times, we had the feeling that he had been everywhere in the world.
Despite being often on the move, Zoltán was very much a family man. He was very proud of his wife Zsuzsanna, their daughter Eszter and their son Robert. He always told us about the latest developments in their lives and was happy about his four grandchildren. We had the pleasure of enjoying Zsuzsanna and Zoltán's exquisite hospitality both in Szeged and in their summer home on Lake Balaton.
Zoltán was very loyal to his friends and would make trips to see them wherever they were living. We were lucky to be amongst them and had the pleasure of hosting him in Aalborg, Florence and Reykjavik, where he visited us a few times and where the thread of his life was cut. We will miss the time we spent doing research or relaxing together, his sense of humour, his conviviality and his hospitality.
## Thursday, September 15, 2016
### LICS 2017: Call for Workshop Proposals
Call for Workshop Proposals
LICS 2017
32nd Annual ACM/IEEE Symposium
on Logic in Computer Science
http://lics.rwth-aachen.de/lics17/
The thirty-second Annual ACM/IEEE Symposium on Logic In Computer Science (LICS'17) will be held in Reykjavik, Iceland on June 20–23, 2017. The workshops will take place on June 18–19, 2017. June 18 will only be used by two-days workshops (if any), or in case the number of workshops is really large. This year, workshop fees should be around 65 euros for a one-day workshop (including lunch and two coffee breaks).
Researchers and practitioners are invited to submit proposals for workshops on topics relating logic – broadly construed – to computer science or related fields. Typically, LICS workshops feature a number of invited speakers and a number of contributed presentations. LICS workshops do not usually produce formal proceedings. However, in the past there have been special issues of journals based in part on certain LICS workshops.
Proposals should include:
• - A short scientific summary and justification of the proposed topic.
This should include a discussion of the particular benefits of the topic to the LICS community.
• - A discussion of the proposed format and agenda.
• - The proposed duration, which is typically one day (two-day workshops can be accommodated too).
• - Procedures for selecting participants and papers.
• - Expected number of participants. This is important for the room!
• - Potential invited speakers.
• - Plans for dissemination (for example, special issues of journals).
Proposals should be sent to Patricia Bouyer: [email protected]
** Important Dates **
Program of the workshops ready: May 19, 2017
Workshops: June 18–19, 2017
LICS conference: June 20–23, 2017
The workshops selection committee consists of the LICS General Chair, LICS Workshops Chair, LICS 2017 PC Chair and LICS 2017 Conference Chair.
## Thursday, September 08, 2016
### An interview with Paul Spirakis, the new EATCS president
During its annual meeting at ICALP 2016 in Rome, the Council of the EATCS elected Paul Spirakis (University of Liverpool, UK, and University of Patras, Greece) as its new president. Paul is a well-known figure in the theoretical'computer-science community and truly needs no introduction. However, I felt that it might be a good idea to interview him briefly in order to give him the opportunity to present himself to the community and to discuss some of his plans for his mandate as president of the EATCS.
I interviewed Paul Spirakis via email and present his answers to my questions in this interview that will appear in the October issue of the Bulletin of the EATCS. In order to preserve the style of Paul’s answers, I did not edit them. I hope that the readers of this blog and of the Bulletin of the EATCS will enjoy reading the text of the interview and will find it as interesting as I did.
## Wednesday, August 24, 2016
### Proceedings of ICALP 2016
The proceedings of ICALP 2016 are now available from the LIPIcs web site. Many thanks to all the colleagues who have worked so hard to make this possible.
I hope that many of you will read the papers in the proceedings, which were selected by Davide, Michael, Yuval and their PCs, and build on their research contributions.
## Thursday, July 21, 2016
### CAV Award 2016
The CAV Award 2016 was presented today to Josh Berdine, Cristiano Calcagno, Dino Distefano, Samin Ishtiaq, Peter O'Hearn, John Reynolds, and Hongseok Yang for "the development of Separation Logic and for demonstrating its applicability in the automated verification of programs that mutate data structures." This is the second major award that is given for work on Separation Logic in the space of roughly a week. Indeed, Steve Brookes and Peter O'Hearn received the 2016 Gödel Prize last week at ICALP 2016 for their invention of Concurrent Separation Logic. (The retrospective article describing Concurrent Separation Logic starts on page 47.)
The award recipients are honoured for the development of the theory of Separation Logic, which includes the key notion of separating conjunction, the work showing its applicability in the analysis of non-trivial programs, and the tool development that culminated in Facebook Infer.
Congratulations to the award recipients!
Those interested in learning about Separation Logic can consult, for instance, the following resources by Peter O'Hearn:
Enjoy!
## Tuesday, July 19, 2016
### Report on the EATCS General Assembly at ICALP 2016
The annual general assembly of the EATCS was held at ICALP 2016 on Thursday, 14 July, from 16:30 till 18:15. The slides I used for the meeting are here, for those who are interested.
I started the general assembly by apologizing to the audience for the problems we had in making the official LIPIcs proceedings available by the conference date. (A preliminary version of the proceedings was available in the form of three large files, one per track, but those were very large and hard to download at the conference hotel. The EATCS Secretary prepared a dedicated web page from which the files of the individual papers could be accessed, but this page was available too late.) This ICALP was the first edition of the conference with LIPIcs proceedings and there were some associated teething problems. (ICALP is the largest conference ever to publish its proceedings with LIPIcs, as far as I know.) I am responsible for this problem and promised that it won't happen again.
During the ensuing discussion, Thore Husfeldt mentioned that, based on his experience as editor of a recent LIPIcs proceedings, he realized that we (theoretical computer scientists) are not good at following the given typesetting guidelines and that this makes the work of the proceedings editors and of the LIPIcs staff harder than it needs to be. (In passing, in a comment to this post, Marc Herbstritt from LIPIcs pointed out that some ICALP papers contains flaws that LIPIcs is still trying to resolve as part of publishing a high-quality proceedings volume. He also noted that most of the authors did not comply with the typesetting instructions they were given, which results in a huge amount of additional work for LIPIcs, and asked: "How come?")
I thanked Thore and asked the audience to help the proceedings chair and the LIPIcs staff by sticking to the typesetting instructions they are given. With electronic proceedings, one or two pages more don't matter and there is no point in trying to gain them by hacking the style files or using fonts that are forbidden by the publisher.
As a counterpoint, Mikkel Thorup and Yuval Rabani stated that they felt authors should not be bothered by strict typesetting guidelines, and that they should spend their time doing good science rather than having to worry about typesetting guidelines from the publishers. Mikkel stated that "if it typesets, it should be good enough". He also suggested that a nice web interface to which authors could upload their papers for checking whether they meet the guidelines of the publisher would be very helpful.
I thanked all the contributors to the discussion. The EATCS will take all the suggestions into account and discuss them with LIPIcs. ICALP will also try to cooperate with other conferences and LIPIcs in order to develop some automated support that can help in preparing the proceedings efficiently and professionally.
I then remembered four colleagues who have left us too early: Hartmuth Ehrig, Zoltán Ésik, David Johnson and Helmut Veith. Obituaries for all these colleagues, apart from Zoltán Ésik, may be found in the June issue of the Bulletin of the EATCS. I trust that contributions honouring the memory of Zoltán Ésik will appear in the October issue of the Bulletin. The EATCS Council decided to offer a small donation to the award in memory of Helmut Veith, established by the University of Vienna to support promising students. As usual, I invite the members of the TCS community to honour the memory of the aforementioned colleagues by building on their work and disseminating it amongst our students.
Tiziana Calamoneri delivered the report from the conference organizers. (Tiziana's slides are here.) ICALP 2016 had 239 registered participants, 205 of whom registered by the early registration deadline. In her presentation, Tiziana also analyzed some of the reasons for the lack of workshops at this year's edition of ICALP.
Yuval Rabani, who chaired the PC for Track A of ICALP, delivered the report on the PC chairs. (The slides are here.) Yuval said that chairing the PC of Track A was an unexpectedly pleasant experience and thanked his PC for the splendid work it had done. Apart from reporting on the figures related to accepted and submitted papers, Yuval described the selection process for Track A, building on his blog posts available here. Quoting from Yuval's blog,
The committee identified around 50 borderline papers, and we had to choose among them 5 or 6 papers. (For those familiar with EasyChair - most papers with scores 2, 1, 1 were rejected.) Choosing those 5-6 papers out of 50 or 51 papers took up about half of the discussion time, because it was indeed a difficult choice. We felt that almost all of the borderline papers could have ended up in the program. The final choice was made, in part, by assessing the “added value” to already chosen papers. For 2 of the 6 slots we ended up voting between 2-3 alternatives for each slot (papers in the same area that were thought to be of about the same quality). Aside from these few last papers, we devoted almost no attention to balancing subareas of theory. Papers were accepted based on pure merit, as judged by experts. Despite the indifference to areas, I think the program came out rather balanced between algorithms and complexity theory, with a nice presence in specialized niche areas. This is a natural outcome of a diverse committee.
Immediately after Yuval's presentation, I handed out the awards for the best papers and the best student papers at ICALP 2016. The best paper awards went to the following papers:
The following papers received the best student paper awards:
Congratulations to the authors of the award-receiving papers!
Mikolaj Bojanczyk gave a short report on the organization of ICALP 2017 on behalf the organizing committee. ICALP 2017 will be held in Warsaw, Poland, in the period 10-14 July 2017. The PC chairs will be Piotr Indyk (MIT, USA) for Track A, Anca Muscholl (LaBRI, France) for Track B and Fabian Kuhn (Freiburg,
Germany) for Track C. Three invited speakers have already been confirmed: Mikolaj Bojanczyk (Warsaw, Poland), Monika Henzinger (Vienna, Austria) and Mikkel Thorup (DIKU, Denmark). A fourth invited speaker will be announced soon.
Mikolaj mentioned that four workshops have already agreed to co-locate with ICALP 2017. If you are interested in organizing a workshop at ICALP 2017, please contact the local organizers.
Jiří Sgall presented a bid to host ICALP 2018, the 45th ICALP, in Prague in the period July 9-13, 2018. The slides for Jiři's presentation are here. The bid from Prague was accepted by the General Assembly. Thanks to Jiří and his colleagues for their kind offer to host ICALP in the beautiful city of Prague! ICALP 2017 and 2018 will also allow us to celebrate the excellent contributions of the Polish and Czech research communities to TCS and discrete mathematics.
After the ICALP-related presentations, I asked the audience the following questions:
• Does ICALP cover TCS sufficiently broadly?
• What do you think of the current acceptance rates at ICALP?
• What would you like to see at ICALP that we don’t do?
• Any criticisms/kudos/suggestions?
There were interesting suggestions from several colleagues. In particular, there was a lively discussion related to the role of the current incarnation of Track C. Despite the best efforts of the PC chairs of the last few years to "brand" this track as a "theory of networking" track, it is fair to say that, despite the high quality of the contributed papers, Track C is still being seen by many as a less competitive version of Track A. This opinion was, for instance, aired by Mikkel Thorup. In particular, Mikkel asked: "What is the role of the current Track C rather than allowing PC members for Track A to submit to the conference?" I reminded the audience that Track C was meant to cover "emerging areas" and that its scope should therefore be regularly considered. During the ensuing discussion, Paul Spirakis suggested that perhaps Track C could be solely devoted to Algorithmic Game Theory. Summing up, the EATCS Council will examine the future of Track C of ICALP in its coming meetings.
Mikkel Thorup also suggested that the submitted versions of the accepted ICALP papers should be posted on the conference web page as soon as they are accepted. This suggestion led to further interesting discussions. IMHO, it would certainly be beneficial to post the final versions of the accepted papers on the conference web site as soon as they arrive.
Thore Husfeldt suggested that the EATCS establish an SC for the conference, possibly independent of the council, and that the EATCS consider establishing a "fast track" for the publication of journal versions of the best ICALP papers. Regarding the first point, I informed the audience that the EATCS already has an ICALP Liaison Committee, but that it would be a good idea to give more power and responsibilities to it. That committee should also revise the current version of the guidelines for ICALP organizers, which are definitely out of date in the light of the new publication outlet for the proceedings and the new awards sponsored by the EATCS. I also informed the audience that the EATCS Council has been discussing the possible establishment of an open-access ournal of the association for some time.
Regarding awards, the audience suggested that the EATCS consider establishing an ICALP Test-of-Time Award. A young researcher even suggested that ICALP should have a best reviewer award.
I thank the attendees for their many suggestions and invite any reader of this post to send theirs to the president of the EATCS or as comments to this post. You are the life and blood of the association. Your input is always most welcome and the EATCS listens to you. We are here to serve.
Next the secretary and the treasurer of the EATCS delivered their annual reports. (The financial report is here and the report from the secretary is here.) We also thanked Dirk Janssens who left his post as treasurer of the EATCS after 27 years of sterling service to the association. We welcomed Jean-Francois Raskin as the new treasurer of the EATCS.
The rest of the general assembly was devoted to a report from the outgoing president (viz. me). I refer you to the slides for my presentation and to the EATCS Annual Report for the details. Here I will limit myself to saying that at the general assembly I announced the new leadership of our association for the coming two-year term. The new president of the EATCS will be Paul Spirakis (University of Liverpool and U. Patras). He will be supported by Leslie Ann Goldberg (University of Oxford), Antonin Kucera (Masaryk University) and Giuseppe Persiano (University of Salerno) as vice-presidents.
During the general assembly, Paul gave a short speech describing some if his objectives as president of the EATCS for the coming two years. The EATCS is in very good hands and I look forward to seeing its influence grow under its new leadership.
Let me close this report by asking my readers and the members of the TCS community at large the questions I posed to the colleagues who attended the general assembly:
• What should the EATCS do for the TCS community?
• What activities should the EATCS support (financially or otherwise)?
• How can we make EATCS membership more attractive (especially among the younger generations)?
Any input you might have will be useful for the new leadership of the EATCS. Make your voice heard, so that the EATCS can serve the TCS community even better than it is already doing.
I thank all of you for the support I have received over the last four years in my role of president of the EATCS. It was a lot of work (to achieve probably very little), but I learned much from many of you. Thank you! You are the life and blood of the EATCS.
## Monday, July 18, 2016
### A peek at ICALP 2016 in Rome
ICALP 2016 took place last week in Rome from the 12th till the 15th of July. The conference, which brought ICALP to Italy for the fifth time, was well organized by Tiziana Calamoneri, Irene Finocchi, Nicola Galesi and Daniele Gorla, whom I thank for the effort they put into making ICALP 2016 a memorable event.
According to the data presented by Tiziana on behalf of the local organizers during the General Assembly of the EATCS held on Thursday, 14 July, ICALP 2016 had 239 registered participants, 74 of which were students. The USA was the country contributing the largest share of attendees (50), followed by France, the UK, Germany and Italy. Let me note, in passing, that I would have expected a larger number of participants from Italy, given the size of the Italian TCS community, the number of TCS researchers based in Rome and in neighbouring cities, and the ease with which Rome can be reached from most of the country. (Italy contributed 21 participants to the conference.)
ICALP 2016 featured four invited talks, which were delivered by Devavrat Shah (MIT, USA), Xavier Leroy (INRIA, France), Seffi Naor (Technion, Israel) and Marta Z. Kwiatkowska (Oxford, UK), as well presentations by the recipients of the Presburger Award, the Gödel Prize and the EATCS Award.
Devavrat Shah kicked off the conference on Monday, 12 July, by delivering a talk entitled Computing Choice. In his talk, Devavrat discussed algorithmic results relating to ranking, rank aggregation and personalized rankings associating intensity to rankings based on partial information resulting from a sparse set of comparisons. The talk, which was excellently paced and interesting, presented many results and I invite you to check Dev's work for the details.This work addresses computational challenges for decision making without a choice model, and offered a glimpse of the exciting possibilities for inter-disciplinary work across disciplines such as CS, EE, OR and Economics.
Xavier Leroy delivered the second invited talk, entitled Formally verifying a compiler: What does it mean exactly?, on Wednesday, 13 July. In his talk, Xavier discussed the context for, and the results of, the CompCert project, which investigates the formal verification of realistic compilers usable for critical embedded software. Such verified compilers come with a mathematical, machine-checked proof that the generated executable code behaves exactly as prescribed by the semantics of the source program. In this project, Coq is used both as a proof assistant and as a programming language.
In his talk, Xavier said that "Pure functional programming is the shortest path to writing and verifying software." He also asked and addressed two fundamental questions arising from this work and related ones:
• Did we prove it (the compiler) right?
• Did we prove the right thing?
In particular, Xavier discussed the latter question in detail and argued that the social consensus underlying the acceptance of proofs in mathematics also plays a role in accepting proofs of software correctness. He also mentioned the "unreasonable effectiveness of labelled transition systems" in semantics and in supporting such correctness proofs.
Seffi Naor's talk took place on Thursday, 14 July, and was entitled Maximatization of submodular functions: Recent progress. Seffi stepped in at the last moment for Subhash Khot, who was unable to make the trip to Rome. On behalf of the EATCS and of the TCS community as a whole, I thank him for delivering an excellent talk at such a short notice.
Research on the topic of Seffi's talk started in the 1950s-1960s and is now thriving. It has applications in the study of social welfare, economics/game theory, combinatorial optimization, machine learning and information theory. In his talk, Seffi first surveyed results on unconstrained maximization of non-monotone functions, with focus on approximation algorithms, and then presented results for the constrained maximization problem. I refer the readers to Seffi's papers and to this Wikipedia page for more information.
The last invited talk at ICALP 2016 was delivered by Marta Z. Kwiatkowska on Friday, 15 July. Marta's talk was entitled Model Checking and Strategy Synthesis for Stochastic Games: From Theory to Practice and is accompanied by a paper that is available here. Marta stated right at the start that, despite the success that model checking and synthesis techniques have had and are having, we have not found yet the right modelling abstractions for autonomous mobile agents such as robots and autonomous vehicles. Software for these vehicles is expected to behave reliably under uncertainty, and its analysis and synthesis require quantitative approaches to specification and verification. As Marta argued cogently in her talk, a game-theoretic point of view is fruitful in the study of such systems. Indeed, games of various kinds have played a fundamental role in the study of the synthesis of correct programs from specifications from the very beginning, and papers on game-theoretic models abound in Volume B conferences. (See the slides for this talk by Moshe Vardi for historical remarks and an overview of the game-theoretic approach to synthesis.) Rather than attempting to summarize Marta's talk, I strongly encourage you to read her accompanying paper, which beautifully summarizes her work on this topic and contains pointers to related literature.
The core of the scientific programme consisted of the papers that were selected for presentation by the PC chairs (Michael Mitzenmacher, Yuval Rabani and Davide Sangiorgi) and their PCs. Because of EATCS commitments, I could not attend as many talks as I would have liked, but all those I did manage to listen to were excellent both scientifically and from the point of view of the quality of the presentation. (For one of the talks, I even had to wear 3D glasses :-)) Thanks to the PC chairs and their PCs for doing a truly great job!
The award ceremony was held on Wednesday, 13 July, and saw the presentation of the EATCS Distinguished Dissertation Awards, of the Presburger Award to Young Scientists, of the Gödel Prize and of the EATCS Award. The event was a festive occasion and celebrated some of the outstanding members of the TCS community.
The EATCS Distinguished Dissertation Award Committee, consisting of Javier Esparza, Michal Feldman, Fedor Fomin, Luke Ong and Giuseppe Persiano (chair), has selected the following three theses for the EATCS Distinguished Dissertation Award for 2015:
• Radu Curticapean, The Simple, Little and Slow Things Count: On Parameterized Counting Complexity. Thesis work carried out at the Department of Computer Science at Saarland University, Saarbrücken, Germany. Supervisor: Markus Bläser.
• Heng Guo. Complexity Classification of Exact and Approximate Counting Problems. Thesis work carried out at the Department: of Computer Sciences in the University of Wisconsin-Madison. Advisor: Jin-Yi Cai,
• Georg Zetzsche. Monoids as storage mechanisms. Thesis work carried out at the Department: of Computer Science at University of Kaiserslautern. Supervisor: Roland Meyer.
The award committee received an impressive set of submissions in terms of quality. The three selected theses are outstanding.
The Presburger Award was presented to Mark Braverman (Princeton University, USA). The Gödel Prize went to Stephen Brookes and Peter O'Hearn for their invention of concurrent separation logic, and the EATCS Award was given to Dexter Kozen. The presentation of each of these three awards was accompanied by an excellent talk by the award recipient(s). As I mentioned during the award ceremony, this might very well be the first time that the Gödel Prize is mentioned in a piece in the New Yorker.
The award session was extremely well attended and preceded a short bus tour in Rome and a social dinner in a popular restaurant in Trastevere.
The annual General Assembly of the EATCS took place on Thursday, 14 July. I'll report on it elsewhere. Here I will limit myself to saying that, at the General Assembly, I formally stepped down as president of the EATCS after two terms of service (four years). The new president of the EATCS will be Paul Spirakis (University of Liverpool and U. Patras). He will be supported by Leslie Ann Goldberg (University of Oxford), Antonin Kucera (Masaryk University) and Giuseppe Persiano (University of Salerno) as vice-presidents. At ICALP 2016 in Rome, Dirk Janssens also left his post as treasurer of the EATCS after 27 years of sterling service. Jean-Francois Raskin kindly accepted to serve as the new treasurer of our association. The association is very grateful to the above-mentioned colleagues for their willingness to serve and to Dirk for his outstanding service over such a long time. I know that the EATCS community will support the members of the new leadership in their work, just like they helped me during the last four years.
If you were at ICALP in Rome and you have any comment, suggestion or criticism, please post them as comments. I'll make sure that they reach the leadership of the EATCS. We are always working on improving an already very successful conference that does its best to provide a bird's eye view of TCS as a whole.
## Monday, July 04, 2016
### Call for guest bloggers at ICALP 2016
I would like to have some blog coverage for ICALP 2016. If you are attending the conference in Rome and you are interested in guest blogging, drop me a line. Ideally, I would like to have a guest blogger for each of the tracks in the conference. You are, of course, also most welcome to blog about the five invited talks, the award ceremony, the general assembly and any other aspect of the conference.
I'll try to write something myself, but the more the merrier!
## Tuesday, June 21, 2016
### EATCS Bulletin Issue 119 is available online
The June 2016 issue of the Bulletin of the EATCS is now available on line. If you prefer, you can download a pdf with the printed version of the Bulletin. As usual, thanks to the support of the members of the EATCS, the Bulletin is open access.
This issue of the Bulletin features the following columns:
Some of you might also be interested in advice to young researchers from Michael Fellows and other Fellows of the EATCS, and in interviews with the recipients of the Gödel Prize 2016 and of the first Alonzo Church Award.
Thanks to Kazuo Iwama, the editor in chief of the Bulletin, and the EATCS Secretary Office for their work on another excellent issue of the Bulletin.
## Monday, June 06, 2016
### One PhD or post-doctoral position at the School of Computer Science, Reykjavik University
Theoretical Foundations for Monitorability
School of Computer Science, Reykjavik University
One PhD or Postdoctoral Position
Applications are invited for one PhD or postdoctoral position at the School of Computer Science, Reykjavik University. The position is part of a research project funded by the Icelandic Research Fund, under the direction of Luca Aceto (Reykjavik University), Adrian Francalanza (University of Malta) and Anna Ingolfsdottir (Reykjavik University). The general aim of the project is to develop further the theoretical foundations of monitorability for fragments of variants of Hennessy-Milner logic with recursion/modal mu-calculus.
The project work will build on the RV 2015 paper by the co-proposers (http://dx.doi.org/10.1007/978-3-319-23820-3_5), and on the experience developed during their previous work on runtime verification and on the tool detectEr (http://www.cs.um.edu.mt/svrg/Tools/detectEr/). The goals of the project will be:
• to explore more stringent conditions for detection than the ones considered in the RV 2015 paper and study whether this has any effect on the monitorable subset of the logic;
• to investigate the monitorability of the logic with respect
to instrumentation set-ups other than the one used in the RV 2015 paper;
• to extend our results from the RV 2015 paper to the setting of real-time systems, modelled as timed automata, and to a real-time variant of Hennessy-Milner Logic with recursion;
• to understand how existing notions of monitorability relate to the one formulated in the RV 2015 paper, thereby consolidating disparate concepts of monitorability;
• to investigate extensions to monitorability that incorporate notions
of enforceability; and
• to apply the results of the theoretical work in the construction of a prototype software tool for the runtime analysis of systems.
The successful candidates will benefit from, and contribute to, the research environment at the Icelandic Centre of Excellence in Theoretical Computer Science (ICE-TCS). For information about ICE-TCS and its activities, see
Moreover, she/he will visit Adrian Francalanza's group at the University of Malta during the project work and will benefit from the research experience on runtime verification within that group.
Qualification requirements
Applicants for the PhD fellowship should have an MSc degree in Computer Science, or closely related fields. Some background in concurrency theory and mathematical competence are desirable.
Applicants for the postdoctoral position should have, or be about to hold, a PhD degree in Computer Science or closely related fields. Previous knowledge of at least one of concurrency theory, process calculi, (structural) operational semantics and logic in computer science is highly desirable.
Remuneration
The PhD position provides a stipend of 290,000 ISK (roughly 2080 € at the current exchange rate) per month before taxes, for three years, starting as early as possible.
The wage for the postdoctoral position is 400,000 ISK (roughly 2870 € at the present exchange rate) per month before taxes. The position is for one year, starting on September 1, 2016 (later starting dates are possible), and is renewable for another year, based on good performance and mutual satisfaction.
Application details
Interested applicants should send their CV, including a list of publications, in PDF to all addresses below, together with a statement outlining their suitability for the project and the names of at least two referees.
Luca Aceto
email: [email protected]
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https://calculator.academy/time-interest-earned-ratio-calculator/
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Enter the total EBITDA (\$) and the total interest expense (\$) into the Time Interest Earned Ratio Calculator. The calculator will evaluate and display the Time Interest Earned Ratio.
## Time Interest Earned Ratio Formula
The following formula is used to calculate the Time Interest Earned Ratio.
TIER = EBITDA / E
• Where TIER is the Time Interest Earned Ratio ( )
• EBITDA is the total EBITDA (\$)
• E is the total interest expense (\$)
## How to Calculate Time Interest Earned Ratio?
The following example problems outline how to calculate Time Interest Earned Ratio.
Example Problem #1:
1. First, determine the total EBITDA (\$).
• The total EBITDA (\$) is given as: 5000.
2. Next, determine the total interest expense (\$).
• The total interest expense (\$) is provided as: 3000.
3. Finally, calculate the Time Interest Earned Ratio using the equation above:
TIER = EBITDA / E
The values given above are inserted into the equation below and the solution is calculated:
TIER = 5000 / 3000 = 1.66 ( )
Example Problem #2:
For this problem, the variables required are provided below:
total EBITDA (\$) = 6000
total interest expense (\$) = 8000
Test your knowledge using the equation and check your answer with the calculator above.
TIER = EBITDA / E = ?
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http://mathhelpforum.com/advanced-algebra/89589-ideals-homomorphisms.html
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# Math Help - Ideals and homomorphisms
1. ## Ideals and homomorphisms
Let I and J be ideals of a ring R and let I be contained in J.
Show that J/I is an ideal of R/I and also show that (R/I)/(J/I) is isomorphic to R/J.
For the second part I am just trying to use a ring homomorphism but am having trouble defining a map.
Also if there is a better way to do the first part than to show that J/I is a sub ring and then an ideal that would be awesome.
Thanks.
2. Originally Posted by curiousmuch
Let I and J be ideals of a ring R and let I be contained in J.
Show that J/I is an ideal of R/I and also show that (R/I)/(J/I) is isomorphic to R/J.
For the second part I am just trying to use a ring homomorphism but am having trouble defining a map.
Also if there is a better way to do the first part than to show that J/I is a sub ring and then an ideal that would be awesome.
Thanks.
for the first part just do what we usually do to prove something is an ideal. for the second part define $f: R/I \longrightarrow R/J$ by $f(r+I)=r+J.$ this map is well-defined because $I \subseteq J.$
it's obviously a surjective ring homomorphism and $\ker f = J/I$ and the result follows.
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http://math.stackexchange.com/questions/293501/ackerman-numbers-arrow-notation?answertab=oldest
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# Ackerman numbers, arrow notation
How to compare 3^3^3^3 and to 3↑(3↑↑3). (Ackerman number, arrow notation) Are these two numbers equal??? How to compare 3↑(3↑↑3) with googol and googolplex???
-
Your first two numbers are equal. By definition $3\uparrow\uparrow 3=3^{3^3}$ and $3\uparrow n=3^n$, so $$\large3\uparrow(3\uparrow\uparrow 3)=3\uparrow 3^{3^3}=3^{3^{3^3}}\;.$$
Now $3\uparrow\uparrow 3=7,625,597,484,987$, so
$$\log_{10}\big(3\uparrow(3\uparrow\uparrow 3)\big)=7,625,597,484,987\log_{10}3>\big(7\times10^{12}\big)\log_{10}3>3\times10^{12}\;,$$
so
$$3\large\uparrow(3\uparrow\uparrow 3)>10^{3\times10^{12}}>10^{100}=1\text{ googol}\;.$$
On the other hand,
$$\log_{10}\big(3\uparrow(3\uparrow\uparrow 3)\big)=7,625,597,484,987\log_{10}3<10^{13}\;,$$
so
$$3\large\uparrow(3\uparrow\uparrow 3)<10^{10^{13}}<10^{10^{100}}=1\text{ googolplex}\;.$$
-
|
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|
https://dsp.stackexchange.com/questions/64624/is-the-laplace-transform-a-special-case-of-fourier-transform-not-the-other-way
|
# Is the Laplace transform a special case of Fourier transform? (Not the other way around)
Always had a thought about why Laplace transform reveals the transient properties of the system? My doubt is based on the following fact, Fourier transform is given as
$$$$\mathscr{F}\left\lbrace f(t)\right\rbrace = \int_{-\infty}^\infty f(t) e^{ -j \omega t} dt$$$$
Where Mathematically and intuitively we believe that the angular frequency $$\omega$$ takes only real value.
What if, instead of taking real angular frequencies, if the variable $$\omega$$ assumes a complex angular frequency in the form $$\beta - j \alpha$$ , then,
$$j \omega t = j (\beta - j \alpha) t = (\alpha + j \beta ) t = s t$$
While taking Fourier transform w.r.t $$\omega$$, the quantity $$\beta$$ will be real angular frequency in radians per second and $$\alpha$$ will be the $$\textbf{imaginary angular }$$ frequency in radians per second.
$$$$\int_{-\infty}^\infty f(t) e^{ -j \omega t} dt = \int_{-\infty}^\infty f(t) e^{ - s t} dt = \mathscr{L}\left\lbrace f(t)\right\rbrace$$$$
Hence is it mathematically correct to consider bilateral Laplace transform as a special case of Fourier transform (not the other way around) when $$\omega$$ takes a complex angular form $$\beta - j \alpha$$ ? I believe the fact that $$\omega$$ can take complex values is the reason why we get transient properties of the system when using Laplace transform.
The Fourier Transform is the Laplace Transform with the complex variable s restricted to be the imaginary axis on the s plane. For this reason the Fourier Transform only exists when the imaginary axis is within the region of convergence. The variable s is called a "complex frequency" as it is the frequency variable that can take on real ($$\sigma$$) and imaginary ($$\omega$$) components. That said, I would view the Fourier Transform as a subset of the Laplace Transform, or the Laplace Transform as an expansion on the Fourier Transform that provides a lot more functionality and can exist when the Fourier Transform can't.
This is also the reason that the frequency response for a system with a general transfer function $$H(s)$$ is given as $$H(j\omega)$$.
When a system is restricted to $$s= j\omega$$ as the input, then the input is restricted to be only sinusoids or signals given by $$e^{st}$$ with $$s = j\omega$$ which maintain a constant magnitude with time. By allowing s to have real and imaginary components as in $$s = \sigma + j\omega$$ then we also allow the input to grow or shrink with time, depending on which point in the s plane is used as the input to the system.
• what is the physical meaning of $\sigma$ ( say $\alpha$ in my question ) – abhilash Mar 16 '20 at 15:37
• Consider the function $e^{-\sigma t}$--- it is simply a decaying exponential for positive t and real $\sigma$. So $\sigma$ provides a decay to the envelope of an otherwise sinusoidal function when you have both $\sigma$ and $\omega$ terms. Thus we see that under the integral how we can have a "region of convergence" for all values of $\omega$ that are greater than the right most pole (for causal functions). Try solving for the integral otherwise and you will see that the solution explodes--- so you can consider $\sigma$ to be a convergence factor for when the Fourier Transform would not exist – Dan Boschen Mar 16 '20 at 16:14
• Agreed, I concur, it’s the decaying exponential, but still, I am unclear about the factor ‘$\sigma$’, let me explain, 1. Suppose we want to find out:- what part of a function $f(t)$ varies along a circle at a particular speed –or-- what component of $f(t)$ is having a periodic variation that moves with a specific time period. What we need to do is to correlate complex function $f(t)$ with a unit circle $e^{ j \omega t}$. $$f(t) \otimes e^{ j \omega t} = \int_{-\infty}^\infty f(t) (e^{ j \omega t})^* dt \hspace{1.5cm} (with zero lag, \tau =0)$$ – abhilash Mar 17 '20 at 19:22
• Which is nothing but our famous Fourier transform. Here $'\omega'$ (speed of variation) is a factor we are throwing into the correlation process to get the magnitude of the variation (amplitude as output). 2. By utilizing a similar thought process, what is the significance of $'\sigma'$, -or- what is the actual meaning of the factor $'\sigma'$ which we are feeding into the transform process; to pull out the amplitude variation. – abhilash Mar 17 '20 at 19:23
• @abhilash it is a decay or growth factor we can apply to the function auch that we can correlate to it and have that converge where it otherwise wouldn’t — and importantly it helps us identify the points of extrema (zeros and poles) that define all dynamics of the system. If you didn’t have the ability to vary the real part of the exponent, you would not find these solutions. – Dan Boschen Mar 17 '20 at 19:29
I think this question is based on a wrong premise: "[...] why Laplace transform reveals the transient properties of the system". It's not true that the transients can only be obtained from the Laplace transform. The Fourier transform can do the same, assuming it exists. What is true is that it is more convenient to use the unilateral Laplace transform for taking into account non-zero initial conditions. But note that even this can be done with the Fourier transform if the initial conditions are modeled as separate sources.
So, to answer your question, no, the Laplace transform is not a special case of the Fourier transform. They are different tools with partially different (but overlapping) applications. For analyzing causal systems with possibly non-zero initial conditions the unilateral Laplace transform is a very practical tool. The Fourier transform is better suited for analyzing ideal systems (such as ideal frequency selective filters) or systems with idealized input signals (such as pure sinusoids). Note that there are signals for which the Fourier transform exists but the (bilateral) Laplace transform doesn't (e.g., sinusoids, complex exponentials, or impulse responses of ideal brick wall filters).
• L wouldn't it be "for which the Fourier Transform exists but the bilateral Laplace transform doesn't"? As I have often seen it go under the assumption that when not mentioned explicitly the unilateral transform is to be assumed. The Laplace transform for a sinusoid for t>=0 and 0 for t<0 does exist. – Dan Boschen Mar 16 '20 at 16:21
• @DanBoschen: Well, that's a matter of definition, but for me it doesn't make sense to talk about the transform of a signal extending from $-\infty$ to $+\infty$ that only takes into account the interval $(0,\infty)$. So in that sense, the Laplace transform of $x(t)=\sin(\omega_0t)$ doesn't exist. What does exist is the Laplace transform of $x(t)=\sin(\omega_0t)u(t)$, but that's not what I was referring to. – Matt L. Mar 16 '20 at 17:19
• @DanBoschen: Anyway, thanks for pointing out a possible misunderstanding, I'll edit my answer. – Matt L. Mar 16 '20 at 17:19
• Right, just a matter of convention really: since the term “Laplace Transform” alone is so ubiquitous- maybe we shouldn’t all be so quick to assume it is the unilateral when not mentioned otherwise; but I think that is typically the case so will avoid misunderstanding indeed. – Dan Boschen Mar 16 '20 at 17:23
• @DanBoschen: I'd say it has to do with the type of convergence we expect from different transforms. With the Fourier transform we're happy with less stringent definitions of convergence. But that would make a great question anyway, even though it might be a better fit at math.SE. – Matt L. Mar 16 '20 at 18:54
|
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|
https://arxiv.org/abs/hep-ph/0203023
|
hep-ph
(what is this?)
# Title: Simple Quark Model with Chiral Phenomenology
Abstract: We propose a new approach to the determination of hadronic observables in which the essential features of chiral symmetry are combined with conventional constituent quark models. To illustrate the approach, we consider the simple quark model in the limit of SU(3) flavour symmetry at the strange quark mass. The comparison with data is made after an analytic continuation which ensures the correct leading nonanalytic behaviour of chiral perturbation theory. The approach not only gives an excellent fit for the octet baryon magnetic moments but the prediction for the $\Delta^{++}$ magnetic moment is also in good agreement with current measurements.
Comments: 8 pages (RevTeX4), 2 figures (PostScript) Subjects: High Energy Physics - Phenomenology (hep-ph) Journal reference: Phys.Rev.C65:062201,2002 DOI: 10.1103/PhysRevC.65.062201 Cite as: arXiv:hep-ph/0203023 (or arXiv:hep-ph/0203023v2 for this version)
## Submission history
From: Ian Cloet [view email]
[v1] Mon, 4 Mar 2002 07:00:12 GMT (38kb)
[v2] Tue, 5 Mar 2002 08:37:45 GMT (37kb)
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|
http://gmrt.ncra.tifr.res.in/gmrt_hpage/Users/doc/WEBLF/LFRA/node88.html
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Next: Weighting, Tapering and Beam Up: Mapping II Previous: Mapping II Contents
# Introduction
An aperture synthesis array measures the visibilities at discrete points in the -domain. The visibilities are Fourier transformed to get the Dirty Map and the weighted -sampling function is Fourier transformed to get the Dirty Beam using the efficient FFT algorithm. This lecture describes the entire chain of data processing required to inverted the visibilities recorded as a function of (), and the resulting errors/distortions in the final image. In this entire lecture, the ' operator represents convolution operation, the .' operator represents point-by-point multiplication and the ' operator represents the Fourier transform operator.
As described earlier, the visibility measured by an aperture synthesis telescope is related to the sky brightness distribution as
(11.1.1)
where denotes the Fourier Transform. The above equation is true only for the case of continuous sampling of the -plane such that is measured for all values of (). However since there are finite antennas in an array, -plane is sampled at descreet points and Eq. 11.1.1 has to be written as
(11.1.2)
where is the Dirty Map, is the true brightness distribution, is the Dirty Beam and is the -sampling function given by
(11.1.3)
where and are the actual () points measured by the telescope. The pattern of all the measured () points is referred to as the -coverage.
This function essentially assigns a weight of unity to all measured points and zero everywhere else in the -plane. Fourier transform of is referred to as the Dirty Beam. As written in Eq. 11.1.2, the Dirty Beam is the transfer function of the instrument used as an imaging device. The shape of the Dirty Beam is a function of the -coverage which in turns is a function of the location of the antennas. Dirty Beam for a fully covered -plane will be equal to where is the largest antenna spacing for which a measurement is available. The width of the main lobe of this function is proportional to . The resolution of such a telescope is therefore roughly and can be interpreted as the size of an equivalent lens. For a real -coverage however, is not flat till and has holes' in between representing un-sampled points. The effect of this missing data is to increase the side-lobes and make the Dirty Beam noisy, but in a deterministic manner. Typically, an elliptical gaussian can be fitted to the main lobe of the Dirty Beam and is used as the resolution element of the telescope. The fitted gaussian is referred to as the Synthesized Beam.
The Dirty Map is a convolution of the true brightness distribution and the Dirty Beam. is almost never a satisfactory final product since the side-lobes of (which are due to missing spacings in the -domain) from a strong source in the map will contaminate the entire map at levels higher than the thermal noise in the map. Without removing the effect of from the map, the effective RMS noise in the map will be much higher than the thermal noise of the telescope and will result into obscuration of faint sources in the map. This will be then equivalent to reduction in the dynamic range of the map. The process of De-convolving is discussed in a later lecture, which effectively attempts to estimate from such that is minimized consistent with the estimated noise in the map.
To use the FFT algorithm for Fourier transforming, the irregularly sampled visibility needs to be gridded onto a regular grid of cells. This operation requires interpolation to the grid points and then re-sampling the interpolated function. To get better control on the shape of the Dirty Beam and on the signal-to-noise ratio in the map, the visibility is first re-weighted before being gridded. These operations are described below.
Next: Weighting, Tapering and Beam Up: Mapping II Previous: Mapping II Contents
NCRA-TIFR
|
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|
https://jp.mathworks.com/help/pde/ug/dynamics-of-a-damped-cantilever-beam.html
|
# Dynamics of Damped Cantilever Beam
This example shows how to include damping in the transient analysis of a simple cantilever beam.
The damping model is basic viscous damping distributed uniformly through the volume of the beam. The beam is deformed by applying an external load at the tip of the beam and then released at time $t=0$. This example does not use any additional loading, so the displacement of the beam decreases as a function of time due to the damping. The example uses plane-stress modal, static, and transient analysis models in its three-step workflow:
1. Perform modal analysis to compute the fundamental frequency of the beam and to speed up computations for the transient analysis.
2. Find the static solution of the beam with a vertical load at the tip to use as an initial condition for a transient model.
3. Perform the transient analysis with and without damping.
Damping is typically expressed as a percentage of critical damping, $\xi$, for a selected vibration frequency. This example uses $\xi =0.03$, which is three percent of critical damping.
The example specifies values of parameters using the imperial system of units. You can replace them with values specified in the metric system. If you do so, ensure that you specify all values throughout the example using the same system.
### Modal Analysis
Create a modal analysis model for a plane-stress problem.
`modelM = createpde("structural","modal-planestress");`
Create the geometry and include it in the model. Suppose, the beam is 5 inches long and 0.1 inches thick.
```width = 5; height = 0.1; gdm = [3;4;0;width;width;0;0;0;height;height]; g = decsg(gdm,'S1',('S1')'); geometryFromEdges(modelM,g);```
Plot the geometry with the edge labels.
```figure; pdegplot(modelM,"EdgeLabels","on"); axis equal title("Geometry With Edge Labels Displayed")```
Define a maximum element size so that there are five elements through the beam thickness. Generate a mesh.
```hmax = height/5; msh = generateMesh(modelM,"Hmax",hmax);```
Specify Young's modulus, Poisson's ratio, and the mass density of steel.
```E = 3.0e7; nu = 0.3; rho = 0.3/386; structuralProperties(modelM,"YoungsModulus",E, ... "PoissonsRatio",nu, ... "MassDensity",rho);```
Specify that the left edge of the beam is a fixed boundary.
`structuralBC(modelM,"Edge",4,"Constraint","fixed");`
Solve the problem for the frequency range from `0` to `1e5`. The recommended approach is to use a value that is slightly smaller than the expected lowest frequency. Thus, use `-0.1` instead of `0`.
`res = solve(modelM,"FrequencyRange",[-0.1,1e5]')`
```res = ModalStructuralResults with properties: NaturalFrequencies: [8x1 double] ModeShapes: [1x1 FEStruct] Mesh: [1x1 FEMesh] ```
By default, the solver returns circular frequencies.
`modeID = 1:numel(res.NaturalFrequencies);`
Express the resulting frequencies in Hz by dividing them by `2π`. Display the frequencies in a table.
```tmodalResults = table(modeID.',res.NaturalFrequencies/(2*pi)); tmodalResults.Properties.VariableNames = {'Mode','Frequency'}; disp(tmodalResults)```
``` Mode Frequency ____ _________ 1 126.94 2 794.05 3 2216.8 4 4325.3 5 7110.7 6 9825.9 7 10551 8 14623 ```
Compute the analytical fundamental frequency (Hz) using the beam theory.
```I = height^3/12; freqAnalytical = 3.516*sqrt(E*I/(width^4*rho*height))/(2*pi)```
```freqAnalytical = 126.9498 ```
Compare the analytical result with the numerical result.
`freqNumerical = res.NaturalFrequencies(1)/(2*pi)`
```freqNumerical = 126.9416 ```
Compute the period corresponding to the lowest vibration mode.
`longestPeriod = 1/freqNumerical`
```longestPeriod = 0.0079 ```
Plot the y-component of the solution for the lowest beam frequency.
```figure; pdeplot(modelM,"XYData",res.ModeShapes.uy(:,1)) title("Lowest Frequency Vibration Mode") axis equal```
### Initial Displacement from Static Solution
The beam is deformed by applying an external load at its tip and then released at time $t=0$. Find the initial condition for the transient analysis by using the static solution of the beam with a vertical load at the tip.
Create a static plane-stress model.
`modelS = createpde("structural","static-planestress");`
Use the same geometry and mesh that you used for the modal analysis.
```geometryFromEdges(modelS,g); modelS.Mesh = msh;```
Specify the same values for Young's modulus, Poisson's ratio, and the mass density of the material.
```structuralProperties(modelS,"YoungsModulus",E, ... "PoissonsRatio",nu, ... "MassDensity",rho); ```
Specify the same constraint on the left end of the beam.
`structuralBC(modelS,"Edge",4,"Constraint","fixed");`
Apply the static vertical load on the right side of the beam.
`structuralBoundaryLoad(modelS,"Edge",2,"SurfaceTraction",[0;1]);`
Solve the static model. The resulting static solution serves as an initial condition for transient analysis.
`Rstatic = solve(modelS);`
### Transient Analysis
Perform the transient analysis of the cantilever beam with and without damping. Use the modal superposition method to speed up computations.
Create a transient plane-stress model.
`modelT = createpde("structural","transient-planestress");`
Use the same geometry and mesh that you used for the modal analysis.
```geometryFromEdges(modelT,g); modelT.Mesh = msh;```
Specify the same values for Young's modulus, Poisson's ratio, and the mass density of the material.
```structuralProperties(modelT,"YoungsModulus",E, ... "PoissonsRatio",nu, ... "MassDensity",rho); ```
Specify the same constraint on the left end of the beam.
`structuralBC(modelT,"Edge",4,"Constraint","fixed");`
Specify the initial condition by using the static solution.
`structuralIC(modelT,Rstatic)`
```ans = NodalStructuralICs with properties: InitialDisplacement: [6511x2 double] InitialVelocity: [6511x2 double] ```
Solve the undamped transient model for three full periods corresponding to the lowest vibration mode.
```tlist = 0:longestPeriod/100:3*longestPeriod; resT = solve(modelT,tlist,"ModalResults",res);```
Interpolate the displacement at the tip of the beam.
`intrpUt = interpolateDisplacement(resT,[5;0.05]);`
The displacement at the tip is a sinusoidal function of time with amplitude equal to the initial y-displacement. This result agrees with the solution to the simple spring-mass system.
```plot(resT.SolutionTimes,intrpUt.uy) grid on title("Undamped Solution") xlabel("Time") ylabel("Tip of beam displacement")```
Now solve the model with damping equal to 3% of critical damping.
```zeta = 0.03; omega = 2*pi*freqNumerical; structuralDamping(modelT,"Zeta",zeta); resT = solve(modelT,tlist,"ModalResults",res);```
Interpolate the displacement at the tip of the beam.
`intrpUt = interpolateDisplacement(resT,[5;0.05]);`
The y-displacement at the tip is a sinusoidal function of time with amplitude exponentially decreasing with time.
```figure hold on plot(resT.SolutionTimes,intrpUt.uy) plot(tlist,intrpUt.uy(1)*exp(-zeta*omega*tlist),"Color","r") grid on title("Damped Solution") xlabel("Time") ylabel("Tip of beam displacement")```
|
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