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http://mathhelpforum.com/discrete-math/184921-equivalence-classes.html | # Thread:
1. ## Equivalence Classes
How do you find the distinct equivalence classes of R?
A = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. R is defined on A as follows:
For all x, y elements of A, x R y <=> 3|(x-y).
I have the answer, but I do not understand the work leading up to the answer. I appreciate any help.
I am h... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/217719/how-do-i-prove-that-a-irreducible-polynomial-in-fx-has-a-root-in-an-extension | How do I prove that a irreducible polynomial in F[x] has a root in an extension E of F.
In order to demonstrate the root extension theorem, I need to prove that if an element of F[x]/(p(x)) is represented as $\overline a =a+(p(x))$ where $p(x)=a_0+a_1x+\cdots+a_nx^n$, then$\overline a_0+\overline a_1\overline x+\cdots... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/27760/advanced-topics-in-string-theory | # Advanced topics in string theory
I'm looking for texts about topics in string theory that are "advanced" in the sense that they go beyond perturbative string theory. Specifically I'm interested in
1. String field theory (including superstrings and closed strings)
2. D-branes and other branes (like the NS5)
3. Duali... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/120601-help-dy-dx-d-2y-dx-2-problem.html | Thread:
1. Help with a dy/dx and d^2y/dx^2 problem!
Hey guys,
Just wondering if someone can please answer this question! Could really use the explanation guys.
Cheers!
Hey guys,
Just wondering if someone can please answer this question! Could really use the explanation guys.
Cheers!
The first and second derivati... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/220605/connectedness-of-two-particular-set-of-matrices/223422 | # connectedness of two particular set of matrices
I need to know whether the $1)$ The set of all symmetric positive definite matrices are connected or not?
Well I guess, This set is convex set, Let $M$ be a symmetric positive definite so $X^TMX>0, X\in \mathbb{R}^n$, now for any two such matrix $A,B$, we have $X^T[tA... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2008/12/30/dimensions-of-symmetric-and-antisymmetric-tensor-spaces/?like=1&_wpnonce=67418a1937 | # The Unapologetic Mathematician
## Dimensions of Symmetric and Antisymmetric Tensor Spaces
We’ve laid out the spaces of symmetric and antisymmetric tensors. We even showed that if $V$ has dimension $d$ and a basis $\{e_i\}$ we can set up bases for $S^n(V)$ and $A^n(V)$. Now let’s count how many vectors are in these ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 43, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/115590/one-problem-in-bounds-and-constructions-for-unconditionally-secure-distributed | ## One problem in “Bounds and constructions for unconditionally secure distributed key distribution schemes for general access structures”
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In this paper "Bounds and constructions for unconditionally secure distr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/625/why-is-the-derivative-of-a-circles-area-its-perimeter-and-similarly-for-sphere?answertab=active | # Why is the derivative of a circle's area its perimeter (and similarly for spheres)?
When differentiated with respect to $r$, the derivative of $\pi r^2$ is $2 \pi r$, which is the circumference of a circle.
Similarly, when the formula for a sphere's volume $\frac{4}{3} \pi r^3$ is differentiated with respect to $r$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 39, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/73719/injective-function-on-a-dense-set | ## Injective Function on a Dense Set
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This is a topological question that came up tangentially to some material I was working on. Suppose $X$ and $Y$ are complete metric spaces and $D$ is a dense subset of $X$. Le... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/33366/the-unprecedented-success-of-the-intersection-operator/33373 | ## The unprecedented success of the “intersection” operator
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You might think that the title is an overstatement of a well-known fact but it is the best title I can come up with for the wonders the intersection ope... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 47, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/19610/help-with-using-some-trig-identities?answertab=oldest | # Help with using some trig identities
Need some help with the steps in converting the derivatives of the following functions.
1. derivative of $\cos(\tan(x))$ to $\frac{-\sin(\tan (x))}{\cos^2(x)}$
I can get $-\sec^2(x) \cdot (\sin(\tan(x))$ using chain rule, but then I am stuck. I guess I just need help on underst... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/279976/show-that-the-distrubtion-function-f-z-of-z-suffices-f-zz-fz2?answertab=oldest | # Show that the distrubtion function $F_Z$ of $Z$ suffices $F_Z(z)=F(z)^2$
Let $X$ and $Y$ be two stochastically independent, equally distributed random variables with distribution function $F$. Define $Z = \max (X, Y)$.
1) Show that the distrubtion function $F_Z$ of $Z$ suffices $F_Z(z)=F(z)^2$.
I got this:
$F_Z(z... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/5647/note | ### Clock Hands
This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.
### Watch the Clock
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest sec... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/7832/list | Return to Answer
2 complex addendum
As long as the form is positive definite and the unit ball is convex, you get a perfectly good Banach space using any symmetric $n$-linear form on a real vector space $V$. The degree $n$ is necessarily even. It is equivalent to defining the norm as the $n$th root of a homogeneous d... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/116026/calculating-the-lebesgue-decomposition-of-a-measure | ## Calculating the Lebesgue decomposition of a measure [closed]
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How we should calculate the Lebesgue decomposition of a measure? Please explain it with an example such I can get the whole idea behind it.
-
Have... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/29300?sort=newest | ## What’s wrong with the surreals?
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Of all the constructions of the reals, the construction of the surreals seems the most elegant to me.
It seems to immediately capture the total ordering and precision of Dedeki... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/166596/when-does-non-negativity-of-the-integral-of-a-function-imply-that-the-function-i | # When does non-negativity of the integral of a function imply that the function itself is non-negative?
Let $(\Omega,\Sigma)$ be a measurable space and $(\omega_k)_{k\in\mathbb{N}}$ a sequence of elements of $\Omega$. Let $$\mathcal{M}:=\left\{\sum_{k=1}^\infty a_k\cdot\delta_{\omega_k}: \quad(a_k)_{k\in\mathbb{N}}\s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/91178/splitting-fields-of-polynomials-over-finite-fields | Splitting fields of polynomials over finite fields
I can't follow a statement in my notes:
"Let $K$ be a finite field, with $f \in K[X]$ an irreducible polynomial of degree $d$. Then any finite extension $L/K$ is normal, and so if $L$ contains one root of $f$ then it contains all the roots of $f$. Therefore, the spli... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/22366-radical-question.html | Thread:
1. Radical Question
I got in a radical 3 and 10 but I don't know what to do next.
2. Originally Posted by fluffy_penguin
I got in a radical 3 and 10 but I don't know what to do next.
$270=3^3 \times 10$
so:
$\root 3 \of{270}=3 \root 3 \of {10}$
RonL | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/52446-easy-complex-equation.html | # Thread:
1. ## easy complex equation
i know this is an easy equation by how the rest of the worksheet is i just dont know how to solve it :s Only just started the topic
solve in x and y
x + iy = 4 - 2i
2. Originally Posted by djmccabie
i know this is an easy equation by how the rest of the worksheet is i just don... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/58107/fast-algorithm-for-adding-an-equation-to-a-system?answertab=oldest | # Fast Algorithm For Adding An Equation To A System?
Assume an $N \times N$ matrix $A$ and a length $N$ vector $b$. I've already solved the system $Ax = b$ for $x$ using standard methods. (If you want you can assume that I have the inverse of $A$ as well.)
Now, I have a block matrix $$A' = \begin{pmatrix} A & V \\ U ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/99984?sort=votes | ## Line bundles and rational singularities
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Hi, I have some problem to understand the proof of lemma 3.2 of this article: http://www.ams.org/journals/jams/2001-14-03/S0894-0347-01-00368-X/.
The lemma states the f... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 31, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/22398-geometric-interpetation-addition-two-dot-products.html | # Thread:
1. ## Geometric interpetation of the addition of two dot products???
Hi,
Let's assume that one needs to calculate the dot product between two 3 dimensional vectors (unit vectors) $u_1$ and $u_2$. This can otherwise be interpreted as finding the angle between them i.e. $\cos\psi_m$.
Further assume that ano... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/58688/subspace-of-mathbbrn-spanned-by-the-image-of-convex-n-1-polyhedra-under | ## Subspace of $\mathbb{R}^n$ spanned by the image of convex $(n-1)$-polyhedra under the face-counting map
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Fix $n \in \mathbb{N}$. A convex polyhedron $C$ in $\mathbb{R}^n$ is the convex hull of finitely many poi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 49, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/37363/prime-numbers-stretch-to-infinity-but-what-about-the-distance-between-them | # Prime numbers stretch to infinity, but what about the distance between them?
That is, let $p_n$ be the nth positive prime number. Does $$L = \lim\limits_{n \to \infty} \left( p_{n+1} - p_n \right)$$ equal infinity?
-
5
I doubt whether the behavior of that sequence is completely known, since it is still unsolved wh... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/1144-number-sequences-drawing-diagram.html | # Thread:
1. ## Number sequences - drawing a diagram
From the book: "Draw a diagram that shows how the sequence of odd numbers can be used to produce the sequence of squares. The diagram can contain numbers, addition symbols, equal signs, and arrows, but it should not contain any words. Your goal is to draw the diagr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/11363/list | ## Return to Answer
4 added 26 characters in body
Regarding a question which arose in comments to another answer: The lambda ring structure is on $RG$ is not enough to reconstruct the group. Dade has given examples (MathSciNet review here; paper does not appear to be available onlinehere) of pairs of groups which hav... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/7775?sort=votes | ## Do DG-algebras have any sensible notion of integral closure?
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Suppose R → S is a map of commutative differential graded algebras over a field of characteristic zero. Under what conditions can we say that there ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 86, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/2120/does-there-exist-a-bijective-f-mathbbn-to-mathbbn-such-that-sum-fn/2122 | # Does there exist a bijective $f:\mathbb{N} \to \mathbb{N}$ such that $\sum f(n)/n^2$ converges?
We know that $\displaystyle\zeta(2)=\sum\limits_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$ and it converges.
• Does there exists a bijective map $f:\mathbb{N} \to \mathbb{N}$ such that the sum $$\sum\limits_{n=1}^{\... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/06/16/fatous-lemma/?like=1&source=post_flair&_wpnonce=9a71b83933 | # The Unapologetic Mathematician
## Fatou’s Lemma
Today we prove Fatou’s Lemma, which is a precursor to the Fatou-Lebesgue theorem, and an important result in its own right.
If $\{f_n\}$ is a sequence of non-negative integrable functions then the function defined pointwise as
$\displaystyle f_*(x)=\liminf\limits_{n... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 19, "mimetex.cgi": 0, "/images/ma... |
http://blog.aggregateknowledge.com/tag/agile-analytics/ | AK Tech Blog
Everything You Need to Know
## HLL Intersections
December 17, 2012 By
### Why?
The intersection of two streams (of user ids) is a particularly important business need in the advertising industry. For instance, if you want to reach suburban moms but the cost of targeting those women on a particular inv... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 87, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/89750/showing-two-matrices-are-similar?answertab=oldest | # Showing two matrices are similar
I have to show that each of the following matrices
$$\frac{1}{\sqrt{2}} \begin{pmatrix} 0&1&0\\ 1&0&1\\ 0&1&0 \end{pmatrix}\quad , \frac{1}{\sqrt{2}} \begin{pmatrix} 0&-i&0\\ i&0&-i\\ 0&i&0 \end{pmatrix} , \begin{pmatrix} 1&0&0\\ 0&0&0\\ 0&0&-1 \end{pmatrix}$$
are equivalent to one... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/relative-motion+inertial-frames | # Tagged Questions
4answers
147 views
### Inertial Frames of Reference - Inertial vs. Accelerated Frames
According to Robert Resnick's book "Introduction to Special Relativity", a line states the following as the definition of an inertial frame of reference: "We define an inertial system as a frame of ...
2answers
7... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/math-topics/24300-four-4-s-urgent-help-needed.html | # Thread:
1. ## Four 4's: Urgent help needed
Hey all,
I could really use some help with this one:
Using four 4's and any combination of math operations, represent as many of the whole numbers 1-100 as you can.
I found operations that result in: 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 16, 20, 24, 36, 60, 64, 65, 68, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 21, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/45702-area-region-between-two-curves-print.html | # Area of the Region Between Two Curves
Printable View
• August 10th 2008, 08:45 PM
MathGeek06
Area of the Region Between Two Curves
Find the area of the region between y = x^2 and y = 4-3x from x = -1 to x = 4/3
• August 10th 2008, 08:52 PM
Chris L T521
Quote:
Originally Posted by MathGeek06
Find the area of the re... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/126028/distance-between-parametric-function-and-a-point/126032 | # Distance between parametric function and a point
Given a parametric function $$\begin{align*} x &= x_o + v_x t + \frac{1}{2} a_x t^2\\ y &= y_o + v_y t + \frac{1}{2} a_y t^2\end{align*}$$
and point $P$ at $(c, d)$ , find all point(s) on the function that are distance $R$ from point $P$, assuming that $R > 0$ and no... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/189307-linear-equation-matrices.html | Thread:
1. Linear Equation and matrices.
It's been a ten years ago when I learning those equations, some how recently my boss just give me a question and asking for help, I d't have any ideal back to carry out those equation where all the knowledge already give back to teacher, i guess.
Therefore, hope some one here... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Laws_of_Kepler | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 43, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/5937/what-happens-if-an-rsa-key-pair-has-identical-public-and-private-exponents/5938 | # What happens if an RSA key pair has identical public and private exponents?
Rather, is it possible for big prime numbers?
Classroom examples usually involve smaller primes, so for example if you are given a prime number pair $p = 3$, $q = 13$ you would get $n = 39$ and $e = d = 5$, making encryption and decryption ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/109603/list | ## Return to Answer
3 edited body
I think that the explanation
"Because the Cartan classification of isomorphism classes of semisimples is discrete (no continuous families), connected components of the space of semisimples are always contained within isomorphism classes"
is a bit simplistic. The real reason, as man... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 99, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/dipole+time-reversal | # Tagged Questions
2answers
106 views
### Power due to dipole radiation and time reversal symmetry in classical E&M
The dipole formula for the power loss emitted by a time varying electric dipole is (in natural units) $P = \frac{\dot d_i^2}{6 \pi}$. This is clearly even under time reversal symmetry $T$, but a ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/library.php?do=view_item&itemid=287 | Physics Forums
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Vi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 58, "mathjax_display_tex": 17, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/45055/hamiltonian-in-position-basis | # Hamiltonian in position basis
Let $H = \frac{-h^2}{2m}\frac{\partial^2 }{\partial x^2}$. I want to find the matrix elements of $H$ in position basis. It is written like this:
$\langle x \mid H \mid x' \rangle = \frac{-h^2}{2m}\frac{\partial^2}{\partial x^2} \delta(x -x')$.
How do we get this? are we allowed to do ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=613582 | Physics Forums
Page 1 of 2 1 2 >
## Why is quantum entanglement special?
Clearly, I am a newb at this. However:
I was reading a bit on qubits and quantum entanglement and -- though I know that QM has no analog to classical mechanics -- the general concept seems to be: two particles interact and become quantum ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/51553-3x3-matrix-eigenvalues.html | # Thread:
1. ## 3x3 Matrix - Eigenvectors
Okey, im trying to find the eigenvectors of a 3x3 matrix.
(I have found the eigenvalues)
I'm going to use an example so I can solve my own matrix myself;
In this example the eigenvectors are found, but how?
So my question is How are the calculations done to recieve the valu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://theoryclass.wordpress.com/2012/09/29/walrasian-with-indivisible-goods/?like=1&_wpnonce=84af3d0b4c | # Walrasian with Indivisible Goods
September 29, 2012 in Auctions, Mechanism design
A paper by Azevdo, Weyl and White in a recent issue of Theoretical Economics caught my eye. It establishes existence of Walrasian prices in an economy with indivisible goods, a continuum of agents and quasilinear utility. The proof us... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 50, "mimetex.cgi": 0, "/images/ma... |
http://scicomp.stackexchange.com/questions/2710/a-sufficient-number-of-distances-to-recover-relative-positions-of-n-points | # A sufficient number of distances to recover relative positions of n points
On several places I found different claims on a sufficient number of distances to recover relative positions of $n$ points in $d$-dimensional space.
For instance, work from
http://www.dimitris-agrafiotis.com/Papers/jcc20078.pdf
(page 5, ri... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/52739/setting-up-a-local-coordinate-system-in-space-time-using-only-a-single-clock-and?answertab=votes | # Setting up a local-coordinate system in space-time using only a single clock and light beams
I have a question to ask about the operationalist view of space-time. I am a mathematician who happens to be interested in physics, so if anyone thinks that my question is a silly or vague one, please feel free to close it.
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikibooks.org/wiki/Haskell/YAHT/Type_basics | # Haskell/YAHT/Type basics
Preamble
Introduction
Getting Started
Language Basics (Solutions)
Type Basics (Solutions)
IO (Solutions)
Modules (Solutions)
Advanced Language (Solutions)
Advanced Types (Solutions)
Monads (Solutions)
Advanced IO
Recursion
Complexity
This box: view • talk • edit
Haskell uses a system of sta... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 35, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/15805/convert-acceleration-as-a-function-of-position-to-acceleration-as-a-function-of | # Convert acceleration as a function of position to acceleration as a function of time?
Suppose I have acceleration defined as a function of position, "a(x)". How to convert it into a function of time "a(t)"? Please give an example for the case a(x)= x/s²
-
It's not a homework but OK. – WindScar Oct 17 '11 at 0:50
T... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/69918/projective-plane-and-some-curves | # Projective plane and some curves
We define a line in the projective plane as a set of the form $$L_{a,b,c} = \left\{ {\left[ {x,y,z} \right] \in P_R^2 :ax + by + cz = 0} \right\}\text{ or just }L$$ Let a finite collection of lines $$\left\{ {L_i } \right\}_{i = 1}^n$$ such that $$\bigcap\limits_{i = 1}^n {L_i }$$ it... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Thurston's_geometrization_conjecture | # Geometrization conjecture
(Redirected from Thurston's geometrization conjecture)
In mathematics, Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the un... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/business-math/148082-minimum-variance-profit-rate.html | # Thread:
1. ## the minimum variance of the profit rate
There are one riskless bond and a bunch of stocks with risk in the market. For the expected profit r>1 (or r=1) the minimum variance of the profit rate for the risk papers is
σ^2(r)=r^2-2r+2.
Let's asume that we have a portfolio with both riskless bonds and st... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=2845564 | Physics Forums
Page 1 of 2 1 2 >
## 2nd order nonlinear differential equation
Hello everybody,
could you please direct me how to solve this nonlinear differential equation analytically, so by mathematica or matlab? I really need to solve it for my research project, so please help me
du/dx=d/dx[a*u^(-1/2)*du/dx... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 18, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/34782/does-frac-mboxlcm1-2-dots-n1-mboxlcm1-2-dots-n-to-infty/34786 | ## Does $\frac{\mbox{lcm}(1,2,\dots,n+1)}{\mbox{lcm}(1,2,\dots,n)}\to\infty$?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I feel that the answer to the title quesiton is "yes". However, I tried using different bounds on such least common multiples to prove... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "mathjax_display_tex": 5, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/114500/list | ## Return to Answer
If you are happy with Frechet bundles here is an alternative approach. Let $\pi \colon {\mathcal G} \times M \to M$ be the projection and consider $\pi^{-1}(TM) \to {\mathcal G} \times M$ a real vector bundle of rank $n$. Following the notation in the paper let $P_{GL^+} \to M$ be the $GL^+(n, {\ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 99, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/69033/help-me-understand-limits | # Help me understand limits
Good day
I'm currently doing some math homework (don't worry I won't ask anyone to solve anything) and I don't think I'm understanding limits correctly. More precisely how the l'Hôpital rule works.
I know I can/should be able to apply it if it is either $\infty/\infty$ or $0/0$ but I was ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Atomic_physics | # Atomic physics
Modern physics
${ i\hbar\frac{\partial}{\partial t} \Psi(\mathbf{r},\,t) = \hat H \Psi(\mathbf{r},\,t)}$
History of modern physics
Founders
Scientists
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/113479-integration-dr-evil-my-teacher.html | # Thread:
1. ## Integration - Dr. Evil is my teacher
Right I won't bore you with a sob story but this is a regular grade 12 class and we've been posed with this problem:
Find the arc length of this function across 0 -> 5:
$s(t) = t^3 - 6t^2 + 9t + 5, {t >= 0}$
I learned the formula of s = Integral of $squareroot(1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/100936/composition-of-two-formal-series | ## Composition of two formal series
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
There are two formal semi-infinite Laurent series
$$f_+(z)=z+\sum_{k=2}^{\infty} a_k z^k$$
and
$$f_-(z)=z+\sum_{k=0}^{\infty} b_k z^{-k}$$
Their composition $f_+(f_-(z))$ i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/29982/has-this-notion-of-product-of-graphs-been-studied/30012 | ## Has this notion of product of graphs been studied?
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Let $n\geq 2$ be a positive integer. For the purposes of this definition, let a colored graph be a finite undirected graph in which each edge is colored with ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 72, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/99169?sort=oldest | ## On Pseudo-finite topological spaces
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We recall that a topological space $(X,\tau)$ is Pseudo-finite, if each compact subset of $X$ is finite.
One of the classical example of Pseudo-finite topological spaces ca... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 54, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.nag.com/numeric/cl/nagdoc_cl23/html/S/s11acc.html | NAG Library Function Documentnag_arccosh (s11acc)
1 Purpose
nag_arccosh (s11acc) returns the value of the inverse hyperbolic cosine, $\mathrm{arccosh}x$. The result is in the principal positive branch.
2 Specification
#include <nag.h>
#include <nags.h>
double nag_arccosh (double x, NagError *fail)
3 Descript... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 31, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/1538/inverses-in-truncated-polynomial-rings/2588 | # Inverses in Truncated Polynomial Rings
I've been trying a long time to understand a thing which is obviously extremely simple, but I just can't get it. Read this, please:
The NTRUEncrypt PKCS uses the ring of truncated polynomials $R$ combined with the modular arithmetic described in Section 1. These are combined b... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/stochastic-integrals+martingales | # Tagged Questions
0answers
20 views
### Supermartingale Lemma + related problems
Given the following Lemma: Let $A_{t}=\int_{0}^{t}a_{s}dB_{s}$ where $a$ is an adapted process satisfying $\mathbb{P}\Big(\int_{0}^{T}a^{2}_{u}du < \infty\Big) = 1$ and $B$ is a standard Brownian ...
1answer
65 views
### Martingale in... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/10496/an-inequality-relating-the-factorial-to-the-primorial/10573 | ## An inequality relating the factorial to the primorial.
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Let [a,b] = {k integer | a < k <= b}. Further let
• Comp[a,b] = product_{c in [a,b]} c composite;
• Fact[a,b] = product_{k in [a,b]} k integer;
• Prim[a,... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://en.wikipedia.org/wiki/Noise_shaping | # Noise shaping
Noise shaping is a technique typically used in digital audio, image, and video processing, usually in combination with dithering, as part of the process of quantization or bit-depth reduction of a digital signal. Its purpose is to increase the apparent signal to noise ratio of the resultant signal. It ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/279980/difference-between-fourier-transform-and-wavelets | Difference between Fourier transform and Wavelets
While understanding difference between wavelets and Fourier transform I came across this point in Wikipedia.
The main difference is that wavelets are localized in both time and frequency whereas the standard Fourier transform is only localized in frequency.
I did not... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/2786/visualization-of-protons-wavefunction?answertab=votes | # Visualization of proton's wavefunction
Visualizations of hydrogen's wavefunctions / electron orbitals are abound.
I could not however locate a visualization of the wavefunction of a proton. The reason I was looking for one is to see whether the three quarks that make it up "occupy" disjoint regions of space (i.e. t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/166579/deducing-results-in-linear-algebra-from-results-in-commutative-algebra/166685 | # Deducing results in linear algebra from results in commutative algebra
Here are two examples of results which can be deduced from commutative algebra:
• Any $n\times n$ complex matrix is conjugate to a Jordan canonical matrix (can be proven using the structure theorem for modules over a PID, in this case $\mathbf{C... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 70, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/82510?sort=newest | The Correlation of the Mobius Function and Dirichlet Characters.
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Let $\chi$ be a Dirichlet character, and define $\phi_\chi (n)$ so that it satisfies $$\sum_{n=1}^\infty \phi_\chi (n)n^{-s}=\frac{\zeta(s-1)}{L(s,\chi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 73, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/105397?sort=oldest | ## There are two slightly different notions of ultraproduct. Why is one said to be better than the other?
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Let $I$ be a set and $\mathcal{U}$ an ultrafilter on $I$. Let $(X_i)_{i \in I}$ be an $I$-indexed family ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 42, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/69845-family-functions-differential-equations.html | # Thread:
1. ## Family of functions, differential equations
Verify that the indicated family of functions is a solution to the given differential equation.
dP/dt=P(1-P); P=(c1*e^t)/(1+c1*e^t)
Do I take the derivative of P first? If so do I just ignore the constants? Thanks for the help.
2. Originally Posted by cow... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/tags/homomorphic-encryption/info | # Tag info
## About homomorphic-encryption
Cryptosystems which support computation on encrypted data. They might be partially homomorphic (support for one operation such as + or *) or they might be fully homomorphic (+ and * at the same time).
Homomorphic cryptosystems are cryptsystems in which, given $c_1\mathcal{E... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.r-bloggers.com/getting-data-from-an-image-introductory-post/ | ## R-bloggers
R news and tutorials contributed by (452) R bloggers
# Getting data from an image (introductory post)
March 5, 2010
By Timothée
(This article was first published on Data visualization (in R), and kindly contributed to R-bloggers)
Hi there!
This blog will be dedicated to data visualization in R. Why?... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/101323?sort=votes | ## Repeated Second Eigenvalue of the Adjacency Matrix of a Graph
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This question is motivated by a talk I went to earlier today.
Suppose we have a $d$-regular graph $G$ with $n$ vertices, with adjacency matrix $A$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://gilkalai.wordpress.com/2009/04/25/a-problem-on-planar-percolation/?like=1&source=post_flair&_wpnonce=a082172354 | Gil Kalai’s blog
## A Problem on Planar Percolation
Posted on April 25, 2009 by
Conjecture (Gady Kozma): Prove that the critical probability for planar percolation on a Cayley graph of the group $Z^2$ is always an algebraic number.
Gady mentioned this conjecture in his talk here about percolation on infinite Cayl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 15, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/6715/can-someone-help-me-understand-what-type-of-problem-i-am-looking-at-not-sure-if | # Can someone help me understand what type of problem I am looking at? Not sure if this classifies as hypothesis-testing
Please pardon me if this question is not clear. I am not sure if I am using the right terminologies.
I have conducted an experiment in different environments multiple times. So my data looks someth... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/statistics/206245-combination.html | # Thread:
1. ## Combination
I need to write this expression with one combination number: C(15,3)-C(16,2)=C(n,k) so I need to find n and k
How can i get one from these two without using factorials?
2. ## Re: Combination
Originally Posted by Serillan
I need to write this expression with one combination number: C(15,3... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/101883/college-euclidean-geometry-textbook-recommendations/101895 | ## College (Euclidean) geometry textbook recommendations
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I will be teaching a mid-level undergraduate course in Euclidean geometry this fall. Has anyone taught such a course, who can recommend a good textbook?
M... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/11832/how-do-you-derive-the-conditional-variance-for-s2-the-ols-estimator-of-sig | How do you derive the conditional variance for $s^2$, the OLS estimator of $\sigma^2$?
I just need a little bit of a push in the right direction. I'm working my way through Hayashi's Econometrics and hit a snag in section 1.4. Review question 7 asks:
Show that, under Assumptions 1.1-1.5,
$Var(s^2|X)=\frac{2\sigma^4}... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/131807/deriving-the-exponential-distribution-from-a-shift-property-of-its-expectation?answertab=votes | # Deriving the exponential distribution from a shift property of its expectation (equivalent to memorylessness).
Suppose $X$ is a continuous, nonnegative random variable with distribution function $F$ and probability density function $f$. If for $a>0,\ E(X|X>a)=a+E(X)$, find the distribution $F$ of $X$.
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2
0% accep... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 65, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/10594/is-there-any-value-in-studying-divisors-with-coefficients-in-a-ring-r | ## Is there any value in studying divisors with coefficients in a ring R?
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As a rule, the various groups and quotients of the divisor group on a variety have coefficients in $\mathbb{Z}$. That is, you take $\mathb... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/135553/using-the-definition-of-a-concave-function-prove-that-fx-4-x2-is-concave-d/135650 | # Using the definition of a concave function prove that $f(x)=4-x^2$ is concave (do not use derivative).
Let $D=[-2,2]$ and $f:D\rightarrow \mathbb{R}$ be $f(x)=4-x^2$. Sketch this function.Using the definition of a concave function prove that it is concave (do not use derivative).
Attempt: $f(x)=4-x^2$ is a down-fac... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/27029/simple-question-on-the-foundations-of-spin-foam-formalism/27030 | Simple question on the foundations of spin foam formalism
To make it simple, take the spin foam formalism of ($SU(2)$) 3D gravity. My question is about the choice of the data that will replace the (smoothly defined) fields $e$ (the triad) and $\omega$ (the connection) on the disretized version of space-time $\mathcal{... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/44897/general-relativity-and-the-microscopic-macroscopic-distinction | # General relativity and the microscopic/macroscopic distinction
Here is Wikipedia's diagram of the stress-energy tensor in general relativity:
I notice that all of its elements are what would be termed "macroscopic" quantities in thermodynamics. That is, in statistical mechanics we would usuallt define these quantit... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 3, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3984303 | Physics Forums
## The meaning of Weyl curvature caused by gravitational waves
In his article The Ricci and Weyl Tensors John Baez states that the tidal stretching and squashing caused by gravitational waves would not change the volume as there is 'only' Weyl- but no Ricci-curvature. No additional meaning is mentioned... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/50034/particle-filter-motion-model?answertab=oldest | # Particle filter motion model
As I understand the basic idea of particle filter is to predict the state of the particle by generating N different possible state. After that, each possible state is evaluated by a predict model (give the weight to each particle).
So...let say, if my particle is (x, y, z). Then, becaus... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/27038/what-hermitian-operators-can-be-observables/27039 | # What Hermitian operators can be observables?
We can construct a Hermitian operator $O$ in the following general way:
1. find a complete set of projectors $P_\lambda$ which commute,
2. assign to each projector a unique real number $\lambda\in\mathbb R$.
By this, each projector defines an eigenspace of the operator ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/78023/genus-and-spinor-genus-of-a-lattice/78025 | ## Genus and Spinor genus of a lattice
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Hi, I'm looking for a motivation for the names genus and spinor genus of a lattice (and spinor norm of an isometry).
Is there any relation between the genus of a lattice an... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/61031/boundness-of-laplacian-eigenfunctions/61041 | ## Boundness of Laplacian eigenfunctions
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Let $A$ be a bounded domain in $\mathbb R^d$, $d>1$, and $\{u_k\}$ is the set of all $L^2$-normalized Laplacian eigenfunctions on $A$ with Dirichlet boundary condition (i.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/179868/how-to-transform-a-stochastic-jump-diffusion-equation-to-a-levy-stochastic-diffe?answertab=votes | # How to transform a stochastic jump diffusion equation to a Levy stochastic differential equation?
If I have this type of stochastic differential equation : $$dX(t) = A(X(t),t)\ dt +B(X(t),t)\ dW(t) + C(X(t),t)\ dP(t)$$ With $$\begin{align} dW(t)& : \text{A wiener process}\\ dP(t)& : \text{A Poisson process with para... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/89533?sort=oldest | ## When a quotient singularity is toric?
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Let $G \subset SL(n,\mathbb{C})$ be a cyclic subgroup of finite order, Is it true that $\mathbb{C}^n /G$ is toric ? If not then when it is ?
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1
The "cyclic" condition i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.haskell.org/haskellwiki/index.php?title=Free_structure&oldid=33900 | # Free structure
### From HaskellWiki
Revision as of 04:24, 2 March 2010 by Dolio (Talk | contribs)
(diff) ←Older revision | Current revision (diff) | Newer revision→ (diff)
## Contents
### 1 Introduction
This article attempts to give a relatively informal understanding of "free" structures from algebra/category ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 25, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.aps.org/articles/v2/67 | # Viewpoint: Melting the world’s smallest raindrop
, Physics & Astronomy, State University of New York, Stony Brook, NY 11794-3800, USA
Published August 10, 2009 | Physics 2, 67 (2009) | DOI: 10.1103/Physics.2.67
Experiments on melting of small water clusters open the door to the study of the size-dependent phase... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 40, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/208295-equation-circles.html | # Thread:
1. ## Equation of circles
So, I've attached both the question and my working inside.
for part 1, I'm not sure how to get the radius and for part 2, how to get the point?
Attached Thumbnails
2. ## Re: Equation of circles
Originally Posted by Thorpelizts
So, I've attached both the question and my working i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/21067/noetherian-rings-of-infinite-krull-dimension/21083 | ## Noetherian rings of infinite Krull dimension?
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Since Noetherian rings satisfy the ascending chain condition, every such ring must contain infinitely many chains of prime ideals s.t. the heights of these chains ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/23212/shors-algorithm-why-throw-away-the-fx/23215 | # Shor's Algorithm: Why throw away the f(x)?
I'm having a little trouble understanding Shor's algorithm - namely, why do we throw away the result f(x) that we get after applying the F gate? Isn't that the answer we need?
My notation: $\newcommand{\ket}[1]{\left|#1\right>}$
$F(\ket x \otimes \ket0) = \ket x \otimes \... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/6870/solution | nrich enriching mathematicsSkip over navigation
### F'arc'tion
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.
### Do Unto Caesar
At the beginning of the night th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 50, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/17711/lagrange-four-squares-theorem-efficient-algorithm-with-units-modulo-a-prime/18081 | ## Lagrange four-squares theorem: efficient algorithm with units modulo a prime?
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I'm looking at algorithms to construct short paths in a particular Cayley graph defined in terms of quadratic residues. This has le... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 58, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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