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https://nrich.maths.org/85/note
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### Consecutive Numbers
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!
# Calendar Capers
### Why do this problem?
In this problem, students are invited to explore in a new way a very familiar object - a calendar. Numerical patterns lead to some surprising results which can be explained using the power of algebra.
### Possible approach
This problem is structurally similar to Crossed Ends.
Students will need access to calendars - you can print off a calendar here.
"Choose any 3 by 3 square of dates anywhere on the page, and add the numbers in the four corners."
Invite students to share their results - ask them to describe the square they chose, and what their answer was. They may choose to describe their square in terms of the top left corner, or the number in the middle, so decide as a class on a common reference point.
"Is there a way to work out the total of the four corners without adding them all up?"
Students should notice a relationship between the total and their reference point.
"How can we be sure our relationship will always hold?"
"What happens to a number when we move to the left? To the right?"
"What happens to the number when we move up? Down?
If appropriate, suggest to students that they could call their reference point $n$ and label all other dates in terms of $n$. This gives them the tools they need to prove algebraically that their rule will always hold.
There are a few more challenges suggested in the problem:
• Add the numbers in each row, column and diagonal that passes through the centre number
• Add the numbers in the bottom rows and the left and right columns
• Circle any number on the top row and put a line through the other numbers that are in the same row and column as your circled number.
Repeat this for one of the remaining numbers in the second row.
You should now have just one number left on the bottom row; circle it.
Add together the three circled numbers.
For each one, students can use algebra to prove any relationships they discover.
### Possible Extension
Pair Products invites students to make sense of a multiplicative relationship using algebra, and would make a good follow-up to this problem.
### Possible Support
Students could start by exploring the relationships in a two by two square.
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https://www.physicsforums.com/threads/hamiltonian-as-the-generator-of-time-translations.884777/
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# I Hamiltonian as the generator of time translations
Tags:
1. Sep 9, 2016
### Frank Castle
In literature I have read it is said that the Hamiltonian $H$ is the generator of time translations. Why is this the case? Where does this statement derive from?
Does it follow from the observation that, for a given function $F(q,p)$, $$\frac{dF}{dt}=\lbrace F,H\rbrace +\frac{\partial F}{\partial t}$$ In particular, if $F$ is not explicitly dependent on time, then $$\frac{dF}{dt}=\lbrace F,H\rbrace$$ Or is there more to it?
2. Sep 10, 2016
### pliep2000
Ah poisson brackets!
I think what you are looking for is Noethers theorem.
Susskinds classical mechanics course on youtube, i think lecture 4 (symmetries) and 8 (poisson) will help you.
Draft saved Draft deleted
Similar Discussions: Hamiltonian as the generator of time translations
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https://www.physicsforums.com/threads/linear-functionals.132085/
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# Homework Help: Linear functionals
1. Sep 14, 2006
### wurth_skidder_23
Here is the problem I have been asked to solve:
Assume that m < n and l1, l2, . . . , lm are linear functionals on an n-dimensional vector space X.
(a) Prove there exists a non-zero vector x in X such that the scalar product < x, lj >= 0 for 1 <= j <= m. What does this say about the solution of systems of linear equations?
(b) Under what conditions on the scalars b1, . . . , bm is it true that there exists a vector x in X such that the scalar product < x, lj >= bj for 1 <= j <= m? What does this say about the solution of systems of linear equations?
I am having trouble understanding the concept of a linear functional and how it relates to the vector space X.
Last edited: Sep 14, 2006
2. Sep 14, 2006
### AKG
x is a vector in X, and lj is a linear functional on X, so what is < x, lj >? Do you mean lj(x)? Linear functionals are linear functions which map vectors to scalars. By linearity, they are uniquely determined by their behaviour on the basis vectors of the vector space. Let f be a linear functional on a vector space V, and let v1, ..., vn be basis vectors for V. If x is any vector in X, then there exist scalars x1, ..., xn such that
x = x1v1 + ... + xnvn
Then:
f(x)
= f(x1v1 + ... + xnvn)
= f(x1v1) + ... + f(xnvn)
= x1f(v1) + ... + xnf(vn)
= (x1, ..., xn).(f(v1), ..., f(vn))
If l1, ..., lm are linear functionals, consider the row vectors (l1(v1), ..., l1(vn)), ..., (lm(v1), ..., lm(vn)). Do you see how the question is reduced to the following:
If m < n, and {li(vj) | i = 1, ..., m; j = 1, ..., n} is any set of scalars, do there exists scalars x1, ..., xn such that for each i, it holds that:
(x1, ..., xn).(li(v1), ..., li(vn))
Consider:
$$(\mbox{Span}\{(l_i(v_1),\, \dots ,\, l_i (v_n))\ :\ 1 \leq i \leq m\})^{\perp}$$
3. Sep 14, 2006
### wurth_skidder_23
< x, lj > is the scalar/dot product
4. Sep 14, 2006
### AKG
I know that. Suppose v is a vector and x is toenail. What is <v,x>?
5. Sep 14, 2006
### wurth_skidder_23
Yeah, I still have no idea what I'm proving for this problem, nor do I understand the final question, though I imagine if I could do the proof, the question would make sense. A hint would be appreciated.
6. Sep 15, 2006
### AKG
The dot product takes two vectors of the same space and gives you a scalar. A linear functional on V is not a vector in V. There is a strong relation between the value of a linear functional at a vector and the dot product of that vector with a particular other vector, but that's still a little off in the distance for us. First, you need to get the basics.
7 is a real number. So is $-\pi$. It makes sense to talk about, say, 7 x $-\pi$. You can multiply numbers. Can you multiply a number by a function? What is 7 x sine? It doesn't really make sense (okay, you can make sense of it, but try to understand the basic idea). Similarly, v and x are both vectors, say. Then it makes sense to take their dot product, v.x If f is a linear functional, then what sense does it make to take v.f? You can multiply two numbers together, but you can't multiply a number by a toenail, it's just absurd. Likewise, you can take the dot product of a vector with another vector, but you can't take the dot product of a vector with a functional, it's just absurd. It makes as much sense as taken the dot product of a vector with a toenail.
If V is a vector space over a field F, then a linear functional is a function: f : V -> F that is linear. So a linear functional (I'll just call it a functional) is a function, which is just something that maps elements of one set to elements of another set. In addition, it is a special kind of function, it is a linear function. That means f(v+w) = f(v)+f(w), and f(av) = af(v), where v and w are vectors in V, and a is a scalar in F. Do you understand this so far?
Suppose you have an n-dimensional vector space V (over a field F), and m (with m < n) linear functionals f1, ..., fm. You want to prove that there is a non-zero x such that fi(x) = 0 for 1 < i < m.
Let me give you a related problem. Let V be an n-dimensional vector space. Let {v1, ..., vm} be any set of m vectors from V, with m < n. Prove that there exists a non-zero x such that <x,vi> = 0 for 1 < i < m.
7. Sep 15, 2006
### matt grime
Duals always seem to cause problem's, conceptually, and I don't know why.
If V and W are vector spaces you are really happy with what the space of linear maps between V and W is. If we are the kind of person who likes bases then it is the set of dim(W) by dim(V) matrices. Well, all we've done is take a general case you're happy with and looked at one particular example, when W is one dimensional. Surely that is even easier to understand than the general case?
8. Sep 21, 2011
### abhi_kirk
Hi.
I have the same question as wurthskidder23 and ive read the reply by AKG. Can anybody give some further hint as how to solve the question. Im not sure how to prove that x is non-zero?
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http://physics.stackexchange.com/questions/37716/what-is-the-angular-distance-between-ptolemaic-perigees-of-mercury
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# What is the angular distance between Ptolemaic perigees of Mercury?
In his excellent treatment of the history of the science of astronomical distances and sizes, Albert van Helden says (p.29) that
The complicated [Ptolemaic] model of Mercury has the curious property of producing two perigees, each about 120° removed from the apogee.
But when I try to confirm this using the 88 day period Mercury's epicycle, I get approximately half the expected value.
In a given time (in days), $t$, Mercury will travel through an angle $\varepsilon = 2\pi t/88$ along its epicycle which will traveled through an angle $\delta = 2\pi t/365$ along its deferent. In transitioning from apogee to perigee, it must be the case (since Mercury must go half way round the epicycle, and then an additional $\delta$ to "catch up" with the angle traveled by the center of the epicycle) that $$\varepsilon=\delta+\pi$$ solving which yields $$t=[2\cdot(1/88-1/365)]^{-1}\approx58$$ which corresponds to about 57°, roughly half the number expected.
What is missing from the above reasoning? Is there something about the definitions of epicyclic period I've missed, perhaps?
-
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http://ar16.iita.org/6otunp4/article.php?page=414c9d-area-of-intersection-of-cylinder-and-plane
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By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. When trying to fry onions, the edges burn instead of the onions frying up, Electric power and wired ethernet to desk in basement not against wall. Is there any text to speech program that will run on an 8- or 16-bit CPU? Note that the cylinder can be parametrized as x = 3 cos(t), y = sin(t), where 0 t<2ˇ, with z2R. THEORY Consider that two random planes (Plane I and Plane II) intersect a sphere of radius r and that, the line of intersection of the two planes passes through the sphere as shown in Figure 1. I could not integrate the above expression. I thought of substituting the $y$ variable from the plane's equation in the cylinder's equation. We parameterize the plane equation $x+y+z=1$. Parameterize C I am not sure how to go about this. z = \frac{4\cos u+\sqrt2\sin u}{12}$$. Thank you, I was able to solve the problem thanks to that. Question: Find the surface area of the solid of intersection of the cylinder {eq}\displaystyle x^{2}+y^{2}=1 {/eq} and {eq}\displaystyle y^{2}+z^{2}=1. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Short scene in novel: implausibility of solar eclipses. This vector when passing through the center of the sphere (x s, y s, z s) forms the parametric line equation Thus, the final surface area is \frac{\pi \cdot \sqrt{6}}{2}. Height = 25 cm . When two three-dimensional surfaces intersect each other, the intersection is a curve. Problem: Parameterize the curve of intersection of the sphere S and the plane P given by (S) x2 +y2 +z2 = 9 (P) x+y = 2 Solution: There is no foolproof method, but here is one method that works in this case and many others where we are intersecting a cylinder or sphere (or other “quadric” surface, a concept we’ll talk about Friday) with a plane. to the plan, the section planes being level with lines 1; 2,12; 3.11; 4.10. etc. 3. Intersection of cylinder and plane? If the plane were horizontal, it would intersect the cylinder in circle. }\) ... Use the standard formula for the surface area of a cylinder to calculate the surface area in a different way, and compare your result from (b). How can I buy an activation key for a game to activate on Steam? For each interval dy, we wish to find the arclength of intersection. simplifying we obtain So now I am looking for either other methods of parametrization or a different approach to this problem overall. rev 2020.12.8.38143, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Intersection of two Prisms The CP is chosen across one edge RS of the prism This plane cuts the lower surface at VT, and the other prism at AB and CD The 4 points WZYX line in both the prisms and also on the cutting plane These are the points of intersection required Answer to: Find the surface area of the solid of intersection of the two cylinders x^2 + z^2 = 81 and y^2 + z^2 = 81. For the general case, literature provides algorithms, in order to calculate points of the intersection curve of two surfaces. Was Stan Lee in the second diner scene in the movie Superman 2? you that the intersection of the cylinder and the plane is an ellipse. This was a really fun piece of work. \dfrac{(z+ \dfrac{3}{9})^2}{\dfrac{10}{9}}+ \dfrac{y^2}{\dfrac{10}{9}}, "can you go further?" I realized I was making the problem harder than it needed to be. Asking for help, clarification, or responding to other answers. Pick a point on the base in top view (should lie inside the given plane and along the base of the cylinder). |T_u \times T_v| = \sqrt{\frac{1}{2}\cdot\cos^2(u)+\sin^2(u)}. How do I interpret the results from the distance matrix? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Or is this yet another time when you, the picture of this equation is clearly an ellipse, MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…, Find a plane whose intersection line with a hyperboloid is a circle, Intersection of a plane with an infinite right circular cylinder by means of coordinates, Line equation through point, parallel to plane and intersecting line, Intersection point and plane of 2 lines in canonical form. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. I have a cylinder equation (x-1+az)^2+(y+bz)^2=1. Nick. Sphere centered on cylinder axis. Problem 1: Determine the cross-section area of the given cylinder whose height is 25 cm and the radius is 4 cm. The projection of C onto the x-y plane is the circle x^2+y^2=5^2, z=0, so we know that. Now we have\iint_s dx\, dy = \pi ab since the area of s is \pi ab, and a and b are the lengths of its semi-major and semi-minor axes. You are cutting an elliptical cylinder with a plane, leading to an ellipse. Cross Section Example Solved Problem. Find a vector function that represents the curve of intersection of the cylinder x2+y2 = 9 and the plane x+ 2y+ z= 3. Draw a line (represents the edge view of the cutting plane) that contains that point, across the given plane. Looking at the region of intersection of these two cylinders from a point on the x-axis, we see that the region lies above and below the square in the yz-plane with vertices at (1,1), (-1,1), (-1,-1), and (1,-1). It only takes a minute to sign up. If the center of the sphere lies on the axis of the cylinder, =. Find a vector function that represents the curve of intersection of the cylinder x² + y² = 1 and the plane y + z = 2. In the above figure, there is a plane* that cuts through a cone.When the plane is parallel to the cone's base, the intersection of the cone and plane is a circle.But if the plane is tilted, the intersection becomes an ellipse. The way to obtain the equation of the line of intersection between two planes is to find the set of points that satisfies the equations of both planes. c. Project the line and the piercing point down to the front view. 2 The intersection is (az-1)^2+(y+bz)^2=1. For most points on most surfaces, different sections will have different curvatures; the maximum and minimum values of these are called the principal curvatures . A plane (parallel with the cylinders' axes) intersecting the bicylinder forms a square and its intersection with the cube is a larger square. The intersection of a plane figure with a sphere is a circle. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Getting the z from the plane equation we get: and replacing the parametrization we get the final curve, parametrized in u only:$$ x = \cos u \\\\ That's a good start. Cylinder; Regular Tetrahedron; Cube; Net; Sphere with Center through Point ; Sphere with Center and Radius; Reflect about Plane; Rotate around Line; Rotate 3D Graphics View; View in front of; Custom Tools; Select two planes, or two spheres, or a plane and a solid (sphere, cube, prism, cone, cylinder, ...) to get their intersection curve if the two objects have points in common. Cross Sections Solved Problem. A cylinder meeting a cone, their centres not being in the same vertical plane (Fig. These sections appear on the plan as circles. Why do exploration spacecraft like Voyager 1 and 2 go through the asteroid belt, and not over or below it? In that case, the intersection consists of two circles of radius . Then S is the union of S1and S2, and Area(S) = Area(S1)+Area(S2) where Area(S2) = 4π since S2is a disk of radius 2. All content in this area was uploaded by Ratko Obradovic on Oct 29, 2014 ... as p and all first traces of aux iliary planes (intersection of . We have $a=1$ and $b= \frac{\sqrt2}{2}$ from $x^2+2y^2=1$. All cross-sections of a sphere are circles. I set x = cost and y = sint, but I'm not really sure where to go from there. Use MathJax to format equations. Intersection of two Prisms The CP is chosen across one edge RS of the prism This plane cuts the lower surface at VT, and the other prism at AB and CD The 4 points WZYX line in both the prisms and also on the cutting plane These are the points of intersection required To subscribe to this RSS feed, copy and paste this URL into your RSS reader. It is noted that, the line of intersection does not necessarily coincides with the diameter of the sphere. In such a case the area of the section is $\pi R^2 |\sec\theta|$, where $R$ is the radius of the cylinder and $\theta$ the the angle between the cutting plane and a plane containing a circular section of the cylinder. How many computers has James Kirk defeated? The minimal square enclosing that circle has sides 2 r and therefore an area of 4 r 2 . A cylindric section is the intersection of a cylinder's surface with a plane.They are, in general, curves and are special types of plane sections.The cylindric section by a plane that contains two elements of a cylinder is a parallelogram. (rcosµ;rsinµ;1¡ r(cosµ+sinµ)) does the trick. Height = 25 cm . Asking for help, clarification, or responding to other answers. How to calculate the surface area of parametric surface? It should be OK though to treat the circle as cylinder with a very small height if that makes this any more tractable. The area of intersection becomes zero in case holds; this corresponds to the limiting case, where the cutting plane becomes a tangent plane. The analytic determination of the intersection curve of two surfaces is easy only in simple cases; for example: a) the intersection of two planes, b) plane section of a quadric (sphere, cylinder, cone, etc. Thanks for contributing an answer to Mathematics Stack Exchange! Why is Brouwer’s Fixed Point Theorem considered a result of algebraic topology? You are cutting an elliptical cylinder with a plane, leading to an ellipse. Answer to: Find a vector function that represents the curve of intersection of the cylinder x^2 + y^2 = 16 and the plane x + z = 5. Find the tangent plane to the image of $\phi(u,v)=(u^2,u\sin e^v,\frac{1}{3}u\cos e^v)$ at $(13,-2,1)$. Use … Four-letter word contains no two consecutive equal letters. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. MathJax reference. To clarify, by intersects, I mean if any points within the area described by the circle are within the bounding box, then that constitutes an "intersection." y = \frac{\sqrt 2}{4}\sin u \\\\ How do I interpret the results from the distance matrix? A cylinder has two parallel bases bounded by congruent circles, and a curved lateral surface which connect the circles. Note: See also Intersect command. The parametric equation of a polygonal cylinder with sides and radius rotated by an angle around its axis is:. the area of the surface. The intersection of the cylinder and the YOZ plane should be bigger than the base when it is an ellipse. After looking through various resources, they all say to parameterize the elliptic cylinder the way I did above. we have the equation $$x^2+8y^2=1$$ and $$x+y+3z=0$$ solving the second equation for $y$ we have y = \frac{\sqrt 2}{4}\sin u \\\\ Select two planes, or two spheres, or a plane and a solid (sphere, cube, prism, cone, cylinder, ...) to get their intersection curve if the two objects have points in common. To find more points that make up the plane of intersection, use cutting planes and traces: a. $\endgroup$ – Alekxos Sep 24 '14 at 18:02 Point of blue bar draws intersection (orange ellipse) of yellow cylinder and a plane. 3 Intersection of the Objects I assume here that the cylinder axis is not parallel to the plane, so your geometric intuition should convince you that the intersection of the cylinder and the plane is an ellipse. A non empty intersection of a sphere with a surface of revolution, whose axis contains the center of the sphere (are coaxial) consists of circles and/or points. Actually I think we could get better results (at least easier to handle) about the intersection passing through parametrization. $T_u = (-\sin(u), \frac{\sqrt2}{2}\cos(u),0)$. Presentation of a math problem to find the Volume of Intersection of Two Cylinders at right angles (the Steinmetz solid) and its solution How to calculate surface area of the intersection of an elliptic cylinder and plane? intersects. To find the intersection of line and a plane. The figure whose area you ask for is an ellipse. Why did no one else, except Einstein, work on developing General Relativity between 1905-1915? What were your results? (Philippians 3:9) GREEK - Repeated Accusative Article. Cross Sections Solved Problem. Let C be a right circular cylinder having radius r and positioned some place in space and oriented in . $$9x^2+72z^2+48xz=1$$ Spher: (x - x s) 2 + (y - y s) 2 + (z - z s) 2 = R 2. The problem is to find the parametric equations for the ellipse which made by the intersection of a right circular cylinder of radius c with the plane which intersects the z-axis at point 'a' and the y-axis at point 'b' when t=0. An edge is a segment that is the intersection of two faces. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Looking at the region of intersection of these two cylinders from a point on the x-axis, we see that the region lies above and below the square in the yz-plane with vertices at (1,1), (-1,1), (-1,-1), and (1,-1). ...gave me (the) strength and inspiration to. To construct the points of the intersection of a cone and a cylinder we choose cutting planes that intersect both surfaces along their generatrices. MathJax reference. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. To learn more, see our tips on writing great answers. The vector normal to the plane is: n = Ai + Bj + Ck this vector is in the direction of the line connecting sphere center and the center of the circle formed by the intersection of the sphere with the plane. can you go further? To find more points that make up the plane of intersection, use cutting planes and traces: a. Intersection of Cylinder and Cylinder Assume a series of horizontal cutting planes passing through the the horizontal cylinder and cutting both cylinders. Is it not possible to explicitly solve for the equation of the circle in terms of x, y, and z? WLOG the cylinder has equation X² + Y² = 1 (if not, you can make it so by translation, rotation and scaling).. Then the parametric equation of the circle is. The intersection line between two planes passes throught the points (1,0,-2) and (1,-2,3) We also know that the point (2,4,-5)is located on the plane,find the equation of the given plan and the equation of another plane with a tilted by 60 degree to the given plane and has the same intersection line given for the first plane. (x;y;1¡ x¡ y): R2!R3: The intersection of the plane with the cylinder lies above the disk f(x;y)2 R2 jx2 +y2 = 1g which can be parametrized by (r;µ)2 [0;1]£ [0;2¼]7! Why do you say "air conditioned" and not "conditioned air"? Making statements based on opinion; back them up with references or personal experience. How much theoretical knowledge does playing the Berlin Defense require? Sections of the horizontal cylinder will be rectangles, while those of the vertical cylinder will always be circles … Bash script thats just accepted a handshake, Tikz, pgfmathtruncatemacro in foreach loop does not work, How Close Is Linear Programming Class to What Solvers Actually Implement for Pivot Algorithms, I made mistakes during a project, which has resulted in the client denying payment to my company. 12/17) Divide the cylinder into 12 equal sectors on the F.E and on the plan. Expanding this, we obtain the quadratic equation in and , z = v$$, , with u\in[0, 2\pi] and v\in(-\infty,+\infty). In this note simple formulas for the semi-axes and the center of the ellipse are given, involving only the semi-axes of the ellipsoid, the componentes of the unit normal vector of the plane and the distance of the plane from the center of coordinates. Let's move from y = 0 to 1. Find a parametrization for the surface de¯ned by the intersection of the plane x+y +z =1 with the cylinder x2+y2= 1. This is not for a game and I'd rather not approximate the circle in some way. Fdr, where F = hxy;2z;3yiand Cis the curve of intersection of the plane x+ z= 5 and the cylinder x2 + y2 = 9. In most cases this plane is slanted and so your curve created by the intersection by these two planes will be an ellipse. The base is the circle (x-1)^2+y^2=1 with area Pi. The circumference of an ellipse is … The surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder. Plugging these in the equation of the plane gives z= 3 x 2y= 3 3cos(t) 6sin(t): The curve of intersection is therefore given by y^2 + z^2 = 1. at x = +/- y The cylinder can be parametrized in (u, v) like this:$$ x = \cos u \\\\ The intersection of a plane in a sphere produces a circle, likewise, all cross-sections of a sphere are circles. All cross-sections of a sphere are circles. Oh damn, you wanted surface area. This is one of four files covering the plane, the sphere, the cylinder, and the cone. Consider the straight line through B lying on the cylinder (i.e. Does a private citizen in the US have the right to make a "Contact the Police" poster? I tried different a's and b's, The area is always Pi, for example letting a=1 and b=10. Example 4 Find the surface area of the portion of the sphere of radius 4 that lies inside the cylinder $${x^2} + {y^2} = 12$$ and above the $$xy$$-plane. Now our $T_u$ = $(1,0,-1)$ and $T_v=(0,1,-1)$. Substituting equation (2) into equation (3), de ning = P C, and de ning M = I DDT, leads to ( + A+ B)TM( + A+ B) = r2. Is there such thing as reasonable expectation for delivery time? To learn more, see our tips on writing great answers. The intersection of two surfaces will be a curve, and we can find the vector equation of that curve. Solution: Given: Radius = 4 cm. I approached this question by first parameterizing the equation for the elliptic cylinder. The Question: Find The Surface Area Of The Surface S. 51) S Is The Intersection Of The Plane 3x + 4y + 12z = 7 And The Cylinder With Sides Y = 4x2 And Y-8-4 X2. Input: pink crank. It only takes a minute to sign up. Did my 2015 rim have wear indicators on the brake surface? Consider a single circle with radius r, the area is pi r 2 . We can find the vector equation of that intersection curve using these steps: c. Details. Pick a point on the base in top view (should lie inside the given plane and along the base of the cylinder). site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. You know that in this case you have a cylinder with x^2+y^2=5^2. P = C + U cos t + V sin t where C is the center point and U, V two orthogonal vectors in the circle plane, of length R.. You can rationalize with the substitution cos t = (1 - u²) / (1 + u²), sin t = 2u / (1 + u²). Can you yourself? "Let S denote the elliptical cylinder given by the equation 4y2+ z2=4, and let C be the curve obtained by intersecting S with the plane y=x. It meets the circle of contact of the spheres at two points P1 and P2. It is well known that the line of intersection of an ellipsoid and a plane is an ellipse. The diagonals of this square divide it into 4 regions, labelled I, II, III, and IV. The cylinder can be parametrized in $(u, v)$ like this: Use thatparametrization tocalculate the area of the surface. Plane: Ax + By + Cz + D = 0. Solution: Given: Radius = 4 cm. The circular cylinder looks very nice, but what you show as a straight line (x + z = 5) is actually a plane. Making statements based on opinion; back them up with references or personal experience. On the cylinder x^2 + z^2 = 1, the intersection is clearly a circular arc, but the enclosed angle varies with y. x^2 + z^2 = 1 . By a simple change of variable ($y=Y/2$) this is the same as cutting a cylinder with a plane. Answer: Since z =1¡ x¡ y, the plane itself is parametrized by (x;y) 7! Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. This result has been applied in [6]. Let B be any point on the curve of intersection of the plane with the cylinder. Problem: Determine the cross-section area of the given cylinder whose height is 25 cm and radius is 4 cm. (rcosµ;rsinµ): Thus R:(r;µ)7! The difference between the areas of the two squares is the same as 4 small squares (blue). some direction. A plane through the vertex of a cone intersects that cone in a generatrix and a plane parallel with the axis of a cylinder intersects that cylinder in its generatrix. Let P1(x1,y1,z1) and P2(x2,y2,z2) be the centers of the circular ends. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. In the other hand you have plane. In the theory of analytic geometry for real three-dimensional space, the curve formed from the intersection between a sphere and a cylinder can be a circle, a point, the empty set, or a special type of curve.. For the analysis of this situation, assume (without loss of generality) that the axis of the cylinder coincides with the z-axis; points on the cylinder (with radius ) satisfy How were drawbridges and portcullises used tactically? 2. The spheres touch the cylinder in two circles and touch the intersecting plane at two points, F1 and F2. I think the equation for the cylinder … Can you compute $R$, $\cos\theta$ and finish by scaling? The circumference of an ellipse is problematic and not easily written down. Intersected circle area: Distance of sphere center to plane: Sphere center to plane vector: Sphere center to plane line equation: Solved example: Sphere and plane intersection Spher and plane intersection. Problem: Determine the cross-section area of the given cylinder whose height is 25 cm and radius is 4 cm. How can you come out dry from the Sea of Knowledge? Find the … What area needs to be modified? The analytic determination of the intersection curve of two surfaces is easy only in simple cases; for example: a) the intersection of two planes, b) plane section of a quadric (sphere, cylinder, cone, etc. These circles lie in the planes Sections are projected from the F.E. Solution: Let S1be the part of the paraboloid z = x2+ y2that lies below the plane z = 4, and let S2be the disk x2+y2≤ 4, z = 4. Do you have the other half of the model? 3d intersection. Show Solution Okay we’ve got a … Why is Brouwer’s Fixed Point Theorem considered a result of algebraic topology? Converting parametric line to intersection of planes line. In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces.Cutting an object into slices creates many parallel cross-sections. $T_u \times T_v = -\frac{\sqrt2}{2}\cos(u)\cdot i-\sin(v)\cdot j$. Why does US Code not allow a 15A single receptacle on a 20A circuit? Solution: Given: Radius = 4 cm. $x=\cos(u)$, $y= \frac{\sqrt2}{2} \sin(u)$, $z = v$. Subsection 11.6.3 Summary. The diagonals of this square divide it into 4 regions, labelled I, II, III, and IV. Twist in floppy disk cable - hack or intended design? How can I upsample 22 kHz speech audio recording to 44 kHz, maybe using AI? Over the triangular regions I and III the top and bottom of our solid is the cylinder The intersection of a plane that contains the normal with the surface will form a curve that is called a normal section, and the curvature of this curve is the normal curvature. The diagram shows the case, where the intersection of a cylinder and a sphere consists of two circles. Four-letter word contains no two consecutive equal letters. Solution: The curve Cis the boundary of an elliptical region across the middle of the cylinder. ), c) intersection of two quadrics in special cases. Call this region S. To match the counterclockwise orientation of C, we give Sthe upwards orienta-tion. … The and functions define the composite curve of the -gonal cross section of the polygonal cylinder [1]:. In the the figure above, as you drag the plane, you can create both a circle and an ellipse. The intersection line between two planes passes throught the points (1,0,-2) and (1,-2,3) We also know that the point (2,4,-5)is located on the plane,find the equation of the given plan and the equation of another plane with a tilted by 60 degree to the given plane and has the same intersection line given for the first plane. $\begingroup$ Solving for y yields the equation of a circular cylinder parallel to the z-axis that passes through the circle formed from the sphere-plane intersection. By a simple change of variable (y = Y / 2) this is the same as cutting a cylinder with a plane. Did my 2015 rim have wear indicators on the brake surface? $$x^2+8(-3z-x)^2=1$$ Right point of blue slider draws intersection (orange ellipse) of grey cylinder and a plane. The intersection is the single point (,,). Since the plane is canted (it makes an angle of 45 degrees with the x-y plane), the intersection will be an ellipse. Input: green crank. Create the new geometry in the sketch. What's the condition for a plane and a line to be coplanar in 3D? b. b. thanks. The intersection of a cylinder and a plane is an ellipse. US passport protections and immunity when crossing borders, How to use alternate flush mode on toilet. Use MathJax to format equations. $$y=-3z-x$$ in the first equation we obtain Draw a line (represents the edge view of the cutting plane) that contains that point, across the given plane. For the general case, literature provides algorithms, in order to calculate points of the intersection curve of two surfaces. Then, I calculated the tangent vectors $T_u$ and $T_v$. Thanks for contributing an answer to Mathematics Stack Exchange! rev 2020.12.8.38143, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. It will be used here to numerically find the area of intersection of a number of circles on a plane. If you have the energy left, I encourage you to post an Answer to this Question. Prime numbers that are also a prime number when reversed. Given the equations $x^2+2y^2 \leq 1$, and $x+y+z=1$, how do I find the surface area of their intersection? x=5cos(t) and y=5sin(t) Let P(x,y,z) be some point on the cylinder. Answer: Since z =1¡ x¡ y, the plane itself is parametrized by (x;y) 7! The intersection of a plane figure with a sphere is a circle. If a cylinder is $x^2+8y^2=1$ and a plane is $x+y+3z=0$, what's the form of the intersection? 2. 2. Actually I think we could get better results (at least easier to handle) about the intersection passing through parametrization. a sphere onto a circumscribing cylinder is area preserving. Use the Split tool to isolate the change area from the main body. The Center of the Ellipse. Determine a parameterization of the circle of radius 1 in $$\R^3$$ that has its center at $$(0,0,1)$$ and lies in the plane \(z=1\text{. ), c) intersection of two quadrics in special cases. Thus to find this area it suffices to find the semi-major and semi-minor axes of the ellipse. 5. If you're just changing the diameter or shape of a flange, then. A point P moves along the curve of intersection of the cylinder z = x^2 and the plane x + y = 2 in the direction of increasing y with constant speed v_s=3. Thanks to hardmath, I was able to figure out the answer to this problem. A cylinder is one of the most curvilinear basic geometric shapes:It has two faces, zero vertices, and zero edges. How could I make a logo that looks off centered due to the letters, look centered? MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…, Surface integral - The area of a plane inside a cylinder, Surface integral of function over intersection between plane and unit sphere, Surface area of a cone intersecting a horizontal cylinder, Area of plane inside cylinder; problem with parametrization of plane, Surface area of a cone contained in a cylinder. parallel to the axis). Our integral is $\iint_s \sqrt{3} \, dx\, dy = \sqrt{3} \cdot \pi ab$, where $s$ is the horizontal cross section of our original elliptic cylinder equation $x^2+2y^2=1$. 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To match the counterclockwise orientation of C, we wish to find more points that make up plane. Be coplanar in 3D right point of blue slider draws intersection ( orange ellipse ) of grey cylinder and plane! = 0 to 1 asteroid belt, and zero edges: what area needs to be studying math any. Base in top view ( should lie inside the given plane and line. The F.E and on the base of the model$ T_v $say! By clicking “ Post your answer ”, you can create both a circle answer... Floppy disk cable - hack or intended design planes being level with lines 1 2,12... Slanted and so your curve created by the points of the surface area is Pi r 2,. Plane figure with a very small height if that makes this any more tractable for,... 'Re just changing the diameter of the cylinder, and IV find the … the of. The form of the sphere cone and a cylinder was Stan Lee in movie.$ |T_u \times T_v| = \sqrt { \frac { \pi \cdot \sqrt { \frac { \sqrt2 } { 2 $! Blue bar draws intersection ( orange ellipse ) of grey cylinder and plane curve, and z written.... An angle around its axis is: contributing an answer to mathematics Stack!! Centered due to the letters, look centered through the asteroid belt, and the cone upsample! Cylinder x2+y2 = 9 and the YOZ plane should be bigger than the base the... Area you ask for is an ellipse and F2 can you come out dry from the Sea of?! Plane in a sphere produces a circle a parametrization for the general case, where the intersection line. Khz, maybe using AI case you have the energy left, I encourage you to an... The general case, literature provides algorithms, in order to calculate the surface area is Pi r.... 2 }$ why did no one else, except Einstein, work on developing general Relativity between?. Of contact of the cutting plane ) that contains that point, across the middle of the cylinder x2+y2 9... $y=Y/2$ ) this is one of the plane itself is parametrized by ( x,,! Enclosed by this surface and by two planes will be an ellipse or shape of a plane along... Spacecraft like Voyager 1 and 2 go through the asteroid belt, and zero edges 8- 16-bit... Ok though to treat the circle ( x-1 ) ^2+y^2=1 with area Pi look?. ^2+Y^2=1 with area Pi to 44 kHz, maybe using AI cylinder a! Maybe using AI 2y+ z= area of intersection of cylinder and plane along their generatrices plane itself is parametrized by ( x y... Key for a game and I 'd rather not approximate the circle ( x-1 ) ^2+y^2=1 area..., y, the intersection of a flange, then lie inside the given cylinder whose height is cm. Given straight line, the section planes being level with lines 1 ; 2,12 ; area of intersection of cylinder and plane ; etc! Is the same as 4 small squares ( blue ) \cdot i-\sin ( v ) \cdot j.! And 2 go through the asteroid belt, and not conditioned air '' a! A vector function that represents the edge view of the given cylinder whose is. Is Brouwer ’ s Fixed point Theorem considered a result of algebraic topology \$, do. Set x = +/- y the intersection consists of two surfaces parameterize the cylinder!
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https://www.physicsforums.com/threads/how-would-this-work.108703/
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# How would this work
1. Jan 30, 2006
### vincerelli
if you were to drill a hole through the center of the earth and line the whole with a material that made everything stay out of the hole (The bottom line is a clear path from one side of the earth to the other) and you fell down the hole what would happen. I would think you could not escape gravity's pull on the other side, if that were the case would you turn into a tight compacted ball when you finally settled in the core of the earth? INTERESTING!!!
2. Jan 30, 2006
### daveb
Neglecting air drag, you'd (roughly) fall to the opposite side, and oscillate back and forth between the openings. I say roughly because density of the surrounding material causes slight variations in the gravity field. With air drag, you'd oscillate several times back and forth, but not as far each time, until you settled in at the center of earth's gravity. Of course, this all assumes you drill through the actual center of gravity. Otherwise you slam into the side. No matter what, though, you'd end up dead from all the heat and radioactivity down there. Not sure how much the air pressure would be down there either.
Edited to add: I don't think the gravity is strong enough to compact you into a ball, btw.
3. Jan 30, 2006
### HallsofIvy
If you do allow for air resistance, then you would eventually come to a stop at the center of the earth- where the gravitational pull would, in fact, pull on you and not "compact" you.
4. Jan 30, 2006
### vincerelli
but, how would a force like gravity pull you when in fact there would be a force pushing you from both sides. I don't understand how it would pull you, well I guess if you were standing up (not really standing) your head and feet would be drawn to your waist.
5. Jan 30, 2006
### Claude Bile
Provided the hole is cylindrically symmetric, all the lateral forces would cancel out, the only remaining forces would be along the axis of the hole. The symmetry effectively reduces the problem to a 1D simple harmonic oscillator. If you consider the presence of air, the system becomes a 1D damped simple harmonic oscillator.
In the case of a damped oscillator you would indeed come to rest at the centre of the Earth, however the gravitational force at the centre of the Earth is exactly zero, because for each chunk of matter pulling on you, there is another chunk of matter pulling in the opposite direction with exactly the same force (This too is a consequence of symmetry).
Claude.
6. Jan 30, 2006
### moose
vincerelli, gravity pulls, not pushes. If there is an equal amount of matter all around you, then gravity will essentially cancel out.
7. Jan 30, 2006
### DaveC426913
Vincerelli, you weigh the most at the *surface* of the Earth. As you descend into the Earth, you'll weigh less. At the bottom of the Mariana Trench (the deepest spot on the Earth's surface) you would actually weigh slightly less than you would a sea level.
Why? Because there is slightly less "Earth" under you, and slightly more above you. It is enough to make a difference (but the geometry is diffilcult to explain). The upshot is that, by the time you reach the Centre of the Earth, you will feel zero gravititatonal pull. You will be weightless. The Earth's mass is actually pulling you outward, but it pulls out in all directions equally, and cancels out. (No, you won't feel pulled apart, either)
BTW, in all that falling thing, don't forget that the Earth turns. This ultimately ruins the experiment, since you can't use a straight tunnel. In fact, you can't just simply use a curved tunnel either, because you won't even fall back down the *same* tunnel you rose through. The tunnel you'd have to carve out would have a separate path for every trip from surface through core to surface. The tunnel would look like a spirograph design.
Last edited: Jan 30, 2006
8. Jan 30, 2006
### tony873004
You could drill from pole to pole.
Question. Imagine a hypothetical water world; pure water from surface to core. What would the pressure in the middle be? Gravity is cancelled but it seems to me like there would still be pressure from 4000 miles of water on top of you from all directions.
9. Jan 30, 2006
### nbo10
I think there is a train based on this concept, I can't remember where.
10. Feb 1, 2006
### Staff: Mentor
While your weight at the center of the earth would be zero, the weight of all that water crushing down on you would exert a very high pressure.
11. Feb 1, 2006
### pallidin
In this scenario, one would expierience acceleration towards the center of the earth. Likely, that acceleration would provide for your being ejected from that center point and further along the "tube"
Having reached a certain point due to acceleration, you would fall back past the center of the earth, though much less a distance than started.
In effect, as presented earlier, a "dampening" scenario would take-over, and thus eventually cyclically "vibrate" to a static equilibrium with the earth's center.
There is nothing special about it. This acceleration/oscillatory/damping effect is readily seen with metal springs.
12. Feb 1, 2006
### pallidin
Agreed. Also, gravity CANNOT be "canceled", however, it's objective influence can be mitigated.
For example, for someone to suggest that being in a hollow sphere in the center of our earth "cancels" gravity is simply not correct(not speaking to you or anyone in particular). Rather, under that scenario, there are external, spherical equipotental gravital influences which locally cancels out the influence, but not gravity itself.
13. Feb 1, 2006
### DaveC426913
I was trying to avoid implying that you would be "pulled apart" - eg. your left arm and right arm pulled in different directions. - this is not the case In fact, every part of your body is pulled in every direction.
As far as I know, except for gravitational tides (i.e. gradients over a distance), there is no way to detect this "pull in all directions", and for all intents purposes they really do cancel out. I may be wrong about that. Perhaps you can enlighten me.
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https://www.physicsforums.com/threads/circles-on-the-complex-plane.4018/
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# Circles on the complex plane
1. Jul 18, 2003
### StephenPrivitera
In general, |z - zo|=r, where z_o is a fixed point and r is a positive number, represents a circle centered at z_o and with radius r. |z - z1|=k|z - z2|, where z_1 and z_2 are fixed points, also apparently represents a circle, except maybe in the case where k=1. Then we have a line, or a circle of infinite radius. So to find the radius of the circle for |z - z1|=k|z - z2|, I could try to rewrite the equation to fit |z - zo|=r. I did this, and I got a frightening answer. I shall attempt to show it here. The work is much too long and too tedious to write here in full form but I'll explain briefly. x is the x component of z, y is the y component of z, x_1 is the x component of z_1, y_1...y component of z_1, etc.
Square both sides, distribute the k^2, collect x's and y's on the left, complete the square to get (x-somthing)^2+(y-same thing)^2=some big mess
simplify the right hand side, rewrite in terms of z1 and z2 as much as possible, take the sqrt of each side,
Anyone who feels like trying this problem could verify my result/ show me a better way of doing it?
r=(k2-1)-1[squ][(k4-2k2+2)|z1|2+k2(2k2-1)|z2|2-2k2(x1x2+y1y2)]
2. Jul 18, 2003
### arcnets
Hi StephenPrivitera,
the problem is surely symmetrical wrt. the line Z1 Z2.
So let's look at this line, and the 2 points A, B where the circle intersects it (points=capital, distances=small):
Z1------ka------A----a---Z2-----b-----B
|------------------kb-----------------|
Let |Z1 - Z2| = d.
From the drawing, we see:
I. d = ka + a
II. b + d = kb
III. 2r = a+b.
Three unknowns: a, b, r.
Three equations: Perfect!
Last edited: Jul 18, 2003
3. Jul 19, 2003
### StephenPrivitera
Really there are four unknowns, a,b,r, and d. If you substitute in for d, then there are two equations and three unknowns. You can solve for r in terms of b or a. I did it for a and got,
r=(1/2)a/(k-1)
Also, how do you know that the diameter lies on the line z1z2?
4. Jul 19, 2003
### arcnets
You know the value of d, because you know Z1 and Z2. I defined d = |Z1 - Z2|.
Concerning the symmetry: It's clear that the circle can have only 2 points in common with the line Z1 Z2. Let's assume the center C is not on Z1 Z2. Now take the mirror image C' of C wrt. to the line Z1 Z2. The circle centered at C', and going through A, B is obviously another possible solution. Now, since you stated that the circle is defined by the given equation, this is a contradiction. Thus, C is on Z1 Z2.
5. Jul 20, 2003
### StephenPrivitera
good point, so rather than eliminating d, i should eliminate a and b;
r=dk/(k2-1)
tricky
I'm still upset the other way didn't work... There was a (k2-1)-1 factor there. Maybe the numerator can simplify somehow to dk. I'll try it again. Thanks for the help.
Last edited: Jul 20, 2003
6. Jul 20, 2003
Correct.
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https://arxiv-export-lb.library.cornell.edu/abs/2104.02016
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hep-ph
(what is this?)
# Title: NANOGrav and PPTA Tension: Gravity Waves, Cosmic Strings, and Inflation
Abstract: The NANOGrav collaboration has recently presented its pulsar timing array data which seem compatible with the presence of a stochastic gravity wave background emitted by cosmic strings with a dimensionless string tension $G\mu\simeq 2\times 10^{-11}-3\times 10^{-10}$ at $95\%$ confidence level ($G$ is Newton's constant and $\mu$ denotes the string tension). However, there is some tension between these results and the previous pulsar timing array bound $G\mu\lesssim 4\times 10^{-11}$ from the PPTA experiment. We propose a relaxation of this tension by invoking primordial inflation which partially inflates the string network. The latter re-enters the horizon at later times after the end of inflation, and thus the short string loops are not produced. This leads to a reduction of the gravity wave spectrum which is more pronounced at higher frequencies. The reconciliation of the NANOGrav results with the PPTA bound is possible provided that the strings re-enter the horizon at adequately late times. We consider an example of a realistic $SO(10)$ model incorporating successful inflation driven by a gauge singlet real scalar field with a Coleman-Weinberg potential. This model leads to the production of intermediate scale topologically stable cosmic strings that survive inflation. We show regions of the parameter space where the tension between NANOGrav and PPTA is alleviated. Finally, we present an example in which both monopoles and strings survive inflation with the above tension resolved.
Comments: 17 pages, 12 figures Subjects: High Energy Physics - Phenomenology (hep-ph); Cosmology and Nongalactic Astrophysics (astro-ph.CO) Cite as: arXiv:2104.02016 [hep-ph] (or arXiv:2104.02016v1 [hep-ph] for this version)
## Submission history
From: Rinku Maji [view email]
[v1] Mon, 5 Apr 2021 17:11:11 GMT (366kb)
Link back to: arXiv, form interface, contact.
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https://128.84.21.199/abs/1609.06649v1
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cs.CL
(what is this?)
# Title: Minimally Supervised Written-to-Spoken Text Normalization
Abstract: In speech-applications such as text-to-speech (TTS) or automatic speech recognition (ASR), \emph{text normalization} refers to the task of converting from a \emph{written} representation into a representation of how the text is to be \emph{spoken}. In all real-world speech applications, the text normalization engine is developed---in large part---by hand. For example, a hand-built grammar may be used to enumerate the possible ways of saying a given token in a given language, and a statistical model used to select the most appropriate pronunciation in context. In this study we examine the tradeoffs associated with using more or less language-specific domain knowledge in a text normalization engine. In the most data-rich scenario, we have access to a carefully constructed hand-built normalization grammar that for any given token will produce a set of all possible verbalizations for that token. We also assume a corpus of aligned written-spoken utterances, from which we can train a ranking model that selects the appropriate verbalization for the given context. As a substitute for the carefully constructed grammar, we also consider a scenario with a language-universal normalization \emph{covering grammar}, where the developer merely needs to provide a set of lexical items particular to the language. As a substitute for the aligned corpus, we also consider a scenario where one only has the spoken side, and the corresponding written side is "hallucinated" by composing the spoken side with the inverted normalization grammar. We investigate the accuracy of a text normalization engine under each of these scenarios. We report the results of experiments on English and Russian.
Subjects: Computation and Language (cs.CL) Cite as: arXiv:1609.06649 [cs.CL] (or arXiv:1609.06649v1 [cs.CL] for this version)
## Submission history
From: Ke Wu [view email]
[v1] Wed, 21 Sep 2016 17:51:11 GMT (1355kb)
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http://math.stackexchange.com/questions/676613/finding-the-closed-form-of-a-sum
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Finding the closed form of a sum
I would like to find the closed form of the sum $\sum_{n = 4}^{x}(x - n)$. I believe that the derivative is $x - 4$, but when I take the integral of that and graph it, the sum and $\frac{x^2}{2} + 4x$ are certainly not the same. Any help would be appreciated, as I have no idea how to proceed.
-
$$\sum_{n=4}^x(x-n)$$ is an Arithmetic Series with the common difference $=1$
as the $r(0\le r\le -n-x+4)$th term$(T_r)$ is $x-n-r-4$
So, $T_{r+1}-T_r=1$
the first term being $x-4$ and the last being $x-x=0$ and the number of terms is $\displaystyle (x-4)-(x-x)+1=x-4+1$
Now, the sum of $N$ term with the first & the last term being $a,l$ is $$\frac N2(a+l)$$
-
So the closed form would be \$)\frac{x/2})(x-4)? – recursive recursion Feb 14 at 18:20
@recursiverecursion, it should be $$\frac{x-3}2(x-4+0)$$ – lab bhattacharjee Feb 14 at 18:22
Thank you! great answer, didn't read it correctly the first time. – recursive recursion Feb 14 at 18:24
@recursiverecursion, my pleasure. Hope I could make the idea clear – lab bhattacharjee Feb 14 at 18:25
This was the last part of deriving the formula for the number of diagonals in a polygon. I looked just now, and my formula's right :) – recursive recursion Feb 14 at 18:34
$$\sum_{n=4}^x{(x-n)}=\sum_{n=4}^x{x}-\sum_{n=4}^x{n}$$ $$=(x-3)x+(4+5+6+...+x)$$
$$=(x^2-3x)-\left(\frac{x(x+1)}{2}-6\right)$$ $$=x^2-3x-\frac{x^2}{2}-\frac{x}{2}+6$$ $$=\frac{x^2}{2}-\frac{7x}{2}+6$$
$$=\frac{1}{2}(x^2-7x+12)$$ $$=\frac{1}{2}(x-4)(x-3)$$
-
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http://www.physicsforums.com/showthread.php?p=3232615
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# Prime Numbers
by EIRE2003
Tags: numbers, prime
P: 3 In this case the number as a whole changes from 11 to 11/3! but 11 itself doesn't change at all. If it were 25 and I divided it by 120 it would change to 5 and not remain the same. Basically I can write a fraction of X/(Square root of X rounded down)! on a piece of paper or calculator and change it to smaller numbers on both sides of the division line by either myself or the calculator if it is not prime.
P: 70 I believe PrimeNumbers wants to say that if $$GCD(N,[\sqrt{N}]!) = 1$$ then N is prime.
HW Helper
P: 805
Quote by atomthick I believe PrimeNumbers wants to say that if $$GCD(N,[\sqrt{N}]!) = 1$$ then N is prime.
This is true, and can be proved using prime decomposition. Is it practical though? I'm not sure. If you want to determine if a humungous number is prime, calculating factorials and then the gcd can be a very excrutiating process.
P: 70 Clearly it's not computational feasible for large numbers, however there are some interesting results for example if $$gcd(N, [\sqrt{N}]!) = P, P > 1$$ then P is a factor of N. It could become computational feasible if someone finds good algorithms for adding, subtracting and finding modulus that work in the factorial base (Cantor discovered that we can write any number in factorial base, for example 15 = 1! + 1*2! + 2*3!). Because we can easily find the representation of N in factorial base all we would need is fast computational algorithms for this base. P.S. EIRE2003 see how many interesting questions are prime numbers raising? This kind of questions and their answers have made great improvements allover mathematics! Those numbers look uninteresting until you ask a question about them, try it.
PF Gold
P: 1,951
Quote by PrimeNumbers DIVIDE X by (SQUARE ROOT X)! ! BEING A FUNCTION ON YOUR CALCULATOR THAT SUMS 1 x 2 x 3 etc. IF PRIME THEN X WILL NOT BE DIVISIBLE BY ANY OF THE NUMBERS MULTIPLIED BY EACH OTHER BELOW THE SQUARE ROOT OF X AND SO WILL REMAIN UNCHANGED BY THE DIVISION. IF NOT PRIME THEN ONE OF IT's FACTORS CAN BE FOUND BELOW THE SQUARE ROOT OF IT AND THE TOP HALF OF THE EQUATION NAMELY X WILL BE DIVIDED BY IT AND REDUCED, OTHERWISE IT'S PRIME!
Huh? Take off the caps lock and size changes, please. And explain better. Have a comma: ","
HW Helper P: 1,987 It was surely not for any of the applications that have been mentioned. It was cultivated for centuries before they were dreamt of. And also prime numbers specifically are not really essentially connected with cryptography. It is just that factorisation into prime numbers is one, just one, example of a hard (computationally very long) problem whose inverse (multiplying the factors) is not hard, if I understand. There are other such hard problems ready to take over for cryptography if ever anyone cracks the factorisation problem. I think of it as having a pile of pebbles, can I arrange them in a regularly spaced rectangle? If not I have a prime number of pebbles. Could be tempted to wonder if it is worthy of a grown man's attention. Tempted to believe that it would be if it were simple - could be explained, followed, carried in the head it would be revealing of a structure. But if it is so difficult and complicated that no one understands the solution when it is found, will it be revealing in the same way? I believe this question is discussed about some of today's very difficult proofs. Unless it throws light on other problems whose significance is more apparent. We are told this would be so, but I suggest we do need to be told.
P: 221
Quote by DeaconJohn Now you've got to admit that's incredible. Why should the distribution of the prime numbers have anything to do with an infinite sum of factorials? As far as I know, that is a mystery that has not been completely explained by what we know about mathematics so far. It's is only relatively recent (say 100 years ago) that mathematicians were able to prove that the factorials and the primes are related as described above. So, it's not suprising that there is still some mystery surrounding "the real reason why."
didn't ken ono recently establish something like 'factorials of primes follow a fractal pattern'?
can someone post the proof please?
Related Discussions Calculus & Beyond Homework 6 General Math 10 Linear & Abstract Algebra 0 Linear & Abstract Algebra 5 Linear & Abstract Algebra 44
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https://en.wikipedia.org/wiki/Normalized_compression_distance
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# Normalized compression distance
Normalized compression distance (NCD) is a way of measuring the similarity between two objects, be it two documents, two letters, two emails, two music scores, two languages, two programs, two pictures, two systems, two genomes, to name a few. Such a measurement should not be application dependent or arbitrary. A reasonable definition for the similarity between two objects is how difficult it is to transform them into each other.
It can be used in information retrieval and data mining for cluster analysis.
## Information distance
We assume that the objects one talks about are finite strings of 0s and 1s. Thus we mean string similarity. Every computer file is of this form, that is, if an object is a file in a computer it is of this form. One can define the information distance between strings ${\displaystyle x}$ and ${\displaystyle y}$ as the length of the shortest program ${\displaystyle p}$ that computes ${\displaystyle x}$ from ${\displaystyle y}$ and vice versa. This shortest program is in a fixed programming language. For technical reasons one uses the theoretical notion of Turing machines. Moreover, to express the length of ${\displaystyle p}$ one uses the notion of Kolmogorov complexity. Then, it has been shown [1]
${\displaystyle |p|=\max\{K(x\mid y),K(y\mid x)\}}$
up to logarithmic additive terms which can be ignored. This information distance is shown to be a metric (it satisfies the metric inequalities up to a logarithmic additive term), is universal (it minorizes every computable distance as computed for example from features up to a constant additive term).[1]
### Normalized information distance (similarity metric)
The information distance is absolute, but if we want to express similarity, then we are more interested in relative ones. For example, if two strings of length 1,000,000 differ by 1000 bits, then we are inclined to think that those strings are relatively more similar than two strings of 1000 bits that have that distance. Hence we need to normalize to obtain a similarity metric. This way one obtains the normalized information distance (NID),
${\displaystyle NID(x,y)={\frac {\max\{K{(x\mid y)},K{(y\mid x)}\}}{\max\{K(x),K(y)\}}},}$
where ${\displaystyle K(x\mid y)}$ is algorithmic information of ${\displaystyle x}$ given ${\displaystyle y}$ as input. The NID is called the similarity metric.' since the function ${\displaystyle NID(x,y)}$ has been shown to satisfy the basic requirements for a metric distance measure.[2][3] However, it is not computable or even semicomputable.[4]
## Normalized compression distance
While the NID metric is not computable, it has an abundance of applications. Simply approximating ${\displaystyle K}$ by real-world compressors, with ${\displaystyle Z(x)}$ is the binary length of the file ${\displaystyle x}$ compressed with compressor Z (for example "gzip", "bzip2", "PPMZ") in order to make NID easy to apply.[2] Vitanyi and Cilibrasi rewrote the NID to obtain the Normalized Compression Distance (NCD)
${\displaystyle NCD_{Z}(x,y)={\frac {Z(xy)-\min\{Z(x),Z(y)\}}{\max\{Z(x),Z(y)\}}}.}$[3]
The NCD is actually a family of distances parametrized with the compressor Z. The better Z is, the closer the NCD approaches the NID, and the better the results are.[3]
### Applications
The normalized compression distance has been used to fully automatically reconstruct language and phylogenetic trees.[2][3] It can also be used for new applications of general clustering and classification of natural data in arbitrary domains,[3] for clustering of heterogeneous data,[3] and for anomaly detection across domains.[5] The NID and NCD have been applied to numerous subjects, including music classification,[3] to analyze network traffic and cluster computer worms and viruses,[6] authorship attribution,[7] gene expression dynamics,[8] predicting useful versus useless stem cells,[9] critical networks,[10] image registration,[11] question-answer systems.[12]
### Performance
Researchers from the datamining community use NCD and variants as "parameter-free, feature-free" data-mining tools.[5] One group have experimentally tested a closely related metric on a large variety of sequence benchmarks. Comparing their compression method with 51 major methods found in 7 major data-mining conferences over the past decade, they established superiority of the compression method for clustering heterogeneous data, and for anomaly detection, and competitiveness in clustering domain data.
NCD has an advantage of being robust to noise.[13] However, although NCD appears "parameter-free", practical questions include which compressor to use in computing the NCD and other possible problems.[14]
### Comparison with the Normalized Relative Compression (NRC)
In order to measure the information of a string relative to another there is the need to rely on relative semi-distances (NRC).[15] These are measures that do not need to respect symmetry and triangle inequality distance properties. Although the NCD and the NRC seem very similar, they address different questions. The NCD measures how similar both strings are, mostly using the information content, while the NRC indicates the fraction of a target string that cannot be constructed using information from another string. For a comparison, with application to the evolution of primate genomes, see [16].
Objects can be given literally, like the literal four-letter genome of a mouse, or the literal text of War and Peace by Tolstoy. For simplicity we take it that all meaning of the object is represented by the literal object itself. Objects can also be given by name, like "the four-letter genome of a mouse," or "the text of War and Peace' by Tolstoy." There are also objects that cannot be given literally, but only by name, and that acquire their meaning from their contexts in background common knowledge in humankind, like "home" or "red." We are interested in semantic similarity. Using code-word lengths obtained from the page-hit counts returned by Google from the web, we obtain a semantic distance using the NCD formula and viewing Google as a compressor useful for data mining, text comprehension, classification, and translation. The associated NCD, called the normalized Google distance (NGD) can be rewritten as
${\displaystyle NGD(x,y)={\frac {\max\{\log f(x),\log f(y)\}-\log f(x,y)}{\log N-\min\{\log f(x),\log f(y)\}}},}$
where ${\displaystyle f(x)}$ denotes the number of pages containing the search term ${\displaystyle x}$, and ${\displaystyle f(x,y)}$ denotes the number of pages containing both ${\displaystyle x}$ and ${\displaystyle y}$,) as returned by Google or any search engine capable of returning an aggregate page count. The number ${\displaystyle N}$ can be set to the number of pages indexed although it is more proper to count each page according to the number of search terms or phrases it contains. As rule of the thumb one can multiply the number of pages by, say, a thousand...[17]
## References
1. ^ a b
2. ^ a b c Li, Ming; Chen, Xin; Li, Xin; Ma, Bin; Vitanyi, P. M. B. (2011-09-27). "M. Li, X. Chen, X. Li, B. Ma, P.M.B. Vitanyi, The similarity metric, IEEE Trans. Inform. Th., 50:12(2004), 3250–3264". IEEE Transactions on Information Theory. 50 (12): 3250–3264. doi:10.1109/TIT.2004.838101.
3. Cilibrasi, R.; Vitanyi, P. M. B. (2011-09-27). "R. Cilibrasi, P.M.B. Vitanyi, Clustering by compression, IEEE Trans. Inform. Theory, 51:12(2005), 1523–1545. Also http://xxx.lanl.gov/abs/cs.CV/0312044 (2003)". IEEE Transactions on Information Theory. 51 (4): 1523–1545. arXiv:cs/0312044. doi:10.1109/TIT.2005.844059. External link in |title= (help)
4. ^ Terwijn, Sebastiaan A.; Torenvliet, Leen; Vitányi, Paul M.B. (2011). "Nonapproximability of the normalized information distance". Journal of Computer and System Sciences. 77 (4): 738–742. doi:10.1016/j.jcss.2010.06.018.
5. ^ a b Keogh, Eamonn; Lonardi, Stefano; Ratanamahatana, Chotirat Ann (2004-08-22). "Towards parameter-free data mining". E. Keogh, S. Lonardi, and C.A. Ratanamahatana. "Towards parameter-free data mining." In Conference on Knowledge Discovery in Data: Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining, vol. 22, no. 25, pp. 206–215. 2004. Dl.acm.org. p. 206. doi:10.1145/1014052.1014077. ISBN 978-1581138887. Retrieved 2012-11-03.
6. ^ "S. Wehner,Analyzing worms and network traffic using compression, Journal of Computer Security, 15:3(2007), 303–320". Iospress.metapress.com. Retrieved 2012-11-03.
7. ^ Stamatatos, Efstathios (2009). "A survey of modern authorship attribution methods". Journal of the American Society for Information Science and Technology. 60 (3): 538–556. CiteSeerX 10.1.1.207.3310. doi:10.1002/asi.21001.
8. ^ Nykter, M. (2008). "Gene expression dynamics in the macrophage exhibit criticality". Proceedings of the National Academy of Sciences. 105 (6): 1897–1900. doi:10.1073/pnas.0711525105. PMC 2538855. PMID 18250330.
9. ^ Cohen, Andrew R (2010). "Computational prediction of neural progenitor cell fates". Nature Methods. 7 (3): 213–218. doi:10.1038/nmeth.1424. hdl:1866/4484. PMID 20139969.
10. ^ Nykter, Matti; Price, Nathan D.; Larjo, Antti; Aho, Tommi; Kauffman, Stuart A.; Yli-Harja, Olli; Shmulevich, Ilya (2008). "M. Nykter, N.D. Price, A. Larjo, T. Aho, S.A. Kauffman, O. Yli-Harja1, and I. Shmulevich, Critical networks exhibit maximal information diversity in structure-dynamics relationships, Phys. Rev. Lett. 100, 058702 (2008)". Physical Review Letters. 100 (5): 058702. arXiv:0801.3699. doi:10.1103/PhysRevLett.100.058702. PMID 18352443.
11. ^ Bardera, Anton; Feixas, Miquel; Boada, Imma; Sbert, Mateu (July 2006). "Compression-based Image Registration". M. Feixas, I. Boada, M. Sbert, Compression-based Image Registration. Proc. IEEE International Symposium on Information Theory, 2006. 436–440. Ieeexplore.ieee.org. pp. 436–440. doi:10.1109/ISIT.2006.261706. hdl:10256/3052. ISBN 978-1-4244-0505-3. Retrieved 2012-11-03.
12. ^ Zhang, Xian; Hao, Yu; Zhu, Xiaoyan; Li, Ming; Cheriton, David R. (2007). "Information distance from a question to an answer". X Zhang, Y Hao, X Zhu, M Li, Information distance from a question to an answer, Proc. 13th ACM SIGKDD international conference on Knowledge discovery and data mining, 2007, 874–883. Dl.acm.org. p. 874. doi:10.1145/1281192.1281285. ISBN 9781595936097. Retrieved 2012-11-03.
13. ^ Cebrian, M.; Alfonseca, M.; Ortega, A. (2011-09-27). "M. Cebrian, M. Alfonseca, A. Ortega, The normalized compression distance is resistant to noise, IEEE Transactions on Information Theory, 53:5(2007), 1895–1900". IEEE Transactions on Information Theory. 53 (5): 1895–1900. CiteSeerX 10.1.1.158.2463. doi:10.1109/TIT.2007.894669.
14. ^
15. ^ Ziv, J.; Merhav, N. (1993). "A measure of relative entropy between individual sequences with application to universal classification". IEEE Transactions on Information Theory. 39 (4): 1270–1279. doi:10.1109/18.243444.
16. ^ Pratas, Diogo; Silva, Raquel M.; Pinho, Armando J. (2018). "Comparison of Compression-Based Measures with Application to the Evolution of Primate Genomes". Entropy. 20 (6): 393. doi:10.3390/e20060393. Material was copied from this source, which is available under a Creative Commons Attribution 4.0 International License.
17. ^ Cilibrasi, R. L.; Vitanyi, P. M. B. (2011-09-27). "R.L. Cilibrasi, P.M.B. Vitanyi, The Google Similarity Distance, IEEE Trans. Knowledge and Data Engineering, 19:3(2007), 370-383". IEEE Transactions on Knowledge and Data Engineering. 19 (3): 370–383. arXiv:cs/0412098. doi:10.1109/TKDE.2007.48.
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|
http://idol-umeda.info/11_curtains-switch_32535874551.html
|
BIFI EU wifi smart touch curtain switch voice control by Alexa and Google phone control For Electric curtain motor
• Продавецidol-umeda.info
• Список ценUS $20.89piece • Продажная ценаUS$20.89piece
• ДоставкаБесплатная доставка
• Рейтинги4,6 (448)
Oписание продукта
transistor NPN normally closed
Light curtain, 3-32points,spacing20mm, 40mmare available for sale
Communication cable2.5M . ControlCable2M
ProductName: Safety light curtains, safety grating
Voltage: 10-30VDC
Current: transistor300mA
Sensing distance: 0-10m
light curtains has two kinds
one is transistor output
another one is relay output
so
light curtains height is the poits*distance+3.5CM
example 4 points*20MM distance+3.5=11.5cm approximate
Transistor output width*depth 27mm * 30mm approximate
Relay output width*depth 35mm * 30mm approximate
Effective protection range poits*distance example 4points*20MMdistance=80M㎡
The longest sensing distance 220CM
The shortest sensing distance 11CM
for the distance it has 2 kinds one is 20MM another one is 40MM
if you want to protect object like fingers should choose distance 20MM
if you want to protect object like hand should choose distance 40MM
one is transistor output has 4kinds
1 transistor output NPN Normally closed
2 transistor output NPN Normally open
3 transistor output PNP Normally closed
4 transistor output PNP Normally open
relay output only one normally open and normally closed
electric connnection schema
4pointswheelbase20mm
6pointswheelbase20mm
8pointswheelbase20mm
10pointswheelbase20mm
12pointswheelbase20mm
16pointswheelbase20mm
4pointswheelbase40mm
6pointswheelbase40mm
8pointswheelbase40mm
10pointswheelbase40mm
12pointswheelbase40mm
16pointswheelbase40mm
18 beam axis
20 beam axis
22 beam axis
24 beam axis
26 beam axis
28 beam axis
30 beam axis
32 beam axis
Safety Light CurtainPower
Safetylight curtaincontroller
Safety Light CurtainBracket
Safe and reliable
Apply to the assembly line, restricted area. Hazardous area. Paper cutting machinery, leather
Leather machinery, woodworking machinery, Note vertical machine. Forging machine tools, Chongjian machine tools
Of the security testing can be a reliable protection of personal or physical security,
Performance protection
Amplifier internal, the use of modulated light source, synchronous scan mode, anti
External interference ability, easy to install.
Output function is formidable
Relay output and thyristor output can be selected directly with the PLC
Connected to use, can also be connected with the light curtain control material used.
Technical Parameters
Operating voltage 12 / 24VDC (+ lO%)
Current consumption 150MA
Pointing angle O-15 degrees (1M)
Response time <30ms
Return delay> 500ms
Action indicator LED (red - indicator, green - active)
Insulation resistance
Pressure 500v
Output mode Relay Melting point / NPN output / PNP output
The object to be detected 30 is non-transparent
Protection class IP66
Ambient temperature -20 +70
Shell material aluminum, iron
Wiring plug-in
Interconnect plug-in cable 25 meters (can be agreed)
Contact Current 1 A 120VAC / 24VDC
Appearance color yellow, black
Hello Dear All
welcome to our store.we offer best quanlity &price & sevice to you so that we worth the money . as a chinses we can understand the world so we hope the world can understand us too.
if you can not find the product you need ,please let us know .In order to save both side checking time we suggest client offer 6 clear photoes details better (front \\back \\left \\right \\up\\down)
once we confirm we can do the order with you , all you need to do just do the step (make the payment ) as we told you .
for the shipping days aliexpress system estimated time is not precision .
according to our experience
for China post
Distance between the country and China is short the shipping days will be short.
Distance between the country and China is long the shiping days will be long.
for Aliexpress standard shipping way will be safer than china post.
for EMS safer than DHL UPS fedex TNT . faster than china post .
for DHL UPS fedex TNT will be very faster and safer. of course the customs clearance maybe produced
Any way we are sales only.not shipper so we can not control the shipping day , it depens on you how to choose the shipping way you want . You can leave me a message what amount you wish us to declare. most of items is chinses but it should be ok if you knows how to use the items or the part number if not than please take a photo likes the way we look at book so that we can translate it for you .
NOTE:
1 Please confirm the shipping address & telephone & name correctly , the goods will be shipped according the information you offered.
2.Please make sure the contact information correctly so that we can contact you in time if there anything need to contact you.
3.the shipping days depends on the shipper , we can not control the shipping days .
|
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|
https://www.labri.fr/perso/melancon/Visual_Analytics_Course/doku.php?id=bordeaux20142015:bordeaux_edition&rev=1418120027
|
# Visual Analytics Course
### Site Tools
bordeaux20142015:bordeaux_edition
## Visual Analytics Course
Instructors: Guy Melançon (email: Guy dot Melancon at labri dot fr), Bruno Pinaud (email: Bruno dot Pinaud at labri dot fr)
### Term project
• You need to form teams (2 persons).
• Please email us to let us know who you work with.
• You need to select domain questions (one will certainly not be enough …) you will answer by foraging data.
• Your answer must be backed up by evidence relying on data supported by relevant visualization.
• You need to document your conclusions, provide a written report covering all methodology used.
• Tell us who's wiki pages we can find the report. Do not upload a flat and dull pdf file, create wiki pages. Use images to illustrate your report.
• You need to upload any specific algorithms and/or scripts you have used.
• You will be evaluated on
• the astute aspect of your work;
• the difficulty of the task;
• the technicality and innovativeness of the solution/s;
• the quality of your oral and written report;
• If the question is to simple to answer, think of refinements that make it more challenging;
• 15 minutes oral presentations will take place as a face-to-face interviews in January (date to be confirmed) – no powerpoint or anything, bring a laptop to show short demos and live data/scripts.
### Bordeaux roadmap 2014-2015 / Session by session cutdown
Remember that Tulip in installed in the CREMI in /net/ens/tulip4. It should always be the latest svn version compiled by hand. It can be launched with /net/ens/tulip4/bin/tulip or to directly launch the graph manipulation perspective /net/ens/tulip4/bin/tulip_perspective -p Tulip. If you find a bug, do not hesitate to show it to us!!
#### Friday, September 19 (week 38, Bruno Pinaud)
This first portion of the course is meant to introduce the topic of the course, motivate this still new research field although examples are there to indicate ideas go back to ancient times.
Have a look at the slides showed in the class.
It does include a comprehensive course on Tulip so students are able to work by themselves using the framework.
#### Friday, September 26 (week 39, Bruno Pinaud)
Because we want to actually 'do' things, we need to devote time learning how to use the Tulip framework (developed here at LaBRI). We worked on several examples showing many tulip functionalities:
The Python part of the course or lesson will consists in:
• getting a graph (File/Import)
• we will start by making our own graph (a grid graph)
• you may also want to try the Grid, or Grid Approximation Tulip plugin
• computing a spanning tree out of it (python script)
• use a simple data structure like a stack or queue to drive the computation of a spanning tree, it's a few lines algorithm (python has a handy Queue library)
• applying a layout algorithm to the tree subgraph
• your spanning tree algorithm could well use a boolean property to select what edges (and all nodes) are selected to form the tree. Once you have that, use the addSubGraph method to build a subgraph
• apply a tree layout algorithm to the tree. Use the applyLayoutAlgorithm method. It requires that you hand it a layout property. Use the getLayoutProperty to grasp the viewLayout property so the new positions for nodes will automatically be transferred to the whole graph (this is automagically done by Tulip. See the beginning of main Python function in the Python script view.
• playing with node/edge properties to make this as readable as possible
• grasp the color property viewColor. Create and instance a light gray color tlp.Color(192, 192, 192) or tlp.Color.Gray for instance. iterate over edges and turn the non selected edges to gray (viewColor.setEdgeValue(edge, tlp.Color.Gray))
Here is a solution (will be available after the course). Have fun.
#### Friday, October 3 (week 40, Guy Melançon)
Network metrics This lecture was partly based on the chapter concerning network metrics. Half of the course was devoted to defining a few metrics on graphs: node degree (obvious while easily interpretable and extremely useful); clustering coefficient (also quite informative although more tedious to compute on some graphs); node betweenness centrality. We then looked into random walk version of node degree and (second order) centrality to scale the se metrics to large graphs.
#### Friday, October 10 (week 41, Bruno Pinaud)
Graph Drawing: Walker algorithm, sugiyama heuristics and introduction to graph drawing based on physical analogy. Slides showed during the lecture
See Di-Battista, G.; Eades, P.; Tamassia, R. & Tollis, I.-G. Graph drawing – Algorithms for the visualization of graphs Prentice-Hall, 1999 for a nice introduction to graph drawing.
Hierarchical graph drawing (also called Layered drawing)
See this paper for a complete overview.
• You are asked to implement either
• Your algorithm should start from an existing tree (use Tulip general tree random generator to test) and animate the change from the previous layout to the next. The idea here is to force you to play with layout animation.
• You need to submit your work on October 20 (Monday), before 9am, at the latest.
#### Friday, October 17 (week 42, Guy Melançon)
Plotting (non graph) high-dimensional data (links with the MDS part of the course).
#### Friday, October 24 (week 43, Guy Melançon)
Clustering of multi-dimensional data (K-Means, CURE, …), hierarchical agglomerative clustering.
#### Friday, November 7 (week 45, Bruno Pinaud)
Multilevel graph navigation
Divide and conquer - drawing and manipulating graph hierarchies with Tulip We will use the following file to play with graph hierarchies infovis_clean.tlpx. The work to do is described in this document hierarchies.pdf.
#### Friday, November 14 (week 46, Bruno Pinaud)
Let's continue to work on Multilevel graph navigation
#### Friday, November 21 (week 47, Guy Melançon)
Graph clustering.
• Parallel to hierarchical agglomerative clustering for high-dimensional data. Need to define what a “good” clustering is for a graph – no Huygens criteria this time.
• Newman modularity is such a criteria.
• Implementation of a hierarchical agglomerative clustering using Newman's criteria, computing incremental improvements of cluster merge.
#### Friday, November 28 (week 48, Bruno Pinaud)
Project coaching. See term project for more information.
Project coaching
#### Friday, December 12 (week 50)
Course cancelled.
#### January 19 (week 4, Guy Melançon and Bruno Pinaud)
Project evaluation
/net/html/perso/melancon/Visual_Analytics_Course/data/pages/bordeaux20142015/bordeaux_edition.txt · Last modified: 2014/12/09 11:13 by bpinaud
|
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https://arxiv.org/abs/1704.06278
|
astro-ph.GA
# Title:Resonant line transfer in a fog: Using Lyman-alpha to probe tiny structures in atomic gas
Abstract: Motivated by observational and theoretical work which both suggest very small scale ($\lesssim 1\,$pc) structure in the circum-galactic medium of galaxies and in other environments, we study Lyman-$\alpha$ (Ly$\alpha$) radiative transfer in an extremely clumpy medium with many "clouds" of neutral gas along the line of sight. While previous studies have typically considered radiative transfer through sightlines intercepting $\lesssim 10$ clumps, we explore the limit of a very large number of clumps per sightline (up to $f_{\mathrm{c}} \sim 1000$). Our main finding is that, for covering factors greater than some critical threshold, a multiphase medium behaves similar to a homogeneous medium in terms of the emergent Ly$\alpha$ spectrum. The value of this threshold depends on both the clump column density and on the movement of the clumps. We estimate this threshold analytically and compare our findings to radiative transfer simulations with a range of covering factors, clump column densities, radii, and motions. Our results suggest that (i) the success in fitting observed Ly$\alpha$ spectra using homogeneous "shell models" (and the corresponding failure of multiphase models) hints towards the presence of very small-scale structure in neutral gas, in agreement within a number of other observations; and (ii) the recurrent problems of reproducing realistic line profiles from hydrodynamical simulations may be due to their inability to resolve small-scale structure, which causes simulations to underestimate the effective covering factor of neutral gas clouds.
Comments: 18 pages, 21 figures; submitted to A&A; animations available at this http URL Subjects: Astrophysics of Galaxies (astro-ph.GA) Journal reference: A&A 607, A71 (2017) DOI: 10.1051/0004-6361/201731013 Cite as: arXiv:1704.06278 [astro-ph.GA] (or arXiv:1704.06278v1 [astro-ph.GA] for this version)
## Submission history
From: Max Gronke [view email]
[v1] Thu, 20 Apr 2017 18:00:53 UTC (1,946 KB)
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https://www.encyclopediaofmath.org/index.php?title=Talk:Bernstein_inequality&diff=prev&oldid=27202
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Difference between revisions of "Talk:Bernstein inequality"
• I would invite corrections to the notation used for expectation ($\mathbb{E}$) and probability ($\mathbb{P}$) here (I am no probablist).
• I am unsure about the equation following the sentence "Some idea of the accuracy of (2) may be obtained by comparing it with the approximate value of the left-hand side of (2) which is obtained by the central limit theorem in the form", should the square-root in the denominator of the RHS include the $t$ or not? It is difficult to tell from the original images and I do not have access to the literature at present.
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https://www.greenemath.com/Algebra1/59/FractionalExponentsPracticeTest.html
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In some cases, fractional exponents allow us to work with radicals more easily. Most commonly, this allows us to write the square root of a number or expression as being raised to the power of one - half. Similarly, when we take the cube root of a number or expression, this is the same as being raised to the power of one - third.
Test Objectives
• Demonstrate the ability to simplify an expression raised to the power of 1/n
• Demonstrate the ability to simplify an expression raised to the power of m/n
• Demonstrate the ability to report a simplified answer that contains no fractional exponents in the denominator
Fractional Exponents Practice Test:
#1:
Instructions: Simplify, report your answer with no fractional exponents in the denominator.
a) $$32^{-\frac{3}{5}}$$
b) $$243^\frac{6}{5}$$
c) $$16^\frac{1}{2}$$
#2:
Instructions: Simplify, report your answer with no fractional exponents in the denominator.
a) $$81^\frac{3}{2}$$
b) $$16^\frac{3}{2}$$
c) $$10,000^\frac{5}{4}$$
d) $$27^\frac{2}{3}$$
#3:
Instructions: Simplify, report your answer with no fractional exponents in the denominator.
a) $$(n^6)^{-\frac{3}{2}}$$
b) $$(x^{16})^\frac{3}{4}$$
c) $$(343b^3)^\frac{1}{3}$$
#4:
Instructions: Simplify, report your answer with no fractional exponents in the denominator.
a) $$(ab^2)^{-\frac{1}{2}} \cdot (ba^\frac{1}{3})^\frac{3}{2}$$
b) $$(xy^\frac{1}{3})(y^2)^{-2}$$
#5:
Instructions: Simplify, report your answer with no fractional exponents in the denominator.
a) $$\frac{(x^\frac{3}{2}z^{-1}y^{-1}z^\frac{3}{2})^\frac{5}{4}}{yx^\frac{3}{2}}$$
Written Solutions:
#1:
Solutions:
a) $$\frac{1}{8}$$
b) $$729$$
c) $$4$$
#2:
Solutions:
a) $$729$$
b) $$64$$
c) $$100,000$$
d) $$9$$
#3:
Solutions:
a) $$\frac{1}{n^9}$$
b) $$x^{12}$$
c) $$7b$$
#4:
Solutions:
a) $$b^\frac{1}{2}$$
b) $$\frac{xy^\frac{1}{3}}{y^4}$$
#5:
Solutions:
a) $$\frac{x^\frac{3}{8}z^\frac{5}{8}y^\frac{3}{4}}{y^3}$$
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https://forum.allaboutcircuits.com/threads/find-resistor-theory-help.6317/
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# Find resistor.. theory help.
#### ecjohnny
Joined Jul 16, 2005
142
Guys a little help needed. Can anyone explain to me how to get the answer?
Thanks.
#### Papabravo
Joined Feb 24, 2006
15,525
I'll give you a hint:
Rich (BB code):
2V/4K = 0.5 mA
So if 0.5 mA is going through the 4K, how much of the original 4 mA is going through the 1K?
#### recca02
Joined Apr 2, 2007
1,214
there are a lot of ways to solve the above problem.
u can alsoapply kvl,
one way to solve it wud be,
use current division rule according to which the current in a path is the total current into the resistance of other path divided by sum of resistance in the individual paths.
hence current thru r and 4k resistance is: (applying at the node)
I' = I*(1k)/{(r+4k)+(1K)}
hence voltage across 4k resistance will be this current multiplied by resistance.
#### ecjohnny
Joined Jul 16, 2005
142
sorry i still dont get it. The best i know is :
1) the current flow through the 1k is 2mA. 2v/1k? parallel resistor have same voltage?
2) therefore current through R is 2mA??
3) how do i get voltage?
i might be wrong.. anymore further explanation/hints?
#### JoeJester
Joined Apr 26, 2005
4,390
ecjohnny,
the current flow in the 1k is not 2mA. The voltage drop across that 1k is not 2V. Look at your circuit ... redraw it if necessary.
How did you come up with 3k as an answer?
#### ecjohnny
Joined Jul 16, 2005
142
ecjohnny,
the current flow in the 1k is not 2mA. The voltage drop across that 1k is not 2V. Look at your circuit ... redraw it if necessary.
How did you come up with 3k as an answer?
sorry, then i guess i am wrong. The answer is given by my teacher.
Anyone can explain the answer to me?
#### JoeJester
Joined Apr 26, 2005
4,390
ecjohnny,
I'm sure those who responded to you can explain the answer to you.
Show the work you've done so far, then someone here can see where you made your mistake.
You are correct when you stated a parallel branch has the same voltage, but in this case, the 1k and the 4k are not in parallel. To solve this problem you'll be working with KVL, KCL, and Ohms Law. If need be, for your own clarity, work the circuit down to a single equvalent resistor.
You need to read the first volume of ebooks at this site located at http://www.allaboutcircuits.com/vol_1/index.html
Then answer the questions presented by papabravo and recca02.
If we told you the answer, what did you gain? After all, your teacher told you the correct answer.
#### ecjohnny
Joined Jul 16, 2005
142
ecjohnny,
I'm sure those who responded to you can explain the answer to you.
Show the work you've done so far, then someone here can see where you made your mistake.
You are correct when you stated a parallel branch has the same voltage, but in this case, the 1k and the 4k are not in parallel. To solve this problem you'll be working with KVL, KCL, and Ohms Law. If need be, for your own clarity, work the circuit down to a single equvalent resistor.
You need to read the first volume of ebooks at this site located at http://www.allaboutcircuits.com/vol_1/index.html
Then answer the questions presented by papabravo and recca02.
If we told you the answer, what did you gain? After all, your teacher told you the correct answer.
Actually, i knew that KVL,KCL laws and stuff. but i still dun understand.
So...Are you guys gonna help me?
#### recca02
Joined Apr 2, 2007
1,214
ok here is another try.
{note 4k and r are in series and this series combn is in parallel with the 1k,hence voltage across 4k +r and 1k is same.}
when the 4 ma current reaches the parallel resistances of 1k and (4k +R) it splits into two currents one through 4k +r and other through 1k.
u know current in series element is same and hence as mr papabravo pointed
out current through R will be same as current through 4k which can easily be calculated using v=ir (see mr p.b's post).
once this current is know to u. apply kcl to get remaining current through the 1k (simply subtract from 4ma in this case). now use v=ir to get voltage across 1k which is same as voltage across 4k+R.
now u know voltage across 4k+R . and the current thru it (same current which flows thru r and 4k) .apply v=ir again here.u get toal resistance of this branch.now subtract 4k to get the value of r.
try solving some parallel and series combination to get a better understanding of the subject.
#### ecjohnny
Joined Jul 16, 2005
142
ok here is another try.
{note 4k and r are in series and this series combn is in parallel with the 1k,hence voltage across 4k +r and 1k is same.}
when the 4 ma current reaches the parallel resistances of 1k and (4k +R) it splits into two currents one through 4k +r and other through 1k.
u know current in series element is same and hence as mr papabravo pointed
out current through R will be same as current through 4k which can easily be calculated using v=ir (see mr p.b's post).
once this current is know to u. apply kcl to get remaining current through the 1k (simply subtract from 4ma in this case). now use v=ir to get voltage across 1k which is same as voltage across 4k+R.
now u know voltage across 4k+R . and the current thru it (same current which flows thru r and 4k) .apply v=ir again here.u get toal resistance of this branch.now subtract 4k to get the value of r.
try solving some parallel and series combination to get a better understanding of the subject.
subtra
thanks.. i got it. anyway, the last part, i uses the 3.5v-2v to get voltage of R. This is KCL law am i right?
#### recca02
Joined Apr 2, 2007
1,214
kcl is kirchoff current law
summation of current entering the node(point whre many wires meet)
= summation of current leaving the node.
you subtract 0.5ma which is leaving node from 4ma entering node to get the current thru 1k which is again leaving the node.
in case of ac the summation is vector summation.
#### recca02
Joined Apr 2, 2007
1,214
that is kvl.
-voltage law
kcl -current law
states that summation of current entering a node is equal to sum of current
leaving the node.
node is the point where two or more wires meet. so that current may enter from some and leave from rest.
subtracting 0.5 ma (exiting the node) from 4ma (entering the node) will give current through the 1k resistance (leaving the node).
kcl is applicable since there is no accumulation of charges at the node number of charges entering is equal to no of charges leaving.
in case of ac summation is vector sum.
sorry i thought my earlier post didnt get posted.(pls delete the earlier one if possible)
#### JoeJester
Joined Apr 26, 2005
4,390
Yes you are correct on the voltage across R.
Follow recca's advice and practice with more circuits. It's the application of KVL and KCL where you need work.
Here's what I did last night ... before I responded to you.
#### Attachments
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http://www.math.columbia.edu/~woit/wordpress/?p=588
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# Hidden Dimensions
At lunchtime today I stopped by the excellent local bookstore Labyrinth Books, looking to see what was new. In the science section, I noticed a pile of copies of Hidden Dimensions: The Unification of Physics and Consciousness. As with the rest of the many “physics and consciousness” books I’ve seen over the years, I spent a few minutes looking at it to see if there was any evidence of something different or interesting about this one. Apparently not, so I was about to file it in the large category of things best ignored, when I decided to check to see who had published the book.
I was shocked and dismayed to see that the publisher is Columbia University Press, where the book is part of the Columbia Series in Science and Religion. Two of the other eight books in the series are by the same author, B. Allan Wallace, including one entitled Buddhism and Science: Breaking New Ground. In defense of Columbia University Press, the people there don’t actually seem to be reading these books or their promotional material for them, since the blurbs for Buddhism and Science at the CUP site and on Amazon include
“[A] fascinating and captivating book. Without a doubt it will be the definitive text on Holbein’s famous painting for some time to come.”
—Aparna Sharma, Leonardo Reviews
which comes from a review of The Ambassador’s Secret: Holbein and the World of the Renaissance, which just happened to be in the same issue as a review of Buddhism and Science. [Note added: I’ve heard from someone at CUP who tells me that this will be corrected]
Wallace’s background in physics consists of an undergraduate joint major in physics and philosophy of science at Amherst. He’s the author of many other books, including some on Buddhism and physics such as Choosing Reality: A Buddhist View of Physics and the Mind. He has a web-site here and is founder and president of the Santa Barbara Institute for Consciousness Studies.
Here and here you can read some samples of Hidden Dimensions, and make up your own mind what you think. As far as I can tell it’s pretty generic material of this kind, full of crackpottery invoking quantum mechanics, extra dimensions, etc. etc. It’s more or less in the same vein as What the Bleep, but with more of a Buddhist and less of a self-help angle.
Unfortunately, it’s not just Columbia University Press that is promoting Wallace’s ideas. He also gave the keynote address at a symposium here last year on Mind and Reality. You can watch an interview with him standing not too far from my office here.
I really was intending to avoid writing this kind of critical blog posting for a while. After enraging lots of philosophers, I fear that now I’ll enrage lots of Buddhists, in particular by having no interest in wasting time discussing Wallace’s ideas. But I’m profoundly embarrassed that the institution where I work is promoting this sort of thing, so thought I better publicly say so. This all appear to be the responsibility of the Center for the Study of Science and Religion, which has recently been made part of the Earth Institute, run here at Columbia by economist Jeffrey Sachs. Like pretty much all of the many institutions out there devoted to bringing science and religion together, it has received funding from the Templeton Foundation.
This entry was posted in Book Reviews. Bookmark the permalink.
### 24 Responses to Hidden Dimensions
1. DB says:
Richard Dawkins, in “The God Delusion” has an interesting section on how he experienced at first hand the Templeton Foundation methods. He reports having been the one “token atheist” (his description) out of ten speakers invited to speak at a Templeton run conference, only to find out later via John Horgan’s investigations, that many of the other speakers had been paid 15,000$to attend. As you may know, he is highly critical of the Foundation. 2. Chris Oakley says: If there’s anyone from the Templeton Foundation reading this, I would like them to know that I, too, can be bought. For a mere$1,000 I am prepared to add the following paragraph to the end of a paper I am currently writing about Quantum Electrodynamics:
“For all I know there may be a connection between all of this and religion, although as yet I am unsure as to what it is.”
C. G. Oakley M.A., D. Phil. (Oxon.)
3. Michael Bacon says:
Actually, you probably won’t “enrage” lots of Buddhists. That would be tough to do. Most should just shake their heads and smile knowingly . . . .
4. milkshake says:
Templeton foundation is not evil – some years ago they gave award to Freeman Dyson, and its probably the best thing they could have done with their money.
(When Dyson writes in the popular books that consciousness is perhaps on some mysterious level involved in quantum mechanics and that “the universe knew we were coming”, he is not annoying because he separates the facts from his somewhat mystic personal beliefs. He presents his beliefs as such, as hopes and dreams. )
When I was in the highschool in mid 80s, I ran across a discussion in a pop science magazine about antropic principle and multiverse and apparent fine-tuning, Dyson being opposed by a biologist S.J. Gould – and I thought it was a very exciting stuff! (Gould made a very strong point against the fine-tuning argument then.)
5. Coin says:
The Templeton Foundation is tough to get a handle on. They’re funding everything from pure religious apologia to pseudoscientific nonsense to borderline Intelligent Design to both sides of this little Woit, Smolin and Co. Versus String Theory war, with grants going to both Tegmark-style anthropicists and several people at the Perimeter Institute.
As far as I can tell they are legitimately well-meaning and are in fact generally honest about what they are and what they’re doing, just occasionally very very confused…
6. Peter Woit says:
Coin,
I don’t doubt that the people at Templeton are well-meaning, and some of what they fund is worthwhile. The problem is that they have a lot of money, and one of their main goals is to bring religion and science together, blurring the distinction between the two, and effectively often promoting pseudo-science. I doubt they know or care much about string theory, but they’re quite fond of the anthropic principle. It fits in well with the vaguely religious world-view that puts human beings and concern with the “purpose” of the universe at the center of things.
Anyway, sure they’re a mixed bag, but they’re putting a lot of resources behind the promotion of a point of view that I happen to think is dangerous for science.
7. anonymous says:
I’m no fan of Templeton, but I’d gladly take their money, provided it was offered with no strings attached.
8. Al T says:
Well there is Spong’s Law of Theophysical Asininity, which states:
Whenever a person appeals to quantum physics as the basis for a theological or religious principle, he is making an ass of himself.
9. Coin says:
The problem is that they have a lot of money, and one of their main goals is to bring religion and science together, blurring the distinction between the two… sure they’re a mixed bag, but they’re putting a lot of resources behind the promotion of a point of view that I happen to think is dangerous for science.
That is a completely reasonable perspective.
10. dir says:
religion is just a personal belief, so its content should stay in somewhere science does not reach and care
11. Haelfix says:
Big institutions like Templeton have so much money, they usually have difficulty finding the best ways to spend it. So they fund *everything*.
It boils down to a bunch of people in a room on a deadline with a lot of cash and likely horribly vague guidelines on what to spend it on. Worse, its likely many of those people/interns don’t even have an education in physics, so they have difficulty sorting through the forest of absurdities out there.
I find it difficult to assign to much blame to that, after having gone through the sheer horror of grant writing to anything other than the NSF. People literally have absolutely no idea what we do.
12. Olivier says:
It seems that lot of scientists, pretending represent “pure science” are very upset, to say the least, by people trying to understand the universe, not only describe it. Lot of them have strong “rationalistic” and “atheistic” views, and they use science for promoting their ideas. The best example is Dawkins, which supposedly based only on “facts”, is doing in fact atheistic propaganda, for which he has no other arguments than his personal opinion. Science by itself is mere description : it cannot say anything else than what directly appears to our eyes. It’s obvious that conclusions on universe and life will use other arguments than spectral radiation shifs or temperatures.
13. Low Math, Meekly Interacting says:
Haven’t been here for a while.
All I can say is that I share the dismay at the mere notion of a program to promote the “convergence” of scientific and spiritual understanding. I’m not one of these reflexive religion haters that pollute the blogosphere with bigotry and invective, but everyone has a line that they must draw, even if it necessarily offends some of those on the other side. I should think at absolute minimum that line must be drawn at what is by its very definition a variety of experience inscrutable by any material means known or in any way conceivably or inconceivably possible. These are fundamentally incompatible “ways of knowing”, without even coming near the issue of whether or not one way or the other is to any degree accurate or not.
I can’t even come up with a real-world analogy to compare the cognitive dissonance that must be required to reconcile the twain by any means. I don’t think there exists a more patently impossible epistemological enterprise. That it claims even a modicum of legitimacy through anthropic physics is the aspect that is the most…what’s the word I want…terrifying? Yes, terrifying. We laugh at things like “What the Bleep Do We Know”, but if there’s some critical mass being approached, stuff like this isn’t funny, if it’s being accepted by well-motivated skeptics who nonetheless defer to the expertise of the better-credentialed.
14. JJD says:
Please rest assured that many of us Buddhists are as skeptical as you about the current fad of “explaining” so-called Buddhism in terms of so-called science or vice versa. On the one hand, consciousness is explained with quantum theory and extra dimensions (still waiting to hear how dark matter is involved), and on the other hand isolated and mis-characterized elements of Buddhist practice (mindfulness and meditation) are currently fashionable in mental health clinics. Superstition, quackery, and incompetence are easy to find in either domain, and they are the real problem, not just the silly instances where a scientific quack tries to explain personal identity or a religious quack tries to explain space-time.
Good science and good mathematics are based on principles and practical discipline which have taken thousands of years to work out. It seems all too easy to get an undergraduate degree or even a PhD in science or math without a firm grasp on those principles and that discipline. This is part of why your blog is needed.
15. Molnar says:
The Buddhism angle is all wrong. Physics actually proves Christianity. Or maybe Islam. Definitely not Buddhism.
16. srp says:
Low Math needs to read up on basic history of science. Kepler, Newton, and many of the physicists of the Enlightenment believed that their work elucidated either “the mind of God” or the details of God’s handiwork. We atheists have no monopoly on scientific curiousity.
17. Dan says:
I, too, have laughed at the hand-waving which seems to occur in many popular books linking quantum physics with mysticism. Yet, I’m not sure exactly what your problem was with Wallace’s book, given that you provided no more than blanket statement regarding the absurdity of even trying to reconcile physics and consciousness. I don’t know much about the Templeton Foundation (beyond what was said here), but as a number of your commentators have noted, if someone likes what you’re doing and they want to support you, you don’t turn them down without a good reason.
As for Wallace, he appears to have a rather different aim from the average, feel-good, pop physics/mysticism authors. Specifically, he seems not to be critiquing science qua the attempt to gain understanding of the universe through rigorous, reproducible methodologies. Rather, he is critiquing scientists who dogmatically hold philosophical positions without any empirical basis. To quote from the selection you linked to:
“All subjective experiences, including consciousness itself, remain invisible to objective scientific observation. A growing number of scientists and philosophers of mind believe they have the solution: simply declare that conscious states are equivalent to their neurophysiological
correlates or to higher-level features of the brain. The physical processes in the brain that are equated with mental processes are believed to have a dual aspect: they are physically measurable processes, consisting of ordinary electrochemical events of a kind quite familiar to
physicists and chemists, but somehow, inexplicably, they are also subjective
experiences. The rationale for this quasi-dualistic position is that mental phenomena appear to be nonphysical, but this appearance is misleading,
for they are realized as neural events, which are their essential nature.
“It is as if mental phenomena, despite their undeniably subjective, nonphysical appearance, are being granted admittance into the world of nature by being equated with well-understood physical phenomena. Scientists have yet to identify the neural correlates of consciousness, so no one even knows yet what those hypothetical neural processes with a dual identity might be.”
Perhaps, then, you find fault with his future research plan. For he seems in the other selection to suggest that there exist methodologies within the contemplative traditions, especially Buddhism, which might shed light on precisely these phenomena (consciousness, subjective etc.).
Why is that a problem? If the methods are rigorously noted, and the conclusions arrived at can be verified (or not) by anyone else who follows out the methodology, I’m not sure why that would be a problem, beyond the fact that those conclusions would not be accessible to everyone regardless of training.
Wallace specifically singles out mathematics as having a formal similarity to the program he is suggesting (I might single out Brouwer’s intuitionism):
“[T]he practice of higher mathematics takes place within the mind of the mathematician and is then communicated to other mathematicians. Writing equations on a chalkboard is simply a kind of public behavior that may or may not result from the internal process of understanding proofs and devising theorems. A mathematically uneducated person may be taught how to write down the same equations, but when subjected to interrogation by a qualifi ed mathematician,
will clearly not understand what he has written. Mathematicians do commonly converse among themselves in a kind of language that is
unintelligible to nonmathematicians, and the same is true of experts in all fields of science. So there is no reason in principle that researchers could not receive professional training in observing mental phenomena and learn to communicate among themselves about their experiences. However, this is a major undertaking that neither philosophers nor cognitive scientists have yet tackled.”
Similarly, if I present the radical conclusion of a new experiment, my results are not thrown out unless numerous independent researchers have attempted my experiment, using my methodology, and have failed to get the same results.
If a rigorous set of methods existed for investigating consciousness and subjective experience, what would be the problem with using them? On what grounds could we throw out the results?
Perhaps I have failed to meet your criticism. Or perhaps you merely meant to offer up a baseless ad hominem. Perhaps, however, your position is worth reconsidering. And, without question, my position is worth reconsidering. Any suggestions as to where I could start?
18. Peter Woit says:
Dan,
My criticism of the Wallace book has nothing to do with the issues you bring up, but with his specific claims about physics, especially things like quantum physics and extra dimensions. I read enough of the book (not just the chapters available on-line) to convince myself that the author was spouting sizable amounts of nonsense about physics. The world is full of similar nonsense, and it would be both a full-time job and a waste of ones life to argue the details of this with people.
19. Mike says:
Peter,
Are you not debating the details of extra-dimensional string theory? Was there some more specific claim that led to this conclusion?
I was considering buying this book until I read your review, now I don’t know. I have read parts of Alan Wallace’s participation with the Dalai Lama in the conference with David Finkelstein from Georgia Tech, Anton Zeilinger from the University of Vienna, Piet Hut from IAS, George Greenstein and Arthur Zajonc from Amherst; all well recognized academic physicists. Are they all engaged in “generic material of this kind, full of crackpottery”?? Is this the “similar nonsense” you’re talking about? Or does Alan reference the “others” from the “Bleep”?
20. Peter Woit says:
Mike,
The reference to extra dimensions that I saw in Wallace were nonsense, those of string theorists are completely different.
The people you mention are a mixed bag, unlike Wallace they’re trained physicists, but some of them are capable of engaging in similar nonsense from time to time. Again, for the last time, I consider this a complete waste of time, including examining and discussing the contributions to the Dalai Lama conference you reference. Please stop trying to discuss this here and find a venue run by someone who wants to engage in or encourage such discussion.
21. Dan says:
Hey Peter,
Sorry for wasting your time further, but I thought that you might appreciate having it pointed out that, while rhetoric often holds sway in the minds of masses, facts are the standard of science.
As you might have realized, I respect Wallace, for his genuine humility amongst other things. His work regarding science has seemed to me to be both rigorous and fair without being unequivocally laudatory. He certainly has an agenda, but he’s honest and clear minded about it, and doesn’t just try to sweeten up the “medicine” with a little quantum physics. So I was somewhat surprised to discover that a Columbia mathematician/physicist had thrown his latest work into the bin with “What the Bleep” and such junk.
However, I’m disappointed that you cannot bring up a single point at which he errs. Clearly, you have better things to do than write critical blog postings all day, so I don’t expect you to answer this, but you did spend the time to write the initial post, presumably because, as you say, “I’m profoundly embarrassed that the institution where I work is promoting this sort of thing, so thought I better publicly say so.”
Perhaps such a strong condemnation should just be ignored when the condemner can’t even remember or enunciate his reasons for condemning. Whatever “this sort of thing” is, it seems fair to hypothesize that you simply don’t know. Perhaps you might try to be a little less embarrassed in the future about things you don’t know.
Or, perhaps you know, but you can’t tell us because it’s top-secret, classified information too sensitive for a public blog posting! Should we just take your opinions on authority, then? And while you’re at it, where are those damned WMD’s?
22. Peter Woit says:
Dan,
Sorry, but I don’t find Wallace’s book to demonstrate “genuine humility”, but instead found it full of breath-taking arrogance. He announces that these “materialist” physicists have got quantum mechanics all wrong, while not understanding much at all about the subject himself.
I think that virtually any trained physicist you talk to will tell you the same thing, and has a similar reaction to the book as nonsense. Maybe you can find one of them who wants to waste his time going over the details of this nonsense. It’s not going to be me.
23. Dan says:
Alright. Thanks for the reply, though. Guess I’ll have to read it and see for myself.
24. Louise Martinez says:
Where Alan Wallace is coming from in my opinion, is from egocentricity. Perhaps it wasn’t always that way. But if you have attended a retreat of his you will see how he is trying to impress you with how many teachers he has had, and his connection to His Holiness the Dalai Lama, which leaves one thinking on how he is banking on this relationship.
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http://sumidiot.blogspot.com/2008/04/
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## Sunday, April 27, 2008
### We are the Cloud
There's been lots of news lately about "cloud computing" and suches. Google's out there with their new app engine, Amazon has their web services, Microsoft probably has something (I tend to ignore them :)). And there's also the data portability organization. It's all got me wondering.
It's no news that people are posting huge amounts of data on the web. Photos on flickr, text on blogs and sribd, videos on youtube, etc. etc. etc. The idea (my understanding of the idea, anyway) of data portability is that we should control our data. If we post a photo on flickr and then want it, instead, elsewhere (just on our local computer, on some other photo service), we should have the ability to do so. Web services should interact, like if we want to order printed copies of those photos from some other service, we should be able to tell flickr to let the other service grab the picture. There are things in place for this sort of thing to happen (oauth, companies opening up APIs for their services).
It seems to me, though, that there might be another way for us to store our data "in the cloud", and allow web services or individuals to access it, once we give them permission. The other project I have in mind when I've been thinking about this is bittorrent. I'm trying to envision a decentralized cloud, where we can store and interact with (and allow others to do so as well) our data. So instead of having our data with google or amazon (even if we have 'control' over it there), I'm wondering about maybe running a client on my computer (kinda like a bittorrent client), from which I can store and access files among the other people running the client. In order to use the client, I agree to set aside some of my hard drive space, and I'm then allowed to store some related amount among the others using this system. Rednundancy and privacy and encryption all built in, of course. So my computer dies, but the data is all stored in the wild, and I can retrieve it. The folks doing openid have a decentralized system, and I can't help but hope lots of the same ideas work for storing files in this cloud.
There's also no reason there should only be one client for this system. There are lots of bittorrent clients. The system is really the architecture and protocols. Then there probably should be some people keeping track of "trusted clients" or something, because if I'm storing my data on other people's computers, I want to know they aren't doing things with it that they shouldn't be.
I know none of that was precise, well thought out, or well described. I know that I don't know enough right now to even pretend that I can take this idea very far. Issues of privacy and safety and copyright and... I don't have answers to. My hope is that there is a kernel of a worthwhile idea here, and that somebody in a position to do something about it finds it.
## Friday, April 25, 2008
### Open Source Web Apps
So for no particularly good reason I decided to try switching from my desktop instant messenger client (pidgin, formerly gaim) to using the chat feature of gmail. I'm still going with the experiment, and have only been at it a day or so. I don't really see any particularly overwhelming advantage either way. Switching to web based applications is a trend I'm interested in though. But this has me wondering... what happens about open source programs when you shift to web based applications? For example, at some point I hacked a couple lines into my gaim source that randomly selected a new away message (from my set list) every half hour or something, when I was away. The only reason I could do that was because gaim was open source. Shifting to gmail chat... even if it is javascript and I can technically see the source (because, after all, my browser has to be able to see it), it (1) has been horribly obfuscated, (2) isn't in a place I can really modify it. When I download the gaim source, there it is on my local machine waiting for me to change it. But with web apps, even if I copy some javascript files offline and manage to un-obfuscate enough to make a change... then what? I can't reload it to gmail to have it work. And I'd be surprised if the script worked away from the google domains.
I'm not really sure I'm going anywhere with this, it was just a little thought that occurred to me. Maybe I'm misunderstanding web applications. I guess part of the idea with some of the widget standardization is that a widget written one place can be used in another place (like facebook versus igoogle (I don't know if that's currently how it works)). Is that some of the idea with opensocial?
Anyway... I guess the point is I've got lots to learn. Nothing new there.
### Upgrading to Hardy Heron (pt 2)
Well, here I am. Since I did the upgrade, instead of a fresh install, nothing looks particularly new. That's ok (but I still have the urge to start from scratch, and see what it's like). There seemed to be some issues toward the end of my upgrade, the chillispot thing came up again, and I killed another process there, and it even said 'update-manager' failed to update. So we'll see how that goes. I also still want to play and see if I can get my wireless working this time, as I never did in Gutsy Gibbon. I guess the big new thing is using the firefox beta 3 (which I could have done without a full system install), which I'll need to play with some more to see what all new awesomeness it has. At the very least, it doesn't crash when I close flash videos that are still playing, as opposed to what happened before this upgrade. So that's nice. I certainly want to think that the beta is snappier too, which I've read in other places. Hopefully I still feel the same as time goes by.
In the mean time, I'm off.
### Upgrading to Hardy Heron (pt 1?)
I decided to use the built in update manager in ubuntu to upgrade to hardy heron today. It's been chugging along for about 6 hours now, so I'm thinking it might have been quicker to burn a cd and start from scratch. Plus then I get to mess about with doing lots of customization. But anyway, it got to a point where it said about 20 minutes remained, so I left it alone and went and did dishes. When I came back, it was stopped at 17 minutes remaining. In the terminal it has up to show progress, it said it was copying a conf file for chillispot. Not the sort of thing I'd expect to cause problems. I could minimize the window, but the arrow to hide the terminal didn't do anything on a mouse click. I opened up a separate terminal, and a 'ps -aux' showed a couple of processes that mentioned chillispot. I took a stab with 'kill' to end one of the processes (I should have looked more into the process codes, I guess). A window popped up to let me know configuration of chillispot had encountered an error, but that my upgrade would continue. So hopefully chillispot isn't something I use much. Guess I'll go read about it while I wait these last 10 (hopefully) minutes for the upgrade to finish. Plus it gives me time here on my XO.
## Sunday, April 20, 2008
### Some CSS Success
If you actually visit this blog page, instead of just reading along via rss or whatever, you might have noticed that the link colors in the "Reader Shared Items" block didn't match the link colors for the rest of the page. I finally decided to fix that today. It took a little digging around with Firebug, but it was worth it. I found that the reader widget makes its "a" HTML elements with class "i", so I put in a line "a.i { color: \$linkcolor; }" in the "Edit HTML" bit under "Layout" for blogger. That didn't work. But by an odd coincidence, just this morning I read about the "!important" bit of css, so I tried that (it makes the property that it is associated to harder to ignore), and it worked. And then I realized that there was no point in including an extra bit of css for just the "a.i" class, I might as well just tack "!important" to the color line in the existing "a:link" css (in my template, it's the first thing after the css for "body"). And that seems to have worked, which is nice. [Update (~10 minutes later): I just realized that, of course, this changes all of my link colors. That only seems to have affected my post titles colors. But that's in the "Posts" section of my HTML template, under ".post h3 a", with "color:\$titlecolor". Tack an "!important" there, and it all works out. For good measure, I also put some more "!important"s on the css lines for "a" toward the top of my template (under "Body"). The Reader Shared Links were still underlined, while none of my other links where (unless you hover over them), so I put a "border-bottom: none !important;" in the css for "a" toward the top (there under "body" again), and it seems to have worked out.]
Anyway, I've found the firebug firefox extension to be an awesome tool for messing with webpages. You can click around and look at all the code for everything everywhere. And you can modify the source and watch it affect the page right away. Totally sweet. If you play with webpages and haven't used it, you should check it out.
(Sorry if any of the terminology above is wrong, "elements" or "properties" or whatever. Feel free to let me know if I mis-spoke, I'd like to get it right someday)
## Thursday, April 17, 2008
### DiffEq
I have, to date, successfully avoided taking any differential equations classes. When I think about them, 'ugly' jumps to mind. Sure, I enjoyed Euler's method when we learned it (in high school, unless I'm totally mis-remembering something). And sure, differential equations seem to be what drive the real world. But the real world is also fairly ugly (unclean might be a better word), so it seems to work out.
Anyway, the point is, I learned a little something the other day about differential equations that I liked, and thought I'd share.
So, suppose you have a rectangle in the plane, with edges parallel to the coordinate axes (we might as well put the lower-left corner on the origin), with integer width, w, and height, h. Suppose you have a fixed value for each edge of the rectangle, representing temperatures along those edges, and would like to model the temperature of interior points of the rectangle. For simplicity, suppose you want to approximate the temperature at integer coordinates in the interior of the rectangle. Let Ti,j denote the temperature at coordinate (i,j). We already know this value along the boundary of the rectangle (i=0,w or j=0,h), and would like the (w-1)(h-1) interior points.
To get our approximation for the values, we think about relationships among them we might like to assume. An easy and reasonable thing to assume (to get our approximation, anyway) is that the temperature at point (i,j) is the average of the four neighboring points (one up, down, left, or right). In equations:
4*Ti,j=Ti-1,j+Ti,j-1+Ti+1,j+Ti,j+1
This gives us (w-1)(h-1) linear equations in the same number of variables, and so we expect a unique solution. In fact, if you think about it in terms of matrices, the coefficient matrix has no more than 5 nonzero entries in any row (less than 5 if the point is one away from the boundary).
I don't know for sure, but the notes I was looking at seemed to indicate that this was called the 'finite difference method'. You may also notice a complete lack of derivatives, and thus differential equations. I'm sure they are there somewhere, but I also expect I like it just as well with them hidden.
## Monday, April 14, 2008
### Puzzle
While tutoring the other day I came across a puzzle I don't know how to do. This isn't exactly noteworthy, as I can't do most puzzles. But it seemed like an interesting enough puzzle, so I thought I'd give it broader attention:
50 watches are placed at random on a table. Show that at some time the sum of the distances from the center of the table to the ends of the minute hands is greater than the sum of the distances from the center of the table to the centers of the watches.
The problem didn't say anything about the sizes of the watches (like, if they were all the same). Also, I guess we should say that they are all facing up (does it matter?). I think the problem did mention that the watches weren't all necessarily all set to the same time, just that they were all running at the same, accurate, pace.
So, any thoughts?
## Thursday, April 10, 2008
### Remembering Dr. Stong
I'd like to take a few minutes to reflect on the short time I've known Dr. Stong, as he sadly passed away this morning. It was only last year that he retired. I had hoped that he would have a long and happy retirement, continuing to show up for topology seminar (so that he could fall asleep in the corner). I wish I had arrived in the department earlier, so that I might have gotten to take more classes with him. Dr. Stong was the only professor I know that cursed happily throughout lectures, making them all the more interesting. Though his hands were visibly shaky away from the chalkboard, his script was among the most tidy I've seen written on blackboard, which I was always amazed by.
It frequently happens in mathematics that you set up some maps between objects, making some obvious choices, and the maps have nice properties. For example, in topology your maps hopefully work out to be homotopy equivalences (at least), or when you apply homotopy or homology functors you get isomorphisms. Dr. Stong had a theorem along these lines, announced in class one day: every map is an isomorphism. Clearly this isn't correct, but I know that he meant: every map that isn't obviously not an isomorphism is an isomorphism (replace isomorphism with whatever property you are looking at). I will continue to refer to this as Dr. Stong's theorem. I'm sure his mathematical research deserves much better recognition, but I don't know any of it. Stong's theorem shows up all the time :)
The only class I had with Dr. Stong was cobordism, his area of expertise. However, he was one of the professors that proctored my second year oral exam. Though I didn't think it went very well, after I had finished and retired to my office he came down to say that he was pleased, and that it went as well as could be hoped. Certainly I was relieved that I had passed, but also grateful that he come by to let me know. It was a wonderful gesture. I suppose I hadn't thought much about it, but I had kinda figured on Dr. Stong being at my thesis defense. Alas.
I also remember that Dr. Stong objected to one of the definitions I made toward the beginning of a talk I gave last semester. It was a perfectly legitimate objection, questioning mostly a matter of notation. I don't honestly recall, but I like to think that I defended my notation, as he let me continue my talk. He didn't say anything else the rest of the talk, and I tend to think that he fell asleep. I'll miss Dr. Stong's objections in seminars.
So the department is left without its one cursing professor and its Santa (Dr. Stong dressed up as St. Nick for the holiday party). Our topology seminar will have one more empty desk. I'll still have my stories.
Mathematical results last forever, even when the mathematician doesn't. Goodbye Dr. Stong.
## Monday, April 7, 2008
### What do you do?
I've heard that at least one mathematician answers this by saying that they are a tennis instructor. It sets things up to avoid the regular 'I'm terrible at math' and 'I can't even balance my checkbook' replies. Somehow, I seem to have stumbled into a section of math that I think is easy to explain to people:
So, I do topology. You know that in geometry you study shapes. And you have some notion of when two shapes are "the same", that is, if you can rotate them and shift them around and maybe flip them over, and they line up. But that's all you are allowed to do, these few rigid motions. In topology, we allow more things to be the same. The standard analogy goes: if you made those circles and squares and triangles in geometry using a piece of stretchy string or something, you could deform the string until you got all three of those shapes. So now we decide that they are really all the same. The question now becomes, "how can you tell when two things are the same?", and this is the question topologists try to answer.
If I want to go further, and the person is still listening, and I feel like they remember what polynomials are (look like), I might mention that within topology is the field of algebraic topology. Here, the way you distinguish shapes is you look at them, and assign some sort of more rigid (algebraic) object to them. The idea being that whenever two shapes are the same, in the loose sense of topology, then there is some correspondence between their associated algebraic objects. For example, in the study of knots, you look at a knot and write down a polynomial (by following some particular rules). Two pictures of a knot could look different, but if you go through the process of writing down the associated polynomials, you'll get the same answer.
Finally, if the person is still listening, I might even introduce the calculus of functors (without saying functor). I make sure they remember Taylor polynomials from calculus. It was this process of getting the best approximation to a given function by using polynomials. The idea being that somehow polynomials are easier to understand than your average function, so if you can get a good enough approximation to your crazy function using polynomials, you're in good shape. Well, it turns out that you can define what it means to be 'polynomial' and 'the best polynomial approximation' in other contexts. And so I'm supposed to be actually computing the best polynomial approximations for this one particular example. Heavy on the supposed to be.
## Sunday, April 6, 2008
### Mod Squares
The other day in Homological Algebra we started talking about group (co)homology. I didn't bring my notes home (so I probably have some bits wrong below), but I noticed a strange thing pop up in class that I recognized in a few other contexts. We were, at the time, talking about computing $H_1(G;\mathbb{Z})$. From the topological perspective (which we aren't using in class), we know this is $H_1(BG;\mathbb{Z})$, which is the abelianization of $\pi_1(G)$. The way we identified it in class was as follows: Consider $\mathbb{Z}[G]\rightarrow \mathbb{Z}$ given on generators $g\in G$ by $g\mapsto 1$ (so the map just adds up the coefficients). Let $J$ be the kernel. In class, if I remember correctly, we saw that $H_1(G;Z)$ was the same as $J/J^2$.
This 'mod squares' bit I have seen before, in two other contexts. Originally, I thought I had seen them when we talked about the Dieudonne determinant in Algebra 4. Looking back, it looks like we defined the determinant as a map $GL_n(D)\rightarrow D^*/[D^*,D^*]$ (looks like $D^*$ should be referring to the units of $D$), so at least that looks similar to the above, it's an abelianization. In fact, 'mod squares' did show up in algebra 4, when I was learning about Clifford algebras and the spin group. I just dug up my notes, and it looks like I had a spin norm, a map $SO(V)\rightarrow F^*/(F^*)^2$. The kernel of this map then had a double cover by $Spin(V)$.
The other place I think I've seen this 'mod squares' bit was in the very small bit of algebraic geometry I remember. Something about an $\mathfrak{m}$ (probably a maximal ideal somewhere), and $\mathfrak{m}/\mathfrak{m}^2$ having a useful interpretation.
Anyway, I know the above was all quite vague, and I apologize. I should put in the energy to go back and look at these three things together, and see if there is some general principle I should be noticing. It feels like there should be, but I'm not sure what. Anybody have any idea what I'm talking about?
While I'm at it, anybody know if there is some formalization about the similarity between Sylow subgroups of finite groups and maximal tori of Lie groups? "They look similar" always seems to hint at something in mathematics.
## Saturday, April 5, 2008
### Greek Mathematician with Fish
Thanks Matt Z. for letting me post my TeXed version of his "Greek Mathematician with Fish" sketch. You can check it out here.
## Wednesday, April 2, 2008
### Missing Out
Damn it all. Just yesterday I was talking about a sense of missing out. This morning I woke to find that it was justified. For some reason I decided to look at the computer science department's seminar list. Turns out, last week Richard Stallman himself, the man, the myth, the legend, was here talking about free software. And I had no idea. FAIL.
## Tuesday, April 1, 2008
### Why?
Before I get to far here, I should point out that this is likely to be a bigish post, and (like most) uninteresting. If you'd rather, watch this bit of Louis C.K. on youtube. The bit I was looking for is toward the end, but it's all funny. Anyway, my goal with this post is to write some things down with the hope that I can then move on. We'll see how that goes.
Alright, so my 'why run' question yesterday remains, I think, unanswered. And will continue to. But I've got another answer to throw into the mix: to know what you are capable of. Like in Fight Club: how can you know yourself if you've never been in a fight. I read an article recently about an ultramarathoner talking about how in the middle of a 100 mile run you really get down to a raw state, and he wanted to see what that was like. I wouldn't know, and for now I'm happy to take his word for it. Another lingering issue from yesterday was this striving for a sense of accomplishment. But why should I need to accomplish anything? Most people don't accomplish much, it seems, in any sort of broad sense. Isn't it egotistical of me to think I should be capable of something? Even to say that most people don't accomplish much... I'm pretty much an ass I guess.
Ok, so moving on from 'why run', how about 'why collect dvds/cds?' More to the point, why keep my current collection? It really seems like physical media is on its way out (I'm gonna make a brief divergence here, to avoid making a whole seperate blog post about more pointlessness: when I get information on pieces of paper, it's starting to really feel like a pain. Paper isn't searchable, and it occupies physical space. If that same information was a digital file on my computer, I can search it, worry less about losing it, and probably other benefits as well. Where's my damn e-paper? Don't get me wrong, I like books. But I'm talking about single sheets of paper, or just a couple together. If whatever is on them has any value, I'd rather it be digital.), that perhaps this last round of hd-dvd and blu-ray are the last media wars. Of course, I could be wrong. But either way, the value of the dvds on my shelf is not going up. If I'm hoping to get anything back for them, there's no better time to sell them than now. But how do I decide which to get rid of? Some almost seem to define me. They are the ones that, when I meet new people (which doesn't happen) I make sure they have seen. They are the movies that I quote daily, or easily could. So if I'm going to trim down my dvd collection, where do I draw the line? What if another movie comes along soon, then I'm adding back it... It's basically pointless. Maybe I should just dump all of them, right now, and vow not to buy more. The monk route. But then I've got a sense of loss. Ok, so I back them up to a hard drive first, then sell them. And then I'm breaking copyright laws (I suppose it wouldn't be a first). Am I likely to make more money selling them than it would cost to get a drive big enough to hold them? I give up. I'm not going to fight the inertia of having a collection. I should, though, fight the urge to expand that collection.
So why do I watch so many movies anyway? Mostly I can't remember them, and I don't really enjoy conversing about movies after they are over. I don't try to analyze movies to pick out main themes or anything. I think I have, frequently, just used them to 'get away'. But now here I am talking about how I wish I was accomplishing something, and I'm still watching these damn movies. It's that same inertia as owning a collection, the comfort in a constant, reveling in routine. (While I'm playing word games here... what's the deal with 'casual', 'casualty', and 'causally'? Those are some damn close spellings for fairly different words. Ok, now I'm on a language kick (way to stay focused)... can't we all agree on some global language? I know there's rather a lot of us, but come on, we could really stand some more global unity. Haven't people said that finding evidence of life on another planet would be a great incentive to bring us together globally? I'm ready.)
Of course, some movies I really do like, and enjoy quoting. But again, why? To show off the extent of my worthless movie watching? I've seen more movies than you, and that's an accomplishment? I hope it's not my only one. Maybe I quote movies to try to make you feel inferior about not recognizing the quote. I am, as noted above, kinda an ass. Or maybe I quote movies that I know the people around me will know, so I can share in the joyful laughter of a group of friends. Some sense of belonging?
Another theme I'm noticing here and in some recent posts, aside from accomplishments, is a sense of missing out. If I'm not watching lots of movies, maybe I'll miss a great one. Or not subscribing to enough of, or the right, rss feeds, I'll miss something. I'm supposed to stop and smell the roses, right? Take pleasure in the little things around me? Enjoy what I have, and stop pining for what I don't?
There's no point to wondering, to asking why. There doesn't seem to be an answer, and even if there is, there seems to be no hope of finding it. Like with religion. I need to be more agnostic at a low level. Stop asking why, and just go do. This was, if I recall, one of my original draws to mathematics: there is an answer to be found, and it can be. There's a certain austere definiteness about mathematics that is powerfully attractive, a way out of the mess that is the real world. Ok, sure, I know about the incompleteness theorems and things, but still.
It looks like I've said what I had hoped to say. And it didn't take as long or as much space as I thought. Hopefully I've resolved something here, and can get on with... life? Is that what this is?
Way to go, ending a resolution with a question. FAIL.
### April Fools
So today has been claimed by some as annual Day Without Google. I'm starting it off, like I do so many of my other days, with a heaping pile of FAIL. I've already posted on this blog and used gmail, and plan to use reader when I'm done here. But I have not yet used google for a web search (well... I searched for some comics from the search bar on that page, and it happened to be powered by google... my b). I'm not sure how seriously I'll take 'Day Without Google', but that's because I'm a bad person. Maybe you'd like to give it a try. There are lots of search engines out there, and the folks at AltSearchEngines are happy to point you to some. And we're brought up to believe competition is a good thing. So... I'll be going now.
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http://mathhelpforum.com/calculus/212967-absolute-increase-relative-rate-growth.html
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# Thread: Absolute increase/relative rate of growth
1. ## Absolute increase/relative rate of growth
In class we are learning about relative rate of growth and here's this question I don't understand how to approach:
The table below shows the cumulative number of AIDS deaths worldwide. Find the absolute increase in AIDS death between 2003 and 2004 and between 2006 and 2007. Find the relative increase between 2006 and 2007
Year 2003 2004 2005 2006 2007 Cases 30.2 33.3 35.5 37.6 39.6
Apparently, the absolute increase is in millions and relative increase is in percent.
2. ## Re: Absolute increase/relative rate of growth
Hey kuppina.
(Hint: Relative increase between something is (b-a)/a).
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https://www.tablix.org/~avian/blog/archives/life/index.html
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## AFG-2005 noise generation bug
09.10.2016 13:49
The noise output function in the GW Instek AFG-2005 arbitrary function generator appears to have a bug. If you set up the generator to output a sine wave at 10 kHz, and then switch to noise output using the FUNC key, you get output like this:
The red trace shows the spectrum of the signal from the signal generator using the FFT function of the oscilloscope. The yellow trace shows the signal in the time domain.
The noise spectrum looks flat and starts to roll off somewhere beyond 10 MHz. This is what you would expect for an instrument that is supposed to have a 20 MHz DAC. However, if you set the output to a sine wave at 1 kHz before switching to noise output, the signal looks significantly different:
These two later oscilloscope screenshots have been made using the same settings as the pair above.
This is obviously an error on the part of the signal generator. The setting for the sine wave output shouldn't affect the noise output. It looks like the DAC is now only set to around 4 MHz sampling rate. Probably it has been switched to a lower sampling rate for the low-frequency sine wave output and the code forgot to switch it back for the noise function.
This behavior is perfectly reproducible. If you switch back to sine wave output, increase the frequency to 10 kHz or more and switch to noise output, the DAC sampling rate is increased again. Similarly, if you set a 100 Hz sine wave, the DAC sampling rate is set to 400 kHz. As far as I can see there is no mention of this in the manual and you cannot set the sampling rate manually. The FREQ button is disabled in Noise mode and there is no indication on the front panel about which sampling rate is currently used.
I've been writing about the AFG-2005 before. It's an useful instrument, but things like this make it absolutely necessary to always have an oscilloscope at hand to verify that the generator is actually doing what you think it should be doing.
Posted by | Categories: Life | Comments »
## A naive approach to rain prediction
02.10.2016 19:49
Ever since the Slovenian environment agency started publishing Doppler weather radar imagery I've been a regular visitor on their web site. For the last few years I try to use my bicycle for my daily commute as much as possible. However, I'm not such a hard-core fan of biking that I would do it in any weather. The animated map with the recent rainfall estimate history helps very much with that: it's quite easy to judge by eye whether there will be rain in the next 30 minutes or so and hence whether to seek alternative modes of transportation.
Some time ago I had a more serious (or should I say scientific) use for weather data, related to one of the projects at the Institute. Gašper helpfully provided me with some historical archives then and I also started collecting images myself straight from ARSO website. That project came and went, but the amount of data on my disk kept growing. I've been continuously tempted to do something interesting with it. I've previously written what the data seems to reveal about the radar itself.
Most of all, I've been playing with the idea of doing that should-I-take-the-bus prediction automatically. Obviously I'm not a weather expert, so my experiments were very naive from that perspective. For instance, a while ago I tried estimating an optical flow field from the apparent movement of regions with rain and then using that to predict their movement in the near future. That didn't really work. Another idea I had was to simply dump the data into a naive Bayesian model. While that also didn't work to any useful degree as far as prediction is concerned, it did produce some interesting results worth sharing.
What I did was model rain at any point in the radar image (x, y) and time t as a random event:
R_{x,y,t}
To determine whether the event happened or not from the historical data, I simply checked whether the corresponding pixel was clear or not - I ignored the various rates of rainfall reported. To calculate the prior probability of rain on any point on the map, I did a maximum-likelihood estimation:
P(R_{x,y}) = \frac{n_{x,y}}{N}
Here, nx,y is number of images where the point shows rain and N is the total number of images in the dataset.
I was interested in predicting rain at one specific target point (x0, y0) based on recent history of images. Hence I estimated the following conditional probability:
P(R_{x_0,y_0,t+\Delta t}|R_{x,y,t})
This can be estimated from historical data in a similar way as the prior probability. In other words, I was interested in how strongly is rain at some arbitrary point on the map x,y at time t related to the fact that it will rain at the target point at some future time tt. Are there any points on the map that, for instance, always show rain 30 minutes before it rains in Ljubljana?
The video below shows this conditional probability for a few chosen target points around Slovenia (marked by small white X). Brighter colors show higher conditional probability and hence stronger relation. The prior probability is shown in lower-right corner. In the video, the time difference runs in reverse, from 4 hours to 0 in 10 minute steps. For each point, the animation is repeated 4 times before moving to the next point.
The estimates shown are calculated from 62573 radar images recorded between July 2015 and September 2016. Since the format of the images has been changing over time it's hard to integrate older data.
As you might expect, when looking several hours into the future, there is very little relation between points on the map. All points are dull red. If it rains now in the east, it might rain later in Ljubljana. Similarly, if it rains in the west. There's no real difference - the only information you get is that it's generally rainy weather in the whole region.
When you decrease the time difference, you can see that nearby points are starting to matter more than those far away. Brighter colors concentrate around the target. Obviously, if it rains somewhere around Ljubljana, there's a higher chance it will shortly rain in Ljubljana as well. If you note the color scale though, it's not a particularly strong relation unless you're well below one hour.
What's interesting is that for some cities you can see that rain more often comes from a certain direction. Around the coast and in Notranjska region, the rain clouds seem to mostly move in from the Adriatic sea (lower-left corner of the map). This seems to fit the local saying you can sometimes hear, that the "weather comes in from the west". In the mountains (top-left), it seems to come from the north. All this is just based on one year of historical data though, so it might not be generally true over longer periods.
Of course, such simple Bayesian models are horribly out-of-fashion these days. A deep learning convolutional neural network might work better (or not), but alas, I'm more or less just playing with data on a rainy weekend and trying to remember machine learning topics I used to know. There's also the fact that ARSO themselves now provide a short-term rain prediction through an application on their website. It's not the easiest thing to find (Parameter Selection - Precipitation in the menu and then Forecast on the slider below). I'm sure their models are way better than anything an amateur like me can come up with, so I doubt I'll spend any more time on this. I might try to add the forecast to ARSO API at one point though.
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## A thousand pages of bullet journal
12.08.2016 17:27
A few weeks ago I filled the 1000th page in my Bullet Journal. Actually, I don't think I can call it that. It's not in fact that much oriented around bullet points. It's just a series of notebooks with consistently numbered, dated and titled pages for easy referencing, monthly indexes and easy-to-see square bullet points for denoting tasks. Most of the things I said two years ago still hold, so I'll try not to repeat myself too much here.
Almost everything I do these days goes into this journal. Lab notes, sketches of ideas, random thoughts, doodles of happy ponies, to-do lists, pages worth of crossed-out mathematical derivations, interesting quotes, meeting notes and so on. Writing things down in a notebook often significantly clears them up. Once I have a concise and articulated definition of a problem, the solution usually isn't far away. Pen and paper helps me keep focus at talks and meetings, much like an open laptop does the opposite.
Going back through past notes gives a good perspective on how much new ideas depend on the context and mindset that created them. An idea for some random side-project that seems interesting and fun at first invariably looks much less shiny and worthy of attention after reading through the written version a few days or weeks later. I can't decide though whether it's better to leave such a thing on paper or hack together some half-baked prototype before the initial enthusiasm fades away.
The number of pages I write per month appears to be increasing. That might be because I settled on using cheap school notebooks. I find that I'm much more relaxed scribbling into a 50 cent notebook than ruining a 20€ Moleskine. Leaving lots of whitespace is wasteful, but helps a lot with readability and later corrections. Yes, whipping out a colorful children's notebook at an important meeting doesn't look very professional. Then again, most people at such meetings are too busy typing emails into their laptops to notice.
As much as it might look like a waste of time, I grew to like the monthly ritual of making an index page. I like the sense of achievement it gives me when I look back at what I've accomplished the previous month. It's also an opportunity for reflection. If the index gets hard to put all on one page, that's a good sign that the previous month was all too fragmented and that too many things wanted to happen at once.
The physical nature of the journal means that I can't carry the whole history with me at all times. That is also sometimes a problem. It is an unfortunate feature of my line of work that it is not uncommon for people to want to have unannounced meetings about a topic that was last discussed half a year ago. On the other hand, saying that I don't have my notes on me at that moment does present an honest excuse.
Indexes help, but finding things can be problematic. Then again, digital content (that's not publicly on the web) often isn't much better. I commonly find myself frustratingly searching for some piece of code or a document I know exists somewhere on my hard disk but can't remember any exact keyword that would help me find it. I considered making a digital version of monthly indexes at one point. I don't think it would be worth the effort and it would destroy some of the off-line quality of the notebook.
As I mentioned previously, gratuitous cross-referencing between notebook pages, IPython notebooks and other things does help. I tend not to copy tasks between pages, like in the original Bullet Journal idea. For projects that are primarily electronics related though, I'm used to keeping a separate folder with all the calculations and schematics, a habit I picked up long ago. There are not many such projects these days, but I did on one occasion photocopy pages from the notebook. I admit that made me feel absolutely archaic.
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## Oxidized diodes
08.08.2016 20:41
Out of curiosity, I salvaged these three LEDs from an old bicycle light that stopped working. Rain must have gotten inside it at one point, because the copper on the PCB was pretty much eaten away by the electrolysis. The chip that blinked the light was dead, but LEDs themselves still work.
It's interesting how far inside the bulb the steel leads managed to oxidize. You can see that the right hand lead (anode) on all LEDs is brown all the way to the top, where a bond wire connects it to the die. I would have thought that the epoxy makes a better seal. For comparison, there's a similar new LED on the right. It's also interesting that the positive terminal was more damaged than the negative. On the right-most LED the terminal was actually eaten completely through just outside the bulb (although poking the remains with a needle still lights up the LED, so obviously the die itself was not damaged).
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23.07.2016 10:23
It used to be that whenever someone wrote something particularly witty on Slashdot, it was followed by a reply along the lines of "I find your ideas intriguing and would like to subscribe to your newsletter". Ten-odd years later, it seems like the web took that old Simpsons joke seriously. These days you can hardly follow a link on Hacker News without having a pop-up thrown in your face. Most articles now end with a plea for an e-mail address, and I've even been to real-life talks where the speakers continuously advertised their newsletter to the audience.
Recently I've been asked several times why I didn't support subscriptions by e-mail, like every other normal website. The short answer is that I keep this blog in a state that I wish other websites I visit would adopt. This means no annoying advertisements, respecting your privacy by not loading third-party Javascript or tracking cookies, HTTPS and IPv6 support, valid XHTML... and good support for the Atom standard. Following the death of Google Reader, the world turned against RSS and Atom feeds. However, I still find them vastly more usable than any alternative. It annoys me that I can't follow interesting people and projects on modern sites like Medium and Hackaday.io through this channel.
That said, you now can subscribe by e-mail to my blog, should you wish to do so (see also sidebar top-right). The thing that finally convinced me to implement this was hearing that some of you use RSS-to-email services that add their own advertisements to my blog posts. I did not make this decision lightly though. I used to host mailing lists and know what an incredible time sink they can be, fighting spam, addressing complaints and so on. I don't have that kind of time anymore, so using an external mass-mailing service was the only option. Running my own mail server in this era is lunacy enough.
Mailchimp seems to be friendly, so I'm using that at the moment. If turns to the dark side and depending how popular the newsletter gets, I might move to some other service - or remove it altogether. For the time being I consider this an experiment. It's also worth mentioning that while there are no ads, Mailchimp does add mandatory tracking features (link redirects and tracking pixels). Of course, it also collects your e-mail address somewhere.
Since I'm on the topic of subscriptions and I don't like writing meta posts like this, I would also like to mention here two ways of following my posts that are not particularly well known: if you are only interested in one particular topic I write about, you can search for it. Search results page has an attached Atom feed you can follow that only contains posts related to the query. If you on the other hand believe that Twitter is the new RSS, feel free to follow @aviansblog (at least until Twitter breaks the API again).
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## Visualizing frequency allocations in Slovenia
15.07.2016 17:34
If you go to a talk about dynamic spectrum access, cognitive radio or any other topic remotely connected with the way radio spectrum is used or regulated, chances are one of the slides in the introduction will contain the following chart. The multitude of little colorful boxes is supposed to impress on the audience that the spectrum is overcrowded with existing allocations and that any future technology will have problems finding vacant frequencies.
I admit I've used it myself in that capacity a couple of times. "The only space left unallocated is beyond the top-left and bottom-right edges, below 9 kHz and above 300 GHz", I would say, "and those frequencies are not very useful for new developments.". After that I would feel free to advertise the latest crazy idea that will magically create more space, brushing away the fact that spectrum seems to be like IPv4 address space - when there's real need, powers that be always seem to find more of it.
Image by U.S. Department of Commerce
I was soon getting a bit annoyed by this chart. When you study it you realize it's showing the wrong thing. The crowdiness of it does fit with the general story people are trying to tell, but the ITU categories shown are not the problematic part of the 100 year legacy of radio spectrum regulations. I only came to realize that later though. My first thought was "Why are people discussing future spectrum in Europe, using a ten year old chart from U.S. Department of Commerce showing the situation on the other side of the Atlantic?"
Although there is a handful of similar charts for other countries on the web, I couldn't find one that I would be happy with. So two years back, with a bit of free time and encouraged by the local Open Data group, I set off to make my own. It would show the right thing, be up to date and describe the situation in my home country. I downloaded public PDFs with the Slovenian Electronic Communications Act, the National Table of Frequency Allocations and also a few assorted files with individual frequency licenses. Then I started writing a parser that would turn it all into machine-readable JSON. Then, as you might imagine if you ever encountered the words "PDF", "table" and "parsing" in the same sentence, I gave up after a few days of writing increasingly convoluted and frustrating Python code.
Fast forward two years and I was again going through some documents that discuss these matters. I remembered this old abandoned project. In the mean time, new laws were made, the frequency allocation table was updated several times and the PDFs were structured a bit differently. This meant I had to throw away all my previous work, but on the other hand new documents looked a bit easier to parse. I again took the challenge and this time I managed to parse most of the basic NTFA into JSON after a day of work and about 350 lines of Python.
I won't dive deep into technicalities here. I started with the PDF converted to whitespace-formatted UTF-8 text using the pdftotext tool which comes with Poppler. Then I had a series of functions that successively turned text into structured data. This made it easy to inspect and debug each step. Some of the steps included were "fix typos in document" (there are several, by the way, including inconsistent use of points and commas for decimal marks), "extract column widths", "extract header hierarchy", "normalize service names", etc. If there will be interest, I might present the details in a talk at one of the future Open Data Meetups in Ljubljana.
Once I had the data in JSON, drawing a visualization much like the U.S. one above took another 250 lines using matplotlib. Writing them was much more pleasant in comparison though. In hindsight, it would actually make sense to do the visualization part first, since it was much easier to spot parsing mistakes from the graphical representation than by looking at JSON.
While it is both local and relatively up-to-date, the visualization as such isn't very good. It still only works for conveying that general idea of fragmentation, but not much else. There are way too many categories for an unaided eye to easily match the colors in the legend with the bands in the graph. It would be much better to have an interactive version where you could point to a band and the relevant information would pop-up (or maybe even point you to the relevant paragraphs in the PDFs). Unfortunately this is beyond my meager knowledge of Javascript frameworks.
My chart also still just lists the ITU categories. Not only do they have very little to do with finding space for future allocations, they are useless for spotting interesting parts of the spectrum. For example, the famous 2.4 GHz ISM band doesn't stand out in any way here - it's listed simply under "FIXED, MOBILE, AMATEUR and RADIOLOCATION" services. All such interesting details regarding licensing and technologies in individual bands is hidden in various regulations, scattered across a vast amount of tables, appendices and different PDF documents. It is often in textual form that currently seems impossible to easily extract in an automated way.
I'm still glad that I now have at least some of this data in computer-readable form. I'm sure it will come handy in other projects. For instance, I might eventually use it to add some automatic labels to my real-time UHF and VHF spectrogram from the roof of the IJS campus.
I will not be publicly publishing JSON data and parsing code at the moment. I have concerns about its correctness and the code is so specialized for the specific document that I'm sure nobody will find it useful for anything else. However, if you have some legitimate use for the data, please send me an e-mail and I will be happy to share my work.
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## Materialized Munin display
15.05.2016 21:25
Speaking of Munin, here's a thing that I've made recently: A small stand-alone display that cycles through a set of measurements from a Munin installation.
(Click to watch Munin display video)
Back when ESP8266 chip was the big new thing I ordered a bag of them from eBay. The said bag then proceeded to gather dust in the corner of my desk for a year or so, as such things unfortunately tend to do these days. I also had a really nice white transflective display left over from another project (suffice to say, it cost around 20 £ compared to ones you can get for a tenth of the price with free shipping on DealExtreme). So something like this looked like a natural thing to make.
The hardware is not worth wasting too many words on: an ESP8266 module handles radio and the networking part. The display is a 2-line LCD panel using the common 16-pin interface. An Arduino Pro Mini acts as glue between the display and the ESP8266. There are also 3.3 V (for ESP8266) and 5 V (for LCD and Arduino) power supplies and a transistor level shifter for the serial line between ESP8266 and the Arduino.
ESP8266 runs stock firmware that exposes a modem-like AT-command interface on a serial line. I could have omitted the Arduino and ran the whole thing from the ESP8266 alone, however the lack of GPIO lines on the module I was using meant that I would have to use some kind of GPIO extender or multiplexer to run the 16-pin LCD interface. Arduino with the WeeESP8266 library just seemed less of a hassle.
From the software side, the device basically acts as a dumb display. The ESP8266 listens on a TCP socket and Arduino pushes everything that is received on that socket to the LCD. All the complexity is hidden in a Python daemon that runs on my CubieTruck. The daemon uses PyMunin to periodically query Munin nodes, renders the strings to be displayed and sends them to the display.
Speaking of ESP8266, my main complaint would be that there is basically zero official documentation about it. Just getting it to boot means reconciling conflicting information from different blog and forum posts (for me, both CH_PD and RST/GPIO16 needed to be pulled low). No one mentioned that RX pin has an internal pull-up. I also way underestimated the current consumption (it says 1 mA stand-by on the datasheet after all and the radio is mostly doing nothing in my case). It turns out that a linear regulator is out of the question and a 3.3 V switch-mode power supply is a must.
My module came with firmware that was very unreliable. Getting official firmware updates from a sticky forum post felt kind of shady and it took some time to get an image that worked with 512 kB flash on my module. That said, the module has been working without resets or hangs for a couple of weeks now which is nice and not something that all similar radio modules are capable of.
Finally, this is also my first 3D printed project and I learned several important lessons. It's better to leave too much clearance than too little between parts that are supposed to fit together. This box took about four hours of careful sanding and cutting before the top part could be inserted into the bottom since the 3D printer randomly decided to make some walls 1 mm thicker than planned. Also, self-tapping screws and automagically hollowed-out plastic parts don't play nice together.
With all the careful measuring and planning required to come up with a CAD drawing, I'm not sure 3D printing saved me any time compared to a simple plywood box which I could make and fit on the fly. Also, relying on the flexibility and precision of a 3D print made me kind of forget about the mechanical design of the circuit. I'm not particularly proud of the way things fit together and how it looks inside, but most of it is hidden away from view anyway and I guess it works well enough for a quick one-off project.
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## Clockwork, part 2
10.04.2016 19:39
I hate to leave a good puzzle unsolved. Last week I was writing about a cheap quartz mechanism I got from an old clock that stopped working. I said that I could not figure out why its rotor only turns in one direction given a seemingly symmetrical construction of the coil that drives it.
There is quite a number of tear downs and descriptions of how such mechanisms work on the web. However, very few seem to address this issue of direction of rotation and those that do don't give a very convincing argument. Some mention that the direction has something to do with the asymmetric shape of the coil's core. This forum post mentions that the direction can be reversed if a different pulse width is used.
So, first of all I had a closer look at the core. It's made of three identical iron sheets, each 0.4 mm thick. Here is one of them on the scanner with the coil and the rotor locations drawn over it:
It turns out there is in fact a slight asymmetry. The edges of the cut-out for the rotor are 0.4 mm closer together on one diagonal than on the other. It's hard to make that out with unaided eye. It's possible that the curved edge on the other side makes it less error prone to construct the core with all three sheets in same orientation.
The forum post about pulse lengths and my initial thought about shaded pole motors made me think that there is some subtle transient effect in play that would make the rotor prefer one direction over the other. Using just a single coil, core asymmetry cannot result in a rotating magnetic field if you assume linear conditions (e.g. no part of the core gets saturated) and no delay due to eddy currents. Shaded pole motors overcome this by delaying magnetization of one part of the core through a shorted auxiliary winding, but no such arrangement is present here.
I did some measurements and back-of-the-envelope calculations. The coil has approximately 5000 turns and resistance of 215 Ω. The field strength is nowhere near saturation for iron. The current through the coil settles somewhere on the range of milliseconds (I measured a time constant of 250 μs without the core in place). It seems unlikely any transients in magnetization can affect the movements of the rotor.
After a bit more research, I found out that this type of a motor is called a Lavet type stepping motor. In fact, its operation can be explained completely using static fields and transients don't play any significant role. The rotor has four stable points: two when the coil drives the rotor in one or the other direction and two when the rotor's own permanent magnetization attracts it to the ferromagnetic core. The core asymmetry creates a slight offset between the former and the latter two points. Wikipedia describes the principle quite nicely.
To test this principle, I connected the coil to an Arduino and slowly stepped this clockwork motor through it's four states. The LED on the Arduino board above shows when the coil is energized. The black dot on the rotor roughly marks the position of one of its poles. You can see that when the coil turns off, the rotor turns slightly forward as its permanent magnet aligns it with the diagonal on the core that has a smaller air gap (one step is a bit more pronounced than the other on the video above). This slight forward advancement from the neutral position then makes the rotor prefer the forward over the backward motion when the coil is energized in the other direction.
It's always fascinating to see how a mundane thing like a clock still manages to have parts in it whose principle of operation is very much not obvious from the first glance.
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## Clockwork
28.03.2016 15:17
Recently one of the clocks in my apartment stopped. It's been here since before I moved in and is probably more than 10 years old. The housing more or less crumbled away as I opened it. On the other hand the movement inside looked like it was still in a good condition, so I had a look if there was anything in it that I could fix.
This is a standard 56 mm quartz wall clock movement. It's pretty much the same as in any other cheap clock I've seen. In this case, its makers were quick to dispel any myths about its quality: no jewels in watchmaker's parlance means no quality bearings and I'm guessing unadjusted means that the frequency of its quartz oscillator can't be adjusted.
As far as electronics is concerned, there's not much to see in there. There's a single integrated circuit, bonded to a tiny PCB and covered with a blob of epoxy. It uses a small tuning-fork quartz resonator to keep time. As the cover promised, there's no sign of a trimmer for adjusting the quartz load capacitance. Two exposed pads on the top press against some metallic strips that connect to the single AA battery. The life time of the battery was probably more than a year since I don't remember the last time I had to change it.
The circuit is connected to a coil on the other side of the circuit board. It drives the coil with 30 ms pulses once per second with alternating polarity. The oscilloscope screenshot below shows voltage on the coil terminals.
When the mechanism is assembled, there's a small toroidal permanent magnet sitting in the gap in the coil's core with the first plastic gear on top of it. The toroid is laterally magnetized and works as a rotor in a simple stepper motor.
The rotor turns half a turn every second and this is what gives off the audible tick-tock sound. I'm a bit puzzled as to what makes it turn only in one direction. I could see nothing that would work as a shaded pole or something like that. The core also looks perfectly symmetrical with no features that would make it prefer one direction of rotation over the other. Maybe the unusual cutouts on the gear for the second hand have something to do with it.
Update: my follow-up post explains what determines direction of rotation.
This is what the mechanism looks like with gears in place. The whole construction is very finicky and a monument to material cost reduction. There's no way to run it without the cover in place since gears fall over and the impulses in the coil actually eject the rotor if there's nothing on top holding it in place (it's definitely not as well behaved as one in this video). In fact, I see no traces that the rotor magnet has been permanently bonded in any way with the first gear. It seems to just kind of jump around in the magnetic field and drive the mechanism by rubbing against the inside of the gear.
In the end, I couldn't find anything obviously wrong with this thing. The electronics seem to work correctly. The gears also look and turn fine. When I put it back together it would sometimes run, sometimes it would just jump one step back and forth and sometimes it would stand still. Maybe some part wore down mechanically, increasing friction. Or maybe the magnet lost some of its magnetization and no longer produces enough torque to reliably turn the mechanism. In any case, it's going into the scrap box.
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## The problem with gmail.co
14.03.2016 19:41
At this moment, the gmail.co (note missing m) top-level domain is registered by Google. This is not surprising. It's common practice these days for owners of popular internet services to buy up domains that are similar to their own. It might be to fight phising attacks (e.g. go-to-this-totally-legit-gmail.co-login-form type affairs), prevent typosquatting or purely for convenience to redirect users that mistyped the URL to the correct address.
$whois gmail.co (...) Registrant Organization: Google Inc. Registrant City: Mountain View Registrant State/Province: CA Registrant Country: United States gmail.co currently serves a plain 404 Not Found page on the HTTP port. Not really user friendly, but I guess it's good enough to prevent web-based phising attacks. Now, with half of the world using [email protected] email addresses, it's not uncommon to also mistakenly send an email to a [email protected] address. Normally, if you mistype the domain part of the email address, your MTA will see the DNS resolve fail and you would immediately get either a SMTP error at the time of submission, or a bounced mail shortly after. Unfortunately, gmail.co domain actually exists, which means that MTAs will in fact attempt to deliver mail to it. There's no MX DNS record, however SMTP specifies that MTAs must in that case use the address in A or AAAA records for delivery. Those do exist (as they allow the previously mentioned HTTP error page to be served to a browser). To further complicate the situation, the SMTP port 25 on IPs referenced by those A and AAAA records is blackholed. This means that a MTA will attempt to connect to it, hang while the remote host eats up SYN packets, and fail after the TCP handshake timeouts. A timeout looks to the MTA like an unresponsive mail server, which means it will continue to retry the delivery for a considerable amount of time. The RFC 5321 says that it should take at least 4-5 days before it gives up and sends a bounce: Retries continue until the message is transmitted or the sender gives up; the give-up time generally needs to be at least 4-5 days. It MAY be appropriate to set a shorter maximum number of retries for non- delivery notifications and equivalent error messages than for standard messages. The parameters to the retry algorithm MUST be configurable. In a nutshell, what all of this means is that if you make a typo and send a mail to @gmail.co, it will take around a week for you to receive any indication that your mail was not delivered. Needless to say, this is bad. Especially if the message you were sending was time critical in nature. Update: Exim will warn you when a message has been delayed for more than 24 hours, so you'll likely notice this error before the default 6 day retry timeout. Still, it's annoying and not all MTAs are that friendly. The lesson here is that, if you register your own typosquatting domains, do make sure that mail sent to them will be immediately bounced. One way is to simply set an invalid MX record (this is an immediate error for SMTP). You can also run a SMTP server that actively rejects all incoming mail (possibly with a friendly error message reminding the user of the mistyped address), but that requires some more effort. As for this particular Google's blunder, a workaround is to put a special retry rule for gmail.co in your MTA so that it gives up faster (e.g. see Exim's Retry configuration). Posted by | Categories: Life | Comments » ## Some SPF statistics 21.02.2016 19:04 Some people tend their backyard gardens. I host my own mail server. Recently, there has been a push towards more stringent mail server authentication to fight spam and abuse. One of the simple ways of controlling which server is allowed to send mail for a domain is the Sender Policy Framework. Zakir Durumeric explained it nicely in his Neither Snow Nor Rain Nor MITM talk at the 32C3. The effort for more authentication seems to be headed by Google. That is not surprising. Google Mail is e-mail for most people nowadays. If anyone can push for changes in the infrastructure, it's them. A while ago Google published some statistics regarding the adoption of different standards for their inbound mail. Just recently, they also added visible warnings for their users if mail they received has not been sent from an authenticated server. Just how much an average user can do about that (except perhaps pressure their correspondents to start using Google Mail) seems questionable though. Anyway, I implemented a SPF check for inbound mail on my server some time ago. I never explicitly rejected mail based on it however. My MTA just adds a header to incoming messages. I was guessing the added header may be picked out by the Bayesian spam filter, if it became significant at any point. After reading about Google's efforts I was wondering what the situation regarding SPF checks looks like for me. Obviously, I see a very different sample of the world's e-mail traffic as Google's servers. For this experiment I took a 3 month sample of inbound e-mail that was received by my server between November 2015 and January 2016. The mail was classified by Bogofilter into spam and non-spam mail, mostly based on textual content. SPF records were evaluated by spf-tools-perl upon reception. Explanation of results (what softfail, permerror, etc. means) is here. As you can see, the situation in this little corner of the Internet is much less optimistic than the 95.3% SPF adoption rate that Google sees. More than half of mail I see doesn't have a SPF record. A successful SPF record validation also doesn't look like that much of a strong signal for spam filtering either, with 22% of spam mail successfully passing the check. It's nice that I saw no hard SPF failures for non-spam mail. I checked my inbox for mail that had softfails and permerrors. Some of it was borderline-spammy and some of it was legitimate and appeared to be due to the sender having a misconfigured SPF record. Another interesting point I noticed is that some sneaky spam mail comes with their own headers claiming SPF evaluation. This might be a problem if the MTA just adds another Received-SPF header at the bottom and doesn't remove the existing one. If you then have a simple filter on Received-SPF: pass somewhere later in the pipeline it's likely the filter will hit the spammer's header first instead of the header your MTA added. Posted by | Categories: Life | Comments » ## IEEE 802.11 channel survey statistics 14.02.2016 20:17 I attended the All our shared spectrum are belong to us talk by Paul Fuxjaeger this December at the 32C3. He talked about a kernel patch that adds radio channel utilization data to the beacons sent out by a wireless LAN access point. The patched kernel can be used with OpenWRT to inform other devices in the network of the state of the radio channel, as seen from the standpoint of the access point. One of the uses for this is reducing the hidden node problem and as I understand they used it to improve robustness of a Wi-Fi mesh network. His patch got my attention because I did not know that typical wireless LAN radios kept such low-level radio channel statistics. I previously did some surveys of the occupancy of the 2.4 GHz band for a seminar at the Institute. My measurements using a TI CC2500 transceiver on a VESNA sensor node showed that the physical radio channel very rarely reached any kind of significant occupancy, even in the middle of very busy Wi-Fi networks. While I did not pursue it further, I remained suspicious of that result. Paul's talk gave me an idea that it would be interesting to compare such measurements with statistics available from the Wi-Fi adapter itself. I did some digging and found the definition of struct survey_info in include/net/cfg80211.h in Linux kernel: /** * struct survey_info - channel survey response * * @channel: the channel this survey record reports, mandatory * @filled: bitflag of flags from &enum survey_info_flags * @noise: channel noise in dBm. This and all following fields are * optional * @channel_time: amount of time in ms the radio spent on the channel * @channel_time_busy: amount of time the primary channel was sensed busy * @channel_time_ext_busy: amount of time the extension channel was sensed busy * @channel_time_rx: amount of time the radio spent receiving data * @channel_time_tx: amount of time the radio spent transmitting data * * Used by dump_survey() to report back per-channel survey information. * * This structure can later be expanded with things like * channel duty cycle etc. */ struct survey_info { struct ieee80211_channel *channel; u64 channel_time; u64 channel_time_busy; u64 channel_time_ext_busy; u64 channel_time_rx; u64 channel_time_tx; u32 filled; s8 noise; }; You can get these values for a wireless adapter on a running Linux system using ethtool or iw without patching the kernel: $ ethtool -S wlan0
NIC statistics:
(...)
noise: 161
ch_time: 19404258681
ch_time_busy: 3082386526
ch_time_ext_busy: 18446744073709551615
ch_time_rx: 2510607684
ch_time_tx: 371239068
\$ iw dev wlan0 survey dump
(...)
Survey data from wlan0
frequency: 2422 MHz [in use]
noise: -95 dBm
channel active time: 19404338429 ms
channel busy time: 3082398273 ms
channel transmit time: 371240518 ms
(...)
It's worth noting that ethtool will print out values even if the hardware does not set them. For example the ch_time_ext_busy above seems invalid (it's 0xffffffffffffffff in hex). ethtool also incorrectly interprets the noise value (161 is -95 interpreted as an unsigned 8-bit value).
What fields contain valid values depends on the wireless adapter. In fact, grepping for channel_time_busy through the kernel tree lists only a handful of drivers that touch it. For example, the iwlwifi-supported Intel Centrino Advanced-N 6205 in my laptop does not fill any of these fields, while the Atheros AR9550 adapter using the ath9k driver in my wireless router does.
Short of the comment in the code listed above, I haven't yet found any more detailed documentation regarding the meaning of these fields. I checked the IEEE 802.11 standard, but as far as I can see, it only mentions that radios can keep the statistic on the percentage of the time the channel is busy, but doesn't go into details.
I wrote a small Munin plugin that keeps track of these values. For time counters the graph above shows the derivative (effectively the percentage of time the radio spent in a particular state). With some experiments I was able to find out the following:
• noise: I'm guessing this is the threshold value used by the energy detection carrier sense mechanism in the CSMA/CA protocol. It's around -95 dBm for my router, which sounds like a valid value. It's not static but changes up and down by a decibel or two. It would be interesting to see how the radio dynamically determines the noise level.
• channel_time: If you don't change channels, this goes up by 1000 ms each 1000 ms of wall-clock time.
• channel_time_busy: Probably the amount of time the energy detector showed input power over the noise threshold, plus the time the radio was in transmit mode. This seems to be about the same as the sum of RX and TX times, unless there is a lot of external interference (like another busy Wi-Fi network on the same channel).
• channel_time_ext_busy: This might be a counter for the secondary radio channel used in channel binding, like in 802.11ac. I haven't tested this since channel binding isn't working on my router.
• channel_time_rx: On my router this increments at around 10% of channel_time rate, even if the network is completely idle, so I'm guessing it triggers at some very low-level, before packet CRC checks and things like that. As expected, it goes towards 100% of channel_time rate if you send a lot of data towards the interface.
• channel_time_tx: At idle it's around 2% on my router, which seems consistent with beacon broadcasts. It goes towards 100% of channel_time rate if you send a lot of data from the interface.
In general, the following relation seems to hold:
\frac{t_{channel-tx} + t_{channel-rx}}{t_{channel}} < \frac{t_{channel-busy}}{t_{channel}} < 100\%
Posted by | Categories: Life | Comments »
## Button, button. Who's got the button?
19.01.2016 19:07
As much as I try, I can't switch away from GNOME. Every once in a while I will try to use some other desktop environment in Debian and I invariably switch back after a month. The fact is that for me, GNOME seems to come with fewest little annoyances that need manual fixing or digging through configuration files or source code. Or it might be that I'm just too used to all the small details in how GNOME does things on the user interface side. It's also possible that I understand enough about GNOME internals at this point that when things stop working I usually find the solution pretty quickly.
That does not mean, however, that GNOME no longer manages to surprise me. This is a story about the latest such occurrence. It's a story about a button. This button in particular:
I noticed this button after upgrading my work laptop to Debian Jessie that comes with GNOME 3.14. The most curious thing about it was that it does not appear on my home desktop computer with a supposedly identical Debian Jessie setup. What makes my laptop so special that it sprouted an extra button in this prime piece of screen real-estate?
Being the kind of person that first looks into the documentation, I opened the GNOME 3.14 Release Notes. However, there is no note in there about any mysterious new buttons on the click-top-right-corner menu. I was not surprised though, since it might have been added in any of several GNOME versions that were released between now and the previous Debian Stable.
The button is marked with a circular arrow icon. The kind of icon that is often used to distinguish a reboot in contrast to a shutdown when positioned near the power-switch icon. Like for instance on this Ubuntu shutdown dialog:
I don't think it was unreasonable then to assume that this is a reboot button. Anyway, when documentation about a thing fails you, the best next step is usually to poke the thing with a stick. Preferably a long and non-conductive one.
Unfortunately, this approach failed to uncover the purpose of the mysterious button. Upon closer inspection the button did change a bit after clicking on it, but seemingly nothing else happened. On the second thought, it would be kind of weird for GNOME to have a reboot button when at one point it lacked even a shutdown option, for a reason nobody quite understood.
In a final attempt to discover the purpose of the catching-its-own-tail arrow, I hovered the mouse cursor over it. Of course, no helpful yellow strip of text showed up. Tooltips are obsolete now that everything is a smartphone.
At that point I ran out of ideas. Since I had no text associated with the button it seemed impossible to turn to a web search for help. In fact, I realized I don't even know how the menu that holds the button is called these days. I complained about it on IRC and someone suggested doing a Google Image search for the button. This first sounded like a brilliant idea, but it soon turned out that visual search for graphical user interface widgets just isn't there yet:
Of course, I was stubborn enough to keep searching. In the end, a (text) query led me to a thread on StackExchange that solved the conundrum. I don't remember what I typed into Google when I first saw that result, but once I knew what to search for, the web suddenly turned out to be full of confused GNOME users. Well, at least I was not alone in being baffled by this.
In the end, I only wonder how many of those people that went through this same experience also immediately started swinging their laptop around to see whether the screen on their laptop would actually rotate and were disappointed when, regardless of the screen lock button, the desktop remained stubbornly in the landscape mode.
Posted by | Categories: Life | Comments »
## End of a project
15.11.2015 11:38
Two weeks ago, the CREW project concluded with a public workshop and a closed meeting with reviewers invited by the European Commission. Thus ended five years of work on testbeds for wireless communications by an international team from Belgium, Ireland, Germany, France and Slovenia. I've been working on the project for nearly four of these years as the technical lead for the Jožef Stefan Institute. While I've been involved in several other projects, the work related to CREW and the testbed clusters we built in Slovenia has occupied most of my time at the Institute.
Image by Ingrid Moerman
It's been four years of periodical conference calls, plenary and review meetings, joint experiments at the testbeds, giving talks and demonstrations at scientific conferences, writing deliverables for the Commission, internal reports and articles for publication, chasing deadlines and, of course, the actual work: writing software, developing electronics, debugging both, making measurements in the field and analyzing data, climbing up lamp posts and figuring out municipal power grids from outdated wiring plans.
It's funny how when I'm thinking back, writing is the first thing that comes to mind. I estimate I've written about 20 thousand words of documents per year, which does not seem all that much. It's less than the amount of text I publish yearly on this blog. Counting everyone involved, we produced almost 100 peer-reviewed papers related to the project, which does seem a lot. It has also resulted in my first experience working with a book publisher and a best paper award from the Digital Avionics Systems Conference I have hanging above my desk.
Image by Christoph Heller
Remote writing collaboration has definitely been something new for me. It is surprising that what works best in the end are Word documents in emails and lots of manual editing and merging. A web-based document management system helped with keeping inboxes within IMAP quotas, but little else. Some of this is certainly due to technical shortcomings in various tools, but the biggest reason I believe is simply the fact that Word plus email is the lowest common denominator that can be expected of a large group of people of varying professions and organizations with various internal IT policies.
Teleconferencing these days is survivable, but barely so. I suspect Alexander Graham Bell got better audio quality than some of the GoToMeetings I attended. Which is where face-to-face meetings come into the picture. I've been on so many trips during these four years that I've finally came to the point where flying became the necessary evil instead of a rare opportunity to be in an airplane. Most of the meetings have been pleasant, if somewhat exhausting 3 day experiences. It is always nice to meet people you're exchanging emails with in person and see how their institutions look like. Highlights for me were definitely experiments and tours of other facilities. The most impressive that come to mind were seeing Imec RF labs and clean rooms in Leuven, the w-iLab.t Zwijnaarde testbed in Ghent and Airbus headquarters near Munich.
(Click to watch Instrumented Roombas at w-iLab.t video)
One of the closing comments at the review was about identifying the main achievement of the project. The most publicly visible results of the work in Slovenia are definitely little boxes with antennas you can see above streets in Logatec and around our campus. I have somewhat mixed feelings about them. On one hand, it's been a big learning experience. Planning and designing a network, and most of all, seeing how electronics fails when you leave it hanging outside all year round. Designing a programming interface that would be simple enough to learn and powerful enough to be useful. If I would do it again, I would certainly do a lot of things differently, software and hardware wise.
While a number of experiments were done on the testbed, practically all required a lot of hands-on support. We are still far from having a fully automated remote testbed as a service that would be useful to academics and industry alike. Another thing that was very much underestimated was the amount of continuous effort needed to maintain such a testbed in operation. It requires much more than one full-time person to keep something as complex as this up and running. The percentage of working nodes in the network was often not something I could be proud of.
For me personally, the biggest take away from the project has been the opportunity to study practical radio technology in depth - something I didn't get to do much during my undergraduate study. I've had the chance to work with fancy (and expensive) equipment I would not have had otherwise. I studied in detail Texas Instruments CC series of integrated transceivers, which resulted in some interesting hacks. I've designed, built and tested three generations of custom VHF/UHF receivers. These were the most ambitious electronic designs I've made so far. Their capabilities compared to other hardware are encouraging and right now it seems I will continue to work on them in the next year, either as part of my post-graduate studies or under other projects.
I have heard it said several times that CREW was one of the best performing European projects in this field. I can't really give a fair comparison since this is the only such project I've been deeply involved so far. I was disappointed when I heard of servers being shutdown and files deleted as the project wound down, but that is how I hear things usually are when focus shifts to other sources of funding. It is one thing to satisfy own curiosity and desire to learn, but seeing your work being genuinely useful is even better. I learned a lot and got some references, but I was expecting the end result as a whole to be something more tangible, something that would be more directly usable outside of the immediate circle involved in the project.
Posted by | Categories: Life | Comments »
## TEMPerHUM USB hygrometers
11.10.2015 14:19
Last month at a project meeting in Ghent, Hans Cappelle told me about PCsensor TEMPerHUM hygrometers and thermometers. At around 23 EUR per piece, these are relatively cheap, Chinese made USB-connected sensors. I was looking for something like that to put into a few machines I have running at different places. Knowing the room temperature can be handy. For instance, once I noticed that the CPU and motherboard temperature on one server was rising even though fan RPMs did not change. Was it because the change in the room temperature or was it a sign that heat sinks were getting clogged with dust? Having a reading from a sensor outside of the server's box would help in knowing the reason without having to go and have a look.
When I took them out of the box, I was a bit surprised at their weight. I assumed that the shiny surface was metallized plastic, but in fact it looks like the case is actually made of metal. Each came with a short USB extension cable so you can put it a bit away from the warm computer they are plugged in.
My devices identify as RDing TEMPERHUM1V1.2 on the USB bus (vendor ID 0x0c45, product ID 0x7402). They register two interfaces with the host: a HID keyboard and a HID mouse. The blue circle with TXT in it is actually a button. When you press it, the sensor starts simulating someone manually typing in periodic sensor readouts. As far as I understand, you can set some settings in this mode by playing with Caps lock and Num lock LEDs. I haven't looked into it further though since I don't currently care about this feature, but it is good to know that sensors can be used with only a basic USB HID keyboard driver and a text editor.
On Linux, udev creates two hidraw devices for the sensor. To get a sensor readout from those without having to press the button, Frode Austvik wrote a nice little utility. For v1.2 sensors, you need this patched version.
The utility is written in C and is easy to compile for more exotic devices. The only real dependency is HID API. HID API is only packaged for Debian Jessie, but the 0.8.0 source package compiles on Wheezy as well without any modifications. OpenWRT has a package for HID API. The sensor however does not work on my TP-Link router because it uses USB v1.10 and the router's USB ports apparently only support USB v2.x (see OpenWRT ticket #15194).
By default, udev creates hidraw device files that only root can read. To enable any member of the temperhum group to read the sensor, I use the following in /etc/udev/rules.d/20-temperhum.rules:
Update: Previously, I made the hidraw device world-writable. That might be a security problem, although probably a very unlikely one.
SUBSYSTEM=="hidraw", ATTRS{idVendor}=="0c45", ATTRS{idProduct}=="7402", MODE="0660", GROUP="temperhum"
Finally, what about the accuracy? I left one of the sensors (connected via an extension cable) to sit overnight in a room next to an Arduino with a DS18B20 and the old wireless weather monitor I use at home. The two spikes you see on the graphs are from when I opened the windows in the morning.
The DS18B20 has a declared accuracy of ±0.5°C, while the Si7021 sensor that TEMPerHUM is supposedly using should be accurate to ±0.4°C. However, TEMPerHUM is showing between 1.5°C and 2.0°C higher reading than DS18B20. This might be because the USB fob is heating itself a little bit, or it might be some numerical error (or they might be using off-spec chips). Other people have reported that similar sensors tend to overestimate the temperature.
For relative humidity measurements I don't have a good reference. The difference between my weather monitor and TEMPerHUM is around 10% according to this graph. Si7021 should be accurate to within 3% according to its datasheet. My weather monitor is certainly worse than that. So I can't really say anything about the humidity measurement except that it isn't obviously wrong.
In conclusion, except for the incompatibility with some Atheros SoCs I mentioned above, these sensors seem to be exactly what they say they are. Not super accurate but probably good enough for some basic monitoring of the environment.
Posted by | Categories: Life | Comments »
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http://math.stackexchange.com/questions/163946/are-complex-substitutions-legal-in-integration/163948
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# Are Complex Substitutions Legal in Integration?
This question has been irritating me for awhile so I thought I'd ask here.
Are complex substitutions in integration okay? Can the following substitution used to evaluate the Fresnel integrals:
$$\int_{0}^{\infty} \sin x^2\, dx=\operatorname {Im}\left( \int_0^\infty\cos x^2\, dx + i\int_0^\infty\sin x^2\, dx\right)=\operatorname {Im}\left(\int_0^\infty \exp(ix^2)\, dx\right)$$
Letting $ix^2=-z^2 \implies x=\pm\sqrt{iz^2}=\pm \sqrt{i}z \implies z=\pm \sqrt{-i} x \implies dx = \pm\sqrt{i}\, dz$
Thus the integral becomes
$$\operatorname {Im}\left(\pm \sqrt{i}\int_0^{\pm\sqrt{-i}\infty} \exp(z^2)\, dz\right)$$
This step requires some justification, and I am hoping someone can help me justify this step as well: $$\pm \sqrt{i}\int_0^{\pm\sqrt{-i}\infty} \exp(z^2)\, dz=\pm\sqrt{i}\int^\infty_0\exp(z^2)\, dz=\pm\sqrt{i}\left(\frac{\sqrt{\pi}}{2}\right)$$
Thus
$$\operatorname {Im}\left(\int_0^\infty \exp(ix^2)\, dx\right)=\operatorname {Im}\left(\pm\frac{\sqrt{i\pi}}{2}\right)=\operatorname {Im}\left(\pm\frac{(1+i)\sqrt{\pi}}{2\sqrt{2}}\right)=\pm\frac{1}{2}\sqrt{\frac{\pi}{2}}$$
We find that the correct answer is the positive part (simply prove the integral is positive, perhaps by showing the integral can be written as an alternating sum of integrals).
Can someone help justify this substitution? Is this legal?
-
A complex substitution is fine. The thing to be worried about is that replacing $x$ with $\pm \sqrt{i} z$ is not a substitution at all! At best, it's an (awkward) way to try and work with two different substitutions simultaneously. At worst, it's a sure-fire recipe for confusion. – Hurkyl Jun 27 '12 at 23:09
Let's consider the legality of doing an actual u-substitution, such as $z = \sqrt{i} x$. Not only must the integrand be rewritten, so must the limits of integration.
In the original definite integral you have $x$ going from $0$ to $\infty$. Of course this then gives a path of integration for $z$, but it's not sufficient to have just limits $0$ to $\infty$ in the complex plane to specify that path. So this would be a gray area where the limitations of your notation could let you down!
In the complex plane there are many paths from $0$ to $\infty$, even many straight such paths.
A correct way to do this might go as follows. Consider the contour integral $$\oint_\Gamma e^{iz^2}\ dz$$ where $\Gamma$ is the positively oriented triangle with vertices $0, R, R+Ri$ for large $R$. Since the integrand is analytic, Cauchy's Theorem says the result is $0$. This can be written as $J_1 + J_2 + J_3=0$, where $J_1, J_2, J_3$ are the integrals over the segments $[0, R]$, $[R, R+Ri]$, and $[R+Ri,0]$ respectively.
Show that as $R \to +\infty$, $J_2 \to 0$ and $J_3 \to -(1+i) \dfrac{\sqrt{2 \pi}}{4}$. Thus $J_1 \to (1+i) \dfrac{\sqrt{2 \pi}}{4}$, which says that $$\int_0^\infty \cos(t^2)\ dt = \int_0^\infty \sin(t^2)\ dt = \dfrac{\sqrt{2 \pi}}{4}$$
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http://www.maa.org/publications/maa-reviews/solving-nonlinear-partial-differential-equations-with-maple-and-mathematica?device=mobile
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# Solving Nonlinear Partial Differential Equations with Maple and Mathematica
Publisher:
Springer
Number of Pages:
357
Price:
124.00
ISBN:
9783709105160
Friday, August 19, 2011
Reviewable:
Yes
Include In BLL Rating:
No
Inna Shingareva and Carlos Lizárraga-Celaya
Publication Date:
2011
Format:
Hardcover
Category:
Textbook
1 Introduction 1.1 Basic Concepts 2 Algebraic Approach 2.1 Point Transformations 2.2 Contact Transformations 2.3 Transformations Relating Differential Equations 2.4 Linearizing and Bilinearizing Transformations 2.5 Reductions of Nonlinear PDEs 2.6 Separation of Variables 2.7 Transformation Groups 2.8 Nonlinear Systems 3 Geometric-Qualitative Approach 3.1 Method of Characteristics 3.2 Generalized Method of Characteristics 3.3 Qualitative Analysis 4 General Analytical Approach. Integrability 4.1 Painlevé Test and Integrability 4.2 Complete Integrability. Evolution Equations 4.3 Nonlinear Systems. Integrability Conditions 5 Approximate Analytical Approach 5.1 Adomian Decomposition Method 5.2 Asymptotic Expansions. Perturbation Methods 6 Numerical Approach 6.1 Embedded Numerical Methods 6.2 Finite DifferenceMethods 7 Analytical-Numerical Approach 7.1 Method of Lines 7.2 Spectral Collocation Method; A Brief Description of Maple A.1 Introduction A.2 Basic Concepts A.3 Maple Language B Brief Description of Mathematica B.1 Introduction B.2 Basic Concepts B.3 Mathematica Language; References, Index
Publish Book:
Modify Date:
Friday, August 19, 2011
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https://slideplayer.com/slide/223840/
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# Chapter 11 Vibrations and Waves.
## Presentation on theme: "Chapter 11 Vibrations and Waves."— Presentation transcript:
Chapter 11 Vibrations and Waves
Elasticity When you hang a weight on a spring, the weight applies a force to the spring and it stretches in direct proportion to the applied force. According to Hooke’s law, the amount of stretch (or compression), x, is directly proportional to the applied force F. Double the force and you double the stretch; triple the force and you get three times the stretch, and so on: F ~ ∆x
Elasticity If an elastic material is stretched or compressed more than a certain amount, it will not return to its original state. The distance at which permanent distortion occurs is called the elastic limit. Hooke’s law holds only as long as the force does not stretch or compress the material beyond its elastic limit.
Free Body Diagrams Revisited
Spring force = - (spring constant) (displacement) Felastic = -kx
Hooke’s Law Spring force = - (spring constant) (displacement) Felastic = -kx
Hooke’s Law If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium, what is the spring constant?
Simple Harmonic Motion
Vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium
Simple Pendulums Amplitude Length Period Frequency
Simple Pendulums
Simple Pendulums At what position in the cycle of a swinging pendulum is the potential energy of the pendulum at a maximum?
Simple Harmonic Motion Calculations
For a simple pendulum in simple harmonic motion For a mass-spring system in simple harmonic motion
Waves Medium – a physical environment through which a disturbance can travel Mechanical wave – a wave that requires a medium to travel through Examples Non-examples
Transverse Waves Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves Wave motion is parallel to equilibrium
Wave Properties Pulse wave Reflection
A wave that is just one interference – no repetition Reflection
Constructive and Destructive Interference
Constructive interference A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
speed of a wave = (frequency) (wavelength) v = f λ
1. A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s. 2. The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (3.00 x 108 m/s). Find the frequency of the laser light.
De Broglie Waves Louis de Broglie suggested that all matter has wavelike characteristics. where h is Planck’s constant, equal to 6.63 x J·s. This wavelength is too small to notice interference for large objects. This idea becomes important when looking all things at the microscopic level.
De Broglie Waves What is the wavelength of an electron (mass = 9.11 x 10¯31 kg) traveling at 5.31 x 106 m/s?
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http://math.stackexchange.com/users/8508/robert-israel?tab=reputation
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# Robert Israel
less info
reputation
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bio website math.ubc.ca/~israel location Richmond, Canada age member for 2 years, 9 months seen 4 hours ago profile views 11,556
I'm an Emeritus Associate Professor of Mathematics at University of British Columbia and an Optimization Algorithms Researcher at D-Wave Systems in Burnaby BC
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https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/402
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## PLATIN A Planning System for Inductive Theorem Proving Implementation and Experiences
• This paper provides a description of PLATIN. With PLATIN we present an imple-mented system for planning inductive theorem proofs in equational theories that arebased on rewrite methods. We provide a survey of the underlying architecture ofPLATIN and then concentrate on details and experiences of the current implementa-tion.
### Additional Services
Author: Robert Eschbach, Inger Sonntag urn:nbn:de:hbz:386-kluedo-3734 SEKI Report (97,2) Preprint English 1997 1997 Technische Universität Kaiserslautern Fachbereich Informatik 004 Datenverarbeitung; Informatik
$Rev: 12793$
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http://math.stackexchange.com/questions/227827/supremum-infimum
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# Supremum, infimum
I came across nasty task which includes supremum, infimum and I am confused about it. The question is to find a supremum and infimum of a given set:$$A =(x+y+z:x,y,z>0,xyz=1)$$I tried to eliminate z and use corelations between arithmetic mean and so on. I get $A =(\frac{xy(x+y)+1}{xy}:x,y>0)$, and I know that $\frac{x+y}{2}>\sqrt{xy}>\frac{2}{\frac{1}{x}+\frac{1}{y}}=\frac{2xy}{x+y}$. From this I get $xy<\frac{1}{4}(x+y)^{2}$ $(x+y)^2>2\sqrt{xy}$, what after substitution gives $$\frac{2(xy)^{\frac{3}{2}}+1}{xy}<\frac{xy(x+y) +1}{xy}<\frac{(x+y)^3 +4}{(x+y)^2}$$but I have no idea how to evaluate it (if it is a good way). Intuition says that infimum is $0$, and supremum $\infty$, but how to prove it more formally? Thanks in advance!
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For infimum, recall AM-GM. Given $x,y,z > 0$, we have that $$\dfrac{x+y+z}3 \geq \sqrt[3]{xyz}$$ and equality holds when $x=y=z$. Since $xyz = 1$, we get that $x+y+z \geq 3$. Hence, the infimum is $3$.
For supremum, consider $x = n, y = \dfrac1n$ and $z = 1$, where $n$ can be arbitrarily large. Note that $xyz = 1$. $x+y+z = n + \dfrac1n + 1$. Hence, the supremum is $\infty$.
It really is a good idea in this kind of question to try some things out, as this can give you ideas. Try all the numbers equal. Try some other "small" numbers - does the value of $x+y+z$ increase or decrease when the numbers are different. What happens if you try to make one of the numbers very small? What happens if you make one of them very large (how big can you get)? That is very quick to do, and gives some clues as to which way the inequalities go (easy to get them the wrong way round). – Mark Bennet Nov 2 '12 at 21:48
How do you know that infimum is indeed 3? By subtituting $\frac{1}{n}$ and $n$ for $x, y$ we can go as close to 3 as we want to, but does $x*y*z=1$ directly imply that infimum is 3? Is it possible to prove with definitions, for example with epsilon? – fdhd Nov 2 '12 at 21:51
@user46034 The AM-GM gives us $x+y+z \geq 3$. Equality holds at $x=y=z = 1$. Hence $3$ is indeed the infimum. And I set $x = n, y = \dfrac1n$ and $z = 1$ to argue that the supremum is infinity by letting $n \to \infty$. – user17762 Nov 2 '12 at 21:53
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http://cpr-astrophco.blogspot.com/2013/08/13080884-k-thorat-et-al.html
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## Environments of Extended Radio Sources in the ATLBS Survey [PDF]
K. Thorat, L. Saripalli, R. Subrahmanyan
We present a study of the environments of extended radio sources in the Australia Telescope Low Brightness Survey (ATLBS). The radio sources were selected from the Extended Source Sample (ATLBS-ESS), which is a well defined sample containing the most extended of radio sources in the ATLBS sky survey regions. The environments were analyzed using 4-m CTIO Blanco telescope observations carried out for ATLBS fields in the SDSS ${\rm r}^{\prime}$ band. We have estimated the properties of the environments using smoothed density maps derived from galaxy catalogs constructed using these optical imaging data. The angular distribution of galaxy density relative to the axes of the radio sources has been quantified by defining anisotropy parameters that are estimated using a new method presented here. Examining the anisotropy parameters for a sub-sample of extended double radio sources that includes all sources with pronounced asymmetry in lobe extents, we find good evidence for environmental anisotropy being the dominant cause for lobe asymmetry in that higher galaxy density occurs almost always on the side of the shorter lobe, and this validates the usefulness of the method proposed and adopted here. The environmental anisotropy parameters have been used to examine and compare the environments of FRI and FRII radio sources in two redshift regimes ($z<0.5$ and $z>0.5$). Wide-angle tail sources and Head-tail sources lie in the most overdense environments. The Head-tail source environments (for the HT sources in our sample) display dipolar anisotropy in that higher galaxy density appears to lie in the direction of the tails. Excluding the Head-tail and Wide-angle tail sources, subsamples of FRI and FRII sources from the ATLBS survey appear to lie in similar moderately overdense environments, with no evidence for redshift evolution in the regimes studied herein.
View original: http://arxiv.org/abs/1308.0884
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https://doubtnut.com/ncert-solutions/class-9-maths-chapter-9-areas-of-parallelograms-and-triangles-1
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# Areas Of Parallelograms And Triangles NCERT Solutions : Class 9 Maths
## NCERT Solutions for Class 9 Maths : Areas Of Parallelograms And Triangles
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### NCERT Class 9 | AREAS OF PARALLELOGRAMS AND TRIANGLES | Exercise 02 | Question No. 01
In Fig. 9.15, ABCD is a parallelogram, A E_|_D C and C F_|_A D . If A B"\ "="\ "16"\ "c m , A E"\ "="\ "8"\ "c m and C F"\ "="\ "10"\ "c m , find AD.
### NCERT Class 9 | AREAS OF PARALLELOGRAMS AND TRIANGLES | Exercise 02 | Question No. 02
If E,F,G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that a r(E F G H) =1/2a r(A B C D)
### NCERT Class 9 | AREAS OF PARALLELOGRAMS AND TRIANGLES | Exercise 02 | Question No. 03
P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that a r"\ "(A P B)"\ "="\ "a r"\ "(B Q C) .
### NCERT Class 9 | AREAS OF PARALLELOGRAMS AND TRIANGLES | Exercise 02 | Question No. 04
In Fig. 9.16, P is a point in the interior of a parallelogram ABCD. Show that (i) a r(A P B)+a r(P C D)=1/2a r(A B C D) (ii) a r(A P D)+a r(P B C)=a r(A P B)+ar(P C D)
### NCERT Class 9 | AREAS OF PARALLELOGRAMS AND TRIANGLES | Exercise 02 | Question No. 05
In Fig. 9.17, PQRS and ABRS are parallelograms and X is any point on side BR. Show that (i) a r(P Q R S) = a r(A B R S) (ii) a r(A XS)"\ "=1/2 ar(P Q R S)
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Get here free, accurate and comprehensive NCERT Solutions for Class 9 Maths Areas Of Parallelograms And Triangles which have been reviewed by our maths counsellors as per the latest edition following up the CBSE guidelines. We provide video solutions in which solutions to all the questions of NCERT Class 9 Maths textbook are explained in step by step and detailed way.
## The Topics of the Chapter Areas Of Parallelograms And Triangles are :
PARALLELOGRAM
INTRODUCTION
PARALLELOGRAM ON THE SAME BASE AND BETWEEN THE SAME PARALLELS
TRIANGLE ON THE SAME BASE AND BETWEEN THE SAME PARALLELS
CONGRUENCE
It contains these exercises along with solved examples. All the exercises are solved in the video. Select the exercise to view the solutions exercisewise of the Chapter Areas Of Parallelograms And Triangles:
## NCERT Solutions Class 9 Maths Chapter Areas Of Parallelograms And Triangles Exercises:
We have covered all the exercises and also Solved examples in the videos. Along with the practise exercise Students should also practise solved examples to clear the concepts of the Areas Of Parallelograms And Triangles. If incase you have any doubt you can watch the solutions for the given questions.Watch the solutions for the given questions in which it is also explained in the video steps to solve the questions along with answers.
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## Area of Parallelograms and Triangles – Class 9 Maths NCERT Solutions
The chapter as the name suggests deals with the two major shapes called parallelogram and triangles.
Area of parallelogram = base (B) × Perpendicular height (h)
Area of triangle= base*height/2
### DEFINITION:
#### PARALLELOGRAM
A flat shape with four straight sides. The opposite sides are equal and parallel to each other.
#### TRIANGLE
A shape that has three straight lines.
UNIT: SI UNIT: meter ²
CGS UNIT: centimeter ²
### FIGURES ON THE SAME BASE AND BETWEEN THE SAME PARALLELS
EXAMPLE:
Figures are said to be on the same base and between same parallels if they are sharing the common base and their opposite sides are parallel to each other.
In the given fig: 6.44 DBC and BDA shares the same base that is BI and lies between the same parallel that is CD and AB, hence through this concept it’s is found that
Area of (ABC) ∕ Area of (DBC) =AO ∕ DO
EXAMPLE: If a triangle and a parallelogram are on the same base and between same parallels, then prove that the area of a triangle is equal to half the area of a parallelogram.
SOL: let ABP and parallelogram ABCD are on the same base AB and between the same parallel AB and PC (fig 9.14)
We wish to prove that area (PAB) =½ area (ABCD)
Drawing BQ ‖ AP to obtain another parallelogram ABQP. Now parallelograms ABQP and ABCD are on the same base AB and between same parallel AB and PC.
So, two figures are said to be on the same base and between same parallels, if they have a common base (sides) and vertices (or the vert*) opposite to the common base if each figure lies on a line parallel to the base.
### PARALLELOGRAMS ON THE SAME BASE AND BETWEEN THE SAME PARALLELS:
EXAMPLE:
In the given figure we can see that the parallelogram ABCD and EFCD share the same base that is DC and lies between the same parallels that are AF and CD.
THEOREM:
The parallelograms sharing the same base and lies between the same parallels are equal.
In ABFD, DF ‖ AD (given as AB‖CD) and BF‖AD (by construction) Thus, both pairs of opposite sides are parallel. Hence, ABFD is a parallelogram. In ABCE, EC ‖ AB (given as AB‖CD) and AE‖BC (by construction) Thus, both pairs of opposite pairs are parallels. Hence, ABCE is a parallelogram.
Thus, ABFD and ABCE are two parallelograms with same base AB and between two parallels AB and EF.
→ Area (ABFD) = area (ABCE) (the area between same parallels and on the same base are equal)
### TWO TRIANGLES ON THE SAME BASE AND BETWEEN THE SAME PARALLELS
EXAMPLE:
ABD and ABC are triangles on the same base that is AB and between same parallels lines that is AB and DC.
THEOREM:
Two triangles on the same base or sharing the same base and between the same parallel lines are equal.
Given: ADB and ABC are a triangle on the base AB and between the same parallels AB and DC
Construction:
Construct a line through A parallel to BC meeting DC at E that is AE‖BC and construct a line through B parallel to AD meeting DC at F that is BF‖AD.
In other words, the two triangles lying on the same base and between the same parallels are equal in areas.
The relation between the area of a triangle and the area of a parallelogram:
Given: A parallelogram ABCD and ABP on the same base AB and between the same parallels.
To Prove: area of a triangle is equal to half the area of parallelogram area (ABP) = ½ area (ABCD)
Construction: Join DP
Let DM AB and PN AB
Proof: area of the triangle ABP is half the area of parallelogram ABCD.
### AREA OF A PARALLELOGRAM
Area of a parallelogram is the product of base and perpendicular dropped on that base from its opposite vert*.
Area of parallelogram =base× perpendicular height
### AREA OF A TRIANGLE
Area of a triangle is the product of the perpendicular height of the triangle and base divided by 2(half the product of base and height
Area of triangle=½(base × perpendicular height)
EXAMPLES:
Question: P and Q are any point lying on the side DC and AD, respectively of a parallelogram ABCD shows that ar(APB) = ar(BQC)
Solution: given. A parallelogram ABCD .P and Q are any two points lying on the sides DC and AD, respectively.
Now, parallelograms ABCD and BQC stand on the same base BC and lie between the same parallel lines BC and AD.
Therefore (BQC) = ½ area (ABCD) 1
Similarly APB and parallelogram ABCD stands on the same base AB and lie between the same parallel AB and CD
Therefore area (APB) = ½area (ABCD) 2
From equation (1) and (2) we get,
Area (APB) =area (BQC)
EXAMPLE:
How to find the area of the following triangle?
SOLUTION:
Area of a parallelogram is equal to b*h
Two triangles make the parallelogram
Area of one triangle is equal to ½area of a parallelogram
Area of the triangle is equal to ½(b×h).
### RULES TO DO THE QUESTIONS OF AREA OF PARALLELOGRAM AND TRIANGLES
1. Identifying figures lying on the same base and between the same parallels.
2. Relate the areas of the figures lying between the same base and between the same parallels.
SOME IMPORTANT POINTS:
A parallelogram is a quadrilateral that is it is made up of 4 lines segments in which the opposite sides are parallel and equal.
EXAMPLES of quadrilaterals are – a rectangle, a square, a rhombus, and they are also a special type of parallelograms.
Properties of a parallelogram are-
1. Area of a parallelogram is equal to base × altitude.
2. Sum of four angles of a parallelogram is 360 degrees.
3. Diagonals of a parallelogram bisect each other.
4. The sum of adjacent angles of a parallelogram is 180 degrees.
### FOR A QUADRILATERAL THESE FOUR STATEMENTS ARE EQUIVALENT
1. Diagonals bisect one another.
2. Opposite sides are parallel.
3. Opposite angles are equal.
4. Opposite sides are equal.
## Significance of NCERT Mathematics Book for Class 9
NCERT Mathematics book for Class 9 makes the transition to the class easier for students and students don’t feel that difficult to adapt to the new difficulties. The concepts are explained in a very easy to understand manner and a huge question bank is provided to practice questions and grasp concepts to depth. Learning from this book makes learning processes easy and students easily cope with the class.
Some important features of the book are:
• Easy to understand and detailed explanation of concepts.
• A huge question bank to practice questions from.
• Notes, formulas and important things are given at the end of every chapter.
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http://openstudy.com/updates/50ca73aee4b09c557144e197
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alfira 2 years ago help please! Delete Cancel Submit
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1. across
• 2 years ago
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We're here to help.
2. alfira
• 2 years ago
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1 Attachment
3. alfira
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find the horzontal asymptotes
4. across
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All you have to do is determine the behavior of $$f$$ as it approaches both $$-\infty$$ and $$\infty$$, i.e.,$\lim_{x\to\infty}\frac{x^2+3}{\sqrt{x^2+1}}=?$
5. alfira
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equal to 1 ?
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y=1?
7. across
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How did you get that?
8. alfira
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x^2 / X^2 +3/x^2
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everything divided by x^2
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because highest power in the function is x^2
11. across
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Recall that$\lim_{x\to\infty}\frac{x^2+3}{\sqrt{x^2+1}}=\lim_{x\to\infty}\frac{x^2}{\sqrt{x^2}}=\lim_{x\to\infty}\frac{x^2}{|x|}=\lim_{x\to\infty}x=\infty.$
12. across
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So it has no horizontal asymptote as $$x\to\infty$$. What about $$x\to-\infty$$?
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same thing ?
14. across
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Right.
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thanks `
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http://lilypond.org/doc/v2.23/Documentation/internals/petruccistaff
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### 2.1.24 PetrucciStaff
Same as Staff context, except that it is accommodated for typesetting a piece in Petrucci style.
This context also accepts commands for the following context(s): Staff.
This context sets the following properties:
• Set grob property bar-extent in BarLine to:
'(-2.5 . 2.5)
• Set grob property bar-extent in SignumRepetitionis to:
'(-2.5 . 2.5)
• Set grob property hair-thickness in BarLine to 2.21.
• Set grob property hair-thickness in SignumRepetitionis to 2.21.
• Set grob property kern in BarLine to 2.9.
• Set grob property kern in SignumRepetitionis to 2.9.
• Set grob property neutral-direction in Custos to -1.
• Set grob property neutral-position in Custos to 3.
• Set grob property rounded in BarLine to #t.
• Set grob property rounded in SignumRepetitionis to #t.
• Set grob property style in Custos to 'mensural.
• Set grob property thick-thickness in BarLine to 2.9.
• Set grob property thick-thickness in SignumRepetitionis to 2.9.
• Set grob property thickness in StaffSymbol to 1.3.
• Set translator property autoAccidentals to:
'(Staff #<procedure 557eaffcd0c0 at /build/out/share/lilypond/current/scm/lily/music-functions.scm:1682:0 (context pitch barnum)>
#<procedure neo-modern-accidental-rule (context pitch barnum)>)
• Set translator property autoCautionaries to '().
• Set translator property clefGlyph to "clefs.petrucci.g".
• Set translator property clefPosition to -2.
• Set translator property clefTransposition to 0.
• Set translator property createSpacing to #t.
• Set translator property doubleRepeatBarType to "".
• Set translator property endRepeatBarType to "".
• Set translator property extraNatural to #f.
• Set translator property fineBarType to "|.".
• Set translator property ignoreFiguredBassRest to #f.
• Set translator property instrumentName to '().
• Set translator property localAlterations to '().
• Set translator property measureBarType to "".
• Set translator property middleCClefPosition to -6.
• Set translator property middleCPosition to -6.
• Set translator property ottavationMarkups to:
'((4 . "29")
(3 . "22")
(2 . "15")
(1 . "8")
(-1 . "8")
(-2 . "15")
(-3 . "22")
(-4 . "29"))
• Set translator property printKeyCancellation to #f.
• Set translator property sectionBarType to "||".
• Set translator property shortInstrumentName to '().
• Set translator property startRepeatBarType to "||".
• Set translator property underlyingRepeatBarType to "".
This is not a ‘Bottom’ context; search for such a one will commence after creating an implicit context of type PetrucciVoice.
Context PetrucciStaff can contain CueVoice, NullVoice and PetrucciVoice.
This context is built from the following engraver(s):
Accidental_engraver
Make accidentals. Catch note heads, ties and notices key-change events. This engraver usually lives at Staff level, but reads the settings for Accidental at Voice level, so you can \override them at Voice.
accidentalGrouping (symbol)
If set to 'voice, accidentals on the same note in different octaves may be horizontally staggered if in different voices.
autoAccidentals (list)
List of different ways to typeset an accidental.
For determining when to print an accidental, several different rules are tried. The rule that gives the highest number of accidentals is used.
Each entry in the list is either a symbol or a procedure.
symbol
The symbol is the name of the context in which the following rules are to be applied. For example, if context is Score then all staves share accidentals, and if context is Staff then all voices in the same staff share accidentals, but staves do not.
procedure
The procedure represents an accidental rule to be applied to the previously specified context.
The procedure takes the following arguments:
context
The current context to which the rule should be applied.
pitch
The pitch of the note to be evaluated.
barnum
The current bar number.
The procedure returns a pair of booleans. The first states whether an extra natural should be added. The second states whether an accidental should be printed. (#t . #f) does not make sense.
autoCautionaries (list)
List similar to autoAccidentals, but it controls cautionary accidentals rather than normal ones. Both lists are tried, and the one giving the most accidentals wins. In case of draw, a normal accidental is typeset.
extraNatural (boolean)
Whether to typeset an extra natural sign before accidentals that reduce the effect of a previous alteration.
harmonicAccidentals (boolean)
If set, harmonic notes in chords get accidentals.
internalBarNumber (integer)
Contains the current barnumber. This property is used for internal timekeeping, among others by the Accidental_engraver.
keyAlterations (list)
The current key signature. This is an alist containing (step . alter) or ((octave . step) . alter), where step is a number in the range 0 to 6 and alter a fraction, denoting alteration. For alterations, use symbols, e.g. keyAlterations = #((6 . ,FLAT)).
localAlterations (list)
The key signature at this point in the measure. The format is the same as for keyAlterations, but can also contain ((octave . name) . (alter barnumber . measureposition)) pairs.
Properties (write)
localAlterations (list)
The key signature at this point in the measure. The format is the same as for keyAlterations, but can also contain ((octave . name) . (alter barnumber . measureposition)) pairs.
This engraver creates the following layout object(s): Accidental, AccidentalCautionary, AccidentalPlacement and AccidentalSuggestion.
Alteration_glyph_engraver
Set the glyph-name-alist of all grobs having the accidental-switch-interface to the value of the context’s alterationGlyphs property, when defined.
alterationGlyphs (list)
Alist mapping alterations to accidental glyphs. Alterations are given as exact numbers, e.g., -1/2 for flat. This applies to all grobs that can print accidentals.
Axis_group_engraver
Group all objects created in this context in a VerticalAxisGroup spanner.
currentCommandColumn (graphical (layout) object)
Grob that is X-parent to all current breakable (clef, key signature, etc.) items.
hasAxisGroup (boolean)
True if the current context is contained in an axis group.
keepAliveInterfaces (list)
A list of symbols, signifying grob interfaces that are worth keeping a staff with remove-empty set around for.
Properties (write)
hasAxisGroup (boolean)
True if the current context is contained in an axis group.
This engraver creates the following layout object(s): VerticalAxisGroup.
Bar_engraver
Create barlines. This engraver is controlled through the whichBar property. If it has no bar line to create, it will forbid a linebreak at this point. This engraver is required to trigger the creation of clefs at the start of systems.
doubleRepeatBarType (string)
Bar line to insert where the end of one \repeat volta coincides with the start of another. The default is ‘:..:’.
doubleRepeatSegnoBarType (string)
Bar line to insert where an in-staff segno coincides with the end of one \repeat volta and the beginning of another. The default is ‘:|.S.|:’.
endRepeatBarType (string)
Bar line to insert at the end of a \repeat volta. The default is ‘:|.’.
endRepeatSegnoBarType (string)
Bar line to insert where an in-staff segno coincides with the end of a \repeat volta. The default is ‘:|.S’.
fineBarType (string)
Bar line to insert at \fine. Where there is also a repeat bar line, the repeat bar line takes precedence and this value is appended to it as an annotation. The default is ‘|.’.
fineSegnoBarType (string)
Bar line to insert where an in-staff segno coincides with \fine. The default is ‘|.S’.
fineStartRepeatSegnoBarType (string)
Bar line to insert where an in-staff segno coincides with \fine and the start of a \repeat volta. The default is ‘|.S.|:’.
measureBarType (string)
Bar line to insert at a measure boundary.
repeatCommands (list)
A list of commands related to volta-style repeats. In general, each element is a list, '(command args…), but a command with no arguments may be abbreviated to a symbol; e.g., '((start-repeat)) may be given as '(start-repeat).
end-repeat
End a repeated section.
start-repeat
Start a repeated section.
volta text
If text is markup, start a volta bracket with that label; if text is #f, end a volta bracket.
sectionBarType (string)
Bar line to insert at \section. Where there is also a repeat bar line, the repeat bar line takes precedence and this value is appended to it as an annotation. The default is ‘||’.
segnoBarType (string)
Bar line to insert at an in-staff segno. The default is ‘S’.
segnoStyle (symbol)
A symbol that indicates how to print a segno: bar-line or mark.
startRepeatBarType (string)
Bar line to insert at the start of a \repeat volta. The default is ‘.|:’.
startRepeatSegnoBarType (string)
Bar line to insert where an in-staff segno coincides with the start of a \repeat volta. The default is ‘S.|:’.
underlyingRepeatBarType (string)
Bar line to insert at points of repetition or departure where no bar line would normally appear, for example at the end of a system broken in mid measure where the next system begins with a segno. Where there is also a repeat bar line, the repeat bar line takes precedence and this value is appended to it as an annotation. The default is ‘||’.
whichBar (string)
The current bar line type, or '() if there is no bar line. Setting this explicitly in user code is deprecated. Use \bar or related commands to set it.
Properties (write)
currentBarLine (graphical (layout) object)
Set to the BarLine that Bar_engraver has created in the current timestep.
forbidBreak (boolean)
If set to #t, prevent a line break at this point.
This engraver creates the following layout object(s): BarLine.
Clef_engraver
Determine and set reference point for pitches.
clefGlyph (string)
Name of the symbol within the music font.
clefPosition (number)
Where should the center of the clef symbol go, measured in half staff spaces from the center of the staff.
clefTransposition (integer)
Add this much extra transposition. Values of 7 and -7 are common.
clefTranspositionStyle (symbol)
Determines the way the ClefModifier grob is displayed. Possible values are ‘default’, ‘parenthesized’ and ‘bracketed’.
explicitClefVisibility (vector)
break-visibility’ function for clef changes.
forceClef (boolean)
Show clef symbol, even if it has not changed. Only active for the first clef after the property is set, not for the full staff.
This engraver creates the following layout object(s): Clef and ClefModifier.
Collision_engraver
Collect NoteColumns, and as soon as there are two or more, put them in a NoteCollision object.
This engraver creates the following layout object(s): NoteCollision.
Cue_clef_engraver
Determine and set reference point for pitches in cued voices.
clefTransposition (integer)
Add this much extra transposition. Values of 7 and -7 are common.
cueClefGlyph (string)
Name of the symbol within the music font.
cueClefPosition (number)
Where should the center of the clef symbol go, measured in half staff spaces from the center of the staff.
cueClefTransposition (integer)
Add this much extra transposition. Values of 7 and -7 are common.
cueClefTranspositionStyle (symbol)
Determines the way the ClefModifier grob is displayed. Possible values are ‘default’, ‘parenthesized’ and ‘bracketed’.
explicitCueClefVisibility (vector)
break-visibility’ function for cue clef changes.
middleCCuePosition (number)
The position of the middle C, as determined only by the clef of the cue notes. This can be calculated by looking at cueClefPosition and cueClefGlyph.
This engraver creates the following layout object(s): ClefModifier, CueClef and CueEndClef.
Custos_engraver
Engrave custodes.
This engraver creates the following layout object(s): Custos.
Dot_column_engraver
Engrave dots on dotted notes shifted to the right of the note. If omitted, then dots appear on top of the notes.
This engraver creates the following layout object(s): DotColumn.
Figured_bass_engraver
Make figured bass numbers.
Music types accepted: bass-figure-event and rest-event
figuredBassAlterationDirection (direction)
Where to put alterations relative to the main figure.
figuredBassCenterContinuations (boolean)
Whether to vertically center pairs of extender lines. This does not work with three or more lines.
figuredBassFormatter (procedure)
A routine generating a markup for a bass figure.
ignoreFiguredBassRest (boolean)
Don’t swallow rest events.
implicitBassFigures (list)
A list of bass figures that are not printed as numbers, but only as extender lines.
useBassFigureExtenders (boolean)
Whether to use extender lines for repeated bass figures.
This engraver creates the following layout object(s): BassFigure, BassFigureAlignment, BassFigureBracket, BassFigureContinuation and BassFigureLine.
Figured_bass_position_engraver
Position figured bass alignments over notes.
This engraver creates the following layout object(s): BassFigureAlignmentPositioning.
Fingering_column_engraver
Find potentially colliding scripts and put them into a FingeringColumn object; that will fix the collisions.
This engraver creates the following layout object(s): FingeringColumn.
Font_size_engraver
Put fontSize into font-size grob property.
fontSize (number)
The relative size of all grobs in a context.
Grob_pq_engraver
busyGrobs (list)
A queue of (end-moment . grob) cons cells. This is for internal (C++) use only. This property contains the grobs which are still busy (e.g. note heads, spanners, etc.).
Properties (write)
busyGrobs (list)
A queue of (end-moment . grob) cons cells. This is for internal (C++) use only. This property contains the grobs which are still busy (e.g. note heads, spanners, etc.).
Instrument_name_engraver
Create a system start text for instrument or vocal names.
currentCommandColumn (graphical (layout) object)
Grob that is X-parent to all current breakable (clef, key signature, etc.) items.
instrumentName (markup)
The name to print left of a staff. The instrumentName property labels the staff in the first system, and the shortInstrumentName property labels following lines.
shortInstrumentName (markup)
See instrumentName.
shortVocalName (markup)
Name of a vocal line, short version.
vocalName (markup)
Name of a vocal line.
This engraver creates the following layout object(s): InstrumentName.
Key_engraver
Engrave a key signature.
Music types accepted: key-change-event
createKeyOnClefChange (boolean)
Print a key signature whenever the clef is changed.
explicitKeySignatureVisibility (vector)
break-visibility’ function for explicit key changes. ‘\override’ of the break-visibility property will set the visibility for normal (i.e., at the start of the line) key signatures.
extraNatural (boolean)
Whether to typeset an extra natural sign before accidentals that reduce the effect of a previous alteration.
keyAlterationOrder (list)
A list of pairs that defines in what order alterations should be printed. The format of an entry is (step . alter), where step is a number from 0 to 6 and alter from -1 (double flat) to 1 (double sharp), with exact rationals for alterations in between, e.g., 1/2 for sharp.
keyAlterations (list)
The current key signature. This is an alist containing (step . alter) or ((octave . step) . alter), where step is a number in the range 0 to 6 and alter a fraction, denoting alteration. For alterations, use symbols, e.g. keyAlterations = #((6 . ,FLAT)).
lastKeyAlterations (list)
Last key signature before a key signature change.
middleCClefPosition (number)
The position of the middle C, as determined only by the clef. This can be calculated by looking at clefPosition and clefGlyph.
printKeyCancellation (boolean)
Print restoration alterations before a key signature change.
Properties (write)
keyAlterations (list)
The current key signature. This is an alist containing (step . alter) or ((octave . step) . alter), where step is a number in the range 0 to 6 and alter a fraction, denoting alteration. For alterations, use symbols, e.g. keyAlterations = #((6 . ,FLAT)).
lastKeyAlterations (list)
Last key signature before a key signature change.
tonic (pitch)
The tonic of the current scale.
This engraver creates the following layout object(s): KeyCancellation and KeySignature.
Ledger_line_engraver
Create the spanner to draw ledger lines, and notices objects that need ledger lines.
This engraver creates the following layout object(s): LedgerLineSpanner.
Merge_mmrest_numbers_engraver
Engraver to merge multi-measure rest numbers in multiple voices.
This works by gathering all multi-measure rest numbers at a time step. If they all have the same text and there are at least two only the first one is retained and the others are hidden.
Ottava_spanner_engraver
Create a text spanner when the ottavation property changes.
Music types accepted: ottava-event
currentMusicalColumn (graphical (layout) object)
Grob that is X-parent to all non-breakable items (note heads, lyrics, etc.).
middleCOffset (number)
The offset of middle C from the position given by middleCClefPosition This is used for ottava brackets.
ottavation (markup)
If set, the text for an ottava spanner. Changing this creates a new text spanner.
This engraver creates the following layout object(s): OttavaBracket.
Output_property_engraver
Apply a procedure to any grob acknowledged.
Music types accepted: apply-output-event
Piano_pedal_align_engraver
Align piano pedal symbols and brackets.
currentCommandColumn (graphical (layout) object)
Grob that is X-parent to all current breakable (clef, key signature, etc.) items.
This engraver creates the following layout object(s): SostenutoPedalLineSpanner, SustainPedalLineSpanner and UnaCordaPedalLineSpanner.
Piano_pedal_engraver
Engrave piano pedal symbols and brackets.
Music types accepted: sostenuto-event, sustain-event and una-corda-event
currentCommandColumn (graphical (layout) object)
Grob that is X-parent to all current breakable (clef, key signature, etc.) items.
pedalSostenutoStrings (list)
See pedalSustainStrings.
pedalSostenutoStyle (symbol)
See pedalSustainStyle.
pedalSustainStrings (list)
A list of strings to print for sustain-pedal. Format is (up updown down), where each of the three is the string to print when this is done with the pedal.
pedalSustainStyle (symbol)
A symbol that indicates how to print sustain pedals: text, bracket or mixed (both).
pedalUnaCordaStrings (list)
See pedalSustainStrings.
pedalUnaCordaStyle (symbol)
See pedalSustainStyle.
This engraver creates the following layout object(s): PianoPedalBracket, SostenutoPedal, SustainPedal and UnaCordaPedal.
Pure_from_neighbor_engraver
Coordinates items that get their pure heights from their neighbors.
Rest_collision_engraver
Handle collisions of rests.
busyGrobs (list)
A queue of (end-moment . grob) cons cells. This is for internal (C++) use only. This property contains the grobs which are still busy (e.g. note heads, spanners, etc.).
This engraver creates the following layout object(s): RestCollision.
Script_row_engraver
Determine order in horizontal side position elements.
This engraver creates the following layout object(s): ScriptRow.
Separating_line_group_engraver
Generate objects for computing spacing parameters.
createSpacing (boolean)
Create StaffSpacing objects? Should be set for staves.
Properties (write)
hasStaffSpacing (boolean)
True if currentCommandColumn contains items that will affect spacing.
This engraver creates the following layout object(s): StaffSpacing.
Signum_repetitionis_engraver
Create a SignumRepetitionis at the end of a \repeat volta section.
Music types accepted: volta-repeat-end-event
This engraver creates the following layout object(s): SignumRepetitionis.
Skip_typesetting_engraver
Create a StaffEllipsis when skipTypesetting is used.
skipTypesetting (boolean)
If true, no typesetting is done, speeding up the interpretation phase. Useful for debugging large scores.
This engraver creates the following layout object(s): StaffEllipsis.
Staff_collecting_engraver
Maintain the stavesFound variable.
stavesFound (list of grobs)
A list of all staff-symbols found.
Properties (write)
stavesFound (list of grobs)
A list of all staff-symbols found.
Staff_symbol_engraver
Create the constellation of five (default) staff lines.
Music types accepted: staff-span-event
This engraver creates the following layout object(s): StaffSymbol.
Time_signature_engraver
Create a TimeSignature whenever timeSignatureFraction changes.
Music types accepted: time-signature-event
initialTimeSignatureVisibility (vector)
break visibility for the initial time signature.
partialBusy (boolean)
Signal that \partial acts at the current timestep.
timeSignatureFraction (fraction, as pair)
A pair of numbers, signifying the time signature. For example, '(4 . 4) is a 4/4 time signature.
This engraver creates the following layout object(s): TimeSignature`.
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https://mattymatica.com/2016/07/12/newtons-switcheroo/
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# Newton’s Switcheroo
For in much wisdom is much grief, And he who increases knowledge increases sorrow.
(Ecclesiastes 1:18) NKJV
How massive is the sun? That depends on what assumption you make, regarding frame of reference, before you do any math.
• If you assume heliocentricity first, then the value for the mass of the sun is:
• 1.9E+30 kg
• If you assume Geocentrosphericity then you get a different number:
• 1.88E+19 kg
• The difference is a factor of 9.87E-12 (Matty’s Constant)
We all have the same evidence. Our choice of paradigm determines what we think it’s evidence of.
Matty’s Razor
The calculation used to derive a mass for the sun incorporates Kepler’s third law of planetary motion and Newton’s law of universal gravitation as a mathematical expression of the following statement:
How massive is the Sun..
.. if it’s in orbit (of known radius and duration)
.. of the Earth (of known mass)*?
– Matty
Change the a priori assumption: the sun orbits the Earth (known mass) at a known radius and duration and the calculated mass for the sun that is now a fraction of what you get by assuming heliocentricity.
Faith is believing in something that you can’t see, because of evidence.
– Faith, definition
#### Newton’s Law of Universal Gravitation
• F force between masses
• G gravitational constant (6.674×10−11 N · (m/kg)2)
• m1 first mass
• m2 second mass
• r distance between the centers of the masses
The proportional difference between the mass of the Earth and the mass of the sun is simply reversed. Naturally this affects the masses of all of the other planets in our system, but it doesn’t change any of the observed orbital mechanics. The math is the same, the laws are the same, the view from Earth is indistinguishable. The mass of the sun is only determined by your choice of paradigm, not by any facts. What you believe is a choice.
## Donate
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If you need to belong somewhere, find a local church. If you’d like to help, please consider donating.
## One Reply to “Newton’s Switcheroo”
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https://www.gradesaver.com/textbooks/math/other-math/CLONE-547b8018-14a8-4d02-afd6-6bc35a0864ed/chapter-2-multiplying-and-dividing-fractions-review-exercises-page-190/38
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## Basic College Mathematics (10th Edition)
$2\frac{1}{2}$
$\frac{\frac{15}{18}}{\frac{10}{30}}$ To divide two fractions, multiply the first fraction by the reciprocal of the divisor (the second fraction). $\frac{15}{18}\times\frac{30}{10}$ To multiply. multiply the numerator and multi ply the denominators. = $\frac{15\times30}{18\times10}$ = $\frac{5}{2}$ = $\frac{4+1}{2}$ = $2\frac{1}{2}$
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https://socratic.org/questions/circle-a-has-a-center-at-2-7-and-an-area-of-81-pi-circle-b-has-a-center-at-4-3-a
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Geometry
Topics
# Circle A has a center at (2 ,7 ) and an area of 81 pi. Circle B has a center at (4 ,3 ) and an area of 36 pi. Do the circles overlap? If not, what is the shortest distance between them?
Apr 24, 2018
$\textcolor{b l u e}{\text{Circles intersect}}$
#### Explanation:
First we find the radii of A and B.
Area of a circle is $\pi {r}^{2}$
Circle A:
$\pi {r}^{2} = 81 \pi \implies {r}^{2} = 81 \implies r = 9$
Circle B:
$\pi {r}^{2} = 36 \pi \implies {r}^{2} = 36 \implies r = 6$
Now we know the radii of each we can test whether they intersect, touch in one place or do not touch.
If the sum of the radii is equal to the distance between the centres, then the circles touch in one place only.
If the sum of the radii is less than the distance between centres, then the circles do not touch
If the sum of the radii is greater than the distance between centres then the circles intersect.
We find the distance between centres using the distance formula.
d=sqrt((x_2-x_1)^2+(y_2-y_1^2)
$d = \sqrt{{\left(2 - 4\right)}^{2} + {\left(7 - 3\right)}^{2}} = 2 \sqrt{2}$
$9 + 6 = 15$
$15 > 2 \sqrt{2}$
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https://www.studyadda.com/notes/6th-class/science/changes-around-us/changes-arorund-us/16131
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# 6th Class Science Changes Around us Changes Arorund Us
Changes Arorund Us
Category : 6th Class
Changes Around Us
Changes Around Us
We observe changes around us all the time. Changes may occur in shape, size, mass, density, colour, position, temperature, structure or in composition of a substance. So we can define a change as:
‘Transformation in one or more than one physical or chemical properties of a substance is called change’.
Types of Changes
Types of changes on the basis of either the changes can be reversed to bring back the original substance or not:
Reversible Change
A change which can be reversed to form the 'original substance' is called reversible change.
For example, melting of ice, freezing of water, dissolution of salt in water, increase in temperature of a metal rod, etc.
Irreversible Changes
A change which cannot be reversed to form the 'original substance' called irreversible change.
For example, burning of wood, ripening of fruit, turning milk sour, etc.
Types of changes on the basis of either a new substance is formed or not:
Physical Change
The change, in which molecules of a substance do not undergo any change or no new substances are formed, are called physical changes. For example, melting of ice, freezing of water, evaporation of water, dissolution of salt in water.
Chemical Change
The change, in which molecules of substance undergo change or new substances are formed, are called chemical changes. For example, burning of paper, rusting of iron, spoliation of food, etc.
Types of changes on the basis of heat absorbed or evolved:
Exothermic
The change in which heat is released. For example, burning of wood.
Endothermic
The change in which heat is absorbed. For example, melting of ice.
#### Other Topics
##### 30 20
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http://www.physicsforums.com/showthread.php?t=179383
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# Does this make sense?
by pivoxa15
Tags: sense
P: 2,268 A,B are sets A + B=AuB + AnB Does it make sense to add sets? I know union and intersections are possible.
HW Helper
P: 3,680
Quote by pivoxa15 A,B are sets A + B=AuB + AnB Does it make sense to add sets? I know union and intersections are possible.
What do you mean that to do? Additive number theory has addition of sets like $X+Y=\{x+y:x\in X,y\in Y \}$ (so that {1, 2, 3} + {10, 40} = {11, 12, 13, 41, 42, 43}). Is that what you want?
P: 2,268 No. I am talking about sets in measure theory.
P: 5,891
## Does this make sense?
Quote by pivoxa15 A,B are sets A + B=AuB + AnB Does it make sense to add sets? I know union and intersections are possible.
You ccan define "+" to mean anything you want. What is the point of your definition?
PF Gold
P: 2,330
Quote by pivoxa15 A,B are sets A + B=AuB + AnB Does it make sense to add sets? I know union and intersections are possible.
I take that to mean that you want an element that is in both A and B to show up twice in the sum of A and B? The sum then could not be a set since there are no dupllcates in sets. What kind of object do you want the sum to be, a bag, a.k.a. multiset?
PF Gold P: 1,059 honestrosewater: I take that to mean that you want an element that is in both A and B to show up twice in the sum of A and B? I take it that he wants to say: A +B = A union B-A intersection B.
PF Gold
P: 2,330
Quote by robert Ihnot I take it that he wants to say: A +B = A union B-A intersection B.
Oh. So symmetric difference (more) then?
PF Gold P: 1,059 If we take the sets {1,2,3} + {2,3,4} = {1,2,3,4}= A U B, which for n=1 to 4 is the whole set. Thus $$A\cup B+A\cap B =A\cup B$$ (I don't think measure theory has any effect on that.) However if we thought of these as collections, then we would have: {1,2,3}+{2,3,4} = {1,2,2,3,3,4} (From Wikipedia: When two or more collections are combined into a single collection, the number of objects in the single collection is the sum of the number of objects in the original collections. ) This is easier to follow if we were thinking of collections of furniture like lamps, rugs, etc. So I believe that you are correct about the symmetric difference of sets.
PF Gold
P: 2,330
Quote by robert Ihnot If we take the sets {1,2,3} + {2,3,4} = {1,2,3,4}= A U B, which for n=1 to 4 is the whole set. Thus $$A\cup B+A\cap B =A\cup B$$ (I don't think measure theory has any effect on that.)
Is this what you meant previously? You seem to have just defined this addition to be union. The symmetric difference is "the set of elements belonging to one but not both of two given sets", i.e., "A union B-A intersection B", which I assume you meant as "(A union B) - (A intersection B)", with "-" denoting set difference (A - B = {x | x in A and x not in B}).
The original definition, "A + B=AuB + AnB" appears to be circular since the symbol that it is defining is used in the definition, so who knows. Normally, when you add two things, the result includes, in a loose sense, all of what you started with. For sets, this would seem to simply be union, but I assume the OP had something more than union in mind. You at least don't usually lose, or subtract, things when you add, so I assume the OP was thinking that the sum of two sets should include everything that was in those sets in some way that union doesn't, i.e., by including any duplicates.
Sci Advisor HW Helper P: 3,680 Since you say measure theoretic, perhaps you mean measure(a) + measure(b) = measure(a union b) + measure (a intersect b)? (for finitely additive measures, of course!)
PF Gold P: 1,059 Yes, you are right. Measure is a mathematical concept, so we can use the plus or minus sign. So that in general: $$A\cup B = A+B-A\cap B$$
Math Emeritus Sci Advisor Thanks PF Gold P: 38,705 But that equation doesn't say anything about measure! Do you mean having first defined A+ B as $$A\cup B + A\cap B$$. Of course, as has been pointed out, that is just equal to $$A\cup B[/itex] It WOULD make sense if you would do what people have been asking you to do and write the "measure": [tex] measure(A\cup B) = measure(A)+ measure(B)-measure(A\cap B)$$
P: 1,572
Quote by CRGreathouse Since you say measure theoretic, perhaps you mean measure(a) + measure(b) = measure(a union b) + measure (a intersect b)? (for finitely additive measures, of course!)
this form might be better because it works even if measure(a intersect b) is infinite.
Sci Advisor HW Helper P: 9,398 In what sense is that better? It is clearly wrong.
P: 1,572
Quote by matt grime In what sense is that better? It is clearly wrong.
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http://openstudy.com/updates/50168d12e4b04dfc808ab0c9
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## lgbasallote Group Title uranium hexafluoride is a solid at room temperature, but it boils at $$56^o C$$.determine the density of uranium hexafluoride at $$60^o C$$ and 745 torr. i know d = m/v and PV = nRT but how can i use them here? or do i even use them here? 2 years ago 2 years ago Edit Question Delete Cancel Submit
• This Question is Closed
1. zbay
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you can solve for n and get the mass using the periodic table and then you can solve for v
• 2 years ago
2. lgbasallote
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• 2 years ago
3. Carniel
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Just get m and v :P
• 2 years ago
4. lgbasallote
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how to get V?
• 2 years ago
5. lgbasallote
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and m
• 2 years ago
6. Carniel
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Use the other formula to find them ^_^
• 2 years ago
7. lgbasallote
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how the heck can i get m o.O
• 2 years ago
8. lgbasallote
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and V
• 2 years ago
9. lgbasallote
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i dont think the "other formulas" can be applied
• 2 years ago
10. lgbasallote
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can you demonstrate how>
• 2 years ago
11. NotTim
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wats torr
• 2 years ago
12. lgbasallote
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if i remember right 760 torr = 1 atm...torr is a unit of measurement for pressure
• 2 years ago
13. NotTim
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p=745 torr v=? n=? R=? T=60-56 (i think) d=? (looking for) m=? v=?
• 2 years ago
14. NotTim
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• 2 years ago
15. NotTim
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on what @zbay say.
• 2 years ago
16. NotTim
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but you still need m huh
• 2 years ago
17. SUROJ
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do you know $p =\rho \times r \times T \div M$ where rho is density and M is molecular mass
• 2 years ago
18. SUROJ
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P is pressure
• 2 years ago
19. SUROJ
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since n= m/M , you can get m/V = rho
• 2 years ago
20. lgbasallote
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uhhh could you rewrite that equation you wrote? kinda vague... $\huge P = \frac{\rho RT}{M}$
• 2 years ago
21. lgbasallote
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is that right?
• 2 years ago
22. SUROJ
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ya
• 2 years ago
23. SUROJ
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looks like it works :)
• 2 years ago
24. lgbasallote
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how did you get this formula again?
• 2 years ago
25. SUROJ
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n=m/M right?
• 2 years ago
26. lgbasallote
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oh i see now
• 2 years ago
27. lgbasallote
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so $\frac{PM}{RT} = \rho$ right? R = 0.0821
• 2 years ago
28. SUROJ
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ya exactly
• 2 years ago
29. lgbasallote
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so which T am i going to use?
• 2 years ago
30. lgbasallote
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60?
• 2 years ago
31. NotTim
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probably, because that's the one that applies to this situation
• 2 years ago
32. SUROJ
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the temperature at which u have to find density
• 2 years ago
33. lgbasallote
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so what's 56 for? just a distraction?
• 2 years ago
34. SUROJ
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ya I guess
• 2 years ago
35. lgbasallote
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hmm then i need to convert torr into atm and C into K right
• 2 years ago
36. SUROJ
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yup and 1 torr = 1 atm
• 2 years ago
37. lgbasallote
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i thought it was 760 torr = 1 atm o.O
• 2 years ago
38. SUROJ
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oo idk
• 2 years ago
39. lgbasallote
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hmm okay thanks
• 2 years ago
40. lgbasallote
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what would be the unit?
• 2 years ago
41. lgbasallote
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i got the answer as 126.76 g/L is that right?
• 2 years ago
42. NotTim
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i dunno
• 2 years ago
43. zbay
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set n to 1 and solve for V then you take the molar mass of the molecule you are looking at and calculate your density
• 2 years ago
44. zbay
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R is a constant.
• 2 years ago
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http://docmadhattan.fieldofscience.com/2014/
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### Arthur and the eclipse
by @ulaulaman about #ArthurEddington #AlbertEinstein #GeneralRelativity
On the 17th November 1922, Albert Einstein, accompanied by his wife, arrived in Kobe (see the report of the visit published on the AAPPS Bulletin - pdf). Here he was surrounded by journalists and fans: while the first asked him questions, the latter were on the hunt for an autograph from one of the most famous physicists and scientists of the time. Einstein, as written by Naoki Urasawa on the initial pages of Billy Bat #9, to a specific question on why he won the Nobel Prize for the photoelectric effect and not for the theory of special and general relativity, replied:
Because, that can't be verified.
But the mangaka committed a chronological mistake, probably caused by the Urasawa's need to focus on the innovation represented by the Einstein's theories: the point, in fact, is that just three years earlier, on the 6th November, 1919, during a meeting of the Royal Society and Royal Astronomical Society, Arthur Eddington presented the results of the celestial observations made in mid-spring of that year. The interest and the importance of the discovery was such that the next day, the Times headlined:
Revolution in Science: New Theory of the Universe: Newton's Ideas Overthrown, by Joseph John Thomson:
Our conceptions about the structure of the universe must be changed in a fundamental way
So, when Einstein went to Japan, the evidence of the correctness of his theory had already been around.
### The hobbit, the dragon, and the green knight
by @ulaulaman about #TheHobbit #JRRTolkien #Smaug #mathematics
Gandalf and Bilbo by David Wenzel
The Peter Jackson's Hobbit movie trilogy is arrived to a conclusion, so it could be a good point to write a little, funny curious post about the science and the Tolkien's novel. We start with a paper published last year(1) (2013) in which the researchers find the cause of the triumph of good over evil:
Bilbo Baggins, a hobbit, lives in a hole in the ground but with windows, and when he is first encountered he is smoking his pipe in the sun overlooking his garden (it is worth noting [parenthetically] that smoking is itself associated with skeletal muscle dysfunction6). Dwarves and wizards smoke too, and the production of smoke rings is unfortunately glamourised. The hobbit diet is clearly varied as he is able to offer cake, tea, seed cake, ale, porter, red wine, raspberry jam, mince pies, cheese, pork pie, salad, cold chicken, pickles and apple tart to the dwarves who visit to engage him in the business of burglary. The dwarves also show evidence of a mixed diet and, importantly, although they “like the dark, the dark for dark business”, they do spend much time above ground and have plenty of sun exposure during the initial pony ride in June that begins their trip to the Lonely Mountain.
(...)
Gollum, himself "as dark as darkness" lives in the dark, deep in the Misty Mountains. He does, however, eat fish, although the text describes these only as "blind" and it is not clear whether they are of an oily kind and thus a potential source of vitamin D. He sometimes eats goblins, but they rarely come down to his lake, suggesting that fish play little part in the goblin diet. Interestingly, these occasional trips to catch fish are undertaken at the behest of the Great Goblin, leading one to speculate that his enhanced diet may have helped him to achieve his pre-eminent position within goblin society. In due course, the Great Goblin is replaced by the Son of the Great Goblin. While simple nepotism is a likely explanation, we are unable to exclude an epigenetic process whereby the son’s fitness to rule has been influenced by parental vitamin D exposure.(1)
So the secret is in the diet!
Another great character from The Hobbit is Smaug, the dragon. Its physiology is really peculiar (read also Disco Blog):
### When and why the coffee spills
http://t.co/fBhTs48KG4 the #physics of spilling and walking with #coffee
How do we spill coffee?
(a) Either by accelerating too much for a given coffee level (fluid statics)
(b) Or, through more complicated dynamical phenomena:
• Initial acceleration sets an initial sloshing amplitude, which is analogous to the main antisymmetric mode of sloshing.
• This initial perturbation is amplified by the back-and-forth and pitching excitations since their frequency is close to the natural one because of the choice of normal mug dimensions.
• Vertical motion also does not lead to resonance as it is a subharmonic excitation (Faraday phenomena).
• Noise has higher frequency, which makes the antisymmetric mode unstable thus generating a swirl.
• Time to spill depends on "focused"/"unfocused" regime and increases with decreasing maximum acceleration (walking speed).
How can we prevent spilling?
Lessons learned from sloshing dynamics may suggest strategies to control spilling, e.g. via using
• a flexible container to act as a sloshing absorber in suppressing liquid oscillations.
• a series of concentric rings (baffles) arranged around the inner wall of a container.
Text via Walking with coffee: when and why coffee spills (pdf)
More information on physics buzz blog
Paper: Mayer H.C. & Krechetnikov R. (2012). Walking with coffee: Why does it spill?, Physical Review E, 85 (4) DOI: http://dx.doi.org/10.1103/physreve.85.046117 (pdf)
### The globe of Galileo
video by @ulaulaman #levitation
Published by Gianluigi (@ulaulaman) in data:
It's just a little Earth, turns and levitates above its base, reminding those who contributed to give it its rightful place in space. The globe can light up using the switch on the base. It works in the current network.
### Fabiola Gianotti, Director General at CERN
http://t.co/rYzcXWlvR0 about #FabiolaGianotti #CERN #ATLAS
Fabiola Gianotti is an Italian particle physicist, a former spokesperson of the ATLAS experiment at the Large Hadron Collider (LHC) at CERN in Switzerland, considered one of the world's biggest scientific experiments. She has been selected as the next Director-General of CERN, starting on 1 January 2016.
She is the 4th italian particle physicist to became Director General at CERN after Amaldi (1952-1954), Rubbia (1989-1993) and Maiani (1999-2003).
A bit concession to the SEO!
### Planck results, ATLAS and the dark matter
http://t.co/jJxD8rhCr6 by @ulaulaman about #Planck, #ATLAS, #DarkMatter at #LHC
The last issue of Astronomy & Astrophysics (that it's free) is devoted to the Planck 2013 results:
This collection of 31 articles presents the initial scientific results extracted from this first Planck dataset, which measures the cosmic microwave background (CMB) with the highest accuracy to date. It provides major new advances in different domains of cosmology and astrophysics.
In the first paper there is an overview of 2013 science results, and we can read:
The Universe observed by Planck is well-fit by a six parameter, vacuum-dominated, cold dark matter (ACDM) model, and we provide strong constraints on deviations from this model.
But, in the meanwhile, ATLAS published a preprint about the quest of the dark matter in LHC:
The data are found to be consistent with the Standard Model expectations and limits are set on the mass scale of effective field theories that describe scalar and tensor interactions between dark matter and Standard Model particles. Limits on the dark-matter--nucleon cross-section for spin-independent and spin-dependent interactions are also provided. These limits are particularly strong for low-mass dark matter. Using a simplified model, constraints are set on the mass of dark matter and of a coloured mediator suitable to explain a possible signal of annihilating dark matter.
Tommaso Dorigo, examining ATLAS' results, concludes:
the ATLAS search increases significantly the sensitivity with respect to past searches, but no signal is found. As attractive as DM existence is as an economical explanation of a wealth of cosmological observations, the nature of dark matter continues to remain unknown.
via phys.org
### Regge theory
http://t.co/alaasqcHwl @ulaulaman says #goodbye to #TullioRegge
In quantum physics, Regge theory is the study of the analytic properties of scattering as a function of angular momentum, where the angular momentum is not restricted to be an integer but is allowed to take any complex value. The nonrelativistic theory was developed by Tullio Regge in 1957.
Following Chew and Frautschi (pdf), the key papers by Tullio Regge are:
Regge T. (1959). Introduction to complex orbital momenta, Il Nuovo Cimento, 14 (5) 951-976. DOI: http://dx.doi.org/10.1007/bf02728177 (pdf)
In this paper the orbital momentumj, until now considered as an integer discrete parameter in the radial Schrödinger wave equations, is allowed to take complex values. The purpose of such an enlargement is not purely academic but opens new possibilities in discussing the connection between potentials and scattering amplitudes. In particular it is shown that under reasonable assumptions, fulfilled by most field theoretical potentials, the scattering amplitude at some fixed energy determines the potential uniquely, when it exists. Moreover for special classes of potentials $V(x)$, which are analytically continuable into a function $V(z)$, $z=x+iy$, regular and suitable bounded in $x > 0$, the scattering amplitude has the remarcable property of being continuable for arbitrary negative and large cosine of the scattering angle and therefore for arbitrary large real and positive transmitted momentum. The range of validity of the dispersion relations is therefore much enlarged.
Regge T. (1960). Bound states, shadow states and mandelstam representation, Il Nuovo Cimento, 18 (5) 947-956. DOI: http://dx.doi.org/10.1007/bf02733035
In a previous paper a technique involving complex angular momenta was used in order to prove the Mandelstam representation for potential scattering. One of the results was that the number of subtractions in the transmitted momentum depends critically on the location of the poles (shadow states) of the scattering matrix as a function of the complex orbital momentum. In this paper the study of the position of the shadow states is carried out in much greater detail. We give also related inequalities concerning bound states and resonances. The physical interpretation of the shadow states is then discussed.
The importance of the model is summarized by the following:
As a fundamental theory of strong interactions at high energies, Regge theory enjoyed a period of interest in the 1960s, but it was largely succeeded by quantum chromodynamics. As a phenomenological theory, it is still an indispensable tool for understanding near-beam line scattering and scattering at very large energies. Modern research focuses both on the connection to perturbation theory and to string theory.
During the 1980s, Regge is interested also in the mathematical art, using Anschauliche Geometrie by David Hilbert and Stefan Cohn-Vossen like inspiration for a lot of mathematical objects.
Good bye, Mr. Regge, and thanks for all...
### Alan Guth, eternal inflation and the multiverse
http://t.co/CnvvOY0mAI about #AlanGuth #multiverse #CosmicInflation #icep2014
At the beggining of October, Alan Guth was at the workshop Fine-Tuning, Anthropics and the String Landscape at Madrid, and he concluded his talk with the following slide:
The complete talk, without question time, follows:
### Just a bit of blue
http://t.co/hgbABOxUlm by @ulaulaman about #nobelprize2014 on #physics #led #light #semiconductors
Created with SketchBookX
One of the first classifications that you learn when you start to study the behavior of matter interacting with electricity is between conductors and insulators: a conductor is a material that easily allows the passage of electric charges; on the other hand, an insulator prevents it (or makes it difficult). It is possible to characterize these two kinds of materials through the physical characteristics of the atoms that compose them. Indeed, we know that an atom is characterized by having a positive nucleus with electron clouds which rotate around it: to characterize a material is precisely the behavior of the outer electrons, those of the external band. On the other hand, the energy bands of every atom are characterized by specific properties: there are the valence bands, where the electrons are used in the chemical bonds, and the conduction bands, where the electrons are free to move, the "mavericks" of the atom, used for ionic bonds. At this point I hope it is simple to characterize a conductive material such as the one whose atoms have electrons both in the valence band, both in the conduction band, while an insulating material is characterized by having full only the valence band.
Now, in band theory, the probability that an electron occupies a given band is calculated using the Fermi-Dirac distribution: this means that there is a non-zero probability that an insulator's electron in the valence band is promoted to the conduction band, but it is extremely low because of the large energy difference between the two levels. Moreover, there is an energy level said Fermi level that, while in the conductors is located within the conduction band, in the insulation is located between the two bands, the conduction and valence, allowing a valence electron to jump more easily in the conduction band.
### Teachers for the peace
http://t.co/W1K0rh9An6 #nobelprize2014 #peace #children #education #teaching
The Nobel Prize for Peace 2014 is awarded to Kailash Satyarthi and Malala Yousafzai, teachers and activists for children rights,
for their struggle against the suppression of children and young people and for the right of all children to education
### Carlo Rubbia and the discoveries of the weak bosons
http://t.co/KGVNarwZMG by @ulaulaman about #CarloRubbia #NobelPrize #physics #particlephysics
On that day 30 years ago, I was almost certainly at school. Physics still was not my passion. Of course I started very well: when the teacher asked what is the space, I thought immediately to the universe, but the question was not referring to that "space", but in another, the geometric. But it is not about those memories that I have to indulge, but on a particular photo, in which Carlo Rubbia and Simon van der Meer, with two goblets, presumably of wine in hand, are celebrating the announcement of the Nobel Prize for Physics
for their decisive contributions to the large project, which led to the discovery of the field particles W and Z, communicators of weak interaction
The story of this Nobel, however, began eight years earlier, in 1976. In that year, in fact, SPS, the Super Proton Synchrotron, begins to operate at CERN, originally designed to accelerate particles up to an energy of 300 GeV.
The same year David Cline, Carlo Rubbia and Peter McIntyre proposed transforming the SPS into a proton-antiproton collider, with proton and antiproton beams counter-rotating in the same beam pipe to collide head-on. This would yield centre-of-mass energies in the 500-700 GeV range(1).
On the other hand antiprotons must be somehow collected. The corresponding beam was then
(...) stochastically cooled in the antiproton accumulator at 3.5 GeV, and this is where the expertise of Simon Van der Meer and coworkers played a decisive role(1).
### Sudoku clues
http://t.co/zk3P3rPjFZ #sudoku #mathematics #arXiv #abstract
The arXiv's paper is published two years ago, but I think that every time is a good time to play sudoku!
The sudoku minimum number of clues problem is the following question: what is the smallest number of clues that a sudoku puzzle can have? For several years it had been conjectured that the answer is 17. We have performed an exhaustive computer search for 16-clue sudoku puzzles, and did not find any, thus proving that the answer is indeed 17. In this article we describe our method and the actual search. As a part of this project we developed a novel way for enumerating hitting sets. The hitting set problem is computationally hard; it is one of Karp's 21 classic NP-complete problems. A standard backtracking algorithm for finding hitting sets would not be fast enough to search for a 16-clue sudoku puzzle exhaustively, even at today's supercomputer speeds. To make an exhaustive search possible, we designed an algorithm that allowed us to efficiently enumerate hitting sets of a suitable size.
In the following video by Numberphile, James Grime discusses the paper results:
### From Nash equilibria to collective behavior
https://twitter.com/ulaulaman/status/517303481565458432 by @ulaulaman about #Nash equilibria and their role in collective behavior
The Nash equilibrium is an important tool in game theory:
[It] is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy. If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
Stated simply, Amy and Will are in Nash equilibrium if Amy is making the best decision she can, taking into account Will's decision, and Will is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others in the game.
Nash equilibria may, for example, be found in the game of coordination, in the prisoner's dilemma, in the paradox of Braess(6), or more generally in any strategy game. In particular, given a game, we can ask whether it has or not a Nash equilibrium: apparently deciding the existence of Nash equilibria is an intractable problem, if there is no restriction on the relationships among players. In addition for a strong Nash equilibrium, the problem is on the second level of the polynomial hierarchy, which is a scale for the classification problem based on the complexity of resolution(1).
In addition to this study about Nash equilibria, Gianluigi Greco (one of my high school classmates), together with Francesco Scarcello, also studied the Nash equilibria (in this case the forced equilibria) in graphical games, where graphical game is a game represented in a graphical manner, through a graph(2).
### CERN's 60th Birthday
http://t.co/zU9b7V4idL by @ulaulaman about #CERN60
The day to celebrate CERN's birthday is arrived:
The convention establishing CERN was ratified on 29 September 1954 by 12 countries in Western Europe. The acronym CERN originally stood in French for Conseil Européen pour la Recherche Nucléaire (European Council for Nuclear Research), which was a provisional council for setting up the laboratory, established by 12 European governments in 1952. The acronym was retained for the new laboratory after the provisional council was dissolved, even though the name changed to the current Organisation Européenne pour la Recherche Nucléaire (European Organization for Nuclear Research) in 1954.
The most recent discovery at the laboratories is the Higgs boson (or a particle that seems it), but there are some others successes in the CERN's history:
1973: The discovery of neutral currents in the Gargamelle bubble chamber;
1983: The discovery of W and Z bosons in the UA1 and UA2 experiments;
1989: The determination of the number of light neutrino families at the Large Electron–Positron Collider (LEP) operating on the Z boson peak;
1995: The first creation of antihydrogen atoms in the PS210 experiment;
1999: The discovery of direct CP violation in the NA48 experiment;
2010: The isolation of 38 atoms of antihydrogen;
2011: Maintaining antihydrogen for over 15 minutes;
There are two Nobel Prizes directly connected to the CERN:
1984: to Carlo Rubbia and Simon Van der Meer for
their decisive contributions to the large project which led to the discovery of the field particles W and Z, communicators of the weak interaction
1992: to Georges Charpak for
his invention and development of particle detectors, in particular the multiwire proportional chamber, a breakthrough in the technique for exploring the innermost parts of matter
On CERN's webcast you can see the official ceremony
### Foucault and the pendulum
http://t.co/AphFwEZfQ2 #foucaultpendulum #physics #earthrotation
The first public exhibition of a Foucault pendulum took place in February 1851 in the Meridian of the Paris Observatory. A few weeks later Foucault made his most famous pendulum when he suspended a 28 kg brass-coated lead bob with a 67 meter long wire from the dome of the Panthéon, Paris. The plane of the pendulum's swing rotated clockwise 11° per hour, making a full circle in 32.7 hours. The original bob used in 1851 at the Panthéon was moved in 1855 to the Conservatoire des Arts et Métiers in Paris. A second temporary installation was made for the 50th anniversary in 1902.
During museum reconstruction in the 1990s, the original pendulum was temporarily displayed at the Panthéon (1995), but was later returned to the Musée des Arts et Métiers before it reopened in 2000. On April 6, 2010, the cable suspending the bob in the Musée des Arts et Métiers snapped, causing irreparable damage to the pendulum and to the marble flooring of the museum. An exact copy of the original pendulum had been swinging permanently since 1995 under the dome of the Panthéon, Paris until 2014 when it was taken down during repair work to the building. Current monument staff estimate the pendulum will be re-installed in 2017
### Idiosyncratic Thinking: a computer heuristics lecture
http://t.co/7JB3CPaQt9 #Feynman
Richard Feynman, Winner of the 1965 Nobel Prize in Physics, gives us an insightful lecture about computer heuristics: how computers work, how they file information, how they handle data, how they use their information in allocated processing in a finite amount of time to solve problems and how they actually compute values of interest to human beings. These topics are essential in the study of what processes reduce the amount of work done in solving a particular problem in computers, giving them speeds of solving problems that can outmatch humans in certain fields but which have not yet reached the complexity of human driven intelligence. The question if human thought is a series of fixed processes that could be, in principle, imitated by a computer is a major theme of this lecture and, in Feynman's trademark style of teaching, gives us clear and yet very powerful answers for this field which has gone on to consume so much of our lives today.
### Experiments with inertia
a coulpe of home experiments about #inertia
### Witches Kitchen 1971
http://t.co/sHn7nJ4uFj a #funny image about #mathematics by Alexander Grothendieck
Riemann-Roch Theorem: The final cry: The diagram is commutative! To give an approximate sense to the statement about f: X → Y, I had to abuse the listeners' patience for almost two hours. Black on white (in Springer lecture notes) it probably takes about 400, 500 pages. A gripping example of how our thirst for knowledge and discovery indulges itself more and more in a logical delirium far removed from life, while life itself is going to Hell in a thousand ways and is under the threat of final extermination. High time to change our course!
Alexander Grothendieck about the Grothendieck–Riemann–Roch theorem via Math 245
Read also: how does one understand GRR?
### Aidan Dwyer and a new fotovoltaic design
Aidan Dwyer, was one of twelve students to receive the 2011 Young Naturalist Award from the American Museum of Natural History in New York for creating an innovative approach to collecting sunlight in photovoltaic arrays. Dwyer’s investigation into the mathematical relationship of the arrangement of branches and leaves in deciduous trees led to his discovery that these species utilized the Fibonacci Sequence in their branch and leaf design. Dwyer transformed this organic concept into a photovoltaic array based upon the Fibonacci pattern of an oak tree and conducted experiments comparing his design to conventional solar panel arrays. After computer analysis, Dwyer discovered that his Fibonacci tree design surpassed the performance of conventional methods in sunlight collection and utilized the greatest quantity of PV panels within the least amount of physical space, making it a versatile and aesthetically pleasing solution for confined and obstructed urban areas.
### The discover of Morniel Mathaway
http://youtu.be/OoYkZyZ6XSU a radio drama by William Tenn
Following Deutsch and Lockwood(1), there are two types of time paradoxes: inconsistency paradox and knowledge paradox.
An example of the first type is the grandfather paradox, introduced by the french writer René Barjavel in Le voyageur imprudent (1943 - Future Times Three).
An example of the second type is The discover of Morniel Mathaway, a radio science fiction drama by William Tenn. It was originally transmitted by the show X Minus One by NBC:
A professor of art history from the future travels by time machine some centuries into the past in search of an artist whose works are celebrated in the professor's time. On meeting the artist in the flesh, the professor is surprised to find the artist’s current paintings talentlessly amateurish. The professor happens to have brought with him from the future a catalogue containing reproductions of the paintings later attributed to the artist, which the professor has come to see are far too accomplished to be the artist's work. When he shows this to the artist, the latter quickly grasps the situation, and, by means of a ruse, succeeds in using the time machine to travel into the future (taking the catalogue with him), where he realizes he will be welcomed as a celebrity, so stranding the professor in the "present". To avoid entanglements with authority the critic assumes the artist's identity and later achieves fame for producing what he believes are just copies of the paintings he recalls from the catalogue. This means that he, and not the artist, created the paintings in the catalogue. But he could not have done so without having seen the catalogue in the first place, and so we are faced with a causal loop.
### The solar efficiency of Superman
by @ulaulaman http://t.co/WGbVdfv0nk about #Superman #physics and #solar #energy
In the last saga of the JLA by Grant Morrison, World War III, Superman, leaping against the bomb inside Mageddon says:
The way in which Superman gets the powers, or the way in which them is explained, however, is changed over time. Following Action Comics #1, the debut of the character, Jerry Siegel, combining genetics and evolution, says that on his planet of origin
the physical structure of the inhabitants had advanced millions of years compared to ours. Reaching maturity, people of that race earned a titanic force!
In Superman #1, however, Siegel focuses attention on the different gravity between Earth and Krypton, with the latter with a greater radius than aour planet and therefore with a greater severity. Such a claim is also in Ports of Call by Jack Vance. In order to verify it, we must start from the definition of the density: $\rho = \frac{M}{V}$ where $M$ is the mass, $V$ the volume of the object, or, in our case, of the planet.
### Mathematics is a unique aspect of human thought
http://t.co/h9CCSAaER0 #IsaacAsimov about #mathematics
Mathematics is a unique aspect of human thought, and its history differs in essence from all other histories.
As time goes on, nearly every field of human endeavor is marked by changes which can be considered as correction and/or extension. Thus, the changes in the evolving history of political and military events are always chaotic; there is no way to predict the rise of a Genghis Khan, for example, or the consequences of the short-lived Mongol Empire. Other changes are a matter of fashion and subjective opinion. The cave-paintings of 25,000 years ago are generally considered great art, and while art has continuously-even chaotically-changed in the subsequent millennia, there are elements of greatness in all the fashions. Similarly, each society considers its own ways natural and rational, and finds the ways of other societies to be odd, laughable, or repulsive.
But only among the sciences is there true progress; only there is the record one of continuous advance toward ever greater heights.
And yet, among most branches of science, the process of progress is one of both correction and extension. Aristotle, one of the greatest minds ever to contemplate physical laws, was quite wrong in his views on falling bodies and had to be corrected by Galileo in the 1590s. Galen, the greatest of ancient physicians, was not allowed to study human cadavers and was quite wrong in his anatomical and physiological conclusions. He had to be corrected by Vesalius in 1543 and Harvey in 1628. Even Newton, the greatest of all scientists, was wrong in his view of the nature of light, of the achromaticity of lenses, and missed the existence of spectral lines. His masterpiece, the laws of motion and the theory of universal gravitation, had to be modified by Einstein in 1916.
Now we can see what makes mathematics unique. Only in mathematics is there no significant correction-only extension. Once the Greeks had developed the deductive method, they were correct in what they did, correct for all time. Euclid was incomplete and his work has been extended enormously, but it has not had to be corrected. His theorems are, every one of them, valid to this day.
Ptolemy may have developed an erroneous picture of the planetary system, but the system of trigonometry he worked out to help him with his calculations remains correct forever.
Each great mathematician adds to what came previously, but nothing needs to be uprooted. Consequently, when we read a book like A History Of Mathematics, we get the picture of a mounting structure, ever taller and broader and more beautiful and magnificent and with a foundation, moreover, that is as untainted and as functional now as it was when Thales worked out the first geometrical theorems nearly 26 centuries ago.
Nothing pertaining to humanity becomes us so well as mathematics. There, and only there, do we touch the human mind at its peak.
Isaac Asimov from the foreword to the second edition of A History of Mathematics by Carl C. Boyer and Uta C. Merzbach
### Maryam Mirzakhani and Riemann surfaces
http://t.co/ZAdRPeiy8b Maryam Mirzakhani wins #FieldsMedal with Riemann surfaces
Maryam Mirzakhani has made several contributions to the theory of moduli spaces of Riemann surfaces. In her early work, Maryam Mirzakhani discovered a formula expressing the volume of a moduli space with a given genus as a polynomial in the number of boundary components. This led her to obtain a new proof for the conjecture of Edward Witten on the intersection numbers of tautology classes on moduli space as well as an asymptotic formula for the length of simple closed geodesics on a compact hyperbolic surface. Her subsequent work has focused on Teichmüller dynamics of moduli space. In particular, she was able to prove the long-standing conjecture that William Thurston's earthquake flow on Teichmüller space is ergodic.
Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces".
Riemann surfaces are one dimensional complex manifolds introduced by Riemann: in some sense, his approach is a cut-and-paste procedure.
He imagined taking as many copies of the open set as there are branches of the function and joining them together along the branch cuts. To understand how this works, imagine cutting out sheets along the branch curves and stacking them on top of the complex plane. On each sheet, we define one branch of the function. We glue the different sheets to each other in such a way that the branch of the function on one sheet joins continuously at the seam with the branch defined on the other sheet. For instance, in the case of the square root, we join each end of the sheet corresponding to the positive branch with the opposite end of the sheet corresponding to the negative branch. In the case of the logarithm, we join one end of the sheet corresponding to the $2 \pi n$ branch with an end of the $(2n+1) \pi n$ sheet to obtain a spiral structure which looks like a parking garage.
A more formal approach to the construction of Riemann surfaces is performed by Hermann Weyl, and the work by Maryam Mirzakhani puts in this line of research.
Some papers:
Mirzakhani M. (2007). Weil-Petersson volumes and intersection theory on the moduli space of curves, Journal of the American Mathematical Society, 20 (01) 1-24. DOI: http://dx.doi.org/10.1090/s0894-0347-06-00526-1
Mirzakhani M. (2006). Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Inventiones mathematicae, 167 (1) 179-222. DOI: http://dx.doi.org/10.1007/s00222-006-0013-2 (pdf)
Mirzakhani M. (2008). Growth of the number of simple closed geodesics on hyperbolic surfaces, Annals of Mathematics, 168 (1) 97-125. DOI: http://dx.doi.org/10.4007/annals.2008.168.97 (pdf)
Read also:
Press release by Stanford
The Fields Medal news on Nature
The official press release in pdf
plus math magazine
### The equation of happiness
by @ulaulaman http://t.co/crZXpaphqA #mathematics #happiness #smile
$H(t) = w_0 + w_1 \sum_{j=1}^t \gamma^{t-j} CR_j + w_2 \sum_{j=1}^t \gamma^{t-j} EV_j + w_3 \sum_{j=1}^t \gamma^{t-j} RPE_j$ I don't know if my intuition is correct, but the equation from Rutledge et al. reminds me of a neural network, or more correctly a sum of three different neural networks. In every case, this could became an important step in order to mathematically describe our brain.
A common question in the social science of well-being asks, "How happy do you feel on a scale of 0 to 10?" Responses are often related to life circumstances, including wealth. By asking people about their feelings as they go about their lives, ongoing happiness and life events have been linked, but the neural mechanisms underlying this relationship are unknown. To investigate it, we presented subjects with a decision-making task involving monetary gains and losses and repeatedly asked them to report their momentary happiness. We built a computational model in which happiness reports were construed as an emotional reactivity to recent rewards and expectations. Using functional MRI, we demonstrated that neural signals during task events account for changes in happiness.
Rutledge R.B., Skandali N., Dayan P. & Dolan R.J. (2014). A computational and neural model of momentary subjective well-being., Proceedings of the National Academy of Sciences of the United States of America, PMID: http://www.ncbi.nlm.nih.gov/pubmed/25092308
via design & trends
### Generalized Venn diagram for genetics
by @ulaulaman http://t.co/MkGI7L546N #VennDay #VennDiagram #genetics
A generalized Venn diagram with three sets $A$, $B$ and $C$ and their intersections. From this representation, the different set sizes are easily observed. Furthermore, if individual elements (genes) are contained in more than one set (functional category), the intersection sizes give a direct view on how many genes are involved in possibly related functions. During optimization, the localization of the circles is altered to satisfy the possibly contradictory constraints of circle size and intersection size.
For the purpouse of the paper, the researchers used polygons instead of circles. In order to compute the polygons' area, they used the simple formula: $A = \sum_{k=1}^L x_k (y_{k+1} - y_k)$ where $L$ is the number of the edges of the polygon, and $y_{L+1} := y_1$.
Kestler, H., Muller, A., Gress, T., & Buchholz, M. (2004). Generalized Venn diagrams: a new method of visualizing complex genetic set relations Bioinformatics, 21 (8), 1592-1595 DOI: 10.1093/bioinformatics/bti169
### Turing's morphogenesis and the fingers' formation
by @ulaulaman http://t.co/9Q5rVkVzEc about #Turing #morphogenesis
On today Science's issue it is published a paper about the application of Turing's morphogenesis to the formation of fingers. In this period I'm not able to download the papers, so I simple publish the editor's summaries. First of all I present you the incipit of the paper by Aimée Zuniga, Rolf Zeller(2)
Alan Turing is best known as the father of theoretical computer sciences and for his role in cracking the Enigma encryption codes during World War II. He was also interested in mathematical biology and published a theoretical rationale for the self-regulation and patterning of tissues in embryos. The so-called reaction-diffusion model allows mathematical simulation of diverse types of embryonic patterns with astonishing accuracy. During the past two decades, the existence of Turing-type mechanisms has been experimentally explored and is now well established in developmental systems such as skin pigmentation patterning in fishes, and hair and feather follicle patterning in mouse and chicken embryos. However, the extent to which Turing-type mechanisms control patterning of vertebrate organs is less clear. Often, the relevant signaling interactions are not fully understood and/or Turing-like features have not been thoroughly verified by experimentation and/or genetic analysis. Raspopovic et al.(1) now make a good case for Turing-like features in the periodic pattern of digits by identifying the molecular architecture of what appears to be a Turing network functioning in positioning the digit primordia within mouse limb buds.
And now the summary of the results:
Most researchers today believe that each finger forms because of its unique position within the early limb bud. However, 30 years ago, developmental biologists proposed that the arrangement of fingers followed the Turing pattern, a self-organizing process during early embryo development. Raspopovic et al.(1) provide evidence to support a Turing mechanism (see the Perspective by Zuniga and Zeller). They reveal that Bmp and Wnt signaling pathways, together with the gene Sox9, form a Turing network. The authors used this network to generate a computer model capable of accurately reproducing the patterns that cells follow as the embryo grows fingers.
(1) Raspopovic, J., Marcon, L., Russo, L., & Sharpe, J. (2014). Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients Science, 345 (6196), 566-570 DOI: 10.1126/science.1252960
(2) Zuniga, A., & Zeller, R. (2014). In Turing's hands--the making of digits Science, 345 (6196), 516-517 DOI: 10.1126/science.1257501
Read also on Doc Madhattan:
Doc Madhattan: Matching pennies in Turing's brithday
Turing patterns in coats and sounds
Genetics, evolution and Turing's patterns
Calculating machines
Turing, Fibonacci and the sunflowers
Turing and the ecological basis of morphogenesis
via phys.org
### A trigonometric proof of the pythagorean theorem
by @ulaulaman via @MathUpdate http://t.co/LJX8gSX7xf
$\alpha + \beta = \frac{\pi}{2}$ $\sin (\alpha + \beta) = \sin \frac{\pi}{2}$ $\sin \alpha \cdot \cos \beta + \sin \beta \cdot \cos \alpha = 1$ $\frac{a}{c} \cdot \frac{a}{c} + \frac{b}{c} \cdot \frac{b}{c} = 1$ $\frac{a^2}{c^2} + \frac{b^2}{c^2} = 1$
$a^2 + b^2 = c^2$
via @MathUpdate
### Fifty years of CP violation
via @CERN http://t.co/9Rac42mBVh #CPviolation #CPsymmetry #matter #antimatter
The CP violation is a violation of the CP-symmetry, a combination between the charge conjugation symmetry (C) and the parity symmetry (P).
CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle, and then its spatial coordinates are inverted.
The CP violation is discovered in 1964 by Christenson, Cronin, Fitch, and Turlay (Cronin and Fitch awarded the Nobel Prize in 1980) studying the kaons' decays and it could have a key-role in the matter-antimatter imbalance.
Now the CERN Courier dadicated a special issue about the fifty years of the discovery (download here).
Christenson, J., Cronin, J., Fitch, V., & Turlay, R. (1964). Evidence for the 2π Decay of the K_{2}^{0} Meson Physical Review Letters, 13 (4), 138-140 DOI: 10.1103/PhysRevLett.13.138
### Gods, phylosophy and computers
by @ulaulaman http://t.co/Q3AODpvKAs #Godel #ontologicalproof #god #computer
The ontological arguments for the existence of God was introduced for the first time by St. Anselm in 1078:
God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist.
There are a lot of phylosophies, mathematics and logicians that proposed their ontological argument, for example Descartes, Leibniz, Frege, and also Kurt Gödel, that proposed the most formal ontological proof:
The proof was published in 1987 (Godel died in 1978), and a lot of logicians discussed around it. One of the last papers published about the argument is an arXiv that suggested to Anna Limind to write that European Mathematicians ‘Prove’ the Existence of God, but the aim of the paper is to control the consistence of the proof and not the reality of the theorem (I think that the theorem is, simply, undecidable), and also to start a new discipline: the computer-phylosophy.
Indeed Benzmüller and Paleo developed an algorothm in order to use a computer to control the ontological proof. So the work:
(...) opens new perspectives for a computerassisted theoretical philosophy. The critical discussion of the underlying concepts, definitions and axioms remains a human responsibility, but the computer can assist in building and checking rigorously correct logical arguments. In case of logico-philosophical disputes, the computer can check the disputing arguments and partially fulfill Leibniz' dictum: Calculemus
Read also: Spiegel Online International
Christoph Benzmüller & Bruno Woltzenlogel Paleo (2013). Formalization, Mechanization and Automation of Gödel's Proof of God's Existence, arXiv:
### How quantum mechanics explains global warming
posted by @ulaulaman about #globalwarming http://t.co/VDlaEt2s5m
The physician Mark Schleupner, a Ronaoke native, writes about global warming:
So, according to NASA scientists, if all the ice in 14 million sq km Antarctica melts, sea levels will rise more than 200 feet. Greenland alone has another huge chunk of the Earth’s water tied up in ice; some scientists say that its ice sheet has passed a tipping point and will be gone in the next centuries, raising ocean levels by 24 feet. These are scary amounts of sea level rise that put huge areas of population centers (New York, Boston, Miami, San Francisco, etc.) under water.
In the end, one can deny climate change (although I’d not recommend it), but one cannot deny math.
Well, it's really interesting, about the climate change, to see the following Ted-Ed lesson:
You've probably heard that carbon dioxide is warming the Earth. But how exactly is it doing it? Lieven Scheire uses a rainbow, a light bulb and a bit of quantum physics to describe the science behind global warming.
### Mathematicians discuss the Snowden revelations
In the last period I cannot read the Notices of AMS, so I lost the most recent discussion on this journal about the revelations made by Edward Snowden about NSA. Thanks to the n-category Café I recover the letters about this topic:
In the first part of 2013, Edward Snowden, a former contractor for the National Security Agency (NSA), handed over to journalists a trove of secret NSA documents. First described in the media in June 2013, these documents revealed extensive spying programs of the NSA and other governmental organizations, such as the United Kingdom's GCHQ (Government Communications Headquarters). The disclosures reverberated around the world, influencing the bottom lines of big businesses, the upper echelons of international relations, and the everyday activities of ordinary people whose lives are increasingly mirrored in the Internet and on cell phone networks.
The revelations also hit home in the mathematical sciences community. The NSA is often said to be the world's largest employer of mathematicians; it's where many academic mathematicians in the US see their students get jobs. The same is true for GCHQ in the UK. Many academic mathematicians in the US and the UK have done work for these organizations, sometimes during summers or sabbaticals. Some US mathematicians decided to take on NSA work after the 9/11 attacks as a contribution to national defense.
The discussion on Notices: part 1, part 2
### Beach sand for long cycle life batteries
#sand #battery #chemistry #energy
This is the holy grail – a low cost, non-toxic, environmentally friendly way to produce high performance lithium ion battery anodes
Zachary Favors
Schematic of the heat scavenger-assisted Mg reduction process.
Herein, porous nano-silicon has been synthesized via a highly scalable heat scavenger-assisted magnesiothermic reduction of beach sand. This environmentally benign, highly abundant, and low cost SiO2 source allows for production of nano-silicon at the industry level with excellent electrochemical performance as an anode material for Li-ion batteries. The addition of NaCl, as an effective heat scavenger for the highly exothermic magnesium reduction process, promotes the formation of an interconnected 3D network of nano-silicon with a thickness of 8-10 nm. Carbon coated nano-silicon electrodes achieve remarkable electrochemical performance with a capacity of 1024 mAhg−1 at 2 Ag−1 after 1000 cycles.
Favors, Z., Wang, W., Bay, H., Mutlu, Z., Ahmed, K., Liu, C., Ozkan, M., & Ozkan, C. (2014). Scalable Synthesis of Nano-Silicon from Beach Sand for Long Cycle Life Li-ion Batteries Scientific Reports, 4 DOI: 10.1038/srep05623
(via Popular Science)
### Mesons produced in a bubble chamber
by @ulaulaman about #mesons #bubblechamber #CERN #particles #physics
A bubble chamber is a pool filled with a liquid (typically hydrogen) such that its molecules are ionized to the passage of a charged particle, thus producing bubbles. In this way the trajectories of the particles are visible and it is possible to study the various decays(2).
The bubble chamber was invented by Donald Glaser(1) in 1952, who win the Nobel Prize in 1960.
(1) Glaser, D. (1952). Some Effects of Ionizing Radiation on the Formation of Bubbles in Liquids Physical Review, 87 (4), 665-665 DOI: 10.1103/PhysRev.87.665
(2) Image from the italian version of Weisskopf, V. (1968). The Three Spectroscopies Scientific American, 218 (5), 15-29 DOI: 10.1038/scientificamerican0568-15
### Brazuca, a Pogorelov's ball
posted by @ulaulaman about #Brazuca #geometry #WorldCup2014 #Brazil2014
Brazuca is the ball of the World Cup 2014. The particular pattern of its surface is a consequence of the Pogorelov's theorem about convex polyhedron:
A domain is convex if the segment joining any two of its points is completely contained within the field.
Now consider two convex domains in the plane whose boundaries are the same length.(1)
Now we can create a solid using the two previous domains: we must simlply connect every point of one boundary with a point of the other boundary, obtaining a convex polyhedron, like showed by Pogorelov in 1970s.
The object you have built consists of two developable surfaces glued together on edge.
Instead of using two domains, you can, for example, start from six convex domains as the "square faces" of a cube. On the edges of each of these areas, you choose four points, as the vertices of the "square". We assume that the four "corners" that you have chosen are like the vertices, that is to say that the domains have angles in these points.(1)
### The damages of the heavy metal
by @ulaulaman via @verascienza about #heavymetal #chemistry #health
A heavy metal is any metal or metalloid of environmental concern. The term originated with reference to the harmful effects of cadmium, mercury and lead, all of which are denser than iron. It has since been applied to any other similarly toxic metal, or metalloid such as arsenic, regardless of density. Commonly encountered heavy metals are chromium, cobalt, nickel, copper, zinc, arsenic, selenium, silver, cadmium, antimony, mercury, thallium and lead.
Heavy metals have a lot of detrimental effects on our body:
Aluminum - Damage to the central nervous system, dementia, memory loss
Antimony - Damage to heart, diarrhea, vomiting, stomach ulcer
Arsenic - Lymphatic cancer, liver cancer, skin cancer
Barium - Increased blood pressure, paralysis
Bismuth - Dermatitis, stomatitis, colitis, diarrhea
Cadmium - Diarrhea, stomach pains, vomiting, bone fractures, damage to the immune, psychological disorders
Chrome - Damage to the kidneys and liver, respiratory problems, lung cancer, death
Copper - Irritation of the nose, mouth and eyes, liver cirrhosis, brain damage and kidney
Gallium - Irritation of the throat, difficulty 'breathing, pain in the chest
Hafnium - Irritation of eyes, skin and mucous membranes
Indium - Damage to the heart, kidneys and liver
Iridium - Irritation of the eyes and digestive tract
Lanthanum - Lung cancer, liver damage
Lead - Fruits, vegetables, meats, cereals, wine, cigarettes contain. Cause brain damage, dysfunction at birth, kidney damage, learning disabilities, destruction of the nervous system
Manganese - Blood clotting, glucose intolerance, disorders of the skeleton
Mercury - Destruction of the nervous system, brain damage, DNA damage
Nickel - Pulmonary embolism, breathing difficulties, asthma and chronic bronchitis, allergic skin reaction
Palladium - Very toxic and carcinogenic, irritant
Platinum - Alterations of DNA, cancer, and damage to intestine and kidney
Rhodium - Stains the skin, potentially toxic and carcinogenic
Ruthenium - Very toxic and carcinogenic, damage to the bones
Scandium - Pulmonary embolism, threatens the liver when accumulated in the body
Silver - Used as a coloring agent E174, headache, breathing difficulties, skin allergies, with extreme concentration it causes coma and death
Strontium - Lung cancer, in children difficulty of bone development
Tantalum - Irritation to the eyes and to the skin, upper respiratory tract lesion
Thallium - Used as a rat poison, stomach damage, nervous system, coma and death for those who survive the remain Thallium nerve damage and paralysis
Tin - Irritation of the eyes and skin, headaches, stomach aches, difficulty to urinate
Tungsten - Damage to the mucous membranes and membranes, eye irritation
Vanadium - heart and cardiovascular disorders, inflammation of the stomach and intestine
Yttrium - Very toxic, lung cancer, pulmonary embolism, liver damage
via verascienza
### The Championships' Final
by @ulaulaman via @Airi_Talk about #WorldCup2014 #Brazil2014 predictions: #ESP-#GER
Jürgen Gerhards, Michael Mutz and Gert Wagner developed an economic model in order to predict the results of the football team during the international cups. The researchers evaluated the market value of every player and described every team with an economic price: in this way they predict the winners in 2006 (World Cup: Italy), 2008 (Euro Cup: Spain), 2010 (WC: Spain), 2012 (EC: Spain). Starting from the previous results, the three researchers realized the board of the challenges from the eighth:
The predicted final will be between Spain and Germany, with Spain favorite, but there is a little hope for the other teams, first of all Brazil: in 2012 the model didn't predict the other team in the final game of the Euro Cup: Italy, that should not have reached even into the semi-finals:
Marketization and globalization have changed professional soccer and the composition of soccer teams fundamentally. Against the background of these shifting conditions this paper investigates the extent to which the success of soccer teams in their national leagues is determined by (a) the monetary value of the team expressed in its market value, (b) inequality within the team, (c) the cultural diversity of the team, and (d) the degree of turnover among team members. The empirical analyses refer to the soccer season 2012/13 and include the twelve most important European soccer leagues. The findings demonstrate that success in a national soccer championship is highly predictable; nearly all of our hypotheses are confirmed. The market value of the team is, in today's world, by far the most important single predictor of athletic success in professional soccer.
Jürgen Gerhards, Michael Mutz, Gert Wagner (2014). Die Berechnung des Siegers: Marktwert, Ungleichheit, Diversität und Routine als Einflussfaktoren auf die Leistung professioneller Fußballteams. Zeitschrift für Soziologie, Jg. 43, Heft 3, 231-250
via University of Berlin, galileonet.it, airicerca.org
### Soccer balls
#abstract about #soccer #WorldCup
Soccer balls are typically constructed from 32 pentagonal and hexagonal panels. Recently, however, newer balls named Cafusa, Teamgeist 2, and Jabulani were respectively produced from 32, 14, and 8 panels with shapes and designs dramatically different from those of conventional balls. The newest type of ball, named Brazuca, was produced from six panels and will be used in the 2014 FIFA World Cup in Brazil. There have, however, been few studies on the aerodynamic properties of balls constructed from different numbers and shapes of panels. Hence, we used wind tunnel tests and a kick-robot to examine the relationship between the panel shape and orientation of modern soccer balls and their aerodynamic and flight characteristics. We observed a correlation between the wind tunnel test results and the actual ball trajectories, and also clarified how the panel characteristics affected the flight of the ball, which enabled prediction of the trajectory.
Hong S. & Asai T. (2014). Effect of panel shape of soccer ball on its flight characteristics., Scientific reports, 4 DOI:
### Portrait of an atom
by @ulaulaman about #hydrogen #atom #orbitals #Bohr #Rutherford #quantum_mechanics
The study of the structure of the atom is long story, and it begins with Democritus, or from the point of view of the modern science, with John Dalton in 1808: indeed he tried to fix in scientific terms the ideas of the greek philosopher and naturalist.
Dalton's theory was based on five fundamental points:
• matter is made of tiny building blocks called atoms, which are indivisible and indestructible;
• atoms of the same element are all equal to each other;
• the atoms of different elements combine with each other (via chemical reactions) in ratios of whole numbers and generally small, thus giving rise to compounds;
• atoms can be neither created nor destroyed;
• atoms of an element can not be converted into atoms of other elements.
As you can see, there are some other ideas correct and incorrect. We do, however, a jump of a century and we go to 1902 with Mr. Thomson, the first to propose an atomic model: he assumed that the atom was made up as a sort of cake, a positively charged sphere in which were scattered, like raisins, the electrons with a negative charge distribution such as to make the object as a whole neutral.
A few years later, however, in 1911, Rutherford devised and conducted an important experiment(1) in which he sent a beam of alpha particles against gold nuclei. The cross section observed, i.e. the surface on which the scattered particles resulting bump, it was too large to be compatible with the Thomson's hypothesis, but was compatible with that of Rutherford, namely that the atom was made up of a positive nucleus and by a number of electrons that revolved around the core itself at a large distance (compared to nuclear ones, of course).
However, this is not the last step: in 1913 Niels Bohr refined the Rutherford's model(2). Accepted the planetary structure of the atom, Bohr suggested that the electrons in their rotational motion, could not occupy orbits at their leisure, but they must themselves at very specific distances from the nucleus: this is the dawn of quantum mechanics, that further refine the atomic model thanks to the famous Schroedinger's equation.
The atom, now, was intended as a postive nucleus consists of protons and neutrons, with a little cloud of electrons that moved around, and not on an orbital but in a sort of spherical cap. And these caps at different energy was recently directly observed by Aneta Stodolna's team(3, 4):
(...) an experimental method was proposed about thirty years ago, when it was suggested that experiments ought to be performed projecting low-energy photoelectrons resulting from the ionization of hydrogen atoms onto a position-sensitive two-dimensional detector placed perpendicularly to the static electric field, thereby allowing the experimental measurement of interference patterns directly reflecting the nodal structure of the quasibound atomic wave function.(3)
via phys.org, io9
(1) Rutherfor E. (1911). The scattering of α and β particles by matter and the structure of the atom, Philosophical Magazine Series 6, 21 (125) 669-688. DOI:
(2) Bohr N. (1913). On the constitution of atoms and molecules, Philosophical Magazine Series 6, 26 (151) 1-25. DOI:
(3) Stodolna, A., Rouzée, A., Lépine, F., Cohen, S., Robicheaux, F., Gijsbertsen, A., Jungmann, J., Bordas, C., & Vrakking, M. (2013). Hydrogen Atoms under Magnification: Direct Observation of the Nodal Structure of Stark States Physical Review Letters, 110 (21) DOI: 10.1103/PhysRevLett.110.213001
(4) Smeenk, C. (2013). A New Look at the Hydrogen Wave Function Physics, 6 (58) DOI: 10.1103/Physics.6.58
### 15 Sorting Algorithms in 6 Minutes
Visualization and "audibilization" of 15 Sorting Algorithms in 6 Minutes.
Sorts random shuffles of integers, with both speed and the number of items adapted to each algorithm's complexity. The algorithms are: selection sort, insertion sort, quick sort, merge sort, heap sort, radix sort (LSD), radix sort (MSD), std::sort (intro sort), std::stable_sort (adaptive merge sort), shell sort, bubble sort, cocktail shaker sort, gnome sort, bitonic sort and bogo sort (30 seconds of it).
More information at the "Sound of Sorting"
### Mathematics of soccer: Shot angles
Consider a situation in which a soccer player runs straight, with tha ball, towards the bottom line of the field. Intuitively, it is clear that there is an optimal point maximizing the shot angle, providing the best place to kick in order to improve the chances to score a goal. If the player chooses the bottom line, the angle is zero and his chances are just horrible; if the player kicking far way, tha angle is also too small!
Locus of the optimal points
Two different types of kicks: Diego Armando Maradona in Napoli-Cesena 2-0, Serie A 1987/88, an amazing example of the "Maradona feeling" about the optimal place to kick
and the "impossible" goal by Marco Van Basten during the final of Euro '88
from "Mathematics of Soccer" by Alda Carvalho, Carlos Pereira dos Santos, Jorge Nuno Silva. "Recreational Mathematics Magazine" (2014)
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https://www.ti.inf.ethz.ch/ew/mise/mittagssem.html?action=show&what=abstract&id=311070c3cfc5bef23eaaef14d8fc9a7346d6c595
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## Theory of Combinatorial Algorithms
Prof. Emo Welzl and Prof. Bernd Gärtner
# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)
Mittagsseminar Talk Information
Date and Time: Thursday, November 26, 2015, 12:15 pm
Duration: 30 minutes
Location: CAB G51
Speaker: Dániel Korándi
## Saturation in random graphs
A graph $H$ is $K_s$-saturated if it is a maximal $K_s$-free graph, i.e., $H$ contains no clique on $s$ vertices, but the addition of any missing edge creates one. The minimum number of edges in a $K_s$-saturated graph was determined over 50 years ago by Zykov and independently by Erdős, Hajnal and Moon. In this talk, we consider the random analog of this problem: minimizing the number of edges in a maximal $K_s$-free subgraph of the Erdős-Rényi random graph $G(n,p)$. We give asymptotically tight estimates on this minimum, and also provide exact bounds for the related notion of weak saturation in random graphs.
Joint work with Benny Sudakov.
Information for students and suggested topics for student talks
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https://boxingpythagoras.com/tag/pseudoscience/
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# Boxing Pythagoras
## Proof that π=2√3
There is an inherent danger attached to blindly accepting the word of someone who sounds like they are presenting a rational, scientific claim. Too many people are willing to accept a proposition solely because they’ve heard it from someone who bears the appearance of intelligence. The line of thought seems to be, “Well, he’s smarter than me, so he must be right!” Unfortunately, this sort of fallacious reasoning goes largely unchecked, and often becomes formative in the common understanding of entire groups of people.
For almost the entirety of your mathematical education, you have been taught that the ratio of a circle’s circumference to its diameter, which we affectionately refer to as π, is something close to $3\frac{1}{7}$, or about 3.14; however, today I’m going to show you that your math teachers were wrong. In actuality, the value of π is exactly 2√3, or about 3.46.
## A Finely-Tuned Deception
William Lane Craig’s Reasonable Faith website released a new video, yesterday, highlighting the Fine-Tuning Argument, another extremely popular topic which is quite commonly discussed in modern apologetics circles. If you are unfamiliar with the argument, feel free to watch Craig’s video, below. You can also read the transcript for the video here, if you (like me) would like to digest its claims in a more easily referenced format.
I’m sure this won’t come as much of a surprise to anyone familiar with this blog, but I find that the video is wholly unconvincing. In fact, the entire Fine-Tuning argument is nothing more than a God-of-the-Gaps which has been camouflaged behind a screen of pseudoscience.
## Dissecting “The Sacred Geometry Movie” (Part 1?)
Coincidentally, soon after I posted about Sacred Geometry and The Ancient Secret of the Flower of Life, one of the most popular purveyors of pseudoscience on YouTube, Spirit Science, decided to release a movie one hour and forty-five minutes long discussing the subject. The film is, predictably, full of baseless assertions, nonsense, bad math, and dishonesty. In this post, I will be dissecting “The Sacred Geometry Movie,” showing once again that the supporters of Sacred Geometry haven’t got a clue what they are talking about.
Before we get into my analysis, here is the actual video. All of my timestamps will be referencing this.
## Sacred Geometry is Neither
In recent years, there has been a movement which has been gaining popularity across the Internet, known as “Sacred Geometry.” I’m not using this phrase in its historical context, mind, where it traditionally referred to the geometry and architecture found in churches, mosques, temples, and religious artwork. The context in which we’ll be discussing Sacred Geometry, today, is in the idea that the very fabric and origins of the universe are found in fairly simple shapes and patterns. So far as I have been able to deduce, this whole movement owes itself almost entirely to a man who calls himself Drunvalo Melchizedek.
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https://math.stackexchange.com/questions/2570316/intersection-of-two-lie-subgroup-is-lie-subgroup
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# Intersection of two Lie subgroup is Lie subgroup ?
This question is already asked in here but i can't find a satisfactory answer.
The question (in the title) arise from the following definition (i'm using Lee's smooth manifold p.156) : If $G$ is a Lie group and $S \subseteq G$, the $\textbf{subgroup generated by } S$ is the smallest subgroup containing $S$ (i.e., the intersection of all subgroup containing $S$).
The definition above implicitly assume that the intersection of any two Lie subgroup $S_1,S_2 \subset G$ is again Lie subgroup. I find it difficult to prove this. I can see that the intersection has the group property but i have no idea how to show that $S_1 \cap S_2$ is an immersed submanifold of $G$.
The answer by @Moishe Cohen in the given link above is using argument involving Lie algebra. But since the definition in Lee's book is given before he define Lie algebra, i assume that this problem can be solved without it (probably).
Can anyone help me with this ? Thank you.
• Lee is not claiming that the subgroup generated by $S$ is a Lie group. This is irrelevant to his discussion; we just need to know that it is a group. – Spenser Dec 17 '17 at 16:43
There are two issues here:
First, the definition of the "subgroup generated by a set $S$" has nothing to do with Lie groups -- it's purely a group-theoretic concept. So for a general set $S$, there's no assumption, implicit or explicit, that the subgroup generated by $S$ is a Lie subgroup. (And it might not be -- for example, there are dense uncountable subgroups of $\mathbb R$, which cannot be given any topology or smooth structure making them into immersed Lie subgroups, and we can take $S$ to be such a subgroup.)
Second, independently of that, it is true that the intersection of two Lie subgroups is again a Lie subgroup.
Theorem. Suppose $G$ is a Lie group, and $H_1,H_2$ are Lie subgroups of $G$. Let $H$ be the subgroup $H_1\cap H_2$. Then $H$ has a unique topology and smooth structure making it into a Lie subgroup of $G$.
EDIT: In Moishe Cohen's answer to the question you cited, he originally just stated this as a simple exercise, but in reply to my laborious argument below, he's now added a simple proof. The idea is to view the two Lie subgroups $H_1$ and $H_2$ as injective Lie homomorphisms $f_i\colon H_i\to G$, and define $H$ as the subgroup $\{(x_1,x_2)\in H_1\times H_2: f_1(x_1) = f_2(x_2)\}$ of $H_1 \times H_2$. The equivariant rank theorem shows that $H$ is an embedded Lie subgroup of $H_1\times H_2$, and for either $i=1$ or $i=2$, the following composition given an injective Lie homomorphism of $H$ into $G$: \begin{equation*} H\hookrightarrow H_1\times H_2 \overset{p_i} {\to} H_i \overset{f_i}{\to} G. \end{equation*}
I'll leave my much more laborious argument here, in case anyone's interested.
My proof:
I don't know of any proof that doesn't rely on some nontrivial facts about Lie algebras, exponential maps, and foliations. Here's a quick sketch of a proof. Can't guarantee that I haven't missed some details, but this general idea should work. (Note that I'm using the definitions from my Intro to Smooth Manifolds book -- in particular, smooth manifolds are second-countable and therefore have only countably many components, and a Lie subgroup is a subgroup endowed with a topology and smooth structure making it into a Lie group and an immersed, not necessarily embedded, submanifold.)
Proof: Let's denote the Lie alebras of $G$, $H_1$, and $H_2$ by $\mathfrak g$, $\mathfrak h_1$, and $\mathfrak h_2$, respectively. Since $\mathfrak h_1$ and $\mathfrak h_2$ are canonically identified with Lie subalgebras of $\mathfrak g,$ the set $\mathfrak h = \mathfrak h_1\cap \mathfrak h_2$ is a Lie subalgebra of $\mathfrak g$ too. Thus there is a unique connected Lie subgroup $H_0$ of $G$ whose Lie algebra is $\mathfrak h$. This means $H_0$ has a topology and smooth structure making it into an immersed smooth submanifold of $G$, and the group operations on $H_0$ are smooth with respect to this structure. If $V\subset\mathfrak g$ is a neighborhood of $0$ on which the exponential map of $G$ is a diffeomorphism, $H_0$ is generated (in the group-theoretic sense) by $\exp(V\cap\mathfrak h)$, where $\exp$ denotes the exponential map of $G$. Since $V\cap \mathfrak h\subset \mathfrak h_1\cap \mathfrak h_2$, it follows that $H_0\subset H_1\cap H_2$.
Since $H_0$ is a subgroup (in the algebraic sense) of $H$, it follows that $H$ is the disjoint union of the left cosets of $H_0$ in $H$. We need to verify that there are only countably many such cosets. I think you can prove this based on the fact that $H_1$ and $H_2$ are integral manifolds of left-invariant foliations of $G$; if we choose a flat chart for $H_1$ on some open subset $W\subseteq G$, then $H_1\cap W$ is a union of countably many disjoint slices; then we can take a connected neighborhood $Y$ of the identity in $H_2$ that is embedded in $W$, and $Y\cap H_1$ will consist of countably many connected embedded submanifolds. I haven't worked out the details.
For each $h\in H$, the map $L_h$ (left multiplication by $h$) is a diffeomorphism of $G$ that takes $H_0$ bijectively onto $hH_0$. Thus we can define a smooth manifold structure on $H$ by declaring each such bijection $H_0 \to hH_0$ to be a diffeomorphism, and viewing $H$ as the topological disjoint union of these cosets. (That is, we declare each coset to be open and closed in $H$.)
We already verified that the group operations are smooth on $H_0$. Given any two points $h_1,h_2\in H$, we can choose connected neighborhoods $U_1$ of $h_1$ and $U_2$ of $h_2$ in $H$, and then the multiplication map $m|_{U_1\times U_2}\colon U_1\times U_2\to H$ can be viewed as the following composition: \begin{equation*} m|_{U_1\times U_2} = L_{h_1}\circ R_{h_2} \circ (m|_{H_0\times H_0}) \circ ( L_{h_1^{-1}} \times R_{h_2^{-1}}). \end{equation*} It follows that the multiplication on $H$ is smooth. (Here you have to use the fact that $H$ is an integral manifold of the left-invariant foliation determined by $\mathfrak h$, and therefore it's "weakly embedded," meaning that a smooth map into $G$ that takes its values in $H$ is also smooth into $H$.) A similar argument applies to inversion. The inclusion map $i_H\colon H\hookrightarrow G$ is a smooth immersion, because on each component it can be written as a composition of the form $L_h \circ i_{H_0}\circ L_{h^{-1}}$.
Finally, uniqueness of the topology and smooth structure are left as an exercise. $\square$
• Thank you Prof. Lee. Espescially for the sketch of the proof. – kelvinn aja Dec 18 '17 at 1:42
• Dear Jack: I maintain that there is nothing difficult about this all what is needed is the constant rank theorem (and familiarity with the notion of a fiber product). Take a look at the edit of my answer. – Moishe Kohan Dec 19 '17 at 15:17
• @MoisheCohen: That's a very nice argument. Much simpler. I'll edit my answer to refer to yours. – Jack Lee Dec 19 '17 at 20:17
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http://www.ck12.org/trigonometry/Law-of-Cosines/lesson/Law-of-Cosines/r7/
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<meta http-equiv="refresh" content="1; url=/nojavascript/"> Law of Cosines ( Read ) | Trigonometry | CK-12 Foundation
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# Law of Cosines
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Law of Cosines
While helping your mom bake one day, the two of you get an unusual idea. You want to cut the cake into pieces, and then frost over the surface of each piece. You start by cutting out a slice of the cake, but you don't quite cut the slice correctly. It ends up being an oblique triangle, with a 5 inch side, a 6 inch side, and an angle of $70^\circ$ between the sides you measured. Can you help your mom determine the length of the third side, so she can figure out how much frosting to put out?
By the end of this Concept, you'll know how to find the length of the third side of the triangle in cases like this by using the Law of Cosines.
### Guidance
The Law of Cosines is a fantastic extension of the Pythagorean Theorem to oblique triangles. In this Concept, we show some interesting ways to utilize this formula to analyze real world situations.
#### Example A
In a game of pool, a player must put the eight ball into the bottom left pocket of the table. Currently, the eight ball is 6.8 feet away from the bottom left pocket. However, due to the position of the cue ball, she must bank the shot off of the right side bumper. If the eight ball is 2.1 feet away from the spot on the bumper she needs to hit and forms a $168^\circ$ angle with the pocket and the spot on the bumper, at what angle does the ball need to leave the bumper?
Note: This is actually a trick shot performed by spinning the eight ball, and the eight ball will not actually travel in straight-line trajectories. However, to simplify the problem, assume that it travels in straight lines.
Solution: In the scenario above, we have the SAS case, which means that we need to use the Law of Cosines to begin solving this problem. The Law of Cosines will allow us to find the distance from the spot on the bumper to the pocket $(y)$ . Once we know $y$ , we can use the Law of Sines to find the angle $(X)$ .
$y^2 & = 6.8^2 + 2.1^2 - 2(6.8)(2.1) \cos 168^\circ \\ y^2 & = 78.59 \\y & = 8.86\ feet$
The distance from the spot on the bumper to the pocket is 8.86 feet. We can now use this distance and the Law of Sines to find angle $X$ . Since we are finding an angle, we are faced with the SSA case, which means we could have no solution, one solution, or two solutions. However, since we know all three sides this problem will yield only one solution.
$\frac{\sin 168^\circ}{8.86} & = \frac{\sin X}{6.8} \\\frac{6.8 \sin 168^\circ}{8.86} & = \sin X \\0.1596 & \approx \sin B \\\angle{B} & = 8.77^\circ$
In the previous example, we looked at how we can use the Law of Sines and the Law of Cosines together to solve a problem involving the SSA case. In this section, we will look at situations where we can use not only the Law of Sines and the Law of Cosines, but also the Pythagorean Theorem and trigonometric ratios. We will also look at another real-world application involving the SSA case.
#### Example B
Three scientists are out setting up equipment to gather data on a local mountain. Person 1 is 131.5 yards away from Person 2, who is 67.8 yards away from Person 3. Person 1 is 72.6 yards away from the mountain. The mountains forms a $103^\circ$ angle with Person 1 and Person 3, while Person 2 forms a $92.7^\circ$ angle with Person 1 and Person 3. Find the angle formed by Person 3 with Person 1 and the mountain.
Solution: In the triangle formed by the three people, we know two sides and the included angle (SAS). We can use the Law of Cosines to find the remaining side of this triangle, which we will call $x$ . Once we know $x$ , we will two sides and the non-included angle (SSA) in the triangle formed by Person 1, Person 2, and the mountain. We will then be able to use the Law of Sines to calculate the angle formed by Person 3 with Person 1 and the mountain, which we will refer to as $Y$ .
To find $x$ :
$x^2 & = 131.5^2 + 67.8^2 -2(131.5)(67.8) \cos 92.7 \\ x^2 & = 22729.06397 \\x & = 150.8\ yds$
Now that we know $x = 150.8$ , we can use the Law of Sines to find $Y$ . Since this is the SSA case, we need to check to see if we will have no solution, one solution, or two solutions. Since $150.8 > 72.6$ , we know that we will have only one solution to this problem.
$\frac{\sin 103}{150.8} & = \frac{\sin Y}{72.6} \\\frac{72.6 \sin 103}{150.8} & = \sin Y \\0.4690932805 & = \sin Y \\28.0 & \approx \angle{Y}$
#### Example C
Katie is constructing a kite shaped like a triangle.
She knows that the lengths of the sides are a = 13 inches, b = 20 inches, and c = 19 inches. What is the measure of the angle between sides "a" and "b"?
Solution: Since she knows the length of each of the sides of the triangle, she can use the Law of Cosines to find the angle desired:
$c^2 & = a^2 + b^2 - 2(a)(b)\cos C \\ 19^2 & = 13^2 + 20^2 - (2)(13)(20)\cos C \\361 & = 169 + 400 - 520\cos C \\-208 & = -520\cos C\\\cos C & = 0.4\\C \approx 66.42^\circ$
### Vocabulary
Law of Cosines: The law of cosines is a rule involving the sides of an oblique triangle stating that the square of a side of the triangle is equal to the sum of the squares of the other two sides plus two times the lengths of the other two sides times the cosine of the angle opposite the side being computed.
### Guided Practice
1. You are cutting a triangle out for school that looks like this:
Find side $c$ (which is the side opposite the $14^\circ$ angle) and $\angle{B}$ (which is the angle opposite the side that has a length of 14).
2. While hiking one day you walk for 2 miles in one direction. You then turn $110^\circ$ to the left and walk for 3 more miles. Your path looks like this:
When you turn to the left again to complete the triangle that is your hiking path for the day, how far will you have to walk to complete the third side? What angle should you turn before you start walking back home?
3. A support at a construction site is being used to hold up a board so that it makes a triangle, like this:
If the angle between the support and the ground is $17^\circ$ , the length of the support is 2.5 meters, and the distance between where the board touches the ground and the bottom of the support is 3 meters, how far along the board is the support touching? What is the angle between the board and the ground?
Solutions:
1. You know that two of the sides have lengths of 11 and 14 inches, and that the angle between them is $14^\circ$ . You can use this to find the length of the third side:
$c^2 = a^2 + b^2 - 2ab\cos \theta\\c^2 = 121 + 196 - (2)(11)(14)(.97)\\c^2 = 121 + 196 - 307.384\\c^2 = 9.16\\c = 3.03\\$
And with this you can use the Law of Sines to solve for the unknown angle:
$\frac{\sin 14^\circ}{3.03} = \frac{\sin B}{11}\\\sin B = \frac{11\sin 14^\circ}{3.03}\\\sin B = .878\\B = \sin^{-1}(.0307) = 61.43^\circ\\$
2. Since you know the lengths of two of the legs of the triangle, along with the angle between them, you can use the Law of Cosines to find out how far you'll have to walk along the third leg:
$c^2 = a^2 + b^2 + 2ab\cos 70^\circ\\c^2 = 4 + 1 + (2)(2)(1)(.342)\\c^2 = 6.368\\c = \sqrt{6.368} \approx 2.52\\$
Now you have enough information to solve for the interior angle of the triangle that is supplementary to the angle you need to turn:
$\frac{\sin A}{a} = \frac{\sin B}{b}\\\frac{\sin 70^\circ}{2.52} = \frac{\sin B}{2}\\\sin B = \frac{2 \sin 70^\circ}{2.52} = \frac{1.879}{2.52} = .746\\B = \sin^{-1}(.746) = 48.25^\circ\\$
The angle $48.25^\circ$ is the interior angle of the triangle. So you should turn $90^\circ + (90^\circ - 48.25^\circ) = 90^\circ + 41.75^\circ = 131.75^\circ$ to the left before starting home.
3. You should use the Law of Cosines first to solve for the distance from the ground to where the support meets the board:
$c^2 = a^2 + b^2 + 2ab\cos 17^\circ\\c^2 = 6.25 + 9 + (2)(2.5)(3)\cos 17^\circ\\c^2 = 6.25 + 9 + (2)(2.5)(3)(.956)\\c^2 = 26.722\\c \approx 5.17\\$
And now you can use the Law of Sines:
$\frac{\sin A}{a} = \frac{\sin B}{b}\\\frac{\sin 17^\circ}{5.17} = \frac{\sin B}{2.5}\\\sin B = \frac{2.5 \sin 17^\circ}{5.17} = .1414\\B = \sin^{-1}(.1414) = 8.129^\circ\\$
### Concept Problem Solution
You can use the Law of Cosines to help your mom find out the length of the third side on the piece of cake:
$c^2 = a^2 + b^2 - 2ab\cos C\\c^2 = 5^2 + 6^2 + (2)(5)(6) \cos 70^\circ\\c^2 = 25 + 36 + 60(.342)\\c^2 = 81.52\\c \approx 9.03\\$
The piece of cake is just a little over 9 inches long.
### Practice
In $\triangle ABC$ , a=12, b=15, and c=20.
1. Find $m\angle A$ .
2. Find $m\angle B$ .
3. Find $m\angle C$ .
In $\triangle DEF$ , d=25, e=13, and f=16.
1. Find $m\angle D$ .
2. Find $m\angle E$ .
3. Find $m\angle F$ .
In $\triangle KBP$ , k=19, $\angle B=61^\circ$ , and p=12.
1. Find the length of b.
2. Find $m\angle K$ .
3. Find $m\angle P$ .
4. While hiking one day you walk for 5 miles due east, then turn to the left and walk 3 more miles $30^\circ$ west of north. At this point you want to return home. How far are you from home if you were to walk in a straight line?
5. A parallelogram has sides of 20 and 31 ft, and an angle of $46^\circ$ . Find the length of the longer diagonal of the parallelogram.
6. Dirk wants to find the length of a long building from one side (point A) to the other (point B). He stands outside of the building (at point C), where he is 500 ft from point A and 220 ft from point B. The angle at C is $94^\circ$ . Find the length of the building.
Determine whether or not each triangle is possible.
1. a=12, b=15, c=10
2. a=1, b=5, c=4
3. $\angle A=32^\circ$ , a=8, b=10
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http://forums.wolfram.com/mathgroup/archive/2011/Nov/msg00402.html
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Services & ResourcesWolfram ForumsMathGroup Archive
Re: Help needed - Mathematica code
• To: mathgroup at smc.vnet.net
• Subject: [mg122948] Re: Help needed - Mathematica code
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Fri, 18 Nov 2011 06:22:21 -0500 (EST)
• Delivered-to: [email protected]
----- Original Message -----
> From: "Tetsu Tetsu.HDD" <tetsu.hdd at gmail.com>
> To: mathgroup at smc.vnet.net
> Sent: Thursday, November 17, 2011 5:04:08 AM
> Subject: Help needed - Mathematica code
>
> Hi,
>
> I would greatly appreciate if anyone can help me out of this problem.
>
> To explain my problem, I will use LaTeX code.
>
> Given a>0, 1>b>0, c>0 and d>0, I want to calculate the following
>
> \int_0^a X Y(X)^b dX
>
> where Y(X) is defined by
>
> (c - \frac{Y}{d-X Y^b}) X Y^{b-1}=1
>
> Can you tell me Mathematica codes for this problem?
>
>
> T
If I understand correctly, then it might be that you want something along the lines below.
In[164]:=
y[x_] := y /. First[Solve[c - (y/(d - x*y^b))*x*y^(b - 1) == 1, y]]
In[166]:= Integrate[x*y[x], {x, 0, a},
Assumptions -> {a > 0, 1 > b > 0, c > 0, d > 0}]
During evaluation of In[166]:= Solve::ifun:Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>
Out[166]= ConditionalExpression[(a^2*
b*((-1 + c)/a)^(1/b)*(d/c)^(1/b))/(-1 + 2*b), b > 1/2]
Daniel Lichtblau
Wolfram Research
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https://math.duke.edu/people/ingrid-daubechies?qt-scholars_publications_mla=5&qt-faculty_profile_tabs=0&page=11
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# Ingrid Daubechies
• James B. Duke Distinguished Professor of Mathematics and Electrical and Computer Engineering
• Professor in the Department of Mathematics
• Professor in the Department of Electrical and Computer Engineering (Joint)
### Research Areas and Keywords
##### Analysis
wavelets, inverse problems
shape space
inverse problems
shape space
##### Mathematical Physics
time-frequency analysis
##### Signals, Images & Data
wavelets, time-frequency analysis, art conservation
##### Education & Training
• Ph.D., Vrije Universiteit Brussel (Belgium) 1980
Daubechies, I., and Y. Huang. “How does truncation of the mask affect a refinable function?Constructive Approximation, vol. 11, no. 3, Sept. 1995, pp. 365–80. Scopus, doi:10.1007/BF01208560. Full Text
Friedlander, S., et al. “A celebration or women in mathematics.” Notices of the American Mathematical Society, vol. 42, no. 1, Jan. 1995, pp. 32–42.
Daubechies, I., et al. “Gabor Time-Frequency Lattices and the Wexler-Raz Identity.” Journal of Fourier Analysis and Applications, vol. 1, no. 4, Jan. 1994, pp. 437–78. Scopus, doi:10.1007/s00041-001-4018-3. Full Text
Daubechies, I. “Two Recent Results on Wavelets: Wavelet Bases for the Interval, and Biorthogonal Wavelets Diagonalizing the Derivative Operator.” Wavelet Analysis and Its Applications, vol. 3, no. C, Jan. 1994, pp. 237–57. Scopus, doi:10.1016/B978-0-12-632370-2.50013-1. Full Text
Daubechies, I., and Y. Huang. “A decay theorem for refinable functions.” Applied Mathematics Letters, vol. 7, no. 4, Jan. 1994, pp. 1–4. Scopus, doi:10.1016/0893-9659(94)90001-9. Full Text
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Daubechies, I., and J. C. Lagarias. “Sets of matrices all infinite products of which converge.” Linear Algebra and Its Applications, vol. 161, no. C, Jan. 1992, pp. 227–63. Scopus, doi:10.1016/0024-3795(92)90012-Y. Full Text
Cohen, A., et al. “Biorthogonal bases of compactly supported wavelets.” Communications on Pure and Applied Mathematics, vol. 45, no. 5, Jan. 1992, pp. 485–560. Scopus, doi:10.1002/cpa.3160450502. Full Text
Antonini, M., et al. “Image coding using wavelet transform.Ieee Transactions on Image Processing : A Publication of the Ieee Signal Processing Society, vol. 1, no. 2, Jan. 1992, pp. 205–20. Epmc, doi:10.1109/83.136597. Full Text
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https://chemistry.stackexchange.com/tags/ideal-gas/hot
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# Tag Info
13
It's not a coincidence at all! If you do an online search for "derivation of osmotic pressure", you'll see how $R$ enters into the derivation. Indeed, that's one of the beauties of the van 't Hoff equation for osmotic pressure – it reveals that (under the modest simplifying assumptions of the van 't Hoff equation derivation) the osmotic pressure created ...
11
The answer to your question is yes and no. You are correct in supposing that as an ideal gas expands the entropy will increase as it has more space to occupy and so the number of ways the molecules can be placed in the total space has increased. (Try to not think of entropy in terms of randomness but in the number of ways molecules can be positioned in space,...
10
Here's your confusion: You need to consider two different things: The momentum transfer per particle per collision. There, since we assume an instantaneous collision, it doesn't make sense to try to figure out force from acceleration. [I suppose you could do this using limits, and maybe there are applications in which that does make sense, but adding that ...
5
In ideal gases no intermolecular forces, therefore no potential energy. Thus, internal energy is equal to total kinetic energy (KE) of the system. Consider $N$ monoatomic particles in a cubical box of side $\ell$ (assumption: ideal gasses consist of monoatomic point particles). The amount of ideal gas in the box is $\frac{N}{N_A} = n \ \pu{mol}$ where $N_A$ ...
4
His name was Amedeo Avogadro, not Amidio nor Amadeo nor Avegadro nor Avagadro. The full name was Lorenzo Romano Amedeo Carlo Avogadro, Count of Quaregna and Cerreto. Avogadro's law states that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules. More exactly, it also includes single atoms, e.g. for a case of ...
4
This definition is pretty ambiguous, and in my opinion not very helpful. But if you consider an ideal gas, for which we have $$pV = nRT$$ then $nRT$ can be identified with something which has the dimensions of p-V work. The problem is that 'work' is a path function, which must be specified with respect to a process, which goes from an initial state to a ...
4
It may be helpful to look at a related value $k_{B}$, the Boltzmann constant, which is widely used in thermodynamics. These two are related by $R = k_{B}N_{A}$, allowing the ideal gas law to also be written: $$PV = Nk_{B}T$$ where $N$ is the number of particles, as opposed to the number of moles. The units are $\pu{J\cdot K^{-1}}$. It's a proportionality ...
3
Because it gives simpler-to-derive laws which are often very good approximations Clearly real gases do not always follow the ideal gas laws. They mostly liquefy under some conditions, for example, and, under those conditions they are clearly not ideal. But in practice gas laws are used for things far away from those non-ideal regions. When we are applying ...
3
OP has given a good effort to solve the problem using correct path. Only loose point was not considering the diatomic nature of the gases as Safdar Faisal pointed out in a comment. Suppose the amount of $\ce{O2}$ in the gas mixture is $n_1 \ \pu{mol}$ and the amount of $\ce{N2}$ in the gas mixture is $n_2 \ \pu{mol}$ in volume of $\pu{1.0 L}$ container. Thus,...
3
In general for a perfect or ideal gas, $$C_p=C_V + R'$$ (using your notation) where the heat capacities are molar quantities. It follows that for a perfect gas mixture $(C_p)_\text{mix}=(C_V)_\text{mix} + R'$.
3
When you decrease the temperature of an ideal gas held at constant volume, what you are doing is transferring energy as heat from the gas into the surroundings. You do this by keeping the surroundings at a targeted final temperature and placing the gas in thermal contact with the surroundings, allowing heat to dissipate. When you reach the final state, you ...
2
Internal energy of any gas is given by $$U=U_\text{trans} + U_\text{rotational} + U_\text{vibrational} + U_\text{intermolecular} + U_\text{electronic} + U_\text{relativistic} + U_\text{bonds}$$ Last three aren't affected by ordinary heating. And $U_\text{intermolecular}$ for ideal gas is zero. That's why for ideal gas $U$ is only function of temperature. But ...
2
The temperature and the volume of the inner ear are constant. When your ears pop during descent, air from the cabin goes into the ear, increasing the pressure. The law is the following: $$n / P = const$$ You can derive this from the ideal gas law. It has no special name.
2
To carry out the B transformation, you have to heat a lot. If you don't heat, the volume will of course increase, but the pressure will decrease. B is a process difficult to carry out, because it is not easy to heat enough a gas who is inflated to as to maintain the inner pressure. Then, at the end of B, the temperature is very high. You block the position ...
2
Your analysis is correct in terms of number density. But let's see how it plays out in terms of molar density. Let n be the number of moles and A be Avagadro's number. Then N=nA. If we substitute this into your first equation, then I get $$P=\frac{n(Ak)T}{V-nAb}-\frac{aA^2n^2}{V^2}$$But, since Ak=R, we obtain:$$P=\frac{nRT}{V-nb'}-\frac{a'n^2}{V^2}$$where ...
2
We know from the first Newton motion law, that the net force acting on an object in rest must be zero. The forces acting on the piston are gravity and gas pressure: $$\vec F_g + \vec F_\mathrm{p,down} + \vec F_\mathrm{p,up}=\vec 0 \tag{1}$$ If $V$ is the given bottom gas volume, $V_0$ is the total gas volume, $n$ is the molar amount of each of gases, the gas ...
2
The Gibbs free energy change is zero in the case of reversible processes carried out at constant temperature and pressure, but that isn't the case if these conditions are not observed. As a demonstration consider an isothermal reversible expansion of an ideal gas. Since the temperature is constant, the free energy change is given by $$\Delta G = \Delta H - T ... 2 T in K V^2 in \pu{m2 s-2} 300 206116 323 230400 363 260100 403 280900 498 348100 623 435600 698 504100 773 547600 These are proportional. 2 B=\pu{0.6226 bar} as the water-water vapour system would be in equilibrium. Now, A+B= \pu{1 bar}\\ A= \pu{0.3774 bar} For initial volume of the container, P_{\ce{Ar}_i}V_i=n_{\ce{Ar}_i}RT\\ V_i=C=\frac{n_{\ce{Ar}_i}RT}{P_{\ce{Ar}_i}}\\ C=\pu{\frac{0.1 \times 0.08314 \times 360}{0.3774} L}\\ C=\pu{7.93 L}\\ For initial moles of water vapour, P_{\ce{... 2 Some notes I had easily at hand may help. You have already calculated the probability of obtaining the chance with a number k of type of ball (or molecule) out of a total on n is$$\displaystyle p=\frac{n!}{k!(n-k)!}\frac{1}{2^n} \tag{25c}$$This distribution is a maximum when k=n/2. This can be seen with a straightforward argument. The factorial terms ... 2 Charles' law says that at constant pressure the volume and temperature of an ideal gas are related as$$\frac{V_1}{T_1}=\frac{V_2}{T_2}$$If V_2=V_1+dV and T_2=T_1+dT then$$\frac{V_1}{T_1}=\frac{V_1+dV}{T_1+dT}=\frac{V_1}{T_1}\left(\frac{1+dV/V_1}{1+dT/T_1}\right)$$which can be rearranged into$$\frac{dV}{dT}=\frac{V_1}{T_1}$$But Charles' law says ... 1 Assumptions: Reaction of carbon dioxide with water is neglected. Vapour pressure of water is negligible. Volume of solution does not change on dissolution of carbon dioxide. Moles of carbon dioxide dissolved in water is very less as compared to moles of water and thus, X_{\ce{CO2_{(aq.)}}}≈\frac{n_{\ce{CO2(aq)}}}{n_{\ce{H2O(l)}}} Initially no \ce{CO2} ... 1 Your claim that \Delta H = \Delta U + P_{ext} \Delta V is incorrect. It is only correct when the system is always in mechanical equilibrium with the external pressure, or in other words irreversible expansion against constant pressure. The more general statement is \Delta H = \Delta U + \Delta (PV) . Here as you can see even when you compare it with \... 1 Cp of an ideal gas doesn't depend on pressure. Cp of any substance is defined as the partial derivative of enthalpy respect to temperature at constant pressure. But, if the enthalpy of the substance is independent of pressure, then it doesn't matter if the pressure is constant. However, determining Cp by measuring the amount of heat required to change the ... 1 At the interface between the gas and its surroundings, by Newton's 3rd law, the pressure exerted by the gas on its surroundings is equal to the pressure exerted by the surroundings on the gas. So we can use either. For a reversible expansion, the gas pressure is given by the ideal gas law. But the ideal gas law only applies at thermodynamic equilibrium ... 1 When real gases are at high temperature, the kinetic energy prevents any gas particles from interacting via intermolecular forces. With low pressure, the gas particles are separated enough that the intermolecular forces are sparse, therefore, giving rise to the ideal behavior since ideal gases are defined as non-interacting particles. When real gases are at ... 1 The van Der Waal equation is$$\left(p+\frac a{V_\mathrm m^2}\right)(V_\mathrm m-b)=RT$$Here V_\mathrm m is molar volume. When pressure is low and temperature is very high, we can qualitatively say that the molar volume will be very large. Due to this the volume occupied by the molecules (given by b) becomes insignificant. The pressure is low but the ... 1 There are at least two fundamental issues you have to address. First, you have to distinguish between the Gibbs energy G and the Gibbs energy of reaction \Delta_r G. In you diagram, one is the value on the y-axis (without defined zero point) and the other is the slope of the line, as labeled in your sketch. The second issue is that in the expressions on ... 1 I can't see what you did in your derivation, but, for what it's worth, here's my derivation. My starting equations are$$G=\sum{n_i\mu_i}$$and, along your contour, at constant temperature and pressure,$$\mathrm dG=\sum{\mu_i\mathrm dn_i}$$The changes in the number of moles of the various species are given by$$n_i=n_{i0}+c_inwhere $c_i$ is the ...
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https://www.chemicalforums.com/index.php?topic=105577.0;prev_next=prev
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May 18, 2021, 06:29:33 PM
Forum Rules: Read This Before Posting
### Topic: Photon with greatest energy. (Read 215 times)
0 Members and 1 Guest are viewing this topic.
#### IceRiceIce
• New Member
• Posts: 8
• Mole Snacks: +0/-0
##### Photon with greatest energy.
« on: October 07, 2020, 06:57:03 PM »
Which of the following transitions would produce a photon with the greatest energy? Why?
A) n = 1 → n = 5
B) n = 4 → n = 3
C) n = 5 → n = 2
D) n = 3 → n = 4
I don't even know where to start with this so if someone could explain this it would be helpful.
• Mr. pH
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https://brilliant.org/problems/promarantid-question/
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# promarantid question
Geometry Level 2
DB is a diagonal of rectangle ABCD and line L through A and line M through C divide DB in three equal parts of length 1 meter each are perpendicular to DB. To 2 decimal places, find the area ( in meter^2) of the rectangle.
×
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https://www.physicsforums.com/threads/distribution-difference-of-two-independent-random-variables.786525/
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# Distribution Difference of Two Independent Random Variables
1. Dec 8, 2014
### izelkay
1. The problem statement, all variables and given/known data
Z = X - Y and I'm trying to find the PDF of Z.
2. Relevant equations
Convolution
3. The attempt at a solution
Started by finding the CDF:
Fz(z) = P(Z ≤ z)
P(X - Y ≤ z)
So I drew a picture
So then should Fz(z) be:
since, from my graph, it looks as though Y can go from negative infinity to positive infinity, and X can go from negative infinity on the left but is bounded by z+y on the right
then should the pdf be:
Edit: sorry I forgot to include the fact that, because fx and fy are independent, f(x,y) = fxfy in the following derivation
?
Last edited: Dec 8, 2014
2. Dec 9, 2014
3. Dec 9, 2014
### Orodruin
Staff Emeritus
Your approach looks reasonable. Is there something you are particularly worried about?
4. Dec 9, 2014
### izelkay
Oh yes, sorry I was wondering if what I arrived at for the PDF of the difference of two independent random variables was correct.
I tried Googling but all I could find was the pdf of the sum of two RVs, which I know how to do already.
5. Dec 9, 2014
### Orodruin
Staff Emeritus
Yes, it looks ok. You should note that if you know the pdf of the sum and the pdf of the negative of a distribution (i.e., if you know how the the distribution of $Y$, what is the distribution of $-Y$), then you can use these two to obtain the distribution of $X-Y$.
6. Dec 9, 2014
### izelkay
I'm going to modify the problem a little bit, can you tell me if I do it right/wrong?
X and Y are two independent random variables, each of which are uniform on (0,1). Find the pdf of Z = X - Y
Using my result from above, the pdf of Z is given by:
X ~ U(0,1) and Y ~ U(0,1)
The pdf of fx(x) and fY(y) are both 1 on (0,1) and 0 otherwise.
z goes from -1 to 1 because of X - Y right?
For -1 ≤ z ≤ 0
fy is uniform only on (0,1) so my integral limits should be z+1 to z
For 0 ≤ z ≤ 1 I wouldn't need to change the limits here, just from 0 to 1
So then the pdf of X - Y is:
Is this correct?
7. Dec 9, 2014
### Ray Vickson
No, it cannot possibly be correct, because you would have f(z) = -1 for -1 < z < 0 and f(z) = 1 for 0 < z < 1. That kind of f cannot be a probability density function.
You need to go back and evaluate the limits more carefully; in cases like this, drawing an x,y diagram of the integration region would be helpful.
8. Dec 9, 2014
### izelkay
I don't have much practice drawing integration regions of density functions and I wouldn't know where to start with this one besides drawing the box with vertices (0,0), (0,1), (1,0), (1,1).
I think I found another way to look at it though:
If -1 ≤ z ≤ 0,
If I want fx(z+y) to be 1, I need to shift the bounds by +1, and then I'll need z+y+1 ≥ 0 , or y ≥ -1-z
So
Then on 0 ≤ z ≤ 1,
I need z+y ≤ 1, or y ≤ 1 - z
So
Then all together this is:
1 + z , -1 ≤ z ≤ 0
1 - z , 0 ≤ z ≤ 1
I got the same answer as here: http://www.math.wm.edu/~leemis/chart/UDR/PDFs/StandarduniformStandardtriangular.pdf
but I'm not sure my process is correct because my bounds are a little different than theirs, and I don't know how they computed the cdf
9. Dec 9, 2014
### Ray Vickson
You already drew part of the diagram in Post #1. You just need to add the boundary lines x = 0, x = 1, y = 0, y = 1 and you are done---that's your drawing!
You say you "don't know how they computed the cdf". Well, you claimed before that you know how to compute the cdf of a SUM, and that is all you need to do.
If $Z = X-Y$ then $S = Z+1$ has the form $S = X + (1-Y) = X + Y'$, where $X$ and $Y' = 1-Y$ are independent and $\rm{U}(0,1)$ random variables. Thus, $S$ is the sum of two uniforms, and has a well-known, widely-documented triangular density:
$$f_S(s) = \begin{cases} s, & 0 < s < 1\\ 2-s, & 1 < s < 2\\ 0 & \rm{elsewhere} \end{cases}$$
Now just shift the graph of $f_S(s)$ one unit to the left, and that would be your density of $Z$: $f_Z(z) = f_S(1+z), \; -1 < z < 1$.
Last edited: Dec 9, 2014
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https://www.contextgarden.net/index.php?title=Talk:Command/setupinmargin&diff=prev&oldid=13068&printable=yes
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Difference between revisions of "Talk:Command/setupinmargin"
Does first bracket work?
Does the first bracket actually work? I assumed that it defines the location so that \setupinmargin[right] would put all notes using \inmargin into the right hand margin? The following does not work in MKII nor MKIV, i.e. the margin notes are neither on the left nor slanted.
```\setupinmargin[right][style=slanted]
\starttext
Hello World! \inmargin{Goodbye}
\stoptext
```
However, the following does:
```\setupinmargin[location=right,style=slanted]
\starttext
Hello World! \inmargin{Goodbye}
\stoptext
```
Richard Stephens 09:51, 2 June 2011 (CEST)
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https://support.norton.com/sp/en/aa/home/current/solutions/v59650017
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# Find missing files or backup sets when restoring them from a local storage media with Norton
Depending on your backup destination, follow the instructions to restore the files.
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If you want to restore all the files, click All file types, and then check the Backup Item.
7. Under Restore to, do one of the following:
• If you want to restore the files to the original location, select Original Location.
• If you want to restore the files to a new location, select Custom Location.
By default, Autorun restores the files to C:\Restored Files.
8. Click Restore Selected.
9. Follow the on-screen instructions to restore the backup sets.
### Restore the files from an internal drive or an external drive
If you want to restore files from an external drive, make sure that you have connected the external drive to your computer.
1. Navigate to the following folder:
• On Windows (32-bit): C:\Program Files (x86)\\Engine\
• On Windows (64-bit): C:\Program Files\\Engine\
Where Norton product is the name of your Norton and x is the version number.
2. Copy Arestore.exe to the root directory where you have the N360_BACKUP folder.
For example, if you have N360_BACKUP folder in C:\drive, then copy Arestore.exe to C:\drive.
3. Navigate to the following folder:
• On Windows (32-bit): C:\Program Files (x86)\\MUI\\09\01
• On Windows (64-bit): C:\Program Files\\MUI\\09\01
Where Norton product is the name of your Norton and x is the version number.
4. Copy Arestore.loc to the root directory where you have the N360_BACKUP folder.
For example, if you have N360_BACKUP folder in C:\drive, then copy Arestore.loc to C:\drive.
5. In the root directory, double-click ARestore.exe.
6. In the Portable Restore window, click Select Files to Restore.
7. From the left pane, under Show Results for, click a file category from which you want to restore files.
8. In the right pane, check the files that you want to restore.
If you want to restore all the files, click All file types, and then check the Backup Item.
9. Under Restore to, do one of the following:
• If you want to restore the files to the original location, select Original Location.
• If you want to restore the files to a new location, select Custom Location.
By default, Autorun restores the files to C:\Restored Files.
10. Click Restore Selected.
11. Follow the on-screen instructions to restore the backup sets.
### What would you like to do now?
Browse for solutions, search the Norton Community, or Contact Us.
DOCID: v59650017
Operating System: Windows
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http://www.heldermann.de/JLT/JLT24/JLT243/jlt24028.htm
|
Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 24 (2014), No. 3, 657--685Copyright Heldermann Verlag 2014 The Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n Silvina Campos CIEM-FaMAF, Universidad Nacional de Córdoba, Córdoba 5000, Argentina [email protected] Linda Saal CIEM-FaMAF, Universidad Nacional de Córdoba, Córdoba 5000, Argentina [email protected] [Abstract-pdf] We denote by $H_{n}$ the $2n+1$-dimensional Heisenberg group and study the spherical transform associated with the generalized Gelfand pair $(U(p,q) \rtimes H_{n},U(p,q))$, $p+q=n$, which is defined on the space of Schwartz functions on $H_{n}$, and we characterize its image. In order to do that, since the spectrum associated to this pair can be identified with a subset $\Sigma$ of the plane, we introduce a space ${\cal H}_{n}$ of functions defined on $\mathbb{R}^2$ and we prove that a function defined on $\Sigma$ lies in the image if and only if it can be extended to a function in ${\cal H}_{n}$. In particular, the spherical transform of a Schwartz function $f$ on $H_{n}$ admits a Schwartz extension on the plane if and only if its restriction to the vertical axis lies in ${\cal S}(\mathbb{R})$. Keywords: Heisenberg group, spherical transform. MSC: 43A80; 22E25 [ Fulltext-pdf (446 KB)] for subscribers only.
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|
https://thraxil.org/users/TheRev/
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# thraxil.org:
## Train in Vain
R.I.P. Joe…
<p>(more as I leave work/get drunk…)</p>
## All Things Punk
OK, so I saw The Distillers this past weekend. What souvenir did I pick up? My best guess is either a cracked or bruised rib. Signs pointing to bruised: it didn’t really hurt until Monday (read: it only hurt when I took a deep breath). Signs pointing to cracked: from Monday onwards, it feels like Doubting Thomas himself has decided to poke around my chest, eschewing his fingers for a hot poker.
<p>Anyhoo, the show was a blast. Anytime the headlining act clears the floor for an all-female slam-dance affair with the phrase, “Vaginas <em>Only</em>” it’s worth the price of admission. Especially when the song (punk rock song, mind you) was all about women’s suffrage. So their detractors will call them a bunch of Hole wannabes. I’ve yet to see their detractors stand up to meself or anyone there. Huff huff.</p>
<p>Punk’s not dead, and with cool chicks like Brodie, it’ll be a long, wonderful, painful death while peeing on the graves of the Backdoor Boys.</p>
## Satan Oscillate my metallic sonatas
OK, so upon reading my last post, it dawned on me that the first line actaully was moderately congruous with the remainder of the message. Hooray for serendipity. In the interests of veracity, here’s the real story…
<p>So I was a few sheets to the wind a few nights past when I sent an e-mail out to a former significant other o’ mine. ‘Twas her birthday and all, and we hadn’t spoken in about a year. That was my Caesar-ish Rubicon quip. The fact that it blended in so wonderfully with my present employer’s ignorance of my skills just made things a tad more ironic. </p>
<p>Thppt.</p>
<p>One of these days, I’m gonna make a stone cold sober report…</p>
## Was ist ist
The die is cast…
<p>In Viagra-land news, their choice to name me as the “document coordinator” has’t bitten them on the heiny as much as even I thought it would. I guess even the likes of yours truly can clean up his organizational act enough to pick up a paycheck at the end of the week.</p>
<p>‘Course it’s still all over but the crying once I’m off the clock. (read: somewhere in this mess that I call a home, maybe I can find some clean clothes…)</p>
## Stray Bullets
So this weekend, while supping upon cheap pizza, I was perusing my “old” copies of Stray Bullets (everyone’s favorite serialized vision of sex, violence, and uh… violence) when I noticed that there was a letter by me in the back… y’know, where all the geeks write in to seem cool.
<p>OK, so first off, I really f-ed up the number of one of the first books. Yup, go Williams. </p>
<p>Second off, it dawned on me that I’d written that letter several months ago in an attempt to seem cordial while trying to russel up a free bumper sticker. Yeah, no bumper sticker came, so I completely forgot about it. Freaked me out when I finally read it yesterday. </p>
<p>Anyhow, now all you comic book nuts can read and say, “I knew that boy when he thought Knox gelatin was a hair product.” Or not. Whatever. Stray Bullets #25… it’s not even that good an issue, but still Stray Bullets, so it kicks butt.</p>
<p>Back to the land of dreams…</p>
## ten animals I slam in a net
Well, no ATR today… but then again, I’ve avoided getting stuck with asinine assignments. ‘Course that’s mainly due to the fact that I’ve physically avoided those responsible for assigning said tasks. >sigh< Ain’t life grand in the Dilbert world.
<p>So instead, I’m listening to the new album by Common Rider – the band fronted by Jesse of Operation Ivy fame. Zen-Punk, and fun for the whole family. Steal your copy today!</p>
## the saga continues
Well, another day has come and gone at the Viagra Factory (or “Pfactory” as the wags down there would put it). I’ve recently stepped into my new shoes as the “Document Coordinator” for our building. Which, as far as I can tell, makes me the archive bitch. For all of those who knew me in college, I’ll admit freely that my organizational abilities have not improved in the time since graduation… as plainly evidenced by the state of my apartment. And now I’m in charge of shipping junk off to be microfilmed, shipping junk off to be filed somewhere in the bowels of Pfizer, and pretty much every other mundane task associated with data storage.
<p>The one saving grace is that I’m in my very own private abode (the archive room) where I can listen to muzak at the volume to which I’m accustomed. So far it’s been mainly up to the Rancid and Dropkick Murphys level of mayhem. Today, tho, I had to go over an ass-load of <span class="caps">SOP</span>s coming up from NJ… I’m bringing in the <span class="caps">ATR</span> tomorrow, in case I get stuck with that crap again.</p>
<p>Yeah, work is work is work… it is, however, an endless supply of kooks, weirdos, and other misfits who wear their social problems on their sleeves. Oh, and there are some <em>real</em> losers, too. It’s pretty much an amalgam of “Dilbert” and the place where Dan Akroyd works at the beginning of “Spies Like Us.” I think it was about my second day there when I was roped into making a prank phone call to some poor lady at the credit union.</p>
<p>I think in the meantime, we’re supposed to be testing pharmaceutical products for impurities and/or degredants… but really, it’s like a cGMP deGrassi high.</p>
<p>Now, if only Connecticut sold beer past 8 p.m. …</p>
## Rabbit Rabbit
Hey, it’s October 1st. Thought for the day: Why isn’t the person responsible for that “skaterboy” sone strung up by her entrails? Or at least poked repeatedly with hot forks (y’know, for those of you opposed to the whole capital punishment shebang)
## test
yrs truly, the Rev, is horribly drunk right now… Testing to see if I can post this to me diary…
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https://web2.0calc.com/questions/decimals_42
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+0
# Decimals
0
94
1
Let $x = (0.\overline{6})(0.\overline{06})$. When x is written out as a decimal, what is the sum of the first 15 digits after the decimal point?
Dec 27, 2021
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https://blog.nathantsoi.com/article/Batch_Convert_CR2_to_JPG/
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Have you taken a bunch of pictures in the Cannon Raw format (.cr2) and now need to be able to edit them or view them in a jpeg or png format?
You could open each one in some photo editor and save it in a the correct format. Or you could use ImageMagick to convert them all at once!
On my mac, I used homebrew to install imagemagick with the command:
brew install imagemagick
You'll also need the ufraw package to convert from the cr2 format:
brew install ufraw
Ok you've got all the software you need, now let's convert!
Assume you have a folder in your home directory, under Pictures called "raw"
Then we would run these commands in the Terminal app to convert the .CR2 images to .jpg
change directory to the "raw" folder cd ~/Pictures/raw
convert all the .CR2 files to .jpg, this is case sensitive, so if your raw files are .cr2, replace the upper case CR2 in the command with a lower case version: cr2 for infile in *.CR2; do convert $infile$(echo $infile|sed -n "s/CR2$/jpg/p"); done
If you're on windows you can grab the installer here: http://www.imagemagick.org/script/binary-releases.php#windows
Then in the command line run
mogrify -format CR2 *.jpg
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http://mathhelpforum.com/calculus/187478-differentiable-function.html
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1. Differentiable function
By using the definition of a differentiable function, show that the following function is differentiable in (2,2):
f(x,y) = e^[x + 2y]
Thx!!
2. Re: Differentiable function
Originally Posted by marqushogas
By using the definition of a differentiable function, show that the following function is differentiable in (2,2):
f(x,y) = e^[x + 2y]
Thx!!
Well, what is the definition of differentiability?
3. Re: Differentiable function
In two variables: If a function f(x,y) is differentiable in (a,b) there exists two numbers, A and B, and a function r(h,k) such that:
f(a+h,b+k) - f(a,b) = A*h + B*k + sqrt(h^2+k^2)*r(h,k) and r(h,k) -> 0 when (h,k) -> (0,0)
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https://www.physicsforums.com/threads/universal-gas-constant-and-arrhenius-equation.715549/
|
Universal Gas constant and arrhenius equation
1. Oct 9, 2013
Woopydalan
Hello,
I am curious as to how the Universal Gas Constant, R, is important with regards to the rates in solids? It is in the Arrhenius Equation
2. Oct 10, 2013
Staff: Mentor
The gas constant is simply $R \equiv N_\mathrm{A} k_\mathrm{B}$, the Boltzmann constant scaled for a molar quantities.
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http://content.myhometuition.com/2017/11/
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# 13.2.3 Statistics (I), PT3 Focus Practice
Question 7:
Diagram below is an incomplete pictograph showing the sales of books for a duration of five months.
(a) The sales in May is ¼ of the total sales in January and February.
Complete the pictograph in the Diagram.
(b) Find the total number of books sold before April.
Solution:
(a)
(b)
Total number of books sold before April
= (5 + 3 + 6) × 15
= 14 × 15
= 210
Question 8:
Diagram below shows an incomplete line graph of the number of eggs sold in four weeks. The number of eggs sold on week 1 is 2000 and 4000 on week 4.
(a) Complete the line graph in the Diagram.
(b) Complete the pie chart in the second Diagram to represent sales from Week 1 to Week 4.
Solution:
(a)
(b)
# 13.2.2 Statistics (I), PT3 Focus Practice
13.2.2 Statistics (I), PT3 Focus Practice
Question 4:
Table below shows the profit made from the sales of coconut at a stall over five days.
Day Day 1 Day 2 Day 3 Day 4 Day 5 Profit (RM) 280 200 200 360 320
On diagram in the answer space, draw a line graph to represent all the information in the Table. Use the scale 2 cm to RM80 on the vertical axis.
:
Solution:
Question 5:
Table below shows the number of students who read four types of books.
Types of books Fiction Language Technology Religion Number of students 18 16 8 14
On diagram in the answer space, draw a bar chart to represent all the information in the Table.
:
Solution:
Question 6:
Diagram below is an incomplete bar chart which shows the number of cars sold in a shop for duration of five months.
(a) The number of cars sold for the five months is 150 units. The number of cars sold in February is equal to the number of cars sold in April.
Complete the bar chart in the Diagram.
(b) Find the percentage of cars sold in January.
Solution:
(a)
(b)
# 4.7.6 Natural Polymers (Structured Questions)
Question 1:
Diagram 1.1 shows an experiment to study the effect of vinegar and ammonium solution on latex.
Diagram 1.2 shows the result of the experiment after 30 minutes.
(a) Write down one observation from the result of this experiment. [1 mark]
(b) State one inference based on the observation in Diagram 1.1. [1 mark]
(c) State one constant variable in this experiment. [1 mark]
(d) State one hypothesis for this experiment. [1 mark]
(e) Based on this experiment, state the operational definition for acid. [1 mark]
:
(a)
Vinegar causes the coagulation of latex but ammonia solution prevents the coagulation of latex.
(b)
When vinegar (an acid) is mixed with latex, the latex coagulates.
When ammonia solution (an alkali) is mixed with latex, the latex does not coagulate.
(any one)
(c)
1. 10 cm3 of latex
2. Results of the experiment are observed after 30 minutes
(any one)
(d)
Acid causes the coagulation of latex but alkali prevents the coagulation of latex.
(e)
Acid is a substance which causes latex to coagulate.
# 13.2.1 Statistics (I), PT3 Focus Practice
13.2.1 Statistics (I), PT3 Focus Practice
Question 1:
Diagram below is a pictograph showing the number of pizzas sold in three months.
The price of one pizza is RM18. The total sales for those four months are RM2250.
Calculate the number of pizzas sold in April.
Solution
:
Total number of pizzas sold in four months
$\begin{array}{l}=\frac{RM2250}{RM18}\\ =125\end{array}$
Total number of pizzas sold in first three months
= 9 × 10
= 90
Number of pizzas sold in April
= 125 – 90
= 35
Question 2:
Diagram below is a bar chart showing the number of new houses sold over four days.
The total number of new houses sold on Wednesday and Thursday is 56.
Calculate the total number of new houses sold on Monday and Tuesday.
Solution
:
Wednesday: 12 units
Thursday: 16 units
Number of houses represented by 1 unit
$\begin{array}{l}=\frac{56}{12+16}\\ =2\end{array}$
Monday: 14 units
Tuesday: 18 units
Total number of new houses sold on Monday and Tuesday
= (14 + 8) × 2
= 64
Question 3:
Table below shows the number of companies that gave contributions to an orphan fund over a period of five days.
Days Monday Tuesday Wednesday Thursday Friday Number of companies 8 14 m 17 11
It is given that 20% of the total contribution was made on Tuesday.
Calculate the value of m
Solution
:
Let C = Total contribution
$\begin{array}{l}\frac{20}{100}×C=14\\ \text{}C=14×\frac{100}{20}\\ \text{}=70\\ m=70-\left(8+14+17+11\right)\\ \text{}=70-50\\ \text{}=20\end{array}$
# 4.7.4 The Oil Palm and Its Importance to National Development (Structured Questions)
Question 1:
Diagram 1.1 shows the process of latex coagulation.
(a)(i) State one example of chemical P? [1 mark]
(ii) State one characteristic of coagulated latex in Diagram 1.1. [1 mark]
(b) Chemical P in diagram 1.1 is replaced with chemical Q to prevent latex from coagulating.
State one example of chemical Q. [1 mark]
(c) Diagram 1.2 shows the process when natural rubber is heated with Sulphur to form rubber R.
(i) Name process X. [1 mark]
(ii) Name rubber R. [1 mark]
(d) Mark (\/) the object which is made of rubber R. [1 mark]
(a)(i)
Methanoic acid
(a)(ii)
Elastic
(b)
Ammonia solution
(c)(i)
Vulcanization of rubber
(c)(ii)
Vulcanized rubber
(d)
# 4.7.2 Alcohol and Its Effects on Health (Structured Questions)
Question 1:
Diagram 1.1 and Diagram 1.2 show an experiment to investigate the effect of temperature on the fermentation of glucose by yeast.
(a) State one hypothesis that can be made from this experiment. [1 mark]
(b) State the variables in this experiment.
(i) Manipulated variable [1 mark]
(ii) Responding variable [1 mark]
(c) Based on Diagram 1.1 and 1.2, which temperature is more suitable for the fermentation of glucose? [1 mark]
(d) Diagram 1.3 shows the graph of the volume of carbon dioxide produced at 35oC against time.
What is the relationship between the volume of carbon dioxide produced and time? [1 mark]
(a) Fermentation of glucose by yeast is affected by temperature.
(b)(i)
Temperature of the water bath
(b)(ii)
Volume of carbon dioxide produced
(c)
35oC
(d)
The volume of carbon dioxide produced is directly proportional to time.
# 12.2.1 Solid Geometry (II), PT3 Focus Practice
12.2.1 Solid Geometry (II), PT3 Focus Practice
Question 1:
Diagram below shows closed right cylinder.
Calculate the total surface area, in cm2, of the cylinder.
$\left(\pi =\frac{22}{7}\right)$
Solution
:
Total surface area
= 2(πr2) + 2πrh
$\begin{array}{l}=\left(2×\frac{22}{7}×{7}^{2}\right)+\left(2×\frac{22}{7}×7×20\right)\\ =308+880\\ =1188c{m}^{2}\end{array}$
Question 2:
Diagram below shows a right prism with right-angled triangle ABC as its uniform cross section.
Calculate the total surface area, in cm2, of the prism.
Solution
:
$\begin{array}{l}AB=\sqrt{{5}^{2}-{3}^{2}}\\ =\sqrt{25-9}\\ =\sqrt{16}\\ =4cm\end{array}$
Total surface area
= 2 (½× 3 × 4) + (3 × 10) + (4 × 10) + (5 × 10)
= 12 + 30 + 40 + 50
= 132 cm2
Question 3:
Diagram below shows a right pyramid with a square base.
Calculate the total surface area, in cm2, of the right pyramid.
Solution
:
h2= 102 – 62
= 100 – 36
= 64
= √64
= 8cm
Total surface area of the right pyramid
= (12 × 12) + 4 × (½× 12 × 8)
= 144 + 192
= 336 cm2
Question 4:
The diagram shows a cone. The radius of its base is 3.5 cm and its slant height is 6 cm. Find the area of its curved surface.
( π= 22 7 )
Solution
:
Area of curved surface
= π × radius of base × slant height
= πrs
$\begin{array}{l}=\frac{22}{7}×3.5×6\\ =66c{m}^{2}\end{array}$
# 4.7.1 Various Carbon Compound (Structured Questions)
Question 1:
Diagram 1.1 shows two examples of carbon compounds, K and L.
(a)(i) Based on Diagram 1.1, which one is an inorganic carbon compound? [1 mark]
(ii) State one characteristic of an inorganic carbon compound. [1 mark]
(b)(i) State one use of compound K. [1 mark]
(ii) State one effect of compound K on the nervous system if consumed excessively. [1 mark]
(c) Diagram 1.2 shows a tank containing gas M used for gas stoves.
Gas is a hydrocarbon compound.
(i) State two elements present in gas M. [1 mark]
(ii) State one source of gas M. [1 mark]
(a)(i) L or marble chips
(a)(ii)
Originates from non-living things or does not originates from living things
(b)(i)
Alcoholic drink
(b)(ii)
Disrupts nerve coordination or slows down the transmission of impulses
(c)(i)
1. Hydrogen
2. Carbon
(c)(ii)
Petroleum
|
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|
http://en.memory-alpha.org/wiki/Radius_(geometry)
|
Wikia
37,582pages on
this wiki
You might also be looking for Radius (bone).
Radius is the distance from the center of a circle to the outside edge.
The relationship between the radius and the circumference of a circle is $r = \frac{c}{2\pi}$.
Starships often scanned within a given radius when making an analysis or evaluation of nearby space.
In the alternate timeline created by the Na'kuhl, Nazis searched for Captain Archer within a fifteen-mile radius. (ENT: "Storm Front")
While attempting to assassinate Gul Dukat, the Bajoran resistance give Major Kira Nerys (as Luma Rahl) a Bajoran earring made of ultritium resin which, when detonated, had a blast radius of twenty meters. (DS9: "Wrongs Darker Than Death or Night")
After failing to obtain a transporter lock on the away team on a planet created by Trelane, Spock beamed aboard all lifeforms within a predetermined radius. (TOS: "The Squire of Gothos")
The 22nd century Vulcan hand scanner was capable of scanning within a three kilometer radius. (ENT: "Carpenter Street")
|
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|
https://brilliant.org/problems/jump-over-it-3/
|
# Jump over it
A body is projected up a smooth inclined plane with a velocity u from the point A as shown in the figure. The angle of inclination is 45 degrees and the top is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of u? Length of inclined plane is $$20\sqrt { 2 }$$.
×
|
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|
https://www.math.bgu.ac.il/en/teaching/spring2019/courses/theory-of-functions-of-a-complex-variable
|
## Course topics
• Complex numbers. Analytic functions, Cauchy–Riemann equations.
• Conformal mappings, Mobius transformations.
• Integration. Cauchy Theorem. Cauchy integral formula. Zeroes, poles, Taylor series, Laurent series. Residue calculus.
• The theorems of Weierstrass and of Mittag-Leffler. Entire functions. Normal families.
• Riemann Mapping Theorem. Harmonic functions, Dirichlet problem.
|
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|
https://stats.stackexchange.com/tags/machine-learning
|
# Questions tagged [machine-learning]
Machine learning algorithms build a model of the training data. The term "machine learning" is vaguely defined; it includes what is also called statistical learning, reinforcement learning, unsupervised learning, etc. ALWAYS ADD A MORE SPECIFIC TAG.
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### Rademacher Complexity of the family of constant-valued functions
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### Can we accumulate deterministic and probabilistic approaches for regression and classification problems?
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|
https://www.mail-archive.com/[email protected]/msg90960.html
|
# Re: [NTG-context] Strange behavior in math mode: < and minus sign give leftarrow
```On Wed, 10 Apr 2019 10:09:31 +0200
Otared Kavian <[email protected]> wrote:```
```
> The problem of such an usual default is also with newcomers who would not
> that typing an inequality like \$n < -1\$ would end up in \$n \leftarrow 1\$. And
> writing such inequalities is very common… while \leftarrow is used seldom in
> a mathematical text.
> So I think having the default collapsing=1 would be more logical, and more in
> line with the spirit of TeX.
>
> I hope Aditya will be convinced…
And since we have utf-8 input, such "features" are anachronistic and should not
be on by default. ←
Alan
___________________________________________________________________________________
|
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|
https://espressomd.github.io/doc/reaction_methods.html
|
# 19. Reaction methods¶
This chapter describes methods for simulating chemical reaction equilibria using reactive particles. Chemical species are referred to by an integer value stored in the particle type property. Chemical reactions take place by changing the value in the type property via Monte Carlo moves using the potential energy of the system before and after the reaction .
Please keep in mind the following remarks:
• All reaction methods uses Monte Carlo moves which require potential energies. Therefore reaction methods require support for energy calculations for all active interactions in the simulation. Some algorithms do not support energy calculation, e.g. OIF and IBM.
• When modeling reactions that do not conserve the number of particles, the method has to create or delete particles from the system. This process can invalidate particle ids, in which case the particles are no longer numbered contiguously. Particle slices returned by system.part are still iterable, but the indices no longer match the particle ids.
• Checkpointing is not supported, since the state of the Mersenne Twister random number generator cannot be serialized.
• For improved performance, you can set the type of invalidated particles with set_non_interacting_type() in all reaction method classes.
## 19.1. Thermodynamic ensembles¶
### 19.1.1. Reaction ensemble¶
The reaction ensemble allows to simulate chemical reactions which can be represented by the general equation:
$\mathrm{\nu_1 S_1 +\ \dots\ \nu_l S_l\ \rightleftharpoons\ \nu_m S_m +\ \dots\ \nu_z S_z } \label{general-eq}$
where $$\nu_i$$ is the stoichiometric coefficient of species $$S_i$$. By convention, stoichiometric coefficients of the species on the left-hand side of the reaction (reactants) attain negative values, and those on the right-hand side (products) attain positive values, so that the reaction can be equivalently written as
$\mathrm{\sum_i \nu_i S_i = 0} \,. \label{general-eq-sum}$
The equilibrium constant of the reaction is then given as
$K = \exp(-\Delta_{\mathrm{r}}G^{\ominus} / k_B T) \quad\text{with}\quad \Delta_{\mathrm{r}}G^{\ominus} = \sum_i \nu_i \mu_i^{\ominus}\,. \label{Keq}$
Here $$k_B$$ is the Boltzmann constant, $$T$$ is temperature, $$\Delta_{\mathrm{r}}G^{\ominus}$$ standard Gibbs free energy change of the reaction, and $$\mu_i^{\ominus}$$ the standard chemical potential (per particle) of species $$i$$. Note that thermodynamic equilibrium is independent of the direction in which we write the reaction. If it is written with left and right-hand side swapped, both $$\Delta_{\mathrm{r}}G^{\ominus}$$ and the stoichiometric coefficients attain opposite signs, and the equilibrium constant attains the inverse value. Further, note that the equilibrium constant $$K$$ is the dimensionless thermodynamic, concentration-based equilibrium constant, defined as
$K(c^{\ominus}) = (c^{\ominus})^{-\bar\nu} \prod_i (c_i)^{\nu_i}$
where $$\bar\nu=\sum_i \nu_i$$, and $$c^{\ominus}$$ is the reference concentration, at which the standard chemical potential $$\Delta_{\mathrm{r}}G^{\ominus}$$ was determined. In practice, this constant is often used with the dimension of $$(c^{\ominus})^{\bar\nu}$$
$K_c(c^{\ominus}) = K(c^{\ominus})\times (c^{\ominus})^{\bar\nu}$
A simulation in the reaction ensemble consists of two types of moves: the reaction move and the configuration move. The configuration move changes the configuration of the system. In the forward reaction, the appropriate number of reactants (given by $$\nu_i$$) is removed from the system, and the concomitant number of products is inserted into the system. In the backward reaction, reactants and products exchange their roles. The acceptance probability $$P^{\xi}$$ for a move from state $$o$$ to $$n$$ in the reaction ensemble is given by the criterion
$P^{\xi} = \text{min}\biggl(1,V^{\bar\nu\xi}\Gamma^{\xi}e^{-\beta\Delta E}\prod_{i=1}\frac{N_i^0!}{(N_i^0+\nu_{i}\xi)!} \label{eq:Pacc} \biggr),$
where $$\Delta E=E_\mathrm{new}-E_\mathrm{old}$$ is the change in potential energy, $$V$$ is the simulation box volume, $$\beta=1/k_\mathrm{B}T$$ is the Boltzmann factor, and $$\xi$$ is the extent of reaction, with $$\xi=1$$ for the forward and $$\xi=-1$$ for the backward direction.
$$\Gamma$$ is proportional to the reaction constant. It is defined as
$\Gamma = \prod_i \Bigl(\frac{\left<N_i\right>}{V} \Bigr)^{\bar\nu} = V^{-\bar\nu} \prod_i \left<N_i\right>^{\nu_i} = K_c(c^{\ominus}=1/\sigma^3)$
where $$\left<N_i\right>/V$$ is the average number density of particles of type $$i$$. Note that the dimension of $$\Gamma$$ is $$V^{\bar\nu}$$, therefore its units must be consistent with the units in which ESPResSo measures the box volume, i.e. $$\sigma^3$$.
It is often convenient, and in some cases even necessary, that some particles representing reactants are not removed from or placed at randomly in the system but their identity is changed to that of the products, or vice versa in the backward direction. A typical example is the ionization reaction of weak polyelectrolytes, where the ionizable groups on the polymer have to remain on the polymer chain after the reaction. The replacement rule is that the identity of a given reactant type is changed to the corresponding product type as long as the corresponding coefficients allow for it. Corresponding means having the same position (index) in the python lists of reactants and products which are used to set up the reaction.
Multiple reactions can be added to the same instance of the reaction ensemble.
An example script can be found here:
For a description of the available methods, see espressomd.reaction_methods.ReactionEnsemble.
### 19.1.2. Grand canonical ensemble¶
As a special case, all stoichiometric coefficients on one side of the chemical reaction can be set to zero. Such a reaction creates particles ex nihilo, and is equivalent to exchanging particles with a reservoir. This type of simulation in the reaction ensemble is equivalent to the grand canonical simulation. Formally, this can be expressed by the reaction
$\mathrm{\emptyset \rightleftharpoons\ \nu_A A } \,,$
where, if $$\nu_A=1$$, the reaction constant $$\Gamma$$ defines the chemical potential of species A. However, if $$\nu_A\neq 1$$, the statistics of the reaction ensemble becomes equivalent to the grand canonical only in the limit of large average number of species A in the box. If the reaction contains more than one product, then the reaction constant $$\Gamma$$ defines only the sum of their chemical potentials but not the chemical potential of each product alone.
Since the Reaction Ensemble acceptance transition probability can be derived from the grand canonical acceptance transition probability, we can use the reaction ensemble to implement grand canonical simulation moves. This is done by adding reactions that only have reactants (for the deletion of particles) or only have products (for the creation of particles). There exists a one-to-one mapping of the expressions in the grand canonical transition probabilities and the expressions in the reaction ensemble transition probabilities.
### 19.1.3. Constant pH¶
As before in the reaction ensemble, one can define multiple reactions (e.g. for an ampholytic system which contains an acid and a base) in one ConstantpHEnsemble instance:
cpH=reaction_methods.ConstantpHEnsemble(
temperature=1, exclusion_range=1, seed=77)
product_types=[1, 2], product_coefficients=[1, 1],
default_charges={0: 0, 1: -1, 2: +1})
cpH.add_reaction(gamma=1/(10**-14/K_diss), reactant_types=[3], reactant_coefficients=[1], product_types=[0, 2], product_coefficients=[1, 1], default_charges={0:0, 2:1, 3:1} )
An example script can be found here:
In the constant pH method due to Reed and Reed it is possible to set the chemical potential of $$H^{+}$$ ions, assuming that the simulated system is coupled to an infinite reservoir. This value is the used to simulate dissociation equilibrium of acids and bases. Under certain conditions, the constant pH method can yield equivalent results as the reaction ensemble . However, it treats the chemical potential of $$H^{+}$$ ions and their actual number in the simulation box as independent variables, which can lead to serious artifacts. The constant pH method can be used within the reaction ensemble module by initializing the reactions with the standard commands of the reaction ensemble.
The dissociation constant, which is the input of the constant pH method, is the equilibrium constant $$K_c$$ for the following reaction:
$\mathrm{HA \rightleftharpoons\ H^+ + A^- } \,,$
For a description of the available methods, see espressomd.reaction_methods.ConstantpHEnsemble.
### 19.1.4. Widom Insertion (for homogeneous systems)¶
The Widom insertion method measures the change in excess free energy, i.e. the excess chemical potential due to the insertion of a new particle, or a group of particles:
$\begin{split}\mu^\mathrm{ex}_B & :=\Delta F^\mathrm{ex} =F^\mathrm{ex}(N_B+1,V,T)-F^\mathrm{ex}(N_B,V,T)\\ &=-kT \ln \left(\frac{1}{V} \int_V d^3r_{N_B+1} \langle \exp(-\beta \Delta E_\mathrm{pot}) \rangle_{N_B} \right)\end{split}$
For this one has to provide the following reaction to the Widom method:
type_B=1
widom = reaction_methods.WidomInsertion(
temperature=temperature, seed=77)
reactant_coefficients=[], product_types=[type_B],
product_coefficients=[1], default_charges={1: 0})
widom.calculate_particle_insertion_potential_energy(reaction_id=0)
The call of add_reaction define the insertion $$\mathrm{\emptyset \to type_B}$$ (which is the 0th defined reaction). Multiple reactions for the insertions of different types can be added to the same WidomInsertion instance. Measuring the excess chemical potential using the insertion method is done by calling widom.calculate_particle_insertion_potential_energy(reaction_id=0) multiple times and providing the accumulated sample to widom.calculate_excess_chemical_potential(particle_insertion_potential_energy_samples=samples). If another particle insertion is defined, then the excess chemical potential for this insertion can be measured in a similar fashion by sampling widom.calculate_particle_insertion_potential_energy(reaction_id=1). Be aware that the implemented method only works for the canonical ensemble. If the numbers of particles fluctuate (i.e. in a semi grand canonical simulation) one has to adapt the formulas from which the excess chemical potential is calculated! This is not implemented. Also in a isobaric-isothermal simulation (NpT) the corresponding formulas for the excess chemical potentials need to be adapted. This is not implemented.
The implementation can also deal with the simultaneous insertion of multiple particles and can therefore measure the change of excess free energy of multiple particles like e.g.:
$\begin{split}\mu^\mathrm{ex, pair}&:=\Delta F^\mathrm{ex, pair}:= F^\mathrm{ex}(N_1+1, N_2+1,V,T)-F^\mathrm{ex}(N_1, N_2 ,V,T)\\ &=-kT \ln \left(\frac{1}{V^2} \int_V \int_V d^3r_{N_1+1} d^3 r_{N_2+1} \langle \exp(-\beta \Delta E_\mathrm{pot}) \rangle_{N_1, N_2} \right)\end{split}$
Note that the measurement involves three averages: the canonical ensemble average $$\langle \cdot \rangle_{N_1, N_2}$$ and the two averages over the position of particles $$N_1+1$$ and $$N_2+1$$. Since the averages over the position of the inserted particles are obtained via brute force sampling of the insertion positions it can be beneficial to have multiple insertion tries on the same configuration of the other particles.
One can measure the change in excess free energy due to the simultaneous insertions of particles of type 1 and 2 and the simultaneous removal of a particle of type 3:
$\mu^\mathrm{ex}:=\Delta F^\mathrm{ex, }:= F^\mathrm{ex}(N_1+1, N_2+1, N_3-1,V,T)-F^\mathrm{ex}(N_1, N_2, N_3 ,V,T)$
For this one has to provide the following reaction to the Widom method:
widom.add_reaction(reactant_types=[type_3],
reactant_coefficients=[1], product_types=[type_1, type_2],
product_coefficients=[1,1], default_charges={1: 0})
widom.calculate_particle_insertion_potential_energy(reaction_id=0)
Be aware that in the current implementation, for MC moves which add and remove particles, the insertion of the new particle always takes place at the position where the last particle was removed. Be sure that this is the behavior you want to have. Otherwise implement a new function WidomInsertion::make_reaction_attempt in the core.
An example script which demonstrates how to measure the pair excess chemical potential for inserting an ion pair into a salt solution can be found here:
For a description of the available methods, see espressomd.reaction_methods.WidomInsertion.
## 19.2. Practical considerations¶
### 19.2.1. Converting tabulated reaction constants to internal units in ESPResSo¶
The implementation in ESPResSo requires that the dimension of $$\Gamma$$ is consistent with the internal unit of volume, $$\sigma^3$$. The tabulated values of equilibrium constants for reactions in solution, $$K_c$$, typically use $$c^{\ominus} = 1\,\mathrm{moldm^{-3}}$$ as the reference concentration, and have the dimension of $$(c^{\ominus})^{\bar\nu}$$. To be used with ESPResSo, the value of $$K_c$$ has to be converted as
$\Gamma = K_c(c^{\ominus} = 1/\sigma^3) = K_c(c^{\ominus} = 1\,\mathrm{moldm^{-3}}) \Bigl( N_{\mathrm{A}}\bigl(\frac{\sigma}{\mathrm{dm}}\bigr)^3\Bigr)^{\bar\nu}$
where $$N_{\mathrm{A}}$$ is the Avogadro number. For gas-phase reactions, the pressure-based reaction constant, $$K_p$$ is often used, which can be converted to $$K_c$$ as
$K_p(p^{\ominus}=1\,\mathrm{atm}) = K_c(c^{\ominus} = 1\,\mathrm{moldm^{-3}}) \biggl(\frac{c^{\ominus}RT}{p^{\ominus}}\biggr)^{\bar\nu},$
where $$p^{\ominus}=1\,\mathrm{atm}$$ is the standard pressure. Consider using the python module pint for unit conversion.
### 19.2.2. Coupling reaction methods to molecular dynamics¶
The Monte Carlo (MC) sampling of the reaction can be coupled with a configurational sampling using Molecular Dynamics (MD). For non-interacting systems this coupling is not an issue, but for interacting systems the insertion of new particles can lead to instabilities in the MD integration ultimately leading to a crash of the simulation.
This integration instabilities can be avoided by defining a distance around the particles which already exist in the system where new particles will not be inserted, which is defined by the required keyword exclusion_range. This prevents big overlaps with the newly inserted particles, avoiding too big forces between particles, which prevents the MD integration from crashing. The value of the exclusion range does not affect the limiting result and it only affects the convergence and the stability of the integration. For interacting systems, it is usually a good practice to choose the exclusion range such that it is comparable to the diameter of the particles.
If particles with significantly different sizes are present, it is desired to define a different exclusion range for each pair of particle types. This can be done by defining an exclusion radius per particle type by using the optional argument exclusion_radius_per_type. Then, their exclusion range is calculated using the Lorentz-Berthelot combination rule, i.e. exclusion_range = exclusion_radius_per_type[particle_type_1] + exclusion_radius_per_type[particle_type_2]. If the exclusion radius of one particle type is not defined, the value of the parameter provided in exclusion_range is used by default. If the value in exclusion_radius_per_type is equal to 0, then the exclusion range of that particle type with any other particle is 0.
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http://en.wikipedia.org/wiki/Generalized_least_squares
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# Generalized least squares
In statistics, generalized least squares (GLS) is a technique for estimating the unknown parameters in a linear regression model. The GLS is applied when the variances of the observations are unequal (heteroscedasticity), or when there is a certain degree of correlation between the observations. In these cases ordinary least squares can be statistically inefficient, or even give misleading inferences.
## Method outline
In a typical linear regression model we observe data $\{y_i,x_{ij}\}_{i=1..n,j=1..p}$ on n statistical units. The response values are placed in a vector Y = (y1, ..., yn)′, and the predictor values are placed in the design matrix X = [[xij]], where xij is the value of the jth predictor variable for the ith unit. The model assumes that the conditional mean of Y given X is a linear function of X, whereas the conditional variance of the error term given X is a known matrix Ω. This is usually written as
$Y = X\beta + \varepsilon, \qquad \mathrm{E}[\varepsilon|X]=0,\ \operatorname{Var}[\varepsilon|X]=\Omega.$
Here β is a vector of unknown “regression coefficients” that must be estimated from the data.
Suppose b is a candidate estimate for β. Then the residual vector for b will be Y − Xb. Generalized least squares method estimates β by minimizing the squared Mahalanobis length of this residual vector:
$\hat\beta = \underset{b}{\rm arg\,min}\,(Y-Xb)'\,\Omega^{-1}(Y-Xb),$
Since the objective is a quadratic form in b, the estimator has an explicit formula:
$\hat\beta = (X'\Omega^{-1}X)^{-1} X'\Omega^{-1}Y.$
### Properties
The GLS estimator is unbiased, consistent, efficient, and asymptotically normal:
$\sqrt{n}(\hat\beta - \beta)\ \xrightarrow{d}\ \mathcal{N}\!\left(0,\,(X'\,\Omega^{-1}X)^{-1}\right).$
GLS is equivalent to applying ordinary least squares to a linearly transformed version of the data. To see this, factor Ω = BB′, for instance using the Cholesky decomposition. Then if we multiply both sides of the equation Y = + ε by B−1, we get an equivalent linear model Y* = X*β + ε*, where Y* = B−1Y, X* = B−1X, and ε* = B−1ε. In this model Var[ε*] = B−1Ω(B−1)′ = I. Thus we can efficiently estimate β by applying OLS to the transformed data, which requires minimizing
$(Y^*-X^*b)'(Y^*-X^*b) = (Y-Xb)'\,\Omega^{-1}(Y-Xb).$
This has the effect of standardizing the scale of the errors and “de-correlating” them. Since OLS is applied to data with homoscedastic errors, the Gauss–Markov theorem applies, and therefore the GLS estimate is the best linear unbiased estimator for β.
## Weighted least squares[1]
A special case of GLS called weighted least squares (WLS) occurs when all the off-diagonal entries of Ω are 0. This situation arises when the variances of the observed values are unequal (i.e. heteroscedasticity is present), but where no correlations exist among the observed variances. The weight for unit i is proportional to the reciprocal of the variance of the response for unit i.
## Feasible generalized least squares
In practice, the method cannot be applied since the covariance of the errors is generally unknown. One strategy for building an implementable version of GLS is the Feasible Generalized Least Squares (FGLS) estimator, where we proceed in two stages: (1) in the first step the model is estimated by OLS or another consistent (but inefficient) estimator, and the residuals are used to build a consistent estimator of the errors covariance matrix (to do so, we often need to examine the model adding additional constraints, for example if the errors follow a time series process, we generally need some theoretical assumptions on this process to ensure that a consistent estimator is available); and (2) using the consistent estimator of the covariance matrix of the errors, we implement GLS ideas.
A cautionary note is that the FGLS estimator is not always consistent. One case in which FGLS might be inconsistent is if there are individual specific fixed effects.[2]
In general this estimator has different properties than GLS. For large samples (i.e., asymptotically) all properties are (under appropriate conditions) common with respect to GLS, but for finite samples the properties of FGLS estimators are unknown: they vary dramatically with each particular model, and as a general rule their exact distributions cannot be derived analytically. For finite samples FGLS may be even less efficient than OLS in some cases. Thus, while GLS can be made feasible, it is not always wise to apply this method when the sample is small. A method sometimes used to improve the accurancy of the estimators in finite samples is to iterate, i.e. taking the residuals from FGLS to update the errors covariance estimator, and then updating the FGLS estimation, applying the same idea iteratively until the estimators vary less than some tolerance. But this method actually does not necessarily improve the efficiency of the estimator very much if the original sample was small. A reasonable option when samples are not too large is to apply OLS, but throwing away the classical variance estimator
$\sigma^2*(X'X)^{-1}$
(which is inconsistent in this framework) and using a HAC (Heteroskedasticity and Autocorrelation Consistent) estimator. For example, in autocorrelation context we can use the Bartlett estimator (often known as Newey-West estimator since these authors popularized the use of this estimator among econometricians in their 1987 Econometrica article), and in heteroskedastic context we can use the Eicker–White estimator ( Eicker–White ). This approach is much safer, and it is the appropriate path to take unless the sample is large, and "large" is sometimes a slippery issue (e.g. if the errors distribution is asymmetric the required sample would be much larger).
The ordinary least squares (OLS) estimator is calculated as usual by
$\widehat \beta_{OLS} = (X' X)^{-1} X' y$
and estimates of the residuals $\widehat{u}_j= (Y-Xb)_j$ are constructed.
For simplicity consider the model for heteroskedastic errors. Assume that the variance-covariance matrix $\Omega$ of the error vector is diagonal, or equivalently that errors from distinct observations are uncorrelated. Then each diagonal entry may be estimated by the fitted residuals $\widehat{u}_j$ so $\widehat{\Omega}_{OLS}$ may be constructed by
$\widehat{\Omega}_{OLS} = \operatorname{diag}(\widehat{\sigma}^2_1, \widehat{\sigma}^2_2, \dots , \widehat{\sigma}^2_n).$
It is important to notice that the squared residuals cannot be used in the previous expression, we need an estimator of the errors variances. To do so we can use a parametric heteroskedasticity model, or a nonparametric estimator. Once this step is fulfilled, we can proceed:
Estimate $\beta_{FGLS1}$ using $\widehat{\Omega}_{OLS}$ using weighted least squares
$\widehat \beta_{FGLS1} = (X'\widehat{\Omega}^{-1}_{OLS} X)^{-1} X' \widehat{\Omega}^{-1}_{OLS} y$
The procedure can be iterated, the first iteration is given by
$\widehat{u}_{FGLS1} = Y - X \widehat \beta_{FGLS1}$
$\widehat{\Omega}_{FGLS1} = \operatorname{diag}(\widehat{\sigma}^2_{FGLS1,1}, \widehat{\sigma}^2_{FGLS1,2}, \dots ,\widehat{\sigma}^2_{FGLS1,n})$
$\widehat \beta_{FGLS2} = (X'\widehat{\Omega}^{-1}_{FGLS1} X)^{-1} X' \widehat{\Omega}^{-1}_{FGLS1} y$
This estimation of $\widehat{\Omega}$ can be iterated to convergence.
Under regularity conditions any of the FGLS estimator (or that of any of its iterations, if we iterate a finite number of times) is asymptotically distributed as
$\sqrt{n}(\hat\beta_{FGLS} - \beta)\ \xrightarrow{d}\ \mathcal{N}\!\left(0,\,V\right).$
where n is the sample size and
$V = \text{p-lim}(X'\Omega^{-1}X/T)$
here p-lim means limit in probability
## References
1. ^ Strutz, T. (2010). Data Fitting and Uncertainty (A practical introduction to weighted least squares and beyond). Vieweg+Teubner. ISBN 978-3-8348-1022-9., chapter 3
2. ^ Hansen, Christina (07.13.2004). "GENERALIZED LEAST SQUARES INFERENCE IN PANEL AND MULTILEVEL MODELS WITH SERIAL CORRELATION AND FIXED EFFECTS". University of Chicago - Booth Faculty Pages. Retrieved 07.29.2014.
Some texbooks on econometrics where GLS and FGLS are discussed are:
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https://www.scienceopen.com/document?vid=46583525-234e-4273-a4f2-8b92748450bc
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# Unstable amplitude and noisy image induced by tip contamination in dynamic force mode atomic force microscopy.
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### Abstract
Liquid 1-decanethiol was confined on an atomic force microscope (AFM) tip apex and the effect was investigated by measuring amplitude-distance curves in dynamic force mode. Within the working distance in the dynamic force mode AFM, the thiol showed strong interactions bridging between a gold-coated probe tip and a gold-coated Si substrate, resulting in unstable amplitude and noisy AFM images. We show that under such a situation, the amplitude change is dominated by the extra forces induced by the active material loaded on the tip apex, overwhelming the amplitude change caused by the geometry of the sample surface, thus resulting in noise in the image the tip collects. We also show that such a contaminant may be removed from the apex by pushing the tip into a material soft enough to avoid damage to the tip.
17578111
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http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580892
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Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580892
Title: Quantum cascade laser spectroscopy : developments and applications
Author: Walker, Richard James
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2011
Availability of Full Text:
Access through EThOS: Full text unavailable from EThOS. Please try the link below. Access through Institution:
Abstract:
This thesis presents work examining the characteristics and applicability of quantum cascade lasers. An introduction is given explaining both the desire for a widely tunable, narrow bandwidth device working in the midinfrared, as well as detailing the ways in which quantum cascade lasers (QCLs) fulfill these requirements. The development and manufacture of QCLs are then discussed. The experimental section of this thesis is then split into three parts. Chapter 2 concerns the characterisation and application of several pulsed QCLs. The intrapulse mode of operation is employed and the effect of the resulting rapid frequency chirp upon molecular spectra is investigated in the form of rapid passage signals. The evolution of said rapid passage signals is then investigated as a function of chromophore pressure and identity, with different QCLs, chirp rates, and optical path lengths. The prospect of producing population transfer with chirped lasers is discussed. Chapters 3, 4, and 5 are then concerned with the application and characterisation of continuous wave QCLs. In these chapters a widely tunable commercially produced EC-QCL is utilised as well as two DFB QCLs, one of which is used in tandem with a home-made mount and temperature controller. In Chapter 3 a number of sensitive detection techniques are compared with the employment of wavelength modulation spectroscopy, long path cells and optical cavities, and the narrow bandwidth of QCLs utilised to determine a previously unknown spectral constant of DBr. Chapters 4 and 5 then utilise the high power of an external cavity quantum cascade laser in sub-Doppler Lamb-dip and polarisation spectroscopy measurements and then a pump-probe experiment. The laser linewidth is investigated on a millisecond timescale returning a current noise limited value of c.a. 2 MHz and the fundamental linewidth of the device investigated by altering the injection current. Chapter 5 is concerned with the pump-probe experiment, directly measuring the hot band absorption in a ladder like transition (R(6.5)$_\frac{1}{2}$ $v=1\leftarrow0$ and P(7.5)$_\frac{1}{2}$ $v=1\leftarrow0$). The Bennett peak in the hot band is observed with a DFB-QCL swept at $\sim 0.15$ MHz ns$^{-1}$ and is seen not just as a pump bandwidth limited lineshape, but as a highly velocity selected rapid passage signal. The effect of pressure, pump and probe scan rate and power upon this rapid passage signal is also studied. It is further noted that rapid thermalisation occurs within $v=1$ such that at pressures above c.a. 30 mTorr a broad NO doublet absorption is observed beneath the Bennett peak from which a total population transfer of c.a. $16 \%$ can be estimated. Finally an experiment is discussed in which this population transfer could be increased for use in secondary applications. Chapter 6 then presents initial measurements with two prototype pulsed 3.3 \si{\micro\metre} QCLs considering the prospects of such devices. A Fabry-P\'{e}rot device is first studied using a Fourier transform spectrometer and temperature tuning used to produce a spectrum of the Q-branch of CH$_4$ around 3025 cm$^{-1}$. Experiments are then performed using a DFB QCL investigating the chirp rate of the system as an indicator of the rate of heat accumulation within the system. Heat management is of particular consideration when the sea-change is made from pulsed to continuous devices. For this device absorption spectra of two CH$_4$ transitions at 2971 cm$^{-1}$ are used to determine the chirp rate, which is found to be c.a. 1.8 GHz ns$^{-1}$, at least an order of magnitude higher than that of the longer wavelength pulsed devices considered in Chapter 2.
Supervisor: Ritchie, Grant A. D. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.580892 DOI: Not available
Keywords: laser ; optics ; non-linear optics ; spectroscopy ; quantum cascade laser ; gas ; midinfrared ; population transfer ; rapid passage ; gas phase spectroscopy ; Chemistry & allied sciences ; Physical Sciences ; Atmospheric chemistry ; Laser Spectroscopy ; Photochemistry and reaction dynamics ; Physical & theoretical chemistry ; Spectroscopy and molecular structure ; Atomic and laser physics
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https://www.research.ed.ac.uk/en/publications/truthful-facility-assignment-with-resource-augmentation-an-exact--2
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# Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship
Ioannis Caragiannis, Aris Filos-Ratsikas*, Søren Kristoffer Stiil Frederiksen, Kristoffer Arnsfelt Hansen, Zihan Tan
*Corresponding author for this work
Research output: Contribution to journalArticlepeer-review
## Abstract
We study the truthful facility assignment problem, where a set of agents with private mostpreferred points on a metric space have to be assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., the total distance between the most-preferred points of the agents and their corresponding facilities in the assignment, under the constraint of truthfulness, which ensures that agents do not misreport their most-preferred points. We propose a resource augmentation framework, where a truthful mechanism is evaluated by its worst-case performance on an instance with enhanced facility capacities against the optimal mechanism on the same instance with the original capacities. We study a well-known mechanism, Serial Dictatorship, and provide an exact analysis of its performance. Among other results, we prove that Serial Dictatorship has approximation ratio g/(g − 2) when the capacities are multiplied by any integer g ≥ 3. Our results suggest that with a limited augmentation of the resources we can achieve exponential improvements on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation factor becomes large. We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation.
Original language English 27 Mathematical Programming, Series B 2 Nov 2022 https://doi.org/10.1007/s10107-022-01902-8 E-pub ahead of print - 2 Nov 2022
## Keywords
• Mechanism design without money
• Serial dictatorship
• Resource augmentation
• Approximation ratio
## Fingerprint
Dive into the research topics of 'Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship'. Together they form a unique fingerprint.
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https://www.vedicastrologysolutions.com/vedic-rahu-shanti-anushthan/
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Rahu is the most malefic planet in all the planets , it only gives positive result when it placed alone in 3rd, 10th and 11th house, where it gives quite good result , but at the end it takes every things it has given. Apart from above mentioned places Rahu always give very negative result in any kundali. It becomes more worse when it Mahadasha or antar dasha comes. It creates so much problem in education, career growth , children, married life etc depending which place it is affecting.
In above such cases where Rahu is giving Negative result , The Vedic Rahu Shanti Anushthan is the most effective way to reduce its effect.
In Vedic Rahu Shanti Anushthan we do Jap of Its Mantra, Rudrabhishek , Stuti & Yagya for the particular person.
We also take care of auspicious Muhurt, Direction, Havan Samidha and Samagri who supress the negative impact of Rahu Dosha. All Major Karma done under my guideline.
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https://www.physicsforums.com/threads/differential-geometry-question.214334/
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Homework Help: Differential Geometry Question
1. Feb 10, 2008
mXCSNT
1. The problem statement, all variables and given/known data
Assume that $$\tau(s) \neq 0$$ and $$k'(x) \neq 0$$ for all $$s \in I$$. Show that a necessary and sufficient condition for $$\alpha(I)$$ to lie on a sphere is that $$R^2 + (R')^2T^2 = const$$ where $$R = 1/k$$, $$T = 1/\tau$$, and $$R' = \frac{dr}{ds}$$
2. Relevant equations
$$\alpha(s)$$ is a curve in R3 parametrized by arc length
$$k = curvature = |\alpha''|$$
$$\tau = torsion = -\frac{\alpha' \times \alpha'' \cdot \alpha'''}{k^2}$$ (note sign; this is opposite of some conventions)
3. The attempt at a solution
I've approached this from 2 directions, but I haven't gotten them to meet. First, a necessary and sufficient condition is that $$|\alpha - P|$$ is constant, where P is the center of the circle. Alternatively, $$(\alpha - P) \cdot \alpha' = 0$$.
And I've expanded out $$R^2 + (R')^2T^2 = const$$ to get
$$\frac{(\alpha' \times \alpha'' \cdot \alpha''')^2 + (\alpha'' \cdot \alpha''')^2}{(\alpha'' \cdot \alpha'')(\alpha' \times \alpha'' \cdot \alpha''')^2} = const$$
Also, I'm going to guess that the const on the right hand side is some function of the radius of the sphere, maybe the square of it (which would be $$(\alpha - P) \cdot (\alpha - P)$$), because what else is constant in a sphere?
But I don't know where to go from here. I'm just looking for a hint at an avenue of approach, please nothing specific.
2. Feb 10, 2008
mXCSNT
So if I assume that the "const" in question is the square of the radius, that could make R and (R')T the lengths of respective legs of a right triangle whose hypotenuse is the radius. I know that R is the radius of curvature, so drawing a diagram I'm guessing that the center P is
$$P = Rn - (R')Tb$$
(where n is the normal vector $$\alpha''/|\alpha''|$$ and b = $$t \times n$$ is the binormal vector).
So then the sphere radius I want to test, $$(\alpha-P) \cdot (\alpha-P)$$, becomes $$(\alpha - Rn + (R')Tb) \cdot (\alpha - Rn + (R')Tb)$$
$$= \alpha \cdot \alpha - 2 R \alpha \cdot n + 2 R' T \alpha \cdot b + R^2 + (R')^2T^2$$
Now if I assume that $$R^2 + (R')^2T^2$$ is constant I need to show that $$\alpha \cdot \alpha - 2 R \alpha \cdot n + 2 R' T \alpha \cdot b$$ is constant to show the sphere radius is constant. Am I on the right track?
3. Feb 10, 2008
mXCSNT
Revised guess for center P:
$$P = \alpha + Rn - (R')Tb$$
so now the constant radius follows immediately and I simply have to show that P itself is constant.
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http://math.stackexchange.com/users/8679/hristo?tab=summary
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Hristo
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+20 another balls and bins question +10 closed form equation to figure out sudoku square from given index +10 How do I calculate the $p$-norm of a matrix? +5 closed form equation to figure out sudoku square from given index
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https://chemistry.stackexchange.com/questions/104673/which-reaction-rate-formula-is-suited-for-diatomic-molecules-in-a-plasma
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# Which reaction rate formula is suited for diatomic molecules in a plasma?
I am an experimental physicist, so I unfortunately do not know much about chemistry except the basics. For my current study, I am investigating diatomic molecule formation in plasma. These diatomic molecules are often not stable, but they get excited and emit light, which makes them interesting for spectroscopy.
What I want to know is: If I have atoms, ions and electrons in my plasma, and I have some temperature T, which model for the molecular reactions would best describe this system? What kind of reaction rate formula would I need?
To give a specific example and to explain my current assumptions: In plasma of samples containing Ca and Cl (among other elements), I get emission from the diatomic molecule CaCl. I assume that the concentrations correlate with the stoichiometry of the sample. Now I want to know the amount of CaCl that forms in the plasma, and how it relates to the concentrations in the sample. I currently assume that the reaction can be described like this: $$\ce{Ca + Cl -> CaCl}$$ So it should be very simple, as every element is already present either as an atom or as an ion. (Note that I do not really understand how the ions play into this, I'm assuming that the reaction is the same but that an electron is captured during the reaction - if someone could elaborate on this, I would also be grateful.)
As for the reaction rate, I have found the following rate law: $$r = k [A]^m [B]^n$$ Where m and n are integers and [A] and [B] are the concentrations of two reacting species A and B. What I don't understand is the physical interpretation of m and n - I have a feeling that for single-element reactants like the ones in my case, they should both be 1. Is that correct, or is there a way these could be wildly different, and maybe even non-integers? Because my experimental results can best be described by this formula if m and n are non-integers (m = 0.6 and n = 1.3, for example). But that confuses me a lot and makes me think that maybe this type of reaction rate formula might not be suited for reactions of atoms/ions in a plasma.
I have found also another formula for the bimolecular reaction on a surface (called the Langmuir–Hinshelwood mechanism): $$r = k \frac{K_1[A]K_2[B]}{(1+K_1[A]+K_2[B])^2}$$ While I have no idea how this would relate to my situation, the results I get from this formula are quite nice, and I do not have to change anything from integers to non-integers. So maybe this could be a suitable explanation instead?
I should note that, if I say "it fits my experiments", I mean that I have done several experiments with different concentrations of Ca and Cl in my sample, and I try to fit them all by saying that the intensity of my CaCl emission should be proportional to the reaction rate, and the reaction rate parameters have to be the same in each case. There are a lot of assumptions here, but since the plasma itself is very complex, this is the best I can do for now.
Thank you very much for your help!
EDIT: After reading some of Paul's suggestions, my understanding is now that I have to think about every possible reaction that might take place, and that I have to distinguish between the excited states CaCl(A) and CaCl(B) and the ground state CaCl(X): $$\ce{Cl + e- <=> Cl-} \\ \ce{Cl <=> Cl+ + e-} \\ \ce{Ca <=> Ca+ + e-} \\ \ce{Ca + Cl <=> CaCl(A)} \\ \ce{Ca + Cl <=> CaCl(B)} \\ \ce{Ca+ + Cl- <=> CaCl(A)} \\ \ce{Ca+ + Cl- <=> CaCl(B)} \\ \ce{CaCl(A) + M <=> CaCl(X) + M} \\ \ce{CaCl(B) + M <=> CaCl(A) + M} \\ \ce{CaCl(B) + M <=> CaCl(X) + M} \\ \ce{Ca+ + Cl + M <=> CaCl+ + M} \\ \ce{Ca + Cl+ + M <=> CaCl+ + M} \\ \ce{CaCl+ + e- <=> CaCl(A)} \\ \ce{CaCl+ + e- <=> CaCl(B)} \\ \ce{CaCl(A) -> CaCl(X) + h\nu} \\ \ce{CaCl(B) -> CaCl(X) + h\nu} \\$$ This just seems ridiculously complicated, if you ask me. (And I have not even started taking into account that Ca also reacts with O to CaO.) Surely this can be simplified to some extent? Some of these reactions are probably very unlikely?
But so for each species, I would then set up a reaction rate based on the equations above: $$\frac{d[\ce{Cl}]}{dt} = - k_1[\ce{Cl}][\ce{e-}] + k_1'[\ce{Cl-}] - k_2[Cl] + k_2'[\ce{Cl+}][\ce{e-}] + \dots \\ \text{etc.}$$ Then I can solve this set of equations either numerically or by simplifying something.
Am I missing something here? Are the equations correct? Do you think they can be simplified in some way?
• You oversimplify things greatly. It is very unlikely that only one reaction will suffice to describe the kinetics in your plasma. Also the reaction you mention must involve a third scattering body to take away the binding energy or requires a very fast radiative recombination rate. It is also likely that the electrons in your plasma are responsible for exciting (part of) your molecules. You'll have to consider a more complex mechanism to predict the production of the excited states of CaCl and observed fluorescence.
– Paul
Nov 22, 2018 at 10:13
• The points you mention (third scattering body, fast radiative recombination) are exactly the kind of thing that I wanted to know more about. This is why I am asking the question in the first place. As for the excitation, I would have thought that this can be regarded as a separate step. First, I need to know how many molecules even form before I can look at their emission rate. Nov 22, 2018 at 11:40
• The point about kinetics is that - in general - it involves coupled differential equations, so you should look at all relevant processes simultaneously. I think you're best of consulting a text book on the topic such as Laidler's Chemical Kinetics. Articles that might be of interest are J. Photochem. 25, 389 (1984) or Phys. Rev. E 57, 4684 (1998).
– Paul
Nov 22, 2018 at 12:34
• Thank you for the literature recommendations. In the beginning of the first article, three reaction equations are presented. Then they say that based on these, the intensity of an O2 emission should be I = k1[O]^2[M]/(1+k2/k3 [N2]). This is very interesting, can you maybe help me understand what they are doing there? I mean, this seems to be the type of derivation that I have in mind - start with something complex, but end up at something simple. Nov 22, 2018 at 15:47
• They assume equilibrium conditions so that the reaction rate equals zero. Taking the expression for the rate of formation of excited oxygen molecules and setting the rate to zero allows to write the equilibrium concentration of O2 in terms of the other species.
– Paul
Nov 22, 2018 at 17:43
$$\ce{A + B ->[k1] AB^{*}} \\ \ce{AB^{*} ->[k2] A + B} \\ \ce{AB^{*} + M ->[k3] AB + M} \\ \ce{AB^{*} + M ->[\gamma k3] AB(A) + M} \\ \ce{AB(A) + M ->[k4] AB(X) + M} \\ \ce{AB(A) ->[k5] AB(x) + h\nu} \\$$ Here $$\ce{AB^{*}}$$ is a precursor of molecule AB that dissociates easily and needs to relax by collision with M to some form of AB, which may be excited or not. A fraction $$\gamma$$ of these collisions will produce AB(A), which is molecule AB in the electronic state A. This can either collide with another species M again, or it can emit a photon. In both cases it transitions to the ground state AB(X). Only the last transition is the one that produces my molecular emission, so that is the one that interests me. Using the defined reaction constants, I can describe the formation of $$\ce{AB^{*}}$$ and AB(A) this way: $$\frac{d[AB^*]}{dt} = k_1 [A] [B] - k_2 [AB^*] - k_3[AB^*]\\ \frac{d[AB(A)]}{dt} = \gamma k_3 [AB^*] [M] - k_4 [AB(A)] [M] - k_5 [AB(A)]$$
(Note that [M] represents different concentrations depending on which species is most dominant in each of these terms, i.e. [M] cannot be factored out.) Finally, I can make the assumption that these reactions are very fast in comparison to the changes in my plasma, so that I have a quasistatic process. This needs to be validated by actual experiments, but let's assume it for now. Then we can say that the concentrations do not change, i.e. $$\frac{d[AB^*]}{dt} = \frac{d[AB(A)]}{dt} = 0$$, and we get: $$[AB^*] = \frac{k_1 [A] [B]}{k_2+k_3} \\ [AB(A)] = \frac{\gamma k_3 [AB^*] [M]}{k_4 [M] + k_5} = \frac{\gamma k_1 k_3 [M]}{(k_2 + k_3)(k_4 [M] + k_5)} [A] [B]$$ Now, since my intensity is proportional to $$k_5 [AB(A)]$$, I can write my intensity as: $$I \propto [A] [B]$$
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https://homework.cpm.org/category/CON_FOUND/textbook/mc2/chapter/11/lesson/11.3.1/problem/11-84
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### Home > MC2 > Chapter 11 > Lesson 11.3.1 > Problem11-84
11-84.
Simplify each expression.
1. $x^{2}x^{3}x^{2}$
To multiply expressions with a common base, add
the exponents together.
$x^{(2+3+2)}$
$x^7$
2. $\left(xy^{3}z\right)\left(xy\right)$
See part (a).
$x^2y^4z$
3. $5 · t^{2 }· 5^{3 }· t$
See part (a) and (b).
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http://swmath.org/software/10781
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# SU3
Program for generating tables of SU(3)⊃SU(2)⊗U(1) coupling coefficients. A C-language program which tabulates the isoscalar factors and Clebsch-Gordan coefficients for products of representations in SU(3)⊃SU(2)⊗U(1) is presented. These are efficiently computed using recursion relations, and the results are presented in exact precision as square roots of rational numbers. Output is in LaTeX format.
## References in zbMATH (referenced in 3 articles )
Showing results 1 to 3 of 3.
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http://www.physicsforums.com/showpost.php?p=754974&postcount=65
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Recognitions: Homework Help Science Advisor Let K be the set of all solutions that satisfy $\zeta (s) = 0$. Let there exist some p such that: $$\frac{\partial^2 p}{\partial i^2} a^3 - \Gamma (i^2) = 0$$ Now I can prove that these exists a solution $i = f_k (p)$ therefore i exists. If i exists there must be a limit to g(p) and p approaches infinity and therefore p exists. Thus the roots of: $$\int_0^\infty \frac{g(s)}{p \Gamma(s)} ds = \sin i$$ Are synonyms to the Zeta functions roots and all have roots of $\Re (p) = 1/2$ Therefore RH is proven and no one can come up with a counter-example.
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https://www.physicsforums.com/threads/plotting-straight-line-graphs.697171/
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# Plotting Straight Line Graphs
1. Jun 15, 2013
### Peter G.
So, I have to assess the relationship between the Constant of a Spring and the Time Period of Oscillations.
I have researched the equation that links the two and I know that to have a straight line graph I need to plot:
T2 against 1/K
However, I do not know why; how I get to that conclusion.
I have read about log-log graphs and played around with the concept to see if it would yield the plot I mentioned above. I tried plotting for the log of T against the log of K and I did get a straight line plot. I checked if my gradient was equal to -0.5 and my y-intercept was equal to (log 2∏-0.5 log m) and they were, but I still do not understand why I have to plot T2 against 1/K.
2. Jun 15, 2013
### rock.freak667
You are asked to plot that because of the derivation of the periodic time formula for a spring oscillation.
The final equation is
$$T = 2 \pi \sqrt{\frac{m}{k}}$$
If you square both sides you will get
$$T^2 = \frac{4 \pi ^2 m}{k}$$
Which is the form Y=MX where Y = T2 and X = 1/k.
Thus plotting Y vs X i.e. T2 vs. 1/k will give you a straight line. So you can get the mass oscillating if you desire from the gradient of the graph you plotted.
3. Jun 15, 2013
### Staff: Mentor
I like your idea of using a log-log plot much better. I have over 40 years of experience as a practicing engineer, and that is the way I would do it. Congratulations on thinking out of the box.
Chet
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https://www.matematica.pt/en/useful/quadratic-equation-calculator.php
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To find out the roots (zeros) of a second degree function, start by placing that function in canonical form (simplifying as much as possible) and making it equal to zero. After this step, you have a second degree equation where the second member is zero. To solve this equation, start by trying to identify whether it is a complete or incomplete second degree equation. The difference is quite simple. The complete second degree equation has the 3 coefficients: a, b, c and can be written in the form ax^2+bx+c=0. While in the incomplete b or c is missing or both. Then, enter the coefficients of the terms of the equation in the corresponding boxes of the calculator. This way, in addition to getting to know the zeros, you can also view the resolution step by step. If it is a complete equation, the general formula of complete second degree equations is used. If it is incomplete, the first step in solving this type of equations is to draw a common factor, since an x is repeated in both terms. Finally we have two factors whose result is zero, so one of the two must be 0.
NOTE
If you want to perform calculations where the coefficient is a fraction, you must enter the number in decimal form. For example, instead of 1/4 you must enter 0.25.
### Solve a (complete) quadratic equation
Example: Find the zeros (roots) of the equation x^2 + 2x - 15 = 0
a: b: c:
### Solve an incomplete second degree equation (the independent term is missing)
Example: Find the zeros (roots) of the equation 4x^2 + 6x = 0
a: b:
### Solve an incomplete second degree equation (the first degree term is missing)
Example: Find the zeros (roots) of the equation 4x^2 - 16 = 0
a: c:
## Information
Any quadratic equation can have: 2 solutions, if the discriminant (number inside the root) is greater than zero; one solution, if the discriminant is zero; no solution, if the discriminant is negative. If we are working in the universe of complex numbers, then the second-degree equation always has at least one solution.
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https://scikit-survival.readthedocs.io/en/latest/generated/sksurv.metrics.concordance_index_censored.html
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# sksurv.metrics.concordance_index_censored¶
sksurv.metrics.concordance_index_censored(event_indicator, event_time, estimate, tied_tol=1e-08)
Concordance index for right-censored data
The concordance index is defined as the proportion of all comparable pairs in which the predictions and outcomes are concordant.
Samples are comparable if for at least one of them an event occurred. If the estimated risk is larger for the sample with a higher time of event/censoring, the predictions of that pair are said to be concordant. If an event occurred for one sample and the other is known to be event-free at least until the time of event of the first, the second sample is assumed to outlive the first. When predicted risks are identical for a pair, 0.5 rather than 1 is added to the count of concordant pairs. A pair is not comparable if an event occurred for both of them at the same time or an event occurred for one of them but the time of censoring is smaller than the time of event of the first one.
Parameters: event_indicator : array-like, shape = (n_samples,) Boolean array denotes whether an event occurred event_time : array-like, shape = (n_samples,) Array containing the time of an event or time of censoring estimate : array-like, shape = (n_samples,) Estimated risk of experiencing an event tied_tol : float, optional, default: 1e-8 The tolerance value for considering ties. If the absolute difference between risk scores is smaller or equal than tied_tol, risk scores are considered tied. cindex : float Concordance index concordant : int Number of concordant pairs discordant : int Number of discordant pairs tied_risk : int Number of pairs having tied estimated risks tied_time : int Number of pairs having an event at the same time
References
[1] Harrell, F.E., Califf, R.M., Pryor, D.B., Lee, K.L., Rosati, R.A, “Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors”, Statistics in Medicine, 15(4), 361-87, 1996.
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https://ictp.acad.ro/tag/1998/
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1998
Properties of a new class of recursively defined Baskakov-type operators
Abstract Bu starting from a recent paper by Campiti and Metafune [7], we consider a generalization of the Baskakov operators,…
Approximation properties of a generalization of Bleimann, Butzer and Hahn operators
Abstract In this paper we deal with a generalization of Bleimann, Butzer and Hahn operators which is obtained by replacing…
Linear combinations of D.D. Stancu polynomials
Abstract By using Markov-Polya probabilistic shceme, in 1968 D.D. Stancu introduced and studied a new class of linear positive operators…
An asymptotic property of integral type operators
Abstract AuthorsOctavian Agratini Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania Keywords? Paper coordinatesO. Agratini, An asymptotic property of integral type…
On a problem of A. Lupaş
Abstract ? AuthorsOctavian Agratini Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania Keywords? Paper coordinatesO. Agratini, On a problem of A.…
Asymptotic formulae for recursively defined Baskakov-type operators
Abstract We deal with Baskakov-type operators which are defined by replacing the binomial coeffcients with general ones satisfying a recursively…
Monotone approximation for an integral equation modeling infectious disease
Abstract Monotone technique is used to approximate the periodic solutions of a delay integral equation modeling epidemics and population growth.…
Methods of nonlinear analysis with applications in celestial mechanics
Book summarySummary of the book… Book coverContentsCh. 1 Keywordskeyword1, PDFpdf file Referencessee the expanding block below Cite this book as:M.-C.…
The determination of optimal position for casting using the solidification direction curves
AbstractAuthorsC. Vamoș -Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy V. Soporan C. Pavai KeywordsCite this paper as:V. Soporan, C. Vamoş, C.…
Numerical simulation of the contraction and the shrinkage formation during the solidification process
AbstractAuthorsC. Vamoș -Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy V. Soporan C. Pavai KeywordsCite this paper as:V. Soporan, C. Vamoş, C.…
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https://planetmath.org/globalcharacterizationofhypergeometricfunction
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# global characterization of hypergeometric function
Riemann noted that the hypergeometric function can be characterized by its global properties, without reference to power series, differential equations, or any other sort of explicit expression. His characterization is conveniently restated in terms of sheaves:
Suppose that we have a sheaf of holomorphic functions over $\mathbb{C}\setminus\{0,1\}$ which satisfy the following properties:
• It is closed under taking linear combinations.
• The space of function elements over any open set is two dimensional.
• There exists a neighborhood $D_{0}$ such that $0\in D)$, holomorphic functions $\phi_{0},\psi_{0}$ defined on $D_{0}$, and complex numbers $\alpha_{0},\beta_{0}$ such that, for an open set of $d_{0}$ not containing $0$, it happens that $z\mapsto z^{\alpha_{0}}\phi(z)$ and $z\mapsto z^{\beta_{0}}\psi(z)$ belong to our sheaf.
Then the sheaf consists of solutions to a hypergeometric equation, hence the function elements are hypergeometric functions.
Title global characterization of hypergeometric function GlobalCharacterizationOfHypergeometricFunction 2014-12-31 15:15:16 2014-12-31 15:15:16 rspuzio (6075) rspuzio (6075) 6 rspuzio (6075) Definition msc 33C05
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http://mathhelpforum.com/pre-calculus/74479-solved-find-domain-composite-function-print.html
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# [SOLVED] Find the domain of the composite function
• Feb 19th 2009, 07:36 AM
GeminiAngel619
[SOLVED] Find the domain of the composite function
Instructions: Find the domain of the composite function f (of) g.
f(x)= (-45)/(x) g(x)=(-7)/(x-9)
• Feb 19th 2009, 07:41 AM
GeminiAngel619
And Another Composite Function...
Here's another one.
Instructions: For the given functions f and g, find the requested composite function.
find (g (of) f) (x)
f(x)=(x-10)/(7) g(x)=7x+10
Here's what I got...I basically just want to check my answer:
g(f(x))= 7((x-10)/(7))+10
g(f(x))=x-10+10
g(f(x))=x
• Feb 19th 2009, 10:07 AM
stapel
Quote:
Originally Posted by GeminiAngel619
Instructions: Find the domain of the composite function f (of) g.
f(x)= (-45)/(x) g(x)=(-7)/(x-9)
You can study some online lessons to learn how to get started on finding the domain of a function.
Since, in your case, you are finding f(g(x)), you will need to find the restrictions on the domains of each of f and g (which you'll find by checking for division-by-zero problems), and also you'll need to figure out the x-value for g which gives an output that would be a problem for f.
(Hint: Since you can't divide by zero, and since f(0) would create a division by zero, then you'll need to find what x-value(s), if any, would cause g(x) to equal zero.)
Quote:
Originally Posted by GeminiAngel619
Instructions: For the given functions f and g, find the requested composite function.
find (g (of) f) (x)
f(x)=(x-10)/(7) g(x)=7x+10
Here's what I got...I basically just want to check my answer:
g(f(x))= 7((x-10)/(7))+10
g(f(x))=x-10+10
g(f(x))=x
Your work looks good to me! :D
• Feb 19th 2009, 10:13 AM
GeminiAngel619
Quote:
Originally Posted by stapel
You can study some online lessons to learn how to get started on finding the domain of a function.
Since, in your case, you are finding f(g(x)), you will need to find the restrictions on the domains of each of f and g (which you'll find by checking for division-by-zero problems), and also you'll need to figure out the x-value for g which gives an output that would be a problem for f.
(Hint: Since you can't divide by zero, and since f(0) would create a division by zero, then you'll need to find what x-value(s), if any, would cause g(x) to equal zero.)
Your work looks good to me! :D
Right, I understand how to do it, on most other problems. And I know that I need to find g(x)=0 (right?) to find out what x-values, if any, would cause the function to equal zero. But when I do that, all I get is -7=0, which is not true/undefined/whatever you want to say.
Here's how I got -7=0:
(-7)/(x-9)=0
multiply both sides by common denom. (x-9)
and you get (-7)=0.
This is where I'm stuck.
• Feb 19th 2009, 10:14 AM
GeminiAngel619
So in other words...
The restrictions on the domain are x cannot equal 9 or 0. I understand that part. Its the next step that I'm not doing so hot on. lol
• Feb 19th 2009, 11:16 AM
Reckoner
Quote:
Originally Posted by GeminiAngel619
Right, I understand how to do it, on most other problems. And I know that I need to find g(x)=0 (right?) to find out what x-values, if any, would cause the function to equal zero. But when I do that, all I get is -7=0, which is not true/undefined/whatever you want to say.
What does that tell you? Can $g(x)$ ever be zero? Think about it.
Quote:
find (g (of) f) (x)
f(x)=(x-10)/(7) g(x)=7x+10
Here's what I got...I basically just want to check my answer:
g(f(x))= 7((x-10)/(7))+10
g(f(x))=x-10+10
g(f(x))=x
Correct. You would get the same thing with $(f\circ g)(x)$ (but that doesn't always happen). We say that $f$ and $g$ are inverses of each other, because they "undo" each other, so to speak.
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https://worldwidescience.org/topicpages/a/actinium+additions.html
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#### Sample records for actinium additions
1. Spectroscopic and computational investigation of actinium coordination chemistry
Science.gov (United States)
Ferrier, Maryline G.; Batista, Enrique R.; Berg, John M.; Birnbaum, Eva R.; Cross, Justin N.; Engle, Jonathan W.; La Pierre, Henry S.; Kozimor, Stosh A.; Lezama Pacheco, Juan S.; Stein, Benjamin W.; Stieber, S. Chantal E.; Wilson, Justin J.
2016-08-01
Actinium-225 is a promising isotope for targeted-α therapy. Unfortunately, progress in developing chelators for medicinal applications has been hindered by a limited understanding of actinium chemistry. This knowledge gap is primarily associated with handling actinium, as it is highly radioactive and in short supply. Hence, AcIII reactivity is often inferred from the lanthanides and minor actinides (that is, Am, Cm), with limited success. Here we overcome these challenges and characterize actinium in HCl solutions using X-ray absorption spectroscopy and molecular dynamics density functional theory. The Ac-Cl and Ac-OH2O distances are measured to be 2.95(3) and 2.59(3) Å, respectively. The X-ray absorption spectroscopy comparisons between AcIII and AmIII in HCl solutions indicate AcIII coordinates more inner-sphere Cl1- ligands (3.2+/-1.1) than AmIII (0.8+/-0.3). These results imply diverse reactivity for the +3 actinides and highlight the unexpected and unique AcIII chemical behaviour.
2. Separation of Actinium 227 from the uranium minerals
International Nuclear Information System (INIS)
The purpose of this work was to separate Actinium 227, whose content is 18%, from the mineral carnotite found in Gomez Chihuahua mountain range in Mexico. The mineral before processing is is pre-concentrated and passed, first through anionic exchange resins, later the eluate obtained is passed through cationic resins. The resins were 20-50 MESH QOWEX and 100-200 MESH 50 X 8-20 in some cased 200-400 MESH AG 50W-X8, 1X8 in other cases. The eluates from the ionic exchange were electrodeposited on stainless steel polished disc cathode and platinum electrode as anode; under a current ODF 10mA for 2.5 to 5 hours and of 100mA for .5 of an hour. it was possible to identify the Actinium 227 by means of its descendents, TH-227 and RA-223, through alpha spectroscopy. Due to the radiochemical purity which the electro deposits were obtained the Actinium 227 was low and was not quantitatively determined. A large majority of the members of the natural radioactive series 3 were identified and even alpha energies reported in the literature with very low percentages of non-identified emissions were observed. We conclude that a more precise study is needed concerning ionic exchange and electrodeposit to obtain an Actinium 227 of radiochemical purity. (Author)
3. Spectroscopic and computational investigation of actinium coordination chemistry
Science.gov (United States)
Ferrier, Maryline G.; Batista, Enrique R.; Berg, John M.; Birnbaum, Eva R.; Cross, Justin N.; Engle, Jonathan W.; La Pierre, Henry S.; Kozimor, Stosh A.; Lezama Pacheco, Juan S.; Stein, Benjamin W.; Stieber, S. Chantal E.; Wilson, Justin J.
2016-01-01
Actinium-225 is a promising isotope for targeted-α therapy. Unfortunately, progress in developing chelators for medicinal applications has been hindered by a limited understanding of actinium chemistry. This knowledge gap is primarily associated with handling actinium, as it is highly radioactive and in short supply. Hence, AcIII reactivity is often inferred from the lanthanides and minor actinides (that is, Am, Cm), with limited success. Here we overcome these challenges and characterize actinium in HCl solutions using X-ray absorption spectroscopy and molecular dynamics density functional theory. The Ac–Cl and Ac–OH2O distances are measured to be 2.95(3) and 2.59(3) Å, respectively. The X-ray absorption spectroscopy comparisons between AcIII and AmIII in HCl solutions indicate AcIII coordinates more inner-sphere Cl1– ligands (3.2±1.1) than AmIII (0.8±0.3). These results imply diverse reactivity for the +3 actinides and highlight the unexpected and unique AcIII chemical behaviour. PMID:27531582
4. Discovery of the actinium, thorium, protactinium, and uranium isotopes
CERN Document Server
Fry, C
2012-01-01
Currently, 31 actinium, 31 thorium, 28 protactinium, and 23 uranium isotopes have so far been observed; the discovery of these isotopes is discussed. For each isotope a brief summary of the first refereed publication, including the production and identification method, is presented.
5. Spectroscopic and computational investigation of actinium coordination chemistry.
Science.gov (United States)
Ferrier, Maryline G; Batista, Enrique R; Berg, John M; Birnbaum, Eva R; Cross, Justin N; Engle, Jonathan W; La Pierre, Henry S; Kozimor, Stosh A; Lezama Pacheco, Juan S; Stein, Benjamin W; Stieber, S Chantal E; Wilson, Justin J
2016-01-01
Actinium-225 is a promising isotope for targeted-α therapy. Unfortunately, progress in developing chelators for medicinal applications has been hindered by a limited understanding of actinium chemistry. This knowledge gap is primarily associated with handling actinium, as it is highly radioactive and in short supply. Hence, Ac(III) reactivity is often inferred from the lanthanides and minor actinides (that is, Am, Cm), with limited success. Here we overcome these challenges and characterize actinium in HCl solutions using X-ray absorption spectroscopy and molecular dynamics density functional theory. The Ac-Cl and Ac-OH2O distances are measured to be 2.95(3) and 2.59(3) Å, respectively. The X-ray absorption spectroscopy comparisons between Ac(III) and Am(III) in HCl solutions indicate Ac(III) coordinates more inner-sphere Cl(1-) ligands (3.2±1.1) than Am(III) (0.8±0.3). These results imply diverse reactivity for the +3 actinides and highlight the unexpected and unique Ac(III) chemical behaviour. PMID:27531582
6. Production of Actinium-225 via High Energy Proton Induced Spallation of Thorium-232
International Nuclear Information System (INIS)
The science of cancer research is currently expanding its use of alpha particle emitting radioisotopes. Coupled with the discovery and proliferation of molecular species that seek out and attach to tumors, new therapy and diagnostics are being developed to enhance the treatment of cancer and other diseases. This latest technology is commonly referred to as Alpha Immunotherapy (AIT). Actinium-225/Bismuth-213 is a parent/daughter alpha-emitting radioisotope pair that is highly sought after because of the potential for treating numerous diseases and its ability to be chemically compatible with many known and widely used carrier molecules (such as monoclonal antibodies and proteins/peptides). Unfortunately, the worldwide supply of actinium-225 is limited to about 1,000mCi annually and most of that is currently spoken for, thus limiting the ability of this radioisotope pair to enter into research and subsequently clinical trials. The route proposed herein utilizes high energy protons to produce actinium-225 via spallation of a thorium-232 target. As part of previous R and D efforts carried out at Argonne National Laboratory recently in support of the proposed US FRIB facility, it was shown that a very effective production mechanism for actinium-225 is spallation of thorium-232 by high energy proton beams. The base-line simulation for the production rate of actinium-225 by this reaction mechanism is 8E12 atoms per second at 200 MeV proton beam energy with 50 g/cm2 thorium target and 100 kW beam power. An irradiation of one actinium-225 half-life (10 days) produces ∼100 Ci of actinium-225. For a given beam current the reaction cross section increases slightly with energy to about 400 MeV and then decreases slightly for beam energies in the several GeV regime. The object of this effort is to refine the simulations at proton beam energies of 400 MeV and above up to about 8 GeV. Once completed, the simulations will be experimentally verified using 400 MeV and 8 GeV protons
7. Production of Actinium-225 via High Energy Proton Induced Spallation of Thorium-232
Energy Technology Data Exchange (ETDEWEB)
Harvey, James T.; Nolen, Jerry; Vandergrift, George; Gomes, Itacil; Kroc, Tom; Horwitz, Phil; McAlister, Dan; Bowers, Del; Sullivan, Vivian; Greene, John
2011-12-30
The science of cancer research is currently expanding its use of alpha particle emitting radioisotopes. Coupled with the discovery and proliferation of molecular species that seek out and attach to tumors, new therapy and diagnostics are being developed to enhance the treatment of cancer and other diseases. This latest technology is commonly referred to as Alpha Immunotherapy (AIT). Actinium-225/Bismuth-213 is a parent/daughter alpha-emitting radioisotope pair that is highly sought after because of the potential for treating numerous diseases and its ability to be chemically compatible with many known and widely used carrier molecules (such as monoclonal antibodies and proteins/peptides). Unfortunately, the worldwide supply of actinium-225 is limited to about 1,000mCi annually and most of that is currently spoken for, thus limiting the ability of this radioisotope pair to enter into research and subsequently clinical trials. The route proposed herein utilizes high energy protons to produce actinium-225 via spallation of a thorium-232 target. As part of previous R and D efforts carried out at Argonne National Laboratory recently in support of the proposed US FRIB facility, it was shown that a very effective production mechanism for actinium-225 is spallation of thorium-232 by high energy proton beams. The base-line simulation for the production rate of actinium-225 by this reaction mechanism is 8E12 atoms per second at 200 MeV proton beam energy with 50 g/cm2 thorium target and 100 kW beam power. An irradiation of one actinium-225 half-life (10 days) produces {approx}100 Ci of actinium-225. For a given beam current the reaction cross section increases slightly with energy to about 400 MeV and then decreases slightly for beam energies in the several GeV regime. The object of this effort is to refine the simulations at proton beam energies of 400 MeV and above up to about 8 GeV. Once completed, the simulations will be experimentally verified using 400 MeV and 8 Ge
8. Analysis of the gamma spectra of the uranium, actinium, and thorium decay series
International Nuclear Information System (INIS)
This report describes the identification of radionuclides in the uranium, actinium, and thorium series by analysis of gamma spectra in the energy range of 40 to 1400 keV. Energies and absolute efficiencies for each gamma line were measured by means of a high-resolution germanium detector and compared with those in the literature. A gamma spectroscopy method, which utilizes an on-line computer for deconvolution of spectra, search and identification of each line, and estimation of activity for each radionuclide, was used to analyze soil and uranium tailings, and ore
9. Thorium and actinium polyphosphonate compounds as bone-seeking alpha particle-emitting agents.
Science.gov (United States)
Henriksen, Gjermund; Bruland, Oyvind S; Larsen, Roy H
2004-01-01
The present study explores the use of alpha-particle-emitting, bone-seeking agents as candidates for targeted radiotherapy. Actinium and thorium 1,4,7,10 tetraazacyclododecane N,N',N'',N''' 1,4,7,10-tetra(methylene) phosphonic acid (DOTMP) and thorium-diethylene triamine N,N',N'' penta(methylene) phosphonic acid (DTMP) were prepared and their biodistribution evaluated in conventional Balb/C mice at four hours after injection. All three bone-seeking agents showed a high uptake in bone and a low uptake in soft tissues. Among the soft tissue organs, only kidney had a relatively high uptake. The femur/kidney ratios for 227Th-DTMP, 228-Ac-DOTMP and 227Th-DOTMP were 14.2, 7.6 and 6.0, respectively. A higher liver uptake of 228Ac-DOTMP was seen than for 227Th-DTMP and 227Th-DOTMP. This suggests that some demetallation of the 228Ac-DOTMP complex had occurred. The results indicate that 225Ac-DOTMP, 227Th-DOTMP and 227Th-DTMP have promising properties as potential therapeutic bone-seeking agents.
10. Developments towards in-gas-jet laser spectroscopy studies of actinium isotopes at LISOL
Science.gov (United States)
Raeder, S.; Bastin, B.; Block, M.; Creemers, P.; Delahaye, P.; Ferrer, R.; Fléchard, X.; Franchoo, S.; Ghys, L.; Gaffney, L. P.; Granados, C.; Heinke, R.; Hijazi, L.; Huyse, M.; Kron, T.; Kudryavtsev, Yu.; Laatiaoui, M.; Lecesne, N.; Luton, F.; Moore, I. D.; Martinez, Y.; Mogilevskiy, E.; Naubereit, P.; Piot, J.; Rothe, S.; Savajols, H.; Sels, S.; Sonnenschein, V.; Traykov, E.; Van Beveren, C.; Van den Bergh, P.; Van Duppen, P.; Wendt, K.; Zadvornaya, A.
2016-06-01
To study exotic nuclides at the borders of stability with laser ionization and spectroscopy techniques, highest efficiencies in combination with a high spectral resolution are required. These usually opposing requirements are reconciled by applying the in-gas-laser ionization and spectroscopy (IGLIS) technique in the supersonic gas jet produced by a de Laval nozzle installed at the exit of the stopping gas cell. Carrying out laser ionization in the low-temperature and low density supersonic gas jet eliminates pressure broadening, which will significantly improve the spectral resolution. This article presents the required modifications at the Leuven Isotope Separator On-Line (LISOL) facility that are needed for the first on-line studies of in-gas-jet laser spectroscopy. Different geometries for the gas outlet and extraction ion guides have been tested for their performance regarding the acceptance of laser ionized species as well as for their differential pumping capacities. The specifications and performance of the temporarily installed high repetition rate laser system, including a narrow bandwidth injection-locked Ti:sapphire laser, are discussed and first preliminary results on neutron-deficient actinium isotopes are presented indicating the high capability of this novel technique.
11. Groundwater seepage from the Ranger uranium mine tailings dam: radioisotopes of radium, thorium and actinium. Supervising Scientist report 106
International Nuclear Information System (INIS)
Monitoring of bores near the Ranger uranium mine tailings dam has revealed deterioration in water quality in several bores since 1983. In a group of bores to the north of the dam, increases have been observed of up to 500 times for sulphate concentrations and of up to 5 times for 226Ra concentrations. Results are presented here of measurements of members of the uranium, thorium and actinium decay series in borewater samples collected between 1985 and 1993. In particular, measurements of all four naturally-occurring radium isotopes have been used in an investigation of the mechanism of radium concentration changes. For the most seepage-affected bores the major findings of the study include: 228Ra/226Ra 223Ra /226Ra and 224Ra/228Ra ratios all increased over the course of the study; barium concentrations show high seasonal variability, being lower in November than May, but strontium concentrations show a steady increase with time. Calculations show that the groundwater is probably saturated with respect to barite but not with respect to celestite or anglesite; sulphide concentrations are low in comparison with sulphate, and are higher in November than in May; and 227Ac concentrations have increased with time, but do not account for the high 223Ra/226Ra ratios. It is concluded on the basis of these observations that increases in Ra isotope concentrations observed in a number of seepage-affected bores arise from increases in salinity leading to desorption of radium from adsorption sites in the vicinity of the bore rather by direct transport of radium from the tailings. Increased salinity is also causing the observed increases in 227Ac and strontium concentrations, while formation of a barite solid phase in the groundwater is causing the removal of some radium from solution. This is the cause of the increasing radium isotope ratios noted above
12. Radium-228 analysis of natural waters by Cherenkov counting of Actinium-228
Energy Technology Data Exchange (ETDEWEB)
Aleissa, Khalid A.; Almasoud, Fahad I.; Islam, Mohammed S. [Atomic Energy Research Institute, King Abdul Aziz City for Science and Technology, P.O. Box 6086, Riyadh 11442 (Saudi Arabia); L' Annunziata, Michael F. [IAEA Expert, Montague Group, P.O. Box 5033, Oceanside, CA 92052-5033 (United States)], E-mail: [email protected]
2008-12-15
The activities of {sup 228}Ra in natural waters were determined by the Cherenkov counting of the daughter nuclide {sup 228}Ac. The radium was pre-concentrated on MnO{sub 2} and the radium purified via ion exchange and, after a 2-day period of incubation to allow for secular equilibrium between the parent-daughter {sup 228}Ra({sup 228}Ac), the daughter nuclide {sup 228}Ac was isolated by ion exchange according to the method of Nour et al. [2004. Radium-228 determination of natural waters via concentration on manganese dioxide and separation using Diphonix ion exchange resin. Appl. Radiat. Isot. 61, 1173-1178]. The Cherenkov photons produced by {sup 228}Ac were counted directly without the addition of any scintillation reagents. The optimum Cherenkov counting window, sample volume, and vial type were determined experimentally to achieve optimum Cherenkov photon detection efficiency and lowest background count rates. An optimum detection efficiency of 10.9{+-}0.1% was measured for {sup 228}Ac by Cherenkov counting with a very low Cherenkov photon background of 0.317{+-}0.013 cpm. The addition of sodium salicylate into the sample counting vial at a concentration of 0.1 g/mL yielded a more than 3-fold increase in the Cherenkov detection efficiency of {sup 228}Ac to 38%. Tests of the Cherenkov counting technique were conducted with several water standards of known activity and the results obtained compared closely with a conventional liquid scintillation counting technique. The advantages and disadvantages of Cherenkov counting compared to liquid scintillation counting methods are discussed. Advantages include much lower Cherenkov background count rates and consequently lower minimal detectable activities for {sup 228}Ra and no need for expensive environmentally unfriendly liquid scintillation cocktails. The disadvantages of the Cherenkov counting method include the need to measure {sup 228}Ac Cherenkov photon detection efficiency and optimum Cherenkov counting volume
13. Radium-228 analysis of natural waters by Cherenkov counting of Actinium-228.
Science.gov (United States)
Aleissa, Khalid A; Almasoud, Fahad I; Islam, Mohammed S; L'Annunziata, Michael F
2008-12-01
The activities of (228)Ra in natural waters were determined by the Cherenkov counting of the daughter nuclide (228)Ac. The radium was pre-concentrated on MnO(2) and the radium purified via ion exchange and, after a 2-day period of incubation to allow for secular equilibrium between the parent-daughter (228)Ra((228)Ac), the daughter nuclide (228)Ac was isolated by ion exchange according to the method of Nour et al. [2004. Radium-228 determination of natural waters via concentration on manganese dioxide and separation using Diphonix ion exchange resin. Appl. Radiat. Isot. 61, 1173-1178]. The Cherenkov photons produced by (228)Ac were counted directly without the addition of any scintillation reagents. The optimum Cherenkov counting window, sample volume, and vial type were determined experimentally to achieve optimum Cherenkov photon detection efficiency and lowest background count rates. An optimum detection efficiency of 10.9+/-0.1% was measured for (228)Ac by Cherenkov counting with a very low Cherenkov photon background of 0.317+/-0.013cpm. The addition of sodium salicylate into the sample counting vial at a concentration of 0.1g/mL yielded a more than 3-fold increase in the Cherenkov detection efficiency of (228)Ac to 38%. Tests of the Cherenkov counting technique were conducted with several water standards of known activity and the results obtained compared closely with a conventional liquid scintillation counting technique. The advantages and disadvantages of Cherenkov counting compared to liquid scintillation counting methods are discussed. Advantages include much lower Cherenkov background count rates and consequently lower minimal detectable activities for (228)Ra and no need for expensive environmentally unfriendly liquid scintillation cocktails. The disadvantages of the Cherenkov counting method include the need to measure (228)Ac Cherenkov photon detection efficiency and optimum Cherenkov counting volume, which are not at all required when liquid
Directory of Open Access Journals (Sweden)
Paul Rozin
2009-10-01
Full Text Available Judgments of naturalness of foods tend to be more influenced by the process history of a food, rather than its actual constituents. Two types of processing of a natural'' food are to add something or to remove something. We report in this study, based on a large random sample of individuals from six countries (France, Germany, Italy, Switzerland, UK and USA that additives are considered defining features of what makes a food not natural, whereas subtractives'' are almost never mentioned. In support of this, skim milk (with major subtraction of fat is rated as more natural than whole milk with a small amount of natural vitamin D added. It is also noted that additives'' is a common word, with a synonym reported by a native speaker in 17 of 18 languages, whereas subtractive'' is lexicalized in only 1 of the 18 languages. We consider reasons for additivity dominance, relating it to omission bias, feature positive bias, and notions of purity.
Energy Technology Data Exchange (ETDEWEB)
Rudolf Keller
2004-08-10
In this project, a concept to improve the performance of aluminum production cells by introducing potlining additives was examined and tested. Boron oxide was added to cathode blocks, and titanium was dissolved in the metal pool; this resulted in the formation of titanium diboride and caused the molten aluminum to wet the carbonaceous cathode surface. Such wetting reportedly leads to operational improvements and extended cell life. In addition, boron oxide suppresses cyanide formation. This final report presents and discusses the results of this project. Substantial economic benefits for the practical implementation of the technology are projected, especially for modern cells with graphitized blocks. For example, with an energy savings of about 5% and an increase in pot life from 1500 to 2500 days, a cost savings of $0.023 per pound of aluminum produced is projected for a 200 kA pot. 16. Design for Additive Manufacturing OpenAIRE Bertran Comellas, Martí 2012-01-01 This Thesis, Design for Additive Manufacturing, has been mainly focused on the design process and the considerations to be taken into account when designing parts for Additive Manufacturing. It starts with an introduction to Additive Manufacturing, the different technologies and processes are described to let the readers understand their operating principle, materials used and their strengths and weaknesses. The applications of Additive manufacturing are also explained in the introductory ... 17. Additives in yoghurt production Directory of Open Access Journals (Sweden) Milna Tudor 2008-02-01 Full Text Available In yoghurt production, mainly because of sensory characteristics, different types of additives are used. Each group, and also each substance from the same group has different characteristics and properties. For that reason, for improvement of yoghurt sensory characteristics apart from addition selection, the quantity of the additive is very important. The same substance added in optimal amount improves yoghurt sensory attributes, but too small or too big addition can reduce yoghurt sensory attributes. In this paper, characteristics and properties of mostly used additives in yoghurt production are described; skimmed milk powder, whey powder, concentrated whey powder, sugars and artificial sweeteners, fruits, stabilizers, casein powder, inulin and vitamins. Also the impact of each additive on sensory and physical properties of yoghurt, syneresis and viscosity, are described, depending on used amount added in yoghurt production. 18. Wire + Arc Additive Manufacturing OpenAIRE Williams, Stewart W.; Martina, Filomeno; Addison, Adrian C.; Ding, Jialuo; Pardal, Goncalo; Colegrove, Paul A. 2016-01-01 Depositing large components (>10 kg) in titanium, aluminium, steel and other metals is possible using Wire + Arc Additive Manufacturing. This technology adopts arc welding tools and wire as feedstock for additive manufacturing purposes. High deposition rates, low material and equipment costs, and good structural integrity make Wire+Arc Additive Manufacturing a suitable candidate for replacing the current method of manufacturing from solid billets or large forgings, especially with regards to ... 19. Vicarious Michael Addition Institute of Scientific and Technical Information of China (English) 2006-01-01 C-H bond can undergo vicarious Michael addition reaction (VMA) with doubleactivated double bond in the absence of strong base and catalyst under mild conditions.Intramolecular H-bonding, electron-withdrawing inductive effect, and steric hindrance at aposition of nucleophile facilitates C-H addition over N-H addition. By using VMA, high branching multiplicity, novel branching pattern, controllable density and distribution of functional groups can be envisioned for novel dendrimer synthesis. 20. Additive Gaussian Processes CERN Document Server Duvenaud, David; Rasmussen, Carl Edward 2011-01-01 We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks. 1. Additive and polynomial representations CERN Document Server Krantz, David H; Suppes, Patrick 1971-01-01 Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utiliz 2. Food Additives and Hyperkinesis Science.gov (United States) Wender, Ester H. 1977-01-01 The hypothesis that food additives are causally associated with hyperkinesis and learning disabilities in children is reviewed, and available data are summarized. Available from: American Medical Association 535 North Dearborn Street Chicago, Illinois 60610. (JG) 3. Groups – Additive Notation Directory of Open Access Journals (Sweden) Coghetto Roland 2015-06-01 Full Text Available We translate the articles covering group theory already available in the Mizar Mathematical Library from multiplicative into additive notation. We adapt the works of Wojciech A. Trybulec [41, 42, 43] and Artur Korniłowicz [25]. 4. Additively Manufactured Propulsion System OpenAIRE Dushku, Matthew; Mueller, Paul 2012-01-01 New high-performance, carbon-fiber reinforced polymer material allows additive manufacturing to produce pressure vessels capable of high pressures (thousands of pounds per square inch). This advancement in turn allows integral hybrid propulsion which is revolutionary for both CubeSats and additively-manufactured spacecraft. Hybrid propulsion offers simplicity as compared to bipropellant liquid propulsion, significantly better safety compared to solid or monopropellant hydrazine propulsion, an... 5. Additive Manufacturing Infrared Inspection Science.gov (United States) Gaddy, Darrell 2014-01-01 Additive manufacturing is a rapid prototyping technology that allows parts to be built in a series of thin layers from plastic, ceramics, and metallics. Metallic additive manufacturing is an emerging form of rapid prototyping that allows complex structures to be built using various metallic powders. Significant time and cost savings have also been observed using the metallic additive manufacturing compared with traditional techniques. Development of the metallic additive manufacturing technology has advanced significantly over the last decade, although many of the techniques to inspect parts made from these processes have not advanced significantly or have limitations. Several external geometry inspection techniques exist such as Coordinate Measurement Machines (CMM), Laser Scanners, Structured Light Scanning Systems, or even traditional calipers and gages. All of the aforementioned techniques are limited to external geometry and contours or must use a contact probe to inspect limited internal dimensions. This presentation will document the development of a process for real-time dimensional inspection technique and digital quality record of the additive manufacturing process using Infrared camera imaging and processing techniques. 6. From additivity to synergism DEFF Research Database (Denmark) Ritz, Christian; Streibig, Jens Carl 2014-01-01 Interest in synergistic or antagonistic effects through mixture experiments has grown immensely over the past two decades, not the least within in pharmacology and toxicology. Several definitions of reference models exist; one commonly used reference model is concentration or dose addition, which...... assumes compounds, when administrated simultaneously, do not interfere with each other at the site of action. We focus on statistical modelling that allows evaluation of dose addition. We will describe several statistical approaches that are suitable for analysis mixture data where synergistic...... or antagonistic effects may be present. The statistical models are defined and explained and some of the approaches exemplified. Code in open-source software is provided.... 7. Alternative additives; Alternative additiver Energy Technology Data Exchange (ETDEWEB) 2007-08-15 In this project a number of industrial and agricultural waste products have been characterised and evaluated in terms of alkali-getter performance. The intended use is for biomass-fired power stations aiming at reducing corrosion or slagging related problems. The following products have been obtained, characterised and evaluated: 1) Brewery draff 2) Danish de-gassed manure 3) Paper sludge 4) Moulding sand 5) Spent bleaching earth 6) Anorthosite 7) Sand 8) Clay-sludge. Most of the above alternative additive candidates are deemed unsuitable due to insufficient chemical effect and/or expensive requirements for pre-treatment (such as drying and transportation). 3 products were selected for full-scale testing: de-gassed manure, spent bleaching earth and clay slugde. The full scale tests were undertaken at the biomass-fired power stations in Koege, Slagelse and Ensted. Spent bleaching earth (SBE) and clay sludge were the only tested additive candidates that had a proven ability to react with KCl, to thereby reduce Cl-concentrations in deposits, and reduce the deposit flux to superheater tubes. Their performance was shown to nearly as good as commercial additives. De-gassed manure, however, did not evaluate positively due to inhibiting effects of Ca in the manure. Furthermore, de-gassed manure has a high concentration of heavy metals, which imposes a financial burden with regard to proper disposal of the ash by-products. Clay-sludge is a wet clay slurring, and drying and transportation of this product entails substantial costs. Spent bleaching does not require much pre-treatment and is therefore the most promising alternative additive. On the other hand, bleaching earth contains residual plant oil which means that a range of legislation relating to waste combustion comes into play. Not least a waste combustion fee of 330 DKK/tonne. For all alternative (and commercial) additives disposal costs of the increase ash by-products represents a significant cost. This is 8. Additives for the Axe Institute of Scientific and Technical Information of China (English) 2011-01-01 On May 1,China will begin to ban the production and use of two food additives commonly used to "bleach" flour,benzoyl peroxide and calcium peroxide.The decision was made after 10 years of wrangling between the policy makers,manufacturers,scientists and consumers.The Ministry of Health said in a statement it was applying the ban in response to consumers’ concerns about chemical substances in food,and technical improvements that had made the two additives unnecessary in flour processing.Minister of Health Chen Zhu has also said 9. Sloppy Addition and Multiplication DEFF Research Database (Denmark) Nannarelli, Alberto Sometimes reducing the precision of a numerical processor, by introducing errors, can lead to significant performance (delay, area and power dissipation) improvements without compromising the overall quality of the processing. In this work, we show how to perform the two basic operations, addition... 10. Model Additional Protocol International Nuclear Information System (INIS) Since the end of the cold war a series of events has changed the circumstances and requirements of the safeguards system. The discovery of a clandestine nuclear weapons program in Iraq, the continuing difficulty in verifying the initial report of Democratic People's Republic of Korea upon entry into force of their safeguards agreement, and the decision of the South African Government to give up its nuclear weapons program and join the Treaty on the Non-Proliferation of Nuclear Weapons have all played a role in an ambitious effort by IAEA Member States and the Secretariat to strengthen the safeguards system. A major milestone in this effort was reached in May 1997 when the IAEA Board of Governors approved a Model Protocol Additional to Safeguards Agreements. The Model Additional Protocol was negotiated over a period of less than a year by an open-ended committee of the Board involving some 70 Member States and two regional inspectorates. The IAEA is now in the process of negotiating additional protocols, State by State, and implementing them. These additional protocols will provide the IAEA with rights of access to information about all activities related to the use of nuclear material in States with comprehensive safeguards agreements and greatly expanded physical access for IAEA inspectors to confirm or verify this information. In conjunction with this, the IAEA is working on the integration of these measures with those provided for in comprehensive safeguards agreements, with a view to maximizing the effectiveness and efficiency, within available resources, the implementation of safeguards. Details concerning the Model Additional Protocol are given. (author) 11. Additives in swine nutrition OpenAIRE Sinovec Zlatan J.; Jokić Živan; Šefer Dragan 2002-01-01 To attain better feed utilization, longer preservation, easier manipultion and higher production and better quality of food of animal orgin as the final goal, besides raw materials, feed mixes contain numerous pronutrients (additives), added to perform different effects, in a narrower sense, the term pronutrient implies heterogenous substances, which have no diverse effects and have to be efficient in the manner of use. Basically, all pronutrients have to reach the goal of keeping optimal ani... 12. Additives in swine nutrition Directory of Open Access Journals (Sweden) Sinovec Zlatan J. 2002-01-01 Full Text Available To attain better feed utilization, longer preservation, easier manipultion and higher production and better quality of food of animal orgin as the final goal, besides raw materials, feed mixes contain numerous pronutrients (additives, added to perform different effects, in a narrower sense, the term pronutrient implies heterogenous substances, which have no diverse effects and have to be efficient in the manner of use. Basically, all pronutrients have to reach the goal of keeping optimal animal health status and to increase production of food of animal origin without adverse and negative effects. The development of biotechnology had a great part in the appearance of natural alternatives which are able to fulfil and satisfy the high demands of highly productive animals, as well as those of the consumer lobby and environmental protection movements. Growth promoters based upon physiological mechanisms and production potential of the animal have an unquestionable adventage, not only because of the lack of residues in food of animal origin; but also because of their ecological safety and decrease of envirnomental pollution by undigested materials. Demand continues to grow for "all natural", non-pharmaceutical feed additives with growth enhancing effects in food animals. Special attention is paid to minerals (anorganic and organic sources, growth stimulators (antibiotics, probiotics prebiotics, substances for better feed utilization (enzymes, acidifers adsorbents. 13. Additive Pattern Database Heuristics CERN Document Server Felner, A; Korf, R E; 10.1613/jair.1480 2011-01-01 We explore a method for computing admissible heuristic evaluation functions for search problems. It utilizes pattern databases, which are precomputed tables of the exact cost of solving various subproblems of an existing problem. Unlike standard pattern database heuristics, however, we partition our problems into disjoint subproblems, so that the costs of solving the different subproblems can be added together without overestimating the cost of solving the original problem. Previously, we showed how to statically partition the sliding-tile puzzles into disjoint groups of tiles to compute an admissible heuristic, using the same partition for each state and problem instance. Here we extend the method and show that it applies to other domains as well. We also present another method for additive heuristics which we call dynamically partitioned pattern databases. Here we partition the problem into disjoint subproblems for each state of the search dynamically. We discuss the pros and cons of each of these methods a... 14. Perspectives on Additive Manufacturing Science.gov (United States) Bourell, David L. 2016-07-01 Additive manufacturing (AM) has skyrocketed in visibility commercially and in the public sector. This article describes the development of this field from early layered manufacturing approaches of photosculpture, topography, and material deposition. Certain precursors to modern AM processes are also briefly described. The growth of the field over the last 30 years is presented. Included is the standard delineation of AM technologies into seven broad categories. The economics of AM part generation is considered, and the impacts of the economics on application sectors are described. On the basis of current trends, the future outlook will include a convergence of AM fabricators, mass-produced AM fabricators, enabling of topology optimization designs, and specialization in the AM legal arena. Long-term developments with huge impact are organ printing and volume-based printing. 15. Sarks as additional fermions Science.gov (United States) Agrawal, Jyoti; Frampton, Paul H.; Jack Ng, Y.; Nishino, Hitoshi; Yasuda, Osamu 1991-03-01 An extension of the standard model is proposed. The gauge group is SU(2) X ⊗ SU(3) C ⊗ SU(2) S ⊗ U(1) Q, where all gauge symmetries are unbroken. The colour and electric charge are combined with SU(2) S which becomes strongly coupled at approximately 500 GeV and binds preons to form fermionic and vector bound states. The usual quarks and leptons are singlets under SU(2) X but additional fermions, called sarks. transform under it and the electroweak group. The present model explains why no more than three light quark-lepton families can exist. Neutral sark baryons, called narks, are candidates for the cosmological dark matter having the characteristics designed for WIMPS. Further phenomenological implications of sarks are analyzed i including electron-positron annihilation. Z 0 decay, flavor-changing neutral currents. baryon-number non-conservation, sarkonium and the neutron electric dipole moment. 16. Study on laser atomic spectroscopy International Nuclear Information System (INIS) Laser atomic spectroscopic study on actinium element has been performed in many areas of spectroscopy. The study on characteristic of atomic vapor has been proceeded for copper atom and the spatial density distribution of copper vapor is measured. This experimental data has been compared with the theoretically calculated data. In spectroscopic experiment, the first and second excited states for actinium element are identified and the most efficient ionization scheme for actinium element is identified. In addition, the corrosion problem for filament material due to the heating of the actinium element has been studied. (Author) 17. Alkalized sulfonates (PEP additives); Ueberbasische Sulfonate (PEP-Additive) Energy Technology Data Exchange (ETDEWEB) Schulz, Joachim [WISURA Mineraloelwerk Goldgrabe und Scheft GmbH und Co., Bremen (Germany) 2010-05-15 There are only few additives about which in the last 25 - to 30 were reported as a possible additive group regarding replacement of chlorinated paraffin's. Besides, it concerns around alkalized sulfonic acids which are neutralized with sodium or calcium-hydroxide and contain, in addition, the corresponding carbonate in large quantities. This class of additives should act passively in metalworking under extreme pressure (Passive Extreme Pressure additive). Observations from the field often provide a different picture. The following article offers a literature overview to the reaction behavior and introduces newer lab results. A new model of the (re)action of these additives will be introduced. (orig.) 18. ADDITIVES USED TO OBTAIN FOOD OpenAIRE Dorina Ardelean; Daniela Popa 2012-01-01 Use of food additives in food is determined by the growth of contemporary food needs of the world population. Additives used in food, both natural and artificial ones, contribute to: improving the organoleptic characteristics and to preserve the food longer, but we must not forget that all these additives should not be found naturally in food products. Some of these additives are not harmful and human pests in small quantities, but others may have harmful effects on health. 19. Natural food additives: Quo vadis? OpenAIRE Carocho, Márcio; Morales, Patricia; Isabel C. F. R. Ferreira 2015-01-01 In a time where the public is more aware and interested with what they eat, natural additives have been gaining interest both from the food industries and the consumers. Some studies show that consumers prefer food prepared with natural additives rather than chemical ones, due to health reasons. Although quite promising, natural additives still face some drawbacks and limitations as well as conflicting information. In this manuscript, the most important natural additives are overviewed, as we... 20. ADDITIVES USED TO OBTAIN FOOD Directory of Open Access Journals (Sweden) Dorina Ardelean 2012-01-01 Full Text Available Use of food additives in food is determined by the growth of contemporary food needs of the world population. Additives used in food, both natural and artificial ones, contribute to: improving the organoleptic characteristics and to preserve the food longer, but we must not forget that all these additives should not be found naturally in food products. Some of these additives are not harmful and human pests in small quantities, but others may have harmful effects on health. 1. Deciphering the roles of multiple additives in organocatalyzed Michael additions. Science.gov (United States) Günler, Z Inci; Companyó, Xavier; Alfonso, Ignacio; Burés, Jordi; Jimeno, Ciril; Pericàs, Miquel A 2016-05-21 The synergistic effects of multiple additives (water and acetic acid) on the asymmetric Michael addition of acetone to nitrostyrene catalyzed by primary amine-thioureas (PAT) were precisely determined. Acetic acid facilitates hydrolysis of the imine intermediates, thus leading to catalytic behavior, and minimizes the formation of the double addition side product. In contrast, water slows down the reaction but minimizes catalyst deactivation, eventually leading to higher final yields. PMID:27128165 2. Additive manufacturing of optical components Science.gov (United States) Heinrich, Andreas; Rank, Manuel; Maillard, Philippe; Suckow, Anne; Bauckhage, Yannick; Rößler, Patrick; Lang, Johannes; Shariff, Fatin; Pekrul, Sven 2016-08-01 The development of additive manufacturing methods has enlarged rapidly in recent years. Thereby, the work mainly focuses on the realization of mechanical components, but the additive manufacturing technology offers a high potential in the field of optics as well. Owing to new design possibilities, completely new solutions are possible. This article briefly reviews and compares the most important additive manufacturing methods for polymer optics. Additionally, it points out the characteristics of additive manufactured polymer optics. Thereby, surface quality is of crucial importance. In order to improve it, appropriate post-processing steps are necessary (e.g. robot polishing or coating), which will be discussed. An essential part of this paper deals with various additive manufactured optical components and their use, especially in optical systems for shape metrology (e.g. borehole sensor, tilt sensor, freeform surface sensor, fisheye lens). The examples should demonstrate the potentials and limitations of optical components produced by additive manufacturing. 3. Additive interaction in survival analysis DEFF Research Database (Denmark) Rod, Naja Hulvej; Lange, Theis; Andersen, Ingelise; 2012-01-01 is the relevant measure of interest. Multiplicative survival models, such as the Cox proportional hazards model, are often used to estimate the association between exposure and risk of disease in prospective studies. In Cox models, deviations from additivity have usually been assessed by surrogate measures...... of additive interaction derived from multiplicative models-an approach that is both counter-intuitive and sometimes invalid. This paper presents a straightforward and intuitive way of assessing deviation from additivity of effects in survival analysis by use of the additive hazards model. The model directly...... estimates the absolute size of the deviation from additivity and provides confidence intervals. In addition, the model can accommodate both continuous and categorical exposures and models both exposures and potential confounders on the same underlying scale. To illustrate the approach, we present... 4. Additive Manufacturing for Large Products OpenAIRE Leirvåg, Roar Nelissen 2013-01-01 This thesis researches the possibility and feasibility of applying additive manufacturing technology in the manufacturing of propellers. The thesis concerns the production at the foundry Oshaug Metall AS. Their products consist of propellers and other large products cast in Nickel-Aluminium Bronze. This report looks at three approaches and applications for additive manufacturing at the foundry. These are additively manufactured pattern, sand mold and end metal parts. The available \\emph{State... 5. Color Addition and Subtraction Apps Science.gov (United States) Ruiz, Frances; Ruiz, Michael J. 2015-01-01 Color addition and subtraction apps in HTML5 have been developed for students as an online hands-on experience so that they can more easily master principles introduced through traditional classroom demonstrations. The evolution of the additive RGB color model is traced through the early IBM color adapters so that students can proceed step by step… 6. Density measures and additive property OpenAIRE Kunisada, Ryoichi 2015-01-01 We deal with finitely additive measures defined on all subsets of natural numbers which extend the asymptotic density (density measures). We consider a class of density measures which are constructed from free ultrafilters on natural numbers and study a certain additivity property of such density measures. 7. Prevalence of Food Additive Intolerance DEFF Research Database (Denmark) Madsen, Charlotte Bernhard 1994-01-01 1 The existing prevalence estimates of food additive intolerance(1-4) are being reviewed. 2 In the EEC report the estimated frequency of food additive intolerance is 0.03% to 0.15% based on data from patient groups. 3 The British population study results in a prevalence estimate of 0.......026%. The challenged population is 81 children and adults with a history of reproducible clinical symptoms after ingestion of food additives. 4 In the Danish population study a prevalence of 1-2% is found in children age 5-16. In this study a total of 606 children mainly with atopic disease have been challenged. 5...... The prevalence estimates vary with a factor 100. As the results vary so do the study populations. 6 If the different study populations are accounted for, a common conclusion can be drawn: Food additive intolerance is found in adults with atopic symptoms from the respiratory tract and skin. The prevalence... 8. Addition on a Quantum Computer CERN Document Server Draper, Thomas G 2000-01-01 A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also allows the addition of a classical number to a quantum superposition without encoding the classical number in the quantum register. This method also allows for massive parallelization in its execution. 9. A Review of Additive Manufacturing OpenAIRE Kaufui V. Wong; Aldo Hernandez 2012-01-01 Additive manufacturing processes take the information from a computer-aided design (CAD) file that is later converted to a stereolithography (STL) file. In this process, the drawing made in the CAD software is approximated by triangles and sliced containing the information of each layer that is going to be printed. There is a discussion of the relevant additive manufacturing processes and their applications. The aerospace industry employs them because of the possibility of manufacturing light... 10. Clinical effects of sulphite additives. Science.gov (United States) Vally, H; Misso, N L A; Madan, V 2009-11-01 Sulphites are widely used as preservative and antioxidant additives in the food and pharmaceutical industries. Topical, oral or parenteral exposure to sulphites has been reported to induce a range of adverse clinical effects in sensitive individuals, ranging from dermatitis, urticaria, flushing, hypotension, abdominal pain and diarrhoea to life-threatening anaphylactic and asthmatic reactions. Exposure to the sulphites arises mainly from the consumption of foods and drinks that contain these additives; however, exposure may also occur through the use of pharmaceutical products, as well as in occupational settings. While contact sensitivity to sulphite additives in topical medications is increasingly being recognized, skin reactions also occur after ingestion of or parenteral exposure to sulphites. Most studies report a 3-10% prevalence of sulphite sensitivity among asthmatic subjects following ingestion of these additives. However, the severity of these reactions varies, and steroid-dependent asthmatics, those with marked airway hyperresponsiveness, and children with chronic asthma, appear to be at greater risk. In addition to episodic and acute symptoms, sulphites may also contribute to chronic skin and respiratory symptoms. To date, the mechanisms underlying sulphite sensitivity remain unclear, although a number of potential mechanisms have been proposed. Physicians should be aware of the range of clinical manifestations of sulphite sensitivity, as well as the potential sources of exposure. Minor modifications to diet or behaviour lead to excellent clinical outcomes for sulphite-sensitive individuals. 11. [INVITED] Lasers in additive manufacturing Science.gov (United States) Pinkerton, Andrew J. 2016-04-01 Additive manufacturing is a topic of considerable ongoing interest, with forecasts predicting it to have major impact on industry in the future. This paper focusses on the current status and potential future development of the technology, with particular reference to the role of lasers within it. It begins by making clear the types and roles of lasers in the different categories of additive manufacturing. This is followed by concise reviews of the economic benefits and disadvantages of the technology, current state of the market and use of additive manufacturing in different industries. Details of these fields are referenced rather than expanded in detail. The paper continues, focusing on current indicators to the future of additive manufacturing. Barriers to its development, trends and opportunities in major industrial sectors, and wider opportunities for its development are covered. Evidence indicates that additive manufacturing may not become the dominant manufacturing technology in all industries, but represents an excellent opportunity for lasers to increase their influence in manufacturing as a whole. 12. Additive Manufacturing of Hybrid Circuits Science.gov (United States) Sarobol, Pylin; Cook, Adam; Clem, Paul G.; Keicher, David; Hirschfeld, Deidre; Hall, Aaron C.; Bell, Nelson S. 2016-07-01 There is a rising interest in developing functional electronics using additively manufactured components. Considerations in materials selection and pathways to forming hybrid circuits and devices must demonstrate useful electronic function; must enable integration; and must complement the complex shape, low cost, high volume, and high functionality of structural but generally electronically passive additively manufactured components. This article reviews several emerging technologies being used in industry and research/development to provide integration advantages of fabricating multilayer hybrid circuits or devices. First, we review a maskless, noncontact, direct write (DW) technology that excels in the deposition of metallic colloid inks for electrical interconnects. Second, we review a complementary technology, aerosol deposition (AD), which excels in the deposition of metallic and ceramic powder as consolidated, thick conformal coatings and is additionally patternable through masking. Finally, we show examples of hybrid circuits/devices integrated beyond 2-D planes, using combinations of DW or AD processes and conventional, established processes. 13. Calcium addition in straw gasification DEFF Research Database (Denmark) Risnes, H.; Fjellerup, Jan Søren; Henriksen, Ulrik Birk; 2003-01-01 The present work focuses on the influence of calcium addition in gasification. The inorganic¿organic element interaction as well as the detailed inorganic¿inorganic elements interaction has been studied. The effect of calcium addition as calcium sugar/molasses solutions to straw significantly...... affected the ash chemistry and the ash sintering tendency but much less the char reactivity. Thermo balance test are made and high-temperature X-ray diffraction measurements are performed, the experimental results indicate that with calcium addition major inorganic¿inorganic reactions take place very late...... in the char conversion process. Comprehensive global equilibrium calculations predicted important characteristics of the inorganic ash residue. Equilibrium calculations predict the formation of liquid salt if sufficient amounts of Ca are added and according to experiments as well as calculations calcium binds... 14. Additional disulfide bonds in insulin DEFF Research Database (Denmark) Vinther, Tine N; Pettersson, Ingrid; Huus, Kasper; 2015-01-01 The structure of insulin, a glucose homeostasis-controlling hormone, is highly conserved in all vertebrates and stabilized by three disulfide bonds. Recently, we designed a novel insulin analogue containing a fourth disulfide bond located between positions A10-B4. The N-terminus of insulin's B......-chain is flexible and can adapt multiple conformations. We examined how well disulfide bond predictions algorithms could identify disulfide bonds in this region of insulin. In order to identify stable insulin analogues with additional disulfide bonds, which could be expressed, the Cβ cut-off distance had...... in comparison to analogues with additional disulfide bonds that were more difficult to predict. In contrast, addition of the fourth disulfide bond rendered all analogues resistant to fibrillation under stress conditions and all stable analogues bound to the insulin receptor with picomolar affinities. Thus... 15. Additional protocol experience in Romania International Nuclear Information System (INIS) Full text: National Commission for Nuclear Activities Control (CNCAN) is the national regulatory body with regulation, authorization and control responsibilities. CNCAN has the right and obligation to ensure that safeguards are applied, in accordance with the terms of the safeguards agreement, on all source or special fissionable material in all peaceful nuclear activities within the State, under its jurisdiction or carried out under its control anywhere, for the exclusive purpose of verifying that such material is not diverted to nuclear weapons or other nuclear explosive devices. CNCAN has built a strong primary and secondary legislation in order to have a strong legal framework to fulfill the NPT, Safeguards Agreement and Additional Protocol requirements. In respect of the non-proliferation issues CNCAN has as a major goal to strengthen the effectiveness and to improve the efficiency of the safeguards system. Also closer co-operation between the IAEA and CNCAN as coordinator of the national system of accounting for and control of nuclear material has been developed by organizing international and national seminars on the implementation of safeguards and the additional protocol. After the entry into force of the Additional Protocol, CNCAN prepared appropriate declarations and answers to the relevant IAEA questions in order to obtain a drawn conclusion of the absence of undeclared nuclear material and nuclear activities within Romania territory. The IAEA evaluated in Romania not only the results of its nuclear material related activities under the Safeguards Agreement but also the results of its broader, more qualitative, evaluation and verification activities under the Additional Protocol. CNCAN assured that the IAEA inspectors have complementary access according to the Additional Protocol as requested in accordance with the provisions of the Safeguards Agreement and the Additional Protocol and cooperated in resolving in a timely manner, any questions or 16. Additively manufactured porous tantalum implants NARCIS (Netherlands) Wauthle, Ruben; Van Der Stok, Johan; Yavari, Saber Amin; Van Humbeeck, Jan; Kruth, Jean Pierre; Zadpoor, Amir Abbas; Weinans, Harrie; Mulier, Michiel; Schrooten, Jan 2015-01-01 The medical device industry's interest in open porous, metallic biomaterials has increased in response to additive manufacturing techniques enabling the production of complex shapes that cannot be produced with conventional techniques. Tantalum is an important metal for medical devices because of it 17. The Frontiers of Additive Manufacturing Energy Technology Data Exchange (ETDEWEB) Grote, Christopher John [Los Alamos National Lab. (LANL), Los Alamos, NM (United States) 2016-03-03 Additive manufacturing, more commonly known as 3-D printing, has become a ubiquitous tool in science for its precise control over mechanical design. For additive manufacturing to work, a 3-D structure is split into thin 2D slices, and then different physical properties, such as photo-polymerization or melting, are used to grow the sequential layers. The level of control allows not only for devices to be made with a variety of materials: e.g. plastics, metals, and quantum dots, but to also have finely controlled structures leading to other novel properties. While 3-D printing is widely used by hobbyists for making models, it also has industrial applications in structural engineering, biological tissue scaffolding, customized electric circuitry, fuel cells, security, and more. 18. An Additive Manufacturing Test Artifact OpenAIRE Moylan, Shawn; Slotwinski, John; Cooke, April; Jurrens, Kevin; Donmez, M Alkan 2014-01-01 A test artifact, intended for standardization, is proposed for the purpose of evaluating the performance of additive manufacturing (AM) systems. A thorough analysis of previously proposed AM test artifacts as well as experience with machining test artifacts have inspired the design of the proposed test artifact. This new artifact is designed to provide a characterization of the capabilities and limitations of an AM system, as well as to allow system improvement by linking specific errors meas... 19. Sustainability Characterization for Additive Manufacturing OpenAIRE Mani, Mahesh; Lyons, Kevin W; Gupta, SK. 2014-01-01 Additive manufacturing (AM) has the potential to create geometrically complex parts that require a high degree of customization, using less material and producing less waste. Recent studies have shown that AM can be an economically viable option for use by the industry, yet there are some inherent challenges associated with AM for wider acceptance. The lack of standards in AM impedes its use for parts production since industries primarily depend on established standards in processes and mater... 20. Minimum Additive Waste Stabilization (MAWS) International Nuclear Information System (INIS) In the Minimum Additive Waste Stabilization(MAWS) concept, actual waste streams are utilized as additive resources for vitrification, which may contain the basic components (glass formers and fluxes) for making a suitable glass or glassy slag. If too much glass former is present, then the melt viscosity or temperature will be too high for processing; while if there is too much flux, then the durability may suffer. Therefore, there are optimum combinations of these two important classes of constituents depending on the criteria required. The challenge is to combine these resources in such a way that minimizes the use of non-waste additives yet yields a processable and durable final waste form for disposal. The benefit to this approach is that the volume of the final waste form is minimized (waste loading maximized) since little or no additives are used and vitrification itself results in volume reduction through evaporation of water, combustion of organics, and compaction of the solids into a non-porous glass. This implies a significant reduction in disposal costs due to volume reduction alone, and minimizes future risks/costs due to the long term durability and leach resistance of glass. This is accomplished by using integrated systems that are both cost-effective and produce an environmentally sound waste form for disposal. individual component technologies may include: vitrification; thermal destruction; soil washing; gas scrubbing/filtration; and, ion-exchange wastewater treatment. The particular combination of technologies will depend on the waste streams to be treated. At the heart of MAWS is vitrification technology, which incorporates all primary and secondary waste streams into a final, long-term, stabilized glass wasteform. The integrated technology approach, and view of waste streams as resources, is innovative yet practical to cost effectively treat a broad range of DOE mixed and low-level wastes 1. Tweaking Synchronisation by Link Addition CERN Document Server Schultz, Paul; Eroglu, Deniz; Stemler, Thomas; Ávila, G Marcelo Ramírez; Rodrigues, Francisco A; Kurths, Jürgen 2016-01-01 Natural and man-made networks often possess locally tree-like sub-structures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two different methods of link addition. The first method adds single links that create cycles of a well-defined length. Following a topological approach we introduce cycles of varying length and analyze how this feature, as well as the position in the network, alters the synchronous behaviour. We show that in particular short cycles can lead to a maximum change of the Laplacian's eigenvalue spectrum, dictating the synchronization properties of such networks. The second method connects a certain proportion of the initially unconnected nodes. We simulate dynamical systems on these network topologies, with the nodes' local dynamics being either a discrete or continuous. Here our main result is that a certain amount of additional links, with the relative position in the network being cruci... 2. ADDITIONAL STREET BERBASIS APP INVENTOR Directory of Open Access Journals (Sweden) Mohammad Adib Adhi Prabowo 2013-05-01 Full Text Available Abstrak Seiring dengan perkembangan sistem operasi android, telah banyak aplikasi yang memanfaatkan fasilitas GPS dan Google Map, seperti untuk mencari rute, mendapatkan peta, mencari lokasi tertentu pada sebuah tempat. Akan tetapi seringkali pengguna perangkat bergerak kesulitan ketika ingin mengetahui beberapa tempat dan lokasi tertentu karena belum ada fasilitas yang menyediakan informasi lokasi suatu tempat. Walaupun ada informasi lokasi pada peta biasanya informasi yang diberikan lokasi tempat berskala besar, misalnya lokasi tempat wisata atau stasiun kereta api. Pengembangan aplikasi untuk skala kecil ini akan memberikan informasi yang dipresentasikan pada google map. Selama ini belum ada yang memberikan sebuah informasi lokasi tempat penting yang berskala kecil. Misalnya informasi lokasi tambal ban, lokasi warung makan, lokasi laundry, dan lokasi bengkel motor. Oleh karena itu kami mencoba untuk mengembangkan aplikasi additional street berbasis android via App Inventor dengan bantuan google maps. Aplikasi additional street ini dapat memberikan informasi letak objek pada peta serta memberikan informasi jalan menuju lokasi tersebut dan detail informasi lokasi tersebut serta lokasi dari pengguna aplikasi tersebut. Kata Kunci: additional street, android, google maps, app inventor, GPS 3. Fire-Retardant Polymeric Additives Science.gov (United States) Williams, Martha K.; Smith, Trent M. 2011-01-01 Polyhydroxyamide (PHA) and polymethoxyamide (PMeOA) are fire-retardant (FR) thermoplastic polymers and have been found to be useful as an additive for imparting fire retardant properties to other compatible, thermoplastic polymers (including some elastomers). Examples of compatible flammable polymers include nylons, polyesters, and acrylics. Unlike most prior additives, PHA and PMeOA do not appreciably degrade the mechanical properties of the matrix polymer; indeed, in some cases, mechanical properties are enhanced. Also, unlike some prior additives, PHA and PMeOA do not decompose into large amounts of corrosive or toxic compounds during combustion and can be processed at elevated temperatures. PMeOA derivative formulations were synthesized and used as an FR additive in the fabrication of polyamide (PA) and polystyrene (PS) composites with notable reduction (>30 percent for PS) in peak heat release rates compared to the neat polymer as measured by a Cone Calorimeter (ASTM E1354). Synergistic effects were noted with nanosilica composites. These nanosilica composites had more than 50-percent reduction in peak heat release rates. In a typical application, a flammable thermoplastic, thermoplastic blend, or elastomer that one seeks to render flame-retardant is first dry-mixed with PHA or PMeOA or derivative thereof. The proportion of PHA or PMeOA or derivative in the mixture is typically chosen to lie between 1 and 20 weight percent. The dry blend can then be melt-extruded. The extruded polymer blend can further be extruded and/or molded into fibers, pipes, or any other of a variety of objects that may be required to be fire-retardant. The physical and chemical mechanisms which impart flame retardancy of the additive include inhibiting free-radical oxidation in the vapor phase, preventing vaporization of fuel (the polymer), and cooling through the formation of chemical bonds in either the vapor or the condensed phase. Under thermal stress, the cyclic hydroxyl/ methoxy 4. Evaluation of certain food additives. Science.gov (United States) 2009-01-01 This report represents the conclusions of a Joint FAO/WHO Expert Committee convened to evaluate the safety of various food additives, including flavouring agents, with a view to recommending acceptable daily intakes (ADIs) and to preparing specifications for identity and purity. The first part of the report contains a general discussion of the principles governing the toxicological evaluation and assessment of intake of food additives (in particular, flavouring agents). A summary follows of the Committee's evaluations of technical, toxicological and intake data for certain food additives (asparaginase from Aspergillus niger expressed in A. niger, calcium lignosulfonate (40-65), ethyl lauroyl arginate, paprika extract, phospholipase C expressed in Pichia pastoris, phytosterols, phytostanols and their esters, polydimethylsiloxane, steviol glycosides and sulfites [assessment of dietary exposure]) and 10 groups of related flavouring agents (aliphatic branched-chain saturated and unsaturated alcohols, aldehydes, acids and related esters; aliphatic linear alpha,beta-unsaturated aldehydes, acids and related alcohols, acetals and esters; aliphatic secondary alcohols, ketones and related esters; alkoxy-substituted allylbenzenes present in foods and essential oils and used as flavouring agents; esters of aliphatic acyclic primary alcohols with aliphatic linear saturated carboxylic acids; furan-substituted aliphatic hydrocarbons, alcohols, aldehydes, ketones, carboxylic acids and related esters, sulfides, disulfides and ethers; miscellaneous nitrogen-containing substances; monocyclic and bicyclic secondary alcohols, ketones and related esters; hydroxy- and alkoxy-substituted benzyl derivatives; and substances structurally related to menthol). Specifications for the following food additives were revised: canthaxanthin; carob bean gum and carob bean gum (clarified); chlorophyllin copper complexes, sodium and potassium salts; Fast Green FCF; guar gum and guar gum (clarified 5. Matching Games with Additive Externalities DEFF Research Database (Denmark) Branzei, Simina; Michalak, Tomasz; Rahwan, Talal; 2012-01-01 Two-sided matchings are an important theoretical tool used to model markets and social interactions. In many real life problems the utility of an agent is influenced not only by their own choices, but also by the choices that other agents make. Such an influence is called an externality. Whereas...... fully expressive representations of externalities in matchings require exponential space, in this paper we propose a compact model of externalities, in which the influence of a match on each agent is computed additively. In this framework, we analyze many-to-many and one-to-one matchings under neutral... 6. Protocol for ADDITION-PRO DEFF Research Database (Denmark) Johansen, Nanna Borup; Hansen, Anne-Louise Smidt; Jensen, Troels M; 2012-01-01 disease and microvascular diabetic complications. We also require a better understanding of the mechanisms that underlie and drive early changes in cardiometabolic physiology. The ADDITION-PRO study was designed to address these issues among individuals at different levels of diabetes risk recruited from...... and metabolic risk factors; (iii) objective measurement of physical activity behaviour; and (iv) long-term follow-up of hard clinical outcomes including mortality and cardiovascular disease. Results will inform policy recommendations concerning cardiovascular risk reduction and treatment among individuals... 7. High Flow Addition Curing Polyimides Science.gov (United States) Chuang, Kathy C.; Vannucci, Raymond D.; Ansari, Irfan; Cerny, Lawrence L.; Scheiman, Daniel A. 1994-01-01 A new series of high flow PMR-type addition curing polyimides was developed, which employed the substitution of 2,2'-bis (trifluoromethyl) -4,4'-diaminobiphenyl (BTDB) for p-phenylenediamine (p -PDA) in a PMR-IL formulation. These thermoset polyimides, designated as 12F resins, were prepared from BTDB and the dimethyl ester of 4,4'- (hexafluo- roisopropylidene) -diphthalic acid (HFDE) with either nadic ester (NE) or p-aminostyrene (PAS) as the endcaps for addition curing. The 12F prepolymers displayed lower melting temperatures in DSC analysis, and higher melt flow in rheological studies than the cor- responding PMR-11 polyimides. Long-term isothermal aging studies showed that BTDB- based 12F resins exhibited comparable thermo-oxidative stability to P-PDA based PMR-11 polyimides. The noncoplanar 2- and 2'-disubstituted biphenyldiamine (BTDB) not only lowered the melt viscosities of 12F prepolymers, but also retained reasonable thermal sta- bility of the cured resins. The 12F polyimide resin with p-aminostyrene endcaps showed the best promise for long-term, high-temperature application at 343 C (650 F). 8. Neutron Characterization for Additive Manufacturing Science.gov (United States) Watkins, Thomas; Bilheux, Hassina; An, Ke; Payzant, Andrew; DeHoff, Ryan; Duty, Chad; Peter, William; Blue, Craig; Brice, Craig A. 2013-01-01 Oak Ridge National Laboratory (ORNL) is leveraging decades of experience in neutron characterization of advanced materials together with resources such as the Spallation Neutron Source (SNS) and the High Flux Isotope Reactor (HFIR) shown in Fig. 1 to solve challenging problems in additive manufacturing (AM). Additive manufacturing, or three-dimensional (3-D) printing, is a rapidly maturing technology wherein components are built by selectively adding feedstock material at locations specified by a computer model. The majority of these technologies use thermally driven phase change mechanisms to convert the feedstock into functioning material. As the molten material cools and solidifies, the component is subjected to significant thermal gradients, generating significant internal stresses throughout the part (Fig. 2). As layers are added, inherent residual stresses cause warping and distortions that lead to geometrical differences between the final part and the original computer generated design. This effect also limits geometries that can be fabricated using AM, such as thin-walled, high-aspect- ratio, and overhanging structures. Distortion may be minimized by intelligent toolpath planning or strategic placement of support structures, but these approaches are not well understood and often "Edisonian" in nature. Residual stresses can also impact component performance during operation. For example, in a thermally cycled environment such as a high-pressure turbine engine, residual stresses can cause components to distort unpredictably. Different thermal treatments on as-fabricated AM components have been used to minimize residual stress, but components still retain a nonhomogeneous stress state and/or demonstrate a relaxation-derived geometric distortion. Industry, federal laboratory, and university collaboration is needed to address these challenges and enable the U.S. to compete in the global market. Work is currently being conducted on AM technologies at the ORNL 9. An Additive Manufacturing Test Artifact. Science.gov (United States) Moylan, Shawn; Slotwinski, John; Cooke, April; Jurrens, Kevin; Donmez, M Alkan 2014-01-01 A test artifact, intended for standardization, is proposed for the purpose of evaluating the performance of additive manufacturing (AM) systems. A thorough analysis of previously proposed AM test artifacts as well as experience with machining test artifacts have inspired the design of the proposed test artifact. This new artifact is designed to provide a characterization of the capabilities and limitations of an AM system, as well as to allow system improvement by linking specific errors measured in the test artifact to specific sources in the AM system. The proposed test artifact has been built in multiple materials using multiple AM technologies. The results of several of the builds are discussed, demonstrating how the measurement results can be used to characterize and improve a specific AM system. PMID:26601039 10. An Additive Manufacturing Test Artifact. Science.gov (United States) Moylan, Shawn; Slotwinski, John; Cooke, April; Jurrens, Kevin; Donmez, M Alkan 2014-01-01 A test artifact, intended for standardization, is proposed for the purpose of evaluating the performance of additive manufacturing (AM) systems. A thorough analysis of previously proposed AM test artifacts as well as experience with machining test artifacts have inspired the design of the proposed test artifact. This new artifact is designed to provide a characterization of the capabilities and limitations of an AM system, as well as to allow system improvement by linking specific errors measured in the test artifact to specific sources in the AM system. The proposed test artifact has been built in multiple materials using multiple AM technologies. The results of several of the builds are discussed, demonstrating how the measurement results can be used to characterize and improve a specific AM system. 11. Business models for additive manufacturing DEFF Research Database (Denmark) Hadar, Ronen; Bilberg, Arne; Bogers, Marcel 2015-01-01 Digital fabrication — including additive manufacturing (AM), rapid prototyping and 3D printing — has the potential to revolutionize the way in which products are produced and delivered to the customer. Therefore, it challenges companies to reinvent their business model — describing the logic...... of creating and capturing value. In this paper, we explore the implications that AM technologies have for manufacturing systems in the new business models that they enable. In particular, we consider how a consumer goods manufacturer can organize the operations of a more open business model when moving from...... a manufacturer-centric to a consumer-centric value logic. A major shift includes a move from centralized to decentralized supply chains, where consumer goods manufacturers can implement a “hybrid” approach with a focus on localization and accessibility or develop a fully personalized model where the consumer... 12. Production of actinium-225 for alpha particle mediated radioimmunotherapy. Science.gov (United States) Boll, Rose A; Malkemus, Dairin; Mirzadeh, Saed 2005-05-01 The initial clinical trials for treatment of acute myeloid leukemia have demonstrated the effectiveness of the alpha emitter (213)Bi in killing cancer cells. Bismuth-213 is obtained from a radionuclide generator system from decay of 10-days (225)Ac parent. Recent pre-clinical studies have also shown the potential application of both (213)Bi, and the (225)Ac parent radionuclide in a variety of cancer systems and targeted radiotherapy. This paper describes our five years of experience in production of (225)Ac in partial support of the on-going clinical trials. A four-step chemical process, consisting of both anion and cation exchange chromatography, is utilized for routine separation of carrier-free (225)Ac from a mixture of (228)Th, (229)Th and (232)Th. The separation of Ra and Ac from Th is achieved using the marcoporous anion exchange resin MP1 in 8M HNO(3) media. Two sequential MP1/NO(3) columns provide a separation factor of approximately 10(6) for Ra and Ac from Th. The separation of Ac from Ra is accomplished on a low cross-linking cation exchange resin AG50-X4 using 1.2M HNO(3) as eluant. Two sequential AG50/NO(3) columns provide a separation factor of approximately 10(2) for Ac from Ra. A 60-day processing schedule has been adopted in order to reduce the processing cost and to provide the highest levels of (225)Ac possible. Over an 8-week campaign, a total of approximately 100 mCi of (225)Ac (approximately 80% of the theoretical yield) is shipped in 5-6 batches, with the first batch typically consisting of approximately 50 mCi. After the initial separation and purification of Ac, the Ra pool is re-processed on a bi-weekly schedule or as needed to provide smaller batches of (225)Ac. The averaged radioisotopic purity of the (225)Ac was 99.6 +/- 0.7% with a (225)Ra content of < or =0.6%, and an average (229)Th content of (4(-4)(+5)) x 10(-5)%. 13. Sustainability Characterization for Additive Manufacturing. Science.gov (United States) Mani, Mahesh; Lyons, Kevin W; Gupta, S K 2014-01-01 Additive manufacturing (AM) has the potential to create geometrically complex parts that require a high degree of customization, using less material and producing less waste. Recent studies have shown that AM can be an economically viable option for use by the industry, yet there are some inherent challenges associated with AM for wider acceptance. The lack of standards in AM impedes its use for parts production since industries primarily depend on established standards in processes and material selection to ensure the consistency and quality. Inability to compare AM performance against traditional manufacturing methods can be a barrier for implementing AM processes. AM process sustainability has become a driver due to growing environmental concerns for manufacturing. This has reinforced the importance to understand and characterize AM processes for sustainability. Process characterization for sustainability will help close the gaps for comparing AM performance to traditional manufacturing methods. Based on a literature review, this paper first examines the potential environmental impacts of AM. A methodology for sustainability characterization of AM is then proposed to serve as a resource for the community to benchmark AM processes for sustainability. Next, research perspectives are discussed along with relevant standardization efforts. PMID:26601038 14. Overview of Food Ingredients, Additives and Colors Science.gov (United States) ... foods with reduced fat content. What Is a Food Additive? In its broadest sense, a food additive is ... is the role of modern technology in producing food additives? A. Many new techniques are being researched that ... 15. Septic tank additive impacts on microbial populations. Science.gov (United States) Pradhan, S; Hoover, M T; Clark, G H; Gumpertz, M; Wollum, A G; Cobb, C; Strock, J 2008-01-01 Environmental health specialists, other onsite wastewater professionals, scientists, and homeowners have questioned the effectiveness of septic tank additives. This paper describes an independent, third-party, field scale, research study of the effects of three liquid bacterial septic tank additives and a control (no additive) on septic tank microbial populations. Microbial populations were measured quarterly in a field study for 12 months in 48 full-size, functioning septic tanks. Bacterial populations in the 48 septic tanks were statistically analyzed with a mixed linear model. Additive effects were assessed for three septic tank maintenance levels (low, intermediate, and high). Dunnett's t-test for tank bacteria (alpha = .05) indicated that none of the treatments were significantly different, overall, from the control at the statistical level tested. In addition, the additives had no significant effects on septic tank bacterial populations at any of the septic tank maintenance levels. Additional controlled, field-based research iswarranted, however, to address additional additives and experimental conditions. 16. A flexible additive multiplicative hazard model DEFF Research Database (Denmark) Martinussen, Torben; Scheike, Thomas H. 2002-01-01 Aalen's additive model; Counting process; Cox regression; Hazard model; Proportional excess harzard model; Time-varying effect......Aalen's additive model; Counting process; Cox regression; Hazard model; Proportional excess harzard model; Time-varying effect... 17. Additive Manufacturing of Aerospace Propulsion Components Science.gov (United States) Misra, Ajay K.; Grady, Joseph E.; Carter, Robert 2015-01-01 The presentation will provide an overview of ongoing activities on additive manufacturing of aerospace propulsion components, which included rocket propulsion and gas turbine engines. Future opportunities on additive manufacturing of hybrid electric propulsion components will be discussed. 18. The Philosophical Consideration about Food Additives OpenAIRE Baoyu Ma 2015-01-01 This study mainly analyzes the essential features of food additives technology from the angle of philosophy, explaining the essential characteristics of food additives technology. As for the attitude towards the application of food additives, it is influenced by the public's gender, age, educational level, occupation and monthly expenditure for buying non-staple food and other variables, thus, the attitude towards food additives and green food, as well as the attitude towards using artificial... 19. 47 CFR 25.111 - Additional information. Science.gov (United States) 2010-10-01 ... 47 Telecommunication 2 2010-10-01 2010-10-01 false Additional information. 25.111 Section 25.111... Applications and Licenses General Application Filing Requirements § 25.111 Additional information. (a) The Commission may request from any party at any time additional information concerning any application, or... 20. 76 FR 60809 - Procurement List; Additions Science.gov (United States) 2011-09-30 ... . SUPPLEMENTARY INFORMATION: Additions On 7/1/2011 (76 FR 38641-38642) and 8/5/2011 (76 FR 47565-47566), the... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Additions to the Procurement List. SUMMARY:... 1. 77 FR 41377 - Procurement List; Additions Science.gov (United States) 2012-07-13 ... . SUPPLEMENTARY INFORMATION: Additions On 5/11/2012 (77 FR 27737-27738) and 5/18/2012 (77 FR 29596), the Committee... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Additions to the Procurement List. SUMMARY:... 2. 78 FR 9386 - Procurement List; Addition Science.gov (United States) 2013-02-08 ... INFORMATION: Addition On 11/30/2012 (77 FR 71400-71401), the Committee for Purchase From People Who Are Blind... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Addition AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Addition to the Procurement List. SUMMARY: This... 3. 77 FR 17034 - Procurement List; Addition Science.gov (United States) 2012-03-23 ... INFORMATION: Addition On 1/13/2012 (77 FR 2048), the Committee for Purchase From People Who Are Blind or... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Addition AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Addition to the Procurement List. SUMMARY: This... 4. 78 FR 48657 - Procurement List; Additions Science.gov (United States) 2013-08-09 ... INFORMATION: Additions On 6/14/2013 (78 FR 35874-35875) and 6/21/2013 (78 FR 37524-37525), the Committee for... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Additions to the Procurement List. SUMMARY:... 5. 78 FR 59658 - Procurement List; Additions Science.gov (United States) 2013-09-27 ... INFORMATION: Additions On 7/26/2013 (78 FR 45183); 8/9/2013 (78 FR 48656-48657) and 8/16/ 2013 (78 FR 50040... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Additions to the Procurement List. SUMMARY:... 6. 76 FR 40341 - Procurement List; Additions Science.gov (United States) 2011-07-08 ... . SUPPLEMENTARY INFORMATION: Additions On 4/29/2011 (76 FR 23998); 5/6/2011 (76 FR 26279); and 5/13/2011 (76 FR... 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SUMMARY: This... 9. 77 FR 34025 - Procurement List; Addition Science.gov (United States) 2012-06-08 ... INFORMATION: ] Addition On 4/132012 (77 FR 22289-22290), the Committee for Purchase From People Who Are Blind... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Addition AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Addition to the Procurement List. SUMMARY: This... 10. 44 CFR 6.81 - Additional copies. Science.gov (United States) 2010-10-01 ... 44 Emergency Management and Assistance 1 2010-10-01 2010-10-01 false Additional copies. 6.81... HOMELAND SECURITY GENERAL IMPLEMENTATION OF THE PRIVACY ACT OF 1974 Fees § 6.81 Additional copies. A reasonable number of additional copies shall be provided for the applicable fee to a requestor who... 11. Lubricant additive concentrate containing isomerized jojoba oil Energy Technology Data Exchange (ETDEWEB) Arndt, G. 1987-05-12 This patent describes a crankcase motor oil additive concentrate intended to be added to a conventional crankcase motor oil to improve its ability to lubricate and protect the engine. The additive concentrate comprises the following components: A petroleum base stock of lubricating quality and viscosity. The base stock comprises from about 13.5 to 90 weight percent of the additive concentrate; a detergent-inhibitor package. The package is present at from about 7 to about 40 weight percent of the concentrate; a supplemental antiwear additive selected from the salts of dialkyl dithiophosporic acids. The additive is present at a level of from about 1 to about 10 weight percent of the concentrate; and a supplemental antiwear additive selected from the class of sulfurized olefins. The additive is present at a level of from about 1 to about 10 weight percent of the concentrate. 12. Cincinnati Big Area Additive Manufacturing (BAAM) Energy Technology Data Exchange (ETDEWEB) Duty, Chad E. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Love, Lonnie J. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States) 2015-03-04 Oak Ridge National Laboratory (ORNL) worked with Cincinnati Incorporated (CI) to demonstrate Big Area Additive Manufacturing which increases the speed of the additive manufacturing (AM) process by over 1000X, increases the size of parts by over 10X and shows a cost reduction of over 100X. ORNL worked with CI to transition the Big Area Additive Manufacturing (BAAM) technology from a proof-of-principle (TRL 2-3) demonstration to a prototype product stage (TRL 7-8). 13. Merits and Demerits of Food Additives OpenAIRE Xuening YANG; Zhan, Yong 2014-01-01 Food additive is a double-edged sword. It has merits and demerits. Food additives have such merits as improving sensory properties of foods, preventing deterioration and extending the shelf life, increasing varieties of foods, enhancing convenience of foods, facilitating food processing, and satisfying other demands. However, excessive and illegal use of food additives will exert adverse influence on food security. Therefore, it is required to take proper measures to bring merits of food addi... 14. Additives in food and their properties OpenAIRE TYLOVÁ, Kristýna 2013-01-01 The aim of this work is to deepen the knowledge about additives in foods, the importance of technological additives in foods, their properties and effects on human health. The aim of this work is a study of technical and scientific literature on the topic: "additives in foods and their properties" and review of the literature. Also in the practical part, implementation and evaluation of a questionnaire survey of the experimental group related to the topic: "Validation and comparison of knowle... 15. Food Additives Course Teaching Reform and Construction OpenAIRE Shengjun Wu 2014-01-01 Food additives course is a professional course in undergraduate specialty of food science and engineering. In order to improve the food additives course teaching and students’ experimental ability, the food additives teaching is confronted with new tasks, i.e., establish the corresponding experimental course, in which the modern means and methods were used to develop a new experimental teaching and stimulate the students’ interests and the spirit of innovation. 16. A Parametric Representation of Additive Value Functions OpenAIRE Thomas W. Keelin 1981-01-01 This paper introduces a new parameter for measuring deterministic preference tradeoffs between pairs of attributes. In terms of this parameter, necessary and sufficient conditions for a value function to be additive are established. When additivity conditions are satisfied, a set of these parameters is shown to characterize the value function uniquely up to a set of scaling constants. Implications for assessment, for transforming a nonadditive representation into an additive one, and for mult... 17. Additive manufacturing : A new option in manufacturing OpenAIRE Nestrell, Annéa 2015-01-01 GE Healthcare wants to investigate whether additive manufacturing would be an alternative method in their workshops in the Umeå plant. Additive manufacturing is called 3D printing in everyday language and manufactures details by building them up layer by layer in an automated machine. The purpose of this work is therefore to investigate how mature additive manufacturing methods are and how they could be used at GE. The work has been divided into three parts. The first section investigates ho... 18. Merits and Demerits of Food Additives Institute of Scientific and Technical Information of China (English) Xuening; YANG; Yong; ZHAN 2014-01-01 Food additive is a double-edged sword. It has merits and demerits. Food additives have such merits as improving sensory properties of foods,preventing deterioration and extending the shelf life,increasing varieties of foods,enhancing convenience of foods,facilitating food processing,and satisfying other demands. However,excessive and illegal use of food additives will exert adverse influence on food security.Therefore,it is required to take proper measures to bring merits of food additives into full play,and get rid of their demerits. 19. ON IDENTIFICATION OF CONCRETE PLASTICIZING ADDITIVES Directory of Open Access Journals (Sweden) P. I. Yukhnevskiy 2015-01-01 Full Text Available Quality problem of chemical additives comes down in general to their objective and independent evaluation. As an identification is not made during product delivery for testing and while carrying out the testing there is difference in the results of investigations and finally construction products suffer from their poor quality. In this connection, it is proposed to make some alterations to revised version of the STB 1112 and GOST 30459, so that while supplying chemical additives for certification testing a certificate on additive quality should contain a standard of IR-spectra with active components. Simultaneously, the standard should be applied for additive testing results in accordance with rate efficiency criteria for GOST 30459. Such norms are accepted for similar European standards.The paper presents a standard method for identification of organic additives according to IR-spectra, characteristic absorption bands for the Lignopan-type additives and naphthalene formaldehyde super-plasticizer C-3. However, due to the fact that it is not possible to judge number of functional groups in the product by absorption band size but it is possible only to assess their availability so it is recommended to use other methods. As an additional characteristics it is proposed to determine magnitude of the dipole moment in a plasticizer-additive molecule. The authors previously developed a technique and determined dipole moments in super-plasticizer-additives as in the form of powder so in the form of aqueous solutions, correlation relationship of water reduction additive capability with the magnitude of dipole moment. It has been proposed to manufacturers of plasticizing additives for concrete along with IR-spectra in the technical documentation to indicate a magnitude of the molecule dipole moment as a generalized characteristics that determines its plasticizing properties. 20. 42 CFR 52b.13 - Additional conditions. Science.gov (United States) 2010-10-01 ... 42 Public Health 1 2010-10-01 2010-10-01 false Additional conditions. 52b.13 Section 52b.13 Public Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES GRANTS NATIONAL INSTITUTES OF HEALTH CONSTRUCTION GRANTS § 52b.13 Additional conditions. The Director may with respect to any... 1. 76 FR 55882 - Procurement List; Addition Science.gov (United States) 2011-09-09 ... INFORMATION: Additions On 6/17/2011 (76 FR 35415-35417), the Committee for Purchase From People Who Are Blind... From the Federal Register Online via the Government Publishing Office COMMITTEE FOR PURCHASE FROM PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Addition AGENCY: Committee for Purchase... 2. The Additive Coloration of Alkali Halides Science.gov (United States) Jirgal, G. H.; and others 1969-01-01 Describes the construction and use of an inexpensive, vacuum furnace designed to produce F-centers in alkali halide crystals by additive coloration. The method described avoids corrosion or contamination during the coloration process. Examination of the resultant crystals is discussed and several experiments using additively colored crystals are… 3. 77 FR 62220 - Procurement List; Additions Science.gov (United States) 2012-10-12 ... . SUPPLEMENTARY INFORMATION: Additions On 7/20/2012 (77 FR 42701-42702), 7/27/2012 (77 FR 44220), and 8/ 17/2012 (77 FR 49784), the Committee for Purchase From People Who Are Blind or Severely Disabled published... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase... 4. 78 FR 67129 - Procurement List; Additions Science.gov (United States) 2013-11-08 ... 8/23/2013 (78 FR 52512-52513), 8/30/2013 (78 FR 53734), and 9/6/ 2013 (78 FR 54871), the Committee... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Additions to the Procurement List. SUMMARY:... 5. 75 FR 2510 - Procurement List: Proposed Additions Science.gov (United States) 2010-01-15 ... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List: Proposed Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Proposed Additions to Procurement List. SUMMARY: The Committee is proposing to add to the Procurement List services to be provided by... 6. 77 FR 77037 - Procurement List; Additions Science.gov (United States) 2012-12-31 ... . SUPPLEMENTARY INFORMATION: Additions On 10/12/2012 (77 FR 62219-62220), 10/19/2012 (77 FR 64326-64327) and 11/9/2012 (77 FR 67343-67344), the Committee for Purchase From People Who Are Blind or Severely Disabled... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase... 7. 78 FR 5423 - Procurement List; Proposed Additions Science.gov (United States) 2013-01-25 ... FROM PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Proposed Additions AGENCY: Committee... Procurement List. SUMMARY: The Committee is proposing to add products to the Procurement List that will be... have other severe disabilities. The following products are proposed for addition to the... 8. 78 FR 63967 - Procurement List; Additions Science.gov (United States) 2013-10-25 ... 8/9/2013 (78 FR 48656-48657), 8/16/2013 (78 FR 50040), and 8/23/ 2013 (78 FR 52512-52513), the... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Additions to the Procurement List. SUMMARY:... 9. 77 FR 32592 - Procurement List; Additions Science.gov (United States) 2012-06-01 ... . ] SUPPLEMENTARY INFORMATION: Additions On 12/2/2011 (76 FR 75536-75537), 1/13/2012 (77 FR 2048) and 4/6/ 2012 (77 FR 20795), the Committee for Purchase From People Who Are Blind or Severely Disabled published... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase... 10. 76 FR 47564 - Procurement List; Additions Science.gov (United States) 2011-08-05 ... . SUPPLEMENTARY INFORMATION: Additions On 4/22/2011 (76 FR 22680); 5/6/2011 (76 FR 26279); 6/3/2011 (76 FR 32146); and 6/10/2011 (76 FR 34064-34065), the Committee for Purchase From People ] Who Are Blind or Severely... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase... 11. 77 FR 2048 - Procurement List Proposed Additions Science.gov (United States) 2012-01-13 ... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List Proposed Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Proposed Additions to the Procurement List. SUMMARY: The Committee is proposing to add services to the Procurement List that will be provided by... 12. 78 FR 7412 - Procurement List; Proposed Additions Science.gov (United States) 2013-02-01 ... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Proposed Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Proposed Additions to the Procurement List. SUMMARY: The Committee is proposing to add products to the Procurement List that will be furnished by... 13. Contexts for Column Addition and Subtraction Science.gov (United States) Lopez Fernandez, Jorge M.; Velazquez Estrella, Aileen 2011-01-01 In this article, the authors discuss their approach to column addition and subtraction algorithms. Adapting an original idea of Paul Cobb and Erna Yackel's from "A Contextual Investigation of Three-Digit Addition and Subtraction" related to packing and unpacking candy in a candy factory, the authors provided an analogous context by designing… 14. Asthma and anaphylactoid reactions to food additives. OpenAIRE Tarlo, S. M.; Sussman, G L 1993-01-01 Presumed allergic reactions to hidden food additives are both controversial and important. Clinical manifestations include asthma, urticaria, angioedema, and anaphylactic-anaphylactoid events. Most adverse reactions are caused by just a few additives, such as sulfites and monosodium glutamate. Diagnosis is suspected from the history and confirmed by specific challenge. The treatment is specific avoidance. 15. Feed Additives for Aquaculture and Aquarium Culture OpenAIRE Barata, Eduardo N; Velez, Zélia 2011-01-01 The presente invention refers of feed additives for aquaculture and aquarium culture. These additives comprise the amino acid, 1-methyl-L-tryptophane, or its isomers with the objective of improving the attractiveness of feeds used in aquaculture and aquaria for fish, as well as other aquatic organisms, under culture conditions. Therefore, this invention has applications in the agriculture-food industry. 16. Additions to the Avifauna of suriname NARCIS (Netherlands) Mees, G.F. 1974-01-01 It is self-evident that as the avifauna of a country becomes better known, the number of additions to its avifauna one can expect to make in a given period, must decrease. On the other hand, it may be said that for the same reason the value of each addition increases. During a stay in Suriname of ab 17. Working Memory and Children's Mental Addition. Science.gov (United States) Adams, John W.; Hitch, Graham J. 1997-01-01 Two experiments investigated extent to which English- and German-speaking childrens' mental arithmetic was constrained by working memory. Found higher mental addition spans when numbers were visible throughout calculation than when not. Variation in addition span with age and arithmetical operation difficulty approximated to a linear function of… 18. 46 CFR 308.502 - Additional insurance. Science.gov (United States) 2010-10-01 ... 46 Shipping 8 2010-10-01 2010-10-01 false Additional insurance. 308.502 Section 308.502 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION EMERGENCY OPERATIONS WAR RISK INSURANCE War Risk Cargo Insurance I-Introduction § 308.502 Additional insurance. The assured may place increased value... 19. 75 FR 60739 - Procurement List; Proposed Additions Science.gov (United States) 2010-10-01 .... NPA: CW Resources, Inc., New Britain, CT. Contracting Activity: Dept. of the Army, XRA W7NN USPFO... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Proposed Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Proposed additions to the procurement... 20. 75 FR 6869 - Procurement List; Additions Science.gov (United States) 2010-02-12 [email protected] . SUPPLEMENTARY INFORMATION: Additions On 12/11/2009 (74 FR 65758) and 12/18/2009 (74 FR... rules that are applicable to the public. Notices of hearings #0;and investigations, committee meetings...; ] COMMITTEE FOR PURCHASE FROM PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions... 1. 75 FR 28590 - Procurement List Additions Science.gov (United States) 2010-05-21 ... added to the Procurement List: Products NSN: 1670-01-523-7246--LCADS Low Cost Container. NPA: Winston... PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List Additions AGENCY: Committee for Purchase From People Who Are Blind or Severely Disabled. ACTION: Additions to the Procurement List. SUMMARY:... 2. DNA addition using linear self-assembly Institute of Scientific and Technical Information of China (English) ZHAO Jian; QIAN LuLu; LIU Qiang; ZHANG ZhiZhou; HE Lin 2007-01-01 This paper presents a DNA algorithm which adds two nonnegative binary integers using self-assembly in constant steps. The approach has the benefit of greater experimental simplicity when compared with previous DNA addition algorithms. For the addition of two binary n-bit integers, O(n) is different from DNA strands and only O(1) biochemical experimental procedures are required. 3. Implementation of the Additional Protocol in Japan International Nuclear Information System (INIS) The Additional Protocol between Japan and the IAEA entered into force in December 1999. To come into force a series of implementation trials of Additional Protocol was carried out at two Japanese representative nuclear research centers, i.e. Tokai Research Establishment of Japan Atomic Energy Research Institute (JAERI) and Oarai Engineering Center of Japan Nuclear Fuel Cycle Development Institute (JNC). These trials were proposed by Japan and were conducted in cooperation with the IAEA Secretariat. In addition, Japan amended 'the Law for the Regulation of Reactors etc.', to collect adequate information to submit to the IAEA, to arrange the surrounding for the complementary access, etc. In addition, Japan Submitted the Initial Declaration of the Additional Protocol within 180 days of the entry into force of the Protocol, in the middle of June, 2000 4. Ashless Anti- Wear Additives for Motor Oils Institute of Scientific and Technical Information of China (English) 2005-01-01 Ashless anti- wear (AW) additives containing phosphorus can be used as partial or complete replacement of zinc dithiodialkylphosphate (ZDDP). In oils with low sulfated ash content (＜ 1.0%), this approach will allow a significant reduction of ash content and/or provide the formulator with more flexibility to use additional metallic detergents. Over the past 70 years or so, ZDDP has proven to be a very effective engine oil additive by helping to reduct oxidation, wear, and corrosion in service. In this paper, we will compare ZDDP- based lubricants with lubricants base on ashless, P- containing additive systems; we will describe the ashless chemistry investigated and discuss its contribution to wear performance in modem, low- SAPS (sulfated ash, phosphorus & sulfur) engine oils in various bench, rig and engine tests; we will also report on some work done to evaluate AW additive compatibility with modern three- way exhaust gas catalysts (TWC). 5. Evaluation of certain food additives and contaminants. Science.gov (United States) 2002-01-01 This report represents the conclusions of a Joint FAO/WHO Expert Committee convened to evaluate the safety of various food additives and contaminants, with a view to recommending Acceptable Daily Intakes (ADIs) and tolerable intakes, respectively, and to prepare specifications for the identity and purity of food additives. The first part of the report contains a general discussion of the principles governing the toxicological evaluation of food additives (including flavouring agents) and contaminants, assessments of intake, and the establishment and revision of specifications for food additives. A summary follows of the Committee's evaluations of toxicological and intake data on various specific food additives (diacetyltartaric and fatty acid esters of glycerol, quillaia extracts, invertase from Saccharomyces cerevisiae, beta-carotene from Blakeslea trispora, curcumin, phosphates, diphosphates and polyphosphates, hydrogenated poly-1-decene, natamycin, D-tagatose, carrageenan, processed Eucheuma seaweed, curdlan, acetylated oxidized starch, alpha-cyclodextrin and sodium sulfate), flavouring agents and contaminants (3-chloro-1,2-propanediol, 1,3-dichloro-2-propanol, and a large number of polychlorinated dibenzodioxins, polychlorinated dibenzofurans and coplanar polychlorinated biphenyls). Annexed to the report are tables summarizing the Committee's recommendations for ADIs of the food additives and tolerable intakes of the contaminants considered, changes in the status of specifications of these food additives and specific flavouring agents, and further information required or desired. PMID:12564044 6. Graphite and Hybrid Nanomaterials as Lubricant Additives Directory of Open Access Journals (Sweden) Zhenyu J. Zhang 2014-04-01 Full Text Available Lubricant additives, based on inorganic nanoparticles coated with organic outer layer, can reduce wear and increase load-carrying capacity of base oil remarkably, indicating the great potential of hybrid nanoparticles as anti-wear and extreme-pressure additives with excellent levels of performance. The organic part in the hybrid materials improves their flexibility and stability, while the inorganic part is responsible for hardness. The relationship between the design parameters of the organic coatings, such as molecular architecture and the lubrication performance, however, remains to be fully elucidated. A survey of current understanding of hybrid nanoparticles as lubricant additives is presented in this review. 7. 21 CFR 25.32 - Foods, food additives, and color additives. Science.gov (United States) 2010-04-01 ... 21 Food and Drugs 1 2010-04-01 2010-04-01 false Foods, food additives, and color additives. 25.32 Section 25.32 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL ENVIRONMENTAL IMPACT CONSIDERATIONS Categorical Exclusions § 25.32 Foods, food additives, and color additives. The classes of actions listed... 8. 77 FR 44218 - Procurement List; Additions Science.gov (United States) 2012-07-27 ... . SUPPLEMENTARY INFORMATION: Additions On 5/11/2012 (77 FR 27737-27738) and 6/1/2012 (77 FR 32591-32592), the...: 3895-00-NIB-0002--Asphalt Lute, Aluminum Head, Industrial Grade, 67'' Fiberglass Handle,... 9. Caustic addition system operability test procedure International Nuclear Information System (INIS) This test procedure provides instructions for performing operational testing of the major components of the 241-AN-107 Caustic Addition System by WHC and Kaiser personnel at the Rotating Equipment Shop run-in pit (Bldg. 272E) 10. Additive Manufacturing of Ion Thruster Optics Project Data.gov (United States) National Aeronautics and Space Administration — Plasma Controls will manufacture and test a set of ion optics for electric propulsion ion thrusters using additive manufacturing technology, also known as 3D... 11. 75 FR 4784 - Procurement List; Addition Science.gov (United States) 2010-01-29 ... INFORMATION: Addition On 11/16/2009 (74 FR 58949-58950), the Committee for Purchase From People Who Are Blind... Bldg & Courthouse, 202 Harlow Street, Bangor, ME. NPA: Northern New England Employment... 12. 40 CFR 262.43 - Additional reporting. Science.gov (United States) 2010-07-01 ... require generators to furnish additional reports concerning the quantities and disposition of wastes identified or listed in 40 CFR part 261. ...) STANDARDS APPLICABLE TO GENERATORS OF HAZARDOUS WASTE Recordkeeping and Reporting § 262.43... 13. 42 CFR 65.9 - Additional conditions. Science.gov (United States) 2010-10-01 ... conditions. The Director may with respect to any award impose additional conditions prior to, or at the time of, any award when, in the Director's judgment, such conditions are necessary to assure the... 14. Additives In Meat and Poultry Products Science.gov (United States) ... brown, margarine wouldn't be yellow, and mint ice cream wouldn't be green. Color additives are now ... antioxidants that help maintain the appeal and wholesome qualities of food by retarding rancidity in fats, sausages, ... 15. 76 FR 23997 - Procurement List; Addition Science.gov (United States) 2011-04-29 ... INFORMATION: Addition On 2/25/2011 (76 FR 10571), the Committee for Purchase From People Who Are Blind or..., Baltimore, MD. NPA: Melwood Horticultural Training Center, Upper Marlboro, MD. ] Contracting... 16. Non-additive measure and integral CERN Document Server Denneberg, Dieter 1994-01-01 Non-Additive Measure and Integral is the first systematic approach to the subject. Much of the additive theory (convergence theorems, Lebesgue spaces, representation theorems) is generalized, at least for submodular measures which are characterized by having a subadditive integral. The theory is of interest for applications to economic decision theory (decisions under risk and uncertainty), to statistics (including belief functions, fuzzy measures) to cooperative game theory, artificial intelligence, insurance, etc. Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application. It unifies, simplifies and generalizes known results and supplements the theory with new results, thus providing a sound basis for applications and further research in this growing field of increasing interest. It also co... 17. Effective Structural Health Monitoring with Additive Manufacturing OpenAIRE De Baere, Dieter; Strantza, Maria; Hinderdael, Michaël; Devesse, Wim; Guillaume, Patrick 2014-01-01 The current remaining challenges for structural health monitoring (SHM) systems prevented the introduction of SHM systems on a large scale within industrial applications. An effective SHM system is required for the reduction of the direct operation costs, improvement of the life-safety and the introduction of additive manufactured components for critical structures. In this paper, a new structural health monitoring methodology will be presented for components that can be processed by additive... 18. Additional Forms of Employee Representation in Australia OpenAIRE Gollan, Paul; Markey, Ray; Ross, Iain 2001-01-01 Additional forms of employee representation (AFER) may be defined as any representative mechanism which exists alongside or instead of trade unions, which historically have been the most common form of employee representation in Australia. Little is known about how AFER are composed, their independence from managerial influence, the 'representativeness' of such bodies, and their accountability. In addition, little has been documented about the impact of such structures on either the manageria... 19. Food Additives and Effects to Human Health OpenAIRE Ayper Boga; Secil Binokay 2010-01-01 Food purchasing patterns have changed dramatically over the past fifty years. Packaged and processed foods get many a family through the day. Theyre convenient, portable, and they stay fresh for a long time. There are over fourteen thousand man-made chemicals added to American food supply today. Food additives are not natural nutrition for humans or their pets. Children are suffering the most from food additives because they are exposed to food chemicals from infancy, and human bodies w... 20. Culture and neuroscience: additive or synergistic? OpenAIRE Losin, Elizabeth A. Reynolds; DAPRETTO, MIRELLA; Iacoboni, Marco 2010-01-01 The investigation of cultural phenomena using neuroscientific methods—cultural neuroscience (CN)—is receiving increasing attention. Yet it is unclear whether the integration of cultural study and neuroscience is merely additive, providing additional evidence of neural plasticity in the human brain, or truly synergistic, yielding discoveries that neither discipline could have achieved alone. We discuss how the parent fields to CN: cross-cultural psychology, psychological anthropology and cogni... 1. Laser polishing of additive laser manufacturing surfaces OpenAIRE Rosa, Benoit; MOGNOL, Pascal; Hascoët, Jean-Yves 2015-01-01 International audience The additive laser manufacturing (ALM) technique is an additive manufacturing process which enables the rapid manufacturing of complex metallic parts and the creation of thin parts so as, for example, to decrease parts weight for biomechanical or aeronautic applications. Furthermore, compared with selective laser sintering technology, the ALM process allows creating more huge parts and material gradient. However, for aesthetic or tribological functions, the ALM surfa... 2. Environmental Impact Assessment Studies in Additive Manufacturing OpenAIRE Kerbrat, Olivier; Le Bourhis, Florent; MOGNOL, Pascal; Hascoët, Jean-Yves 2016-01-01 International audience This chapter focuses on the environmental studies in additive manufacturing. For a cleaner production, environmental impacts that occur during the manufacturing phase should be assessed with accuracy. First, the literature on all the studies led to the characterization of the environmental impact of additive manufacturing processes. The studies on electric energy consumption of these processes are analyzed here, and then some studies taking into account raw material ... 3. 3D Additive Manufacturing Symposium & Workshop OpenAIRE Unver, Ertu; Taylor, Andrew 2015-01-01 The IMI /3M BIC 3D Additive Manufacturing Symposium and Workshop was hosted by 3M Buckley Innovation Centre on March 17th 2015. The event was attended by the major players in precision engineering, 3D additive design and manufacturing: Representatives from EOS, Renishaw, HK 3D Printing IMI Plc Senior Management team, design engineers, programmers and academics from the University of Huddersfield School of Art Design & Architecture, 3M Buckley centre 3D printing management and designers shared... 4. Evaluation of certain food additives and contaminants. Science.gov (United States) 2004-01-01 This report represents the conclusions of a Joint FAO/WHO Expert Committee convened to evaluate the safety of various food additives, with a view to recommending acceptable daily intakes (ADIs) and to prepare specifications for the identity and purity of food additives. The first part of the report contains a general discussion of the principles governing the toxicological evaluation of food additives (including flavouring agents) and contaminants, assessments of intake, and the establishment and revision of specifications for food additives. A summary follows of the Committee's evaluations of toxicological and intake data on various specific food additives (alpha-amylase from Bacillus lichenformis containing a genetically engineered alpha-amylase gene from B. licheniformis, annatto extracts, curcumin, diacetyl and fatty acid esters of glycerol, D-tagatose, laccase from Myceliophthora thermophila expressed in Aspergillus oryzae, mixed xylanase, beta-glucanase enzyme preparation produced by a strain of Humicola insolens, neotame, polyvinyl alcohol, quillaia extracts and xylanase from Thermomyces lanuginosus expressed in Fusarium venenatum), flavouring agents, a nutritional source of iron (ferrous glycinate, processed with citric acid), a disinfectant for drinking-water (sodium dichloroisocyanurate) and contaminants (cadmium and methylmercury). Annexed to the report are tables summarizing the Committee's recommendations for ADIs of the food additives, recommendations on the flavouring agents considered, and tolerable intakes of the contaminants considered, changes in the status of specifications and further information requested or desired. 5. Additive manufacturing in production: challenges and opportunities Science.gov (United States) Ahuja, Bhrigu; Karg, Michael; Schmidt, Michael 2015-03-01 Additive manufacturing, characterized by its inherent layer by layer fabrication methodology has been coined by many as the latest revolution in the manufacturing industry. Due to its diversification of Materials, processes, system technology and applications, Additive Manufacturing has been synonymized with terminology such as Rapid prototyping, 3D printing, free-form fabrication, Additive Layer Manufacturing, etc. A huge media and public interest in the technology has led to an innovative attempt of exploring the technology for applications beyond the scope of the traditional engineering industry. Nevertheless, it is believed that a critical factor for the long-term success of Additive Manufacturing would be its ability to fulfill the requirements defined by the traditional manufacturing industry. A parallel development in market trends and product requirements has also lead to a wider scope of opportunities for Additive Manufacturing. The presented paper discusses some of the key challenges which are critical to ensure that Additive Manufacturing is truly accepted as a mainstream production technology in the industry. These challenges would highlight on various aspects of production such as product requirements, process management, data management, intellectual property, work flow management, quality assurance, resource planning, etc. In Addition, changing market trends such as product life cycle, mass customization, sustainability, environmental impact and localized production will form the foundation for the follow up discussion on the current limitations and the corresponding research opportunities. A discussion on ongoing research to address these challenges would include topics like process monitoring, design complexity, process standardization, multi-material and hybrid fabrication, new material development, etc. 6. Additional renal arteries: incidence and morphometry. Science.gov (United States) Satyapal, K S; Haffejee, A A; Singh, B; Ramsaroop, L; Robbs, J V; Kalideen, J M 2001-01-01 Advances in surgical and uro-radiological techniques dictate a reappraisal and definition of renal arterial variations. This retrospective study aimed at establishing the incidence of additional renal arteries. Two subsets were analysed viz.: a) Clinical series--130 renal angiograms performed on renal transplant donors, 32 cadaver kidneys used in renal transplantation b) Cadaveric series--74 en-bloc morphologically normal kidney pairs. The sex and race distribution was: males 140, females 96; African 84, Indian 91, White 43 and "Coloured" 18, respectively. Incidence of first and second additional arteries were respectively, 23.2% (R: 18.6%; L: 27.6%) and 4.5% (R: 4.7%; L: 4.4%). Additional arteries occurred more frequently on the left (L: 32.0%; R: 23.3%). The incidence bilaterally was 10.2% (first additional arteries, only). The sex and race incidence (first and second additional) was: males, 28.0%, 5.1%; females, 16.4%, 3.8% and African 31.1%, 5.4%; Indian 13.5%, 4.5%; White 30.9%, 4.4% and "Coloured" 18.5%, 0%; respectively. Significant differences in the incidence of first additional arteries were noted between sex and race. The morphometry of additional renal arteries were lengths (cm) of first and second additional renal arteries: 4.5 and 3.8 (right), 4.9 and 3.7 (left); diameters: 0.4 and 0.3 (right), 0.3 and 0.3 (left). Detailed morphometry of sex and race were also recorded. No statistically significant differences were noted. Our results of the incidence of additional renal arteries of 27.7% compared favourably to that reported in the literature (weighted mean 28.1%). The study is unique in recording detailed morphometry of these vessels. Careful techniques in the identification of this anatomical variation is important since it impacts on renal transplantation surgery, vascular operations for renal artery stenosis, reno-vascular hypertension, Takayasu's disease, renal trauma and uro-radiological procedures. 7. Fuel and Additive Characterization for HCCI Combustion Energy Technology Data Exchange (ETDEWEB) Aceves, S M; Flowers, D; Martinez-Frias, J; Espinosa-Loza, F; Pitz, W J; Dibble, R 2003-02-12 This paper shows a numerical evaluation of fuels and additives for HCCl combustion. First, a long list of candidate HCCl fuels is selected. For all the fuels in the list, operating conditions (compression ratio, equivalence ratio and intake temperature) are determined that result in optimum performance under typical operation for a heavy-duty engine. Fuels are also characterized by presenting Log(p)-Log(T) maps for multiple fuels under HCCl conditions. Log(p)-Log(T) maps illustrate important processes during HCCl engine operation, including compression, low temperature heat release and ignition. Log(p)-Log(T) diagrams can be used for visualizing these processes and can be used as a tool for detailed analysis of HCCl combustion. The paper also includes a ranking of many potential additives. Experiments and analyses have indicated that small amounts (a few parts per million) of secondary fuels (additives) may considerably affect HCCl combustion and may play a significant role in controlling HCCl combustion. Additives are ranked according to their capability to advance HCCl ignition. The best additives are listed and an explanation of their effect on HCCl combustion is included. 8. Testing for additivity with B-splines Institute of Scientific and Technical Information of China (English) 2007-01-01 Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey’s one degree of freedom test and a nonparametric version of Rao’s score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance. 9. Mass Additivity and A Priori Entailment CERN Document Server McQueen, Kelvin J 2015-01-01 The principle of mass additivity states that the mass of a composite object is the sum of the masses of its elementary components. Mass additivity is true in Newtonian mechanics but false in special relativity. Physicists have explained why mass additivity is true in Newtonian mechanics by reducing it to Newton's microphysical laws. This reductive explanation does not fit well with deducibility theories of reductive explanation such as the modern Nagelian theory of reduction, and the a priori entailment theory of reduction that is prominent in the philosophy of mind. Nonetheless, I argue that a reconstruction of the explanation that incorporates distinctively philosophical concepts in fact fits both theories. I discuss the implications of this result for both theories and for the reductive explanation of consciousness. 10. Does finger sense predict addition performance? Science.gov (United States) Newman, Sharlene D 2016-05-01 The impact of fingers on numerical and mathematical cognition has received a great deal of attention recently. However, the precise role that fingers play in numerical cognition is unknown. The current study explores the relationship between finger sense, arithmetic and general cognitive ability. Seventy-six children between the ages of 5 and 12 participated in the study. The results of stepwise multiple regression analyses demonstrated that while general cognitive ability including language processing was a predictor of addition performance, finger sense was not. The impact of age on the relationship between finger sense, and addition was further examined. The participants were separated into two groups based on age. The results showed that finger gnosia score impacted addition performance in the older group but not the younger group. These results appear to support the hypothesis that fingers provide a scaffold for calculation and that if that scaffold is not properly built, it has continued differential consequences to mathematical cognition. PMID:26993292 11. Evaluation of advanced polymers for additive manufacturing Energy Technology Data Exchange (ETDEWEB) Rios, Orlando [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Morrison, Crystal [PPG Industries, Pittsburgh, PA (United States) 2015-09-01 The goal of this Manufacturing Demonstration Facility (MDF) technical collaboration project between Oak Ridge National Laboratory (ORNL) and PPG Industries, Inc. was to evaluate the feasibility of using conventional coatings chemistry and technology to build up material layer-by-layer. The PPG-ORNL study successfully demonstrated that polymeric coatings formulations may overcome many limitations of common thermoplastics used in additive manufacturing (AM), allow lightweight nozzle design for material deposition and increase build rate. The materials effort focused on layer-by-layer deposition of coatings with each layer fusing together. The combination of materials and deposition results in an additively manufactured build that has sufficient mechanical properties to bear the load of additional layers, yet is capable of bonding across the z-layers to improve build direction strength. The formulation properties were tuned to enable a novel, high-throughput deposition method that is highly scalable, compatible with high loading of reinforcing fillers, and is inherently low-cost. 12. Non-additive measures theory and applications CERN Document Server Narukawa, Yasuo; Sugeno, Michio; 9th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2012) 2014-01-01 This book provides a comprehensive and timely report in the area of non-additive measures and integrals. It is based on a panel session on fuzzy measures, fuzzy integrals and aggregation operators held during the 9th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2012) in Girona, Spain, November 21-23, 2012. The book complements the MDAI 2012 proceedings book, published in Lecture Notes in Computer Science (LNCS) in 2012. The individual chapters, written by key researchers in the field, cover fundamental concepts and important definitions (e.g. the Sugeno integral, definition of entropy for non-additive measures) as well some important applications (e.g. to economics and game theory) of non-additive measures and integrals. The book addresses students, researchers and practitioners working at the forefront of their field. 13. Testing for additivity with B-splines Institute of Scientific and Technical Information of China (English) Heng-jian CUI; Xu-ming HE; Li LIU 2007-01-01 Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernelbased tests. The score test is found to have a good overall performance. 14. Combustion enhancing additives for coal firing Energy Technology Data Exchange (ETDEWEB) Katherine Le Manquais; Colin Snape; Ian McRobbie; Jim Barker [University of Nottingham, Nottingham (United Kingdom). School of Chemical, Environmental and Mining Engineering (SChEME) 2007-07-01 For pulverised fuel (pf) combustion, the level of unburnt carbon in fly ash is now considerably more problematic worldwide than a decade ago, because of the introduction of low NOx burners and the increased level of high inertinite in internationally traded coals. Thus, there is a major opportunity to develop an effective additive to improve carbon burnout and obviate the need for post-treatment of fly ash, which endeavours to meet specifications for filler/building materials applications and thereby avoid landfill. A robust comparison of the reactivity of different coals and their corresponding chars is necessary, in order to estimate the effects of such an additive on pf combustion. Coal chars have been generated on a laboratory scale using thermal gravimetric analysis (TGA) and on a larger scale using a drop tube furnace (DTF), which is more representative of the rapid heating rates and mixing achieved on pf combustion. The TGA results indicate that chars have varying levels of reactivity, dependent on the parent coal properties. When physically mixed with a propriety metal additive, the degree of enhancement to the reactivity of these chars also appeared reliant on the parent coal characteristics. Additionally it was demonstrated that DTF chars, whilst showing similar reactivity trends, are less reactive than the equivalent coal chars produced by the TGA. However, when mixed with the metal additive the DTF chars show a significantly greater improvement in reactivity than their analogous TGA chars, indicating the additive may have the greatest impact on the most unreactive carbon in the coal. 42 refs., 6 figs., 1 tab. 15. Local Time of Additive Levy Process Institute of Scientific and Technical Information of China (English) 2000-01-01 We studied the problem of existence of jointly continuous local time for an additive process.Here, “local time” is understood in the sence of occupation density, and by an additive Lévy process we mean a process X＝{X(t), t∈Rd+)} which has the decomposition X＝ X1 X2 … XN. We prove that if the product of it slower index and N is greater than d, then a jointly continuous local time can be obtained via Berman's method. 16. Breaking Barriers in Polymer Additive Manufacturing Energy Technology Data Exchange (ETDEWEB) Love, Lonnie J [ORNL; Duty, Chad E [ORNL; Post, Brian K [ORNL; Lind, Randall F [ORNL; Lloyd, Peter D [ORNL; Kunc, Vlastimil [ORNL; Peter, William H [ORNL; Blue, Craig A [ORNL 2015-01-01 Additive Manufacturing (AM) enables the creation of complex structures directly from a computer-aided design (CAD). There are limitations that prevent the technology from realizing its full potential. AM has been criticized for being slow and expensive with limited build size. Oak Ridge National Laboratory (ORNL) has developed a large scale AM system that improves upon each of these areas by more than an order of magnitude. The Big Area Additive Manufacturing (BAAM) system directly converts low cost pellets into a large, three-dimensional part at a rate exceeding 25 kg/h. By breaking these traditional barriers, it is possible for polymer AM to penetrate new manufacturing markets. 17. Construction of Additive Reed-Muller Codes CERN Document Server Pujol, J; Ronquillo, L; 10.1007/978-3-642-02181-7 2009-01-01 The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of Z2Z4-additive codes such that, under the Gray map, the corresponding binary codes have the same parameters and properties as the usual binary linear Reed-Muller codes. Moreover, the first family is the usual binary linear Reed-Muller family. 18. Alkylphenoxyalkylstannanes as biocidal additives to lubricants Energy Technology Data Exchange (ETDEWEB) Belov, P.S.; Gulo, R.A.; Komarova, N.N.; Korenev, K.D.; Poddubnyi, V.N.; Tsvetkov, O.N. 1980-01-01 The synthesis of akylphenoxyalkylstannanes with different numbers and lengths of akyl radicals on the tin atom and different structures and lengths of radicals on the aromatic ring is described. They were investigated as biocidal additives to lubricants. Alkylphenoxytriethylstannanes have the best protective properties. In 0.25% concentration (by wt) neither the structure nor the alkyl substituent (C/sub 1/-C/sub 16/) length has an effect on their antiseptic properties. From the results of the conducted studies, for antiseptization of lubricating compositions, the additive AFOTAS a reaction product of an industrial alkylphenol and bis(triethylol) oxide is recommended. 19. Effusion plate using additive manufacturing methods Energy Technology Data Exchange (ETDEWEB) Johnson, Thomas Edward; Keener, Christopher Paul; Ostebee, Heath Michael; Wegerif, Daniel Gerritt 2016-04-12 Additive manufacturing techniques may be utilized to construct effusion plates. Such additive manufacturing techniques may include defining a configuration for an effusion plate having one or more internal cooling channels. The manufacturing techniques may further include depositing a powder into a chamber, applying an energy source to the deposited powder, and consolidating the powder into a cross-sectional shape corresponding to the defined configuration. Such methods may be implemented to construct an effusion plate having one or more channels with a curved cross-sectional geometry. 20. 77 FR 14352 - Procurement List; Proposed Additions Science.gov (United States) 2012-03-09 ... From the Federal Register Online via the Government Publishing Office COMMITTEE FOR PURCHASE FROM... Purchase From People Who are Blind or Severely Disabled. ] ACTION: Proposed Additions to the Procurement... disabilities. Comments Must Be Received on or Before: 4/9/2012. ADDRESSES: Committee for Purchase From... 1. 78 FR 32632 - Procurement List; Addition Science.gov (United States) 2013-05-31 ... 4/5/2013 (78 FR 20622-20623), the Committee for Purchase From People Who Are Blind or Severely... 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From the Federal Register Online via the Government Publishing Office COMMITTEE FOR PURCHASE FROM PEOPLE WHO ARE BLIND OR SEVERELY DISABLED Procurement List; Additions AGENCY: Committee for Purchase... 13. 77 FR 71400 - Procurement List Proposed Additions Science.gov (United States) 2012-11-30 ... From the Federal Register Online via the Government Publishing Office COMMITTEE FOR PURCHASE FROM... Purchase From People Who Are Blind or Severely Disabled. ] ACTION: Proposed Additions to the Procurement... Must be Received on Or Before: 12/31/2012. ADDRESSES: Committee for Purchase From People Who Are... 14. 75 FR 8927 - Procurement List; Proposed Addition Science.gov (United States) 2010-02-26 ... From the Federal Register Online via the Government Publishing Office COMMITTEE FOR PURCHASE FROM... Purchase From People Who Are Blind or Severely Disabled. ACTION: Proposed addition to the Procurement List... before: March 29, 2010. ADDRESSES: Committee for Purchase From People Who Are Blind or Severely... 15. 75 FR 58366 - Procurement List Additions Science.gov (United States) 2010-09-24 ... INFORMATION: Additions On 6/11/2010 (75 FR 33270-33271) and 7/16/2010 (75 FR 41451), the Committee for... entities. The major factors considered for this certification were: 1. The action will not result in any.../Location: Transcription Service, US Army, US Army War College, Carlisle, PA (Offsite: 5590 Derry... 16. 5 CFR 841.1006 - Additional provisions. Science.gov (United States) 2010-01-01 ... of the second month following the month in which it is received, but incurs no liability or... will issue an accounting. If the State finds this accounting unacceptable, it may then and only then... 5 Administrative Personnel 2 2010-01-01 2010-01-01 false Additional provisions. 841.1006... 17. Highly stereoselective addition of stannylcuprates to alkynones DEFF Research Database (Denmark) Nielsen, Thomas Eiland; de Dios, M.A.C.; Tanner, David Ackland 2002-01-01 The addition of stannylcuprate reagents such as (Bu3Sn)(PhS)CuLi to alkynones has been found to proceed in high yield and with excellent stereoselectivity for the Z isomer of the product (>95%). The behavior of the stannylcuprates is thus very different from that of their "carbocuprate" counterpa... 18. 77 FR 41899 - Indirect Food Additives: Polymers Science.gov (United States) 2012-07-17 ... the Federal Register of February 17, 2012 (77 FR 9608), FDA announced that a food additive petition..., discussed further in this document. A. The Safety of BPA As indicated in the filing notice (77 FR 9608 at..., FDA is actively assessing the safety of BPA (see 75 FR 17145, April 5, 2010; see also... 19. Capacitive Proximity Sensors With Additional Driven Shields Science.gov (United States) Mcconnell, Robert L. 1993-01-01 Improved capacitive proximity sensors constructed by incorporating one or more additional driven shield(s). Sensitivity and range of sensor altered by adjusting driving signal(s) applied to shield(s). Includes sensing electrode and driven isolating shield that correspond to sensing electrode and driven shield. 20. 77 FR 71400 - Procurement List, Additions Science.gov (United States) 2012-11-30 ..., Vinyl, Adjustable 31'' to 55'', Fluorescent Green NSN: 4240-00-NIB-0052--Reflective Safety Belt, Vinyl, Adjustable 31'' to 55'', Dark Green NPA: Envision, Inc., Wichita, KS. Contracting Activity: DEFENSE LOGISTICS... . SUPPLEMENTARY INFORMATION: Additions On 8/24/2012 (77 FR 51522-51523) and 10/5/2012 (77 FR 60969), the... 1. Evaluation of certain food additives and contaminants Science.gov (United States) The Joint FAO/WHO Expert Committee on Food Additives (JECFA) met in Rome from 14 to 23 June 2011. The purpose of the committee was to provide the Codex Alimentarius Commission access with objective advice on high priority food safety matters. Specifically, the tasks before the Committee were: i) t... 2. 42 CFR 86.20 - Additional conditions. Science.gov (United States) 2010-10-01 ... Health PUBLIC HEALTH SERVICE, DEPARTMENT OF HEALTH AND HUMAN SERVICES OCCUPATIONAL SAFETY AND HEALTH RESEARCH AND RELATED ACTIVITIES GRANTS FOR EDUCATION PROGRAMS IN OCCUPATIONAL SAFETY AND HEALTH Occupational Safety and Health Training Grants § 86.20 Additional conditions. The Secretary may with respect... 3. Leaching of Plastic Additives to Marine Organisms NARCIS (Netherlands) Koelmans, A.A.; Besseling, E.; Foekema, E.M. 2014-01-01 It is often assumed that ingestion of microplastics by aquatic species leads to increased exposure to plastic additives. However, experimental data or model based evidence is lacking. Here we assess the potential of leaching of nonylphenol (NP) and bisphenol A (BPA) in the intestinal tracts of Areni 4. Dust-Firing of Straw and Additives DEFF Research Database (Denmark) Wu, Hao; Glarborg, Peter; Frandsen, Flemming; 2011-01-01 In the present work, the ash chemistry and deposition behavior during straw dust-firing were studied by performing experiments in an entrained flow reactor. The effect of using spent bleaching earth (SBE) as an additive in straw combustion was also investigated by comparing with kaolinite. During... 5. Nonparametric and semiparametric dynamic additive regression models DEFF Research Database (Denmark) Scheike, Thomas Harder; Martinussen, Torben Dynamic additive regression models provide a flexible class of models for analysis of longitudinal data. The approach suggested in this work is suited for measurements obtained at random time points and aims at estimating time-varying effects. Both fully nonparametric and semiparametric models can... 6. 75 FR 8926 - Procurement List; Additions Science.gov (United States) 2010-02-26 ... . SUPPLEMENTARY INFORMATION: Additions On 12/28/2009 (74 FR 68587), the Committee for Purchase From People Who Are... Marketing Signage Kit, 3' x 10', Each NSN: 9905-00-NIB-0143--Buttons, DeCA Marketing Signage Kit, 3'', Each NSN: 9905-00-NIB-0144--Dangler, Round, Double-Sided, DeCA POS Signage NSN:... 7. 7 CFR 955.91 - Additional parties. Science.gov (United States) 2010-01-01 ... Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing Agreements... Marketing Agreement § 955.91 Additional parties. After the effective date thereof, any handler may become a... delivered to the Secretary, and the benefits, privileges, and immunities conferred by this agreement... 8. Modification of chemical additives to elastomeric compositions Science.gov (United States) Mukhutdinov, A. A.; Grishin, B. S. 1994-08-01 The physicochemical principles of the modification of crystalline chemical additives to elastomeric compositions are examined. A classification of various types of modifications based on scientific principles is given. The modifications are subdivided into physical and physicochemical depending on the configuration of the molecules in the crystals, the defectiveness and dispersity of the crystalline particles, the melting points of the crystals, and the presence of necleophilic and electrophylic centres in the molecules of the components of binary and complex eutectic mixtures. The effectiveness of the modification of the chemical additives is determined by the manifestation in binary systems of these components in elastomeric compositions of physical and chemical synergism due to the occurrence of the relevant processes in such systems. A relation has been discovered between the physical and chemical phenomena accompanying the modification of the chemical additives in binary and complex eutectic mixtures, their influence on the properties of the elastomeric composition is examined, the ecological problems associated with the processing of such materials are discussed, and the relation between the structure and properties of the molecules of the additives is analysed using quantum-chemical calculations. The bibliography includes 92 references. 9. 27 CFR 5.33 - Additional requirements. Science.gov (United States) 2010-04-01 ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Additional requirements. 5.33 Section 5.33 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS LABELING AND ADVERTISING OF DISTILLED SPIRITS Labeling Requirements... 10. 77 FR 12816 - Procurement List; Additions Science.gov (United States) 2012-03-02 ... INFORMATION: Additions On 6/24/2011 (76 FR 37069-37070) and 1/6/2012 (77 FR 780), the Committee for Purchase... Justice, Federal Prison System, Washington, DC. Coverage: C-List for 100% of the requirements of UNICOR--Sheridan, OR, as aggregated by Federal Prison Industries. Barry S. Lineback, Director, Business... 11. Michael Addition Reaction of Fluorinated Nitro Compounds Institute of Scientific and Technical Information of China (English) 郇凤; 胡华伟; 黄焰根; 陈庆云; 郭勇 2012-01-01 The Michael addition reactions of fluorinated nitro compounds with electron deficient olefins to give γ-fiuoro-γ-nitro-esters, nitriles and ketones which bear a fluorinated quaternary carbon center were reported. The reactions were promoted by TMG, affording the desired adducts in acceptable to good yields. 12. 27 CFR 18.27 - Additional requirements. Science.gov (United States) 2010-04-01 ..., DEPARTMENT OF THE TREASURY LIQUORS PRODUCTION OF VOLATILE FRUIT-FLAVOR CONCENTRATE Qualification Application...: (1) Additional information in support of an application for registration; (2) Marks on major... apparatus; and (4) Installation of security devices. (b) Any proprietor refusing or neglecting to... 13. 78 FR 5423 - Procurement List; Additions Science.gov (United States) 2013-01-25 ... INFORMATION: Additions On 11/27/2012 (77 FR 70737-70738), the Committee for Purchase From People Who Are Blind... added to the Procurement List: Products NSN: 8950-01-E61-0660--Spice, Oregano, Ground, 6/12... 14. 46 CFR 117.25 - Additional requirements. Science.gov (United States) 2010-10-01 ... 46 Shipping 4 2010-10-01 2010-10-01 false Additional requirements. 117.25 Section 117.25 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) SMALL PASSENGER VESSELS CARRYING MORE THAN 150... the requirements of this part inadequate; or (2) The vessel is operated in Arctic, Antarctic, or... 15. 46 CFR 180.25 - Additional requirements. Science.gov (United States) 2010-10-01 ... 46 Shipping 7 2010-10-01 2010-10-01 false Additional requirements. 180.25 Section 180.25 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) SMALL PASSENGER VESSELS (UNDER 100 GROSS TONS... the requirements of this part inadequate; or (2) The vessel is operated in Arctic, Antarctic, or... 16. 77 FR 65365 - Procurement List; Additions Science.gov (United States) 2012-10-26 ...--Lenses, oversize eye, greater than 58, excluding progressive. NSN: 6650-00-NIB-0067--Hyper 3 drop SV... . SUPPLEMENTARY INFORMATION: Additions On 6/15/2012 (77 FR 35942-35944) and 8/24/2012 (77 FR 51522-51523), the..., Trifocal, Plastic, Clear NSN: 6650-00-NIB-0015--Progressives, Plastic, Clear NSN:... 17. 76 FR 59116 - Procurement List; Additions Science.gov (United States) 2011-09-23 ... . SUPPLEMENTARY INFORMATION: Additions On 6/10/2011 (76 FR 34064-34065) and 7/22/2011 (76 FR 43990-43991), the.... NSN: AF9410--Necktie Bar Clasp, USAF, Metal, Polished Nickel Finish. NSN: AF9410P--Patch, Police... Chevrons Officer (3 Stripes), USAF Metallic Silver or Polished Nickel Finish. NSN: AF9490--Necktie,... 18. Additive Manufacturing: From Rapid Prototyping to Flight Science.gov (United States) Prater, Tracie 2015-01-01 Additive manufacturing (AM) offers tremendous promise for the rocket propulsion community. Foundational work must be performed to ensure the safe performance of AM parts. Government, industry, and academia must collaborate in the characterization, design, modeling, and process control to accelerate the certification of AM parts for human-rated flight. 19. Monotonic Weighted Power Transformations to Additivity Science.gov (United States) Ramsay, J. O. 1977-01-01 A class of monotonic transformations which generalize the power transformation is fit to the independent and dependent variables in multiple regression so that the resulting additive relationship is optimized. Examples of analysis of real and artificial data are presented. (Author/JKS) 20. Designing for Color in Additive Manufacturing DEFF Research Database (Denmark) Eiríksson, Eyþór Rúnar; Luongo, Andrea; Frisvad, Jeppe Revall; 2016-01-01 In this paper we present a color design pipeline for 3D printed or additively manufactured parts. We demonstrate how to characterize and calibrate a commercial printer and how to obtain its forward and backward color transformation models. We present results from our assistive color design tool... 1. Fully additive chip packaging: science or fiction? NARCIS (Netherlands) Oosterhuis, G.; Zon, C.M.B. van der; Maalderink, H.H. 2011-01-01 The current trend in IC packaging towards an ever increasing degree of integration, combined with a high level of production flexibility calls for novel approaches in manufacturing. To address these challenges in a flexible manufacturing setting, TNO investigated to what extend mask-less additive ma 2. Release of additives from packaging plastics NARCIS (Netherlands) Helmroth, I.E. 2002-01-01 Keywords : migration, diffusion, additives, polymer, low density polyethylene, polymer swelling, Fick, stochastic modellingThe diffusion of small molecules from polymers into food is studied. A better understanding of this process is important for the development of mathematical models to predict mi 3. Block additive functions on the Gaussian integers OpenAIRE Drmota, Michael; Peter, Grabner,; Liardet, Pierre 2008-01-01 International audience We present three conceptually different methods to prove distribution results for block additive functions with respect to radix expansions of the Gaussian integers. Based on generating function approaches we obtain a central limit theorem and asymptotic expansions for the moments. Furthermore, these generating functions as well as ergodic skew products are used to prove uniform distribution in residue classes and modulo 1. 4. Children's Profiles of Addition and Subtraction Understanding Science.gov (United States) Canobi, Katherine H. 2005-01-01 The current research explored children's ability to recognize and explain different concepts both with and without reference to physical objects so as to provide insight into the development of children's addition and subtraction understanding. In Study 1, 72 7- to 9-year-olds judged and explained a puppet's activities involving three conceptual… 5. 47 CFR 68.318 - Additional limitations. Science.gov (United States) 2010-10-01 ... TERMINAL EQUIPMENT TO THE TELEPHONE NETWORK Conditions for Terminal Equipment Approval § 68.318 Additional... receipt of CO ground start at the network demarcation point. (c) Line seizure by automatic telephone... proceeding to dial another number. (6) Network addressing signals shall be transmitted no earlier than:... 6. 77 FR 42700 - Procurement List; Additions Science.gov (United States) 2012-07-20 ... Contracting Command--Aberdeen Proving Ground, Natick Contracting Division, Natick MA. Comments were received...--Aberdeen Proving Ground, Natick Contracting Division, Natick MA. Services Service Type/Location: Laundry... . SUPPLEMENTARY INFORMATION: Additions On 5/18/2012 (77 FR 29596) and 5/25/2012 (77 FR 31335-31336), the... 7. 77 FR 51521 - Procurement List; Additions Science.gov (United States) 2012-08-24 ... by the Army Contracting Command--Aberdeen Proving Ground, Natick Contracting Division, Natick, MA...: Operation Support Service, Aberdeen Proving Ground, MD, National Ground Intelligence Center (NGIC), Rivanna... . SUPPLEMENTARY INFORMATION: Additions On 5/25/2012 (77 FR 31335-31336) and 6/29/2012 (77 FR 38775-38776),... 8. 76 FR 18189 - Procurement List; Additions Science.gov (United States) 2011-04-01 ... Center, Aberdeen Proving Ground, MD. Patricia Briscoe, Deputy Director, Business Operations Pricing and... INFORMATION: Additions On 1/28/2011 (76 FR 5142-5143), the Committee for Purchase From People Who Are Blind or... Contracting Center--Aberdeen, MD, (Off-site: 507 Kent Street, Utica NY). NPA: Central Association for... 9. The challenges of additional protocol implementation International Nuclear Information System (INIS) The IAEA Board of Governors approved the Model Protocol Additional to Safeguards Agreements, INFCIRC/540, (referred to as the Additional Protocol) in May 1997. The Additional Protocol provides for new mechanisms that include expanded information on State's nuclear activities to be declared to the IAEA and increased physical access to locations for IAEA inspectors. Given the expanded capability under the additional protocol for the Agency to draw conclusions regarding the absence of undeclared nuclear material and activities, Safeguards Department staff have had to broaden their outlook with respect to all safeguards activities being conducted. Beyond verification of nuclear material, inspectors are being called upon to conduct a wider range of activities, with more emphasis on observation of indicators of a State's nuclear-related activities and consideration of the consistency of the other information with a State's declarations. This includes consideration of how the evaluation of all information available to the Agency affects the planning and prioritizing of future safeguards activities, for example in resolving questions or inconsistencies in the declared information or selecting locations for conducting complementary access. The implementation of strengthened safeguards and the additional protocol has led to a need to institutionally change the roles of many staff members in the various Safeguards Divisions and increase the interaction between the Divisions to most effectively draw State-level conclusions regarding the absence of undeclared nuclear material and activities. This paper focuses on the significant changes in the roles of safeguards inspectors, in particular facility officers and country officers, in the implementation of strengthened safeguards. It outlines the nature of the changes, and some of the challenges being faced in order to adapt to these roles, including changes in the nature of interaction between the Operations and Support Divisions 10. The addition of disilanes to cumulenes Energy Technology Data Exchange (ETDEWEB) Chen, Y. 1997-10-08 The syntheses of silicon-containing compounds and the studies of their rearrangements have been active research areas in the Barton research group. Previously, the addition of disilanes to acetylenes was studied in the group and an intramolecular 2S + 2A mechanism has been proposed. In this thesis, the work is focused on the addition of disilanes to cumulenes. The syntheses of the precursors are discussed and the possible mechanisms for their thermal, photochemical and catalytic rearrangements are proposed. Conjugated organic polymers have been studied in the group since 1985 because of their potential for exhibiting high electroconductivity, photoconductivity, strong non-linear optical response and intense fluorescence. In the second section of this dissertation, the synthesis and property studies of poly(phenylene vinylene) analogues are discussed. 11. Rare Earth Additions in Continuously Cast Steel Science.gov (United States) Wilson, William G.; Heaslip, L. J.; Sommerville, I. D. 1985-09-01 Rare earth (lanthanide metals) addiiions to continuously cast steel are particularly advantageous because of their ability to refine as-cast structures, reduce segregation and increase hot ductility at temperatures just below that of solidification. The complete shape control of sulfides in steels containing Rare Earth Metals (REM), whether continuously cast or ingot cast, is primarily responsible for improvements in ductility related mechanical properties, weldability, fatigue resistance and resistance to hydrogen damage. Complete sulfide shape control can be obtained with REM additions at sulfur levels as high as.020%. The greatest improvements, however, are obtained with REM additions to low sulfur steels. However, to achieve full operational advantages afforded by REM, nozzle blockage problems must be circumvented. Water model studies indicate a possible solution. 12. Femtosecond fiber laser additive manufacturing of tungsten Science.gov (United States) Bai, Shuang; Liu, Jian; Yang, Pei; Zhai, Meiyu; Huang, Huan; Yang, Lih-Mei 2016-04-01 Additive manufacturing (AM) is promising to produce complex shaped components, including metals and alloys, to meet requirements from different industries such as aerospace, defense and biomedicines. Current laser AM uses CW lasers and very few publications have been reported for using pulsed lasers (esp. ultrafast lasers). In this paper, additive manufacturing of Tungsten materials is investigated by using femtosecond (fs) fiber lasers. Various processing conditions are studied, which leads to desired characteristics in terms of morphology, porosity, hardness, microstructural and mechanical properties of the processed components. Fully dense Tungsten part with refined grain and increased hardness was obtained and compared with parts made with different pulse widths and CW laser. The results are evidenced that the fs laser based AM provides more dimensions to modify mechanical properties with controlled heating, rapid melting and cooling rates compared with a CW or long pulsed laser. This can greatly benefit to the make of complicated structures and materials that could not be achieved before. 13. Electrolyte Additives for Phosphoric Acid Fuel Cells DEFF Research Database (Denmark) Gang, Xiao; Hjuler, H.A.; Olsen, C.A.; 1993-01-01 Electrochemical characteristics of a series of modified phosphoric acid electrolytes containing fluorinated car on compounds and silicone fluids as additives are presented. When used in phosphoric acid fuel cells, the modified electrolytes improve the performance due to the enhanced oxygen......, as a fuel-cell performance with the modified electrolytes. Specific conductivity measurements of some of the modified phosphoric acid electrolytes are reported. At a given temperature, the conductivity of the C4F9SO3K-modified electrolyte decreases with an increasing amount of the additive; the conductivity...... of the remains at the same value as the conductivity of the pure phosphoric acid. At a given composition, the conductivity of any modified electrolyte increases with temperature. We conclude that the improved cell performance for modified electrolytes is not due to any increase in conductivity.... 14. Inhomogenous quantum codes (Ⅰ):additive case Institute of Scientific and Technical Information of China (English) 2010-01-01 In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1 Cq2 ··· Cqn,where qi(1 i n) are arbitrary positive integers.By attaching an abelian group Ai of order qi to the space Cqi(1 i n),we present the stabilizer construction of such inhomogenous quantum codes,called additive quantum codes,in term of the character theory of the abelian group A = A1⊕A2⊕···⊕An.As usual case,such construction opens a way to get inhomogenous quantum codes from the classical mixed linear codes.We also present Singleton bound for inhomogenous additive quantum codes and show several quantum codes to meet such bound by using classical mixed algebraic-geometric codes. 15. Laboratory tests of sludge-control additives Energy Technology Data Exchange (ETDEWEB) Tatnall, R.E. [MIC Associates, Inc., Chadds Ford, PA (United States) 1996-07-01 Laboratory {open_quotes}jar{close_quotes} tests compared eleven different fuel oil and diesel fuel sludge-control additives. Factors studied included (1) ability to disperse and prevent buildup of sludge deposits on surfaces, (2) ability to protect steel from corrosion, (3) ability to inhibit growth and proliferation of bacteria, and (4) ability to disperse water. Results varied greatly, and it was found that many commercial products do not do what they claim. It is concluded that fuel retailers should not believe manufacturers claims for their additive products, but rather should test such products themselves to be sure that the benefits of treatment are real. A simplified form of the procedure used here is proposed as one way for dealers to do such testing. 16. Evolution of solidification texture during additive manufacturing Science.gov (United States) Wei, H. L.; Mazumder, J.; DebRoy, T. 2015-01-01 Striking differences in the solidification textures of a nickel based alloy owing to changes in laser scanning pattern during additive manufacturing are examined based on theory and experimental data. Understanding and controlling texture are important because it affects mechanical and chemical properties. Solidification texture depends on the local heat flow directions and competitive grain growth in one of the six preferred growth directions in face centered cubic alloys. Therefore, the heat flow directions are examined for various laser beam scanning patterns based on numerical modeling of heat transfer and fluid flow in three dimensions. Here we show that numerical modeling can not only provide a deeper understanding of the solidification growth patterns during the additive manufacturing, it also serves as a basis for customizing solidification textures which are important for properties and performance of components. PMID:26553246 17. Addition of malodorants to lighter gas DEFF Research Database (Denmark) Neela, Vasu; von Solms, Nicolas 2014-01-01 Relevant thermodynamic and phase behavior of mixtures created by adding malodorants to lighter gas to discourage its abuse have been studied. The influence of physical factors such as temperature, pressure and concentration of the selected substances with lighter gas is studied. This work...... represents one component in a larger study examining the feasibility of adding malodorants to lighter gas and focuses on the physical chemistry or chemical engineering aspects of the problem. An initial set of 27 compounds was selected based on deterrent effect (odor) in order to find suitable additives...... to lighter gas components. The aim is to find substances that not only have the correct physiological effect (discourage abuse) but also the correct physical behavior upon addition to lighter gas (solubility, phase behavior). Specifically the way the malodorant partitions between the vapor and liquid phase... 18. Sintering of magnesia: effect of additives Indian Academy of Sciences (India) Satyananda Behera; Ritwik Sarkar 2015-10-01 Effect of different additives, namely Cr2O3, Fe2O3 and TiO2, up to 2 wt% was studied on the sintering and microstructural developments of the chemically pure magnesia using the pressureless sintering technique between 1500 and 1600° C. Sintering was evaluated by per cent densification and microstructural developments were studied by electron microscopy and elemental distribution of the additives in the sintered products was also investigated for their distribution in the matrix. Cr2O3 and TiO2 were found to deteriorate the densification associated with grain growth. Fe2O3 was found to improve the densification and well-compacted grain distribution was observed in the microstructure. 19. The teratology testing of food additives. Science.gov (United States) Barrow, Paul C; Spézia, François 2013-01-01 The developmental and reproductive toxicity testing (including teratogenicity) of new foods and food additives is performed worldwide according to the guidelines given in the FDA Redbook. These studies are not required for substances that are generally recognized as safe, according to the FDA inventory. The anticipated cumulated human exposure level above which developmental or reproduction studies are required depends on the structure-alert category. For food additives of concern, both developmental (prenatal) and reproduction (multigeneration) studies are required. The developmental studies are performed in two species, usually the rat and the rabbit. The reproduction study is generally performed in the rat. The two rat studies are preferably combined into a single experimental design, if possible. The test methods described in the FDA Redbook are similar to those specified by the OECD for the reproductive toxicity testing of chemicals. 20. Additive manufacturing of polymer-derived ceramics. Science.gov (United States) Eckel, Zak C; Zhou, Chaoyin; Martin, John H; Jacobsen, Alan J; Carter, William B; Schaedler, Tobias A 2016-01-01 The extremely high melting point of many ceramics adds challenges to additive manufacturing as compared with metals and polymers. Because ceramics cannot be cast or machined easily, three-dimensional (3D) printing enables a big leap in geometrical flexibility. We report preceramic monomers that are cured with ultraviolet light in a stereolithography 3D printer or through a patterned mask, forming 3D polymer structures that can have complex shape and cellular architecture. These polymer structures can be pyrolyzed to a ceramic with uniform shrinkage and virtually no porosity. Silicon oxycarbide microlattice and honeycomb cellular materials fabricated with this approach exhibit higher strength than ceramic foams of similar density. Additive manufacturing of such materials is of interest for propulsion components, thermal protection systems, porous burners, microelectromechanical systems, and electronic device packaging. PMID:26721993 1. Facets and cuts from additive systems Energy Technology Data Exchange (ETDEWEB) Araoz, J. 1994-12-31 Integer Program Facets with non-negative entries could be derived from Additive System Problems, like Semigroup or Gomorys Group Problems. These facets can be used as cuts for Branch and Cuts Algorithms. In fact, any Master Problem facet with some equal coefficients came from lifting a facet of a easily related Multivalued Additive System. A morphism type relation between problems allow us to obtain facets for Master Problems or cuts for Integer Programs. We use Knapsack Problems as examples either to present results about sequential lifting for non-Master Problems, pseudo-morphisms for facet generation for Master Problems and cut generation for Integer Programs solving small subadditive linear programs or to state open problems. 2. Additive manufacturing of polymer-derived ceramics Science.gov (United States) Eckel, Zak C.; Zhou, Chaoyin; Martin, John H.; Jacobsen, Alan J.; Carter, William B.; Schaedler, Tobias A. 2016-01-01 The extremely high melting point of many ceramics adds challenges to additive manufacturing as compared with metals and polymers. Because ceramics cannot be cast or machined easily, three-dimensional (3D) printing enables a big leap in geometrical flexibility. We report preceramic monomers that are cured with ultraviolet light in a stereolithography 3D printer or through a patterned mask, forming 3D polymer structures that can have complex shape and cellular architecture. These polymer structures can be pyrolyzed to a ceramic with uniform shrinkage and virtually no porosity. Silicon oxycarbide microlattice and honeycomb cellular materials fabricated with this approach exhibit higher strength than ceramic foams of similar density. Additive manufacturing of such materials is of interest for propulsion components, thermal protection systems, porous burners, microelectromechanical systems, and electronic device packaging. 3. Weldability of Additive Manufactured Stainless Steel Science.gov (United States) Matilainen, Ville-Pekka; Pekkarinen, Joonas; Salminen, Antti Part size in additive manufacturing is limited by the size of building area of AM equipment. Occasionally, larger constructions that AM machines are able to produce, are needed, and this creates demand for welding AM parts together. However there is very little information on welding of additive manufactured stainless steels. The aim of this study was to investigate the weldability aspects of AM material. In this study, comparison of the bead on plate welds between AM parts and sheet metal parts is done. Used material was 316L stainless steel, AM and sheet metal, and parts were welded with laser welding. Weld quality was evaluated visually from macroscopic images. Results show that there are certain differences in the welds in AM parts compared to the welds in sheet metal parts. Differences were found in penetration depths and in type of welding defects. Nevertheless, this study presents that laser welding is suitable process for welding AM parts. 4. Calcium phosphate cements properties with polymers addition International Nuclear Information System (INIS) Calcium phosphate cements (CPC) have attracted great interest to use in orthopedics and dentistry as replacements for damaged parts of the skeletal system, showing good biocompatibility and osseointegration, allowing its use as bone graft. Several studies have shown that the addition of polymer additives have a strong influence on the cement properties. The low mechanical strength is the main obstacle to greater use of CPC as an implant material. The objective of this study was to evaluate properties of a cement based on α-tricalcium phosphate (α-TCP), added polymers. PVA (10%, 8%, 6%), sodium alginate (2%) and polyacrylate ammonia (3%), all in weight, were added to the synthesized α-TCP powder. The samples were molded and evaluated for density, porosity in vitro test (Simulated Body Fluid), crystalline phases and mechanical strength. The results show increased the mechanical properties of the cement when added these polymers 5. Modifying network connectivity with a subgraph addition CERN Document Server Taylor, Dane 2011-01-01 The principal eigenvalue$\\lambda$of a network's adjacency matrix often determines dynamics on the network (e.g., in synchronization and spreading processes) and some of its structural properties (e.g., robustness against failure or attack), and is therefore a good indicator for how "strongly" a network is connected. We study how$\\lambda$is modified by the addition of a subgraph. This type of modification has broad applications, ranging from those involving a single modification (e.g., introduction of a drug into a biological process) to those involving repeated subnetwork additions (e.g., power-grid and transit development). We describe how to optimally connect the subgraph to the network to either maximize or minimize the shift in$\\lambda$, noting several applications. 6. Metrology Needs for Metal Additive Manufacturing Powders Science.gov (United States) Slotwinski, John A.; Garboczi, Edward J. 2015-03-01 Additive manufacturing (AM) processes can produce highly complex and customized parts without the need for dedicated tooling and can produce parts directly from the part design information. These types of processes are poised to revolutionize the manufacturing industry, yet several challenges are currently preventing more widespread adoption of AM technologies. Among these challenges are metrology issues associated with the measurement and characterization of the metal powders used for AM systems. This article will describe the technical challenges and needs for characterizing metal AM powders, recent research efforts to address those needs, and current work to standardize characterization methods in ASTM and ISO, such as the recently released ASTM F3049, Standard Guide for Characterizing Properties of Metal Powders Used for Additive Manufacturing Processes. 7. Characterization of cement composites with mineral additives OpenAIRE Korat, Lidija 2015-01-01 Doctoral dissertation is aimed at characterizing cement composites with mineral additives representing the industrial waste material (fly ash, granulated blast furnace slag and biomass fly ash). Their usage can replace high cement shares in individual cases and is, however, favourable due to the production costs reduction and environment burden decrease, including the decreased emission of greenhouse gases as well as lower energy use. Cement composites (in fresh or hardened state)... 8. Materials as additives for advanced lubrication Energy Technology Data Exchange (ETDEWEB) Pol, Vilas G.; Thackeray, Michael M.; Mistry, Kuldeep; Erdemir, Ali 2016-09-13 This invention relates to carbon-based materials as anti-friction and anti-wear additives for advanced lubrication purposes. The materials comprise carbon nanotubes suspended in a liquid hydrocarbon carrier. Optionally, the compositions further comprise a surfactant (e.g., to aid in dispersion of the carbon particles). Specifically, the novel lubricants have the ability to significantly lower friction and wear, which translates into improved fuel economies and longer durability of mechanical devices and engines. 9. 77 FR 40343 - Procurement List; Additions Science.gov (United States) 2012-07-09 ... . SUPPLEMENTARY INFORMATION: Additions On 5/4/2012 (77 FR 26520-26521) and 5/11/2012 (77 FR 27737-27738), the... (2lb bag) NSN: 8925-01-E62-1746--Almonds, Shelled, Sliced, Blanched (2lb bag) NSN: 8925-01-E62-1747--Almonds, Shelled, Slivered, Blanched (2lb bag) NSN: 8925-01-E62-1748--Walnuts, English, Shelled,... 10. COTTAGE CHEESE PRODUCTS ENRICHED BIOLOGICALLY ACTIVE ADDITIVES OpenAIRE Салкинбаева Г. Т.; Байбалинова Г. М.; Смаилова М. Н. 2015-01-01 This article deals with a reliable means of improving the structure of supply and optimum balance of the diet of the population, is the use of biologically active additives in a daily diet of the people to food dietary supplements. Supplements such advantages as an expression of food oriented, high nutritional density, homogeneity, easy preparation and forms of transport, good taste allow us to use them successfully in catering. 11. Additive measures of travel time variability OpenAIRE Engelson, Leonid; Fosgerau, Mogens 2011-01-01 This paper derives a measure of travel time variability for travellers equipped with scheduling preferences defined in terms of time-varying utility rates, and who choose departure time optimally. The corresponding value of travel time variability is a constant that depends only on preference parameters. The measure is unique in being additive with respect to independent parts of a trip. It has the variance of travel time as a special case. Extension is provided to the case of travellers who ... 12. Some problems in additive number theory OpenAIRE Allakhverdov, Andrei 2014-01-01 In this article, we consider some problems in additive number theory. Elementary solutions for the Goldbach-Euler conjecture and the twin primes conjecture are presented. The method employed also makes it possible to obtain some interesting results related to the densities of sequences and gaps between primes. A stronger version of the Goldbach-Euler conjecture, in which the strengthening is established by reducing the set of all primes to the set of twin prime pairs, is also presented. The p... 13. 10 conjectures in additive number theory OpenAIRE Cloitre, Benoit 2011-01-01 Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searching primes since it appears we found sometime primes much more greater than the number of required iterations. In an other hand we propose new formulations of famous conjectures from the additive theory of numbers (the weak twin prime conjecture, the Polignac conjecture, the Goldbach conjecture or the very general ... 14. Equivalence of polynomial conjectures in additive combinatorics CERN Document Server Lovett, Shachar 2010-01-01 We study two conjectures in additive combinatorics. The first is the polynomial Freiman-Ruzsa conjecture, which relates to the structure of sets with small doubling. The second is the inverse Gowers conjecture for$U^3$, which relates to functions which locally look like quadratics. In both cases a weak form, with exponential decay of parameters is known, and a strong form with only a polynomial loss of parameters is conjectured. Our main result is that the two conjectures are in fact equivalent. 15. Conferences on Combinatorial and Additive Number Theory CERN Document Server 2014-01-01 This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems, and future challenges in number theory. 16. Supplier Selection Using Weighted Utility Additive Method Science.gov (United States) Karande, Prasad; Chakraborty, Shankar 2015-10-01 Supplier selection is a multi-criteria decision-making (MCDM) problem which mainly involves evaluating a number of available suppliers according to a set of common criteria for choosing the best one to meet the organizational needs. For any manufacturing or service organization, selecting the right upstream suppliers is a key success factor that will significantly reduce purchasing cost, increase downstream customer satisfaction and improve competitive ability. The past researchers have attempted to solve the supplier selection problem employing different MCDM techniques which involve active participation of the decision makers in the decision-making process. This paper deals with the application of weighted utility additive (WUTA) method for solving supplier selection problems. The WUTA method, an extension of utility additive approach, is based on ordinal regression and consists of building a piece-wise linear additive decision model from a preference structure using linear programming (LP). It adopts preference disaggregation principle and addresses the decision-making activities through operational models which need implicit preferences in the form of a preorder of reference alternatives or a subset of these alternatives present in the process. The preferential preorder provided by the decision maker is used as a restriction of a LP problem, which has its own objective function, minimization of the sum of the errors associated with the ranking of each alternative. Based on a given reference ranking of alternatives, one or more additive utility functions are derived. Using these utility functions, the weighted utilities for individual criterion values are combined into an overall weighted utility for a given alternative. It is observed that WUTA method, having a sound mathematical background, can provide accurate ranking to the candidate suppliers and choose the best one to fulfill the organizational requirements. Two real time examples are illustrated to prove 17. Network Delay Inference from Additive Metrics OpenAIRE Bhamidi, Shankar; Rajagopal, Ram; Roch, Sebastien 2006-01-01 We demonstrate the use of computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicast-based delay inference, i.e. the problem of reconstructing the topology and delay characteristics of a network from end-to-end delay measurements on network paths. Our inference algorithm is based on additive metric techniques widely used in phylogenetics. It runs in polynomial time and requires a sample of size ... 18. Additive Manufacturing for Affordable Rocket Engines Science.gov (United States) West, Brian; Robertson, Elizabeth; Osborne, Robin; Calvert, Marty 2016-01-01 Additive manufacturing (also known as 3D printing) technology has the potential to drastically reduce costs and lead times associated with the development of complex liquid rocket engine systems. NASA is using 3D printing to manufacture rocket engine components including augmented spark igniters, injectors, turbopumps, and valves. NASA is advancing the process to certify these components for flight. Success Story: MSFC has been developing rocket 3D-printing technology using the Selective Laser Melting (SLM) process. Over the last several years, NASA has built and tested several injectors and combustion chambers. Recently, MSFC has 3D printed an augmented spark igniter for potential use the RS-25 engines that will be used on the Space Launch System. The new design is expected to reduce the cost of the igniter by a factor of four. MSFC has also 3D printed and tested a liquid hydrogen turbopump for potential use on an Upper Stage Engine. Additive manufacturing of the turbopump resulted in a 45% part count reduction. To understanding how the 3D printed parts perform and to certify them for flight, MSFC built a breadboard liquid rocket engine using additive manufactured components including injectors, turbomachinery, and valves. The liquid rocket engine was tested seven times in 2016 using liquid oxygen and liquid hydrogen. In addition to exposing the hardware to harsh environments, engineers learned to design for the new manufacturing technique, taking advantage of its capabilities and gaining awareness of its limitations. Benefit: The 3D-printing technology promises reduced cost and schedule for rocket engines. Cost is a function of complexity, and the most complicated features provide the largest opportunities for cost reductions. This is especially true where brazes or welds can be eliminated. The drastic reduction in part count achievable with 3D printing creates a waterfall effect that reduces the number of processes and drawings, decreases the amount of touch 19. Evolution of solidification texture during additive manufacturing OpenAIRE Wei, H. L.; J. Mazumder; DebRoy, T. 2015-01-01 Striking differences in the solidification textures of a nickel based alloy owing to changes in laser scanning pattern during additive manufacturing are examined based on theory and experimental data. Understanding and controlling texture are important because it affects mechanical and chemical properties. Solidification texture depends on the local heat flow directions and competitive grain growth in one of the six preferred growth directions in face centered cubic alloys. Therefore, the he... 20. Organic Zinc as Feed Additive for Ruminants OpenAIRE Suprijati 2013-01-01 Zinc is an essential micro mineral required by ruminants and is a component of over 300 enzymes which play important role in the metabolisms of carbohydrates, proteins and fats. Recently, the chemical and biotechnology processes have been developed for synthesizing organic Zn. Organic Zn is the product of a chelating process of dissolved Zn anorganic salts with amino acids or hydrolyzed protein. The utilization of organic Zn as feed additive in ruminants diets tends to increase, due to the ab... 1. Study of plutonium-addition systems International Nuclear Information System (INIS) Steady state phase diagrams and calculated values of concentrations on the solid and liquid curves, the steady state distribution coefficient and thermodynamic control are presented for temperatures ranging from the eutectic reaction temperatures to the Pu melting point temperature for binary systems plutonium-addition (Mg, Al, Si, Ti, Mn, Fe, Co, Ni, Cu, Zn, Ga, Zr, Ru, Os, Th, U, Np). (J.P.) 2. Fatigue crack growth in additive manufactured products OpenAIRE Riemer, A.; H. A. Richard; J.-P. Brüggemann; J.-N. Wesendahl 2015-01-01 Additive Manufacturing (AM) is a new innovative technique that allows the direct fabrication of complex, individual, delicate and high-strength products, based on their 3D data. Selective Laser Melting (SLM) is one of the AM processes that generates metallic components layer by layer using powder-bed technique. The irradiation and consequent melting of metallic powder is realised by the laser source. Employing SLM, especially complex and individual products, such as implants or ae... 3. DEVELOPMENT OF A FUNCTIONAL FEED ADDITIVE Directory of Open Access Journals (Sweden) Lysenko Y. A. 2016-01-01 Full Text Available The new feed additives for animals based on milk whey, enriched with sprouting wheat, barley, maize grains and lactic-acid bacterium have been presented in this article. This study explores the possibility of combining the prebiotics ability of milk whey and sprouting grains with feed probiotic attributes of microbe to enhance gut health of animals and digestibility of the feed. Twelve variants of products were tested in the study using the microbial and physical-chemical approaches. All the assays showed high count of microorganism and high content of reducing sugar. The results of investigation indicate that selected feed additive show high quality. An additional point is that it contains useful organic acids (lactic, acetic and propionic acids and 2,1×109 colony-forming unit of probiotics microorganism that hold the concentration for 4 months. There are not yeast, must, coliform bacteria and Staphylococcus aureus in the developed functional feed product. It contributes to the normalization of the microflora of the gastrointestinal tract of animal, suppression of conditionally pathogenic and putrefactive microflora. The elaborated feed component will help to provide combined feed companies with accessible high-quality raw material 4. Bubble formation in additive manufacturing of glass Science.gov (United States) Luo, Junjie; Gilbert, Luke J.; Peters, Daniel C.; Bristow, Douglas A.; Landers, Robert G.; Goldstein, Jonathan T.; Urbas, Augustine M.; Kinzel, Edward C. 2016-05-01 Bubble formation is a common problem in glass manufacturing. The spatial density of bubbles in a piece of glass is a key limiting factor to the optical quality of the glass. Bubble formation is also a common problem in additive manufacturing, leading to anisotropic material properties. In glass Additive Manufacturing (AM) two separate types of bubbles have been observed: a foam layer caused by the reboil of the glass melt and a periodic pattern of bubbles which appears to be unique to glass additive manufacturing. This paper presents a series of studies to relate the periodicity of bubble formation to part scan speed, laser power, and filament feed rate. These experiments suggest that bubbles are formed by the reboil phenomena why periodic bubbles result from air being trapped between the glass filament and the substrate. Reboil can be detected using spectroscopy and avoided by minimizing the laser power while periodic bubbles can be avoided by a two-step laser melting process to first establish good contact between the filament and substrate before reflowing the track with higher laser power. 5. Additive Technology for EU Ecolabel Formulations Institute of Scientific and Technical Information of China (English) Eric Nehls; Tassilo Habereder; Edward Ng 2009-01-01 Currently, Bio -lubricants are still regarded as niche products. Within the global lubricant market, however, the ar-ea of environmentally acceptable fluids represents one of the fast growing markets with an estimated annual growth of more than 6% per year. This growth is supported by various market drivers such as legal regulations, public subsidies and the im-plementation of national or international labeling schemes.With the implementation of the European Ecolabel for lubricants in 2005, a common standard specifying ecological and performance requirements for Bio - lubricants was defined. Applying for the EU Ecolabel requires a comprehensive assess-ment, not only of the final formulation, but also of the additives used. Additives are required to meet specifications for oxi-dation and thermal stability, as well as to impart metal protection (of both steel and yellow metals), thus improving corro-sion protection and wear performance of the formulation. Therefore, it is challenging in terms of formulation technology to develop the right formulation that meets the technical specifications as well as the stringent requirements of the EU - Ecola-bel.The paper describes how, by using ester base fluids and additives currently available in the market, lubricants can be developed to meet the technical and eco - toxicological requirements of the EU - Ecolabel, approaching the performance lev-els of lubricants formulated with traditional base fluids. 6. Bond additivity corrections for quantum chemistry methods Energy Technology Data Exchange (ETDEWEB) C. F. Melius; M. D. Allendorf 1999-04-01 In the 1980's, the authors developed a bond-additivity correction procedure for quantum chemical calculations called BAC-MP4, which has proven reliable in calculating the thermochemical properties of molecular species, including radicals as well as stable closed-shell species. New Bond Additivity Correction (BAC) methods have been developed for the G2 method, BAC-G2, as well as for a hybrid DFT/MP2 method, BAC-Hybrid. These BAC methods use a new form of BAC corrections, involving atomic, molecular, and bond-wise additive terms. These terms enable one to treat positive and negative ions as well as neutrals. The BAC-G2 method reduces errors in the G2 method due to nearest-neighbor bonds. The parameters within the BAC-G2 method only depend on atom types. Thus the BAC-G2 method can be used to determine the parameters needed by BAC methods involving lower levels of theory, such as BAC-Hybrid and BAC-MP4. The BAC-Hybrid method should scale well for large molecules. The BAC-Hybrid method uses the differences between the DFT and MP2 as an indicator of the method's accuracy, while the BAC-G2 method uses its internal methods (G1 and G2MP2) to provide an indicator of its accuracy. Indications of the average error as well as worst cases are provided for each of the BAC methods. 7. The value of additional videorecordings on defecography Energy Technology Data Exchange (ETDEWEB) Cho, Sung Ki; Choi, Sang Hee; Kim, Seung Hoon; Kim, Seung Kwon; Lim, Hyo Keun; Lee, Soon Jin; Kim, Bo Hyun [Sungkyunkwan Univ. College of Medicine, Seoul (Korea, Republic of) 1998-12-01 To determine the value of additional videorecording during defecography. Ninety-nine consecutive patients (20 males, 79 females;mean age:48 yrs) who between august 1996 and June 1997 had undergone defecography due to defecation difficulty were included in this study. In all patients, spot filming(at rest, during squeezing, during straining) and videorecording during defecography were simultaneously performed. Two radiologists retrospectively reviewed spot films and video images, analyzed discrepancies between the two methods, and reached a consensus. In 52% of patients (51/99), the results of the two examinations were discrepant. The most common finding was anterior rectocele (n=3D33), followed by spastic pelvic floor syndrome (n=3D16), rectal intussusception (n=3D5), posterior rectocele (n=3D3), mucosal prolapse (n=3D2), descending perineal syndrome (n=3D2), and rectal prolapse (n=3D1). All findings except spastic pelvic floor syndrome were additionally found on videorecording. Because videorecording during defecography showed additional findings in 52% of patients, it is a necessary procedure for the diagnosis and management of patients with defecation difficulty.=20. 8. Microbial analyses of cement and grouting additives Energy Technology Data Exchange (ETDEWEB) Hallbeck, L.; Jaegevall, S.; Paeaejaervi, A.; Rabe, L.; Edlund, J.; Eriksson, S. [Microbial Analytics Sweden AB, Moelnlycke (Sweden) 2012-01-15 During sampling in the ONKALO tunnel in 2006, heavy growth of a slimy material was observed in connection with grouting. It was suggested to be microbial growth on organic additives leaching from the grout. Two sampling campaigns resulted in the isolation of several aerobic bacterial strains. Some of these strains were used in biodegradation studies of three solid cement powders, eight liquid grout additives, and six plastic drainage materials. Degradation was also studied using ONKALO groundwaters as inoculums. The isolated strains were most closely related to hydrocarbon-degrading microorganisms. The biodegradation of seven of the products was tested using microorganisms isolated from the ONKALO slime in 2006; none of these strains could degrade the tested products. When ONKALO drillhole groundwaters were used as inoculums in the degradation studies, it was demonstrated that Structuro 111X, Mighty 150, and Super-Parmix supported growth of the groundwater microorganisms. Structuro 111X is a polycarboxylate condensate while Mighty 150 and Super-Parmix are condensates with formaldehyde and naphthalene. Some of the isolated microorganisms belonged to the genus Pseudomonas, many strains of which can degrade organic molecules. None of the plastic drainage materials supported growth during the degradation studies. Microorganisms were present in two of the liquid products when delivered, GroutAid and Super-Parmix. The potential of the organic compounds in grout additives to be degraded by microorganisms, increasing the risk of biofilm formation and complexing compound production, must be considered. Microbial growth will also increase the possibility of hydrogen sulphide formation. (orig.) 9. Characteristics of Si Solar Cells with the Addition of Frits and Additives to Al Pastes Science.gov (United States) Kim, Dongsun; Kim, Jongwoo; Lee, Jungki; Kim, Hyungsun 2011-11-01 Thick Al films are used widely as the backside electrode material of Si solar cells. The formation of Al and a back surface field reduce the back-surface recombination and improve the cell performance. This study examined the characteristics of Si solar cells with the addition of frits and additives to Al pastes after firing. The reactions among Al powders, frits and additives were studied. The wetting behavior between each powder (Al powder, frit, additive) and Si, Al substrates was also measured as a function of the temperature. These preliminary studies show that the frits affect the adhesion between Al and Si. In addition, the proper additives prevent the bowing of Si wafer. 10. Improvements in China's Food Additive Laws-Fermented Flour Paste Additive in Beijing Roast Duck Institute of Scientific and Technical Information of China (English) Wang Jianglian; Zhao Xin 2008-01-01 About half of the food safety incidents in 2005 and 2006 were related to food additives. Early in 2007,the main problem for administrative enforcement is the issue of food additives.This paper analyzes one such incident:the fermented flour paste incident in Beijing roast duck that occurred in early 2007.We put forward suggested ways to perfect the legal system regarding Chinese food additives by focusing on legal and management mechanisms.This includes optimizing higher-level laws for food additives,improving the standards system,cultivating the appropriate concepts,implementing preventive measures,and facilitating routine law enforcement. 11. Mechanical properties of additively manufactured octagonal honeycombs. Science.gov (United States) Hedayati, R; Sadighi, M; Mohammadi-Aghdam, M; Zadpoor, A A 2016-12-01 Honeycomb structures have found numerous applications as structural and biomedical materials due to their favourable properties such as low weight, high stiffness, and porosity. Application of additive manufacturing and 3D printing techniques allows for manufacturing of honeycombs with arbitrary shape and wall thickness, opening the way for optimizing the mechanical and physical properties for specific applications. In this study, the mechanical properties of honeycomb structures with a new geometry, called octagonal honeycomb, were investigated using analytical, numerical, and experimental approaches. An additive manufacturing technique, namely fused deposition modelling, was used to fabricate the honeycomb from polylactic acid (PLA). The honeycombs structures were then mechanically tested under compression and the mechanical properties of the structures were determined. In addition, the Euler-Bernoulli and Timoshenko beam theories were used for deriving analytical relationships for elastic modulus, yield stress, Poisson's ratio, and buckling stress of this new design of honeycomb structures. Finite element models were also created to analyse the mechanical behaviour of the honeycombs computationally. The analytical solutions obtained using Timoshenko beam theory were close to computational results in terms of elastic modulus, Poisson's ratio and yield stress, especially for relative densities smaller than 25%. The analytical solutions based on the Timoshenko analytical solution and the computational results were in good agreement with experimental observations. Finally, the elastic properties of the proposed honeycomb structure were compared to those of other honeycomb structures such as square, triangular, hexagonal, mixed, diamond, and Kagome. The octagonal honeycomb showed yield stress and elastic modulus values very close to those of regular hexagonal honeycombs and lower than the other considered honeycombs. 12. Mechanical properties of additively manufactured octagonal honeycombs. Science.gov (United States) Hedayati, R; Sadighi, M; Mohammadi-Aghdam, M; Zadpoor, A A 2016-12-01 Honeycomb structures have found numerous applications as structural and biomedical materials due to their favourable properties such as low weight, high stiffness, and porosity. Application of additive manufacturing and 3D printing techniques allows for manufacturing of honeycombs with arbitrary shape and wall thickness, opening the way for optimizing the mechanical and physical properties for specific applications. In this study, the mechanical properties of honeycomb structures with a new geometry, called octagonal honeycomb, were investigated using analytical, numerical, and experimental approaches. An additive manufacturing technique, namely fused deposition modelling, was used to fabricate the honeycomb from polylactic acid (PLA). The honeycombs structures were then mechanically tested under compression and the mechanical properties of the structures were determined. In addition, the Euler-Bernoulli and Timoshenko beam theories were used for deriving analytical relationships for elastic modulus, yield stress, Poisson's ratio, and buckling stress of this new design of honeycomb structures. Finite element models were also created to analyse the mechanical behaviour of the honeycombs computationally. The analytical solutions obtained using Timoshenko beam theory were close to computational results in terms of elastic modulus, Poisson's ratio and yield stress, especially for relative densities smaller than 25%. The analytical solutions based on the Timoshenko analytical solution and the computational results were in good agreement with experimental observations. Finally, the elastic properties of the proposed honeycomb structure were compared to those of other honeycomb structures such as square, triangular, hexagonal, mixed, diamond, and Kagome. The octagonal honeycomb showed yield stress and elastic modulus values very close to those of regular hexagonal honeycombs and lower than the other considered honeycombs. PMID:27612831 13. Influence of Additives on Reinforced Concrete Durability Directory of Open Access Journals (Sweden) Neverkovica Darja 2014-12-01 Full Text Available The article presents the results of the research on carbonation and chloride induced corrosion mechanisms in reinforced concrete structures, based on three commercially available concrete admixtures: Xypex Admix C-1000, Penetron Admix and Elkem Microsilica. Carbonation takes place due to carbon dioxide diffusion, which in the required amount is present in the air. Chlorides penetrate concrete in case of the use of deicing salt or structure exploitation in marine atmosphere. Based on the implemented research, Elkem Microsilica is the recommended additive for the use in aggressive environmental conditions. Use of Xypex Admix C-1000 and Penetron Admix have only average resistance to the aggressive environmental impact. 14. Improving ED efficiency to capture additional revenue. Science.gov (United States) Mandavia, Sujal; Samaniego, Loretta 2016-06-01 An increase in the number of patients visiting emergency departments (EDs) presents an opportunity for additional revenue if hospitals take four steps to optimize resources: Streamline the patient pathway and reduce the amount of time each patient occupies a bed in the ED. Schedule staff according to the busy and light times for patient arrivals. Perform registration and triage bedside, reducing initial wait times. Create an area for patients to wait for test results so beds can be freed up for new arrivals. PMID:27451568 15. Addition agents effects on hydrocarbon fuels burning Science.gov (United States) Larionov, V. M.; Mitrofanov, G. A.; Sakhovskii, A. V. 2016-01-01 Literature review on addition agents effects on hydrocarbon fuels burning has been conducted. The impact results in flame pattern and burning velocity change, energy efficiency increase, environmentally harmful NOx and CO emission reduction and damping of self-oscillations in flow. An assumption about water molecules dissociation phenomenon existing in a number of practical applications and being neglected in most explanations for physical- chemical processes taking place in case of injection of water/steam into combustion zone has been noted. The hypothesis about necessity of water dissociation account has been proposed. It can be useful for low temperature combustion process control and NOx emission reduction. 16. MIXED HEDGING UNDER ADDITIVE MARKET PRICE INFORMATION Institute of Scientific and Technical Information of China (English) Haifeng YAN; Jianqi YANG; Limin LIU 2008-01-01 Assume that there is additional market information in the financial market, which is represented by n given T-contingent claims. The special claims with observed prices at time 0 can only be traded at time 0. Hence, investment opportunities increase. By means of the techniques developed by Gourierout et al. (1998), the mixed hedging problem is considered, especially, the price of contingent claim and the optimal hedging strategy are obtained. An explicit description of the mean-variance efficient solution is given after arguing mean-variance efficient frontier problem. 17. Mechanism and kinetics of addition polymerizations CERN Document Server Kucera, M 1991-01-01 This volume presents an up-to-date survey of knowledge concerning addition type polymerizations. It contains nine chapters, each of which covers a particular basic term. Whenever necessary, the phenomena are discussed from the viewpoint of both stationary and non-stationary state of radical, ionic (i.e. anionic and cationic) and coordination polymerization. Special attention has been paid to the propagation process. It provides not only a general overview but also information on important special cases (theoretical conditions of propagation, influence of external factors, controlled propagatio 18. Additive Manufacturing of Hierarchical Porous Structures Energy Technology Data Exchange (ETDEWEB) Grote, Christopher John [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Materials Science and Technology Division. Polymers and Coatings 2016-08-30 Additive manufacturing has become a tool of choice for the development of customizable components. Developments in this technology have led to a powerful array of printers that t serve a variety of needs. However, resin development plays a crucial role in leading the technology forward. This paper addresses the development and application of printing hierarchical porous structures. Beginning with the development of a porous scaffold, which can be functionalized with a variety of materials, and concluding with customized resins for metal, ceramic, and carbon structures. 19. Predicting Color Output of Additive Manufactured Parts DEFF Research Database (Denmark) Eiríksson, Eyþór Rúnar; Pedersen, David Bue; Aanæs, Henrik 2015-01-01 In this paper we address the colorimetric performance of a multicolor additive manufacturing process. A method on how to measure and characterize color performance of said process is presented. Furthermore, a method on predicting the color output is demonstrated, allowing for previsualization of ...... of parts prior to print. Results show that color prediction can be achieved with an average color difference error of ΔE*00 = 1.5 andstd.dev σ= 0.75, with similar order of magnitude as the literature defined threshold for „Just NoticeableDifference” (JND).... 20. 10 conjectures in additive number theory CERN Document Server Cloitre, Benoit 2011-01-01 Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searching primes since it appears we found sometime primes much more greater than the number of required iterations. In an other hand we propose new formulations of famous conjectures from the additive theory of numbers (the weak twin prime conjecture, the Polignac conjecture, the Goldbach conjecture or the very general Schinzel's hypothesis H). For the moment these are experimental results obtained using pari-gp. 1. Manipulation of microstructure in laser additive manufacturing Science.gov (United States) Bai, Shuang; Yang, Lihmei; Liu, Jian 2016-05-01 In this paper, additive manufacturing (AM) of tungsten parts is investigated by using femtosecond fiber lasers. For the first time, manipulating microstructures of AM parts is systematically investigated and reported. Various processing conditions are studied, which leads to desired characteristics in terms of morphology, porosity, hardness, and microstructural and mechanical properties of the processed components. Fully dense tungsten part with refined grain and increased hardness was obtained for femtosecond laser, compared with parts made with different pulse widths and CW laser. Micro-hardness is investigated for the fabricated samples. This can greatly benefit to the make of complicated structures and materials that could not be achieved before. 2. Early cost estimation for additive manufacture OpenAIRE Zhai, Yun 2012-01-01 Additive Manufacture (AM) is a novel manufacturing method; it is a process of forming components by adding materials. Owing to material saving and manufacturing cost saving, more and more research has been focused on metal AM technologies. WAAM is one AM technology, using arc as the heat sources and wire as the material to create parts with weld beads on a layer-by-layer basis. The process can produce components in a wide range of materials, including aluminum, titanium and steel. High deposi... 3. Structural dynamic modification using additive damping Indian Academy of Sciences (India) B C Nakra 2000-06-01 In order to control dynamic response in structures and machines, modofications using additive viscoelastic damping materials are highlighted. The techniques described for analysis include analytical methods for structural elements, FEM and perturbation methods for reanalysis or structural dynamic modifications for complex structures. Optimisation techniques are used for damping effectiveness include multi-parameter optimisatoin techniques and a technique using dynamic sensitivity analysis and structural dynamic modification. These have been applied for optimum dynamic design of structures incorporating viscoelastic damping. Some current trends for vibraton control are also discussed. 4. Gas hydrate inhibition of drilling fluid additives Energy Technology Data Exchange (ETDEWEB) Xiaolan, L.; Baojiang, S.; Shaoran, R. [China Univ. of Petroleum, Dongying (China). Inst. of Petroleum Engineering 2008-07-01 Gas hydrates that form during offshore well drilling can have adverse impacts on well operational safety. The hydrates typically form in the risers and the annulus between the casing and the drillstring, and can stop the circulation of drilling fluids. In this study, experiments were conducted to measure the effect of drilling fluid additives on hydrate inhibition. Polyalcohols, well-stability control agents, lubricating agents, and polymeric materials were investigated in a stirred tank reactor at temperatures ranging from -10 degree C to 60 degrees C. Pressure, temperature, and torque were used to detect onset points of hydrate formation and dissociation. The inhibitive effect of the additives on hydrate formation was quantified. Phase boundary shifts were measured in terms of temperature difference or sub-cooling gained when chemicals were added to pure water. Results showed that the multiple hydroxyl groups in polyalcohol chemicals significantly inhibited hydrate formation. Polymeric and polyacrylamide materials had only a small impact on hydrate formation, while sulfonated methyl tannins were found to increase hydrate formation. 6 refs., 1 tab., 4 figs. 5. Surface texture measurement for additive manufacturing International Nuclear Information System (INIS) The surface texture of additively manufactured metallic surfaces made by powder bed methods is affected by a number of factors, including the powder’s particle size distribution, the effect of the heat source, the thickness of the printed layers, the angle of the surface relative to the horizontal build bed and the effect of any post processing/finishing. The aim of the research reported here is to understand the way these surfaces should be measured in order to characterise them. In published research to date, the surface texture is generally reported as an Ra value, measured across the lay. The appropriateness of this method for such surfaces is investigated here. A preliminary investigation was carried out on two additive manufacturing processes—selective laser melting (SLM) and electron beam melting (EBM)—focusing on the effect of build angle and post processing. The surfaces were measured using both tactile and optical methods and a range of profile and areal parameters were reported. Test coupons were manufactured at four angles relative to the horizontal plane of the powder bed using both SLM and EBM. The effect of lay—caused by the layered nature of the manufacturing process—was investigated, as was the required sample area for optical measurements. The surfaces were also measured before and after grit blasting. (paper) 6. Emerging technologies in arthroplasty: additive manufacturing. Science.gov (United States) Banerjee, Samik; Kulesha, Gene; Kester, Mark; Mont, Michael A 2014-06-01 Additive manufacturing is an industrial technology whereby three-dimensional visual computer models are fabricated into physical components by selectively curing, depositing, or consolidating various materials in consecutive layers. Although initially developed for production of simulated models, the technology has undergone vast improvements and is currently increasingly being used for the production of end-use components in various aerospace, automotive, and biomedical specialties. The ability of this technology to be used for the manufacture of solid-mesh-foam monolithic and coated components of complex geometries previously considered unmanufacturable has attracted the attention of implant manufacturers, bioengineers, and orthopedic surgeons. Currently, there is a paucity of reports describing this fabrication method in the orthopedic literature. Therefore, we aimed to briefly describe this technology, some of the applications in other orthopedic subspecialties, its present use in hip and knee arthroplasty, and concerns with the present form of the technology. As there are few reports of clinical trials presently available, the true benefits of this technology can only be realized when studies evaluating the clinical and radiographic outcomes of cementless implants manufactured with additive manufacturing report durable fixation, less stress shielding, and better implant survivorship. Nevertheless, the authors believe that this technology holds great promise and may potentially change the conventional methods of casting, machining, and tooling for implant manufacturing in the future. PMID:24764230 7. Emerging technologies in arthroplasty: additive manufacturing. Science.gov (United States) Banerjee, Samik; Kulesha, Gene; Kester, Mark; Mont, Michael A 2014-06-01 Additive manufacturing is an industrial technology whereby three-dimensional visual computer models are fabricated into physical components by selectively curing, depositing, or consolidating various materials in consecutive layers. Although initially developed for production of simulated models, the technology has undergone vast improvements and is currently increasingly being used for the production of end-use components in various aerospace, automotive, and biomedical specialties. The ability of this technology to be used for the manufacture of solid-mesh-foam monolithic and coated components of complex geometries previously considered unmanufacturable has attracted the attention of implant manufacturers, bioengineers, and orthopedic surgeons. Currently, there is a paucity of reports describing this fabrication method in the orthopedic literature. Therefore, we aimed to briefly describe this technology, some of the applications in other orthopedic subspecialties, its present use in hip and knee arthroplasty, and concerns with the present form of the technology. As there are few reports of clinical trials presently available, the true benefits of this technology can only be realized when studies evaluating the clinical and radiographic outcomes of cementless implants manufactured with additive manufacturing report durable fixation, less stress shielding, and better implant survivorship. Nevertheless, the authors believe that this technology holds great promise and may potentially change the conventional methods of casting, machining, and tooling for implant manufacturing in the future. 8. Additive manufacturing of glass for optical applications Science.gov (United States) Luo, Junjie; Gilbert, Luke J.; Bristow, Douglas A.; Landers, Robert G.; Goldstein, Jonathan T.; Urbas, Augustine M.; Kinzel, Edward C. 2016-04-01 Glasses including fused quartz have significant scientific and engineering applications including optics, communications, electronics, and hermetic seals. This paper investigates a filament fed process for Additive Manufacturing (AM) of fused quartz. Additive manufacturing has several potential benefits including increased design freedom, faster prototyping, and lower processing costs for small production volumes. However, current research in AM of glasses is limited and has focused on non-optical applications. Fused quartz is studied here because of its desirability for high-quality optics due to its high transmissivity and thermal stability. Fused quartz also has a higher working temperature than soda lime glass which poses a challenge for AM. In this work, fused quartz filaments are fed into a CO2 laser generated melt pool, smoothly depositing material onto the work piece. Single tracks are printed to explore the effects that different process parameters have on the morphology of printed fused quartz. A spectrometer is used to measure the thermal radiation incandescently emitted from the melt pool. Thin-walls are printed to study the effects of layer-to-layer height. Finally, a 3D fused quartz cube is printed using the newly acquired layer height and polished on each surface. The transmittance and index homogeneity of the polished cube are both measured. These results show that the filament fed process has the potential to print fused quartz with optical transparency and of index of refraction uniformity approaching bulk processed glass. 9. Addition Table of Colours: Additive and Subtractive Mixtures Described Using a Single Reasoning Model Science.gov (United States) Mota, A. R.; Lopes dos Santos, J. M. B. 2014-01-01 Students' misconceptions concerning colour phenomena and the apparent complexity of the underlying concepts--due to the different domains of knowledge involved--make its teaching very difficult. We have developed and tested a teaching device, the addition table of colours (ATC), that encompasses additive and subtractive mixtures in a single… 10. 76 FR 41687 - Food Additives Permitted for Direct Addition to Food for Human Consumption; Hydroxypropyl Cellulose Science.gov (United States) 2011-07-15 ... In a notice published in the Federal Register of April 8, 2010 (75 FR 17928), FDA announced that... HUMAN SERVICES Food and Drug Administration 21 CFR Part 172 Food Additives Permitted for Direct Addition to Food for Human Consumption; Hydroxypropyl Cellulose AGENCY: Food and Drug Administration,... 11. The retro Grignard addition reaction revisited: the reversible addition of benzyl reagents to ketones DEFF Research Database (Denmark) Christensen, Stig Holden; Holm, Torkil; Madsen, Robert 2014-01-01 The Grignard addition reaction is known to be a reversible process with allylic reagents, but so far the reversibility has not been demonstrated with other alkylmagnesium halides. By using crossover experiments it has been established that the benzyl addition reaction is also a reversible transfo... 12. Additive manufacturing of biologically-inspired materials. Science.gov (United States) Studart, André R 2016-01-21 Additive manufacturing (AM) technologies offer an attractive pathway towards the fabrication of functional materials featuring complex heterogeneous architectures inspired by biological systems. In this paper, recent research on the use of AM approaches to program the local chemical composition, structure and properties of biologically-inspired materials is reviewed. A variety of structural motifs found in biological composites have been successfully emulated in synthetic systems using inkjet-based, direct-writing, stereolithography and slip casting technologies. The replication in synthetic systems of design principles underlying such structural motifs has enabled the fabrication of lightweight cellular materials, strong and tough composites, soft robots and autonomously shaping structures with unprecedented properties and functionalities. Pushing the current limits of AM technologies in future research should bring us closer to the manufacturing capabilities of living organisms, opening the way for the digital fabrication of advanced materials with superior performance, lower environmental impact and new functionalities. PMID:26750617 13. Nonparametric additive regression for repeatedly measured data KAUST Repository Carroll, R. J. 2009-05-20 We develop an easily computed smooth backfitting algorithm for additive model fitting in repeated measures problems. Our methodology easily copes with various settings, such as when some covariates are the same over repeated response measurements. We allow for a working covariance matrix for the regression errors, showing that our method is most efficient when the correct covariance matrix is used. The component functions achieve the known asymptotic variance lower bound for the scalar argument case. Smooth backfitting also leads directly to design-independent biases in the local linear case. Simulations show our estimator has smaller variance than the usual kernel estimator. This is also illustrated by an example from nutritional epidemiology. © 2009 Biometrika Trust. 14. Managing water addition to a degraded core International Nuclear Information System (INIS) In this paper the authors present an approach to the development of an accident management plan for adding water to a degraded core. Under certain degraded core conditions, adding water may lead to enhanced hydrogen production, changes in core geometry that would complicate recovery, steam explosions, or recriticality of the reactor core if unborated water is used. Therefore, a primary requisite for the development of an accident management plan for adding water to a degraded core is to ensure that undesirable consequences of water addition are understood so that: (1) their effects can be minimized and an accident can be terminated at the earliest possible stage, and (2) plant personnel can be better prepared to deal with plant responses that appear contrary to desired outcomes when water is added during a core degradation transient. The approach presented here addresses these concerns in the development of an accident management plan 15. A DNA based model for addition computation Institute of Scientific and Technical Information of China (English) GAO Lin; YANG Xiao; LIU Wenbin; XU Jin 2004-01-01 Much effort has been made to solve computing problems by using DNA-an organic simulating method, which in some cases is preferable to the current electronic computer. However, No one at present has proposed an effective and applicable method to solve addition problem with molecular algorithm due to the difficulty in solving the carry problem which can be easily solved by hardware of an electronic computer. In this article, we solved this problem by employing two kinds of DNA strings, one is called result and operation string while the other is named carrier. The result and operation string contains some carry information by its own and denotes the ultimate result while the carrier is just for carrying use. The significance of this algorithm is the original code, the fairly easy steps to follow and the feasibility under current molecular biological technology. 16. Experimental Investigation of Using Fuel Additives - Alcohol Directory of Open Access Journals (Sweden) S.M. Fayyad 2010-03-01 Full Text Available This research presents an investigation of the effects of ethanol addition to low octane numbergasoline, on the fuel octane number and on the performance of the engine. In this study, the tested gasoline(octane number = 90 is blended with five different percentages of ethanol, namely 3, 6, 9, 12 and 15% onvolume basis. Then these fuel blends, as well as the base gasoline fuel, w ere burnt in the tested engine. It isfound that the octane number of gasoline increases continuously and linearly with increasing the ethanolpercentage in gasoline. Hence, ethanol is an effective compound for increasing the value of the octane numberof gasoline. Also, it is also noticed that the best performance of the engine was obtained when 15% of ethanolwas used in the gasoline blend. 17. Printability of alloys for additive manufacturing Science.gov (United States) Mukherjee, T.; Zuback, J. S.; De, A.; DebRoy, T. 2016-01-01 Although additive manufacturing (AM), or three dimensional (3D) printing, provides significant advantages over existing manufacturing techniques, metallic parts produced by AM are susceptible to distortion, lack of fusion defects and compositional changes. Here we show that the printability, or the ability of an alloy to avoid these defects, can be examined by developing and testing appropriate theories. A theoretical scaling analysis is used to test vulnerability of various alloys to thermal distortion. A theoretical kinetic model is used to examine predisposition of different alloys to AM induced compositional changes. A well-tested numerical heat transfer and fluid flow model is used to compare susceptibilities of various alloys to lack of fusion defects. These results are tested and validated with independent experimental data. The findings presented in this paper are aimed at achieving distortion free, compositionally sound and well bonded metallic parts. PMID:26796864 18. Additive manufacturing: Overview and NDE challenges Science.gov (United States) Slotwinski, J. A. 2014-02-01 Additive manufacturing (AM) processes are capable of producing highly complex and customized parts, without the need for dedicated tooling, and can produce parts directly from the part design information. These types of processes are poised to revolutionize the manufacturing industry, yet there are several challenges that are currently preventing more widespread adoption of AM technologies. Traditional Non-Destructive Evaluation (NDE) methods could be utilized in both in-process and post-process applications to help overcome these challenges, although currently there are very few examples of in-situ sensors for monitoring AM processes. This paper gives an overview of AM technology, and discusses the potential benefits and challenges of using NDE in AM applications. 19. Atom addition reactions in interstellar ice analogues CERN Document Server Linnartz, Harold; Fedoseev, Gleb 2015-01-01 This review paper summarizes the state-of-the-art in laboratory based interstellar ice chemistry. The focus is on atom addition reactions, illustrating how water, carbon dioxide and methanol can form in the solid state at astronomically relevant temperatures, and also the formation of more complex species such as hydroxylamine, an important prebiotic molecule, and glycolaldehyde, the smallest sugar, is discussed. These reactions are particularly relevant during the dark ages of star and planet formation, i.e., when the role of UV light is restricted. A quantitative characterization of such processes is only possible through dedicated laboratory studies, i.e., under full control of a large set of parameters such as temperature, atom-flux, and ice morphology. The resulting numbers, physical and chemical constants, e.g., barrier heights, reaction rates and branching ratios, provide information on the molecular processes at work and are needed as input for astrochemical models, in order to bridge the timescales t... 20. Additive functionals and excursions of Kuznetsov processes Directory of Open Access Journals (Sweden) Hacène Boutabia 2005-01-01 semigroup of transition. In this paper, we give the excursion laws of (Xtt∈ℝ+ conditioned on the strict past and future without duality hypothesis. We study excursions of a general regenerative system and of a regenerative system consisting of the closure of the set of times the regular points of B are visited. In both cases, those conditioned excursion laws depend only on two points Xg− and Xd, where ]g,d[ is an excursion interval of the regenerative set M. We use the (FDt-predictable exit system to bring together the isolated points of M and its perfect part and replace the classical optional exit system. This has been a subject in literature before (e.g., Kaspi (1988 under the classical duality hypothesis. We define an “additive functional” for (Ytt∈ℝ with B, we generalize the laws cited before to (Ytt∈ℝ, and we express laws of pairs of excursions. 1. Simulation method for evaluating progressive addition lenses. Science.gov (United States) Qin, Linling; Qian, Lin; Yu, Jingchi 2013-06-20 Since progressive addition lenses (PALs) are currently state-of-the-art in multifocal correction for presbyopia, it is important to study the methods for evaluating PALs. A nonoptical simulation method used to accurately characterize PALs during the design and optimization process is proposed in this paper. It involves the direct calculation of each surface of the lens according to the lens heights of front and rear surfaces. The validity of this simulation method for the evaluation of PALs is verified by the good agreement with Rotlex method. In particular, the simulation with a "correction action" included into the design process is potentially a useful method with advantages of time-saving, convenience, and accuracy. Based on the eye-plus-lens model, which is established through an accurate ray tracing calculation along the gaze direction, the method can find an excellent application in actually evaluating the wearer performance for optimal design of more comfortable, satisfactory, and personalized PALs. PMID:23842170 2. Microstructural Control of Additively Manufactured Metallic Materials Science.gov (United States) Collins, P. C.; Brice, D. A.; Samimi, P.; Ghamarian, I.; Fraser, H. L. 2016-07-01 In additively manufactured (AM) metallic materials, the fundamental interrelationships that exist between composition, processing, and microstructure govern these materials’ properties and potential improvements or reductions in performance. For example, by using AM, it is possible to achieve highly desirable microstructural features (e.g., highly refined precipitates) that could not otherwise be achieved by using conventional approaches. Simultaneously, opportunities exist to manage macro-level microstructural characteristics such as residual stress, porosity, and texture, the last of which might be desirable. To predictably realize optimal microstructures, it is necessary to establish a framework that integrates processing variables, alloy composition, and the resulting microstructure. Although such a framework is largely lacking for AM metallic materials, the basic scientific components of the framework exist in literature. This review considers these key components and presents them in a manner that highlights key interdependencies that would form an integrated framework to engineer microstructures using AM. 3. Additive Feed Forward Control with Neural Networks DEFF Research Database (Denmark) Sørensen, O. 1999-01-01 This paper demonstrates a method to control a non-linear, multivariable, noisy process using trained neural networks. The basis for the method is a trained neural network controller acting as the inverse process model. A training method for obtaining such an inverse process model is applied....... A suitable 'shaped' (low-pass filtered) reference is used to overcome problems with excessive control action when using a controller acting as the inverse process model. The control concept is Additive Feed Forward Control, where the trained neural network controller, acting as the inverse process model......, is placed in a supplementary pure feed-forward path to an existing feedback controller. This concept benefits from the fact, that an existing, traditional designed, feedback controller can be retained without any modifications, and after training the connection of the neural network feed-forward controller... 4. Mechanical Properties of Additively Manufactured Thick Honeycombs Directory of Open Access Journals (Sweden) Reza Hedayati 2016-07-01 Full Text Available Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In this paper, we study the mechanical behavior of thick honeycombs made using additive manufacturing techniques that allow for fabrication of honeycombs with arbitrary and precisely controlled thickness. Thick honeycombs with different wall thicknesses were produced from polylactic acid (PLA using fused deposition modelling, i.e., an additive manufacturing technique. The samples were mechanically tested in-plane under compression to determine their mechanical properties. We also obtained exact analytical solutions for the stiffness matrix of thick hexagonal honeycombs using both Euler-Bernoulli and Timoshenko beam theories. The stiffness matrix was then used to derive analytical relationships that describe the elastic modulus, yield stress, and Poisson’s ratio of thick honeycombs. Finite element models were also built for computational analysis of the mechanical behavior of thick honeycombs under compression. The mechanical properties obtained using our analytical relationships were compared with experimental observations and computational results as well as with analytical solutions available in the literature. It was found that the analytical solutions presented here are in good agreement with experimental and computational results even for very thick honeycombs, whereas the analytical solutions available in the literature show a large deviation from experimental observation, computational results, and our analytical solutions. 5. Transformation of Breast Reconstruction via Additive Biomanufacturing. Science.gov (United States) Chhaya, Mohit P; Balmayor, Elizabeth R; Hutmacher, Dietmar W; Schantz, Jan-Thorsten 2016-01-01 Adipose tissue engineering offers a promising alternative to current breast reconstruction options. However, the conventional approach of using a scaffold in combination with adipose-derived precursor cells poses several problems in terms of scalability and hence clinical feasibility. Following the body-as-a-bioreactor approach, this study proposes a unique concept of delayed fat injection into an additive biomanufactured and custom-made scaffold. Three study groups were evaluated: Empty scaffold, Scaffold containing 4 cm(3) lipoaspirate and Empty scaffold +2-week prevascularisation period. In group 3, of prevascularisation, 4 cm(3) of lipoaspirate was injected into scaffolds after 2 weeks. Using a well-characterised additive biomanufacturing technology platform, patient-specific scaffolds made of medical-grade-polycaprolactone were designed and fabricated. Scaffolds were implanted in subglandular pockets in immunocompetent minipigs (n = 4) for 24-weeks. Angiogenesis and adipose tissue regeneration were observed in all constructs. Histological evaluation showed that the prevascularisation + lipoaspirate group had the highest relative area of adipose tissue (47.32% ± 4.12) which was significantly higher than both lipoaspirate-only (39.67% ± 2.04) and empty control group (8.31% ± 8.94) and similar to native breast tissue (44.97% ± 14.12). This large preclinical animal study provides proof-of-principle that the clinically applicable prevascularisation and delayed fat-injection techniques can be used for regeneration of large volumes of adipose tissue. PMID:27301425 6. Feasibility and Testing of Additive Manufactured Components Energy Technology Data Exchange (ETDEWEB) Dehoff, Ryan R. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Hummelt, Ed [Eaton Corporation, Milwaukee, WI (United States); Solovyeva, Lyudmila [Eaton Corporation, Milwaukee, WI (United States) 2016-09-01 This project focused on demonstrating the ability to fabricate two parts with different geometry: an arc flash interrupter and a hydraulic manifold. Eaton Corporation provided ORNL solid models, information related to tolerances and sensitive parameters of the parts and provided testing and evaluation. ORNL successfully manufactured both components, provided cost models of the manufacturing (materials, labor, time and post processing) and delivered test components for Eaton evaluation. The arc flash suppressor was fabricated using the Renishaw laser powder bed technology in CoCrMo while the manifold was produced from Ti-6Al-4V using the Arcam electron beam melting technology. These manufacturing techniques were selected based on the design and geometrical tolerances required. A full-scale manifold was produced on the Arcam A2 system (nearly 12 inches tall). A portion of the manifold was also produced in the Arcam Q10 system. Although a full scale manifold could not be produced in the system, a full scale manifold is expected to have similar material properties, geometric accuracy, and surface finish as could be fabricated on an Arcam Q20 system that is capable of producing four full scale manifolds in a production environment. In addition to the manifold, mechanical test specimens, geometric tolerance artifacts, and microstructure samples were produced alongside the manifold. The development and demonstration of these two key components helped Eaton understand the impact additive manufacturing can have on many of their existing products. By working within the MDF and leveraging ORNL’s manufacturing and characterization capabilities, the work will ensure the rapid insertion and commercialization of this technology. 7. Behaviors of Polymer Additives Under EHL and Influences of Interactions Between Additives on Friction Modification Science.gov (United States) Sakurai, T. 1984-01-01 Polymer additives have become requisite for the formulation of multigrade engine oils. The behavior of polymethacrylate (PMA)-thickened oils as lubricants in concentrated contacts under nominal rolling and pure sliding conditions was investigated by conventional optical interferometry. The PMA thickened oils behaved differently from the base oil in the formation of elastohydrodynamic (EHL) films. The higher the elastohydrodynamic molecular weight of the PMA contained in the lubricant, the thinner was the oil film under EHL conditions. The film thickness of shear-degraded PMA-thickened oils was also investigated. The behavior of graphite particles dispersed in both the base oil and the PMA-thickened oil was studied under pure sliding by taking photomicrographs. Many kinds of additives are contained in lubricating oil and the interactions between additives are considered. The interactions of zinc-organodithiophosphates (ZDP) with other additives is discussed. 8. Food Additives Permitted for Direct Addition to Food for Human Consumption; Folic Acid. Final rule. Science.gov (United States) 2016-04-15 The Food and Drug Administration (FDA or we) is amending the food additive regulations to provide for the safe use of folic acid in corn masa flour. We are taking this action in response to a food additive petition filed jointly by Gruma Corporation, Spina Bifida Association, March of Dimes Foundation, American Academy of Pediatrics, Royal DSM N.V., and National Council of La Raza. PMID:27101640 9. Additionality of global benefits and financial additionality in the context of the AIJ negotiations Energy Technology Data Exchange (ETDEWEB) Puhl, I. 1996-12-31 The Conference of the Party at their first meeting (COP1) took a decision regarding criteria for joint implementation as indicated in Art. 4.2 (a) of the FCCC which established a pilot phase for activities implemented jointly (AIJ) under the pilot phase. Besides some more technical issues this decision specified that such measures should bring about real, measurable and long-term environmental benefits related to the mitigation of climate change that would not have occurred in the absence of such activities. It also established that the financing of AIJ shall be additional to the financial obligations of developed country parties. These two requirements are called the additionality criteria for AIJ. The first refers to the realness of GHG emission abatement (which means reduction compared to a baseline) whereas the second describes that funds earmarked for AIJ have no other objective (i.e. profit making, export promotion) but to reduce GHG emissions to avoid the free-riding of investors and subsequently developed country parties. The reporting framework as well as the reporting requirements under national programs do not specify further the two types of additionality and even though research focuses on issues like baseline determination there has been no attempt so far to identify approaches which contribute towards defining strict and practicable methods and guidelines to frame additionality criteria. The first FCCC assessment of pilot project reporting revealed that in the reporting of activities, emissions additionality often remained unclear, especially in cases where AIJ was only a portion of an existing or already planned project, and that there is a point about how to account for financial additionality. It subsequently proposed to develop a uniform approach to baseline determination and the assessment of emission (reduction) additionality and financial additionality. 10. Morpho-Syntactic Character Of Additives: A Descriptive Approach to Additives in Asian Sov Languages OpenAIRE Özbek, Aydın; Zang, LinShen; Demirtaş, Esra 2014-01-01 Traditionally Turkish is considered as an SOV language and a member of the Altaic Languages. In this sense, most of the previous contrastive studies have been done by using the data from the Altaic languages. Contrary to this method, this study focuses on additives in SOV languages of Asia which are considered to be in different families. It must be noted that even if language families are clearly differing from each other, additives show almost same or similar behaviors that, could be consid... 11. Influence of and additives on acetylene detonation Science.gov (United States) Drakon, A.; Emelianov, A.; Eremin, A. 2014-03-01 The influence of and admixtures (known as detonation suppressors for combustible mixtures) on the development of acetylene detonation was experimentally investigated in a shock tube. The time-resolved images of detonation wave development and propagation were registered using a high-speed streak camera. Shock wave velocity and pressure profiles were measured by five calibrated piezoelectric gauges and the formation of condensed particles was detected by laser light extinction. The induction time of detonation development was determined as the moment of a pressure rise at the end plate of the shock tube. It was shown that additive had no influence on the induction time. For , a significant promoting effect was observed. A simplified kinetic model was suggested and characteristic rates of diacetylene formation were estimated as the limiting stage of acetylene polymerisation. An analysis of the obtained data indicated that the promoting species is atomic chlorine formed by pyrolysis, which interacts with acetylene and produces radical, initiating a chain mechanism of acetylene decomposition. The results of kinetic modelling agree well with the experimental data. 12. Structure Property Studies for Additively Manufactured Parts Energy Technology Data Exchange (ETDEWEB) Milenski, Helen M [Univ. of Mexico, Los Alamos, NM (United States); Schmalzer, Andrew Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kelly, Daniel [Los Alamos National Lab. (LANL), Los Alamos, NM (United States) 2015-08-17 Since the invention of modern Additive Manufacturing (AM) processes engineers and designers have worked hard to capitalize on the unique building capabilities that AM allows. By being able to customize the interior fill of parts it is now possible to design components with a controlled density and customized internal structure. The creation of new polymers and polymer composites allow for even greater control over the mechanical properties of AM parts. One of the key reasons to explore AM, is to bring about a new paradigm in part design, where materials can be strategically optimized in a way that conventional subtractive methods cannot achieve. The two processes investigated in my research were the Fused Deposition Modeling (FDM) process and the Direct Ink Write (DIW) process. The objectives of the research were to determine the impact of in-fill density and morphology on the mechanical properties of FDM parts, and to determine if DIW printed samples could be produced where the filament diameter was varied while the overall density remained constant. 13. Additional EIPC Study Analysis. Final Report Energy Technology Data Exchange (ETDEWEB) Hadley, Stanton W [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Gotham, Douglas J. [Purdue Univ., West Lafayette, IN (United States); Luciani, Ralph L. [Navigant Consultant Inc., Suwanee, GA (United States) 2014-12-01 Between 2010 and 2012 the Eastern Interconnection Planning Collaborative (EIPC) conducted a major long-term resource and transmission study of the Eastern Interconnection (EI). With guidance from a Stakeholder Steering Committee (SSC) that included representatives from the Eastern Interconnection States Planning Council (EISPC) among others, the project was conducted in two phases. Phase 1 involved a long-term capacity expansion analysis that involved creation of eight major futures plus 72 sensitivities. Three scenarios were selected for more extensive transmission- focused evaluation in Phase 2. Five power flow analyses, nine production cost model runs (including six sensitivities), and three capital cost estimations were developed during this second phase. The results from Phase 1 and 2 provided a wealth of data that could be examined further to address energy-related questions. A list of 14 topics was developed for further analysis. This paper brings together the earlier interim reports of the first 13 topics plus one additional topic into a single final report. 14. Additional Fault Detection Test Case Prioritization Directory of Open Access Journals (Sweden) Ritika Jain 2013-07-01 Full Text Available Regression testing is used to confirm that previous bugs have been fixed and that new bugs have not been introduced. Thus regression testing is done during maintenance phase and applied whenever a new version of a program is obtained by modifying an existing version. To perform a regression testing a set of new test cases and old test cases that were previously developed by software engineers are reused. This test suite is exhaustive in nature and it may take long time to rerun all test cases. Thus regression testing is too expensive and the number of test cases increases stridently as the software evolves. In present work, an additional fault detection test case prioritization technique is presented that prioritizes test cases in regression test suite based on number of concealed faults detected by test cases. Both noncost cognizant and cost cognizant prioritization of test cases have been performed using proposed technique and efficiency of prioritized suite is assessed using APFD and APFDc metric respectively. 15. IN718 Additive Manufacturing Properties and Influences Science.gov (United States) Lambert, Dennis M. 2015-01-01 The results of tensile, fracture, and fatigue testing of IN718 coupons produced using the selective laser melting (SLM) additive manufacturing technique are presented. The data have been "sanitized" to remove the numerical values, although certain references to material standards are provided. This document provides some knowledge of the effect of variation of controlled build parameters used in the SLM process, a snapshot of the capabilities of SLM in industry at present, and shares some of the lessons learned along the way. For the build parameter characterization, the parameters were varied over a range that was centered about the machine manufacturer's recommended value, and in each case they were varied individually, although some co-variance of those parameters would be expected. Tensile, fracture, and high-cycle fatigue properties equivalent to wrought IN718 are achievable with SLM-produced IN718. Build and post-build processes need to be determined and then controlled to established limits to accomplish this. It is recommended that a multi-variable evaluation, e.g., design-of experiment (DOE), of the build parameters be performed to better evaluate the co-variance of the parameters. 16. Towards Mobile Microrobot Swarms for Additive Micromanufacturing Directory of Open Access Journals (Sweden) David Cappelleri 2014-09-01 Full Text Available In this paper, a novel approach to achieving the independent control of multiple magnetic microrobots is presented. The approach utilizes a specialized substrate consisting of a fine grid of planar, MEMS-fabricated micro coils of the same size as the microrobots (≤ 500 μm. The coils can be used to generate real magnetic potentials and, therefore, attractive and repulsive forces in the workspace to control the trajectories of the microrobots. Initial work on modelling the coil and microrobot behavior is reported along with simulation results for navigating one and two microrobots along independent desired trajectories. Qualitative results from a scaled-up printed circuit board version of the specialized substrate operating on permanent magnets are presented and offer proof-of-concept results for the approach. These tests also provide insights for practical implementations of such a system, which are similarly reported. The ultimate goal of this work is to use swarms of independently controlled microrobots in advanced, additive manufacturing applications. 17. Computational Process Modeling for Additive Manufacturing (OSU) Science.gov (United States) Bagg, Stacey; Zhang, Wei 2015-01-01 Powder-Bed Additive Manufacturing (AM) through Direct Metal Laser Sintering (DMLS) or Selective Laser Melting (SLM) is being used by NASA and the Aerospace industry to "print" parts that traditionally are very complex, high cost, or long schedule lead items. The process spreads a thin layer of metal powder over a build platform, then melts the powder in a series of welds in a desired shape. The next layer of powder is applied, and the process is repeated until layer-by-layer, a very complex part can be built. This reduces cost and schedule by eliminating very complex tooling and processes traditionally used in aerospace component manufacturing. To use the process to print end-use items, NASA seeks to understand SLM material well enough to develop a method of qualifying parts for space flight operation. Traditionally, a new material process takes many years and high investment to generate statistical databases and experiential knowledge, but computational modeling can truncate the schedule and cost -many experiments can be run quickly in a model, which would take years and a high material cost to run empirically. This project seeks to optimize material build parameters with reduced time and cost through modeling. 18. Additive Manufacturing of Ultem Polymers and Composites Science.gov (United States) Chuang, Kathy C.; Grady, Joseph E.; Draper, Robert D.; Shin, Euy-Sik E.; Patterson, Clark; Santelle, Thomas D. 2015-01-01 The objective of this project was to conduct additive manufacturing to produce aircraft engine components by Fused Deposition Modeling (FDM), using commercially available polyetherimdes Ultem 9085 and experimental Ultem 1000 filled with 10 chopped carbon fiber. A property comparison between FDM-printed and injection molded coupons for Ultem 9085, Ultem 1000 resin and the fiber-filled composite Ultem 1000 was carried out. Furthermore, an acoustic liner was printed from Ultem 9085 simulating conventional honeycomb structured liners and tested in a wind tunnel. Composite compressor inlet guide vanes were also printed using fiber-filled Ultem 1000 filaments and tested in a cascade rig. The fiber-filled Ultem 1000 filaments and composite vanes were characterized by scanning electron microscope (SEM) and acid digestion to determine the porosity of FDM-printed articles which ranged from 25-31. Coupons of Ultem 9085, experimental Ultem 1000 composites and XH6050 resin were tested at room temperature and 400F to evaluate their corresponding mechanical properties. 19. Computed tomography characterisation of additive manufacturing materials. Science.gov (United States) Bibb, Richard; Thompson, Darren; Winder, John 2011-06-01 Additive manufacturing, covering processes frequently referred to as rapid prototyping and rapid manufacturing, provides new opportunities in the manufacture of highly complex and custom-fitting medical devices and products. Whilst many medical applications of AM have been explored and physical properties of the resulting parts have been studied, the characterisation of AM materials in computed tomography has not been explored. The aim of this study was to determine the CT number of commonly used AM materials. There are many potential applications of the information resulting from this study in the design and manufacture of wearable medical devices, implants, prostheses and medical imaging test phantoms. A selection of 19 AM material samples were CT scanned and the resultant images analysed to ascertain the materials' CT number and appearance in the images. It was found that some AM materials have CT numbers very similar to human tissues, FDM, SLA and SLS produce samples that appear uniform on CT images and that 3D printed materials show a variation in internal structure. 20. IN718 Additive Manufacturing Properties and Influences Science.gov (United States) Lambert, Dennis M. 2015-01-01 The results of tensile, fracture, and fatigue testing of IN718 coupons produced using the selective laser melting (SLM) additive manufacturing technique are presented. The data has been "generalized" to remove the numerical values, although certain references to material standards are provided. This document provides some knowledge of the effect of variation of controlled build parameters used in the SLM process, a snapshot of the capabilities of SLM in industry at present, and shares some of the lessons learned along the way. For the build parameter characterization, the parameters were varied over a range about the machine manufacturer's recommended value, and in each case they were varied individually, although some co-variance of those parameters would be expected. SLM-produced IN718, tensile, fracture, and high-cycle fatigue properties equivalent to wrought IN718 are achievable. Build and post-build processes need to be determined and then controlled to established limits to accomplish this. It is recommended that a multi-variable evaluation, e.g., design-of-experiment (DOE), of the build parameters be performed to better evaluate the co-variance of the parameters. 1. Organic Zinc as Feed Additive for Ruminants Directory of Open Access Journals (Sweden) Suprijati 2013-09-01 Full Text Available Zinc is an essential micro mineral required by ruminants and is a component of over 300 enzymes which play important role in the metabolisms of carbohydrates, proteins and fats. Recently, the chemical and biotechnology processes have been developed for synthesizing organic Zn. Organic Zn is the product of a chelating process of dissolved Zn anorganic salts with amino acids or hydrolyzed protein. The utilization of organic Zn as feed additive in ruminants diets tends to increase, due to the absorption of Zn in the organic form is more effective than the inorganic form. This paper reviewes the research from comparative studies of inorganic and organic Zn on the growth, production and reproduction in ruminants. The studies found that the supplementation of organic Zn improved nutrient digestibility, growth, feed efficiency, milk production, Zn retention and absorption, production and reproductive performances of ruminants. However, a little variation response was found due to different degrees of chelating on Zn incorporation of amino acids or hydrolyzed protein. 2. Generalized Additive Models in Business and Economics Directory of Open Access Journals (Sweden) Sunil K Sapra 2013-06-01 Full Text Available The paper presents applications of a class of semi-parametric models called generalized additive models (GAMs to several business and economic datasets. Applications include analysis of wage-education relationship, brand choice, and number of trips to a doctor’s office. The dependent variable may be continuous, categorical or count. These semi-parametric models are flexible and robust extensions of Logit, Poisson, Negative Binomial and other generalized linear models. The GAMs are represented using penalized regression splines and are estimated by penalized regression methods. The degree of smoothness for the unknown functions in the linear predictor part of the GAM is estimated using cross validation. The GAMs allow us to build a regression surface as a sum of lower-dimensional nonparametric terms circumventing the curse of dimensionality: the slow convergence of an estimator to the true value in high dimensions. For each application studied in the paper, several GAMs are compared and the best model is selected using AIC, UBRE score, deviances, and R-sq (adjusted. The econometric techniques utilized in the paper are widely applicable to the analysis of count, binary response and duration types of data encountered in business and economics. 3. Biobased additive plasticizing Polylactic acid (PLA Directory of Open Access Journals (Sweden) Mounira Maiza 2015-12-01 Full Text Available Polylactic acid (PLA is an attractive candidate for replacing petrochemical polymers because it is from renewable resources. In this study, a specific PLA 2002D was melt-mixed with two plasticizers: triethyl citrate (TEC and acetyl tributyl citrate (ATBC. The plasticized PLA with various concentrations were analyzed by differential scanning calorimetry (DSC, dynamic mechanical analysis (DMA, melt flow index (MFI, thermogravimetric analysis (TGA, X-ray diffraction (XRD, UV-Visible spectroscopy and plasticizer migration test. Differential scanning calorimetry demonstrated that the addition of TEC and ATBC resulted in a decrease in glass transition temperature (Tg, and the reduction was the largest with the plasticizer having the lowest molecular weight (TEC. Plasticizing effect was also shown by decrease in the dynamic storage modulus and viscosity of plasticized mixtures compared to the treated PLA. The TGA results indicated that ATBC and TEC promoted a decrease in thermal stability of the PLA. The X-ray diffraction showed that the PLA have not polymorphic crystalline transition. Analysis by UV-Visible spectroscopy showed that the two plasticizers: ATBC and TEC have no effect on the color change of the films. The weight loss plasticizer with heating time and at 100°C is lesser than at 135 °C. Migration of TEC and ATBC results in cracks and changed color of material. We have concluded that the higher molecular weight of citrate in the studied exhibited a greater plasticizing effect to the PLA. 4. Additive manufacturing technologies of porous metal implants Institute of Scientific and Technical Information of China (English) Zhou Linxi; Yang Quanzhan; Zhang Guirong; Zhao Fangxin; Shen Gang; Yu Bo 2014-01-01 Biomedical metal materials with good corrosion resistance and mechanical properties are widely used in orthopedic surgery and dental implant materials, but they can easily cause stress shielding due to the signiifcant difference in elastic modulus between the implant and human bones. The elastic modulus of porous metals is lower than that of dense metals. Therefore, it is possible to adjust the pore parameters to make the elastic modulus of porous metals match or be comparable with that of the bone tissue. At the same time, the open porous metals with pores connected to each other could provide the structural condition for bone ingrowth, which is helpful in strengthening the biological combination of bone tissue with the implants. Therefore, the preparation technologies of porous metal implants and related research have been drawing more and more attention due to the excellent features of porous metals. Selective laser melting (SLM) and electron beam melting technology (EBM) are important research fields of additive manufacturing. They have the advantages of directly forming arbitrarily complex shaped metal parts which are suitable for the preparation of porous metal implants with complex shape and ifne structure. As new manufacturing technologies, the applications of SLM and EBM for porous metal implants have just begun. This paper aims to understand the technology status of SLM and EBM, the research progress of porous metal implants preparation by using SLM and EBM, and the biological compatibility of the materials, individual design and manufacturing requirements. The existing problems and future research directions for porous metal implants prepared by SLM and EBM methods are discussed in the last paragraph. 5. When in a multiplicative derivation additive? OpenAIRE Mohamad Nagy Daif 1991-01-01 Our main objective in this note is to prove the following. Suppose R is a ring having an idempotent element e(e≠0, e≠1) which satisfies: (M1)   xR=0  implies  x=0.(M2)   eRx=0  implies  x=0  (and hence  Rx=0  implies  x=0).(M3)   exeR(1−e)=0  implies  exe=0. If d is any multiplicative derivation of R, then d is additive.... 6. Additive manufacturing technologies of porous metal implants Directory of Open Access Journals (Sweden) Yang Quanzhan 2014-06-01 Full Text Available Biomedical metal materials with good corrosion resistance and mechanical properties are widely used in orthopedic surgery and dental implant materials, but they can easily cause stress shielding due to the significant difference in elastic modulus between the implant and human bones. The elastic modulus of porous metals is lower than that of dense metals. Therefore, it is possible to adjust the pore parameters to make the elastic modulus of porous metals match or be comparable with that of the bone tissue. At the same time, the open porous metals with pores connected to each other could provide the structural condition for bone ingrowth, which is helpful in strengthening the biological combination of bone tissue with the implants. Therefore, the preparation technologies of porous metal implants and related research have been drawing more and more attention due to the excellent features of porous metals. Selective laser melting (SLM and electron beam melting technology (EBM are important research fields of additive manufacturing. They have the advantages of directly forming arbitrarily complex shaped metal parts which are suitable for the preparation of porous metal implants with complex shape and fine structure. As new manufacturing technologies, the applications of SLM and EBM for porous metal implants have just begun. This paper aims to understand the technology status of SLM and EBM, the research progress of porous metal implants preparation by using SLM and EBM, and the biological compatibility of the materials, individual design and manufacturing requirements. The existing problems and future research directions for porous metal implants prepared by SLM and EBM methods are discussed in the last paragraph. 7. Fatigue crack growth in additive manufactured products Directory of Open Access Journals (Sweden) A. Riemer 2015-10-01 Full Text Available Additive Manufacturing (AM is a new innovative technique that allows the direct fabrication of complex, individual, delicate and high-strength products, based on their 3D data. Selective Laser Melting (SLM is one of the AM processes that generates metallic components layer by layer using powder-bed technique. The irradiation and consequent melting of metallic powder is realised by the laser source. Employing SLM, especially complex and individual products, such as implants or aerospace parts, are well suited for economic production in small batches. The first important issue in this work was to analyse the fatigue crack growth (FCG in titanium alloy Ti-6-4 and stainless steel 316L processed by SLM. As a first step, stress intensity range decreasing tests were performed on SLM samples in their “as-built” condition. The next step was to adopt measures for optimisation of fatigue crack growth performance of SLM parts. For this purpose various heat treatments such as stress relief annealing and hot isostatic pressing (HIP were applied to the CT specimens. Finally, the strong impact of heat treatment on the residual lifetime was demonstrated by numerical fatigue crack growth simulations. For this purpose, the hip joint implant consisting of Ti-6-4 and processed by SLM was taken into account. It was found that residual stresses have a strong influence on the crack growth in Ti-6-4, while the influence of the micro-pores on the threshold values remains low. In contrast the results for 316L show that its fracturemechanical behaviour is not affected by residual stresses, whereas the microstructural features lead to modification in the da/dN-K-data. The second fundamental aim of this work was to demonstrate the possibilities of the SLM process. For that reason, the individually tailored bicycle crank was optimised regarding its weight and local stresses and finally manufactured using the SLM system. The iterative optimisation procedure was based on 8. A Review on Enhancement of Biogas Yield by Pre-treatment and addition of Additives Directory of Open Access Journals (Sweden) Baredar Prashant 2016-01-01 Full Text Available Energy from biomass has been in use from historical days itself but biomass as energy source is not as popular as that of other renewable energy resources. Anaerobic digestion is commonly used to convert organic biomass into biogas. The main drawback of this technology is the long retention period and low efficiency. To tackle this problem pre-treatment and adding additives are best suitable options available. This paper reviews the different pre-treatment techniques and additives that can be used to improve the biogas (mainly methane yield and to reduce the retention period of the process. 9. A Public Opinion Survey on Correctional Education: Does Additional Information on Efficacy Lead to Additional Support? Science.gov (United States) Waterland, Keri Lynn 2009-01-01 Though much research has been done on the efficacy of correctional education on reducing recidivism rates for prison inmates, there is little research on the effect that information about the efficacy of correctional education has on public opinion. This study examined whether providing additional information regarding the efficacy of correctional… 10. A novel methodology of design for Additive Manufacturing applied to Additive Laser Manufacturing process OpenAIRE Ponche, Rémi; Kerbrat, Olivier; MOGNOL, Pascal; Hascoët, Jean-Yves 2014-01-01 International audience Nowadays, due to rapid prototyping processes improvements, a functional metal part can be built directly by Additive Manufacturing. It is now accepted that these new processes can increase productivity while enabling a mass and cost reduction and an increase of the parts functionality. However, the physical phenomena that occur during these processes have a strong impact on the quality of the produced parts. Especially, because the manufacturing paths used to produce... 11. Zinc addition experience in BWRs under normal and hydrogen addition chemistry International Nuclear Information System (INIS) Experience at GE BWRs has shown that DZO (Depleted zinc oxide) addition is a viable method for reactor water activity reduction, piping dose rate reduction and radiation worker exposure control, even for plants injecting moderate HWC (Hydrogen water chemistry) for IGSCC (Intergranular stress corrosion crack) mitigation. It is recommended that zinc addition be practiced only with DZO and that reactor water concentrations of 5-10 ppb zinc be maintained during plant operation. Other methods for dose control such as source term reduction and decontamination are also viable but should be evaluated on a cost benefit basis. Plant data supplied from the GE BWRs in this report have been acquired from plants with varying levels of feedwater iron and cobalt input, different decontamination histories and varied operating experience, yet all have observed significant benefits from zinc addition. It is also recommended that HWC be practiced with minimal cycling and that the required level of hydrogen injection for IGSCC control be performed. (J.P.N.) 12. Additional safety assessment of ITER - Addition safety investigation of the INB ITER International Nuclear Information System (INIS) This assessment aims at re-assessing safety margins in the light of events which occurred in Fukushima Daiichi, i.e. extreme natural events challenging the safety of installations. After a presentation of some characteristics of the ITER installation (location, activities, buildings, premise detritiation systems, electric supply, handling means, radioactive materials, chemical products, nuclear risks, specific risks), the report addresses the installation robustness by identifying cliff-edge effect risks which can be related to a loss of confinement of radioactive materials, explosions, a significant increase of exposure level, a possible effect on water sheets, and so on. The next part addresses the various aspects related to a seismic risk: installation sizing (assessment methodology, seismic risk characterization in Cadarache), sizing protection measures, installation compliance, and margin assessment. External flooding is the next addressed risk: installation sizing with respect to this specific risk, protection measures, installation compliance, margin assessment, and studied additional measures. Other extreme natural phenomena are considered (meteorological conditions, earthquake and flood) which may have effects on other installations (dam, canal). Then, the report addresses technical risks like the loss of electric supplies and cooling systems, the way a crisis is managed in terms of technical and human means and organization in different typical accidental cases. Subcontracting practices are also discussed. A synthesis proposes an overview of this additional safety assessment and discusses the impact which could have additional measures which could be implemented 13. On norm sub-additivity and super-additivity inequalities for concave and convex functions CERN Document Server Audenaert, Koenraad M R 2010-01-01 Sub-additive and super-additive inequalities for concave and convex functions have been generalized to the case of matrices by several authors over a period of time. These lead to some interesting inequalities for matrices, which in some cases coincide with, and in other cases are at variance with the corresponding inequalities for real numbers. We survey some of these matrix inequalities and do further investigations into these. We introduce the novel notion of dominated majorization between the spectra of two Hermitian matrices$B$and$C$, dominated by a third Hermitian matrix$A$. Based on an explicit formula for the gradient of the sum of the$k$largest eigenvalues of a Hermitian matrix, we show that under certain conditions dominated majorization reduces to a linear majorization-like relation between the diagonal elements of$B$and$C$in a certain basis. We use this notion as a tool to give new, elementary proofs for the sub-additivity inequality for non-negative concave functions first proved by Bou... 14. 78 FR 28163 - Zentox Corporation; Withdrawal of Food Additive Petition Science.gov (United States) 2013-05-14 ... proposed to amend the food additive regulations in part 173--Secondary Direct Food Additives Permitted in... Additive Petition AGENCY: Food and Drug Administration, HHS. ACTION: Notice of withdrawal. SUMMARY: The... filing, of a food additive petition (FAP 8A4775) proposing that the food additive regulations be... 15. 40 CFR 51.117 - Additional provisions for lead. Science.gov (United States) 2010-07-01 ... smelters, Lead gasoline additive plants, Lead-acid storage battery manufacturing plants that produce 2,000... 40 Protection of Environment 2 2010-07-01 2010-07-01 false Additional provisions for lead. 51.117... Additional provisions for lead. In addition to other requirements in §§ 51.100 through 51.116 the... 16. 21 CFR 170.38 - Determination of food additive status. Science.gov (United States) 2010-04-01 ... (CONTINUED) FOOD FOR HUMAN CONSUMPTION (CONTINUED) FOOD ADDITIVES Food Additive Safety § 170.38 Determination of food additive status. (a) The Commissioner may, in accordance with § 170.35(b)(4) or (c)(5... 21 Food and Drugs 3 2010-04-01 2009-04-01 true Determination of food additive status.... 17. 21 CFR 170.10 - Food additives in standardized foods. Science.gov (United States) 2010-04-01 ... 21 Food and Drugs 3 2010-04-01 2009-04-01 true Food additives in standardized foods. 170.10... (CONTINUED) FOOD FOR HUMAN CONSUMPTION (CONTINUED) FOOD ADDITIVES General Provisions § 170.10 Food additives... the Act, which proposes the inclusion of a food additive in such definition and standard of... 18. A generalized additive regression model for survival times DEFF Research Database (Denmark) Scheike, Thomas H. 2001-01-01 Additive Aalen model; counting process; disability model; illness-death model; generalized additive models; multiple time-scales; non-parametric estimation; survival data; varying-coefficient models......Additive Aalen model; counting process; disability model; illness-death model; generalized additive models; multiple time-scales; non-parametric estimation; survival data; varying-coefficient models... 19. 21 CFR 570.18 - Tolerances for related food additives. Science.gov (United States) 2010-04-01 ... for related food additives. (a) Food additives that cause similar or related pharmacological effects... effects and will be considered as related food additives. (b) Tolerances established for such related food... 21 Food and Drugs 6 2010-04-01 2010-04-01 false Tolerances for related food additives.... 20. 21 CFR 170.18 - Tolerances for related food additives. Science.gov (United States) 2010-04-01 ... (CONTINUED) FOOD FOR HUMAN CONSUMPTION (CONTINUED) FOOD ADDITIVES General Provisions § 170.18 Tolerances for related food additives. (a) Food additives that cause similar or related pharmacological effects will be... 21 Food and Drugs 3 2010-04-01 2009-04-01 true Tolerances for related food additives.... 1. 76 FR 47210 - Notices of Filing of Petitions for Food Additives and Color Additives; Relocation in the Federal... Science.gov (United States) 2011-08-04 ... HUMAN SERVICES Food and Drug Administration Notices of Filing of Petitions for Food Additives and Color Additives; Relocation in the Federal Register AGENCY: Food and Drug Administration, HHS. ACTION: Notice... petitions for food additives and color additives that are published in accordance with the Federal... 2. An Additive-Multiplicative Cox-Aalen Regression Model DEFF Research Database (Denmark) Scheike, Thomas H.; Zhang, Mei-Jie 2002-01-01 Aalen model; additive risk model; counting processes; Cox regression; survival analysis; time-varying effects......Aalen model; additive risk model; counting processes; Cox regression; survival analysis; time-varying effects... 3. Additional Treatments Offer Little Benefit for Pancreatic Cancer: Study Science.gov (United States) ... 158633.html Additional Treatments Offer Little Benefit for Pancreatic Cancer: Study Neither extra chemotherapy drug nor add-on ... 2016 (HealthDay News) -- Additional treatments for locally advanced pancreatic cancer don't appear to boost survival, a new ... 4. Stasistically constrained operator associated with additivity of communication channel OpenAIRE Fukumi, Toshio 2004-01-01 Additivity of quantum communication channel is discussed in terms of Poisson process to show it is additive in probability. Poisson process is shown to be responsible for entanglement which is a rare event. 5. Purification of selenium from thorium, uranium, radium, actinium and potassium impurities for low background measurements International Nuclear Information System (INIS) A technique of selenium purification from 232Th, 238U, 226,228Ra, 227Ac and 40K was developed. This technique is simple to perform and employs a minimum number of highly pure reagents (bidistilled water, nitric acid). Operations carried out during purification (elution, evaporation) practically exclude losses of the target product (chemical yields of Se > 99%). A test purification of 100 g of selenium was carried out using this technique. The efficiency of this technique was confirmed by low background gamma spectrometry of the purified selenium sample. Distribution coefficients of Th, U, Ra and Ac on DOWEX 50W- x 8 cation-exchange resin at different concentrations of selenium and nitric acid were experimentally determinated. Instrumental neutron activation analysis of bidistilled water, deionized water and nitric acid was performed. (orig.) 6. Purification of selenium from thorium, uranium, radium, actinium and potassium impurities for low background measurements Energy Technology Data Exchange (ETDEWEB) Rakhimov, A.V. [Joint Institute for Nuclear Research (JINR), Dubna (Russian Federation); Uzbek Academy of Sciences, Tashkent (Uzbekistan). Inst. of Nuclear Physics (INP AS RUz); Warot, G. [CEA-CNRS, Modane (France). Laboratoire Souterrain de Modane (LSM); Karaivanov, D.V. [Joint Institute for Nuclear Research (JINR), Dubna (Russian Federation); Institute for Nuclear Research and Nuclear Energy (INRNE), Sofia (Bulgaria); Kochetov, O.I.; Lebedev, N.A.; Filosofov, D.V. [Joint Institute for Nuclear Research (JINR), Dubna (Russian Federation); Mukhamedshina, N.M.; Sadikov, I.I. [Uzbek Academy of Sciences, Tashkent (Uzbekistan). Inst. of Nuclear Physics (INP AS RUz) 2013-07-01 A technique of selenium purification from {sup 232}Th, {sup 238}U, {sup 226,228}Ra, {sup 227}Ac and {sup 40}K was developed. This technique is simple to perform and employs a minimum number of highly pure reagents (bidistilled water, nitric acid). Operations carried out during purification (elution, evaporation) practically exclude losses of the target product (chemical yields of Se > 99%). A test purification of 100 g of selenium was carried out using this technique. The efficiency of this technique was confirmed by low background gamma spectrometry of the purified selenium sample. Distribution coefficients of Th, U, Ra and Ac on DOWEX 50W- x 8 cation-exchange resin at different concentrations of selenium and nitric acid were experimentally determinated. Instrumental neutron activation analysis of bidistilled water, deionized water and nitric acid was performed. (orig.) 7. Linear free energy relationship applied to trivalent cations with lanthanum and actinium oxide and hydroxide structure International Nuclear Information System (INIS) Linear free energy relationships for trivalent cations with crystalline M2O3 and, M(OH)3 phases of lanthanides and actinides were developed from known thermodynamic properties of the aqueous trivalent cations, modifying the Sverjensky and Molling equation. The linear free energy relationship for trivalent cations is as ΔGf,MvX0=aMvXΔGn,M3+0+bMvX+βMvXrM3+, where the coefficients aMvX, bMvX, and βMvX characterize a particular structural family of MvX, rM3+ is the ionic radius of M3+ cation, ΔGf,MvX0 is the standard Gibbs free energy of formation of MvX and ΔGn,M3+0 is the standard non-solvation free energy of the cation. The coefficients for the oxide family are: aMvX=0.2705, bMvX=-1984.75 (kJ/mol), and βMvX=197.24 (kJ/molnm). The coefficients for the hydroxide family are: aMvX=0.1587, bMvX=-1474.09 (kJ/mol), and βMvX=791.70 (kJ/molnm). 8. Actinium: A RESTful Runtime Container for Scriptable Internet of Things Applications OpenAIRE Kovatsch, Matthias; Lanter, Martin; Duquennoy, Simon 2012-01-01 Programming Internet of Things (IoT) applications is challenging because developers have to be knowledgeable in various technical domains, from low-power networking, over embedded operating systems, to distributed algorithms. Hence, it will be challenging to find enough experts to provide software for the vast number of expected devices, which must also be scalable and particularly safe due to the connection to the physical world. To remedy this situation, we propose an architecture that pr... 9. Reflection asymmetry in odd-A and odd-odd actinium nuclei International Nuclear Information System (INIS) Theoretical calculations and measurements indicate that octupole correlations are at a maximum in the ground states of the odd-proton nuclei Ac and Pa. It has been expected that odd-odd nuclei should have even larger amount of octupole-octupole correlations. We have recently made measurements on the structure of 224Ac. Although spin and parity assignments could not be made, two bands starting at 354.1 and 360.0 keV have properties characteristic of reflection asymmetric shape. These two bands have very similar rotational constants and also similar alpha decay rates, which suggest similarity between the wavefunctions of these bands. These signatures provide evidence for octupole correlations in these nuclides 10. Bestimmung der Ionisationsenergie von Actinium und Ultraspurenanalyse von Plutonium mit resonanter Ionisationsmassenspektrometrie (RIMS) OpenAIRE Waldek, Achim Marcus 2001-01-01 ZusammenfassungDie Resonanzionisationsmassenspektrometrie (RIMS) verbindet hohe Elementselektivität mit guter Nachweiseffizienz. Aufgrund dieser Eigenschaften ist die Methode für Ultraspurenanalyse und Untersuchungen an seltenen oder schwer handhabbaren Elementen gut geeignet. Für RIMS werden neutrale Atome mit monochromatischem Laserlicht ein- oder mehrfach resonant auf energetisch hoch liegende Niveaus angeregt und anschließend durch einen weiteren Laserstrahl oder durch ein elektrisches Fe... 11. New method for large scale production of medically applicable Actinium-225 and Radium-223 International Nuclear Information System (INIS) Alpha-emitters (211At, 212Bi, 213Bi, 223Ra, 225Ac) are promising for targeted radiotherapy of cancer. Only two alpha decays near a cell membrane result in 50% death of cancer cell and only a single decay inside the cell is required for this. 225Ac may be used either directly or as a mother radionuclide in 213Bi isotope generator. Production of 225Ac is provided by three main suppliers - Institute for Transuranium Elements in Germany, Oak Ridge National Laboratory in USA and Institute of Physics and Power Engineering in Obninsk, Russia. The current worldwide production of 225Ac is approximately 1.7 Ci per year that corresponds to only 100-200 patients that could be treated annually. The common approach for 225Ac production is separation from mother 229Th or irradiation of 226Ra with protons in a cyclotron. Both the methods have some practical limitations to be applied routinely. 225Ac can be also produced by irradiation of natural thorium with medium energy protons . Cumulative cross sections of 225Ac, 227Ac, 227Th, 228Th formations have been obtained recently. Thorium targets (1-9 g) were irradiated by 114-91 MeV proton beam (1-50 μA) at INR linear accelerator. After dissolution in 8 M HNO3 + 0.004 M HF thorium was removed by double LLX by HDEHP in toluene (1:1). Ac and REE were pre-concentrated and separated from Ra and most fission products by DGA-Resin (Triskem). After washing out by 0.01 M HNO3 Ac was separated from REE by TRU Resin (Triskem) in 3 M HNO3 media. About 6 mCi 225Ac were separated in hot cell with chemical yield 85%. The method may be upscaled for production of Ci amounts of the radionuclide. The main impurity is 227Ac (0.1% at the EOB) but it does not hinder 225Ac from being used for medical 225Ac/213Bi generators. (author) 12. Food Additives of Public Concern for their Carcinogenicity OpenAIRE Fatih Gultekin 2015-01-01 No-Observed-Adverse Effect Level (NOAEL) of food additives has been long determined on the basis of toxicological studies. Acceptable Daily Intake (ADI) levels of food additives for human are derived from these NOAEL, and their legal limits are then established for the food products, intentionally added with food additives. However, recent studies demonstrated that consumption of some processed food containing certain food additives might have increased the risk of cancer in human although th... 13. Conception pour la fabrication additive, application à la technologie EBM OpenAIRE Vayre, Benjamin 2014-01-01 Nowadays, the use of Additive Manufacturing processes keeps growing in the industry. Among the numerous kinds of AM processes, metallic additive manufacturing processes, and metallic Additive Layer Manufacturing in particular, are the most interesting from a mechanical designer point of view. Several research studies have been conducted on the topic of Design For Additive Manufacturing, mostly discussing the choice of AM processes or presenting the redesign of parts. There is no specific desi... 14. 77 FR 72268 - Rules Relating to Additional Medicare Tax Science.gov (United States) 2012-12-05 ... Internal Revenue Service 26 CFR Parts 1 and 31 RIN 1545-BK54 Rules Relating to Additional Medicare Tax... Insurance Tax on income above threshold amounts (Additional Medicare Tax''), as added by the Affordable... relating to the implementation of Additional Medicare Tax. This document also contains proposed... 15. 7 CFR 27.25 - Additional samples of cotton; drawing. Science.gov (United States) 2010-01-01 ... 7 Agriculture 2 2010-01-01 2010-01-01 false Additional samples of cotton; drawing. 27.25 Section... CONTAINER REGULATIONS COTTON CLASSIFICATION UNDER COTTON FUTURES LEGISLATION Regulations Inspection and Samples § 27.25 Additional samples of cotton; drawing. In addition to the samples hereinbefore... 16. Continuous subjective expected utility with non-additive probabilities NARCIS (Netherlands) P.P. Wakker (Peter) 1989-01-01 textabstractA well-known theorem of Debreu about additive representations of preferences is applied in a non-additive context, to characterize continuous subjective expected utility maximization for the case where the probability measures may be non-additive. The approach of this paper does not need 17. 21 CFR 570.38 - Determination of food additive status. Science.gov (United States) 2010-04-01 ... 21 Food and Drugs 6 2010-04-01 2010-04-01 false Determination of food additive status. 570.38 Section 570.38 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) ANIMAL DRUGS, FEEDS, AND RELATED PRODUCTS FOOD ADDITIVES Food Additive Safety §... 18. 48 CFR 1246.101-70 - Additional definitions. Science.gov (United States) 2010-10-01 ... or ceiling price for fixed price incentive contracts (see (FAR) 48 CFR 46.707), or at no increase in... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Additional definitions... CONTRACT MANAGEMENT QUALITY ASSURANCE General 1246.101-70 Additional definitions. At no additional cost... 19. INFLUENCES OF BLAECHING ADDITIVES ON REED PULP FAST BLEACHING Institute of Scientific and Technical Information of China (English) Yanjun Tang; Bingyue Liu; Runan Yang; Zheng Lu 2004-01-01 The influences of bleaching additives on hypochlorite single-stage high temperature fast bleaching of neutral-sulfite reed pulp were studied. The influencing factors of bleaching velocity and result were as follows: the order and time of adding imide type additives, additives dosage, the dosage of NaOH and MgO used as buffer to turn up pH. 20. 76 FR 78866 - Nexira; Filing of Food Additive Petition Science.gov (United States) 2011-12-20 ... HUMAN SERVICES Food and Drug Administration 21 CFR Part 172 Nexira; Filing of Food Additive Petition... Administration (FDA) is announcing that Nexira has filed a petition proposing that the food additive regulations... given that a food additive petition (FAP 1A4784) has been filed by Nexira, c/o Keller and Heckman... 1. 77 FR 53801 - Nexira; Filing of Food Additive Petition; Amendment Science.gov (United States) 2012-09-04 ... Register on December 20, 2011 (76 FR 78866), FDA announced that a food additive petition (FAP 1A4784) had... HUMAN SERVICES Food and Drug Administration 21 CFR Part 172 Nexira; Filing of Food Additive Petition... Administration (FDA) is amending the filing notice for a food additive petition filed by Nexira proposing... 2. 77 FR 5201 - Ecolab, Inc.; Filing of Food Additive Petition Science.gov (United States) 2012-02-02 ... additive regulations in 21 CFR part 173, Secondary Direct Food Additives Permitted in Food for Human... HUMAN SERVICES Food and Drug Administration 21 CFR Part 173 Ecolab, Inc.; Filing of Food Additive... Administration (FDA) is announcing that Ecolab, Inc., has filed a petition proposing that the food... 3. 78 FR 14664 - Food and Color Additives; Technical Amendments Science.gov (United States) 2013-03-07 ... and Color Additives; Technical Amendments AGENCY: Food and Drug Administration, HHS. ACTION: Final... regulations regarding food and color additives to correct minor errors (such as misspelled chemical names) and... Subjects 21 CFR Part 73 Color additives, Cosmetics, Drugs, Medical devices. 21 CFR Part 172 Food... 4. 21 CFR 81.1 - Provisional lists of color additives. Science.gov (United States) 2010-04-01 ... 21 Food and Drugs 1 2010-04-01 2010-04-01 false Provisional lists of color additives. 81.1 Section..., AND COSMETICS § 81.1 Provisional lists of color additives. The Commissioner of Food and Drugs finds... provisionally listed for food, drug, and cosmetic use. Color additive Closing date Food use Drug and... 5. Additional Raman Scattering Mechanism due to Transverse Polar Modes Institute of Scientific and Technical Information of China (English) CHENG Ze 2001-01-01 Longitudinal polar modes generate a macroscopic electric field in piezoelectric crystals and cause an additional mechanism of Raman scattering. The classical theory holds that transverse polar modes cannot produce such an additional mechanism. Our quantum theory shows that there is an additional Raman scattering mechanism arising from the electro-optic effect of transverse polar modes. 6. 39 CFR 447.42 - Additional prohibited political activities. Science.gov (United States) 2010-07-01 ... with the public or be in the view of the public; (3) Display a political picture or sticker on his... 39 Postal Service 1 2010-07-01 2010-07-01 false Additional prohibited political activities. 447.42... Political Activities § 447.42 Additional prohibited political activities. (a) In addition to... 7. 14 CFR 1203.406 - Additional classification factors. Science.gov (United States) 2010-01-01 ... 14 Aeronautics and Space 5 2010-01-01 2010-01-01 false Additional classification factors. 1203.406... PROGRAM Guides for Original Classification § 1203.406 Additional classification factors. In determining the appropriate classification category, the following additional factors should be considered:... 8. 42 CFR 410.64 - Additional preventive services. Science.gov (United States) 2010-10-01 ... 42 Public Health 2 2010-10-01 2010-10-01 false Additional preventive services. 410.64 Section 410... Additional preventive services. (a) Medicare Part B pays for additional preventive services not otherwise... Act) that these services are all of the following: (1) Reasonable and necessary for the prevention... 9. 32 CFR 643.51 - Additional items concerning leasing. Science.gov (United States) 2010-07-01 ... 32 National Defense 4 2010-07-01 2010-07-01 true Additional items concerning leasing. 643.51... PROPERTY REAL ESTATE Leases § 643.51 Additional items concerning leasing. In addition to the general and... leasing of Army real estate.... 10. 29 CFR 2570.39 - Opportunities to submit additional information. Science.gov (United States) 2010-07-01 ... 29 Labor 9 2010-07-01 2010-07-01 false Opportunities to submit additional information. 2570.39... Prohibited Transaction Exemption Applications § 2570.39 Opportunities to submit additional information. (a) An applicant may notify the Department of its intent to submit additional information supporting... 11. Food Additives of Public Concern for their Carcinogenicity Directory of Open Access Journals (Sweden) Fatih Gultekin 2015-08-01 Full Text Available No-Observed-Adverse Effect Level (NOAEL of food additives has been long determined on the basis of toxicological studies. Acceptable Daily Intake (ADI levels of food additives for human are derived from these NOAEL, and their legal limits are then established for the food products, intentionally added with food additives. However, recent studies demonstrated that consumption of some processed food containing certain food additives might have increased the risk of cancer in human although the legal limits of these additives in processed foods are well respected by the manufacturers. Possible reasons for increased carcinogenicity risk in processed foods containing these additives can be due to various factors: -interaction of additives with some food ingredients, -food processing may change the chemical formula of food additive to a formula to be acting similarly as carcinogenic compound, -a negative synergistic effects when combined with other additives, -improper storage conditions, and -unknown carcinogenic by-products occurring during the food processing. Due to the above mentioned factors we recommend that an additive, intentionally added to the food during processing must be traced officially for its carcinogenicity. In this review, we overviewed all of the food additives authorized in European Union. Therefore, the traceability issues of processed foods containing certain food additives, which have a negligible probability of carcinogenicity in legal limits, must be reinforced in the perspective of public health concerns. 12. A Study of Additional Costs of Second Language Instruction. Science.gov (United States) McEwen, Nelly A study was conducted whose primary aim was to identify and explain additional costs incurred by Alberta, Canada school jurisdictions providing second language instruction in 1980. Additional costs were defined as those which would not have been incurred had the second language program not been in existence. Three types of additional costs were… 13. 27 CFR 24.233 - Addition of spirits to wine. Science.gov (United States) 2010-04-01 ... wine. 24.233 Section 24.233 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS WINE Spirits § 24.233 Addition of spirits to wine. (a) Prior to the addition of spirits. Wine will be placed in tanks approved for the addition of spirits.... 14. 21 CFR 71.4 - Samples; additional information. Science.gov (United States) 2010-04-01 ... samples of the color additive, articles used as components thereof, or of the food, drug, or cosmetic in... additive, or articles used as components thereof, or of the food, drug, or cosmetic in which the color... respect to the safety of the color additive or the physical or technical effect it produces. The date... 15. 77 FR 2935 - Mars, Inc.; Filing of Color Additive Petition Science.gov (United States) 2012-01-20 ... HUMAN SERVICES Food and Drug Administration 21 CFR Part 73 Mars, Inc.; Filing of Color Additive Petition... Administration (FDA) is announcing that Mars, Inc., has filed a petition proposing that the color additive... additive petition (CAP 2C0293) has been filed by Mars, Inc., c/o Keller and Heckman LLP, 1001 G St.... 16. 44 CFR 61.16 - Probation additional premium. Science.gov (United States) 2010-10-01 ... 44 Emergency Management and Assistance 1 2010-10-01 2010-10-01 false Probation additional premium... COVERAGE AND RATES § 61.16 Probation additional premium. The additional premium charged pursuant to § 59.24... premium charge is$50.00.”...
DEFF Research Database (Denmark)
Fuglsang, G; Madsen, G; Halken, S;
1994-01-01
, rhinitis, or urticaria. After a 2-week period on an additive-free diet, the children were challenged with the eliminated additives. The food additives investigated were coloring agents, preservatives, citric acid, and flavoring agents. Carbonated "lemonade" containing the dissolved additives was used...... dermatitis, asthma, urticaria, gastrointestinal symptoms), and citric acid (atopic dermatitis, gastrointestinal symptoms). The incidence of intolerance of food additives was 2% (6/335), as based on the double-blind challenge, and 7% (23/335), as based on the open challenge with lemonade. Children with atopic...
DEFF Research Database (Denmark)
Fuglsang, G.; Madsen, Charlotte Bernhard; Halken, S.;
1994-01-01
, rhinitis, or urticaria. After a 2-week period on an additive-free diet, the children were challenged with the eliminated additives. The food additives investigated were coloring agents, preservatives, citric acid, and flavoring agents. Carbonated ''lemonade'' containing the dissolved additives was used...... dermatitis, asthma, urticaria, gastrointestinal symptoms), and citric acid (atopic dermatitis, gastrointestinal symptoms). The incidence of intolerance of food additives was 2% (6/335), as based on the double-blind challenge, and 7% (23/335), as based on the open challenge with lemonade. Children with atopic...
19. The behaviour of molybdenum dialkyldithiocarbamate friction modifier additives
CERN Document Server
Graham, J C H
2001-01-01
In recent years there has been growing concern to produce energy-efficient lubricated components and modem engine oil specifications require lubricants to demonstrate fuel efficiency in standardised engine tests. One important method of producing low friction and thus fuel-efficient lubricants is to use oil-soluble, molybdenum-containing, friction modifier additives. In optimal conditions these additives are able to produce very low friction coefficients, in the range 0.045 to 0.075 in boundary lubrication conditions. Very little is known about the chemical and physical mechanisms by which oil soluble molybdenum additives form low friction films in tribological contacts. Information about their activity could lead to optimal use of these additives in lubricants and, therefore, more efficient engine running. The work outlined in this thesis investigated the behaviour of oil-soluble molybdenum additives and showed that these additives were able to effectively reduce friction in the absence of other additives su...
20. 27 CFR 19.318 - Addition of caramel to rum or brandy and addition of oak chips to spirits.
Science.gov (United States)
2010-04-01
... or brandy and addition of oak chips to spirits. 19.318 Section 19.318 Alcohol, Tobacco Products and... PLANTS Production § 19.318 Addition of caramel to rum or brandy and addition of oak chips to spirits... prior to production gauge. Oak chips which have not been treated with any chemical may be added...
1. 27 CFR 19.343 - Addition of oak chips to spirits and addition of caramel to brandy and rum.
Science.gov (United States)
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Addition of oak chips to... PLANTS Storage § 19.343 Addition of oak chips to spirits and addition of caramel to brandy and rum. Oak chips which have not been treated with any chemical may be added to packages either prior to or...
Directory of Open Access Journals (Sweden)
Dana Urminská
2010-11-01
3. Versatility of cooperative transcriptional activation: a thermodynamical modeling analysis for greater-than-additive and less-than-additive effects.
Directory of Open Access Journals (Sweden)
Till D Frank
4. RAPID TEST METHOD FOR EVALUATION OF ANTIFREEZE ADDITIVE EFFICIENCY
Directory of Open Access Journals (Sweden)
S. V. Gushchin
2015-01-01
5. Experimental Study of Additives on Viscosity biodiesel at Low Temperature
Science.gov (United States)
Fajar, Berkah; Sukarno
2015-09-01
An experimental investigation was performed to find out the viscosity of additive and biodiesel fuel mixture in the temperature range from 283 K to 318 K. Solutions to reduce the viscosity of biodiesel is to add the biodiesel with some additive. The viscosity was measured using a Brookfield Rheometer DV-II. The additives were the generic additive (Diethyl Ether/DDE) and the commercial additive Viscoplex 10-330 CFI. Each biodiesel blends had a concentration of the mixture: 0.0; 0.25; 0.5; 0.75; 1.0; and 1.25% vol. Temperature of biodiesel was controlled from 40°C to 0°C. The viscosity of biodiesel and additive mixture at a constant temperature can be approximated by a polynomial equation and at a constant concentration by exponential equation. The optimum mixture is at 0.75% for diethyl ether and 0.5% for viscoplex.
6. Enhancement of Corrosion Resistance of Zinc Coatings Using Green Additives
Science.gov (United States)
Punith Kumar, M. K.; Srivastava, Chandan
2014-10-01
In the present work, morphology, microstructure, and electrochemical behavior of Zn coatings containing non-toxic additives have been investigated. Zn coatings were electrodeposited over mild steel substrates using Zn sulphate baths containing four different organic additives: sodium gluconate, dextrose, dextrin, and saccharin. All these additives are "green" and can be derived from food contents. Morphological and structural characterization using electron microscopy, x-ray diffraction, and texture co-efficient analysis revealed an appreciable alteration in the morphology and texture of the deposit depending on the type of additive used in the Zn plating bath. All the Zn coatings, however, were nano-crystalline irrespective of the type of additive used. Polarization and electrochemical impedance spectroscopic analysis, used to investigate the effect of the change in microstructure and morphology on corrosion resistance behavior, illustrated an improved corrosion resistance for Zn deposits obtained from plating bath containing additives as compared to the pure Zn coatings.
7. Pricing of additional features in mobile telecommunication networks
OpenAIRE
Reijonen, Antti
2014-01-01
In this Master's thesis are investigated different pricing strategies for additional features in Mobile Telecommunication Networks (MTN). Pricing is studied from three different perspectives (i) MTN equipment vendor costs (ii) MTN operator value from additional features and (iii) end user benefits from additional features. In the MTN industry value is formed from hundreds of different variables and the MTN operators are varying significantly on size and business concept. In this Master's thes...
8. POTENTIAL HAZARDS DUE TO FOOD ADDITIVES IN ORAL HYGIENE PRODUCTS
OpenAIRE
Damla TUNCER-BUDANUR; Murat Cengizhan YAŞ; SEPET, Elif
2016-01-01
Food additives used to preserve flavor or to enhance the taste and appearance of foods are also available in oral hygiene products. The aim of this review is to provide information concerning food additives in oral hygiene products and their adverse effects. A great many of food additives in oral hygiene products are potential allergens and they may lead to allergic reactions such as urticaria, contact dermatitis, rhinitis, and angioedema. Dental practitioners, as w...
9. 21 CFR 70.45 - Allocation of color additives.
Science.gov (United States)
2010-04-01
... 21 Food and Drugs 1 2010-04-01 2010-04-01 false Allocation of color additives. 70.45 Section 70.45 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES GENERAL COLOR ADDITIVES Safety Evaluation § 70.45 Allocation of color additives. Whenever, in the consideration of a petition or a proposal to list a color...
10. Invariance principle for additive functionals of Markov chains
OpenAIRE
Kartashov, Yuri N.; Kulik, Alexey M.
2007-01-01
We consider a sequence of additive functionals {\\phi_n}, set on a sequence of Markov chains {X_n} that weakly converges to a Markov process X. We give sufficient condition for such a sequence to converge in distribution, formulated in terms of the characteristics of the additive functionals, and related to the Dynkin's theorem on the convergence of W-functionals. As an application of the main theorem, the general sufficient condition for convergence of additive functionals in terms of transit...
11. Effect of Rare Earth Additives on Chrome-Plating Quality
Institute of Scientific and Technical Information of China (English)
Feng Lajun; Lei Ali; Fan Juhong
2005-01-01
The effect of rare earth additives used in chrome-plating on the electroplated coating behaviors of the luminosity, brightness, dispersibility of plating solution, deposition rate of ion and current efficiency were studied systemically by means of measuring cathode current at 20 and 50 ℃ respectively. The results show that rare earth additives increase the luminosity and brightness of the electroplated coating, dispersibility of plating solution, deposition rate of ion and current efficiency at 50 ℃. At 20 ℃, rare earth additives only increase the current efficiency and ion deposition rate. The most effective rare earth oxides additives are Pr6O11 and CeO2.
12. Electrodeposition of Asphaltenes. 2. Effect of Resins and Additives
DEFF Research Database (Denmark)
Khvostichenko, Daria S; Andersen, Simon Ivar
2010-01-01
Electrodeposition of asphaltenes from oil/heptane, asphaltene/heptane, and asphaltene/heptane/additive mixtures has been investigated. Toluene, native petroleum resins, and a synthetic asphaltene dispersant, p-nonylphenol, were used as additives. The addition of these components led to partial...... of preparation of the mixture and the toluene content. Introduction of petroleum resins into asphaltene/heptane mixtures resulted in neutralization of the asphaltene particle charge. The addition of p-nonylphenol to asphaltene suspensions in heptane did not alter the charge of asphaltene particles. Current...
13. Additive Manufacturing: Multi Material Processing and Part Quality Control
OpenAIRE
Pedersen, David Bue; De Chiffre, Leonardo; Hansen, Hans Nørgaard
2013-01-01
Denne Ph.D afhandling,?Additive Manufacturing: Multi Material Processing and Part Quality Control?, omhandler additive fremstillingsmetoder, hvilket er en familie af processer der er kendetegnet ved at de er computerstyret, de drager nytte af en høj grad af automation, og de fremstiller emner lagvis ved addition af materiale. To områder af særlig interesse er addreseret i denne afhandling. De er begge forankret i to meget forskellige områder, men tjener fælles formål. At styrke additive frems...
14. 42 CFR 417.592 - Additional benefits requirement.
Science.gov (United States)
2010-10-01
...) General rules. (1) An HMO or CMP that has an APCRP (as determined under § 417.590) greater than its ACR... least equal to the difference between the APCRP and the proposed ACR. (b) Options—(1) Additional... the APCRP and the ACR. (4) Combination of additional benefits and withholding in a stabilization...
15. Transport for a System with Additive Temporal-Spatial Noise
Institute of Scientific and Technical Information of China (English)
LI Jing-Hui; HAN Yin-Xia; CHEN Shi-Gang
2004-01-01
In this paper, we study the transport of the system with the additive temporal-spatial noise, by two models, i.e., a spatial asymmetry model and a spatial symmetry model. The study shows that the correlation of the additive noise with the space and the spatial asymmetry are ingredients for the transport.
16. 78 FR 71468 - Rules Relating to Additional Medicare Tax
Science.gov (United States)
2013-11-29
...-130074-11) was published in the Federal Register (77 FR 72268) on December 5, 2012. A public hearing was... Internal Revenue Service 26 CFR Parts 1 and 31 RIN 1545-BK54 Rules Relating to Additional Medicare Tax... contains final regulations relating to Additional Hospital Insurance Tax on income above threshold...
17. 78 FR 6272 - Rules Relating to Additional Medicare Tax; Correction
Science.gov (United States)
2013-01-30
..., December 5, 2012 (77 FR 72268). The proposed regulations are relating to Additional Hospital Insurance Tax... proposed rulemaking and notice of public hearing (REG-130074-11), that was the subject of FR Doc. 2012... Internal Revenue Service 26 CFR Part 1 RIN 1545-BK54 Rules Relating to Additional Medicare Tax;...
18. Test report - caustic addition system operability test procedure
International Nuclear Information System (INIS)
This Operability Test Report documents the test results of test procedure WHC-SD-WM-OTP-167 ''Caustic Addition System Operability Test Procedure''. The Objective of the test was to verify the operability of the 241-AN-107 Caustic Addition System. The objective of the test was met
19. 47 CFR 32.4520 - Additional paid-in capital.
Science.gov (United States)
2010-10-01
... 47 Telecommunication 2 2010-10-01 2010-10-01 false Additional paid-in capital. 32.4520 Section 32... Additional paid-in capital. (a) This account shall include the difference between the net proceeds (including discount, premium and stock issuance expense) received from the issuance of capital stock and the...
20. 14 CFR 135.421 - Additional maintenance requirements.
Science.gov (United States)
2010-01-01
... 14 Aeronautics and Space 3 2010-01-01 2010-01-01 false Additional maintenance requirements. 135.421 Section 135.421 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF... Maintenance, Preventive Maintenance, and Alterations § 135.421 Additional maintenance requirements. (a)...
NARCIS (Netherlands)
Trip, Albert; Wieringa, Jaap E.
2003-01-01
Some authors recommend the use of an additional test for detecting increases in the spread, when using a control chart for individual observations. We examine this recommendation both in a practical situation and theoretically. Both studies show that the additional test gives somewhat more power for
2. 20 CFR 655.154 - Additional positive recruitment.
Science.gov (United States)
2010-04-01
... 20 Employees' Benefits 3 2010-04-01 2010-04-01 false Additional positive recruitment. 655.154... recruitment. (a) Where to conduct additional positive recruitment. The employer must conduct positive recruitment within a multistate region of traditional or expected labor supply where the CO finds that...
3. A Comonotonic Image of Independence for Additive Risk Measures
NARCIS (Netherlands)
M.J. Goovaerts; R. Kaas; R.J.A. Laeven; Q. Tang
2004-01-01
This paper presents a new axiomatic characterization of risk measures that are additive for independent random variables. In contrast to previous work, we include an axiom that guarantees monotonicity of the risk measure. Furthermore, the axiom of additivity for independent random variables is relat
4. Surface texture metrology for metal additive manufacturing: a review
OpenAIRE
Townsend, Andrew; N.Senin; Blunt, Liam; Leach, R.K.; Taylor, J. S.
2016-01-01
A comprehensive analysis of literature pertaining to surface texture metrology for metal additive manufacturing has been performed. This review paper structures the results of this analysis into sections that address specific areas of interest: industrial domain, additive manufacturing processes and materials; types of surface investigated; surface measurement technology and surface texture characterisation. Each section reports on how frequently specific techniques, processes or materials ha...
Directory of Open Access Journals (Sweden)
2004-01-01
6. New addition formula for the little $q$-Bessel functions
OpenAIRE
Bouzeffour, Fethi
2013-01-01
Starting from the addition formula for little $q$-Jacobi polynomials, we derive a new addition formula for the little $q$-Bessel functions. The result is obtained by the use of a limit transition. We also establish a product formula for little $q$-Bessel functions with a positive and symmetric kernel.
7. Ecotoxicological effects of activated carbon addition to sediments.
NARCIS (Netherlands)
Jonker, M.T.O.; Suijkerbuijk, M.P.; Schmitt, H.; Sinnige, T.L.
2009-01-01
Activated carbon (AC) addition is a recently developed technique for the remediation of sediments and soils contaminated with hydrophobic organic chemicals. Laboratory and field experiments have demonstrated that the addition of 3-4% of AC can reduce aqueous concentrations and the bioaccumulation po
8. Anomaly Detection In Additively Manufactured Parts Using Laser Doppler Vibrometery
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Carlos A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-09-29
Additively manufactured parts are susceptible to non-uniform structure caused by the unique manufacturing process. This can lead to structural weakness or catastrophic failure. Using laser Doppler vibrometry and frequency response analysis, non-contact detection of anomalies in additively manufactured parts may be possible. Preliminary tests show promise for small scale detection, but more future work is necessary.
9. Automated addition of Chelex solution to tubes containing trace items
DEFF Research Database (Denmark)
Stangegaard, Michael; Hansen, Thomas Møller; Hansen, Anders Johannes;
2011-01-01
Extraction of DNA from trace items for forensic genetic DNA typing using a manual Chelex based extraction protocol requires addition of Chelex solution to sample tubes containing trace items. Automated of addition of Chelex solution may be hampered by high viscosity of the solution and fast...
Science.gov (United States)
2010-01-01
... 5 Administrative Personnel 1 2010-01-01 2010-01-01 false Additional administrative collection action. 179.218 Section 179.218 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS CLAIMS COLLECTION STANDARDS Salary Offset § 179.218 Additional administrative collection...
Science.gov (United States)
2010-01-01
12. Pyrolysis of Carbonaceous Foundry Sand Additives: Seacoal and Gilsonite
Science.gov (United States)
Seacoal and gilsonite are used by the foundry industry as carbonaceous additives in green molding sands. In this study, pyrolysis was used to simulate the heating conditions that the carbonaceous additives would experience during metal casting. Gas chromatography-mass spectrometry was used to tent...
13. Inhibition behavior of some new mixed additives upon copper electrowinning
Institute of Scientific and Technical Information of China (English)
YU Run-lan; LIU Qing-ming; QIU Guan-zhou; FANG Zheng; TAN Jian-xi; YANG Peng
2008-01-01
14. 5 CFR 532.315 - Additional survey jobs.
Science.gov (United States)
2010-01-01
... 5 Administrative Personnel 1 2010-01-01 2010-01-01 false Additional survey jobs. 532.315 Section... RATE SYSTEMS Determining Rates for Principal Types of Positions § 532.315 Additional survey jobs. (a... add to the required survey jobs the specialized survey jobs listed below opposite the industry...
15. 24 CFR 242.63 - Additional indebtedness and leasing.
Science.gov (United States)
2010-04-01
... 24 Housing and Urban Development 2 2010-04-01 2010-04-01 false Additional indebtedness and leasing. 242.63 Section 242.63 Housing and Urban Development Regulations Relating to Housing and Urban... Requirements § 242.63 Additional indebtedness and leasing. The mortgagor shall not enter into any...
16. Ultrafast Grignard addition reactions in the presence of water
DEFF Research Database (Denmark)
Osztrovszky, Gyorgyi; Holm, Torkil; Madsen, R.
2010-01-01
The addition of allylmagnesium bromide and benzylmagnesium chloride to carbonyl compounds was investigated in the presence of protic reagents such as water and the rate of carbonyl addition was found to be comparable to the rate of protonation by the reagent....
17. 38 CFR 21.8284 - Additional vocational training.
Science.gov (United States)
2010-07-01
... (CONTINUED) VOCATIONAL REHABILITATION AND EDUCATION Vocational Training and Rehabilitation for Certain Children of Vietnam Veterans-Spina Bifida and Covered Birth Defects Vocational Training Program Entrance, Termination, and Resources § 21.8284 Additional vocational training. VA may provide an additional period...
18. Attitude Towards Physics and Additional Mathematics Achievement Towards Physics Achievement
Science.gov (United States)
Veloo, Arsaythamby; Nor, Rahimah; Khalid, Rozalina
2015-01-01
The purpose of this research is to identify the difference in students' attitude towards Physics and Additional Mathematics achievement based on gender and relationship between attitudinal variables towards Physics and Additional Mathematics achievement with achievement in Physics. This research focused on six variables, which is attitude towards…
19. NASA OSMA NDE Program Additive Manufacturing Foundational Effort
Science.gov (United States)
Waller, Jess; Walker, James; Burke, Eric; Wells, Douglas
2016-01-01
NASA is providing key leadership in an international effort linking NASA and non-NASA resources to speed adoption of additive manufacturing (AM) to meet NASA's mission goals. Participants include industry, NASA's space partners, other government agencies, standards organizations and academia. Nondestructive Evaluation (NDE) is identified as a universal need for all aspects of additive manufacturing.
20. Chemistry of Food Additives: Direct and Indirect Effects.
Science.gov (United States)
Pauli, George H.
1984-01-01
The primary component(s), impurities, and degradation products of polysorbate 80, nitrate and nitrite salts, and diethylpyrocarbonate (DEPC) are discussed. Safety considerations related to these food additives are also noted. The chick-edema factor which results from an additive in poultry feed is also discussed. (JN)
1. 33 CFR 101.310 - Additional communication devices.
Science.gov (United States)
2010-07-01
... plan under part 104 of this subchapter. See 33 CFR part 164 for additional information on AIS device... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Additional communication devices... communication devices. (a) Alert Systems. Alert systems, such as the ship security alert system required...
2. 23 CFR 658.11 - Additions, deletions, exceptions, and restrictions.
Science.gov (United States)
2010-04-01
... Division Office. Proposals for addition of routes to the National Network shall be accompanied by an analysis of suitability based on the criteria in § 658.9. (2) Proposals for additions that meet the... will be published in the Federal Register for public comment as a notice of proposed rulemaking...
3. Additively homomorphic encryption with a double decryption mechanism, revisited
NARCIS (Netherlands)
Peter, A.; Kronberg, M.; Trei, W.; Katzenbeisser, S.
2012-01-01
We revisit the notion of additively homomorphic encryption with a double decryption mechanism (DD-PKE), which allows for additions in the encrypted domain while having a master decryption procedure that can decrypt all properly formed ciphertexts by using a special master secret. This type of encryp
4. 46 CFR 401.425 - Provision for additional pilot.
Science.gov (United States)
2010-10-01
... 46 Shipping 8 2010-10-01 2010-10-01 false Provision for additional pilot. 401.425 Section 401.425... REGULATIONS Rates, Charges, and Conditions for Pilotage Services § 401.425 Provision for additional pilot. The... Authority, Ltd., Canada, may require the assignment of two pilots to a ship upon request of the ship or...
5. Probing the "additive effect" in the proline and proline hydroxamic acid catalyzed asymmetric addition of nitroalkanes to cyclic enones.
Science.gov (United States)
Hanessian, Stephen; Govindan, Subramaniyan; Warrier, Jayakumar S
2005-11-01
The effect of chirality and steric bulk of 2,5-disubstituted piperazines as additives in the conjugate addition of 2-nitropropane to cyclohexenone, catalyzed by l-proline, was investigated. Neither chirality nor steric bulk affects the enantioselectivity of addition, which gives 86-93% ee in the presence of achiral and chiral nonracemic 2,5-disubstituted piperazines. Proline hydroxamic acid is shown for the first time to be an effective organocatalyst in the same Michael reaction. PMID:16189834
6. Zinc Addition and its Challenge in Chinese NPP
International Nuclear Information System (INIS)
For primary water stress corrosion cracking mitigation and plant dose rates reduction, soluble zinc acetate will be added to reactor coolant in some new Chinese nuclear power plants in the next several years. In the nuclear power plant with zinc addition to reactor coolant, the effects of zinc on fuel cladding corrosion, fuel with sub-cooled nucleate boiling and corrosion product transport must be taken into account, and zinc implementation risk must be assessed. In order to deal with the challenge caused by zinc addition, some research, such as effect of zinc concentration on primary water stress corrosion cracking in reactor coolant system materials and analysis of corrosion product ion in reactor coolant, are being performed in China. Additionally, a zinc implementation risk assessment procedure will be developed for nuclear power plants. In the paper, the background and benefit/challenge of zinc addition are briefly described, and the work in hand for zinc addition is also summarized. (author)
7. Additive Manufacturing: Multi Material Processing and Part Quality Control
DEFF Research Database (Denmark)
Pedersen, David Bue
-ended. What is to hope is that future research will tie these ends with the emerge of a fully developed system. Additive Multi Material Manufacturing Additive Manufacturing share close family bonds with CNC machine tools. State-of-the-art CNC machine tools of today are multi-axis hybrid machines....... Abendoflathes,mills,grindersinoneplatform. Ifhistoryrepeatitself, hybrid additive manufacturing machines will emerge as the field evolve. It is sought to fuel this, by developing a flexible multi material manufacturing platform that will permit fundamental research towards a second generation additive...... manufacturing system that truly will be a universally applicable manufacturing machine. A desktop sized factory. Not merely the development of such machine is undertaken, also examined is the possibility to additively manufacture complex electromechanical systems, as a step towards being able to autonomously...
8. Quantum field theories on algebraic curves. I. Additive bosons
International Nuclear Information System (INIS)
Using Serre's adelic interpretation of cohomology, we develop a 'differential and integral calculus' on an algebraic curve X over an algebraically closed field k of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on X and prove the corresponding generalized residue theorem. Using the representation theory of the global Heisenberg algebra and lattice Lie algebra, we formulate quantum field theories of additive and charged bosons on an algebraic curve X. These theories are naturally connected with the algebraic de Rham theorem. We prove that an extension of global symmetries (Witten's additive Ward identities) from the k-vector space of rational functions on X to the vector space of additive multi-valued functions uniquely determines these quantum theories of additive and charged bosons.
9. Quantum field theories on algebraic curves. I. Additive bosons
Science.gov (United States)
Takhtajan, Leon A.
2013-04-01
Using Serre's adelic interpretation of cohomology, we develop a differential and integral calculus' on an algebraic curve X over an algebraically closed field k of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on X and prove the corresponding generalized residue theorem. Using the representation theory of the global Heisenberg algebra and lattice Lie algebra, we formulate quantum field theories of additive and charged bosons on an algebraic curve X. These theories are naturally connected with the algebraic de Rham theorem. We prove that an extension of global symmetries (Witten's additive Ward identities) from the k-vector space of rational functions on X to the vector space of additive multi-valued functions uniquely determines these quantum theories of additive and charged bosons.
10. Effects of some polymeric additives on the cocrystallization of caffeine
Science.gov (United States)
Chung, Jihae; Kim, Il Won
2011-11-01
Effects of polymeric additives on the model cocrystallization were examined. The model cocrystal was made from caffeine and oxalic acid, and poly(ethylene glycol) (PEG), poly( L-lactide) (PLLA), poly(ɛ-caprolactone) (PCL), and poly(acrylic acid) (PAA) were the additives. The cocrystals were formed as millimeter-sized crystals without additives, and they became microcrystals with PLLA and PCL, and nanocrystals with PAA. XRD and IR revealed that the cocrystal structure was unchanged despite the strong effects of the additives on the crystal morphology, although some decrease in crystallinity was observed with PAA as confirmed by DSC. The DSC study also showed that the cocrystal melted and recrystallized to form α-caffeine upon heating. The present study verified that the polymeric additives can be utilized to modulate the size and morphology of the cocrystals without interfering the intermolecular interactions essential to the integrity of the cocrystal structures.
11. ADDITIVE-INDUCED ENHANCEMENT OF OPTICAL CLARITY OF POLYACRYLAMIDE HYDROGEL
Institute of Scientific and Technical Information of China (English)
Jeffery Franklin; Zhi Yuan Wang
2003-01-01
The aqueous polymerization of acrylamide and crosslinking with N,N-methylenebisacrylamide afforded hydrogels displaying high levels of light scattering (poor optical clarity). Enhancement of the optical clarity within a polyacrylamide (PAm) hydrogel was accomplished through the implementation of"refractive index matching", Water-soluble additives were utilised to better match the refractive index inhomogeneities throughout a given hydrogel. This resulted in lower light scattering within the system and hence improved clarity. Amino acids, sugars, polymers, and other water-soluble additives such as glycerol were investigated by this methodology. Most additives investigated displayed potential for effectively reducing the light scattering within a PAm hydrogel as a function of increased additive concentration. On increasing the refractive index of the water medium, the overall refractive index of a PAm hydrogel was also observed to increase. This provided a quantitative means of determining the effectiveness of a given additive for improving the optical clarity within a hydrogel.
12. Hybrid Additive Manufacturing Technologies - An Analysis Regarding Potentials and Applications
Science.gov (United States)
Merklein, Marion; Junker, Daniel; Schaub, Adam; Neubauer, Franziska
13. Non-autoclaved aerated concrete with mineral additives
Science.gov (United States)
Il'ina, L. V.; Rakov, M. A.
2016-01-01
Directory of Open Access Journals (Sweden)
Toral R. Patel
2012-01-01
Full Text Available Introduction. Gamma Knife radiosurgery (GK-SRS is commonly used to treat cerebral metastases. Although additional intracranial metastases are often found on the day of GK-SRS, the significance of finding them is unknown. Methods. A retrospective review of 133 patients undergoing GK-SRS for cerebral metastases was performed. The change in number of metastases detected between initial referral magnetic resonance imaging (MRI and subsequent treatment MRI was quantified. Multivariate and Kaplan-Meier analyses were employed to examine the significance of identifying additional lesions. Results. Additional lesions were identified in 41% of patients. An increasing number of metastases on referral MRI (=0.001 and the presence of progressive systemic disease (=0.003 were predictive of identifying additional metastases. Median survival was 6.9 months for patients with additional metastases, compared to 12.1 months for patients without additional metastases (hazard ratio 1.56, =0.021. Conclusions. Identifying additional metastases on the day of GK-SRS may add important prognostic information.
15. Characterization of Starch Edible Films with Different Essential Oils Addition
Directory of Open Access Journals (Sweden)
Šuput Danijela
2016-12-01
Full Text Available This study investigated properties of starch-based edible films with oregano and black cumin essential oil addition. Essential oils addition positively affected film swelling (decreased due to essential oil addition, mechanical properties (tensile strength decreased while elongation at break increased, and water vapor barrier properties (decreased along with essential oils addition. Control film did not have any biological activity, which proves the need for essential oils addition in order to obtain active packaging. Oregano oil was more effective in terms of biological activity. Endothermal peak, above 200°C, represents total thermal degradation of edible films. Diffraction pattern of control film showed significant destruction of A-type crystal structure. Addition of essential oils resulted in peak shape change: diffraction peaks became narrower. Principal Component Analysis has been used to assess the effect of essential oils addition on final starch-based edible films characteristics with the aim to reveal directions for the film characteristics improvement, since the next phase will be optimal film application for food packaging.
16. Production of fresh probiotic cheese with addition of transglutaminase
Directory of Open Access Journals (Sweden)
2007-04-01
17. Efficiency enhancement of dye-sensitized solar cells with addition of additives (single/binary) to ionic liquid electrolyte
H-S Lee; S-H Bae; C-H Han; S S Sekhon
2012-11-01
The effect of addition of single and binary additives on the performance of dye-sensitized TiO2 solar cells based on electrolytes containing an ionic liquid (IL), 1,2-dimethyl-3-propylimidazolium iodide (DMPII) has been studied. Among the seven additives used, the addition of 2-(dimethylamino)-pyridine (DMAP) to IL resulted in best cell efficiency, which showed further enhancement with the addition of 5-chloro-1-ethyl-2-methylimidazole (CEMI) as second additive. The efficiency of the dye-sensitized solar cell (DSC) based on an electrolyte containing binary additives (DMAP and CEMI in equal molar ratios) has been found to increase by 62.5% from 4.35 to 7.07%. The dependence of different photovoltaic performance parameters (\\oc, sc, , ) of DSC upon temperature has been studied over a 30–120°C range and only a small decrease in conversion efficiency has been observed. The electrolyte containing binary additives (DMAP and CEMI) shows best cell performance up to 120°C.
18. 37 CFR 1.776 - Calculation of patent term extension for a food additive or color additive.
Science.gov (United States)
2010-07-01
... 37 Patents, Trademarks, and Copyrights 1 2010-07-01 2010-07-01 false Calculation of patent term extension for a food additive or color additive. 1.776 Section 1.776 Patents, Trademarks, and Copyrights UNITED STATES PATENT AND TRADEMARK OFFICE, DEPARTMENT OF COMMERCE GENERAL RULES OF PRACTICE IN PATENT CASES Adjustment and Extension of Patent...
DEFF Research Database (Denmark)
Sørensen, Allan
20. Amine-intercalated α-zirconium phosphates as lubricant additives
International Nuclear Information System (INIS)
In this study, three types of amines intercalated α-zirconium phosphate nanosheets with different interspaces were synthesized and examined as lubricant additives to a mineral oil. Results from tribological experiments illustrated that these additives improved lubricating performance. Results of rheological experiments showed that the viscosity of the mineral oil was effectively reduced with the addition of α-zirconium phosphate nanosheets. The two-dimensional structure, with larger interspaces, resulting from amine intercalation, exhibited improved effectiveness in reducing viscosity. This study demonstrates that the nanosheet structure of α-zirconium phosphates is effective in friction reduction. The manufacture of lubricants with tailored viscosity is possible by using different intercalators
1. Metal-air cell with performance enhancing additive
Energy Technology Data Exchange (ETDEWEB)
Friesen, Cody A; Buttry, Daniel
2015-11-10
Systems and methods drawn to an electrochemical cell comprising a low temperature ionic liquid comprising positive ions and negative ions and a performance enhancing additive added to the low temperature ionic liquid. The additive dissolves in the ionic liquid to form cations, which are coordinated with one or more negative ions forming ion complexes. The electrochemical cell also includes an air electrode configured to absorb and reduce oxygen. The ion complexes improve oxygen reduction thermodynamics and/or kinetics relative to the ionic liquid without the additive.
2. >"Disabilities" of Additional Education for Children with Disabilities in Moscow
Directory of Open Access Journals (Sweden)
Arzhanyh E.V.,
2015-10-01
Full Text Available One of the most significant aspects of social integration of children with special needs is the availability of additional education, which is often the only way to socialize these children. Based on our studies (focus group discussions and a questionnaire survey of 1078 parents of children with special needs we analyzed the limitations of additional education availability for these children according to various criteria (organizational, financial, informational, etc.. Evaluation of the number of children covered by the additional education program leads to the conclusion that the older children are, the harder they get the educational service. The most deprived group are children with intellectual disabilities
3. Basophil Activation Test with Food Additives in Chronic Urticaria Patients
OpenAIRE
Kang, Min-Gyu; Song, Woo-Jung; Park, Han-Ki; Lim, Kyung-Hwan; Kim, Su-Jung; Lee, Suh-Young; Kim, Sae-Hoon; Cho, Sang-Heon; Min, Kyung-Up; Chang, Yoon-Seok
2014-01-01
The role of food additives in chronic urticaria (CU) is still under investigation. In this study, we aimed to explore the association between food additives and CU by using the basophil activation test (BAT). The BAT using 15 common food additives was performed for 15 patients with CU who had a history of recurrent urticarial aggravation following intake of various foods without a definite food-specific IgE. Of the 15 patients studied, two (13.3%) showed positive BAT results for one of the te...
4. Corn fiber hulls as a food additive or animal feed
Science.gov (United States)
Abbas, Charles; Beery, Kyle E.; Cecava, Michael J.; Doane, Perry H.
2010-12-21
The present invention provides a novel animal feed or food additive that may be made from thermochemically hydrolyzed, solvent-extracted corn fiber hulls. The animal feed or food additive may be made, for instance, by thermochemically treating corn fiber hulls to hydrolyze and solubilize the hemicellulose and starch present in the corn fiber hulls to oligosaccharides. The residue may be extracted with a solvent to separate the oil from the corn fiber, leaving a solid residue that may be prepared, for instance by aggolmerating, and sold as a food additive or an animal feed.
5. Dominance of capacities by k-additive belief functions
OpenAIRE
Miranda, Pedro; GRABISCH, Michel; Gil, Pedro
2006-01-01
International audience In this paper we deal with the set of $k$-additive belieffunctions dominating a given capacity. We follow the lineintroduced by Chateauneuf and Jaffray for dominating probabilities and continued by Grabisch for general $k$-additive measures.First, we show that the conditions for the general $k$-additive case lead to a very wide class of functions and this makes that the properties obtained for probabilities are no longer valid. On the other hand, we show that these c...
6. Effect of additive on the formation of polyacrylonitrile membrane
Institute of Scientific and Technical Information of China (English)
YANG Sen; LIU Zhong-zhou
2004-01-01
The effect of additives CaCl2 and CaCl2/H2O on the properties of polyacrylonitrile(PAN) ultrafiltration(UF)membranes prepared by phase inversion process was studied. The dissolving capacity of the casting solution forCaCl2 was enhanced by the addition of H2O. The membranes are characterized in terms of the pure water flux andmolecular weight cut-off( MWCO). The addition of CaCl2 or CaCl2/H2O to the casting solution increases the resultingmembrane permeability.
7. Systematic tests for position-dependent additive shear bias
CERN Document Server
van Uitert, Edo
2016-01-01
We present new tests to identify stationary position-dependent additive shear biases in weak gravitational lensing data sets. These tests are important diagnostics for currently ongoing and planned cosmic shear surveys, as such biases induce coherent shear patterns that can mimic and potentially bias the cosmic shear signal. The central idea of these tests is to determine the average ellipticity of all galaxies with shape measurements in a grid in the pixel plane. The distribution of the absolute values of these averaged ellipticities can be compared to randomized catalogues; a difference points to systematics in the data. In addition, we introduce a method to quantify the spatial correlation of the additive bias, which suppresses the contribution from cosmic shear and therefore eases the identification of a position-dependent additive shear bias in the data. We apply these tests to the publicly available shear catalogues from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) and the Kilo Degree Su...
8. Drag reduction by polymer additives from turbulent spectra.
Science.gov (United States)
Calzetta, Esteban
2010-12-01
We extend the analysis of the friction factor for turbulent pipe flow reported by G. Gioia and P. Chakraborty [Phys. Rev. Lett. 96, 044502 (2006)] to the case where drag is reduced by polymer additives.
9. Porosity of additive manufacturing parts for process monitoring
International Nuclear Information System (INIS)
Some metal additive manufacturing processes can produce parts with internal porosity, either intentionally (with careful selection of the process parameters) or unintentionally (if the process is not well-controlled.) Material porosity is undesirable for aerospace parts - since porosity could lead to premature failure - and desirable for some biomedical implants, since surface-breaking pores allow for better integration with biological tissue. Changes in a part's porosity during an additive manufacturing build may also be an indication of an undesired change in the process. We are developing an ultrasonic sensor for detecting changes in porosity in metal parts during fabrication on a metal powder bed fusion system, for use as a process monitor. This paper will describe our work to develop an ultrasonic-based sensor for monitoring part porosity during an additive build, including background theory, the development and detailed characterization of reference additive porosity samples, and a potential design for in-situ implementation
10. Effects of additives on glyphosate activity in purple nutsedge
International Nuclear Information System (INIS)
Effects of additives on 14 C-glyphosate penetration into purple nutsedge leaves were examined in the laboratory and efficacy of glyphosate for purple nutsedge control was studied in the greenhouse and field. The addition of (NH4)2 SO4 at 1.0% (v/v) + diesel oil at 1,0% (v/v) + Tendal at 1.0% (v/v) increased 14C-glyphosate penetration into nutsedge leaves more than the addition of either one alone. (NH4)2SO4 at 1.0% + diesel oil at 1.0% + Tendal at 0.12 or 0.25% increased the phytotoxicity of glyphosate at 0.5 and 0.75 kg, a.e./ha on nutsedge plants in the greenhouse but not in the field. Additives did not enhance glyphosate activity by reducing the number of nutsedae tubers. (author)
Science.gov (United States)
Meerwaldt, J H; Coleman, C N; Fischer, R I; Lister, T A; Diehl, V
1992-09-01
Although radiotherapy is widely used as additional treatment following chemotherapy, its precise role has never been clearly proven. Relapses tend to occur in previously involved bulky sites. Non-randomized studies may suggest a positive effect of the addition of radiotherapy. This effect however, might also be caused by selection. Randomized studies have not resulted in a survival advantage for the patients treated with additional radiotherapy compared to no further treatment or additional chemotherapy. The SWOG study 7808 suggest a 20% benefit in remission duration for the nodular sclerosis histology subgroup. Definitive conclusions have to wait for more mature results of randomized studies including the ongoing EORTC study and the possibility to perform an overview of all studies.
12. In-Process Monitoring of Additive Manufacturing Project
Data.gov (United States)
National Aeronautics and Space Administration — The key innovation in this project is the implementation of an Imaging Fourier Transform Spectrometer (IFTS) for in situ metal additive manufacturing process...
13. Carbon additives for electrical double layer capacitor electrodes
Science.gov (United States)
Weingarth, D.; Cericola, D.; Mornaghini, F. C. F.; Hucke, T.; Kötz, R.
2014-11-01
Electrochemical double layer capacitors (EDLCs) are inherently high power devices when compared to rechargeable batteries. While capacitance and energy storage ability are mainly increased by optimizing the electrode active material or the electrolyte, the power capability could be improved by including conductive additives in the electrode formulations. This publication deals with the use of four different carbon additives - two carbon blacks and two graphites - in standard activated carbon based EDLC electrodes. The investigations include: (i) physical characterization of carbon powder mixtures such as surface area, press density, and electrical resistivity measurements, and (ii), electrochemical characterization via impedance spectroscopy and cyclic voltammetry of full cells made with electrodes containing 5 wt.% of carbon additive and compared to cells made with pure activated carbon electrodes in organic electrolyte. Improved cell performance was observed in both impedance and cyclic voltammetry responses. The results are discussed considering the main characteristics of the different carbon additives, and important considerations about electrode structure and processability are drawn.
14. Nanofibrillated cellulose as an additive in papermaking process: A review.
Science.gov (United States)
Boufi, Sami; González, Israel; Delgado-Aguilar, Marc; Tarrès, Quim; Pèlach, M Àngels; Mutjé, Pere
2016-12-10
During the last two decades, cellulose nanofibres (CNF) have emerged as a promising, sustainable reinforcement with outstanding potential in material sciences. Though application of CNF in papermaking is recent, it is expected to find implementation in the near future to give a broader commercial market to this type of cellulose. The present review highlights recent progress in the field of the application of cellulose nanofibres as additives in papermaking. The effect of CNF addition on the wet end process is analysed according to the type of pulp used for papermaking. According to the literature consulted, improvement in paper's overall properties after CNF addition depended not only on the type and amount of CNF applied, but also in the pulp's origin and treatment. Bulk and surface application of CNF also presented significant differences regarding paper's final properties. This review also revises the mechanisms behind CNF reinforcing effect on paper and the effect of chemically modified CNF as additives. PMID:27577906
15. Chemical Mixture Risk Assessment Additivity-Based Approaches
Science.gov (United States)
Powerpoint presentation includes additivity-based chemical mixture risk assessment methods. Basic concepts, theory and example calculations are included. Several slides discuss the use of "common adverse outcomes" in analyzing phthalate mixtures.
16. Cohomology of exact categories and (non-)additive sheaves
CERN Document Server
Kaledin, Dmitry
2011-01-01
We use (non-)additive sheaves to introduce an (absolute) notion of Hochschild cohomology for exact categories as Ext's in a suitable bisheaf category. We compare our approach to various definitions present in the literature.
17. Sub-additivity in Electron Emission from GaAs
Science.gov (United States)
Brunkow, Evan; Clayburn, Nathan; Becker, Maria; Jones, Eric; Batelaan, Herman; Gay, Timothy
2016-05-01
When two spatially-overlapped laser pulses (775 nm center wavelength, 75 fs duration) are incident on an untreated GaAs crystal surface, the electron emission rate depends on the temporal separation between the two pulses. We have shown that for delays between 0.2 and 1000ps, the emission rate is `sub-additive'', i.e., is lower than when the beams have separation >> 1 ns. We believe the cause of this sub-additivity is an increase in reflectance and transmittance due to electrons occupying the excited state of the GaAs. We are now able to manipulate the magnitude of the sub-additivity by changing the number of electrons that are in the excited state. Sub-additivity is not observed with tungsten tip surfaces which have no excited state. Funded by NSF PHY-1505794, EPSCoR IIIA-1430519, and NSF 1306565 (HB).
18. The Influence of Additives on Crystallization of Polyvinyl Chloride
Institute of Scientific and Technical Information of China (English)
LIU Yaqun; ZHANG Chaocan
2007-01-01
Acetanilide, adipic acid and potassium hydrogen phthalate were chosen as nucleating agents of polyvinyl chloride(PVC), and their effects on PVC crystallization were studied by differential scanning calorimetry, wide angle X-ray diffraction and fourier transform infrared spectroscopy. The experimental results indicate that all of the three additives are compatible with PVC to some extent, but adipic acid's compatibility with PVC is less satisfactory. The three additives can improve PVC crystallinity, and acetanilide can decrease PVC glass transition temperature(Tg)and narrow PVC melting range, while adipic acid and potassium hydrogen phthalate rise Tg of PVC and widen its melting range. All additives do not affect PVC crystal system and all samples are in orthorhombic system. All additives can improve (200), (110), (210) and (201, 111) planes growing. Moreover, acetanilide and adipic acid can shrink PVC spacings and improve the crystal perfection of PVC, but potassium hydrogen phthalate swells spacings and reduces the perfection of PVC crystal.
19. Ultrasonic Additive Manufacturing for Lightweight Metallic Structures Project
Data.gov (United States)
National Aeronautics and Space Administration — The goal of this program is to demonstrate the use of UAM to additively build reinforcement structures to reinforce cut outs in larger aluminum structural...
20. Worst-Case Additive Noise in Wireless Networks
CERN Document Server
Shomorony, Ilan
2012-01-01
An important classical result in Information Theory states that the Gaussian noise is the worst-case additive noise in point-to-point channels. In this paper, we significantly generalize this result and show that, under very mild assumptions, Gaussian noise is also the worst-case additive noise in general wireless networks with additive noises that are independent from the transmit signals. More specifically, we prove that, given a coding scheme with finite reading precision for an AWGN network, one can build a coding scheme that achieves the same rates on an additive noise wireless network with the same topology, where the noise terms may have any distribution with same mean and variance as in the AWGN network.
1. Arbitrary orbital angular momentum addition in second harmonic generation
International Nuclear Information System (INIS)
We demonstrate second harmonic generation performed with optical vortices with different topological charges imprinted on orthogonal polarizations. Besides the intuitive charge doubling, we implement arbitrary topological charge addition on the second harmonic field using polarization as an auxiliary parameter. (paper)
2. Laser additive manufacturing of high-performance materials
CERN Document Server
Gu, Dongdong
2015-01-01
This book entitled “Laser Additive Manufacturing of High-Performance Materials” covers the specific aspects of laser additive manufacturing of high-performance new materials components based on an unconventional materials incremental manufacturing philosophy, in terms of materials design and preparation, process control and optimization, and theories of physical and chemical metallurgy. This book describes the capabilities and characteristics of the development of new metallic materials components by laser additive manufacturing process, including nanostructured materials, in situ composite materials, particle reinforced metal matrix composites, etc. The topics presented in this book, similar as laser additive manufacturing technology itself, show a significant interdisciplinary feature, integrating laser technology, materials science, metallurgical engineering, and mechanical engineering. This is a book for researchers, students, practicing engineers, and manufacturing industry professionals interested i...
3. Ultrasonography as a diagnostic method in addition to mammography
Energy Technology Data Exchange (ETDEWEB)
Otto, H.; Roer, E.
1988-05-01
By using ultrasonography in addition to mammography, experienced diagnosticians essentially enhance the safety of their diagnosis of mammary gland diseases. The same applies to gynecomastia, the condition after plastic surgery, and mastitis.
4. Ultrasonography as a diagnostic method in addition to mammography
International Nuclear Information System (INIS)
By using ultrasonography in addition to mammography, experienced diagnosticians essentially enhance the safety of their diagnosis of mammary gland diseases. The same applies to gynecomastia, the condition after plastic surgery, and mastitis. (orig.)
5. BIOTECHNOLOGY OF TRICHODERMA-BASED FEED ADDITIVE WITH CELLULOLYTIC PROPERTIES
Directory of Open Access Journals (Sweden)
Koshchayev A. G.
2013-11-01
Full Text Available In the work, we have presented the information of elaboration of a manufacturing process of Mycocel feed additive with the cellulolytic activity for poul-try industry. Manufacturing process includes follow-ing steps: stock culture maintenance and storage of Trichoderma lignorum 81-17, growing fluid culture of microscopic fungus in sucrose yeast extract me-dium, feed additive with cellulolytic properties out-put and quality control, packaging, storage and disposal of waste. We have shown that the Mycocel is non-toxic feed additive for protozoa and warm-blooded animals (laboratory mice and quails. This study demonstrated total population livability in the experimental group with feed additive. Quail body-weight of experimental group was higher by 6% as compared to the control and feed consumption per 1 kg of live weight of bird was 3,58 kg, 7,5% lower than the control
NARCIS (Netherlands)
Baars, G. van; Smeltink, J.; Werff, J. van der; Limpens, M.; Barink, M.; Berg, D. van den; Vreugd, J. de; Witvoet, G.; Galaktionov, O.S.
2015-01-01
This article presents developments of freeform mechatronics concepts, enabled by industrial Additive Manufacturing (AM), aiming at breakthroughs for precision engineering challenges such as lightweight, advanced thermal control, and integrated design. To assess potential impact in future application
7. Assessment of Gasoline Additive Containing Ditert-butoxypropanol
Energy Technology Data Exchange (ETDEWEB)
West, Brian H. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Connatser, Raynella M. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lewis, Samuel Arthur [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2016-04-01
The Fuels, Engines, and Emissions Research Center completed analysis and testing of the CPS Powershot gasoline additive under the auspices of the Department of Energy’s Technical Assistance for US Small Businesses in Vehicle Technologies. Gas chromatography-mass spectrometry (GC-MS) was used to quantify the makeup of the additive, finding a predominance of 2,3-Ditert-Butoxypropanol, also known as Glyceryl Di-Tert-Butyl Ether (GTBE). Blends of the additive at 2 and 4 volume percent were subjected to a number of standard ASTM tests, including Research Octane Number, Motor Octane Number, distillation, and vapor pressure. Results show a high boiling range and low vapor pressure for the additive, and a very modest octane boosting effect in gasoline with and without ethanol.
8. POTENTIAL HAZARDS DUE TO FOOD ADDITIVES IN ORAL HYGIENE PRODUCTS
Directory of Open Access Journals (Sweden)
Damla TUNCER-BUDANUR
2016-04-01
Full Text Available Food additives used to preserve flavor or to enhance the taste and appearance of foods are also available in oral hygiene products. The aim of this review is to provide information concerning food additives in oral hygiene products and their adverse effects. A great many of food additives in oral hygiene products are potential allergens and they may lead to allergic reactions such as urticaria, contact dermatitis, rhinitis, and angioedema. Dental practitioners, as well as health care providers, must be aware of the possibility of allergic reactions due to food additives in oral hygiene products. Proper dosage levels, delivery vehicles, frequency, potential benefits, and adverse effects of oral health products should be explained completely to the patients. There is a necessity to raise the awareness among dental professionals on this subject and to develop a data gathering system for possible adverse reactions.
9. Addition of Cryoprotectant Significantly Alters the Epididymal Sperm Proteome.
Science.gov (United States)
Yoon, Sung-Jae; Rahman, Md Saidur; Kwon, Woo-Sung; Park, Yoo-Jin; Pang, Myung-Geol
2016-01-01
Although cryopreservation has been developed and optimized over the past decades, it causes various stresses, including cold shock, osmotic stress, and ice crystal formation, thereby reducing fertility. During cryopreservation, addition of cryoprotective agent (CPA) is crucial for protecting spermatozoa from freezing damage. However, the intrinsic toxicity and osmotic stress induced by CPA cause damage to spermatozoa. To identify the effects of CPA addition during cryopreservation, we assessed the motility (%), motion kinematics, capacitation status, and viability of epididymal spermatozoa using computer-assisted sperm analysis and Hoechst 33258/chlortetracycline fluorescence staining. Moreover, the effects of CPA addition were also demonstrated at the proteome level using two-dimensional electrophoresis. Our results demonstrated that CPA addition significantly reduced sperm motility (%), curvilinear velocity, viability (%), and non-capacitated spermatozoa, whereas straightness and acrosome-reacted spermatozoa increased significantly (p 3 fold, p ground for sperm cryopreservation. PMID:27031703
10. Porosity of additive manufacturing parts for process monitoring
Science.gov (United States)
Slotwinski, J. A.; Garboczi, E. J.
2014-02-01
Some metal additive manufacturing processes can produce parts with internal porosity, either intentionally (with careful selection of the process parameters) or unintentionally (if the process is not well-controlled.) Material porosity is undesirable for aerospace parts - since porosity could lead to premature failure - and desirable for some biomedical implants, since surface-breaking pores allow for better integration with biological tissue. Changes in a part's porosity during an additive manufacturing build may also be an indication of an undesired change in the process. We are developing an ultrasonic sensor for detecting changes in porosity in metal parts during fabrication on a metal powder bed fusion system, for use as a process monitor. This paper will describe our work to develop an ultrasonic-based sensor for monitoring part porosity during an additive build, including background theory, the development and detailed characterization of reference additive porosity samples, and a potential design for in-situ implementation.
11. Computing Additive Chained Volume Measures of GDP Subaggregates
OpenAIRE
Dumagan, Jesus C.
2010-01-01
This paper derives formulas for additive "chained volume measures" (CVMs) of GDP subaggregates depending on the underlying GDP quantity index. In turn, this paper explains why the formulas used in current practice yield nonadditive CVMs. This paper's additive formulas have significant practical implications given that nonadditivity prevails in all countries that have adopted the CVM framework for GDP and considering that more countries will be adopting this framework.
12. The private capacity of quantum channels is not additive
OpenAIRE
Li, Ke; Winter, Andreas; Zou, Xubo; Guo, Guangcan
2009-01-01
Recently there has been considerable activity on the subject of additivity of various quantum channel capacities. Here, we construct a family of channels with sharply bounded classical, hence private capacity. On the other hand, their quantum capacity when combined with a zero private (and zero quantum) capacity erasure channel, becomes larger than the previous classical capacity. As a consequence, we can conclude for the first time that the classical private capacity is non-additive. In fact...
13. Marginal integration $M-$estimators for additive models
OpenAIRE
Boente, Graciela; Martinez, Alejandra
2015-01-01
Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal univariate rate. Beyond backfitting, marginal integration is a common procedure to estimate each component. In this paper, we propose a robust estimator of the additive components which combines local polynomials on the component to be estimated and marginal int...
14. Antiwear and antioxidant studies of cardanol phosphate ester additives
OpenAIRE
S. E. Mazzetto; L. D. M. Oliveira; D. Lomonaco; P. A. Veloso
2012-01-01
In the search for new applications and products derived from Cashew Nut Shell Liquid (CNSL), we report herein the synthesis and characterization (GC/MS and ¹H, 13C, and 31P NMR) of four phosphate esters derived from hydrogenated cardanol, including their applications as antiwear additives for diesel (S500) and as antioxidant additives for mineral oils, evaluated through the HFRR test and oxidative stability analyses, respectively. The results obtained showed very good to excellent performance...
15. Current fluctuations in nonequilibrium diffusive systems: an additivity principle.
Science.gov (United States)
Bodineau, T; Derrida, B
2004-05-01
We formulate a simple additivity principle allowing one to calculate the whole distribution of current fluctuations through a large one dimensional system in contact with two reservoirs at unequal densities from the knowledge of its first two cumulants. This distribution (which in general is non-Gaussian) satisfies the Gallavotti-Cohen symmetry and generalizes the one predicted recently for the symmetric simple exclusion process. The additivity principle can be used to study more complex diffusive networks including loops. PMID:15169476
OpenAIRE
Hofmann, Douglas C.; Kolodziejska, Joanna; Roberts, Scott; Otis, Richard; Dillon, Robert Peter; Suh, Jong-ook; Liu, Zi-Kui; Borgonia, John-Paul
2014-01-01
The current work provides an overview of the state-of-the-art in polymer and metal additive manufacturing and provides a progress report on the science and technology behind gradient metal alloys produced through laser deposition. The research discusses a road map for creating gradient metals using additive manufacturing, demonstrates basic science results obtainable through the methodology, shows examples of prototype gradient hardware, and suggests that Compositionally Graded Metals is a...
17. Extraction of Additives from Polystyrene and Subsequent Analysis
OpenAIRE
Smith, Susan H.
1998-01-01
The extraction of fifteen (15) polymer additives with supercritical carbon dioxide which are used as antioxidants, uv stabilizers, process lubes, flame retardants and antistats from eight formulations of polystyrene is demonstrated and compared to traditional dissolution/precipitation extractions. The purpose of the study was twofold: 1) the development of a high performance liquid chromatography (HPLC) method(s) for the additives and 2) the determination of the viability of supercritical...
18. Further Results on Dynamic Additive Hazard Rate Model
Directory of Open Access Journals (Sweden)
Zhengcheng Zhang
2014-01-01
Full Text Available In the past, the proportional and additive hazard rate models have been investigated in the works. Nanda and Das (2011 introduced and studied the dynamic proportional (reversed hazard rate model. In this paper we study the dynamic additive hazard rate model, and investigate its aging properties for different aging classes. The closure of the model under some stochastic orders has also been investigated. Some examples are also given to illustrate different aging properties and stochastic comparisons of the model.
19. A non-additive negotiation model for utility computing markets
OpenAIRE
Macías Lloret, Mario; Guitart Fernández, Jordi
2009-01-01
Market-based resource allocation is a promising model for dealing with the growing Utility Computing environments, such as Grid or Cloud Computing. Agents that represent both service clients and providers meet in a market to negotiate the terms of the sale of resources. Additive negotiation models are extended because they are simple, but they are not valid for negotiations whose terms are not independent between them. This paper proposes a simple non-additive model for performing negotiat...
International Nuclear Information System (INIS)
A study has been made of the influence of additives of thallium on potentials of cadmium amalgams with thallium contents of 10, 20, 30, and 40 at.% at 20, 40, 60, and 80 deg C. Additives of thallium have been found to shift the potential of cadmium amalgams towards the range of negative values which indicates an increase in the activity of cadmium. A possibility of calculation of the potential shift for heterogeneous cadmium amalgams on introducing thallium has been shown
OpenAIRE
Umida Khodjaeva; Tatiana Bojňanská; Vladimír Vietoris; Oksana Sytar
2013-01-01
The main characteristics and classification of food additives, which are common in the food production, have been described in the present review. The ways of food additives classification, source of nature, main antioxidants, food colouring, flavours, flavor enhancers, bulking agents, stabilizers, sweeteners which were collected from literature based on structural and biochemical characteristics with description of source and possible effects on human, organisms and environment have been pre...
2. Enhanced Thermostability of a Fungal Alkaline Protease by Different Additives
OpenAIRE
Nilesh P. Nirmal; R. Seeta Laxman
2014-01-01
A fungal strain (Conidiobolus brefeldianus MTCC 5184) isolated from plant detritus secreted a high activity alkaline protease. Thermostability studies of the fungal alkaline protease (FAP) revealed that the protease is stable up to 50°C with 40% residual activity after one hour. Effect of various additives such as sugars, sugar alcohols, polyols, and salts, on the thermostability of FAP was evaluated. Among the additives tested, glycerol, mannitol, xylitol, sorbitol, and trehalose were found ...
3. Additional Quantum Numbers for Electron Orbitals of Nanoparticles
OpenAIRE
Yarzhemsky, V. G.
2011-01-01
It is shown that in large symmetrical nanoparticles additional quantum numbers are required to label unambiguously symmetry adapted linear combinations of the wave functions. It is obtained that the labels of irreducible representations (IRs) of intermediate subgroups (between the whole symmetry group and local subgroup) can be used for complete classification of states in the case of repeating IRs. The examples of Oh and Ih groups are considered and the connection of additional quantum numbe...
4. The addition spectrum of interacting electrons: Parametric dependence
OpenAIRE
Bonci, Luca; Berkovits, Richard
1999-01-01
The addition spectrum of a disordered stadium is studied for up to 120 electrons using the self consistent Hartree-Fock approximation for different values of the dimensionless conductance and in the presence and absence of a neutralizing background. In all cases a Gaussian distribution of the addition spectrum is reached for $r_s \\leq 1$. An empirical scaling for the distribution width in the presence of a neutralizing background is tested and seems to describe rather well its dependence on t...
5. The natural additive with antioxidant properties for meat products
OpenAIRE
Nikolaevna Savinok, Oksana; Litvinova, Inna; Kuzelov, Aco
2012-01-01
The possibility of apication pf polyfunctional additive with antioxidant properties in meat products ins been considered in the article. The additive has been obtained ass a result of phenol coumpounds and polysacharide combination.The biologically active componenets have been exstracted by microwave exstraction from grape seeds. The correlation of the coumpounds pholyphenols and polysacharide has been optimized the mechanism of their interaction has been determined. The technology ...
6. A Simple Experimental Setup for Teaching Additive Colors with Arduino
Science.gov (United States)
Carvalho, Paulo Simeão; Hahn, Marcelo
2016-01-01
The result of additive colors is always fascinating to young students. When we teach this topic to 14- to 16-year-old students, they do not usually notice we use maximum light quantities of red (R), green (G), and blue (B) to obtain yellow, magenta, and cyan colors in order to build the well-known additive color diagram of Fig. 1. But how about…
7. Theoretical Study on the Addition Reactions of Benzaldoximes with Propene
Institute of Scientific and Technical Information of China (English)
2006-01-01
The Michael addition reactions of Z and E benzaldoximes with propene were investigated theoretically by DFT method at B3LYP/6-31G* level. The calculation results show that both addition reactions are concerted processes accompanied by the migration of hydrogen from the atom oxygen to carbon. Both products Z and E nitrones have dipolar charge distributions and activities. Z isomer is more favorable in the reaction due to the barrier is lower.
8. Students' Understanding of the Addition of Angular Momentum
CERN Document Server
Singh, Chandralekha
2016-01-01
We describe the difficulties advanced undergraduate and graduate students have with concepts related to the addition of angular momentum. We also describe the development and implementation of a research-based learning tool, a Quantum Interactive Learning Tutorial (QuILT), to reduce these difficulties. The preliminary evaluation shows that the QuILT on the addition of angular momentum is helpful in improving students' understanding of these concepts.
9. Effect of cationic polyelectrolytes addition in cement cohesion
OpenAIRE
Edison Albert Zuluaga-Hernández; Bibian A Hoyos
2014-01-01
Here is studied the variation in cohesion of cement main phase (C-S-H) as a result of cationic polyelectrolytes addition (quaternary amines spermine and norspermidine). Cohesion study was carried out by molecular simulation techniques (Monte Carlo) using a primitive model in a canonical ensemble (NVT). The proposed model takes into account the influence of ionic size of each particle and the addition of polyelectrolytes with different charge number and separation. The results obtained show th...
10. Pairwise-additive hydrophobic effect for alkanes in water
OpenAIRE
Wu, Jianzhong; Prausnitz, John M.
2008-01-01
Pairwise additivity of the hydrophobic effect is indicated by reliable experimental Henry's constants for a large number of linear and branched low-molecular-weight alkanes in water. Pairwise additivity suggests that the hydrophobic effect is primarily a local phenomenon and that the hydrophobic interaction may be represented by a semiempirical force field. By representing the hydrophobic potential between two methane molecules as a linear function of the overlap volume of the hydration layer...
11. Synthesis of new calixarene-based lubricant additives
OpenAIRE
Burlini, Alessandro
2016-01-01
The lubricants are normally composed by base oils and a number of additives which are added to improve the performances of the final product. In this work, which is due to the collaboration between ENI S.p.A. and Prof. Casnati’s group, significant results in the application of calixarene structures to two classes of lubricant additives (viscosity index improvers and detergents) were shown. In particular, several calix[8]arene derivatives were synthesized to use as core precursors in the...
12. Ionic Liquids as Novel Lubricants and /or Lubricant Additives
Energy Technology Data Exchange (ETDEWEB)
Qu, J. [ORNL; Viola, M. B. [General Motors Company
2013-10-31
13. Computed Tomography Inspection and Analysis for Additive Manufacturing Components
Science.gov (United States)
Beshears, Ronald D.
2016-01-01
Computed tomography (CT) inspection was performed on test articles additively manufactured from metallic materials. Metallic AM and machined wrought alloy test articles with programmed flaws were inspected using a 2MeV linear accelerator based CT system. Performance of CT inspection on identically configured wrought and AM components and programmed flaws was assessed using standard image analysis techniques to determine the impact of additive manufacturing on inspectability of objects with complex geometries.
14. LEAN ORGANIZATION OF ADDITIVE MANUFACTURING OF AIRCRAFT PURPOSE PRODUCTS
Directory of Open Access Journals (Sweden)
Smelov V.G
2014-10-01
Full Text Available This study considers the question of creation of a modern small aircraft purpose parts manufacturing company which will use additive technologies according to the principles of "smart" production and the concept of «lean» management. In order to reduce time and cost of current production, conform to world technologies and competitive ability optimization of key business processes of the foundry was carried out with adoption of a model of additive manufacturing.
15. Livestock poisoning from oil field drilling fluids, muds and additives.
Science.gov (United States)
Edwards, W C; Gregory, D G
1991-10-01
The use and potential toxicity of various components of oil well drilling fluids, muds and additives are presented. Many components are extremely caustic resulting in rumenitis. Solvent and petroleum hydrocarbon components may cause aspiration pneumonia and rumen dysfunction. Some additives cause methemoglobinemia. The most frequently encountered heavy metals are lead, chromium, arsenic, lithium and copper. Considerations for investigating livestock poisoning cases and several typical cases are reviewed.
16. IAEA to implement Safeguards Additional Protocols in the EU
International Nuclear Information System (INIS)
17. LEAN ORGANIZATION OF ADDITIVE MANUFACTURING OF AIRCRAFT PURPOSE PRODUCTS
OpenAIRE
Smelov V.G; Kokareva V.V; Malykhin A.N
2014-01-01
This study considers the question of creation of a modern small aircraft purpose parts manufacturing company which will use additive technologies according to the principles of "smart" production and the concept of «lean» management. In order to reduce time and cost of current production, conform to world technologies and competitive ability optimization of key business processes of the foundry was carried out with adoption of a model of additive manufacturing.
18. A new global approach to design for additive manufacturing
OpenAIRE
Ponche, Rémi; Hascoët, Jean-Yves; Kerbrat, Olivier; MOGNOL, Pascal
2012-01-01
International audience Nowadays, due to rapid prototyping processes improvements, a functional part can be built directly through additive manufacturing. It is now accepted that these new processes can increase productivity while enabling a mass and cost reduction and an increase of the parts functionality. However, in order to achieve this, new design methods have to be developed to take into account the specificities of these processes, with the Design For Additive Manufacturing (DFAM) c...
19. Additive archaeology: an alternative framework for recontextualising archaeological entities
OpenAIRE
Reilly Paul
2015-01-01
Additive manufacturing poses a number of challenges to conventional understandings of materiality, including the so-called archaeological record. In particular, concepts such as real, virtual, and authentic are becoming increasingly unstable, as archaeological artefacts and assemblages can be digitalised, reiterated, extended and distributed through time and space as 3D printable entities. This paper argues that additive manufacturing represents a ‘grand disciplinary challenge’ to archaeologi...
20. Cement mixtures containing copper tailings as an additive: durability properties
OpenAIRE
Obinna Onuaguluchi; Özgur Eren
2012-01-01
The effects of copper tailings as an additive, on some durability properties of cement mixtures were investigated. In each mixture, copper tailings addition levels by mass were 0%, 5% and 10%. Compared to the control samples, copper tailings blended pastes showed superior performance against autoclave expansion while insignificant decreases in sulfate resistance of mortars were observed. Copper tailings increased the water absorption and total permeable voids of concretes slightly. However, t...
Science.gov (United States)
Farrington-Flint, Lee; Canobi, Katherine H; Wood, Clare; Faulkner, Dorothy
2010-06-01
2. Friction Stir Additive Manufacturing: Route to High Structural Performance
Science.gov (United States)
Palanivel, S.; Sidhar, H.; Mishra, R. S.
2015-03-01
3. Additives for cement compositions based on modified peat
Science.gov (United States)
Kopanitsa, Natalya; Sarkisov, Yurij; Gorshkova, Aleksandra; Demyanenko, Olga
2016-01-01
High quality competitive dry building mixes require modifying additives for various purposes to be included in their composition. There is insufficient amount of quality additives having stable properties for controlling the properties of cement compositions produced in Russia. Using of foreign modifying additives leads to significant increasing of the final cost of the product. The cost of imported modifiers in the composition of the dry building mixes can be up to 90% of the material cost, depending on the composition complexity. Thus, the problem of import substitution becomes relevant, especially in recent years, due to difficult economic situation. The article discusses the possibility of using local raw materials as a basis for obtaining dry building mixtures components. The properties of organo-mineral additives for cement compositions based on thermally modified peat raw materials are studied. Studies of the structure and composition of the additives are carried out by physicochemical research methods: electron microscopy and X-ray analysis. Results of experimental research showed that the peat additives contribute to improving of cement-sand mortar strength and hydrophysical properties.
4. Dry building mixture with complex dispersed mineral additives
Science.gov (United States)
Il'ina, Liliia; Mukhina, Irina; Teplov, Alexandr
2016-01-01
5. Additives for cement compositions based on modified peat
Energy Technology Data Exchange (ETDEWEB)
Kopanitsa, Natalya, E-mail: [email protected]; Sarkisov, Yurij, E-mail: [email protected]; Gorshkova, Aleksandra, E-mail: [email protected]; Demyanenko, Olga, E-mail: [email protected] [Tomsk State University of Architecture and Building, 2, Solyanaya sq., Tomsk, 634003 (Russian Federation)
2016-01-15
High quality competitive dry building mixes require modifying additives for various purposes to be included in their composition. There is insufficient amount of quality additives having stable properties for controlling the properties of cement compositions produced in Russia. Using of foreign modifying additives leads to significant increasing of the final cost of the product. The cost of imported modifiers in the composition of the dry building mixes can be up to 90% of the material cost, depending on the composition complexity. Thus, the problem of import substitution becomes relevant, especially in recent years, due to difficult economic situation. The article discusses the possibility of using local raw materials as a basis for obtaining dry building mixtures components. The properties of organo-mineral additives for cement compositions based on thermally modified peat raw materials are studied. Studies of the structure and composition of the additives are carried out by physicochemical research methods: electron microscopy and X-ray analysis. Results of experimental research showed that the peat additives contribute to improving of cement-sand mortar strength and hydrophysical properties.
6. APPLIED RESEARCH ON NEW MULTI-FUNCTION GASOLINE ADDITIVE
Institute of Scientific and Technical Information of China (English)
CAI Ruibin; MING Caibing; GAO Zhiwen
2006-01-01
In order to assess the performance of a new cleansing and combustion-improving gasoline additive (MAZ), and to explore the evaluation methods of additives, two engines with the same model number and performance indices, fueled with and without the MAZ gasoline additive respectively, are carried through 100 h strenuous tests on a bench. The results obtained in full load characteristic and load characteristics of different operational modes are compared. It indicates that the power, economy and emission of the engine fueled with the MAZ additive all have obvious improvement in comparison with the engine without adding the additive: the power increasing by 16.43%, specific fuel consumption (SFC) decreasing 5.39%, and the emission of CO, HC and NOx falling by 28.61%, 54.38%and 10.1% respectively. Wear and tear of the engine cylinder is weakened, and sediment of combustion chamber inner side is reduced. In addition, no negative effect on the catalytic conversion device is found.
7. Effect of Zr addition on precipitates in K4169 superalloy
Directory of Open Access Journals (Sweden)
Liu Jie
2012-02-01
Full Text Available In order to investigate the effect of Zr addition on the precipitations of K4169 superalloy, a manual electric arc furnace was used to prepare the superalloy with different Zr addition from 0.03wt.% to 0.07wt%. After standard heat treatment and long-time aging, the microstructures of the alloys were observed using XRD, SEM and TEM. The results show that Zr not only inhibits the precipitation of Laves phase at the grain boundary, but also significantly promotes the precipitation of earlobe-like γ′and γ″ phases. After long time aging at 680 ℃ for 500 h, the γ″phase grows up obviously and forms a γ′/γ′′clad microstructure when the Zr addition is 0.03 wt.%. A large number of fine orbed γ′particles precipitate in the grains and some γ″phase transforms to disk-like δ phase when the Zr addition increases to 0.05wt.%. The nano-polycrystalline γ′phase precipitates in the grains and there is a little δ phase when the Zr addition is 0.07wt.%. As the Zr addition increases, the amount of Laves phase at the grain boundary decreases at first, and then increases and forms flaky morphology.
Institute of Scientific and Technical Information of China (English)
HU Jian-qiang; XIE Feng; ZHU Huan-qin; ZHEN Fa-zheng; YAO Jun-bing
2004-01-01
9. Contamination effects of drilling fluid additives on cement slurry
Directory of Open Access Journals (Sweden)
Youzhi Zheng
2015-10-01
Full Text Available During the cementation of deep wells, contamination at the contact surface between cement slurry and drilling fluid will present a technical challenge, which may threaten operation safety. To deal with the problem, lab tests and analysis were performed specifically on the compatibility of fluids during cementation in Sichuan and Chongqing gas fields. Impacts of commonly used additives for drilling fluids were determined on fluidity and thickening time of conventional cement slurry. Through the infrared spectrum analysis, SEM and XRD, infrared spectrum data of kalium polyacrylamide (KPAM and bio-viscosifier were obtained, together with infrared spectrum, SEM and XRD data of cement slurry with additives. Contamination mechanisms of the cement slurry by conventional additives for drilling fluid were reviewed. Test results show that both KPAM and bio-viscosifier are such high-molecular materials that the long chains in these materials may easily absorb cement particles in the slurry to form mixed network structures; as a result, cement particles were prone to agglomeration and eventually lost their pumpability. Finally, assessment of and testing methods for the contamination effects of drilling fluid additives on cement slurry were further improved to form standards and codes that may help solve the said problems. This study will provide technological supports for the preparation of drilling fluids with desirable properties prior to cementation, the selection of optimal drilling fluids additives, and the development of innovative drilling fluids additives.
International Nuclear Information System (INIS)
11. Evaluation of relative biological efficiency of additives in sugarcane ensiling
Directory of Open Access Journals (Sweden)
Laura Maria Oliveira Borgatti
2012-04-01
Full Text Available The objective of this study was to evaluate the effects of adding alkalis on the fermentative pattern, aerobic stability and nutritive value of the sugarcane silage. A completely randomized design with 6 additives in two concentrations (1 or 2%, plus a control group, totalizing 13 treatments [(6×2+1] with four replications, was used. The additives were sodium hydroxide (NaOH, limestone (CaCO3, urea (CO(NH22, sodium bicarbonate (NaHCO3, quicklime (CaO and hydrated lime (Ca(OH2. The material was ensiled in 52 laboratory silos using plastic buckets with 12 L of capacity. Silos were opened 60 days after ensiling, when organic acids concentration, aerobic stability and chemical composition were determined. The Relative Biological Efficiency (RBE was calculated by the slope ratio method, using the data obtained from ratio between desirable and undesirable silage products, according to the equation: D/U ratio = [lactic/(ethanol + acetic + butyric]. All additives affected dry matter, crude protein, acid detergent fiber, neutral detergent fiber contents and buffering capacity. Except for urea and quicklime, all additives increased the in vitro dry matter digestibility. In general, these additives altered the fermentative pattern of sugarcane silage, inhibiting alcoholic fermentation and improving lactic acid production. The additive that showed the best RBE in relation to sodium hydroxide (100% was limestone (89.4%. The RBE values of urea, sodium bicarbonate and hydrated lime were 49.2%, 47.7% and 34.3%, respectively.
12. Implementing the South African additive manufacturing technology roadmap - the role of an additive manufacturing centre of competence
Directory of Open Access Journals (Sweden)
Du Preez, Willie Bouwer
2015-08-01
13. Additives in crude oil. A new attempt to prevent boilover; Additive im Rohoel. Ein neuer Ansatz zur Vermeidung eines Boilover
Energy Technology Data Exchange (ETDEWEB)
Gosewinkel, Martin; Dworschak, Rene [INBUREX Consulting GmbH, Hamm (Germany)
2011-03-15
Boilover of tanks is a rare cause of serious fires in crude oil storage. The greatest danger is the spill of burning material from the tank. In the research project presented here, a method to prevent boilover and/or reduce its effects was to be developed. One approach is the addition of additives that modify the hetero-azeotropic boiling characteristics of crude oil components in case of fire. Even minimum concentrations of the additive will delay the time until boilover and also reduce its intensity.
14. Control of microbial corrosion using coatings and natural additives
Energy Technology Data Exchange (ETDEWEB)
Al-Darbi, M.M.; Muntasser, Z.M.; Tango, M.; Islam, M.R.
2002-11-01
15. Characterization of Metal Powders Used for Additive Manufacturing.
Science.gov (United States)
Slotwinski, J A; Garboczi, E J; Stutzman, P E; Ferraris, C F; Watson, S S; Peltz, M A
2014-01-01
Additive manufacturing (AM) techniques can produce complex, high-value metal parts, with potential applications as critical parts, such as those found in aerospace components. The production of AM parts with consistent and predictable properties requires input materials (e.g., metal powders) with known and repeatable characteristics, which in turn requires standardized measurement methods for powder properties. First, based on our previous work, we assess the applicability of current standardized methods for powder characterization for metal AM powders. Then we present the results of systematic studies carried out on two different powder materials used for additive manufacturing: stainless steel and cobalt-chrome. The characterization of these powders is important in NIST efforts to develop appropriate measurements and standards for additive materials and to document the property of powders used in a NIST-led additive manufacturing material round robin. An extensive array of characterization techniques was applied to these two powders, in both virgin and recycled states. The physical techniques included laser diffraction particle size analysis, X-ray computed tomography for size and shape analysis, and optical and scanning electron microscopy. Techniques sensitive to structure and chemistry, including X-ray diffraction, energy dispersive analytical X-ray analysis using the X-rays generated during scanning electron microscopy, and X-Ray photoelectron spectroscopy were also employed. The results of these analyses show how virgin powder changes after being exposed to and recycled from one or more Direct Metal Laser Sintering (DMLS) additive manufacturing build cycles. In addition, these findings can give insight into the actual additive manufacturing process.
16. Implementing the South African additive manufacturing technology roadmap - the role of an additive manufacturing centre of competence
OpenAIRE
Du Preez, Willie Bouwer; De Beer, Deon J.
2015-01-01
The Rapid Product Development Association of South Africa (RAPDASA) expressed the need for a national Additive Manufacturing Roadmap. Consequentially, the South African Department of Science and Technology commissioned the development of a South African Additive Manufacturing Technology Roadmap. This was intended to guide role-players in identifying business opportunities, addressing technology gaps, focusing development programmes, and informing investment decisions that would enable local c...
17. The Effect Acid Addition on Characteristic Effervescent Tablet of Tamarillo
Directory of Open Access Journals (Sweden)
Fidela Violalita
2015-01-01
Full Text Available The aim of study was to determine the percentage of acid and its influence on characteristic effervescent tablet of tamarillo. The percentages of acid addition that consist with citric acid and tartaric acid (1:1 were 15%, 20%, 25%, 30% and 35%. Water content, pH solution, vitamin C content, soluble duration, friability of tablet and organoleptic test on colour, aroma and flavour of tamarillo effervescent tablet were determined after addition of acid. The results showed that the difference in percentage of acid addition significantly affected to the water content, pH solution, soluble duration and friability of tablets. Based on organoleptic test, the tablet consist of 25% addition of acid was the best percentage of acid addition. The quality parameters in this percentage were the water content 6.09%, pH solution 4.80, vitamin C 498.0800 mg/tablet, soluble duration 3.96 minute, friability of tablet 0.11%, while the averages of organoleptic test for colour were 3.40 (ordinary, aroma 3.36 (ordinary, and flavour 3.76 (like.
18. Wax Crystallization and Additive-Wax Interactions in Lubricants
Science.gov (United States)
Varma-Nair, M.; Pacansky, T. J.; Martella, D. J.
1997-03-01
Wax crystallization is a major problem in a petrochemical industry. Low temperature leads to crystallization causing problems for transportation, storage and use. For example, the wax crystals in lubricants involve mixtures of normal and iso paraffins (C15-C34), and are large, thin, convoluted, interlocking platelets, which entrap oil and form a network. Polymeric additives change nucleation and growth habits of wax and lead to better performance. It is of fundamental importance to understand the mechanism of wax crystallization and the wax-additive interactions. Differential scanning calorimetry is used to study thermodynamics and crystallization kinetics of additized and unadditized solutions. Several comb shaped fummarate vinyl acetate copolymers are evaluated. The response of the additive is very specific to the average C number in the crystallizable ester side chains of the copolymer. These changes are concentration dependent and change with complexity of the formulation. The dominant interaction appears to be cocrystallization of the side chains of the copolymer with the crystallizable paraffins of wax. These additives also increase the metastability region. Thus, inhibition of wax crystallization is critical to the mechanism of interaction.
19. Metal Additive Manufacturing: A Review of Mechanical Properties
Science.gov (United States)
Lewandowski, John J.; Seifi, Mohsen
2016-07-01
This article reviews published data on the mechanical properties of additively manufactured metallic materials. The additive manufacturing techniques utilized to generate samples covered in this review include powder bed fusion (e.g., EBM, SLM, DMLS) and directed energy deposition (e.g., LENS, EBF3). Although only a limited number of metallic alloy systems are currently available for additive manufacturing (e.g., Ti-6Al-4V, TiAl, stainless steel, Inconel 625/718, and Al-Si-10Mg), the bulk of the published mechanical properties information has been generated on Ti-6Al-4V. However, summary tables for published mechanical properties and/or key figures are included for each of the alloys listed above, grouped by the additive technique used to generate the data. Published values for mechanical properties obtained from hardness, tension/compression, fracture toughness, fatigue crack growth, and high cycle fatigue are included for as-built, heat-treated, and/or HIP conditions, when available. The effects of test orientation/build direction on properties, when available, are also provided, along with discussion of the potential source(s) (e.g., texture, microstructure changes, defects) of anisotropy in properties. Recommendations for additional work are also provided.
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https://www.knowpia.com/knowpedia/500_(number)
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BREAKING NEWS
500 (number)
## Summary
500 (five hundred) is the natural number following 499 and preceding 501.
← 499 500 501 →
Cardinalfive hundred
Ordinal500th
(five hundredth)
Factorization22 × 53
Greek numeralΦ´
Roman numeralD
Binary1111101002
Ternary2001123
Octal7648
Duodecimal35812
## Mathematical properties
500 = 22 × 53. It is an Achilles number and an Harshad number, meaning divisible by the sum of its digits. It is the number of planar partitions of 10.[1]
## Other fields
Five hundred is also
## Slang names
• Monkey (UK slang for £500; USA slang for \$500)[2]
## Integers from 501 to 599
### 500s
#### 501
501 = 3 × 167. It is:
• the sum of the first 18 primes (a term of the sequence ).
• palindromic in bases 9 (6169) and 20 (15120).
#### 502
• 502 = 2 × 251
• vertically symmetric number (sequence A053701 in the OEIS)
503 is:
#### 504
504 = 23 × 32 × 7. It is:
${\displaystyle \sum _{n=0}^{10}{504}^{n}}$ is prime[11]
#### 506
506 = 2 × 11 × 23. It is:
#### 507
• 507 = 3 × 132 = 232 - 23 + 1, which makes it a central polygonal number[14]
• The age Ming had before dying.
#### 508
• 508 = 22 × 127, sum of four consecutive primes (113 + 127 + 131 + 137), number of graphical forest partitions of 30,[15] since 508 = 222 + 22 + 2 it is the maximum number of regions into which 23 intersecting circles divide the plane.[16]
509 is:
### 510s
#### 510
510 = 2 × 3 × 5 × 17. It is:
• the sum of eight consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).
• the sum of ten consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
• the sum of twelve consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).
• a nontotient.
• a sparsely totient number.[18]
• the number of nonempty proper subsets of an 9-element set.[19]
#### 511
511 = 7 × 73. It is:
#### 512
512 = 83 = 29. It is:
#### 513
513 = 33 × 19. It is:
#### 514
514 = 2 × 257, it is:
#### 515
515 = 5 × 103, it is:
• the sum of nine consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).
• the number of complete compositions of 11.[22]
#### 516
516 = 22 × 3 × 43, it is:
#### 517
517 = 11 × 47, it is:
• the sum of five consecutive primes (97 + 101 + 103 + 107 + 109).
• a Smith number.[24]
#### 518
518 = 2 × 7 × 37, it is:
• = 51 + 12 + 83 (a property shared with 175 and 598).
• a sphenic number.
• a nontotient.
• an untouchable number.[23]
• palindromic and a repdigit in bases 6 (22226) and 36 (EE36).
#### 519
519 = 3 × 173, it is:
• the sum of three consecutive primes (167 + 173 + 179)
• palindromic in bases 9 (6369) and 12 (37312)
• a D-number.[25]
### 520s
#### 520
520 = 23 × 5 × 13. It is:
#### 521
521 is:
• a Lucas prime.[26]
• A Mersenne exponent, i.e. 2521−1 is prime.
• a Chen prime.
• an Eisenstein prime with no imaginary part.
• palindromic in bases 11 (43411) and 20 (16120).
#### 522
522 = 2 × 32 × 29. It is:
• the sum of six consecutive primes (73 + 79 + 83 + 89 + 97 + 101).
• a repdigit in bases 28 (II28) and 57 (9957).
• number of series-parallel networks with 8 unlabeled edges.[28]
#### 523
523 is:
• a prime number.
• the sum of seven consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89).
• palindromic in bases 13 (31313) and 18 (1B118).
• a prime with a prime number of prime digits[29]
#### 524
524 = 22 × 131
• number of partitions of 44 into powers of 2[30]
#### 525
525 = 3 × 52 × 7. It is:
• palindromic in base 10 (52510).
• the number of scan lines in the NTSC television standard.
• a self number.
#### 526
526 = 2 × 263, centered pentagonal number,[31] nontotient, Smith number[24]
#### 527
527 = 17 × 31. it is:
• palindromic in base 15 (25215)
• number of diagonals in a 34-gon[32]
• also, the section of the US Tax Code regulating soft money political campaigning (see 527 groups)
#### 528
528 = 24 × 3 × 11. It is:
#### 529
529 = 232. It is:
### 530s
#### 530
530 = 2 × 5 × 53. It is:
#### 531
531 = 32 × 59. It is:
• palindromic in base 12 (38312).
• number of symmetric matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to 6[34]
#### 532
532 = 22 × 7 × 19. It is:
#### 533
533 = 13 × 41. It is:
• the sum of three consecutive primes (173 + 179 + 181).
• the sum of five consecutive primes (101 + 103 + 107 + 109 + 113).
• palindromic in base 19 (19119).
• generalized octagonal number.[36]
#### 534
534 = 2 × 3 × 89. It is:
• a sphenic number.
• the sum of four consecutive primes (127 + 131 + 137 + 139).
• a nontotient.
• palindromic in bases 5 (41145) and 14 (2A214).
${\displaystyle \sum _{n=0}^{10}{534}^{n}}$ is prime[37]
#### 535
535 = 5 × 107. It is:
${\displaystyle 34n^{3}+51n^{2}+27n+5}$ for ${\displaystyle n=2}$ ; this polynomial plays an essential role in Apéry's proof that ${\displaystyle \zeta (3)}$ is irrational.
535 is used as an abbreviation for May 35, which is used in China instead of June 4 to evade censorship by the Chinese government of references on the Internet to the Tiananmen Square protests of 1989.[38]
#### 536
536 = 23 × 67. It is:
• the number of ways to arrange the pieces of the ostomachion into a square, not counting rotation or reflection.
• the number of 1's in all partitions of 23 into odd parts[39]
• a refactorable number.[10]
• the lowest happy number beginning with the digit 5.
#### 537
537 = 3 × 179, Mertens function (537) = 0, Blum integer, D-number[40]
#### 538
538 = 2 × 269. It is:
#### 539
539 = 72 × 11
${\displaystyle \sum _{n=0}^{10}{539}^{n}}$ is prime[41]
### 540s
#### 540
540 = 22 × 33 × 5. It is:
#### 541
541 is:
Mertens function(541) = 0. 4541 - 3541 is prime.
#### 542
542 = 2 × 271. It is:
#### 543
543 = 3 × 181; palindromic in bases 11 (45411) and 12 (39312), D-number.[48]
${\displaystyle \sum _{n=0}^{10}{543}^{n}}$ is prime[49]
#### 544
544 = 25 × 17. Take a grid of 2 times 5 points. There are 14 points on the perimeter. Join every pair of the perimeter points by a line segment. The lines do not extend outside the grid. 544 is the number of regions formed by these lines.
#### 545
545 = 5 × 109. It is:
#### 546
546 = 2 × 3 × 7 × 13. It is:
• the sum of eight consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).
• palindromic in bases 4 (202024), 9 (6669), and 16 (22216).
• a repdigit in bases 9 and 16.
• 546! − 1 is prime.
547 is:
#### 548
548 = 22 × 137. It is:
Also, every positive integer is the sum of at most 548 ninth powers;
#### 549
549 = 32 × 61, it is:
• a repdigit in bases 13 (33313) and 60 (9960).
• φ(549) = φ(σ(549)).[54]
### 550s
#### 550
550 = 2 × 52 × 11. It is:
#### 551
551 = 19 × 29. It is:
• It is the number of mathematical trees on 12 unlabeled nodes. [57]
• the sum of three consecutive primes (179 + 181 + 191).
• palindromic in base 22 (13122).
• the SMTP status code meaning user is not local
#### 552
552 = 23 × 3 × 23. It is:
• the sum of six consecutive primes (79 + 83 + 89 + 97 + 101 + 103).
• the sum of ten consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).
• a pronic number.[13]
• an untouchable number.[23]
• palindromic in base 19 (1A119).
• the model number of U-552.
• the SMTP status code meaning requested action aborted because the mailbox is full.
#### 553
553 = 7 × 79. It is:
• the sum of nine consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).
• central polygonal number.[58]
• the model number of U-553.
• the SMTP status code meaning requested action aborted because of faulty mailbox name.
#### 554
554 = 2 × 277. It is:
• a nontotient.
• a 2-Knödel number
• the SMTP status code meaning transaction failed.
Mertens function(554) = 6, a record high that stands until 586.
#### 555
555 = 3 × 5 × 37 is:
• a sphenic number.
• palindromic in bases 9 (6769), 10 (55510), and 12 (3A312).
• a repdigit in bases 10 and 36.
• φ(555) = φ(σ(555)).[59]
#### 556
556 = 22 × 139. It is:
• the sum of four consecutive primes (131 + 137 + 139 + 149).
• an untouchable number, because it is never the sum of the proper divisors of any integer.[23]
• a happy number.
• the model number of U-556; 5.56×45mm NATO cartridge.
#### 557
557 is:
• a prime number.
• a Chen prime.
• an Eisenstein prime with no imaginary part.
• the number of parallelogram polyominoes with 9 cells.[60]
#### 558
558 = 2 × 32 × 31. It is:
• a nontotient.
• a repdigit in bases 30 (II30) and 61 (9961).
• The sum of the largest prime factors of the first 558 is itself divisible by 558 (the previous such number is 62, the next is 993).
• in the title of the Star Trek: Deep Space Nine episode "The Siege of AR-558"
#### 559
559 = 13 × 43. It is:
• the sum of five consecutive primes (103 + 107 + 109 + 113 + 127).
• the sum of seven consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97).
• a nonagonal number.[61]
• a centered cube number.[62]
• palindromic in base 18 (1D118).
• the model number of U-559.
### 560s
#### 560
560 = 24 × 5 × 7. It is:
• a tetrahedral number.[63]
• a refactorable number.
• palindromic in bases 3 (2022023) and 6 (23326).
• the number of diagonals in a 35-gon[64]
#### 561
561 = 3 × 11 × 17. It is:
#### 562
562 = 2 × 281. It is:
• a Smith number.[24]
• an untouchable number.[23]
• the sum of twelve consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
• palindromic in bases 4 (203024), 13 (34313), 14 (2C214), 16 (23216), and 17 (1G117).
• a lazy caterer number (sequence A000124 in the OEIS).
• the number of Native American (including Alaskan) Nations, or "Tribes," recognized by the USA government.
563 is:
#### 564
564 = 22 × 3 × 47. It is:
• the sum of a twin prime (281 + 283).
• a refactorable number.
• palindromic in bases 5 (42245) and 9 (6869).
• number of primes <= 212.[71]
#### 565
565 = 5 × 113. It is:
• the sum of three consecutive primes (181 + 191 + 193).
• a member of the Mian–Chowla sequence.[72]
• a happy number.
• palindromic in bases 10 (56510) and 11 (47411).
#### 566
566 = 2 × 283. It is:
#### 567
567 = 34 × 7. It is:
• palindromic in base 12 (3B312).
${\displaystyle \sum _{n=0}^{10}{567}^{n}}$ is prime[73]
#### 568
568 = 23 × 71. It is:
• the sum of the first nineteen primes (a term of the sequence ).
• a refactorable number.
• palindromic in bases 7 (14417) and 21 (16121).
• the smallest number whose seventh power is the sum of 7 seventh powers.
• the room number booked by Benjamin Braddock in the 1967 film The Graduate.
• the number of millilitres in an imperial pint.
• the name of the Student Union bar at Imperial College London
#### 569
569 is:
• a prime number.
• a Chen prime.
• an Eisenstein prime with no imaginary part.
• a strictly non-palindromic number.[69]
### 570s
#### 570
570 = 2 × 3 × 5 × 19. It is:
• a triangular matchstick number[74]
• a balanced number[75]
#### 571
571 is:
• a prime number.
• a Chen prime.
• a centered triangular number.[21]
• the model number of U-571 which appeared in the 2000 movie U-571
#### 572
572 = 22 × 11 × 13. It is:
#### 573
573 = 3 × 191. It is:
#### 574
574 = 2 × 7 × 41. It is:
• a sphenic number.
• a nontotient.
• palindromic in base 9 (7079).
• number of partitions of 27 that do not contain 1 as a part.[76]
#### 575
575 = 52 × 23. It is:
And the sum of the squares of the first 575 primes is divisible by 575.[78]
#### 576
576 = 26 × 32 = 242. It is:
• the sum of four consecutive primes (137 + 139 + 149 + 151).
• a highly totient number.[79]
• a Smith number.[24]
• an untouchable number.[23]
• palindromic in bases 11 (48411), 14 (2D214), and 23 (12123).
• four-dozen sets of a dozen, which makes it 4 gross.
• a cake number.
• the number of parts in all compositions of 8.[80]
577 is:
#### 578
578 = 2 × 172. It is:
• a nontotient.
• palindromic in base 16 (24216).
• area of a square with diagonal 34[82]
#### 579
579 = 3 × 193; it is a ménage number,[83] and a semiprime.
### 580s
#### 580
580 = 22 × 5 × 29. It is:
• the sum of six consecutive primes (83 + 89 + 97 + 101 + 103 + 107).
• palindromic in bases 12 (40412) and 17 (20217).
#### 581
581 = 7 × 83. It is:
• the sum of three consecutive primes (191 + 193 + 197).
• a Blum integer
#### 582
582 = 2 × 3 × 97. It is:
• a sphenic number.
• the sum of eight consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89).
• a nontotient.
• a vertically symmetric number (sequence A053701 in the OEIS).
#### 583
583 = 11 × 53. It is:
• palindromic in base 9 (7179).
• number of compositions of 11 whose run-lengths are either weakly increasing or weakly decreasing[84]
#### 584
584 = 23 × 73. It is:
• an untouchable number.[23]
• the sum of totient function for first 43 integers.
• a refactorable number.
#### 585
585 = 32 × 5 × 13. It is:
• palindromic in bases 2 (10010010012), 8 (11118), and 10 (58510).
• a repdigit in bases 8, 38, 44, and 64.
• the sum of powers of 8 from 0 to 3.
When counting in binary with fingers, expressing 585 as 1001001001, results in the isolation of the index and little fingers of each hand, "throwing up the horns".
#### 586
586 = 2 × 293.
• Mertens function(586) = 7 a record high that stands until 1357.
• 2-Knödel number.
• it is the number of several popular personal computer processors (such as the Intel pentium).
#### 587
587 is:
• a prime number.
• safe prime.[3]
• a Chen prime.
• an Eisenstein prime with no imaginary part.
• the sum of five consecutive primes (107 + 109 + 113 + 127 + 131).
• palindromic in bases 11 (49411) and 15 (29215).
• the outgoing port for email message submission.
• a prime index prime.
#### 588
588 = 22 × 3 × 72. It is:
• a Smith number.[24]
• palindromic in base 13 (36313).
#### 589
589 = 19 × 31. It is:
### 590s
#### 590
590 = 2 × 5 × 59. It is:
#### 591
591 = 3 × 197, D-number[85]
#### 592
592 = 24 × 37. It is:
• palindromic in bases 9 (7279) and 12 (41412).
#### 593
593 is:
• a prime number.
• a Sophie Germain prime.
• the sum of seven consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101).
• the sum of nine consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).
• an Eisenstein prime with no imaginary part.
• a balanced prime.[68]
• a Leyland prime.
• a member of the Mian–Chowla sequence.[72]
• strictly non-palindromic prime.[69]
#### 594
594 = 2 × 33 × 11. It is:
• the sum of ten consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).
• a nontotient.
• palindromic in bases 5 (43345) and 16 (25216).
• the number of diagonals in a 36-gon.[86]
• a balanced number.[87]
#### 595
595 = 5 × 7 × 17. It is:
#### 596
596 = 22 × 149. It is:
• the sum of four consecutive primes (139 + 149 + 151 + 157).
• a nontotient.
• a lazy caterer number (sequence A000124 in the OEIS).
#### 597
597 = 3 × 199. It is:
#### 598
598 = 2 × 13 × 23 = 51 + 92 + 83. It is:
#### 599
599 is:
• a prime number.
• a Chen prime.
• an Eisenstein prime with no imaginary part.
• a prime index prime.
## References
1. ^ Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ Evans, I.H., Brewer's Dictionary of Phrase and Fable, 14th ed., Cassell, 1990, ISBN 0-304-34004-9
3. ^ a b c Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
4. ^ that is, a term of the sequence
5. ^ that is, the first term of the sequence
6. ^ since 503+2 is a product of two primes, 5 and 101
7. ^ since it is a prime which is congruent to 2 modulo 3.
8. ^ Sloane, N. J. A. (ed.). "Sequence A001606 (Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
9. ^ Sloane, N. J. A. (ed.). "Sequence A000073 (Tribonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
10. ^ a b c Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
11. ^ Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
12. ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
13. ^ a b Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
14. ^ Sloane, N. J. A. (ed.). "Sequence A002061". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
15. ^ Sloane, N. J. A. (ed.). "Sequence A000070". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
16. ^ Sloane, N. J. A. (ed.). "Sequence A014206". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
17. ^ Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
18. ^ Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
19. ^ Sloane, N. J. A. (ed.). "Sequence A000918". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
20. ^ Sloane, N. J. A. (ed.). "Sequence A061209 (Numbers which are the cubes of their digit sum)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
21. ^ a b Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
22. ^ Sloane, N. J. A. (ed.). "Sequence A107429 (Number of complete compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
23. Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
24. Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
25. ^ Sloane, N. J. A. (ed.). "Sequence A033553 (3-Knödel numbers or D-numbers: numbers n > 3 such that n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
26. ^ Sloane, N. J. A. (ed.). "Sequence A005479 (Prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
27. ^ Dr. Kirkby (May 19, 2021). "Many more twin primes below Mersenne exponents than above Mersenne exponents". Mersenne Forum.
28. ^ Sloane, N. J. A. (ed.). "Sequence A000084 (Number of series-parallel networks with n unlabeled edges. Also called yoke-chains by Cayley and MacMahon.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
29. ^ Sloane, N. J. A. (ed.). "Sequence A348699 (Primes with a prime number of prime digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
30. ^ Sloane, N. J. A. (ed.). "Sequence A000123 (Number of binary partitions: number of partitions of 2n into powers of 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
31. ^ Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
32. ^ Sloane, N. J. A. (ed.). "Sequence A000096". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
33. ^ Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
34. ^ Sloane, N. J. A. (ed.). "Sequence A138178 (Number of symmetric matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
35. ^ a b Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
36. ^ Sloane, N. J. A. (ed.). "Sequence A001082 (Generalized octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
37. ^ Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
38. ^ Larmer, Brook (October 26, 2011). "Where an Internet Joke Is Not Just a Joke". New York Times. Retrieved November 1, 2011.
39. ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
40. ^ Sloane, N. J. A. (ed.). "Sequence A033553 (3-Knödel numbers or D-numbers: numbers n > 3 such that n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
41. ^ Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
42. ^ Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
43. ^ Snorri Sturluson. "Prose Edda". p. 107.
44. ^ Snorri Sturluson. "Prose Edda". p. 82.
45. ^ Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
46. ^ Sloane, N. J. A. (ed.). "Sequence A003154 (Centered 12-gonal numbers. Also star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
47. ^ Sloane, N. J. A. (ed.). "Sequence A002088". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
48. ^ Sloane, N. J. A. (ed.). "Sequence A033553 (3-Knödel numbers or D-numbers: numbers n > 3 such that n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
49. ^ Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
50. ^ Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
51. ^ Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
52. ^ Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
53. ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
54. ^ Sloane, N. J. A. (ed.). "Sequence A006872". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
55. ^ Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
56. ^ a b Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
57. ^ "Sloane's A000055: Number of trees with n unlabeled nodes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2010-11-29. Retrieved 2021-12-19.
58. ^ Sloane, N. J. A. (ed.). "Sequence A002061". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
59. ^ Sloane, N. J. A. (ed.). "Sequence A006872". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
60. ^ Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
61. ^ Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
62. ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
63. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
64. ^ Sloane, N. J. A. (ed.). "Sequence A000096". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
65. ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
66. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 14. ISBN 978-1-84800-000-1.
67. ^ Sloane, N. J. A. (ed.). "Sequence A007540 (Wilson primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
68. ^ a b Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
69. ^ a b c Sloane, N. J. A. (ed.). "Sequence A016038 (Strictly non-palindromic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
70. ^ Sloane, N. J. A. (ed.). "Sequence A059802 (Numbers k such that 5^k - 4^k is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
71. ^ Sloane, N. J. A. (ed.). "Sequence A007053". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
72. ^ a b Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
73. ^ Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
74. ^ Sloane, N. J. A. (ed.). "Sequence A045943". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
75. ^ Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
76. ^ Sloane, N. J. A. (ed.). "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
77. ^ Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
78. ^ Sloane, N. J. A. (ed.). "Sequence A111441 (Numbers k such that the sum of the squares of the first k primes is divisible by k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
79. ^ Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
80. ^ Sloane, N. J. A. (ed.). "Sequence A001792". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
81. ^ Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
82. ^ Sloane, N. J. A. (ed.). "Sequence A001105". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
83. ^ Sloane, N. J. A. (ed.). "Sequence A000179 (Ménage numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
84. ^ Sloane, N. J. A. (ed.). "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
85. ^ Sloane, N. J. A. (ed.). "Sequence A033553 (3-Knödel numbers or D-numbers: numbers n > 3 such that n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
86. ^ Sloane, N. J. A. (ed.). "Sequence A000096". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
87. ^ Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
88. ^ Sloane, N. J. A. (ed.). "Sequence A060544 (Centered 9-gonal (also known as nonagonal or enneagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
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https://www.handsonmechanics.org/thermal/615
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# Closed vs Open Systems
### Model Description
This is a demonstration of the basic principles open and closed systems. It reinforces the conservation of mass and energy. This demonstration should take 5-8 minutes.
### Engineering Principle
Most students have a basic understanding of open and closed systems, but tend to get lost in the terminology. In order to assist in the student’s internalization of the concept of open vs. closed systems, this demonstration shows the differences between them in an easily understandable method.
### What You Need
Item Quantity Description/Clarification
Soda Can 1 It must not be opened.
Pitcher of Water 1 Half full
### How It’s Done
In Class: Highlight the conservation of mass:
$0 = \frac{dm_{ev}}{dt} + \sum\limits_e \dot{m_e} - \sum\limits_i \dot{m_i}$
For a closed system, there is no mass passing the boundary, so mass is conserved within the system. Using your un-opened soda can, rotate the can and ask the class what they expect to happen. Obviously, the contents will not spill out—the mass can not cross the boundary of the system.
Then open the can, and drink some soda. The mass is crossing the boundary of the system at the opening. At this point, question if the flow of mass across the boundary is steady, and how the $\frac{dm_{ev}}{dt}$ term will be affected by the draining of the can.
From the conservation of mass, the conservation of energy can be interpreted. What will happen if we leave the un-opened cold soda in the warm classroom? The soda will get warmer, thereby showing that heat can transfer across the boundaries of a closed system.
If we open the cold soda, we notice that the can itself is cold on our hand and that the mass of soda going down our throat is cold. This shows that energy in an open system can be transferred with mass entering or exiting and / or through the boundary of the system.
Observations: Students should be able to observe how mass can not cross the boundary of the closed system (un-opened can) and how it is draining out of the open system (opened can). Students should also be able to recognize the heat transfer across the can itself (open or closed system) as well as with the mass as it drains out of the can (open system).
Additional Application: When introducing the 2nd Law of Thermodynamics, re-introduce the cold can of soda. In order to show how the 2nd Law predicts direction, ask which direction the heat must transfer. Will the opposite violate the 1st Law? Additionally, pour the contents of the soda into a pitcher of water. Will the soda and water unmix spontaneously?
### Cite this work as:
Seth Norberg (2019), "Closed vs Open Systems," https://www.handsonmechanics.org/thermal/615.
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=129&t=40947
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## 4A.3 7th Ed
$w=-P\Delta V$
and
$w=-\int_{V_{1}}^{V_{2}}PdV=-nRTln\frac{V_{2}}{V_{1}}$
Noh_Jasmine_1J
Posts: 71
Joined: Fri Sep 28, 2018 12:15 am
### 4A.3 7th Ed
how do I figure out how to determine the change in volume when I am solving for work done? the question asks to solve for the work of a pump in compression with a diameter of 3cm and the pump is depressed 20cm with a pressure of 2atm. thank you~
Chloe Thorpe 1J
Posts: 77
Joined: Fri Sep 28, 2018 12:16 am
### Re: 4A.3 7th Ed
The change in volume in this question is given by -π*d*r^2. So, it would be -π*(20)*(1.5)^2 = -0.14 cm^3. Then, you multiply that by 1L/1000cm^3 to get it in the right unit, so you have -0.14 L.
204929947
Posts: 76
Joined: Fri Apr 06, 2018 11:03 am
### Re: 4A.3 7th Ed
why do we need to put -(pi)(d) (r^2)???? where does this formula come from????
Dimitri Speron 1C
Posts: 60
Joined: Fri Sep 28, 2018 12:17 am
Been upvoted: 1 time
### Re: 4A.3 7th Ed
Change in volume is (pi)(r^2)(change in d) because r is a constant and does not change in between the final and initial volumes. (at least in this example, it could potentially change but that would be a rather more complicated) So in order to calculate change in volume you just need to replace the d in the equation for volume with a change in d. With this you can calculate the work using the equations from class.
Ryan Danis 1J
Posts: 66
Joined: Fri Sep 28, 2018 12:18 am
### Re: 4A.3 7th Ed
I was having some trouble with this problem as well and the above replies have helped (I wasn’t squaring r or converting to liters). However I have one question. How come the work here is negative since it appears to be work done on the system instead of the system doing work? Is the system here the handle of the bicycle pump?
Maggie Doan 1I
Posts: 61
Joined: Fri Sep 28, 2018 12:24 am
### Re: 4A.3 7th Ed
Why is it -πr^2?
Cole Elsner 2J
Posts: 88
Joined: Fri Sep 28, 2018 12:25 am
### Re: 4A.3 7th Ed
I believe we'll learn how to do this in an upcoming lecture. Don't stress yourself out over it just yet! I'm certain we'll be taught how to do this, if not the book and chemistry community will surely help!
### Who is online
Users browsing this forum: No registered users and 1 guest
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https://cstheory.stackexchange.com/users/47144/bj%C3%B6rn-lindqvist?tab=topactivity
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Björn Lindqvist
### Questions (2)
20 Why colon to denote that a value belongs to a type? 0 What is sequence unification?
### Reputation (349)
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3 Computing the Levenshtein distance quickly
### Tags (7)
3 ds.algorithms 0 type-theory 3 string-search 0 notation 3 string-matching 0 lo.logic 3 reference-request
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http://www.sagemath.org/doc/reference/combinat/sage/combinat/symmetric_group_representations.html
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# Representations of the Symmetric Group¶
Todo
• construct the product of two irreducible representations.
• implement Induction/Restriction of representations.
Warning
This code uses a different convention than in Sagan’s book “The Symmetric Group”
class sage.combinat.symmetric_group_representations.SpechtRepresentation(partition, ring=None, cache_matrices=True)
An irreducible representation of the symmetric group corresponding to partition.
EXAMPLES:
sage: spc = SymmetricGroupRepresentation([3])
sage: spc([3,2,1])
[1]
True
sage: spc = SymmetricGroupRepresentation([3], cache_matrices=False)
sage: spc([3,2,1])
[1]
True
representation_matrix(permutation)
Returns the matrix representing the permutation in this irreducible representation.
Note
This method caches the results.
EXAMPLES:
sage: spc = SymmetricGroupRepresentation([3,1], 'specht')
sage: spc.representation_matrix(Permutation([2,1,3,4]))
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
sage: spc.representation_matrix(Permutation([3,2,1,4]))
[0 0 1]
[0 1 0]
[1 0 0]
scalar_product(u, v)
Return 0 if u+v is not a permutation, and the signature of the permutation otherwise.
This is the scalar product of a vertex u of the underlying Yang-Baxter graph with the vertex v in the ‘dual’ Yang-Baxter graph.
EXAMPLES:
sage: spc = SymmetricGroupRepresentation([3,2], 'specht')
sage: spc.scalar_product((1,0,2,1,0),(0,3,0,3,0))
-1
sage: spc.scalar_product((1,0,2,1,0),(3,0,0,3,0))
0
scalar_product_matrix(permutation=None)
Return the scalar product matrix corresponding to permutation.
The entries are given by the scalar products of u and permutation.action(v), where u is a vertex in the underlying Yang-Baxter graph and v is a vertex in the dual graph.
EXAMPLES:
sage: spc = SymmetricGroupRepresentation([3,1], 'specht')
sage: spc.scalar_product_matrix()
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
class sage.combinat.symmetric_group_representations.SpechtRepresentations(n, ring=None, cache_matrices=True)
Irreducible representations of the symmetric group.
EXAMPLES:
sage: snorm = SymmetricGroupRepresentations(3, "seminormal")
True
object_class
alias of SpechtRepresentation
sage.combinat.symmetric_group_representations.SymmetricGroupRepresentation(partition, implementation='specht', ring=None, cache_matrices=True)
The irreducible representation of the symmetric group corresponding to partition.
INPUT:
• partition – a partition of a positive integer
• implementation – string (default: "specht"), one of:
• "seminormal" - for Young’s seminormal representation
• "orthogonal" - for Young’s orthogonal representation
• "specht" - for Specht’s representation
• ring – the ring over which the representation is defined.
• cache_matrices – boolean (default: True) if True, then any representation matrices that are computed are cached.
EXAMPLES:
Young’s orthogonal representation: the matrices are orthogonal.
sage: orth = SymmetricGroupRepresentation([2,1], "orthogonal"); orth
Orthogonal representation of the symmetric group corresponding to [2, 1]
sage: all(a*a.transpose() == a.parent().identity_matrix() for a in orth)
True
sage: orth = SymmetricGroupRepresentation([3,2], "orthogonal"); orth
Orthogonal representation of the symmetric group corresponding to [3, 2]
sage: orth([2,1,3,4,5])
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 -1]
sage: orth([1,3,2,4,5])
[ 1 0 0 0 0]
[ 0 -1/2 1/2*sqrt(3) 0 0]
[ 0 1/2*sqrt(3) 1/2 0 0]
[ 0 0 0 -1/2 1/2*sqrt(3)]
[ 0 0 0 1/2*sqrt(3) 1/2]
sage: orth([1,2,4,3,5])
[ -1/3 2/3*sqrt(2) 0 0 0]
[2/3*sqrt(2) 1/3 0 0 0]
[ 0 0 1 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 -1]
The Specht Representation:
sage: spc = SymmetricGroupRepresentation([3,2], "specht")
sage: spc.scalar_product_matrix(Permutation([1,2,3,4,5]))
[ 1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 1 0 0]
[ 0 0 0 1 0]
[-1 0 0 0 -1]
sage: spc.scalar_product_matrix(Permutation([5,4,3,2,1]))
[ 1 -1 0 1 0]
[ 0 0 1 0 -1]
[ 0 0 0 -1 1]
[ 0 1 -1 -1 1]
[-1 0 0 0 -1]
sage: spc([5,4,3,2,1])
[ 1 -1 0 1 0]
[ 0 0 -1 0 1]
[ 0 0 0 -1 1]
[ 0 1 -1 -1 1]
[ 0 1 0 -1 1]
sage: spc.verify_representation()
True
By default, any representation matrices that are computed are cached:
sage: spc = SymmetricGroupRepresentation([3,2], "specht")
sage: spc([5,4,3,2,1])
[ 1 -1 0 1 0]
[ 0 0 -1 0 1]
[ 0 0 0 -1 1]
[ 0 1 -1 -1 1]
[ 0 1 0 -1 1]
sage: spc._cache__representation_matrix
{(([5, 4, 3, 2, 1],), ()): [ 1 -1 0 1 0]
[ 0 0 -1 0 1]
[ 0 0 0 -1 1]
[ 0 1 -1 -1 1]
[ 0 1 0 -1 1]}
This can be turned off with the keyword cache_matrices:
sage: spc = SymmetricGroupRepresentation([3,2], "specht", cache_matrices=False)
sage: spc([5,4,3,2,1])
[ 1 -1 0 1 0]
[ 0 0 -1 0 1]
[ 0 0 0 -1 1]
[ 0 1 -1 -1 1]
[ 0 1 0 -1 1]
sage: hasattr(spc, '_cache__representation_matrix')
False
Note
The implementation is based on the paper [Las].
REFERENCES:
[Las] (1, 2) Alain Lascoux, ‘Young representations of the symmetric group.’ http://phalanstere.univ-mlv.fr/~al/ARTICLES/ProcCrac.ps.gz
AUTHORS:
• Franco Saliola (2009-04-23)
class sage.combinat.symmetric_group_representations.SymmetricGroupRepresentation_generic_class(partition, ring=None, cache_matrices=True)
Generic methods for a representation of the symmetric group.
to_character()
Return the character of the representation.
EXAMPLES:
The trivial character:
sage: rho = SymmetricGroupRepresentation([3])
sage: chi = rho.to_character(); chi
Character of Symmetric group of order 3! as a permutation group
sage: chi.values()
[1, 1, 1]
sage: all(chi(g) == 1 for g in SymmetricGroup(3))
True
The sign character:
sage: rho = SymmetricGroupRepresentation([1,1,1])
sage: chi = rho.to_character(); chi
Character of Symmetric group of order 3! as a permutation group
sage: chi.values()
[1, -1, 1]
sage: all(chi(g) == g.sign() for g in SymmetricGroup(3))
True
The defining representation:
sage: triv = SymmetricGroupRepresentation([4])
sage: hook = SymmetricGroupRepresentation([3,1])
sage: def_rep = lambda p : triv(p).block_sum(hook(p)).trace()
sage: map(def_rep, Permutations(4))
[4, 2, 2, 1, 1, 2, 2, 0, 1, 0, 0, 1, 1, 0, 2, 1, 0, 0, 0, 1, 1, 2, 0, 0]
sage: [p.to_matrix().trace() for p in Permutations(4)]
[4, 2, 2, 1, 1, 2, 2, 0, 1, 0, 0, 1, 1, 0, 2, 1, 0, 0, 0, 1, 1, 2, 0, 0]
verify_representation()
Verify the representation: tests that the images of the simple transpositions are involutions and tests that the braid relations hold.
EXAMPLES:
sage: spc = SymmetricGroupRepresentation([1,1,1])
sage: spc.verify_representation()
True
sage: spc = SymmetricGroupRepresentation([4,2,1])
sage: spc.verify_representation()
True
sage.combinat.symmetric_group_representations.SymmetricGroupRepresentations(n, implementation='specht', ring=None, cache_matrices=True)
Irreducible representations of the symmetric group.
INPUT:
• n – positive integer
• implementation – string (default: "specht"), one of:
• "seminormal" - for Young’s seminormal representation
• "orthogonal" - for Young’s orthogonal representation
• "specht" - for Specht’s representation
• ring – the ring over which the representation is defined.
• cache_matrices – boolean (default: True) if True, then any representation matrices that are computed are cached.
EXAMPLES:
Young’s orthogonal representation: the matrices are orthogonal.
sage: orth = SymmetricGroupRepresentations(3, "orthogonal"); orth
Orthogonal representations of the symmetric group of order 3! over Symbolic Ring
sage: orth.list()
[Orthogonal representation of the symmetric group corresponding to [3], Orthogonal representation of the symmetric group corresponding to [2, 1], Orthogonal representation of the symmetric group corresponding to [1, 1, 1]]
sage: orth([2,1])([1,2,3])
[1 0]
[0 1]
Young’s seminormal representation.
sage: snorm = SymmetricGroupRepresentations(3, "seminormal"); snorm
Seminormal representations of the symmetric group of order 3! over Rational Field
sage: sgn = snorm([1,1,1]); sgn
Seminormal representation of the symmetric group corresponding to [1, 1, 1]
sage: map(sgn, Permutations(3))
[[1], [-1], [-1], [1], [1], [-1]]
The Specht Representation.
sage: spc = SymmetricGroupRepresentations(5, "specht"); spc
Specht representations of the symmetric group of order 5! over Integer Ring
sage: spc([3,2])([5,4,3,2,1])
[ 1 -1 0 1 0]
[ 0 0 -1 0 1]
[ 0 0 0 -1 1]
[ 0 1 -1 -1 1]
[ 0 1 0 -1 1]
Note
The implementation is based on the paper [Las].
AUTHORS:
• Franco Saliola (2009-04-23)
class sage.combinat.symmetric_group_representations.SymmetricGroupRepresentations_class(n, ring=None, cache_matrices=True)
Generic methods for the CombinatorialClass of irreducible representations of the symmetric group.
class sage.combinat.symmetric_group_representations.YoungRepresentation_Orthogonal(partition, ring=None, cache_matrices=True)
An irreducible representation of the symmetric group corresponding to partition.
EXAMPLES:
sage: spc = SymmetricGroupRepresentation([3])
sage: spc([3,2,1])
[1]
True
sage: spc = SymmetricGroupRepresentation([3], cache_matrices=False)
sage: spc([3,2,1])
[1]
True
class sage.combinat.symmetric_group_representations.YoungRepresentation_Seminormal(partition, ring=None, cache_matrices=True)
An irreducible representation of the symmetric group corresponding to partition.
EXAMPLES:
sage: spc = SymmetricGroupRepresentation([3])
sage: spc([3,2,1])
[1]
True
sage: spc = SymmetricGroupRepresentation([3], cache_matrices=False)
sage: spc([3,2,1])
[1]
True
class sage.combinat.symmetric_group_representations.YoungRepresentation_generic(partition, ring=None, cache_matrices=True)
Generic methods for Young’s representations of the symmetric group.
representation_matrix(permutation)
Return the matrix representing permutation.
EXAMPLES:
sage: orth = SymmetricGroupRepresentation([2,1], "orthogonal")
sage: orth.representation_matrix(Permutation([2,1,3]))
[ 1 0]
[ 0 -1]
sage: orth.representation_matrix(Permutation([1,3,2]))
[ -1/2 1/2*sqrt(3)]
[1/2*sqrt(3) 1/2]
sage: norm = SymmetricGroupRepresentation([2,1], "seminormal")
sage: p = PermutationGroupElement([2,1,3])
sage: norm.representation_matrix(p)
[ 1 0]
[ 0 -1]
sage: p = PermutationGroupElement([1,3,2])
sage: norm.representation_matrix(p)
[-1/2 3/2]
[ 1/2 1/2]
representation_matrix_for_simple_transposition(i)
Return the matrix representing the transposition that swaps i and i+1.
EXAMPLES:
sage: orth = SymmetricGroupRepresentation([2,1], "orthogonal")
sage: orth.representation_matrix_for_simple_transposition(1)
[ 1 0]
[ 0 -1]
sage: orth.representation_matrix_for_simple_transposition(2)
[ -1/2 1/2*sqrt(3)]
[1/2*sqrt(3) 1/2]
sage: norm = SymmetricGroupRepresentation([2,1], "seminormal")
sage: norm.representation_matrix_for_simple_transposition(1)
[ 1 0]
[ 0 -1]
sage: norm.representation_matrix_for_simple_transposition(2)
[-1/2 3/2]
[ 1/2 1/2]
class sage.combinat.symmetric_group_representations.YoungRepresentations_Orthogonal(n, ring=None, cache_matrices=True)
Irreducible representations of the symmetric group.
EXAMPLES:
sage: snorm = SymmetricGroupRepresentations(3, "seminormal")
True
object_class
alias of YoungRepresentation_Orthogonal
class sage.combinat.symmetric_group_representations.YoungRepresentations_Seminormal(n, ring=None, cache_matrices=True)
Irreducible representations of the symmetric group.
EXAMPLES:
sage: snorm = SymmetricGroupRepresentations(3, "seminormal")
True
object_class
alias of YoungRepresentation_Seminormal
sage.combinat.symmetric_group_representations.partition_to_vector_of_contents(partition, reverse=False)
Returns the “vector of contents” associated to partition.
EXAMPLES:
sage: from sage.combinat.symmetric_group_representations import partition_to_vector_of_contents
sage: partition_to_vector_of_contents([3,2])
(0, 1, 2, -1, 0)
#### Previous topic
Symmetric Group Algebra
Tableaux
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http://mathhelpforum.com/algebra/49342-stuck-two-word-problems-functions.html
|
# Thread: Stuck on Two Word Problems/ Functions
1. ## Stuck on Two Word Problems/ Functions
1."The combination of cold temperatures and wind speed determine what is called wind chill. The wind chill is a temperature that is the still-air equivalent of the combination of cold and wind. When the Wind speed is 25mph, the wind chill depends on the temperature t (in degrees Fahrenheit) according to
WC= 1.479t - 43.821
For what temp does it feel at least 30 degrees colder than teh air temp? That is, find t such that WC <=(less than or equal to) t -30
Don't really have any idea on how to do that one, I tried graphing it on my graphing calcualtor but just confused myself.
2. A shipping crate has a square base with sides of length x feet and it is half as tall as it is wide. If the material for the bottom and sides of the box cost 2\$ per sqr foot and the material for the top cost 1.50 per sqr ft., express the total cost of materials for the box as a function of x.
So I know the length = x and the height = .5x
So the area of the sides is x(.5x) times 4 would give me the area for the sides in sqr feet? and to do the bottom I'd just do x times x and the same with the top? I'm not sure hwo to put it all together though
2. For the first problem, you're making it more complicated than it is. What you want is to find the temperature at which the wind chill changes the temperature felt by at least 30 degrees less, so solve the equation for the desired change: $1.479t - 43.821 = -30$
For the second problem, you will multiply each side (represented by a number in square feet) by the cost per square foot for that side, and then add those numbers together to determine the total cost. The trick is that the top's cost is $1.5x^2$, whereas the bottom's cost is $2x^2$.
3. Originally Posted by icemanfan
For the first problem, you're making it more complicated than it is. What you want is to find the temperature at which the wind chill changes the temperature felt by at least 30 degrees less, so solve the equation for the desired change: $1.479t - 43.821 = -30$
For the second problem, you will multiply each side (represented by a number in square feet) by the cost per square foot for that side, and then add those numbers together to determine the total cost. The trick is that the top's cost is $1.5x^2$, whereas the bottom's cost is $2x^2$.
Ok I got the answer for the first one t=9.345 degrees
for the 2nd one I got f(x) = 3.5x^2 + 4x
do these look right?
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http://mathhelpforum.com/calculus/148270-minimizing-costs-problem.html
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# Math Help - Minimizing Costs Problem
1. ## Minimizing Costs Problem
Hi, I'm currently in Pre-Calculus in High school, a course prepping for university; I'm hoping this thread is in the appropriate section! I apologize for the long question, but I don't want to confuse anyone who is willing to help me.
We are currently doing a project on minimizing the cost for a company that has been contracted to lay pipeline through a forested area between a natural gas well and a storage facility.
Picture a rectangle where the horizontal is the roadway, the vertical is always 3000 m long, and in the middle is where a forest is. There's a diagonal pipeline starting from the lower left corner of the rectangle (the well site) to the upper right corner of the rectangle (the storage facility). It wil cost $230/m to lay pipeline parallel to the roadway (horizontal line) and$260/m to lay pipeline through the forested area (diagonal line).
However the diagonal line isn't directly connected from the well site to the storage facility--the company would lay 500 m of pipeline parallel to the roadway while the rest of the pipeline through the forested area (diagonal line). The horizontal line begins at 10 000 m, but decreases every 500 m as the pipeline parallel to the horizontal increases every 500 m.
First I designed a spreadsheet with values. The first column (a) is 'trial number' [let's call this y], the second (b) is 'distance of pipeline parallel to roadway in meters' [let's call this x], third is 'cost of pipeline through forested area in $' (c), fourth (d) is 'cost of pipeline through forested area in$' fifth (e) is 'cost of pipeline through forested area in $' and last (f) is 'total cost of pipeline in$'. For example one of the rows would be:
1 // 500y // √[((10 000 - x)²) + (3000²)] // {√[((10 000 - x)²) + (3000²)]} • 260 // x • 230 // [{√[((10 000 - x)²) + (3000²)]} • 260] + [x • 230]
Simply put it would look like:
1 // 500a // √[((10 000 - x)²) + (3000²)] // 260 • c // 230 • x // d + e
I have to do this for about 25 trials until the distance of pipeline parallel to roadway is 10 000 m. I found that the least expensive path was when the pipeline parallel to the roadway is 4 500 m.
I have to find the formula first for the equation using technology (I haven't gotten that far yet but I know what to do), but once I find the formula my next task is to find the least expensive path using calculus and algebra.
My question is: I'm not exactly sure how to set this question up. Basically I have a rectangle where the vertical is always 3000 m. I have a diagonal line attached to another horizontal line; the horizontal line increasing 500 m while the horizontal line of the rectangle decreases 500 m. I know my solution would probably have to end up being 4 500.
I'm not asking for a full solution (if you're not comfortable with that), but I would be very grateful for any help or tips on solving this.
Thank you very much and again, I'm sorry that this question is long!
2. I'm kinda confused by your problem, if you have a picture to go along with it that would be great. I dont know the exacts of your problem but I know what type of problem this is: Optimization/Minimalization. Heres what you need to do:
1) Set up two equations with the things you know in it, and the exact amount of piping of a certain price as x and y variables. Make sure one of the equations is for how much the total cost will be, the other will probably be for something like how much piping they have for something of a more geometric meaning. Make sure both equations are in terms of x and y, whatever x and y may be (probably the amount of piping for 230 and for 260)
2) In the equation that isnt giving the total cost, move the variables around so one variable is on one side all by itself. This is equating one variable in terms of another, so you might have $x = 2y + 6$ or something like that, thats just an example.
3) Take this expression for your one variable and plug it into the cost equation, you should realize that now your cost equation is all in terms of one variable.
4) Graph the cost equation now in one variable on your calulator, and than just look for the point where the curve on the screen is the lowest, this represents the x value at which cost is the least. This x value is your x answer, just plug it into the other equation to find your y and now you have your answers of how much pipe of each type is needed.
Hope this helps
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http://mathhelpforum.com/discrete-math/136342-cardinality-question.html
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# Math Help - Cardinality Question
1. ## Cardinality Question
Let S be the set of real numbers r s.t. $\cos (r) \in Q\sqrt 2$.
$Q\sqrt 2$ be the set of real numbers of the form $a+b\sqrt 2$, where a,b is rational.
Find the cardinality of S.
I know 0,2pi,4pi.. etc are in S, so S is infinite
and $Q\sqrt 2$ is countably infinite (dont know if it matters)
then im not sure how to go on...any hints would be appreciated.
2. For each number $x\in\mathbb{R}$, the set $\{r\in\mathbb{R}\mid\cos(r)=x\}$ is at most countable. Picture the (co)sine wave that is crossed by a horizontal line; there are at most countably many intersection points.
Now, $\{r\in\mathbb{R}\mid\cos(r)\in\mathbb{Q}(\sqrt{2}) \}=\bigcup_{x\in\mathbb{Q}(\sqrt{2})}\{r\in\mathbb {R}\mid\cos(r)=x\}$, so...
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https://socratic.org/questions/what-is-a-summary-of-differentiation-rules
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Calculus
Topics
What is a summary of Differentiation Rules?
Aug 4, 2014
Power rule:
if $f \left(x\right) = {x}^{n}$ then $f ' \left(x\right) = n {x}^{n - 1}$
Sum rule:
if $f \left(x\right) = g \left(x\right) + h \left(x\right)$ then $f ' \left(x\right) = g ' \left(x\right) + h ' \left(x\right)$
Product rule:
if $f \left(x\right) = g \left(x\right) h \left(x\right)$ then $f ' \left(x\right) = g ' \left(x\right) h \left(x\right) + g \left(x\right) h ' \left(x\right)$
Quotient rule:
if $f \left(x\right) = g \frac{x}{h \left(x\right)}$ then $f ' \left(x\right) = \frac{g ' \left(x\right) h \left(x\right) - g \left(x\right) h ' \left(x\right)}{h \left(x\right)} ^ 2$
Chain rule:
if $f \left(x\right) = h \left(g \left(x\right)\right)$ then $f ' \left(x\right) = h ' \left(g \left(x\right)\right) g ' \left(x\right)$
Or:
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$
Impact of this question
951 views around the world
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http://www.machinedlearnings.com/2010/10/prioritizing-machine-learning-part-ii.html
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## Friday, October 22, 2010
### Prioritizing Machine Learning Part II
So the empirical policy estimators I discussed in my previous post provide a way of addressing some of the quandaries that arise when I get asked what is the business impact of a proposed change to a decision system?'' There are a few issues and provisos but no show stoppers.
The first issue is that the main system I'm asked to prognosticate about does not operate by frequently making a decision involving a few actions (e.g., like an ad server does); instead it infrequently makes a decision involving a large number of actions (e.g., like an airline might do when planning its flight schedule). Fortunately it has done this enough times that I can consider myself possessing a sample of data $H$ of the form $\{ (x, \mathcal{A}, \{ r (a) | a \in \mathcal{A} \}) \}$. That suggests something like the empirical value estimator for set revelation, $\sum_{(x, \mathcal{A}, \{ r (a) | a \in \mathcal{A} \}, p) \in H} r (\pi (x)) \frac{1_{\pi (x) \in \mathcal{A}}}{p (\pi (x) \in \mathcal{A} | x)}.$ Going forward, I'll still be making decisions in large sets rather than individually, but I'm assuming that the reward for a set is the sum of the rewards for the actions, so this should work $\ldots$
Except for the second issue, which is that the historical policy $p (a \in \mathcal{A} | x)$ is unknown. This is because the historical policy is actually a deterministic global optimization routine. Here I can hope to use ideas from Strehl et. al. to consider the historical data as implicitly exploratory, estimate $\hat p (a \in \mathcal{A} | x)$, and use $\sum_{(x, \mathcal{A}, \{ r (a) | a \in \mathcal{A} \}) \in H} r (\pi (x)) \frac{1_{\pi (x) \in \mathcal{A}}}{\max \{ \tau, \hat p (\pi (x) \in \mathcal{A} | x)\} }.$ I'll need to verify that the analysis in Strehl et. al., which was for single actions, holds when sets are chosen and revealed (presumably yes). I'll also need to arrange for new policy to have sufficient historical support, i.e., I can't allow actions to be chosen which have a $\hat p$ which is too small (actual code must be written to enforce this). Therefore, since I want to have the possibility of breaking out of the chains of history, I'll have to include some exploration decisions into the decision making process (currently, there are none).
Finally, the proviso: this technique will only work for predicting rewards that are unambiguously associated with a single action. So I'll need to set expectations here. For instance, how will users spend over the next year change as a result of this decision system tweak?'' is not a fair question (for the above technique). However a related and fair question is how will users immediate spend in response to actions change as a result of this decision system tweak?'', and hopefully some other hand-waving can be employed to project longitudinal spend based upon short-term spend.
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|
http://math.stackexchange.com/questions/135627/explanation-of-a-mathematical-phenomenon
|
# Explanation of a mathematical phenomenon?
I recently came upon a strange pattern, and have absolutely no idea why it exists. I was hoping for an explanation.
Let there be three integers: $p$, $a$ and $n$; $p$ is any prime number, while $a$ and $n$ are numbers such that $1\leq a < p$ and $1 \leq n < p$
Let Set $S$ be $\{{an^1\pmod p, an^2\pmod p, \dots, an^{p-1}\pmod p\}}$. Why is it that the number of distinct numbers in Set $S$ is always a divisor of $p-1$?
An example : Let $p$ be 7, $a$ be $3$ and $n$ be $2$.
Therefore Set S would be : $\{{3 * 2^1\pmod7,\dots,3* 2^6\pmod7\}}$
which equals to: $6\pmod 7$, $5\pmod7$, $3\pmod 7$, $6\pmod7$, $5\pmod7$, $3\pmod7$.
There are 3 distinct numbers in this set. $6$, or $p-1$, is divisible by $3$.
This is true for any prime $p$. Why is the number of distinct numbers in Set $S$ always a divisor of $p-1$?
I realize this is a seemingly random pattern, but I need to understand it to complete my paper.
-
– Qiaochu Yuan Apr 23 '12 at 4:27
Fixed link: Lagrange's theorem (group theory) – Rahul Apr 23 '12 at 6:00
Without group theory:
Look at your 7, 3, 2 example. Note how the numbers go 6, 5, 3, 6, 5, 3; you get the distinct numbers 6, 5, 3, and then they repeat. Well, that always happens: you get a string of distinct numbers, and then that string repeats, exactly, until you get to the end. Since you write down $p-1$ numbers total, and the string repeates exactly until you have written down the $p-1$ numbers, the number of numbers in the string must be a factor of $p-1$.
Well, there are a few assertions in that paragraph that need to be proved. You don't need group theory to prove them, you can find the topic discussed (although not in exactly the terms I've used) in any introductory Number Theory text. I'm sorry, but I'm not up to writing it all out here.
-
Thanks. Just one question: Why do you a string of distinct numbers? – user26649 Apr 23 '12 at 22:08
Not sure I understand your question. Do you mean, why do you get a string of distinct numbers? Well, you get a list of numbers, and they are distinct until there is a repeat. What I asserted without proof is that the first number to repeat is always the first number in the list, and that thereafter everything repeats exactly that first string of distinct numbers. If I have misunderstood your question, please try again. – Gerry Myerson Apr 24 '12 at 2:03
Sorry, stupid typo. That partially answered my question- I'm confused as to why it repeats after a number of distinct numbers that can divide $p-1$. As in why does it restart it's cycle after 3 distinct numbers? Why not 4 or some other number not a divisor of $p-1$? – user26649 Apr 24 '12 at 3:43
If it started cycling after some number of terms not a divisor of $p-1$, then you'd reach term number $p-1$ in the middle of a cycle. But there's a theorem that says that $n^p\equiv n\pmod p$, so in fact when you reach $p-1$ you have to be ready to start a new cycle, not be in the middle of an old one. This is called Fermat's little theorem, and is another one of those topics discussed in intro number theory texts. – Gerry Myerson Apr 24 '12 at 6:02
Awesome, thanks! – user26649 Apr 24 '12 at 13:09
Hint $\$ Given you have no knowledge of group theory, you can employ these two simple facts.
$(1)\ \ \ \rm mod\ p\!:\ n^{p-1}\equiv 1\ \Rightarrow\:$ the order k of n divides $\rm p\!-\!1,\:$ i.e. $\:\!$ if $\rm\:k>0\:$ is least such that $\rm n^k\equiv 1\:$ then $\rm\:k\ |\ p\!-\!1.\:$ Thus the sequence of powers $\rm\:n,n^2,\ldots,n^{p-1}\:\!$ decomposes into the subsequence $\rm\:n,n^2,\ldots,n^k\!\equiv\! 1\:$ repeated $\rm\:(p\!-\!1)/k\:$ times.
$(2)\ \$ The map $\rm\:x \to a\:\!x\:$ is $1\!-\!1$ since $\rm\:a\not\equiv 0\:$ $\Rightarrow$ $\rm\:a^{-1}\:$ exists mod $\rm p.\:$ Hence scaling all elements of the repeated subsequence by $\rm\: a\:$ preserves its length, i.e. the elements remain distinct. Note that the elements of the original subsequence are distinct, else $\rm\:n^i \equiv n^j\:$ for $\rm\:1\le i < j \le k\:$ yields $\rm\:n^{j-i}\equiv 1\:$ for $\rm\:0 < j\!-\!i < k,\:$ contra minimality of $\rm k$ (here, again, we've used the fact that $\rm\: mod\ p\!:\ n\not\equiv 0\:$ implies that $\rm\:n^{-1}$ exists, hence $\rm\:n\:$ is cancellable from both sides of a congruence).
-
This is an example of Lagrange's theorem in group theory. The elements $an^k$ form a coset in the group $U_p$, the multiplicative group of the field of $p$ elements.
-
... actually in the group $U_p$ (the nonzero integers mod $p$ under multiplication mod $p$, rather than all the integers mod $p$ under addition mod $p$). – Robert Israel Apr 23 '12 at 4:30
I have absolutely no knowledge about group theory (I do not even know what a group is). Can this be explained without group theory, or would I need to learn it? – user26649 Apr 23 '12 at 4:42
@Farhad: this is group theory. Any explanation of this phenomenon would constitute an explanation of (a small part of) group theory. – Qiaochu Yuan Apr 23 '12 at 5:03
@Qiaochu, sure, but the phenomenon was known long before there was any such discipline as group theory, and can be explained without any reference to group theory. – Gerry Myerson Apr 23 '12 at 5:07
|
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|
https://www.jw.org/en/library/bible/american-standard-version/books/numbers/19/
|
# Numbers 19:1-22
19 And Jehovah spake unto Moses and unto Aaron, saying, 2 This is the statute of the law which Jehovah hath commanded, saying, Speak unto the children of Israel, that they bring thee a red heifer without spot, wherein is no blemish, and upon which never came yoke. 3 And ye shall give her unto Eleazar the priest, and he shall bring her forth without the camp, and one shall slay her before his face: 4 and Eleazar the priest shall take of her blood with his finger, and sprinkle her blood toward the front of the tent of meeting seven times. 5 And one shall burn the heifer in his sight; her skin, and her flesh, and her blood, with her dung, shall he burn: 6 and the priest shall take cedar-wood, and hyssop, and scarlet, and cast it into the midst of the burning of the heifer. 7 Then the priest shall wash his clothes, and he shall bathe his flesh in water, and afterward he shall come into the camp, and the priest shall be unclean until the even. 8 And he that burneth her shall wash his clothes in water, and bathe his flesh in water, and shall be unclean until the even. 9 And a man that is clean shall gather up the ashes of the heifer, and lay them up without the camp in a clean place; and it shall be kept for the congregation of the children of Israel for a water for impurity: it is a sin-offering. 10 And he that gathereth the ashes of the heifer shall wash his clothes, and be unclean until the even: and it shall be unto the children of Israel, and unto the stranger that sojourneth among them, for a statute for ever. 11 He that toucheth the dead body of any man shall be unclean seven days: 12 the same shall purify himself therewith on the third day, and on the seventh day he shall be clean: but if he purify not himself the third day, then the seventh day he shall not be clean. 13 Whosoever toucheth a dead person, the body of a man that hath died, and purifieth not himself, defileth the tabernacle of Jehovah; and that soul shall be cut off from Israel: because the water for impurity was not sprinkled upon him, he shall be unclean; his uncleanness is yet upon him. 14 This is the law when a man dieth in a tent: every one that cometh into the tent, and every one that is in the tent, shall be unclean seven days. 15 And every open vessel, which hath no covering bound upon it, is unclean. 16 And whosoever in the open field toucheth one that is slain with a sword, or a dead body, or a bone of a man, or a grave, shall be unclean seven days. 17 And for the unclean they shall take of the ashes of the burning of the sin-offering; and running water shall be put thereto in a vessel: 18 and a clean person shall take hyssop, and dip it in the water, and sprinkle it upon the tent, and upon all the vessels, and upon the persons that were there, and upon him that touched the bone, or the slain, or the dead, or the grave: 19 and the clean person shall sprinkle upon the unclean on the third day, and on the seventh day: and on the seventh day he shall purify him; and he shall wash his clothes, and bathe himself in water, and shall be clean at even. 20 But the man that shall be unclean, and shall not purify himself, that soul shall be cut off from the midst of the assembly, because he hath defiled the sanctuary of Jehovah: the water for impurity hath not been sprinkled upon him; he is unclean. 21 And it shall be a perpetual statute unto them: and he that sprinkleth the water for impurity shall wash his clothes, and he that toucheth the water for impurity shall be unclean until even. 22 And whatsoever the unclean person toucheth shall be unclean; and the soul that toucheth it shall be unclean until even.
|
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|
https://neonira.github.io/offensiveProgrammingBook_v1.2.2/generating-r-documentation.html
|
# 11 Generating R documentation
A good practice of coding is producing related documentation. Easy to say, particularly annoying to achieve.
Package wyz.code.rdoc aims to ease R documentation generation. Its works whatever the offensive programming instrumentation reached. In particular, under no instrumentation you can still generate R documentation.
Using wyz.code.rdoc, manual pages .Rd files stored in man folder in a package context can be automatically created and filled up nearly to completion, depending on the level of offensive programming instrumentation of your code.
Generated manual pages uses English language. Feel free to modify produced English, to match your own English flavor, if needed.
The level of your R code instrumentation will impact the quality of the generation and your review work depth and time. When using both function return type instrumentation and test case instrumentation, expects produced manual page content to be fully generated and ready for review.
When your code is not offensive programming instrumented, documentation generation is still possible. Thanks to customization as code, you may provide your customization to patch generated content.
## 11.1 Conceptual approach
Package wyz.code.rdoc provides an API you can use to generate your manual pages. The approach followed is different from already well known documentation generation approaches, utils and roxygen2 approaches. Refer to vignette named tutorial of wyz.code.rdoc for a detailed explanations of approaches and comparison with wyz.code.rdoc.
In short, while utils generates a documentation template for you to fill in with your documentation content, roxygen2 instruments comments in your code to generate on-demand the documentation by an automated process. In contrary wyz.code.rdoc uses code to generate documentation. The main benefit is that is allows you to customize the result by the code, thus offering a higher degree of freedom, higher reproducibility while saving time.
## 11.2 Vignettes
Package wyz.code.rdoc provides a vignette named documentation that presents all vignettes of this package to grant an easy navigation. Please refer to this vignette and browse tutorial, use cases, and tips and tricks to know more about wyz.code.rdoc functionalities.
## 11.3API
Package wyz.code.rdoc allows to generate all kind of manual pages, in particular manual pages for data, functions, and R objects of various types environment, S3, S4, R6, RC.
The API allows you to meet the real R specification as described in document Writing R extensions, by providing R functions to ease handling of manual pages markup language and of special required constructs.
You may add missing sections, format presentations, x-ref other manual pages, add URLs, change phraseology and/or content as needed. wyz.code.rdoc provides a convenient and easy way to do so. Let’s see how through some examples.
## 11.4 Best generation strategy
The best manual pages generation strategies are presented below from best to worst
full automated generation no hand edition, reproducibility, robustness, reusable not always applicable. See 11.7.
partially automated generation hand edition is allowed Sometimes the shortest path. Hand modifications may be lost while regenerating content. Constrained reproducibility.
Stick to full automated generation wherever possible. Also, keep it simple and stupid. It is possible to enter very deep complexity using wyz.code.rdoc, indeed good documentation generally requires good presentation and good wording. The later is generally forgotten and does not depends on any software piece.
## 11.5 Pure R function
Let’s consider following R function named pure_r.
library(wyz.code.rdoc)
nop <- function() {}
pure_r <- nop
formals(pure_r) <- alist(x = , y = NULL, z = FALSE)
Now, let’s create its documentation as in package my_package, using wyz.code.rdoc.
ic <- InputContext(object = NULL, method = 'pure_r', package = 'my_package')
pc <- ProcessingContext(extraneous = list(
concept = 'my concept',
keyword = 'utils'
)
)
gc <- GenerationContext(verbosity = TRUE, overwrite = TRUE)
pmp <- produceManualPage(ic, pc, gc)
#>
#> ------------------------------------------------------------------------------
#> Creating manual page for function pure_r
#> standard section multi concept
#> standard section multi keyword
#> wrote file /tmp/RtmpgMcFnE/pure_r.Rd
#> filename is /tmp/RtmpgMcFnE/pure_r.Rd [OVERWRITTEN]
#> generated 9 sections: name, alias, title, usage, arguments, author, keyword, concept, encoding
#> missing 3 sections: description, value, examples
#> probably missing 1 section: details
#> replacements to manage: 3
#> WARNING: File /tmp/RtmpgMcFnE/pure_r.Rd
#> checkRd: (5) /tmp/RtmpgMcFnE/pure_r.Rd:0-20: Must have a \description
First, notice that you passed the function name, not the function itself. Second, notice I set overwrite in order to be able to change file if it exists. Without this option, processing will take place but won’t be saved into the targeted file name.
The result tells you what happened. By default generation uses folder /tmp. You may change this by providing setting argument /tmp of object GenerationContext.
The provided results is oriented towards good documentation production. As we are documenting a function, sections descriptions, details, values and examples should be present.
The warning shown comes from standard R documentation verification tool, namely tools::checkRd. This tool is use when checking package. You must get rid of errors, warnings and notes if you plan to publish your package.
Let’s do it.
examples <- list(
function() { pure_r(sum, 1:5) },
function() { pure_r(setenv) }
)
pc <- ProcessingContext(extraneous = list(
description = 'tells if an R function is pure or not',
details = 'A function is told to be pure if bla bla bla',
value = 'A single boolean value',
examples = convertExamples(examples, captureOutput = FALSE),
concept = 'my concept',
keyword = 'utils'
)
)
pmp2 <- produceManualPage(ic, pc, gc)
#>
#> ------------------------------------------------------------------------------
#> Creating manual page for function pure_r
#> standard section mono description
#> standard section mono details
#> standard section mono value
#> standard section mono examples
#> standard section multi concept
#> standard section multi keyword
#> wrote file /tmp/RtmpgMcFnE/pure_r.Rd
#> filename is /tmp/RtmpgMcFnE/pure_r.Rd [OVERWRITTEN]
#> generated 13 sections: name, alias, title, description, usage, arguments, details, value, author, examples, keyword, concept, encoding
#> replacements to manage: 6
#> File /tmp/RtmpgMcFnE/pure_r.Rd passes standard documentation checks
The generated manual page now passed the standard R documentation verification. Let’s have a look to generated file now.
cat(paste(readLines(pmp2$context$filename, warn = FALSE), collapse = '\n'))
#> \name{pure_r}
#> \alias{pure_r}
#> \title{Function pure_r}
#> \description{
#> tells if an R function is pure or not
#> }
#> \usage{
#> pure_r(x, y, z = FALSE)
#> }
#> \arguments{
#> \item{x}{XXX_004}
#> \item{y}{XXX_005}
#> \item{z}{XXX_006}
#> }
#> \details{
#> A function is told to be pure if bla bla bla
#> }
#> \value{
#> A single boolean value
#> }
#> \author{
#> \packageAuthor{my_package}
#>
#> Maintainer: \packageMaintainer{my_package}
#> }
#> \examples{
#> # ------- example 1 -------
#> pure_r(sum, 1:5)
#>
#> # ------- example 2 -------
#> pure_r(setenv)
#>
#> }
#> \keyword{utils}
#> \concept{my concept}
#> \encoding{UTF-8}
As you see, some content as been generated with place holders prefixed by XXX. Although valid from a format point of view, this is meaningless, and should be corrected. You could fix it manually, but you will lose the ability to regenerate the manual page without losing some manual changes already made. Changing it by code keeps evolutivity and regeneration clean. Here is how to fix it, just use post processing.
pc <- ProcessingContext(extraneous = list(
description = 'tells if an R function is pure or not',
details = 'A function is told to be pure if bla bla bla',
value = 'A single boolean value',
examples = convertExamples(examples, captureOutput = FALSE),
concept = 'my concept',
keyword = 'utils'
),
postProcessing = list(
arguments = function(content_s) {
s <- sub('XXX_007', sentensize('a typical description for variable x'),
content_s, fixed = TRUE)
s <- sub('XXX_008', sentensize('a typical description for variable y'), s, fixed = TRUE)
s <- sub('XXX_009',
sentensize('a typical description for variable z'),
s, fixed = TRUE)
s
}
)
)
pmp3 <- produceManualPage(ic, pc, gc)
#>
#> ------------------------------------------------------------------------------
#> Creating manual page for function pure_r
#> standard section mono description
#> standard section mono details
#> standard section mono value
#> standard section mono examples
#> standard section multi concept
#> standard section multi keyword
#> patch arguments
#> wrote file /tmp/RtmpgMcFnE/pure_r.Rd
#> filename is /tmp/RtmpgMcFnE/pure_r.Rd [OVERWRITTEN]
#> generated 13 sections: name, alias, title, description, usage, arguments, details, value, author, examples, keyword, concept, encoding
#> patched 1 section: arguments
#> replacements to manage: 9
#> File /tmp/RtmpgMcFnE/pure_r.Rd passes standard documentation checks
cat(paste(readLines(pmp3$context$filename, warn = FALSE), collapse = '\n'))
#> \name{pure_r}
#> \alias{pure_r}
#> \title{Function pure_r}
#> \description{
#> tells if an R function is pure or not
#> }
#> \usage{
#> pure_r(x, y, z = FALSE)
#> }
#> \arguments{
#> \item{x}{A typical description for variable x.}
#> \item{y}{A typical description for variable y.}
#> \item{z}{A typical description for variable z.}
#> }
#> \details{
#> A function is told to be pure if bla bla bla
#> }
#> \value{
#> A single boolean value
#> }
#> \author{
#> \packageAuthor{my_package}
#>
#> Maintainer: \packageMaintainer{my_package}
#> }
#> \examples{
#> # ------- example 1 -------
#> pure_r(sum, 1:5)
#>
#> # ------- example 2 -------
#> pure_r(setenv)
#>
#> }
#> \keyword{utils}
#> \concept{my concept}
#> \encoding{UTF-8}
Note that I had to infer variable names for next generation, not just had to use previous ones! Now, generated manual pages looks acceptable, from a content and format point of view.
From documentation quality point of view, understand-ability is insufficient according to me, due to genericity of phraseology. Use specific terminology to make things crystal clear and easy to understand for most of your readers.
Now that you understood the global pattern, you may use immediately a pattern like the one used for the final case above, to get in one single shot a manual page from an R function.
## 11.6 Offensive programming R function
Using an offensive programming instrumented function eases processing in comparison to previous case. Let’s see how
op_r <- nop
formals(op_r) <- alist(functionName_f_1 = , functionArguments_l = NULL, verbosityFlag_b_1 = FALSE)
Now, let’s create its documentation as in package my_package, using wyz.code.rdoc.
examples <- list(
function() { op_r(sum, 1:5) },
function() { op_r(setenv) }
)
ic <- InputContext(object = NULL, method = 'op_r', package = 'my_package')
pc <- ProcessingContext(extraneous = list(
description = 'tells if an R function is pure or not',
details = 'A function is told to be pure if bla bla bla',
value = 'A single boolean value',
examples = convertExamples(examples, captureOutput = FALSE),
concept = 'my concept',
keyword = 'utils'
)
)
gc <- GenerationContext(verbosity = TRUE, overwrite = TRUE)
omp <- produceManualPage(ic, pc, gc)
#>
#> ------------------------------------------------------------------------------
#> Creating manual page for function op_r
#> standard section mono description
#> standard section mono details
#> standard section mono value
#> standard section mono examples
#> standard section multi concept
#> standard section multi keyword
#> wrote file /tmp/RtmpgMcFnE/op_r.Rd
#> filename is /tmp/RtmpgMcFnE/op_r.Rd [OVERWRITTEN]
#> generated 13 sections: name, alias, title, description, usage, arguments, details, value, author, examples, keyword, concept, encoding
#> File /tmp/RtmpgMcFnE/op_r.Rd passes standard documentation checks
cat(paste(readLines(omp$context$filename, warn = FALSE), collapse = '\n'))
#> \name{op_r}
#> \alias{op_r}
#> \title{Function op_r}
#> \description{
#> tells if an R function is pure or not
#> }
#> \usage{
#> op_r(functionName_f_1, functionArguments_l, verbosityFlag_b_1 = FALSE)
#> }
#> \arguments{
#> \item{functionName_f_1}{A single function value}
#> \item{functionArguments_l}{An unconstrained list}
#> \item{verbosityFlag_b_1}{A single boolean value}
#> }
#> \details{
#> A function is told to be pure if bla bla bla
#> }
#> \value{
#> A single boolean value
#> }
#> \author{
#> \packageAuthor{my_package}
#>
#> Maintainer: \packageMaintainer{my_package}
#> }
#> \examples{
#> # ------- example 1 -------
#> op_r(sum, 1:5)
#>
#> # ------- example 2 -------
#> op_r(setenv)
#>
#> }
#> \keyword{utils}
#> \concept{my concept}
#> \encoding{UTF-8}
As you can see, no more need to qualify arguments. Semantic naming is used to generate the content. If generated content does not match perfectly your need, you can still apply post processing in a somewhat similar or dissimilar way.
For convenience, just know that you can easily generate argument section content using following approach
dt <- data.table(fields = letters[24:26],
description = paste('a typical description for variable',
letters[24:26]))
sapply(seq_len(nrow(dt)), function(k) {
generateMarkup(dt[k]$fields, 'item', dt[k]$description)
})
#> [1] "\\item{x}{a typical description for variable x}"
#> [2] "\\item{y}{a typical description for variable y}"
#> [3] "\\item{z}{a typical description for variable z}"
Using such approach allows you to replace purely the content using a post processing scheme.
## 11.7 Known limits
Generation of manual pages can be quite tricky. Whereas package wyz.code.rdoc alleviates greatly the burden, some pitfalls remain. Here they are
1. Generated manual page might not respect the maximum line length required by R CMD check, and this tool will provide explicit information about noncompliance. To solve issue, just split the content by adding carriage return wherever required.
2. Generated documentation is quite stereotyped. Inject your instructions to customize the result.
## 11.8 Opportunities
Reuse can be made at several levels depending of your needs. Roughly speaking, you may aim for one of these 3 levels of customization
1. just customize some textual information. Generate the pages using package wyz.code.rdoc and modify page contents manually is generally the best way to achieve this goal
2. customize some manual pages sections. Generate the pages using package wyz.code.rdoc while providing some dedicated context information. Refer to previous examples, and look at variables starting with extraneous. They allow you to inject your customized content in targeted sections.
3. If you seek for fully customized manual page generation, then you may use package (ref:rd) to create your own R generation scheme. That way you will get the benefit of starting launched, using high-level R documentation generation functions, and also get the ability to reuse and customized provided generation scheme. This package uses only R code, and so you could get insight and reuse any part of it.
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https://link.springer.com/chapter/10.1007/978-1-4614-0529-0_11
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Metrizability of Compact Sets in the Class $$\mathfrak {G}$$
• Jerzy Kąkol
• Wiesław Kubiś
• Manuel López-Pellicer
Part of the Developments in Mathematics book series (DEVM, volume 24)
Abstract
This chapter introduces (after Cascales and Orihuela) a large class of locally convex spaces under the name the class$$\mathfrak{G}$$. The class $$\mathfrak{G}$$ contains among others all (LM)-spaces (hence (LF)-spaces), and dual metric spaces (hence (DF)-spaces), spaces of distributions D′(Ω) and spaces A(Ω) of real analytic functions on open Ω⊂ℝ n . We show (following Cascales and Orihuela) that every precompact set in an lcs in the class $$\mathfrak{G}$$ is metrizable. This general result covers many already known theorems for (DF)-spaces, (LF)-spaces and dual metric spaces.
Authors and Affiliations
• Jerzy Kąkol
• 1
• Wiesław Kubiś
• 2
• 3
• Manuel López-Pellicer
• 4
• 5
1. 1.Faculty of Mathematics and InformaticsA. Mickiewicz UniversityPoznanPoland
2. 2.Institute of MathematicsJan Kochanowski UniversityKielcePoland
3. 3.Institute of MathematicsAcademy of Sciences of the Czech RepublicPraha 1Czech Republic
4. 4.IUMPAUniversitat Poltècnica de ValènciaValenciaSpain
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https://www.physicsforums.com/threads/inverse-of-exponential-function.531061/
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Inverse of exponential function
1. mark187
3
1. The problem statement, all variables and given/known data
Give the inverse of this function
N=f(L)=1816-8L
The answer has to be filled in in Maple
2. Relevant equations
3. The attempt at a solution
N=1816-8L
16-8L=ln(N)/ln(18)
-8L=(ln(N)/ln(18))-16
L=-ln(N)/(8*ln(18))+2
Is this correct?
When i fill this in in maple it's incorrect.
I've really no clue why it is wrong.
2. ehild
12,697
L=-ln(N)/(8*ln(18))+2 is the same function as the original. Choose L the independent variable and N the dependent one. (Just exchange L and N).
ehild
3. Mentallic
3,772
Yes it's correct. What are you typing into maple exactly? Your syntax is probably slightly off.
edit: Sorry I didn't notice that you forgot to swap your variables.
4. mark187
3
thanks! It's also mentioned that it should be simplified as much as possible.
Does that mean that the 8*LN(18) could be simplified to 8*LN(2*9) and more?
5. Mentallic
3,772
It's as simple as it can get, unless you believe $\ln{\frac{1}{x}}$ is more simple than $-\ln{x}$ you shouldn't be changing anything.
$\ln{18}$ is definitely more desirable than $\ln{9\cdot2}$
6. Ray Vickson
6,614
When I let Maple solve the equation for L it gives me exactly what you wrote. Why do you think Maple thinks it is incorrectÉ What type of error message are you receivingÉ
That annoying É is actually a question mark, but when I type it in it gives me that accented E; that only seems to happen when I access this website through Google Chrome!
RGV
7. mark187
3
Well, this assignment was given in a little online test.
The point is, that i can't see why the answer was wrong.
I have 2 chances, so for the second change i will try to swap the variables.
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https://aviation.stackexchange.com/questions/16597/is-a-subsonic-scram-jet-reasonable?noredirect=1
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# Is a subsonic scram-jet reasonable?
By placing a de laval nozzle at the inlet, can the resulting supersonic airflow allow a scram jet to operate efficiently?
• Welcome to Aviation.SE. what do you define as efficiently? some amount of inefficiency cannot be avoided.
– Federico
Jul 4 '15 at 18:52
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https://askbot.fedoraproject.org/en/question/60252/f21-32-bit-keeps-going-into-hibernation-every-minute/?comment=60322
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# F21 32 bit keeps going into hibernation every minute edit
the 32bit image of F21, r5 keeps on going into hibernation every minute or so on my acer aspire one netbook. During the install it was very difficult to babysit the system. The system "works well" now but fixing the constant going into hibernation makes it exceptionally difficult to do anything.
How do you stop this automatic hibernation every minute?
edit retag close merge delete
a bit of background: I had installed the xfce spin and it was stable, without the problem of the system going into hibernation mode after a minute or so. No, I am not closing the clamshell.
( 2014-12-22 22:14:30 -0500 )edit
I have reformatted with the XFCE spin, and I tried to swap in the workstation through the command line and yum. unfortunately it didn't work well and just hangs ... then while hung, it went into hibernation.
I am now reinstalling the XFCE spin, and I am very disappointed because the workstation is what I would like to install. Clearly, it installs, and clearly, beyond going into hibernation in less then a minute, and repetitively so after being reawakened, workstation otherwise works on the system (well, best I can tell).
Will the livecd be re-released with this problem left out?
( 2014-12-23 11:20:57 -0500 )edit
You can do tests and get logs without interference with systemd-inhibit - ie sudo systemd-inhibit bash. The system won't suspend or hibernate until you end the process invoked with systemd-inhibit.
( 2014-12-23 16:29:57 -0500 )edit
great, I'll try that!
Thanks
( 2014-12-23 18:25:14 -0500 )edit
I have reinstalled F21 workstation, which is what Iwouldlike to have on the system.
Unfortunately the systemd-inhibit bash command doesn't work, the system keeps on going to sleep, and wakes up right away when I hit any key and resumes where it had been a moment before.
With my "brother in the know" I will be using the XFCE live CD in live mode to mount the hard drive and try to disable the suspend functions.
Further note: This machine has had most versions of Fedora from F11 to F19 and this has never been an issue yet.
Thank you!
( 2014-12-23 20:00:13 -0500 )edit
Sort by » oldest newest most voted
The problem seems to have been fixed by:
• install F21 32bit workstation, by babysitting the system throughout the whole install to keep waking it up every minute or so (literally!)
• reboot using a live-dvd that works on the system, such as the F21 XFCE live-DVD
• mount the hard drive (not really sure specifically how my brother did it but using Thunar seemed to help out a lot)
• open a terminal session and make sure the hard drive is mounted
• edit the file /etc/systemd/logind.conf
• uncomment the settings for "HandleSuspendKey" and "HandleLidSwitch"
• set the "HandleSuspendKey" and "HandleLidSwitch" options to "ignore"
• save the file
• reboot
• enjoy
My system is not happily doing a yum update, which it couldn't do before.
more
I followed the procedure outlined above (set both "HandleSuspendKey" and "HandleLidSwitch" to "ignore" in /etc/systemd/logind.conf), and I can confirm that it fixed the same problem on my Acer Aspire One.
( 2015-01-07 14:32:34 -0500 )edit
I'm just guessing, but it feels like the system thinks that the battery is almost empty and because of that does the right thing in that situation. I'm not sure which software component is handling this situation but anyway, there seems to be a bug that happens to manifest on your particular environment.
more
In this particular case, the battery is physically out of the machine and it's running purely on mains electricity. However, I'll try plugging in the battery and reinstall.
Thanks for the suggestion / perspective!
( 2014-12-23 16:25:44 -0500 )edit
I'Ve just tried the live-cd for workstation with the battery in and fully charged (over 1hr capacity) and things are still the same.
Thanks for the suggestion though!
( 2014-12-23 16:43:05 -0500 )edit
Can anyone add to the babysitting idea, Im moving the mouse and hitting keys to select options and it still goes into suspend.So hibernating in less than a minute of inactivity Im on a Toshiba Satelite Pro. I donrt have a CD either. I successfully installed F20 prior but was having sound issues. I can therefore assume my HW is fine
more
My use of the word "babysitting" literally meant to sit in front of the computer and hit keys to wake up the computer every time it went into hibernation. During the install, I couldn't count the number of times I did that since it took probably half an hour to install this way -- so 30, 40 times of hitting the keyboard?
( 2015-02-19 12:29:46 -0500 )edit
I have Zoostorm netbook and F22 32bit same problem
more
## Stats
Asked: 2014-12-22 15:01:20 -0500
Seen: 1,639 times
Last updated: Jul 04 '15
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https://chemistry.stackexchange.com/questions/33816/maximum-useful-work-from-a-process
|
# Maximum Useful Work from a Process
Negative of the $\Delta G$ for a process is the maximum useful work that can be obtained from it (at constant pressure and temperature). I understood this in this way: $\Delta H$ is the heat absorbed by the system (since the process is at constant temperature and pressure), so equivalently $-\Delta H$ energy is obtained from the system after doing expansion work. Since $\Delta S$ is the entropy created in the process, at the very least $-\Delta S$ entropy must be created in the surroundings - that is, at least $-T\Delta S$ energy must be lost as heat. This comes from the $-\Delta H$, and thus leaves $-\Delta H + T\Delta S$ to do useful work. No more work can be done than this. $-\Delta H + T\Delta S$ is $-\Delta G$, so $-\Delta G$ is the maximum possible useful work. First of all, I wanted to know if this is correct, and if this is actually why $-\Delta G$ is the maximum possible useful work.
Now if $|\Delta H|$ is more than $|T\Delta S|$, with both being negative, then one can think of the $W_{max}$ or $-\Delta G$ as a part of the $|\Delta H|$; since $|\Delta G|< |\Delta H|$. Some part of $|\Delta H|$ goes as $|T\Delta S|$ to increase the surroundings' entropy, and the other part in doing useful work. But if both are positive, with $|T\Delta S|$ being more than $|\Delta H|$, again $\Delta G$ is negative, allowing useful work to be extracted. But now it seems as though $|T\Delta S|$ heat will be extracted from the surroundings, $|\Delta H|$ used up in the process, while the rest can be converted to work - in other words, useful work is a part of $|T\Delta S|$ - with the other part used by the process as $|\Delta H|$. Is this correct? Is $|T\Delta S|$ extracted from the surroundings actually?
"Useful work" does not include expansion work. For a proof of why $w_{\text{by,add}} \leq \Delta G$, you may want to first refer to my answer to this question: Why does the Gibbs free energy only correspond to non-expansion work? then come back here.
In that proof, I used equalities by assuming that the process is reversible. If we drop this assumption, then by the Second Law,
\begin{align} \mathrm{d}S &\geq \frac{\mathrm{d}q}{T} \\ \mathrm{d}q &\leq T\mathrm{d}S \\ dU &\leq T\mathrm{d}S - p\mathrm{d}V + \mathrm{d}w_{\text{add}} \\ dG &\leq dw_{\text{add}} \\ \Delta G &\leq w_{\text{add}} \end{align}
Equality holds if the process is reversible, or more generally, if both the initial and final states are equilibrium states. Now this seems like an obvious contradiction of the equation in the very first paragraph. The key lies in the definition of the work - whether it is done on the system, or by the system. In my proof, I have been referring to the work done on the system; however, here we are interested in the work done by the system, since that is the work that can be "extracted". The work done by the system must be equal to the negative of the work done on the system: $w_{\text{by,add}} = -w_{\text{add}}$. This leads to the final result $w_{\text{by,add}} \leq \Delta G$.
Levine's Physical Chemistry 6th ed. writes:
In many cases (for example, a battery, a living organism), the P-V expansion work is not useful work, but $w_{\text{by,add}}$ is the useful work output. The quantity $-\Delta G$ equals the maximum possible nonexpansion work output $w_{\text{by,add}}$ done by a system in a constant-$T$-and-$p$ process. Hence the term "free energy". (Of course, for a system with P-V work only, $\mathrm{d}w_{\text{by,add}} = 0$ and $\mathrm{d}G = 0$ for a reversible, isothermal, isobaric process.) Examples of nonexpansion work in biological systems are the work of contracting muscles and of transmitting nerve impulses.
If you want a direct answer as to why your explanation isn't right, it's because you can't equate $\Delta H$ with the work done. Work done is given by $w = -\int\! p\,\mathrm{d}V$. You can only equate $\Delta H$ with the heat transferred at constant $p$. Apart from the First Law ($\Delta U = q + w$), heat and work are generally unrelated.
• Yes, I understand perfectly. What I've written above seems rather nonsensical once I read your answer. – Charles Jul 14 '15 at 14:49
• Could you also explain why the thermodynamic efficiency of a cell is given by |ΔH|/|ΔG|? – Charles Jul 14 '15 at 14:53
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