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https://proceedings.mlr.press/v167/su22a.html
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# Faster Rates of Private Stochastic Convex Optimization
Jinyan Su, Lijie Hu, Di Wang
Proceedings of The 33rd International Conference on Algorithmic Learning Theory, PMLR 167:995-1002, 2022.
#### Abstract
In this paper, we revisit the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) and provide excess population risks for some special classes of functions that are faster than the previous results of general convex and strongly convex functions. In the first part of the paper, we study the case where the population risk function satisfies the Tysbakov Noise Condition (TNC) with some parameter $\theta>1$. Specifically, we first show that under some mild assumptions on the loss functions, there is an algorithm whose output could achieve an upper bound of $\tilde{O}((\frac{1}{\sqrt{n}}+\frac{d}{n\epsilon})^\frac{\theta}{\theta-1})$ and $\tilde{O}((\frac{1}{\sqrt{n}}+\frac{\sqrt{d\log(1/\delta)}}{n\epsilon})^\frac{\theta}{\theta-1})$ for $\epsilon$-DP and $(\epsilon, \delta)$-DP, respectively when $\theta\geq 2$, here $n$ is the sample size and $d$ is the dimension of the space. Then we address the inefficiency issue, improve the upper bounds by $\text{Poly}(\log n)$ factors and extend to the case where $\theta\geq \bar{\theta}>1$ for some known $\bar{\theta}$. Next we show that the excess population risk of population functions satisfying TNC with parameter $\theta\geq 2$ is always lower bounded by $\Omega((\frac{d}{n\epsilon})^\frac{\theta}{\theta-1})$ and $\Omega((\frac{\sqrt{d\log(1/\delta)}}{n\epsilon})^\frac{\theta}{\theta-1})$ for $\epsilon$-DP and $(\epsilon, \delta)$-DP, respectively, which matches our upper bounds. In the second part, we focus on a special case where the population risk function is strongly convex. Unlike the previous studies, here we assume the loss function is non-negative and the optimal value of population risk is sufficiently small. With these additional assumptions, we propose a new method whose output could achieve an upper bound of $O(\frac{d\log(1/\delta)}{n^2\epsilon^2}+\frac{1}{n^{\tau}})$ and $O(\frac{d^2}{n^2\epsilon^2}+\frac{1}{n^{\tau}})$ for any $\tau> 1$ in $(\epsilon,\delta)$-DP and $\epsilon$-DP model respectively if the sample size $n$ is sufficiently large. These results circumvent their corresponding lower bounds in (Feldman et al., 2020) for general strongly convex functions. Finally, we conduct experiments of our new methods on real world data. Experimental results also provide new insights into established theories.
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https://math.stackexchange.com/questions/1172119/how-to-prove-x3-y3-x-yx2xyy2-without-expand-the-right-side
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# How to prove $x^3-y^3 = (x-y)(x^2+xy+y^2)$ without expand the right side?
I can prove that $x^3-y^3 = (x-y)(x^2+xy+y^2)$ by expanding the right side.
1. $x^3-y^3 = (x-y)x^2 + (x-y)(xy) + (x-y)y^2$
2. $\implies x^3 - x^2y + x^2y -xy^2 + xy^2 - y^3$
3. $\implies x^3 - y^3$
I was wondering what are other ways to prove that $x^3-y^3 = (x-y)(x^2+xy+y^2)$
Let $\omega$ be a complex cube root of unity. Then $x^{3} - y^{3} = (x-y)(x- \omega y)(x-\omega^{2}y)$ since both sides vanish when $x \in \{y,\omega y,\omega^{2}y \}$ and the degrees are right. Since $1 + \omega + \omega^{2} = 0$ we have $\omega + \omega^{2} = -1.$ We also have $\omega \omega^{2} = 1$, so we have $(x - \omega y)(x-\omega^{2}y) = x^{2}+xy + y^{2}.$
Divide $x^3-y^3$ by $x-y$ as polynomials
First, notice that for all $u$, \begin{align*}(1-u)(1 + u + u^2) &= 1 + u + u^2 - (u - u^2 - u^3)\\ &= 1 + (u-u) + (u^2-u^2) - u^3\\ &= 1 - u^3.\end{align*} Now, take $u = \frac{y}{x}$ and multiply by $x^3$.
They agree at $\,x = 0,\pm y\,$ so their difference is a quadratic in $\,x\,$ with $3$ roots, hence zero.
• Here the coefficient ring is the integral domain $\,\Bbb Z[y]\,$ where $\,0,y,-y\,$ are distinct. Recall that a nonzero polynomial over a domain has no more roots than its degree. – Bill Dubuque Mar 2 '15 at 18:32
Since $x=y$ is clearly a root, one may divide $x^3-y^3$ by $x-y$ directly.
Well there are two ways that come to mind.
It is clear that when $x=y$ we have $x^3-y^3=0$. Then use long division to divide $x^3-y^3$ by $x-y$ and the result will be the equation on the right.
Another way would be to write:
$$\left(\frac{x}{y}\right)^3 - 1$$
Now we wish to find the zeros of this polynomial. These correspond to $\frac{x}{y} = 1$, $\frac{x}{y} = e^{i\frac{2\pi}{3}}$ and $\frac{x}{y} = e^{i\frac{4\pi}{3}}$.
Then we can factor the polynomial as:
$$\left(\frac{x}{y}\right)^3 - 1 = \left( \frac{x}{y} - 1 \right) \left(\frac{x}{y} - e^{i\frac{2\pi}{3}}\right) \left( \frac{x}{y} - e^{i\frac{4\pi}{3}} \right)$$
If we multiply the last two factors together we find:
$$\left(\frac{x}{y}\right)^3 - 1 = \left( \frac{x}{y} - 1 \right) \left(\frac{x^2}{y^2} - \frac{x}{y} \left(e^{i \frac{2\pi}{3}} + e^{i \frac{4 \pi}{3}}\right) + 1 \right)$$ $$=\left( \frac{x}{y} - 1 \right) \left(\frac{x^2}{y^2} - \frac{x}{y} \left( 2 \cos(2\pi/3) \right) + 1 \right) = \left( \frac{x}{y} - 1 \right) \left(\frac{x^2}{y^2} + \frac{x}{y} + 1 \right).$$
Thus $$\left(\frac{x}{y}\right)^3 - 1 = \left( \frac{x}{y} - 1 \right) \left(\frac{x^2}{y^2} + \frac{x}{y} + 1 \right).$$ Multiplying by $y^3$ on both sides gives the result.
Another way is as follows: $$(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3 = (x^3 - y^3) -3xy(x - y) \quad \Rightarrow$$ $$x^3 - y^3 = (x - y)^3 + 3xy(x - y) = (x - y)[(x - y)^2 + 3xy] \quad \Rightarrow$$ $$x^3 - y^3 = (x - y)(x^2 + xy + y^2)$$
$x^3-y^3=x^2(x-y)+yx^2-y^3=x^2(x-y)+yx(x-y)+xy^2-y^3=...$ (Simly insert $x^2y-yx^2$, then insert $y^2x-xy^2$,...)
You can rearrange it into two possible ways.
Show, by left side, that $$\frac{x^3-y^3}{x-y} = x^2+xy+y^2,$$ or $$\frac{x^3-y^3}{x^2+xy+y^2} = x-y.$$
You could do the enclidian division of $X^3 - Y^3$ by $X-Y$ in the ring $A[X]$, where $A = \mathbf{Z}[Y]$, has $X-Y$ has unit leading coefficient.
You can use "Long Division of Polynomials"
$\frac {1-(\frac y x)^3}{1-(\frac y x)}=1+\frac y x+(\frac y x)^2$
Multiply both sides by $x^3$
$\frac {x^3-y^3}{1-(\frac y x)}=x(x^2+xy+y^2)$
Then you have
$x^3-y^3=(x-y)(x^2+xy+y^2)$
• What's the point of using $\frac yx$ in the first place? Why can't you just perform your long division on $1-x^3$? – BigbearZzz Aug 8 '16 at 8:21
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https://nrhstat.org/publication/2002-geometric-drift/
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# Establishing geometric drift via the Laplace transform of symmetric measures
Publication
Statistics & Probability Letters, 60(3), 289-295
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http://jakobschwichtenberg.com/larger-symmetries/
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# Larger Symmetries
“Further progress lies in the direction of making our equations invariant under wider and still wider transformations.”
These prophetic lines were written in 1930 by P. A. M. Dirac in his famous book “The Principles of Quantum Mechanics”. In the following centuries, tremendous progress was made exactly as he predicted.
Weak interactions were described perfectly using $SU(2)$ symmetry, strong interactions using $SU(3)$ symmetry and it is well known that electrodynamics can be derived from $U(1)$ symmetry. Other aspects of elementary particles, like their spin, can be understood using the symmetry of special relativity.
A symmetry is a transformation that leaves our equations invariant, i.e. that does not change the equations. A set of symmetry transformations is called a group and, for example, the set of transformations that leaves the equations of special relativity invariant is called the Poincare group.
By making our equations invariant under the quite large set of transformations:
$$\text{Poincare Group} \times U(1) \times SU(2) \times SU(3) ,$$
we are able to describe all known interactions of elementary particles, except for gravity. This symmetry is the core of the standard model of modern physics, which is approximately 40 years old. Since then it has been confirmed many times, for example, through the discovery of the Higgs boson. Just as Dirac predicted, we gained incredible insights into the inner workings of nature, by making the symmetry of our equations larger and larger.
Unfortunately, since the completion of the standard model $\sim 40$ years ago, there was no further progress in this direction. No further symmetry of nature was revealed by experiments. (At least that’s the standard view, but I don’t think it’s true. More on that later). In 2017 our equations are still simply invariant under $\text{Poincare Group} \times U(1) \times SU(2) \times SU(3) ,$ but no larger symmety.
I’m a big believer in Dirac’s mantra. Despite the lack of new experimental insights, I do think there are many great ideas for how symmetries could guide us towards the correct theory beyond the standard model.
Before, we can discuss some of these ideas, there is one additional thing that should be noted. Although the four groups $\text{Poincare Group} \times U(1) \times SU(2) \times SU(3)$ are written equally next to each other, they aren’t treated equally in the standard model. The Poincare group is a spacetime symmetry, whereas all other groups describe inner symmetries of quantum fields. Therefore, we must divide the quest for a larger symmetry into two parts. On the one hand, we can enlarge the spacetime symmetry and on the other hand, we can enlarge the inner symmetry. In addition to these two approaches, we can also try to treat the symmetries equally and enlarge them at the same time.
## Enlargement of the Spacetime Symmetry
The symmetry group of special relativity is the set of transformations that describe transformations between iinertialframes of reference and leave the speed of light invariant. As already noted, this set of transformations is called the Poincare group.
Before Einstein discovered special relativity, people used a spacetime symmetry that is called the Galilean group. The Galilean group also describes transformations between inertial frames of reference, but does not care about the speed of light.
The effects of special relativity are only important for objects that are moving fast. For everything that moves slowly compared to the speed of light, the Galilean group is sufficient. The Galilean group is an approximate symmetry when objects move slowly. Mathematically this means that the Galilean group is the contraction of the Poincare group in the limit where the speed of light goes to infinity. For an infinite speed of light, nothing can move with a speed close to the speed of light and thus the Galilean group would be the correct symmetry group.
It is natural to wonder if the Poincare group is an approximate symmetry, too.
One hint in this direction is that the Poincare group is an “ugly” group. The Poincare group is the semi-direct product of the group of translations and the Lorentz group, which described rotations and boosts. Therefore the Poincare group not a simple group. The simply groups are the “atoms of groups” that can be used to construct all other group from. However, the spacetime symmetry group that we use in the standard model is not one of these truly fundamental groups.
Already in 1967 Monique Levy‐Nahas studied the question which groups could yield the Poincare group as a limit, analogous to how the Poincare group yields the Galilean group as a limit.
The answer she found was stunningly simple: “the only groups which can be contracted in the Poincaré group are $SO(4, 1)$ and $SO(3, 2)$”. These groups are called the de Sitter and the anti de Sitter group.
They consist of transformations that describe transformations between inertial frames of reference, leave the speed of light invariant and leave additionally an energy scale invariant. The de Sitter group leaves a positive energy scale invariant, whereas the anti deSitter group leaves a negative energy scale invariant. Both contract to the Poincare group in the limit where the invariant energy scale goes to zero.
Levy‐Nahas’ discovery is great news. There isn’t some large pool of symmetries that we can choose from, but only two. In addition, the groups she found are simple groups and therefore much “prettier” than the Poincare group.
Following Dirac’s mantra and remembering the fact that the deformation: Galilean Group $\to$ Poincare Group led to incredible progress, we should take the idea of replacing the Poincare group with the de Sitter or anti de Sitter group seriously. This point was already emphasized in 1972 by Freeman J. Dyson in his famous talk “Missed opportunities”.
Nevertheless, I didn’t hear about the de Sitter groups in any particle physics lecture or read about them in any particle physics book. Maybe because the de Sitter symmetry is not a symmetry of nature? Because there are no experimental evidence?
To answer these questions, we must first answer the question: what is the energy scale that is left invariant?
The answer is: it’s the cosmological constant!
The present experimental status is that the cosmological constant is tiny, but nonzero and positive: $\Lambda \approx 10^{-12}$ eV! This smallness explains why the Poincare group works so well. Nevertheless, the correct spacetime symmetry group is the de Sitter group. I’m a bit confused why this isn’t mentioned in the textbooks or lectures. If you have an idea, please let me know!
Can we enlarge the spacetime symmetry even further?
Yes, we can. But as we know from Levy‐Nahas’ paper, only a different kind of symmetry enlargement is possible. There isn’t any other symmetry that could be more exact and yield the de Sitter group in some limit. Instead, we can think about the question, if there could be a larger broken spacetime symmetry.
Nowadays the idea of a broken symmetry is well known and already an important part of the standard model. In the standard model the Higgs field triggers the breaking $SU(2) \times U(1) \to U(1)$.
Something similar could’ve been happend to a spacetime symmetry in the early universe. A good candidate for such a broken spacetime symmetry is the conformal group $SO(4,2)$.
The temperature in the early universe was incredibly high and “[i]t is an old idea in particle physics that, in some sense, at sufficiently high energies the masses of the elementary particles should become unimportant” (Sidney Coleman in Aspects of Symmetry). In the massless limit our equations become invariant under the conformal group (source) . The de Sitter group and the Poincare group are subgroups of the conformal group. Therefore it is possible that the conformal group was broken to the de Sitter group in the early universe.
This idea is interesting for a different reason, too. The only parameter in the standard model that breaks conformal symmetry at tree level is the Higgs mass parameter. This parameter is the most problematic aspect of the standard model and possibly the Higgs mass fine-tuning problem can be solved with the help of the conformal group. (See: On naturalness in the standard model by William A. Bardeen.)
## Enlargement of the Inner Symmetry
The inner symmetry group of the standard model $U(1) \times SU(2) \times SU(3)$ is quite ugly, too. Like the Poincare group it is not a simple group.
There is an old idea by Howard Georgi and Sheldon Glashow that instead of $U(1) \times SU(2) \times SU(3)$ we use a larger, simple group $G_{GUT}$ . These kind of theories are called Grand Unified Theories (GUTs).
While GUTs have problems, they are certainly beautiful. On obvious “problem” is that in present day colliders, we do not observe effects of a $G_{GUT}$ structure and thus we assume the unified gauge symmetry is broken at some high energy scale:
\label{eq:schematicgutbreaking}
G_{GUT} \stackrel{M_{GUT}}{\rightarrow} \ldots \stackrel{M_I}{\rightarrow} G_{SM} \stackrel{M_Z}{\rightarrow} SU(3)_C \times U(1)_Q \, ,
where the dots indicate possible intermediate scales between $G_{GUT}$ and $G_{SM}$. In the following, we discuss some of the “mysteries” of the standard model that can be resolved by a GUT.
### Quantization of Electric Charge
In the standard model the electric charges of the various particles must be put in by hand and there is no reason why there should be any relation between the electron and proton charge. However from experiments it is known that $Q_{\text{proton}}+Q_{\text{electron}}= \mathcal{O}(10^{-20})$. In GUTs one multiplet of $G_{GUT}$ contains quarks and leptons. This way, GUTs provide an elegant explanation for the experimental fact of charge quantization. For example in $SU(5)$ GUTs the conjugate $5$-dimensional representation contains the down quark and the lepton doublet
\bar{5} = \begin{pmatrix} \nu_L \\ e_L \\ (d_R^c)_{\text{red}} \\ (d_R^c)_{\text{blue}} \, .\\ (d_R^c)_{\text{green}} \end{pmatrix}
The standard model generators must correspond to generators of $G_{GUT}$. Thus the electric charge generator must correspond to one Cartan generator of $G_{GUT}$ (The eigenvalues of the Cartan generators of a given gauge group correspond to the quantum numbers commonly used in particle physics.). In $SU(5)$ the Cartan generators can be written as diagonal $5\times 5$ matrices with trace zero. (In $SU(5)$ is the set of $5 \times 5$ matrices $U$ with determinant $1$ that fulfil $U^\dagger U = 1$. For the generators $T_a$ this means $\text{det}(e^{i \alpha_a T_a})=e^{i \alpha_a \text{Tr}(T_a)} \stackrel{!}{=}1$. Therefore $Tr(T_a) \stackrel{!}{=} 0$) Therefore we have
\begin{align}
\text{Tr}(Q)&= \text{Tr} \begin{pmatrix} Q(\nu_L) & 0 & 0 & 0 &0 \\ 0 & Q(e_L) & 0 & 0 &0 \\ 0 & 0 & Q((d_R^c)_{\text{red}}) & 0 &0\\ 0 & 0 & 0 & Q((d_R^c)_{\text{blue}})&0\\ 0 & 0 & 0 & 0 &Q((d_R^c)_{\text{green}}) \end{pmatrix} \stackrel{!}{=} 0 \notag \\
&\rightarrow Q(\nu_L) + Q(e_L) + 3Q(d_R^c) \stackrel{!}{=} 0 \notag \\
&\rightarrow Q(d_R^c) \stackrel{!}{=} -\frac{1}{3} Q(e_L) \, .
\end{align}
Analogously, we can derive a relation between $e_R^c$, $u_L$ and $u_R^c$. Thus $Q_{\text{proton}}+Q_{\text{electron}}= \mathcal{O}(10^{-20})$ is no longer a miracle, but rather a direct consequence of of the embedding of $G_{SM}$ in an enlarged gauge symmetry.
### Coupling Strengths
The standard model contains three gauge couplings, which are very different in strength. Again, this is not a real problem of the standard model, because we can simply put these values in by hand. However, GUTs provide a beautiful explanation for this difference in strength. A simple group $G_{GUT}$ implies that we have only one gauge coupling as long as $G_{GUT}$ is unbroken. The gauge symmetry $G_{GUT}$ is broken at some high energy scale in the early universe. Afterwards, we have three distinct gauge couplings with approximately equal strength. The gauge couplings are not constant, but depend on the energy scale. This is described by the renormalization group equations (RGEs). The RGEs for a gauge coupling depend on the number of particles that carry the corresponding charge. Gauge bosons have the effect that a given gauge coupling becomes stronger at lower energies and fermions have the opposite effect. The adjoint of $SU(3)$ is $8$-dimensional and therefore we have $8$ corresponding gauge bosons. In contrast the adjoint of $SU(2)$ is $3$-dimensional and thus we have $3$ gauge bosons. For $U(1)$ there is only one gauge boson. As a result for $SU(3)$ the gauge boson effect dominates and the corresponding gauge coupling becomes stronger at lower energies. For $SU(2)$ the fermion and boson effect almost cancel each other and thus the corresponding gauge coupling is approximately constant. For $U(1)$ the fermions dominate and the $U(1)$ gauge coupling becomes much weaker at low energies. This is shown schematically in the figure below. This way GUTs provide an explanation why strong interactions are strong and weak interactions are weak.
Another interesting aspect of the renormalization group evolution of the gauge couplings is that there is a close between the GUT scale and the proton lifetime . Thus proton decay experiments yield directly a bound on the GUT scale $M_{GUT} \gtrsim 10^{15}$ GeV. On the other hand we can use the measured values of the gauge couplings and the standard model particle content to compute how the three standard model gauge couplings change with energy. Thus we can approximate the GUT scale as the energy scale at which the couplings become approximately equal. The exact scale depends on the details of the GUT model, but the general result is a very high scale, which is surprisingly close to the value from proton decay experiments. This is not a foregone conclusion. With a different particle content or different measured values of the gauge coupling this calculation could yield a much lower scale and this would be a strong argument against GUTs. In addition, the gauge couplings could run in the “wrong direction” as shown in the figure. The fact that the gauge coupling run sufficiently slow and become approximately equal at high energies are therefore hints in favor of the GUT idea.
### Further Postdictions
In addition to the “classical” GUT postdictions described in the last two sections, I want to mention two additional postdictions:
• A quite generic implication of grand unification small neutrino masses through the type-1 seesaw mechanism. Models based on the popular $SO(10)$ or $E_6$ groups contain automatically a right-handed neutrino $\nu_R$. As a result of the breaking chain this standard model singlet $\nu_R$ gets a superheavy mass $M$. After the last breaking step $G_{SM}\rightarrow SU(3)_C \times U(1)_Y$ the right-handed and left-handed neutrinos mix. This yields a surpressed mass of the left-handed neutrino of order $\frac{m^2}{M}$, where $m$ denotes a typical standard model mass.
• GUTs provide a natural framework to explain the observed matter-antimatter asymmetry in the universe. As already noted above a general implication of GUTs is that protons are no longer stable. Formulated differently, GUTs allow baryon number-violating interactions. This is one of three central ingredients, known as Sakharov condition, needed to produce more baryons than antibaryons in the early universe. Thus, as D. V. Nanopoulos put it, “if the proton was stable it would not exist”.
## What’s next?
While the unification of spacetime symmetries was already confirmed by the measurement of the cosmological constant, so far, there is no experimental evidence for the correctness of the GUT idea. Thus the unification of internal symmetries still has to wait. However, proton decay could be detected anytime soon. When Hyper-Kamiokande will start operating the limits on proton lifetime will become one order of magnitude better and this means there is a realistic chance that we finally find evidence for Grand Unification.
This however, would by no means be the end of the road.
Arguably, it would be awesome if we could unify spacetime and internal symmetries into one large symmetry. However, there is one no-go theorem that blocked progress in this direction: the famous Coleman-Mandula theorem.
Nevertheless, no-go theorem in physics never really mean that something is impossible, only that it isn’t as trivial as one might think. There are several loopholes in the theorem, that potentially allow the unification of spacetime and internal symmetries.
At least to me it seems as Dirac was right and larger symmetries is the way to go. However, so far, we don’t know which way we should follow.
P.S. I wrote a textbook, which is, in some sense, the book I wished had existed when I started my journey in physics. It's called "Physics from Symmetry" and you can buy it, for example, at Amazon. And I'm now on Twitter too if you'd like to get updates about what I'm recently up to.
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|
https://jackmckew.dev/3d-gradient-descent-in-python.html
|
# 3D Gradient Descent in Python
Posted on Wed 26 February 2020 in Python • 40 min read
Visualising gradient descent in 3 dimensions
Building upon our terrain generator from the blog post: https://jackmckew.dev/3d-terrain-in-python.html, today we will implement a demonstration of how gradient descent behaves in 3 dimensions and produce an interactive visualisation similar to the terrain visualisation. Note that my understanding of gradient descent this does not behave in the similar manner as the gradient descent function used heavily in optimisation problems, although this does make for a demonstration.
The premise behind gradient descent is at a point in an a 'function' or array, you can determine the minimum value or maximum value by taking the steepest slope around the point till you get to the minimum/maximum. As optimising functions is one of the main premises behind machine learning, gradient descent is used to reduce computation time & resources.Image Source
### What can I use this for?¶
At it's core, gradient descent is a optimisation algorithm used to minimise a function. The benefit of gradient shines when searching every single possible combination isn't feasible, so taking an iterative approach to finding the minimum is favourable.
In machine learning, we use gradient descent to update the parameters of our model. Parameters refer weights on training data, coefficients in Linear Regression, weights in neural networks and more.
### How?¶
A way of imagining this is if you are at the top of a hill, and want to get to the bottom in the quickest way possible, if you take a step in each time in the direction of the steepest slope, you should hopefully get to the bottom a quick as possible.
### What could go wrong?¶
The common pitfalls behind gradient descent is that the algorithm can get 'stuck' within holes, ridges or plateaus meaning the algorithm converges on a local minimum, rather than the global minimum. Another problem being the step size can be difficult to estimate before calculation, in that if you take too small of steps it will take too long to converge.
## Let's get started!¶
First of all, we need to import all the packages we will need to use, then we will use the numpy array from last time which we generated with Perlin Noise. Next we will find the global maximum and minimum, and plot this all on a 2D contour plot. The maximum (highest point) is show by the red dot, while the minimum (lowest point) is shown by the yellow dot.
In [11]:
from IPython.core.display import HTML
import plotly
import plotly.graph_objects as go
import noise
import numpy as np
import matplotlib
from mpl_toolkits.mplot3d import axes3d
%matplotlib inline
In [12]:
z = world
matplotlib.pyplot.imshow(z,origin='lower',cmap='terrain')
# Find maximum value index in numpy array
indices = np.where(z == z.max())
max_z_x_location, max_z_y_location = (indices[1][0],indices[0][0])
matplotlib.pyplot.plot(max_z_x_location,max_z_y_location,'ro',markersize=15)
# Find minimum value index in numpy array
indices = np.where(z == z.min())
min_z_x_location, min_z_y_location = (indices[1][0],indices[0][0])
matplotlib.pyplot.plot(min_z_x_location,min_z_y_location,'yo',markersize=15)
Out[12]:
[<matplotlib.lines.Line2D at 0x1d927058b88>]
For our implementation in this blog post, rather than computing the gradient at each point (typical implementation), we will evaluate our array by searching through the 'neighbouring' values around a certain index. Luckily, an answer from pv on Stackoverflow had already solved this problem for us.
In [13]:
# Source: https://stackoverflow.com/questions/10996769/pixel-neighbors-in-2d-array-image-using-python
# This code by pv (https://stackoverflow.com/users/108184/pv), is to find all the adjacent values around a specific index
import numpy as np
from numpy.lib.stride_tricks import as_strided
def sliding_window(arr, window_size):
""" Construct a sliding window view of the array"""
arr = np.asarray(arr)
window_size = int(window_size)
if arr.ndim != 2:
raise ValueError("need 2-D input")
if not (window_size > 0):
raise ValueError("need a positive window size")
shape = (arr.shape[0] - window_size + 1,
arr.shape[1] - window_size + 1,
window_size, window_size)
if shape[0] <= 0:
shape = (1, shape[1], arr.shape[0], shape[3])
if shape[1] <= 0:
shape = (shape[0], 1, shape[2], arr.shape[1])
strides = (arr.shape[1]*arr.itemsize, arr.itemsize,
arr.shape[1]*arr.itemsize, arr.itemsize)
return as_strided(arr, shape=shape, strides=strides)
def cell_neighbours(arr, i, j, d):
"""Return d-th neighbors of cell (i, j)"""
w = sliding_window(arr, 2*d+1)
ix = np.clip(i - d, 0, w.shape[0]-1)
jx = np.clip(j - d, 0, w.shape[1]-1)
i0 = max(0, i - d - ix)
j0 = max(0, j - d - jx)
i1 = w.shape[2] - max(0, d - i + ix)
j1 = w.shape[3] - max(0, d - j + jx)
return w[ix, jx][i0:i1,j0:j1].ravel()
Now we will implement our function which will calculate the gradient descent of an array from a point in the array with nominated maximum number of steps & size of step.
This works by:
• extracting a smaller subset array of all the values around a specified point (in this post we will start a the maximum point),
• locating the minimum in this array (inferring the greatest slope from the current point),
• move our current location to the minimum
• repeat till the point stays the same as previous step
We also store of all our previous steps in gradient descent in a list such that we can use this to plot later on.
In [14]:
from dataclasses import dataclass
@dataclass
class descent_step:
"""Class for storing each step taken in gradient descent"""
value: float
x_index: float
y_index: float
# Initial point to start gradient descent at
step = descent_step(array[y_start][x_start],x_start,y_start)
# Store each step taken in gradient descent in a list
step_history = []
step_history.append(step)
# Plot 2D representation of array with startng point as a red marker
if plot:
matplotlib.pyplot.imshow(array,origin='lower',cmap='terrain')
matplotlib.pyplot.plot(x_start,y_start,'ro')
current_x = x_start
current_y = y_start
# Loop through specified number of steps of gradient descent to take
for i in range(steps):
prev_x = current_x
prev_y = current_y
# Extract array of neighbouring cells around current step location with size nominated
neighbours=cell_neighbours(array,current_y,current_x,step_size)
# Locate minimum in array (steepest slope from current point)
next_step = neighbours.min()
indices = np.where(array == next_step)
# Update current point to now be the next point after stepping
current_x, current_y = (indices[1][0],indices[0][0])
step = descent_step(array[current_y][current_x],current_x,current_y)
step_history.append(step)
# Plot each step taken as a black line to the current point nominated by a red marker
if plot:
matplotlib.pyplot.plot([prev_x,current_x],[prev_y,current_y],'k-')
matplotlib.pyplot.plot(current_x,current_y,'ro')
# If step is to the same location as previously, this infers convergence and end loop
if prev_y == current_y and prev_x == current_x:
print(f"Converged in {i} steps")
break
return next_step,step_history
Next, to ensure that we get to our global minimum in the end, we loop through each step size until we reach a step size large enough to reach the global minimum.
Note that this is possibly not feasible in some implementations of gradient descent, but for demonstration purposes we will use it here
We then randomise a point for the algorithm to start at and then compute the gradient descent until we have a large enough step size to reach the global minimum (see below for a step size smaller than the required size).
In [15]:
np.random.seed(42)
global_minimum = z.min()
indices = np.where(z == global_minimum)
print(f"Target: {global_minimum} @ {indices}")
step_size = 0
found_minimum = 99999
# Random starting point
start_x = np.random.randint(0,50)
start_y = np.random.randint(0,50)
# Increase step size until convergence on global minimum
while found_minimum != global_minimum:
step_size += 1
print(f"Optimal step size {step_size}")
print(f"Steps: {steps}")
Target: -0.0994970053434372 @ (array([16], dtype=int64), array([0], dtype=int64))
Converged in 9 steps
Converged in 5 steps
Converged in 7 steps
Converged in 6 steps
Converged in 4 steps
Converged in 4 steps
Converged in 3 steps
Converged in 3 steps
Converged in 3 steps
Converged in 5 steps
Optimal step size 10
Converged in 5 steps
Steps: [descent_step(value=0.10347005724906921, x_index=38, y_index=28), descent_step(value=0.007558110170066357, x_index=28, y_index=38), descent_step(value=-0.03461135923862457, x_index=18, y_index=39), descent_step(value=-0.03682023286819458, x_index=8, y_index=35), descent_step(value=-0.07587684690952301, x_index=0, y_index=26), descent_step(value=-0.0994970053434372, x_index=0, y_index=16), descent_step(value=-0.0994970053434372, x_index=0, y_index=16)]
Moving from each point to the next is typically represented as a vector, in our case, this will be in 3D space. In 2D space, you would use a quiver plot to show this, in 3D, you can use a Cone Plot. To calculate the vector between each of our steps, we again turn to Stackoverflow from an answer by teclnol.
In [16]:
# Source https://stackoverflow.com/questions/51272288/how-to-calculate-the-vector-from-two-points-in-3d-with-python
def multiDimenDist(point1,point2):
#find the difference between the two points, its really the same as below
deltaVals = [point2[dimension]-point1[dimension] for dimension in range(len(point1))]
runningSquared = 0
#because the pythagarom theorm works for any dimension we can just use that
for coOrd in deltaVals:
runningSquared += coOrd**2
return runningSquared**(1/2)
def findVec(point1,point2,unitSphere = False):
#setting unitSphere to True will make the vector scaled down to a sphere with a radius one, instead of it's orginal length
finalVector = [0 for coOrd in point1]
for dimension, coOrd in enumerate(point1):
#finding total differnce for that co-ordinate(x,y,z...)
deltaCoOrd = point2[dimension]-coOrd
finalVector[dimension] = deltaCoOrd
if unitSphere:
totalDist = multiDimenDist(point1,point2)
unitVector =[]
for dimen in finalVector:
unitVector.append( dimen/totalDist)
return unitVector
else:
return finalVector
Finally, we build a function that can generate 3D plots with Plotly, similar to the terrain visualisation with the steps in gradient descent visualised as cones and lines.
In [17]:
def generate_3d_plot(step_history):
# Initialise empty lists for markers
step_markers_x = []
step_markers_y = []
step_markers_z = []
step_markers_u = []
step_markers_v = []
step_markers_w = []
for index, step in enumerate(step_history):
step_markers_x.append(step.x_index)
step_markers_y.append(step.y_index)
step_markers_z.append(step.value)
# If we haven't reached the final step, calculate the vector between the current step and the next step
if index < len(steps)-1:
vec1 = [step.x_index,step.y_index,step.value]
vec2 = [steps[index+1].x_index,steps[index+1].y_index,steps[index+1].value]
result_vector = findVec(vec1,vec2)
step_markers_u.append(result_vector[0])
step_markers_v.append(result_vector[1])
step_markers_w.append(result_vector[2])
else:
step_markers_u.append(0.1)
step_markers_v.append(0.1)
step_markers_w.append(0.1)
# Include cones at each marker to show direction of step, scatter3d is to show the red line between points and surface for the terrain
fig = go.Figure(data=[
go.Cone(
x=step_markers_x,
y=step_markers_y,
z=step_markers_z,
u=step_markers_u,
v=step_markers_v,
w=step_markers_w,
sizemode="absolute",
sizeref=2,
anchor='tail'),
go.Scatter3d(
x=step_markers_x,
y=step_markers_y,
z=step_markers_z,
mode='lines',
line=dict(
color='red',
width=2
)),
go.Surface(colorscale=terrain,z=world,opacity=0.5)])
# Z axis is limited to the extent of the terrain array
fig.update_layout(
scene = dict(zaxis = dict(range=[world.min(),world.max()],),),)
return fig
# Generate 3D plot from previous random starting location
fig = generate_3d_plot(steps)
Out[17]:
To demonstrate how gradient descent can be stuck, by setting the gradient descent algorithm to start a the maximum point with a step size of 5, we can see how it falls straight into the nearest ditch (local minima) but then cannot get out of it.
In [18]:
found_minimum,steps = gradient_descent_3d(z,max_z_x_location,max_z_y_location,step_size=5,plot=True)
fig = generate_3d_plot(steps)
Converged in 3 steps
|
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|
https://tex.stackexchange.com/questions/187725/how-to-install-mathtools-package
|
# How to install mathtools package?
I'm new to Latex so forgive me if the questions are dumb...
I was trying to right left-top corner superscript, someone recommended mathtools package on this forum: Left and right subscript / superscript.
So I downloaded mathtools.zip from CTAN, unzip it, there's an "mathtools.dtx". In the package there are documents but none talked about how to install, I fancy the installation is just too primary to real Latex users.
OK, then, there's still another thread here explained the steps: How can I manually install a package on MiKTeX (Windows) . So here I follow
1. I ran "tex XXX.dtx" (there's no *.ins files) on all the .dtx files under the extracted folder, that includes: breqn.dtx, flexisym.dtx, mathstyle.dtx, empheq.dtx, mathtools.
2. Then I created a folder "C:\athos\localtexmf\mathtools" and put all the new files in.
3. Then I go to "Windows -> Start -> Programs -> MikTex 2.9 -> Maintenance (Admin) -> Settings (Admin) "; in "Roots" tab I added path "C:\athos\localtexmf"; in "General" tab I clicked "Refresh FNDB" and then clicked "OK" to close it.
4. I restarted my WinEdt, added "\usepackage{mathtools}" under "\documentclass..."; and added "test $\prescript{14}{2}{\mathbf{C}}$ " in the main body.
After that when I try to "MikTex", the error still comes up: "The required file tex\latex\mh\mathtools\sty is missing. It is a part of the following pakage: mh . The package will be installed from ..."
Seems the folder "C:\athos\localtexmf\mathtools" is not captured by MikTex?
Then in the error message dialog, I choose "Change", choose "Package shall be installed from a directory", click "Next", choose ""C:\athos\localtexmf\" or "C:\athos\localtexmf\mathtools", in either try it says "Not a local package repository".
What shall I do?
I'm on Microsoft Windows XP Prefessional SP3, WinEdt 8 (Build: 20140613 (v. 8.2) - 32-bit), and MikTex 2.9.
• You should install mh from MiKTeX's package manager, you'll have no problem. Why do you want to install manually a package that's in the distribution? Jul 3, 2014 at 1:52
• @Bernard let's say rookies shoot their foot :p Jul 3, 2014 at 1:58
• Hi. I try to install the mathtools from mh bundles in the package manager, but it shows 'Error response from server: 404' . May I know how to solve this problem? Aug 26, 2014 at 4:06
• @idonknow my problem was that in my company there was a proxy, it works perfect for browsers but seems the TeX update does not recognize it. Not knowing how to config TeX proxy, I did the update at home , where my WiFi has no proxy Aug 26, 2014 at 13:56
• In August 2014, the mh bundle of packages was broken up into two parts. The advice sought (and given) in this posting about installing the mh bundle is no longer applicable for versions of TeXLive and MikTeX more recent than August 2014.
– Mico
Jul 6, 2015 at 22:59
If you have installed MikTeX 2.9 (on Windows) is very easy. You can go to
Home->Programs->MiKTeX 2.9->Maintenance (Admin)->Package Manager (Admin)
Alternative path to admin exe file C:\Program Files (x86)\MiKTeX 2.9\miktex\bin
or without (Admin) if you want to install the new packages in a local directory. There you can choose any package and to install it by clicking in + button. In case of the mathtools package you can find it in the mh bundle (it appears in the list of installable packages) and provides a series of packages designed to enhance the appearance of documents containing a lot of mathematics (mathtools included).
## Edit
From August 19'th 2014 the mh bundle has disappeared in MiKTeX, now it's possible to find the mathtools package separately.
• It started to download and failed : "connect failed in tcp_connect()" -- I'm behind a firewall, may I check how to set the proxy? Jul 3, 2014 at 2:04
• @athos Try again, and make sure you have a good internet connection or choose another download server (mirror). Jul 3, 2014 at 2:10
• do you mean that i don't need to set up the proxy server ip etc? mmm, if so i guess the reason is the proxy prohibited some files (.exe or too big file), let me try it at home. Jul 3, 2014 at 2:23
• So... no longer possible to use mathtools at all? Your Oct 1, 2014 edit is not very clear to a tex noob. Oct 6, 2014 at 23:10
• I can use tool mathtool with MiKTeX. In my package manager it is listed with the packaging date 2014-08-19 and I can run it! So edit 2 seems to be obsolet ... Oct 14, 2014 at 14:48
@romkyns
I had the same problem with mathtools and MiKTeX today, the same initial error about the missing .sty file. Going to:
MiKTeX 2.9\miktex\bin
I ran mpm_mfc_admin, went to the Repository tab at the top and clicked synchronise. mathtools is now in my package list and I can confirm it works; no more missing .sty file.
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|
https://iwaponline.com/wst/article-abstract/71/3/412/18799/Photodegradation-of-sulfonamide-antimicrobial?redirectedFrom=fulltext
|
This study used Na2S2O8, NaBrO8 and H2O2 to degrade sulfadiazine (SDZ), sulfamethizole (SFZ), sulfamethoxazole (SMX) and sulfathiazole (STZ) under ultraviolet (UV) irradiation. The initial concentration of sulfonamide and oxidant in all experiments was 20 mg/L and 5 mM, respectively. The degradation rate for sulfonamides satisfies pseudo-first-order kinetics in all UV/oxidant systems. The highest degradation rate for SDZ, SFZ, SMX and STZ was in the UV/Na2S2O8, UV/NaBrO3, UV/Na2S2O8 and UV/H2O2 system, respectively. In the UV/Na2S2O8 system, the photodegradation rate of SDZ, SFZ, SMX and STZ was 0.0245 min−1, 0.0096 min−1, 0.0283 min−1 and 0.0141 min−1, respectively; moreover, for the total organic carbon removal rate for SDZ, SFZ, SMX and STZ it was 0.0057 min−1, 0.0081 min−1, 0.0130 min−1 and 0.0106 min−1, respectively. Experimental results indicate that the ability of oxidants to degrade sulfonamide varied with pollutant type. Moreover, UV/Na2S2O8 had the highest mineralization rate for all tested sulfonamides.
You do not currently have access to this content.
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https://mom6.readthedocs.io/en/dev-gfdl/api/generated/pages/Vertical_Diffusion.html
|
# Vertical Diffusion¶
Vertical diffusion of tracers
The MOM6 tracer registry takes care of the tracer advection as well as horizontal diffusion, but it is up to each individual tracer package to define its own vertical diffusion.
|
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|
http://mathoverflow.net/questions/14805/when-do-equivariant-sheaves-on-a-formal-neighborhood-extend
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# When do equivariant sheaves on a formal neighborhood extend?
Suppose that $X$ is a variety (in char 0) with an action of an affine algebraic group $G$. Let $Y \subset X$ be a subvariety fixed by $G$--the action map agrees with projection upon restriction to $Y$. Let $\widehat{Y}$ be the formal completion of $X$ along $Y$. Furthermore let $\widehat{G}$ be the the completion of $G$ at the identity, viewed as a formal group. There is a restriction functor $j^*$ from the $Qcoh^G(X)$, the category of $G$-equivariant quasicoherent sheaves on $X$, to $Qcoh^{\widehat{G}}(\widehat{Y})$, the category of $\widehat{G}$-equivariant quasicoherent sheaves on $\widehat{Y}$.
1) Is this situation considered in the literature? Where?
2) What tools are available to control this functor? How might one describe the essential image?
Although curious about this general package, I specifically care about the case $G =\mathbb{G}_m$.
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http://dsp.stackexchange.com/questions/6192/interpretation-of-a-periodogram-the-effect-of-window-sizes
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# Interpretation of a periodogram: the effect of window sizes
I am specifically working on a categorical time series of best n number of parallel threads (for n=1..16) for a multicore workstation. I constructed the Walsh-Fourier periodogram for size 2^10 and 2^11 data points. Both of the images are with the first value removed to allow a scaled image. The difference is dramatic as you can see.
My naive interpretation is that there is something stationary going on with the $2^{11}$ range that isn't happening in the $2^{10}$ range. In particular my data covers minute intervals and if I am looking for background programs that will effect the the best thread policy, if they are scheduled nightly (antivirus, back-up etc) then in terms of 1440 minutes=1 day they will fall within $2^{11}$ minutes because $2^{10}<1440<2^{11}$. Am I making the correct assumption here?
Because I am too new on this particular stackexchange I am not allowed to post the periodograms but they are hosted here.
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When you say 2^10 or 2^11, you are talking about the number of samples pre-FFT correct, or are you talking about FFT size? Also, can you please scale the images properly on both axes. – Mohammad Dec 6 '12 at 6:16
I'm a little concerned that I am in over my head but by 2^10 and 2^11, I meant number of samples. However I have a much larger sample size, but since I thought I might use a fast Walsh-Hadamard transform I got used to sub-selecting sample sizes as powers of two to fit the algorithm. Since I'm not yet using that, and my computer is fast enough, I should stick to a 1440 sample size (1 day). Also I'm embarrassed to say, I don't know what is wrong with my axes scales. – Meadowlark Bradsher Dec 6 '12 at 7:10
I realized I had neglected to average my periodograms. When they were averaged they both looked very similar. However I still don't know the explanation for the difference between those two un-averaged periodograms. It doesn't appear adequately random. – Meadowlark Bradsher Dec 6 '12 at 8:52
Yes, the averaging is crucial to a smoothed periodogram, or Bartletts Method. Make sure you do that. I am still not clear as to the sizes in question here. Can you put some images of the total signal, its length, the FFT size, etc etc. This will make the problem more easily attacked by everyone. – Mohammad Dec 6 '12 at 15:46
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http://mathhelpforum.com/algebra/161138-word-problem-help.html
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1. ## Word problem help,
The slurry that leaves the reactor on a plant manufacturing phosphoric acid contains 20% w/w solids together with a solution of phosphoric and sulphuric acids
In water. The solution consists of 38% w/w H3PO4 , 2.5% w/w H2SO4 , the
Remainder being water.
The slurry is filtered and all the solids are removed in the filter cake. The filter
cake that is produced contains 50% w/w solids and 50% w/w liquid. The filter
Cake is then re-slurried with water and subjected to a second filtration. The second
Filter cake contains 55% w/w solids and 45% w/w liquid. In this case also, all the
Solids are present in the filter cake.
If 1% of the phosphoric acid present in the initial slurry is retained in the liquid
Trapped in the second filter cake then, using a basis of 1000 kg initial slurry,
Calculate:
(a) The composition of the first filter cake,
(b) The composition of the second fillter cake,
(c) The amount of water used to reslurry the first filter cake.
I have drawn a diagram, and I still not sure how to calculate the composition of the first filtration,
From the question it says that the slurry contains 20% solids, so of the 1000kg, 200kg is solid and the rest must be liquid, of which 38% is H3PO4 and 2.5% is H2SO4. Which means 59.9% must be water.
Attached Thumbnails
2. of the 1000kg, 200kg is solid and the rest must be liquid, of which 38% is H3PO4 and 2.5% is H2SO4. Which means 59.9% must be water.
It's 59.5% that is the percentage of water.
First, you can calculate the mass of H3PO4 in the original 1000kg slurry and thus find 1% of the phosphoric acid present in the initial slurry. This will be used later.
It is not clear from the problem text in what proportions the components of the solution are retained by the filtration. I mean, there is 2.5% w/w H2SO4 in the solution, but filtration theoretically may retain all H2SO4 and some water, but none of H3PO4. I don't think it is possible to calculate anything without this information.
Most likely, however, filtration preserves the ratio of the solution components. Since the solids account for 50% of the first cake, the cake's mass is 400kg, and the solution's mass is also 200kg. Using the proportions above, you can find the mass of each solution component.
After that let x kg of water has been added. Then the concentrations of the three components of the liquid solution in the new slurry can be expressed through x.
In the second cake, the same 200kg of solids constitute 55%, so you know the mass of the cake and the mass of its liquid part. Therefore, using the concentration of H3PO4 you found, you can calculate the mass of H3PO4 as an expression of x. Finally, it is equated to the 1% of the H3PO4in the initial slurry that you found in the beginning to form an equation for x.
3. Originally Posted by emakarov
It's 59.5% that is the percentage of water.
First, you can calculate the mass of H3PO4 in the original 1000kg slurry and thus find 1% of the phosphoric acid present in the initial slurry. This will be used later.
It is not clear from the problem text in what proportions the components of the solution are retained by the filtration. I mean, there is 2.5% w/w H2SO4 in the solution, but filtration theoretically may retain all H2SO4 and some water, but none of H3PO4. I don't think it is possible to calculate anything without this information.
Most likely, however, filtration preserves the ratio of the solution components. Since the solids account for 50% of the first cake, the cake's mass is 400kg, and the solution's mass is also 200kg. Using the proportions above, you can find the mass of each solution component.
After that let x kg of water has been added. Then the concentrations of the three components of the liquid solution in the new slurry can be expressed through x.
In the second cake, the same 200kg of solids constitute 55%, so you know the mass of the cake and the mass of its liquid part. Therefore, using the concentration of H3PO4 you found, you can calculate the mass of H3PO4 as an expression of x. Finally, it is equated to the 1% of the H3PO4in the initial slurry that you found in the beginning to form an equation for x.
Thank you,
I also quite confused with the wording of the problem, because when it says all of the solids is removed, does that mean, the filtration contains 800kg of the liquid, which is than separated into 50% solid 50% liquid? which would mean, there is still the original 200kg of solids that is not in the filter.
before filtration:
mass of solid = 0.20 x 1000 = 200kg
mass of liquid = 0.80x1000= 800kg
of that 800kg liquid:
304kg H3PO4
20kg-H2S04
479.2kg-H20
right, now how do I work out the proportions that is in the first filtration?
The correct answers for part a is: 200kg solids, 76kg H3PO4, 5kg H2S04, and 119kg of H20
Is it half of 800kg is liquid and half solid?
800 x 0.5 = 400kg than work out the percentages of acid in that amount of liquid, which does not give the correct answer.
How did you work out that the cake's mass is 400kg and that the solution's mass is 200kg?
4. I also quite confused with the wording of the problem, because when it says all of the solids is removed, does that mean, the filtration contains 800kg of the liquid, which is than separated into 50% solid 50% liquid?
The first cake contains all the solids and some of the liquid. Namely, 200kg liquid of the original 800kg (see below).
of that 800kg liquid:
304kg H3PO4
20kg-H2S04
479.2kg-H20
Again, there is 59.5% of water, which is 476kg.
Is it half of 800kg is liquid and half solid?
No, 800kg is completely liquid.
How did you work out that the cake's mass is 400kg and that the solution's mass is 200kg?
Since all of solids (200kg) are in the first cake and they constitute 50% of the cake, the cake is 400kg and its liquid part is 400 - 200 = 200kg.
right, now how do I work out the proportions that is in the first filtration?
Of the original 800kg liquid, 200kg is still in the first cake. This is 1/4 of the liquid in the original slurry. If the concentrations of H2S04, H3PO4 and H2O in the liquid part of the slurry and in the liquid part of the cake are the same, you can multiply 304, 20 and 476 by 1/4 to find the component masses of the liquid part of the cake. This is the same as the answer you have.
5. Since all of solids (200kg) are in the first cake and they constitute 50% of the cake, the cake is 400kg and its liquid part is 400 - 200 = 200kg.
Sorry, still a little confused, Is that 400kg of liquid and solid? So the mass of the first filter cake is 400kg? How do you know this?
to work out the amount of solid present in the first filter cake; you could just set up this equation.
200kg = 0.5S
solving for s = 400kg
wont you do the same for the liquid?
800kg = 0.5L
L = 1600kg
I know this does not work, because than the total is more than 1000kg, but as the question says 50% of liquid and solid, why are you not just taking 50% of the original masses?
Thank you
6. Actually, I understand now why is it 200kg, liquid and 200kg solid. For the second part, we know that 55% is the orignal 200kg of solid, but from that how would I know the mass of the liquid? is it 0.45 x 800 = 360 ?
7. Let C2 be the mass of the second cake. We know that 55% of it is 200kg (solids). Therefore, 0.55 * C2 = 200, from where C2 = 200 / 0.55 = 364 kg (approximately). So, the second cake has 364 - 200 = 164 kg of liquid.
Now suppose that x kg of water was added during re-slurrying. Then the mass of liquid in the second slurry is (200 + x) kg. Since there was 76kg of H3PO4 in the second cake, the concentration of H3PO4 in the liquid part of the second slurry is 76 / (200 + x). H3PO4 has the same concentration in the liquid part of the second cake, so the second cake has 164 * 76 / (200 + x) kg of H3PO4. Finally, we are told that this is 1% of the amount of H3PO4 in the original slurry, or 304kg. From here, x can be found.
8. Originally Posted by emakarov
Let C2 be the mass of the second cake. We know that 55% of it is 200kg (solids). Therefore, 0.55 * C2 = 200, from where C2 = 200 / 0.55 = 364 kg (approximately). So, the second cake has 364 - 200 = 164 kg of liquid.
Now suppose that x kg of water was added during re-slurrying. Then the mass of liquid in the second slurry is (200 + x) kg. Since there was 76kg of H3PO4 in the second cake, the concentration of H3PO4 in the liquid part of the second slurry is 76 / (200 + x). H3PO4 has the same concentration in the liquid part of the second cake, so the second cake has 164 * 76 / (200 + x) kg of H3PO4. Finally, we are told that this is 1% of the amount of H3PO4 in the original slurry, or 304kg. From here, x can be found.
Hello,
Can you please post a full solution for this problem, as I am not able to follow through. I don't quite understand, why do you not multiply by the amount that the question has given?
if you could please start from the beginning.
Thank you.
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http://firewords.net/definitions/moisture_of_extinction.htm
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# Moisture of extinction [Extinction moisture content]
n. The dead fuel moisture content at which the Rothermel’s (1972) surface fire spread model predicts spread rate will fall to zero.
• Discussion
Moisture of extinction is a parameter of fire behavior fuel models. The use of the term in the Rothermel (1972) surface fire model is misleading because it is not designed to predict extinction; rather, it is included as a way to predict the effect of moisture content on fire behavior (through the moisture damping coefficient). The greater the difference between actual moisture content and the moisture of extinction, the smaller the moisture damping coefficient and therefore the greater the spread rate.
•
Fuel moisture content is most commonly expressed as the mass of water as a fraction or percentage of oven-dry mass. The term moisture fraction is sometimes used when moisture content is expressed as a fraction. Multiply moisture fraction by 100 to get moisture content as a percentage.
•
• Rothermel, R.C. 1972. A mathematical model for predicting fire spread in wildland fuels. Res. Pap. INT-115. Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Forest and Range Experiment Station. 42 p.
• Notes
• Joe Scott, Research Forester
Systems for Environmental Management
• August 2007
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https://www.physicsforums.com/threads/standard-error.333378/
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Homework Help: Standard Error
1. Aug 29, 2009
needhelp83
Weight of turkeys is normally distributed with a standard deviation of 9 pounds. Farmer Jones samples 25 turkeys from his farm in order to estimate their mean weight. What is the probability that his sampling error will not exceed 2 pounds?
I hate this because I can't figure out what formula to use? I found one for the standard error of the mean where
$$SE = \frac{s}{\sqrt{n}}$$
This gives me the answer of 1.8. Now if I figure out the probability of exceeding 2 lbs how do I determine this with my given answer?
2. Aug 29, 2009
You know the weights are normally distributed, correct? You know the value of $$\sigma$$ but not $$\mu$$, so using the normal distribution is out of the question.
Here's a hint masquerading as a question: what do you know about the distribution of the sample variance when you sample from a normal distribution?
3. Aug 29, 2009
needhelp83
I am not sure if I am answering exactly what you are looking for, but if you know the standard deviation you will know the standard variance since it is sd squared. What this exactly tells me about the distribution I am unsure.
4. Aug 30, 2009
needhelp83
Ok...sorry, but I am still not understanding what exactly I am supposed to see with this problem. Any help?
5. Aug 31, 2009
needhelp83
Any help, anybody? More than happy to figure it out if just given a push in right direction.
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http://mathoverflow.net/feeds/question/103152
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Determinant of integer lattice basis of $L=\{(x_1,\ldots,x_n): a_1x_1+\cdots+a_nx_n=0\}$ - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T07:01:44Z http://mathoverflow.net/feeds/question/103152 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/103152/determinant-of-integer-lattice-basis-of-l-x-1-ldots-x-n-a-1x-1-cdotsa-n Determinant of integer lattice basis of $L=\{(x_1,\ldots,x_n): a_1x_1+\cdots+a_nx_n=0\}$ Victor Wang 2012-07-26T03:44:45Z 2012-07-26T03:44:45Z <blockquote> <p><strong>Question:</strong> Suppose <code>$\{v_1,\ldots,v_{n-1}\}$</code> is an integer basis for the lattice <code>$$L=\{(x_1,\ldots,x_n)\in\mathbb{Z}^n: a_1x_1+\cdots+a_nx_n=0\},$$</code> where the $a_i$ are fixed nonzero integers. Is the volume <code>$V(P)=\det(L)$</code> (see <a href="http://numbertheoryreadinggroup.wordpress.com/2008/04/24/geometry-of-numbers-lecture-2-determinant-of-the-lattice-and-the-fundamental-parallelepiped-lee/" rel="nofollow">this</a> for a proof that they are equal) of its fundamental parallelotope <code>$P=\{t_1v_1+\cdots+t_{n-1}v_{n-1} \mid t_i\in[0,1)\}$</code> necessarily equal to <code>$$\frac{\sqrt{a_1^2+\cdots+a_n^2}}{\gcd(a_1,\ldots,a_n)}?$$</code></p> </blockquote> <p>I used the case $n=3$ along with <a href="http://en.wikipedia.org/wiki/Minkowski%27s_theorem" rel="nofollow">Minkowski's theorem</a> (in the <a href="http://en.wikipedia.org/wiki/Geometry_of_numbers" rel="nofollow">geometry of numbers</a>) to solve the following <a href="http://www.math.u-szeged.hu/~mmaroti/schweitzer/schweitzer-2000-eng.pdf" rel="nofollow">Miklos problem</a> from 2000:</p> <blockquote> <p>Let <code>$a<b<c$</code> be positive integers. Prove that there exist integers <code>$x,y,z$</code>, not all zero, such that <code>$ax+by+cz=0$</code> and <code>$\max(|x|,|y|,|z|)\le 1+\frac{2}{\sqrt3}\sqrt{c}$</code>, and show that the constant <code>$\frac{2}{\sqrt3}$</code> cannot be improved.</p> </blockquote> <p>However, I was only able to find a brute force proof for this special case (see lemma 1 in my AoPS post <a href="http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2471417#p2471417" rel="nofollow">here</a>), and I'm not sure if it's as easy for larger values of $n$.</p> <p>But I'm pretty sure this should be true in general (I've tried several cases for $n=4$ and $n=5$), so I would appreciate it if someone could give a (clean?) proof, reference, or counterexample. Thanks!</p>
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https://rd.springer.com/article/10.1007%2Fs00500-018-3547-5
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Soft Computing
, Volume 23, Issue 1, pp 197–210
# Duality-based branch–bound computational algorithm for sum-of-linear-fractional multi-objective optimization problem
• Deepika Agarwal
• Pitam Singh
• Deepak Bhati
• Saru Kumari
• Fellow of IEEE and Fellow of SCS
Methodologies and Application
## Abstract
Optimizing the sum-of-fractional functions under the bounded feasible space is a very difficult optimization problem in the research area of nonlinear optimization. All the existing solution methods in the literature are developed to find the solution of single-objective sum-of-fractional optimization problems only. Sum-of-fractional multi-objective optimization problem is not attempted to solve much by the researchers even when the fractional functions are linear. In the present article, a duality-based branch and bound computational algorithm is proposed to find a global efficient (non-dominated) solution for the sum-of-linear-fractional multi-objective optimization (SOLF-MOP) problem. Charnes–Cooper transformation technique is applied to convert the original problem into non-fractional optimization problem, and equivalence is shown between the original SOLF-MOP and non-fractional MOP. After that, weighted sum method is applied to transform MOP into a single-objective problem. The Lagrange weak duality theorem is used to develop the proposed algorithm. This algorithm is programmed in MATLAB (2016b), and three numerical illustrations are done for the systematic implementation. The non-dominance of obtained solutions is shown by comparison with the existing algorithm and by taking some feasible solution points from the feasible space in the neighborhood of obtained global efficient solution. This shows the superiority of the developed method.
## Keywords
Multi-objective programming Sum-of-ratio Multi-objective linear fractional programming Duality Branch and bound
## Notes
### Acknowledgements
This work is financially supported by DST-SERB, Government of India, Vide Sanction No. SB/EMEQ - 049/2014. Also, Authors would like to acknowledge the help of Mr. Abhishek Chaurasiya, B.Tech. final year student of MNNIT Allahabad for his help in developing the MATLAB code of the method.
### Conflict of interest
All the authors declare that they have no conflict of interest.
### Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
## References
1. Benson HP (2001) Global optimization algorithm for the non-linear sum of ratios problem. J Math Anal Appl 263:301–315
2. Benson HP (2002) Global optimization algorithm for the non-linear sum of ratios problem. J Optim Theory Appl 112(1):1–29
3. Benson HP (2007a) A simplicial branch and bound duality-bounds algorithm for the linear sum-of-ratio problem. Eur J Oper Res 182:597–611
4. Benson HP (2007b) Solving sum of ratios fractional programs via concave minimization. J Optim Theory Appl 135:1–17
5. Benson HP (2010) Branch-and-bound outer approximation algorithms for sum-of-ratios fractional programs. J Optim Theory Appl 146:1–18
6. Bhati D, Singh P (2016) Branch and bound computational method for multi-objective linear fractional optimization problem. Neural Comput Appl. Google Scholar
7. Chen HJ (2009) Generic algorithm for generalized fractional programming. J Optim Theory Appl 141:93–105
8. Freund RW, Jarre F (2001) Solving the sum-of-ratios problem by an interior-point method. J Glob Optim 19:83–102
9. Gao Y, Jin S (2013) A global optimization algorithm for sum of linear ratios problem. J Appl Math.
10. Horst R, Tuy H (1996) Global optimization: deterministic approaches. Springer, Berlin
11. Jaberipour M, Khorram E (2010) Solving the sum-of-ratios problem by a harmony search algorithm. J Comput Appl Math 234:733–742
12. Jiao HW, Liu SY (2015) A practicable branch and bound algorithm for sum of linear ratios problem. Eur J Oper Res 243:723–730
13. Jiao H, Shen P (2007) A note on the paper global optimization of non-linear sum of ratios. Appl Math Comput 188:1812–1815
14. Jin L, Hou XP (2014) Global optimization for a class non-linear sum of ratios problems. Probl Eng. Google Scholar
15. Kanno H, Tsuchiya K, Yamamoto R (2007) Minimization of ratio of function defined as sum of the absolute values. J Optim Theory Appl 135:399–410
16. Qu SJ, Zhang KC, Zhao JK (2007) An efficient algorithm for globally minimizing sum of quadratics ratios problem with non-convex quadratics constraints. Appl Math Comput 189:1624–1636
17. Schaible S (1977) A note on the sum of a linear and linear fractional functions. Naval Res Logist Q 24:61–963
18. Schaible S, Shi J (2003) Fractional programming: the sum-of-ratio case. Optim Method Softw 18(2):219–229
19. Scott CH, Jefferson TR (1998) Duality of non-convex sum of ratios. J Optim Theory Appl 98(1):151–159
20. Shen PP, Jin L (2010) Using canonical partition to globally maximizing the non-linear sum of ratios. Appl Math Model 34:2396–2413
21. Shen PP, Wang CF (2006) Global optimization for sum of ratios problem with coefficient. Appl Math Comput 176:219–229
22. Shen PP, Wang CF (2008) Global optimization for sum of generalization fractional functions. J Comput Appl Math 214:1–12
23. Shen PP, Chen Y, Yuan M (2009a) Solving sum of quadratic ratios fractional programs via monotonic function. Appl Math Comput 212:234–244
24. Shen PP, Duan YP, Pei YG (2009b) A simplicial branch and duality bound algorithm for the sum of convex–convex ratios problem. J Comput Appl Math 223:145–158
25. Shen PP, Li W, Bai X (2013) Maximizing for the sum of ratios of two convex functions over a convex set. Comput Oper Res 40:2301–2307
26. Singh P, Dutta D (2012) Sum of ratios multi-objective programming problem: a fuzzy goal programming approach. Nonlinear Dyn Syst Theory 12(3):289–302
27. Singh S, Gupta P (2010) On multiparametric analysis in sum-of-ratios programming. In: Proceeding of the international multiconference of engineers and computer scientist, IMECS-2010, Hong Kong, 17–19 Mar 2010Google Scholar
28. Wang YJ, Zhang KC (2004) Global optimization of non-linear sum of ratios problem. Appl Math Appl 158:319–330
© Springer-Verlag GmbH Germany, part of Springer Nature 2018
## Authors and Affiliations
• Deepika Agarwal
• 1
• Pitam Singh
• 1
Email author
• Deepak Bhati
• 2
• Saru Kumari
• 3
|
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|
https://export.arxiv.org/abs/2010.00602
|
astro-ph.GA
(what is this?)
Title: HOLISMOKES -- IV. Efficient mass modeling of strong lenses through deep learning
Abstract: Modelling the mass distributions of strong gravitational lenses is often necessary to use them as astrophysical and cosmological probes. With the high number of lens systems ($>10^5$) expected from upcoming surveys, it is timely to explore efficient modeling approaches beyond traditional MCMC techniques that are time consuming. We train a CNN on images of galaxy-scale lenses to predict the parameters of the SIE mass model ($x,y,e_x,e_y$, and $\theta_E$). To train the network, we simulate images based on real observations from the HSC Survey for the lens galaxies and from the HUDF as lensed galaxies. We tested different network architectures, the effect of different data sets, and using different input distributions of $\theta_E$. We find that the CNN performs well and obtain with the network trained with a uniform distribution of $\theta_E$ $>0.5"$ the following median values with $1\sigma$ scatter: $\Delta x=(0.00^{+0.30}_{-0.30})"$, $\Delta y=(0.00^{+0.30}_{-0.29})"$, $\Delta \theta_E=(0.07^{+0.29}_{-0.12})"$, $\Delta e_x = -0.01^{+0.08}_{-0.09}$ and $\Delta e_y = 0.00^{+0.08}_{-0.09}$. The bias in $\theta_E$ is driven by systems with small $\theta_E$. Therefore, when we further predict the multiple lensed image positions and time delays based on the network output, we apply the network to the sample limited to $\theta_E>0.8"$. In this case, the offset between the predicted and input lensed image positions is $(0.00_{-0.29}^{+0.29})"$ and $(0.00_{-0.31}^{+0.32})"$ for $x$ and $y$, respectively. For the fractional difference between the predicted and true time delay, we obtain $0.04_{-0.05}^{+0.27}$. Our CNN is able to predict the SIE parameters in fractions of a second on a single CPU and with the output we can predict the image positions and time delays in an automated way, such that we are able to process efficiently the huge amount of expected lens detections in the near future.
Comments: 17 pages, 14 Figures Subjects: Astrophysics of Galaxies (astro-ph.GA) DOI: 10.1051/0004-6361/202039574 Cite as: arXiv:2010.00602 [astro-ph.GA] (or arXiv:2010.00602v2 [astro-ph.GA] for this version)
Submission history
From: Stefan Schuldt [view email]
[v1] Thu, 1 Oct 2020 18:00:03 GMT (789kb,D)
[v2] Fri, 18 Dec 2020 12:19:05 GMT (4865kb,D)
Link back to: arXiv, form interface, contact.
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|
http://efavdb.com/gpu-accelerated-theano-keras-with-windows-10/
|
GPU-accelerated Theano & Keras with Windows 10
There are many tutorials with directions for how to use your Nvidia graphics card for GPU-accelerated Theano and Keras for Linux, but there is only limited information out there for you if you want to set everything up with Windows and the current CUDA toolkit. This is a shame however because there are a large number of computers out there with very nice video cards that are only running windows, and it is not always practical to use a Virtual Machine, or Dual-Boot. So for today’s post we will go over how to get everything running in Windows 10 by saving you all the trial and error I went through. (All of these steps should also work in earlier versions of Windows).
Dependencies
Before getting started, make sure you have the following:
• NVIDIA card that supports CUDA (link)
• Python 2.7 (Anaconda preferably)
• Compilers for C/C++
• CUDA 7.5
• GCC for code generated by Theano
Setup
Visual Studio 2013 Community Edition Update 4
First, go and download the installer for Visual Studio 2013 Community Edition Update 4. You can not use the 2015 version because it is still not supported by CUDA. When installing, there is no need to install any of the optional packages. When you are done add the compiler, C:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin, to your windows path.
System → Advanced system settings → Environment Variables → Path.
CUDA
Next, go the NVIDIA’s website and download the CUDA 7.5 toolkit. Select the right version for you computer. When you are installing it, make sure to pick custom install if you don’t want your video card drivers to be overwritten with the version that comes with the toolkit, which are often out of date. If it turns out that your version of the drivers are older than what comes with the toolkit,then there is no harm in updating your drivers, otherwise only pick the three boxes starting with CUDA.
GCC
The last thing we need to do GCC compiler, I recommend TDM-gcc. Install the 64 bit version, and then add the compiler to your windows path, the install has an option to do that for you automatically if you wish.
To make sure that everything is working at this point, run the the following command on the command line (cmd.exe) . If if finds the path for everything you are good to go.
where gcc where cl where nvcc where cudafe where cudafe++
Theano and Keras
At this point it is easy to install Theano and Keras, just you pip (or conda and pip)!
conda install mingw libpython
pip install theano
pip install keras
After installing the python libraries you need to tell Theano to use the GPU instead of the CPU. A lot of older posts would have you set this in the system environment, but it is possible to make a config file in your home directory named “.theanorc.txt” instead. This also makes it easy to switch out config files. Inside the file put the following:
[global]
device = gpu
floatX = float32
[nvcc]
compiler_bindir=C:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin
Lastly, set up the Keras config file ~/.keras/keras.json. If you haven’t started Keras yet, the folder and file won’t be there but you can create it. Inside the config put the following.
{
"image_dim_ordering": "tf",
"epsilon": 1e-07,
"floatx": "float32",
"backend": "theano"
}
Testing Theano with GPU
Using the following python code, check if your installation of Theano is using your GPU.
from theano import function, config, shared, sandbox
import theano.tensor as T
import numpy
import time
vlen = 10 * 30 * 768 # 10 x #cores x # threads per core
iters = 1000
rng = numpy.random.RandomState(22)
x = shared(numpy.asarray(rng.rand(vlen), config.floatX))
f = function([], T.exp(x))
print(f.maker.fgraph.toposort())
t0 = time.time()
for i in range(iters):
r = f()
t1 = time.time()
print("Looping %d times took %f seconds" % (iters, t1 - t0))
print("Result is %s" % (r,))
if numpy.any([isinstance(x.op, T.Elemwise) for x in f.maker.fgraph.toposort()]):
print('Used the cpu')
else:
print('Used the gpu')
Testing Keras with GPU
This code will make sure that everything is working and train a model on some random data. The first time might take a little longer because it the software needs to do some compiling.
from keras.models import Sequential
from keras.layers import Dense, Activation
# for a single-input model with 2 classes (binary):
model = Sequential()
model.compile(optimizer='rmsprop',
loss='binary_crossentropy',
metrics=['accuracy'])
# generate dummy data
import numpy as np
data = np.random.random((1000, 784))
labels = np.random.randint(2, size=(1000, 1))
# train the model, iterating on the data in batches
# of 32 samples
model.fit(data, labels, nb_epoch=10, batch_size=32)
If everything works you will see something like this!
Now you can start playing with neural networks using your GPU!
• IngeSpring
Awesome, thank you.
• Damien
The link changed after publication, but I went ahead an updated. Thanks for the heads up. As far as the other packages, at least in my case the normal scipy and numpy dependencies worked fine. It is also true that it takes longer the first time because of the time it takes the libraries to compile, I might not have made that clear enough, thanks for your feedback!
• Iván Vallés Pérez
Amazing! Thank you. Can you specify exactly how should I determine the exact keras.json path? Is it C:/Users/MyUserName/.keras?? Thank you
• Damien
That’s correct, worse case you can try starting Keras and it will make the folder for you.
|
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|
https://tongfamily.com/2021/01/05/long-distance-tesla-travel-in-the-age-of-covid/
|
OK, suppose that you are too paranoid to get on an airplane and instead decide that any trip within 1,200 km of your home city are fair game for a road trip. What do you need to make the trip as safely as possible. Here are some notes 🙂
## Safety Stuff: Of Snow tires and things
Well the first thing is that with a Tesla you do get road side assistance, but it could definitely take a while if you are 100 miles from the nearest city (yes the American West is a vast place). So here are some of the things you need:
1. Real snow tires and wheels. Yes, this is particularly true if you have a Model 3 Performance with those very cool and fast performance tires. First of all, should not be driven when it is below freezing nor should it be stored when it is 20F. So fortunately from Tesla or Tirerack, you can get approved snow tires. One trick here is that if you have 20-inch performance wheels, the stepped hub on the Performance is really big, so the stock 18-inch wheels won't fit. You need a wheelset that will fit around it. We've used the Pirelli Sottozero 3 which is the special Tesla T0 PCNS version with sound deadening inside. Tesla offers these in a Winter Snow Package with 19" Gemini wheels that look nice and have decent fuel economy too for $3,500 which is definitely a lot to pay, but you get a car that is really stable everywhere. We actually got our snow set before the Gemini's were available and ended up using a Fast Wheels EV01+ 18" set with the same kind of "ugly" aero covers but they are really efficient. We spent a fortune getting these from Canada, but they are now$1,200 from Evannex.
2. Snow Shovel and Brush. Yes, you will need these. We have some no-name ones, but the ORIENTOOLS looks great as it is folding and the SNOBRUM is just 17" when closed and has a foam top
3. Inflater, Flashlight, LED Emergency Beacon, Emergency Mylar Blankets, Smart Spair Tire Repair Kit, LifeHammer and Jump Starting Power Pack. Yes, it has a huge battery, but there is also a 12V that can give out. Plus you need something that will let you flash things in the real world. The nerdiest thing is the Life Hammer which breaks a side window if you need to get out in a hurray 🙂
4. Covers for the rear seats. Assuming you are going to be piling junk in there, this is perfect for covering the seat. it's a pet cover, so really works well.
## Really planning your trip: A Better Route Planner
If you are taking a 12-15 hour trip in your Tesla, then minimizing charge time is going to really matter. Using A Better Route Planner and paying for the premium features is a great idea. With it, you can see the exact road conditions and also learn how to optimize charge time. In this time of COVID-19, you probably don't want to lounge around in strange restaurants, so having a place to use the bathroom and have a snack in the car is vital:
1. A Better Route Planner tuning parameters. This tool let's you do long term planning. There are two things to know. First is that tuning the application to your driving really matters. For us for instance, the default parameters that matter are your energy consumption to 65 mph and the speed parameter which is what percent of the speed limit are you going (not that you should ever go above the speed limit). As an example, the Model 3 Performance is 295 Wh/mi at 65 mph and we've found that pretty high given our style of driving and also with the EV01+ we get better mileage. So careful tuning shows we are doing about 265 Wh/mi. And 103-107% on the second parameter seems to match times well.
2. Monitoring real performance. If you leave ABRP on with your phone, you can see how you are doing vs forecast, it has buttons that let you adjust the actual State of Charge (SoC) and see what you are really doing. That's useful to tune the two parameters above.
3. Always have a bailout plan. When you are planning to drive down to 12%, make sure you have a bailout plan. We only do this on routes we know because if you get to a charger and it doesn't work, you need enough charge to get somewhere else, so it is a good idea to know a bunch of alternative sites. The Supercharger network is pretty good, but we have seen cases where half the chargers are down and you have to go somewhere else.
4. Charging Strategy. With the Model 3 battery, you get the best charge times when you are between 10 and 50%, so you will see that the built in Tesla planner tends to optimize for fewer but longer charges. So it will try to charge to 80% which sounds good except the taper is very steep after 50%. The optimal balance between stops which means you slow down and charging time is hard to estimate, but usually, if you get down to 12% and then charge to 60%, you are going to be driving for two hours before a charge of 10 minutes or so. When you factor in slowing down and parking this makes some sense. In truth really just a 10 minute stop is really short, so the reality is that you start a plan with ABRP and then see how you are really doing in charging time.
5. Bias to 250W chargers. Of course, there is another factor, the older 150W chargers are slower and when they are full, you share charging power with another stall, so you can definitely have long charging times with the 150W. When modifying a ABRP plan, we tend to bias towards getting to the 250W 12% (if you go lower than 10%, charging slows again) and then pushing for enough to the next 250W charge if it is in range. There are definitely some routes like I-5 in California where there is a 250W charger every 90 miles or so, that's nearly ideal as you can run from 10-50% and stop for 8 minutes at a time.
6. Charger load factor. It is a good idea to look at see what the busy chargers are. Some are just never busy (try the ones in Idaho), but in California, you can really wait a long time, so it's good to hit the busy station either at the 250W ones or early in the morning. Also, those chargers close to the city oftentimes have local folks with free unlimited charging taking up lots of spots
## Napping and Sleeping in the Car
Finally, there could come a time after 12 hours of driving that you need a little shut-eye. Fortunately, there's a big discussion forum about how to do this thanks to the relatively long (6' 4") length with the seats folded. The knee room is a little tight in a Model 3 and its twin-sized so not big for two full-sized people 🙂
1. Tesmat Camping Mattress. It's expensive at $270 direct, but it is a nice 2" thick memory foam with a board underneath that helps bridge the 6" gap between the rear seat and the front seat back. There are even fitted twin sheets for it. 2. Dreamcase. This is a big more expensive and has a case prop instead of a board to cover the last six inches. Comes from Europe so would take 2-3 weeks to get to the US. They sell them for a huge number of cars, for the Model 3 including sheets, so this is direct$658.
3. Exped Megamat Duo 10. This is a whopping \$349, but is air inflatable so theoretically smaller and insulated. Plus it is self inflating. You will still need a board or something to bridge the gap at the top.
4. Zinio 4" foam folding mattress. It's huge but comfortable and much cheaper.
|
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|
https://nlpforhackers.io/tf-idf/
|
# Weighting words using Tf-Idf
If I ask you “Do you remember the article about electrons in NY Times?” there’s a better chance you will remember it than if I asked you “Do you remember the article about electrons in the Physics books?”. Here’s why: an article about electrons in NY Times is far less common than in a collection of physics books. It is less likely to stumble upon the “electron” concept in NY Times than in a physics book.
Let’s consider now the scenario of a single article. Suppose you read an article and you’re asked to rank the concepts found in the article by importance. The chances are you’ll basically order the concepts by frequency. The reason is simply that important stuff would be mentioned repeatedly because the narrative gravitates around them.
Combining the 2 insights, given a term, a document and a collection of documents we can loosely say that:
`importance ~ appearances(term, document) / count(documents containing term in collection)`
This technique is called Tf-IdfTerm Frequency – Inverse Document Frequency. Here’s how the measure is defined:
• `tf = count(word, document) / len(document)` – term frequency
• `idf = log( len(collection) / count(document_containing_term, collection)` – inverse document frequency )
• `tf-idf = tf * idf` – term frequency – inverse document frequency
Let’s test this theory on some data. We’re going to use the Reuters dataset bundles inside NLTK.
Let’s build a tokenizer that ignores punctuation and stopwords:
We now need to know all the words inside the collection
Let’s compute the Idf for every word in the vocabulary:
Let’s write, as an exercise, the numpy parallelized version of the Idf computation:
Since Idf doesn’t depend on the current document but only on the collection we can preprocess the results as we did above. Here’s the code for the final computation:
Let’s run a few computations:
Notice how I sneakily computed the words in the order of the Tf-Idf score.
That’s how we compute the Tf-Idf ourselves. Let’s also use some libraries to make the job a bit easier. Note that the scores might be different but the order should be the same. The difference is probably due to different smoothing strategies.
Here’s the code for computing the Tf-Idf score using scikit-learn:
Here’s the code for computing the Tf-Idf score using gensim:
## Conclusions
• TfIdf is a really popular technique for weighting the importance of the terms inside a collection of documents
• It is used in Information Retrieval to rank results
• It is used for extracting keywords on web pages
Shares
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https://cs.stackexchange.com/users/2353/xavierm02?tab=favorites&sort=newest
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xavierm02
# 27 Favorites
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### Expression Problem: Why are simple parameterized types a non-solution?
Sep 15 '17 at 9:04 Bengt 141
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### Sorting in place & stable in linear time
Feb 3 '17 at 12:46 Riley 260
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### Canonical definition of suitable encoding
May 25 '16 at 22:59 xavierm02 1,167
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https://codeforces.com/blog/entry/80202
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### kratos99's blog
By kratos99, history, 4 weeks ago, ,
I need help to solve this problem.
Thanks in advance.
Happy Coding :)
• +13
» 4 weeks ago, # | ← Rev. 5 → +6 1.Use Linear Sieve to take primes no more than $n$ out, store them. Linear Sievevectorpr; bool p[500000005];//this array consumes ~500MB of space. The Memory limit is 1024MB, so it's enough. void primes(){ for(int i=2;i<=n;i++){ if(!p[i])pr.push_back(i); for(int j=0;j
• » » 3 weeks ago, # ^ | 0 I did this and got AC but I think purpose of problem setter is behind this question is not this so I asked.
• » » » 3 weeks ago, # ^ | +5 There's a time constraint of $10$ seconds, with $1024$ MB memory avaliable.I think the purpose of the author could be that ( enumerate primes )
|
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https://scholar.archive.org/work/3oomnyn2qvcdrpfoy2f3bhoqbe
|
### Large-momentum-transfer Bragg interferometer with strontium atoms
T. Mazzoni, X. Zhang, R. Del Aguila, L. Salvi, N. Poli, G. M. Tino
2015 Physical Review A. Atomic, Molecular, and Optical Physics
We report on the first atom interferometer based on Bragg diffraction in a fountain of alkaline-earth atoms, namely $^{88}$Sr. We demonstrate large momentum transfer to the atoms up to eight photon recoils and the use of the interferometer as a gravimeter with a sensitivity $\delta g/g=4\times 10^{-8}$. Thanks to the special characteristics of strontium atoms for precision measurements, this result opens a new way for experiments in fundamental and applied physics.
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https://notenik.app/knowledge-base/EPUB/html/custom-url-scheme.html
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5.12 Custom URL Scheme
Notenik has its own custom URL scheme, which can be invoked by other apps as a means of integrating Notenik with these other applications.
Note that URLs must in general be percent encoded. The most common encoding is done by replacing each space with %20.
The following commands are supported.
### Open
Following is a sample URL:
notenik://open?shortcut=todo&id=pickupmilk
Let's break this down:
• notenik:// - The custom scheme that will invoke the Notenik app.
• open - The Notenik command to open a Collection and optionally a specific Note within the Collection.
• ? - A question mark indicates the end of the command and the beginning of the query string.
• shortcut=todo - The shortcut identifying the Collection to be opened. Note that shortcuts are defined in such a way that they will generally not need to be percent encoded.
• path=Users/user1/Sites/site1 - Specifying the complete path would be an alternate way of identifying the Collection to be opened. Path values generally will require percent encoding.
• & - An ampersand is used to separate each label=value parameter from the next.
• id=pickupmilk - The ID identifying the Note to be selected for Display. Note than a Note ID is defined in such a way (removing spaces, etc.) that it will not need to be percent encoded.
An easy way to obtain a complete URL that can be used to later open a specific Note is to right-click the Note's row on the List tab within Notenik, and then select Copy Notenik URL from the contextual menu that will pop up. This will copy a complete Notenik URL to the clipboard, from which it can then be pasted into another location.
Following is a sample URL:
notenik://add?shortcut=todo&title=Pick%20up%20milk&body=You%20gotta
Again, let's break this down.
• notenik:// - The custom scheme that will invoke the Notenik app.
• add - The Notenik command to add a new Note to an existing Collection.
• ? - A question mark indicates the end of the command and the beginning of the query string.
• shortcut=todo - The shortcut identifying the Collection to which the new Note is to be added.
• path=Users/user1/Sites/site1 - Again, specifying the complete path would be an alternate way of identifying the Collection to be used.
• & - An ampersand is used to separate each label=value parameter from the next.
• title=Pick%20up%20milk - The title for the new Note. This will amost always require percent encoding, as in this example.
• & - An ampersand is used to separate each label=value parameter from the next.
• body=You%20gotta - The body of the new Note. Again, this will almost always require percent encoding.
Other fields may also be specified for a new Note, using a similar label=value convention.
### Help
Following is a sample URL:
notenik://help?id=versionhistory
Once more, let's break this down:
• notenik:// - The custom scheme that will invoke the Notenik app.
• help - The Notenik command to open the Notenik Knowledge Base supplied with Notenik.
• ? - A question mark indicates the end of the command and the beginning of the query string.
• id=versionhistory - The ID identifying the Note to be selected for Display.
The query string is optional. If it is not supplied, then the Knowledge Base will be opened at the first Note in the Collection.
Next: Markdown
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|
https://math.stackexchange.com/questions/2222589/is-fracdydx-fracdycdx
|
# Is $\frac{dy}{dx} = \frac{d(y+c)}{dx}$?
Is the following true?
$$\frac{dy}{dx} = \frac{d(y+c)}{dx}$$
where $c$ is an arbitrary real constant.
I believe it is true, and my reasoning goes like this:
$dy$ is an infinitesimal, so the addition of another constant would still be an infinitesimal. I do not know if my reasoning is correct.
Do note that I'm not familiar with epilson delta and university calculus. I would appreciate it if someone could explain the above simply.
EDIT: I couldn't see why $d(y+c)= dy+dc$. What is $d$? Is it a number, or a function?
• You conclusion is correct. As you are reasoning by "non-standard" analysis, it is tough to call it "correct" but your intuition is leading you to the right places. Apr 7, 2017 at 16:24
• @DougM Inasmuch as the OP is unfamiliar with "university calculus," it is a safe bet that the OP is equally unfamiliar with non-standard analysis. ;-)) Apr 7, 2017 at 16:26
• I have some knowledge about the difference between standard and non-standard calculus analysis. It would be great if someone could explain this through simple, non-standard perspective. Apr 7, 2017 at 16:29
• How about this... differentiation is a "linear operation" that is $\frac {d}{dx} (f(x) + g(x)) = \frac {df}{dx} + \frac {dg}{dx}$ and since $c$ is constant $\frac {d}{dx} (y + c) = \frac {dy}{dx}$ Apr 7, 2017 at 16:31
• I'm also just learning about the non-standard approach, but I think the story is the same in the standard and non-standard approaches. Since $c$ is constant, an infinitesimal change in the "argument" of $c$ changes nothing. If $c$ were a function, then we would argue that $d(y+c) = dy + dc$, since an infinitesimal change in the argument produces an infinitesimal change in both terms. Apr 7, 2017 at 16:34
$$\mathrm{d}(y+c) = \mathrm{d}y + \mathrm{d} c$$
However, if $c$ is a constant, then
$$\mathrm{d} c = 0$$
so we get
$$\mathrm{d}(y+c) = \mathrm{d}y$$
Consequently, if one side of the following makes sense, then both sides do and they are equal:
$$\frac{\mathrm{d}(y+c)}{\mathrm{d}x} = \frac{\mathrm{d}y}{\mathrm{d}x}$$
• I couldn't see why $d(y + c) = dy + dc$. What is $d$? Is it a number, or a function? Apr 8, 2017 at 8:20
let $g(x) = y(x) + c\;$ $\forall x \in D_y$
\begin{align} & \frac{d(y+c)}{dx} = \frac{dg}{dx} = g'(x)= \lim_{h\to0} \frac{g(x+h)-g(x)}{h} =\lim_{h\to0} \frac{y(x+h)+c-y(x)-c}{h} \\[10pt] = {} & \lim_{h\to0} \frac{y(x+h)-y(x)}{h} = y'(x) = \frac{dy}{dx} \end{align}
|
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|
http://math.stackexchange.com/questions/285310/name-of-trigonometric-identity
|
Name of trigonometric identity
Is there a name of this trigonometric identity: $$\cos(a+b) \cos(a+c+b) \equiv \frac{1}{2} \left[\cos(c) + \cos(2a+2b+c) \right]$$
Bsaically we are "changing" a product of cosines into a sum of cosines.
-
– Fabian Jan 23 '13 at 20:33
$\cos(a+b) = \cos(a)\cos(b)-\sin(a)\sin(b)$
$\cos(a-b) = \cos(a)\cos(b)+\sin(a)\sin(b)$
$\cos(a)\cos(b) = \frac{1}{2}(\cos(a+b)+\cos(a-b))$
|
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|
http://www.koreascience.or.kr/search.page?keywords=Waist+circumference
|
• Title, Summary, Keyword: Waist circumference
### Characteristocs of the Somatotypes of Korean Farmer (한국 남녀 농업인의 체형 특성)
• Baek, Yoon-Jeong;Lee, Kyung-Suk;Hwang, Kyoung-Sook;Kim, Kyung-Ran;Kim, Hyo-Cher
• Journal of the Korean Society of Clothing and Textiles
• /
• v.32 no.3
• /
• pp.431-442
• /
• 2008
• This study was to research the characteristics of the somatotype of Korean farmers. 836 Korean farmers(Male: 361 persons, Female: 475 persons) volunteered for this study. They volunteered from 9 different area such as Kumi, Damyang, Iksan, Injae, Chungju, Choongju, Haman, Whasung, and Whasoon. The reusults were as follows: 1. The subcutaneous body fat thickness were decreased as they aged(p<.05). 2. The thicker the subcutaneous body fat thickness of Korean farmer, the wider the circumference size by the Korean famer's physical parts(p<.05-p<.001). 3. There were no significant differences in the circumference size such as upper arm, chest, bust, waist, umbilical waist, hip, and calf between Korean farmers and Korean standard size. 4. Korean women farmer showed significantly differences in the upper arm circumference(p<.01), the chest circumference(p<.01), the bust circumference(p<.01), the waist circumference(p<.01), the umbilical waist circumference(p<.01), and the calf circumference(p<.05) from Korean women standard by ages. Especially, Korean women farmer had thicker the umbilical waist circumference(the 40's: 103.2mm, the 50's 52.3mm, the 60's 22.3mm, over 70's 22.1mm) than Korean women standard. 5. The 40's women farmer had thicker the upper arm circumference, the chest circumference, the bust circumference, the waist circumference, the umbilical waist circumference, and the calf circumference than Korean women standard. The 70's women farmer had skinner circumferences except the umbilical waist circumference than Korean women standard. 6. Korean farmers showed the crooked back shape, the broad-knee length and also front-bending knee shape as they aged.
### Optimal Waist Circumference for the Prevention of Cardiovascular Disease (심혈관계질환의 발병 위험을 선별할 수 있는 적정 허리둘레의 임계점)
• Baik, In-Kyung;Shin, Chol
• Korean Journal of Community Nutrition
• /
• v.15 no.2
• /
• pp.275-283
• /
• 2010
• There are few studies reporting optimal waist circumference that can be utilized to prevent the incidence of cardiovascular disease (CVD). We evaluated the association of waist circumference and waist and hip circumference ratio (WHR) with incident cases of CVD developed over 6 years in a population-based prospective study including Korean adults. Analyses for receiver-operating characteristic (ROC) curve were performed with data for 1,733 men and 1,579 women who were aged 40 to 69 years and were free of a physician-diagnosis of CVD at baseline. Information on the diagnosis of CVD was periodically reported using interviewer-administered questionnaires and anthropometric measures were obtained by biennial health examinations. We newly identified 77 cases of CVD during a follow-up period between 2003 and 2008. On the basis of measures of diagnostic accuracy including minimum distance to ROC curve and Youden index, waist circumference of 85 cm for men, in particular for male nonsmokers, and of 80 cm for women and WHR of 0.88 to 0.90 for men and of 0.83 for women were found to be optimal cutoff points to identify individuals at CVD risks. The study also found that the use of the suggested optimal values for waist circumference show higher sensitivity and lower specificity compared with 90 cm for men and 85 cm for women, which are waist cutoff points given by the Korean Society for the Study of Obesity to define abdominal obesity for Korean adults. Although lower cutoff points of waist circumference (83 cm) and WHR (0.87) were observed to be optimal for male smokers compared with male nonsmokers, whether suggesting waist cutoff points specific to smokers is needed warrants further studies. After taking into account other cardiovascular risk factors including smoking, men with waist circumference of 85 cm or greater and women with 80 cm or greater were at an increased risk of CVD. Thus, these cutoff points of waist circumference may be able to capture more individuals at CVD risks contributing to the prevention of future development of CVD.
### Eco Resort Wear Sizing System Targeting Jeju's Medical Tourists
• Kwon, Sookhee;Hong, Jiun
• Journal of the Ergonomics Society of Korea
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• v.31 no.6
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• pp.765-772
• /
• 2012
• Objective: The purpose of this research was to aid creating an effective sizing system for the vacation wear intended for Jeju's medical tourists, specifically females from the major countries including the USA, Japan, and Korea. Background: Medical tourism makes the gains of every year 40,000,000,000 dollar, every year 30% it is increasing. Thus the Jeju-do is propelling medical tourism. The body size each country is different. Consequently must set the body size standard for the women. Method: (1) It observed the body size of the Korean women of 2004 years and 2010 years. (2) It analyzed the body size of the women of the USA, China, Japan and Korea. (3) It set the sizing system of the women of the USA(ASTM), China (GB), Japan(JIS) and Korea(KS). Results: Korean adult females' height in 2010 has increased from 2004. The Waist Back Length, Waist Front Length, Arm Length etc has also increased along with the Height. The upper body has become slimmer at the same time; the Chest Circumference, Bust Circumference, and Underbust Circumference have decreased. The lower body on the other hand has become bigger: the Waist Circumference and Hip Circumference have increased. The BMI has decreased by 0.4 from 2004 - the Height has increased while Weight has decreased. The Chest Circumference and Under Bust Circumference of Korean women across all age groups have increased at a proportional rate to other parts of body; however, the rate of increase in Chest Circumference was far greater. American females(Caucasians) had the greatest ratio of waist to bust (Waist Circumference/Chest Circumference), smallest ratio of Neck Base Circumference to Bust Circumference (neck/bust). Korean females had smallest ratio of Waist Circumference to Underbust Circumference(waist/bust). As for the drop of Chest Circumference and Waist Circumference, American females had the highest and Koreans had the lowest. As for the drop of Hip Circumference and Chest Circumference, Japanese had the highest and Americans had the lowest, but Japanese women at the same time showed the A line body shapes. As for difference of Chest Circumference and Underbust Circumference, American females had the biggest(13.73) followed by Korean(11.1), Japanese(10.9) and Chinese(10.5). Conclusion: The women of the USA, China, Japan and Korea body size is different. Especially the value of the Bust Circumference - the Underbust Circumference is different. Thus, it set the sizing system(Table 8).
### Differences of Chest and Waist Circumferences in Spastic Diplegic and Hemiplegic Cerebral Palsy
• Nam, Ki Seok;Lee, Hye Young
• The Journal of Korean Physical Therapy
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• v.25 no.3
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• pp.155-159
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• 2013
• Purpose: Circumference of the chest and waist can be one of clinical indicator to reflect respiratory function in children with cerebral palsy. In this study, we compared to differences in the chest/waist circumference and maximal phonation time between children with spastic diplegia and hemiplegia. Methods: Seventeen children with spastic diplegic and hemiplegic cerebral palsy were recruited, who were matched to gender, age, height, weight, and body mass index for control of the known factors affected to respiratory function. The chest/waist circumference and were measured in each group, when children took a breath at rest and at maximal voluntary inspiration/expiration. Results: No significant differences were found in the chest and waist circumference and expansion between the two groups. However, only in the waist expansion, children with diplegic CP were significantly lower extensibility of lung, compared to the other group. In comparison of the maximal phonation time, a significant lower score was shown in children with spastic diplegic CP, compared to children with hemiplegic CP. Conclusion: Our results indicated that children with spastic diplegic CP had smaller chest wall and waist, compared to children with spastic hemiplegic CP. In addition, they showed a shorter time for sustaining phonation than spastic hemiplegic CP did. Therefore, spastic diplegic CP will be required for careful monitor regarding respiratory function in rehabilitation settings.
### Study on a Clothes Sizing System for Elderly Men (노년 남성의 의복사이즈 체계연구)
• Seong, Ok Jin;Ha, Hee Jung
• Journal of the Korean Society of Clothing and Textiles
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• v.39 no.1
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• pp.147-160
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• 2015
• This study suggests a detailed apparel sizing system for brands that target elderly men between the ages of 60 to 79 by studying body type differences of the age group based on data from 'The $5^{th}$ Korean Anthropometric survey'. Compared to middle aged men, elderly men body measurements appear to be smaller except in the midriff area, such as the natural waist circumference, waist circumference (omphalion), waist depth and waist depth (omphalion). The size chart in the study was established according to the KS size chart system with a size jump of 5cm in height, 5cm and 3cm in chest circumference, 2cm in waist circumference (omphalion) and 2cm in hip circumference. A total of 8 sizes were established with heights between 160cm and 170cm and chest measurements between 85cm to 100cm for casual tops. For suit tops, a total of 11 sizes were established with heights between 160cm and 170cm and chest measurements between 88cm to 100cm. For bottoms, detailed sizes were suggested by dividing basic and reference areas with 13 sizes between 84cm to 94cm in the waist circumference (omphalion) and between 90cm to 98cm in the hip circumference.
### Evaluation of Waist Circumference Cut-off Values as a Marker for Fatty Liver among Japanese Workers
• Abe, Naomi;Honda, Sumihisa;Jahng, Doosub
• Safety and Health at Work
• /
• v.3 no.4
• /
• pp.287-293
• /
• 2012
• Objectives: Metabolic syndrome has received attention as a risk factor for cardiovascular disease, with particular importance attached to visceral fat accumulation, which is associated with lifestyle-related diseases and is strongly correlated with waist circumference. In this study, our aim is to propose waist circumference cut-off values that can be used as a marker for fatty liver based on a sample of workers receiving health checkups in Japan. Methods: This study was conducted in a total of 21,866 workers who underwent periodic health checkups between January 2007 and December 2007. The mean age of the subjects was 47.4 years for men (standard deviation [SD]: 8.0) and 44.7 years for women (SD: 6.9). Evaluation included abdominal ultrasound and measurement of waist circumference, body mass index, fasting blood glucose, triglycerides, high-density lipoprotein cholesterol, and blood pressure. Results: Based on receiver operating characteristic curve analysis, the optimal waist circumference cut-off values were shown as 85.0 cm (sensitivity 0.72, specificity 0.69) for men and 80.0 cm (sensitivity 0.75, specificity 0.78) for women. Conclusion: Abdominal ultrasound is the most efficient means of diagnosing fatty liver, but this examination seldom occurs because the test is not routinely performed at workers' health checkups. In people found to have a high risk of fatty liver, recommendations can be made for abdominal ultrasound based on the waist circumference cut-off values obtained in this study. That is, waist circumference can be used in high risk individuals as an effective marker for early detection of fatty liver.
### An Analysis of The Preferred Ease of Torso Sloper by Body Size (신체크기에 따른 토르소원형의 부위별 선호여유량 분석)
• Kang, Yeo-Sun
• Journal of the Korean Society of Clothing and Textiles
• /
• v.36 no.1
• /
• pp.112-125
• /
• 2012
• This study researches the preferred ease of torso sloper according to body sizes and drop. For this, the eases of main body parts such as chest circumference, waist circumference, hip circumference, biacromion length, and waist back length were analysed; in addition, the drop differences of body and pattern were explored to find out characteristics of silhouette changes. The subjects were 55 women in their early 20s (aged from 20 to 24) and individual torso block made with muslin was corrected 1-3 times by a personal fitting. There were 3 meaningful results. First, the preferred ease were individually various; however, the eases of all torso blocks should be same at the pattern making step. Second, the eases were also significantly different among body size groups and the bigger group preferred less ease at the biacromion length, waist back length, armhole-depth, chest circumference, and waist circumference. Third, the eases of chest circumference and hip circumference were significantly changed among drop groups. To change their body drop, H-shape drop adopted less ease at chest circumference and more ease at hip circumference; however, A-shape drop adopted more ease at chest circumference and less ease at hip circumference.
### The Usefulness of Obesity Indices for the Coronary Risk Factors in an Urban Inhabitants (도시지역 주민의 관상동맥질환 위험인자에 관련한 비만지표의 유용성 검토)
• Park, Sung-Kyeong;Kim, Kwang-Hwan;Cho, Young-Chae
• Journal of Preventive Medicine and Public Health
• /
• v.39 no.6
• /
• pp.447-454
• /
• 2006
• Objectives : To determine obesity for the screening of individuals at high risk of coronary heart disease in urban areas. Methods : Data were obtained from 4,137 adults between 19 and 85 years of age (2,372 males, 1,765 females), not recognized as taking medicines for cardiovascular diseases, who underwent a health check-up at the health promotion center of university hospitals in cities between Jan. 2003 and Dec. 2004. The variables studied were divided into two broad categories, and their relationships examined. obesity indices and risk factors for coronary heart disease. To reveal the relation between each of the obesity indices and the proportion of individuals at risk of coronary heart disease, the obesity indices were stratified and odds ratios obtained after age adjustment. Results : From a gender comparison of anthropometric measures, men were found to have significantly greater heights, weights, and waist and hip circumferences than women. From a gender comparison by the obesity indices, women were found to have significantly higher BMI, %Fat, waist to hip and waist to stature ratios than men. As obesity indices, the waist to stature ratio and the waist circumference were strongly correlated with coronary risk factors, both in men and women. The age-adjusted odds ratio of coronary risk factors increased significantly with increasing waist circumference, BMI, %fat, waist to hip and waist to stature ratios, and were highest specifically for the waist to stature ratio and the waist circumference. Conclusions : The study results showed that the waist to stature ratio and the waist circumference, as obesity indices, were most closely correlated with coronary risk factors. It is suggested that the waist to stature ratio and, specifically, the waist circumference can be effectively used in the field of health management for screening those with high levels of coronary risk factors.
### A Study on the Body Characteristics of Korean Obese Women (Part I)
• Yi, Kyong-Hwa
• Journal of the Korean Society of Clothing and Textiles
• /
• v.34 no.6
• /
• pp.937-954
• /
• 2010
• This study analyzes the body characteristics of Korean obese women using 2004 Size Korea data. For selecting the obesity sample, 7 obesity judgment indices were chosen from previous clothing-related studies. A total of 636 females defined as "obese" by 5 out of 7 indices were selected as subjects for this study. 54 body measurements and obesity judgment indices were used. First, the subjects had a BMI 27.11, R$\ddot{o}$hrer index 1.76, Vervaeck index 104.77, Relative weight 133.00, and WHR 0.90. In the case of the distribution by age groups, the twenties were 6.4% of the entire subjects, the thirties were 18.2%, the forties were 16.4%, the fifties were 37.4%, and the sixties were 21.5%. The result of the ANOVAs (divided into 5 age groups) showed significant differences in 41 measurement items except for bust circumference, waist length front, and all of obesity judgment indices. Second, according to the ANOVAs among stature groups divided by 5cm pitches there are significant differences in all measurements except for bust circumference. The results of the ANOVAs among bust circumference groups divided by 5cm pitches show that significant differences were observed in all measurements except four measurement items (including body rise). According to the ANOVAs among the waist circumference groups divided by 5cm pitches, there are no significant differences in all height measurements and shoulder length, waist to hip length, and crotch length. It is confirmed that stature and bust circumference have a deep relationship with measurements other than waist circumference. Third, as the factor analysis were conducted using 39 measurement items to extract the body characteristics of obese women Factor 1 is "circumference measurements & obesity judgment indices," Factor 2 is "heights & arm-related lengths," and Factor 3 is "size and ratio of waist circumference & hip circumference." Factor 4 was "lengths in upper body," Factor 5 was "back width in upper body," Factor 6 was "side neck point to bust & bust circumference," Factor 7 was "length in lower body & arm circumferences," and Factor 8 was "neck base circumference & front widths in upper body." These 8 factors explained 76.54% of the total variance.
### Cross-sectional Study of Obesity Indices in Stroke (초발 뇌경색 환자의 비만지표에 관한 단면적 연구)
• Kim, Jin-Ah;Park, Jung-Mi;Kim, Hyung-Do
• Journal of Korean Medicine for Obesity Research
• /
• v.4 no.1
• /
• pp.55-60
• /
• 2004
• Objective: Obesity is an established risk factor for Coronary Heart Disease, but its role as risk factor for Stroke remains controversial. And we examined association between Obesity indices and Stroke cross sectionally. Methods: The subjects were 30 stroke patients admitted in hospital. We measured obesity indices of BMI, waist circumference and waist-to-height ratio. Result: There was a significant correlation among BMI, waist circumference and waist-to-height ratio. 47% of subjects were obese in BMI and 93% of subjects were obese in waist-to-height ratio. Conclusion: Abdominal obesity measured by waist circumference and waist-to-height ratio may be a better predictor of stroke than BMI.
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https://crackexams99.com/free-fall-equation-with-definition/
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# Free Fall Equation With Definition
Free Fall Equation With Definition: In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. Or we can say that acceleration due to gravity. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.
## Free Fall Equation With Explanation
1. h= 1/2gt²
2. v²= 2gh
3. v=gt
where, h = height traveled
v = final velocity
g = acceleration due to gravity
t = time taken
The free fall equation can be derived from the equations of motion.
• s= ut+1/2at²
• v² =u²+ 2as
• v=u+at
initial velocity u=0,
acceleration, a=g.
distance traveled, s = h,
After placing these values we get.
Free Fall Equations, i.e.
• h= 1/2gt²
• v² =2gh
• v=gt
Share on:
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http://meshugga.ugent.be/snaut/
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## snaut
snaut allows to measure semantic distance between words or documents and explore distributional semantics models through a convenient interface.
You can find the associated paper here (Mandera, Keuleers, & Brysbaert, in press).
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http://mathhelpforum.com/algebra/162031-sum-squares-all-numbers-between-10-70-divisible-4-a-print.html
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# sum of squares of all numbers between 10 and 70 and which are divisible by 4.
• Nov 3rd 2010, 07:26 PM
rickrishav
sum of squares of all numbers between 10 and 70 and which are divisible by 4.
Find the sum of squares of all numbers between 10 and 70 and which are divisible by 4.
• Nov 4th 2010, 08:19 AM
Wilmer
All evens are divisible by 4; so "sum of even squares":
n = 70/2 = 35; f = (10-2)/2 = 4
2n(n+1)(2n+1)/3 - 2f(f+1)(2f+1)/3 = 59640 - 120 = 59520
"See" that?
• Nov 4th 2010, 10:13 AM
Soroban
Hello, rickrishav!
I hope I interpreted the problem correctly . . .
Quote:
Find the sum of squares of all integers between 10 and 70 which are divisible by 4.
The integers between 10 and 70 which are multiple of 4 are:
. . $\{12,16,20,24,\,\hdots\,68\} \;=\;\{3\!\cdot\!4,\:4\!\cdot\!4,\:5\!\cdot\!4,\:6 \!\cdot\!6,\:\hdots\:17\!\cdot\!4\}$
The sum of their squares is:
. . $S \;=\;3^2\!\cdot\!4^2 + 4^2\!\cdot\!4^2 + 5^2\!\cdot\!4^2 + 5^2\!\cdot4^2 + \hdots + 17^2\!\cdot\!4^2$
. . . . $=\;4^2\left(3^2 + 4^2 + 5^2 + \hdots + 17^2\right)$
. . . . $\displaystyle = \;4^2\left(\sum^{17}_{k=1} k^2 - \sum^2_{k=1}k^2\right)$
. . . . $-\; 4^2\left(\dfrac{17\!\cdot\!18\!\cdot\!35}{6} - \dfrac{2\!\cdot\!3\!\cdot\!5}{6}\right)$ .**
. . . . $=\;16\cdot 1780$
. . . . $=\;28,\!480$
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
**
The sum of the first $\,n$ squares is:
. . $\displaystyle \sum^n_{k+1} k^2 \;=\; 1^2 + 2^2 + 3^2 + \hdots + n^2 \;=\;\frac{n(n+1)(2n+1)}{6}$
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https://beesbuzz.biz/blog/5206-Thirds
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## Thirds
Kitt wrote an entry about splitting a pastry in thirds, which has a few different solutions. I hashed out what I thought was a correct solution in the comments but I’d actually made a pretty big mistake that came from me not actually drawing a diagram. So here’s a version with diagrams.
## The problem
Let’s say you have a pastry that’s X units wide and Y units tall, and you want to split it into even thirds.
## Trivial: trisection
One simple solution is to bisect the pastry 1/3 across, then to bisect the larger segment:
This gives you three sections, $$A$$, $$B$$, and $$C$$, which each have an area of $$\frac{XY}{3}$$.
But this has a problem: inequal distribution of crust! $$A$$’s crust length is $$\frac{2X}{3} + Y$$ whereas $$B$$ and $$C$$ have a crust length of $$\frac{2X}{3} + \frac{Y}{2}$$, meaning $$A$$ will always get $$\frac{Y}{2}$$ more crust than $$B$$ and $$C$$. This is clearly unfair!
How else can we solve this problem?
## Trangular cut
Another approach is to make $$A$$ a triangular cut out of the side, and $$B$$ and $$C$$ into trapezoids:
This gives us areas of $$A=\frac{2X}{3}\frac{Y}{2}$$ (i.e. $$A=\frac{XY}{3}$$) and $$B=C=\frac{X+\frac{X}{3}}{2}\frac{Y}{2}$$ which, as you might expect, also simplifies to $$\frac{XY}{3}$$. The crust allotments are now $$A=Y$$ and $$B=C=X+\frac{Y}{2}$$. So we can work out the appropriate pastry size to get equal area and crust:
$Y=X+\frac{Y}{2} \\ \frac{Y}{2}=X$
Or, to check our math a bit differently, we want the $$Y$$ edge to be 1/3 of the total edge length $$2(X+Y)$$, so:
$Y=\frac{2X+2Y}{3} \\ 3Y=2X+2Y \\ Y=2X$
which says exactly the same thing.
So if the pastry is twice as tall as it is wide, we’re done! So in this particular pastry we’d actually want the cuts to look more like this:
Where in the above situation, the areas and the crusts are equal for all three pieces.
However, this isn’t good enough! We want to generalize a solution to all possible pastry aspect ratios!
## Generalized solution
So, first, let’s orient the pastry so that $$X > Y$$, i.e. it’s a “lansdcape” aspect, as above.
Now, we know that if $$Y=\frac{X}{2}$$, both constraints are satisfied. But the crust allocation for $$A$$ is always $$X$$ and $$B=C=Y+\frac{X}{2}$$. Which means that if the aspect of the pastry tends more square, then $$A$$ gets less crust proportionally, and if the rectangular gets more elongated, $$A$$ gets proportionally more crust.
So we need to work out two solutions, one for pastries which are less than a 2:1 aspect, and ones which are more than 2:1.
### When $$X < 2Y$$
We add two offsets, $$a$$ and $$b$$, which affect the pastry division thusly:
In this case, section $$A$$’s crust amount is $$X+2a$$, and so we can solve for $$a$$:
$X+2a=\frac{2X + 2Y}{3} \\ 3X+6a=2X+2Y \\ 6a=2Y-X \\ a=\frac{2Y - X}{6}$
So, from this we can see that $$a$$ is only a sensible (i.e. non-negative) value if $$X \leq 2Y$$, so this setup continues to make sense with our preconditions.
Anyway, now that we’ve solved for $$a$$, we can solve for $$b$$:
$\frac{X}{2} \times \frac{b + Y - a}{2} = \frac{XY}{3} \\ \frac{X(b + Y - a)}{4} = \frac{XY}{3} \\ 3X(b + Y - a) = 4XY \\ b + Y - a = \frac{4Y}{3} \\ b = \frac{Y}{3} + a$
So let’s take a look at Kitt’s pastry conundrum and work out how it could have been split into perfect thirds. We can do an approximate measurement on the image; let’s just use pixels as the size unit here and assume that perspective more or less averages out:
Just to keep life simple let’s say that it’s $$X=270$$ and $$Y=240$$, which happens to be an aspect ratio of 9:8 although that doesn’t really matter right now. If we plug those values into the equation, we get $$a=35$$ and $$b=115$$, so this trisection of the pastry should produce equal area and edge:
We should, of course, double-check our math here.
The total edge of this pastry is $$2(270+240) = 1020$$, so each section should have an edge of 340. The edge of section $$A$$ is $$270 + 2 \times 35 = 340$$, so that checks out. (For that matter, it would be even easier to see that $$B$$ and $$C$$ both have $$135 + 205 = 340$$ crust units.)
The total area of this pastry is $$270 \times 240 = 64800$$, so each section should have an area of 21600. The area of section $$B$$ is $$135 \times \frac{240 - 35 + 115}{2} = 21600$$. So at least for this pastry, the math works out!
The theoretical limit for this setup (since we want to restrict ourselves to orienting the pastry such that $$X \geq Y$$) is a width and a height of 1. In that case, we’d have $$a = \frac{1}{6}$$ and $$b = \frac{1}{3} + \frac{1}{6} = \frac{1}{2}$$. Or in other words, it would look like this:
Theoretically the pastry could continue to get narrower as long as $$0 \leq a \leq Y$$ and $$0 \leq b \leq Y$$. We know $$a \geq 0$$ as long as $$X \leq 2Y$$, and we know $$b \geq 0$$ as long as
$\frac{Y}{3} + \frac{2Y - X}{6} \geq 0 \\ \frac{4Y - X}{6} \geq 0 \\$
or, in other words, $$4Y \geq X$$ – which is always true given the above. But what about the other conditions? First, we check that $$a \leq Y$$:
$\frac{2Y - X}{6} \leq Y \\ 2Y - X \leq 6Y \\ {-X} \leq 4Y 0 \leq 4Y + X$
Well, since $$X$$ and $$Y$$ are always positive, it’s safe to say that this condition is true. What about $$b \leq Y$$?
$\frac{Y}{3} + \frac{2Y - X}{6} \leq Y \\ 2Y + 2Y - X \leq 6Y \\ 0 \leq 2Y + X$
Which is, again, always true. So, this setup can always be used for any pastry; if it’s more than twice as wide than it is tall, simply turn it sideways. But this might make for some very slim cuts, so we still want a general solution that works for an extra-wide pastry. Also, it would get weird if we ever have a situation where $$Y - a < b$$. Does that ever happen?
$Y - a < b \\ Y - a < \frac{Y}{3} + a \\ \frac{2Y}{3} < 2a \\ \frac{2Y}{3} < \frac{2Y - X}{3} \\ 2Y < 2Y - X \\ 0 < -X \\ X < 0$
Okay, so we never actually get into that situation, at least.
### When $$X > 2Y$$
So how can we solve for pastries which are wider than a 2:1 aspect? Let’s try this setup:
In this case, section $$A$$’s crust amount is $$X-2a$$, so we again solve for $$a$$:
$X - 2a = \frac{2X + 2Y}{3} \\ 3X - 6a = 2X + 2Y \\ -6a = 2Y - X \\ a = \frac{X - 2Y}{6}$
And now $$a$$ is only sensible (i.e. non-negative) if $$X \geq 2Y$$, so this setup once again makes sense with our preconditions.
So again, now we solve for $$b$$; this time we can use the area of section $$A$$ as our guide, as it’s much more straightforward to compute:
$\frac{(X - 2a)(Y - b)}{2} = \frac{XY}{3} \\ 3(X - 2a)(Y - b) = 2XY \\ 3(XY - 2aY - bX + 2ab) = 2XY \\ 3XY - 6aY - 3bX + 6ab = 2XY \\ 6ab - 3Xb = 6aY - XY \\ b = \frac{6aY - XY}{6a - 3X}\\ b = \frac{(X - 2Y)Y - XY}{X - 2Y - 3X} \\ b = \frac{2Y^2}{2X + 2Y} \\ b = \frac{Y^2}{X + Y}$
So, hey, that simplifies pretty nicely. So, let’s say we have a pastry that’s, say, 3 units wide and 1 unit tall. In this case, $$a=\frac{1}{6}$$ and $$b = \frac{1}{4}$$. Let’s verify that this makes sense!
This theoretical pastry would have a total area of 3, and a total edge of 8. So we’d need section $$A$$ to have 1 unit of area and $$\frac{8}{3}$$ units of edge. How does this work out?
Edge length is $$X-2a = 3 - \frac{2}{6} = \frac{8}{3}$$. Phew!
And the area is $$\frac{(X - 2a)(Y - b)}{2} = \frac{\frac{8}{3} \times \frac{3}{4}}{2} = 1$$. Alright!
Are there any limits to how wide the pastry can be? As always, we want $$a \geq 0$$ and $$b \geq 0$$. We already know this to be true for $$a$$ as long as $$X \geq 2Y$$ (which is the situation we have this setup for anyway), and it’s pretty obvious that $$b \geq 0$$ as long as $$X$$ and $$Y$$ are non-negative real numbers. This will not hold for imaginary pastry heights, though.
We also need $$2a \leq X$$ and $$b \leq Y$$. First thing first:
$2a \leq X \\ \frac{X - 2Y}{3} \leq X \\ X - 2Y \leq 3X \\ {-2Y} \leq 2X \\ 0 \leq X + Y$
Which is always true. And now the other thing:
$\frac{Y^2}{X + Y} \leq Y \\ Y^2 \leq XY + Y^2 \\ 0 \leq XY$
which is also always true.
So, now we know how to always trisect a pastry and keep the same amount of edge and area between all three parts!
## Left as an exercise for the reader
• Figuring out the volume of filling
• Accounting for the width of the crimping
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https://www.mi.fu-berlin.de/math/groups/discgeom/projects/ERC/Publications_old2/Preprints/Equivariant_topology_of_configuration_spaces/index.html
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Springe direkt zu Inhalt
# Equivariant topology of configuration spaces
## Pavle V. M. Blagojević, Wolfgang Lück, Günter M. Ziegler – 2012
Focus Area 3: Topological connectivity and diameter of Discrete Structures We study the Fadell-Husseini index of the configuration space F(R^d,n) with respect to different subgroups of the symmetric group S_n. For p prime and d>0, we completely determine Index_{Z/p}(F(R^d,p);F_p) and partially describe Index{(Z/p)^k}(F(R^d,p^k);F_p). In this process we obtain results of independent interest, including: (1) an extended equivariant Goresky-MacPherson formula, (2) a complete description of the top homology of the partition lattice Pi_p as an F_p[Z_p]-module, and (3) a generalized Dold theorem for elementary abelian groups. The results on the Fadell-Husseini index yield a new proof of the Nandakumar & Ramana Rao conjecture for a prime. For n=p^k a prime power, we compute the Lusternik-Schnirelmann category cat(F(R^d,n)/S_n)=(d-1)(n-1), and for spheres obtain the bounds (d-1)(n-1)\le cat(F(S^d,n)/S_n)\le (d-1)(n-1)+1. Moreover, we extend coincidence results related to the Borsuk-Ulam theorem, as obtained by Cohen & Connett, Cohen & Lusk, and Karasev & Volovikov.
Titel
Equivariant topology of configuration spaces
Verfasser
Pavle V. M. Blagojević, Wolfgang Lück, Günter M. Ziegler
Datum
2012-07
Art
Text
Größe oder Länge
40 pages
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https://homework.cpm.org/category/CON_FOUND/textbook/gc/chapter/11/lesson/11.1.3/problem/11-36
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### Home > GC > Chapter 11 > Lesson 11.1.3 > Problem11-36
11-36.
Find the volume and surface area of a square-based right pyramid if the base edge has length 6 units and the height of the pyramid is $4$ units. Assume the diagram at right is not to scale.
$\text{Volume }= \frac{1}{3} (\text{volume of the corresponding prism})$
$\frac{1}{3} (\text{number of cubes in the bottom layer)(number of layers)}$
$\frac{1}{3}(l)(w)(h)$
$\frac{1}{3}(6^2\cdot4)$
$\text{Surface Area} = 4\text{(area of triangle) + (area of base)}$
You will need to find the slant height of the pyramid.
$96$ square units
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https://physics.stackexchange.com/questions/625977/transformation-law-of-vector-fields-on-mathbbrn
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# Transformation law of vector fields on $\mathbb{R}^n$
So suppose we have a function $$F$$ from $$\mathbb R^2$$ to $$\mathbb R^2$$ defined by $$F(x,y) = (g(x,y),h(x,y))$$ where $$g$$ and $$h$$ represent temperate and pressure respectively (the point is, they are both scalar fields). From the viewpoint of differential geometry the above function can be seen as a (coordinate representation of a) vector field (i.e. a map from the manifold to the tangent bundle); and here's where my confusion lies: Mathematically, since this is a section of the projection map it is forced to obey the vector transformation law, yet physically it's intuitively clear that this is not a vector field but rather just a bunch of scalars so do we implement a vector transformation law or not (under a change of coordinates); does it even make sense to talk about? I'm having trouble putting the rigorous definitions of differential geometry into physical context.
More generally if we have an n-dimensional smooth manifold $$\cal M$$ (so think of a Riemannian 4-manifold for instance) and a function $$F$$ from $$\cal M$$ to $$\mathbb R^n$$, will the physical nature of this function (i.e. depending on what physical quantity it represents) govern its transformation behavior? If yes, where is this (if at all) taken into account in the mathematical framework of differential geometry?
• The tangent space of a point on manifold needs to be defined before you can talk about vectors. This can be done with directional derivatives. This is also why the dimension of the vector space is the dimension of the manifold. The pressure and temperature have no relationship to tangent space. You could define these on a 1D manifold, but the vector space of a 1D manifold must have dimension 1. Mar 31 at 2:37
• The transformation law of a vector field on a manifold is that of a contravariant vector (field). Mar 31 at 2:37
• @Jbag1212 what do you mean the tangent space needs to be defined? It is defined in the obvious way for $R^2$. And I am aware of all that, what i'm saying is this: I have a function as defined above and it can be easily shown to be a section of the projection map from $TR^2$ to $R^2$, so mathematically it satisfies the definition of a vector field (which is just a section of the projection map), so give me a reason why it shouldn't obey the vector transformation law. Mar 31 at 2:43
• Things obey the vector transformation law if they are vectors which are elements of the tangent space at each point. In $\mathbb{R}^2$ suppose we have a basis for the tangent space, and physically we call it "north-south" and "east-west." Physically speaking, the temperature and pressure do not depend the direction of "north-south" and "east-west." So this vector of temperature and pressure is not in the tangent space. Mar 31 at 2:52
• In physics we look for physical quantities which transform like tensors. If you were just given a function that you don't actually know what it physically represents, then of course you wouldn't be able to proceed. Just because something has multiple indices doesn't mean that it is a tensor. Spinors are one example, And in answer to your question, yes. Mar 31 at 3:07
TL;DR - I suspect your confusion lies in the Physics 101 example that e.g. the ordered pair ("temperature","pressure") does not define a vector because when we change our coordinates, temperature and pressure don't transform. However, if we are working in cartesian coordinates, the object (temperature)$$\hat x$$ + (pressure)$$\hat y$$ is a linear combination of our basis vectors, and therefore does transform appropriately. This is just as well-defined as the vector $$\mathbf V = 3\hat x + 4\hat y$$.
In other words, if you write down a physically meaningless (but perfectly well-defined) vector field in some coordinate system, then it will change in the usual way when you move to a different coordinate system.
So suppose we have a function $$F$$ from $$\mathbb R^2$$ to $$\mathbb R^2$$ defined by $$F(x,y)=(g(x,y),h(x,y))$$ where $$g$$ and $$h$$ represent temperature and pressure respectively (the point is, they are both scalar fields).
Okay, subtlety number one: Is the domain of $$F$$ the manifold $$\mathcal M =\mathbb R^2$$, or the image of $$\mathcal M$$ under a cartesian coordinate chart? $$x :\mathcal M \rightarrow \mathbb R^2$$ $$(a,b) \mapsto (a,b)$$
Mathematical Interlude
Despite being one of the simplest possible manifolds, $$\mathbb R^2$$ is actually terrible from a pedagogical point of view precisely because it's so easy to get confused on this issue. The manifold $$\mathcal M = \mathbb R^2$$ is abstract; points $$p\in \mathbb R^2$$ consist of ordered pairs of real numbers $$(a,b)$$, but those numbers are not coordinates for $$p$$. We can introduce coordinates by defining a coordinate chart on some open neighborhood of $$p$$. For example, we might coordinatize the upper half-plane via the polar coordinate chart: $$\pi : \mathbb R_+^2 \rightarrow \mathbb R \times(0,\pi)$$ $$(a,b) \mapsto \left(\sqrt{a^2+b^2},\sin^{-1}\left(\frac{b}{\sqrt{a^2+b^2}}\right)\right)$$ where the first coordinate is interpreted as the radial coordinate and the second as the angular coordinate. Any function which is defined at the manifold level - e.g. some $$f:\mathcal M \rightarrow \mathbb R$$ - has a corresponding expression in each coordinate chart. For example, let $$f:\mathcal M \rightarrow \mathbb R$$ be defined by $$(a,b)\mapsto a$$. If we descend into the polar coordinate chart, we could consider the function $$f_\pi: \mathbb R\times (0,\pi)$$ $$(r,\theta) \mapsto (f\circ \pi^{-1})(r,\theta) = f\big(r\cos(\theta),r\sin(\theta)\big) = r\cos(\theta)$$ $$f_\pi$$ is the expression of the (manifold-level) function $$f$$ in the $$\pi$$ coordinate chart. Changing to a different chart entails mapping points back to $$\mathcal M$$ via $$\pi^{-1}$$, then applying the new coordinate chart. For example, if we wanted to use the cartesian chart defined above, we would have $$f_x = f\circ x^{-1} = f\circ \pi^{-1} \circ \pi \circ x^{-1} = f_\pi \circ (\pi\circ x^{-1})$$ The map $$\pi \circ x^{-1}$$ is called the chart transition map between the cartesian chart $$x$$ and the polar chart $$\pi$$; it is easily seen to be $$\pi \circ x^{-1}: \mathbb R_+^2 \rightarrow \mathbb R\times(0,\pi)$$ $$(a,b) \mapsto \left(\sqrt{a^2+b^2},\sin^{-1}\left(\frac{b}{\sqrt{a^2+b^2}}\right)\right)$$ and so $$f_x : (r,\theta)\in \mathbb R\times(0,\pi) \mapsto r\cos(\theta)$$ as anticipated.
End Interlude
The point of that somewhat length example is that when you say $$F:\mathbb R^2\rightarrow \mathbb R^2$$, its not clear whether you are defining an express at the manifold level - in which case there are no coordinates being used at all, and no transformations to consider - or at the level of (presumably cartesian) coordinates, in which case your $$F$$ is really $$F_x \equiv F \circ x^{-1}$$, and a change of chart is effected by simply inserting a chart transition map, e.g. $$F_\pi \equiv F_x \circ (x\circ \pi^{-1})$$.
From the viewpoint of differential geometry the above function can be seen as a (coordinate representation of a) vector field (i.e. a map from the manifold to the tangent bundle)
Okay. Based on this, I will assume we are working in cartesian coordinates. You are defining a vector field $$\mathbf V$$ on $$\mathbb R^2$$ whose $$x$$-component is the temperature and whose $$y$$-component is the pressure. That defines a little directional derivative which sits at each point, with the vector field being
$$\mathbf V = g(x,y)\frac{\partial}{\partial x} + h(x,y) \frac{\partial}{\partial y}$$
Mathematically, since this is a section of the projection map it is forced to obey the vector transformation law, yet physically it's intuitively clear that this is not a vector field but rather just a bunch of scalars so do we implement a vector transformation law or not (under a change of coordinates); does it even make sense to talk about?
I don't know what you mean here. It is a perfectly well-defined vector field. It doesn't have any physical significance, as far as I can tell, but that doesn't mean it isn't a vector field.
A change of coordinates induces a change of basis, so you're asking whether the components of $$\mathbf V$$ change when we go from the cartesian basis $$\left\{\frac{\partial}{\partial x},\frac{\partial}{\partial y}\right\}$$ to e.g. the polar basis $$\left\{\frac{\partial}{\partial r}, \frac{\partial}{\partial \theta}\right\}$$, and the answer is obviously yes - the polar coordinate unit vectors generally point in different directions than the cartesian unit vectors, after all. If you replace $$\frac{\partial}{\partial x}\mapsto \frac{\partial r}{\partial x} \frac{\partial}{\partial r} + \frac{\partial \theta}{\partial x} \frac{\partial}{\partial \theta}$$ $$\frac{\partial}{\partial y}\mapsto \frac{\partial r}{\partial y} \frac{\partial}{\partial r} + \frac{\partial \theta}{\partial y} \frac{\partial}{\partial \theta}$$ in our original expression for $$\mathbf V$$, then when the dust settles you'll have something of the form
$$\mathbf V = V^r \frac{\partial}{\partial r} + V^\theta \frac{\partial}{\partial \theta}$$
where $$V^{r}$$ and $$V^\theta$$ are some (position-dependent) linear combinations of $$g$$ and $$h$$. That's all the vector transformation rule is - expressing the same vector field using different basis vectors requires different components, which should be fairly obvious.
Actually, this isn't quite right - your functions $$g$$ and $$h$$ are really $$g_x=g\circ x^{-1}$$ and $$h_x = h\circ x^{-1}$$, so under change of chart they would also be replaced by $$g_\pi = g_x \circ (x\circ \pi^{-1})$$ and $$h_\pi = h_x \circ (x\circ \pi^{-1})$$.
More generally if we have an $$n$$-dimensional smooth manifold $$\mathcal M$$ (so think of a Riemannian 4-manifold for instance) and a function $$F$$ from $$M$$ to $$\mathbb R^n$$, will the physical nature of this function (i.e. depending on what physical quantity it represents) govern its transformation behavior?
No. As long as you have a well-defined function at the manifold level, that immediately translates into an expression in whatever coordinate chart you wish to work in. There is nothing transformative about this idea - if you have a point $$p$$ which is being mapped to some other space and you label $$p$$ by some coordinates, then you get a function which eats those coordinates. If you change coordinates, you change the function.
In this case, that other space was the tangent bundle, and we performed a corresponding chart transformation on that (i.e. a change of basis) which was induced by the chart transformation on the manifold $$\mathcal M=\mathbb R^2$$, which added a layer of complexity.
• I posted 4 pages from Chapter 4 of "Flanders" on imgur.com/gallery/CZSR28w . Every point is attached to a local orthogonal frame $\mathbf{e}_i$ where for each $i=1,2,3$ is a smooth vector field. Flanders writes: "What we shall do is express everything in terms of the $\mathbf {e}_i$, ... apply$d$, and $d\mathbf{x}=\sigma_1 \mathbf{e}_1+\sigma_2 \mathbf{e}_2+\sigma_3 \mathbf{e}_3$" Mar 31 at 13:49
• How can we apply "$d$" to a vector field when it is defined in Chapter 3 for forms but not tangent vectors? What sort of creature $d\mathbf{x}$ is: a covariant or a contravariant vector? Mar 31 at 13:56
• @hyportnex Flanders does the following. The underlying set for Euclidean space is $\mathbb R^3$; consider a cartesian chart $x$ as per my answer, which eat a point $p$ and spit out its cartesian coordinates, $x(p)=(x^1(p),x^2(p),x^3(p))$. Each $x^i$ is a function from $\mathcal M\rightarrow \mathbb R$, so we can define cooresponding 1-forms $\mathrm dx^i$; we then throw these together into a one-form valued vector $\mathrm d\mathbf x= dx^i \frac{\partial}{\partial x^i}$. Mar 31 at 14:10
• @hyportnex More formally, $\mathrm d\mathbf x$ is a $(1,1)$-tensor whose cartesian coordinate form is $\mathrm d\mathbf x = \mathrm dx^i \otimes \frac{\partial}{\partial x^i}$, i.e. its components are $(\mathrm d\mathbf x)^i_{\ \ j}= \delta^i_j$. In a different coordinate system, its components will of course be different. Mar 31 at 14:14
• Thank you for clearing this up. Would you also say that what Flanders does is a bit of a stealthy underhanded way by which he introduces (mixed) tensors? Mar 31 at 14:24
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http://mathhelpforum.com/statistics/195334-help-how-much-allocate-varying-probabilities-get-specific-probability.html
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# Math Help - Help with how much to allocate to varying probabilities to get specific probability?
1. ## Help with how much to allocate to varying probabilities to get specific probability?
Problem:
I must spend $1000. I have 3 strategies that have different Probabilities Of Success (POS). Strategy A POS = 70% Strategy B POS = 50% Strategy C POS = 25% How much do I spend on each strategy (must spend total of$1000) to have an overall POS of 65%?
4. ## Re: Help with how much to allocate to varying probabilities to get specific probabili
If X is success, then the probability of success $P(X)=0.65 = 0.70 \cdot P(A) + 0.50 \cdot P(B) + 0.25 \cdot P(C)$
If you let $b=0$ then you end up with $0.7a + 0.50 \cdot 0 + 0.25 \cdot (1000-a)=650$
Law of total probability - Wikipedia, the free encyclopedia
5. ## Re: Help with how much to allocate to varying probabilities to get specific probabili
Originally Posted by dmbeas12
.65 = .70x + .5x + .25x
This is where you went wrong. Your solution assumes that you bet the same amount on each betting strategy. The percentages you've posted can be interpreted as conditional probabilities. Given a betting strategy A, B or C, what is the probability X that it success. This is where the law of total probability comes into the picture. If you have a sample space where the probability of all events add up to 1, then you can write the probability for an arbitrary event A as:
$P(A)=P(A|H_1)P(H_1) + P(A|H_2)P(H_2)+ ... + P(A|H_N)P(H_N)$, $P(H_1)+P(H_2)+...+P(H_N)=1$
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http://www.health-ground.com/tag/deflazacort-manufacture/
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# Our goal was to determine the role of the inflammatory cytokine
Our goal was to determine the role of the inflammatory cytokine interleukin\23 (IL\23) in promoting neutrophil recruitment, inflammatory cytokine expression and intestinal histopathology in response to infection. was also a trend towards less severe colonic Deflazacort manufacture histopathology in the absence of IL\23. The induction of and was also significantly abrogated in IL\23KO mice. Inflammatory cytokine expression and neutrophilic inflammation were not reduced in IL\17a\deficient mice or in mice treated with anti\IL\22 depleting monoclonal antibody. However, induction of was significantly reduced in animals treated with anti\IL\22 antibody. Taken together, these data indicate that IL\23, but not IL\17a or IL\22,
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https://worldwidescience.org/topicpages/p/protandrous+black+porgy.html
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#### Sample records for protandrous black porgy
1. Biological characteristics and probiotic effect of Leuconostoc lactis strain isolated from the intestine of black porgy fish
Directory of Open Access Journals (Sweden)
Wei Zhang
2013-09-01
Full Text Available A strain of lactic acid bacteria, Leuconostoc lactis, was isolated from the intestinal tract of black porgy, Sparus macrocephalus, and identified by conventional biochemical characteristics and 16S rDNA gene sequence analysis. The isolated strain had the ability of bile tolerance and resistance to low pH, and survived well in the trypsinase and pepsin solution. But the highly concentrated dose of trypsinase and pepsin affect the viability of the isolated strain. The isolate was resistant to several antibiotics, including Cephalothin, Ceftriaxone, Imipenem and Tobramycin. The isolate could autoaggregate itself and coaggregate with other bacteria in vitro. The autoaggregation percentage increased to 23.29% after 20 h of incubation. The percentage of coaggregation were respectively 31.21%, 29.44%, 10.74%, 16.49%, 24.36%, 24.41% and 20.99% for Vibrio parahaemolyticus, Listeria monocytogenes, Escherichia coli O157, Salmonella typhimurium, Shigella, Staphylococcus aureus and Proteusbacillus vulgaris after 20 h incubation of a mixed suspension. The supernatant of the strain inhibited the growth of several pathogens, such as V.parahaemolyticus, Vibrio harveyi, Vibrio alginolyticus, Staphylococcus aureus, Escherichia coli O157, Salmonella typhimurium, Bacillus subtilis, Proteusbacillus vulgaris and Shigella. These results indicated that the isolate, Leuconostoc lactis, might be an attractive candidate for perspectival strain for probiotics in marine aquaculture.
2. Reproductive biology of black seabream Acanthopagrus schlegelii, threadfin porgy Evynnis cardinalis and red pargo Pagrus major in the northern South China Sea with consideration of fishery status and management needs.
Science.gov (United States)
Law, C S W; Sadovy de Mitcheson, Y
2017-07-01
The reproductive biology of three commercially significant seabream species (family: Sparidae) Acanthopagrus schlegelii, Evynnis cardinalis and Pagrus major, taken from Hong Kong and adjacent northern South China Sea (SCS) waters, were investigated for their sexual patterns, spawning seasons, length at maturity and exploitation in relation to their conservation and management status. Histological analysis showed E. cardinalis and P. major to be functionally gonochoristic, the latter having a bisexual juvenile stage and being a rudimentary hermaphrodite. Acanthopagrus schlegelii is a protandric hermaphrodite. Standard length (L S ) at 50% sex change for A. schlegelii is 291 mm. L S at 50% female maturity for E. cardinalis and P. major are 117 and 332 mm, respectively. For all three species, the spawning period falls between November and March. The study highlights geographical differences in reproductive biology among the species and a paucity of fishery or other population-related data. While heavy fishing pressure, life-history characteristics and absence of effective management throughout the geographic ranges of these species make them susceptible to overfishing, they nonetheless appear to be generally more resilient than many other taxa that comprise the multi-species fisheries of the region, possibly due to their relatively rapid sexual maturation and spatial movement patterns. Overall, however, little is known of the biology, fishing history and current fishery status of sparids in general in the northern SCS and the current study is one of the first to examine such aspects of this family in the region and to consider appropriate management options. © 2017 The Fisheries Society of the British Isles.
3. Isolation, identification and biological characteristics of an exopolysaccharide-producing lactic acid bacteria strain from intestinal tract of black porgy (Sparus macrocephalus)%产胞外多糖的黑鲷肠道乳酸菌的分离鉴定及其生物学特性
Institute of Scientific and Technical Information of China (English)
戴贤君; 章蔚; 刘明启; 黄晓林
2011-01-01
通过常规鉴定和16S rDNA序列分析,从黑鲷(Sparus macrocephalus)肠道中分离鉴定出1株明串珠菌属(Leuconostoc)乳酸菌菌株;该分离株对酸、胆盐、蛋白酶具有良好耐受性,但对温度耐受能力较差;分离株培养上清液对哈维氏弧菌(Vibrio harveyi)、溶藻弧菌(Vibrio algnolyticus)、副溶血弧菌(Vibrio parahaemolyticus)的抑菌圈直径为1.12～1.22 cm,不同培养时间的抑菌效果差异无统计学意义(P＞0.05);分离株在培养24、32、40、48和56 h时的胞外多糖质量浓度为167.24～184.45 mg·L-1,不同取样时间的胞外多糖质量浓度差异无统计学意义(P＞0.05);灌服胞外多糖20 d后黑鲷血液的红细胞、白细胞数量和血红素浓度、淋巴细胞比率均显著升高(P＜0.05).综上,该分离株为产胞外多糖的明串珠属乳酸菌,可作为开发海水鱼用微生态制剂的候选菌株.%A strain of exopolysaccharide-producing lactic acid bacteria was isolated from intestines of black porgy, Sparus macrocephalus, and was identified as Leuconostoc lactis by conventional biochemical characteristics, 16S rDNA gene sequence analysis. Physiological-biochemical tests for the isolate showed that it had good tolerance to acid, bile salt and protease, but couldn' t live above 70 ℃. The culture supernatant of the isolate could inhibit the growth of Vibrio parahaemolyticus, Vibrio harveyi and Vibrio alginolyticus, and the inhibition zone diameters were 1.12-1.22 cm and had not significant difference (P＞ 0.05) at different culture time of 24, 32, 40, 48, 56 h, The concentrations of exopolysaccharides in the culture medium were 167. 24-184.45 mg· L-1 with no significant difference (P＞0. 05) at the culture time of 24, 32, 40, 48, 56 h. The erythrocyte and leukocyte counts,hemoglobin concentration and lymphocyte ratio of black porgies increased significantly (P＜0. 05) after being fed orally exopolysaccharides from the isolate culture for 20 d. The results above
4. The acute stress response of red porgy, Pagrus pagrus, kept on a red or white background
NARCIS (Netherlands)
Salm, A.L. van der; Pavlidis, M; Flik, G.; Wendelaar Bonga, S.E.
2005-01-01
The skin colour of red porgy, Pagrus pagrus, can be modified by exposure to different background colours. Red and white background colours brighten the dark skin colour that develops under common culture conditions in red porgy. To assess whether skin colour is also modified by aquaculture related
5. Strategy-Driven Exploration for Rule-Based Models of Biochemical Systems with Porgy
OpenAIRE
Andrei , Oana; Fernández , Maribel; Kirchner , Hélène; Pinaud , Bruno
2016-01-01
This paper presents Porgy – an interactive visual environment for rule-based modelling of biochemical systems. We model molecules and molecule interactions as port graphs and port graph rewrite rules, respectively. We use rewriting strategies to control which rules to apply, and where and when to apply them. Our main contributions to rule-based modelling of biochemical systems lie in the strategy language and the associated visual and interactive features offered by Porgy. These features faci...
6. Effects of husbandry conditions on the skin colour and stress response of red porgy, Pagrus pagrus
NARCIS (Netherlands)
Salm, A.L. van der; Martinez, M.; Flik, G.; Wendelaar Bonga, S.E.
2004-01-01
Red porgy, Pagrus pagrus, is a potential candidate for aquaculture. However, darkening of the body occurs after capture of wild fish and during fanning of cultured animals. In fish, skin pigmentation is hormonally controlled and the main hormone involved in skin darkening,
7. Redescription and biology of Diopatra neapolitana (Annelida: Onuphidae), a protandric hermaphrodite with external spermaducal papillae
Science.gov (United States)
Arias, Andrés; Paxton, Hannelore; Budaeva, Nataliya
2016-06-01
A one-year study of the reproductive biology of a population of Diopatra neapolitana at Villaviciosa estuary, northern Spain, was undertaken. Field observations together with a histological study of monthly collected individuals revealed that the population was iteroparous, had a discontinuous reproductive season with a resting period during August and September and a spawning season from March to July. The study showed that D. neapolitana was not dioecious as previously suggested but consisted of protandric sequential hermaphrodites, pure males and pure females with a male biased sex ratio of 3:1. During the peak reproductive period from May to August we observed simultaneous hermaphrodites with two dorsal papillae per segment in the branchial region. Histological studies demonstrated that the papillae were acting as seminal vesicles, storing own sperm, and also as sperm ducts, providing an exit route; hence we termed them 'spermaducal papillae'. The papillae are not the only sperm repositories as the coelom of males and simultaneous hermaphrodites in smaller size classes is also filled with sperm. The worms are broadcast spawners with a brief pelagic larval stage as previously reported but the finer points of this unusual fertilisation system need still to be elaborated. Diopatra cryptornata was recently described as a new species, supposedly differing from D. neapolitana in chaetal detail and the possession of the papillae. We have shown conclusively with morphological and genetical studies that the former species is a junior synonym of the latter. In the absence of type material we are here designating a neotype from recently collected material from Naples.
8. In vitro metabolism of radioactive progesterone and testosterone by the gonads of the protandrous Rhabdosargus sarba at various sexual phases
International Nuclear Information System (INIS)
Yeung, W.S.; Chan, S.T.
1985-01-01
The in vitro steroidogenic capacity of the gonadal tissue in the protandrous Rhabdosargus sarba was studied. Testicular and ovarian tissues from various sexual phases were used either separately or combined. With progesterone as precursor, high yield of 5 beta-reduced metabolites, and no 11-ketotestosterone or 11 beta-hydroxytestosterone were found. The production of 5 beta-pregnan-3 alpha-ol-20-one and 5 beta-pregnane-3,20-dione was very high in incubations with testicular tissue from intersexes or males and was low in those with ovarian tissue only. The production of 17 alpha-hydroxyprogesterone was high in the female but was low in other sexual phases. With testosterone as precursor, 11-ketotestoterone and 11 beta-hydroxytestosterone were identified. 5 beta-Reductase activity was high in the male and relatively low in the female. 5 alpha-Reduced products, however, were absent. There was an increase in the production of androstenedione as the animal underwent sex reversal. The significance of this change in steroidogenesis in this protandrous fish is at present under investigation. Experimental results also indicated that in the intersexual gonad there may be interaction between the testicular component and the ovarian component in steroidgenesis
9. The Size Advantage Model of Sex Allocation in the Protandrous Sex-Changer Crepidula fornicata: Role of the Mating System, Sperm Storage, and Male Mobility.
Science.gov (United States)
Broquet, Thomas; Barranger, Audrey; Billard, Emmanuelle; Bestin, Anastasia; Berger, Rémy; Honnaert, Gaelle; Viard, Frédérique
2015-09-01
Sequential hermaphroditism is adaptive when the reproductive value of an individual varies with size or age, and this relationship differs between males and females. In this case, theory shows that the lifetime reproductive output of an individual is increased by changing sex (a hypothesis referred to as the size-advantage model). Sex-linked differences in size-fitness curves can stem from differential costs of reproduction, the mating system, and differences in growth and mortality between sexes. Detailed empirical data is required to disentangle the relative roles of each of these factors within the theory. Quantitative data are also needed to explore the role of sperm storage, which has not yet been considered with sequential hermaphrodites. Using experimental rearing and paternity assignment, we report relationships between size and reproductive success of Crepidula fornicata, a protandrous (male-first) gastropod. Male reproductive success increased with size due to the polygamous system and stacking behavior of the species, but females nonetheless had greater reproductive success than males of the same size, in agreement with the size-advantage theory. Sperm storage appeared to be a critical determinant of success for both sexes, and modeling the effect of sperm storage showed that it could potentially accelerate sex change in protandrous species.
10. Black to Black
DEFF Research Database (Denmark)
Langkjær, Michael Alexander
2012-01-01
Pop musicians performing in black stage costume take advantage of cultural traditions relating to matters black. Stylistically, black is a paradoxical color: although a symbol of melancholy, pessimism, and renunciation, black also expresses minimalist modernity and signifies exclusivity (as is hi...
11. Black rings
International Nuclear Information System (INIS)
Emparan, Roberto; Reall, Harvey S
2006-01-01
A black ring is a five-dimensional black hole with an event horizon of topology S 1 x S 2 . We provide an introduction to the description of black rings in general relativity and string theory. Novel aspects of the presentation include a new approach to constructing black ring coordinates and a critical review of black ring microscopics. (topical review)
12. Black holes
International Nuclear Information System (INIS)
Feast, M.W.
1981-01-01
This article deals with two questions, namely whether it is possible for black holes to exist, and if the answer is yes, whether we have found any yet. In deciding whether black holes can exist or not the central role in the shaping of our universe played by the forse of gravity is discussed, and in deciding whether we are likely to find black holes in the universe the author looks at the way stars evolve, as well as white dwarfs and neutron stars. He also discusses the problem how to detect a black hole, possible black holes, a southern black hole, massive black holes, as well as why black holes are studied
13. Black Alcoholism.
Science.gov (United States)
Watts, Thomas D.; Wright, Roosevelt
1988-01-01
Examines some aspects of the problem of alcoholism among Blacks, asserting that Black alcoholism can best be considered in an ecological, environmental, sociocultural, and public health context. Notes need for further research on alcoholism among Blacks and for action to reduce the problem of Black alcoholism. (NB)
14. Black holes
OpenAIRE
Brügmann, B.; Ghez, A. M.; Greiner, J.
2001-01-01
Recent progress in black hole research is illustrated by three examples. We discuss the observational challenges that were met to show that a supermassive black hole exists at the center of our galaxy. Stellar-size black holes have been studied in x-ray binaries and microquasars. Finally, numerical simulations have become possible for the merger of black hole binaries.
15. Black Tea
Science.gov (United States)
... mental alertness as well as learning, memory, and information processing skills. It is also used for treating headache; ... of carbamazepine. Since black tea contains caffeine, in theory taking black tea with carbamazepine might decrease the ...
16. Black Holes
OpenAIRE
Townsend, P. K.
1997-01-01
This paper is concerned with several not-quantum aspects of black holes, with emphasis on theoretical and mathematical issues related to numerical modeling of black hole space-times. Part of the material has a review character, but some new results or proposals are also presented. We review the experimental evidence for existence of black holes. We propose a definition of black hole region for any theory governed by a symmetric hyperbolic system of equations. Our definition reproduces the usu...
17. Black Holes
OpenAIRE
Horowitz, Gary T.; Teukolsky, Saul A.
1998-01-01
Black holes are among the most intriguing objects in modern physics. Their influence ranges from powering quasars and other active galactic nuclei, to providing key insights into quantum gravity. We review the observational evidence for black holes, and briefly discuss some of their properties. We also describe some recent developments involving cosmic censorship and the statistical origin of black hole entropy.
18. Black Culture
Directory of Open Access Journals (Sweden)
Angela Khristin Brown
2013-07-01
Full Text Available The migration of blacks in North America through slavery became united. The population of blacks past downs a tradition of artist through art to native born citizens. The art tradition involved telling stories to each generation in black families. The black culture elevated by tradition created hope to determine their personal freedom to escape from poverty of enslavement and to establish a way of life through tradition. A way of personal freedoms was through getting a good education that lead to a better foundation and a better way of life.
19. The Crisis in Black and Black.
Science.gov (United States)
Hutchinson, Earl Ofari
These essays explore why the historic conflict between blacks and whites in the United States has become a crisis that divides many African Americans. The changing racial dynamic is not marked by conflicts. between the black middle class and the poor, black men and women, the black intellectual elite and rappers, black politicians and the urban…
20. Counseling Blacks
Science.gov (United States)
Vontress, Clemmont E.
1970-01-01
Blacks have developed unique environmental perceptions, values, and attitudes, making it difficult for counselors to establish and maintain positive rapport. This article examines attitudinal ingredients posited by Carl Rogers for relevance to this problem, and suggests in-service training to help counselors and other professionals relate…
1. Black Willow
Science.gov (United States)
R. M. Krinard
1980-01-01
Black willow and other species of Salix together comprise a majority of the stocking. Cottonwood is the chief associate, particularly in the early stages, but green ash, sycamore, pecan, persimmon, waterlocust, American elm, baldcypress, red maple, sugarberry, box-elder, and in some areas, silver maple are invaders preceding the next successional stage.
2. Black Psyllium
Science.gov (United States)
... by mouth for up to 6 weeks reduces blood sugar in people with type 2 diabetes. Cancer. Diarrhea. Irritable bowel syndrome (IBS). Other conditions. ... with the dose. Diabetes: Black psyllium can lower blood sugar levels ... with type 2 diabetes by slowing down absorption of carbohydrates. Monitor blood ...
3. Black hole astrophysics
International Nuclear Information System (INIS)
Blandford, R.D.; Thorne, K.S.
1979-01-01
Following an introductory section, the subject is discussed under the headings: on the character of research in black hole astrophysics; isolated holes produced by collapse of normal stars; black holes in binary systems; black holes in globular clusters; black holes in quasars and active galactic nuclei; primordial black holes; concluding remarks on the present state of research in black hole astrophysics. (U.K.)
4. Contemporary Black Theatre.
Science.gov (United States)
Thomas, Pearl
The distinguishable black theatre in America, mirroring a distinguishable black experience, is an artistic product which demands audience involvement. Both the Afro-American oral tradition and the art of gesture are integral aspects of black theatre. In addition, the tragedy found black theatre is not tragedy in the classic sense, as blacks feel…
5. Black widow spider
Science.gov (United States)
... medlineplus.gov/ency/article/002858.htm Black widow spider To use the sharing features on this page, please enable JavaScript. The black widow spider (Latrodectus) has a shiny black body with a ...
6. Black Urine
Directory of Open Access Journals (Sweden)
Rahim Vakili
2016-06-01
Full Text Available A 2-year-old boy was born at term of healthy, non-consanguineous Iranian parents. His mother attended in the clinic with the history of sometimes discoloration of diapers after passing urine. She noticed that first at the age of one month with intensified in recent months. His Physical examination and growth parameters were normal. His mother denied taking any medication (sorbitol, nitrofurantoin, metronidazole, methocarbamol, sena and methyldopa (5. Qualitative urine examination showed dark black discoloration. By this history, alkaptonuria was the most clinical suspicious. A 24-hour-urine sample was collected and sent for quantitative measurements. The urine sample was highly positive for homogentisic acid and negative for porphyrin metabolites.
7. Megadenus atrae n. sp., an endoparasitic eulimid gastropod (Mollusca) from the black sea cucumber Holothuria atra Jaeger (Aspidochirotida: Holothuriidae) in the Indo-West Pacific.
Science.gov (United States)
Takano, Tsuyoshi; Warén, Anders; Kano, Yasunori
2017-07-01
An eulimid gastropod, Megadenus atrae n. sp., endoparasitic in the cloacal chamber of the black sea cucumber Holothuria atra Jaeger is described from Okinawa, Japan, as the fifth species of the genus. Conspecific specimens have also been found from southeast India, northeast Australia and New Caledonia. The generic assignment is justified by the presence of (i) a thick, long proboscis that bears a large fold (pseudopallium) near the base and a collar-like structure at the middle, (ii) a thin, globose shell that is covered by the pseudopallium, and (iii) sexual dimorphism with the female generally larger than the male. The new species is distinguishable from the four previously described congeners by its cauldron-shaped pseudopallium, moderately-developed collar of the proboscis and rounded basal lip of the shell. The comparisons of the size and sex of solitary and paired individuals support a previous hypothesis that the species of Megadenus Rosén, 1910 are protandrous with environmental sex determination. The present species occurs mostly as monogamous pairs despite its very low population density, implying that the presence of a conspecific individual acts as a cue for larval settlement. Both mechanisms would increase individual reproductive success in such permanent parasites with low prevalence and abundance as the species of Megadenus.
8. Black Silicon Solar Cells with Black Ribbons
DEFF Research Database (Denmark)
Davidsen, Rasmus Schmidt; Tang, Peter Torben; Mizushima, Io
2016-01-01
We present the combination of mask-less reactive ion etch (RIE) texturing and blackened interconnecting ribbons as a method for obtaining all-black solar panels, while using conventional, front-contacted solar cells. Black silicon made by mask-less reactive ion etching has total, average...... in the range 15.7-16.3%. The KOH-textured reference cell had an efficiency of 17.9%. The combination of black Si and black interconnecting ribbons may result in aesthetic, all-black panels based on conventional, front-contacted silicon solar cells....... reflectance below 0.5% across a 156x156 mm2 silicon (Si) wafer. Black interconnecting ribbons were realized by oxidizing copper resulting in reflectance below 3% in the visible wavelength range. Screen-printed Si solar cells were realized on 156x156 mm2 black Si substrates with resulting efficiencies...
9. Black holes. Chapter 6
International Nuclear Information System (INIS)
Penrose, R.
1980-01-01
Conditions for the formation of a black hole are considered, and the properties of black holes. The possibility of Cygnus X-1 as a black hole is discussed. Einstein's theory of general relativity in relation to the formation of black holes is discussed. (U.K.)
10. Search for black holes
International Nuclear Information System (INIS)
Cherepashchuk, Anatolii M
2003-01-01
Methods and results of searching for stellar mass black holes in binary systems and for supermassive black holes in galactic nuclei of different types are described. As of now (June 2002), a total of 100 black hole candidates are known. All the necessary conditions Einstein's General Relativity imposes on the observational properties of black holes are satisfied for candidate objects available, thus further assuring the existence of black holes in the Universe. Prospects for obtaining sufficient criteria for reliably distinguishing candidate black holes from real black holes are discussed. (reviews of topical problems)
11. A Dancing Black Hole
Science.gov (United States)
Shoemaker, Deirdre; Smith, Kenneth; Schnetter, Erik; Fiske, David; Laguna, Pablo; Pullin, Jorge
2002-04-01
Recently, stationary black holes have been successfully simulated for up to times of approximately 600-1000M, where M is the mass of the black hole. Considering that the expected burst of gravitational radiation from a binary black hole merger would last approximately 200-500M, black hole codes are approaching the point where simulations of mergers may be feasible. We will present two types of simulations of single black holes obtained with a code based on the Baumgarte-Shapiro-Shibata-Nakamura formulation of the Einstein evolution equations. One type of simulations addresses the stability properties of stationary black hole evolutions. The second type of simulations demonstrates the ability of our code to move a black hole through the computational domain. This is accomplished by shifting the stationary black hole solution to a coordinate system in which the location of the black hole is time dependent.
12. Black hole critical phenomena without black holes
large values of Ф, black holes do form and for small values the scalar field ... on the near side of the ridge ultimately evolve to form black holes while those configu- ... The inset shows a bird's eye view looking down on the saddle point.
13. The Black Studies Boondoggle
Science.gov (United States)
Long, Richard A.
1970-01-01
Indicates tendencies dangerous to the basic purpose of Black Studies, and identifies four external challeges--imperialism, paternalism, nihilism, and materialism. An internal challenge is considered to be the use of European and Establishment constructs to analyze black reality. (DM)
14. Black hole hair removal
International Nuclear Information System (INIS)
Banerjee, Nabamita; Mandal, Ipsita; Sen, Ashoke
2009-01-01
Macroscopic entropy of an extremal black hole is expected to be determined completely by its near horizon geometry. Thus two black holes with identical near horizon geometries should have identical macroscopic entropy, and the expected equality between macroscopic and microscopic entropies will then imply that they have identical degeneracies of microstates. An apparent counterexample is provided by the 4D-5D lift relating BMPV black hole to a four dimensional black hole. The two black holes have identical near horizon geometries but different microscopic spectrum. We suggest that this discrepancy can be accounted for by black hole hair - degrees of freedom living outside the horizon and contributing to the degeneracies. We identify these degrees of freedom for both the four and the five dimensional black holes and show that after their contributions are removed from the microscopic degeneracies of the respective systems, the result for the four and five dimensional black holes match exactly.
15. Noncommutative black holes
Energy Technology Data Exchange (ETDEWEB)
Lopez-DomInguez, J C [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); RamIrez, C [Facultad de Ciencias FIsico Matematicas, Universidad Autonoma de Puebla, PO Box 1364, 72000 Puebla (Mexico); Sabido, M [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico)
2007-11-15
We study noncommutative black holes, by using a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate Hawking's temperature and entropy for the 'noncommutative' Schwarzschild black hole.
16. Black holes without firewalls
Science.gov (United States)
Larjo, Klaus; Lowe, David A.; Thorlacius, Larus
2013-05-01
The postulates of black hole complementarity do not imply a firewall for infalling observers at a black hole horizon. The dynamics of the stretched horizon, that scrambles and reemits information, determines whether infalling observers experience anything out of the ordinary when entering a large black hole. In particular, there is no firewall if the stretched horizon degrees of freedom retain information for a time of the order of the black hole scrambling time.
17. Black holes are hot
International Nuclear Information System (INIS)
Gibbons, G.
1976-01-01
Recent work, which has been investigating the use of the concept of entropy with respect to gravitating systems, black holes and the universe as a whole, is discussed. The resulting theory of black holes assigns a finite temperature to them -about 10 -7 K for ordinary black holes of stellar mass -which is in complete agreement with thermodynamical concepts. It is also shown that black holes must continuously emit particles just like ordinary bodies which have a certain temperature. (U.K.)
18. Monopole Black Hole Skyrmions
OpenAIRE
Moss, Ian G; Shiiki, N; Winstanley, E
2000-01-01
Charged black hole solutions with pion hair are discussed. These can be\\ud used to study monopole black hole catalysis of proton decay.\\ud There also exist\\ud multi-black hole skyrmion solutions with BPS monopole behaviour.
19. What is black hole?
First page Back Continue Last page Overview Graphics. What is black hole? Possible end phase of a star: A star is a massive, luminous ball of plasma having continuous nuclear burning. Star exhausts nuclear fuel →. White Dwarf, Neutron Star, Black Hole. Black hole's gravitational field is so powerful that even ...
20. Genocide and Black Ecology
Science.gov (United States)
Sinnette, Calvin H.
1972-01-01
Contends that the survival of black people is in serious jeopardy as is evidenced in contemporary discussions on the worldwide plight of black people, and that an exhaustive study of the problem in its many dimensions is seriously lacking; the moral and ethical issues of genocide require examination from a black perspective. (JW)
1. Black holes in binary stars
NARCIS (Netherlands)
Wijers, R.A.M.J.
1996-01-01
Introduction Distinguishing neutron stars and black holes Optical companions and dynamical masses X-ray signatures of the nature of a compact object Structure and evolution of black-hole binaries High-mass black-hole binaries Low-mass black-hole binaries Low-mass black holes Formation of black holes
2. Black hole levitron
International Nuclear Information System (INIS)
Arsiwalla, Xerxes D.; Verlinde, Erik P.
2010-01-01
We study the problem of spatially stabilizing four dimensional extremal black holes in background electric/magnetic fields. Whilst looking for stationary stable solutions describing black holes placed in external fields we find that taking a continuum limit of Denef et al.'s multicenter supersymmetric black hole solutions provides a supergravity description of such backgrounds within which a black hole can be trapped within a confined volume. This construction is realized by solving for a levitating black hole over a magnetic dipole base. We comment on how such a construction is akin to a mechanical levitron.
3. Primary black holes
International Nuclear Information System (INIS)
Novikov, I.; Polnarev, A.
1981-01-01
Proves are searched for of the formation of the so-called primary black holes at the very origin of the universe. The black holes would weigh less than 10 13 kg. The formation of a primary black hole is conditional on strong fluctuations of the gravitational field corresponding roughly to a half of the fluctuation maximally permissible by the general relativity theory. Only big fluctuations of the gravitational field can overcome the forces of the hot gas pressure and compress the originally expanding matter into a black hole. Low-mass black holes have a temperature exceeding that of the black holes formed from stars. A quantum process of particle formation, the so-called evaporation takes place in the strong gravitational field of a black hole. The lower the mass of the black hole, the shorter the evaporation time. The analyses of processes taking place during the evaporation of low-mass primary black holes show that only a very small proportion of the total mass of the matter in the universe could turn into primary black holes. (M.D.)
4. Astrophysical black holes
CERN Document Server
Gorini, Vittorio; Moschella, Ugo; Treves, Aldo; Colpi, Monica
2016-01-01
Based on graduate school lectures in contemporary relativity and gravitational physics, this book gives a complete and unified picture of the present status of theoretical and observational properties of astrophysical black holes. The chapters are written by internationally recognized specialists. They cover general theoretical aspects of black hole astrophysics, the theory of accretion and ejection of gas and jets, stellar-sized black holes observed in the Milky Way, the formation and evolution of supermassive black holes in galactic centers and quasars as well as their influence on the dynamics in galactic nuclei. The final chapter addresses analytical relativity of black holes supporting theoretical understanding of the coalescence of black holes as well as being of great relevance in identifying gravitational wave signals. With its introductory chapters the book is aimed at advanced graduate and post-graduate students, but it will also be useful for specialists.
5. Black branes as piezoelectrics.
Science.gov (United States)
Armas, Jay; Gath, Jakob; Obers, Niels A
2012-12-14
We find a realization of linear electroelasticity theory in gravitational physics by uncovering a new response coefficient of charged black branes, exhibiting their piezoelectric behavior. Taking charged dilatonic black strings as an example and using the blackfold approach we measure their elastic and piezolectric moduli. We also use our results to draw predictions about the equilibrium condition of charged dilatonic black rings in dimensions higher than six.
6. Accreting Black Holes
OpenAIRE
Begelman, Mitchell C.
2014-01-01
I outline the theory of accretion onto black holes, and its application to observed phenomena such as X-ray binaries, active galactic nuclei, tidal disruption events, and gamma-ray bursts. The dynamics as well as radiative signatures of black hole accretion depend on interactions between the relatively simple black-hole spacetime and complex radiation, plasma and magnetohydrodynamical processes in the surrounding gas. I will show how transient accretion processes could provide clues to these ...
7. Nonextremal stringy black hole
International Nuclear Information System (INIS)
Suzuki, K.
1997-01-01
We construct a four-dimensional BPS saturated heterotic string solution from the Taub-NUT solution. It is a nonextremal black hole solution since its Euler number is nonzero. We evaluate its black hole entropy semiclassically. We discuss the relation between the black hole entropy and the degeneracy of string states. The entropy of our string solution can be understood as the microscopic entropy which counts the elementary string states without any complications. copyright 1997 The American Physical Society
8. Naked black holes
International Nuclear Information System (INIS)
Horowitz, G.T.; Ross, S.F.
1997-01-01
It is shown that there are large static black holes for which all curvature invariants are small near the event horizon, yet any object which falls in experiences enormous tidal forces outside the horizon. These black holes are charged and near extremality, and exist in a wide class of theories including string theory. The implications for cosmic censorship and the black hole information puzzle are discussed. copyright 1997 The American Physical Society
9. The Black Family as Educator.
Science.gov (United States)
Wallace, Joan
The black family is the primary socializing agent of the black child and, thus, the primary educator. The culture of blacks in America, in which the child is steeped, is unique, complex and rich-the result of a convergence and fusion of African, American, and European influences. In its education of the black child, the black family must deal,…
10. Black hole Berry phase
NARCIS (Netherlands)
de Boer, J.; Papadodimas, K.; Verlinde, E.
2009-01-01
Supersymmetric black holes are characterized by a large number of degenerate ground states. We argue that these black holes, like other quantum mechanical systems with such a degeneracy, are subject to a phenomenon which is called the geometric or Berry’s phase: under adiabatic variations of the
11. Black holes are warm
International Nuclear Information System (INIS)
Ravndal, F.
1978-01-01
Applying Einstein's theory of gravitation to black holes and their interactions with their surroundings leads to the conclusion that the sum of the surface areas of several black holes can never become less. This is shown to be analogous to entropy in thermodynamics, and the term entropy is also thus applied to black holes. Continuing, expressions are found for the temperature of a black hole and its luminosity. Thermal radiation is shown to lead to explosion of the black hole. Numerical examples are discussed involving the temperature, the mass, the luminosity and the lifetime of black mini-holes. It is pointed out that no explosions corresponding to the prediction have been observed. It is also shown that the principle of conservation of leptons and baryons is broken by hot black holes, but that this need not be a problem. The related concept of instantons is cited. It is thought that understanding of thermal radiation from black holes may be important for the development of a quantified gravitation theory. (JIW)
12. on black ironbark (Eucalyptus
African Journals Online (AJOL)
(Apis meOifera) on black ironbark. (Eucalyptus sideroxylon). B. Buys. Plant Protection Research Institute, Private Bag X5017,. Stellenbosch, 7600 Republic of South Africa. Received May /984; accepted 28 November /986. Black ironbark trees secrete nectar during the night. Argentine ants collected 42% of the nectar before ...
13. Black holes matter
DEFF Research Database (Denmark)
Kragh, Helge Stjernholm
2016-01-01
Review essay, Marcia Bartusiak, Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled On by Hawking Became Loved (New Haven: Yale University Press, 2015).......Review essay, Marcia Bartusiak, Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled On by Hawking Became Loved (New Haven: Yale University Press, 2015)....
14. Quantum black holes
OpenAIRE
Hooft, G. 't
1987-01-01
This article is divided into three parts. First, a systematic derivation of the Hawking radiation is given in three different ways. The information loss problem is then discussed in great detail. The last part contains a concise discussion of black hole thermodynamics. This article was published as chapter $6$ of the IOP book "Lectures on General Relativity, Cosmology and Quantum Black Holes" (July $2017$).
15. Protecting Black Girls
Science.gov (United States)
Morris, Monique W.
2016-01-01
Statistics show that black girls in U.S. K-12 public schools are overrepresented among students who face disciplinary approaches (such as suspensions) that exclude or even criminalize them. Morris explains how black girls face conditions that make them vulnerable to a phenomenon she calls "school to confinement pathways"--conditions like…
16. Black hole levitron
NARCIS (Netherlands)
Arsiwalla, X.D.; Verlinde, E.P.
2010-01-01
We study the problem of spatially stabilizing four dimensional extremal black holes in background electric/magnetic fields. Whilst looking for stationary stable solutions describing black holes placed in external fields we find that taking a continuum limit of Denef et al.’s multicenter
17. The Black Woman's Burden
Science.gov (United States)
Hayes, Dianne
2012-01-01
Not even the first lady of the most powerful nation in the world is immune to stereotypes that have plagued Black women since first setting foot on American soil. Stereotypes of being the "angry Black woman" and curiosity about differences in appearance still persist from the academy to 1600 Pennsylvania Ave. As African-American women rise in…
18. Black Boycott: Gainsville, Florida
Science.gov (United States)
White, Arthur O.
1975-01-01
A case study of the events precipitating a black student boycott in 1969 in Gainesville, Flordia, when school board manuevering to avoid school integration led to the threatened closing of Lincoln High School, a reputable black community school. Also described are the subsequent transformations of Lincoln into a vocational-technical school and…
19. Lifshitz topological black holes
International Nuclear Information System (INIS)
Mann, R.B.
2009-01-01
I find a class of black hole solutions to a (3+1) dimensional theory gravity coupled to abelian gauge fields with negative cosmological constant that has been proposed as the dual theory to a Lifshitz theory describing critical phenomena in (2+1) dimensions. These black holes are all asymptotic to a Lifshitz fixed point geometry and depend on a single parameter that determines both their area (or size) and their charge. Most of the solutions are obtained numerically, but an exact solution is also obtained for a particular value of this parameter. The thermodynamic behaviour of large black holes is almost the same regardless of genus, but differs considerably for small black holes. Screening behaviour is exhibited in the dual theory for any genus, but the critical length at which it sets in is genus-dependent for small black holes.
20. Legitimizing Blacks in Philosophy
Directory of Open Access Journals (Sweden)
Jameliah Shorter-Bourhanou
2017-12-01
Full Text Available In its efforts toward improving diversity, the discipline of philosophy has tended to focus on increasing the number of black philosophers. One crucial issue that has received less attention is the extent to which black philosophers are delegitimized in the discipline because their philosophical contributions challenge the status quo. A systematic problem that bars black philosophers from equal and full participation, this delegitimization precludes the emergence of genuine diversity and reveals the importance of interrogating broader attitudes toward black philosophical contributions. In this essay, I argue for radical systematic changes to disciplinary hallmarks of professionalization such as pedagogy, mentoring, publishing, and hiring practices with the aim of legitimizing black philosophers and their contributions.
1. ULTRAMASSIVE BLACK HOLE COALESCENCE
International Nuclear Information System (INIS)
Khan, Fazeel Mahmood; Holley-Bockelmann, Kelly; Berczik, Peter
2015-01-01
Although supermassive black holes (SMBHs) correlate well with their host galaxies, there is an emerging view that outliers exist. Henize 2-10, NGC 4889, and NGC 1277 are examples of SMBHs at least an order of magnitude more massive than their host galaxy suggests. The dynamical effects of such ultramassive central black holes is unclear. Here, we perform direct N-body simulations of mergers of galactic nuclei where one black hole is ultramassive to study the evolution of the remnant and the black hole dynamics in this extreme regime. We find that the merger remnant is axisymmetric near the center, while near the large SMBH influence radius, the galaxy is triaxial. The SMBH separation shrinks rapidly due to dynamical friction, and quickly forms a binary black hole; if we scale our model to the most massive estimate for the NGC 1277 black hole, for example, the timescale for the SMBH separation to shrink from nearly a kiloparsec to less than a parsec is roughly 10 Myr. By the time the SMBHs form a hard binary, gravitational wave emission dominates, and the black holes coalesce in a mere few Myr. Curiously, these extremely massive binaries appear to nearly bypass the three-body scattering evolutionary phase. Our study suggests that in this extreme case, SMBH coalescence is governed by dynamical friction followed nearly directly by gravitational wave emission, resulting in a rapid and efficient SMBH coalescence timescale. We discuss the implications for gravitational wave event rates and hypervelocity star production
2. On the Charter Question: Black Marxism and Black Nationalism
Science.gov (United States)
Stern, Mark; Hussain, Khuram
2015-01-01
This article brings two black intellectual traditions to bear on the question of charter schools: black Marxism and black nationalism. The authors examine the theoretical and rhetorical devices used to talk about charters schools by focusing on how notions of "black liberation" are deployed by the charter movement, and to what end. The…
3. "Black Like Me": Reframing Blackness for Decolonial Politics
Science.gov (United States)
Dei, George J. Sefa
2018-01-01
From a particular vantage point, as an African-born scholar with a politics to affirm my Black subjectivity and Indigeneity in a diasporic context, my article engages a (re)theorization of Blackness for decolonial politics. Building on existing works of how Black scholars, themselves, have theorized Blackness, and recognizing the fluid,…
4. Black holes new horizons
CERN Document Server
Hayward, Sean Alan
2013-01-01
Black holes, once just fascinating theoretical predictions of how gravity warps space-time according to Einstein's theory, are now generally accepted as astrophysical realities, formed by post-supernova collapse, or as supermassive black holes mysteriously found at the cores of most galaxies, powering active galactic nuclei, the most powerful objects in the universe. Theoretical understanding has progressed in recent decades with a wider realization that local concepts should characterize black holes, rather than the global concepts found in textbooks. In particular, notions such as trapping h
5. Understanding the Black Aesthetic Experience.
Science.gov (United States)
Curtis, Marvin V.
1988-01-01
Discussing the importance of the Black aesthetic experience, Curtis examines Black cultural heritage and participatory style, the spiritual, and the creation and recreation of Black music. Advocating multicultural music education in teacher training, he suggests that Black music be studied for its value and contribution to society. Lists five ways…
6. New Directions for Black Women?
Science.gov (United States)
McGuigan, Dorothy, Ed.
1978-01-01
This collection of papers deals with various aspects of the black female experience in America. "The Black Woman in Transition" discusses the effects of sexism and racism on black women with particular reference to employment and education; it is noted that black women, in comparison with other groups in society, suffer a proportionately higher…
7. Black Writers' Views of America.
Science.gov (United States)
Hairston, Loyle
1979-01-01
This article argues that the stagnation, pessimism, and self-pity evident in recent Black writing results in part from the alienation of Black writers from the mainstream of Black life, and in part from the illusions that they share with other Blacks who have embraced the American value system. (Author/EB)
8. Black holes with halos
Science.gov (United States)
Monten, Ruben; Toldo, Chiara
2018-02-01
We present new AdS4 black hole solutions in N =2 gauged supergravity coupled to vector and hypermultiplets. We focus on a particular consistent truncation of M-theory on the homogeneous Sasaki–Einstein seven-manifold M 111, characterized by the presence of one Betti vector multiplet. We numerically construct static and spherically symmetric black holes with electric and magnetic charges, corresponding to M2 and M5 branes wrapping non-contractible cycles of the internal manifold. The novel feature characterizing these nonzero temperature configurations is the presence of a massive vector field halo. Moreover, we verify the first law of black hole mechanics and we study the thermodynamics in the canonical ensemble. We analyze the behavior of the massive vector field condensate across the small-large black hole phase transition and we interpret the process in the dual field theory.
9. Tuberculosis in Blacks
Science.gov (United States)
... are reported in blacks received training to enhance skills for engaging communities, develop strategies, and sustain partnerships for reducing TB rates. Other CDC activities include a study to identify the socio-cultural, racial, and health ...
10. Introducing the Black Hole
Science.gov (United States)
Ruffini, Remo; Wheeler, John A.
1971-01-01
discusses the cosmology theory of a black hole, a region where an object loses its identity, but mass, charge, and momentum are conserved. Include are three possible formation processes, theorized properties, and three way they might eventually be detected. (DS)
11. Colliding black hole solution
International Nuclear Information System (INIS)
Ahmed, Mainuddin
2005-01-01
A new solution of Einstein equation in general relativity is found. This solution solves an outstanding problem of thermodynamics and black hole physics. Also this work appears to conclude the interpretation of NUT spacetime. (author)
12. Black Sea aerosols
International Nuclear Information System (INIS)
Hacisalihoglu, G.; Eliyakut, F.; Anwari, M.A.; Ataman, O.Y.; Balkas, T.I.; Tuncel, G.; Olmez, I.
1991-01-01
Shipboard, high volume air particulate samples were collected from the Black Sea atmosphere and analyzed by instrumental neutron activation analysis, atomic absorption spectrophotometry and ion chromatography for about 40 elements and ions. Concentrations of elements in the eastern and western parts of the Black Sea are different at the 95% confidence level, with lower concentrations in the eastern Black Sea. Back-trajectories and concentrations of elements in trajectory groups show that Europe accounts for more than 70% of the anthropogenic elements in the atmosphere. The average sulfate concentration was 7 μg/m 3 , which is comparable with rural sulfate levels in western Europe. Fluxes of elements from the atmosphere to the Black Sea are in good agreement with the results of similar flux calculations for other regions
13. Black Teenage Pregnancy
Directory of Open Access Journals (Sweden)
Loretta I. Winters
2012-01-01
Full Text Available This article examines the relative importance of race and socioeconomic status (SES in determining whether Black and White teenagers report having ever been pregnant. Data gathered from 1999 to 2006 by the National Center for Health Statistics of the Center for Disease Control and Prevention included 1,580 Black and White females aged 15 to 19 years. Results supported the effects of race and SES, with SES having the stronger effect. However, the effects of race and SES differ when controlling for the state of the economy. No difference between Blacks and Whites was found during better economic times. During 2003-2004, the period of greatest economic stress, race was determined to be the only predictor of teenage pregnancy. In particular, during 2005-2006, the reduction in pregnancy rates for Black minors (15-17 fell below those for White minors within their respective SES categories. Policy implications are discussed in light of these findings.
14. Black-hole thermodynamics
International Nuclear Information System (INIS)
Bekenstein, J.D.
1980-01-01
Including black holes in the scheme of thermodynamics has disclosed a deep-seated connection between gravitation, heat and the quantum that may lead us to a synthesis of the corresponding branches of physics
15. White dwarfs - black holes
International Nuclear Information System (INIS)
Sexl, R.; Sexl, H.
1975-01-01
The physical arguments and problems of relativistic astrophysics are presented in a correct way, but without any higher mathematics. The book is addressed to teachers, experimental physicists, and others with a basic knowledge covering an introductory lecture in physics. The issues dealt with are: fundamentals of general relativity, classical tests of general relativity, curved space-time, stars and planets, pulsars, gravitational collapse and black holes, the search for black holes, gravitational waves, cosmology, cosmogony, and the early universe. (BJ/AK) [de
16. Supersymmetric black holes
OpenAIRE
de Wit, Bernard
2005-01-01
The effective action of $N=2$, $d=4$ supergravity is shown to acquire no quantum corrections in background metrics admitting super-covariantly constant spinors. In particular, these metrics include the Robinson-Bertotti metric (product of two 2-dimensional spaces of constant curvature) with all 8 supersymmetries unbroken. Another example is a set of arbitrary number of extreme Reissner-Nordstr\\"om black holes. These black holes break 4 of 8 supersymmetries, leaving the other 4 unbroken. We ha...
17. Bumpy black holes
OpenAIRE
Emparan, Roberto; Figueras, Pau; Martinez, Marina
2014-01-01
We study six-dimensional rotating black holes with bumpy horizons: these are topologically spherical, but the sizes of symmetric cycles on the horizon vary non-monotonically with the polar angle. We construct them numerically for the first three bumpy families, and follow them in solution space until they approach critical solutions with localized singularities on the horizon. We find strong evidence of the conical structures that have been conjectured to mediate the transitions to black ring...
18. British Dance: Black Routes
OpenAIRE
2016-01-01
British Dance: Black Routes re-examines the distinctive contributions made to British dance by dancers who are Black. Covering the period 1946 to the present, it presents a radical re-reading of dancers and their companies, placing their achievements within a broader historical, cultural and artistic context. The result of a two year research project, British Dance and the African Diaspora, led by editors Christy Adair and Ramsay Burt, the collection looks at artists working with contempor...
19. Black Holes and Thermodynamics
OpenAIRE
Wald, Robert M.
1997-01-01
We review the remarkable relationship between the laws of black hole mechanics and the ordinary laws of thermodynamics. It is emphasized that - in analogy with the laws of thermodynamics - the validity the laws of black hole mechanics does not appear to depend upon the details of the underlying dynamical theory (i.e., upon the particular field equations of general relativity). It also is emphasized that a number of unresolved issues arise in ordinary thermodynamics'' in the context of gener...
20. Black holes and beyond
Energy Technology Data Exchange (ETDEWEB)
NONE
2002-02-01
Belief in the existence of black holes is the ultimate act of faith for a physicist. First suggested by the English clergyman John Michell in the year 1784, the gravitational pull of a black hole is so strong that nothing - not even light - can escape. Gravity might be the weakest of the fundamental forces but black-hole physics is not for the faint-hearted. Black holes present obvious problems for would-be observers because they cannot, by definition, be seen with conventional telescopes - although before the end of the decade gravitational-wave detectors should be able to study collisions between black holes. Until then astronomers can only infer the existence of a black hole from its gravitational influence on other matter, or from the X-rays emitted by gas and dust as they are dragged into the black hole. However, once this material passes through the 'event horizon' that surrounds the black hole, we will never see it again - not even with X-ray specs. Despite these observational problems, most physicists and astronomers believe that black holes do exist. Small black holes a few kilometres across are thought to form when stars weighing more than about two solar masses collapse under the weight of their own gravity, while supermassive black holes weighing millions of solar masses appear to be present at the centre of most galaxies. Moreover, some brave physicists have proposed ways to make black holes - or at least event horizons - in the laboratory. The basic idea behind these 'artificial black holes' is not to compress a large amount of mass into a small volume, but to reduce the speed of light in a moving medium to less than the speed of the medium and so create an event horizon. The parallels with real black holes are not exact but the experiments could shed new light on a variety of phenomena. The first challenge, however, is to get money for the research. One year on from a high-profile meeting on artificial black holes in London, for
1. Surface geometry of 5D black holes and black rings
International Nuclear Information System (INIS)
Frolov, Valeri P.; Goswami, Rituparno
2007-01-01
We discuss geometrical properties of the horizon surface of five-dimensional rotating black holes and black rings. Geometrical invariants characterizing these 3D geometries are calculated. We obtain a global embedding of the 5D rotating black horizon surface into a flat space. We also describe the Kaluza-Klein reduction of the black ring solution (along the direction of its rotation) which, though it is nakedly singular, relates this solution to the 4D metric of a static black hole distorted by the presence of external scalar (dilaton) and vector ('electromagnetic') fields. The properties of the reduced black hole horizon and its embedding in E 3 are briefly discussed
2. Merging Black Holes
Science.gov (United States)
Centrella, Joan
2012-01-01
The final merger of two black holes is expected to be the strongest source of gravitational waves for both ground-based detectors such as LIGO and VIRGO, as well as future. space-based detectors. Since the merger takes place in the regime of strong dynamical gravity, computing the resulting gravitational waveforms requires solving the full Einstein equations of general relativity on a computer. For many years, numerical codes designed to simulate black hole mergers were plagued by a host of instabilities. However, recent breakthroughs have conquered these instabilities and opened up this field dramatically. This talk will focus on.the resulting 'gold rush' of new results that is revealing the dynamics and waveforms of binary black hole mergers, and their applications in gravitational wave detection, testing general relativity, and astrophysics
3. Black hole gravitohydromagnetics
CERN Document Server
Punsly, Brian
2008-01-01
Black hole gravitohydromagnetics (GHM) is developed from the rudiments to the frontiers of research in this book. GHM describes plasma interactions that combine the effects of gravity and a strong magnetic field, in the vicinity (ergosphere) of a rapidly rotating black hole. This topic was created in response to the astrophysical quest to understand the central engines of radio loud extragalactic radio sources. The theory describes a "torsional tug of war" between rotating ergospheric plasma and the distant asymptotic plasma that extracts the rotational inertia of the black hole. The recoil from the struggle between electromagnetic and gravitational forces near the event horizon is manifested as a powerful pair of magnetized particle beams (jets) that are ejected at nearly the speed of light. These bipolar jets feed large-scale magnetized plasmoids on scales as large as millions of light years (the radio lobes of extragalactic radio sources). This interaction can initiate jets that transport energy fluxes exc...
4. Turbulent black holes.
Science.gov (United States)
Yang, Huan; Zimmerman, Aaron; Lehner, Luis
2015-02-27
We demonstrate that rapidly spinning black holes can display a new type of nonlinear parametric instability-which is triggered above a certain perturbation amplitude threshold-akin to the onset of turbulence, with possibly observable consequences. This instability transfers from higher temporal and azimuthal spatial frequencies to lower frequencies-a phenomenon reminiscent of the inverse cascade displayed by (2+1)-dimensional fluids. Our finding provides evidence for the onset of transitory turbulence in astrophysical black holes and predicts observable signatures in black hole binaries with high spins. Furthermore, it gives a gravitational description of this behavior which, through the fluid-gravity duality, can potentially shed new light on the remarkable phenomena of turbulence in fluids.
5. Anyon black holes
Science.gov (United States)
Aghaei Abchouyeh, Maryam; Mirza, Behrouz; Karimi Takrami, Moein; Younesizadeh, Younes
2018-05-01
We propose a correspondence between an Anyon Van der Waals fluid and a (2 + 1) dimensional AdS black hole. Anyons are particles with intermediate statistics that interpolates between a Fermi-Dirac statistics and a Bose-Einstein one. A parameter α (0 quasi Fermi-Dirac statistics for α >αc, but a quasi Bose-Einstein statistics for α quasi Bose-Einstein statistics. For α >αc and a range of values of the cosmological constant, there is, however, no event horizon so there is no black hole solution. Thus, for these values of cosmological constants, the AdS Anyon Van der Waals black holes have only quasi Bose-Einstein statistics.
6. Black holes go supersonic
Energy Technology Data Exchange (ETDEWEB)
Leonhardt, Ulf [School of Physics and Astronomy, University of St. Andrews (United Kingdom)
2001-02-01
In modern physics, the unification of gravity and quantum mechanics remains a mystery. Gravity rules the macroscopic world of planets, stars and galaxies, while quantum mechanics governs the micro-cosmos of atoms, light quanta and elementary particles. However, cosmologists believe that these two disparate worlds may meet at the edges of black holes. Now Luis Garay, James Anglin, Ignacio Cirac and Peter Zoller at the University of Innsbruck in Austria have proposed a realistic way to make an artificial 'sonic' black hole in a tabletop experiment (L J Garay et al. 2000 Phys. Rev. Lett. 85 4643). In the February issue of Physics World, Ulf Leonhardt of the School of Physics and Astronomy, University of St. Andrews, UK, explains how the simulated black holes work. (U.K.)
International Nuclear Information System (INIS)
Joshi, Pankaj S.; Narayan, Ramesh
2016-01-01
We propose here that the well-known black hole paradoxes such as the information loss and teleological nature of the event horizon are restricted to a particular idealized case, which is the homogeneous dust collapse model. In this case, the event horizon, which defines the boundary of the black hole, forms initially, and the singularity in the interior of the black hole at a later time. We show that, in contrast, gravitational collapse from physically more realistic initial conditions typically leads to the scenario in which the event horizon and space-time singularity form simultaneously. We point out that this apparently simple modification can mitigate the causality and teleological paradoxes, and also lends support to two recently suggested solutions to the information paradox, namely, the ‘firewall’ and ‘classical chaos’ proposals. (paper)
8. Bringing Black Holes Home
Science.gov (United States)
Furmann, John M.
2003-03-01
Black holes are difficult to study because they emit no light. To overcome this obstacle, scientists are trying to recreate a black hole in the laboratory. The article gives an overview of the theories of Einstein and Hawking as they pertain to the construction of the Large Hadron Collider (LHC) near Geneva, Switzerland, scheduled for completion in 2006. The LHC will create two beams of protons traveling in opposing directions that will collide and create a plethora of scattered elementary particles. Protons traveling in opposite directions at very high velocities may create particles that come close enough to each other to feel their compacted higher dimensions and create a mega force of gravity that can create tiny laboratory-sized black holes for fractions of a second. The experiments carried out with LHC will be used to test modern string theory and relativity.
9. Slowly balding black holes
International Nuclear Information System (INIS)
Lyutikov, Maxim; McKinney, Jonathan C.
2011-01-01
The 'no-hair' theorem, a key result in general relativity, states that an isolated black hole is defined by only three parameters: mass, angular momentum, and electric charge; this asymptotic state is reached on a light-crossing time scale. We find that the no-hair theorem is not formally applicable for black holes formed from the collapse of a rotating neutron star. Rotating neutron stars can self-produce particles via vacuum breakdown forming a highly conducting plasma magnetosphere such that magnetic field lines are effectively ''frozen in'' the star both before and during collapse. In the limit of no resistivity, this introduces a topological constraint which prohibits the magnetic field from sliding off the newly-formed event horizon. As a result, during collapse of a neutron star into a black hole, the latter conserves the number of magnetic flux tubes N B =eΦ ∞ /(πc(ℎ/2π)), where Φ ∞ ≅2π 2 B NS R NS 3 /(P NS c) is the initial magnetic flux through the hemispheres of the progenitor and out to infinity. We test this theoretical result via 3-dimensional general relativistic plasma simulations of rotating black holes that start with a neutron star dipole magnetic field with no currents initially present outside the event horizon. The black hole's magnetosphere subsequently relaxes to the split-monopole magnetic field geometry with self-generated currents outside the event horizon. The dissipation of the resulting equatorial current sheet leads to a slow loss of the anchored flux tubes, a process that balds the black hole on long resistive time scales rather than the short light-crossing time scales expected from the vacuum no-hair theorem.
10. Modeling black hole evaporation
CERN Document Server
Fabbri, Alessandro
2005-01-01
The scope of this book is two-fold: the first part gives a fully detailed and pedagogical presentation of the Hawking effect and its physical implications, and the second discusses the backreaction problem, especially in connection with exactly solvable semiclassical models that describe analytically the black hole evaporation process. The book aims to establish a link between the general relativistic viewpoint on black hole evaporation and the new CFT-type approaches to the subject. The detailed discussion on backreaction effects is also extremely valuable.
11. Characterizing Black Hole Mergers
Science.gov (United States)
Baker, John; Boggs, William Darian; Kelly, Bernard
2010-01-01
Binary black hole mergers are a promising source of gravitational waves for interferometric gravitational wave detectors. Recent advances in numerical relativity have revealed the predictions of General Relativity for the strong burst of radiation generated in the final moments of binary coalescence. We explore features in the merger radiation which characterize the final moments of merger and ringdown. Interpreting the waveforms in terms of an rotating implicit radiation source allows a unified phenomenological description of the system from inspiral through ringdown. Common features in the waveforms allow quantitative description of the merger signal which may provide insights for observations large-mass black hole binaries.
12. Better Physician's 'Black Bags'
Science.gov (United States)
1976-01-01
The "black bag" is outgrowth of astronaut monitoring technology from NASA's Johnson Space Center. Technically known as the portable medical status system, a highly advanced physician's "black bag" weighs less than 30 pounds, yet contains equipment for monitoring and recording vital signs, electrocardiograms, and electroencephalograms. Liquid crystal displays are used to present 15 digits of data simultaneously for long periods of time without excessive use of battery power. Single printed circuit card contains all circuitry required to measure and display vital signs such as heart and respiration rate, temperature, and blood pressure.
13. Bulletproof Black Man
DEFF Research Database (Denmark)
Højer, Henrik
2016-01-01
Netflix’ kommende serie om den sorte Marvel-helt Luke Cage lander snart – midt i de aktuelle racekonflikter i USA. I GIF-anatomien "Bulletproof Black Man" sætter Henrik Højer serien ind i dens amerikanske kontekst.......Netflix’ kommende serie om den sorte Marvel-helt Luke Cage lander snart – midt i de aktuelle racekonflikter i USA. I GIF-anatomien "Bulletproof Black Man" sætter Henrik Højer serien ind i dens amerikanske kontekst....
14. Moulting Black Holes
OpenAIRE
Bena, Iosif; Chowdhury, Borun D.; de Boer, Jan; El-Showk, Sheer; Shigemori, Masaki
2011-01-01
We find a family of novel supersymmetric phases of the D1-D5 CFT, which in certain ranges of charges have more entropy than all known ensembles. We also find bulk BPS configurations that exist in the same range of parameters as these phases, and have more entropy than a BMPV black hole; they can be thought of as coming from a BMPV black hole shedding a "hair" condensate outside of the horizon. The entropy of the bulk configurations is smaller than that of the CFT phases, which indicates that ...
15. Are black holes springlike?
Science.gov (United States)
Good, Michael R. R.; Ong, Yen Chin
2015-02-01
A (3 +1 )-dimensional asymptotically flat Kerr black hole angular speed Ω+ can be used to define an effective spring constant, k =m Ω+2. Its maximum value is the Schwarzschild surface gravity, k =κ , which rapidly weakens as the black hole spins down and the temperature increases. The Hawking temperature is expressed in terms of the spring constant: 2 π T =κ -k . Hooke's law, in the extremal limit, provides the force F =1 /4 , which is consistent with the conjecture of maximum force in general relativity.
16. Dancing with Black Holes
Science.gov (United States)
Aarseth, S. J.
2008-05-01
We describe efforts over the last six years to implement regularization methods suitable for studying one or more interacting black holes by direct N-body simulations. Three different methods have been adapted to large-N systems: (i) Time-Transformed Leapfrog, (ii) Wheel-Spoke, and (iii) Algorithmic Regularization. These methods have been tried out with some success on GRAPE-type computers. Special emphasis has also been devoted to including post-Newtonian terms, with application to moderately massive black holes in stellar clusters. Some examples of simulations leading to coalescence by gravitational radiation will be presented to illustrate the practical usefulness of such methods.
17. Scattering from black holes
International Nuclear Information System (INIS)
Futterman, J.A.H.; Handler, F.A.; Matzner, R.A.
1987-01-01
This book provides a comprehensive treatment of the propagation of waves in the presence of black holes. While emphasizing intuitive physical thinking in their treatment of the techniques of analysis of scattering, the authors also include chapters on the rigorous mathematical development of the subject. Introducing the concepts of scattering by considering the simplest, scalar wave case of scattering by a spherical (Schwarzschild) black hole, the book then develops the formalism of spin weighted spheroidal harmonics and of plane wave representations for neutrino, electromagnetic, and gravitational scattering. Details and results of numerical computations are given. The techniques involved have important applications (references are given) in acoustical and radar imaging
18. Virtual Black Holes
OpenAIRE
Hawking, Stephen W.
1995-01-01
One would expect spacetime to have a foam-like structure on the Planck scale with a very high topology. If spacetime is simply connected (which is assumed in this paper), the non-trivial homology occurs in dimension two, and spacetime can be regarded as being essentially the topological sum of $S^2\\times S^2$ and $K3$ bubbles. Comparison with the instantons for pair creation of black holes shows that the $S^2\\times S^2$ bubbles can be interpreted as closed loops of virtual black holes. It is ...
19. Superfluid Black Holes.
Science.gov (United States)
Hennigar, Robie A; Mann, Robert B; Tjoa, Erickson
2017-01-13
We present what we believe is the first example of a "λ-line" phase transition in black hole thermodynamics. This is a line of (continuous) second order phase transitions which in the case of liquid ^{4}He marks the onset of superfluidity. The phase transition occurs for a class of asymptotically anti-de Sitter hairy black holes in Lovelock gravity where a real scalar field is conformally coupled to gravity. We discuss the origin of this phase transition and outline the circumstances under which it (or generalizations of it) could occur.
20. Partons and black holes
International Nuclear Information System (INIS)
Susskind, L.; Griffin, P.
1994-01-01
A light-front renormalization group analysis is applied to study matter which falls into massive black holes, and the related problem of matter with transplankian energies. One finds that the rate of matter spreading over the black hole's horizon unexpectedly saturates the causality bound. This is related to the transverse growth behavior of transplankian particles as their longitudinal momentum increases. This growth behavior suggests a natural mechanism to implement 't Hooft's scenario that the universe is an image of data stored on a 2 + 1 dimensional hologram-like projection
1. Black Musicians Leading the Way.
Science.gov (United States)
Music Educators Journal, 1982
1982-01-01
Describes the careers and musical achievements of Blacks who were forerunners in jazz, blues, gospel, music, spirituals, band music, classical music, ragtime, and opera. The list was compiled to provide teachers with historical background information for "Black History Month." (AM)
2. Black holes and quantum mechanics
CERN Document Server
Wilczek, Frank
1995-01-01
1. Qualitative introduction to black holes : classical, quantum2. Model black holes and model collapse process: The Schwarzschild and Reissner-Nordstrom metrics, The Oppenheimer-Volkov collapse scenario3. Mode mixing4. From mode mixing to radiance.
3. Black Sea Bass genetic connectivity
Data.gov (United States)
National Oceanic and Atmospheric Administration, Department of Commerce — Microsatellite analysis of black sea bass was undertaken to determine magnitude and direction of mixing of black seabass across the Hatteras boundary, as well as...
4. Quantum Mechanics of Black Holes
OpenAIRE
Giddings, Steven B.
1994-01-01
These lectures give a pedagogical review of dilaton gravity, Hawking radiation, the black hole information problem, and black hole pair creation. (Lectures presented at the 1994 Trieste Summer School in High Energy Physics and Cosmology)
5. Quantum aspects of black holes
CERN Document Server
2015-01-01
Beginning with an overview of the theory of black holes by the editor, this book presents a collection of ten chapters by leading physicists dealing with the variety of quantum mechanical and quantum gravitational effects pertinent to black holes. The contributions address topics such as Hawking radiation, the thermodynamics of black holes, the information paradox and firewalls, Monsters, primordial black holes, self-gravitating Bose-Einstein condensates, the formation of small black holes in high energetic collisions of particles, minimal length effects in black holes and small black holes at the Large Hadron Collider. Viewed as a whole the collection provides stimulating reading for researchers and graduate students seeking a summary of the quantum features of black holes.
6. Aspects of hairy black holes
Energy Technology Data Exchange (ETDEWEB)
Anabalón, Andrés, E-mail: [email protected] [Departamento de Ciencias, Facultad de Artes Liberales y Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Viña del Mar (Chile); Astefanesei, Dumitru [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile)
2015-03-26
We review the existence of exact hairy black holes in asymptotically flat, anti-de Sitter and de Sitter space-times. We briefly discuss the issue of stability and the charging of the black holes with a Maxwell field.
7. Black Holes in Higher Dimensions
Directory of Open Access Journals (Sweden)
Reall Harvey S.
2008-09-01
Full Text Available We review black-hole solutions of higher-dimensional vacuum gravity and higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers–Perry solutions, black rings, and solution-generating techniques. We discuss black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.
8. Nonsingular black hole
Energy Technology Data Exchange (ETDEWEB)
Chamseddine, Ali H. [American University of Beirut, Physics Department, Beirut (Lebanon); I.H.E.S., Bures-sur-Yvette (France); Mukhanov, Viatcheslav [Niels Bohr Institute, Niels Bohr International Academy, Copenhagen (Denmark); Ludwig-Maximilians University, Theoretical Physics, Munich (Germany); MPI for Physics, Munich (Germany)
2017-03-15
We consider the Schwarzschild black hole and show how, in a theory with limiting curvature, the physical singularity ''inside it'' is removed. The resulting spacetime is geodesically complete. The internal structure of this nonsingular black hole is analogous to Russian nesting dolls. Namely, after falling into the black hole of radius r{sub g}, an observer, instead of being destroyed at the singularity, gets for a short time into the region with limiting curvature. After that he re-emerges in the near horizon region of a spacetime described by the Schwarzschild metric of a gravitational radius proportional to r{sub g}{sup 1/3}. In the next cycle, after passing the limiting curvature, the observer finds himself within a black hole of even smaller radius proportional to r{sub g}{sup 1/9}, and so on. Finally after a few cycles he will end up in the spacetime where he remains forever at limiting curvature. (orig.)
9. Suburban Black Lives Matter
Science.gov (United States)
Lewis-McCoy, R. L'Heureux
2018-01-01
This article explores the range of experiences and meanings of Black life in suburban space. Drawing from educational, historical, and sociological literatures, I argue that an underconsideration of suburban space has left many portraits of educational inequality incomplete. The article outlines the emergence of American suburbs and the formation…
10. and black cumin
African Journals Online (AJOL)
Keywords: Black Cumin Seed, Co-pressing, Screw Speed, Oxidative Stability, Niger Seed Oil ... against oxidation resulting in rapid development of .... The machine ... apparatus (Metrohm, Herisau, model Switzerland) at .... present study indicates the need to optimize SS for ..... Mathematical simulation of an oilseed press.
11. Black and white holes
International Nuclear Information System (INIS)
Zeldovich, Ya.; Novikov, I.; Starobinskij, A.
1978-01-01
The theory is explained of the origination of white holes as a dual phenomenon with regard to the formation of black holes. Theoretically it is possible to derive the white hole by changing the sign of time in solving the general theory of relativity equation implying the black hole. The white hole represents the amount of particles formed in the vicinity of a singularity. For a distant observer, matter composed of these particles expands and the outer boundaries of this matter approach from the inside the gravitational radius Rsub(r). At t>>Rsub(r)/c all radiation or expulsion of matter terminates. For the outside observer the white hole exists for an unlimited length of time. In fact, however, it acquires the properties of a black hole and all processes in it cease. The qualitative difference between a white hole and a black hole is in that a white hole is formed as the result of an inner quantum explosion from the singularity to the gravitational radius and not as the result of a gravitational collapse, i.e., the shrinkage of diluted matter towards the gravitational radius. (J.B.)
12. Black and white holes
Energy Technology Data Exchange (ETDEWEB)
Zeldovich, Ya; Novikov, I; Starobinskii, A
1978-07-01
The theory is explained of the origination of white holes as a dual phenomenon with regard to the formation of black holes. Theoretically it is possible to derive the white hole by changing the sign of time in solving the general theory of relativity equation implying the black hole. The white hole represents the amount of particles formed in the vicinity of a singularity. For a distant observer, matter composed of these particles expands and the outer boundaries of this matter approach from the inside the gravitational radius R/sub r/. At t>>R/sub r//c all radiation or expulsion of matter terminates. For the outside observer the white hole exists for an unlimited length of time. In fact, however, it acquires the properties of a black hole and all processes in it cease. The qualitative difference between a white hole and a black hole is in that a white hole is formed as the result of an inner quantum explosion from the singularity to the gravitational radius and not as the result of a gravitational collapse, i.e., the shrinkage of diluted matter towards the gravitational radius.
13. Annotated black walnut literature
Science.gov (United States)
J. W. Van Sambeek
2006-01-01
Many of our publications on the establishment, management, and utilization of black walnut, butternut, and associated high-value hardwoods are printed in conference proceedings or scientific journals that are not readily available at most public libraries or on the internet. As Chair of the Education Committee, I have tried to summarize for you the relevant findings of...
14. When Black Holes Collide
Science.gov (United States)
Baker, John
2010-01-01
Among the fascinating phenomena predicted by General Relativity, Einstein's theory of gravity, black holes and gravitational waves, are particularly important in astronomy. Though once viewed as a mathematical oddity, black holes are now recognized as the central engines of many of astronomy's most energetic cataclysms. Gravitational waves, though weakly interacting with ordinary matter, may be observed with new gravitational wave telescopes, opening a new window to the universe. These observations promise a direct view of the strong gravitational dynamics involving dense, often dark objects, such as black holes. The most powerful of these events may be merger of two colliding black holes. Though dark, these mergers may briefly release more energy that all the stars in the visible universe, in gravitational waves. General relativity makes precise predictions for the gravitational-wave signatures of these events, predictions which we can now calculate with the aid of supercomputer simulations. These results provide a foundation for interpreting expect observations in the emerging field of gravitational wave astronomy.
15. Dictionary of Black Culture.
Science.gov (United States)
This dictionary is an encyclopedic survey of the cultural background and development of the black American, covering the basic issues, events, contributions and biographies germane to the subject. The author-compiler is Chairman of Classical Languages Department at Southeastern State College, Durant, Oklahoma. Richard Runes is practicing law as a…
16. Newborn Black Holes
Science.gov (United States)
Science Teacher, 2005
2005-01-01
Scientists using NASA's Swift satellite say they have found newborn black holes, just seconds old, in a confused state of existence. The holes are consuming material falling into them while somehow propelling other material away at great speeds. "First comes a blast of gamma rays followed by intense pulses of x-rays. The energies involved are much…
17. Black coal. [Australia
Energy Technology Data Exchange (ETDEWEB)
Pratt, R
1973-01-01
Statistics are given for the Australian black coal industry for 1970-3 (production, value, employment, wages and salaries, productivity, trade, stocks, consumption, export contracts, exploration, etc.). In less detail, world coal trade is reviewed and coke production is mentioned briefly. (LTN )
18. Australian black coal statistics 1990
Energy Technology Data Exchange (ETDEWEB)
1991-01-01
This second edition of Australian black coal statistics replaces the Joint Coal Board's publication 'Black coal in Australia'. It includes an expanded international coal trade supplement. Sections cover resources of black coal, coal supply and demand, coal production, employment and productivity of mines, export data, coal consumption and a directory of producers.
19. Uncovering Black Womanhood in Engineering
Science.gov (United States)
Gibson, Sheree L.; Espino, Michelle M.
2016-01-01
Despite the growing research that outlines the experiences of Blacks and women undergraduates in engineering, little is known about Black women in this field. The purpose of this qualitative study was to uncover how eight Black undergraduate women in engineering understood their race and gender identities in a culture that can be oppressive to…
20. Watchable Wildlife: The Black Bear
Science.gov (United States)
Lynn L. Rogers
1992-01-01
Black bears are the bears people most often encounter. Black bears live in forests over much of North America, unlike grizzlies that live only in Alaska, northern and western Canada, and the northern Rocky Mountains. This brochure presents the latest information on black bear life and how this species responds to an ever-increasing number of campers, hikers, and...
1. Black-spot poison ivy.
Science.gov (United States)
Schram, Sarah E; Willey, Andrea; Lee, Peter K; Bohjanen, Kimberly A; Warshaw, Erin M
2008-01-01
In black-spot poison ivy dermatitis, a black lacquerlike substance forms on the skin when poison ivy resin is exposed to air. Although the Toxicodendron group of plants is estimated to be the most common cause of allergic contact dermatitis in the United States, black-spot poison ivy dermatitis is relatively rare.
2. Queering Black Racial Identity Development
Science.gov (United States)
Johnson, Alandis A.; Quaye, Stephen John
2017-01-01
We used queer theory to encourage readers to think differently about previous theories about Black racial identity development. Queer theory facilitates new and deeper understandings of how Black people develop their racial identities, prompting more fluidity and nuance. Specifically, we present a queered model of Black racial identity development…
3. A Typology of Black Leadership.
Science.gov (United States)
Tryman, Donald L.
1977-01-01
A leadership typology is developed which describes the relationship of Black leadership styles to the Black masses. The role that such leadership plays in the political integration of Blacks as an ethnic group is analyzed. Four authority types are discussed: traditional brokerage, cultural nationalist, religious nationalist, and faddist…
4. Warped products and black holes
International Nuclear Information System (INIS)
Hong, Soon-Tae
2005-01-01
We apply the warped product space-time scheme to the Banados-Teitelboim-Zanelli black holes and the Reissner-Nordstroem-anti-de Sitter black hole to investigate their interior solutions in terms of warped products. It is shown that there exist no discontinuities of the Ricci and Einstein curvatures across event horizons of these black holes
5. Magnetohydrodynamics near a black hole
International Nuclear Information System (INIS)
Wilson, J.R.
1975-01-01
A numerical computer study of hydromagnetic flow near a black hole is presented. First, the equations of motion are developed to a form suitable for numerical computations. Second, the results of calculations describing the magnetic torques exerted by a rotating black hole on a surrounding magnetic plasma and the electric charge that is induced on the surface of the black hole are presented. (auth)
6. Black silicon with black bus-bar strings
DEFF Research Database (Denmark)
Davidsen, Rasmus Schmidt; Tang, Peter Torben; Mizushima, Io
2016-01-01
We present the combination of black silicon texturing and blackened bus-bar strings as a potential method for obtaining all-black solar panels, while using conventional, front-contacted solar cells. Black silicon was realized by mask-less reactive ion etching resulting in total, average reflectance...... below 0.5% across a 156x156 mm2 silicon wafer. Black bus-bars were realized by oxidized copper resulting in reflectance below 3% in the entire visible wavelength range. The combination of these two technologies may result in aesthetic, all-black panels based on conventional, front-contacted solar cells...
7. Looking for the invisible universe - Black matter, black energy, black holes
International Nuclear Information System (INIS)
Elbaz, David
2016-01-01
As the discovery of the expansion of the universe and of black holes put the study of cosmology into question again because it now refers to invisible things such as black holes, black energy and black matter, the author proposes an other view on the universe within such a context. He first discusses these three enigmas of black matter, black energy and black holes. In a second part, he addresses, discusses and comments five illusions: the Uranian illusion (questions of the existence of an anti-world, of black matter temperature), the Mercurian illusion (quantum gravity, the string theory), the Martian illusion (a patchwork universe, the illusion of the infinite), the cosmic Maya (the John Wheeler's cup, the holographic universe), and the narcissistic illusion
8. From binary black hole simulation to triple black hole simulation
International Nuclear Information System (INIS)
Bai Shan; Cao Zhoujian; Han, Wen-Biao; Lin, Chun-Yu; Yo, Hwei-Jang; Yu, Jui-Ping
2011-01-01
Black hole systems are among the most promising sources for a gravitational wave detection project. Now, China is planning to construct a space-based laser interferometric detector as a follow-on mission of LISA in the near future. Aiming to provide some theoretical support to this detection project on the numerical relativity side, we focus on black hole systems simulation in this work. Considering the globular galaxy, multiple black hole systems also likely to exist in our universe and play a role as a source for the gravitational wave detector we are considering. We will give a progress report in this paper on our black hole system simulation. More specifically, we will present triple black hole simulation together with binary black hole simulation. On triple black hole simulations, one novel perturbational method is proposed.
9. Statistical mechanics of black holes
International Nuclear Information System (INIS)
Harms, B.; Leblanc, Y.
1992-01-01
We analyze the statistical mechanics of a gas of neutral and charged black holes. The microcanonical ensemble is the only possible approach to this system, and the equilibrium configuration is the one for which most of the energy is carried by a single black hole. Schwarzschild black holes are found to obey the statistical bootstrap condition. In all cases, the microcanonical temperature is identical to the Hawking temperature of the most massive black hole in the gas. U(1) charges in general break the bootstrap property. The problems of black-hole decay and of quantum coherence are also addressed
10. BlackBerry For Dummies
CERN Document Server
Kao, Robert
2010-01-01
Get the most juice out of your BlackBerry handheld!. Feature-rich and complex, the BlackBerry is the number one smartphone in the corporate world is among the most popular handhelds for business users. This new and updated edition includes all the latest and greatest information on new and current BlackBerry mobile devices. Covering a range of valuable how-to topics, this helpful guide explores the BlackBerry's most useful features, techniques for getting the most out of your BlackBerry, and practical information about power usage.: Covers all aspects of the number one smartphone in the corpor
11. Over spinning a black hole?
Energy Technology Data Exchange (ETDEWEB)
Bouhmadi-Lopez, Mariam; Cardoso, Vitor; Nerozzi, Andrea; Rocha, Jorge V, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [CENTRA, Department de Fisica, Instituto Superior Tecnico, Av. Rovisco Pais 1, 1049 Lisboa (Portugal)
2011-09-22
A possible process to destroy a black hole consists on throwing point particles with sufficiently large angular momentum into the black hole. In the case of Kerr black holes, it was shown by Wald that particles with dangerously large angular momentum are simply not captured by the hole, and thus the event horizon is not destroyed. Here we reconsider this gedanken experiment for black holes in higher dimensions. We show that this particular way of destroying a black hole does not succeed and that Cosmic Censorship is preserved.
12. Internal structure of black holes
International Nuclear Information System (INIS)
Cvetic, Mirjam
2013-01-01
Full text: We review recent progress that sheds light on the internal structure of general black holes. We first summarize properties of general multi-charged rotating black holes both in four and five dimensions. We show that the asymptotic boundary conditions of these general asymptotically flat black holes can be modified such that a conformal symmetry emerges. These subtracted geometries preserve the thermodynamic properties of the original black holes and are of the Lifshitz type, thus describing 'a black hole in the asymptotically conical box'. Recent efforts employ solution generating techniques to construct interpolating geometries between the original black hole and their subtracted geometries. Upon lift to one dimension higher, these geometries lift to AdS 3 times a sphere, and thus provide a microscopic interpretation of the black hole entropy in terms of dual two-dimensional conformal field theory. (author)
13. Caged black holes: Black holes in compactified spacetimes. I. Theory
International Nuclear Information System (INIS)
Kol, Barak; Sorkin, Evgeny; Piran, Tsvi
2004-01-01
In backgrounds with compact dimensions there may exist several phases of black objects including a black hole and a black string. The phase transition between them raises questions and touches on fundamental issues such as topology change, uniqueness, and cosmic censorship. No analytic solution is known for the black hole, and moreover one can expect approximate solutions only for very small black holes, while phase transition physics happens when the black hole is large. Hence we turn to numerical solutions. Here some theoretical background to the numerical analysis is given, while the results will appear in a subsequent paper. The goals for a numerical analysis are set. The scalar charge and tension along the compact dimension are defined and used as improved order parameters which put both the black hole and the black string at finite values on the phase diagram. The predictions for small black holes are presented. The differential and the integrated forms of the first law are derived, and the latter (Smarr's formula) can be used to estimate the 'overall numerical error'. Field asymptotics and expressions for physical quantities in terms of the numerical values are supplied. The techniques include the 'method of equivalent charges', free energy, dimensional reduction, and analytic perturbation for small black holes
14. Black-hole astrophysics
Energy Technology Data Exchange (ETDEWEB)
Bender, P. [Univ. of Colorado, Boulder, CO (United States); Bloom, E. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Cominsky, L. [Sonoma State Univ., Rohnert Park, CA (United States). Dept. of Physics and Astronomy] [and others
1995-07-01
Black-hole astrophysics is not just the investigation of yet another, even if extremely remarkable type of celestial body, but a test of the correctness of the understanding of the very properties of space and time in very strong gravitational fields. Physicists excitement at this new prospect for testing theories of fundamental processes is matched by that of astronomers at the possibility to discover and study a new and dramatically different kind of astronomical object. Here the authors review the currently known ways that black holes can be identified by their effects on their neighborhood--since, of course, the hole itself does not yield any direct evidence of its existence or information about its properties. The two most important empirical considerations are determination of masses, or lower limits thereof, of unseen companions in binary star systems, and measurement of luminosity fluctuations on very short time scales.
15. Black Holes and Firewalls
Science.gov (United States)
Polchinski, Joseph
2015-04-01
Our modern understanding of space, time, matter, and even reality itself arose from the three great revolutions of the early twentieth century: special relativity, general relativity, and quantum mechanics. But a century later, this work is unfinished. Many deep connections have been discovered, but the full form of a unified theory incorporating all three principles is not known. Thought experiments and paradoxes have often played a key role in figuring out how to fit theories together. For the unification of general relativity and quantum mechanics, black holes have been an important arena. I will talk about the quantum mechanics of black holes, the information paradox, and the latest version of this paradox, the firewall. The firewall points to a conflict between our current theories of spacetime and of quantum mechanics. It may lead to a new understanding of how these are connected, perhaps based on quantum entanglement.
16. Forging a Black identity
Directory of Open Access Journals (Sweden)
Barry Chevannes
1992-07-01
Full Text Available [First paragraph] The Rastafarians: sounds of cultural dissonance [revised and updated editionj. LEONARD E. BARRETT, SR. Boston: Beacon Press, 1988. xviii + 302 pp. (Paper US$11.95 Rasta and resistance: from Marcus Garvey to Walter Rodney. HORACE CAMPBELL. Trenton NJ: Africa World Press, 1987. xiii + 236 pp. (Cloth US$32.95, Paper US10.95 Garvey's children: the legacy of Marcus Garvey. TONY SEWELL. London: Macmillan Caribbean, 1990. 128 pp. (Paper £ 17.95 The central theme linking these three titles is the evolution of a black identity among English-speaking Caribbean peoples, in particular Jamaicans. Consequently all three authors cover the two most important historical phenomena in Caribbean black nationalism, namely Garveyism and Rastafari, one focusing on the former and the other two focusing on the latter. 17. Beyond the black hole International Nuclear Information System (INIS) Boslough, J. 1985-01-01 This book is about the life and work of Stephen Hawking. It traces the development of his theories about the universe and particularly black holes, in a biographical context. Hawking's lecture 'Is the end in sight for theoretical physics' is presented as an appendix. In this, he discusses the possibility of achieving a complete, consistent and unified theory of the physical interactions which would describe all possible observations. (U.K.) 18. Magnonic black holes OpenAIRE Roldán-Molina, A.; Nunez, A.S.; Duine, R. A. 2017-01-01 We show that the interaction between spin-polarized current and magnetization dynamics can be used to implement black-hole and white-hole horizons for magnons - the quanta of oscillations in the magnetization direction in magnets. We consider three different systems: easy-plane ferromagnetic metals, isotropic antiferromagnetic metals, and easy-plane magnetic insulators. Based on available experimental data, we estimate that the Hawking temperature can be as large as 1 K. We comment on the imp... 19. Black Friday = Broget Branding? DEFF Research Database (Denmark) Hansen, Heidi 2015-01-01 ? Essensen ved Black Friday er lave priser, og det er der ved første øjekast ikke mange brandingmuligheder forbundet ved, hvis man forstår branding som en måde at skabe ekstra værdi omkring sit produkt eller sin virksomhed. Som brand bliver man dog alligevel nødt til at forholde sig til konceptet, da det er... 20. France in Black Africa, Science.gov (United States) 1989-01-01 Difficulties with this romantic concept developed, however, when General Faidherbe began to expand French control into the Senegalese hinterland. He was...and his German 45 France in Black Africa friends to gain greater control of the AOF.6 The tragi- comedy ended with the 1942 Allied landings in North...service]). Trinquier’s own stay in Africa was short-lived. Belgian resistance to a French invasion of their turf was fierce. Trinquier’s romantic 1. Black Sea challenges International Nuclear Information System (INIS) Drevet, J.F. 2008-01-01 In this month's European column, Jean-Francois Drevet examines the issues that arise for Europe from the Black Sea region. The Black Sea is increasingly becoming a crucial place of transit for hydrocarbon imports from the Caspian and Russia into the European Union. The considerable increase in this traffic raises both environmental problems (the risk of oil slicks) and issues of security of supply, on account of the economic and political fragility of some of the bordering or neighbouring states (Ukraine, Georgia, Armenia, Azerbaijan, Russia/Chechnya etc.). This is why, as Jean-Francois Drevet stresses, the European Union has been trying since the mid-1990's to claim a role in the management of the affairs of the region. With two bordering states (Rumania and Bulgaria) joining the EU in 2007, cooperation in the Black Sea has become a priority within the framework of the European Neighbourhood Policy, and this column delineates a number of the obstacles that still have to be surmounted. (author) 2. Black silicon solar cells with black bus-bar strings DEFF Research Database (Denmark) Davidsen, Rasmus Schmidt; Tang, Peter Torben; Mizushima, Io 2016-01-01 We present the combination of black silicon texturing and blackened bus-bar strings as a potential method for obtaining all-black solar panels, while using conventional, front-contacted solar cells. Black silicon was realized by maskless reactive ion etching resulting in total, average reflectance...... below 0.5% across a 156x156 mm2 silicon wafer. Four different methods to obtain blackened bus-bar strings were compared with respect to reflectance, and two of these methods (i.e., oxidized copper and etched solder) were used to fabricate functional allblack solar 9-cell panels. The black bus-bars (e.......g., by oxidized copper) have a reflectance below 3% in the entire visible wavelength range. The combination of black silicon cells and blackened bus-bars results in aesthetic, all-black panels based on conventional, front-contacted solar cells without compromising efficiency.... 3. Black Hole Area Quantization rule from Black Hole Mass Fluctuations OpenAIRE Schiffer, Marcelo 2016-01-01 We calculate the black hole mass distribution function that follows from the random emission of quanta by Hawking radiation and with this function we calculate the black hole mass fluctuation. From a complete different perspective we regard the black hole as quantum mechanical system with a quantized event horizon area and transition probabilities among the various energy levels and then calculate the mass dispersion. It turns out that there is a perfect agreement between the statistical and ... 4. Black Swan Tropical Cyclones Science.gov (United States) Emanuel, K.; Lin, N. 2012-12-01 Virtually all assessments of tropical cyclone risk are based on historical records, which are limited to a few hundred years at most. Yet stronger TCs may occur in the future and at places that have not been affected historically. Such events lie outside the realm of historically based expectations and may have extreme impacts. Their occurrences are also often made explainable after the fact (e.g., Hurricane Katrina). We nickname such potential future TCs, characterized by rarity, extreme impact, and retrospective predictability, "black swans" (Nassim Nicholas Taleb, 2007). As, by definition, black swan TCs have yet to happen, statistical methods that solely rely on historical track data cannot predict their occurrence. Global climate models lack the capability to predict intense storms, even with a resolution as high as 14 km (Emanuel et al. 2010). Also, most dynamic downscaling methods (e.g., Bender et al. 2010) are still limited in horizontal resolution and are too expensive to implement to generate enough events to include rare ones. In this study, we apply a simpler statistical/deterministic hurricane model (Emanuel et al. 2006) to simulate large numbers of synthetic storms under a given (observed or projected) climate condition. The method has been shown to generate realistic extremes in various basins (Emanuel et al. 2008 and 2010). We also apply a hydrodynamic model (ADCIRC; Luettich et al. 1992) to simulate the storm surges generated by these storms. We then search for black swan TCs, in terms of the joint wind and surge damage potential, in the generated large databases. Heavy rainfall is another important TC hazard and will be considered in a future study. We focus on three areas: Tampa Bay in the U.S., the Persian Gulf, and Darwin in Australia. Tampa Bay is highly vulnerable to storm surge as it is surrounded by shallow water and low-lying lands, much of which may be inundated by a storm tide of 6 m. High surges are generated by storms with a broad 5. 77 FR 70423 - Black Bear Hydro Partners, LLC and Black Bear Development Holdings, LLC and Black Bear SO, LLC... Science.gov (United States) 2012-11-26 ... Bear Hydro Partners, LLC and Black Bear Development Holdings, LLC and Black Bear SO, LLC; Notice of..., 2012, Black Bear Hydro Partners, LLC, sole licensee (transferor) and Black Bear Development Holdings, LLC and Black Bear SO, LLC (transferees) filed an application for the partial the transfer of licenses... 6. Quantum effects in black holes International Nuclear Information System (INIS) Frolov, V.P. 1979-01-01 A strict definition of black holes is presented and some properties with regard to their mass are enumerated. The Hawking quantum effect - the effect of vacuum instability in the black hole gravitational field, as a result of shich the black hole radiates as a heated body is analyzed. It is shown that in order to obtain results on the black hole radiation it is sufficient to predetermine the in-vacuum state at a time moment in the past, when the collapsing body has a large size, and its gravitational field can be neglected. The causes and the place of particle production by the black hole, and also the space-time inside the black hole, are considered 7. Particle creation by black holes International Nuclear Information System (INIS) Hawking, S.W. 1975-01-01 In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 10 15 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law: S + 1/4 A never decreases where S is the entropy of matter outside black holes and A is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon. (orig.) [de 8. Black Hole's 1/N Hair CERN Document Server Dvali, Gia 2013-01-01 According to the standard view classically black holes carry no hair, whereas quantum hair is at best exponentially weak. We show that suppression of hair is an artifact of the semi-classical treatment and that in the quantum picture hair appears as an inverse mass-square effect. Such hair is predicted in the microscopic quantum description in which a black hole represents a self-sustained leaky Bose-condensate of N soft gravitons. In this picture the Hawking radiation is the quantum depletion of the condensate. Within this picture we show that quantum black hole physics is fully compatible with continuous global symmetries and that global hair appears with the strength B/N, where B is the global charge swallowed by the black hole. For large charge this hair has dramatic effect on black hole dynamics. Our findings can have interesting astrophysical consequences, such as existence of black holes with large detectable baryonic and leptonic numbers. 9. Acceleration of black hole universe Science.gov (United States) Zhang, T. X.; Frederick, C. 2014-01-01 Recently, Zhang slightly modified the standard big bang theory and developed a new cosmological model called black hole universe, which is consistent with Mach's principle, governed by Einstein's general theory of relativity, and able to explain all observations of the universe. Previous studies accounted for the origin, structure, evolution, expansion, and cosmic microwave background radiation of the black hole universe, which grew from a star-like black hole with several solar masses through a supermassive black hole with billions of solar masses to the present state with hundred billion-trillions of solar masses by accreting ambient matter and merging with other black holes. This paper investigates acceleration of the black hole universe and provides an alternative explanation for the redshift and luminosity distance measurements of type Ia supernovae. The results indicate that the black hole universe accelerates its expansion when it accretes the ambient matter in an increasing rate. In other words, i.e., when the second-order derivative of the mass of the black hole universe with respect to the time is positive . For a constant deceleration parameter , we can perfectly explain the type Ia supernova measurements with the reduced chi-square to be very close to unity, χ red˜1.0012. The expansion and acceleration of black hole universe are driven by external energy. 10. On black hole horizon fluctuations International Nuclear Information System (INIS) Tuchin, K.L. 1999-01-01 A study of the high angular momentum particles 'atmosphere' near the Schwarzschild black hole horizon suggested that strong gravitational interactions occur at invariant distance of the order of 3 √M [2]. We present a generalization of this result to the Kerr-Newman black hole case. It is shown that the larger charge and angular momentum black hole bears, the larger invariant distance at which strong gravitational interactions occur becomes. This invariant distance is of order 3 √((r + 2 )/((r + - r - ))). This implies that the Planckian structure of the Hawking radiation of extreme black holes is completely broken 11. Black holes and the multiverse International Nuclear Information System (INIS) Garriga, Jaume; Vilenkin, Alexander; Zhang, Jun 2016-01-01 Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spherical domain walls nucleating during inflation. As an illustrative example, we studied the black hole mass spectrum in the domain wall scenario, assuming that domain walls interact with matter only gravitationally. Our results indicate that, depending on the model parameters, black holes produced in this scenario can have significant astrophysical effects and can even serve as dark matter or as seeds for supermassive black holes. The mechanism of black hole formation described in this paper is very generic and has important implications for the global structure of the universe. Baby universes inside super-critical black holes inflate eternally and nucleate bubbles of all vacua allowed by the underlying particle physics. The resulting multiverse has a very non-trivial spacetime structure, with a multitude of eternally inflating regions connected by wormholes. If a black hole population with the predicted mass spectrum is discovered, it could be regarded as evidence for inflation and for the existence of a multiverse 12. Black holes and the multiverse Energy Technology Data Exchange (ETDEWEB) Garriga, Jaume [Departament de Fisica Fonamental i Institut de Ciencies del Cosmos, Universitat de Barcelona, Marti i Franques, 1, Barcelona, 08028 Spain (Spain); Vilenkin, Alexander; Zhang, Jun, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Institute of Cosmology, Tufts University, 574 Boston Ave, Medford, MA, 02155 (United States) 2016-02-01 Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spherical domain walls nucleating during inflation. As an illustrative example, we studied the black hole mass spectrum in the domain wall scenario, assuming that domain walls interact with matter only gravitationally. Our results indicate that, depending on the model parameters, black holes produced in this scenario can have significant astrophysical effects and can even serve as dark matter or as seeds for supermassive black holes. The mechanism of black hole formation described in this paper is very generic and has important implications for the global structure of the universe. Baby universes inside super-critical black holes inflate eternally and nucleate bubbles of all vacua allowed by the underlying particle physics. The resulting multiverse has a very non-trivial spacetime structure, with a multitude of eternally inflating regions connected by wormholes. If a black hole population with the predicted mass spectrum is discovered, it could be regarded as evidence for inflation and for the existence of a multiverse. 13. Black report up-date International Nuclear Information System (INIS) 1988-12-01 In 1984, the Black Report published its results on the incidence of cancer and leukaemia in under 25-year olds in the village of Seascale and the surrounding area near the Sellafield nuclear reprocessing plant. Since then the pressure group core, as a result of their own independent research, has discovered ten additional cases of childhood cancer which should have been included in the Black Report and a Further two cases since the Black Report was written. This represents an additional 31% over the initial numbers considered and a review of the Black Report is sought. (UK) 14. Statistical Hair on Black Holes International Nuclear Information System (INIS) Strominger, A. 1996-01-01 The Bekenstein-Hawking entropy for certain BPS-saturated black holes in string theory has recently been derived by counting internal black hole microstates at weak coupling. We argue that the black hole microstate can be measured by interference experiments even in the strong coupling region where there is clearly an event horizon. Extracting information which is naively behind the event horizon is possible due to the existence of statistical quantum hair carried by the black hole. This quantum hair arises from the arbitrarily large number of discrete gauge symmetries present in string theory. copyright 1996 The American Physical Society 15. Thermodynamics of Accelerating Black Holes. Science.gov (United States) Appels, Michael; Gregory, Ruth; Kubizňák, David 2016-09-23 We address a long-standing problem of describing the thermodynamics of an accelerating black hole. We derive a standard first law of black hole thermodynamics, with the usual identification of entropy proportional to the area of the event horizon-even though the event horizon contains a conical singularity. This result not only extends the applicability of black hole thermodynamics to realms previously not anticipated, it also opens a possibility for studying novel properties of an important class of exact radiative solutions of Einstein equations describing accelerated objects. We discuss the thermodynamic volume, stability, and phase structure of these black holes. 16. Drifting black aurorae? International Nuclear Information System (INIS) Schoute-Vanneck, H.; Scourfield, M.W.J.; Nielsen, E. 1990-01-01 Characteristics of eastward drifting forms, previously described in the literature as black aurorae, have been identified in low-light level TV camera data. The TV field of view was within the field of view of STARE and that of an all-sky camera. On the basis of these observations the authors propose that these auroral forms are a manifestation of folds or waves on the borders of auroral bands propagating along the dark regions between neighboring auroral bands. Conditions under which the folds or waves occur are compatible with their formation by the Kelvin-Helmholtz electrostatic instability 17. Black lung disease Energy Technology Data Exchange (ETDEWEB) Ramani, R.V.; Frantz, R.L. [Pennsylvania State University, University Park, PA (United States) 1995-12-31 Coal workers pneumoconiosis (CWP), often called Black Lung Disease is a occupational disease which results from inhalation of coal mine dust which usually contains small amounts of free crystalline silica. This chapter reviews the current knowledge of the epidemiology and clinical aspects of CWP and how it has been controlled in the USA through the 1969 Coal Mine Act and dust level standards. It describes the sampling methods used. Medical control methods and engineering control of the disease is discussed. Work of the Generic Mineral Technology Center for Respirable Dust is described. 28 refs., 6 figs. 18. Artificial black holes CERN Document Server Visser, Matt; Volovik, Grigory E 2009-01-01 Physicists are pondering on the possibility of simulating black holes in the laboratory by means of various "analog models". These analog models, typically based on condensed matter physics, can be used to help us understand general relativity (Einstein's gravity); conversely, abstract techniques developed in general relativity can sometimes be used to help us understand certain aspects of condensed matter physics. This book contains 13 chapters - written by experts in general relativity, particle physics, and condensed matter physics - that explore various aspects of this two-way traffic. 19. Thermal BEC Black Holes Directory of Open Access Journals (Sweden) Roberto Casadio 2015-10-01 Full Text Available We review some features of Bose–Einstein condensate (BEC models of black holes obtained by means of the horizon wave function formalism. We consider the Klein–Gordon equation for a toy graviton field coupled to a static matter current in a spherically-symmetric setup. The classical field reproduces the Newtonian potential generated by the matter source, while the corresponding quantum state is given by a coherent superposition of scalar modes with a continuous occupation number. An attractive self-interaction is needed for bound states to form, the case in which one finds that (approximately one mode is allowed, and the system of N bosons can be self-confined in a volume of the size of the Schwarzschild radius. The horizon wave function formalism is then used to show that the radius of such a system corresponds to a proper horizon. The uncertainty in the size of the horizon is related to the typical energy of Hawking modes: it decreases with the increasing of the black hole mass (larger number of gravitons, resulting in agreement with the semiclassical calculations and which does not hold for a single very massive particle. The spectrum of these systems has two components: a discrete ground state of energy m (the bosons forming the black hole and a continuous spectrum with energy ω > m (representing the Hawking radiation and modeled with a Planckian distribution at the expected Hawking temperature. Assuming the main effect of the internal scatterings is the Hawking radiation, the N-particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy M = Nm and Entropy 2015, 17 6894 a Planckian distribution for E > M at the same Hawking temperature. This can be used to compute the partition function and to find the usual area law for the entropy, with a logarithmic correction related to the Hawking component. The backreaction of modes with ω > m is also shown to reduce 20. Magnonic Black Holes. Science.gov (United States) Roldán-Molina, A; Nunez, Alvaro S; Duine, R A 2017-02-10 We show that the interaction between the spin-polarized current and the magnetization dynamics can be used to implement black-hole and white-hole horizons for magnons-the quanta of oscillations in the magnetization direction in magnets. We consider three different systems: easy-plane ferromagnetic metals, isotropic antiferromagnetic metals, and easy-plane magnetic insulators. Based on available experimental data, we estimate that the Hawking temperature can be as large as 1 K. We comment on the implications of magnonic horizons for spin-wave scattering and transport experiments, and for magnon entanglement. 1. Black American and Nigerian Pentecostalism: A Black Religious ... African Journals Online (AJOL) Black American and Nigerian Pentecostalism: A Black Religious Schizophrenia, 1910-2010. ... in American and African Pentecostalism as is related to social crisis, the dislocation of masses brought on by economic deprivation, urbanization, the break up of traditional society and consequence loss of traditional values. 2. The Effect of Black Peers on Black Test Scores Science.gov (United States) Armor, David J.; Duck, Stephanie 2007-01-01 Recent studies have used increasingly complex methodologies to estimate the effect of peer characteristics--race, poverty, and ability--on student achievement. A paper by Hanushek, Kain, and Rivkin using Texas state testing data has received particularly wide attention because it found a large negative effect of school percent black on black math… 3. Black Interpretation, Black American Literature, and Grey Audiences. Science.gov (United States) Washington, Earl M. 1981-01-01 Defines and illustrates language techniques used by Black authors writing to and for Blacks in the 1960s and 1970s. Suggests how language and theme barriers of such literature might be overcome in a contemporary integrated oral interpretation classroom. (PD) 4. Black hole thermodynamical entropy International Nuclear Information System (INIS) Tsallis, Constantino; Cirto, Leonardo J.L. 2013-01-01 As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy S BG of a (3+1) black hole is proportional to its area L 2 (L being a characteristic linear length), and not to its volume L 3 . Similarly it exists the area law, so named because, for a wide class of strongly quantum-entangled d-dimensional systems, S BG is proportional to lnL if d=1, and to L d-1 if d>1, instead of being proportional to L d (d ≥ 1). These results violate the extensivity of the thermodynamical entropy of a d-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is not to be identified with the BG additive entropy but with appropriately generalized nonadditive entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle. (orig.) 5. Black holes and holography International Nuclear Information System (INIS) Mathur, Samir D 2012-01-01 The idea of holography in gravity arose from the fact that the entropy of black holes is given by their surface area. The holography encountered in gauge/gravity duality has no such relation however; the boundary surface can be placed at an arbitrary location in AdS space and its area does not give the entropy of the bulk. The essential issues are also different between the two cases: in black holes we get Hawking radiation from the 'holographic surface' which leads to the information issue, while in gauge/gravity duality there is no such radiation. To resolve the information paradox we need to show that there are real degrees of freedom at the horizon of the hole; this is achieved by the fuzzball construction. In gauge/gravity duality we have instead a field theory defined on an abstract dual space; there are no gravitational degrees of freedom at the holographic boundary. It is important to understand the relations and differences between these two notions of holography to get a full understanding of the lessons from the information paradox. 6. Statistical black-hole thermodynamics International Nuclear Information System (INIS) Bekenstein, J.D. 1975-01-01 Traditional methods from statistical thermodynamics, with appropriate modifications, are used to study several problems in black-hole thermodynamics. Jaynes's maximum-uncertainty method for computing probabilities is used to show that the earlier-formulated generalized second law is respected in statistically averaged form in the process of spontaneous radiation by a Kerr black hole discovered by Hawking, and also in the case of a Schwarzschild hole immersed in a bath of black-body radiation, however cold. The generalized second law is used to motivate a maximum-entropy principle for determining the equilibrium probability distribution for a system containing a black hole. As an application we derive the distribution for the radiation in equilibrium with a Kerr hole (it is found to agree with what would be expected from Hawking's results) and the form of the associated distribution among Kerr black-hole solution states of definite mass. The same results are shown to follow from a statistical interpretation of the concept of black-hole entropy as the natural logarithm of the number of possible interior configurations that are compatible with the given exterior black-hole state. We also formulate a Jaynes-type maximum-uncertainty principle for black holes, and apply it to obtain the probability distribution among Kerr solution states for an isolated radiating Kerr hole 7. Introduction: Teaching Black Lives Matter OpenAIRE Paula Austin; Erica Cardwell; Christopher Kennedy; Robyn Spencer 2016-01-01 An introduction to Radical Teacher, Issue 106: Teaching Black Lives Matter. This issue brings together a diverse collection of articles exploring educator’s responses, strategies, and stories on how #BlackLivesMatter has informed their teaching practice, the content of their courses, and their personal relationship to colleagues, family, friends, and self. 8. Introduction: Teaching Black Lives Matter Directory of Open Access Journals (Sweden) Paula Austin 2016-11-01 Full Text Available An introduction to Radical Teacher, Issue 106: Teaching Black Lives Matter. This issue brings together a diverse collection of articles exploring educator’s responses, strategies, and stories on how #BlackLivesMatter has informed their teaching practice, the content of their courses, and their personal relationship to colleagues, family, friends, and self. 9. Teaching Black History after Obama Science.gov (United States) Sotiropoulos, Karen 2017-01-01 This article is a reflection on the teaching of black history after the Obama presidency and at the dawn of the Trump era. It is both an analysis of the state of the academic field and a primer on how to integrate the past few decades of scholarship in black history broadly across standard K-12 curriculum. It demonstrates the importance of… 10. Black-Hole Mass Measurements DEFF Research Database (Denmark) Vestergaard, Marianne 2004-01-01 The applicability and apparent uncertainties of the techniques currently available for measuring or estimating black-hole masses in AGNs are briefly summarized.......The applicability and apparent uncertainties of the techniques currently available for measuring or estimating black-hole masses in AGNs are briefly summarized.... 11. School Desegregation and Black Achievement. Science.gov (United States) Cook, Thomas; And Others Seven papers commissioned by the National Institute of Education in order to clarify the state of recent knowledge about the effects of school desegregation on the academic achievement of black students are contained in this report. The papers, which analyze 19 "core" empirical studies on this topic, include: (1) "What Have Black Children Gained… 12. ATLAS simulated black hole event CERN Multimedia Pequenão, J 2008-01-01 The simulated collision event shown is viewed along the beampipe. The event is one in which a microscopic-black-hole was produced in the collision of two protons (not shown). The microscopic-black-hole decayed immediately into many particles. The colors of the tracks show different types of particles emerging from the collision (at the center). 13. Black holes in brane worlds Indian Academy of Sciences (India) Abstract. A Kerr metric describing a rotating black hole is obtained on the three brane in a five-dimensional Randall-Sundrum brane world by considering a rotating five-dimensional black string in the bulk. We examine the causal structure of this space-time through the geodesic equations. 14. Black holes and quantum processes in them International Nuclear Information System (INIS) Frolov, V.P. 1976-01-01 The latest achievements in the physics of black holes are reviewed. The problem of quantum production in a strong gravitational field of black holes is considered. Another parallel discovered during investigation of interactions between black holes and between black holes and surrounding media, is also drawn with thermodynamics. A gravitational field of rotating black holes is considered. Some cosmological aspects of evaporation of small black holes are discussed as well as possibilities to observe them 15. Black hole decay as geodesic motion International Nuclear Information System (INIS) Gupta, Kumar S.; Sen, Siddhartha 2003-01-01 We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The equation governing black hole decay can be identified as the geodesic equation in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. Moreover, this approach predicts a precise correction term to the usual expression for the decay rate of black holes 16. Black holes and everyday physics International Nuclear Information System (INIS) Bekenstein, J.D. 1982-01-01 Black holes have piqued much curiosity. But thus far they have been important only in ''remote'' subjects like astrophysics and quantum gravity. It is shown that the situation can be improved. By a judicious application of black hole physics, one can obtain new results in ''everyday physics''. For example, black holes yield a quantum universal upper bound on the entropy-to-energy ratio for ordinary thermodynamical systems which was unknown earlier. It can be checked, albeit with much labor, by ordinary statistical methods. Black holes set a limitation on the number of species of elementary particles-quarks, leptons, neutrinos - which may exist. And black holes lead to a fundamental limitation on the rate at which information can be transferred for given message energy by any communication system. (author) 17. The search for black holes International Nuclear Information System (INIS) Torn, K. 1976-01-01 Conceivable experimental investigations to prove the existence of black holes are discussed. Double system with a black hole turning around a star-satellite are in the spotlight. X-radiation emmited by such systems and resulting from accretion of the stellar gas by a black hole, and the gas heating when falling on the black hole might prove the model suggested. A source of strong X-radiation observed in the Cygnus star cluster and referred to as Cygnus X-1 may be thus identified as a black hole. Direct registration of short X-ray pulses with msec intervals might prove the suggestion. The lack of appropriate astrophysic facilities is pointed out to be the major difficulty on the way of experimental verifications 18. Black hole final state conspiracies International Nuclear Information System (INIS) McInnes, Brett 2009-01-01 The principle that unitarity must be preserved in all processes, no matter how exotic, has led to deep insights into boundary conditions in cosmology and black hole theory. In the case of black hole evaporation, Horowitz and Maldacena were led to propose that unitarity preservation can be understood in terms of a restriction imposed on the wave function at the singularity. Gottesman and Preskill showed that this natural idea only works if one postulates the presence of 'conspiracies' between systems just inside the event horizon and states at much later times, near the singularity. We argue that some AdS black holes have unusual internal thermodynamics, and that this may permit the required 'conspiracies' if real black holes are described by some kind of sum over all AdS black holes having the same entropy 19. String-Corrected Black Holes Energy Technology Data Exchange (ETDEWEB) Hubeny, V. 2005-01-12 We investigate the geometry of four dimensional black hole solutions in the presence of stringy higher curvature corrections to the low energy effective action. For certain supersymmetric two charge black holes these corrections drastically alter the causal structure of the solution, converting seemingly pathological null singularities into timelike singularities hidden behind a finite area horizon. We establish, analytically and numerically, that the string-corrected two-charge black hole metric has the same Penrose diagram as the extremal four-charge black hole. The higher derivative terms lead to another dramatic effect--the gravitational force exerted by a black hole on an inertial observer is no longer purely attractive. The magnitude of this effect is related to the size of the compactification manifold. 20. Compressibility of rotating black holes International Nuclear Information System (INIS) Dolan, Brian P. 2011-01-01 Interpreting the cosmological constant as a pressure, whose thermodynamically conjugate variable is a volume, modifies the first law of black hole thermodynamics. Properties of the resulting thermodynamic volume are investigated: the compressibility and the speed of sound of the black hole are derived in the case of nonpositive cosmological constant. The adiabatic compressibility vanishes for a nonrotating black hole and is maximal in the extremal case--comparable with, but still less than, that of a cold neutron star. A speed of sound v s is associated with the adiabatic compressibility, which is equal to c for a nonrotating black hole and decreases as the angular momentum is increased. An extremal black hole has v s 2 =0.9 c 2 when the cosmological constant vanishes, and more generally v s is bounded below by c/√(2). 1. When Supermassive Black Holes Wander Science.gov (United States) Kohler, Susanna 2018-05-01 Are supermassive black holes found only at the centers of galaxies? Definitely not, according to a new study in fact, galaxies like the Milky Way may harbor several such monsters wandering through their midst.Collecting Black Holes Through MergersIts generally believed that galaxies are built up hierarchically, growing in size through repeated mergers over time. Each galaxy in a major merger likely hosts a supermassive black hole a black hole of millions to billions of times the mass of the Sun at its center. When a pair of galaxies merges, their supermassive black holes will often sink to the center of the merger via a process known as dynamical friction. There the supermassive black holes themselves will eventually merge in a burst of gravitational waves.Spatial distribution and velocities of wandering supermassive black holes in three of the authors simulated galaxies, shown in edge-on (left) and face-on (right) views of the galaxy disks. Click for a closer look. [Tremmel et al. 2018]But if a galaxy the size of the Milky Way was built through a history of many major galactic mergers, are we sure that all its accumulated supermassive black holes eventually merged at the galactic center? A new study suggests that some of these giants might have escaped such a fate and they now wander unseen on wide orbits through their galaxies.Black Holes in an Evolving UniverseLed by Michael Tremmel (Yale Center for Astronomy Astrophysics), a team of scientists has used data from a large-scale cosmological simulation, Romulus25, to explore the possibility of wandering supermassive black holes. The Romulus simulations are uniquely suited to track the formation and subsequent orbital motion of supermassive black holes as galactic halos are built up through mergers over the history of the universe.From these simulations, Tremmel and collaborators find an end total of 316 supermassive black holes residing within the bounds of 26 Milky-Way-mass halos. Of these, roughly a third are 2. Complicated Contradictions Amid Black Feminism and Millennial Black Women Teachers Creating Curriculum for Black Girls Science.gov (United States) Nyachae, Tiffany M. 2016-01-01 Millennial Black women teachers wrestle with two simultaneous burdens: disrupting the racist and sexist status quo of schooling through curriculum, and employing tactics to survive school politics among their majority White women colleagues. This article describes how the "Sisters of Promise" (SOP) curriculum aligned with Black feminism… 3. Black Lives Matter of Black Identity Extremist? : The FBI, Black Activists and the Struggle for Victimhood NARCIS (Netherlands) Mutsaers, Paul 2017-01-01 The question 'who is the victim?' is an important social directive that shapes the struggles for victimhood in which Black Lives Matters, U.S. police forces and their various (counter)publics are currently engaging. This column begins with a controversial FBI report on so-called Black Identity 4. A nonsingular rotating black hole International Nuclear Information System (INIS) Ghosh, Sushant G. 2015-01-01 The spacetime singularities in classical general relativity are inevitable, as predicated by the celebrated singularity theorems. However, it is a general belief that singularities do not exist in Nature and that they are the limitations of the general relativity. In the absence of a welldefined quantum gravity, models of regular black holes have been studied. We employ a probability distribution inspired mass function m(r) to replace the Kerr black hole mass M to represent a nonsingular rotating black hole that is identified asymptotically (r >> k, k > 0 constant) exactly as the Kerr-Newman black hole, and as the Kerr black hole when k = 0. The radiating counterpart renders a nonsingular generalization of Carmeli's spacetime as well as Vaidya's spacetime, in the appropriate limits. The exponential correction factor changing the geometry of the classical black hole to remove the curvature singularity can also be motivated by quantum arguments. The regular rotating spacetime can also be understood as a black hole of general relativity coupled to nonlinear electrodynamics. (orig.) 5. The renaissance of black phosphorus. Science.gov (United States) Ling, Xi; Wang, Han; Huang, Shengxi; Xia, Fengnian; Dresselhaus, Mildred S 2015-04-14 One hundred years after its first successful synthesis in the bulk form in 1914, black phosphorus (black P) was recently rediscovered from the perspective of a 2D layered material, attracting tremendous interest from condensed matter physicists, chemists, semiconductor device engineers, and material scientists. Similar to graphite and transition metal dichalcogenides (TMDs), black P has a layered structure but with a unique puckered single-layer geometry. Because the direct electronic band gap of thin film black P can be varied from 0.3 eV to around 2 eV, depending on its film thickness, and because of its high carrier mobility and anisotropic in-plane properties, black P is promising for novel applications in nanoelectronics and nanophotonics different from graphene and TMDs. Black P as a nanomaterial has already attracted much attention from researchers within the past year. Here, we offer our opinions on this emerging material with the goal of motivating and inspiring fellow researchers in the 2D materials community and the broad readership of PNAS to discuss and contribute to this exciting new field. We also give our perspectives on future 2D and thin film black P research directions, aiming to assist researchers coming from a variety of disciplines who are desirous of working in this exciting research field. 6. Black Hole Grabs Starry Snack Science.gov (United States) 2006-01-01 [figure removed for brevity, see original site] Poster Version This artist's concept shows a supermassive black hole at the center of a remote galaxy digesting the remnants of a star. NASA's Galaxy Evolution Explorer had a 'ringside' seat for this feeding frenzy, using its ultraviolet eyes to study the process from beginning to end. The artist's concept chronicles the star being ripped apart and swallowed by the cosmic beast over time. First, the intact sun-like star (left) ventures too close to the black hole, and its own self-gravity is overwhelmed by the black hole's gravity. The star then stretches apart (middle yellow blob) and eventually breaks into stellar crumbs, some of which swirl into the black hole (cloudy ring at right). This doomed material heats up and radiates light, including ultraviolet light, before disappearing forever into the black hole. The Galaxy Evolution Explorer was able to watch this process unfold by observing changes in ultraviolet light. The area around the black hole appears warped because the gravity of the black hole acts like a lens, twisting and distorting light. 7. Black holes at neutrino telescopes International Nuclear Information System (INIS) Kowalski, M.; Ringwald, A.; Tu, H. 2002-01-01 In scenarios with extra dimensions and TeV-scale quantum gravity, black holes are expected to be produced in the collision of light particles at center-of-mass energies above the fundamental Planck scale with small impact parameters. Black hole production and evaporation may thus be studied in detail at the large hadron collider (LHC). But even before the LHC starts operating, neutrino telescopes such as AMANDA/IceCube, ANTARES, Baikal, and RICE have an opportunity to search for black hole signatures. Black hole production in the scattering of ultrahigh energy cosmic neutrinos on nucleons in the ice or water may initiate cascades and through-going muons with distinct characteristics above the Standard Model rate. In this Letter, we investigate the sensitivity of neutrino telescopes to black hole production and compare it to the one expected at the Pierre Auger Observatory, an air shower array currently under construction, and at the LHC. We find that, already with the currently available data, AMANDA and RICE should be able to place sensible constraints in black hole production parameter space, which are competitive with the present ones from the air shower facilities Fly's Eye and AGASA. In the optimistic case that a ultrahigh energy cosmic neutrino flux significantly higher than the one expected from cosmic ray interactions with the cosmic microwave background radiation is realized in nature, one even has discovery potential for black holes at neutrino telescopes beyond the reach of LHC. (orig.) 8. Black-hole driven winds International Nuclear Information System (INIS) Punsly, B.M. 1988-01-01 This dissertation is a study of the physical mechanism that allows a large scale magnetic field to torque a rapidly rotating, supermassive black hole. This is an interesting problem as it has been conjectured that rapidly rotating black holes are the central engines that power the observed extragalactic double radio sources. Axisymmetric solutions of the curved space-time version of Maxwell's equations in the vacuum do not torque black holes. Plasma must be introduced for the hole to mechanically couple to the field. The dynamical aspect of rotating black holes that couples the magnetic field to the hole is the following. A rotating black hole forces the external geometry of space-time to rotate (the dragging of inertial frames). Inside of the stationary limit surface, the ergosphere, all physical particle trajectories must appear to rotate in the same direction as the black hole as viewed by the stationary observers at asymptotic infinity. In the text, it is demonstrated how plasma that is created on field lines that thread both the ergosphere and the equatorial plane will be pulled by gravity toward the equator. By the aforementioned properties of the ergosphere, the disk must rotate. Consequently, the disk acts like a unipolar generator. It drives a global current system that supports the toroidal magnetic field in an outgoing, magnetically dominated wind. This wind carries energy (mainly in the form of Poynting flux) and angular momentum towards infinity. The spin down of the black hole is the ultimate source of this energy and angular momentum flux 9. Black powder in gas pipelines Energy Technology Data Exchange (ETDEWEB) Sherik, Abdelmounam [Saudi Aramco, Dhahran (Saudi Arabia) 2009-07-01 Despite its common occurrence in the gas industry, black powder is a problem that is not well understood across the industry, in terms of its chemical and physical properties, source, formation, prevention or management of its impacts. In order to prevent or effectively manage the impacts of black powder, it is essential to have knowledge of its chemical and physical properties, formation mechanisms and sources. The present paper is divided into three parts. The first part of this paper is a synopsis of published literature. The second part reviews the recent laboratory and field work conducted at Saudi Aramco Research and Development Center to determine the compositions, properties, sources and formation mechanisms of black powder in gas transmission systems. Microhardness, nano-indentation, X-ray Diffraction (XRD), X-ray Fluorescence (XRF) and Scanning Electron Microscopy (SEM) techniques were used to analyze a large number of black powder samples collected from the field. Our findings showed that black powder is generated inside pipelines due to internal corrosion and that the composition of black powder is dependent on the composition of transported gas. The final part presents a summary and brief discussion of various black powder management methods. (author) 10. Thermodynamic theory of black holes Energy Technology Data Exchange (ETDEWEB) Davies, P C.W. [King' s Coll., London (UK). Dept. of Mathematics 1977-04-21 The thermodynamic theory underlying black hole processes is developed in detail and applied to model systems. It is found that Kerr-Newman black holes undergo a phase transition at a = 0.68M or Q = 0.86M, where the heat capacity has an infinite discontinuity. Above the transition values the specific heat is positive, permitting isothermal equilibrium with a surrounding heat bath. Simple processes and stability criteria for various black hole situations are investigated. The limits for entropically favoured black hole formation are found. The Nernst conditions for the third law of thermodynamics are not satisfied fully for black holes. There is no obvious thermodynamic reason why a black hole may not be cooled down below absolute zero and converted into a naked singularity. Quantum energy-momentum tensor calculations for uncharged black holes are extended to the Reissner-Nordstrom case, and found to be fully consistent with the thermodynamic picture for Q < M. For Q < M the model predicts that 'naked' collapse also produces radiation, with such intensity that the collapsing matter is entirely evaporated away before a naked singularity can form. 11. Black holes and Higgs stability CERN Document Server Tetradis, Nikolaos 2016-09-20 We study the effect of primordial black holes on the classical rate of nucleation of AdS regions within the standard electroweak vacuum. We find that the energy barrier for transitions to the new vacuum, which characterizes the exponential suppression of the nucleation rate, can be reduced significantly in the black-hole background. A precise analysis is required in order to determine whether the the existence of primordial black holes is compatible with the form of the Higgs potential at high temperature or density in the Standard Model or its extensions. 12. Vacuum metastability with black holes Energy Technology Data Exchange (ETDEWEB) Burda, Philipp [Centre for Particle Theory, Durham University,South Road, Durham, DH1 3LE (United Kingdom); Gregory, Ruth [Centre for Particle Theory, Durham University,South Road, Durham, DH1 3LE (United Kingdom); Perimeter Institute, 31 Caroline Street North,Waterloo, ON, N2L 2Y5 (Canada); Moss, Ian G. annd [School of Mathematics and Statistics, Newcastle University,Newcastle Upon Tyne, NE1 7RU (United Kingdom) 2015-08-24 We consider the possibility that small black holes can act as nucleation seeds for the decay of a metastable vacuum, focussing particularly on the Higgs potential. Using a thin-wall bubble approximation for the nucleation process, which is possible when generic quantum gravity corrections are added to the Higgs potential, we show that primordial black holes can stimulate vacuum decay. We demonstrate that for suitable parameter ranges, the vacuum decay process dominates over the Hawking evaporation process. Finally, we comment on the application of these results to vacuum decay seeded by black holes produced in particle collisions. 13. Orbital resonances around black holes. Science.gov (United States) Brink, Jeandrew; Geyer, Marisa; Hinderer, Tanja 2015-02-27 We compute the length and time scales associated with resonant orbits around Kerr black holes for all orbital and spin parameters. Resonance-induced effects are potentially observable when the Event Horizon Telescope resolves the inner structure of Sgr A*, when space-based gravitational wave detectors record phase shifts in the waveform during the resonant passage of a compact object spiraling into the black hole, or in the frequencies of quasiperiodic oscillations for accreting black holes. The onset of geodesic chaos for non-Kerr spacetimes should occur at the resonance locations quantified here. 14. Vacuum metastability with black holes International Nuclear Information System (INIS) Burda, Philipp; Gregory, Ruth; Moss, Ian G. annd 2015-01-01 We consider the possibility that small black holes can act as nucleation seeds for the decay of a metastable vacuum, focussing particularly on the Higgs potential. Using a thin-wall bubble approximation for the nucleation process, which is possible when generic quantum gravity corrections are added to the Higgs potential, we show that primordial black holes can stimulate vacuum decay. We demonstrate that for suitable parameter ranges, the vacuum decay process dominates over the Hawking evaporation process. Finally, we comment on the application of these results to vacuum decay seeded by black holes produced in particle collisions. 15. Tunnelling from Goedel black holes International Nuclear Information System (INIS) Kerner, Ryan; Mann, R. B. 2007-01-01 We consider the spacetime structure of Kerr-Goedel black holes, analyzing their parameter space in detail. We apply the tunnelling method to compute their temperature and compare the results to previous calculations obtained via other methods. We claim that it is not possible to have the closed timelike curve (CTC) horizon in between the two black hole horizons and include a discussion of issues that occur when the radius of the CTC horizon is smaller than the radius of both black hole horizons 16. Quantum mechanics of black holes. Science.gov (United States) Witten, Edward 2012-08-03 The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely. 17. Gravitational polarizability of black holes International Nuclear Information System (INIS) Damour, Thibault; Lecian, Orchidea Maria 2009-01-01 The gravitational polarizability properties of black holes are compared and contrasted with their electromagnetic polarizability properties. The 'shape' or 'height' multipolar Love numbers h l of a black hole are defined and computed. They are then compared to their electromagnetic analogs h l EM . The Love numbers h l give the height of the lth multipolar 'tidal bulge' raised on the horizon of a black hole by faraway masses. We also discuss the shape of the tidal bulge raised by a test-mass m, in the limit where m gets very close to the horizon. 18. Black layers on historical architecture. Science.gov (United States) Toniolo, Lucia; Zerbi, Carlotta M; Bugini, Roberto 2009-03-01 The external surface of any building in urban polluted environment is unavoidably destined to be covered with layers that assume a grey to black colour and are generally called 'black crusts'. These, according to standard protocols and glossary, are deteriorated surface layers of stone material; they can have variable thickness, are hard and fragile and can detach spontaneously from the substrate, which, in general, is quite decayed. Plain visual examination may lead to consider 'black crusts' all similar, whilst only a careful diagnostic investigation can distinguish 'black crusts' and the consequences of their formation on stone substrates. In this paper, various black layers on marble are studied and compared and the morphological and compositional characteristics discussed according to the related mechanisms of formation. Differences between old (hundred years) and recent crusts (30 years) are investigated and pointed out. Samples of black crusts collected from the Milan Cathedral façade (Candoglia Marble) have been studied and compared with the careful and synergic employ of traditional techniques: optical (transmission and reflected VIS light) and electron microscopy, X-ray spectrometry and micro-Fourier transform infrared spectroscopy. Visual examination of loose fragments does not allow to point out outstanding differences amongst the various samples; black layers have similar main mineral components, gypsum and airborne particles, with different spatial distribution. The microscopic studies allowed to point out the porosity differences, the gypsum crystallisation habit, different amount of embedded particles, level and progress of marble decay. The observations lead to define three main types of black crusts: black crust deriving from marble sulphation, compact deposit and encrustation due to exogenic materials deposition. Black crusts show evidence of sulphation in progress, without a clear continuity solution between crust and marble; the lack of 19. Erratic Black Hole Regulates Itself Science.gov (United States) 2009-03-01 New results from NASA's Chandra X-ray Observatory have made a major advance in explaining how a special class of black holes may shut off the high-speed jets they produce. These results suggest that these black holes have a mechanism for regulating the rate at which they grow. Black holes come in many sizes: the supermassive ones, including those in quasars, which weigh in at millions to billions of times the mass of the Sun, and the much smaller stellar-mass black holes which have measured masses in the range of about 7 to 25 times the Sun's mass. Some stellar-mass black holes launch powerful jets of particles and radiation, like seen in quasars, and are called "micro-quasars". The new study looks at a famous micro-quasar in our own Galaxy, and regions close to its event horizon, or point of no return. This system, GRS 1915+105 (GRS 1915 for short), contains a black hole about 14 times the mass of the Sun that is feeding off material from a nearby companion star. As the material swirls toward the black hole, an accretion disk forms. This system shows remarkably unpredictable and complicated variability ranging from timescales of seconds to months, including 14 different patterns of variation. These variations are caused by a poorly understood connection between the disk and the radio jet seen in GRS 1915. Chandra, with its spectrograph, has observed GRS 1915 eleven times since its launch in 1999. These studies reveal that the jet in GRS 1915 may be periodically choked off when a hot wind, seen in X-rays, is driven off the accretion disk around the black hole. The wind is believed to shut down the jet by depriving it of matter that would have otherwise fueled it. Conversely, once the wind dies down, the jet can re-emerge. "We think the jet and wind around this black hole are in a sort of tug of war," said Joseph Neilsen, Harvard graduate student and lead author of the paper appearing in the journal Nature. "Sometimes one is winning and then, for reasons we don 20. Black Hole Complementary Principle and Noncommutative Membrane International Nuclear Information System (INIS) Wei Ren 2006-01-01 In the spirit of black hole complementary principle, we have found the noncommutative membrane of Scharzchild black holes. In this paper we extend our results to Kerr black hole and see the same story. Also we make a conjecture that spacetimes are noncommutative on the stretched membrane of the more general Kerr-Newman black hole. 1. The Black Man in American Society. Science.gov (United States) Framingham Public Schools, MA. GRADE OR AGES: Junior high school. SUBJECT MATTER: The black man in American society. ORGANIZATION AND PHYSICAL APPEARANCE: There are four major parts each with an overview. The four parts concern a) the African heritage of the black man, b) the American exploitation of the black man, c) the black man's contribution to American society, d) the… 2. The Core Journal Concept in Black Studies Science.gov (United States) Weissinger, Thomas 2010-01-01 Black Studies scholars have shown interest in the core journal concept. Indeed, the idea of core journals for the study of the Black experience has changed several times since 1940. While Black Studies scholars are citing Black Studies journals with frequency, they also cite traditional disciplinary journals a great deal of the time. However,… 3. Accretion, primordial black holes and standard cosmology Indian Academy of Sciences (India) Primordial black holes evaporate due to Hawking radiation. We find that the evaporation times of primordial black holes increase when accretion of radiation is included. Thus, depending on accretion efficiency, more primordial black holes are existing today, which strengthens the conjecture that the primordial black holes ... 4. The Black Journalist in South Africa. Science.gov (United States) Hachten, William A. The role of the black journalist in South Africa is contradictory, precarious, and permeated with politics. There is little freedom of expression for blacks in South Africa, yet white-owned newspapers have expanded their coverage of black news, and some have special editions for black readers. As a result, the English language press is using more… 5. Black Films in Search of a Home. Science.gov (United States) Taylor, Clyde 1983-01-01 Black filmmakers have produced many films that successfully showcase African-American culture, yet this work is rarely exposed to its intended audience. The Black bourgeoisie, because of their money and social status, must play a role in supporting Black filmmaking and fostering the perception of Black film as part of American popular culture. (GC) 6. Then and Now: Black Boycott in Waterloo. Science.gov (United States) Anderson, Ruth B. 1983-01-01 Discusses events following the desegregation of Waterloo, Iowa, schools. Describes the 1978 Black boycott of Hoover Junior High, which led to improvements in the treatment of Black students. Lists administrative responses to each Black grievance, and presents interviews with ten Black students three years after the boycott. (KH) 7. Black hole evaporation: a paradigm International Nuclear Information System (INIS) Ashtekar, Abhay; Bojowald, Martin 2005-01-01 A paradigm describing black hole evaporation in non-perturbative quantum gravity is developed by combining two sets of detailed results: (i) resolution of the Schwarzschild singularity using quantum geometry methods and (ii) time evolution of black holes in the trapping and dynamical horizon frameworks. Quantum geometry effects introduce a major modification in the traditional spacetime diagram of black hole evaporation, providing a possible mechanism for recovery of information that is classically lost in the process of black hole formation. The paradigm is developed directly in the Lorentzian regime and necessary conditions for its viability are discussed. If these conditions are met, much of the tension between expectations based on spacetime geometry and structure of quantum theory would be resolved 8. Axion-dilation black holes International Nuclear Information System (INIS) Kallosh, R. 1993-01-01 In this talk some essential features of stringy black holes are described. The author considers charged U(1) and U(1) x U(1) four-dimensional axion-dilaton black holes. The Hawking temperature and the entropy of all solutions are shown to be simple functions of the squares of supercharges, defining the positivity bounds. Spherically symmetric and multi black hole solutions are presented. The extreme solutions with zero entropy (holons) represent a ground state of the theory and are characterized by elementary dilaton, axion, electric, and magnetic charges. The attractive gravitational and axion-dilaton force is balanced by the repulsive electromagnetic force. The author discusses the possibility of splitting of nearly extreme black holes. 11 refs 9. Black Sprayable Molecular Adsorber Coating Data.gov (United States) National Aeronautics and Space Administration — The main objective of this technology project is to develop, optimize, and flight qualify a black version of the molecular adsorber coating and a conductive version... 10. Black holes by analytic continuation CERN Document Server Amati, Daniele 1997-01-01 In the context of a two-dimensional exactly solvable model, the dynamics of quantum black holes is obtained by analytically continuing the description of the regime where no black hole is formed. The resulting spectrum of outgoing radiation departs from the one predicted by the Hawking model in the region where the outgoing modes arise from the horizon with Planck-order frequencies. This occurs early in the evaporation process, and the resulting physical picture is unconventional. The theory predicts that black holes will only radiate out an energy of Planck mass order, stabilizing after a transitory period. The continuation from a regime without black hole formation --accessible in the 1+1 gravity theory considered-- is implicit in an S matrix approach and provides in this way a possible solution to the problem of information loss. 11. "Be Real Black for Me": Imagining BlackCrit in Education Science.gov (United States) Dumas, Michael J.; ross, kihana miraya 2016-01-01 The authors put forward a theorization of a Black Critical Theory, or what might be called BlackCrit, within, and in response to, Critical Race Theory, and then outline ways that BlackCrit in education helps us to more incisively analyze how the specificity of (anti)blackness matters in explaining how Black bodies become marginalized, disregarded,… 12. A radiant black market International Nuclear Information System (INIS) Roser, T. 1993-01-01 On the 13 October the Bavarian police seized 2.2kg of uranium and arrested a group of seven people who had offered to sell it for500.000. The existence of a black market for uranium may be a proliferation risk but it is not a serious health hazard - even if the material is negligently packed, as it seems to have been in all the recent cases. The situation is quite different when it comes to dealing with highly radioactive materials such as fission productions. Two such cases have been reported this summer involving Cs-137 and Sr-90, both emitters of hard beta rays. Little is known about the provenance of the radioactive and fissile material discovered. Obviously it originates from the ex-USSR, and the absence of highly enriched material suggests a civil rather than a military source. The governments of ex-Soviet states have apparently tried to intercept smugglers at their western frontiers, but have so far been unable to pinpoint the breaches in their security. It is also uncertain whether the occurrences discovered and reported are merely the tip of an iceberg. (author)
13. Black hole meiosis
Science.gov (United States)
van Herck, Walter; Wyder, Thomas
2010-04-01
The enumeration of BPS bound states in string theory needs refinement. Studying partition functions of particles made from D-branes wrapped on algebraic Calabi-Yau 3-folds, and classifying states using split attractor flow trees, we extend the method for computing a refined BPS index, [1]. For certain D-particles, a finite number of microstates, namely polar states, exclusively realized as bound states, determine an entire partition function (elliptic genus). This underlines their crucial importance: one might call them the ‘chromosomes’ of a D-particle or a black hole. As polar states also can be affected by our refinement, previous predictions on elliptic genera are modified. This can be metaphorically interpreted as ‘crossing-over in the meiosis of a D-particle’. Our results improve on [2], provide non-trivial evidence for a strong split attractor flow tree conjecture, and thus suggest that we indeed exhaust the BPS spectrum. In the D-brane description of a bound state, the necessity for refinement results from the fact that tachyonic strings split up constituent states into ‘generic’ and ‘special’ states. These are enumerated separately by topological invariants, which turn out to be partitions of Donaldson-Thomas invariants. As modular predictions provide a check on many of our results, we have compelling evidence that our computations are correct.
14. New regular black hole solutions
International Nuclear Information System (INIS)
Lemos, Jose P. S.; Zanchin, Vilson T.
2011-01-01
In the present work we consider general relativity coupled to Maxwell's electromagnetism and charged matter. Under the assumption of spherical symmetry, there is a particular class of solutions that correspond to regular charged black holes whose interior region is de Sitter, the exterior region is Reissner-Nordstroem and there is a charged thin-layer in-between the two. The main physical and geometrical properties of such charged regular black holes are analyzed.
15. Black holes from extended inflation
International Nuclear Information System (INIS)
Hsu, S.D.H.; Lawrence Berkeley Lab., CA
1990-01-01
It is argued that models of extended inflation, in which modified Einstein gravity allows a graceful exit from the false vacuum, lead to copious production of black holes. The critical temperature of the inflationary phase transition must be >10 8 GeV in order to avoid severe cosmological problems in a universe dominated by black holes. We speculate on the possibility that the interiors of false vacuum regions evolve into baby universes. (orig.)
16. Linezolid induced black hairy tongue
OpenAIRE
Govindan Balaji; B Maharani; Velappan Ravichandran; Thiyagarajan Parthasarathi
2014-01-01
Black hairy tongue (BHT) also called as lingua villosa nigra, is a self limiting benign condition characterized by hypertrophy and elongation of filiform papillae of tongue with brown or black discoloration. Smoking, poor oral hygiene, xerostomia, using peroxide containing mouth washes, substance abuse and drugs (steroids, methyldopa, olanzapine, etc) are the predisposing factors. However its occurrence in relation to linezolid ingestion among south Indians has not been reported in PubMed dat...
17. Theorizing black (African) transnational masculinities
OpenAIRE
Pasura, Dominic; Christou, Anastasia
2017-01-01
Just as masculinity is crucial in the construction of nationhood, masculinity is also significant in the making and unmaking of transnational communities. This article focuses on how black African men negotiate and perform respectable masculinity in transnational settings, such as the workplace, community, and family. Moving away from conceptualizations of black transnational forms of masculinities as in perpetual crisis and drawing on qualitative data collected from the members of the new Af...
18. Black strings and classical hair
International Nuclear Information System (INIS)
Horowitz, G.T.; Yang, H.
1997-01-01
We examine the geometry near the event horizon of a family of black string solutions with traveling waves. It has previously been shown that the metric is continuous there. Contrary to expectations, we find that the geometry is not smooth, and the horizon becomes singular whenever a wave is present. Both five-dimensional and six-dimensional black strings are considered with similar results. copyright 1997 The American Physical Society
19. Black coal. Annual report 1997
International Nuclear Information System (INIS)
1997-01-01
An overview is given of the situation of the world energy industry with regard to all energy carriers. Then energy-political conclusions are drawn for German black coal and the resulting prospects are detailed. Finally, some socio-political aspects are considered with regard to German black-coal mining: Workforce policy, tariff policy, social security and social safeguards for the adaptation process. (orig.) [de
20. What is a black hole
International Nuclear Information System (INIS)
Tipler, F.J.
1979-01-01
A definition of a black hole is proposed that should work in any stably causal space-time. This is that a black hole is the closure of the smaller future set that contains all noncosmological trapped surfaces and which has its boundary generated by null geodesic segments that are boundary generators of TIPs. This allows precise definitions of cosmic censorship and white holes. (UK)
1. Black holes and cosmic censorship
International Nuclear Information System (INIS)
Hiscock, W.A.
1979-01-01
It is widely accepted that the complete gravitational collapse of a body always yields a black hole, and that naked singularities are never produced (the cosmic censorship hypothesis). The local (or strong) cosmic censorship hypothesis states that singularities which are even locally naked (e.g., to an observer inside a black hole) are never produced. This dissertation studies the validity of these two conjectures. The Kerr-Newman metrics describes the black holes only when M 2 greater than or equal to Q 2 + P 2 , where M is the mass of the black hole, a = J/M its specific angular momentum, Q its electric charge, and P its magnetic charge. In the first part of this dissertation, the possibility of converting an extreme Kerr-Newman black hole (M 2 = a 2 + Q 2 + P 2 ) into a naked singularity by the accretion of test particles is considered. The motion of test particles is studied with a large angular momentum to energy ratio, and also test particles with a large charge to energy ratio. The final state is always found to be a black hole if the angular momentum, electric charge, and magnetic charge of the black hole are all much greater than the corresponding angular momentum, electric charge, and magnetic charge of the test particle. In Part II of this dissertation possible black hole interior solutions are studied. The Cauchy horizons and locally naked timelike singularities of the charged (and/or rotating) solutions are contrasted with the spacelike all-encompassing singularity of the Schwarzschild solution. It is determined which portions of the analytic extension of the Reissner-Nordstroem solution are relevant to realistic gravitational collapse
2. Are Black Holes Elementary Particles?
OpenAIRE
Ha, Yuan K.
2009-01-01
Quantum black holes are the smallest and heaviest conceivable elementary particles. They have a microscopic size but a macroscopic mass. Several fundamental types have been constructed with some remarkable properties. Quantum black holes in the neighborhood of the Galaxy could resolve the paradox of ultra-high energy cosmic rays detected in Earth's atmosphere. They may also play a role as dark matter in cosmology.
3. Black holes in the universe
International Nuclear Information System (INIS)
Camenzind, M.
2005-01-01
While physicists have been grappling with the theory of black holes (BH), as shown by the many contributions to the Einstein year, astronomers have been successfully searching for real black holes in the Universe. Black hole astrophysics began in the 1960s with the discovery of quasars and other active galactic nuclei (AGN) in distant galaxies. Already in the 1960s it became clear that the most natural explanation for the quasar activity is the release of gravitational energy through accretion of gas onto supermassive black holes. The remnants of this activity have now been found in the centers of about 50 nearby galaxies. BH astrophysics received a new twist in the 1970s with the discovery of the X-ray binary (XRB) Cygnus X-1. The X-ray emitting compact object was too massive to be explained by a neutron star. Today, about 20 excellent BH candidates are known in XRBs. On the extragalactic scale, more than 100.000 quasars have been found in large galaxy surveys. At the redshift of the most distant ones, the Universe was younger than one billion year. The most enigmatic black hole candidates identified in the last years are the compact objects behind the Gamma-Ray Bursters. The formation of all these types of black holes is accompanied by extensive emission of gravitational waves. The detection of these strong gravity events is one of the biggest challenges for physicists in the near future. (author)
4. Stationary black holes as holographs
Energy Technology Data Exchange (ETDEWEB)
Racz, Istvan [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-01 (Japan); MTA KFKI, Reszecske- es Magfizikai Kutatointezet, H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)
2007-11-21
Smooth spacetimes possessing a (global) one-parameter group of isometries and an associated Killing horizon in Einstein's theory of gravity are investigated. No assumption concerning the asymptotic structure is made; thereby, the selected spacetimes may be considered as generic distorted stationary black holes. First, spacetimes of arbitrary dimension, n {>=} 3, with matter satisfying the dominant energy condition and allowing a non-zero cosmological constant are investigated. In this part, complete characterization of the topology of the event horizon of 'distorted' black holes is given. It is shown that the topology of the event horizon of 'distorted' black holes is allowed to possess a much larger variety than that of the isolated black hole configurations. In the second part, four-dimensional (non-degenerate) electrovac distorted black hole spacetimes are considered. It is shown that the spacetime geometry and the electromagnetic field are uniquely determined in the black hole region once the geometry of the bifurcation surface and one of the electromagnetic potentials are specified there. Conditions guaranteeing the same type of determinacy, in a neighbourhood of the event horizon, on the domain of outer communication side are also investigated. In particular, they are shown to be satisfied in the analytic case.
5. Atomic structure in black hole
International Nuclear Information System (INIS)
Nagatani, Yukinori
2006-01-01
We propose that any black hole has atomic structure in its inside and has no horizon as a model of black holes. Our proposal is founded on a mean field approximation of gravity. The structure of our model consists of a (charged) singularity at the center and quantum fluctuations of fields around the singularity, namely, it is quite similar to that of atoms. Any properties of black holes, e.g. entropy, can be explained by the model. The model naturally quantizes black holes. In particular, we find the minimum black hole, whose structure is similar to that of the hydrogen atom and whose Schwarzschild radius is approximately 1.1287 times the Planck length. Our approach is conceptually similar to Bohr's model of the atomic structure, and the concept of the minimum Schwarzschild radius is similar to that of the Bohr radius. The model predicts that black holes carry baryon number, and the baryon number is rapidly violated. This baryon number violation can be used as verification of the model. (author)
6. Intermediate-Mass Black Holes
Science.gov (United States)
Miller, M. Coleman; Colbert, E. J. M.
2004-01-01
The mathematical simplicity of black holes, combined with their links to some of the most energetic events in the universe, means that black holes are key objects for fundamental physics and astrophysics. Until recently, it was generally believed that black holes in nature appear in two broad mass ranges: stellar-mass (M~3 20 M⊙), which are produced by the core collapse of massive stars, and supermassive (M~106 1010 M⊙), which are found in the centers of galaxies and are produced by a still uncertain combination of processes. In the last few years, however, evidence has accumulated for an intermediate-mass class of black holes, with M~102 104 M⊙. If such objects exist they have important implications for the dynamics of stellar clusters, the formation of supermassive black holes, and the production and detection of gravitational waves. We review the evidence for intermediate-mass black holes and discuss future observational and theoretical work that will help clarify numerous outstanding questions about these objects.
7. Regular black hole in three dimensions
OpenAIRE
Myung, Yun Soo; Yoon, Myungseok
2008-01-01
We find a new black hole in three dimensional anti-de Sitter space by introducing an anisotropic perfect fluid inspired by the noncommutative black hole. This is a regular black hole with two horizons. We compare thermodynamics of this black hole with that of non-rotating BTZ black hole. The first-law of thermodynamics is not compatible with the Bekenstein-Hawking entropy.
8. Black holes, qubits and octonions
International Nuclear Information System (INIS)
Borsten, L.; Dahanayake, D.; Duff, M.J.; Ebrahim, H.; Rubens, W.
2009-01-01
We review the recently established relationships between black hole entropy in string theory and the quantum entanglement of qubits and qutrits in quantum information theory. The first example is provided by the measure of the tripartite entanglement of three qubits (Alice, Bob and Charlie), known as the 3-tangle, and the entropy of the 8-charge STU black hole of N=2 supergravity, both of which are given by the [SL(2)] 3 invariant hyperdeterminant, a quantity first introduced by Cayley in 1845. Moreover the classification of three-qubit entanglements is related to the classification of N=2 supersymmetric STU black holes. There are further relationships between the attractor mechanism and local distillation protocols and between supersymmetry and the suppression of bit flip errors. At the microscopic level, the black holes are described by intersecting D3-branes whose wrapping around the six compact dimensions T 6 provides the string-theoretic interpretation of the charges and we associate the three-qubit basis vectors, |ABC>(A,B,C=0 or 1), with the corresponding 8 wrapping cycles. The black hole/qubit correspondence extends to the 56 charge N=8 black holes and the tripartite entanglement of seven qubits where the measure is provided by Cartan's E 7 contains [SL(2)] 7 invariant. The qubits are naturally described by the seven vertices ABCDEFG of the Fano plane, which provides the multiplication table of the seven imaginary octonions, reflecting the fact that E 7 has a natural structure of an O-graded algebra. This in turn provides a novel imaginary octonionic interpretation of the 56=7x8 charges of N=8: the 24=3x8 NS-NS charges correspond to the three imaginary quaternions and the 32=4x8 R-R to the four complementary imaginary octonions. We contrast this approach with that based on Jordan algebras and the Freudenthal triple system. N=8 black holes (or black strings) in five dimensions are also related to the bipartite entanglement of three qutrits (3-state systems
9. Black hole quantum spectrum
Energy Technology Data Exchange (ETDEWEB)
Corda, Christian [Institute for Theoretical Physics and Advanced Mathematics (IFM) Einstein-Galilei, Prato (Italy); Istituto Universitario di Ricerca ' ' Santa Rita' ' , Prato (Italy); International Institute for Applicable Mathematics and Information Sciences (IIAMIS), Hyderabad (India)
2013-12-15
Introducing a black hole (BH) effective temperature, which takes into account both the non-strictly thermal character of Hawking radiation and the countable behavior of emissions of subsequent Hawking quanta, we recently re-analysed BH quasi-normal modes (QNMs) and interpreted them naturally in terms of quantum levels. In this work we improve such an analysis removing some approximations that have been implicitly used in our previous works and obtaining the corrected expressions for the formulas of the horizon's area quantization and the number of quanta of area and hence also for Bekenstein-Hawking entropy, its subleading corrections and the number of micro-states, i.e. quantities which are fundamental to realize the underlying quantum gravity theory, like functions of the QNMs quantum ''overtone'' number n and, in turn, of the BH quantum excited level. An approximation concerning the maximum value of n is also corrected. On the other hand, our previous results were strictly corrected only for scalar and gravitational perturbations. Here we show that the discussion holds also for vector perturbations. The analysis is totally consistent with the general conviction that BHs result in highly excited states representing both the ''hydrogen atom'' and the ''quasi-thermal emission'' in quantum gravity. Our BH model is somewhat similar to the semi-classical Bohr's model of the structure of a hydrogen atom. The thermal approximation of previous results in the literature is consistent with the results in this paper. In principle, such results could also have important implications for the BH information paradox. (orig.)
10. Black hole quantum spectrum
Science.gov (United States)
Corda, Christian
2013-12-01
Introducing a black hole (BH) effective temperature, which takes into account both the non-strictly thermal character of Hawking radiation and the countable behavior of emissions of subsequent Hawking quanta, we recently re-analysed BH quasi-normal modes (QNMs) and interpreted them naturally in terms of quantum levels. In this work we improve such an analysis removing some approximations that have been implicitly used in our previous works and obtaining the corrected expressions for the formulas of the horizon's area quantization and the number of quanta of area and hence also for Bekenstein-Hawking entropy, its subleading corrections and the number of micro-states, i.e. quantities which are fundamental to realize the underlying quantum gravity theory, like functions of the QNMs quantum "overtone" number n and, in turn, of the BH quantum excited level. An approximation concerning the maximum value of n is also corrected. On the other hand, our previous results were strictly corrected only for scalar and gravitational perturbations. Here we show that the discussion holds also for vector perturbations. The analysis is totally consistent with the general conviction that BHs result in highly excited states representing both the "hydrogen atom" and the "quasi-thermal emission" in quantum gravity. Our BH model is somewhat similar to the semi-classical Bohr's model of the structure of a hydrogen atom. The thermal approximation of previous results in the literature is consistent with the results in this paper. In principle, such results could also have important implications for the BH information paradox.
11. Black holes: the membrane paradigm
International Nuclear Information System (INIS)
Thorne, K.S.; Price, R.H.; Macdonald, D.A.
1986-01-01
The physics of black holes is explored in terms of a membrane paradigm which treats the event horizon as a two-dimensional membrane embedded in three-dimensional space. A 3+1 formalism is used to split Schwarzschild space-time and the laws of physics outside a nonrotating hole, which permits treatment of the atmosphere in terms of the physical properties of thin slices. The model is applied to perturbed slowly or rapidly rotating and nonrotating holes, and to quantify the electric and magnetic fields and eddy currents passing through a membrane surface which represents a stretched horizon. Features of tidal gravitational fields in the vicinity of the horizon, quasars and active galalctic nuclei, the alignment of jets perpendicular to accretion disks, and the effects of black holes at the center of ellipsoidal star clusters are investigated. Attention is also given to a black hole in a binary system and the interactions of black holes with matter that is either near or very far from the event horizon. Finally, a statistical mechanics treatment is used to derive a second law of thermodynamics for a perfectly thermal atmosphere of a black hole
12. Cosmology with primordial black holes
International Nuclear Information System (INIS)
Lindley, D.
1981-09-01
Cosmologies containing a substantial amount of matter in the form of evaporating primordial black holes are investigated. A review of constraints on the numbers of such black holes, including an analysis of a new limit found by looking at the destruction of deuterium by high energy photons, shows that there must be a negligible population of small black holes from the era of cosmological nucleosynthesis onwards, but that there are no strong constraints before this time. The major part of the work is based on the construction of detailed, self-consistent cosmological models in which black holes are continually forming and evaporating The interest in these models centres on the question of baryon generation, which occurs via the asymmetric decay of a new type of particle which appears as a consequence of the recently developed Grand Unified Theories of elementary particles. Unfortunately, there is so much uncertainty in the models that firm conclusions are difficult to reach; however, it seems feasible in principle that primordial black holes could be responsible for a significant part of the present matter density of the Universe. (author)
13. Black holes: a slanted overview
International Nuclear Information System (INIS)
Vishveshwara, C.V.
1988-01-01
The black hole saga spanning some seventy years may be broadly divided into four phases, namely, (a) the dark ages when little was known about black holes even though they had come into existence quite early through the Schwarzschild solution, (b) the age of enlightenment bringing in deep and prolific discoveries, (c) the age of fantasy that cast black holes in all sorts of extraordinary roles, and (d) the golden age of relativistic astrophysics - to some extent similar to Dirac's characterisation of the development of quantum theory - in which black holes have been extensively used to elucidate a number of astrophysical phenomena. It is impossible to give here even the briefest outline of the major developments in this vast area. We shall only attempt to present a few aspects of black hole physics which have been actively pursued in the recent past. Some details are given in the case of those topics that have not found their way into text books or review articles. (author)
14. Black women in menopausal transition.
Science.gov (United States)
Im, Eun-Ok; Lee, Seung Hee; Chee, Wonshik
2010-01-01
To describe the experience of menopausal symptoms of midlife Black women in the United States. Qualitative online forum using a feminist perspective. Internet communities for midlife women and Blacks. Twenty midlife Black women recruited using a quota sampling method. A 6-month online forum was conducted with seven discussion topics on menopausal symptoms. The discussion topics were posted sequentially on the forum site, and the women posted messages at their convenience over 6 months. The data were analyzed using thematic analysis. The identified themes were raised to be strong, accepting a natural aging process, silent and without knowledge, and our own experience. The women tried to be strong during their menopausal transitions while dealing with other important family matters. The women did not report their menopausal symptoms and were silent about or downplayed their symptoms, but many emphasized the importance of education about menopausal symptoms and highlighted their own lack of knowledge. These women generally did not talk about their symptoms because they believed that nobody except other Black midlife women could understand their menopausal experience. Health care providers need to develop a mechanism to deliver the necessary knowledge about menopausal symptoms and management strategies to Black midlife women in their health care practices.
15. Time dependent black holes and scalar hair
International Nuclear Information System (INIS)
2014-01-01
We show how to correctly account for scalar accretion onto black holes in scalar field models of dark energy by a consistent expansion in terms of a slow roll parameter. At leading order, we find an analytic solution for the scalar field within our Hubble volume, which is regular on both black hole and cosmological event horizons, and compute the back reaction of the scalar on the black hole, calculating the resulting expansion of the black hole. Our results are independent of the relative size of black hole and cosmological event horizons. We comment on the implications for more general black hole accretion, and the no hair theorems. (paper)
16. Black holes a very short introduction
CERN Document Server
Blundell, Katherine
2015-01-01
Black holes are a constant source of fascination to many due to their mysterious nature. Black Holes: A Very Short Introduction addresses a variety of questions, including what a black hole actually is, how they are characterized and discovered, and what would happen if you came too close to one. It explains how black holes form and grow—by stealing material that belongs to stars—as well as how many there may be in the Universe. It also explores the large black holes found in the centres of galaxies, and how black holes power quasars and lie behind other spectacular phenomena in the cosmos.
17. Why Blue-Collar Blacks Help Less
OpenAIRE
Smith, Sandra Susan; Young, Kara Alexis
2013-01-01
Why are blue-collar blacks less likely to help jobseekers than jobholders from other ethnoracial groups or even than more affluent blacks? Drawing from in-depth, semi-structured interviews with 97 black and Latino workers at one large, public sector employer, we find that blue-collar black workers both helped less proactively and rejected more requests for assistance than did blue-collar Latino and white-collar black workers. We attribute blue-collar blacks’ more passive engagement to their...
18. Lee–Wick black holes
Directory of Open Access Journals (Sweden)
Cosimo Bambi
2017-01-01
Full Text Available We derive and study an approximate static vacuum solution generated by a point-like source in a higher derivative gravitational theory with a pair of complex conjugate ghosts. The gravitational theory is local and characterized by a high derivative operator compatible with Lee–Wick unitarity. In particular, the tree-level two-point function only shows a pair of complex conjugate poles besides the massless spin two graviton. We show that singularity-free black holes exist when the mass of the source M exceeds a critical value Mcrit. For M>Mcrit the spacetime structure is characterized by an outer event horizon and an inner Cauchy horizon, while for M=Mcrit we have an extremal black hole with vanishing Hawking temperature. The evaporation process leads to a remnant that approaches the zero-temperature extremal black hole state in an infinite amount of time.
19. The black hole quantum atmosphere
Science.gov (United States)
Dey, Ramit; Liberati, Stefano; Pranzetti, Daniele
2017-11-01
Ever since the discovery of black hole evaporation, the region of origin of the radiated quanta has been a topic of debate. Recently it was argued by Giddings that the Hawking quanta originate from a region well outside the black hole horizon by calculating the effective radius of a radiating body via the Stefan-Boltzmann law. In this paper we try to further explore this issue and end up corroborating this claim, using both a heuristic argument and a detailed study of the stress energy tensor. We show that the Hawking quanta originate from what might be called a quantum atmosphere around the black hole with energy density and fluxes of particles peaked at about 4 MG, running contrary to the popular belief that these originate from the ultra high energy excitations very close to the horizon. This long distance origin of Hawking radiation could have a profound impact on our understanding of the information and transplanckian problems.
20. The black hole quantum atmosphere
Directory of Open Access Journals (Sweden)
Ramit Dey
2017-11-01
Full Text Available Ever since the discovery of black hole evaporation, the region of origin of the radiated quanta has been a topic of debate. Recently it was argued by Giddings that the Hawking quanta originate from a region well outside the black hole horizon by calculating the effective radius of a radiating body via the Stefan–Boltzmann law. In this paper we try to further explore this issue and end up corroborating this claim, using both a heuristic argument and a detailed study of the stress energy tensor. We show that the Hawking quanta originate from what might be called a quantum atmosphere around the black hole with energy density and fluxes of particles peaked at about 4MG, running contrary to the popular belief that these originate from the ultra high energy excitations very close to the horizon. This long distance origin of Hawking radiation could have a profound impact on our understanding of the information and transplanckian problems.
1. Massive Black Holes and Galaxies
CERN Multimedia
CERN. Geneva
2016-01-01
Evidence has been accumulating for several decades that many galaxies harbor central mass concentrations that may be in the form of black holes with masses between a few million to a few billion time the mass of the Sun. I will discuss measurements over the last two decades, employing adaptive optics imaging and spectroscopy on large ground-based telescopes that prove the existence of such a massive black hole in the Center of our Milky Way, beyond any reasonable doubt. These data also provide key insights into its properties and environment. Most recently, a tidally disrupting cloud of gas has been discovered on an almost radial orbit that reached its peri-distance of ~2000 Schwarzschild radii in 2014, promising to be a valuable tool for exploring the innermost accretion zone. Future interferometric studies of the Galactic Center Black hole promise to be able to test gravity in its strong field limit.
2. Criticality for charged black branes
Science.gov (United States)
Hennigar, Robie A.
2017-09-01
We show that the inclusion of higher curvature terms in the gravitational action can lead to phase transitions and critical behaviour for charged black branes. The higher curvature terms considered here belong to the recently constructed generalized quasi-topological class [arXiv:1703.01631], which possess a number of interesting properties, such as being ghost-free on constant curvature backgrounds and non-trivial in four dimensions. We show that critical behaviour is a generic feature of the black branes in all dimensions d ≥ 4, and contextualize the results with a review of the properties of black branes in Lovelock and quasi-topological gravity, where critical behaviour is not possible. These results may have interesting implications for the CFTs dual to this class of theories.
3. Geometric inequalities for black holes
International Nuclear Information System (INIS)
Dain, Sergio
2013-01-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
4. Control of black hole evaporation?
International Nuclear Information System (INIS)
Ahn, Doyeol
2007-01-01
Contradiction between Hawking's semi-classical arguments and the string theory on the evaporation of a black hole has been one of the most intriguing problems in fundamental physics. A final-state boundary condition inside the black hole was proposed by Horowitz and Maldacena to resolve this contradiction. We point out that the original Hawking effect can also be regarded as a separate boundary condition at the event horizon for this scenario. Here, we found that the change of the Hawking boundary condition may affect the information transfer from the initial collapsing matter to the outgoing Hawking radiation during the evaporation process and as a result the evaporation process itself, significantly
5. Geometric inequalities for black holes
Energy Technology Data Exchange (ETDEWEB)
Dain, Sergio [Universidad Nacional de Cordoba (Argentina)
2013-07-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
6. Black Psychology and Black Personality: Some Issues for Considerations
Science.gov (United States)
Baldwin, Joseph A.
1976-01-01
Discusses an emerging body of psychological literature by black behavioral scientists assumed to represent a radical departure in its conceptual orientation from the social pathology tradition advanced primarily by white behavioral scientists; and focuses on the construct of Self-Extension Orientation, a dynamic process which is assumed to…
7. Moodulitest komplekteeritav diivan Black = A modular sofa called Black
Index Scriptorium Estoniae
2007-01-01
Autor Tiina Mang pälvis diivanikomplekti Black eest Eesti Sisearhitektide Liidu 2006. a. esemepreemia. T. Mangist, objektid, kuhu on valitud T. Mangi projekteeritud mööblit, näitused. 3 värv. vaadet, foto T. Mangist
8. Black supernovae and black holes in non-local gravity
Energy Technology Data Exchange (ETDEWEB)
Bambi, Cosimo [Center for Field Theory and Particle Physics and Department of Physics, Fudan University,200433 Shanghai (China); Theoretical Astrophysics, Eberhard-Karls Universität Tübingen,72076 Tübingen (Germany); Malafarina, Daniele [Department of Physics, Nazarbayev University,010000 Astana (Kazakhstan); Modesto, Leonardo [Center for Field Theory and Particle Physics and Department of Physics, Fudan University,200433 Shanghai (China)
2016-04-22
In a previous paper, we studied the interior solution of a collapsing body in a non-local theory of gravity super-renormalizable at the quantum level. We found that the classical singularity is replaced by a bounce, after which the body starts expanding. A black hole, strictly speaking, never forms. The gravitational collapse does not create an event horizon but only an apparent one for a finite time. In this paper, we solve the equations of motion assuming that the exterior solution is static. With such an assumption, we are able to reconstruct the solution in the whole spacetime, namely in both the exterior and interior regions. Now the gravitational collapse creates an event horizon in a finite comoving time, but the central singularity is approached in an infinite time. We argue that these black holes should be unstable, providing a link between the scenarios with and without black holes. Indeed, we find a non catastrophic ghost-instability of the metric in the exterior region. Interestingly, under certain conditions, the lifetime of our black holes exactly scales as the Hawking evaporation time.
9. Interior structure of rotating black holes. III. Charged black holes
International Nuclear Information System (INIS)
Hamilton, Andrew J. S.
2011-01-01
This paper extends to the case of charged rotating black holes the conformally stationary, axisymmetric, conformally separable solutions presented for uncharged rotating black holes in a companion paper. In the present paper, the collisionless fluid accreted by the black hole may be charged. The charge of the black hole is determined self-consistently by the charge accretion rate. As in the uncharged case, hyper-relativistic counterstreaming between ingoing and outgoing streams drives inflation at (just above) the inner horizon, followed by collapse. If both ingoing and outgoing streams are charged, then conformal separability holds during early inflation, but fails as inflation develops. If conformal separability is imposed throughout inflation and collapse, then only one of the ingoing and outgoing streams can be charged: the other must be neutral. Conformal separability prescribes a hierarchy of boundary conditions on the ingoing and outgoing streams incident on the inner horizon. The dominant radial boundary conditions require that the incident ingoing and outgoing number densities be uniform with latitude, but the charge per particle must vary with latitude such that the incident charge densities vary in proportion to the radial electric field. The subdominant angular boundary conditions require specific forms of the incident number- and charge-weighted angular motions. If the streams fall freely from outside the horizon, then the prescribed angular conditions can be achieved by the charged stream, but not by the neutral stream. Thus, as in the case of an uncharged black hole, the neutral stream must be considered to be delivered ad hoc to just above the inner horizon.
10. Erratum: Quantum corrections and black hole spectroscopy
Science.gov (United States)
Jiang, Qing-Quan; Han, Yan; Cai, Xu
2012-06-01
In my paper [Qing-Quan Jiang, Yan Han, Xu Cai, Quantum corrections and black hole spectroscopy, JHEP 08 (2010) 049], there was an error in deriving the black hole spectroscopy. In this erratum, we attempt to rectify them.
11. Entropy of black holes with multiple horizons
Directory of Open Access Journals (Sweden)
Yun He
2018-05-01
Full Text Available We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and “quintessence horizon” for the black holes surrounded by quintessence. Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.
12. Black hole entropy, curved space and monsters
International Nuclear Information System (INIS)
Hsu, Stephen D.H.; Reeb, David
2008-01-01
We investigate the microscopic origin of black hole entropy, in particular the gap between the maximum entropy of ordinary matter and that of black holes. Using curved space, we construct configurations with entropy greater than the area A of a black hole of equal mass. These configurations have pathological properties and we refer to them as monsters. When monsters are excluded we recover the entropy bound on ordinary matter S 3/4 . This bound implies that essentially all of the microstates of a semiclassical black hole are associated with the growth of a slightly smaller black hole which absorbs some additional energy. Our results suggest that the area entropy of black holes is the logarithm of the number of distinct ways in which one can form the black hole from ordinary matter and smaller black holes, but only after the exclusion of monster states
13. Entropy of black holes with multiple horizons
Science.gov (United States)
He, Yun; Ma, Meng-Sen; Zhao, Ren
2018-05-01
We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and "quintessence horizon" for the black holes surrounded by quintessence). Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.
14. Black and White Differentials in Mortality.
Science.gov (United States)
Rene, Antonio A.; Clifford, Patrick R.
1986-01-01
Overviews vital statistics data, emphasizing differences in health status between the Black and White populations with respect to specific diseases and mortality. Discusses major causes of death among US Blacks. (GC)
15. Atypical features of hyperthyroidism in Blacks
International Nuclear Information System (INIS)
Kalk, W.J.
1980-01-01
Hyperthyroidism is reportedly uncommon in the indigenous populations of Africa. The presenting symptoms volunteered, the symptoms elicited by direct questioning, and the results of physical examination were therefore prospectively compared in 60 Black and 56 White patients with thyrotoxicosis attending a single thyroid clinic. Fewer Blacks than Whites volunteered information about weight loss, while more Blacks complained only of the presence of a goitre. A 'chance' diagnosis of hyperthyroidism was made more frequently in Blacks. Symptomatology elicited by direct questioning and findings on physical examination were generally similar in each group, except that Blacks presented more frequently with complicated disease (cardiac failure and overt myopathy) and infiltrative ophthalmopathy. The frequency with which hyperthyroidism presents 'atypically' in Black compared with White patients may reflect educational, socio-economic and cultural differences in the Black and White populations, and may partly explain the infrequency with which this disease is diagnosed in Blacks
16. Charge Fluctuations of an Uncharged Black Hole
OpenAIRE
Schiffer, Marcelo
2016-01-01
In this paper we calculate charge fluctuations of a Schwarzschild black-hole of mass $M$ confined within a perfectly reflecting cavity of radius R in thermal equilibrium with various species of radiation and fermions . Charge conservation is constrained by a Lagrange multiplier (the chemical potential). Black hole charge fluctuations are expected owing to continuous absorption and emission of particles by the black hole. For black holes much more massive than $10^{16} g$ , these fluctuations ...
17. Bosonic instability of charged black holes
International Nuclear Information System (INIS)
Gaina, A.B.; Ternov, I.M.
1986-01-01
The processes of spontaneous and induced production and accumulation of charged bosons on quasibound superradiant levels in the field of Kerr-Newman black hole is analysed. It is shown that bosonic instability may be caused exclusively by the rotation of the black hole. Particulary, the Reissner-Nordstrom configuration is stable. In the case of rotating and charged black hole the bosonic instability may cause an increase of charge of the black hole
18. Will black holes eventually engulf the Universe?
International Nuclear Information System (INIS)
2006-01-01
The Babichev-Dokuchaev-Eroshenko model for the accretion of dark energy onto black holes has been extended to deal with black holes with non-static metrics. The possibility that for an asymptotic observer a black hole with large mass will rapidly increase and eventually engulf the Universe at a finite time in the future has been studied by using reasonable values for astronomical parameters. It is concluded that such a phenomenon is forbidden for all black holes in quintessential cosmological models
19. Event horizon image within black hole shadow
OpenAIRE
Dokuchaev, V. I.; Nazarova, N. O.
2018-01-01
The external border of the black hole shadow is washed out by radiation from matter plunging into black hole and approaching the event horizon. This effect will crucially influence the results of future observations by the Event Horizon Telescope. We show that gravitational lensing of the luminous matter plunging into black hole provides the event horizon visualization within black hole shadow. The lensed image of the event horizon is formed by the last highly red-shifted photons emitted by t...
20. Electromagnetic black holes'' in hyperbolic metamaterials
Science.gov (United States)
Smolyaninov, Igor
2013-03-01
We demonstrate that spatial variations of the dielectric tensor components in a hyperbolic metamaterial may lead to formation of electromagnetic black holes'' inside this metamaterial. Similar to real black holes, horizon area of the electromagnetic black holes'' is quantized in units of the effective Planck scale'' squared. Potential experimental realizations of such electromagnetic black holes'' will be considered. For example, this situation may be realized in a hyperbolic metamaterial in which the dielectric component exhibits critical opalescence.
1. Quantum Black Holes As Elementary Particles
OpenAIRE
Ha, Yuan K.
2008-01-01
Are black holes elementary particles? Are they fermions or bosons? We investigate the remarkable possibility that quantum black holes are the smallest and heaviest elementary particles. We are able to construct various fundamental quantum black holes: the spin-0, spin 1/2, spin-1, and the Planck-charge cases, using the results in general relativity. Quantum black holes in the neighborhood of the Galaxy could resolve the paradox posed by the Greisen-Zatsepin-Kuzmin limit on the energy of cosmi...
2. Catastrophic Instability of Small Lovelock Black Holes
OpenAIRE
Takahashi, Tomohiro; Soda, Jiro
2010-01-01
We study the stability of static black holes in Lovelock theory which is a natural higher dimensional generalization of Einstein theory. We show that Lovelock black holes are stable under vector perturbations in all dimensions. However, we prove that small Lovelock black holes are unstable under tensor perturbations in even-dimensions and under scalar perturbations in odd-dimensions. Therefore, we can conclude that small Lovelock black holes are unstable in any dimensions. The instability is ...
3. The Black Lives Matter Movement and Historically Black Colleges and Universities
Science.gov (United States)
Gasman, Marybeth
2017-01-01
This article looks at the Black Lives Matter Movement and Historically Black Colleges and Universities. Historically Black Colleges and Universities (HBCUs) continue to play an important role in society. However, what the Black Lives Matter movement shows consistently is that predominantly White institutions need to change, to step up and embrace…
4. Black Hawkid harjutasid Pakri poolsaarel
Index Scriptorium Estoniae
2014-01-01
USA 173. õhudessantbrigaadi Eestis viibiv kompanii ja Scoutspataljoni C-kompanii jalaväerühma kaitseväelased alustasid eile ühisõppust, mille käigus harjutatakse kahe Black Hawk UH-60 helikopteriga nelja Pakri poolsaarel asuva õppeobjekti ründamist
5. Sexuality Attitudes of Black Adults.
Science.gov (United States)
Timberlake, Constance A.; Carpenter, Wayne D.
1990-01-01
Assessed sexuality attitudes of black middle-class sample (N=124) concerning communication regarding sexuality information, adolescent contraception, adolescent pregnancy, nonmarital intercourse, responsibility for contraception and pregnancy, abortion, pornography, and masturbation. Results suggest that participants were well-informed, moderate,…
6. Why Black Officers Still Fail
Science.gov (United States)
2010-01-01
that ROTC programs were being staffed with lower performing and less qualified officers to educate young black officers. He based this conclusion on...come to mutually supporting conclusions. In a 2008 USAWC Strategy Research Project, while exploring the effects of ethnocentrism and its affect on
7. Black Holes: A Selected Bibliography.
Science.gov (United States)
Fraknoi, Andrew
1991-01-01
Offers a selected bibliography pertaining to black holes with the following categories: introductory books; introductory articles; somewhat more advanced articles; readings about Einstein's general theory of relativity; books on the death of stars; articles on the death of stars; specific articles about Supernova 1987A; relevant science fiction…
8. Black Holes in Our Universe
are humanity's high-technology windows onto the universe. For reasons that will ... instrument ever built; and it was the first direct ... gravity will drive it to collapse into a black hole. Indeed, in 2007, ... Given their large X-ray power, it has been ...
9. Satellite monitoring of black bear.
Science.gov (United States)
Craighead, J. J.; Craighead, F. C., Jr.; Varney, J. R.; Cote, C. E.
1971-01-01
Description of a feasibility experiment recently performed to test the use of a satellite system for telemetering environmental and physiological data from the winter den of a 'hibernating' black bear, Ursus americanus. The instrumentation procedure and evaluations of the equipment performance and sensory data obtained are discussed in detail.
10. Why I Teach "Black Boy."
Science.gov (United States)
Mahle, Benjamin
1983-01-01
Argues that Richard Wright's "Black Boy" is appropriate for ninth-grade students because it combines an exciting story of survival with effective prose, forces readers to try to understand their own experiences in the light of the protagonist's, and intimately involves students in such universal concerns as suffering, violence, and…
11. Wands of the Black Ring
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena
2005-01-01
Roč. 37, č. 7 (2005), s. 1277-1287 ISSN 0001-7701 R&D Projects: GA ČR GP202/03/P017; GA AV ČR KJB1019403 Institutional research plan: CEZ:AV0Z10190503 Keywords : algebraic classification * Petrov classification * black ring Subject RIV: BA - General Mathematics Impact factor: 1.550, year: 2005
12. Android for the Beaglebone Black
CERN Document Server
Henderson, Andrew
2015-01-01
If you are an Android app developer who wants to experiment with the hardware capabilities of the BeagleBone Black platform, then this book is ideal for you. You are expected to have basic knowledge of developing Android apps but no prior hardware experience is required.
13. Black and grey neutron detectors
International Nuclear Information System (INIS)
Gabbard, F.
1977-01-01
Recent progress in the development and use of ''black'' and ''grey'' detectors is reviewed. Such detectors are widely used for counting neutrons in (p,n) and (α,n) experiments and in neutron cross section measurements. Accuracy of each detector is stressed. 19 figures
14. From Pinholes to Black Holes
Energy Technology Data Exchange (ETDEWEB)
Fenimore, Edward E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-10-06
Pinhole photography has made major contributions to astrophysics through the use of “coded apertures”. Coded apertures were instrumental in locating gamma-ray bursts and proving that they originate in faraway galaxies, some from the birth of black holes from the first stars that formed just after the big bang.
15. Black Womanhood and Feminist Standpoints.
Science.gov (United States)
Allen, Brenda J.
1998-01-01
Discusses challenges and consequences of being a member of two historically oppressed groups in the United States--Blacks and females. Relies on feminist standpoint theory--a distinctive element of contemporary feminist thought about how knowledge is constructed. Focuses on academe as a discursive site for constructing identity. (PA)
16. The Award Winning Black Suns
Science.gov (United States)
Holbrook, Jarita
2018-01-01
Black Suns: An Astrophysics Adventure is a documentary film focusing on the annular and total solar eclipses of 2012. We made a different kind of astronomy documentary showing the human aspects rather than just focusing on pretty astronomy pictures. The film combines personal stories with science. Our heroes are Hakeem Oluseyi and Alphonse Sterling, who valiantly travel to study the solar corona during total solar eclipses. The goals of the film included presenting three dimensional scientists, to show their paths to becoming astrophysicists, and to show them as they collect data and work as scientists. Drama and tension surround taking data during the small window of time during totality. The Black Suns was filmed in Tokyo, Cairns, Tucson, and Melbourne Florida. Uniquely, the film began through a Kickstarter campaign to fund travel and filming in Tokyo. Many American Astronomical Society members donated to the film! Black Suns won the Jury Prize at the 2017 Art of Brooklyn Film Festival. Black Suns will be screening in full on ???.
17. Paths toward understanding black holes
NARCIS (Netherlands)
Mayerson, D.R.
2015-01-01
This work can be summarized as trying to understand aspects of black holes, gravity, and geometry, in the context of supergravity and string theory in high-energy theoretical physics. The two parts of this thesis have been written with entirely different audiences in mind. The first part consists of
18. Black holes and trapped points
International Nuclear Information System (INIS)
Krolak, A.
1981-01-01
Black holes are defined and their properties investigated without use of any global causality restriction. Also the boundary at infinity of space-time is not needed. When the causal conditions are brought in, the equivalence with the usual approach is established. (author)
19. Black Holes and Exotic Spinors
Directory of Open Access Journals (Sweden)
J. M. Hoff da Silva
2016-05-01
Full Text Available Exotic spin structures are non-trivial liftings, of the orthogonal bundle to the spin bundle, on orientable manifolds that admit spin structures according to the celebrated Geroch theorem. Exotic spin structures play a role of paramount importance in different areas of physics, from quantum field theory, in particular at Planck length scales, to gravity, and in cosmological scales. Here, we introduce an in-depth panorama in this field, providing black hole physics as the fount of spacetime exoticness. Black holes are then studied as the generators of a non-trivial topology that also can correspond to some inequivalent spin structure. Moreover, we investigate exotic spinor fields in this context and the way exotic spinor fields branch new physics. We also calculate the tunneling probability of exotic fermions across a Kerr-Sen black hole, showing that the exotic term does affect the tunneling probability, altering the black hole evaporation rate. Finally we show that it complies with the Hawking temperature universal law.
20. and black cumin (Nigella sativa)
African Journals Online (AJOL)
USER
2016-03-30
Mar 30, 2016 ... Feed additive antibiotics reduce the cost and improve the quantity of food production through more ... similar antibiotics used in human medicine as the result of food chain ... The main active components of black cumin ... Another plant of nutritional and medicinal importance is buckwheat (Fagopyrum ...
1. On Being an Angry Black Man
Science.gov (United States)
Quaye, Stephen John
2017-01-01
Black men are often seen as problems, threats, and thugs. The mere existence of a Black body is often met with fear. Using autoethnographic mystory, I blend personal stories, poetry, song lyrics, and analysis to subvert the angry Black man mantra and explore the productive use of anger to stimulate change.
2. Compensating Scientism through "The Black Hole."
Science.gov (United States)
Roth, Lane
The focal image of the film "The Black Hole" functions as a visual metaphor for the sacred, order, unity, and eternal time. The black hole is a symbol that unites the antinomic pairs of conscious/unconscious, water/fire, immersion/emersion, death/rebirth, and hell/heaven. The black hole is further associated with the quest for…
3. Hawking radiation of black rings from anomalies
International Nuclear Information System (INIS)
Chen Bin; He Wei
2008-01-01
We derive Hawking radiation of five-dimensional black rings from gauge and gravitational anomalies using the method proposed by Robinson and Wilczek. We find, as in the black hole case, that the problem could reduce to a (1+1)-dimensional field theory and the anomalies result in correct Hawking temperature for neutral, dipole and charged black rings
4. Area spectra of near extremal black holes
International Nuclear Information System (INIS)
Chen, Deyou; Yang, Haitang; Zu, Xiaotao
2010-01-01
Motivated by Maggiore's new interpretation of quasinormal modes, we investigate area spectra of a near extremal Schwarzschild-de Sitter black hole and a higher-dimensional near extremal Reissner-Nordstrom-de Sitter black hole. The result shows that the area spectra are equally spaced and irrelevant to the parameters of the black holes. (orig.)
5. A Black Hole in Our Galactic Center
Science.gov (United States)
Ruiz, Michael J.
2008-01-01
An introductory approach to black holes is presented along with astronomical observational data pertaining to the presence of a supermassive black hole at the center of our galaxy. Concepts of conservation of energy and Kepler's third law are employed so students can apply formulas from their physics class to determine the mass of the black hole…
6. White holes and eternal black holes
International Nuclear Information System (INIS)
Hsu, Stephen D H
2012-01-01
We investigate isolated white holes surrounded by vacuum, which correspond to the time reversal of eternal black holes that do not evaporate. We show that isolated white holes produce quasi-thermal Hawking radiation. The time reversal of this radiation, incident on a black hole precursor, constitutes a special preparation that will cause the black hole to become eternal. (paper)
7. Extremal black holes in N=2 supergravity
NARCIS (Netherlands)
2011-01-01
An explanation for the entropy of black holes has been an outstanding problem in recent decades. A special case where this is possible is that of extremal black holes in N=2 supergravity in four and five dimensions. The best developed case is for black holes preserving some supersymmetry (BPS),
8. New entropy formula for Kerr black holes
Directory of Open Access Journals (Sweden)
González Hernán A.
2018-01-01
Full Text Available We introduce a new entropy formula for Kerr black holes inspired by recent results for 3-dimensional black holes and cosmologies with soft Heisenberg hair. We show that also Kerr–Taub–NUT black holes obey the same formula.
9. On black holes and gravitational waves
CERN Document Server
Loinger, Angelo
2002-01-01
Black holes and gravitational waves are theoretical entities of today astrophysics. Various observed phenomena have been associated with the concept of black hole ; until now, nobody has detected gravitational waves. The essays contained in this book aim at showing that the concept of black holes arises from a misinterpretation of general relativity and that gravitational waves cannot exist.
10. Will Integration Hurt My Black Son's Education?
Science.gov (United States)
Latimer, Leah Y.
1987-01-01
In integrated schools, the educational system is slow to encourage black youngsters to participate at all levels of school life. Black participation is also inhibited by an insidious peer pressure and immature code of racial pride that defines blackness in terms that often exclude excellence in efforts beyond music, dance, and sports. (PS)
11. Black Films and Film-Makers.
Science.gov (United States)
Patterson, Lindsay, Ed.
The development of black films and the attitudes of the film industry toward black films and black actors are some of the topics examined in this anthology of essays. Section 1, "Nigger to Supernigger," contains such articles as "The Death of Rastus: Negroes in American Films" by Thomas R. Cripps and "Folk Values in a New Medium" by Alain Locke…
12. SAAB Tackling the Black, Brown Male Crisis
Science.gov (United States)
Pluviose, David
2007-01-01
Increasingly, dropping out of high school is a one-way ticket to prison for Black men. Recent research conducted by sociologists Becky Pettit and Bruce Western indicates that 3 percent of Whites and 20 percent of Blacks born between 1965 and 1969 had served time in prison by their early thirties. The crisis among Black and Hispanic men mobilized…
13. How Well Are We Housed? 3. Blacks.
Science.gov (United States)
Limmer, Ruth
Blacks are housed poorly compared to the total American population. Black housing suffers frequently from deficiencies in every category except heating and electricity. It is estimated that 37% of blacks, but only 20% of the total population, need to spend more than a quarter of their cash incomes to live in unflawed, uncrowded housing. The…
14. Black Hole Monodromy and Conformal Field Theory
NARCIS (Netherlands)
Castro, A.; Lapan, J.M.; Maloney, A.; Rodriguez, M.J.
2013-01-01
The analytic structure of solutions to the Klein-Gordon equation in a black hole background, as represented by monodromy data, is intimately related to black hole thermodynamics. It encodes the "hidden conformal symmetry" of a nonextremal black hole, and it explains why features of the inner event
15. On Quantum Contributions to Black Hole Growth
NARCIS (Netherlands)
Spaans, M.
2013-01-01
The effects of Wheeler’s quantum foam on black hole growth are explored from an astrophysical per- spective. Quantum fluctuations in the form of mini (10−5 g) black holes can couple to macroscopic black holes and allow the latter to grow exponentially in mass on a time scale of 109 years.
16. 5D Black Holes and Matrix Strings
CERN Document Server
Dijkgraaf, R; Verlinde, Herman L
1997-01-01
We derive the world-volume theory, the (non)-extremal entropy and background geometry of black holes and black strings constructed out of the NS IIA fivebrane within the framework of matrix theory. The CFT description of strings propagating in the black hole geometry arises as an effective field theory.
17. Therapeutic Dimensions of the Black Aesthetic
Science.gov (United States)
Toldson, Ivory L.; Pasteur, Alfred B.
1976-01-01
The authors of this article see the black aesthetic largely in terms of the affective component. Emotional oneness which is foreign to the white world view is the means by which the black man can achieve optimal mental health and development. The therapeutic implications of the black aesthetic are outlined. (NG)
18. A Black Hole Spectral Signature
Science.gov (United States)
Titarchuk, Lev; Laurent, Philippe
2000-03-01
An accreting black hole is, by definition, characterized by the drain. Namely, the matter falls into a black hole much the same way as water disappears down a drain matter goes in and nothing comes out. As this can only happen in a black hole, it provides a way to see a black hole'', an unique observational signature. The accretion proceeds almost in a free-fall manner close to the black hole horizon, where the strong gravitational field dominates the pressure forces. In this paper we present analytical calculations and Monte-Carlo simulations of the specific features of X-ray spectra formed as a result of upscattering of the soft (disk) photons in the converging inflow (CI) into the black hole. The full relativistic treatment has been implemented to reproduce these spectra. We show that spectra in the soft state of black hole systems (BHS) can be described as the sum of a thermal (disk) component and the convolution of some fraction of this component with the CI upscattering spread (Greens) function. The latter boosted photon component is seen as an extended power-law at energies much higher than the characteristic energy of the soft photons. We demonstrate the stability of the power spectral index over a wide range of the plasma temperature 0 - 10 keV and mass accretion rates (higher than 2 in Eddington units). We also demonstrate that the sharp high energy cutoff occurs at energies of 200-400 keV which are related to the average energy of electrons mec2 impinging upon the event horizon. The spectrum is practically identical to the standard thermal Comptonization spectrum when the CI plasma temperature is getting of order of 50 keV (the typical ones for the hard state of BHS). In this case one can see the effect of the bulk motion only at high energies where there is an excess in the CI spectrum with respect to the pure thermal one. Furthermore we demonstrate that the change of spectral shapes from the soft X-ray state to the hard X-ray state is clearly to be
19. Phase transition for black holes with scalar hair and topological black holes
International Nuclear Information System (INIS)
Myung, Yun Soo
2008-01-01
We study phase transitions between black holes with scalar hair and topological black holes in asymptotically anti-de Sitter spacetimes. As the ground state solutions, we introduce the non-rotating BTZ black hole in three dimensions and topological black hole with hyperbolic horizon in four dimensions. For the temperature matching only, we show that the phase transition between black hole with scalar hair (Martinez-Troncoso-Zanelli black hole) and topological black hole is second-order by using differences between two free energies. However, we do not identify what order of the phase transition between scalar and non-rotating BTZ black holes occurs in three dimensions, although there exists a possible decay of scalar black hole to non-rotating BTZ black hole
20. Gamma ray bursts of black hole universe
Science.gov (United States)
Zhang, T. X.
2015-07-01
Slightly modifying the standard big bang theory, Zhang recently developed a new cosmological model called black hole universe, which has only a single postulate but is consistent with Mach's principle, governed by Einstein's general theory of relativity, and able to explain existing observations of the universe. In the previous studies, we have explained the origin, structure, evolution, expansion, cosmic microwave background radiation, quasar, and acceleration of black hole universe, which grew from a star-like black hole with several solar masses through a supermassive black hole with billions of solar masses to the present state with hundred billion-trillions of solar masses by accreting ambient matter and merging with other black holes. This study investigates gamma ray bursts of black hole universe and provides an alternative explanation for the energy and spectrum measurements of gamma ray bursts according to the black hole universe model. The results indicate that gamma ray bursts can be understood as emissions of dynamic star-like black holes. A black hole, when it accretes its star or merges with another black hole, becomes dynamic. A dynamic black hole has a broken event horizon and thus cannot hold the inside hot (or high-frequency) blackbody radiation, which flows or leaks out and produces a GRB. A star when it collapses into its core black hole produces a long GRB and releases the gravitational potential energy of the star as gamma rays. A black hole that merges with another black hole produces a short GRB and releases a part of their blackbody radiation as gamma rays. The amount of energy obtained from the emissions of dynamic star-like black holes are consistent with the measurements of energy from GRBs. The GRB energy spectra derived from this new emission mechanism are also consistent with the measurements.
1. Chandra Catches "Piranha" Black Holes
Science.gov (United States)
2007-07-01
Supermassive black holes have been discovered to grow more rapidly in young galaxy clusters, according to new results from NASA's Chandra X-ray Observatory. These "fast-track" supermassive black holes can have a big influence on the galaxies and clusters that they live in. Using Chandra, scientists surveyed a sample of clusters and counted the fraction of galaxies with rapidly growing supermassive black holes, known as active galactic nuclei (or AGN). The data show, for the first time, that younger, more distant galaxy clusters contained far more AGN than older, nearby ones. Galaxy clusters are some of the largest structures in the Universe, consisting of many individual galaxies, a few of which contain AGN. Earlier in the history of the universe, these galaxies contained a lot more gas for star formation and black hole growth than galaxies in clusters do today. This fuel allows the young cluster black holes to grow much more rapidly than their counterparts in nearby clusters. Illustration of Active Galactic Nucleus Illustration of Active Galactic Nucleus "The black holes in these early clusters are like piranha in a very well-fed aquarium," said Jason Eastman of Ohio State University (OSU) and first author of this study. "It's not that they beat out each other for food, rather there was so much that all of the piranha were able to really thrive and grow quickly." The team used Chandra to determine the fraction of AGN in four different galaxy clusters at large distances, when the Universe was about 58% of its current age. Then they compared this value to the fraction found in more nearby clusters, those about 82% of the Universe's current age. The result was the more distant clusters contained about 20 times more AGN than the less distant sample. AGN outside clusters are also more common when the Universe is younger, but only by factors of two or three over the same age span. "It's been predicted that there would be fast-track black holes in clusters, but we never
2. Dyonic black hole in heterotic string theory
International Nuclear Information System (INIS)
Jatkar, D.P.; Mukherji, S.
1997-01-01
We study some features of the dyonic black hole solution in heterotic string theory on a six-torus. This solution has 58 parameters. Of these, 28 parameters denote the electric charge of the black hole, another 28 correspond to the magnetic charge, and the other two parameters are the mass and the angular momentum of the black hole. We discuss the extremal limit and show that in various limits it reduces to the known black hole solutions. The solutions saturating the Bogomolnyi bound are identified. An explicit solution is presented for the non-rotating dyonic black hole. (orig.)
3. Modified dispersion relations and black hole physics
International Nuclear Information System (INIS)
Ling Yi; Li Xiang; Hu Bo
2006-01-01
A modified formulation of the energy-momentum relation is proposed in the context of doubly special relativity. We investigate its impact on black hole physics. It turns out that such a modification will give corrections to both the temperature and the entropy of black holes. In particular, this modified dispersion relation also changes the picture of Hawking radiation greatly when the size of black holes approaches the Planck scale. It can prevent black holes from total evaporation, as a result providing a plausible mechanism to treat the remnant of black holes as a candidate for dark matter
4. Black-hole creation in quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Zhong Chao, Wu [Rome, Univ. La Sapienza (Italy). International Center for Relativistic Astrophysics]|[Specola Vaticana, Vatican City State (Vatican City State, Holy See)
1997-11-01
It is proven that the probability of a black hole created from the de Sitter space-time background, at the Wkb level, is the exponential of one quarter of the sum of the black hole and cosmological horizon areas, or the total entropy of the universe. This is true not only for the spherically symmetric cases of the Schwarzschild or Reissner-Nordstroem black holes, but also for the rotating cases of the Kerr black hole and the rotating charged case of the Newman black hole. The de Sitter metric is the most probable evolution at the Planckian era of the universe.
5. Black holes escaping from domain walls
International Nuclear Information System (INIS)
Flachi, Antonino; Sasaki, Misao; Pujolas, Oriol; Tanaka, Takahiro
2006-01-01
Previous studies concerning the interaction of branes and black holes suggested that a small black hole intersecting a brane may escape via a mechanism of reconnection. Here we consider this problem by studying the interaction of a small black hole and a domain wall composed of a scalar field and simulate the evolution of this system when the black hole acquires an initial recoil velocity. We test and confirm previous results, however, unlike the cases previously studied, in the more general set-up considered here, we are able to follow the evolution of the system also during the separation, and completely illustrate how the escape of the black hole takes place
6. Few-layer black phosphorus nanoparticles.
Science.gov (United States)
Sofer, Zdenek; Bouša, Daniel; Luxa, Jan; Mazanek, Vlastimil; Pumera, Martin
2016-01-28
Herein, black phosphorus quantum dots and nanoparticles of a few layer thickness were prepared and characterized using STEM, AFM, dynamic light scattering, X-ray photoelectron spectroscopy, X-ray diffraction, Raman spectroscopy and photoluminescence. Impact electrochemistry of the induvidual black phosphorus nanoparticles allows their size determination. The centrifugation of colloidal black phosphorus nanoparticles allowed separation of quantum dots with sizes up to 15 nm. These black phosphorus nanoparticles exhibit a large band gap and are expected to find a wide range of applications from semiconductors to biomolecule tags. The use of black phosphorus nanoparticles for vapour sensing was successfully demonstrated.
7. [Black urine or black sclera of the eyes? Consider alkaptonuria].
Science.gov (United States)
Gubbels, Nanda P; Sijbrand, Merijn H; Onstenk, Ron
2014-01-01
Alkaptonuria is a rare metabolic disorder due to a defect in the gene for homogentisic acid oxidase. This results in an accumulation of homogentisic acid, which leads to the deposit of pigment in the connective tissue in the body. This causes problems and symptoms in various organ systems, such as early artropathy, dark-coloured urine, black sclerae, dark-coloured aortic valves and an increased risk of kidney stones and gall stones. Various specialists may see patients with this disease. The diagnosis is often missed. We describe a 69-year-old woman who underwent surgery due to joint problems, which showed up black cartilage. It turned out that for many years she had also had eye and heart problems. Not until later in life was she diagnosed with alkaptonuria. There is no curative treatment for alkaptonuria at the moment. Early recognition of the disease can increase the quality of life. Preventative check-ups and guidance are also therefore necessary.
8. Extremal vacuum black holes in higher dimensions
International Nuclear Information System (INIS)
Figueras, Pau; Lucietti, James; Rangamani, Mukund; Kunduri, Hari K.
2008-01-01
We consider extremal black hole solutions to the vacuum Einstein equations in dimensions greater than five. We prove that the near-horizon geometry of any such black hole must possess an SO(2,1) symmetry in a special case where one has an enhanced rotational symmetry group. We construct examples of vacuum near-horizon geometries using the extremal Myers-Perry black holes and boosted Myers-Perry strings. The latter lead to near-horizon geometries of black ring topology, which in odd spacetime dimensions have the correct number of rotational symmetries to describe an asymptotically flat black object. We argue that a subset of these correspond to the near-horizon limit of asymptotically flat extremal black rings. Using this identification we provide a conjecture for the exact 'phase diagram' of extremal vacuum black rings with a connected horizon in odd spacetime dimensions greater than five.
9. Quantum information erasure inside black holes
International Nuclear Information System (INIS)
Lowe, David A.; Thorlacius, Larus
2015-01-01
An effective field theory for infalling observers in the vicinity of a quasi-static black hole is given in terms of a freely falling lattice discretization. The lattice model successfully reproduces the thermal spectrum of outgoing Hawking radiation, as was shown by Corley and Jacobson, but can also be used to model observations made by a typical low-energy observer who enters the black hole in free fall at a prescribed time. The explicit short distance cutoff ensures that, from the viewpoint of the infalling observer, any quantum information that entered the black hole more than a scrambling time earlier has been erased by the black hole singularity. This property, combined with the requirement that outside observers need at least of order the scrambling time to extract quantum information from the black hole, ensures that a typical infalling observer does not encounter drama upon crossing the black hole horizon in a theory where black hole information is preserved for asymptotic observers.
10. Collision of two rotating Hayward black holes
Energy Technology Data Exchange (ETDEWEB)
Gwak, Bogeun [Sejong University, Department of Physics and Astronomy, Seoul (Korea, Republic of)
2017-07-15
We investigate the spin interaction and the gravitational radiation thermally allowed in a head-on collision of two rotating Hayward black holes. The Hayward black hole is a regular black hole in a modified Einstein equation, and hence it can be an appropriate model to describe the extent to which the regularity effect in the near-horizon region affects the interaction and the radiation. If one black hole is assumed to be considerably smaller than the other, the potential of the spin interaction can be analytically obtained and is dependent on the alignment of angular momenta of the black holes. For the collision of massive black holes, the gravitational radiation is numerically obtained as the upper bound by using the laws of thermodynamics. The effect of the Hayward black hole tends to increase the radiation energy, but we can limit the effect by comparing the radiation energy with the gravitational waves GW150914 and GW151226. (orig.)
11. From Black Holes to Quivers
CERN Document Server
Manschot, Jan; Sen, Ashoke
2012-01-01
Middle cohomology states on the Higgs branch of supersymmetric quiver quantum mechanics - also known as pure Higgs states - have recently emerged as possible microscopic candidates for single-centered black hole micro-states, as they carry zero angular momentum and appear to be robust under wall-crossing. Using the connection between quiver quantum mechanics on the Coulomb branch and the quantum mechanics of multi-centered black holes, we propose a general algorithm for reconstructing the full moduli-dependent cohomology of the moduli space of an arbitrary quiver, in terms of the BPS invariants of the pure Higgs states. We analyze many examples of quivers with loops, including all cyclic Abelian quivers and several examples with two loops or non-Abelian gauge groups, and provide supporting evidence for this proposal. We also develop methods to count pure Higgs states directly.
12. Cosmic strings and black holes
International Nuclear Information System (INIS)
Aryal, M.; Ford, L.H.; Vilenkin, A.
1986-01-01
The metric for a Schwarzschild black hole with a cosmic string passing through it is discussed. The thermodynamics of such an object is considered, and it is shown that S = (1/4)A, where S is the entropy and A is the horizon area. It is noted that the Schwarzschild mass parameter M, which is the gravitational mass of the system, is no longer identical to its energy. A solution representing a pair of black holes held apart by strings is discussed. It is nearly identical to a static, axially symmetric solution given long ago by Bach and Weyl. It is shown how these solutions, which were formerly a mathematical curiosity, may be given a more physical interpretation in terms of cosmic strings
13. Symmetries of supergravity black holes
International Nuclear Information System (INIS)
Chow, David D K
2010-01-01
We investigate Killing tensors for various black hole solutions of supergravity theories. Rotating black holes of an ungauged theory, toroidally compactified heterotic supergravity, with NUT parameters and two U(1) gauge fields are constructed. If both charges are set equal, then the solutions simplify, and then there are concise expressions for rank-2 conformal Killing-Staeckel tensors. These are induced by rank-2 Killing-Staeckel tensors of a conformally related metric that possesses a separability structure. We directly verify the separation of the Hamilton-Jacobi equation on this conformally related metric and of the null Hamilton-Jacobi and massless Klein-Gordon equations on the 'physical' metric. Similar results are found for more general solutions; we mainly focus on those with certain charge combinations equal in gauged supergravity but also consider some other solutions.
14. Dynamics of test black holes
International Nuclear Information System (INIS)
Epikhin, E.N.
1981-01-01
A concept of a test object is introduced. This definition includes also small black holes. Reduced approximation of testing permits to unambiguously introduce a concept of background space-time. Dynamic values for test objects are introduced by means of the Noether theorem which gave the possibility to covariantly generalize pseudotensor of the Papapetru energy-momentum for the case of curved background space-time. Additional use of radiation approximation and the accountancy of the zero and first momenta of dynamic values lead to the conclusion that motion of the test object (including small black holes) is subordinated to the Matthiessen-Papapetru equations. The above results are testified to the accountancy of a proper gravitational field of the test object in integrated dynamic values [ru
15. Some Simple Black Hole Thermodynamics
Science.gov (United States)
Lopresto, Michael C.
2003-05-01
In his recent popular book The Universe in a Nutshell, Steven Hawking gives expressions for the entropy1 and temperature (often referred to as the Hawking temperature''2 ) of a black hole:3 S = kc34ℏG A T = ℏc38πkGM, where A is the area of the event horizon, M is the mass, k is Boltzmann's constant, ℏ = h2π (h being Planck's constant), c is the speed of light, and G is the universal gravitational constant. These expressions can be used as starting points for some interesting approximations on the thermodynamics of a Schwarzschild black hole, of mass M, which by definition is nonrotating and spherical with an event horizon of radius R = 2GMc2.4,5
16. Lifetime of a black hole
International Nuclear Information System (INIS)
Carlitz, R.D.; Willey, R.S.
1987-01-01
We study the constraints placed by quantum mechanics upon the lifetime of a black hole. In the context of a moving-mirror analog model for the Hawking radiation process, we conclude that the period of Hawking radiation must be followed by a much longer period during which the remnant mass (of order m/sub P/) may be radiated away. We are able to place a lower bound on the time required for this radiation process, which translates into a lower bound for the lifetime of the black hole. Particles which are emitted during the decay of the remnant, like the particles which comprise the Hawking flux, may be uncorrelated with each other. But each particle emitted from the decaying remnant is correlated with one particle emitted as Hawking radiation. The state which results after the remnant has evaporated is one which locally appears to be thermal, but which on a much larger scale is marked by extensive correlations
17. Black hole with quantum potential
Energy Technology Data Exchange (ETDEWEB)
Ali, Ahmed Farag, E-mail: [email protected] [Department of Physics, Faculty of Science, Benha University, Benha 13518 (Egypt); Khalil, Mohammed M., E-mail: [email protected] [Department of Electrical Engineering, Alexandria University, Alexandria 12544 (Egypt)
2016-08-15
In this work, we investigate black hole (BH) physics in the context of quantum corrections. These quantum corrections were introduced recently by replacing classical geodesics with quantal (Bohmian) trajectories and hence form a quantum Raychaudhuri equation (QRE). From the QRE, we derive a modified Schwarzschild metric, and use that metric to investigate BH singularity and thermodynamics. We find that these quantum corrections change the picture of Hawking radiation greatly when the size of BH approaches the Planck scale. They prevent the BH from total evaporation, predicting the existence of a quantum BH remnant, which may introduce a possible resolution for the catastrophic behavior of Hawking radiation as the BH mass approaches zero. Those corrections also turn the spacelike singularity of the black hole to be timelike, and hence this may ameliorate the information loss problem.
18. Black hole with quantum potential
Directory of Open Access Journals (Sweden)
Ahmed Farag Ali
2016-08-01
Full Text Available In this work, we investigate black hole (BH physics in the context of quantum corrections. These quantum corrections were introduced recently by replacing classical geodesics with quantal (Bohmian trajectories and hence form a quantum Raychaudhuri equation (QRE. From the QRE, we derive a modified Schwarzschild metric, and use that metric to investigate BH singularity and thermodynamics. We find that these quantum corrections change the picture of Hawking radiation greatly when the size of BH approaches the Planck scale. They prevent the BH from total evaporation, predicting the existence of a quantum BH remnant, which may introduce a possible resolution for the catastrophic behavior of Hawking radiation as the BH mass approaches zero. Those corrections also turn the spacelike singularity of the black hole to be timelike, and hence this may ameliorate the information loss problem.
19. Accidents, 'black swans' and risks
International Nuclear Information System (INIS)
Luxat, J.C.
2013-01-01
Major accidents and natural disasters with severe consequences have occurred in all sectors of industrial activity with relatively high frequency. The severe consequences of concern involve either significant loss of life or major economic loss, or both loss of life and economic loss. Such events have the last two years been referred to as 'black swan' events following publication of Taleb's bestselling book. These events demonstrate limits to PRA application that arise from the underlying high uncertainty associated with the estimation of frequency of occurrence of such events. An approach is proposed in this paper that, consistent with the concept of defense in depth employed by the nuclear industry, augments probabilistic risk assessment with a methodology based upon 'threat - risk assessment'. This approach shifts these very low frequency high consequence 'black swan' events out of the probabilistic risk assessment domain into a deterministic emergency response assessment domain. (author)
20. Framing black boys: parent, teacher, and student narratives of the academic lives of black boys.
Science.gov (United States)
Rowley, Stephanie J; Ross, Latisha; Lozada, Fantasy T; Williams, Amber; Gale, Adrian; Kurtz-Costes, Beth
2014-01-01
The discourse on Black boys tends to suggest that Black boys are in complete peril. We begin with evidence that Black boys are excelling in certain contexts (i.e., in certain states, in certain schools, and in certain courses). We then discuss the ways in which the narratives used by parents, teachers, and Black boys themselves may serve to further reinforce views that Black boys are beyond hope. Research on Black parents suggests that they tend to view their sons as vulnerable and have lower expectations for sons than for daughters. Studies of teachers show that they tend to view Black boys as unteachable, as social problems, and as scary. Research on Black boys shows that they are sometimes complicit in supporting these narratives by engaging in negative or ste reotypical behavior. We also include recent research that includes counter-narratives of Black boys. We end with suggestions for future research.
1. The phase structure of higher-dimensional black rings and black holes
International Nuclear Information System (INIS)
Emparan, Roberto; Harmark, Troels; Niarchos, Vasilis; Obers, Niels A.; RodrIguez, Maria J.
2007-01-01
We construct an approximate solution for an asymptotically flat, neutral, thin rotating black ring in any dimension D ≥ 5 by matching the near-horizon solution for a bent boosted black string, to a linearized gravity solution away from the horizon. The rotating black ring solution has a regular horizon of topology S 1 x S D-3 and incorporates the balancing condition of the ring as a zero-tension condition. For D = 5 our method reproduces the thin ring limit of the exact black ring solution. For D ≥ 6 we show that the black ring has a higher entropy than the Myers-Perry black hole in the ultra-spinning regime. By exploiting the correspondence between ultra-spinning black holes and black membranes on a two-torus, we take steps towards qualitatively completing the phase diagram of rotating blackfolds with a single angular momentum. We are led to propose a connection between MP black holes and black rings, and between MP black holes and black Saturns, through merger transitions involving two kinds of 'pinched' black holes. More generally, the analogy suggests an infinite number of pinched black holes of spherical topology leading to a complicated pattern of connections and mergers between phases
2. Black ringoids: spinning balanced black objects in d≥5 dimensions — the codimension-two case
International Nuclear Information System (INIS)
Kleihaus, Burkhard; Kunz, Jutta; Radu, Eugen
2015-01-01
We propose a general framework for the study of asymptotically flat black objects with k+1 equal magnitude angular momenta in d≥5 spacetime dimensions (with 0≤k≤[((d−5)/2)]). In this approach, the dependence on all angular coordinates but one is factorized, which leads to a codimension-two problem. This framework can describe black holes with spherical horizon topology, the simplest solutions corresponding to a class of Myers-Perry black holes. A different set of solutions describes balanced black objects with S"n"+"1×S"2"k"+"1 horizon topology. The simplest members of this family are the black rings (k=0). The solutions with k>0 are dubbed black ringoids. Based on the nonperturbative numerical results found for several values of (n,k), we propose a general picture for the properties and the phase diagram of these solutions and the associated black holes with spherical horizon topology: n=1 black ringoids repeat the k=0 pattern of black rings and Myers-Perry black holes in 5 dimensions, whereas n>1 black ringoids follow the pattern of higher dimensional black rings associated with ‘pinched’ black holes and Myers-Perry black holes.
3. Van der Waals black hole
Directory of Open Access Journals (Sweden)
Aruna Rajagopal
2014-10-01
Full Text Available In the context of extended phase space, where the negative cosmological constant is treated as a thermodynamic pressure in the first law of black hole thermodynamics, we find an asymptotically AdS metric whose thermodynamics matches exactly that of the Van der Waals fluid. We show that as a solution of Einstein's equations, the corresponding stress energy tensor obeys (at least for certain range of metric parameters all three weak, strong, and dominant energy conditions.
4. Australian black coal statistics 1991
Energy Technology Data Exchange (ETDEWEB)
1992-01-01
This third edition of Australian black coal statistics covers anthracite, bituminous and subbituminous coals. It includes maps and figures on resources and coal fields and statistics (mainly based on the calendar year 1991) on coal demand and supply, production, employment and productivity in Australian coal mines, exports, prices and ports, and domestic consumption. A listing of coal producers by state is included. A final section presents key statistics on international world trade in 1991. 54 tabs.
5. Black holes, singularities and predictability
International Nuclear Information System (INIS)
Wald, R.M.
1984-01-01
The paper favours the view that singularities may play a central role in quantum gravity. The author reviews the arguments leading to the conclusion, that in the process of black hole formation and evaporation, an initial pure state evolves to a final density matrix, thus signaling a breakdown in ordinary quantum dynamical evolution. Some related issues dealing with predictability in the dynamical evolution, are also discussed. (U.K.)
6. A black-hole cosmology
International Nuclear Information System (INIS)
Debney, G.; Farnsworth, D.
1983-01-01
Motivated by the fact that 2m/r is of the order of magnitude unity for the observable universe, we explore the possibility that a Schwarzschild or black hole cosmological model is appropriate. Luminosity distance and frequency shifts of freely-falling, standard, monochromatic objects are viewed by a freely-falling observer. The observer is inside r=2m. The observer in such a world does not see the same universe as do astronomers. (author)
7. Black esophagus: exploring the dark
Directory of Open Access Journals (Sweden)
Robert Forster
2013-10-01
Full Text Available Black esophagus is a rare but underdiagnosed disease. It occurs most frequently in severely ill patients and carries a high mortality rate. Cause of death is usually attributed to the comorbid conditions. Treatment is directed at the underlying cause, acid suppression and keeping the patient nil-per-os. Surgery is needed in complicated cases and stenosis is the most feared longterm sequel. In the present article, two cases are described and literature is reviewed.
8. Electrically charged dilatonic black rings
International Nuclear Information System (INIS)
Kunduri, Hari K.; Lucietti, James
2005-01-01
In this Letter we present (electrically) charged dilatonic black ring solutions of the Einstein-Maxwell-dilaton theory in five dimensions and we consider their physical properties. These solutions are static and as in the neutral case possess a conical singularity. We show how one may remove the conical singularity by application of a Harrison transformation, which physically corresponds to supporting the charged ring with an electric field. Finally, we discuss the slowly rotating case for arbitrary dilaton coupling
9. Brown dwarfs and black holes
International Nuclear Information System (INIS)
Tarter, J.C.
1978-01-01
The astronomical missing-mass problem (the discrepancy between the dynamical mass estimate and the sum of individual masses in large groupings) is considered, and possible explanations are advanced. The existence of brown dwarfs (stars not massive enough to shine by nuclear burning) and black holes (extremely high density matter contraction such that gravitation allows no light emission) thus far provides the most plausible solutions
10. Working with young black people.
OpenAIRE
Sallah, Momodou; Howson, Carlton
2007-01-01
This is an important collection, integrating research with messages for practitioners in an area where there has as yet been insufficient material published. This book also formed the focal point for a major international conference in the Summer of 2006. As well as jointly editing the publication, the author contributed a chapter to it. Bringing together this work's different dimensions and perspectives, this book seeks to challenge both the accepted status quo of Black young people s neg...
11. Broken links and black boxes
DEFF Research Database (Denmark)
Sindbæk, Søren Michael
2013-01-01
Long-distance communication has emerged as a particular focus for archaeological exploration using network theory, analysis, and modelling. Initial attempts to adapt methods from social network analysis to archaeological data have, however, struggled to produce decisive results. This paper argues...... observable distributions and patterns of association in the archaeological record. In formal terms this is not a problem of network analysis, but network synthesis: the classic problem of cracking codes or reconstructing black-box circuits....
12. Nectar sugar production across floral phases in the Gynodioecious Protandrous Plant Geranium sylvaticum [corrected].
Science.gov (United States)
Varga, Sandra; Nuortila, Carolin; Kytöviita, Minna-Maarit
2013-01-01
Many zoophilous plants attract their pollinators by offering nectar as a reward. In gynodioecious plants (i.e. populations are composed of female and hermaphrodite individuals) nectar production has been repeatedly reported to be larger in hermaphrodite compared to female flowers even though nectar production across the different floral phases in dichogamous plants (i.e. plants with time separation of pollen dispersal and stigma receptivity) has rarely been examined. In this study, sugar production in nectar standing crop and secretion rate were investigated in Geranium sylvaticum, a gynodioecious plant species with protandry (i.e. with hermaphrodite flowers releasing their pollen before the stigma is receptive). We found that flowers from hermaphrodites produced more nectar than female flowers in terms of total nectar sugar content. In addition, differences in nectar production among floral phases were found in hermaphrodite flowers but not in female flowers. In hermaphrodite flowers, maximum sugar content coincided with pollen presentation and declined slightly towards the female phase, indicating nectar reabsorption, whereas in female flowers sugar content did not differ between the floral phases. These differences in floral reward are discussed in relation to visitation patterns by pollinators and seed production in this species.
13. Nectar Sugar Production across Floral Phases in the Gynodioecious Protandrous Plant Geranium sylvaticum
Science.gov (United States)
Varga, Sandra; Nuortila, Carolin; Kytöviita, Minna-Maarit
2013-01-01
Many zoophilous plants attract their pollinators by offering nectar as a reward. In gynodioecious plants (i.e. populations are composed of female and hermaphrodite individuals) nectar production has been repeatedly reported to be larger in hermaphrodite compared to female flowers even though nectar production across the different floral phases in dichogamous plants (i.e. plants with time separation of pollen dispersal and stigma receptivity) has rarely been examined. In this study, sugar production in nectar standing crop and secretion rate were investigated in Geranium sylvaticum, a gynodioecious plant species with protandry (i.e. with hermaphrodite flowers releasing their pollen before the stigma is receptive). We found that flowers from hermaphrodites produced more nectar than female flowers in terms of total nectar sugar content. In addition, differences in nectar production among floral phases were found in hermaphrodite flowers but not in female flowers. In hermaphrodite flowers, maximum sugar content coincided with pollen presentation and declined slightly towards the female phase, indicating nectar reabsorption, whereas in female flowers sugar content did not differ between the floral phases. These differences in floral reward are discussed in relation to visitation patterns by pollinators and seed production in this species. PMID:23614053
14. Glory scattering by black holes
International Nuclear Information System (INIS)
Matzner, R.A.; DeWitte-Morette, C.; Nelson, B.; Zhang, T.
1985-01-01
We present a physically motivated derivation of the JWKB backward glory-scattering cross section of massless waves by Schwarzschild black holes. The angular dependence of the cross section is identical with the one derived by path integration, namely, dsigma/dΩ = 4π 2 lambda -1 B/sub g/ 2 (dB mWπ, where lambda is the wavelength, B(theta) is the inverse of the classical deflection function CTHETA(B), B/sub g/ is the glory impact parameter, s is the helicity of the scattered wave, and J/sub 2s/ is the Bessel function of order 2s. The glory rings formed by scalar waves are bright at the center; those formed by polarized waves are dark at the center. For scattering of massless particles by a spherical black hole of mass M, B(theta)/Mapprox.3 √3 + 3.48 exp(-theta), theta > owigπ. The numerical values of dsigma/dΩ for this deflection function are found to agree with earlier computer calculations of glory cross sections from black holes
15. Black holes and random matrices
Energy Technology Data Exchange (ETDEWEB)
Cotler, Jordan S.; Gur-Ari, Guy [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Hanada, Masanori [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); The Hakubi Center for Advanced Research, Kyoto University,Kyoto 606-8502 (Japan); Polchinski, Joseph [Department of Physics, University of California,Santa Barbara, CA 93106 (United States); Kavli Institute for Theoretical Physics, University of California,Santa Barbara, CA 93106 (United States); Saad, Phil; Shenker, Stephen H. [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Stanford, Douglas [Institute for Advanced Study,Princeton, NJ 08540 (United States); Streicher, Alexandre [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Department of Physics, University of California,Santa Barbara, CA 93106 (United States); Tezuka, Masaki [Department of Physics, Kyoto University,Kyoto 606-8501 (Japan)
2017-05-22
We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function |Z(β+it)|{sup 2} as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.
16. Soft Hair on Black Holes
Science.gov (United States)
Hawking, Stephen W.; Perry, Malcolm J.; Strominger, Andrew
2016-06-01
It has recently been shown that Bondi-van der Burg-Metzner-Sachs supertranslation symmetries imply an infinite number of conservation laws for all gravitational theories in asymptotically Minkowskian spacetimes. These laws require black holes to carry a large amount of soft (i.e., zero-energy) supertranslation hair. The presence of a Maxwell field similarly implies soft electric hair. This Letter gives an explicit description of soft hair in terms of soft gravitons or photons on the black hole horizon, and shows that complete information about their quantum state is stored on a holographic plate at the future boundary of the horizon. Charge conservation is used to give an infinite number of exact relations between the evaporation products of black holes which have different soft hair but are otherwise identical. It is further argued that soft hair which is spatially localized to much less than a Planck length cannot be excited in a physically realizable process, giving an effective number of soft degrees of freedom proportional to the horizon area in Planck units.
17. On The Black Sea Surozhian
Science.gov (United States)
Caraivan, Glicherie; Corneliu, Cerchia
2016-04-01
Some Black Sea researchers still support the idea of no other connection to the Mediterranean Sea between LGM and Karangatian Stage (Riss - Wurm). We try to clarify the source of these disagreements. C14 AMS age data (HERAS Project) made on undisturbed samples from a new Mamaia drilling hole where compared with the classical Black Sea stratigraphic schemes. A first transgressive event (Zone D) is found between 38.00 - 20.20 m depth. Zone D4 shows a fairly rapid rise of sea level, about 10 m below the present one indicating an inner shelf marine polyhaline environment. AMS age data show 14C ages between 53690 - 47359 y (MIS 1), corresponding to the "Surozhian Beds" of Popov. The "beach rock" from Zone E marks the decrease of the sea level after the maximum reached in Zone D4. Zone E mollusc shells AMS data, indicate 14C ages of 48724 - 44604 y, suggesting a long-time reworked material from the previous D4 zone sediments, and represents the beginning of the "regressive Tarkankutian" sequence.The Last Glacial Maximum (LGM) led to the retreat of the sea level down to about 100 m below the current one (27-17 ky BP), followed by an retreat of the shoreline to the present position. At the beginning of the Holocene - MIS 1 (8408-8132 cal. y BP), Black Sea brackish water level grew rapidly, up to -14 m below the present one (Zone F: 22, 57-20, 20 m). Zone F deposits could be correlated with the Bugazian strata. Then, a continuous rising of the Black Sea level is recorded up to a maximum of -2 m under the present one, about 6789 - 7063 cal. y BP, when a transgressive spurt ("Neolithic transgression") may have taken place. After that, given a weak Danubian sedimentary input, coastal erosion intensified. The coarse sandy sediments were reworked and pushed over the previous peat deposits, and suggest a classical "sedimentary regression", not a sea-level decrease. During the last 1.5 ky, sea level has risen towards the current one. Previous C14 dates from "Karangatian
18. Soft Hair on Black Holes.
Science.gov (United States)
Hawking, Stephen W; Perry, Malcolm J; Strominger, Andrew
2016-06-10
It has recently been shown that Bondi-van der Burg-Metzner-Sachs supertranslation symmetries imply an infinite number of conservation laws for all gravitational theories in asymptotically Minkowskian spacetimes. These laws require black holes to carry a large amount of soft (i.e., zero-energy) supertranslation hair. The presence of a Maxwell field similarly implies soft electric hair. This Letter gives an explicit description of soft hair in terms of soft gravitons or photons on the black hole horizon, and shows that complete information about their quantum state is stored on a holographic plate at the future boundary of the horizon. Charge conservation is used to give an infinite number of exact relations between the evaporation products of black holes which have different soft hair but are otherwise identical. It is further argued that soft hair which is spatially localized to much less than a Planck length cannot be excited in a physically realizable process, giving an effective number of soft degrees of freedom proportional to the horizon area in Planck units.
19. Black hole vacua and rotation
International Nuclear Information System (INIS)
Krishnan, Chethan
2011-01-01
Recent developments suggest that the near-region of rotating black holes behaves like a CFT. To understand this better, I propose to study quantum fields in this region. An instructive approach for this might be to put a large black hole in AdS and to think of the entire geometry as a toy model for the 'near-region'. Quantum field theory on rotating black holes in AdS can be well-defined (unlike in flat space), if fields are quantized in the co-rotating-with-the-horizon frame. First, some generalities of constructing Hartle-Hawking Green functions in this approach are discussed. Then as a specific example where the details are easy to handle, I turn to 2+1 dimensions (BTZ), write down the Green functions explicitly starting with the co-rotating frame, and observe some structural similarities they have with the Kerr-CFT scattering amplitudes. Finally, in BTZ, there is also an alternate construction for the Green functions: we can start from the covering AdS 3 space and use the method of images. Using a 19th century integral formula, I show the equality between the boundary correlators arising via the two constructions.
20. The stable problem of the black-hole connected region in the Schwarzschild black hole
OpenAIRE
Tian, Guihua
2005-01-01
The stability of the Schwarzschild black hole is studied. Using the Painlev\\'{e} coordinate, our region can be defined as the black-hole-connected region(r>2m, see text) of the Schwarzschild black hole or the white-hole-connected region(r>2m, see text) of the Schwarzschild black hole. We study the stable problems of the black-hole-connected region. The conclusions are: (1) in the black-hole-connected region, the initially regular perturbation fields must have real frequency or complex frequen...
1. Stationary black holes: large D analysis
International Nuclear Information System (INIS)
Suzuki, Ryotaku; Tanabe, Kentaro
2015-01-01
We consider the effective theory of large D stationary black holes. By solving the Einstein equations with a cosmological constant using the 1/D expansion in near zone of the black hole we obtain the effective equation for the stationary black hole. The effective equation describes the Myers-Perry black hole, bumpy black holes and, possibly, the black ring solution as its solutions. In this effective theory the black hole is represented as an embedded membrane in the background, e.g., Minkowski or Anti-de Sitter spacetime and its mean curvature is given by the surface gravity redshifted by the background gravitational field and the local Lorentz boost. The local Lorentz boost property of the effective equation is observed also in the metric itself. In fact we show that the leading order metric of the Einstein equation in the 1/D expansion is generically regarded as a Lorentz boosted Schwarzschild black hole. We apply this Lorentz boost property of the stationary black hole solution to solve perturbation equations. As a result we obtain an analytic formula for quasinormal modes of the singly rotating Myers-Perry black hole in the 1/D expansion.
2. Charged spinning black holes as particle accelerators
International Nuclear Information System (INIS)
Wei Shaowen; Liu Yuxiao; Guo Heng; Fu Chune
2010-01-01
It has recently been pointed out that the spinning Kerr black hole with maximal spin could act as a particle collider with arbitrarily high center-of-mass energy. In this paper, we will extend the result to the charged spinning black hole, the Kerr-Newman black hole. The center-of-mass energy of collision for two uncharged particles falling freely from rest at infinity depends not only on the spin a but also on the charge Q of the black hole. We find that an unlimited center-of-mass energy can be approached with the conditions: (1) the collision takes place at the horizon of an extremal black hole; (2) one of the colliding particles has critical angular momentum; (3) the spin a of the extremal black hole satisfies (1/√(3))≤(a/M)≤1, where M is the mass of the Kerr-Newman black hole. The third condition implies that to obtain an arbitrarily high energy, the extremal Kerr-Newman black hole must have a large value of spin, which is a significant difference between the Kerr and Kerr-Newman black holes. Furthermore, we also show that, for a near-extremal black hole, there always exists a finite upper bound for center-of-mass energy, which decreases with the increase of the charge Q.
3. BSW process of the slowly evaporating charged black hole
OpenAIRE
Wang, Liancheng; He, Feng; Fu, Xiangyun
2015-01-01
In this paper, we study the BSW process of the slowly evaporating charged black hole. It can be found that the BSW process will also arise near black hole horizon when the evaporation of charged black hole is very slow. But now the background black hole does not have to be an extremal black hole, and it will be approximately an extremal black hole unless it is nearly a huge stationary black hole.
4. NASA's Chandra Finds Black Holes Are "Green"
Science.gov (United States)
2006-04-01
Black holes are the most fuel efficient engines in the Universe, according to a new study using NASA's Chandra X-ray Observatory. By making the first direct estimate of how efficient or "green" black holes are, this work gives insight into how black holes generate energy and affect their environment. The new Chandra finding shows that most of the energy released by matter falling toward a supermassive black hole is in the form of high-energy jets traveling at near the speed of light away from the black hole. This is an important step in understanding how such jets can be launched from magnetized disks of gas near the event horizon of a black hole. Illustration of Fuel for a Black Hole Engine Illustration of Fuel for a Black Hole Engine "Just as with cars, it's critical to know the fuel efficiency of black holes," said lead author Steve Allen of the Kavli Institute for Particle Astrophysics and Cosmology at Stanford University, and the Stanford Linear Accelerator Center. "Without this information, we cannot figure out what is going on under the hood, so to speak, or what the engine can do." Allen and his team used Chandra to study nine supermassive black holes at the centers of elliptical galaxies. These black holes are relatively old and generate much less radiation than quasars, rapidly growing supermassive black holes seen in the early Universe. The surprise came when the Chandra results showed that these "quiet" black holes are all producing much more energy in jets of high-energy particles than in visible light or X-rays. These jets create huge bubbles, or cavities, in the hot gas in the galaxies. Animation of Black Hole in Elliptical Galaxy Animation of Black Hole in Elliptical Galaxy The efficiency of the black hole energy-production was calculated in two steps: first Chandra images of the inner regions of the galaxies were used to estimate how much fuel is available for the black hole; then Chandra images were used to estimate the power required to produce
5. Boosting jet power in black hole spacetimes.
Science.gov (United States)
Neilsen, David; Lehner, Luis; Palenzuela, Carlos; Hirschmann, Eric W; Liebling, Steven L; Motl, Patrick M; Garrett, Travis
2011-08-02
The extraction of rotational energy from a spinning black hole via the Blandford-Znajek mechanism has long been understood as an important component in models to explain energetic jets from compact astrophysical sources. Here we show more generally that the kinetic energy of the black hole, both rotational and translational, can be tapped, thereby producing even more luminous jets powered by the interaction of the black hole with its surrounding plasma. We study the resulting Poynting jet that arises from single boosted black holes and binary black hole systems. In the latter case, we find that increasing the orbital angular momenta of the system and/or the spins of the individual black holes results in an enhanced Poynting flux.
6. The membrane paradigm for black holes
International Nuclear Information System (INIS)
Price, R.H.; Thorne, K.S.
1988-01-01
It is now widely accepted that black holes exist and have an astrophysical role, in particular as the likely power source of quasars. To understand this role with ease, the authors and their colleagues have developed a new paradigm for black holes - a new way to picture, think about and describe them. As far as possible it treats black holes as ordinary astrophysical objects, made of real material. A black hole in this description is a spherical or oblate surface made of a thin, electrically conducting membrane. It was the author's quest to understand the Blandford-Znajek process intuitively that led them to create the membrane paradigm. Their strategy was to translate the general-relativistic mathematics of black holes into the same language of three-dimensional space that is used for magnetized plasmas and to create a new set of black-hole diagrams and pictures to go along with the language. 9 figs
7. Production of spinning black holes at colliders
International Nuclear Information System (INIS)
Park, S. C.; Song, H. S.
2003-01-01
When the Planck scale is as low as TeV, there will be chances to produce Black holes at future colliders. Generally, black holes produced via particle collisions can have non-zero angular momenta. We estimate the production cross-section of rotating Black holes in the context of low energy gravitation theories by taking the effects of rotation into account. The production cross section is shown to be enhanced by a factor of 2 - 3 over the naive estimate σ = π ∼ R S 2 , where R S denotes the Schwarzschild radius of black hole for a given energy. We also point out that the decay spectrum may have a distinguishable angular dependence through the grey-body factor of a rotating black hole. The angular dependence of decaying particles may give a clear signature for the effect of rotating black holes.
8. Hawking temperature of constant curvature black holes
International Nuclear Information System (INIS)
Cai Ronggen; Myung, Yun Soo
2011-01-01
The constant curvature (CC) black holes are higher dimensional generalizations of Banados-Teitelboim-Zanelli black holes. It is known that these black holes have the unusual topology of M D-1 xS 1 , where D is the spacetime dimension and M D-1 stands for a conformal Minkowski spacetime in D-1 dimensions. The unusual topology and time-dependence for the exterior of these black holes cause some difficulties to derive their thermodynamic quantities. In this work, by using a globally embedding approach, we obtain the Hawking temperature of the CC black holes. We find that the Hawking temperature takes the same form when using both the static and global coordinates. Also, it is identical to the Gibbons-Hawking temperature of the boundary de Sitter spaces of these CC black holes.
9. Black-hole bomb and superradiant instabilities
International Nuclear Information System (INIS)
Cardoso, Vitor; Dias, Oscar J.C.; Lemos, Jose P.S.; Yoshida, Shijun
2004-01-01
A wave impinging on a Kerr black hole can be amplified as it scatters off the hole if certain conditions are satisfied, giving rise to superradiant scattering. By placing a mirror around the black hole one can make the system unstable. This is the black-hole bomb of Press and Teukolsky. We investigate in detail this process and compute the growing time scales and oscillation frequencies as a function of the mirror's location. It is found that in order for the system black hole plus mirror to become unstable there is a minimum distance at which the mirror must be located. We also give an explicit example showing that such a bomb can be built. In addition, our arguments enable us to justify why large Kerr-AdS black holes are stable and small Kerr-AdS black holes should be unstable
10. Instability of ultra-spinning black holes
International Nuclear Information System (INIS)
Emparan, Roberto; Myers, Robert C.
2003-01-01
It has long been known that, in higher-dimensional general relativity, there are black hole solutions with an arbitrarily large angular momentum for a fixed mass. We examine the geometry of the event horizon of such ultra-spinning black holes and argue that these solutions become unstable at large enough rotation. Hence we find that higher-dimensional general relativity imposes an effective 'Kerr-bound' on spinning black holes through a dynamical decay mechanism. Our results also give indications of the existence of new stationary black holes with 'rippled' horizons of spherical topology. We consider various scenarios for the possible decay of ultra-spinning black holes, and finally discuss the implications of our results for black holes in braneworld scenarios. (author)
11. Black Feminism: An Integrated Review of Literature.
Science.gov (United States)
Love, Katie L
2016-01-01
This study presents a systematic literature review exploring the uses and potential benefits of Black Feminism in nursing research. Black Feminism may benefit knowledge development for nursing in a variety of ways, such as illuminating the multifaceted factors of Black women's identities in helping scholars move away from generalization of experiences, to improve understanding of health disparities, and making such changes by broadening the social consciousness of the nurse researchers, who are predominantly White. Discrimination in health disparities may be deconstructed if the focus is placed on asking different research questions and offering different interventions with the social structures that contributes to such actions. When Black Feminism guides the research method (including research questions and analysis), the accuracy of representing the experiences of Black women is increased. In this research, Black Feminism highlights experience, coping mechanisms, spiritual values, a tradition of strength, and a holistic view of identity.
12. Posttraumatic stress disorder among black Vietnam veterans.
Science.gov (United States)
Allen, I M
1986-01-01
Because of racism in the military and racial and social upheaval in the United States during the Vietnam War years, as well as limited opportunities for blacks in the postwar period, black veterans of the Vietnam War often harbor conflicting feelings about their wartime experiences and have difficulty rationalizing brutality against the Vietnamese. As a result, black veterans suffer from posttraumatic stress disorder (PTSD) at a higher rate than white veterans. Diagnosis and treatment of PTSD in black veterans is complicated by the tendency to misdiagnose black patients, by the varied manifestations of PTSD, and by patients' frequent alcohol and drug abuse and medical, legal, personality, and vocational problems. The author presents his and others' recommendations about ways to treat black veterans with PTSD.
13. Braneworld black holes and entropy bounds
Directory of Open Access Journals (Sweden)
2018-01-01
Full Text Available The Bousso's D-bound entropy for the various possible black hole solutions on a 4-dimensional brane is checked. It is found that the D-bound entropy here is apparently different from that of obtained for the 4-dimensional black hole solutions. This difference is interpreted as the extra loss of information, associated to the extra dimension, when an extra-dimensional black hole is moved outward the observer's cosmological horizon. Also, it is discussed that N-bound entropy is hold for the possible solutions here. Finally, by adopting the recent Bohr-like approach to black hole quantum physics for the excited black holes, the obtained results are written also in terms of the black hole excited states.
14. Charged topological black hole pair creation
International Nuclear Information System (INIS)
Mann, R.B.
1998-01-01
I examine the pair creation of black holes in space-times with a cosmological constant of either sign. I consider cosmological C-metrics and show that the conical singularities in this metric vanish only for three distinct classes of black hole metric, two of which have compact event horizons on each spatial slice. One class is a generalization of the Reissner-Nordstroem (anti-)de Sitter black holes in which the event horizons are the direct product of a null line with a 2-surface with topology of genus g. The other class consists of neutral black holes whose event horizons are the direct product of a null conoid with a circle. In the presence of a domain wall, black hole pairs of all possible types will be pair created for a wide range of mass and charge, including even negative mass black holes. I determine the relevant instantons and Euclidean actions for each case. (orig.)
15. Reversible Carnot cycle outside a black hole
International Nuclear Information System (INIS)
Xi-Hao, Deng; Si-Jie, Gao
2009-01-01
A Carnot cycle outside a Schwarzschild black hole is investigated in detail. We propose a reversible Carnot cycle with a black hole being the cold reservoir. In our model, a Carnot engine operates between a hot reservoir with temperature T 1 and a black hole with Hawking temperature T H . By naturally extending the ordinary Carnot cycle to the black hole system, we show that the thermal efficiency for a reversible process can reach the maximal efficiency 1 – T H /T 1 . Consequently, black holes can be used to determine the thermodynamic temperature by means of the Carnot cycle. The role of the atmosphere around the black hole is discussed. We show that the thermal atmosphere provides a necessary mechanism to make the process reversible. (general)
16. Charged black holes with scalar hair
Energy Technology Data Exchange (ETDEWEB)
Fan, Zhong-Ying; Lü, H. [Center for Advanced Quantum Studies, Department of Physics,Beijing Normal University, Beijing 100875 (China)
2015-09-10
We consider a class of Einstein-Maxwell-Dilaton theories, in which the dilaton coupling to the Maxwell field is not the usual single exponential function, but one with a stationary point. The theories admit two charged black holes: one is the Reissner-Nordstrøm (RN) black hole and the other has a varying dilaton. For a given charge, the new black hole in the extremal limit has the same AdS{sub 2}×Sphere near-horizon geometry as the RN black hole, but it carries larger mass. We then introduce some scalar potentials and obtain exact charged AdS black holes. We also generalize the results to black p-branes with scalar hair.
17. Information Retention by Stringy Black Holes
CERN Document Server
Ellis, John
2015-01-01
Building upon our previous work on two-dimensional stringy black holes and its extension to spherically-symmetric four-dimensional stringy black holes, we show how the latter retain information. A key r\\^ole is played by an infinite-dimensional $W_\\infty$ symmetry that preserves the area of an isolated black-hole horizon and hence its entropy. The exactly-marginal conformal world-sheet operator representing a massless stringy particle interacting with the black hole necessarily includes a contribution from $W_\\infty$ generators in its vertex function. This admixture manifests the transfer of information between the string black hole and external particles. We discuss different manifestations of $W_\\infty$ symmetry in black-hole physics and the connections between them.
18. What does a black hole look like?
CERN Document Server
Bailyn, Charles D
2014-01-01
Emitting no radiation or any other kind of information, black holes mark the edge of the universe--both physically and in our scientific understanding. Yet astronomers have found clear evidence for the existence of black holes, employing the same tools and techniques used to explore other celestial objects. In this sophisticated introduction, leading astronomer Charles Bailyn goes behind the theory and physics of black holes to describe how astronomers are observing these enigmatic objects and developing a remarkably detailed picture of what they look like and how they interact with their surroundings. Accessible to undergraduates and others with some knowledge of introductory college-level physics, this book presents the techniques used to identify and measure the mass and spin of celestial black holes. These key measurements demonstrate the existence of two kinds of black holes, those with masses a few times that of a typical star, and those with masses comparable to whole galaxies--supermassive black holes...
19. Hidden conformal symmetry of extremal black holes
International Nuclear Information System (INIS)
Chen Bin; Long Jiang; Zhang Jiaju
2010-01-01
We study the hidden conformal symmetry of extremal black holes. We introduce a new set of conformal coordinates to write the SL(2,R) generators. We find that the Laplacian of the scalar field in many extremal black holes, including Kerr(-Newman), Reissner-Nordstrom, warped AdS 3 , and null warped black holes, could be written in terms of the SL(2,R) quadratic Casimir. This suggests that there exist dual conformal field theory (CFT) descriptions of these black holes. From the conformal coordinates, the temperatures of the dual CFTs could be read directly. For the extremal black hole, the Hawking temperature is vanishing. Correspondingly, only the left (right) temperature of the dual CFT is nonvanishing, and the excitations of the other sector are suppressed. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction.
20. Shaping Globular Clusters with Black Holes
Science.gov (United States)
Kohler, Susanna
2018-03-01
How many black holes lurk within the dense environments of globular clusters, and how do these powerful objects shape the properties of the cluster around them? One such cluster, NGC 3201, is now helping us to answer these questions.Hunting Stellar-Mass Black HolesSince the detection of merging black-hole binaries by the Laser Interferometer Gravitational-Wave Observatory (LIGO), the dense environments of globular clusters have received increasing attention as potential birthplaces of these compact binary systems.The central region of the globular star cluster NGC 3201, as viewed by Hubble. The black hole is in orbit with the star marked by the blue circle. [NASA/ESA]In addition, more and more stellar-mass black-hole candidates have been observed within globular clusters, lurking in binary pairs with luminous, non-compact companions. The most recent of these detections, found in the globular cluster NGC 3201, stands alone as the first stellar-mass black hole candidate discovered via radial velocity observations: the black holes main-sequence companion gave away its presence via a telltale wobble.Now a team of scientists led by Kyle Kremer (CIERA and Northwestern University) is using models of this system to better understand the impact that black holes might have on their host clusters.A Model ClusterThe relationship between black holes and their host clusters is complicated. Though the cluster environment can determine the dynamical evolution of the black holes, the retention rate of black holes in a globular cluster (i.e., how many remain in the cluster when they are born as supernovae, rather than being kicked out during the explosion) influences how the host cluster evolves.Kremer and collaborators track this complex relationship by modeling the evolution of a cluster similar to NGC 3201 with a Monte Carlo code. The code incorporates physics relevant to the evolution of black holes and black-hole binaries in globular clusters, such as two-body relaxation
1. Seeding black holes in cosmological simulations
Science.gov (United States)
Taylor, P.; Kobayashi, C.
2014-08-01
We present a new model for the formation of black holes in cosmological simulations, motivated by the first star formation. Black holes form from high density peaks of primordial gas, and grow via both gas accretion and mergers. Massive black holes heat the surrounding material, suppressing star formation at the centres of galaxies, and driving galactic winds. We perform an investigation into the physical effects of the model parameters, and obtain a best' set of these parameters by comparing the outcome of simulations to observations. With this best set, we successfully reproduce the cosmic star formation rate history, black hole mass-velocity dispersion relation, and the size-velocity dispersion relation of galaxies. The black hole seed mass is ˜103 M⊙, which is orders of magnitude smaller than that which has been used in previous cosmological simulations with active galactic nuclei, but suggests that the origin of the seed black holes is the death of Population III stars.
2. Is there life inside black holes?
International Nuclear Information System (INIS)
Dokuchaev, V I
2011-01-01
Bound inside rotating or charged black holes, there are stable periodic planetary orbits, which neither come out nor terminate at the central singularity. Stable periodic orbits inside black holes exist even for photons. These bound orbits may be defined as orbits of the third kind, following the Chandrasekhar classification of particle orbits in the black hole gravitational field. The existence domain for the third-kind orbits is rather spacious, and thus there is place for life inside supermassive black holes in the galactic nuclei. Interiors of the supermassive black holes may be inhabited by civilizations, being invisible from the outside. In principle, one can get information from the interiors of black holes by observing their white hole counterparts. (paper)
3. Measuring the spins of accreting black holes
International Nuclear Information System (INIS)
McClintock, Jeffrey E; Narayan, Ramesh; Gou, Lijun; Kulkarni, Akshay; Penna, Robert F; Steiner, James F; Davis, Shane W; Orosz, Jerome A; Remillard, Ronald A
2011-01-01
A typical galaxy is thought to contain tens of millions of stellar-mass black holes, the collapsed remnants of once massive stars, and a single nuclear supermassive black hole. Both classes of black holes accrete gas from their environments. The accreting gas forms a flattened orbiting structure known as an accretion disk. During the past several years, it has become possible to obtain measurements of the spins of the two classes of black holes by modeling the x-ray emission from their accretion disks. Two methods are employed, both of which depend upon identifying the inner radius of the accretion disk with the innermost stable circular orbit, whose radius depends only on the mass and spin of the black hole. In the Fe Kα method, which applies to both classes of black holes, one models the profile of the relativistically broadened iron line with a special focus on the gravitationally redshifted red wing of the line. In the continuum-fitting (CF) method, which has so far only been applied to stellar-mass black holes, one models the thermal x-ray continuum spectrum of the accretion disk. We discuss both methods, with a strong emphasis on the CF method and its application to stellar-mass black holes. Spin results for eight stellar-mass black holes are summarized. These data are used to argue that the high spins of at least some of these black holes are natal, and that the presence or absence of relativistic jets in accreting black holes is not entirely determined by the spin of the black hole.
4. Gravitational lensing by a Horndeski black hole
Energy Technology Data Exchange (ETDEWEB)
Badia, Javier [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Eiroa, Ernesto F. [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2017-11-15
In this article we study gravitational lensing by non-rotating and asymptotically flat black holes in Horndeski theory. By adopting the strong deflection limit, we calculate the deflection angle, from which we obtain the positions and the magnifications of the relativistic images. We compare our results with those corresponding to black holes in General Relativity. We analyze the astrophysical consequences in the case of the nearest supermassive black holes. (orig.)
5. Influence functionals and black body radiation
OpenAIRE
Anglin, J. R.
1993-01-01
The Feynman-Vernon formalism is used to obtain a microscopic, quantum mechanical derivation of black body radiation, for a massless scalar field in 1+1 dimensions, weakly coupled to an environment of finite size. The model exhibits the absorption, thermal equilibrium, and emission properties of a canonical black body, but shows that the thermal radiation propagates outwards from the body, with the Planckian spectrum applying inside a wavefront region of finite thickness. The black body enviro...
6. Unified geometric description of black hole thermodynamics
International Nuclear Information System (INIS)
Alvarez, Jose L.; Quevedo, Hernando; Sanchez, Alberto
2008-01-01
In the space of thermodynamic equilibrium states we introduce a Legendre invariant metric which contains all the information about the thermodynamics of black holes. The curvature of this thermodynamic metric becomes singular at those points where, according to the analysis of the heat capacities, phase transitions occur. This result is valid for the Kerr-Newman black hole and all its special cases and, therefore, provides a unified description of black hole phase transitions in terms of curvature singularities.
7. Effective Stringy Description of Schwarzschild Black Holes
OpenAIRE
Krasnov , Kirill; Solodukhin , Sergey N.
2004-01-01
We start by pointing out that certain Riemann surfaces appear rather naturally in the context of wave equations in the black hole background. For a given black hole there are two closely related surfaces. One is the Riemann surface of complexified tortoise'' coordinate. The other Riemann surface appears when the radial wave equation is interpreted as the Fuchsian differential equation. We study these surfaces in detail for the BTZ and Schwarzschild black holes in four and higher dimensions....
8. Gravitational lensing by a Horndeski black hole
International Nuclear Information System (INIS)
2017-01-01
In this article we study gravitational lensing by non-rotating and asymptotically flat black holes in Horndeski theory. By adopting the strong deflection limit, we calculate the deflection angle, from which we obtain the positions and the magnifications of the relativistic images. We compare our results with those corresponding to black holes in General Relativity. We analyze the astrophysical consequences in the case of the nearest supermassive black holes. (orig.)
9. Statistical Mechanics and Black Hole Thermodynamics
OpenAIRE
Carlip, Steven
1997-01-01
Black holes are thermodynamic objects, but despite recent progress, the ultimate statistical mechanical origin of black hole temperature and entropy remains mysterious. Here I summarize an approach in which the entropy is viewed as arising from would-be pure gauge'' degrees of freedom that become dynamical at the horizon. For the (2+1)-dimensional black hole, these degrees of freedom can be counted, and yield the correct Bekenstein-Hawking entropy; the corresponding problem in 3+1 dimension...
10. A New Model of Black Hole Formation
Directory of Open Access Journals (Sweden)
Thayer G. D.
2013-10-01
Full Text Available The formation of a black hole and its event horizon are described. Conclusions, which are the result of a thought experiment, show that Schwarzschild [1] was correct: A singularity develops at the event horizon of a newly-formed black hole. The intense gravitational field that forms near the event horizon results in the mass-energy of the black hole accumulating in a layer just inside the event horizon, rather than collapsing into a central singularity.
11. Semiclassical Approach to Black Hole Evaporation
OpenAIRE
Lowe, David A.
1992-01-01
Black hole evaporation may lead to massive or massless remnants, or naked singularities. This paper investigates this process in the context of two quite different two dimensional black hole models. The first is the original CGHS model, the second is another two dimensional dilaton-gravity model, but with properties much closer to physics in the real, four dimensional, world. Numerical simulations are performed of the formation and subsequent evaporation of black holes and the results are fou...
12. Observability of Quantum State of Black Hole
CERN Document Server
David, J R; Mandal, G; Wadia, S R; David, Justin R.; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R.
1997-01-01
We analyze terms subleading to Rutherford in the $S$-matrix between black hole and probes of successively high energies. We show that by an appropriate choice of the probe one can read off the quantum state of the black hole from the S-matrix, staying asymptotically far from the BH all the time. We interpret the scattering experiment as scattering off classical stringy backgrounds which explicitly depend on the internal quantum numbers of the black hole.
13. Black-swan events in animal populations
OpenAIRE
Anderson, Sean C.; Branch, Trevor A.; Cooper, Andrew B.; Dulvy, Nicholas K.
2017-01-01
Black swans?statistically improbable events with profound consequences?happen more often than expected in financial, social, and natural systems. Our work demonstrates the rare but systematic presence of black-swan events in animal populations around the world (mostly birds, mammals, and insects). These events are predominantly downward, implying that unexpected population crashes occur more frequently than increases. Black-swan events are not driven by life history (e.g., lifespan) but by ex...
14. Test fields cannot destroy extremal black holes
International Nuclear Information System (INIS)
Natário, José; Queimada, Leonel; Vicente, Rodrigo
2016-01-01
We prove that (possibly charged) test fields satisfying the null energy condition at the event horizon cannot overspin/overcharge extremal Kerr–Newman or Kerr–Newman–anti de Sitter black holes, that is, the weak cosmic censorship conjecture cannot be violated in the test field approximation. The argument relies on black hole thermodynamics (without assuming cosmic censorship), and does not depend on the precise nature of the fields. We also discuss generalizations of this result to other extremal black holes. (paper)
15. #BlackBabiesMatter: Analyzing Black Religious Media in Conservative and Progressive Evangelical Communities
Directory of Open Access Journals (Sweden)
Monique Moultrie
2017-11-01
Full Text Available This article explores how conservative and progressive black Protestants interrogate the theological theme of the sacrality of black life through digital media. The innovations of religious media in black evangelical communities remain an understudied phenomenon in African American religion, making this an apt arena for further discovery. This current intervention into the study of African American Religion examines digital activism through examples of religious media produced by blacks for black audiences. This article begins its interrogation of the sacrality of black life by juxtaposing those who contend that Black Babies Matter as pro-birth-oriented, religiously motivated activists with those religious opponents asserting Black Lives Matter who present an intersectional pro-life approach. The comparison of views relies on womanist cultural analysis as its main methodology to analyze and interpret digital media and explore its ramifications for African American Religion.
16. Low-mass black holes as the remnants of primordial black hole formation.
Science.gov (United States)
Greene, Jenny E
2012-01-01
Bridging the gap between the approximately ten solar mass 'stellar mass' black holes and the 'supermassive' black holes of millions to billions of solar masses are the elusive 'intermediate-mass' black holes. Their discovery is key to understanding whether supermassive black holes can grow from stellar-mass black holes or whether a more exotic process accelerated their growth soon after the Big Bang. Currently, tentative evidence suggests that the progenitors of supermassive black holes were formed as ∼10(4)-10(5) M(⊙) black holes via the direct collapse of gas. Ongoing searches for intermediate-mass black holes at galaxy centres will help shed light on this formation mechanism.
17. Magnetized black holes and black rings in the higher dimensional dilaton gravity
International Nuclear Information System (INIS)
2006-01-01
In this paper we consider magnetized black holes and black rings in the higher dimensional dilaton gravity. Our study is based on exact solutions generated by applying a Harrison transformation to known asymptotically flat black hole and black ring solutions in higher dimensional spacetimes. The explicit solutions include the magnetized version of the higher dimensional Schwarzschild-Tangherlini black holes, Myers-Perry black holes, and five-dimensional (dipole) black rings. The basic physical quantities of the magnetized objects are calculated. We also discuss some properties of the solutions and their thermodynamics. The ultrarelativistic limits of the magnetized solutions are briefly discussed and an explicit example is given for the D-dimensional magnetized Schwarzschild-Tangherlini black holes
18. Spin One Hawking Radiation from Dirty Black Holes
OpenAIRE
Petarpa Boonserm; Tritos Ngampitipan; Matt Visser
2013-01-01
A “clean” black hole is a black hole in vacuum such as the Schwarzschild black hole. However in real physical systems, there are matter fields around a black hole. Such a black hole is called a “dirty black hole”. In this paper, the effect of matter fields on the black hole and the greybody factor is investigated. The results show that matter fields make a black hole smaller. They can increase the potential energy to a black hole to obstruct Hawking radiation to propagate. This causes the gre...
19. Hawking radiation and strong gravity black holes
International Nuclear Information System (INIS)
1979-01-01
It is shown that the strong gravity theory of Salam et al. places severe restrictions on black hole evaporation. Two major implications are that: mini blck holes (down to masses approximately 10 -16 kg) would be stable in the present epoch; and that some suggested mini black hole mechanisms to explain astrophysical phenomena would not work. The first result implies that f-gravity appears to make black holes much safer by removing the possibility of extremely violent black hole explosions suggested by Hawking. (Auth.)
20. Tidal interactions with Kerr black holes
International Nuclear Information System (INIS)
Hiscock, W.A.
1977-01-01
The tidal deformation of an extended test body falling with zero angular momentum into a Kerr black hole is calculated. Numerical results for infall along the symmetry axis and in the equatorial plane of the black hole are presented for a range of values of a, the specific angular momentum of the black hole. Estimates of the tidal contribution to the gravitational radiation are also given. The tidal contribution in equatorial infall into a maximally rotating Kerr black hole may be of the same order as the center-of-mass contribution to the gravitational radiation
1. Noncommutative Black Holes at the LHC
Science.gov (United States)
Villhauer, Elena Michelle
2017-12-01
Based on the latest public results, 13 TeV data from the Large Hadron Collider at CERN has not indicated any evidence of hitherto tested models of quantum black holes, semiclassical black holes, or string balls. Such models have predicted signatures of particles with high transverse momenta. Noncommutative black holes remain an untested model of TeV-scale gravity that offers the starkly different signature of particles with relatively low transverse momenta. Considerations for a search for charged noncommutative black holes using the ATLAS detector will be discussed.
2. Entropy evaporated by a black hole
International Nuclear Information System (INIS)
Zurek, W.H.
1982-01-01
It is shown that the entropy of the radiation evaporated by an uncharged, nonrotating black hole into vacuum in the course of its lifetime is approximately (4/3) times the initial entropy of this black hole. Also considered is a thermodynamically reversible process in which an increase of black-hole entropy is equal to the decrease of the entropy of its surroundings. Implications of these results for the generalized second law of thermodynamics and for the interpretation of black-hole entropy are pointed out
3. Black hole evaporation in conformal gravity
Energy Technology Data Exchange (ETDEWEB)
Bambi, Cosimo; Rachwał, Lesław [Center for Field Theory and Particle Physics and Department of Physics, Fudan University, 220 Handan Road, 200433 Shanghai (China); Modesto, Leonardo [Department of Physics, Southern University of Science and Technology, 1088 Xueyuan Road, Shenzhen 518055 (China); Porey, Shiladitya, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Department of Physics, Indian Institute of Technology, 208016 Kanpur (India)
2017-09-01
We study the formation and the evaporation of a spherically symmetric black hole in conformal gravity. From the collapse of a spherically symmetric thin shell of radiation, we find a singularity-free non-rotating black hole. This black hole has the same Hawking temperature as a Schwarzschild black hole with the same mass, and it completely evaporates either in a finite or in an infinite time, depending on the ensemble. We consider the analysis both in the canonical and in the micro-canonical statistical ensembles. Last, we discuss the corresponding Penrose diagram of this physical process.
4. On algebraically special perturbations of black holes
International Nuclear Information System (INIS)
Chandrasekhar, S.
1984-01-01
Algebraically special perturbations of black holes excite gravitational waves that are either purely ingoing or purely outgoing. Solutions, appropriate to such perturbations of the Kerr, the Schwarzschild, and the Reissner-Nordstroem black-holes, are obtained in explicit forms by different methods. The different methods illustrate the remarkable inner relations among different facets of the mathematical theory. In the context of the Kerr black-hole they derive from the different ways in which the explicit value of the Starobinsky constant emerges, and in the context of the Schwarzschild and the Reissner-Nordstroem black-holes they derive from the potential barriers surrounding them belonging to a special class. (author)
5. New geometries for black hole horizons
Energy Technology Data Exchange (ETDEWEB)
Armas, Jay [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine CP231, B-1050 Brussels (Belgium); Blau, Matthias [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland)
2015-07-10
We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D≥6.
6. The statistical clustering of primordial black holes
International Nuclear Information System (INIS)
Carr, B.J.
1977-01-01
It is shown that Meszaros theory of galaxy formation, in which galaxies form from the density perturbations associated with the statistical fluctuation in the number density of primordial black holes, must be modified if the black holes are initially surrounded by regions of lower radiation density than average (as is most likely). However, even in this situation, the sort of effect Meszaros envisages does occur and could in principle cause galactic mass-scales to bind at the conventional time. In fact, the requirement that galaxies should not form prematurely implies that black holes could not have a critical density in the mass range above 10 5 M(sun). If the mass spectrum of primordial black holes falls off more slowly than m -3 (as expected), then the biggest black holes have the largest clustering effect. In this case the black hole clustering theory of galaxy formation reduces to the black hole seed theory of galaxy formation, in which each galaxy becomes bound under the gravitational influence of a single black hole nucleus. The seed theory could be viable only if the early Universe had a soft equation of state until a time exceeding 10 -4 s or if something prevented black hole formation before 1 s. (orig.) [de
7. The horizon of the lightest black hole
Energy Technology Data Exchange (ETDEWEB)
Calmet, Xavier [University of Sussex, Physics and Astronomy, Falmer, Brighton (United Kingdom); Casadio, Roberto [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, Bologna (Italy)
2015-09-15
We study the properties of the poles of the resummed graviton propagator obtained by resumming bubble matter diagrams which correct the classical graviton propagator. These poles have been previously interpreted as black holes precursors. Here, we show using the horizon wave-function formalism that these poles indeed have properties which make them compatible with being black hole precursors. In particular, when modeled with a Breit-Wigner distribution, they have a well-defined gravitational radius. The probability that the resonance is inside its own gravitational radius, and thus that it is a black hole, is about one half. Our results confirm the interpretation of these poles as black hole precursors. (orig.)
8. Black Artists' Music Videos: Three Successful Strategies
Science.gov (United States)
Peterson-Lewis, Sonja; Chennault, Shirley A.
1986-01-01
Identifies three successful self-presentational patterns used by black artists to penetrate the music television market. Discusses the historical relationship between minorities and the mass media. (MS)
9. Rotating black holes and Coriolis effect
Directory of Open Access Journals (Sweden)
Chia-Jui Chou
2016-10-01
Full Text Available In this work, we consider the fluid/gravity correspondence for general rotating black holes. By using the suitable boundary condition in near horizon limit, we study the correspondence between gravitational perturbation and fluid equation. We find that the dual fluid equation for rotating black holes contains a Coriolis force term, which is closely related to the angular velocity of the black hole horizon. This can be seen as a dual effect for the frame-dragging effect of rotating black hole under the holographic picture.
10. Black holes with Yang-Mills hair
International Nuclear Information System (INIS)
Kleihaus, B.; Kunz, J.; Sood, A.; Wirschins, M.
1998-01-01
In Einstein-Maxwell theory black holes are uniquely determined by their mass, their charge and their angular momentum. This is no longer true in Einstein-Yang-Mills theory. We discuss sequences of neutral and charged SU(N) Einstein-Yang-Mills black holes, which are static spherically symmetric and asymptotically flat, and which carry Yang-Mills hair. Furthermore, in Einstein-Maxwell theory static black holes are spherically symmetric. We demonstrate that, in contrast, SU(2) Einstein-Yang-Mills theory possesses a sequence of black holes, which are static and only axially symmetric
11. Dirac particle tunneling from black rings
International Nuclear Information System (INIS)
Jiang Qingquan
2008-01-01
Recent research shows that Hawking radiation can be treated as a quantum tunneling process, and Hawking temperatures of Dirac particles across the horizon of a black hole can be correctly recovered via the fermion tunneling method. In this paper, motivated by the fermion tunneling method, we attempt to apply the analysis to derive Hawking radiation of Dirac particles via tunneling from black ring solutions of 5-dimensional Einstein-Maxwell-dilaton gravity theory. Finally, it is interesting to find that, as in the black hole case, fermion tunneling can also result in correct Hawking temperatures for the rotating neutral, dipole, and charged black rings.
12. Micro black holes and the democratic transition
International Nuclear Information System (INIS)
Dvali, Gia; Pujolas, Oriol
2009-01-01
Unitarity implies that the evaporation of microscopic quasiclassical black holes cannot be universal in different particle species. This creates a puzzle, since it conflicts with the thermal nature of quasiclassical black holes, according to which all of the species should see the same horizon and be produced with the same Hawking temperatures. We resolve this puzzle by showing that for the microscopic black holes, on top of the usual quantum evaporation time, there is a new time scale which characterizes a purely classical process during which the black hole loses the ability to differentiate among the species and becomes democratic. We demonstrate this phenomenon in a well-understood framework of large extra dimensions, with a number of parallel branes. An initially nondemocratic black hole is the one localized on one of the branes, with its high-dimensional Schwarzschild radius being much shorter than the interbrane distance. Such a black hole seemingly cannot evaporate into the species localized on the other branes that are beyond its reach. We demonstrate that in reality the system evolves classically in time, in such a way that the black hole accretes the neighboring branes. The end result is a completely democratic static configuration, in which all of the branes share the same black hole and all of the species are produced with the same Hawking temperature. Thus, just like their macroscopic counterparts, the microscopic black holes are universal bridges to the hidden sector physics.
13. Black Holes and Gravitational Properties of Antimatter
CERN Document Server
Hajdukovic, D
2006-01-01
We speculate about impact of antigravity (i.e. gravitational repulsion between matter and antimatter) on the creation and emission of particles by a black hole. If antigravity is present a black hole made of matter may radiate particles as a black body, but this shouldn't be true for antiparticles. It may lead to radical change of radiation process predicted by Hawking and should be taken into account in preparation of the attempt to create and study mini black holes at CERN. Gravity, including antigravity is more than ever similar to electrodynamics and such similarity with a successfully quantized interaction may help in quantization of gravity.
14. Rotating black holes and Coriolis effect
Energy Technology Data Exchange (ETDEWEB)
Chou, Chia-Jui, E-mail: [email protected] [Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan, ROC (China); Wu, Xiaoning, E-mail: [email protected] [Institute of Mathematics, Academy of Mathematics and System Science, CAS, Beijing, 100190 (China); Yang, Yi, E-mail: [email protected] [Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan, ROC (China); Yuan, Pei-Hung, E-mail: [email protected] [Institute of Physics, National Chiao Tung University, Hsinchu, Taiwan, ROC (China)
2016-10-10
In this work, we consider the fluid/gravity correspondence for general rotating black holes. By using the suitable boundary condition in near horizon limit, we study the correspondence between gravitational perturbation and fluid equation. We find that the dual fluid equation for rotating black holes contains a Coriolis force term, which is closely related to the angular velocity of the black hole horizon. This can be seen as a dual effect for the frame-dragging effect of rotating black hole under the holographic picture.
15. Black Hole Universe Model and Dark Energy
Science.gov (United States)
Zhang, Tianxi
2011-01-01
Considering black hole as spacetime and slightly modifying the big bang theory, the author has recently developed a new cosmological model called black hole universe, which is consistent with Mach principle and Einsteinian general relativity and self consistently explains various observations of the universe without difficulties. According to this model, the universe originated from a hot star-like black hole and gradually grew through a supermassive black hole to the present universe by accreting ambient material and merging with other black holes. The entire space is infinitely and hierarchically layered and evolves iteratively. The innermost three layers are the universe that we lives, the outside space called mother universe, and the inside star-like and supermassive black holes called child universes. The outermost layer has an infinite radius and zero limits for both the mass density and absolute temperature. All layers or universes are governed by the same physics, the Einstein general relativity with the Robertson-Walker metric of spacetime, and tend to expand outward physically. When one universe expands out, a new similar universe grows up from its inside black holes. The origin, structure, evolution, expansion, and cosmic microwave background radiation of black hole universe have been presented in the recent sequence of American Astronomical Society (AAS) meetings and published in peer-review journals. This study will show how this new model explains the acceleration of the universe and why dark energy is not required. We will also compare the black hole universe model with the big bang cosmology.
16. On the thermodynamics of hairy black holes
Energy Technology Data Exchange (ETDEWEB)
Anabalón, Andrés [Departamento de Ciencias, Facultad de Artes Liberales y Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Viña del Mar (Chile); Astefanesei, Dumitru [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Choque, David, E-mail: [email protected] [Universidad Técnica Federico Santa María, Av. España 1680, Valparaiso (Chile)
2015-04-09
We investigate the thermodynamics of a general class of exact 4-dimensional asymptotically Anti-de Sitter hairy black hole solutions and show that, for a fixed temperature, there are small and large hairy black holes similar to the Schwarzschild–AdS black hole. The large black holes have positive specific heat and so they can be in equilibrium with a thermal bath of radiation at the Hawking temperature. The relevant thermodynamic quantities are computed by using the Hamiltonian formalism and counterterm method. We explicitly show that there are first order phase transitions similar to the Hawking–Page phase transition.
17. Destroying black holes with test bodies
Energy Technology Data Exchange (ETDEWEB)
Jacobson, Ted [Center for Fundamental Physics, University of Maryland, College Park, MD 20742-4111 (United States); Sotiriou, Thomas P, E-mail: [email protected], E-mail: [email protected] [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)
2010-04-01
If a black hole can accrete a body whose spin or charge would send the black hole parameters over the extremal limit, then a naked singularity would presumably form, in violation of the cosmic censorship conjecture. We review some previous results on testing cosmic censorship in this way using the test body approximation, focusing mostly on the case of neutral black holes. Under certain conditions a black hole can indeed be over-spun or over-charged in this approximation, hence radiative and self-force effects must be taken into account to further test cosmic censorship.
18. Charged black holes in phantom cosmology
Energy Technology Data Exchange (ETDEWEB)
Jamil, Mubasher; Qadir, Asghar; Rashid, Muneer Ahmad [National University of Sciences and Technology, Center for Advanced Mathematics and Physics, Rawalpindi (Pakistan)
2008-11-15
In the classical relativistic regime, the accretion of phantom-like dark energy onto a stationary black hole reduces the mass of the black hole. We have investigated the accretion of phantom energy onto a stationary charged black hole and have determined the condition under which this accretion is possible. This condition restricts the mass-to-charge ratio in a narrow range. This condition also challenges the validity of the cosmic-censorship conjecture since a naked singularity is eventually produced due to accretion of phantom energy onto black hole. (orig.)
19. Destroying black holes with test bodies
International Nuclear Information System (INIS)
Jacobson, Ted; Sotiriou, Thomas P
2010-01-01
If a black hole can accrete a body whose spin or charge would send the black hole parameters over the extremal limit, then a naked singularity would presumably form, in violation of the cosmic censorship conjecture. We review some previous results on testing cosmic censorship in this way using the test body approximation, focusing mostly on the case of neutral black holes. Under certain conditions a black hole can indeed be over-spun or over-charged in this approximation, hence radiative and self-force effects must be taken into account to further test cosmic censorship.
20. Statistical clustering of primordial black holes
Energy Technology Data Exchange (ETDEWEB)
Carr, B J [Cambridge Univ. (UK). Inst. of Astronomy
1977-04-01
It is shown that Meszaros theory of galaxy formation, in which galaxies form from the density perturbations associated with the statistical fluctuation in the number density of primordial black holes, must be modified if the black holes are initially surrounded by regions of lower radiation density than average (as is most likely). However, even in this situation, the sort of effect Meszaros envisages does occur and could in principle cause galactic mass-scales to bind at the conventional time. In fact, the requirement that galaxies should not form prematurely implies that black holes could not have a critical density in the mass range above 10/sup 5/ M(sun). If the mass spectrum of primordial black holes falls off more slowly than m/sup -3/ (as expected), then the biggest black holes have the largest clustering effect. In this case the black hole clustering theory of galaxy formation reduces to the black hole seed theory of galaxy formation, in which each galaxy becomes bound under the gravitational influence of a single black hole nucleus. The seed theory could be viable only if the early Universe had a soft equation of state until a time exceeding 10/sup -4/ s or if something prevented black hole formation before 1 s.
1. Schwarzschild black holes can wear scalar wigs.
Science.gov (United States)
Barranco, Juan; Bernal, Argelia; Degollado, Juan Carlos; Diez-Tejedor, Alberto; Megevand, Miguel; Alcubierre, Miguel; Núñez, Darío; Sarbach, Olivier
2012-08-24
We study the evolution of a massive scalar field surrounding a Schwarzschild black hole and find configurations that can survive for arbitrarily long times, provided the black hole or the scalar field mass is small enough. In particular, both ultralight scalar field dark matter around supermassive black holes and axionlike scalar fields around primordial black holes can survive for cosmological times. Moreover, these results are quite generic in the sense that fairly arbitrary initial data evolve, at late times, as a combination of those long-lived configurations.
2. Particle accelerators inside spinning black holes.
Science.gov (United States)
Lake, Kayll
2010-05-28
On the basis of the Kerr metric as a model for a spinning black hole accreting test particles from rest at infinity, I show that the center-of-mass energy for a pair of colliding particles is generically divergent at the inner horizon. This shows not only that classical black holes are internally unstable, but also that Planck-scale physics is a characteristic feature within black holes at scales much larger that the Planck length. The novel feature of the divergence discussed here is that the phenomenon is present only for black holes with rotation, and in this sense it is distinct from the well-known Cauchy horizon instability.
3. Causticizing for Black Liquor Gasifiers
Energy Technology Data Exchange (ETDEWEB)
Scott Sinquefeld; James Cantrell; Xiaoyan Zeng; Alan Ball; Jeff Empie
2009-01-07
The cost-benefit outlook of black liquor gasification (BLG) could be greatly improved if the smelt causticization step could be achieved in situ during the gasification step. Or, at a minimum, the increase in causticizing load associated with BLG could be mitigated. A number of chemistries have been proven successful during black liquor combustion. In this project, three in situ causticizing processes (titanate, manganate, and borate) were evaluated under conditions suitable for high temperature entrained flow BLG, and low temperature steam reforming of black liquor. The evaluation included both thermodynamic modeling and lab experimentation. Titanate and manganate were tested for complete direct causticizing (to thus eliminate the lime cycle), and borates were evaluated for partial causticizing (to mitigate the load increase associated with BLG). Criteria included high carbonate conversion, corresponding hydroxide recovery upon hydrolysis, non process element (NPE) removal, and economics. Of the six cases (three chemistries at two BLG conditions), only two were found to be industrially viable: titanates for complete causticizing during high temperature BLG, and borates for partial causticizing during high temperature BLG. These two cases were evaluated for integration into a gasification-based recovery island. The Larsen [28] BLG cost-benefit study was used as a reference case for economic forecasting (i.e. a 1500 tpd pulp mill using BLG and upgrading the lime cycle). By comparison, using the titanate direct causticizing process yielded a net present value (NPV) of $25M over the NPV of BLG with conventional lime cycle. Using the existing lime cycle plus borate autocausticizing for extra capacity yielded a NPV of$16M.
4. Ten Myths, Half-Truths and Misunderstandings About Black History.
Science.gov (United States)
Ruffins, Paul
1997-01-01
Common myths and misconceptions about Blacks in American history and evidence that refutes them are presented. Issues addressed include Black enslavement patterns, social status within the Black community based on skin color, the legality of slaves learning to read, resistance to slavery, African influences in modern Black culture, Black names and…
5. The Films of Oscar Micheaux: America's First Fabulous Black Filmmaker.
Science.gov (United States)
Peterson, Bernard L., Jr.
1979-01-01
Although Oscar Micheaux was not the first Black American filmmaker, he was undoubtedly the most prolific Black American movie producer. He is credited with making the first full-length, all-Black silent film produced by a Black company, as well as the first full-length, all-Black sound film. (Author/MC)
6. Thermodynamic light on black holes
International Nuclear Information System (INIS)
Davies, P.
1977-01-01
The existence of black holes and their relevance to our understanding of the nature of space and time are considered, with especial reference to the application of thermodynamic arguments which can reveal their energy-transfer processes in a new light. The application of thermodynamics to strongly gravitating systems promises some fascinating new insights into the nature of gravity. Situations can occur during gravitational collapse in which existing physics breaks down. Under these circumstances, the application of universal thermodynamical principles might be our only guide. (U.K.)
7. Falling into a black hole
OpenAIRE
Mathur, Samir D.
2007-01-01
String theory tells us that quantum gravity has a dual description as a field theory (without gravity). We use the field theory dual to ask what happens to an object as it falls into the simplest black hole: the 2-charge extremal hole. In the field theory description the wavefunction of a particle is spread over a large number of loops', and the particle has a well-defined position in space only if it has the same `position' on each loop. For the infalling particle we find one definition of ...
8. Black Sea coastal forecasting system
Directory of Open Access Journals (Sweden)
A. I. Kubryakov
2012-03-01
Full Text Available The Black Sea coastal nowcasting and forecasting system was built within the framework of EU FP6 ECOOP (European COastalshelf sea OPerational observing and forecasting system project for five regions: the south-western basin along the coasts of Bulgaria and Turkey, the north-western shelf along the Romanian and Ukrainian coasts, coastal zone around of the Crimea peninsula, the north-eastern Russian coastal zone and the coastal zone of Georgia. The system operates in the real-time mode during the ECOOP project and afterwards. The forecasts include temperature, salinity and current velocity fields. Ecosystem model operates in the off-line mode near the Crimea coast.
9. REFRACTORY FOR BLACK LIQUOR GASIFIERS
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr; Musa Karakus; Jun Wei
2005-03-01
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the material problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
10. Black History, Inc! Investigating the Production of Black History through Walmart's Corporate Web Site
Science.gov (United States)
King, LaGarrett J.; Brown, Anthony L.
2012-01-01
Social and public sites are becoming a popular medium for intellectual consumption of Black history. Given the educational climate in which many students' exposure to Black history may come from outside of schools, the authors examine how Walmart's Black History Month Web site produced simplistic and safe narratives about African American history.
11. Adaptability of black walnut, black cherry, and Northern red oak to Northern California
Science.gov (United States)
Philip M. McDonald
1987-01-01
When planted in sheltered sites in northern California, only 49% of black walnut (Juglans nigra L.) and 58% of black cherry (Prunus serotina Ehrh.) survived for 15 years, and 20% of northern red oak (Quercus rubra L.) survived for 10 years. The black walnut trees averaged 0.6 inches diameter at breast...
12. Is It because I'm Black? A Black Female Research Experience
Science.gov (United States)
Maylor, Uvanney
2009-01-01
This article examines what it means to be a Black female researcher in contemporary Britain. Drawing on Black feminist theory and critical race theory (CRT), this article seeks to highlight some of the experiences and challenges that Black female researchers face when undertaking research, particularly research that has diversity, equality or…
13. Retaining Black Teachers: An Examination of Black Female Teachers' Intentions to Remain in K-12 Classrooms
Science.gov (United States)
Farinde, Abiola A.; Allen, Ayana; Lewis, Chance W.
2016-01-01
Sixty years after "Brown v. Board of Education," retention trends indicate that there is a Black teacher shortage. Research shows that Black teachers' retention rates are often lower than the retention rates of White teachers. Black teachers report low salaries, lack of administrative support, and other school variables as reasons for…
14. Why Are Black Employers More Likely Than White Employers To Hire Blacks? Discussion Paper.
Science.gov (United States)
Stoll, Michael A.; Raphael, Steven; Holzer, Harry J.
This study investigated why black employers tend to hire blacks at higher rates than do white employers and examined individual steps in the hiring process, the role of the hiring agent's race, and the degree to which variation in black application rates related to differences in observable characteristics, such as an establishment's physical…
15. "Styled by Their Perceptions": Black Adolescent Girls Interpret Representations of Black Females in Popular Culture
Science.gov (United States)
Muhammad, Gholnecsar E.; McArthur, Sherell A.
2015-01-01
Identity formation is a critical process shaping the lives of adolescents and can present distinct challenges for Black adolescent girls who are positioned in society to negotiate ideals of self when presented with false and incomplete images representing Black girlhood. Researchers have found distorted images of Black femininity derived from…
16. From Black Power to Black Studies: How a Radical Social Movement became an Academic Discipline
Science.gov (United States)
Rojas, Fabio
2007-01-01
The black power movement helped redefine African Americans' identity and establish a new racial consciousness in the 1960s. As an influential political force, this movement in turn spawned the academic discipline known as Black Studies. Today there are more than a hundred Black Studies degree programs in the United States, many of them located in…
17. NASA Observatory Confirms Black Hole Limits
Science.gov (United States)
2005-02-01
The very largest black holes reach a certain point and then grow no more, according to the best survey to date of black holes made with NASA's Chandra X-ray Observatory. Scientists have also discovered many previously hidden black holes that are well below their weight limit. These new results corroborate recent theoretical work about how black holes and galaxies grow. The biggest black holes, those with at least 100 million times the mass of the Sun, ate voraciously during the early Universe. Nearly all of them ran out of 'food' billions of years ago and went onto a forced starvation diet. Focus on Black Holes in the Chandra Deep Field North Focus on Black Holes in the Chandra Deep Field North On the other hand, black holes between about 10 and 100 million solar masses followed a more controlled eating plan. Because they took smaller portions of their meals of gas and dust, they continue growing today. "Our data show that some supermassive black holes seem to binge, while others prefer to graze", said Amy Barger of the University of Wisconsin in Madison and the University of Hawaii, lead author of the paper describing the results in the latest issue of The Astronomical Journal (Feb 2005). "We now understand better than ever before how supermassive black holes grow." One revelation is that there is a strong connection between the growth of black holes and the birth of stars. Previously, astronomers had done careful studies of the birthrate of stars in galaxies, but didn't know as much about the black holes at their centers. DSS Optical Image of Lockman Hole DSS Optical Image of Lockman Hole "These galaxies lose material into their central black holes at the same time that they make their stars," said Barger. "So whatever mechanism governs star formation in galaxies also governs black hole growth." Astronomers have made an accurate census of both the biggest, active black holes in the distance, and the relatively smaller, calmer ones closer by. Now, for the first
18. Spacetime and orbits of bumpy black holes
International Nuclear Information System (INIS)
Vigeland, Sarah J.; Hughes, Scott A.
2010-01-01
Our Universe contains a great number of extremely compact and massive objects which are generally accepted to be black holes. Precise observations of orbital motion near candidate black holes have the potential to determine if they have the spacetime structure that general relativity demands. As a means of formulating measurements to test the black hole nature of these objects, Collins and Hughes introduced ''bumpy black holes'': objects that are almost, but not quite, general relativity's black holes. The spacetimes of these objects have multipoles that deviate slightly from the black hole solution, reducing to black holes when the deviation is zero. In this paper, we extend this work in two ways. First, we show how to introduce bumps which are smoother and lead to better behaved orbits than those in the original presentation. Second, we show how to make bumpy Kerr black holes--objects which reduce to the Kerr solution when the deviation goes to zero. This greatly extends the astrophysical applicability of bumpy black holes. Using Hamilton-Jacobi techniques, we show how a spacetime's bumps are imprinted on orbital frequencies, and thus can be determined by measurements which coherently track the orbital phase of a small orbiting body. We find that in the weak field, orbits of bumpy black holes are modified exactly as expected from a Newtonian analysis of a body with a prescribed multipolar structure, reproducing well-known results from the celestial mechanics literature. The impact of bumps on strong-field orbits is many times greater than would be predicted from a Newtonian analysis, suggesting that this framework will allow observations to set robust limits on the extent to which a spacetime's multipoles deviate from the black hole expectation.
19. Quantum criticality and black holes
International Nuclear Information System (INIS)
Sachdev, Subir; Mueller, Markus
2009-01-01
Many condensed matter experiments explore the finite temperature dynamics of systems near quantum critical points. Often, there are no well-defined quasiparticle excitations, and so quantum kinetic equations do not describe the transport properties completely. The theory shows that the transport coefficients are not proportional to a mean free scattering time (as is the case in the Boltzmann theory of quasiparticles), but are completely determined by the absolute temperature and by equilibrium thermodynamic observables. Recently, explicit solutions of this quantum critical dynamics have become possible via the anti-de Sitter/conformal field theory duality discovered in string theory. This shows that the quantum critical theory provides a holographic description of the quantum theory of black holes in a negatively curved anti-de Sitter space, and relates its transport coefficients to properties of the Hawking radiation from the black hole. We review how insights from this connection have led to new results for experimental systems: (i) the vicinity of the superfluid-insulator transition in the presence of an applied magnetic field, and its possible application to measurements of the Nernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Dirac electrons in graphene and the prediction of a hydrodynamic cyclotron resonance.
20. Gravitating discs around black holes
International Nuclear Information System (INIS)
Karas, V; Hure, J-M; Semerak, O
2004-01-01
Fluid discs and tori around black holes are discussed within different approaches and with the emphasis on the role of disc gravity. First reviewed are the prospects of investigating the gravitational field of a black hole-disc system using analytical solutions of stationary, axially symmetric Einstein equations. Then, more detailed considerations are focused to the middle and outer parts of extended disc-like configurations where relativistic effects are small and the Newtonian description is adequate. Within general relativity, only a static case has been analysed in detail. Results are often very inspiring. However, simplifying assumptions must be imposed: ad hoc profiles of the disc density are commonly assumed and the effects of frame-dragging are completely lacking. Astrophysical discs (e.g. accretion discs in active galactic nuclei) typically extend far beyond the relativistic domain and are fairly diluted. However, self-gravity is still essential for their structure and evolution, as well as for their radiation emission and the impact on the surrounding environment. For example, a nuclear star cluster in a galactic centre may bear various imprints of mutual star-disc interactions, which can be recognized in observational properties, such as the relation between the central mass and stellar velocity dispersion. (topical review)
1. Emissions & Measurements - Black Carbon | Science ...
Science.gov (United States)
Emissions and Measurement (EM) research activities performed within the National Risk Management Research Lab NRMRL) of EPA's Office of Research and Development (ORD) support measurement and laboratory analysis approaches to accurately characterize source emissions, and near source concentrations of air pollutants. They also support integrated Agency research programs (e.g., source to health outcomes) and the development of databases and inventories that assist Federal, state, and local air quality managers and industry implement and comply with air pollution standards. EM research underway in NRMRL supports the Agency's efforts to accurately characterize, analyze, measure and manage sources of air pollution. This pamphlet focuses on the EM research that NRMRL researchers conduct related to black carbon (BC). Black Carbon is a pollutant of concern to EPA due to its potential impact on human health and climate change. There are extensive uncertainties in emissions of BC from stationary and mobile sources. Emissions and Measurement (EM) research activities performed within the National Risk Management Research Lab NRMRL) of EPA's Office of Research and Development (ORD)
2. Wavy strings: Black or bright?
International Nuclear Information System (INIS)
Kaloper, N.; Myers, R.C.; Roussel, H.
1997-01-01
Recent developments in string theory have brought forth considerable interest in time-dependent hair on extended objects. This novel new hair is typically characterized by a wave profile along the horizon and angular momentum quantum numbers l,m in the transverse space. In this work, we present an extensive treatment of such oscillating black objects, focusing on their geometric properties. We first give a theorem of purely geometric nature, stating that such wavy hair cannot be detected by any scalar invariant built out of the curvature and/or matter fields. However, we show that the tidal forces detected by an infalling observer diverge at the open-quotes horizonclose quotes of a black string superposed with a vibration in any mode with l≥1. The same argument applied to longitudinal (l=0) waves detects only finite leading-order tidal forces. We also provide an example with a manifestly smooth metric, proving that at least a certain class of these longitudinal waves have regular horizons. copyright 1997 The American Physical Society
3. Superluminality, black holes and EFT
Energy Technology Data Exchange (ETDEWEB)
Goon, Garrett [Department of Applied Mathematics and Theoretical Physics,Cambridge University, Cambridge, CB3 0WA (United Kingdom); Hinterbichler, Kurt [CERCA, Department of Physics, Case Western Reserve University,10900 Euclid Ave, Cleveland, OH 44106 (United States)
2017-02-27
Under the assumption that a UV theory does not display superluminal behavior, we ask what constraints on superluminality are satisfied in the effective field theory (EFT). We study two examples of effective theories: quantum electrodynamics (QED) coupled to gravity after the electron is integrated out, and the flat-space galileon. The first is realized in nature, the second is more speculative, but they both exhibit apparent superluminality around non-trivial backgrounds. In the QED case, we attempt, and fail, to find backgrounds for which the superluminal signal advance can be made larger than the putative resolving power of the EFT. In contrast, in the galileon case it is easy to find such backgrounds, indicating that if the UV completion of the galileon is (sub)luminal, quantum corrections must become important at distance scales of order the Vainshtein radius of the background configuration, much larger than the naive EFT strong coupling distance scale. Such corrections would be reminiscent of the non-perturbative Schwarzschild scale quantum effects that are expected to resolve the black hole information problem. Finally, a byproduct of our analysis is a calculation of how perturbative quantum effects alter charged Reissner-Nordstrom black holes.
4. Exp(1076) Shades of Black: Aspects of Black Hole Microstates
Science.gov (United States)
Vasilakis, Orestis
In this thesis we examine smooth supergravity solutions known as "microstate geometries". These solutions have neither a horizon, nor a singularity, yet they have the same asymptotic structure and conserved charges as black holes. Specifically we study supersymmetric and extremal non-supersymmetric solutions. The goal of this program is to construct enough microstates to account for the correct scaling behavior of the black hole entropy with respect to the charges within the supergravity approximation. For supersymmetric systems that are ⅛-BPS, microstate geometries account so far only for Q5/4 of the total entropy S ˜ Q3/2, while for non-supersymmetric systems the known microstate geometries are sporadic. For the supersymmetric case we construct solutions with three and four charges. Five-dimensional systems with three and four charges are ⅛-BPS. Thus they admit macroscopic horizons making the supergravity approximation valid. For the three-charge case we present some steps towards the construction of the superstratum, a microstate geometry depending on arbitrary functions of two variables, which is expected to provide the necessary entropy for this class of solutions. Specifically we construct multiple concentric solutions with three electric and two dipole magnetic charges which depend on arbitrary functions of two variables and examine their properties. These solutions have no KKM charge and thus are singular. For the four-charge case we construct microstate geometries by extending results available in the literature for three charges. We find smooth solutions in terms of bubbled geometries with ambipolar Gibbons-Hawking base space and by constructing the relevant supertubes. In the non-supersymmetric case we work with a three-charge system of extremal black holes known as almost-BPS, which provides a controlled way of breaking sypersymmetry. By using supertubes we construct the first systematic example of a family of almost-BPS microstate geometries and
5. REFRACTORY FOR BLACK LIQUOR GASIFIERS
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr.; Alireza Rezaie
2003-12-01
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the materials problems encountered during the operation of low-pressure high-temperature (LFHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
6. Refractory for Black Liquor Gasifiers
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr; Alireza Rezaie
2003-12-01
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the materials problems encountered during the operation of low-pressure high-temperature (LFHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
7. Refractory for Black Liquor Gasifiers
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr; Alireza Rezaie; Xiaoting Liang; Musa Karakus; Jun Wei
2005-12-01
The University of Missouri-Rolla identified materials that permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project was to resolve the material problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study attempted to define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials were selected or developed that reacted with the gasifier environment to form protective surfaces in
8. Refractory for Black Liquor Gasifiers
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr; Musa Karakus; Xiaoting Liang
2005-10-01
The University of Missouri-Rolla identified materials that permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project was to resolve the material problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study attempted to define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials were selected/developed that either react with the gasifier environment to form protective surfaces in
9. Refractory for Black Liquor Gasifiers
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick; Musa Karakus; Alireza Rezaie
2004-03-30
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the material problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
10. REFRACTORY FOR BLACK LIQUOR GASIFIERS
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr; Musa Karakus; Xiaoting Liang; Alireza Rezaie
2004-07-01
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the material problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
11. REFRACTORY FOR BLACK LIQUOR GASIFIERS
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr; Musa Karakus; Xiaoting Liang; Alireza Rezaie
2004-10-01
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the material problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
12. REFRACTORY FOR BLACK LIQUOR GASIFIERS
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr; Musa Karakus; Xiaoting Liang; Jun Wei
2005-01-01
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the material problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
13. REFRACTORY FOR BLACK LIQUOR GASIFIERS
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr; Musa Karakus; Xiaoting Liang; Jun Wei
2005-04-01
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the material problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
14. REFRACTORY FOR BLACK LIQUOR GASIFIERS
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr; Musa Karakus; Xiaoting Liang
2005-07-01
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the material problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
15. REFRACTORY FOR BLACK LIQUOR GASIFIERS
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr.; Alireza Rezaie
2004-04-01
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the materials problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
16. Black Perceptions of the Mayor: An Empirical Test.
Science.gov (United States)
Foster, Lorn S.
1978-01-01
During the past ten years Blacks have increased their participation in the urban political process. In a few urban areas, such as Newark and Detroit, Blacks constitute an electoral majority and have elected Black mayors. (Author/RLV)
17. How Black women make sense of 'White' and 'Black' fashion magazines: a qualitative think aloud study.
Science.gov (United States)
Ogden, Jane; Russell, Sheriden
2013-12-01
This qualitative think aloud study explored how Black women (n = 32) processed information from a White or Black fashion magazine. Comments to the 'White' magazine were characterised by rejection, being critical of the media and ambivalence, whereas they responded to the 'Black' magazine with celebration, identification and a search for depth. Transcending these themes was their self-identity of being a Black woman that was brought to the fore either by a sense of exclusion (White magazine) or engagement (Black magazine). Such an identity provides resilience against the media's thin ideals by minimising the processes of social comparison and internalisation.
18. Quantum capacity of quantum black holes
Science.gov (United States)
2014-03-01
The fate of quantum entanglement interacting with a black hole has been an enduring mystery, not the least because standard curved space field theory does not address the interaction of black holes with matter. We discuss an effective Hamiltonian of matter interacting with a black hole that has a precise analogue in quantum optics and correctly reproduces both spontaneous and stimulated Hawking radiation with grey-body factors. We calculate the quantum capacity of this channel in the limit of perfect absorption, as well as in the limit of a perfectly reflecting black hole (a white hole). We find that the white hole is an optimal quantum cloner, and is isomorphic to the Unruh channel with positive quantum capacity. The complementary channel (across the horizon) is entanglement-breaking with zero capacity, avoiding a violation of the quantum no-cloning theorem. The black hole channel on the contrary has vanishing capacity, while its complement has positive capacity instead. Thus, quantum states can be reconstructed faithfully behind the black hole horizon, but not outside. This work sheds new light on black hole complementarity because it shows that black holes can both reflect and absorb quantum states without violating the no-cloning theorem, and makes quantum firewalls obsolete.
19. BHDD: Primordial black hole binaries code
Science.gov (United States)
Kavanagh, Bradley J.; Gaggero, Daniele; Bertone, Gianfranco
2018-06-01
BHDD (BlackHolesDarkDress) simulates primordial black hole (PBH) binaries that are clothed in dark matter (DM) halos. The software uses N-body simulations and analytical estimates to follow the evolution of PBH binaries formed in the early Universe.
20. Black Hole Interior in Quantum Gravity.
Science.gov (United States)
Nomura, Yasunori; Sanches, Fabio; Weinberg, Sean J
2015-05-22
We discuss the interior of a black hole in quantum gravity, in which black holes form and evaporate unitarily. The interior spacetime appears in the sense of complementarity because of special features revealed by the microscopic degrees of freedom when viewed from a semiclassical standpoint. The relation between quantum mechanics and the equivalence principle is subtle, but they are still consistent.
1. Breeding phenology of African Black Oystercatchers Haematopus ...
African Journals Online (AJOL)
The timing of the start and duration of breeding and the effect of these on breeding productivity were analysed for African Black Oystercatchers Haematopus moquini on Robben Island, South Africa, over three breeding seasons from 2001 to 2004. African Black Oystercatchers have a long breeding season, from November ...
2. The quantum structure of black holes
International Nuclear Information System (INIS)
Mathur, Samir D
2006-01-01
We give an elementary review of black holes in string theory. We discuss black hole entropy from string microstates and Hawking radiation from these states. We then review the structure of two-charge microstates and explore how 'fractionation' can lead to quantum effects over macroscopic length scales of the order of the horizon radius. (topical review)
3. Black Colleges: An Alternative Strategy for Survival.
Science.gov (United States)
Whiting, Albert N.
1988-01-01
Joseph Perkins argued in the "Wall Street Journal" that one-third of the 100 traditionally Black colleges should become two-year institutions. This rebuttal suggests that Black institutions' survival involves planning for new and broader missions in an unsheltered, integrated, competitive environment. (MLW)
4. ATLAS: Black hole production and decay
CERN Multimedia
2004-01-01
This track is an example of simulated data modelled for the ATLAS detector on the Large Hadron Collider (LHC) at CERN, which will begin taking data in 2008. These tracks would be produced if a miniature black hole was produced in the proton-proton collision. Such a small black hole would decay instantly to various particles via a process known as Hawking radiation.
5. Black and white human skin differences
DEFF Research Database (Denmark)
Andersen, Klaus Ejner; Maibach, H I
1979-01-01
This review of black and white human skin differences emphasizes the alleged importance of factors other than the obvious, i.e., skin color. Physicochemical differences and differences in susceptibility to irritants and allergens suggest a more resistant black than white skin. Differences appear...
6. Black Student Retention in Higher Education.
Science.gov (United States)
Lang, Marvel, Ed.; Ford, Clinita A., Ed.
This collection focuses on problems in the recruitment, enrollment and retention of Blacks in higher education in America. The following chapters are provided: "The Black Student Retention Problem in Higher Education: Some Introductory Perspectives" (Marvel Lang); "Early Acceptance and Institutional Linkages in a Model Program of Recruitment,…
7. Educating for Service: Black Studies for Premeds.
Science.gov (United States)
Henderson, Algo; Gumas, Natalie
Traditional undergraduate liberal arts courses, required of most premedical and predental students, have failed dismally to motivate doctors and dentists to become concerned with the health problems of the poor, be they black or white. Examination of black studies programs leads the authors to believe that these programs, if planned with the…
8. Super-horizon primordial black holes
International Nuclear Information System (INIS)
2005-01-01
We discuss a new class of solutions to the Einstein equations which describe a primordial black hole (PBH) in a flat Friedmann background. Such solutions arise if a Schwarzschild black hole is patched onto a Friedmann background via a transition region. They are possible providing the black hole event horizon is larger than the cosmological apparent horizon. Such solutions have a number of strange features. In particular, one has to define the black hole and cosmological horizons carefully and one then finds that the mass contained within the black hole event horizon decreases when the black hole is larger than the Friedmann cosmological apparent horizon, although its area always increases. These solutions involve two distinct future null infinities and are interpreted as the conversion of a white hole into a black hole. Although such solutions may not form from gravitational collapse in the same way as standard PBHs, there is nothing unphysical about them, since all energy and causality conditions are satisfied. Their conformal diagram is a natural amalgamation of the Kruskal diagram for the extended Schwarzschild solution and the conformal diagram for a black hole in a flat Friedmann background. In this paper, such solutions are obtained numerically for a spherically symmetric universe containing a massless scalar field, but it is likely that they exist for more general matter fields and less symmetric systems
9. Do stringy corrections stabilize colored black holes?
International Nuclear Information System (INIS)
Kanti, P.; Winstanley, E.
2000-01-01
We consider hairy black hole solutions of Einstein-Yang-Mills-dilaton theory, coupled to a Gauss-Bonnet curvature term, and we study their stability under small, spacetime-dependent perturbations. We demonstrate that stringy corrections do not remove the sphaleronic instabilities of colored black holes with the number of unstable modes being equal to the number of nodes of the background gauge function. In the gravitational sector and in the limit of an infinitely large horizon, colored black holes are also found to be unstable. Similar behavior is exhibited by magnetically charged black holes while the bulk of neutral black holes are proved to be stable under small, gauge-dependent perturbations. Finally, electrically charged black holes are found to be characterized only by the existence of a gravitational sector of perturbations. As in the case of neutral black holes, we demonstrate that for the bulk of electrically charged black holes no unstable modes arise in this sector. (c) 2000 The American Physical Society
10. Gravitational lensing by a regular black hole
International Nuclear Information System (INIS)
Eiroa, Ernesto F; Sendra, Carlos M
2011-01-01
In this paper, we study a regular Bardeen black hole as a gravitational lens. We find the strong deflection limit for the deflection angle, from which we obtain the positions and magnifications of the relativistic images. As an example, we apply the results to the particular case of the supermassive black hole at the center of our galaxy.
11. Gravitational lensing by a regular black hole
Energy Technology Data Exchange (ETDEWEB)
Eiroa, Ernesto F; Sendra, Carlos M, E-mail: [email protected], E-mail: [email protected] [Instituto de Astronomia y Fisica del Espacio, CC 67, Suc. 28, 1428, Buenos Aires (Argentina)
2011-04-21
In this paper, we study a regular Bardeen black hole as a gravitational lens. We find the strong deflection limit for the deflection angle, from which we obtain the positions and magnifications of the relativistic images. As an example, we apply the results to the particular case of the supermassive black hole at the center of our galaxy.
12. Communities for and with Black Male Students
Science.gov (United States)
Jett, Christopher C.; Stinson, David W.; Williams, Brian A.
2015-01-01
The social and educational status of black male youth in the United States has been receiving increasing attention. In February 2014, President Barack Obama announced a new national initiative--My Brother's Keeper--for helping black boys and male youth or, to speak more generally, boys and young men of color, to "stay on track; providing the…
13. Blacks in Pop Music: A Short Story.
Science.gov (United States)
Rickelman, Melinda
1991-01-01
A short history of black pop music includes artists who have changed pop music or culture and highlights from the 1920s into the 1980s, from Fats Waller to Michael Jackson. In black pop music, there is a direct line of influence from the sharecropper to the current Top 40. (SLD)
14. Black America: Looking Inward or Outward?
Science.gov (United States)
Jordan, Vernon E.
1996-01-01
Presents some observations on what the recent attacks on affirmative action, the O. J. Simpson trial, and the Million Man March say about racism in America. In particular, the author assesses the Million Man March in terms of black leadership and its influence in helping black men to become more involved in constructive community service. (GR)
15. Partition functions for supersymmetric black holes
NARCIS (Netherlands)
Manschot, J.
2008-01-01
This thesis presents a number of results on partition functions for four-dimensional supersymmetric black holes. These partition functions are important tools to explain the entropy of black holes from a microscopic point of view. Such a microscopic explanation was desired after the association of a
16. Recent advances on bioactivities of black rice.
Science.gov (United States)
Dias, Aécio L de S; Pachikian, Barbara; Larondelle, Yvan; Quetin-Leclercq, Joëlle
2017-11-01
Black rice has been consumed for centuries in Asian countries such as China, Korea or Japan. Nowadays, extracts and derivatives are considered as beneficial functional foods because of their high content in several bioactive molecules such as anthocyanins, other phenolics and terpenoids. The purpose of this review is to summarize and discuss recent developments on black rice bioactivities. Some sterols and triterpenoids with potential anticancer properties already tested in vitro and in vivo have been isolated and identified from bran extracts of black rice. Protection against osteoporosis has been suggested for the first time for black rice extracts. Because of its antioxidant and anti-inflammatory properties, black rice also protects liver and kidney from injuries. One clinical study reported the interest of black rice in case of alcohol withdrawal. Several advances have been recently achieved on the understanding of the potential biological effects of black rice and its derivatives. They further confirm that black rice should be considered as a promising source of health-promoting functional foods targeting a large set of noninfectious diseases. However, more clinical studies are needed to support the findings highlighted in this review.
17. Mass inflation in the loop black hole
International Nuclear Information System (INIS)
Brown, Eric G.; Mann, Robert; Modesto, Leonardo
2011-01-01
In classical general relativity the Cauchy horizon within a two-horizon black hole is unstable via a phenomenon known as mass inflation, in which the mass parameter (and the spacetime curvature) of the black hole diverges at the Cauchy horizon. Here we study this effect for loop black holes - quantum gravitationally corrected black holes from loop quantum gravity - whose construction alleviates the r=0 singularity present in their classical counterparts. We use a simplified model of mass inflation, which makes use of the generalized Dray-'t Hooft relation, to conclude that the Cauchy horizon of loop black holes indeed results in a curvature singularity similar to that found in classical black holes. The Dray-'t Hooft relation is of particular utility in the loop black hole because it does not directly rely upon Einstein's field equations. We elucidate some of the interesting and counterintuitive properties of the loop black hole, and corroborate our results using an alternate model of mass inflation due to Ori.
18. Quantum aspects of black hole entropy
Four dimensional supersymmetric extremal black holes in string-based ... elements in the construction of black holes are our concepts of space and time. They are, thus, almost by definition, the most perfect macroscopic objects there are in ... Appealing to the Cardy formula for the asymptotic degeneracy of these states, one.
19. Otosclerosis among South African indigenous blacks | Tshifularo ...
African Journals Online (AJOL)
Objective: To report cases of clinical otosclerosis histologically confirmed among indigenous South African blacks. Design: A retrospective study. Setting: Referral tertiary center, MEDUNSA, Garankuwa Hospital, South Africa. Subjects: All fifteen indigenous South African blacks diagnosed with clinical otosclerosis at ...
20. Black+Brown: Institutions of Higher Education
Science.gov (United States)
Frederick D. Patterson Research Institute, UNCF, 2014
2014-01-01
Historically Black Colleges and Universities (HBCUs) and Hispanic-Serving Institutions (HSIs) represent a small percentage of all institutions in the U.S. but educate a large portion of all black and Latino students, many of whom are low-income and first-generation college attendees. Given the population growth of these students overall, both HSIs…
1. Quantum aspects of black hole entropy
Quantum corrections to the semiclassical Bekenstein–Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black ...
2. Primordial braneworld black holes: significant enhancement of ...
Abstract. The Randall-Sundrum (RS-II) braneworld cosmological model with a frac- tion of the total energy density in primordial black holes is considered. Due to their 5d geometry, these black holes undergo modified Hawking evaporation. It is shown that dur- ing the high-energy regime, accretion from the surrounding ...
3. Black Hole Dynamic Potentials Koustubh Ajit Kabe
Abstract. In the following paper, certain black hole dynamic potentials have been developed definitively on the lines of classical thermodynam- ics. These potentials have been refined in view of the small differences in the equations of the laws of black hole dynamics as given by Bekenstein and those of thermodynamics.
4. Black Thyroid Associated with Thyroid Carcinoma
Directory of Open Access Journals (Sweden)
2010-01-01
Full Text Available Objective. Black thyroid is a rare pigmented change seen almost exclusively in patients upon minocycline ingestion, and the process has previously been thought to be generally benign. There have been 61 reported cases of black thyroid. We are aware of 13 cases previously reported in association with thyroid carcinoma. This paper reports six patients with black thyroid pigmentation in association with thyroid carcinoma. Design. The medical records of six patients who were diagnosed with black thyroid syndrome, all of whom underwent thyroid surgery, were reviewed. Data on age, gender, race, preoperative fine needle aspiration biopsy (FNA, thyroid function levels, and pathology reports were collected. Main Outcome. The mean age was 60 years. There were 5 females, 4 of whom were African American. All patients were clinically and biochemically euthyroid. Black pigmentation was not diagnosed in preoperative FNA, and only one patient had a preoperative diagnosis of papillary thyroid carcinoma. The other patients underwent surgery and were found to have black pigmentation of the thyroid associated with carcinoma. Conclusions. FNA does not diagnose black thyroid, which is associated with thyroid carcinoma. Thyroid glands with black pigmentation deserve thorough pathologic examination, including several sections of each specimen.
5. Black Self-Esteem and Desegregated Schools.
Science.gov (United States)
Drury, Darrel W.
1980-01-01
Discusses a study to determine attitudes among Black and White students in 194 southern high schools regarding desegregation. Data are presented on differences between schools; test-score achievement; and variations in self-esteem among students in predominantly White, Black, and racially mixed schools. Findings are interpreted in light of…
6. How bees distinguish black from white
Directory of Open Access Journals (Sweden)
Horridge A
2014-10-01
Full Text Available Adrian Horridge Biological Sciences, Australian National University, Canberra, ACT, AustraliaAbstract: Bee eyes have photoreceptors for ultraviolet, green, and blue wavelengths that are excited by reflected white but not by black. With ultraviolet reflections excluded by the apparatus, bees can learn to distinguish between black, gray, and white, but theories of color vision are clearly of no help in explaining how they succeed. Human vision sidesteps the issue by constructing black and white in the brain. Bees have quite different and accessible mechanisms. As revealed by extensive tests of trained bees, bees learned two strong signals displayed on either target. The first input was the position and a measure of the green receptor modulation at the vertical edges of a black area, which included a measure of the angular width between the edges of black. They also learned the average position and total amount of blue reflected from white areas. These two inputs were sufficient to help decide which of two targets held the reward of sugar solution, but the bees cared nothing for the black or white as colors, or the direction of contrast at black/white edges. These findings provide a small step toward understanding, modeling, and implementing in silicon the anti-intuitive visual system of the honeybee, in feeding behavior. Keywords: vision, detectors, black/white, color, visual processing
7. Black cohosh Actaea racemosa: an annotated bibliography
Science.gov (United States)
Mary L. Predny; Patricia De Angelis; James L. Chamberlain
2006-01-01
Black cohosh (Actaea racemosa, Syn.: Cimicifuga racemosa), a member of the buttercup family (Ranunculaceae), is an erect perennial found in rich cove forests of Eastern North America from Georgia to Ontario. Native Americans used black cohosh for a variety of ailments including rheumatism, malaria, sore throats, and complications...
8. Black holes and the weak cosmic censorship
International Nuclear Information System (INIS)
Krolak, A.
1984-01-01
A theory of black holes is developed under the assumption of the weak cosmic censorship. It includes Hawking's theory of black holes in the future asymptotically predictable space-times as a special case but it also applies to the cosmological situations including models with nonzero cosmological constant of both signs. (author)
9. Black holes and the strong cosmic censorship
International Nuclear Information System (INIS)
Krolak, A.
1984-01-01
The theory of black holes developed by Hawking in asymptotically flat space-times is generalized so that black holes in the cosmological situations are included. It is assumed that the strong version of the Penrose cosmic censorship hypothesis holds. (author)
10. Charged black rings at large D
Energy Technology Data Exchange (ETDEWEB)
Chen, Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Collaborative Innovation Center of Quantum Matter,5 Yiheyuan Rd, Beijing 100871 (China); Center for High Energy Physics, Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Li, Peng-Cheng; Wang, Zi-zhi [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,5 Yiheyuan Rd, Beijing 100871 (China)
2017-04-28
We study the charged slowly rotating black holes in the Einstein-Maxwell theory in the large dimensions (D). By using the 1/D expansion in the near regions of the black holes we obtain the effective equations for the charged slowly rotating black holes. The effective equations capture the dynamics of various stationary solutions, including the charged black ring, the charged slowly rotating Myers-Perry black hole and the charged slowly boosted black string. Via different embeddings we construct these stationary solutions explicitly. For the charged black ring at large D, we find that the charge lowers the angular momentum due to the regularity condition on the solution. By performing the perturbation analysis of the effective equations, we obtain the quasinormal modes of the charge perturbation and the gravitational perturbation analytically. Like the neutral case the charged thin black ring suffers from the Gregory-Laflamme-like instability under the non-axisymmetric perturbations, but the charge weakens the instability. Besides, we find that the large D analysis always respects the cosmic censorship.
11. Simulations of nearly extremal binary black holes
Science.gov (United States)
Giesler, Matthew; Scheel, Mark; Hemberger, Daniel; Lovelace, Geoffrey; Kuper, Kevin; Boyle, Michael; Szilagyi, Bela; Kidder, Lawrence; SXS Collaboration
2015-04-01
Astrophysical black holes could have nearly extremal spins; therefore, nearly extremal black holes could be among the binaries that current and future gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass m and spin S exceeding the Bowen-York limit of S /m2 = 0 . 93 . Using improved methods we simulate an unequal-mass, precessing binary black hole coalescence, where the larger black hole has S /m2 = 0 . 99 . We also use these methods to simulate a nearly extremal non-precessing binary black hole coalescence, where both black holes have S /m2 = 0 . 994 , nearly reaching the Novikov-Thorne upper bound for holes spun up by thin accretion disks. We demonstrate numerical convergence and estimate the numerical errors of the waveforms; we compare numerical waveforms from our simulations with post-Newtonian and effective-one-body waveforms; and we compare the evolution of the black-hole masses and spins with analytic predictions.
12. Black Hole Entanglement and Quantum Error Correction
NARCIS (Netherlands)
Verlinde, E.; Verlinde, H.
2013-01-01
It was recently argued in [1] that black hole complementarity strains the basic rules of quantum information theory, such as monogamy of entanglement. Motivated by this argument, we develop a practical framework for describing black hole evaporation via unitary time evolution, based on a holographic
13. Black hole complementarity: The inside view
Directory of Open Access Journals (Sweden)
David A. Lowe
2014-10-01
Full Text Available Within the framework of black hole complementarity, a proposal is made for an approximate interior effective field theory description. For generic correlators of local operators on generic black hole states, it agrees with the exact exterior description in a region of overlapping validity, up to corrections that are too small to be measured by typical infalling observers.
14. Black English Annotations for Elementary Reading Programs.
Science.gov (United States)
This report describes a program that uses annotations in the teacher's editions of existing reading programs to indicate the characteristics of black English that may interfere with the reading process of black children. The first part of the report provides a rationale for the annotation approach, explaining that the discrepancy between written…
15. Ambivalence toward Black English: Some Tentative Solutions.
Science.gov (United States)
Taylor, Hanni
1991-01-01
Describes the writing problems of a poor, black, urban student who wants to succeed in college but doesn't know how. Asserts that language use, particularly the use of Black English, plays a major role in their lack of academic success. Offers drills and strategies to help with this problem. (PRA)
16. Holographic Lovelock gravities and black holes
NARCIS (Netherlands)
de Boer, J.; Kulaxizi, M.; Parnachev, A.
2010-01-01
We study holographic implications of Lovelock gravities in AdS spacetimes. For a generic Lovelock gravity in arbitrary spacetime dimensions we formulate the existence condition of asymptotically AdS black holes. We consider small fluctuations around these black holes and determine the constraint on
17. Black Holes at the LHC: Progress since 2002
International Nuclear Information System (INIS)
Park, Seong Chan
2008-01-01
We review the recent noticeable progresses in black hole physics focusing on the up-coming super-collider, the LHC. We discuss the classical formation of black holes by particle collision, the greybody factors for higher dimensional rotating black holes, the deep implications of black hole physics to the 'energy-distance' relation, the security issues of the LHC associated with black hole formation and the newly developed Monte-Carlo generators for black hole events.
18. Black hole as a wormhole factory
Directory of Open Access Journals (Sweden)
Sung-Won Kim
2015-12-01
Full Text Available There have been lots of debates about the final fate of an evaporating black hole and the singularity hidden by an event horizon in quantum gravity. However, on general grounds, one may argue that a black hole stops radiation at the Planck mass (ħc/G1/2∼10−5 g, where the radiated energy is comparable to the black hole's mass. And also, it has been argued that there would be a wormhole-like structure, known as “spacetime foam”, due to large fluctuations below the Planck length (ħG/c31/2∼10−33 cm. In this paper, as an explicit example, we consider an exact classical solution which represents nicely those two properties in a recently proposed quantum gravity model based on different scaling dimensions between space and time coordinates. The solution, called “Black Wormhole”, consists of two different states, depending on its mass parameter M and an IR parameter ω: For the black hole state (with ωM2>1/2, a non-traversable wormhole occupies the interior region of the black hole around the singularity at the origin, whereas for the wormhole state (with ωM2<1/2, the interior wormhole is exposed to an outside observer as the black hole horizon is disappearing from evaporation. The black hole state becomes thermodynamically stable as it approaches the merging point where the interior wormhole throat and the black hole horizon merges, and the Hawking temperature vanishes at the exact merge point (with ωM2=1/2. This solution suggests the “Generalized Cosmic Censorship” by the existence of a wormhole-like structure which protects the naked singularity even after the black hole evaporation. One could understand the would-be wormhole inside the black hole horizon as the result of microscopic wormholes created by “negative” energy quanta which have entered the black hole horizon in Hawking radiation process; the quantum black hole could be a wormhole factory! It is found that this speculative picture may be consistent with the
19. Distortion of Schwarzschild-anti-de Sitter black holes to black strings
International Nuclear Information System (INIS)
Tomimatsu, Akira
2005-01-01
Motivated by the existence of black holes with various topologies in four-dimensional spacetimes with a negative cosmological constant, we study axisymmetric static solutions describing any large distortions of Schwarzschild-anti-de Sitter black holes parametrized by the mass m. Under the approximation such that m is much larger than the anti-de Sitter radius, it is found that a cylindrically symmetric black string is obtained as a special limit of distorted spherical black holes. Such a prolonged distortion of the event horizon connecting a Schwarzschild-anti-de Sitter black hole to a black string is allowed without violating both the usual black hole thermodynamics and the hoop conjecture for the horizon circumference
20. STU black holes and string triality
International Nuclear Information System (INIS)
Behrndt, K.; Kallosh, R.; Rahmfeld, J.; Shmakova, M.; Wong, W.K.
1996-01-01
We find double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F=STU. The area formula is STU-moduli independent and has [SL(2,Z)] 3 symmetry in space of charges. The dual version of this theory without a prepotential treats the dilaton S asymmetric vs T,U moduli. We display the dual relation between new (STU) black holes and stringy (S|TU) black holes using a particular Sp(8,Z) transformation. The area formula of one theory equals that of the dual theory when expressed in terms of dual charges. We analyze the relation between (STU) black holes to string triality of black holes: (S|TU), (T|US), (U|ST) solutions. In the democratic STU-symmetric version we find that all three S, T, and U duality symmetries are nonperturbative and mix electric and magnetic charges. copyright 1996 The American Physical Society
1. Plasma horizons of a charged black hole
International Nuclear Information System (INIS)
Hanni, R.S.
1977-01-01
The most promising way of detecting black holes seems to be through electromagnetic radiation emitted by nearby charged particles. The nature of this radiation depends strongly on the local electromagnetic field, which varies with the charge of the black hole. It has often been purported that a black hole with significant charge will not be observed, because, the dominance of the Coulomb interaction forces its neutralization through selective accretion. This paper shows that it is possible to balance the electric attraction of particles whose charge is opposite that of the black hole with magnetic forces and (assuming an axisymmetric, stationary solution) covariantly define the regions in which this is possible. A Kerr-Newman hole in an asymptotically uniform magnetic field and a current ring centered about a Reissner-Nordstroem hole are used as examples, because of their relevance to processes through which black holes may be observed. (Auth.)
2. Bumpy black holes from spontaneous Lorentz violation
International Nuclear Information System (INIS)
Dubovsky, Sergei; Tinyakov, Peter; Zaldarriaga, Matias
2007-01-01
We consider black holes in Lorentz violating theories of massive gravity. We argue that in these theories black hole solutions are no longer universal and exhibit a large number of hairs. If they exist, these hairs probe the singularity inside the black hole providing a window into quantum gravity. The existence of these hairs can be tested by future gravitational wave observatories. We generically expect that the effects we discuss will be larger for the more massive black holes. In the simplest models the strength of the hairs is controlled by the same parameter that sets the mass of the graviton (tensor modes). Then the upper limit on this mass coming from the inferred gravitational radiation emitted by binary pulsars implies that hairs are likely to be suppressed for almost the entire mass range of the super-massive black holes in the centers of galaxies
3. Magnetized black holes and nonlinear electrodynamics
Science.gov (United States)
Kruglov, S. I.
2017-08-01
A new model of nonlinear electrodynamics with two parameters is proposed. We study the phenomenon of vacuum birefringence, the causality and unitarity in this model. There is no singularity of the electric field in the center of pointlike charges and the total electrostatic energy is finite. We obtain corrections to the Coulomb law at r →∞. The weak, dominant and strong energy conditions are investigated. Magnetized charged black hole is considered and we evaluate the mass, metric function and their asymptotic at r →∞ and r → 0. The magnetic mass of the black hole is calculated. The thermodynamic properties and thermal stability of regular black holes are discussed. We calculate the Hawking temperature of black holes and show that there are first-order and second-order phase transitions. The parameters of the model when the black hole is stable are found.
4. Surface effects in black hole physics
International Nuclear Information System (INIS)
Damour, T.
1982-01-01
This contribution reviews briefly the various analogies which have been drawn between black holes and ordinary physical objects. It is shown how, by concentrating on the properties of the surface of a black hole, it is possible to set up a sequence of tight analogies allowing one to conclude that a black hole is, qualitatively and quantitatively, similar to a fluid bubble possessing a negative surface tension and endowed with finite values of the electrical conductivity and of the shear and bulk viscosities. These analogies are valid simultaneously at the levels of electromagnetic, mechanical and thermodynamical laws. Explicit applications of this framework are worked out (eddy currents, tidal drag). The thermostatic equilibrium of a black hole electrically interacting with its surroundings is discussed, as well as the validity of a minimum entropy production principle in black hole physics. (Auth.)
5. Black hole accretion: the quasar powerhouse
International Nuclear Information System (INIS)
Anon.
1983-01-01
A program is described which calculates the effects of material falling into the curved space-time surrounding a rotation black hole. The authors have developed a two-dimensional, general-relativistic hydrodynamics code to simulate fluid flow in the gravitational field of a rotating black hole. Such calculations represent models that have been proposed for the energy sources of both quasars and jets from radiogalaxies. In each case, the black hole that powers the quasar or jet would have a mass of about 100 million times the mass of the sun. The black hole would be located in the center of a galaxy whose total mass is 1000 time greater than the black hole mass. (SC)
6. Tension perturbations of black brane spacetimes
International Nuclear Information System (INIS)
Traschen, Jennie; Fox, Daniel
2004-01-01
We consider black brane spacetimes that have at least one spatial translation Killing field that is tangent to the brane. A new parameter, the tension of a spacetime, is defined. The tension parameter is associated with spatial translations in much the same way that the ADM mass is associated with the time translation Killing field. In this work, we explore the implications of the spatial translation symmetry for small perturbations around a background black brane. For static-charged black branes we derive a law which relates the tension perturbation to the surface gravity times the change in the horizon area, plus terms that involve variations in the charges and currents. We find that as a black brane evaporates the tension decreases. We also give a simple derivation of a first law for black brane spacetimes. These constructions hold when the background stress-energy is governed by a Hamiltonian, and the results include arbitrary perturbative stress-energy sources
7. Phases of Kaluza-Klein Black Holes
DEFF Research Database (Denmark)
Harmark, Troels; Obers, N. A.
2005-01-01
We review the latest progress in understanding the phase structure of static and neutral Kaluza-Klein black holes, i.e. static and neutral solutions of pure gravity with an event horizon that asymptote to a d-dimensional Minkowski-space times a circle. We start by reviewing the (mu,n) phase diagram...... and the split-up of the phase structure into solutions with an internal SO(d-1) symmetry and solutions with Kaluza-Klein bubbles. We then discuss the uniform black string, non-uniform black string and localized black hole phases, and how those three phases are connected, involving issues such as classical...... instability and horizon-topology changing transitions. Finally, we review the bubble-black hole sequences, their place in the phase structure and interesting aspects such as the continuously infinite non-uniqueness of solutions for a given mass and relative tension....
8. Mass formula for quasi-black holes
International Nuclear Information System (INIS)
Lemos, Jose P. S.; Zaslavskii, Oleg B.
2008-01-01
A quasi-black hole, either nonextremal or extremal, can be broadly defined as the limiting configuration of a body when its boundary approaches the body's quasihorizon. We consider the mass contributions and the mass formula for a static quasi-black hole. The analysis involves careful scrutiny of the surface stresses when the limiting configuration is reached. It is shown that there exists a strict correspondence between the mass formulas for quasi-black holes and pure black holes. This perfect parallelism exists in spite of the difference in derivation and meaning of the formulas in both cases. For extremal quasi-black holes the finite surface stresses give zero contribution to the total mass. This leads to a very special version of Abraham-Lorentz electron in general relativity in which the total mass has pure electromagnetic origin in spite of the presence of bare stresses.
9. Kerr black holes are not fragile
Energy Technology Data Exchange (ETDEWEB)
McInnes, Brett, E-mail: [email protected] [Centro de Estudios Cientificos (CECs), Valdivia (Chile); National University of Singapore (Singapore)
2012-04-21
Certain AdS black holes are 'fragile', in the sense that, if they are deformed excessively, they become unstable to a fundamental non-perturbative stringy effect analogous to Schwinger pair-production [of branes]. Near-extremal topologically spherical AdS-Kerr black holes, which are natural candidates for string-theoretic models of the very rapidly rotating black holes that have actually been observed to exist, do represent a very drastic deformation of the AdS-Schwarzschild geometry. One therefore has strong reason to fear that these objects might be 'fragile', which in turn could mean that asymptotically flat rapidly rotating black holes might be fragile in string theory. Here we show that this does not happen: despite the severe deformation implied by near-extremal angular momenta, brane pair-production around topologically spherical AdS-Kerr-Newman black holes is always suppressed.
10. Black hole thermodynamics based on unitary evolutions
International Nuclear Information System (INIS)
Feng, Yu-Lei; Chen, Yi-Xin
2015-01-01
In this paper, we try to construct black hole thermodynamics based on the fact that the formation and evaporation of a black hole can be described by quantum unitary evolutions. First, we show that the Bekenstein–Hawking entropy S BH may not be a Boltzmann or thermal entropy. To confirm this statement, we show that the original black hole's ‘first law’ may not simply be treated as the first law of thermodynamics formally, due to some missing metric perturbations caused by matter. Then, by including those (quantum) metric perturbations, we show that the black hole formation and evaporation can be described effectively in a unitary manner, through a quantum channel between the exterior and interior of the event horizon. In this way, the paradoxes of information loss and firewall can be resolved effectively. Finally, we show that black hole thermodynamics can be constructed in an ordinary way, by constructing statistical mechanics. (paper)
11. STU Black Holes and String Triality
Energy Technology Data Exchange (ETDEWEB)
Shmakova, Marina
2003-05-23
We found double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F = STU. The area formula is STU-moduli independent and has [SL(2, Z)]{sup 3} symmetry in space of charges. The dual version of this theory without prepotential treats the dilaton S asymmetric versus T,U-moduli. We display the dual relation between new (STU) black holes and stringy (S|TU) black holes using particular Sp(8,Z) transformation. The area formula of one theory equals the area formula of the dual theory when expressed in terms of dual charges. We analyze the relation between (STU) black holes to string triality of black holes: (S|TU), (T|US), (U|ST) solutions. In democratic STU-symmetric version we find that all three S and T and U duality symmetries are non-perturbative and mix electric and magnetic charges.
12. Eating pathology among Black and White smokers.
Science.gov (United States)
Sánchez-Johnsen, Lisa A P; Fitzgibbon, Marian L; Ahluwalia, Jasjit S; Spring, Bonnie J
2005-02-01
Among White smokers, many females use smoking as a weight control strategy. Little is known about the relationship between eating pathology and smoking among Black females, and whether smokers who enroll in treatment differ in eating pathology from smokers who decline treatment. We examined eating pathology among Black and White smokers who enrolled in a smoking cessation treatment and those who declined treatment. Participants were 100 Black and 100 White female smokers (ages 18-65) who completed three measures of eating pathology. After controlling for BMI, Whites reported greater levels of overall eating pathology than Blacks [F(1,195)=4.1; pWhite than Black smokers. However, once females seek smoking cessation treatment, these ethnic differences are not apparent.
13. Black hole thermodynamics with conical defects
Energy Technology Data Exchange (ETDEWEB)
Appels, Michael [Centre for Particle Theory, Durham University,South Road, Durham, DH1 3LE (United Kingdom); Gregory, Ruth [Centre for Particle Theory, Durham University,South Road, Durham, DH1 3LE (United Kingdom); Perimeter Institute,31 Caroline Street North, Waterloo, ON, N2L 2Y5 (Canada); Kubiznák, David [Perimeter Institute,31 Caroline Street North, Waterloo, ON, N2L 2Y5 (Canada)
2017-05-22
Recently we have shown https://www.doi.org/10.1103/PhysRevLett.117.131303 how to formulate a thermodynamic first law for a single (charged) accelerated black hole in AdS space by fixing the conical deficit angles present in the spacetime. Here we show how to generalise this result, formulating thermodynamics for black holes with varying conical deficits. We derive a new potential for the varying tension defects: the thermodynamic length, both for accelerating and static black holes. We discuss possible physical processes in which the tension of a string ending on a black hole might vary, and also map out the thermodynamic phase space of accelerating black holes and explore their critical phenomena.
14. Magnetic charge, black holes, and cosmic censorship
International Nuclear Information System (INIS)
Hiscock, W.H.
1981-01-01
The possibility of converting a Reissner-Nordstroem black hole into a naked singularity by means of test particle accretion is considered. The dually charged Reissner-Nordstroem metric describes a black hole only when M 2 >Q 2 +P 2 . The test particle equations of motion are shown to allow test particles with arbitrarily large magnetic charge/mass ratios to fall radially into electrically charged black holes. To determine the nature of the final state (black hole or naked singularity) an exact solution of Einstein's equations representing a spherical shell of magnetically charged dust falling into an electrically charged black hole is studied. Naked singularities are never formed so long as the weak energy condition is obeyed by the infalling matter. The differences between the spherical shell model and an infalling point test particle are examined and discussed
15. Thin accretion disk around regular black hole
Directory of Open Access Journals (Sweden)
QIU Tianqi
2014-08-01
Full Text Available The Penrose′s cosmic censorship conjecture says that naked singularities do not exist in nature.So,it seems reasonable to further conjecture that not even a singularity exists in nature.In this paper,a regular black hole without singularity is studied in detail,especially on its thin accretion disk,energy flux,radiation temperature and accretion efficiency.It is found that the interaction of regular black hole is stronger than that of the Schwarzschild black hole. Furthermore,the thin accretion will be more efficiency to lost energy while the mass of black hole decreased. These particular properties may be used to distinguish between black holes.
16. Dual jets from binary black holes.
Science.gov (United States)
Palenzuela, Carlos; Lehner, Luis; Liebling, Steven L
2010-08-20
The coalescence of supermassive black holes--a natural outcome when galaxies merge--should produce gravitational waves and would likely be associated with energetic electromagnetic events. We have studied the coalescence of such binary black holes within an external magnetic field produced by the expected circumbinary disk surrounding them. Solving the Einstein equations to describe black holes interacting with surrounding plasma, we present numerical evidence for possible jets driven by these systems. Extending the process described by Blandford and Znajek for a single, spinning black hole, the picture that emerges suggests that the electromagnetic field extracts energy from the orbiting black holes, which ultimately merge and settle into the standard Blandford-Znajek scenario. Emissions along these jets could potentially be observable at large distances.
17. Magnetohydrodynamic Simulations of Black Hole Accretion
Science.gov (United States)
Avara, Mark J.
Black holes embody one of the few, simple, solutions to the Einstein field equations that describe our modern understanding of gravitation. In isolation they are small, dark, and elusive. However, when a gas cloud or star wanders too close, they light up our universe in a way no other cosmic object can. The processes of magnetohydrodynamics which describe the accretion inflow and outflows of plasma around black holes are highly coupled and nonlinear and so require numerical experiments for elucidation. These processes are at the heart of astrophysics since black holes, once they somehow reach super-massive status, influence the evolution of the largest structures in the universe. It has been my goal, with the body of work comprising this thesis, to explore the ways in which the influence of black holes on their surroundings differs from the predictions of standard accretion models. I have especially focused on how magnetization of the greater black hole environment can impact accretion systems.
18. FEASTING BLACK HOLE BLOWS BUBBLES
Science.gov (United States)
2002-01-01
A monstrous black hole's rude table manners include blowing huge bubbles of hot gas into space. At least, that's the gustatory practice followed by the supermassive black hole residing in the hub of the nearby galaxy NGC 4438. Known as a peculiar galaxy because of its unusual shape, NGC 4438 is in the Virgo Cluster, 50 million light-years from Earth. These NASA Hubble Space Telescope images of the galaxy's central region clearly show one of the bubbles rising from a dark band of dust. The other bubble, emanating from below the dust band, is barely visible, appearing as dim red blobs in the close-up picture of the galaxy's hub (the colorful picture at right). The background image represents a wider view of the galaxy, with the central region defined by the white box. These extremely hot bubbles are caused by the black hole's voracious eating habits. The eating machine is engorging itself with a banquet of material swirling around it in an accretion disk (the white region below the bright bubble). Some of this material is spewed from the disk in opposite directions. Acting like high-powered garden hoses, these twin jets of matter sweep out material in their paths. The jets eventually slam into a wall of dense, slow-moving gas, which is traveling at less than 223,000 mph (360,000 kph). The collision produces the glowing material. The bubbles will continue to expand and will eventually dissipate. Compared with the life of the galaxy, this bubble-blowing phase is a short-lived event. The bubble is much brighter on one side of the galaxy's center because the jet smashed into a denser amount of gas. The brighter bubble is 800 light-years tall and 800 light-years across. The observations are being presented June 5 at the American Astronomical Society meeting in Rochester, N.Y. Both pictures were taken March 24, 1999 with the Wide Field and Planetary Camera 2. False colors were used to enhance the details of the bubbles. The red regions in the picture denote the hot gas
19. Refractory for Black Liquor Gasifiers
Energy Technology Data Exchange (ETDEWEB)
William L. Headrick Jr; Musa Karakus; Xiaoting Laing
2005-10-01
The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the material problems encountered during the operation of low-pressure high-temperature (LPHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective
20. Notes on Phase Transition of Nonsingular Black Hole
International Nuclear Information System (INIS)
Ma Meng-Sen; Zhao Ren
2015-01-01
On the belief that a black hole is a thermodynamic system, we study the phase transition of nonsingular black holes. If the black hole entropy takes the form of the Bekenstein—Hawking area law, the black hole mass M is no longer the internal energy of the black hole thermodynamic system. Using the thermodynamic quantities, we calculate the heat capacity, thermodynamic curvature and free energy. It is shown that there will be a larger black hole/smaller black hole phase transition for the nonsingular black hole. At the critical point, the second-order phase transition appears. (paper)
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HOME> 논문 > 논문 검색상세
## 논문 상세정보
### 여고생의 의복치수 설정을 위한 연구 -주로 서울시내 17세 여고생을 중심으로- A Study on Establishment of the Standard Size for High School Girls -The Girls of Seventeen Years Old in Seoul-
손원교 (서울대학교 농과대학UU0000691 );
• #### 초록
'Adolescence' is a critical period in the process of growing and aging but important in that an adolescent becomes aware of and begins to look about him or her self. Especially with girls in their late teens (15 $\~$ 18), they pay more attention to their looks and clothes than the boys do, which affects to some extent the formation of their personality and their behavior. From this point .of view. it is significant to establish the standard size of high-school girls' clothes. This study aims to measure high-school girls in size and to establish the standard size of their clothes; furthermore. to enable them to lead a satisfactory living with more appropriate size of clothes. The results, analyzed by two different representing items which resulted in little difference, are as belows: 1) Stature had a significant correlation with posterior waist height; bust girth had the most significant correlation with weight. and also some considerable correlation with other representing items; 2) The F-test result showed significant difference on $1\%$ level over all the items between the measured (Y) and the estimated (Y); the correlation among the representing items was considerable also; 3) When the measurement increases in stature by 4cm, bust girth by 4cm. and posterior shoulder width by 2cm respectively, the increase or decrease in other items are as shown on Table 4. Since this study was carried out in girls' high-schools in Seoul, it is expected to extend its further study throughout the nation. thus contributing to comprehending the whole truth of people's body-size and promoting the fabrication and modelling of the original clothes for the nation by the strict standard size up to making ready-made clothes with no difficulty in setting the standard and model size.
• #### 이 논문을 인용한 문헌 (1)
1. 2002. "High School Girls'Satisfaction with Korean Trditional Style School Uniform and Their Clothing Behaviour" 한국의류학회지 = Journal of the Korean Society of Clothing and Textiles, 26(5): 654~662
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• #### 손원교 (1) 관련메뉴
1. 1974 "한국 여고생의 표준치수 설정을 위한 연구 (II)" 대한가정학회지 = Journal of the Korean Home Economics Association 12 (2): 621~631
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https://learnzillion.com/lesson_plans/4071-4-doggie-dilemma-estimate-whether-a-sum-will-be-greater-or-less-than-a-whole-number-a
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Lesson plan
# 4. Doggie Dilemma: Estimate whether a sum will be greater or less than a whole number (A)
teaches Common Core State Standards 5.NF.A.1 http://corestandards.org/Math/Content/5/NF/A/1
teaches Common Core State Standards 5.NF.A.2 http://corestandards.org/Math/Content/5/NF/A/2
teaches Common Core State Standards MP2 http://corestandards.org/Math/Practice/MP2
teaches Common Core State Standards MP4 http://corestandards.org/Math/Practice/MP4
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https://cs.stackexchange.com/questions/3112/how-to-disambiguate-symbolic-regular-expressions
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# How to disambiguate symbolic regular expressions
What I mean by a "symbolic regular expression" (if there already is a different name for this I'm not aware of it) is a regular expression that may include exponents that are symbolic arithmetic expressions.
Example 1: $a^k|b^*$ means "either $k$ copies of $a$ or zero or more copies of $b$".
Example 2: $a^{k+1}|a^k$ means "either $k$ or $k+1$ copies of $a$".
What I'd like to do is disambiguate such regular expressions. I know that to disambiguate a normal regular expression, you can convert it to an NFA, then a DFA, then back to a regular expression.
The problem is not completely straightforward. For example, $a^k|a^j$ is ambiguous if $j=k$ and unambiguous otherwise. Thus, the appropriate output would be, for example, $$a^k \text{ if } k=j, \qquad a^k|a^j \text{ otherwise.}$$
• Hmmm. So, you might want to convert an expression such as $\bigl[(a^3)^\ast \mathrel| (a^5)^\ast\bigr]$ to $\bigl[\varepsilon \mathrel| a^3 \mathrel| a^5 \mathrel| a^6 \mathrel| a^8a^\ast\bigr]$, that is separating out all possibilities exhaustively into disjoint collections (a sort of sum-of-products)? – Niel de Beaudrap Aug 10 '12 at 0:15
• There is a problem: if you require a case analysis for all possible values of the symbolic exponents, an example such as I gave yields either an indeterminate number of disjuncts in the formula (it is not an augmented-regular-expression, but a schema for such expressions), or an infinite number of cases. If we consider $\bigl[(a^j)^\ast \mathrel| (a^k)^\ast\bigr]$, the number of disjuncts in the result doesn't just depend on whether $j=k$. For example, $k=nj+r$ (for $n,r\geqslant0$) has at least $\lcm(j,k)+1 = \frac{nj^2+rj}{\gcd(j,r)}+1$ disjuncts, which for $n,r,j$ arbitrary is unbounded. – Niel de Beaudrap Aug 10 '12 at 9:45
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https://math.stackexchange.com/questions/447715/history-question-on-continued-fractions
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# History Question on Continued Fractions
I worked out the periodicity of some infinite continued fractions last night by hand. (Don't ask me why)
For example, $\sqrt{13}= [3,1,1,1,1,6,1,1,1,1,6,\ldots]$. Last night I worked out the first period of this continued fraction and the algebra was a little meh. I was wondering, what is the largest continued fraction period ever worked out by hand before?
For example: $\sqrt{D}$ may have the continued fraction expansion: $[\text{repeat}(a_1,a_2,a_3,\ldots, a_n)]$. Define the "first period worked out by hand" to be:
The discovery of the first $a_1,a_2,a_3,\ldots,a_n$ of the infinite continued fraction $\sqrt{D}$ using nothing but pencil, and paper.
Any stories for me?
• No story, but there are efficient ways to compute the continued fraction of square roots. – André Nicolas Jul 19 '13 at 23:08
• How is that related to math history? – lhf Jul 20 '13 at 1:35
Lagrange's method uses just integer arithmetic and is suitable for use by hand. See How to detect when continued fractions period terminates
If you need more detail let me know.
Note that I used precisely that in Minimum of $n$? $123456789x^2 - 987654321y^2 =n$ ($x$,$y$ and $n$ are positive integers) although it was by computer.
Not by the way, if you are primarily interested in the square root of positive a integer $D,$ then the triple indicating a first form in the cycle is given by finding $$a_0 = \lfloor \sqrt D \rfloor$$ and then forming the triple $$\langle 1, 2 a_0, a_0^2 - D \rangle$$
Here, the triple $\langle a, b, c \rangle$ refers to the quadratic form $$f(x,y) = a x^2 + b x y + c y^2.$$ The form is "reduced" if both $ac <0$ and $b > |a+c|.$
jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$./Pell Input n for Pell 991 0 form 1 62 -30 delta -2 1 form -30 58 5 delta 12 2 form 5 62 -6 delta -10 3 form -6 58 25 delta 2 4 form 25 42 -22 delta -2 5 form -22 46 21 delta 2 6 form 21 38 -30 delta -1 7 form -30 22 29 delta 1 8 form 29 36 -23 delta -2 9 form -23 56 9 delta 6 10 form 9 52 -35 delta -1 11 form -35 18 26 delta 1 12 form 26 34 -27 delta -1 13 form -27 20 33 delta 1 14 form 33 46 -14 delta -3 15 form -14 38 45 delta 1 16 form 45 52 -7 delta -8 17 form -7 60 13 delta 4 18 form 13 44 -39 delta -1 19 form -39 34 18 delta 2 20 form 18 38 -35 delta -1 21 form -35 32 21 delta 2 22 form 21 52 -15 delta -3 23 form -15 38 42 delta 1 24 form 42 46 -11 delta -4 25 form -11 42 50 delta 1 26 form 50 58 -3 delta -20 27 form -3 62 10 delta 6 28 form 10 58 -15 delta -4 29 form -15 62 2 delta 31 30 form 2 62 -15 delta -4 31 form -15 58 10 delta 6 32 form 10 62 -3 delta -20 33 form -3 58 50 delta 1 34 form 50 42 -11 delta -4 35 form -11 46 42 delta 1 36 form 42 38 -15 delta -3 37 form -15 52 21 delta 2 38 form 21 32 -35 delta -1 39 form -35 38 18 delta 2 40 form 18 34 -39 delta -1 41 form -39 44 13 delta 4 42 form 13 60 -7 delta -8 43 form -7 52 45 delta 1 44 form 45 38 -14 delta -3 45 form -14 46 33 delta 1 46 form 33 20 -27 delta -1 47 form -27 34 26 delta 1 48 form 26 18 -35 delta -1 49 form -35 52 9 delta 6 50 form 9 56 -23 delta -2 51 form -23 36 29 delta 1 52 form 29 22 -30 delta -1 53 form -30 38 21 delta 2 54 form 21 46 -22 delta -2 55 form -22 42 25 delta 2 56 form 25 58 -6 delta -10 57 form -6 62 5 delta 12 58 form 5 58 -30 delta -2 59 form -30 62 1 delta 62 60 form 1 62 -30 disc 3964 Automorph, written on right of Gram matrix: 5788591406539787767296194303 361672073709940783423276163010 12055735790331359447442538767 753244210407084073508733597857 Pell automorph 379516400906811930638014896080 11947234168218377212415555918097 12055735790331359447442538767 379516400906811930638014896080 Pell unit 379516400906811930638014896080^2 - 991 * 12055735790331359447442538767^2 = 1 ========================================= 991 991 jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$ date
Fri Jul 19 16:34:12 PDT 2013
jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus\$
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https://artofproblemsolving.com/wiki/index.php?title=2008_iTest_Problems/Problem_83&diff=prev&oldid=98939
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# Difference between revisions of "2008 iTest Problems/Problem 83"
## Problem
Find the greatest natural number such that and is a perfect square.
## Solution
Notice that , so Thus, . In order for the expression to be a perfect square, must be a perfect square.
By using the Euclidean Algorithm, . Thus, the GCD of and must be factors of 6. Now, split the factors as different casework. Note that the quadratic residues of 7 are 0, 1, 2, and 4.
• If , then . Let , so . Since 6 is divided out of and , and are relatively prime, so and must be perfect squares. However, since 6 is not a quadratic residue of 7, the GCD of and can not be 6.
• If , then . Let , so . Since 3 is divided out of and , and are relatively prime, so and must be perfect squares. However, since 5 is not a quadratic residue of 7, the GCD of and can not be 3.
• If , then . Let , so . Since 2 is divided out of and , and are relatively prime, so and must be perfect squares. We also know that and do not share a factor of 3, so . That means , so . After trying values of that are one less than a perfect square, we find that the largest value that makes a perfect square is . That means .
• If , then (to avoid common factors that are factors of 6), so . After trying values of that are one less than a perfect square, we find that the largest value that makes a perfect square is (we could also stop searching once gets below 1921).
From the casework, the largest natural number that makes is a perfect square is .
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https://rd.springer.com/article/10.1007/s00229-017-0951-6
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manuscripta mathematica
, Volume 156, Issue 1–2, pp 117–125
# A remark on Beauville’s splitting property
• Robert Laterveer
Article
## Abstract
Let X be a hyperkähler variety. Beauville has conjectured that a certain subring of the Chow ring of X should inject into cohomology. This note proposes a similar conjecture for the ring of algebraic cycles on X modulo algebraic equivalence: a certain subring (containing divisors and codimension 2 cycles) should inject into cohomology. We present some evidence for this conjecture.
## Mathematics Subject Classification
Primary 14C15 14C25 14C30
## Preview
Unable to display preview. Download preview PDF.
## References
1. 1.
Abdulali, S.: Filtrations on the cohomology of Abelian varieties. In: Brent Gordon, B., et al. (eds.) The Arithmetic and Geometry of Algebraic Cycles, Banff 1998, CRM Proceedings and Lecture Notes. American Mathematical Society Providence (2000)Google Scholar
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Abdulali, S.: Tate twists of Hodge structures arising from Abelian varieties. In: Kerr, M., et al. (eds.) Recent Advances in Hodge Theory: Period Domains, Algebraic Cycles, and Arithmetic, London Mathematical Society Lecture Note Series 427. Cambridge University Press, Cambridge (2016)Google Scholar
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Arapura, D.: Motivation for Hodge cycles. Adv. Math. 207, 762–781 (2006)
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Beauville, A.: Sur l’anneau de Chow d’une variété abélienne. Math. Ann. 273, 647–651 (1986)
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Beauville, A.: On the splitting of the Bloch–Beilinson filtration. In: Nagel, J., et al. (eds.) Algebraic Cycles and Motives, London Mathematical Society Lecture Notes 344. Cambridge University Press, Cambridge (2007)Google Scholar
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Beauville, A., Voisin, C.: On the Chow ring of a $$K3$$ surface. J. Algebraic Geom. 13, 417–426 (2004)
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Charles, F., Pacienza, G.: Families of Rational Curves on Holomorphic Symplectic Varieties and Applications to $$0$$-Cycles. arXiv:1401.4071
8. 8.
Fu, L.: Beauville–Voisin conjecture for generalized Kummer varieties. Int. Math. Res. Not. 12, 3878–3898 (2015)
9. 9.
Fu, L., Tian, Z., Vial, C.: Motivic Hyperkähler Resolution Conjecture for Generalized Kummer Varieties. arXiv:1608.04968
10. 10.
Jannsen, U.: Equivalence relations on algebraic cycles. In: The Arithmetic and Geometry of Algebraic Cycles, Banff 1998. In: Gordon, B., et al. (eds.) CRM Proceedings and Lecture Notes. American Mathematical Society Providence (2000)Google Scholar
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Kahn, B., Murre, J., Pedrini, C.: On the transcendental part of the motive of a surface. In: Nagel, J., et al. (eds.) Algebraic Cycles and Motives. Cambridge University Press, Cambridge (2007)Google Scholar
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Kimura, S.: Chow groups are finite dimensional, in some sense. Math. Ann. 331, 173–201 (2005)
13. 13.
Laterveer, R.: Hard Lefschetz for Chow groups of generalized Kummer varieties. Abh. Math. Semin. Univ. Hambg. 87(1), 135–144 (2017)
14. 14.
Rieß, U.: On Beauville’s conjectural weak splitting property. Int. Math. Res. Not. 20, 6133–6150 (2016)
15. 15.
Shen, M., Vial, C.: The Fourier transform for certain hyper Kähler fourfolds. Mem. AMS 240(1139) vii+163 (2016)Google Scholar
16. 16.
Shen, M., Vial, C.: The motive of the Hilbert cube $$X^{[3]}$$. Forum Math. Sigma 4, 1–55 (2016)
17. 17.
Vial, C.: On the motive of some hyperkähler varieties. J. für Reine u. Angew. Math. 725, 235–247 (2017)
18. 18.
Voisin, C.: On the Chow ring of certain algebraic hyper-Kähler manifolds. Pure Appl. Math. Q. 4(3), 613–649 (2008)
19. 19.
Voisin, C.: Chow rings and decomposition theorems for $$K3$$ surfaces and Calabi–Yau hypersurfaces. Geom. Topol. 16, 433–473 (2012)
20. 20.
Voisin, C.: Chow Rings, Decomposition of the Diagonal, and the Topology of Families. Princeton University Press, Princeton (2014)
21. 21.
Voisin, C.: Remarks and questions on coisotropic subvarieties and $$0$$-cycles of hyper-Kähler varieties. In: Faber, C., et al. (eds.) K3 Surfaces and Their Moduli, Proceedings of the Schiermonnikoog Conference 2014, Progress in Mathematics 315. Birkhäuser (2016)Google Scholar
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Xu, Z.: Algebraic Cycles on a Generalized Kummer Variety. arXiv:1506.04297v1
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Yin, Q.: Finite-dimensionality and cycles on powers of $$K3$$ surfaces. Comment. Math. Helv. 90, 503–511 (2015)
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http://math.stackexchange.com/users/26975/kiss-my-armpit?tab=activity&sort=accepts
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kiss my armpit
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https://socratic.org/questions/a-container-has-a-volume-of-4-l-and-holds-9-mol-of-gas-if-the-container-is-expan
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Physics
Topics
# A container has a volume of 4 L and holds 9 mol of gas. If the container is expanded such that its new volume is 36 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?
Mar 2, 2017
We must inject $72 m o l$ of gas
#### Explanation:
The Ideal Gas Law is
$P V = n R T$
$\frac{V}{n} = R \frac{T}{P}$
$\frac{V}{n} = k$
Where $k =$constant
${V}_{1} / {n}_{1} = {V}_{2} / {n}_{2}$
${V}_{1} = 4 L$
${n}_{1} = 9 m o l$
${V}_{2} = 36 L$
${n}_{2} = {V}_{2} / {V}_{1} \cdot {n}_{1}$
$= \frac{36}{4} \cdot 9 = 81 m o l$
##### Impact of this question
119 views around the world
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http://www.ck12.org/geometry/Distance-Formula-in-the-Coordinate-Plane/exerciseint/True-or-False--Distance-Between-Two-Points/r1/
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<meta http-equiv="refresh" content="1; url=/nojavascript/"> Distance Formula in the Coordinate Plane ( Assessments ) | Geometry | CK-12 Foundation
# Distance Formula in the Coordinate Plane
%
Best Score
Practice Distance Formula in the Coordinate Plane
Best Score
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# True or False--Distance Between Two Points Teacher Contributed
The distance between the points (3, 4) and (1, 4) is 2.00.
qid: 100122
# Reviews
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https://www.r-bloggers.com/2014/02/three-ways-to-call-cc-from-r/
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Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
By Ben Ogorek
Introduction
I only recently discovered the fundamental connection between the C and R languages. It was during a Bay Area useR Group meeting, where presenter J.J. Allaire shared two points to motivate his talk on Rcpp. The first explained just how much of modern R really is C and C++. For illustration, he used the librestats language composition analysis of Core R, which might not have been so interesting if it did not extend to R’s contributed packages. Allaire’s second point emphasized R’s roots as an interactive mechanism for calling code from compiled languages like C and Fortran (which you can also hear from S inventor John Chambers). While I didn’t understand all of the finer points at the time, I never thought of R in the same way again.
The big three
The .C function interface
Of R’s native functions, the .C interface is the simplest but also the most limited way to call C from R. Inside a running R session, the .C interface allows objects to be directly accessed in an R session’s active memory. Thus, to write a compatible C function, all arguments must be pointers. No matter the nature of your function’s return value, it too must be handled using pointers. The C function you will write is effectively a subroutine.
Our function f(x)= 2x, implemented as double_me in the file doubler.c, is shown below.
void double_me(int* x) {
// Doubles the value at the memory location pointed to by x
*x = *x + *x;
}
To compile the C code, run the following line at your terminal:
$R CMD SHLIB doubler.c In an R interactive session, run: dyn.load("doubler.so") .C("double_me", x = as.integer(5))$x
[1] 10
Notice that the output of .C is a list with names corresponding to the arguments. While the above code is pure C, adding C++ code (instead of C) is made possible by using the extern wrapper.
.Call
The .Call interface is the more fully featured and complex cousin of the .C interface. Unlike .C, .Call requires header files that come standard with every R installation. These header files provide access to a new data type, SEXP. The following code, stored in the file, doubler2.c, illustrates its use.
#include
#include
SEXP double_me2(SEXP x) {
// Doubles the value of the first integer element of the SEXP input
SEXP result;
PROTECT(result = NEW_INTEGER(1)); // i.e., a scalar quantity
INTEGER(result)[0] = INTEGER(x)[0] * 2;
UNPROTECT(1); // Release the one item that was protected
return result;
}
Unlike our experience with the .C interface, double_me2 is a function and does return a value. While that appeals to intuition, no matter what the native input and output types, they must now live in a SEXP object. To code double_me2, you must know that there’s an integer in the input x, and extract it as if it were the first item in a C array. For the return value, you must add your integer result to a SEXP object in an equally unnatural way. The PROTECT function must be used to prevent R’s automatic garbage collection from destroying all the objects.
As before, use R at the command line to compile doubler2.c:
\$ R CMD SHLIB doubler2.c
Back in the R interactive console, the steps are very similar.
dyn.load("doubler2.so")
.Call("double_me2", as.integer(5))
[1] 10
Notice now that the output is an integer vector instead of a list.
Rcpp and the sourceCpp function
The .C and .Call examples above owe a debt to Jonathan Callahan’s entries 8 and 10 of his Using R series. When the examples started working, I tweeted to share my excitement. An hour later, I saw a familiar face:
Let’s check it out.
In terms of the code alone, it’s easy to see where Hadley is coming from. It’s readable, looks just like standard C++ code, and features data types that make intuitive sense. Our simple function is implemented below, saved in the final static file doubler3.cpp (though, in all humility, it’s really just C).
#include
using namespace Rcpp;
// [[Rcpp::export]]
int double_me3(int x) {
// takes a numeric input and doubles it
return 2 * x;
}
I’ll refer you to Hadley’s article High performance functions with Rcpp for details on Rcpp, but for now, note the “// [[Rcpp::export]]” comment, necessary before each C/C++ function, and the updated #include statement. Most importantly, notice how the pointers and SEXP objects have been replaced. Just like our original function f(x), double_me3 takes one integer input and returns one integer output.
After installing the Rcpp package, we’re back to the console one final time.
library(Rcpp)
sourceCpp("doubler3.cpp")
double_me3(5)
[1] 10
With Rcpp, the function is waiting for us in the global environment, without even compiling at the command line. Pretty convenient!
Discussion
With the disclaimer that I am a C++ novice, I summarize my thoughts on the three options below.
I like the simplicity of the C code written for the .C interface. It doesn’t rely on external header files and it is possible to test using a C compiler alone. On the other hand, I don’t like that a function has to be morphed into a subroutine that uses pointers.
In the .Call interface, SEXP objects are also pointers, though that is perhaps superfluous. My biggest complaint is the verboseness that was added to our short example. As Jonathan Callahan points out, .Call “requires much more knowledge of R internals [but] is the recommended, modern approach for serious C [and C++] programmers.”
After seeing Rccp in action, it’s not hard to understand why Hadley sent me directly to Rcpp. The C code looks great, there were fewer steps, and our function was ready for us inside the R global environment.
Perhaps you’re wondering if there is any reason not to use Rcpp. According Murray Stokely, Google Software Engineer, it could be risky on a very large project. “Rcpp’s heavy reliance on C macros can make it unsafe to use with large code bases,” says Stokely. For example, the Rcpp FAQ (Section 3.9) describes an unresolved issue casting 64-bit integer types. The implication, Stokely explains, is that a loss of precision could occur without any errors or warnings. The Rcpp FAQ considers such examples “corner cases,” and perhaps the typical user will not have to worry.
Whatever your decision, I wish you the best on your C++ journey!
Acknowledgements
Thanks to Max Ghenis and Mindy Greenberg for expedited proofreadings. Keep up with ours and other articles featuring the R language on R-bloggers.
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https://math.msu.edu/seminars/TalkView.aspx?talk=26797
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## Applied Mathematics
• Ben Adcock, Simon Fraser University
• The troublesome kernel: instabilities in deep learning for inverse problems; zoom link @ https://sites.google.com/view/minds-seminar/home
• 06/04/2020
• 2:30 PM - 3:30 PM
•
(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home) Due to their stunning success in traditional machine learning applications such as classification, techniques based on deep learning have recently begun to be actively investigated for problems in computational science and engineering. One of the key areas at the forefront of this trend is inverse problems, and specifically, inverse problems in imaging. The last few years have witnessed the emergence of many neural network-based algorithms for important imaging modalities such as MRI and X-ray CT. These claim to achieve competitive, and sometimes even superior, performance to current state-of-the-art techniques. However, there is a problem. Techniques based on deep learning are typically unstable. For example, small perturbations in the data can lead to a myriad of artefacts in the recovered images. Such artifacts can be hard to dismiss as obviously unphysical, meaning that this phenomenon has potentially serious consequences for the safe deployment of deep learning in practice. In this talk, I will first showcase the instability phenomenon empirically in a range of examples. I will then focus on its mathematical underpinnings, the consequences of these insights when it comes to potential remedies, and the future possibilities for computing genuinely stable neural networks for inverse problems in imaging. This is joint work with Vegard Antun, Nina M. Gottschling, Anders C. Hansen, Clarice Poon, and Francesco Renna Papers: https://www.pnas.org/content/early/2020/05/08/1907377117 https://arxiv.org/abs/2001.01258
## Contact
Department of Mathematics
Michigan State University
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https://planetmath.org/keepflipchange
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# keep-flip-change
Let $a,b,c,d\in\mathbb{Z}-\{0\}$. A mnemonic device for calculating
$\frac{a}{b}\div\frac{c}{d}$
is KFC. This stands for ”keep-flip-change”. This means that you keep the first fraction as it is, flip the second fraction, and change the problem to a multiplication problem. Thus, the expression above becomes
$\frac{a}{b}\cdot\frac{d}{c}.$
This yields that
$\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\cdot\frac{d}{c}=\frac{ad}{bc}.$
Title keep-flip-change Keepflipchange 2013-03-22 15:59:52 2013-03-22 15:59:52 Wkbj79 (1863) Wkbj79 (1863) 4 Wkbj79 (1863) Definition msc 97D40 KFC K.F.C.
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https://www.kdnuggets.com/2018/08/mxnet-tensor-basics-simple-derivatives.html
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KDnuggets Home » News » 2018 » Aug » Tutorials, Overviews » A Crash Course in MXNet Tensor Basics & Simple Automatic Differentiation ( 18:n32 )
# A Crash Course in MXNet Tensor Basics & Simple Automatic Differentiation
This is an overview of some basic functionality of the MXNet ndarray package for creating tensor-like objects, and using the autograd package for performing automatic differentiation.
I originally intended to play around with MXNet long ago, around the time that Gluon was released publicly. Things got busy. I got sidetracked.
I finally started using MXNet recently. In the interests of getting to know my way around, I thought covering some basics, such as how tensors and derivatives are handled, might be a good place to start (such as I did here and here with PyTorch).
This won't repeat what is in those previous PyTorch articles step by step, so look at those if you want any further context. What's below should be relatively straightforward, however.
MXNet is an open source neural network framework, a "flexible and efficient library for deep learning." Gluon is the imperative high-level API for MXNet, which provides additional flexibility and ease of use. You can think of the relationship between MXNet and Gluon as being similar to TensorFlow and Keras. We won't cover Gluon any further herein, but will explore it in future posts.
MXNet's tensor implementation comes in the form of the ndarray package. Here you will find what's needed to build multidimensional (n-dimensional) arrays and perform some of the operations on them required for implementing neural networks, along with the autograd package. It is this package we will make use of below.
ndarray (Very) Basics
First, let's import what we need from the library, in such a way as to simplify making our API calls:
import mxnet as mx
from mxnet import autograd as ag
from mxnet import nd
Now, let's create a basic ndarray (on the CPU):
# Create CPU array
a = nd.ones((3, 2))
print(a)
[[1. 1.]
[1. 1.]
[1. 1.]]
<NDArray 3x2 @cpu(0)>
Note that printing an ndarray also prints out the type of the object (again, NDArray), as well as its size and the device to which it is attached (in this case, CPU).
What if we wanted to create an ndarray object with a GPU context (note that a context is the device type and ID which should be used to perform operations on the object)? First, let's determine whether or not there is a GPU available to MXNet:
# Test if GPU is recognized
def gpu_device(gpu_number=0):
try:
_ = mx.nd.array([1, 2, 3], ctx=mx.gpu(gpu_number))
except mx.MXNetError:
return None
return mx.gpu(gpu_number)
gpu_device()
gpu(0)
This response denotes that there is a GPU device, and its ID is 0.
Let's create an ndarray on this device:
# Create GPU array
b = nd.zeros((2, 2), ctx=mx.gpu(0))
print(b)
[[0. 0.]
[0. 0.]]
<NDArray 2 x 2 @gpu(0)>
The output here confirms that an ndarray of zeros of size 2 x 2 was created with a context of GPU.
To get a returned transposed ndarray (as opposed to simply a transpose view of the original):
# Transpose
T = c.T
print(T)
[[1. 2. 3.]
[4. 5. 6.]]
<NDArray 2x3 @cpu(0)>
Reshape an ndarray as a view, without alteration of the original data:
# Reshape
r = T.reshape(3,2)
print(r)
[[1. 2.]
[3. 4.]
[5. 6.]]
<NDArray 3x2 @cpu(0)>
Some ndarray info:
# ndarray info
print('ndarray shape:', r.shape)
print('Number of dimensions:', r.ndim)
print('ndarray type:', r.dtype)
ndarray shape: (3, 2)
Number of dimensions: 2
ndarray type: <class 'numpy.float32'>
See here for more on ndarray basics.
MXNet ndarray To and From Numpy ndarray
It's easy to go from Numpy ndarrays to MXNet ndarrays and vice versa.
import numpy as np
# To numpy ndarray
n = c.asnumpy()
print(n)
print(type(n))
[[1. 4.]
[2. 5.]
[3. 6.]]
<class 'numpy.ndarray'>
# From numpy ndarray
a = np.array([[1, 10], [2, 20], [3, 30]])
b = nd.array(a)
print(b)
print(type(b))
[[ 1. 10.]
[ 2. 20.]
[ 3. 30.]]
<class 'mxnet.ndarray.ndarray.NDArray'>
Matrix-matrix multiplication
Here's how to compute a matrix-matrix dot product:
# Compute dot product
t1 = nd.random.normal(-1, 1, shape=(3, 2))
t2 = nd.random.normal(-1, 1, shape=(2, 3))
t3 = nd.dot(t1, t2)
print(t3)
[[1.8671514 2.0258508 1.1915313]
[9.009048 8.481084 6.7323728]
[5.0241795 4.346245 4.0459785]]
<NDArray 3x3 @cpu(0)>
See here for more on linear algebra operations with ndarray.
Using autograd to Find and Solve a Derivative
On to solving a derivative with the MXNet autograd package for automatic differentiation.
First we will need a function for which to find the derivative. Arbitrarily, let's use this:
$\boldsymbol{\mathbf{f(x) = 5 x^4 + 3 x^3 + 7 x^2 + 9 x - 5}}$
To see us work out the first order derivative of this function by hand, as well as find the value of our derivative function for a given value of x, see this post.
For reasons which should be obvious, we have to represent our function in Python as such:
y = 5*x**4 + 3*x**3 + 7*x**2 + 9*x - 5
Now let's find the value of our derivative function for a given value of x. Let's arbitrarily use 2:
x = nd.array([2])
with ag.record():
y = 5*x**4 + 3*x**3 + 7*x**2 + 9*x - 5
y.backward()
Line by line, the above code:
• defines the value (2) we want to compute the derivative with regard to as an MXNet ndarray object
• uses attach_grad() to allocate space for the gradient to be computed
• the code block denoted with ag.record() contains the computation to be performed with regard to computing and tracking the gradient
• defines the function we want to compute the derivative of
• uses autograd's backward() to compute the sum of gradients, using the chain rule
• outputs the value stored in the x ndarray's grad attribute, which, as shown below
tensor([ 233.])
This value, 233, matches what we calculated by hand in this post.
See here for more on automatic differentiation with autograd.
This has been a very basic overview of simple ndarray operations and derivatives in MXNet. As these are 2 of the staples of building neural networks, this should provide some familiarity with the library's approaches to these basic buildings blocks, and allow for diving in to some more complex code. Next time we will create some simple neural networks with MXNet and Gluon, exploring the libraries more in-depth.
For more (right now!) on MXNet, Gluon, and deep learning in general, the freely-available book Deep Learning - The Straight Dope, written by those intimately involved in the development and evangelizing of these libraries, is definitely worth looking at.
Related:
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https://www.physicsforums.com/threads/b-mode-plots-spherical-harmonics-fundamental-modes.744349/
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# B-mode plots, spherical harmonics?, fundamental modes?
1. Mar 20, 2014
### Spinnor
If the B-mode sky plots could be Fourier transformed what would be a plot of the lowest order B-mode harmonic plotted on a sphere look like?
I guess we need two functions of spherical coordinates, one function for amplitude at points on a sphere and one function for the orientation at the same points on a sphere?
Is there a hypothetical "gravitational wave" that gives rise to this lowest order harmonic?
Thanks for any help!
Last edited: Mar 20, 2014
2. Mar 20, 2014
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http://math.stackexchange.com/users/60079/easy?tab=activity
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Easy
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Jul2 awarded Curious May24 revised Does every function with $f_x,f_y>0,f_{xx},f_{yy}<0$ with particular condition have to satisfy $f_{xy}/f_{xx} = -x/y$? deleted 3 characters in body May24 comment Does every function with $f_x,f_y>0,f_{xx},f_{yy}<0$ with particular condition have to satisfy $f_{xy}/f_{xx} = -x/y$? When you say $\infty$, it is $+\infty$ or $-\infty$? May21 answered Inverse of a sum of positive definite matrices May20 answered Proving $A+2B+3C+4D < 2.5$ with given conditions May20 comment If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant? You may want to consider the fundamental theorem of Lebesgue integral calculus, which requires $f'(x)=0$ almost everywhere to get to your result. However, $\mathbb{Q}$ is far away from almost everywhere.. Feb12 awarded Nice Answer Jan29 awarded Yearling Sep12 accepted Maximal abelian subgroups in a $p$-group are always normal? Sep12 comment Maximal abelian subgroups in a $p$-group are always normal? thanks, I didn't realise it was so simple. Sep11 comment Maximal abelian subgroups in a $p$-group are always normal? @DonAntonio, yeah, I am assuming the $p$-group is finite. But I am talking about maximal among abelian subgroups, not just maximal among any subgroups. Sep11 asked Maximal abelian subgroups in a $p$-group are always normal? Aug5 comment $\frac {dy}{dx} \sin y = (1-x\cos y)\cos y$ Hint: $\sin ydy=-d\cos y$. Jul31 asked How to choose the adjacency set Jul22 comment Are these 2 graphs isomorphic? @MarkMcClure, do you know this kind of animation is available by tex coding or not? Jul22 answered Group Theory Normal Subgroups Jul21 comment Solving $x^2-7[x]+5=0.$ to find values of $x$. Hint: find the intersection of $y=x^2+5$ and $y=7[x]$. Jul15 comment Splitting an electricity bill I suggest to assume every equal length period consumes the same amount of electricity. We know there are a lot of electric facilities consume the same amount of electricity regardless of the number of tenancy. For example, fridge, tv, heater, etc. More people just means more usage on the light bulbs in their own rooms, maybe? Jul9 comment What is the structure of the Coxeter groups of type $\text{D}_n$ @JyrkiLahtonen, sorry, I still don't quite get it. For example, where $\sigma_2\circ\sigma_n$ is mapped to? And why $|ker f|=2^{n-1}$ but not $2^{n\choose 2}$? Jul9 comment What is the structure of the Coxeter groups of type $\text{D}_n$ @TobiasKildetoft, by the base group I meant $\mathbb{Z}_2^{n-1}$.
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http://www.zora.uzh.ch/53837/
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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-53837
# Tohge, T; Ramos, M S; Nunes-Nesi, A; Mutwil, M; Giavalisco, P; Steinhauser, D; Schellenberg, M; Willmitzer, L; Persson, S; Martinoia, E; Fernie, A R (2011). Toward the storage metabolome: profiling the barley vacuole. Plant Physiology, 157(3):1469-82.
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## Abstract
While recent years have witnessed dramatic advances in our capacity to identify and quantify an ever-increasing number of plant metabolites, our understanding of how metabolism is spatially regulated is still far from complete. In an attempt to partially address this question, we studied the storage metabolome of the barley (Hordeum vulgare) vacuole. For this purpose, we used highly purified vacuoles isolated by silicon oil centrifugation and compared their metabolome with that found in the mesophyll protoplast from which they were derived. Using a combination of gas chromatography-mass spectrometry and Fourier transform-mass spectrometry, we were able to detect 59 (primary) metabolites for which we know the exact chemical structure and a further 200 (secondary) metabolites for which we have strong predicted chemical formulae. Taken together, these metabolites comprise amino acids, organic acids, sugars, sugar alcohols, shikimate pathway intermediates, vitamins, phenylpropanoids, and flavonoids. Of the 259 putative metabolites, some 12 were found exclusively in the vacuole and 34 were found exclusively in the protoplast, while 213 were common in both samples. When analyzed on a quantitative basis, however, there is even more variance, with more than 60 of these compounds being present above the detection limit of our protocols. The combined data were also analyzed with respect to the tonoplast proteome in an attempt to infer specificities of the transporter proteins embedded in this membrane. Following comparison with recent observations made using nonaqueous fractionation of Arabidopsis (Arabidopsis thaliana), we discuss these data in the context of current models of metabolic compartmentation in plants.
## Citations
38 citations in Web of Science®
41 citations in Scopus®
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http://www.zora.uzh.ch/58318/
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# Measurement of photon production in the very forward direction in deep-inelastic scattering at HERA
H1 Collaboration; Aaron, F D; Alexa, C; Andreev, V; Müller, K; Robmann, P; Straumann, U; Truöl, P (2011). Measurement of photon production in the very forward direction in deep-inelastic scattering at HERA. European Physical Journal C - Particles and Fields, 71(10):1771.
## Abstract
The production of photons at very small angles with respect to the proton beam direction is studied in deep-inelastic positron–proton scattering at HERA. The data are taken with the H1 detector in the years 2006 and 2007 and correspond to an integrated luminosity of 126 pb−1. The analysis covers the range of negative four momentum transfer squared at the positron vertex 6<Q 2<100 GeV2 and inelasticity 0.05<y<0.6. Cross sections are measured for the most energetic photon with pseudorapidity η>7.9
as a function of its transverse momentum pTlead and longitudinal momentum fraction of the incoming proton xLlead. In addition, the cross sections are studied as a function of the sum of the longitudinal momentum fraction xLsum of all photons in the pseudorapidity range η>7.9. The cross sections are normalised to the inclusive deep-inelastic scattering cross section and compared to the predictions of models of deep-inelastic scattering and models of the hadronic interactions of high energy cosmic rays.
The production of photons at very small angles with respect to the proton beam direction is studied in deep-inelastic positron–proton scattering at HERA. The data are taken with the H1 detector in the years 2006 and 2007 and correspond to an integrated luminosity of 126 pb−1. The analysis covers the range of negative four momentum transfer squared at the positron vertex 6<Q 2<100 GeV2 and inelasticity 0.05<y<0.6. Cross sections are measured for the most energetic photon with pseudorapidity η>7.9
as a function of its transverse momentum pTlead and longitudinal momentum fraction of the incoming proton xLlead. In addition, the cross sections are studied as a function of the sum of the longitudinal momentum fraction xLsum of all photons in the pseudorapidity range η>7.9. The cross sections are normalised to the inclusive deep-inelastic scattering cross section and compared to the predictions of models of deep-inelastic scattering and models of the hadronic interactions of high energy cosmic rays.
## Citations
5 citations in Web of Science®
2 citations in Scopus®
## Altmetrics
Detailed statistics
Item Type: Journal Article, refereed, original work 07 Faculty of Science > Physics Institute 530 Physics English 2011 12 Feb 2012 14:05 05 Apr 2016 15:34 Springer 1434-6044 (P) 1434-6052 (E) The original publication is available at www.springerlink.com 10.1140/epjc/s10052-011-1771-6 http://arxiv.org/abs/1106.5944
Permanent URL: http://doi.org/10.5167/uzh-58318
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http://math.stackexchange.com/questions/69433/an-action-of-a-group-on-a-covering-space
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# An action of a group on a covering space
We see $S_3$ as the quotient of the free group on two elements and the normal subgroup $R$ generated by $\langle\sigma^3,\tau^2,\sigma\tau\sigma\tau\rangle$ where $\sigma$ and $\tau$ are the generators of the free group. The covering space corresponding to $R$ of the bouquet of 2 circle sould be the following:
Now $S_3$ acts on this covering space, and the action should have two orbits. Could you explain me how is this action? (I mean, what are the images of the single edges?)
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Let us write $t=(12)$ and $s=(123)$, two elements of the symmetric group $S_3$ of degree $3$.
Construct a directed graph $\Gamma$ as follows:
• the vertices are the elements of $S_3$,
• if $g\in S_3$ is a vertex, there are two edges coming out of $g$ in $\Gamma$: one going from $g$ to $gt$ and the other going from $g$ to $gs$.
In other words, the set of edges is $$E=\{(g,gt)\in S_3\times S_3:g\in S_3\}\cup \{(g,gs)\in S_3\times S_3:g\in S_3\}.$$
We can draw a picture:
There is an action of $S_3$ on $\Gamma$ as follows: if $h\in S_3$, then
• the action of $h$ on the vertices of $\Gamma$ is by left multiplication by $h$: that is, a vertex $g\in S_3$ is mapped to $hg$;
• on the other hand, the action of $h$ on the edges is the induced one: if $(g_1,g_2)$ is one of the edges, then $h\cdot(g_1,g_2)=(hg_1,hg_2)$. It is easy to see that this latter element is, indeed, an edge of $\Gamma$.
It is very easy to see that the action of $S_3$ on the vertices of $\Gamma$ is simply transitive, so that the quotient graph $\Gamma/S_3$ has exactly one vertex, and that the action of $S_3$ on the edges of $\Gamma$ has exactly two orbits. It thus follows that $\Gamma/S_3$ is a two-leaved rose.
$$♦ ♦ ♦$$
Can you see how to go from this action of $S_3$ on $\Gamma$ to an action of $S_3$ on a CW-complex of dimension $1$, which is what you want?
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It might help to remember that $S_3$ is the same thing as $D_3$. So let's look for a "triangle-ish" shape for $D_3$ to act on. As you've drawn your picture, you can almost see it: the upper and lower three-cycles form a pair of triangles; in this way the whole graph is best visualized as a sort of triangular prism. Now $\sigma$ will act as a rotation, and $\tau$ will swap the upper and lower triangles. From this way of looking at things, it's perhaps easier to see that $S_3$ acts transitively on triangle edges (the non-vertical edges in your picture) and also acts transitively on the vertical edges. So these are your two orbits.
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http://www.drumtom.com/q/please-help-find-the-absolute-maximum-and-absolute-minimum-values-of-f-on-the-given-interval-f-x-x-3-7x-8-0-3
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# Please help! Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x^3 − 7x + 8, [0, 3]?
• Please help! Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x^3 − 7x + 8, [0, 3]?
Minimum and Maximum Values ... Finding Absolute Extrema of f(x) on ... Here we are really asking for the absolute extrema of A(t) on the interval [0,10].
Positive: 24 %
If we replace the interval $[0,\frac{3\pi ... and absolute minimum values of f on the given interval.$f ... to find the absolute maximum of \$f(x) = ...
Positive: 21 %
### More resources
Determine absolute maximum value of: f(x ... Determine absolute maximum value of: f(x) = 4 sin x - 3 ... graph is given by 6 10.0 points 001 1 Find all the ...
Positive: 24 %
find edges. Gaussian blur with ... Please check your URL and try again. ... Help Wolfram|Alpha grow! We respond to as many substantial suggestions as possible.
Positive: 19 %
Critical Points Definition of a ... has a local minimum at x 0. If f '(x 0) = 0 and ... in a closed interval I, then the absolute maximum of f(x) in I is ...
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https://uwaterloo.ca/combinatorics-and-optimization/events/archive/2013
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# Events - 2013
Friday, December 6, 2013 — 3:30 PM EST
## Tutte seminar - Hamid Mahini
### Behavioral Cascades with Opposing Influences
Speaker: Hamid Mahini University of Maryland Mathematics and Computer Building (MC) 5158
#### Abstract:
Thursday, November 28, 2013 — 1:00 PM EST
## Seminar - algebraic graph theory
### Linear Cayley Graphs, Codes and Geometry
Speaker: Mario Huang University of Waterloo Mathematics and Computer Building (MC) 5136
#### Abstract:
Monday, November 25, 2013 — 4:00 PM EST
### Ear-decompositions of nonbipartite matching-covered graphs
Speaker: Nishad Kothari University of Waterloo Mathematics and Computer Building (MC) 5168
#### Abstract:
Friday, November 22, 2013 — 3:30 PM to 4:30 PM EST
## Tutte seminar - Alan Sokal
### Some wonderful conjectures (but very few theorems) at the boundary between analysis, combinatorics and probability
Speaker: Andrew Childs University of Waterloo Mathematics and Computer Building (MC) 5158
Thursday, November 21, 2013 — 1:00 PM EST
## Seminar - algebraic graph theory
### University theorem for polynomial invartiants on ribbon graphs with flags.
Speaker: Avohou Remi Cocou University d'Abomey Calavi Mathematics and Computer Building (MC) 5136
#### Abstract:
In my presentation, I will recall the Bollobas-Riordan polynomial
for ribbon graphs and its universality property. This polynomial finds
Friday, November 15, 2013 — 3:30 PM to 4:30 PM EST
## Tutte seminar - Jane Gao
### Solution geometry of a random k-XORSAT near the clustering threshold
Speaker: Jane Gao University of Toronto Mathematics and Computer Building (MC) 5158
#### Abstract
Friday, November 8, 2013 — 3:30 PM to 4:30 PM EST
## Seminar - Christiane Sato
### Counting Connected Uniform Hypergraphs
Speaker: Christiane Sato University of Waterloo Mathematics and Computer Building (MC) 5158
#### Abstract:
Tuesday, November 5, 2013 — 3:30 PM to 4:30 PM EST
## Seminar - Michael P. Friedlander
### Sparsity and gauge optimization
Speaker: Michael P. Friedlander Department of Computer Science, University of British Columbia Mathematics and Computer Building (MC) 5158
#### Abstract:
Tuesday, November 5, 2013 — 2:30 PM to 3:30 PM EST
## Seminar - Shuzhong Zhang
### Recent Results on Tensor and Polynomial Optimization
Speaker: Shuzhong Zhang University of Minnesota Mathematics and Computer Building (MC) 5158
#### Abstract
Friday, November 1, 2013 — 3:30 PM to 4:30 PM EDT
## Tutte seminar - Laura Sanita
### Finding small stabilizers for unstable graphs
Speaker: Andrew Childs University of Waterloo Mathematics and Computer Building (MC) 5158
#### Abstract:
A vertex v of a graph G is called inessential if there exists a maximum matching in G that exposes v. G is said to be stable if the set of its inessential vertices forms a stable set.
Friday, October 25, 2013 — 3:30 PM to 4:30 PM EDT
## Tutte seminar - Jane Gao
### Solution geometry of a random k-XORSAT near the clustering threshold
Speaker: Jane Gao University of Waterloo Mathematics and Computer Building (MC) 5158
#### Abstract:
Since early 2000s statistical physicists predicted, using a non-rigorous
technique called the "cavity method", that the solution spaces of many
Thursday, October 24, 2013 — 1:00 PM to 2:30 PM EDT
## Algebraic graph theory
### Problems in Algebraic Graph Theory
Speaker: Chris Godsil University of Waterloo Mathematics and Computer Building (MC) 5158
#### Abstract:
Problems in algebraic graph theory will be discussed.
Friday, October 18, 2013 — 3:30 PM to 4:30 PM EDT
## Tutte seminar - Karthekeyan Chandraskearan
### Faster private release of marginals on small databases
Speaker: Professor Karthekeyan Chandraskearan Harvard University Mathematics and Computer Building (MC) 5158
#### Abstract:
Thursday, October 17, 2013 — 3:30 PM to 4:30 PM EDT
## Algebraic graph theory
### Stable Polynomials and Ramanujan Graphs
Speaker: David Wagner University of Waterloo Mathematics and Computer Building (MC) 5158
Abstract:
We show how Marcus, Spielman and Srivastava use stable polynomials to construct bipartite Ramunujan graphs of degree $k$ whenever $k\ge3$. (This will be the second of two lectures.)
Friday, October 11, 2013 — 3:30 PM to 4:30 PM EDT
## Tutte seminar - Marcel Silva
### The Boundary Structure of Spectrahedra Arising from the Lovász Theta Function
Speaker: Marcel Silva University of Waterloo Mathematics and Computer Building (MC) 5158
#### Abstract:
The theta body TH(G) of a graph G is a semidefinite relaxation of
STAB(G), the stable set polytope of G, and it is contained in QSTAB(G),
Thursday, October 10, 2013 — 3:30 PM to 4:30 PM EDT
## Graph Theory seminar
### A Proof of the Manickam-Mikl\'{o}s-Singhi Conjecture for Vector Spaces
Speaker: Ameera Chowdhury Carnegie Melon University Mathematics and Computer Building (MC) 5158
#### Abstract:
Let $V$ be an $n$-dimensional vector space over a finite field.
Assign a real-valued weight to each $1$-dimensional subspace in $V$ so
Friday, October 4, 2013 — 3:30 PM to 4:30 PM EDT
## Tutte seminar - Jim Geelen
### Rota's Conjecture
Speaker: Jim Geelen University of Waterloo Mathematics and Computer Building (MC) 5158
#### Abstract:
In 1970, Gian-Carlo Rota posed a conjecture giving a succinct
combinatorial characterization of the linear dependencies among a finite set of vectors in a vector space over any given finite field.
Thursday, October 3, 2013 — 3:30 PM to 4:30 PM EDT
## Algebraic Graph Theory seminar
### Stable Polynomials and Ramanujan Graphs
Speaker: Andrew Childs University of Waterloo Mathematics and Computer Building (MC) 5158
#### Abstract:
We show how Marcus, Spielman and Srivastava use stable polynomials to
construct bipartite Ramunujan graphs of degree $k$ whenever $k\ge3$. (This will be the first of two lectures.)
Friday, September 27, 2013 — 3:30 PM to 4:30 PM EDT
## Tutte seminar - Anna Bertiger
### The Rim Hook Rule: Relating Quantum Cohomology of the Grassmannian to Ordinary Cohomology of the Grassmannian
Speaker: Anna Bertiger University of Waterloo Mathematics and Computer Building (MC) 5158
#### Abstract:
Friday, September 20, 2013 — 3:30 PM to 4:30 PM EDT
## Tutte seminar - Eric Katz
### Line arrangements and intersection theory on algebraic surfaces
Speaker: Eric Katz University of Waterloo Mathematics and Computer Building (MC) 5158
#### Abstract:
Thursday, September 19, 2013 — 1:00 PM to 2:30 PM EDT
## Algebraic Graph Theory seminar
### Matching Polynomials, Real Stable Polynomials and Ramanujan Graphs
Speaker: Chris Godsil and Dave Wagner University of Waterloo Mathematics and Computer Building (MC) 5158
#### Abstract:
Friday, September 13, 2013 — 3:30 PM to 4:30 PM EDT
## Tutte seminar - Luke Postle
### 3-Coloring and 3-List-Coloring Graphs of Girth at least Five on Surfaces
Speaker: Luke Postle University of Waterloo and Emory University Mathematics and Computer Building (MC) 5158
#### Abstract:
Tuesday, August 20, 2013 — 1:30 PM to 2:30 PM EDT
## Seminar - Sebi Ciaoba
### Connectivity and matching properties of distance-regular graphs
Speaker: Sebi Ciaoba University of Delaware Mathematics and Computer Building (MC) 5158
#### Abstract:
Tuesday, August 13, 2013 — 3:30 PM to 4:30 PM EDT
## Graph Theory seminar - Mike Molloy
### Frozen vertices in colourings of a random graph
Speaker: Mike Molloy University of Toronto Mathematics and Computer Building (MC) 5158
#### Abstract:
Monday, July 29, 2013 (all day) to Friday, August 2, 2013 (all day)
## Workshop on Flexible Network Design
### Flexible network design
#### Topics include
• Theoretical computer science
• Graph algorithms
• Discrete optimization
#### Local organizers
• Joseph Cheriyan (Waterloo)
• Anupam Gupta (Carnegie Mellon)
• Jochen Könemann (Waterloo)
• Stefano Leonardi (Sapienza U. of Rome)
• R. Ravi (Carnegie Mellon)
• Laura Sanita (Waterloo)
• Chaitanya Swamy (Waterloo)
#### Plenary speakers
• Julia Chuzhoy (Toyota Technological Institute at Chicago)
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### January 2013
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http://www.gradesaver.com/textbooks/math/precalculus/precalculus-mathematics-for-calculus-7th-edition/chapter-1-section-1-6-complex-numbers-1-6-exercises-page-64/14
|
## Precalculus: Mathematics for Calculus, 7th Edition
The real part of the complex number $i\sqrt 3$ is 0 and the imaginary part is $\sqrt 3$.
Complex numbers are written in the form a+bi, with a being the real number and b being the imaginary number. Since there is no "a" in this complex number a must be equal to zero. Therefore, b=$\sqrt 3$, so the real part is 0 and the imaginary part is $\sqrt 3$.
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https://www.physicsforums.com/threads/quick-question-with-the-antederivative.148033/
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# Quick question with the antederivative
1. Dec 13, 2006
### ddr
hi!
who help me to find the antiderivative of:
(x^3 + 3x^2)/(x^2 + 4x + 4)
thanks
2. Dec 13, 2006
### HallsofIvy
Staff Emeritus
You sure this is not homework?
First divide so that you have p(x)+ (Ax+ B)/x^2+ 4x+ 4): a polynomial plus a linear term over x^2+ 4x+ 4. You should be able to integrate the polynomial easily. Now use the fact that x^2+ 4x+ 4= (x+2)^2 and partial fractions.
(I just did the division myself: Ax+ B is simple enough that you don't need partial fractions!)
Last edited: Dec 13, 2006
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https://aps.arxiv.org/list/cond-mat.quant-gas/2009?skip=0&show=100
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# Quantum Gases
## Authors and titles for cond-mat.quant-gas in Sep 2020
[ total of 112 entries: 1-100 | 101-112 ]
[ showing 100 entries per page: fewer | more | all ]
[1]
Title: Disconnecting a Traversable Wormhole: Universal Quench Dynamics in Random Spin Models
Comments: 9 pages, 4 figures + supplementary
Journal-ref: Phys. Rev. Research 3, 022024 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
[2]
Title: Robust and Ultrafast State Preparation by Ramping Artificial Gauge Potentials
Comments: Accepted in New Journal of Physics
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[3]
Title: Universal duality transformations in interacting one-dimensional quantum systems
Authors: Manuel Valiente
Comments: 5 pages, 1 figure. See accompanying article "Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime", arXiv:2009.00624
Journal-ref: Phys. Rev. A 103, 021302 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[4]
Title: Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime
Authors: Manuel Valiente
Comments: 22 pages, 5 figures. Accepted version. See accompanying shorter article "Universal duality transformations in interacting one-dimensional quantum systems", arXiv:2009.00614
Journal-ref: Phys. Rev. A 102, 053304 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[5]
Title: Rectification in Nonequilibrium Steady States of Open Many-Body Systems
Comments: 7+5 pages, 4+2 figures, to appear in Physical Review Research
Journal-ref: Phys. Rev. Research 2, 043343 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
[6]
Title: A new form of liquid matter: quantum droplets
Comments: A brief review article to be published in Frontiers in Physics
Subjects: Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS)
[7]
Title: Quantum Zeno effects across a parity-time symmetry breaking transition in atomic momentum space
Journal-ref: npj Quantum information 7, 78 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas)
[8]
Title: Realization of a Bosonic Antiferromagnet
Journal-ref: Nature Physics (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
[9]
Title: Effect of interactions in the interference pattern of Bose Einstein condensates
Comments: 10 pages, 14 figures; published version
Journal-ref: Phys. Rev. A 102, 043314 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[10]
Title: Coherent Manipulation of the Internal State of Ultracold $^{87}$Rb$^{133}$Cs Molecules with Multiple Microwave Fields
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph)
[11]
Title: On-demand generation of dark soliton trains in Bose-Einstein condensates
Journal-ref: Phys. Rev. A 103, 023329 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS); Quantum Physics (quant-ph)
[12]
Title: Anderson Molecules
Journal-ref: Phys. Rev. A 103, 023320 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Atomic and Molecular Clusters (physics.atm-clus); Quantum Physics (quant-ph)
[13]
Title: Energy-Resolved Information Scrambling in Energy-Space Lattices
Comments: Note revised title and completely rewritten text
Journal-ref: Phys. Rev. Lett. 126, 070601 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[14]
Title: Wannier-Stark flatbands in Bravais lattices
Comments: 11 pages, 3 figures. Similar to the published version. Comments are welcome
Journal-ref: Phys. Rev. Research 3, 013174 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Materials Science (cond-mat.mtrl-sci); Quantum Physics (quant-ph)
[15]
Title: Temperature Dependence of the Density and Excitations of Dipolar Droplets
Comments: 11 pages, 6 figures to appear in PRA
Journal-ref: Phys. Rev. A 102, 033329 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas)
[16]
Title: Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates
Journal-ref: Phys. Rev. A 103, 043321 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
[17]
Title: Scattering of two heavy Fermi polarons: resonances and quasibound states
Comments: 7 pages, 6 figures; published version
Journal-ref: Phys. Rev. A 102, 063321 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas)
[18]
Title: Exactly-solvable system of one-dimensional trapped bosons with short and long-range interactions
Journal-ref: Phys. Rev. Lett. 125, 220602 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
[19]
Title: Neutral vortex necklace in a trapped planar superfluid
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
[20]
Title: Quantum Elliptic Vortex in a Nematic-Spin Bose-Einstein Condensate
Journal-ref: Phys. Rev. Lett. 126, 195302 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Other Condensed Matter (cond-mat.other)
[21]
Title: Quantized transport induced by topology transfer between coupled one-dimensional lattice systems
Authors: Lukas Wawer (1), Rui Li (1), Michael Fleischhauer (1) ((1) Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Germany)
Journal-ref: Phys. Rev. A 104, 012209 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas)
[22]
Title: Exact $\mathcal{N}$-point function mapping between pairs of experiments with Markovian open quantum systems
Comments: 16 pages, 2 figures, article in Press
Journal-ref: Phys. Rev. A 102, 043320 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas)
[23]
Title: Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid
Subjects: Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)
[24]
Title: Phonon redshift and Hubble friction in an expanding BEC
Comments: Typos fixed, minor clarifications, version published in SciPost
Journal-ref: SciPost Phys. 10, 064 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Atomic Physics (physics.atom-ph)
[25]
Title: Plane and Stripe Wave Phases of a Spin-Orbit Coupled Bose-Einstein Condensate in an Optical Lattice with a Zeeman Field
Comments: 12 pages, 6 figures, accepted in Physical Review A
Journal-ref: Phys. Rev. A 102, 053318 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas)
[26]
Title: Structured hetero-symmetric quantum droplets
Comments: 6 pages, 5 figures, to appear in Physical Review Research
Journal-ref: Phys. Rev. Research 2, 033522 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)
[27]
Title: Two Rydberg-dressed atoms escaping from an open well
Journal-ref: Phys. Rev. A 103, 013304 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas)
[28]
Title: Pauli crystals -- interplay of symmetries
Journal-ref: Symmetry 12, 1886 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[29]
Title: Open Fermi-Hubbard model: Landauer's vs. master equation approaches
Authors: A. R. Kolovsky
Journal-ref: Phys. Rev. B 102, 174310 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[30]
Title: Searching for the Kardar-Parisi-Zhang phase in microcavity polaritons
Journal-ref: Phys. Rev. B 105, 205301 (2022)
Subjects: Quantum Gases (cond-mat.quant-gas)
[31]
Title: Two-dimensional vortex quantum droplets get thick
Comments: 9pages,6 figures,to be published in Communications in Nonlinear Science and Numerical Simulation
Subjects: Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS)
[32]
Title: Chaos and ergodicity across the energy spectrum of interacting bosons
Comments: 4 pages, 4 figures + supplemental material
Journal-ref: Phys. Rev. Lett. 126, 150601 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[33]
Title: Negative refraction and rotons in the relativistic Bose gas
Subjects: Quantum Gases (cond-mat.quant-gas); High Energy Physics - Theory (hep-th)
[34]
Title: Inflationary Dynamics and Particle Production in a Toroidal Bose-Einstein Condensate
Journal-ref: Phys. Rev. A 103, 023322 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); General Relativity and Quantum Cosmology (gr-qc)
[35]
Title: Large Chern numbers in a dissipative dice model
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[36]
Title: Spin-polarized fermions with $p$-wave interactions
Authors: Furkan Çağrı Top (1), Yair Margalit (1), Wolfgang Ketterle (1) ((1) Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, and Department of Physics, Massachusetts Institute of Technology)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[37]
Title: Molecular Impurities as a Realization of Anyons on the Two-Sphere
Comments: 6 pages, 3 figures with a Supplemental Material
Journal-ref: Phys. Rev. Lett. 126, 015301 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)
[38]
Title: Perfect transmission and perfect reflection of Bogoliubov quasiparticles in a dynamically unstable Bose-Einstein condensate
Subjects: Quantum Gases (cond-mat.quant-gas)
[39]
Title: Many-Body Phases of a Planar Bose-Einstein Condensate with Cavity-Induced Spin-Orbit Coupling
Journal-ref: Phys. Rev. A 103, 023302 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[40]
Title: Propagation of first and second sound in a two-dimensional Fermi superfluid
Comments: 6 pages, 3 figures; published version, correction of journal reference
Journal-ref: Phys. Rev. A 103, L061303 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas)
[41]
Title: Generalized hydrodynamics in strongly interacting 1D Bose gases
Comments: 21 pages, 4 main text figures, 10 extended data figures
Journal-ref: Science 373, 1129 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph)
[42]
Title: Stable two-dimensional soliton complexes in Bose-Einstein condensates with helicoidal spin-orbit coupling
Comments: minor corrections, published version, 2020 New J. Phys. 22 103014
Subjects: Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)
[43]
Title: Quantum Monte Carlo simulation of BEC-impurity tunneling
Journal-ref: Phys. Rev. B 103, 155406 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas)
[44]
Title: Twist-and-store entanglement in bimodal and spin-1 Bose-Einstein condensates
Comments: 16 pages, 10 figures, 1 video file
Journal-ref: Phys. Rev. A 102, 053315 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[45]
Title: Numerically exact mimicking of quantum gas microscopy for interacting lattice fermions
Comments: 5 + 10 pages, 3 + 8 figures, including link to program code, published version
Journal-ref: Phys. Rev. B 104, 075155 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el)
[46]
Title: Resonant collisional shielding of reactive molecules using electric fields
Journal-ref: Science 370, 1324-1327 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Chemical Physics (physics.chem-ph); Quantum Physics (quant-ph)
[47]
Title: Quasi-condensation of bilayer excitons in a periodic potential
Journal-ref: Phys. Rev. Lett. 126, 067404 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas)
[48]
Title: Fate of Lattice Gauge Theories Under Decoherence
Comments: 6 pages and 2 figures, journal paper
Subjects: Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph)
[49]
Title: Interaction induced doublons and embedded topological subspace in a complete flat-band system
Journal-ref: Phys. Rev. A 102, 063325 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Superconductivity (cond-mat.supr-con)
[50]
Title: Chiral condensates in a polariton hexagonal ring
Journal-ref: Optics Letters 45, 5700-5703 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas)
[51]
Title: Edge dynamics of an Integer Quantum Hall system
Authors: Alberto Nardin
Comments: Master thesis work for the Universit\`a degli Studi di Trento, under the supervision of Pr. Iacopo Carusotto
Subjects: Quantum Gases (cond-mat.quant-gas); Other Condensed Matter (cond-mat.other)
[52]
Title: Pattern formation of correlated impurities subjected to an impurity-medium interaction pulse
Journal-ref: Phys. Rev. A 103, 023313 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
[53]
Title: Density Fluctuations across the Superfluid-Supersolid Phase Transition in a Dipolar Quantum Gas
Comments: 11 pages, 5 + 3 figures
Journal-ref: Phys. Rev. X 11, 011037 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph)
[54]
Title: Preparation of the 1/2-Laughlin state with atoms in a rotating trap
Journal-ref: Phys. Rev. A 103, 063325 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)
[55]
Title: Time-optimal variational control of bright matter-wave soliton
Journal-ref: Phys. Rev. A 102, 053313 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS)
[56]
Title: Poincaré crystal on the one-dimensional lattice
Authors: Pei Wang
Journal-ref: J. Phys. A: Math. Theor. 54, 115003 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph)
[57]
Title: Collisionless drag for a one-dimensional two-component Bose-Hubbard model
Comments: 7 pages, 6 figures. Final version published as Letter in PRR
Journal-ref: Phys. Rev. Research 3, 022017 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas)
[58]
Title: Periodic driving induced helical Floquet channels with ultracold atoms in momentum space
Comments: partial overlap with the last section of arxiv:1906.12016V1, which was left out of the published version
Journal-ref: The European Physical Journal D, 74,152 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas)
[59]
Title: Observation and control of quantized scattering halos
Journal-ref: New J. Phys. 22 (2020) 123032
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[60]
Title: Superstripes and quasicrystals in bosonic systems with hard-soft corona interactions
Subjects: Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
[61]
Title: Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder
Comments: 18 pages, 5 figures, submission to SciPost
Journal-ref: SciPost Phys. 10, 008 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)
[62]
Title: Dynamics of a vortex lattice in an expanding polariton quantum fluid
Comments: Main 6 pages, 4 figures, SM 4 pages, 5 figures
Journal-ref: Phys. Rev. Lett. 127, 047401 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Fluid Dynamics (physics.flu-dyn)
[63]
Title: Stückelberg interferometry using spin-orbit-coupled cold atoms in an optical lattice
Comments: 9 pages, 6 figures, close to published version
Journal-ref: Phys. Rev. A 102, 033332 (2020)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[64]
Title: Doubly Modulated Optical Lattice Clock Interference and Topology
Journal-ref: Phys. Rev. Lett. 127, 033601 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[65]
Title: Dynamical control of the conductivity of an atomic Josephson junction
Journal-ref: Phys. Rev. Research 3, 013111 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[66]
Title: Hydrodynamic stabilization of self-organized criticality in a driven Rydberg gas
Journal-ref: Phys. Rev. Lett. 126, 123401 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas)
[67]
Title: Many-body collisional dynamics of impurities injected into a double-well trapped Bose-Einstein condensate
Journal-ref: Phys. Rev. Research 3, 023068 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
[68]
Title: Quantum dark solitons in ultracold one-dimensional Bose and Fermi gases
Authors: Andrzej Syrwid
Comments: 60 pages, 37 figures, Tutorial on quantum solitons in exactly solvable many-body systems (The Version of Record is available online at this https URL)
Journal-ref: Journal of Physics B: Atomic, Molecular and Optical Physics, Volume 54, Number 10 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
[69]
Title: Novel soliton in dipolar BEC caused by the quantum fluctuations
Authors: Pavel A. Andreev
Subjects: Quantum Gases (cond-mat.quant-gas)
[70]
Title: Key role of the moire potential for the quasi-condensation of interlayer excitons in van der Waals heterostructures
Journal-ref: Phys. Rev. B 103, 041406 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas)
[71]
Title: Squeezing-induced Topological Gap Opening on Bosonic Bogoliubov Excitations
Journal-ref: Phys. Rev. A 103, 013308 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas)
[72]
Title: Fermions meet two bosons -- the heteronuclear Efimov effect revisited
Journal-ref: Braz J Phys (2020)
Subjects: Quantum Gases (cond-mat.quant-gas)
[73]
Title: Quantum Simulation of Lattice Gauge Theories on Superconducting Circuits: Quantum Phase Transition and Quench Dynamics
Journal-ref: Chin. Phys. B 31, 020304 (2022)
Subjects: Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)
[74]
Title: Two-Particle Interference with Double Twin-Atom Beams
Journal-ref: Phys. Rev. Lett. 126, 083603 (2021)
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
[75]
Title: Spin-1 spin-orbit- and Rabi-coupled Bose-Einstein condensate solver
Journal-ref: Comput. Phys. Commun. 259 (2021) 107657
Subjects: Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS); Computational Physics (physics.comp-ph); Quantum Physics (quant-ph)
[76]
Title: Quantum reflection of a Bose-Einstein condensate from a rapidly varying potential: the role of dark soliton
Comments: 7 pages of RevTex4-1, 5 figures
Subjects: Quantum Gases (cond-mat.quant-gas)
[77] arXiv:2009.01250 (cross-list from cond-mat.supr-con) [pdf, other]
Title: Boundary Topological Superconductors
Comments: 7+3 pages, 5 figures, some typos are corrected and new references are added
Journal-ref: Phys. Rev. B 103, 064512 (2021)
Subjects: Superconductivity (cond-mat.supr-con); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Materials Science (cond-mat.mtrl-sci); Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el)
[78] arXiv:2009.01491 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: Prethermalization with negative specific heat
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[87] arXiv:2009.09817 (cross-list from cond-mat.dis-nn) [pdf, other]
Title: Out of equilibrium Phase Diagram of the Quantum Random Energy Model
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https://www.proc-iahs.net/379/43/2018/
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Journal cover Journal topic
Proceedings of the International Association of Hydrological Sciences An open-access publication for refereed proceedings in hydrology
Journal topic
Proc. IAHS, 379, 43-47, 2018
https://doi.org/10.5194/piahs-379-43-2018
Proc. IAHS, 379, 43-47, 2018
https://doi.org/10.5194/piahs-379-43-2018
Pre-conference publication 05 Jun 2018
Pre-conference publication | 05 Jun 2018
# Centralized versus distributed reservoirs: an investigation of their implications on environmental flows and sustainable water resources management
Centralized versus distributed reservoirs
• 1International Water Management Institute, Battaramulla, 10120, Sri Lanka
• 2UNU Institute for Water Environment and Health, Hamilton, Ontario, Canada
• 3Department of Civil Engineering, The Open University of Sri Lanka, Nugegoda, 10250, Sri Lanka
Abstract
Storage of surface water is widely regarded as a form of insurance against rainfall variability. However, creation of surface storage often endanger the functions of natural ecosystems, and, in turn, ecosystem services that benefit humans. The issues of optimal size, placement and the number of reservoirs in a river basin – which maximizes sustainable benefits from storage – remain subjects for debate. This study examines the above issues through the analysis of a range of reservoir configurations in the Malwatu Oya river basin in the dry zone of Sri Lanka. The study produced multiple surface storage development pathways for the basin under different scenarios of environmental flow (EF) releases and reservoir network configurations. The EF scenarios ranged from “zero” to “very healthy” releases. It is shown that if the “middle ground” between the two extreme EF scenarios is considered, the theoretical maximum “safe” yield from surface storage is about 65–70 % of the mean annual runoff (MAR) of the basin. It is also identified that although distribution of reservoirs in the river network reduces the cumulative yield from the basin, this cumulative yield is maximized if the ratio among the storage capacities placed in each sub drainage basin is equivalent to the ratio among their MAR. The study suggests a framework to identify drainage regions having higher surface storage potential, to plan for the right distribution of storage capacity within a river basin, as well as to plan for EF allocations.
1 Introduction
Storage of water is widely regarded as a form of insurance against rainfall variability. Although the debate over the most appropriate forms of water storage continues, historically, the “natural” first choice among water planners and managers has been surface storage. This is evidenced by the ancient tank irrigation systems that existed in Sri Lanka from around 300 BC, as well as multiple large dams that were constructed all over the world, during the latter half of the twentieth century. However, creation of surface storage often endanger the functions of natural ecosystems, and, in turn, ecosystem services that benefit humans. The optimal size, placement, and the number of reservoirs in a river basin, which maximizes sustainable benefits, while minimizing negative impacts on ecosystems, remain subjects for debate. This study examines some of the above issues through the analysis of a range of reservoir configurations in the Malwatu Oya river basin in the dry zone of Sri Lanka. Optimal sustainable limits to surface storage development for water supply, and the differences between centralized large reservoirs and distributed small reservoirs, are examined, by studying the behaviour of “water supply yield” versus “environmental flow (EF) yield” with increasing storage under each configuration.
2 Study Area
The Malwatu Oya basin in the dry zone of Sri Lanka (Fig. 1) has a drainage area of 3246 km2 and a mean annual runoff (MAR) of 0.79 km3. It is dotted with small tank cascade systems, an ancient irrigation system consisting of a series of interconnected tanks, acting as storage and regulating reservoirs (Panabokke et al., 2002; Jayatillake et al., 2003). Apart from these small tanks the basin also consists of a number of larger irrigation reservoirs, also built in ancient times, but subsequently modified to suit present day demands. The combination of small and large reservoirs satisfy irrigation and other needs of the basin particularly during the long dry period from May to September.
Figure 1The Malwatu Oya basin and river network.
3 Methodology
## 3.1 Simulation of Natural River Flow
A Water Evaluation and Planning (WEAP) Model (Yates et al., 2005a, b) of the Malwatu Oya basin was developed in order to model its current hydrological processes, physical infrastructure and water abstractions. The larger basin was disaggregated into 147 sub watersheds (Fig. 1), for which climate input was provided with data acquired from six gauging stations in the vicinity. The sub watersheds were delineated in such a manner that they overlapped with the watersheds of the existing tank cascades as much as possible. The average area of a sub watershed was 22.7 km2. Water inflows, outflows, demands and currently available storage capacity (large reservoirs and small tanks) within a sub watershed were lumped together. The model was calibrated and validated (R2= 0.92; Nash–Sutcliffe Coefficient = 0.84) for the period 1961–2013 against measured flow data, and simulated discharges output by a calibrated Soil and Water Assessment Tool (SWAT) model (R2= 0.88; Nash–Sutcliffe Coefficient = 0.86), set up by the International Water Management Institute, for the same basin. Once the model calibration was completed, natural river discharge of each branch of the river was simulated by removing all reservoirs and water abstractions. This natural river discharge served as the basis for analysing different storage and environmental flow scenarios.
## 3.2 Behaviour of Water Supply and EF Yields under a Centralized Large Reservoir
The maximum potential annual “Safe Yield” from reservoir storage in the basin was estimated under a range of reservoir sizes and network configurations while allowing different (with respect to magnitude and timing) EF releases. The “Safe Yield” is the target draft that can be supplied at 100 % reliability for a given flow record by a reservoir which starts full and refills at least once after the worst drought on record (Vogel et al., 2007). The Sequent Peak Algorithm (Thomas and Burden, 1963), implemented in WEAP, which is the automated equivalent of the mass curve approach developed by Rippl (1883) was used for this purpose.
### 3.2.1 Mean Annual Safe Water Supply Yield and EF Yield under a Centralized Large Reservoir
In the initial configuration, the cumulative runoff from the basin was routed through a hypothetical reservoir of increasing capacity while a varying monthly water demand, closely aligned with the actual demand distribution (which is mainly for irrigating rice) of the basin, was imposed on the reservoir. EF releases below the reservoir ranged from “zero” to “very healthy”. Six EF scenarios (time series of flow releases) were generated using the method of Smakhtin and Anputhas (2006). In this approach, the natural monthly flow time series at the outlet of the Malwatu Oya basin is used as input to develop six other monthly flow time series, which differ in magnitude, but are similar in pattern (following the monthly pattern of the natural flows – the pattern considered as the ideal for EF releases). The flow time series correspond to six Environmental Management Classes (EMCs), named A through F, and represent the EF requirements at the downstream end of the basin for the river to be maintained in each of the EMCs. Class A represents the ecological status of a protected healthy river whereas class F represents that of a highly degraded river. Table 1 summarises the mean annual “EF yield” required to maintain the river in each of the EMCs.
The behaviour of the Safe Yield under the zero EF (no EF) and the six EMC scenarios (with equal priorities assigned to both water supply and EF yields) is shown in Fig. 2. The yields shown are gross yields with no evaporation or seepage losses, and, no flood control, buffer or inactive storage assumed for the reservoir. The reservoir storage was allowed to become zero if it was necessary to satisfy the demands, but was required to fill up at least once during the total simulation period (53 years) in order to ensure continuity of storage. The curves represent the theoretical upper thresholds for cumulative annual surface water withdrawals (in units of MAR) from reservoir storage in the basin under a range of ecological protection categories. The curve for Class A provides the highest level of protection, while the curve with no EF requirements provides the lowest level of protection. The “middle ground” between the two extreme scenarios is shown as the “Mid” curve. The inverse of the curves correspond to the annual EF yields under the same set of scenarios, but are not shown on the figure for clarity.
Table 1Mean annual EF requirements (yields) under each Environmental Management Class (EMC).
### 3.2.2 Monthly Distribution of Safe Water Supply Yield and EF Yield under a Centralized Large Reservoir
The monthly distribution (quantity and timing) of both water supply and EF yields is as important as the mean annual quantity. The monthly water supply yield determines the “health” of the supply delivered, whereas the monthly EF yield determines the “health” of the river. Following the well documented reliability, resilience vulnerability and sustainability criteria (Hashimoto et al., 1982; Loucks, 1997) to evaluate the effectiveness of water storage, a Water Supply Sustainability (WSS) index and an Environmental Flow Sustainability (EFS) index (Eq. 1) was adopted to evaluate: how well a given demand is met by a given storage capacity and withdrawal scenario; and how well a prescribed EF regime is met by the in-stream flow releases below a reservoir, in terms of quantity and timing. Although the index of sustainability has been formulated in a number of ways by different authors, its formulation here (Eq. 1) follows that of McCartney et al. (2013). The optimum storage development pathway in a river basin should attempt to maximise both WSS and EFS.
$\begin{array}{ll}\text{(1)}& & \mathrm{Sustainability}=& \phantom{\rule{1em}{0ex}}\frac{\mathrm{Reliability}+\mathrm{Resilience}+\left(\mathrm{1}-\mathrm{Relative}\phantom{\rule{0.125em}{0ex}}\mathrm{Vulnerability}\right)}{\mathrm{3}}\end{array}$
The WSS versus EFS space was mapped out for the two reservoir sizes of 0.4 and 1.0 MAR assuming: (a) the “health of the water supply” is at its best (i.e. WSS = 1) when the water supply yield is at the level of the no EF scenario, and deteriorates when gradually increasing levels of EF is released, and, (b) the health of the river is at its best (i.e. EFS = 1) if the water supply yield is at the level of EMC scenario A, and deteriorates when gradually increasing levels of yields are drawn out. The resulting graphs of WSS versus EFS for scenarios (a) and (b) above for a reservoir size of 1.0 MAR (with different assigned priorities to water supply (WS), EF releases and reservoir filling) are shown on Fig. 3. The Safe Yields at which a compromise is reached between scenarios (a) and (b) for reservoir sizes of 0.4 and 1.0 MAR (when equal priorities to water supply and EF yields, and a lower priority to reservoir filling are assigned) are shown on Fig. 2 as “Compromise” points.
Figure 2Behaviour of Safe Yield for a centralized hypothetical reservoir under different EF releases, compared with those for two distributed reservoir configurations under which no explicit EF releases are made.
## 3.3 Behaviour of Water Supply and EF Yields under Distributed Small Reservoirs
In the second reservoir configuration, hypothetical reservoirs were placed at the outlets of 14 major sub drainage basins (identified by the Department of Agrarian Development) of the Malwatu Oya basin. Maximum potential Safe Yield curves for each of these drainage basins under the no EF scenario were developed, considering only the runoff generated within each sub drainage basin. This exercise helped to identify drainage regions having higher surface storage potential. Next, the cumulative Safe Yield curve for the entire basin was estimated by aggregating the individual yields under two sub scenarios as follows: (a) reservoirs placed in each sub drainage basin are of equal capacity, and, (b) reservoirs placed in each sub drainage basin follow a capacity ratio equivalent to the MAR ratio among sub drainage basins. The above exercise was then repeated under a third configuration where hypothetical reservoirs were placed at the outlets of the 147 sub watersheds delineated in the initial WEAP model. These 147 sub watersheds represent a further sub division of the 14 major drainage basins considered in scenario 2. The resulting Safe Yield curves under both distributed reservoir configurations are also shown on Fig. 2 (Dist. Con.1 MAR ratio, Dist. Con.2 MAR ratio), along with the earlier curves for the centralized reservoir configuration.
Figure 3Variation of WSS and EFS when increasing levels of yields are extracted while trying to satisfy EF at EMC “A” (a); when increasing levels of EF are released while trying to extract yields at “No EF” level (b) for a storage capacity of 1 MAR with different priorities assigned to water supply and EF demands.
4 Results and discussion
When attempting to compromise the mean annual water supply and EF yields for the entire basin (Mid curve of Fig. 2), for cumulative storage capacities below 1.5 MAR units, the EMC scenario C curve represents a reasonable “middle ground” storage development pathway to be adopted, unless there is a specific need for the river to be at a higher state of protection. However, as storage capacities become larger than 1.5 MAR units, adoption of the EMC scenario B curve is more appropriate. Considering the Mid curve, the theoretical maximum (gross) Safe Yield for the Malwatu Oya basin is about 65–70 % of the MAR.
For any given storage capacity, the performance of the two indicators, EFS and WSS (which assess the “health” of the actual pattern of EF releases and water supply yields withdrawn), depend on the magnitude of the yield withdrawn, and the order of priority assigned to meeting each demand and filling up of the reservoir (Fig. 3). Considering where a compromise is reached between WSS and EFS for 0.4 and 1.0 MAR capacities (Fig. 2), the EMC Scenario C curve represents a reasonable storage development pathway to be adopted for cumulative storage capacities below 1.0 MAR units. For storage capacities above 1.0 MAR units, adoption of the Class B scenario is more appropriate.
Figure 2 illustrates that the maximum achievable yield from a lumped reservoir of a certain capacity is higher than the cumulative yield obtained from a network of distributed reservoirs of the same aggregated capacity. The cumulative yield is maximized when the storage capacity in each sub drainage basin follows a ratio equivalent to the MAR ratio of each sub drainage basin (also observed by Pitman, 1995). The cumulative yield of the entire basin declines with subsequent levels of distribution of reservoirs. When the cumulative Safe Yield curves for the two distributed reservoir configurations were compared with the EMC scenario curves in Fig. 2, it was observed that they closely follow the curves for EMC scenarios F and D respectively up to a reservoir size of 0.5 MAR. This implies that more releases are available at the downstream of the basin as EF, even though no explicit EF releases were made. Therefore, planned distribution of reservoirs in the river network, and limiting abstractions from them to a fraction of the local runoff generated within their individual watersheds is a strategy that can be adopted (subject to other requirements in the basin) to ensure that sufficient environmental flow releases are maintained in the river. It is also possible to identify the appropriate distribution of storage capacity in individual watersheds, and threshold levels of withdrawals to ensure that the entire basin stays on an identified sustainable storage development pathway. The actual reservoir configuration in the Malwatu Oya basin is even more densely distributed than any of the ones examined here. The position of the current cumulative storage capacity and current annual yield (approximately 0.43 and 0.31 MAR units respectively) shown on Fig. 2 also agrees with the finding that higher levels of distribution lowers cumulative yields. The current position is almost coincident with the “Mid” curve (Fig. 2). Although this implies that there is a reasonable quantity of annual EF releases at the downstream end, their temporal and spatial distribution (especially during the dry season) needs to be further investigated.
5 Conclusions
The objective of this research was to analyse a series of surface storage scenarios, consisting of hypothetical reservoirs of increasing storage capacity, placed at three levels of distribution across the river network, to investigate how an optimum reservoir arrangement (which maximizes water supply yields) under a given EF release scenario may be formulated. It provides tools and approaches to identify “sustainable” storage development pathways and theoretical maximum “safe” yields for whole river basins. Developing storage yield relationships for sub drainage regions (sub watersheds) helps to identify: regions in a river basin having higher surface storage potential; and, the right distribution of storage capacity (and allowable withdrawals) in individual drainage regions, to stay on an identified storage development pathway, which maximizes water supply yields while accommodating targeted EF yields.
When modelling current river flow, all water transfers and available storage capacity within a sub watershed was lumped together in order to reduce model complexity and processing time. Although the model may have not captured the heterogeneity within a sub watershed, it was still able to simulate river flows at sub watershed outlets (the hydrological resolution of our interest) reasonably well. However, use of simulated flow data in subsequent analyses introduces uncertainty into the end results, no matter how well the hydrological models have performed. Therefore, the use of measured flow time series, wherever possible, is recommended in order to reduce this uncertainty. In addition, further research should also investigate the impact of river fragmentation when reservoirs are distributed across the river network.
Data availability
Data availability.
The daily climate data and monthly flow data used in this study were obtained from the recording gauges of the Meteorological and Irrigation Departments of Sri Lanka respectively. They are currently not publicly available.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Special issue statement
Special issue statement.
This article is part of the special issue “Innovative water resources management – understanding and balancing interactions between humankind and nature”. It is a result of the 8th International Water Resources Management Conference of ICWRS, Beijing, China, 13–15 June 2018.
Acknowledgements
Acknowledgements.
This research was supported by the International Water Management Institute (IWMI) as part of the CGIAR Research Programs on Climate Change Agriculture and Food Security (CCAFS) and Water Land and Ecosystems (WLE). The authors would like to acknowledge the support provided by Madusanka Thilakarathne for processing the data required by the WEAP model.
Edited by: Zongxue Xu
Reviewed by: two anonymous referees
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Yates, D., Purkey, D., Sieber, J., Huber-Lee, A., and Galbraith, H, WEAP21: A demand, priority, and preference-driven water planning model: 2. Aiding freshwater ecosystem service evaluation, Water Int., 30, 501–512, 2005b.
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https://appliedprobability.blog/2017/05/18/weighted-majority-algorithm/
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# Weighted Majority Algorithm
The Weighted Majority Algorithm is a randomized rule used to learn the best action amongst a fixed reference set.
We consider the following setting
• There are a fixed set of actions $i=1,...,N$ which one may choose. There are a set of outcomes $y\in{\mathcal Y}$.
• After choosing an action $i$, an outcome $y$ occurs and you receives a reward $r(i,y)\in [0,1]$. Over time a policy $\pi$ chooses actions $\pi_t$ $t=1,...,T$ and outcomes $y_t$, $t=1,...,T$ occur.
• It is assumed that the function $r:\{1,...,N\}\times {\mathcal Y} \rightarrow [0,1]$ is known by the policy.
• The accumulated a net reward is
We are interested in how our dynamic policy $\pi$ performs in comparison to each fixed policy $i=1,...,N$, that is a policy that chooses the same action $i$ at each time. In particular, we are interested in how this compares to the fixed policy which is retrospectively the best.
• For this reason, we consider the regret of policy $\pi$
• We can only retrospectively find the best fixed policy, whilst our policy $\pi$ must behave adaptively based on historical information. Thus $R(\pi,T)$ quantifies how we regret not having had the information to have chosen the best fixed policy.
• Note a ‘good’ policy would have low regret. For instance, we might hope our dynamic policy is as good as the best fixed policy, i.e. $R(\pi,T)\leq 0$.
Using Blackwell’s Approachability Theorem, we saw that low regret policies exist. See Section [Blackwell]Theorem [blackwell:regret]. One of the key advantages of such algorithms is that is does not place statistical assumptions on the outcome sequence $y_1,...,y_T$. The Weighted Majority Algorithm is a further example of an algorithm that has asymptotically low regret and does not require statistical assumptions to be placed on the input sequence.
Weighted Majority Algorithm
For parameter $\eta>0$, the \emph{(exponentially) weighted majority algorithm} is a randomized policy which chooses a policy $\latex i=1,…,N$ at time $t$ with probability $P(i,N)=\frac{1}{N}$ for $t=1$ and for $t\geq 1$
$P(i,t)=\frac{w_{i,t}}{W(t)},\qquad\text{where}\qquad w_{i,t}=e^{\eta\rho(i,t-1)} \quad\text{and}\quad W(t)=\sum_{i=1}^N e^{\eta \rho(i,t)}.$
We can derived the following regret bound
Theorem: If policy $\pi$ is the the weighted majority algorithm
(1) With $\eta$ fixed,
for choice $\eta=\sqrt{2T^{-1}\log(N)}$, the above bound states
(2) For $\eta$ fixed the policy,
(3) For $\eta_t$ varrying over time and increasing, we have
for choice $\eta_t=\sqrt{4t^{-1}\log(N)}$, the above bound states
Proof:
(1) Observe
In the second inequaltiy, we apply the Azuma-Hoeffding Inequality, see Section [Azuma]. Taking logs and rearranging, we gain the required expression . Substituting $\eta=\sqrt{2T^{-1}\log(N)}$, we gain expression .
(2) We note the following inequality holds
In the first inequality, we bound with the line segment above the exponential. In the second inequality, we apply the bound $1+x\leq e^x$. Applying bound to inequality , we have
Taking logs and rearranging gives the required bound.
(3) The crux of the proof (1) was that the function $N^{-1} W(T) \exp\{-\eta {\mathbb E} \rho(\pi,T) - \eta^2 T^2/2\}$ is decreasing and thus bounded above by $1$. We apply the same prinicple, but we have to take account of the change in parameter $\eta_t$.
We can express our weights differently, notice,
$S(t)^{\eta_t^{-1}}$ will play a similar role to that of $N^{-1} W(T) \exp\{-\eta {\mathbb E} \rho(\pi,T) - \eta^2 T^2/2\}$ in the proof of (1):
Since $S(0)=1$, the sequence is decreasing and bounded above by $1$. Thus, as $\frac{1}{N}s_{i,T}\leq S(T)\leq 1$, we get the result. $\square$
|
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|
https://www.imath.kiev.ua/~sigma/2019/058/
|
### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
SIGMA 15 (2019), 058, 15 pages arXiv:1901.09951 https://doi.org/10.3842/SIGMA.2019.058
Contribution to the Special Issue on Algebraic Methods in Dynamical Systems
### Linear Differential Systems with Small Coefficients: Various Types of Solvability and their Verification
Moulay A. Barkatou a and Renat R. Gontsov bc
a) Laboratoire XLIM (CNRS UMR 72 52), Département Mathématiques-Informatique, Université de Limoges, Faculté des Sciences et Techniques, 123 avenue Albert Thomas, F-87060 LIMOGES Cedex, France
b) Institute for Information Transmission Problems RAS, Bolshoy Karetny per. 19, build. 1, Moscow 127051, Russia
c) Moscow Power Engineering Institute, Krasnokazarmennaya 14, Moscow 111250, Russia
Received January 30, 2019, in final form July 31, 2019; Published online August 09, 2019
Abstract
We study the problem of solvability of linear differential systems with small coefficients in the Liouvillian sense (or, by generalized quadratures). For a general system, this problem is equivalent to that of solvability of the Lie algebra of the differential Galois group of the system. However, dependence of this Lie algebra on the system coefficients remains unknown. We show that for the particular class of systems with non-resonant irregular singular points that have sufficiently small coefficient matrices, the problem is reduced to that of solvability of the explicit Lie algebra generated by the coefficient matrices. This extends the corresponding Ilyashenko-Khovanskii theorem obtained for linear differential systems with Fuchsian singular points. We also give some examples illustrating the practical verification of the presented criteria of solvability by using general procedures implemented in Maple.
Key words: linear differential system; non-resonant irregular singularity; formal exponents; solvability by generalized quadratures; triangularizability of a set of matrices.
pdf (373 kb) tex (20 kb)
References
1. Barkatou M.A., An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system, Appl. Algebra Engrg. Comm. Comput. 8 (1997), 1-23.
2. Barkatou M.A., Cluzeau T., On simultaneous triangularization of a set of matrices, in preparation.
3. Barkatou M.A., Cluzeau T., Weil J.A., Di Vizio L., Computing the Lie algebra of the differential Galois group of a linear differential system, in Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2016, 63-70.
4. Barkatou M.A., Pflügel E., ISOLDE: a Maple package for solving systems of linear ODEs (1996), available at http://sourceforge.net/projects/isolde/.
5. Compoint E., Singer M.F., Computing Galois groups of completely reducible differential equations, J. Symbolic Comput. 28 (1999), 473-494.
6. Feng R., Hrushovski's algorithm for computing the Galois group of a linear differential equation, Adv. in Appl. Math. 65 (2015), 1-37, arXiv:1312.5029.
7. Gontsov R.R., On the dimension of the subspace of Liouvillian solutions of a Fuchsian system, Math. Notes 102 (2017), 149-155.
8. Gontsov R.R., Vyugin I.V., Solvability of linear differential systems with small exponents in the Liouvillian sense, Arnold Math. J. 1 (2015), 445-471.
9. Hrushovski E., Computing the Galois group of a linear differential equation, in Differential Galois Theory (Bęedlewo, 2001), Banach Center Publ., Vol. 58, Polish Acad. Sci. Inst. Math., Warsaw, 2002, 97-138.
10. Humphreys J.E., Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York - Berlin, 1972.
11. Kaplansky I., An introduction to differential algebra, Actualités Sci. Ind., Vol. 1251, Hermann, Paris, 1957.
12. Khovanskii A.G., On solvability and unsolvability of equations in explicit form, Russian Math. Surveys 59 (2004), 661-736.
13. Khovanskii A.G., Topological Galois theory: solvability and unsolvability of equations in finite terms, Springer Monographs in Mathematics, Springer, Heidelberg, 2014.
14. Kimura T., On Riemann's equations which are solvable by quadratures, Funkcial. Ekvac. 12 (1970), 269-281.
15. Kolchin E.R., Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations, Ann. of Math. 49 (1948), 1-42.
16. Maciejewski A., Moulin-Ollagnier J., Nowicki A., Simple quadratic derivations in two variables, Comm. Algebra 29 (2001), 5095-5113.
17. Morales Ruiz J.J., Differential Galois theory and non-integrability of Hamiltonian systems, Progress in Mathematics, Vol. 179, Birkhäuser Verlag, Basel, 1999.
18. van der Hoeven J., Around the numeric-symbolic computation of differential Galois groups, J. Symbolic Comput. 42 (2007), 236-264.
19. Vidunas R., Differential equations of order two with one singular point, J. Symbolic Comput. 28 (1999), 495-520.
20. Vyugin I.V., Gontsov R.R., On the question of solubility of Fuchsian systems by quadratures, Russian Math. Surveys 67 (2012), 585-587.
21. Wasow W., Asymptotic expansions for ordinary differential equations, Pure and Applied Mathematics, Vol. 14, Interscience Publishers John Wiley & Sons, Inc., New York - London - Sydney, 1965.
22. Żoładek H., Polynomial Riccati equations with algebraic solutions, in Differential Galois Theory (Będlewo, 2001), Banach Center Publ., Vol. 58, Polish Acad. Sci. Inst. Math., Warsaw, 2002, 219-231.
23. Żoładek H., The monodromy group, Monografie Matematyczne, Vol. 67, Birkhäuser Verlag, Basel, 2006.
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http://www.sphinx-doc.org/en/master/development/tutorials/helloworld.html
|
# Developing a “Hello world” extension¶
The objective of this tutorial is to create a very basic extension that adds a new directive. This directive will output a paragraph containing “hello world”.
Only basic information is provided in this tutorial. For more information, refer to the other tutorials that go into more details.
Warning
For this extension, you will need some basic understanding of docutils and Python.
## Overview¶
We want the extension to add the following to Sphinx:
• A helloworld directive, that will simply output the text “hello world”.
## Prerequisites¶
We will not be distributing this plugin via PyPI and will instead include it as part of an existing project. This means you will need to use an existing project or create a new one using sphinx-quickstart.
We assume you are using separate source (source) and build (build) folders. Your extension file could be in any folder of your project. In our case, let’s do the following:
1. Create an _ext folder in source
2. Create a new Python file in the _ext folder called helloworld.py
Here is an example of the folder structure you might obtain:
└── source
├── _ext
│ └── helloworld.py
├── _static
├── conf.py
├── somefolder
├── index.rst
├── somefile.rst
└── someotherfile.rst
## Writing the extension¶
Open helloworld.py and paste the following code in it:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 from docutils import nodes from docutils.parsers.rst import Directive class HelloWorld(Directive): def run(self): paragraph_node = nodes.paragraph(text='Hello World!') return [paragraph_node] def setup(app): app.add_directive("helloworld", HelloWorld) return { 'version': '0.1', 'parallel_read_safe': True, 'parallel_write_safe': True, }
Some essential things are happening in this example, and you will see them for all directives.
The directive class
Our new directive is declared in the HelloWorld class.
1 2 3 4 5 class HelloWorld(Directive): def run(self): paragraph_node = nodes.paragraph(text='Hello World!') return [paragraph_node]
This class extends the docutilsDirective class. All extensions that create directives should extend this class.
This class contains a run method. This method is a requirement and it is part of every directive. It contains the main logic of the directive and it returns a list of docutils nodes to be processed by Sphinx. These nodes are docutils’ way of representing the content of a document. There are many types of nodes available: text, paragraph, reference, table, etc.
The nodes.paragraph class creates a new paragraph node. A paragraph node typically contains some text that we can set during instantiation using the text parameter.
The setup function
This function is a requirement. We use it to plug our new directive into Sphinx.
1 2 3 4 5 6 7 8 def setup(app): app.add_directive("helloworld", HelloWorld) return { 'version': '0.1', 'parallel_read_safe': True, 'parallel_write_safe': True, }
The simplest thing you can do it call the add_directive() method, which is what we’ve done here. For this particular call, the first argument is the name of the directive itself as used in a reST file. In this case, we would use helloworld. For example:
Some intro text here...
.. helloworld::
Some more text here...
We also return the extension metadata that indicates the version of our extension, along with the fact that it is safe to use the extension for both parallel reading and writing.
## Using the extension¶
The extension has to be declared in your conf.py file to make Sphinx aware of it. There are two steps necessary here:
1. Add the _ext directory to the Python path using sys.path.append. This should be placed at the top of the file.
2. Update or create the extensions list and add the extension file name to the list
For example:
import os
import sys
sys.path.append(os.path.abspath("./_ext"))
extensions = ['helloworld']
Tip
We’re not distributing this extension as a Python package, we need to modify the Python path so Sphinx can find our extension. This is why we need the call to sys.path.append.
You can now use the extension in a file. For example:
Some intro text here...
.. helloworld::
Some more text here...
The sample above would generate:
Some intro text here...
Hello World!
Some more text here...
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https://stats.stackexchange.com/questions/505437/example-of-curved-exponential-family-with-t-being-a-complete-statistic
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# Example of curved exponential family with $T$ being a complete statistic?
Is there any example of curved exponential family with $$T$$ being a complete statistic? Here $$T$$ is the sufficient statistic.
• "Curved exponential families may arise when the parameters of an exponential family satisfy constraints. For these families the minimal sufficient statistic may not be complete, and UMVU estimation may not be possible." R. Keener Jan 18 '21 at 20:05
• Keener gives the example of two Normal samples with both variances being equal, in which case there exists a complete sufficient statistic. Jan 18 '21 at 20:07
2. When $$X\sim \mathcal B(p)$$ and $$Y\sim\mathcal B(h(p))$$, the joint distribution of $$(X,Y)$$ is curved except for a specific function $$h_0(p)$$. Give two functions $$h(p)$$ for which $$(X,Y)$$ is minimal sufficient but not complete and for which $$(X,Y)$$ is complete.
• One solution to this problem is $h(p)=cp$, then $(X,Y)$ is not complete. When $h(p)=p^c$, $(X,Y)$ is complete. Here $c$ is a non-zero constant. Other solutions are also possible.
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https://dsp.stackexchange.com/questions/27280/how-do-we-find-the-capacity-of-mimo-wideband-point-to-point-system
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# How do we find the capacity of MIMO wideband point to point system?
This question is in the context of digital communication .
In many text books (wireless communication), when people derive the capacity of point to point communication system (one transmit one receive end) with multiple transmit and multiple receive antennas, people consider the narrow band flat fading channel. Below I write down the output equation of system with $N$ transmit antennas and $M$ receive antennas
$${\bf Y_{M\times 1} = H_{M\times N}X_{ N\times 1}+ Z_{M\times 1}}$$
The solution to find the maximum capacity is to do Singular Value Decomposition (SVD) of the channel as follows
$${\bf H = U D V^H}$$
The transmitter uses matrix ${\bf V}$ that is the transmit signal is $${\bf X'= VX}$$ while the receiver uses matrix ${\bf U}$ as follows
$${\bf Y'= U^HY}$$
My question is what about wideband channels, time varying frequency selective channels that is systems with channel such as
$${\bf H_{M\times N}(t)} \,\,\,\,\,\, t =0... T_{Delay}$$
How do we find the MIMO capacity of such channels. In one case, I think once can assume multicarrier (OFDM) system and divide the wideband channel into smaller narrow band and apply the algorithm I mentioned above. But what if its not multicarrier system? What is the optimal scheme, what should the transmitter and receiver do?
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https://artofproblemsolving.com/wiki/index.php/User:Temperal/The_Problem_Solver%27s_Resource6
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# User:Temperal/The Problem Solver's Resource6
Introduction | Other Tips and Tricks | Methods of Proof | You are currently viewing page 6.
## Beginner/Intermediate Number Theory
This section covers number theory, specifically Fermat's Little Theorem, Wilson's Theorem,Euler's Totient Theorem, Quadratic residues, and the Euclidean algorithm.
To use this page, we recommend knowing the basics of Linear congruence, Modular arithmetic, and have a grasp of basic number theory needed for the AMC 10 and 12.
## Definitions
• if is the remainder when is divided by to give an integral amount. Also, this means b divides (n-a).
• (or divides ) if for some integer .
• is the greek letter phi. is the number of integers less than or equal to m that are at the same time relatively prime to n. If the prime factorization of n is , .
## Special Notation
Occasionally, if two equivalent expressions are both modulated by the same number, the entire equation will be followed by the modulo.
refers to the greatest common factor of and refers to the lowest common multiple of .
## Properties
For any number there will be only one congruent number modulo between and .
If and , then .
• , where is a positive integer that divides and .
### Fundamental Theorem of Arithmetic
The Fundamenal Theorem of Arithmetic is fairly clear, yet is extremely important. It states that any integer n greater than one has a unique representation as a product of primes. It has a very interesting proof; attempt to prove it using contradiction.
### Fermat's Little Theorem
For a prime and a number such that , . A frequently used result of this is .
#### Example Problem 1
Find all primes p such that .
##### Solution
Firstly, p=2 clearly does not work. Now, as all other primes are odd, and hence . After adding one, we have since p divides . However, that means p must divide 3, so the only prime possible is 3. Indeed, is a multiple of 3.
### Wilson's Theorem
For a prime , .
#### Example Problem 2
Let be an integer such that . Find the remainder when is divided by .
##### Solution
After multiplying through by , we know that every term on the left-hand-side will be divisible by 13 except for . We wish to find the remainder when is divided by 13. From Wilson's Theorem, we know that so we consider (mod 13). Thus, the remainder is which comes out to be 7. Thus, our answer is 7.
### Euler's Phi Theorem
If , then , where is the number of relatively prime numbers lower than . This is mostly a generalization of Fermat's Little Theorem, although much more useful.
An integer n is a quadratic residue (mod m) if and only if there exists an integer p such that . Some useful facts are that all quadratic residues are or and , , or . All cubic residues (mod 9) are 0, 1, or -1.
#### Example Problem 3
Does there exist an integer such that its cube is equal to , where n is an integer? (IMO longlist 1967)
##### Solution
Consider (mod 9), and n (mod 3). If n is divisible by 3, is clearly divisible by 9. If n is congruent to 1 (mod 3), is congruent to 6 (mod 9). If n is congruent to 2 (mod 3), then . As n+1 is divisible by 3, it is congruent to 0 (mod 9). Hence, is either 7 or 4 (mod 9). However, all cubes are 0,1, or -1 (mod 9), so there does not exist such an integer.
### Solving Linear Congruences
As mentioned at the top, you should at least know how to solve simple linear congruences, with just one linear congruence. However, solving with two or more congruences is more complex, and many times there is not even a solution. The Chinese Remainder Theorem shows when the congruences do have a unique solution. *to be continued*
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http://experiment-ufa.ru/x+y=177;x=97
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# x+y=177;x=97
## Simple and best practice solution for x+y=177;x=97. Check how easy it is, to solve this system of equations and learn it for the future. Our solution is simple, and easy to understand, so dont hesitate to use it as a solution of your homework.
If it's not what You are looking for type in the system of equations solver your own equations and let us solve it.
Remember to put linear equations with variables x and y.
for example:
2x+y=8
x+3y=14
## Solution for x+y=177;x=97 system of equations:
We try to solve the equation: We insert the solution into one of the initial equations of our system of equationsWe get a system of equations:We insert the solution into one of the initial equations of our system of equationsFor :We get a system of equations:`
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https://ask.sagemath.org/question/48215/how-to-load-in-jupyter/?answer=48222
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# how to Load in Jupyter edit
This doesn't works (latex_milp.py is on my desktop) on Windows10
What can I test ?
edit retag close merge delete
Hi Cyrille
on which OS do you work?,, but I do not know your userName and the dir of your ipynb is surely not the same as mine(you need to double the \ , i did it but it disseapear when the message is displayed:
on my W10 OS:
on my UBUNTU OS (do not double the /):
if you do not want to have to add the full path , then simply copy your file in the directory where you code is (the file *.ipynb)
to know the Desktop path on W10/8 open an explorer and click right on the Desktop icon in the tree, and look at the path in the general tab.
( 2019-10-07 08:31:08 +0200 )edit
it would be nicer, Cyrille, to say when someone answers your question if it helped to solve your problem or not.
if that's not the case can you tell us what's wrong
( 2019-10-07 15:53:24 +0200 )edit
Sorry Ortollj, I have a very busy day because of courses but also because I must taught tomorrow with S&ageMAth and I cannot obtain what I espect. Of course there are some difference in the managment of path between windows 10 and linux. In my case if I put the file in the good directory there is no problem but for all the other case not one of the suggestion works. And sincerely I appreciate your help.
( 2019-10-07 20:23:36 +0200 )edit
Ok >Cyrille ,But what is your OS ? if it is W10/8 did you think about doubling slashes ? , \\
but I imagine that as you are overwhelmed, the option to put the file in the code folder is enough. Good luck for tomorrow. but if you have time tick the @dsejas answer below in a way to pass this question solved the tick just under the 1 answer below.
( 2019-10-07 23:13:30 +0200 )edit
sorry I forget this question. I have found, but I do not know where that insertig a r before the " works for windows10 which is my os. But I do not know why. I have found no references.
( 2020-06-07 14:02:02 +0200 )edit
Sort by » oldest newest most voted
Hello, @Cyrille! I am not completely sure if there are differences between Windows and Linux (I use Linux), but I think the following three procedures are OS-independent:
1. If you launch the Sage Notebook from the terminal (command line), you can move first to the same directory where your latex_milp.py file is, and then launch the Sage Notebook with sage -n jupyter.
2. When you open the Sage Notebook, the first screen that is shown to you has a tree of folder through which you can navigate on your computer. Just move to the folder where your latex_milp.py is, and then open a new notebook with the "new" menu on you right.
3. When I am feeling a little lazy, I look for the file, I make right click on it, and select the "copy" option. Then I move to my Sage Notebook, write load(""), and in the middle of the quotation marks, I make right click and give the "paste" command. That copies the complete location of my file. For example, suppose I have my file on "/home/user/Documents/latex_milp.py". Exactly that location should appear in the middle of the load command. (I am not completely sure that this works on Windows.)
I hope this helps! If not, you should follow @ortollj's suggestion, and give us a little bit of additional info on the location of your file, so we can help.
more
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http://water.huji.ac.il/publications/year/2012
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## פרסומים של בוגרי התוכנית
רבים מבוגרי התוכנית פרסמו מאמרים אקדמים בתחומי הידרולוגיה שונים.
# Publications
2012
Peleg, N. & Morin, E., 2012. Convective rain cells: Radar-derived spatiotemporal characteristics and synoptic patterns over the eastern Mediterranean. Journal of Geophysical Research , 117 , 'עמ. D15116. Publisher's Versionתקציר
This paper examines the spatiotemporal characteristics of convective rain cells over the eastern Mediterranean (northern Israel) and their relationship to synoptic patterns. Information on rain cell features was extracted from high-resolution weather radar data. The radar-gauge adjustment, validation, cell segmentation and tracking techniques are discussed at length at the beginning of the paper. Convective rain cells were clustered into three synoptic types (two winter lows—deep Cyprus lows and shallow lows—and one tropical intrusion, Active Red Sea Trough) using several NCEP/NCAR parameters, and empirical distributions were computed for their spatial and temporal features. In the study region, it was found that the Active Red Sea Trough rain cells are larger, live for less time and possess lower rain intensities than the rain cells generated by the winter lows. The Cyprus low rain cells were found to be less intense and slightly larger on average than the shallow low rain cells. It was further discovered that the preferential orientation of the rain cells is associated with the direction and velocity of the wind. The effect of distance from the coastline was also examined. An increase in the number and area of the rain cells near the coastline was observed, presumably due to the sea breeze convection. The mean rainfall intensity was found to peak near the shore and decrease with distance inland. This information is of great importance for understanding rain patterns and can be further applied in exploring the hydrological responses of the basins in this region.
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https://www.physicsforums.com/threads/find-velocity-of-a-long-jumper.438570/
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Find Velocity of a long jumper
• Start date
• #1
5
0
Homework Statement
An athlete executing a long jump leaves the ground at an angle of 30 degrees and travels 8.90m. What was the take-off speed?
Homework Equations
d(vertical)=(vi)(t) + 0.5at^2
The Attempt at a Solution
0=Vsin30t + (0.5)(-9.8)(t^2)
I cannot solve for two separate variables, how can I solve this problem?
• #2
2,745
22
EDIT: I see what you've done.
Right, in your attempt, d does not equal 0. There has to be some vertical height.
For horizontal you know:
d = 8.9m
For vertical you know:
a = -9.8 for the ascent and 9.8 for the descent.
You know vf for the ascent = 0 and vi for the descent = 0.
Last edited:
• #3
5
0
that is the vertical, there is no horizontal acceleration
Vertical:
Vi=?
Vf=?
a=-9.8m/s^2
t=?
d=0
Horizontal:
Vave=?
t=?
d=8.90m
• #4
2,745
22
that is the vertical, there is no horizontal acceleration
Vertical:
d=0
d does not equal 0. There has to be vertical height.
The vertical phase is split in two. See previous post for details.
Unless you know the flight time, this question all comes down to the vertical components.
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http://aas.org/archives/BAAS/v26n2/aas184/abs/S6104.html
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In Search of $\ldots$ Dwarfs in the Tidal Debris of Compact Groups
Session 61 -- Properties and Evolution of Clusters of Galaxies
Display presentation, Thursday, 2, 1994, 9:20-6:30
[61.04] In Search of $\ldots$ Dwarfs in the Tidal Debris of Compact Groups
S. D. Hunsberger (Penn State), D. Zaritsky (Carnegie Observatories), $\;$ J. C. Charlton (Penn State)
Tidal forces extract material from interacting galaxies and form bridges and tails of gas and stars. Recent observational results support the idea, presented by Zwicky (1956) and confirmed by N-body simulations (Barnes and Hernquist 1992), that self-gravitating objects within such tidal debris could evolve into small galaxies. For example, Mirabel et al. (1991) observed a region of active star formation at the tip of the southern tail of the Superantennae, and Mirabel et al. (1992) observed a nascent dwarf irregular galaxy at the tip of the Antennae. \par We present moderately deep CCD images of 52 Hickson compact groups and results from a search for condensed objects in tidal tails within these groups. Tidal tails are expected in compact groups because the number density of galaxies is similar to that of rich clusters, where interactions are common. However, because the groups were not chosen due to the presence of tidal tails, this work presents an unbiased study of dwarf galaxy formation in tidal tails within an environment where such tails should be common. The results to date are presented here. \bigskip \par \noindent Barnes, J.E. \& Hernquist, L.E. 1992, Nature , {\bf360}, 715 \newline Mirabel, I.F., Dottori, H. \& Lutz, D. 1992, A\&A, {\bf256}, L19 \newline Mirabel, I.F., Lutz, D. \& Maza, J. 1991, A\&A, {\bf243}, 367 \newline Zwicky, F. 1956, Ergebnisse der Exakten Naturwissenschaften , {\bf29}, 344
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|
http://codereview.stackexchange.com/questions/21408/calculating-scores-for-predictions-of-football-scores
|
# Calculating scores for predictions of football scores
I am writing a program which calculates the scores for participants of a small "Football Score Prediction" game.
Rules are:
1. if the match result(win/loss/draw) is predicted correctly: 1 point
2. if the match score is predicted correctly(exact score): 3 points (and +1 point because 1st rule is automatically satisfied)
Score is calculated after every round of matches (10 matches in a round).
The program I've written is as follows:
import numpy as np
import re
players = {0:'Alex',1:'Charlton',2:'Vineet'}
results = np.array(range(40),dtype='a20').reshape(4,10)
eachPrediction = np.array(range(20),dtype='a2').reshape(2,10)
score = np.zeros(3)
correctScore=3
correctResult=1
allPredictions = []
done = False
def takeFixtures():
filename='bplinput.txt'
file = open(filename)
fixtures = [line.strip() for line in text]
file.close()
i=0
for eachMatch in fixtures:
x=re.match("(.*) ([0-9]+) ?- ?([0-9]+) (.*)", eachMatch)
results[0,i]=x.group(1)
results[1,i]=x.group(2)
results[2,i]=x.group(3)
results[3,i]=x.group(4)
i+=1
def takePredictions(noOfParticipants):
for i in range(0,noOfParticipants):
print("Enter predictions by "+players[i]+" in x-y format")
for i in range(0,10):
eachFixturePrediction = raw_input("Enter prediction for "+results[0,i]+" vs "+results[3,i]+": ")
x=eachFixturePrediction.split('-')
eachPrediction[0,i]=str(x[0])
eachPrediction[1,i]=str(x[1])
allPredictions.append(eachPrediction)
def scoreEngine():
for i in range(0,len(players)):
for j in range(0,10):
resultH=int(results[1,j])
resultA=int(results[2,j])
result=resultH-resultA
predictionH=int(allPredictions[i][0][j])
predictionA=int(allPredictions[i][1][j])
pResult = predictionH-predictionA
if result == pResult or (result<0 and pResult<0) or (result>0 and pResult>0):
score[i]+=correctResult
if resultH==predictionH and resultA==predictionA:
score[i]+=correctScore
noOfParticipants=len(players)
takeFixtures()
takePredictions(noOfParticipants)
scoreEngine()
print("Scores are:")
print(score)
for player in players:
print(players[player]+" has scored "+ str(score[player])+" points" )
The file used to take list of fixtures looks like this:
West Bromwich Albion 0-1 Tottenham Hotspur
Manchester City 2-2 Liverpool
Queens Park Rangers 0-0 Norwich City
Arsenal 1-0 Stoke City
Everton 3-3 Aston Villa
Newcastle United 3-2 Chelsea
West Ham United 1-0 Swansea City
Wigan Athletic 2-2 Southampton
Fulham 0-1 Manchester United
I want advice on how this program can be improved in any way (decreasing the code/ making it efficient).
-
## Style
The first thing to do is to follow PEP 8: it's a style guide that says how you should indent your code, name your variables, and so on. For example, prefer results[0, i] = x.group(1) to results[0,i]=x.group(1).
## Files
Opening files in Python should be done using the with idiom: your file is then guaranteed to be close correctly. takeFixtures now becomes:
def takeFixtures():
with open('bplinput.txt') as file:
for eachMath in file:
x=re.match("(.*) ([0-9]+) ?- ?([0-9]+) (.*)", eachMatch.strip)
results[0,i]=x.group(1)
results[1,i]=x.group(2)
results[2,i]=x.group(3)
results[3,i]=x.group(4)
i+=1
## Data structures
I you didn't use numpy, you could have written results[i] = x.groups(), and then used zip(*results) to transpose the resulting matrix. More generally, as pointed out by Josay, you should use Python data structures, and only switch to numpy if you find out that this is where the inefficiency lies.
## Formatting
The last thing that the other reviewers didn't mention is that concatenating strings is poor style, and format() should be preferred since it's more readable and more efficient:
for player in players:
print("{} has scored {} points".format(players[player], score[player]))
-
thanks,Can you give me suggestion on a better way to take input from all the players? right now I have to manually input the score predictions by all players, and if there is some mistake i have to do it all over again. ie. one mistake and i have to input 30 predictions all over again – vineetrok Feb 7 '13 at 15:29
You need to catch the exception that comes out and ask the input to be made again. You would need some kind of loop to make the input until it worked correctly. This would be a good question on StackOverflow unless it has alread been asked. – Quentin Pradet Feb 7 '13 at 16:14
First thing, let's talk about the players array :
• you define it with players = {0:'Alex',1:'Charlton',2:'Vineet'}.
• you iterate on it using :
for i in range(0,noOfParticipants):
or
for player in players:
# Something about : players[player] and str(score[player])
First passing the length of an array without passing the array is a bit awkward (not to say useless). Then, the way you loop is not very pythonic. If what you want is a list of names, define it as a list of names: players = ['Alex','Charlton','Vineet'] (if you define the index yourself and you iterate using only the size of the loop, you might get troubles). Then, if you want to iterate over the names, it's pretty straightforward: for player in players:. You want the index as well ? Enumerate is what you want: for i,name in enumerate(players). How cool is this ?
However, it might be a good idea to make this array a little bit more complicated and use it to store not only the players' names but also their prediction and their score. Then, a dictionary would be a good solution.
Then, a few details :
• I think you should get rid of the magic numbers: I have no idea what the different numbers are for.
• I think correctScore and correctResult are not very good names to express number of points (pointCorrectScore and pointCorrectResult are my suggestions) but storing this in variable is a pretty good idea. Also, I would advise you to create a function returning the score from an estimation and an actual score. Your variables correctScore and correctResult could then be local to your function.
I have no time to go further in the code I didn't quite understand at first glance but I'll try to do it eventually.
-
I'd change something in the style of your application in order to decrease the coupling.
Why do you use global variables? I'd change the design to have the following functions:
• takeFixtures(fileName) returning the fixtures;
• takePredictions(numberOfParticipants, fixtures) returning the predictions for each player. This should be decomposed in a function that takes the predictions of a player and another that takes the prediction for a single game;
• computeScores(fixtures, predictions) that returns a list of pair (player, score). That function should be decomposed to other functions computing the score for a player and the score for a single game.
In addition to that, why do you limit your code to work only if you have 10 games? Wouldn't it be better if you replace the 10 in for j in range(0,10): with len(games) or something similar? That would also benefit from the functional point of view as your code would support out of the box any league regardless of the number of games played each turn.
-
the reason I limited to 10 games because its for Barclays premier league which has 20 teams. but its a good suggestion, i'll take it :) thanks – vineetrok Feb 7 '13 at 15:23
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https://human.libretexts.org/Bookshelves/Composition/Introductory_Composition/Book%3A_Horse_of_a_Different_Color_-_English_Composition_and_Rhetoric/Part_I%3A_The_Writing_Process/3%3A_Drafting/3.2%3A_During_the_Drafting_Process
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# 3.2: During the Drafting Process
“My starting point [in writing] is always a feeling of partisanship, a sense of injustice . . . I write because there is some lie that I want to expose, some fact to which I wish to draw attention, and my initial concern is to get a hearing.” —George Orwell
## Let it Flow
As you draft, do not stop to edit or look up small pieces of information; there will be time for precision later. Luke Sullivan, author of Hey Whipple, Squeeze This, suggests that you must “write hot and edit cold.” In other words, write off the top of your head and allow your thoughts to be spontaneous. You never want to leave a good idea out. However, when it comes to polishing the final product, become critical by taking out unnecessary words or ideas that stray from the main message. Do not keep text that distracts or causes misunderstandings. If you have a question, place it in brackets or make a note of it and refer back to it later. First, just get your ideas out without worrying about punctuation or spelling. Similarly, if you notice a big gap which requires more research, skip it and work on other sections. The important thing is to let your ideas keep coming and make progress on the page. No matter how irrelevant your words may appear, keep writing. If you have to stop, be sure to end in a place where it will be easy to pick up from later. Don't get distracted when your initial drafts aren’t “A” quality work. That’s the reason they are drafts. The important thing is to get your ideas down on paper. You can spend time evaluating them later on.
“Write 1,000 words a day. That’s only about four pages, but force yourself to do it. Put your finger down your throat and throw up. That’s what writing’s all about.” —Ray Bradbury
Figure $$\PageIndex{1}$$ - Photo credit: fotoleder via Visualhunt.com/CC BY-NC-ND
## Dealing with Writer’s Block
Writer’s block can occur at any point during the writing process. You may find yourself sitting down to write when you suddenly realize that you can't think of a single thing to say. Don't panic! It’s a common problem with a variety of solutions.
Here are a few...
• Staring at a blank screen can be intimidating. Try writing out your dilemma in the form of a question: “What is it I’m trying to say?” “What are my goals?” Then brainstorm to answer these questions.
• Take a break. Ten minutes away from your work will usually recharge your creativity.
• Review the literature on your topic to see what other people are saying. Even opposing views can be inspiring.
• Bounce ideas off someone else. Speaking about your writer’s block with friends, family, and fellow students may help untangle ideas or generate new ones.
• Read aloud what you’ve already written to see if the juices start flowing again.
## Experiment
How do you start your draft? While the occasional flash of inspiration can lead you to scribble out great work on the back of an envelope with a stubby pencil, paying brief attention not only to “what you write,” but “how you write,” can inspire you to write differently or even more effectively.
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https://www.r-bloggers.com/2011/01/r-tutorial-series-two-way-anova-with-pairwise-comparisons/
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Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
By extending our one-way ANOVA procedure, we can test the pairwise comparisons between the levels of several independent variables. This tutorial will demonstrate how to conduct pairwise comparisons in a two-way ANOVA.
Tutorial Files
Before we begin, you may want to download the sample data (.csv) used in this tutorial. Be sure to right-click and save the file to your R working directory. This dataset contains a hypothetical sample of 27 participants who are divided into three stress reduction treatment groups (mental, physical, and medical) and three age groups (young, mid, and old). The stress reduction values are represented on a scale that ranges from 0 to 10. This dataset can be conceptualized as a comparison between three stress treatment programs, one using mental methods, one using physical training, and one using medication, across three age groups. The stress reduction values represent how effective the treatment programs were at reducing participant’s stress levels, with higher numbers indicating higher effectiveness. Note that the numbers in this dataset are not very realistic and are simply used to make this example possible.
Beginning Steps
To begin, we need to read our dataset into R and store its contents in a variable.
1. > #read the dataset into an R variable using the read.csv(file) function
3. > #display the data
4. > dataTwoWayComparisons
The first ten rows of our dataset.
Omnibus Test
Let’s run a general omnibus test to assess the main effects and interactions present in the dataset.
1. > #use anova(object) to test the omnibus hypothesis
2. > #Are main effects or interaction effects present in the independent variables?
3. > anova(lm(StressReduction ~ Treatment * Age, dataTwoWayComparisons))
The omnibus ANOVA test
Pairwise Comparisons
Since the omnibus test was significant for both variables and no interaction effect was present, we can proceed to testing the main effect pairwise comparisons. To accomplish this, we will apply our pairwise.t.test() function to each of our independent variables. For more details on the pairwise.t.test() function, see the One-Way ANOVA with Pairwise Comparisons tutorial.
1. > #use pairwise.t.test(x, g, p.adj) to test the pairwise comparisons between the treatment group means
2. > #What significant differences are present amongst the treatment means?
3. > pairwise.t.test(dataTwoWayComparisons$StressReduction, dataTwoWayComparisons$Treatment, p.adj = “none”)
4. > #use pairwise.t.test(x, g, p.adj) to test the pairwise comparisons between the age group means
5. > #What significant differences are present amongst the age group means?
6. > pairwise.t.test(dataTwoWayComparisons$StressReduction, dataTwoWayComparisons$Age, p.adj = “none”)
Pairwise comparisons of treatment group means
Pairwise comparisons of age group means
Note that the desired p-adjustment method will vary by researcher, study, etc. Here, we will assume an alpha level of .05 for all tests, effectively making no adjustment for the family-wise Type I error rate.
These results indicate that there are are no statistically significant pairwise differences between the treatment groups and that all of the comparisons between age groups are statistically significant. The age group means are 8 for young, 5 for mid, and 2 for old. Consequently, we are inclined to conclude that, regardless of treatment, young patients are going to be most responsive, followed by middle aged patients, followed by older ones. However, there is insufficient support to differentiate between the effectiveness of the treatment methods themselves.
Complete Two-Way ANOVA with Pairwise Comparisons Example
To see a complete example of how two-way ANOVA pairwise comparisons can be conducted in R, please download the two-way ANOVA comparisons example (.txt) file.
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http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0003919
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Research Article
# Reference Intervals in Healthy Adult Ugandan Blood Donors and Their Impact on Conducting International Vaccine Trials
• [email protected]
Affiliations: U.S. Military HIV Research Program, Rockville, Maryland, United States of America, Makerere University Walter Reed Project, Kampala, Uganda
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• Affiliations: U.S. Military HIV Research Program, Rockville, Maryland, United States of America, Makerere University Walter Reed Project, Kampala, Uganda
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• Affiliation: Makerere University Walter Reed Project, Kampala, Uganda
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• Affiliation: Uganda National Blood Transfusion Service, Kampala, Uganda
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• Affiliation: Makerere University Walter Reed Project, Kampala, Uganda
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• Affiliation: Makerere University Walter Reed Project, Kampala, Uganda
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• Affiliation: Makerere University Walter Reed Project, Kampala, Uganda
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• Affiliation: Makerere University Walter Reed Project, Kampala, Uganda
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• Affiliation: U.S. Military HIV Research Program, Rockville, Maryland, United States of America
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• Affiliation: Makerere University Walter Reed Project, Kampala, Uganda
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• Affiliation: Makerere University Walter Reed Project, Kampala, Uganda
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• Affiliation: U.S. Military HIV Research Program, Rockville, Maryland, United States of America
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• Affiliation: Walter Reed Army Institute of Research, Rockville, Maryland, United States of America
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• Affiliations: U.S. Military HIV Research Program, Rockville, Maryland, United States of America, Armed Forces Research Institute of Medical Sciences, Bangkok, Thailand
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• Published: December 11, 2008
• DOI: 10.1371/journal.pone.0003919
## Abstract
### Background
Clinical trials are increasingly being conducted internationally. In order to ensure enrollment of healthy participants and proper safety evaluation of vaccine candidates, established reference intervals for clinical tests are required in the target population.
### Methodology/Principal Findings
We report a reference range study conducted in Ugandan adult blood bank donors establishing reference intervals for hematology and clinical chemistry parameters. Several differences were observed when compared to previously established values from the United States, most notably in neutrophils and eosinophils.
### Conclusions/Significance
In a recently conducted vaccine trial in Uganda, 31 percent (n = 69) of volunteers screened (n = 223) were excluded due to hematologic abnormalities. If local reference ranges had been employed, 83% of those screened out due to these abnormalities could have been included in the study, drastically reducing workload and cost associated with the screening process. In addition, toxicity tables used in vaccine and drug trial safety evaluations may need adjustment as some clinical reference ranges determined in this study overlap with grade 1 and grade 2 adverse events.
### Introduction
Substantial efforts are underway to develop and test HIV vaccines internationally. The first priority in vaccine development is the evaluation of safety and tolerability in the clinically “normal” adult population. In order to accurately assess what is healthy, reference intervals for standard laboratory tests in the target population are necessary. Use of improper clinical reference ranges may falsely exclude otherwise eligible volunteers from participating in vaccine trials, making the process of trial enrollment and execution more challenging. In addition, clinical reference intervals in a population are necessary in order to accurately assess potential adverse vaccine reactions observed during the course of a clinical trial.
Common practice in Uganda, both in hospitals and research laboratories, is to use the manufacturer's ranges for a given clinical laboratory assay system. Many of these assay systems are procured from Europe or the United States and use reference values based on their populations, which may not be representative of the Ugandan population. Numerous publications describe differences between clinical reference ranges in African populations compared to industrialized countries [1], [2], [3], [4], [5]. A small number of publications address reference values in Uganda [4], [6], but these are limited in scope to hematologic and selected lymphocyte parameters or restricted geographically to rural areas of Uganda.
In November 2004, screening for enrollment in a Phase I HIV vaccine trial to assess the safety and immunogenicity of a multiclade HIV-1 DNA plasmid vaccine (VRC-HIVDNA009-00-VP, Vaccine Research Center, National Institute of Health, Bethesda, Maryland) began at the Makerere University Walter Reed Project (MUWRP) in Kampala, Uganda. [7] The trial enrolled 31 healthy Ugandan volunteers, with inclusion criteria based on clinical reference ranges obtained from US sources. Due to numerous exclusions based on laboratory abnormalities, the screening to enrollment ratio was extremely high (7 volunteers screened for every 1 trial participant). These numbers present enormous logistical, personnel and financial issues for movement of vaccine candidates into phase II and phase III trials, thus more appropriate reference ranges are needed. In addition, population relevant clinical reference ranges would aid clinicians in patient management in Uganda.
This study establishes the reference ranges for hematology and chemistry values in anonymous, healthy, adult Ugandan blood bank donors in the Kampala region and evaluates their potential implications in vaccine trials.
### Materials and Methods
#### Blood Bank
The Nakasero Blood Bank, in Kampala, is the central laboratory for the Uganda Blood Transfusion Service (UBTS). The UBTS supplies over 140,000 units of blood per year to Ugandan hospitals. Blood donations are derived from the donation center in Kampala and at multiple donation centers throughout the country. In accordance with Ugandan National blood donation policy and practices, a confidential pre-donation evaluation is conducted by a trained health counselor to determine eligibility to donate blood. Questions include information about blood transfusion history‚ number of sexual partners‚ use of non-sterilized needles‚ prolonged fever or frequent infections‚ history of liver disease or hepatitis‚ and medication history. In addition‚ a general physical examination including general appearance‚ lymphadenopathy‚ weight, height‚ blood pressure‚ and temperature is performed by a health specialist trained by the UBTS. A copper sulfate test is used to ensure adequate hemoglobin levels in blood donors. As a result of the screening process‚ the HIV prevalence in the blood donor population has been reduced from approximately 14 percent in 1987 to 2 percent in 2003. (personal communication, Dr. Peter Kataaha, Director UBTS) These procedures ensured that blood collection occurred in those donors that were generally healthy.
Participation in this study was anonymous as no linkage was present between the blood donor and samples. The only demographic information collected was gender, age and regional collection site. All donors found eligible as a result of the blood bank screening process were asked to participate in this study. Donors willing to participate were required to complete a written donor affidavit form, consenting to donate residual blood for research purposes. The study received ethical approval from the Makerere University Faculty of Medicine Research and Ethics Committee and the Uganda National Council of Science and Technology in Uganda and from the Walter Reed Army Institute of Research Institutional Review Board in the United States.
#### Sample collection
After standard blood collection in a polyethylene donation bag, residual blood remaining in the tubing was collected into 3ml EDTA and serum collection vacutainers. The tubing was manually clamped at the bag to prevent backflow of blood and/or anticoagulant from the bag into the tubing. Samples were transported at room temperature in sealed boxes to the College of American Pathologists (CAP) accredited MUWRP laboratory, located in Kampala, Uganda. Only those samples received in the laboratory within 8 hours of phlebotomy were included in the study. All samples were collected between July and September 2005.
#### Hematology and Chemistry Testing
Hematology analysis, including a complete blood count and five part differential, was performed on EDTA anticoagulated blood using the Coulter AcT5 diff (Beckman Coulter, Fullerton, California). Serum vacutainers were centrifuged at 800×g and serum was aliquoted for use on Roche Cobas Integra 400 plus analyzer (Roche, Indianapolis, Indiana). Tests were performed on both platforms in strict adherence to manufacturer's instructions.
#### Exclusion from reference range data set
All samples were tested for HIV antibody, Hepatitis B surface Antigen, Hepatitis C Antibody, and pregnancy. All test kits were approved by the US Food and Drug Administration (FDA). Samples found to be positive in any of these tests were excluded from the data set.
Initial screening for anti-HIV-1 antibody was conducted using Genetic Systems rLAV ELISA (BioRad Laboratories, Redmond, WA). Reactive samples were repeated in duplicate using the Vironostika HIV-1 Microelisa Systems (Organon Teknika, Durham, North Carolina). Samples repeatedly reactive by both ELISAs were tested using the Genetic Systems HIV-1 Western Blot (BioRad Laboratories, Redmond, WA). Screening for Hepatitis B surface antigen (HBsAg) was performed using the Genetic Systems HBsAg EIA 3.0 (BioRad Laboratories, Redmond, WA). Repeatedly reactive samples were confirmed using the Genetic Systems Confirmatory Assay 3.0 (BioRad Laboratories, Redmond, WA). Screening for anti-Hepatitis C antibody was performed using the Ortho HCV Version 3.0 ELISA Tests System. Repeatedly reactive samples were tested in the Chiron RIBA HCV 3.0 SIA (Chiron Corporation, Emeryville, CA). Serum pregnancy testing was performed on all females using Wampole PreVue hCG cassettes. (Wampole Laboratories, Inc Dist., Princeton, NJ)
#### Statistical methods
Ranges were calculated using JMP 5.1 (SAS Institute, Cary, NC, USA). The reference range intervals were calculated as the range between those values at the 2.5% and 97.5% limits for the population after exclusions listed above, stratified by gender, thus providing the reference range encompassing 95% of the population. The non-parametric Wilcoxon test was used to determine any statistically significant differences between laboratory values for men and women.
### Results
#### Sample collection results
Of 960 samples collected and received in the laboratory, 8% (78/960) were excluded due to laboratory abnormalities (1% positive for HIV Antibody; 4% positive for Hepatitis B Surface Antigen; 3% positive or indeterminate for Hepatitis C Antibody; 3% of females were pregnant). Another 2% (20/960) were excluded from the analysis due to missing data. Following these exclusions, 862 samples were included for clinical reference range determination. Most analytes had far fewer samples included due to issues with sample volume or test availability (Tables 1 and 2), but the number of subjects tested for each analyte was within the sample size (N = 120) suggested by CLSI.[8] The gender distribution was 20% female and 80% male and the median age was 23 years (male:24, female:20), with a range of 18 to 56. Most volunteers (73%) were below the age of 30.
#### Hematology and Chemistry Reference Ranges
Hematologic reference ranges, mean and median values are presented in Table 1. Statistically significant (p<0.05) gender differences were seen in most parameters, with the exception of the red blood cell indices (MCV, MCH, MCHC), absolute monocyte count and absolute basophil count, but these differences were not clinically relevant. In comparing these values with those obtained from the Massachusetts General Hospital (MGH) in the United States [9], there were several noticeable differences. The lower limit of the neutrophil percentage range was considerably decreased in the Ugandan population (22%) compared with the MGH population (40%), while the upper limit of eosinophil percentages was drastically increased (25% in Uganda vs. 8% at MGH). The lower range of the red blood cell parameters (RBC, Hemoglobin, Hematocrit) was also decreased in the Ugandan population.
Chemistry reference intervals were established for 24 analytes including electrolytes, liver function tests, renal function tests, lipid profile, cardiac enzymes and others. Mean and median values along with the 2.5–97.5% ranges are presented in Table 2. There were statistically significant (p < 0.05) differences between men and women for fifteen laboratory parameters. Most tests were in agreement with reference intervals published in the US.[9] Differences in cholesterol and triglyceride values are likely due to the fact that samples in our study were not collected from fasting individuals. Two enzymes, Creatine Kinase (CK) and Lactose Dehydrogenase (LDH) had upper ranges that were substantially higher than the published MGH ranges(See Table 2)[9]. In contrast, the upper limit of the Lipase range was much lower in the Ugandan population (68 U/L) compared to the MGH upper range (160 U/L) although it was within the range given by the instrument manufacturer. (13–60 U/L).[10]
### Discussion
Reference ranges were established for hematology and chemistry parameters using samples derived from anonymous blood bank donors. Although the number of females was disproportionate to males (20% vs. 80%) in this study, the number of females included in reference range determination for each analyte was well within the guidelines of CLSI of 120 subjects[8]. The lower proportion of females is likely due to less frequent participation in blood drives and other medical research due to cultural issues. The low prevalence of Hepatitis B surface antigen, Hepatitis C Antibody and HIV antibody in this group demonstrates the success of the blood bank's screening questionnaire as a method for eliminating donors with pathological conditions or acute illnesses that may have an impact on blood safety. Although a detailed medical history outlined by the CLSI guideline[8], including history of tobacco use, diet, alcohol consumption, fasting status, exercise history, genetic or environmental factors, occupation and socio-economic status could not be obtained and utilized in this study, the rigorous screening process employed by the blood bank presumably resulted in collection from overall healthy adults. Furthermore, the blood bank population is likely to be similar to one that would participate in vaccine trials, making these reference ranges directly applicable to that population.
Hematology ranges derived in this study were comparable to published values in Uganda using identical methodology[4], despite the fact that the previous study focused on rural areas and the health status of the volunteers was largely unknown. Red blood cell parameter and platelet findings were consistent with other published African values[2], [4], [5], with Ugandans having lower levels than subjects from industrialized nations. As has been previously shown in other African countries[11], [12], [13], our analysis revealed drastically higher eosinophil counts than published values derived from the United Sates[9] and is likely a result of the high prevalence of parasitic infestations in Africa[4]. The observed neutropenia in this study has also been previously documented[1], [11], [12], [14], 15, although the cause is still unknown. In contrast with other African studies[2], [4], [16], our data showed significant gender differences between white blood cells and most differential parameters.
Clinical chemistry reference values have not been previously published in Uganda. In contrast with hematologic ranges, chemistry ranges were similar to those published in the United States with a few exceptions. CK and LDH values were substantially higher than those published for the US. Exercise is known to elevate levels of these enzymes[17] and perhaps the topography of Kampala combined with the socio-economic status of the donors compared to the US and Europe may lead to more daily physical exercise in the Ugandan group. Additionally, racial differences in creatine kinase levels have been documented and may be contributing to this disparity.[18]
Calculation of region specific reference ranges is not only important for improving quality of health care, but also for implementation of vaccine trials. The impact of utilization of local reference ranges may be significant in reducing screening to enrollment ratios in clinical trials. Our program recently screened 223 volunteers for a phase I vaccine trial in Kampala, Uganda in 2004–2005. As local reference ranges had not been established, US based reference ranges were used for inclusion/exclusion criteria. These inclusion/exclusion criteria included: 1) White blood cell count: 3,300–12,000 cells/µl; 2) Hemoglobin: >11g/L (females) and >12.5 g/L (males); 3) Neutrophils: 32–66% or >1,500 cells/µl 4)Lymphocytes: 28–61% or >800 cells/µl; 5) Eosinophils: 0–8% or ≤400 cells/µl; 6)Platelet count: 125,000–550,000 cells/µl. A total of 69 volunteers were excluded due to apparent hematology abnormalities. However if locally derived reference intervals had been utilized, 57 of these volunteers (83%) could have been included (Table 3). Additionally, the time period for trial enrollment could have theoretically been reduced from 4 months to approximately 3 months. A reduction in the number of volunteers screened would impact dramatically both daily workload and cost. For example, the personnel cost (clinic and laboratory) for conducting screening visits for the additional 57 volunteers in this vaccine study was approximately $17,000 (US). The extra clinical supplies and lab tests associated with the additional screening cost approximately$10,300 (US). In personnel and lab supply costs alone these additional volunteers increased the cost of the study by \$27,000 (US).
Equally important, the toxicity tables used for grading adverse events may need re-evaluation based on clinical reference ranges from the developing world (Table 4). In particular, the NIH Division of AIDS (DAIDS) table for grading the severity of adult and pediatric adverse events (http://www3.niaid.nih.gov/research/resources/DMIDClinRsrch/toxtables.htm) used in many clinical trials may not reflect locally established country specific reference ranges. For example, the range for absolute neutrophils established in this study has a lower limit of 0.9×10ˆ3 cells/ul, although this value would qualify as a grade 2 adverse event. Similarly, ranges for hemoglobin, platelets and CO2 coincide with a grade 1 adverse event.
Ideally, a reference range study should be conducted as an independent investigation, with carefully designed questionnaires, exclusion/inclusion criteria and a comprehensive sampling plan, according to CLSI guidelines[8]. These studies are time consuming, logistically difficult and quite expensive. Most published reference range studies in Africa [2], [3], [4], [5], [6] have used existing studies/protocols (cohort development, HIV studies, etc) in order to gather data. Some studies have had strict criteria for sample inclusion [2] while the two studies in Uganda required only a negative HIV test [4], [6]. Our study used a similar approach as the previous African studies, although a brief physical exam as described earlier went one step further towards ensuring participation of generally healthy donors. Several limitations are apparent in the design of our study, mostly importantly the lack of detailed information to rule out subclinical conditions. We conducted this study within the framework of the bloodbank's existing procedures, without additional staff or infrastructure and without resources spent on volunteer recruitment. In order to minimize interference in daily activities, very limited extraneous information was collected. A second limitation of this study is the calculation of ranges based on a very specific population. Although the blood bank population can be described as a self-selected population, this is in fact, similar to a population that might participate in clinical trials. In a developing country, where resources are limited, we believe that our study methods were adequate to determine reference ranges in a setting where this type of information is limited.
Despite the stated limitations of the study, we assert that the ranges generated in this study would be suitable for use in a more generalized setting, especially in the absence of other relevant data. It is possible that these ranges could be extrapolated to other regions in East Africa or other regions of Africa, of similar altitudes and environments, however small bridging studies according to CLSI guidelines[8] should be performed in order to validate these ranges in a new population. Our study confirms previous findings that regional differences exist for clinical reference intervals. These intervals are critical for successful evaluation of vaccines and drugs internationally and also for advancing basic health care services in the developing world.
### Acknowledgments
The authors would like to thank the Ugandan Blood Bank donors who agreed to participate in this study, the Blood Bank staff who collected samples and obtained consent from the blood donors and the hard work and dedication of the staff in all departments of the Makerere University Walter Reed Project. We thank Dr. Robert O'Connell for his critical review of the manuscript. Material has been reviewed by the Walter Reed Army Institute of Research. There is no objection to its presentation and/or publication. The opinions or assertions contained herein are the private views of the author, and are not to be construed as official, or as reflecting true views of the Department of the Army or the Department of Defense.
### Author Contributions
Conceived and designed the experiments: LAE MAE PK FWM HK MR NM MdS. Performed the experiments: BO DK RT JW RS. Analyzed the data: LAE MAE BO WBS. Contributed reagents/materials/analysis tools: PK. Wrote the paper: LAE MAE MdS.
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1. 1. Bain BJ (1996) Ethnic and sex differences in the total and differential white cell count and platelet count. J Clin Pathol 49: 664–666.
2. 2. Tsegaye A, Messele T, Tilahun T, Hailu E, Sahlu T, et al. (1999) Immunohematological reference ranges for adult Ethiopians. Clin Diagn Lab Immunol 6: 410–414.
3. 3. Menard D, Mandeng MJ, Tothy MB, Kelembho EK, Gresenguet G, et al. (2003) Immunohematological reference ranges for adults from the Central African Republic. Clin Diagn Lab Immunol 10: 443–445.
4. 4. Lugada ES, Mermin J, Kaharuza F, Ulvestad E, Were W, et al. (2004) Population-based hematologic and immunologic reference values for a healthy Ugandan population. Clin Diagn Lab Immunol 11: 29–34.
5. 5. Saathoff E, Schneider P, Kleinfeldt V, Geis S, Haule D, et al. (2008) Laboratory reference values for healthy adults from southern Tanzania. Trop Med Int Health 13: 612–625.
6. 6. Tugume SB, Piwowar EM, Lutalo T, Mugyenyi PN, Grant RM, et al. (1995) Hematological reference ranges among healthy Ugandans. Clin Diagn Lab Immunol 2: 233–235.
7. 7. Eller MA, Eller LA, Opollo MS, Ouma BJ, Oballah PO, et al. (2007) Induction of HIV-specific functional immune responses by a multiclade HIV-1 DNA vaccine candidate in healthy Ugandans. Vaccine 25: 7737–7742.
8. 8. NCCLS (2000) How to define and determine reference intervals in the clinical laboratory; approved guideline-Second Edition. National Committee for Clinical Laboratory Standards, Wayne, PA C28-A2, Vol.20 No 13. 2ed
9. 9. Kratz A, Ferraro M, Sluss PM, Lewandrowski KB (2004) Case records of the Massachusetts General Hospital. Weekly clinicopathological exercises. Laboratory reference values. N Engl J Med 351: 1548–1563.
10. 10. Diagnostics R (2007) Instructions for use, Roche Laboratory Analyzers: Cobas Integra
11. 11. Shaper AG, Lewis P (1971) Genetic neutropenia in people of African origin. Lancet 2: 1021–1023.
12. 12. Ezeilo GC (1972) Non-genetic neutropenia in Africans. Lancet 2: 1003–1004.
13. 13. Badenhorst CJ, Fourie J, Steyn K, Jooste PL, Lombard CJ, et al. (1995) The haematological profile of urban black Africans aged 15-64 years in the Cape Peninsula. East Afr Med J 72: 19–24.
14. 14. Ezeilo GC (1971) Neutropenia in Africans. Trop Geogr Med 23: 264–267.
15. 15. Ezeilo GC (1974) The aetiology of neutropenia in healthy Africans. East Afr Med J 51: 936–942.
16. 16. Menard D, Mavolomade EE, Mandeng MJ, Talarmin A (2003) Advantages of an alternative strategy based on consecutive HIV serological tests for detection of HIV antibodies in Central African Republic. J Virol Methods 111: 129–134.
17. 17. Pilis W, Langfort J, Pilsniak A, Pyzik M, Btasiak M (1988) Plasma lactate dehydrogenase and creatine kinase after anaerobic exercise. Int J Sports Med 9: 102–103.
18. 18. Black HR, Quallich H, Gareleck CB (1986) Racial differences in serum creatine kinase levels. Am J Med 81: 479–487.
Ambra 2.10.8 Managed Colocation provided
by Internet Systems Consortium.
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http://cowlark.com/cowbel/runtime-library.html
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#### Introduction
The cowbel runtime library is a work in progress and mainly exists to support the test suite. If you actually want to write a real program in cowbel, you're advised to copy the files you want to protect yourself from future changes.
Currently the actual library is so much in flux that the only sensible documentation is in the header files themselves. Formal documentation here will follow once I've written a documentation generator.
#### Primitive types
Unlike cowbel 0.1, primitive types are now represented by interfaces and are described in Stdlib.ch above.
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http://mathhelpforum.com/calculus/202933-limit-proof-required-special-case-chain-rule-print.html
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# Limit proof required for special case of chain rule
• September 4th 2012, 06:06 PM
lamp23
Limit proof required for special case of chain rule
I am trying to figure out how to prove the equality I circled below in red. I have figured out how to prove the text in blue but don't know how to use that to prove the equality I circled in red.
Below I will post the givens I'm trying to use and my guess of how to prove it.
P.S. I understand this only proves the chain rule in the special case where $\Delta u \neq 0$. This is from Stewart's Calculus and he does mention that this is not a full proof but I'm very curious how to prove this special case anyway.
http://i900.photobucket.com/albums/a...amp23/calc.jpg
I'm not sure if I'm using the right givens below.
In their blue form it looks like I will be able to use the transitive property of implication $(a \rightarrow b \wedge b \rightarrow c) \rightarrow (a \rightarrow c)$ if I can always let the $\epsilon$ from the 1st given equal the $\delta$ from the second line.
http://i900.photobucket.com/albums/a...3/deltau-2.jpg
• September 4th 2012, 07:15 PM
Prove It
Re: Limit proof required for special case of chain rule
• September 4th 2012, 09:52 PM
lamp23
Re: Limit proof required for special case of chain rule
I'm not looking for a way to prove the product of the limits is the limit of the product. I'm looking for a way to prove the two expressions I circled in red are equal, i.e. $\lim_{\Delta x\to 0}\frac{\Delta y}{\Delta x} = \lim_{\Delta u\to 0}\frac{\Delta y}{\Delta x}$
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https://bestbinaryoptionstradingsystem.com/how-to-learn-forex-trading-for-beginner-do-i-pay-tax-on-forex-trading.html
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If we denote by S the FOR/DOM exchange rate (i.e., 1 unit of foreign currency is worth S units of domestic currency) we can observe that paying out 1 unit of the domestic currency if the spot at maturity is above or below the strike is exactly like a cash-or nothing call and put respectively. Similarly, paying out 1 unit of the foreign currency if the spot at maturity is above or below the strike is exactly like an asset-or nothing call and put respectively. Hence if we now take {\displaystyle r_{\mathrm {FOR} }} , the foreign interest rate, {\displaystyle r_{DOM}} , the domestic interest rate, and the rest as above, we get the following results.
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Articles and other publications on this site are current as of their date of publication and do not necessarily reflect the present law or regulations. BinaryOptions.net accepts no responsibility for loss which may arise from accessing or reliance on information contained in this site. BinaryOptions.net is not responsible for the content of external internet sites that link to this site or which are linked from it. USA REGULATION NOTICE: Please note if you are from the USA: some binary options companies are not regulated within the United States. These companies are not supervised, connected or affiliated with any of the regulatory agencies such as the Commodity Futures Trading Commission (CFTC), National Futures Association (NFA), Securities and Exchange Commission (SEC) or the Financial Industry Regulatory Authority (FINRA). We warn US citizens of the dangers of trading with such entities and strongly advise that they take legal advice on this in the US. 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https://physics.stackexchange.com/questions/600502/s-acting-on-a-spin-chain-raises-the-entropy-by-at-most-ln2/633636#633636
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# $S^+$ acting on a spin chain raises the entropy by at most $\ln(2)$
Consider the operator $$S^+ = \sum_{i=1}^L S^+_i$$ acting on a spin-chain of spin-1/2 particles. Denote the half-chain Von Neumann entanglement entropy of a state $$|\psi\rangle$$ by $$\mathbb{S}[|\psi\rangle]$$. (For simplicity in notation in the following, take $$\mathbb{S}[0] = 0$$.)
Consider the following example. Define the state $$|\Omega\rangle$$ as having all spins down: $$|\Omega\rangle = \otimes_{i=1}^L|\downarrow\rangle$$. Then $$\mathbb{S}[|\Omega\rangle] =0$$ because $$|\Omega\rangle$$ is a product state, while $$\mathbb{S}[S^+|\Omega\rangle] = \ln(2)$$, as can be seen by a quick Schmidt decomposition by hand. Notice in particular that
$$\mathbb{S}[S^+|\Omega\rangle] - \mathbb{S}[|\Omega\rangle] = \ln(2)$$
After playing around a little with numerics, I have the following conjecture: $$\max_{|\psi\rangle \in \mathscr{H}} \left( \mathbb{S}[S^+|\psi\rangle] - \mathbb{S}[|\psi\rangle] \right)= \ln(2)$$
That is, $$S^+$$ can only increase the entropy of a state by $$\ln(2)$$ and no more. Similarly, I conjecture that $$\max_{|\psi\rangle \in \mathscr{H}} \left( \mathbb{S}[(S^+)^n|\psi\rangle] - \mathbb{S}[|\psi\rangle] \right)=\mathbb{S}[(S^+)^n|\Omega\rangle] - \mathbb{S}[|\Omega\rangle]$$
Are these conjectures correct? How can I prove these conjectures?
A small piece of supporting evidence (not near a proof) for the first conjecture is that it is easy to check that all product states $$|p\rangle$$ in the $$S^z$$-basis obey $$\mathbb{S}[S^+|p\rangle] \leq \ln(2)$$, as the resulting state's Schmidt decomposition has at most two states. Another small piece of supporting evidence, when I feed in random states for $$|\psi\rangle$$, the entanglement entropy decreases relative to the entropy of the random state. However, this is just supporting evidence that is far from a statement about all possible states in the Hilbert space.
• Only saw this now: The point is that the operator S+ has Schmidt rank 2 (as an operator), and thus, it can increase the Schmidt rank of any state by at most a factor of 2. However, what happens to the Schmidt coefficients can be rather different, as you correctly note in your answer. May 2 at 22:03
• @NorbertSchuch Thanks, that adds clarity to what's happening. May 2 at 22:34
My conjectures in my question were incorrect. Since $$S^+$$ can destroy certain states, it's possible to begin with a low entanglement entropy state that gains a high entropy after being acted upon by $$S^+$$.
For example, consider (for some large $$L$$) a state $$|\psi\rangle = \sqrt{.999999999} \otimes_{i=1}^L|\uparrow\rangle_i + \sqrt{.000000001} (\text{scrambled, normalized superposition of a massive number of states}).$$ The entropy of this initial state arising from the second term is suppressed by the tiny coefficient. However, the action of $$S^+$$ will destroy the first term, removing the suppression of the second term after normalizing. The second term after being acted upon by $$S^+$$ will still have some large amount of entanglement, perhaps smaller than the second term had before, but still a much larger amount than the full initial state. Thus, the entanglement of the final state will be much larger than the initial state, easily exceeding $$\ln(2)$$.
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https://www.physicsforums.com/threads/sum-of-i-2-4-i-where-i-is-from-0-to-infinity.31966/
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# Sum of (i^2)/(4^i) where i is from 0 to infinity.
1. Jun 21, 2004
### Johnny Leong
Sum of (i^2)/(4^i) where i is from 0 to infinity.
2. Jun 21, 2004
### NateTG
You mean $$\sum_{i=1}^\infty \frac{i^2}{4^i}$$? (I don't like $$\frac{0^2}{4^0}$$ - it's not necessarily clear what it is.)
Well, for $$i \geq 4$$ ,
$$2^i \geq i^2$$,
so
$$\frac{i^2}{4^i} < \frac{2^i}{4^i} = \frac{1}{2^i}$$
so
$$\sum_{i=1}^\infty \frac{i^2}{4^i} < \frac{1}{4}+\frac{4}{16}+\frac{9}{64} + \sum_{i=4}^{\infty} \frac{1}{2^i}$$
Perhaps you can find some better bounds?
3. Jun 21, 2004
### Muzza
I'm sorry, but what's unclear about 0^2/4^0?
4. Jun 21, 2004
### Gokul43201
Staff Emeritus
$$\sum_{i=1}^\infty \frac{i^2}{4^i} > \frac{1}{4}+\frac{4}{16}+\frac{9}{64} + \sum_{i=4}^{\infty} \frac{1}{4^i}$$
That gives a range of 0.7 to 0.9. Wonder if it isn't just 3/4 or 4/5 ?
5. Jun 21, 2004
Mathematica's saying 20/27 (~.740741). But, like most things Mathematica, I have no idea how it produced that number.
6. Jun 21, 2004
### Johnny Leong
Actually, this question could not give an accurate answer. The answer should just be an approximation, right? Because the terms in the summation are not having some sequence properties.
7. Jun 22, 2004
### Johnny Leong
I think Gokul43201's answer would not be a good one because after I have read a book, I found that when we do some approximation, the approximation's value had better dominate the value of the original question.
8. Jun 22, 2004
### HallsofIvy
What in the world does that mean? What do you mean by "dominate the value of the original question? An approximation is an approximation. There exist good approximations and bad approximations. The ideal is to get as close as possible to the true value for the work done.
9. Jun 22, 2004
### arildno
$$F(x)=\sum_{i=0}^{\infty}i^{2}x^{i}$$
$$\sum_{i=0}^{\infty}i^{2}x^{i}=\sum_{i=0}^{\infty}xi\frac{d}{dx}x^{i}$$
$$\sum_{i=0}^{\infty}xi\frac{d}{dx}x^{i}=\frac{d}{dx}\sum_{i=0}^{\infty}ix^{i+1}-\sum_{i=0}^{\infty}ix^{i}$$
$$\sum_{i=0}^{\infty}ix^{i}=x\frac{d}{dx}\sum_{i=0}^{\infty}x^{i}$$
Hence, we have:
$$F(x)=\frac{d}{dx}(x^{2}\frac{d}{dx}\frac{1}{1-x})-x\frac{d}{dx}\frac{1}{1-x}$$
or:
$$F(x)=\frac{x^{2}+x}{(1-x)^{3}}$$
The sum of the original series is found by evaluating $$F(\frac{1}{4})$$
Last edited: Jun 22, 2004
10. Jun 22, 2004
### Gokul43201
Staff Emeritus
Which is 20/27, as Mathematica magically guessed.
Nice, arildno.
11. Jun 22, 2004
A very clever little trick, indeed.
12. Jun 23, 2004
### Johnny Leong
I mean the approximation should be an upper bound to the accurate answer to the original question.
13. Jun 23, 2004
### Johnny Leong
What are you doing, arildno? You are professional but I do not understand. Why you do like this?
14. Jun 23, 2004
### arildno
OK, I'll break up this in tiny pieces; then pin-point what you don't understand.
1. Changing perspective from number to function:
We start out with the series:
$$S=\sum_{i=0}^{\infty}i^{2}(\frac{1}{4})^{i}$$
Our aim is to find the number S!
However, this is difficult to do as it stands; what I want to do, is to change the problem slightly, so that:
a) I gain access to powerful solving techniques in the new problem to be solved
(which is not accessible in the original problem)
b) I can easily find the answer to the original problem once I have found the answer to the new problem
That is why I change perspectives to try to simplify the expression for the following function:
$$F(x)=\sum_{i=0}^{\infty}i^{2}x^{i}$$
a): Since I now have a power series function , I can use the extraordinarily powerful teqnique of differentiation to help me solve the new problem (simplifying the expression for F(x)!)
b) If I can do this, then I can find the answer to my original problem simply by
computing $$F(\frac{1}{4})$$
I'll let you ponder on this for a while, if you have some specific questions, pleasy notify..
Similar Discussions: Sum of (i^2)/(4^i) where i is from 0 to infinity.
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https://wellness-trends.com/does-the-cold-climate-affect-the-spread-of-coronavirus/health/
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## A study conducted by the GVN, the Global Virus Network, would have identified a correlation between temperature and diffusion rate of the coronavirus: let’s find out.
Is there a relationship between the temperature and the rate at which coronavirus spreads? The answer comes from the GVN, the Global Virus Network. The prestigious international coalition would have conducted a study based on the observation of the diffusion rate of COVID-19, in relation to the climate of a given place.
The study gave us an answer : the temperature affects the propagation of the coronavirus. Like? Let’s find out.
### Coronavirus, does the climate affect?
The study conducted by the Global Virus Network (GVN) stems from the observation that in hot countries the virus would seem to progress more slowly than in other countries.
In fact, through the analysis of the statistics , it is possible to establish that the coronavirus would seem to spread differently according to the temperature. In particular, it would have spread more insistently in areas with colder or temperate climates, where the average temperature is between 5 and 11 degrees on the Celsius scale.
Not surprisingly, COVID-19 has spread significantly in Europe and the United States, without however being able to effectively hit the hottest countries of South Asia and Africa. Obviously, the virus has also reached these areas, but the spread would seem slower and the number of significant outbreaks less.
### Coronavirus and seasonal flu: cold weather helps spread
Like seasonal flu , the work of coronavirus would appear to be greatly influenced by temperature. Both would spread more easily in colder climates. The hope is that, with the arrival of spring and then of summer, the emergency can slowly return until it completely disappears .
However, the fact that the virus tends to expand more easily in colder areas does not necessarily mean that with the arrival of the heat it will disappear. However, it could slow down its spread, helping doctors to better treat patients and allowing more time for scientists to find a possible vaccine .
Photo source: https://pixabay.com/it/photos/termometro-estate-heiss-di-calore-4294021/
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https://www.physicsforums.com/threads/double-integrals-in-polar-coordinates.325701/
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# Double integrals in polar coordinates
1. Jul 18, 2009
### compliant
1. The problem statement, all variables and given/known data
Find
$$\int{\int_{D}x dA}$$
where D is the region in Q1 between the circles x2+y2=4 and x2+y2=2x using only polar coordinates.
3. The attempt at a solution
Well, the two circles give me r=2 and r=2 cos $$\theta$$, and the integrand is going to be r2cos $$\theta$$, but I have no idea how to determine the bounds of integration in this case.
2. Jul 18, 2009
### tiny-tim
Hi compliant!
(have a theta: θ and a pi: π )
Just integrate θ from 0 to 2π (or -π and π), and integrate r between whatever values it goes between for a fixed value of θ.
3. Jul 18, 2009
### HallsofIvy
Staff Emeritus
I would recommend first drawing a picture. $x^2+ y^2= 4$ is, of course, a circle with center at (0,0) and radius 2. $x^2+ y^2= 2x= x^2- 2x+ y^2= 0$ or $x^2- 2x+ 1+ y^2= (x- 1)^2+ y^2= 1$ is a circle with center at (1, 0) and radius 1: it is tangent to the y-axis at (0,0) and tangent to the first circle at (2, 0). Now think in terms of polar coordinates. Both equations become very simple in polar coordinates. What drawing the graph tells you is that you will want to handle the integration in three parts: $\theta= 0$ to $\pi/2$, $\theta= \pi/2$ to $3\pi/2$, and $\theta= 3\pi/2$ to $2\pi$.
suggested, the outside radius (the upper limit of integration) is always 2 and the inner radius (the lower limit of integration, for $\theta= 0$ to $\pi/2$ is
4. Jul 19, 2009
### compliant
tiny-tim, thanks for those. desperately needed.
hallsofivy, I did draw the diagram, and found that it was rather inconveniently symmetrical, which was why I got stumped. going by your suggestion, from θ = 0 to θ = π/2, I would be integrating along the right side of the curve, where the upper bound is r = 2, and the lower bound is r = 2 cos θ. I would then solve accordingly, with r2 cos θ as the integrand.
I'm just wondering though, how is the left side of the curve from θ = π/2 to θ = 3π/2 and not θ = π/2 to θ = π ? And as for the third part of the curve that goes from θ = 3π/2 to θ = 2π, that's...a straight line. =/
Argh.
5. Jul 21, 2009
### compliant
sorry to do this, but bump.
6. Jul 22, 2009
### tiny-tim
Hi compliant !
I'm confused
The area is between two circles, one touching both the edge and the centre of the other.
So there are two regions:
the "left" region, which is simply a semicircle, so you know the answer already, and you needn't integrate at all (though if you did, you would integrate a constant, over the whole angle π/2 to 3π/2)
and the "right" region, which is from -π/2 to π/2, which you seem to be ok with.
Similar Discussions: Double integrals in polar coordinates
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https://fluidpower.pro/author/admin-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2/page/15/
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# Author Archive: Dzyanis
## Hydraulic oil viscosity
Summary:
• Dynamic and kinematic viscosity in SI and British unit
• Understanding the optimum operating viscosity range
• Selecting the ISO VG (Viscosity Grade) for your system
• Understanding the Viscosity Index
~~~ // ~~~
The viscosity is a measure of the fluid’s resistance to flow.
There are dynamic and kinematic viscosity are usually common for calculations.
The symbol for dynamic viscosity is the Greek letter mu (µ). The SI unit for dynamic viscosity is the pascal-second (Pa·s), but the more common unit is the centipoise (cP):
1 P = 0.1 Pa·s
1 cP = 0.001 Pa·s = 0.001 N·s/m2.
For example, the dynamic viscosity of water at 20°C is 1.00 cP
## Cylinder’s Area Ratio
Summary:
• Understanding the Cylinder Area Ratio
~~~ // ~~~
By the definition, the “Cylinder Area Ratio” is the relation between the complete area of the bore and the same area minus the area of the rod:
$CR = \frac{A_b}{A_b – A_r}$
For the ratio there is important a diameter of the rod (but not rod side annular area!) because when you choose the cylinders for your project in hydraulic catalogs you pick out them using Piston and Rod diameters.
This is why the area ratio CR is always >1.
Sometimes, you can meet records like:
$\frac{A_b}{A_b – A_r} : 1$
For example, for cylinder 4″ bore diameter and 2.5″ rod diameter, the ratio is:
$CR=\frac{A_b}{A_b-A_r}=\frac{\pi\frac{D^2_b}{4}}{\pi\frac{D^2_b}{4}-\pi\frac{D^2_r}{4}}=\frac{D^2_b}{D^2_b-D^2_r}=\frac{4^2}{4^2-2.5^2}=1.64$
So, $$CR=1.64$$ or $$1.64:1$$
## Hydraulic manifolds material
Summary:
• Selecting the type of material for manifold
• Manifold’s Blackening
~~~ // ~~~
Choosing between ductile steel and aluminum can mean the difference between a failed product or machine and a reliable, productive machine. Consider the following factors:
System Pressures
When system pressure will be consistently above 3500 psi, ductile steel is required. Also, when normal operating pressures are at or near or at 3500 psi, and when pressure “spikes” might exceed 3500 psi, ductile steel should be considered.
## Pilot ratio & pilot pressure of counterbalance valves
Summary:
• Understanding the pilot ratio of the counterbalance valves
• Calculations the pilot pressure of the counterbalance valves for different applications
~~~ // ~~~
Lower pilot ratios will increase system stability and provide better motion control. Therefore, the vast majority of counterbalance applications are satisfied with a 3:1 pilot ratio.
Higher ratios will be more efficient (reduce heat generation) but at the cost of stability and smooth motion control. This is why 10:1 pilot ratio valves, generally, should be avoided. But, sometimes, on motors high pilot ratios will provide adequate dynamic control.
Two areas work to open a counterbalance valve, the relief area (port 3) and the pilot area (port 1); the pilot area divided by the relief area equals the pilot ratio:
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https://www.datanovia.com/en/blog/how-to-change-ggplot-facet-labels/
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# How to Change GGPlot Facet Labels
Contents:
#### Related Book
GGPlot2 Essentials for Great Data Visualization in R
## Prerequisites
Load required packages and set the theme function theme_light() [ggplot2] as the default theme:
library(ggplot2)
theme_set(
theme_light() + theme(legend.position = "top")
)
## Basic ggplot with facet
Create a box plot filled by groups:
# Load data and convert dose to a factor variable
data("ToothGrowth")
ToothGrowth$dose <- as.factor(ToothGrowth$dose)
# Box plot, facet accordding to the variable dose and supp
p <- ggplot(ToothGrowth, aes(x = dose, y = len)) +
geom_boxplot(aes(fill = supp), position = position_dodge(0.9)) +
scale_fill_viridis_d()
p + facet_grid(dose ~ supp)
## Change the text of facet labels
Facet labels can be modified using the option labeller, which should be a function.
• In the following R code, facets are labelled by combining the name of the grouping variable with group levels. The labeller function label_both is used.
p + facet_grid(dose ~ supp, labeller = label_both)
• A simple way to modify facet label text, is to provide new labels as a named character vector:
# New facet label names for dose variable
dose.labs <- c("D0.5", "D1", "D2")
names(dose.labs) <- c("0.5", "1", "2")
# New facet label names for supp variable
supp.labs <- c("Orange Juice", "Vitamin C")
names(supp.labs) <- c("OJ", "VC")
# Create the plot
p + facet_grid(
dose ~ supp,
labeller = labeller(dose = dose.labs, supp = supp.labs)
)
• An alternative solution to change the facet labels, is to modify the data:
df <- ToothGrowth
# Modify the data
df$dose <- factor(df$dose, levels = c("0.5", "1", "2"),
labels = c("D0.5", "D1", "D2"))
df$supp <- factor(df$supp, levels = c("OJ", "VC"),
labels = c("Orange Juice", "Vitamin C")
)
# Create the plot
ggplot(df, aes(x = dose, y = len)) +
geom_boxplot(aes(fill = supp)) +
facet_grid(dose ~ supp)
## Customize facet labels appearance
# Change facet text font. Possible values for the font style:
#'plain', 'italic', 'bold', 'bold.italic'.
p + facet_grid(dose ~ supp)+
theme(
strip.text.x = element_text(
size = 12, color = "red", face = "bold.italic"
),
strip.text.y = element_text(
size = 12, color = "red", face = "bold.italic"
)
)
## Change facet background color
The rectangle around facet labels can be modified using the function element_rect().
p + facet_grid(dose ~ supp)+
theme(
strip.background = element_rect(
color="black", fill="#FC4E07", size=1.5, linetype="solid"
)
)
• Another great and very useful post,
(with clear code examples).
Thanks you again, Kassambara.
You are a Pro!.
SFer
San Francisco
• Thank you SFer for your feedback, always appreciated!
• Fringse
Thanks for these information!
On top of what you describe here: How can I change the font of only once facet and leave the others untouched?
Say have one facet label in italic and the others in plain?
• Hi,
I don’t know how to modify the font of only one panel. If you find any solution, I would appreciate if you can share it.
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http://math.stackexchange.com/questions/712482/on-number-of-different-factorizations-over-integers-of-a-number-field
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# On number of different factorizations over integers of a number field
Let $K$ be a finite field extension of the rational numbers and let $\mathcal{O}_K$ denote its ring of integers. If a rational integer $n$ factors into two distinct ways into irreducible elements in $\mathcal{O}_K$, that is,
$$n = \prod{a_j} = \prod{b_j},$$
where $a_j, b_j$ are irreducible and no $a_j$ is associate to any $b_j$, then $n^2 = \prod{a_j}^2 = \prod{b_j}^2 = \prod{a_j}\prod{b_j}$ has at least three distinct factorizations; by taking powers of $n$ one thus can see that the number of distinct factorizations of rational integers is unbounded. Is the number of distinct "primitive" factorizations of rational integers over $\mathcal{O}_K$ bounded, that is, factorizations that do not arise from a construction as above (that is, cannot be split into different "sub-factorizations")? If yes, can this bound be given explicitly in terms of the size of the class group and $[K : \mathbb{Q}]$?
-
You might be interested in this question: math.stackexchange.com/questions/538959/… – John M Mar 17 '14 at 14:38
The question has been answered here: mathoverflow.net/questions/162916/… – streetcar277 Jun 19 '14 at 11:42
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https://www.albert.io/ie/ap-physics-1-and-2/radiation-ranking
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# AP® Physics 1 & 2
Free Version
Easy
APPH12-XEAXUP
Students are creating a chart with the various forms of electromagnetic radiation. They are listing the radiation from long wavelength to short wavelength and have included the following types of radiation:
• Gamma
• Microwave
• Visible Light
• X-Rays
Based on the wavelength ranges, which of the following is the best order for listing them long to short wavelength?
A
Visible Light, X-Rays, Microwaves, Gamma Waves, Radio.
B
Gamma Waves, Visible Light, X-Rays, Microwaves, Radio.
C
Radio, Microwaves, Visible Light, X-rays, Gamma Waves.
D
Radio, Visible Light, Microwaves, Gamma Waves, X-Rays.
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https://ru.scribd.com/document/390591295/Chapter-1
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Вы находитесь на странице: 1из 16
# Chapter One
## Stresses in Soils from Surface Loads
1. Introduction
Various types of loads are applied to soils. For example, an oil tank will impose a uniform circular,
vertical stress on the surface of the soil while an unsymmetrical building may impose a non-uniform
vertical stress. We would like to know how the surface stresses are distributed within the soil mass
and the resulting deformations.
The distribution of surface stresses within a soil is determined by assuming that the soil is a semi-
infinite, homogeneous, linear, isotropic, elastic material. A semi-infinite mass is bounded on one
side and extends infinitely in all other directions; this is also called an “elastic half space.” For soils,
the horizontal surface is the bounding side. Equations and charts for several types of surface loads based
on the above assumptions are presented in this chapter.
## 1.1 Definitions of key Terms
Stress or intensity of loading is the load per unit area. The fundamental definition of a stress is the ratio
of the force ΔP acting on a plane to the area of the plane ΔS when ΔS tends to zero; Δ denotes a small
quantity.
Strain or intensity of deformation is the ratio of the change in dimension to the original dimension
or the ratio of change in length to the original length.
Sample Practical Situation Two storage tanks are to be founded on a deep layer of stiff saturated
clay. Your client and the mechanical engineer, who is designing the pipe works, need an estimate of
the settlement of the tanks when they are completely filled. Because of land restrictions, your client
desires that the tanks be as close as possible to each other. You should realize that if two separate
foundations are placed too close to each other, the stresses in the soil induced by each foundation
overlap and cause intolerable tilting of the structures and their foundations.
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 1
1.2. Stresses and Strains
## 1.2.1. Normal Stresses and Strains
Consider a cube of dimensions x = y = z that is subjected to forces Px, Py, Pz, normal to the
three adjacent sides as shown in Fig. 1.1.
## The normal stresses are:
Let as assume that under these forces the cube compresses by x, y, and z in the X, Y, and Z
directions. The strains in these directions, assuming they are small (infinitesimal), are:
## 1.2.2 Volumetric Strain
The volumetric strain which is the sum of strains in X, Y,and Z direction is expressed as follows:
## 1.2.3 Shear Stresses and Shear Strains
Let us consider, for simplicity, the XZ plane and apply a force F that causes the square to distort into a
parallelogram as shown in Fig. 1.2. The force F is a shearing force and the shear stress is expressed as
follows:
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 2
The simple shear strain, also called engineering shear strain, is a measure of the angular
distortion of a body by shearing forces. If the horizontal displacement is Dx, the shear
strain or simple shear strain, γzx , is expressed as:
## For small strains tanγzx=γzx and therefore,
If the shear stress on a plane is zero, the normal stress on that plane is called a principal stress. In
geotechnical engineering, compressive stresses in soils are assumed to be positive. Soils cannot
sustain any appreciable tensile stresses and we normally assume that the tensile strength of soils is
negligible. Strains can be compressive or tensile.
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 3
1.3 Stresses in Soil from Surface Loads
## 1.3.1 Point Load
Boussinesq (1885) presented a solution for the distribution of stresses for a point load applied on the
soil surface. An example of a point load is the vertical load transferred to the soil from an electric
power line pole. The increases in stresses on a soil element located at point A (Fig. 1.3a) due to a point
load, Q, are:
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 4
Equations (1.10) to (1.13) represent the same stresses in terms of the angle and depth z.
Where is Poisson’s ratio. Most often, the increase in vertical stress is needed in practice. Equation
(1.6) can be written as:
## Where I is an influence factor, and
The distribution of the increase in vertical stress from Eq. (1.14) reveals that the increase in
vertical stress decreases with depth (Fig. 1.3 b) and radial distance (Fig.1.3c).
EXAMPLE 1.1
A pole carries a vertical load of 200 kN. Determine the vertical stress increase at a depth 5 m (a)
directly below the pole and (b) at a radial distance of 2 m.
EXAMPLE 1.2
## Under a concentrated vertical load of 100 kN, determine:
a) The distribution of σz on horizontal planes at depths of 1 m, 2 m, and 3 m below the
ground surface - vary r/z from 0.0 to 3.0 in 0.25 increments,
b) The distribution of σz on the vertical planes at 1 m, 2 m, and 3 m from the applied
concentrated load and the position of the maximum vertical stress on these planes - vary z
in 0.5 m increments up to 6 m.
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 5
1.3.2 Line Load
With reference to Fig. 1.4a, the increase in stresses due to a line load, Q (force/length), are:
A practical example of line load is the load from a long brick wall.
## 1.3.3 Line Load Near a Buried Earth Retaining Structure
The increase in lateral stress on a buried earth retaining structure (Fig. 1.4b) due to a line load of
intensity Q (force/length) is:
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 6
1.3.4 Strip Load
A strip load is the load transmitted by a structure of finite width and infinite length on a soil surface. Two
types of strip loads are common in geotechnical engineering. One is a load that imposes a uniform stress on
the soil, for example, the middle section of a long embankment (Fig. 1.5a). The other is a load that induces a
triangular stress distribution over an area of width B (Fig. 1.5b). An example of a strip load with a triangular
stress distribution is the stress under the side of an embankment. The increases in stresses due to a
surface stress qs (force/area) are as follows:
Figure 1.5: Strip load imposing (a) a uniform stress and (b) a linearly varying stress. (c) Strip load
near a retaining wall and (b) lateral force near a retaining wall from a strip load.
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 7
(b) Area transmitting triangular stress (Fig. 1.5b)
## (c) Area transmitting triangular stress (Fig. 1.5c, d)
The lateral force and its location were derived by Jarquio (1981) and are expressed as follows:-
where
## 1.3.5 Uniformly Loaded Circular Area
An example of circular area that transmits stresses to a soil mass in a circular foundation of an oil
or water tank. The increase in vertical and radial stresses under a circular area of radial distance
ro are articulated as follows:
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 8
and the increase in radial stress is:
The vertical elastic settlement at the surface of due to a circular flexible loaded area is:
## 1.3.6 Uniformly Loaded Rectangular Area
Many structural foundations are rectangular or approximately rectangular in shape. The increase
in stresses below the corner of a rectangular area of width B and length L are:
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 9
These equations can be written as
follows:
Where I denotes the influence factor. The influence factor for the vertical stress is
where m= B/ z and n= L /z . You can program your calculator or use a spreadsheet to find Iz.
You must be careful in the last term (tan-1) in programming. If m2 + n2 +1 < m2n2 , then you
have to add P to the quantity in the last term. In general, the vertical stress increase is less than
10% of the surface stress when z > 3B. The vertical elastic settlement at the ground surface under
a rectangular surface load is:
Where Is is a settlement influence factor that is a function of the L/B ratio (L is length and B is
width). Setting ξs =L /B , the equations for Is are:
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 10
The above equations can be simplified to the following for ξs > 1.
## 1.3.7 Approximate Method for Rectangular Loads
In preliminary analyses of vertical stress increases under the center of rectangular loads,
geotechnical engineers often use an approximate method (sometimes called the 2:1 method). The
surface load on an area, BxL , is dispersed at a depth z over an area (B + z)x (L + z) as illustrated
in Fig. 1.6.
The vertical load increase under the center of the rectangle is:
EXAMPLE 1.3
A rectangular concrete slab, 3 m×4.5 m, rests on the surface of a soil mass (Fig. E1.3). The load
on the slab is 2025 kN. Determine the vertical stress increase at a depth of 3 m (a) under the
center of the slab, point A, (b) under point B, and (c) at a distance of 1.5 m from a corner, point C.
Strategy: The slab is rectangular and the equations for a uniformly loaded rectangular area are
for the corner of the area. You should divide the area so that the point of interest is the corner of
a rectangle(s). You may have to extend the loaded area if the point of interest is outside it
(loaded area). The extension is fictitious so you have to subtract the fictitious increase in stress
for the extended area.
Figure E1.3
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 12
1.3.8 Vertical Stress below Arbitrarily Shaped Area
## Figure 1.7: Newmark's chart for increase in vertical stress.
Newmark (1942) developed a chart to determine the increase in vertical stress due to a uniformly
loaded area of any shape. The chart consists of concentric circles divided by radial lines (Fig.1.7).
The area of each segment represents an equal proportion of the applied surface stress at depth z
below the surface. If there are 10 concentric circles (only 9 are shown because the 10th extends
to infinity) and 20 radial lines, the stress on each circle is qs/10 and on each segment isqs (10x20).
The radius to depth ratio of the first (inner) circle is found by setting Dσz =0.1qs in Eq. (1.30),
that is,
from which r/ z=0.27 . For the other circles, substitute the appropriate value for sz; for example,
for the second circle, sz = 0.2qs , and find r/z . The chart is normalized to the depth; that is, all
dimensions are scaled by a factor initially determined for the depth. Every chart should show a
scale and an influence factor IN, which for our case is 1/(10x20) = 0.005.
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 13
The procedure for using Newmark’s chart is as follows:
1. Set the scale, shown on the chart, equal to the depth at which the increase in vertical stress is required.
We will call this the depth scale.
2. Identify the point on the loaded area below which the stress is required. Let us say this point is point A.
3. Plot the loaded area using the depth scale with point A at the center of the chart.
4. Count the number of segments (Ns) covered by the scaled loaded area. If certain segments are not fully
covered, you can estimate what fraction is covered.
5. Calculate the increase in vertical stress as z q s I N N s .
EXAMPLE 1.4
The plan of a foundation of uniform thickness for a building is shown in Fig. E1.4a. Determine
the vertical stress increase at a depth of 4 m below the centroid. The foundation applies a vertical
stress of 200 kPa on the soil surface.
Figure E1.4 a, b
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 14
Strategy: You need to locate the centroid of the foundation, which you can find using the given
dimensions. The shape of the foundation does not fit nearly into one of the standard shapes (e.g.,
rectangles or circles) discussed. The convenient method to use for this (odd) shape foundation is
Newmark’s chart
## Soil Mechanics II Lecture Notes Instructor: Nuru I. 15
Individual Assignment to be submitted
1. A shallow Foundation 25m x 18m carries a uniform pressure of 175kN/m2. Determine the
vertical stress at a point 12m below the midpoint of one of the longer sides.
## a. Using influence factors
b. By means of Newmark's chart
2. A line load of 150 kN/m acts 2m behind the sub-surface of an earth retaining structure of
4m high. Calculate the total thrust and plot the distribution of the pressure on the
structure due to the line load.
## Нижнее меню
### Получите наши бесплатные приложения
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http://mathoverflow.net/questions/112618/leray-spectral-sequence?sort=newest
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# Leray Spectral Sequence
Let $f:X\to Y$ be a smooth map between paracompact differential manifolds $X$ and $Y$. Let $U$ be an open and dense subset of $Y$. For any $y\in U$, let $f^{-1}(y)=F$ be a generic fiber that is a submanifold of $F$.
Assume the singular fibers are $F/\Gamma_t$, where for each $t\in Y\setminus U$, $\Gamma_t$ is a finite subgroup (depending on $t$) of the automorphism group of $F$ that is acting properly discontinuously on $F/\Gamma_t$, i.e., the latter is also a smooth manifold.
If $\Gamma_t$ is the identity for all $t$, and $f$ is a fibration, then there is a Leray spectral sequence relating the homology of $X$ to that of $F$ and $Y$. Is there some spectral sequence for the case when $\Gamma_t$ is not always the identity, and if so what? A reference for this would be appreciated too.
-
As Algori mentions, the answer is yes, and it's also the Leray spectral sequence. What reference are you using? – Ryan Budney Nov 16 '12 at 23:37
Ru -- the Leray spectral sequence exists for any map $f:X\to Y$ of arbitrary topological spaces and any sheaf $F$ on $X$ and its second term is $$E_2^{p,q}=H^p(Y,R^q f_*F)$$ where $R^q f_*F$ are the sheaves on $Y$ that are obtained by sheafifying the presheaves $U\mapsto H^q(f^{-1}(U),F)$. Here are some remarks that might help:
1. If $f$ is a locally trivial fibration and $F$ is constant then all $R^q f_*F$ are locally constant; if in addition $Y$ is simply-connected then the sheaves are constant and we can express $E_2$ in terms of the constant cohomology of $Y$.
2. It may happen that all fibers $f^{-1}(y),y\in Y$ are homeomorphic but some or all $R^q f_*F$ are non-constant; take e.g. $X=(\mathbb{R}\setminus \{ 0\})\sqcup \{ 0\}, Y=\mathbb{R},f$ the identity map.
3. Nevertheless, if $f:X\to X/G$ where $G$ is a connected Lie group that acts nicely on $X$ (say so that the quotient is Hausdorff) with finite stabilizers, and $F$ is a constant sheaf with stalk $\mathbb{Q}$ (or $\mathbb{R}$ or $\mathbb{C}$) then any sheaf $R^q f_*F$ is constant with stalk $H^q(G,\mathbb{Q})$ (resp., $H^q(G,\mathbb{R})$ and $H^q(G,\mathbb{C})$).
Two possible references (which means, to be honest, that there may be better references but that's where I first learned this from) are Godement, Topologie alg\'ebrique et th\'eorie des faisceaux, the very end of chapter 4, and Griffiths-Harris, the very end of vol.1
-
Thanks Algori, As you mentioned spectral sequence argument seems to work for cohomology - how about homology? – user13559 Nov 18 '12 at 20:48
Ru -- welcome. Re how about homology: it depends: for locally trivial fibrations everyng works fine in a similar way; for more general maps the homological version exists but is quite a bit more complicated (the strategy basically consists in reducing everything to the cohomological case via the Verdier duality). – algori Nov 18 '12 at 22:49
Thanks again. Do you know of any reference about homological case? – user13559 Nov 19 '12 at 18:34
Ru -- I've never seen it done in detail in the homological case but if I had to guess I would define, following Borel-Moore, Homology theory for locally compact spaces, Michigan Math. J. 7, 2, 1960, thm 3.8 and \S 5, $H_i(X,F)=\mathbb{H}_c^{-i}(X,DF)$ where $\mathbb{H}_c$ stands for compactly supported hypercohomology and $D$ for the Verdier dual, and then see how it goes. For a careful introduction to constructible sheaves and related things see e.g. Borel, Intersection cohomology. Also, there was an Asterisque volume called "Etale homology" by Deligne et al, which may also be relevant. – algori Nov 20 '12 at 2:12
Thanks Algori! Have a good day. – user13559 Nov 23 '12 at 0:51
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https://arxiv.org/abs/math/0307405
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# Title:On the topology of graph picture spaces
Abstract: We study the space ${\mathcal X}^{d}(G)$ of pictures of a graph $G$ in complex projective $d$-space. The main result is that the homology groups (with integer coefficients) of ${\mathcal X}^{d}(G)$ are completely determined by the Tutte polynomial of $G$. One application is a criterion in terms of the Tutte polynomial for independence in the {\it $d$-parallel matroids} studied in combinatorial rigidity theory. For certain special graphs called \defterm{orchards}, the picture space is smooth and has the structure of an iterated projective bundle. We give a Borel presentation of the cohomology ring of the picture space of an orchard, and use this presentation to develop an analogue of the classical Schubert calculus.
Comments: LaTeX (uses xypic package), 22 pages. Final version, to appear in Advances in Mathematics. The title has been changed slightly, the exposition improved, the material in Section 6 clarified, and some open problems added Subjects: Combinatorics (math.CO); Algebraic Geometry (math.AG); Algebraic Topology (math.AT) MSC classes: 05C10 (Primary) 05B35, 14N20, 52C35 (Secondary) Journal reference: Adv. Math. 191, no. 2 (2005), 312--338 Cite as: arXiv:math/0307405 [math.CO] (or arXiv:math/0307405v2 [math.CO] for this version)
## Submission history
From: Jeremy L. Martin [view email]
[v1] Thu, 31 Jul 2003 18:38:30 UTC (23 KB)
[v2] Wed, 28 Apr 2004 21:41:39 UTC (26 KB)
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https://export.arxiv.org/abs/2003.14068
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math.CO
(what is this?)
# Title: On subspaces of Kloosterman zeros and permutations of the form $L_1(x^{-1})+L_2(x)$
Abstract: Permutations of the form $F=L_1(x^{-1})+L_2(x)$ with linear functions $L_1,L_2$ are closely related to several interesting questions regarding CCZ-equivalence and EA-equivalence of the inverse function. In this paper, we show that $F$ cannot be a permutation if the kernel of $L_1$ or $L_2$ is too large. A key step of the proof is a new result on the maximal size of a subspace of $\mathbb{F}_{2^n}$ that contains only Kloosterman zeros, i.e. a subspace $V$ such that $K_n(v)=0$ for all $v \in V$ where $K_n(v)$ denotes the Kloosterman sum of $v$.}
Comments: Included reviewers comments. To appear in the proceedings of WAIFI 2020 Subjects: Combinatorics (math.CO); Information Theory (cs.IT) Cite as: arXiv:2003.14068 [math.CO] (or arXiv:2003.14068v2 [math.CO] for this version)
## Submission history
From: Lukas Kölsch [view email]
[v1] Tue, 31 Mar 2020 10:13:19 GMT (25kb)
[v2] Tue, 22 Sep 2020 17:13:15 GMT (30kb)
Link back to: arXiv, form interface, contact.
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http://www.investopedia.com/articles/06/probabilitydistribution.asp
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Almost regardless of your view about the predictability or efficiency of markets, you'll probably agree that asset returns are uncertain or risky. This is with rare exception. If we ignore the math that underlies probability distributions, we can see they are pictures that describe a particular view of uncertainty.
Uncertainty refers to randomness and is different from a lack of predictability, or market inefficiency. An emergent research view holds that financial markets are both uncertain and predictable. Also, markets can be efficient but also uncertain. In finance, we use probability distributions to draw pictures that illustrate our view of an asset return's sensitivity when we think the asset return can be considered a random variable. In this article, we'll go over a few of the most popular probability distributions and show you how to calculate them.
What Are They?
There are two ways of categorizing distributions: by whether it is discrete or continuous, and by whether it is a probability density function (PDF) or a cumulative distribution.
Discrete refers to a random variable drawn from a finite set of possible outcomes. A six-sided die, for example, has six discrete outcomes. A continuous distribution refers to a random variable drawn from an infinite set. Examples of continuous random variables include speed, distance and some asset returns. A discrete random variable is illustrated typically with dots or dashes, while a continuous variable is illustrated with a solid line. Figure 1 shows discrete and continuous distributions for a normal distribution with mean (expected value) of 50 and standard deviation of 10:
Figure 1
The distribution is an attempt to chart uncertainty. In this case, an outcome of 50 is the most likely but only will happen about 4% of the time; an outcome of 40 is one standard deviation below the mean and it will occur just under 2.5% of the time.
The other distinction is between the probability density function and the cumulative distribution function.
The PDF is the probability that our random variable reaches a specific value (or in the case of a continuous variable, of falling between an interval). We show that by indicating the probability that a random variable ‘X' will equal an actual value 'x':
P[x=X]
The cumulative distribution is the probability that random variable 'X' will be less than or equal to actual value 'x':
P[x<=X]
For example, if your height is a random variable with an expected value of 5'10" inches (your parents' average height), then the PDF question is, "What's the probability that you will reach a height of 5'4"?" The corresponding cumulative distribution function question is, "What's the probability you'll be shorter than 5'4"?"
Figure 1 showed two normal distributions. You can now see these are probability density function (PDF) plots. If we re-plot the exact same distribution as a cumulative distribution, we'll get the following:
Figure 2
The cumulative distribution must eventually reach 1.0 or 100% on the y-axis. If we raise the bar high enough, then at some point, virtually all outcomes will fall under that bar (we could say the distribution is typically asymptotic to 1.0).
Finance, as a social science, is not as clean as physical sciences. Gravity, for example, has an elegant formula that we can depend on, time and again. Financial asset returns, on the other hand cannot be replicated so consistently. A staggering amount of money has been lost over the years by clever people who confused the accurate distributions (i.e., as if derived from physical sciences) with the messy, unreliable approximations that try to depict financial returns. In finance, probability distributions are little more than crude pictorial representations.
Uniform
The simplest and most popular distribution is the uniform distribution in which all outcomes have an equal chance of occurring. A six-sided die has a uniform distribution. Each outcome has a probability of about 16.67% (1/6). Our plot below shows the solid line (so you can see it better), but keep in mind that this is a discrete distribution - you can't roll 2.5 or 2.11:
Figure 3
Now roll two dice together, as shown in Figure 4, and the distribution is no longer uniform. It peaks at seven, which happens to have a 16.67% chance. In this case, all the other outcomes are less likely:
Figure 4
Now roll three dice together, as shown in Figure 4. We start to see the effects of a most amazing theorem: the central limit theorem. The central limit theorem boldly promises that the sum or average of a series of independent variables will tend to become normally distributed, regardless of their own distribution. Our dice are individually uniform but combine them and - as we add more dice - almost magically their sum will tend toward the familiar normal distribution!
Figure 5
Binomial
The binomial distribution reflects a series of "either/or" trials, such as a series of coin tosses. These are called Bernoulli trials but you don't need even (50/50) odds. A Bernoulli trial refers to events that have only two outcomes. The binomial distribution below plots a series of 10 coin tosses where the probability of heads is 50% (p-0.5). You can see in Figure 6 that the chance of flipping exactly five heads and five tails (order doesn't matter) is just shy of 25%:
Figure 6
If the binomial distribution looks normal to you, you are correct about that. As the number of trials increase, the binomial tends toward the normal distribution.
Lognormal
The lognormal distribution is very important in finance because many of the most popular models assume that stock prices are distributed lognormally. It is easy to confuse asset returns with price levels:
Asset returns are often treated as normal - a stock can go up 10% or down 10%. Price levels are often treated as lognormal - a \$10 stock can go up to \$30 but it can't go down to -\$10. The lognormal distribution is non-zero and skewed to the right (again, a stock can't fall below zero but it has no theoretical upside limit):
Figure 7
Poisson
The Poisson distribution is used to describe the odds of a certain event (e.g., a daily portfolio loss below 5%) occurring over a time interval. So, in the example below, we assume that some operational process has an error rate of 3%. We further assume 100 random trials; the Poisson distribution describes the likelihood of getting a certain number of errors over some period of time, such as a singe day.
Figure 8
Student's T
The student's T distribution is also very popular because it has a slightly "fatter tail" than the normal distribution. The student's T is used typically when our sample size is small (i.e. less than 30). In finance, the left tail represents the losses. Therefore, if the sample size is small, we dare underestimate the odds of a big loss. The fatter tail on the student's T will help us out here. Even so, it happens that this distribution's fat tail is often not fat enough. Financial returns tend to exhibit, on rare catastrophic occasion, really fat-tail losses (i.e. fatter than predicted the distributions). Large sums of money have been lost making this point.
Figure 9
Beta Distribution
Finally, the beta distribution (not to be confused with the beta parameter in the capital asset pricing model) is popular with models that estimate the recovery rates on bond portfolios. The beta distribution is the utility player of distributions. Like the normal, it needs only two parameters (alpha and beta), but they can be combined for remarkable flexibility. Four possible beta distributions are illustrated in Figure 10 below:
Figure 10
The Bottom Line
Like so many shoes in our statistical shoe closet, we try to choose the best fit for the occasion, but we don't really know what the weather holds for us. We may choose a normal distribution then find out it underestimated left-tail losses; so we switch to a skewed distribution, only to find the data looks more "normal" in the next period. The elegant math underneath may seduce you into thinking these distributions reveal a deeper truth, but it is more likely that they are mere human artifacts. For example, all of the distributions we reviewed are quite smooth, but some asset returns jump discontinuously.
The normal distribution is omnipresent and elegant and it only requires two parameters (mean and distribution). Many other distributions converge toward the normal (e.g., binomial and Poisson). However, many situations, such as hedge fund returns, credit portfolios and severe loss events, don't deserve the normal distributions..
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https://www.gamedev.net/forums/topic/651445-how-to-split-up-pathfinding-how-to-implement-divide-and-conquer-on-pathfinding/
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# How to split up pathfinding? How to implement divide-and-conquer on pathfinding?
This topic is 1429 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
When pathfinding itself becomes a time hog, it's usually because it's calculating a long path from point A to point B. My hypothesis is that if the path from point A to point B is split up into halves, it may cut down the time it needs to calculate from point A to point B.
I'm trying to use divide and conquer on my A* 2D-grid pathfinding algorithm. I was thinking of splitting up my long path into two shorter paths, with point M (M for median) in the center of the long path. So, a character starts from point A to point M, would mean that I just have to calculate path from point A to point M. And then redo the calculations for the next path from point M to point B.
• Do I just have to find the median point of a path from point A to point B when I'm about to start calculating the path?
• Where do I start updating my character when a smaller path has just completed and it's about to start calculating the next path?
Here's a Java pseudo-code:
public ArrayList<Node> createHalfPath(Node start, Node goal) {
return createPath(null, getEstimatedMedianNode(start, goal));
}
private Node getEstimatedMedianNode(Node start, Node goal) {
Node result = null;
double dist = Math.hypot((start.x - goal.x), (start.y - goal.y));
if (dist > 16.0) {
int dx = (start.x - goal.x) / 2;
int dy = (start.y - goal.y) / 2;
result = new Node(dx, dy);
result.distanceFromStart = dist / 2.0;
result.hueristicDistanceToGoal = this.getEstimatedDistanceToGoal(result, goal);
}
return result;
}
I've realized I can only get the first half of the path, but not the second part of the path. I have the theory in place, but the logic is where I'm stuck at. Does anyone know how to work it out?
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I work with huge terrains and navigation meshes. We can't even build the entire navmesh due to memory constraints(it uses the popular voxellization techniques), so we built the navmesh in tiles. In order to facilitate long distance pathfinding, which would be extremely slow for long paths, I use the resolution of these tiles as part of the hierarchial pathfinding, which I recommend you do here as well. it's much simpler with tile maps.
The idea is just to group your navigation into larger tiles, and then build a higher level graph on this information. You can do it with a higher level grid or create tile groupings.
http://www.gamasutra.com/view/feature/3000/gdc_2002_polygon_soup_for_the_.php
Depending on the size and complexity of the map, this can simplify the pathfinding hugely. Pathfinding could boil down to a simple search inside the region you are in, and once the search hits the high level sector border, it can skip entirely over all sectors in between, using the cached connectivity of the high level graph. Once it reaches the destination sector, it can fall back down to the tile grid for the rest of the path. Once you have that path through, which includes a mix of high and low level paths, the high level edges would need to be filled in for each tile, but this can be done incrementally as you follow the path. I ended up not doing incremental updates though, because it caused problems such as not having enough path context into the future in order to do my string pulling properly, so I ended up building out the whole path by the time I returned it, but the multi-level pathing is still a huge performance improvement, and filling in those high level sectors is basically a flood fill from the starting polygon/tile until it reaches the next expected high level tile.
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May I ask, did you use recursive methods to complete this task?
public ArrayList<Node> createRecursivePath(Node start, Node goal) {
Node median = getEstimatedMedianNode(start, goal);
if (median != null) {
ArrayList<Node> results1 = createPath(start, median);
ArrayList<Node> results2 = createPath(median, goal);
return results1;
}
else {
ArrayList<Node> results = createRecursivePath(start, getEstimatedMedianNode(start, median));
return results;
}
}
I know my recursive skills are bad, but I'm thinking I might be going in the right direction. Somehow...
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Here's an attachment of a ZIP-ed JAR file, containing the current working state of the divide-and-conquer A* pathfinding.
To start, click anywhere in the screen. The pink pixel means the starting node, and the green pixel means the ending node. The background is grayed out, so that the whiter, lighter colors of the path can be displayed easily to the eyes.
[attachment=19207:astar_pixel.zip]
One of the paths generated created this path, shown below:
I followed your advice on splitting the screen up into 4 sectors, with each sectors having their portals connecting to each adjacent sectors. I don't know what I've done to get this path. Here's the code for the path above:
public ArrayList<Node> makePath(Node start, Node goal) {
System.out.println("Making path from sectors...");
if (tempPath == null)
tempPath = new ArrayList<Node>();
Sector startingSector = findSector(start);
Sector endingSector = findSector(goal);
if (startingSector == null || endingSector == null) {
System.out.println("Something is wrong...");
return null;
}
System.out.println("Calculating different segments of paths from each sectors...");
System.out.println("The first path...");
tempPath = createPath(start, startingSector.centerNode);
System.out.println("The second path...");
System.out.println("The last path...");
System.out.println("Paths complete.");
return tempPath;
}
private Sector findSector(Node node) {
for (Sector sector : sectors) {
if (sector.boundingBox.hasNode(node))
return sector;
}
return null;
}
//Box class - the "boundingBox" member is a Box object.
public boolean hasNode(Node node) {
int x1 = this.width + this.x;
int y1 = this.height + this.y;
if (node.x >= this.x && node.x < x1 && node.y >= this.y && node.y < y1)
return true;
return false;
}
I wanted to ask myself, what else could go wrong?
Java out-of-memory error. There's an infinite loop that for some reasons, the parent of the node is always that same node. (node.parent == node is always true).
So, just to make sure, I did this, in order to stop the infinite loop:
private ArrayList<Node> recreatePath(Node node) {
int counter = 0;
ArrayList<Node> results = new ArrayList<Node>();
while (node.parent != null) {
if (node.equals(node.parent)) {
counter++;
if (counter > 5)
break;
}
node = node.parent;
}
//DEBUG
System.out.println("Size of path: " + results.size());
return results;
}
It might be possible this can cause the weird path in the picture shown above. Got any hints?
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You don't have to make things recursive, any recursion can also be programmed iteratively. (Though sometimes recursion can be cleaner/easier)
I suggest spitting out some more debug info graphically. It looks like the path is trying to go to the wrong median node? I would draw all the sectors, and the entrances/exits to the sectors. I think it will make tracking down why the path looks like it does easier.
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I suggest spitting out some more debug info graphically. It looks like the path is trying to go to the wrong median node?
Yeah, it's going to the wrong median node. The old code was hardwired to reach that node before advancing on to the next node.
But to be honest, I can hardly see any difference in speed when comparing the old method of "going from node A to node B directly", and the new method of "going through portal A to portal B, then connect node X in portal A to node Y in portal B, finally connect."; the speed difference is minimal. In fact, I'd say it's slower than the old method, because the new method has to be called 3 times to make the path, rather than the old method of calling 1 time.
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An empty map is probably not the best test, that's the worst case scenario, and could probably be optimized out in a game with lots of open spaces with a simple raycast to the goal check, before doing any pathfinding.
A super cluttered map is where you'd save time, as the agent only has to look at it's local surroundings before starting to move, it wouldn't have to wait for the pathfind to complete.
To test it though, you can do two things. First, I suggest more visualization, perhaps color all nodes that are visited by each algorithm (different shades), and then I suggest also profiling the results as well (with visualizations off)
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The portal (hierarchical) method can help alot (on sufficiently large maps where the extra complexity of the hierarchical mechanism overhead is insignificant) when there are restricted paths (saving alot of blind alley checking in typical solid wall maze like maps).
For some games actually saving a path and reusing/sharing it (ie- units being sent to the same destination) and portal (high) level paths are alot less data to store if you have many combinations of reused source + destination paths
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Splitting the path in two is faster because you reduce the number of nodes explored, still, keep in mind that you will only notice difference in huge maps. Also, the median point doesn't really have to be part of the path, so you may end up with a non-optimal path.
That being said, I'd rather use JPS (assuming you don't have different weight restrictions), it is much faster than any other approach.
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An empty map is probably not the best test, that's the worst case scenario, and could probably be optimized out in a game with lots of open spaces with a simple raycast to the goal check, before doing any pathfinding.
Isn't an empty test a good way to test the performance of optimized A* pathfinding for worst case scenarios? If I were to optimize my own derivation of A* pathfinding for my game, so that it's logic is adapted into what my game wants, I could use an empty map in order to see exactly how the most lagging scenario it is and how it's affecting my game.
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I guess you can make sure that you're new algorithm isn't terrible at empty maps, but modifying your pathfinder so it does a check to see if it can do a direct walk from the start to the goal, and just returns that straight path would bypass that case entirely.
You're also not going to see any speedup compared to the standard A* algorithm, so you'd mostly just be doing a sanity test to make sure the more complicated algorithm isn't overdoing it.
The most lagging scenario would be when the paths are not straightforward, or when the goal cannot be reached at all. Though the latter, again is a scenario that's best optimized out entirely if possible.
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You should consider several approaches. The hierachy is a really good solution for really large maps. If you just have issues with performance (stuttering due to long calculations), then you should consider to split up your A* calculation. This works quite fine, just explore maybe 100 nodes per frame to equally distribute the performance hit on severaly frames. I use this technique by calculating several paths over one or more frames distributed on multiple cores. This should work for small to medium sized maps.
If you want an immediate reaction of the entity start with an A* and take the result of the first frame (the A* heuristic should point into the right direction). This path is a good guess of where the final path will point to, and it should be good enough to let your entity start to move in the right direction, though it only works if you have one potential goal. After the final path has been calculated you can "connect" the entity to the final path (maybe a small A* is necessary to connect them).
Edited by Ashaman73
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https://proxies-free.com/functional-analysis-measurement-and-characterization-of-local-correlation-matrices/
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# Functional Analysis – Measurement and Characterization of Local Correlation Matrices
Definition: A matrix $$C in mathbb R ^ {m times n}$$ is a local correlation matrix if there are true random variables $$x_1, dots, x_m, y_1, dots, y_n$$ defined on a common probability space in which values are recorded $$[-1,+1]$$ so that $$C_ {ij} = mathbb E[x_iy_j]$$ holds with everyone $$(i, j) in {1, dots, m } times {1, dots, n }$$,
Set of all $$m times n$$ local correlation matrices $$mathsf {LC} _ {m, n}$$,
1. What is the measure of $$mathsf {LC} _ {m, n} cap[-1,+1]^ {m times n}$$ in the $$[-1,+1]^ {m times n}$$?
2. Is there a nontrivial geometric or functional characterization of $$mathsf {LC} _ {m, n}$$?
3. Are there explicit template families in $$[-1,+1]^ {m times n}$$ they are not$$mathsf {LC} _ {m, n}$$?
4. Given a $$m times n$$ Matrix, there is a simple test if it is a member $$mathsf {LC} _ {m, n}$$?
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|
https://hal-univ-tlse3.archives-ouvertes.fr/INRIA/search/index/?q=%2A&sort=producedDate_tdate+asc&authFullName_s=Ferran+Hurtado
|
inria-00098848v1 Journal articles
Stabbing information of a simple polygon
Discrete Applied Mathematics, Elsevier, 1999, 91 (1-3), pp.67-92
hal-01179059v1 Conference papers
Separating Several Point Sets in the Plane
|
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|
https://blender.stackexchange.com/questions/659/how-can-i-discover-the-author-of-a-blendfile
|
# How can I discover the author of a blendfile?
I know how to set the "Author" attribute for the blendfiles that I create, using Blender User Preferences > File. However, I have not found out how to view the author of a blendfile. How can I do this?
• I don't usually like to provide alternatives, but seeing as this feature is largely useless to the average user (and cannot provide much info), I would suggest using a Text block for author info and packing it with the Blender file. – A Wild RolandiXor Jun 5 '13 at 19:42
• @rolandixor Whenever they are useful, alternatives are great and broaden the horizon. – Haunt_House Sep 21 '13 at 7:58
You can't, This author field is only ever used in exporters. In the COLLADA export to be precise, where the COLLADA format can have an author tag, and I wanted it to be possible for users to have a configurable content for this, so I added the author field to user preferences.
Not everybody will have this set, either, so best not to rely on this for 'correct' user data.
You can query this in the Python Console or in a script using:
bpy.context.user_preferences.system.author
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|
http://www.epsilon-delta.org/2012/06/i-have-bone-to-pick-with-product-and.html?showComment=1348404608736
|
## Friday, June 29, 2012
### I have a bone to pick with the Product and Quotient Rules
First of all, American idioms were the hardest part of high school grammar for me. While English is now my best language, it is not my first. I would never say growing up in a family where neither parent's native language was English ever inhibited my performance in school...except when it came to that darn chapter on idioms in English class.
I clearly remember having assignments where we had to identity the idiom in the given sentence and replace it by a less trite, but similar-in-meaning phrase.
I could always identify the idiom (because it was the only part of the sentence I had never heard in my life). But I could never replace it with the correct meaning.
Clearly, my Googling skills were not up to par in 2003.
To this day, I hardly ever get idioms right. I try. But I usually fail. I'll say things like, "Don't put all your chickens in one basket," "You hit the nail with the head," or, "Don't count your eggs before they hatch."
So, when I was typing the title for this post, I had double check to make sure I was using "I have a bone to pick" correctly.
I believe I did use it correctly. And for your further educational value, according to wikianswers:
"Bone to pick," dates back to the 16th century, simply refers to a dog chewing endlessly on, and "picking clean," a large bone. A "bone to pick" is thus a subject or issue that is expected to require considerable discussion or argument.
You probably already knew that since--somehow--natural-born American citizens seem to come out of the womb with an understanding for these types of phrases. I was not born with this. Thankfully, there's Google.
So, yes. I have an issue with the Product and Quotient Rules. This is an issue I remember having even as a student. Here's what I don't get. In the texts I've used, the Product Rule is typically presented as:
While the Quotient Rule is given as:
$\frac{d\left( \frac{u}{v} \right)}{dx}\; =\; \frac{\left[ v\frac{du}{dx}-u\frac{dv}{dx} \right]}{v^{2}}$
I cannot be the only one who has a problem with this. Why are we making the two rules as different as possible, and hence (in my opinion) as hard as possible, for students to memorize?
As a student, I tried to come up with a way where I could memorize both rules with as little effort as possible, because I was convinced my brain could only hold a finite amount of information. And I had already stuffed it with a lot of nonsense about idioms. So, for both rules, I committed to memory:
(Mess the first)(Hold the second) (Hold the first)(Mess the second)
Btw, Mess=Derive.
Then, for the Product Rule, I would insert a plus sign in the space; for the Quotient Rule, a minus, and put it all over the square of the second. I loved this because I could just move from left to right or up to down in either case. For both rules, u is the first; v is the second.
And so this is how I've been teaching the two rules. As an added bonus, I feel like I'm sending the subliminal message: Differentiating a function can mess it up, or make it "worse." As in, the derivative of a [continuous] function is not necessarily continuous.
Ok, it's very subliminal, but maybe some will catch on.
I know, I know, the standard proofs typically do not yield the rules in this fashion. But what is keeping textbook authors from adding one more little line to the proofs, saying, "And with a little rearranging, we get..."
I know I can't be the only one who teaches it in this way. But I do know I was only ever taught the "textbook" way. And I never understood why my teachers wanted to make it so hard on us.
I'm trying to convert my own students to my method now. Unfortunately, their books present the rules the "standard" way, and so that sometimes gets me in trouble.
1. I also re-arrange the product rule to make it 'match'. I do have a few students who just prefer to do things 'by the book' and that always gives us an opportunity to practice algebra and show the order is not critical. They always chuckle when I bring up the commutative properties - they thought they left that behind in middle school.
2. I am so glad to hear this! It seems so much more natural to me.
3. Nice!
I never thought of doing it this way. When I was in a test in college, I'd derive the quotient rule from the product and chain rules. Otherwise I wouldn't know which term came before the minus. (The rest felt easy to remember.)
Now I call the function t/b (top over bottom), and start the derivative with the bottom squared, then I remember to start the top with b: bottom * derivative of top - top * derivative of bottom.
One more way to get the order right is to use either order, and then check whether your answer makes sense in comparison to the graph
Tell me what you think!
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http://math.stackexchange.com/questions/223897/if-b-is-a-continuous-bilinear-function-such-that-bh-k-o-lverth-k-rvert
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# If $B$ is a continuous bilinear function such that $B(h,k) = o(\lVert(h,k)\rVert^2)$, then $B=0$.
Suppose that $B: H \times K \Rightarrow F$ is a continuous bilinear function, where $H,K$ and $F$ are real normed spaces.
I have to prove (not as homework) that if $B(h,k) = o(\lVert(h,k)\rVert^2)$, then $B=0$.
Since $B$ is bilinear and continuous, we have that $\lVert B(h,k)\rVert \leq \lVert B\rVert \lVert h \rVert \lVert k\rVert \leq \lVert B\rVert \lVert(h,k)\rVert^2$, where $\lVert B\rVert$ is the operator norm.
Hence we have $$0=\lim_{(h,k)\rightarrow 0} \frac{\lVert B(h,k)\rVert}{\lVert (h,k) \rVert^2} \leq \lim_{(h,k)\rightarrow 0} \frac{\lVert B\rVert \lVert(h,k)\rVert^2}{\lVert (h,k) \rVert^2}= \lVert B\rVert.$$
If there is some way for me to get that the last limit is also $0$, I have what has to be proven. But I don't see a way to this. Could anyone provide me with a tiny hint? (No full answers please)
-
Could you please edit in some examples of the kind of $B$ you are talking about? I am unable to combine things in the way you indicate. Mostly I have no clue what $\parallel B \parallel$ should mean here. Anyway, please type in a few actual $B(h,k),$ which would appear to be a function taking real values. Plus, if this is what I think, the word continuous is superfluous. – Will Jagy Oct 30 '12 at 0:29
@WillJagy, Is this ok? – sxd Oct 30 '12 at 0:36
Let $f, g$ be arbitrary and take $\epsilon > 0$ some parameter. Then look at the behaviour $\epsilon^{-2} B(\epsilon f, \epsilon g)$ as $\epsilon \to 0$.
This is a hint how you can prove your proposition, i.e. that $B = 0$ if $B$ is bilinear and satisfies $B(h,k) = o(\| (h,k) \|^2 )$. I'm afraid your attempt just shows $\| B \| \geq 0$ which you know anyway. To get $\| B \| = 0$ try what I suggested. – DanielM Oct 31 '12 at 20:01
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https://askdev.io/questions/995543/dealing-with-tychonoffs-theorem
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# Dealing with Tychonoff's Theorem.
Here are my few questions that I encountered while going through Tychonoff's theorem in .
a) First of all, so far I was thinking that Heine Borel definition of compactness implies sequential compactness but not the other way around ( although i am failing to find some examples to appreciate it). But what wikipedia says is that " but NEITHER implies the other in general topological space . What am i missing here ?
b) It is easy to see that finite product ( countable product is not true, right ? ) of sequentially compact spaces is compact which we can see using diagonalization argument . and it discusses of embedding X ( completely regular Hausdorff space ) into $[0,1]^{C(X,[0,1])}$ (what does $[0,1]^{C(X,[0,1])}$ mean? I am not able to make any sense) , where $C(X,[0,1])$ is the set of continuous map from $X$ to $[0,1]$. I would appreciate your help.
Thanks!
3
2022-07-25 20:47:13
Source Share
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https://www.kidbrooke.com/knowledge-base/part-ii-portfolio-construction-sampling-optimisation/
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# Part II - Portfolio Construction - Sampling & Optimisation
The main findings of the first part of the “Portfolio Construction”- series suggest that the parameter uncertainty has a significant impact on the optimal portfolio allocations. Therefore, a Bayesian sampling method is proposed to introduce the parameter uncertainty to the model. This section presents and compares the results from the Bayesian simulation model to those obtained through using a regular multivariate normal model.
Portfolio Construction New
Portfolio Construction New
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https://gitlab.lrde.epita.fr/spot/spot/-/commit/54b25b8c8ec03c0b9210cd57cd54410abf1423b6
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Commit 54b25b8c by Alexandre Duret-Lutz
### ltlcross: more documentation
* doc/org/ltlcross.org: Describe statistics, and mention --products=N.
parent 9b82d755
... ... @@ -31,7 +31,8 @@ The core of =ltlcross= is a loop that does the following steps: If there are 3 translators, the positive and negative translations will be denoted =P0=, =N0=, =P1=, =N1=, =P2=, =N2=. - Build the products of these automata with a random state-space (the same state-space for all translations). state-space for all translations). (If the =--products=N= option is given, =N= products are performed instead.) - Perform sanity checks between all these automata to detect any problem. - Gather statistics if requested. ... ... @@ -109,6 +110,8 @@ Detailed statistics about the result of each translation, and the product of that resulting automaton with the random state-space, can be obtained using the =--csv=FILE= or =--json=FILE= option. ** CSV or JSON output (or both!) The following compare =ltl2tgba=, =spin=, and =lbt= on three random formula (where =W= and =M= operators have been rewritten away because they are not supported by =spin= and =lbt=). ... ... @@ -179,9 +182,9 @@ This can be loaded in any spreadsheet application. Although we only supplied 2 random generated formulas, the output contains 4 formulas because =ltlcross= had to translate the positive and negative version of each. If we had used the option =--json=results.json= instead of =--cvs=results.csv=, the file =results.json= would have contained the following [[http://www.json.org/][JSON]] output. If we had used the option =--json=results.json= instead of (or in addition to) =--cvs=results.csv=, the file =results.json= would have contained the following [[http://www.json.org/][JSON]] output. #+BEGIN_SRC sh :results verbatim :exports results cat results.json ... ... @@ -271,6 +274,112 @@ bogus automata are still included: as shown below =ltlcross= will report inconsistencies between automata as errors, but it does not try to guess who is incorrect. ** Description of the columns =formula= and =tool= contain the formula translated and the command run to translate it. In the CSV, these columns contain the actual text. In the JSON output, these column contains an index into the =formula= and =tool= table declared separately. =states=, =edged=, =transitions=, =acc= are size measures for the automaton that was translated. =acc= counts the number of acceptance sets. When building (degeneralized) Büchi automata, it will always be =1=, so its value is meaningful only when evaluating translations to generalized Büchi automata. =edges= counts the actual number of edges in the graph supporting the automaton; an edge (labeled by a Boolean formula) might actually represent several transitions (each labeled by assignment of all atomic propositions). For instance in an automaton where the atomic proposition are $a$ and $b$, one edge labeled by $a\lor b$ actually represents three transitions $a b$, $a\bar b$, and $\bar a b$. The following picture displays two automata for the LTL formula =a U b=. They both have 2 states and 3 edges, however they differ in the number of transitions (7 versus 8), because the initial self-loop is more constrained in the first automaton. A smaller number of transition is therefore an indication of a more constrained automaton. #+BEGIN_SRC dot :file edges.png :cmdline -Tpng :exports results digraph G { 0 [label="", style=invis, height=0] 0 -> 1 1 [label="A1"] 1 -> 2 [label="b\n"] 1 -> 1 [label="a & !b\n"] 2 [label="B1", peripheries=2] 2 -> 2 [label="1"] 3 [label="", style=invis, height=0] 3 -> 4 4 [label="A2"] 4 -> 5 [label="b\n"] 4 -> 4 [label="a\n"] 5 [label="B2", peripheries=2] 5 -> 5 [label="1"] } #+END_SRC #+RESULTS: [[file:edges.png]] =scc= counts the number of strongly-connected components in the automaton. These SCCs are also partitioned on four sets based on their strengths: - =nonacc_scc= for non-accepting SCCs (such as states A1 and A2 in the previous picture) - =terminal_scc= for SCCs that consist of a single state with an accepting self-loop labeled by true (such as states B1 and B2 in the previous picture) - =weak_scc= for non-terminal SCCs in which all cycles are accepting - and =strong_scc= for accepting SCCs in which some cycles are not accepting. These SCC strengths can be used to compute the strength of the automaton as a whole: - an automaton is terminal if it contains only non-accepting or terminal SCCs, - an automaton is weak if it it contains only non-accepting, terminal, or weak SCCs, - an automaton is strong if it contains at least one strong SCC. This classification is used to fill the =terminal_aut=, =weak_aut=, =strong_aut= columns with Boolean values. Only one of these should contain =1=. We usually prefer terminal automata over weak automata, and weak automata over strong automata, because the emptiness check of terminal (and weak) automata is easier. =nondetstates= counts the number of non-deterministic states in the automaton. =nondeterministic= is a Boolean value indicating if the automaton is not deterministic. For instance in the previous picture showing two automata for =a U b=, the first automaton is deterministic (these two fields will contain 0), while the second automaton contain a nondeterministic state (state A2 has two possible successors for the assignment $ab$) and is therefore not deterministic. =time= obviously contains the time used by the translation. Time is measured with some high-resolution clock when available (that's nanosecond accuracy under Linux), but because translator commands are executed through a shell, it also includes the time to start a shell. (This extra cost apply identically to all translators, so it is not unfair.) Finally, =product_states=, =product_transitions=, and =product_scc= count the number of state, transitions and strongly-connect components in the product that has been built between the translated automaton and a random model. For a given formula, the same random model is of course used against the automata translated by all tools. Comparing the size of these product might give another indication of the "conciseness" of a translated automaton. There is of course a certain "luck factor" in the size of the product. Maybe some translator built a very dumb automaton, with many useless states, in which just a very tiny part is translated concisely. By luck, the random model generated might synchronize with this tiny part only, and ignore the part with all the useless states. A way to lessen this luck factor is to increase the number of products performed against the translated automaton. If option =--products=N= is used, =N= products are builds instead of one, and the fields =product_states=, =product_transitions=, and =product_scc= contain average values. * Detecting problems If a translator exits with a non-zero status code, or fails to output ... ... @@ -318,6 +427,11 @@ positive and negative formulas by the ith translator). : error: {P0,P2,P3,P4,P5,P6,P7,P8,P9} disagree with {P1} when evaluating the state-space If =--products=N= is used with =N= greater than one, the number of the state-space is also printed. This number is of no use by itself, except to explain why you may get multiple disagreement between the same sets of automata. - Consistency check: For each $i$, the products $P_i\otimes S$ and $N_i\otimes S$ ... ... @@ -329,7 +443,11 @@ positive and negative formulas by the ith translator). : error: inconsistency between P1 and N1 The above checks are the same that are performed by [[http://www.tcs.hut.fi/Software/lbtt/][LBTT]]. If =--products=N= is used with =N= greater than one, the number of the state-space in which the inconsistency was detected is also printed. The above checks are similar to those that are performed by [[http://www.tcs.hut.fi/Software/lbtt/][LBTT]]. If any problem was reported during the translation of one of the formulas, =ltlcheck= will exit with an exit status of =1=. Statistics ... ...
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