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http://physics.stackexchange.com/questions/52699/how-can-one-determine-at-which-distance-the-lennard-jones-potential-reaches-a-gi/52704 | # How can one determine at which distance the Lennard-Jones potential reaches a given value?
My question is fairly simple, but I do need clarification on how to get the inverse of the Lennard-Jones potential V(x).
I am working with the following expression: $$V(x) = e\times[(R/x)^{12} -2\times(R/x)^6]$$
So given a v... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/31035?sort=votes | ## Deeper meanings of barycentric subdivision
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I just want to ask if there is any deeper motivation or clear geometric "sense" behind the barycentric subdivision. Some friend asked me about this a few months ago, ... | {"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": 83, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/33404-proof-26-only-number-between-cubed-squared-number.html | # Thread:
1. ## proof that 26 is the only number between a cubed and a squared number
I was reading Singh's Fermats Last Theorem, and it mentioned that fermat was the first person to prove that 26 is the only number between a cubed and a squared number. I have been unable to prove this, so i thought I'd ask, apologie... | {"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": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2008/03/03/the-riemann-stieltjes-integral-iii/?like=1&source=post_flair&_wpnonce=c1c9c39881 | # The Unapologetic Mathematician
## The Riemann-Stieltjes Integral III
Last Friday we explained the change of variables formula for Riemann integrals by using Riemann-Stieltjes integrals. Today let’s push it a little further and prove a change of variables formula for Riemann-Stieltjes integrals.
We start with a fun... | {"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": 77, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=568686 | Physics Forums
## What is a photon in respect to electromagnetic waves?
I've always thought that photons and electromagnetic waves are one in the same. And I still do, but I'm trying to get a better grasp on the idea and am finding it difficult.
1) As I understand it, they are the same. But an electromagnetic wave w... | {"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": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/153369-equality-binomial-sums.html | # Thread:
1. ## An Equality of Binomial Sums
If $n\ge 0$, show that
$\displaystyle \sum_{k=0}^{n}\binom{2n}{k}\binom{2n-2k}{n-k} = \sum_{k=0}^{n}\binom{2n+1}{k} = \sum_{k=0}^{2n}\binom{2n}{k}$
2. Originally Posted by Vandermonde
If $n\ge 0$, show that
$\displaystyle \sum_{k=0}^{n}\binom{2n}{k}\binom{2n-2k}{n-k} = ... | {"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://www.physicsforums.com/showthread.php?p=1194482 | Physics Forums
## intuitive explanation why frequency is fixed
From treating light as a wave it is possible using Huygen’s theory to deduce that the frequency of the light will not change whether in vacuum or some other material. I have seen a mathematical proof of it and understand it but is there an intuitive expla... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/69141/atkin-lehner-involution-and-class-number/69294 | ## Atkin-Lehner involution and class number
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I was told of a relation between the number of fixed points of the Atkin-Lehner involution and the class number of certain number fields.
Can someone point me to a ref... | {"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": 129, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/36815/a-simple-explanation-of-eigenvectors-and-eigenvalues-with-big-picture-ideas-of/36818 | # A simple explanation of eigenvectors and eigenvalues with 'big picture' ideas of why on earth they matter
A number of areas I'm studying in my degree (not a maths degree) involve eigenvalues and eigvenvectors, which have never been properly explained to me. I find it very difficult to understand the explanations giv... | {"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": 28, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/15931-rectangle-within-semicircle-print.html | # Rectangle Within Semicircle
Printable View
• June 13th 2007, 01:45 PM
blueridge
Rectangle Within Semicircle
A rectangle is inscribed in a semicircle of radius 2. Let P = (x,y) be the point in quadrant 1 that is a vertex of the rectangle and is on the circle.
(a) Express the area A of the rectangle as a function of... | {"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://mathhelpforum.com/differential-equations/166274-non-homogeneous-pde-non-homogeneous-bc-s-eigenfunction-expansion.html | Thread:
1. Non-homogeneous PDE with Non-homogeneous BC's - Eigenfunction Expansion
I have an exam tomorrow, and I came across one question that I don't really know how to start and I was really hoping someone could help me out with it.
Use the method of eigenfunction expansion to obtain a solution to
$u_t = u_{xx} ... | {"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": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/114697/an-invariant-method-of-stationary-phase | ## An invariant method of stationary phase
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The method of stationary phase is very well-known and employed in many areas of physics and mathematics, and, of course, included in various versions as theorem in textb... | {"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": 81, "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/9169/request-for-reference-banach-type-spaces-as-algebraic-theories | ## Request for reference: Banach-type spaces as algebraic theories.
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Sparked by Yemon Choi's answer to Is the category of Banach spaces with contractions an algebraic theory? I've just spent a merry time reading 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": 3, "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/228692/is-u-fx-fx-in-p-3-operatornamedeg-fx-3-a-subspace-of-p/228693 | # Is $U = \{f(x)| f(x) \in P_{3}, \operatorname{deg} f(x) = 3\}$ a subspace of $P_{3}$?
Given : $U = \{f(x)| f(x) \in P_{3}, \operatorname{deg} f(x) = 3\}$
Does: U is a subspaces of $P_{3}$
I think the answer is yes. But in my textbook, they say no. And explain that zero is not in set, and scalar multiplication and ... | {"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://math.stackexchange.com/questions/53026/finite-abelian-group/53036 | # Finite Abelian Group
Let $G$ be a finite abelian group, $G = \{e, a_{1}, a_{2}, ..., a_{n} \}$. Prove that $(a_{1}a_{2}\cdot \cdot \cdot a_{n})^{2}$ = $e$.
I've been stuck on this problem for quite some time. Could someone give me a hint?
Thanks in advance.
-
1
every element has an inverse, and you can reorder 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": 79, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4111273 | Physics Forums
Quadruples of Integers
This should be a simple combinatorial problem. Suppose I have a number n which is a positive integer. Suppose, that there are four numbers a,b,c,d such that 0<=a<=b<=c<=d<=n.
The question is how many quadruples of the form (a,b,c,d) can be formed out such arrangement?
I realize ... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/4959/how-do-you-calculate-the-expectation-of-left-sum-i-1n-x-i-right2 | # How do you calculate the expectation of $\left(\sum_{i=1}^n {X_i} \right)^2$?
If $X_i$ is exponentially distributed $(i=1,...,n)$ with parameter $\lambda$ and $X_i$'s are mutually independent, what is the expectation of
$$\left(\sum_{i=1}^n {X_i} \right)^2$$
in terms of $n$ and $\lambda$ and possibly other constan... | {"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": 32, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/177424-complex-number-proof.html | # Thread:
1. ## Complex Number Proof
For the complex equation $z^4 = cosx + isinx$, prove that the sum of the four solutions is always zero, no matter what size $x$ is.
This is what I've done so far.
$Z = (cis(x + 360k))^1^/^4<br /> = cis(x/4 + 90k)$
Can someone please teach me how to do the rest? Thanks in advanc... | {"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": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/74770/distribution-of-the-normal-cdf | # distribution of the normal cdf
I am wondering what is the probability density function for the normal cdf $\Phi (aX+b)$, where $\phi$ is the usual standard normal cumulative distribution function
I want to calculate $\mathbb{E}[\Phi(aX+b)]$ but i am stuck on how to get the distribution. thank you =]
-
What does $... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/12/16/dimensions-of-young-tabloid-modules/?like=1&_wpnonce=d19428bcb3 | # The Unapologetic Mathematician
## Dimensions of Young Tabloid Modules
Last time our efforts to calculate the characters of the modules $M^\lambda$ were stymied. But at least we can calculate their dimensions. The dimension of $M^\lambda$ is the number of Young tabloids of shape $\lambda$.
Again, we pick some canon... | {"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": 44, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/55097/can-homologous-submanifolds-be-connected-by-an-immersed-manifold-with-boundary/55102 | ## Can homologous submanifolds be connected by an immersed manifold with boundary?
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Supposed I have an n-dimensional manifold M with a k-dimensional submanifold that is homologous to zero (or, equivalently, two ho... | {"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://mathoverflow.net/questions/18636/number-of-invertible-0-1-real-matrices/18639 | ## Number of invertible {0,1} real matrices?
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This question is inspired from here, where it was asked what possible determinants an $n \times n$ matrix with entries in {0,1} can have over $\mathbb{R}$.
My questio... | {"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": 30, "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/28496/what-should-be-learned-in-a-first-serious-schemes-course/28594 | What should be learned in a first serious schemes course?
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I've just finished teaching a year-long "foundations of algebraic geometry" class. It was my third time teaching it, and my notes are gradually converging. 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": 150, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/65418?sort=newest | ## Birational Contractions on Moduli of pointed Curves
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On the Moduli space $\overline{M}_{g}$ of genus $g$ stable curves the Hodge class $\lambda$ induces a birational morphism $f$ on a projective variety contrac... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/statistics/85801-permutation-problem-4-a.html | # Thread:
1. ## permutation problem 4
hey guys, need some help with this problem. this is one of four permutation problems that our teacher gave us to solve but haven't really figured it out, plus i was sick so i missed the lecture..
4) 3 balls are to be drawn one at a time from an urn containing 8 distinct ones. Fi... | {"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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/73326/closed-but-not-rational-points-of-a-real-cubic | ## Closed but not rational points of a real cubic
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In Mumford's Red Book of Varieties and Schemes, page 102, he gave the example of the closed but not rational points (that is to say points having residue field 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": 133, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://en.wikipedia.org/wiki/Kernel_(statistics) | # Kernel (statistics)
It has been suggested that this article be into multiple articles accessible from a disambiguation page. (December 2012)
The term kernel has two separate meanings in statistics.
## In Bayesian statistics
In statistics, especially in Bayesian statistics, the kernel of a probability density fun... | {"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": 32, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/9586/range-of-binomial-probability-given-a-certain-number-of-observations/9590 | ## Range of binomial probability, given a certain number of observations?
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Let's say I am given $n$ flips of a coin, $k$ of which are heads. These are iid flips.
Can I say, with probability $p > 1/2$, that the tr... | {"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://mathhelpforum.com/calculus/33042-need-help-hurry.html | # Thread:
1. ## Need Help!! in a hurry
A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 110 meters, the radius of the slick is expanding by 0.6 meter/minute and its thickness is 0.03 meter.
(a) At that moment, how fast is the area of the slick expanding?
(b) The circ... | {"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": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/100514/separable-l-1-predual | ## Separable $L_1$-predual
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Some isometric preduals of $\ell_1$ are of the form $C_0(K)$ where $K$ is countable. I am wondering whether this is a general rule.
Question: Is there a measure $\mu$ and a (preferably... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/75902/is-the-disk-quasiconformally-isomorphic-to-the-plane | ## Is the disk quasiconformally isomorphic to the plane?
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(This question might turn out to be too elementary for this site,
if so I'm sorry, but I can't find the answer anywhere.)
Does there exist a function `$\;... | {"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://en.wikibooks.org/wiki/Special_Relativity/Print_version | Special Relativity/Print version
The latest reviewed version was checked on 12 March 2013. There are template/file changes awaiting review.
This is the print version of Special_relativity You won't see this message or any elements not part of the book's content when you print or preview this page.
Note: current vers... | {"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": 1074, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathhelpforum.com/advanced-algebra/157769-prove-ab-aa-b-ab.html | # Thread:
1. ## Prove a(AB)=(aA)B=A(aB) ..
Prove a(AB)=(aA)B=A(aB) for any scalar a. At first I started out like:
a(AB)=(aA)(aB) and quickly noticed that that was very wrong. And then I kept trying to play around with it in different ways and I seem to get tangled and I know this is such an easy concept.
2. I suppo... | {"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": 39, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/150936-solving-problem-involving-nonlinear-functions-equations.html | # Thread:
1. ## Solving a problem involving nonlinear functions and equations
Hello, quick question. I'm pretty sure I know how to do this, but it's just slipping my mind right now. Could anyone tell me how to solve this problem?
If a≠0 and 5/x=5+a/x+a, what is the value of x?
2. I'm guessing you meant
$\dfrac{5}{... | {"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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/17830/how-should-i-proceed-in-proving-this-tautology/17890 | # How should I proceed in proving this tautology?
I know that following is a tautology because I've checked its truth table. I am now attempting to prove that it is a tautology by using the rules of logic, which is more difficult. How should I proceed?
$(p\land(p\implies q))\implies q$
$(p\land(\lnot p \lor q))\impl... | {"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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://chorasimilarity.wordpress.com/2013/02/14/towards-qubits-graphic-lambda-calculus-over-conical-groups-and-the-barycentric-move/ | # chorasimilarity
computing with space
Home > Uncategorized > Towards qubits: graphic lambda calculus over conical groups and the barycentric move
## Towards qubits: graphic lambda calculus over conical groups and the barycentric move
February 14, 2013
In this post I want to pave the way to the application of graph... | {"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": 18, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/75009/local-finiteness-and-coarse-bounded-geometry/75025 | ## Local finiteness and coarse bounded geometry
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I've just started learning these things and so probably my questions will be very easy. Please forgive me.
A metric space $(X,d)$ is called locally finite if every... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/130014/finding-an-equivalent-of-u-n-u-infty-where-u-n-sum-k-1n-frac | # Finding an equivalent of $u_{n}-u_{\infty}$ where $u_{n}= \sum_{k=1}^{n} \frac{n}{n^2+k^2}$
I would like to find an equivalent of
$$u_{n}-u_{\infty}=\sum_{k=1}^{n} \frac{n}{n^2+k^2}-u_{\infty}$$
Using Riemann sums, it is easy to show that:
$$u_{n} \sim \frac{\pi}{4}=u_{\infty}$$
Using integrals, we have:
$$\int... | {"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": 14, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/246794/how-to-prove-that-mathrmgl-2-bbb-z-2-has-only-six-subgroups | How to prove that $\mathrm{GL}_2(\Bbb Z_2)$ has only six subgroups
I have found the six subgroups that I know that $\mathrm{GL}_2(\Bbb Z_2)$ has, but now I want to prove that this is all. How can I do this? I am currently thinking that I should argue using the fact that if $H \le G$ is a subgroup, then $|H|$ must divi... | {"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": 14, "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/9026/how-do-you-handle-the-floor-and-ceiling-function-in-an-equation?answertab=active | # How do you handle the floor and ceiling function in an equation?
I tried to do some math in a blog post of mine and came to one with a floor function. I wasn't sure how to deal with it so I just ignored it, and then added the ceiling function in my final equation as that seemed to give me the result I wanted. I'm wo... | {"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": 14, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/88269-congruence.html | # Thread:
1. ## Congruence
Can somebody help with this question please?
Prove that
(e^x)(e^x2/2)(e^x^3/3)...=1+x+x^2+... when |x|<1.
Show that the coefficient of x^19 in the power series expansion on the LHS has the form
1/19! + 1/19 + r/s,
where 19 does not divide s.
Deduce that 18!= -1(mod 19).
2. Hi
$\prod... | {"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": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/spacetime+string-theory | # Tagged Questions
1answer
69 views
### Can the fuzzball conjecture be applied to microscopically explain the entropy of a region beyond the gravitational observer horizon?
In this article discussing this and related papers, it is explained among other things, how the neighborhood of an observer's worldline can be 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": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/121543-question-semi-elliptical-arch-bridge.html | # Thread:
1. ## question on semi elliptical arch bridge
the arch bridge takes the shape of a circular arc. the portion of the arch bridge above the water has a span of 30m and a rise of 10m. a boat passes through the arch bridge. if the cross section of the boat is modeled by a rectangle with vertical sides, find cor... | {"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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/38123/what-do-you-feel-when-crossing-the-event-horizon | # What do you feel when crossing the event horizon?
I have heard the claim over and over that you won't feel anything when crossing the event horizon as the curvature is not very large. But the fundamental fact remains that information cannot pass through the event horizon so you cannot feel your feet when they have p... | {"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://mathoverflow.net/revisions/45247/list | ## Return to Answer
2 more details
I think it would be NP complete. One NP complete problem is to determine if a graph has an Vertex Cover of size $k$: given graph with m vertices and e edges is there a set of k vertices including at least on endpoint of each edge. TO ? To encode this in your problem, assign a unique... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathforum.org/mathimages/index.php?title=Logistic_Bifurcation&oldid=27246 | # Logistic Bifurcation
### From Math Images
Revision as of 01:23, 26 July 2011 by 144.118.94.68 (Talk)
(diff) ←Older revision | Current revision (diff) | Newer revision→ (diff)
Logistic Bifurcation
Field: Dynamic Systems
Created By: Diana Patton
Website: [ ]
Logistic Bifurcation
This is a section of a bifurcation 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 24, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/543 | ### Real(ly) Numbers
If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?
### Overturning Fracsum
Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7
### Bang's Theorem
If all 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": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.cfd-online.com/W/index.php?title=Baldwin-Lomax_model&diff=13274&oldid=13267 | [Sponsors]
Home > Wiki > Baldwin-Lomax model
# Baldwin-Lomax model
### From CFD-Wiki
(Difference between revisions)
| | ... | {"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": 38, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/29161?sort=newest | ## Does the concept of a basis for a topology on a category exist?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
If we want to define a sheaf F on a topological space X and we have a basis B for the topology of X, what we can do is to define objects and rest... | {"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": 55, "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/24270?sort=oldest | ## A number encoding all primes
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This may be a soft question, but it's just something I thought of one night before sleeping. It's not my field at all, so I am just asking out of curiosity. Has anyone studied 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": 10, "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/315050/using-pigeonhole-principle-to-prove-two-numbers-in-a-subset-of-2n-divide-eac | # Using Pigeonhole Principle to prove two numbers in a subset of $[2n]$ divide each other
Let $n$ be greater or equal to $1$, and let $S$ be an $(n+1)$-subset of $[2n]$. Prove that there exist two numbers in $S$ such that one divides the other.
Any help is appreciated!
-
## 1 Answer
HINT: Create a pigeonhole for 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://mathoverflow.net/revisions/100391/list | ## Return to Answer
3 Item #3 added.
Here are a couple of few others:
1. Let $H_n=\sum_{j=1}^n 1/j$. Then for all $n\geq 1$, $$\sum_{d|n}d\leq H_n+(\log H_n)e^{H_n}.$$ Jeff Lagarias showed that this is equivalent to the Riemann hypothesis!
2. Let $x_0=2$, $x_{n+1}=x_n-\frac{1}{x_n}$ for $n\geq 0$. Then $x_n$ is unb... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/177767-division-algorithm-polynomials-print.html | # Division algorithm for polynomials
Printable View
• April 15th 2011, 06:39 AM
worc3247
Division algorithm for polynomials
Let M and N be positive integers with M > N. The division algorithm for Z implies that
there exist integers Q and R such that M = QN + R, where 0=<R<N. The division algorithm for $\mathbb{R}[x]$... | {"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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/111890?sort=newest | ## Geometrically connected curve
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What is the definition of a geometrically connected curve?
-
6
Seriously, the first hit on google gives you the answer... google.fr/search?q=geometrically+connected – Lierre Nov... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://jwbales.us/precal/part5/part5.2.html | ## Discovering other identities
Other trigonometric identities can be derived from the elementary identities.
For example, an identity for $$\cot A\sin A$$ can be found by replacing $$\cot A$$ with $$\dfrac{\cos A}{\sin A}$$ and simplifing to $$\cos A$$.
Thus $$\cot A\sin A = \cos A$$ is an identity.
## A caveat
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": 20, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2007/02/24/generators-and-relations/?like=1&source=post_flair&_wpnonce=c1c9c39881 | # The Unapologetic Mathematician
## Generators and Relations
Now it’s time for the reason why free groups are so amazingly useful. Let $X$ be any set, $F(X)$ be the free group on $X$, and $G$ be any other group. Now, every function $f$ from $X$ into $G$ extends to a unique homomorphism $f: F(X)\rightarrow G$. Just wr... | {"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": 67, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/217291/figure-out-a-function-expression-from-graph-sine-and-cosine?answertab=votes | # Figure out a function expression from graph (sine and cosine)
I am trying to recreate the following image in latex (pgfplots), but in order to do so I need to figure out the mathematical expressions for the functions
So far I am sure that the gray line is $\sin x$, and that the redline is some version of $\sin x / ... | {"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": 16, "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/116313?sort=votes | ## Homotopy Transfer Theorem for Differential Graded Associative Algebras
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As in Algebra+Homotopy=Operad by Bruno Vallette, let $A$ with multiplication $\nu$ be a differential graded associative algebra equipped w... | {"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": 100, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://citizendia.org/Diffraction | The intensity pattern formed on a screen by diffraction from a square aperture
Colors seen in a spider web are partially due to diffraction, according to some analyses. [1]
Diffraction is normally taken to refer to various phenomena which occur when a wave encounters an obstacle. Very similar effects are observed when... | {"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": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/17305?sort=oldest | ## ray class field of rational function field
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Let $f \in \mathbf{F}_q[T]$ be irreducible. I know that the ray class field for $\mathrm{Cl}((f)) \cong (\mathbf{F}_q[T]/(f))^\times$ can be constructed by adjoining ... | {"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": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.m.wikibooks.org/wiki/Modern_Physics/Characteristics_of_Relativistic_Waves | # Modern Physics/Characteristics of Relativistic Waves
Special Relativity
1 - 2 - 3 - 4 - 5 - 6
In classical physics, ω and k for light are related by
$\omega = c k \,$
In relativistic physics, we've seen that for waves with no special reference frame, such as light, ω and k are related by
$\omega^2 = c^2 k^2 + \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": 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/139995/representation-of-compactly-supported-distribution | # Representation of compactly supported distribution
Is this true?
Any compactly supported distribution $T\in \cal D'$ can be represented as finite sum of partial derivatives of functions.
-
If $T$ is compactly supported, then $T$ can be extended to the space of infinitely differentiable function, and hence have 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": 3, "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/90794/is-a-semicontinuous-real-function-borel-measurable/91669 | ## Is a semicontinuous real function Borel measurable?
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Let $f(x,u): [0,1]^2 \mapsto \mathbb{R}$ be a continuous function.
[Q] Is $g(x) = \inf_{u\in [0,1]} f(x,u)$ always Borel measurable? If not, can one find 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": 35, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/97259/differential-equations-exact-differential-equations | # Differential equations - exact differential equations
I am self studying ode from boyce diprima book and while doing exercises on chapter 2.6.
I couldnt undestand how question 17 is derived I checked the solution manual and I found the same answer which I have already found by myself but what the the question asks ... | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/53073/diffusion-sample-paths-as-deformed-brownian-sample-paths/69299 | ## Diffusion sample paths as deformed Brownian sample paths
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Suppose $X$ is a non-explosive diffusion with dynamics
$dX_t = \mu(X_t)dt + \sigma(X_t)dW_t$,
where $W$ is a standard Brownian motion. My intuition ab... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/dipole+coordinate-systems | # Tagged Questions
1answer
907 views
### Force from point charge on perfect dipole
Have a point charge and a perfect dipole $\vec{p}$ a distance $r$ away. Angle between $\vec{p}$ and $\hat{r}$ is $\theta$. Want to find force on dipole. I'm having more than a little difficulty ... | {"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://physics.stackexchange.com/questions/45858/root-mean-square-value-for-dc/45859 | Root mean square value for DC
The mean value of alternating current comes to be zero because of half of the cycle being positive while the other half negative. so, take the root means square value of Alternating current given by:
$I_{rms} = 0.707\times I_{max}$
But why do we take "rms" for direct current? if we take... | {"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": 9, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://openwetware.org/index.php?title=User:Timothee_Flutre/Notebook/Postdoc/2011/11/10&diff=672771&oldid=565816 | # User:Timothee Flutre/Notebook/Postdoc/2011/11/10
### From OpenWetWare
(Difference between revisions)
| | ... | {"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": 85, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/tagged/tensor | ## Tagged Questions
0answers
44 views
### Null vector fields given Bondi metric
I'm trying to understand how to compute the null future-directed vector fields if I have a given (Bondi) metric $g=-e^{2\nu}du^{2}-2e^{\nu+\lambda}dudr+r^{2}d\Omega$ with \$d\Omeg …
0answers
61 views
### Geometric interpretation of trac... | {"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": 28, "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/34241/laplacian-operator-and-relation-to-the-laplace-transform | ## Laplacian operator and relation to the Laplace Transform
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I'm trying to understand why the Laplacian operator is used in blob detection in image analysis. I must admit that in trying to figure out why the Lapla... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://motls.blogspot.cz/2013/03/lhcb-7-sigma-and-9-sigma-anomalies-in.html?m=1 | # The Reference Frame
Our stringy Universe from a conservative viewpoint
## Monday, March 04, 2013
### LHCb: $$7$$-$$\sigma$$ and $$9$$-$$\sigma$$ anomalies in CP-violation
First, let me start with Tommaso Dorigo. He reviewed a recent paper by Carena et al. that tried to find the best parameters of the MSSM Higgs 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": 0, "mathjax_display_tex": 44, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/64652-volume-integral.html | # Thread:
1. ## volume by integral
if we rotate the area between the curve $f(x)=2x^2-x^3$ and the line $y=0$ around the y-axis,how can we find the volume of the shape by silindirical method? | {"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/2581/cutting-sticks-puzzle/4059 | # Cutting sticks puzzle
This was asked on sci.math ages ago, and never got a satisfactory answer.
Given a number of sticks of integral length $\ge n$ whose lengths add to $n(n+1)/2$. Can these always be broken (by cuts) into sticks of lengths $1,2,3, \ldots ,n$?
You are not allowed to glue sticks back together. Assu... | {"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": 55, "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/114605/solve-equation-with-matrix-variable | ## Solve equation with matrix variable
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I want to solve a matrix $\Omega$ from a equation $\sum_k (\Omega + \Theta_k)^{-1} = Q$. The $Q$ and $\Theta, \forall k=1...K$ are known, and are positive definite matrices.... | {"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": 40, "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/236625/find-groups-g-h-and-a-surjective-homomorphism-alpha-g-to-h-such-that/236706 | # Find groups $G$, $H$ and a surjective homomorphism $\alpha: G\to H$ such that $\alpha(Z(G)) \neq Z(H)$
Question:
Find groups $G$ and $H$ and a surjective homomorphism $\alpha: G \to H$ such that $\alpha(Z(G)) \neq Z(H)$
My answer:
Let $G$ and $H$ both be cyclic groups of order 4.
Define $\alpha: G \to H$ such 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": 66, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cs.stackexchange.com/questions/tagged/algorithm-design | # Tagged Questions
The algorithm-design tag has no wiki summary.
1answer
51 views
### How to repeat a mapreduce process? [closed]
How can I repeat the map and reduce process and feed the output of reduce into map function (in the next round)? My second question is how to define a global variable with is accessible ... | {"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://pgraycode.wordpress.com/2009/09/03/looking-for-the-lost-harmony/?like=1&_wpnonce=07995c002f | # Code and Bugs
Coding things
### Looking for the lost harmony
#### by Mithrandir
In fact, this is only a successful attempt at trying the Harmony Search for a toy problem.
I began by creating a library for random numbers, taking into account the things gathered from the Monte Carlo articles and other sources of 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": 0, "wp_latex": 2, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/71415/list | 2 edited tags
1
# Manifolds and Polynomials
Given a compact smooth manifold $M \subset R^k$ there is a Polynom $f\in R[x_1,..x_n]$ such that the zero set of $f$ is diffeomorphic to $M$. Can the coefficients of $f$ be pertubated slightly to a Polynomial $g \in Q[x_1,..x_n]$ such that the zero set of $g$ is diffeotopic... | {"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": 9, "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/294973/is-the-quotient-of-the-injective-envelope-a-torsion | # Is the quotient of the injective envelope a torsion?
We know that every module $M$ is embedded in an injective module $D$. Is it true that the module $D/M$ is torsion?
-
## 1 Answer
No, let $A = \frac{k[x, y]}{x^2, y^2}$ where $k$ is a field of characteristic $2$. This is a Frobenius algebra, hence it's self inje... | {"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": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/78223-exponential-equations-print.html | Exponential Equations
Printable View
• March 11th 2009, 03:50 PM
hotblonde
Exponential Equations
Can anyone please help me figure out how to solve the following problem? I believe you take the natural log of both sides, but I'm still left with 2 x's.
Solve the problem. Round answers to the nearest hundredth.
70.47x ... | {"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://www.physicsforums.com/showthread.php?p=4214035 | Physics Forums
## Graphical to Mathematical representation of changing the order of some elements
I have a question that is a little hard to explain, since i don't know the name of this method, but I'll try my best, if anyone knows the name please do tell me.
So let's say we have three numbers, 1 2 3 (in this order)... | {"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://physics.stackexchange.com/questions/tagged/magnetic-monopoles+electromagnetism | # Tagged Questions
1answer
85 views
### What is the action for an electromagnetic field if including magnetic charge
Recently, I try to write an action of an electromagnetic field with magnetic charge and quantize it. But it seems not as easy as it seems to be. Does anyone know anything or think of anything like ...... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/179024/why-does-a-langle-m-1-m-2-m-3-rangle-lm-1-cap-lm-2-ne-lm-3-isn?answertab=votes | # Why does A=$\{\langle M_1,M_2,M_3 \rangle : L(M_1) \cap L(M_2) \ne L(M_3)\}$ isn't in $RE$.
I'm trying to figure out what's wrong with this following Turing machine which determinate that the following language
A=$\{\langle M_1,M_2,M_3 \rangle : L(M_1) \cap L(M_2) \ne L(M_3)\}$ is in $RE$.
I said that we can build... | {"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": 41, "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/182101/appropriate-notation-equiv-versus/182120 | # Appropriate Notation: $\equiv$ versus $:=$
With respect to assignments/definitions, when is it appropriate to use $\equiv$ as in
$$M \equiv \max\{b_1, b_2, \dots, b_n\}$$
which I encountered in my analysis textbook as opposed to the "colon equals" sign, where this example is taken from Terence Tao's blog :
$$S(x,... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://jdueck.net/article/shoveling-less-with-math | The Local Yarn
Wednesday January 16, 2013
Shoveling Less With Math
Having been born and raised in Minnesota, I’ve had a lot of time to think about the most efficient way to shovel snow. Being as it’s now the dead of winter, I thought I’d formalize my findings on the subject so far. If you are also a long-time reside... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/104576/a-linear-program-related-question | ## A linear program related question
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Dear all, recently, I encountered the following problem. It is closely related to the order of growth for UMD constants of all $n$-dimensional Banach lattice.
Let $\alpha^k \... | {"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": 10, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/discrete-math/183154-solving-equation-parts-sum-sum.html | # Thread:
1. ## Solving equation with parts of a sum and a sum
Is it possible to solve any of these equations and thus find $\Delta x_{n}$ or $\sum_{0}^{n}\Delta x_{n}$?
Define
$\Delta x_{0}=V\frac{l}{v_{0}}$
and
$\Delta x_{1}=V\frac{l-\Delta x_{0}}{v_{0}+V}$
and
$\Delta x_{n+1}=V\frac{l-\sum_{0}^{n}\Delta x_{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": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.exampleproblems.com/wiki/index.php/Cumulative_distribution_function | # Cumulative distribution function
### From Exampleproblems
In probability theory, the cumulative distribution function (abbreviated cdf) completely describes the probability distribution of a real-valued random variable, X. For every real number x, the cdf is given by
$F(x) = \operatorname{P}(X\leq x),$
where 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": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/35180?sort=newest | Topology of function spaces?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $X,Y$ be finite-dimensional differentiable manifolds, and let's assume that they are connected. In fact, in applications I would like both $X$ and $Y$ to be riemannian manifolds.
Let... | {"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": 122, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/85751/proving-that-the-graph-is-symmetric-about-the-origin | # Proving That The Graph Is Symmetric About The Origin
I know that the graph of an equation in x and y is symmetric with respect to the origin if replacing x by -x and y by -y yeilds the same equation.
How can one prove that if the graph is symmetric with respect to it's x and y axis's,then it's also symmetric with 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": 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/97432?sort=newest | ## When is a three-manifold deck transformation group solvable?
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Suppose that $\pi:Y \to Y'$ is a regular covering of closed, connected, orientable three-manifolds and let $G$ be the deck transformation group. Fur... | {"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.aps.org/articles/v2/18 | # Viewpoint: Peaceful coexistence of nuclear shapes
, National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA
Published March 2, 2009 | Physics 2, 18 (2009) | DOI: 10.1103/Physics.2.18
Experiments show that spherical and nonspherical states of a light nucleus near neu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 48, "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://mathoverflow.net/questions/tagged/absolute-galois-group | ## Tagged Questions
3answers
908 views
### Subgroups of GL(2,q)
I have been wondering about something for a while now, and the simplest incarnation of it is the following question: Find a finite group that is not a subgroup of any $GL_2(q)$ …
2answers
475 views
### Is it known if the absolute Galois group is “divis... | {"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/questions/119744/completion-time-of-a-process-on-a-tree/119790 | ## Completion time of a process on a tree
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Given is a constant degree rooted tree of depth $D$. It is also known that the total number of nodes in the tree is at most $D^2$. There is a probabilistic process with 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": 31, "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/183924/undergraduate-approach-to-a-problem-about-convex-functions/183934 | # Undergraduate approach to a problem about convex functions
I am preparing some sheets of exercises that I'll assign to my undergraduate students in biology (sophomore class, or first academic year in italian universities). This is the problem:
Exercise. Let $f \colon [a,b] \to \mathbb{R}$ be a continuous and convex... | {"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": 21, "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/12283/if-you-place-a-spring-on-a-neodymium-hard-drive-magnet-it-appears-to-vibrate-in | # If you place a spring on a neodymium hard-drive magnet, it appears to vibrate in slow-motion. Why is that so?
By chance(playing around really) I saw that a spring(mainly from a pen) placed on a neodymium hard-disk magnet(and then flicked by your finger at the top) makes a nice-effect (see youtube video ). It appears... | {"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://physics.stackexchange.com/questions/tagged/volume+work | # Tagged Questions
2answers
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### How is it possible to equate the internal energy at constant volume with the internal energy of an adiabatic process?
I hope my question makes sense. My problem is that, I have read through numerous textbooks that nC(cons. volume)dT = -PdV when deriving the relationship betwe... | {"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/27367?sort=newest | Good reference for homology of $K(\mathbb{Z}, 2n)$?
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The homology algebra $H_*( K(\mathbb{Z},2n); \mathbb{Z})$ contains a divided polynomial algebra on a generator $x$ of dimension $2n$.
I suppose I could read through... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/72913/centerlessness-of-reduced-free-group | Centerlessness of reduced free group
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Let F_n be the free group with n generators, where n is an interger greater than 1. Let RF_n be the reduced free group, which is defined to be the quotient group of F_n obtained 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": 26, "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/98615?sort=oldest | ## Affine “real algebraic geometry” of hyperbolic space?
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Real algebraic geometry, at least to start with, traditionally studies the zero-sets of real polynomials in a given set of variables. But treating, say, 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": 52, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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