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http://math.stackexchange.com/questions/7266/why-does-this-process-when-iterated-tend-towards-a-certain-number-the-golden | # Why does this process, when iterated, tend towards a certain number? (the golden ratio?)
1. Take any number $x$ (edit: x should be positive, heh)
2. Add 1 to it $x+1$
3. Find its reciprocal $1/(x+1)$
4. Repeat from 2
So, taking $x = 1$ to start:
• 1
• 2 (the + 1)
• 0.5 (the reciprocal)
• 1.5 (the + 1)
• 0.666... (... | {"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": 80, "mathjax_display_tex": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://regularize.wordpress.com/tag/convex-sets/ | # regularize
Trying to keep track of what I stumble upon
November 15, 2012
## What is convexity?
Posted by Dirk under Math, Optimization | Tags: convex functions, convex sets, convexity, non-convex optimization |
1 Comment
There are several answers to the following question:
1. What is a convex set?
For a 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 74, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/138797/is-there-a-function-or-anything-else-that-gives-the-same-result-on-an-interval | # Is there a function or anything else that gives the same result on an interval? [duplicate]
Possible Duplicate:
Is there a function or anything else that gives the same result on a set?
I want to know if there is a function, for example, that gives the same result on the interval $[10,15]$. I want to have these 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": 14, "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/201169/what-is-the-relevance-of-the-supremum-in-this-question/201182 | # What is the relevance of the supremum in this question?
Prove that $d$ is a metric on the set $X$.
$d_u(f,g) = \sup\{|f(x) - g(x)|: x \in I \}, X = C(I)$ the set of all continuous functions from the closed bounded interval $I = [a,b]$ to $\mathbb{R}$
I don't understand what difference using the supremum of $|f(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": 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/218402/proper-orthogonal-matrix | # Proper Orthogonal Matrix
Prove that, for any $\theta$, $\lambda$, $\mu$
$Q = \pmatrix{\cos{\lambda}\cos{\mu} - \cos{\theta}\sin{\lambda}\sin{\mu}&\sin{\lambda}\cos{\mu} + \cos{\theta}\cos{\lambda}\sin{\mu}&\sin{\theta}\sin{\mu}\\-\cos{\lambda}\sin{\mu} - \cos{\theta}\sin{\lambda}\cos{\mu}&-\sin{\lambda}\sin{\mu} + ... | {"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://unapologetic.wordpress.com/2010/07/26/the-measures-of-ordinate-sets/ | # The Unapologetic Mathematician
## The Measures of Ordinate Sets
If $(X,\mathcal{S})$ is a $\sigma$-algebra and $f:X\to\mathbb{R}$ is a Borel-measurable function we defined the upper and lower ordinate sets $V^*(f)$ and $V_*(f)$ to be measurable subsets of $X\times\mathbb{R}$. Now if we have a measure $\mu$ on $X$ 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 32, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/6984-help-trees.html | # Thread:
1. ## Help with trees
ok, so i'm supposed to draw all the trees with five vertices and their complements. now, i have all the trees with five vertices down. but i don't know how to draw their complements. can anyone help me with this and show me an example of one? i would be really grateful.
2. Originally ... | {"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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/55222/can-a-black-hole-bounce/55231 | # Can a black hole bounce?
Is there a limit to the amount of matter that a black hole can accrete per second and if so could a certain sized black hole bounce off a dense enough surface?
-
## 2 Answers
Let's answer the first part of your question first. In general, astrophysical objects are limited in the amount 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": 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/115458/smallest-lipschitz-constant-on-non-convex-domains/115459 | ## Smallest Lipschitz constant on non-convex domains
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It is well known that if a function $f:U\to \mathbb C^n$, $U\subset \mathbb C^m$ satisfies $\sup_{x\in U}\|Df(x)\|_{\infty} = C < \infty$ uniformly on $U$ 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": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/120270-sequence-lebesgue-space.html | # Thread:
1. ## Sequence, Lebesgue Space
Show that if $|| f_n ||_1 \leq 2^{-n}$ for every $n \geq 1$ then $(f_n)_n$ converges to zero a.e.
If $(f_n)_n$ is a sequence in $L^1[0, 1]$ is such that $\sum_{n=1}^{\infty} || f_n ||_1 < \infty$ then $\sum_{n=1}^{\infty} | f_n(s) | < \infty$ for almost every $s \in [0, 1]$.
... | {"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": 42, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/5626 | ### Quaternions and Rotations
Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.
### Quaternions and Reflections
See how 4 dimensional quaternions involve vectors in 3-space and how the quaternion function F(v) = nvn gives a simple algebraic meth... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/29711/ra-leq-rbrc-given-a-leq-bc | # $r^a \leq r^b+r^c$ given $a \leq b+c$?
Apologies for the (maybe obvious) question. It's come up as part of a proof of the triangle inequality for a metric function I'd like to work with.
For real number $r \geq 1$ and positive integers a, b, c:
Is it generally true that $r^a \leq r^b+r^c$? Given that $a \leq b + 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": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.arachnoid.com/relativity/index.html | Home | Science | * Evolution * Answers * Dark Energy * Gravitation Equations * Gravity * The Doubt Factory * What is Science? * Why Science Needs Theories Are You Overweight? Gravitation Physics / 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": 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/3776?sort=newest | ## When are two proofs of the same theorem really different proofs
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Many well-known theorems have lots of "different" proofs. Often new proofs of a theorem arise surprisingly from other branches of mathematics tha... | {"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/2699-e-question.html | # Thread:
1. ## e question
How are $\lim_{x \to \infty}(1+\frac{1}{x})^x$ and $1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} ...$ similar or related to each other, other than their results being $e$?
2. It should be $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right )^x$ and I don't really know how ... | {"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": 25, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/geometric-optics?sort=votes&pagesize=15 | # Tagged Questions
The subfield of optics in which light propagation is approximated in terms of rays. It mainly includes reflection and refraction on surfaces.
14answers
41k views
### A mirror flips left and right, but not up and down
Why is it that when you look in the mirror left and right directions appear flip... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/87631-help-finding-rate-increase-using-product-quotient-rule.html | # Thread:
1. ## Help with finding rate of increase using product/quotient rule
I've been having trouble with a particular problem from my Calculus book in the Product and Quotient rules chapter.
I was hoping someone on this forum could help me out. Thanks in advance!
Question:
Suppose the price of an object is \$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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/48528/evaporation-of-water-content-from-a-solid-material-by-applying-low-pressure?answertab=oldest | # Evaporation of water content from a solid material by applying low pressure
I have a raw material which melts at $96\ ^\circ C$. My aim is to make water content evaporate at temperature below this temperature. I can apply vaccume oven for this. I want to know at what pressure the water evaporates by keeping low temp... | {"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://mathoverflow.net/questions/43286?sort=newest | ## How and how much do the notations and diagrams influence our understanding of mathematical concepts?
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How and how much do the notations and diagrams influence our understanding of mathematical concepts?
This q... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cogsci.stackexchange.com/questions/3187/how-to-adjust-sse-or-rmse-for-the-number-of-free-parameters-in-the-model/3191 | # How to adjust SSE or RMSE for the number of free parameters in the model?
How do I adjust SSE (sum of squared errors) or RMSE (root-mean-square errors) for the number of free parameters in the model?
Is there an "adjusted" RMSD metric similar to the adjusted r-squared metric?
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please don't assume that we know wha... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/53374/solving-the-time-independent-schrodinger-equation-does-a-complex-solution-make?answertab=oldest | # Solving the time independent Schrodinger equation: Does a complex solution make sense?
In my notes, I have the Time Independent Schrodinger equation for a free particle $$\frac{\partial^2 \psi}{\partial x^2}+\frac{p^2}{\hbar^2}\psi=0\tag1$$
The solution to this is given, in my notes, as $$\Large \psi(x)=C e^\left(\... | {"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": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/21453/for-which-lie-groups-is-the-convolution-of-any-two-nonzero-integrable-compactly-s | ## For which Lie groups is the convolution of any two nonzero integrable compactly supported functions nonzero?
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The Titchmarsh convolution theorem implies that the convolution of two nonzero functions $f,g\in L^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": 32, "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/Engineering_Analysis/MISO_Transformations | # Engineering Analysis/MISO Transformations
Consider now a system with two inputs, both of which are random (or pseudorandom, in the case of non-deterministic data). For instance, let's consider a system with the following inputs and outputs:
• X: non-deterministic data input
• Y: disruptive noise
• Z: System output
... | {"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://physics.stackexchange.com/questions/54949/gaussian-wave-packet/54969 | # Gaussian wave packet
At our QM intro our professor said that we derive uncertainty principle using the integral of plane waves $\psi = \psi_0(k) e^{i(kx - \omega t)}$ over wave numbers $k$. We do it at $t=0$ hence $\psi = \psi_0(k) e^{ikx}$
$$\psi = \int\limits_{-\infty}^{+\infty} \psi_0\!(k) \cdot e^{ikx} \, \text... | {"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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/77348/how-to-prove-that-lim-limits-h-to-0-fracah-1h-ln-a/77368 | # How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$
In order to find the derivative of a exponential function, on its general form $a^x$ by the definition, I used limits.
$\begin{align*} \frac{d}{dx} a^x & = \lim_{h \to 0} \left [ \frac{a^{x+h}-a^x}{h} \right ]\\ \\ & =\lim_{h \to 0} \left [ \frac{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": 29, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/46316/angle-brackets-for-tuples?answertab=active | # Angle brackets for tuples
I've recently noticed that use of angle brackets for writing tuples, e.g. $\langle x, y \rangle$ instead of the usual round brackets in a few books I've been reading — Lawvere's Sets for Mathematics, Mac Lane's Categories for the Working Mathematician, Forster's Logic, induction and sets, 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": 33, "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/87601/techniques-for-visualising-n-dimensional-space/87749 | # Techniques for visualising $n$-dimensional space
Can you guys point me to the types of things I should read about (I'm a maths lay person really) if I want to learn about the current thinking how $n$ dimensional spaces can be visualised and thus navigated?
Sorry this question seems a bit vague, but I'm trying think... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/12599/will-a-hole-cut-into-a-metal-disk-expand-or-shrink-when-the-disc-is-heated/22436 | # Will a hole cut into a metal disk expand or shrink when the disc is heated?
Suppose you take a metal disc and cut a small, circular hole in the center. When you heat the whole thing, will the hole's diameter increase or decrease? and why?
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4
Sometimes answers become clear when you think about various extremes. 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": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2008/06/03/the-category-of-matrices-ii/?like=1&source=post_flair&_wpnonce=671450efa2 | # The Unapologetic Mathematician
## The Category of Matrices II
As we consider the category $\mathbf{Mat}(\mathbb{F})$ of matrices over the field $\mathbb{F}$, we find a monoidal structure.
We define the monoidal product $\boxtimes$ on objects by multiplication — $m\boxtimes n=mn$ — and on morphisms by using the Kro... | {"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://mathhelpforum.com/differential-geometry/183728-absolute-value-convergence-vs-convergence-they-same-print.html | # Absolute value convergence vs. convergence (Are they the same?)
Printable View
• June 27th 2011, 11:42 PM
CountingPenguins
Absolute value convergence vs. convergence (Are they the same?)
The question is if the absolute value of a sequence converges then does the sequence itself converge. My gut reaction to this is ... | {"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://mathoverflow.net/revisions/61079/list | ## Return to Answer
UPDATE: There is an error at the end of this answer, addressed here and in comments. I am leaving the original answer here because it is discussed elsewhere.
Ugh, this turned out to be a nasty bit of brute forcing and I found myself grappling with notation before I got it (I think) right.
Write $... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/55085/new-proofs-to-major-theorems-leading-to-new-insights-and-results/55093 | ## New proofs to major theorems leading to new insights and results?
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I am wondering, historically, when has a new proof of an old theorem been particularly fruitful. A few examples I have in mind (all number theo... | {"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://mathhelpforum.com/advanced-applied-math/18815-temperature-room.html | # Thread:
1. ## Temperature in a Room
Say I have a rectangular room (so its volume is easy to find) and an air conditioner that cools this room. I know the initial state of the room without the air conditioner and cool this room eventually to the same temperature as the air conditioner. I turn off the air conditioner... | {"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/141579/associativity-of-norms-in-inseparable-extensions | # Associativity of norms in inseparable extensions
Let $K$ be a field. Let $L/K$ and $E/L$ be finite extensions. Let $α$ be an element of E. Let $N_{E/K}(α)$ be the norm of $α$, i.e. the determinant of the regular representaion matrix of $α$. It is well known that $N_{E/K}(α)$ $=$ $N_{L/K}(N_{E/L}(α))$ if $E/K$ is sep... | {"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://math.stackexchange.com/questions/7511/functions-that-are-their-own-nth-derivatives-for-real-n/7517 | # Functions that are their Own nth Derivatives for Real n
Consider (non-trivial) functions that are their own nth derivatives. For instance
$\frac{\mathrm{d}}{\mathrm{d}x} e^x = e^x$
$\frac{\mathrm{d}^2}{\mathrm{d}x^2} e^{-x} = e^{-x}$
$\frac{\mathrm{d}^3}{\mathrm{d}x^3} e^{\frac{-x}{2}}\sin(\frac{\sqrt{3}x}{2}) = ... | {"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": 119, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathhelpforum.com/algebra/185809-speed-earth-around-sun.html | # Thread:
1. ## Speed of the Earth around the Sun.
"The Earth revolves around the sun in an elliptical orbit, however for this problem you can assume that the orbit is circular with a radius of 9.3 * 10^7 miles.
In what speed in feet per second does Earth travel around the sun?"
I know this problem has something to... | {"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-geometry/97767-differential-geometry-straight-lines-shortest-connections.html | # Thread:
1. ## Differential Geometry: Straight lines as shortest connections
I started this problem, but got stuck shortly after beginning
Basically, I started with the middle peice of math from the in/equation above.
Since v is a constant vector, I took it out the front of the integral and used the fundamental 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": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathforum.org/mathimages/index.php/Talk:Differentiability | # Talk:Differentiability
## Anna 6/26
Can you say that $y=x^2$ is an everywhere differentiable function? I feel like that a subtlety missing in this page. Also I'd retitle the "basic description" section to be something else, for the same reasons in Alan's comment below.
## David 6/25
I think you have a typo in 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": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/64843?sort=oldest | ## Cohomology of the infinite loop space of the affine grassmanian (as in the generalized Mumford conjecture)
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I've been reading Hatcher's survey "A short exposition of the Madsen-Weiss theorem". In it, he outline... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/119377?sort=newest | Automorphism of finite groups and Hurwitz spaces
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If $G$ is a finite group, embedded as a transitive subgroup of $S_n$ for some $n$, will every automorphism of $G$ extend to an inner automorphism of $S_n$?
I'm trying... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/176425-find-limits-integral.html | Thread:
1. Find limits for integral
why does the unit circle with center in (1,0) have period $-\frac{\pi}{2} , \frac{\pi}{2}$ and not $0, 2\pi$ ?
2. The problem statement here makes no sense. Can you please either give the context of the problem, or better yet, simply state the original problem? Thanks!
3. As Ackb... | {"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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/223032/smooth-monotone-mathbbr3-curve-with-constant-nontrivial-curvature?answertab=votes | # Smooth Monotone $\mathbb{R}^3$ curve with constant (nontrivial) curvature
So I was trying to construct a closed curve in $\mathbb{R}^3$ with constant positive curvature and non-trivial torsion. To do this I tried to glue two helices together in a smooth way with a curve that is: Smooth, Monotone, and has the same cu... | {"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/tags/classifying-spaces/hot | Tag Info
Hot answers tagged classifying-spaces
13
What functor does $K(G, 1)$ represent for nonabelian $G$?
K(G,1) aka BG classifies G-bundles — i.e. G-coverings, if G is discrete. (Details can be found e.g. in May's Concise Course in Algebraic Topology.) Usual definition of Cech cohomology works for $H^1(X;G)$ eve... | {"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": 69, "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/57870/count-the-number-of-homogeneous-polynomials/57874 | ## Count the number of homogeneous polynomials
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Is there a general way of counting the number of homogeneous polynomials of certain degree in a complex projective space or a weighted complex projective space, mod ... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Quaternions | # Quaternion
(Redirected from Quaternions)
Quaternion multiplication
× 1 i j k
1 1 i j k
i i −1 k −j
j j −k −1 i
k k j −i −1
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843[1][2] and applied to mecha... | {"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": 76, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://sciencehouse.wordpress.com/2009/10/ | # Scientific Clearing House
Carson C. Chow
## Archive for October, 2009
### Hurdles for mathematical thinking
October 30, 2009
From my years as both a math professor and observer of people, I’ve come up with a list of hurdles for mathematical thinking. These are what I believe to be the essential set of skills ... | {"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": 12, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=592229 | Physics Forums
Mentor
## Simple question about simple functions
I feel like this should be really easy, but for some reason I don't see how to finish it. I'm probably missing something obvious.
The integral of an integrable simple function ##f=\sum_{k=1}^n a_k\chi_{E_k}## is
$$\int f\,\mathrm{d}\mu=\sum_{k=1}^n a_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": 13, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-challenge-problems/95364-quadratic-residues.html | Thread:
1. Quadratic Residues
Let $p$ be a prime such that $p>(n^2+n+k)^2+k$. ( $<br /> n,k \in \mathbb{Z}^ + <br />$ )
Consider the sequence: $<br /> n^2 ,n^2 + 1,...,\left( {n^2 + n + k} \right)^2 + k<br />$.
Prove that there's a pair $(m,m+k)$ of integers from our sequence, such that $<br /> \left( {\tfrac{m}<br... | {"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": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/84824?sort=newest | ## an operation on binary strings
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Recently, as part of some joint research, Tom Roby was led to a curious operation on strings of L's and R's which he calls "bounce-reading": We start by reading the string at 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": 28, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/170578-perimeter-equilateral-triangle.html | # Thread:
1. ## Perimeter of an equilateral triangle
The perimeter of an equilateral triangle exceeds the perimeter of a square by 1989cm. The length of each side of the triangle exceeds the length of each side of the square by d cm. The square has perimter greater than 0. How many positive integers are not possible ... | {"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://mathforum.org/mathimages/index.php?title=Parametric_Equations&diff=6423&oldid=6415 | # Parametric Equations
### From Math Images
(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": 12, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=79794 | Physics Forums
## Common source amplifier
Just out of interest guys have I got this right?
Function of certain components of a common source amplifier:
Capacitors at input and output: They are coupling capacitors and simply block the DC voltage, but allow the AC voltage through.
Gate Resistance: Is the purpose 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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikibooks.org/wiki/Cellular_Automata/Global_Dynamics | Cellular Automata/Global Dynamics
Attractor Basin
When discussing global dynamics of cellular automata the word state is used to describe configurations.
Graphic conventions
The following diagrams/captions are based on the original figure State-space and basins of attraction on the DDLab website. Sub-trees, basins ... | {"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": 16, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/absolute-value | # Tagged Questions
The absolute-value tag has no wiki summary.
1answer
28 views
### Simplifying $\left|\left|\sqrt{-x^2}-1\right|-2\right|$
How do we simplify the expression $\left|\left|\sqrt{-x^2}-1\right|-2\right|$? This is very confusing. Do they cancel out and become just simply $\sqrt{-x^2}-1-2$?
0answers
34 ... | {"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": 152, "mathjax_display_tex": 18, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathhelpforum.com/differential-geometry/180307-singularity.html | # Thread:
1. ## singularity
$f(z)=\frac{1}{sinh(z)}$
It's ok that z=0 is a singularity, but why
$2ik\pi$, where k is a integer, are singularities too? sinh(z)=0 only when z=0
Regards
2. $\sinh (2k\pi i)=\dfrac{e^{2k\pi i}-e^{-2k\pi i}}{2}=\dfrac{1-1}{2}=0$
3. Originally Posted by FernandoRevilla
$\sinh (2k\pi 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": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.m.wikibooks.org/wiki/Space_Transport_and_Engineering_Methods/Orbital_Mechanics | # Section 1.2 - Orbital Mechanics
## Introduction
Astrodynamics or Orbital Mechanics is mainly concerned with motions under gravity, either purely as a single force, or in combination with forces like thrust, drag, lift, light pressure, and others. As a topic it has a long history, with the motions of the planets, Mo... | {"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": 20, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/170256-uniformly-integrable.html | # Thread:
1. ## uniformly integrable
Hallo!
Is the following sequence of integrable random variables $(X_h)_{h \in [0,1]}$ also uniformly integrable?
$X_h=\prod\limits_{n=1}^{\frac{T}{h}}(1+\alpha_{(n-1)h}(\exp\{\mu_{(n-1)h}h+ \sigma (W_{nh}-W_{(n-1)h})\} -1))^\gamma$
whereas
$W$ is a standard Brownian motion,
$\sig... | {"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": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/continued-fractions?page=3&sort=newest&pagesize=15 | # Tagged Questions
For questions on continued fractions.
1answer
221 views
### Is the Iterated Continued fraction from Convergents for Pi/2 exactly 3/2?
Iterated continued fraction from convergents are described at https://oeis.org/wiki/Convergents_constant and https://oeis.org/wiki/Table_of_convergents_constants.... | {"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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/39735/induced-map-on-eilenberg-maclane-space | # Induced map on Eilenberg-MacLane space
Let $X$ be an $n-1$ connected space. Why does a map $X\rightarrow K(\pi_n(X),n)$ that induces an isomorphism on $\pi_n$ exist and what is this map?
-
## 3 Answers
If $X$ is a CW-complex, then you can build a $K(\pi_n(X),n)$ by attaching cells (of dimension $n+2$ and above) 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": 26, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/3789/are-there-any-standard-techniques-for-adding-realistic-synthetic-microstructure?answertab=oldest | # Are there any standard techniques for adding realistic synthetic microstructure noise to a price series?
This may seem like a strange question, but for my particular application we need to actually add synthetic microstructure noise to real time charts. The signal should still be representative of the aggregate mark... | {"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://math.stackexchange.com/questions/tagged/computational-mathematics+computer-algebra-systems | # Tagged Questions
2answers
53 views
### What free software can I use to solve a system of linear equations containing an unknown?
Question: What free software can I use to solve a system of linear equations $M\mathbf{x}=\mathbf{y}$ where the entries of $\mathbf{y}$ vary with an unknown quantity $n$? Presumably I co... | {"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://mathoverflow.net/questions/70657/hyperbolic-coxeter-polytopes-and-del-pezzo-surfaces/71606 | ## Hyperbolic Coxeter polytopes and Del-Pezzo surfaces
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Added. In the following link there is a proof of the observation made in this question: http://dl.dropbox.com/u/5546138/DelpezzoCoxeter.pdf
I would like to ... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.scholarpedia.org/article/Aloha_random_access | # Aloha random access
From Scholarpedia
Norman Abramson (2009), Scholarpedia, 4(10):7020.
Jump to: navigation, search
Curator and Contributors
1.00 - Norman Abramson
Figure 1: Multiple Transmitters Sharing an ALOHA channel.
Aloha random access is a widely used technique for coordinating the access of large numbers... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/271527/region-of-convergence-of-z-transform-connected-area | # Region of convergence of Z-Transform connected area?
Shouldn't the Region of Convergence of the Z transform be a connected area ? In Oppenheim solution manual, I've found this answer of a question that asks to determine the different forms of the impulse response of a certain system
in the (d) option it shows that ... | {"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://www.physicsforums.com/showthread.php?p=4158805 | Physics Forums
Page 3 of 4 < 1 2 3 4 >
The problem with infinity.
Quote by bahamagreen How about addressing my previous post #28 first?
Quote by bahamagreen I'm suggesting that is a flaw because you are defining some persons as both a non-customer and a customer - because 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": 2, "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/37142/integral-int-0a-frac-exp-2-pi-iwxx-idx | Integral $\int_{0}^{A}\frac{\exp(-2\pi iwx)}{x-i}dx$
Here $A>0$, $w$-real,$\mathtt{i}$-complex. Mathematica gives the answer: $$\frac{1}{2}e^{2\pi w}(\mathtt{i}\pi+2\Gamma(0,2\pi w)-2\Gamma(0,2(1+\mathtt{i}A)\pi w)+2\ln(-\mathtt{i}+A)+2\ln(w)-2\ln(w+iA))$$ My questions: 1. How to obtain this results without mathematic... | {"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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/51008?sort=oldest | ## Limit of a sequence of polygons.
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Begin with a polygon $P_0$.
Place two points on every edge of the polygon such that they divide each side equally into three parts. Create a new polygon $P_1$ by connecting al... | {"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://unapologetic.wordpress.com/2009/09/08/the-special-linear-group-and-others/?like=1&source=post_flair&_wpnonce=c1c9c39881 | # The Unapologetic Mathematician
## The Special Linear Group (and others)
We’ve got down the notion of the general linear group $\mathrm{GL}(V)$ of a vector space $V$, including the particular case of the matrix group $\mathrm{GL}(n,\mathbb{F})$ of the space $\mathbb{F}^n$. We also have defined the orthogonal group $... | {"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": 27, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/178851-need-help-changing-irrational-number-into-rational-number-involving-polar-coord.html | # Thread:
1. ## Need help changing an irrational number into a rational number, involving polar coord
I am working with problems of changing from Polar to Cartesian coordinates.
the problem is (-5, pi/3)
I know x=-5cos pi/3 = -5/2
and y = -5sin pi/3 \approx 4.33 or = 5sqrt3/2 but I only know that it can be written 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": 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/54534/is-it-possible-for-delta-x-sigma-x-of-any-free-particle-wave-packet-to-b/54537 | # Is it possible for $\Delta x$ ($\sigma_x$) of any free particle wave packet to be decreasing at any time?
Consider any wave packet describing a free particle (so no potential or other forces acting on it). Then it can be shown that $\Delta p$ does not change in time. However, my question is what happens with $\Delta... | {"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": 69, "mathjax_display_tex": 23, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/9733?sort=oldest | ## Matrix factorizations and physics
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I have heard during some seminar talks that there are applications of the theory of matrix factorizations in string theory. A quick search shows mostly papers written by physi... | {"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/78627?sort=newest | ## Is it consistent relative to ZF that $\frak c = \aleph_\omega$?
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In ZFC we know that the continuum cannot have cofinality $\omega$.
However, in the Feferman-Levy model we have that $\frak c=\aleph_1$, and that... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/49724?sort=newest | ## The functional equation $f(f(x))=x+f(x)^2$
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I'd like to gather information and references on the following functional equation for power series $$f(f(x))=x+f(x)^2,$$$$f(x)=\sum_{k=1}^\infty c_k x^k$$
(so $c_0=... | {"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": 345, "mathjax_display_tex": 20, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://math.stackexchange.com/questions/155589/schur-weyl-duality-for-sl-2-and-s-n | # Schur -Weyl duality for $sl_2$ and $S_n$
$V$ is an $m$ dimensional vector space having a structure of $sl_2(\mathbb{C})$-module, where $sl_2(\mathbb{C})$ is the Lie algebra of the Lie group $SL_2(\mathbb{C})$. The symmetric group $S_n$ acts on the tensor product $V^{\otimes n}$.
What does Schur-Weyl duality say 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": 37, "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/40161/why-do-we-care-about-the-hilbert-scheme-of-points/40180 | ## Why do we care about the Hilbert scheme of points?
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If $X$ is a scheme, the Hilbert scheme of points $X^{[n]}$ parameterizes zero dimensional subschemes of $X$ of degree $n$.
Why do we care about it?
Of cours... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://tcsmath.wordpress.com/2010/06/15/majorizing-measures/ | # tcs math – some mathematics of theoretical computer science
## June 15, 2010
### Majorizing measures
Filed under: Math — Tags: chaining, cover time, Gaussian process, majorizing measures, Talagrand — James Lee @ 12:44 am
At STOC 2010 last week, Talagrand gave a presentation on some of his favorite open problems, ... | {"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": 59, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2007/03/page/3/ | The Unapologetic Mathematician
Flag varieties
As another part of preparing for the digestion of the $E_8$ result, I need to talk about flag vareties. You’ll need at least some linear algebra to follow from this point.
A flag in a vector space is a chain of nested subspaces of specified dimensions. In three-dimension... | {"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": 109, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/57951?sort=newest | ## Lifting of projective representations of a torus over a valuation ring
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Let $R$ be a valuation ring. We don't assume it to be discrete or have a finite residue field. Let $T$ be a split torus over $R$, so $T\co... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://te.wikipedia.org/wiki/%E0%B0%A6%E0%B1%83%E0%B0%B7%E0%B1%8D%E0%B0%9F%E0%B0%BF_%E0%B0%95%E0%B1%8B%E0%B0%A3%E0%B0%82 | # దృష్టి కోణం
వికీపీడియా నుండి
ఇక్కడికి గెంతు: పేజీకి సంబంధించిన లింకులు, వెతుకు
ఈ వ్యాసాన్ని పూర్తిగా తరువాత ఈ మూసను తీసివేయండి. అనువాదం చేయాల్సిన వ్యాస భాగం ఒకవేళ ప్రధాన పేరుబరిలో వున్నట్లయితే పాఠ్యం సవరించు నొక్కినప్పుడు కనబడవచ్చు.
దృష్టి కోణం(Angle of view)
A camera's angle of view can be measured horizontall... | {"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": 31, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/263496/properties-of-fourier-transform-of-distributions?answertab=votes | # Properties of Fourier transform of distributions
For distributions the scaling property, $f(ax) = \frac{1}{|a|} \mathcal{F(\frac{u}{a})}$, of the Fourier transform is no longer true. Is there a source that lists which properties of the Fourier transform remain true even for distributions and which are false?
-
3
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": 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/54549/how-deep-is-the-well-given-this-data?answertab=oldest | # How deep is the well, given this data?
A rock is dropped into a well. A timer starts when the rock is dropped and is stopped when the noise of the rock hitting the ground of the well is heard. How deep is the well?
Here's what I have so far: $t = \left(\left(\frac{2\times h}{g}\right)^{\frac{1}{2}}+\left(\frac{h}{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": 13, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/842/why-is-compactness-in-logic-called-compactness | Why is compactness in logic called compactness?
In logic, a semantics is said to be compact iff if every finite subset of a set of sentences has a model, then so to does the entire set.
Most logic texts either don't explain the terminology, or allude to the topological property of compactness. I see an analogy as, gi... | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/126512-determine-whether-function-solution-de.html | # Thread:
1. ## Determine whether the function is a solution of the DE?
Determine whether the function is a solution of the differential equation
y''' - 8y = 0
(a) y = cos(2x)
(b) y = e^(2x)
What exactly is one suppose to do here? Is this suppose to be the third degree because we only covered first degree DE?
2. 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/50779-disproving-prime-numbers.html | # Thread:
1. ## disproving prime numbers
how do you prove that number is not Prime?
the example in my book says prove that 2 to the power of 66 is not prime and then says the keys lies in this simple algebra $x squared-1=(x-1)(x+1)$ it says to use that to write a proof that the number is not prime so what am suppose... | {"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": 23, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/101969/calculate-the-maximum-number-of-linearly-independent-subsets | # calculate the maximum number of linearly independent subsets
I am not sure if this question has been asked before, apologies if I am repeating this question again.
My question is as follows:
given a set i know how to find all the subsets of the set.
But what I would really like to know is how do i find all linear... | {"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://en.wikipedia.org/wiki/Faraday's_law_of_induction | # Electromagnetic induction
(Redirected from Faraday's law of induction)
For the relationship between a time-varying magnetic field and an induced electric field, see Maxwell's equations.
Electromagnetism
• Electromagnetic induction
Scientists
Electromagnetic induction is the production of a potential difference (vol... | {"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": 28, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/05/page/2/ | # The Unapologetic Mathematician
## Commutativity in Series II
We’ve seen that commutativity fails for conditionally convergent series. It turns out, though, that things are much nicer for absolutely convergent series. Any rearrangement of an absolutely convergent series is again absolutely convergent, and to the sam... | {"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": 201, "mimetex.cgi": 0, "/images/m... |
http://gilkalai.wordpress.com/2008/09/07/diameter-problem-3/?like=1&source=post_flair&_wpnonce=b19f116cf4 | Gil Kalai’s blog
## Diameter Problem (3)
Posted on September 7, 2008 by
### 3. What we will do in this post and and in future posts
We will now try all sorts of ideas to give good upper bounds for the abstract diameter problem that we described. As we explained, such bounds apply to the diameter of graphs of simple... | {"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": 78, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=337830 | Physics Forums
## electrical potential difference given velocity
1. The problem statement, all variables and given/known data
An electron moving parallel to the x axis has in initial speed of 3.7x10^6m/s at the origin. Its speed is reduced to 1.4x10^5m/s at the point x=2.0 cm. What is the potential difference between... | {"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://www.physicsforums.com/showthread.php?s=86e0cba3bcf2c774e27f1eb960bc99b0&p=4083425 | Physics Forums
## Finding a basis for a set of polynomials and functions
Find a basis for and the dimension of the subspaces defined for each of the following sets of conditions:
{p $\in$ P3(R) | p(2) = p(-1) = 0 }
{ f$\in$Span{ex, e2x, e3x} | f(0) = f'(0) = 0}
Attempt: Having trouble getting started...
So I thin... | {"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://mathoverflow.net/questions/38943?sort=oldest | ## An orthogonal companion matrix
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Let $P\in{\mathbb R}[X]$ be a monic polynomial with roots on the unit circle. For the problem below, we may assume wlog that the roots are simple and distinct from $\pm1$. It can... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/22065?sort=oldest | ## Algebraic properties of the algebra of continuous functions on a manifold.
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Does the algebra of continuous functions from a compact manifold to $\mathbb{C}$ satisfy any specific algebraic property?
I'm not sur... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/63580/is-a-double-centralizer-type-theorem-encountered-in-semisimple-algebras-true | ## Is a double centralizer type theorem ( encountered in semisimple algebras) true for algebraic groups ?
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Let, $G(k^{al})$ be an algebraic group, over an algebraically closed field, and $\Gamma_{G}$ is the set o... | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/15707/for-what-functions-fx-is-fxfy-convex | # For what functions $f(x)$ is $f(x)f(y)$ convex?
For which functions $f\colon [0,1] \to [0,1]$ is the function $g(x,y)=f(x)f(y)$ convex over $(x,y) \in [0,1]\times [0,1]$ ? Is there a nice characterization of such functions $f$?
The obvious examples are exponentials of the form $e^{ax+b}$ and their convex combinatio... | {"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": 56, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/135480-operation.html | # Thread:
1. ## Operation
Hi,
$_* \$is a binary operation in E,
C is a set defined as:
$C={ y \in E/ (\forall x \in E): y_*x=x_*y }$
I must determine the specifications of $(C,_*)$: associativity, commutativity, neutral element, inverse element...
I found that $_*$ is commutative but for the others i don't know ... | {"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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/135796-find-centroid.html | Thread:
1. Find the centroid
$x=y^2, y=x-2$
I have the formulas
$<br /> \bar{x}=\frac{1}{A}\int_{a}^b x[f(x)-g(x)]\,dx<br />$
and
$<br /> \bar{y}=\frac{1}{A}\int_{a}^b \frac{1}{2}[(f(x))^{2}-(g(x))^{2}]\,dx$
I found A= 9/2
Now I do not know how to write $x=y^2$ as f(x) function, since $x=y^2$would be $f(x) = y = ... | {"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": 20, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/281413/effective-well-ordering-of-reals | # Effective Well ordering of reals
Is there an effective (constructive) well order on reals ?
I know several questions were already asked on this topic, and the answers were very good to this well known problem. My question is more specific :
Is there some axiom $A$ ($A$ is equivalent to "there exists some large car... | {"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://physics.stackexchange.com/questions/38077/quark-compositions-in-pi-to-pi0-pion-decay?answertab=votes | # Quark compositions in $\pi^+$ to $\pi^0$ pion decay
Pions can undergo a rare beta-like decay into leptons:
Pion beta decay (with probability of about $10^{−8}$) into a neutral pion plus an electron and electron antineutrino (or for positive pions, a neutral pion, positron, and electron neutrino).
• Why is the quar... | {"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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/221153/find-the-directions-in-which-the-directional-derivative-has-the-value-1 | # Find the directions in which the directional derivative has the value 1
Can anyone show me how to adjust my work below so that it is a correct answer? This is question number 14.6.28 in the 7th edition of Stewart Calculus.
Find the directions in which the directional derivative of $f(x,y)=ye^{-xy}$ at the point $(0... | {"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": 53, "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/waves+acoustics | # Tagged Questions
1answer
75 views
### Why do sound waves travel at the same speed moleculewise? (Same medium)
I don't understand what happens in reality (outside of wave theories). If I clap my hands I invest energy in the nearby air molecules, which move and transfer their energy to nearby molecules which ...
0an... | {"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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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