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http://mathhelpforum.com/calculus/168667-how-do-i-find-relative-extrema-points-inflection-function-print.html | # How do I find the relative extrema and points of inflection of this function?
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• January 17th 2011, 08:38 PM
onanyc
How do I find the relative extrema and points of inflection of this function?
y = (x)/(x^2+9)
• January 17th 2011, 08:57 PM
Prove It
Local Maxima: The points where $\displaystyle \frac{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": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/189895-does-uniquely-determine-g.html | # Thread:
1. ## Does this uniquely determine G?
(up to isomorphism)
$1\longrightarrow \mathbb{Z}_4 \longrightarrow^{\!\!\!\!\!\!\!\!\!\beta}\ \, G \longrightarrow^{\!\!\!\!\!\!\!\!\!\alpha}\ \, \mathbb{Z}_2 \longrightarrow 1$
$\mathbb{Z}_2\longrightarrow^{\!\!\!\!\!\!\!\gamma} \ \, G$
$\gamma \circ \alpha = 1_{\ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/61761/topological-sort-of-partial-order-into-sorted-sets | ## Topological sort of partial order into sorted sets
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Given a partial order of elements, one can use topological sorting to produce a sorted list of elements. For example, if we have the partial order A->B and 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": 10, "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/31/lay-explanation-of-the-theory-of-relativity | # Lay explanation of the theory of relativity?
What is Einstein's theory of Special relativity, in terms a lay person can follow?
-
5
How lay are we talking about here? Do you have some knowledge of Galilean dynamics and Newtonian mechanics? – j.c. Nov 2 '10 at 20:24
3
The problem is : after the beta we will 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": 7, "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/41589/reading-list-in-topological-qft/41729 | # Reading list in topological QFT
I'm interested in learning about topological QFT including Chern Simons theory, Jones polynomial, Donaldson theory and Floer homology - basically the kind of things Witten worked on in the 80s. I'm looking for pedagogical reviews rather than original articles. Though these things sit ... | {"extraction_info": {"found_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/3164/how-is-a-spherical-electromagnetic-wave-emitted-from-an-antenna-described-in-ter/3167 | # How is a spherical electromagnetic wave emitted from an antenna described in terms of photons?
When an atenna transmits radiowaves isn't it true that the electromagnetic pulse is radiated away from the accelerating electron as a spherical wave in all directions simultaneously, and if so how can the associated photon... | {"extraction_info": {"found_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/tagged/eigenvector | ## Tagged Questions
1answer
131 views
### Coercive Symmetric Bilinear form on a Hilbert space
I need to show one of the two following equivalent results. If true, it must be a simple proof but I do not seem to be able to make it work. Thank you in advance. 1) Consider a co …
1answer
156 views
### Coercive Symmetric... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/42594?sort=newest | ## Concavity of $\det^{1/n}$ over $HPD_n$.
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One of my beloved theorems in matrix analysis is the fact that the map $H\mapsto (\det H)^{1/n}$, defined over the convex cone $HPD_n$ of Hermitian positive definite mat... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/80986?sort=votes | ## Question on geometric measure theory
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I want to know the following is well-known or not:
Let X be a metric space with Hausdorff dimension $\alpha$. Then for any $\beta < \alpha$, X contains a closed subset who... | {"extraction_info": {"found_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://math.stackexchange.com/questions/214533/variation-of-monty-hall-game-homework-need-checking | # Variation of Monty Hall game. Homework. Need checking.
Assume that you are playing the following variation of the Monty Hall game: A valuable prize is randomly placed behind one of the four doors, numbered from 1 to 4, and nothing behind the remaining three doors. You are allowed to select a door. After your selecti... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/tagged/teaching+general-topology | # Tagged Questions
4answers
156 views
### Motivation for the importance of topology
Starting from tomorrow, I will be tutoring some undergraduate students following a course in general topology. I am looking for examples motivating the importance of topology in mathematics which can ...
1answer
179 views
### Compac... | {"extraction_info": {"found_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/advanced-algebra/49185-solved-determinant-3x3-matrix.html | # Thread:
1. ## [SOLVED] Determinant of a 3x3 matrix
I've done the problem but I just want to know if I'm on the right track because I've solved many others this way. In other words, is my answer correct?
Determine for which values of $c$ the following matrix is invertible :
$\left[ \begin{array}{ccc} 1 & c & -1 \\ 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/152039/question-related-to-some-class-of-nowhere-dense-sets | # Question related to some class of nowhere dense sets
Let $\Omega\subset (0,1)$ be a nowhere dense set which has no lower and upper bound in $(0,1)$ and for which $\Omega^{d}\cap(0,1)=\Omega$ ($\Omega^{d}$ denotes here the set of all limit points of $\Omega$; let also $\Omega^{\pm d}$ denote the set of all two-sided ... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/2705/standard-symbol-notation-for-x-knows-y-or-the-inverse/2725 | # Standard symbol / notation for “x knows y”, or the inverse
What's the standard way to express "$x$ knows about $y$", or "$x$ has no knowledge of $y$" in cryptographic notation?
Example (PRNG predictor):
$\exists f : P(f(G(k)|_{0..n}) = G(k)|_{n+1}) \geq 0.5 + \epsilon$, for non negligable $\epsilon$, where $f$ has... | {"extraction_info": {"found_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/tagged/limit | # Tagged Questions
Questions on the evaluation of limits.
2answers
33 views
### Proving if $f(x)$ is differentiable at $x = x_0$ then $f(x)$ is continuous at $x = x_0$.
Please, see if I made some mistake in the proof below. I mention some theorems in the proof: The condition to $f(x)$ be continuous at $x=x_0$ 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": 145, "mathjax_display_tex": 33, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://www.sagemath.org/doc/reference/combinat/sage/combinat/rigged_configurations/bij_abstract_class.html | # Abstract classes for the rigged configuration bijections¶
This file contains two sets of classes, one for the bijection from KR tableaux to rigged configurations and the other for the reverse bijection. We do this for two reasons, one is because we can store a state in the bijection locally, so we do not have to con... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/35972/observation-of-violation-of-the-uncertainty-principle?answertab=votes | # Observation of violation of the uncertainty principle?
I stumbled upon this piece of news in the BBC's website http://www.bbc.co.uk/news/science-environment-19489385, discussing this paper http://prl.aps.org/abstract/PRL/v109/i10/e100404, which reports the "Violation of Heisenberg’s Measurement-Disturbance Relations... | {"extraction_info": {"found_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://en.m.wikibooks.org/wiki/Basic_Algebra/Working_with_Numbers/Dividing_Rational_Numbers | # Basic Algebra/Working with Numbers/Dividing Rational Numbers
## Vocabulary
↑Jump back a section
## Lesson
Dividing rational numbers.
Dividing rational numbers covers a general area of equations. For an equation that is such has only to have a numerator and denominator that are both rational numbers. In turn, one... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 17, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/50472?sort=newest | ## Sums of arctangents
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```$$
\begin{align}
\arctan(x) & = \arctan(1) + \arctan\left(\frac{x-1}{2}\right) \\
& {} - \arctan\left(\frac{(x-1)^2}{4} \right) + \arctan\left(\frac{(x-1)^3}{8}\right) - \cdots
\end{alig... | {"extraction_info": {"found_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": 14, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/revisions/39653/list | ## Return to Answer
2 deleted 2 characters in body
One way to approach this question quantitatively is suggested by probability. One can put various measures on the space of all simplicial complexes on $n$ vertices. One perhaps fairly natural measure is to take a random graph and then take the clique complex. This do... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "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/72147?sort=newest | ## Is this polynomial irreducible?
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I'm just curious about the polynomial $\det (x_k^iy_k^j)_{0\leq i\leq d-1, 0\leq j\leq e-1, 1\leq k\leq de}$ (determinant of $de\times de$-matrix, $x_k$, $y_k$ are all independe... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/black-holes+string-theory | # Tagged Questions
1answer
87 views
### Where and how is the entropy of a black hole stored?
Where and how is the entropy of a black hole stored? Is it around the horizon? Most of the entanglement entropy across the event horizon lies within Planck distances of it and are short lived. Is ...
0answers
51 views
### 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": 3, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://sciencehouse.wordpress.com/2009/07/03/why-consciousness/ | # Scientific Clearing House
Carson C. Chow
## Why consciousness?
If we believe in materialism then we must accept that the function of our brain is the collective action of the biological parts. This doesn’t imply reductionism (i.e. just knowing the parts is enough), but it does imply that there is nothing beyond 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/99270/a-simple-question-about-the-difference-between-directional-derivatives-and-deriv | # A simple question about the difference between directional derivatives and derivatives
As the topic, let $\mathbf{u}=u\hat{i}+v\hat{j}$.
Why $$D_ug(0,0) = \lim_{h\rightarrow0}\frac{g(hu,hv)-g(0,0)}{h}$$ while
$$Dg(0,0)= \lim_{(h,k)\rightarrow (0,0)}\frac{g(h,k)-L(0,0)}{\sqrt{h^2+k^2}},$$we don't need to use the li... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2007/04/23/homomorphisms-of-modules/?like=1&source=post_flair&_wpnonce=a832ba55c5 | # The Unapologetic Mathematician
## Homomorphisms of modules
Again, once we have a new structure it’s important to understand what sort of functions connect different instancees of the structure. For modules we have module homomorphisms.
By now this should be pretty straightforward. A left $R$-module $M$ is an abeli... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/412/verify-product-without-revealing-multipliers/465 | # Verify product without revealing multipliers
Situation:
Several participants contribute encrypted random numbers. These numbers will be used to generate community-agreed random (by simple multiplication).
Question:
Is there any way to detect same products values without revealing multipliers? Maybe it is 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": 45, "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/27749/what-are-some-correct-results-discovered-with-incorrect-or-no-proofs/27753 | ## What are some correct results discovered with incorrect (or no) proofs?
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Many famous results were discovered through non-rigorous proofs, with correct proofs being found only later and with greater 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": 42, "mathjax_display_tex": 3, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/9691 | ### Fence It
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
# Perimeter Possibilities
##### Stage: 3 Challenge Level:
Watch the video below.
How many other possible perimeters can you find, for a rectangle with an area of $24cm^2$?
Now watch the video to see 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": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2009/01/29/extracting-the-determinant-from-the-characteristic-polynomial/?like=1&source=post_flair&_wpnonce=3fdfac1636 | # The Unapologetic Mathematician
## Extracting the Determinant from the Characteristic Polynomial
This one’s a pretty easy entry. If we know the characteristic polynomial of an endomorphism $T$ on a vector space $V$ of finite dimension $d$, then we can get its determinant from the constant term.
First let’s look at ... | {"extraction_info": {"found_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://mathhelpforum.com/discrete-math/73551-solved-difficult-binomial-theorem-question-involving-greatest-integer-function.html | # Thread:
1. ## [SOLVED] Difficult binomial theorem question(involving greatest integer function)?
If (3√3 + 5)^9 = R and [R] denotes the greatest integer less than or equal to R, then:
A) [R] is divisible by 10
B) [R^2] is divisible by 512
C) [R] is divisible by 15
D) [R] is an even number
More than one options ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/42127?sort=newest | ## generalization of Bezout’s Theorem?
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I learned Bezout's Theorem in class, stated for plane curves (if irreducible, sum of intersection multiplicities equals product of degrees). What is the proper general state... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/45089/what-is-the-length-of-a-sine-wave-from-0-to-2-pi/45092 | # What is the length of a sine wave from $0$ to $2\pi$?
What is the length of a sine wave from $0$ to $2\pi$? Physically I would plot $$y=\sin(x),\quad 0\le x\le {2\pi}$$ and measure line length.
I think part of the answer is to integrate this: $$\int_0^{2\pi} \sqrt{ 1 + (\sin(x))^2} \ \rm{dx}$$
Any ideas?
-
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": 29, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/52144/relationship-between-mars-and-earth-rotation | # Relationship between Mars and Earth rotation
Is it by pure random chance that Mars and the Earth have nearly the same day duration (Mars day is barely 40 minutes longer, which is just 3% difference), or there is some causal relationship between the two?
-
## 1 Answer
The length of the day on Earth has been changi... | {"extraction_info": {"found_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://mathforum.org/mathimages/index.php/Talk:Prime_spiral_(Ulam_spiral) | # Talk:Prime spiral (Ulam spiral)
### From Math Images
Iris6/28
I made all the changes to pf Maurer, Abram, and Anna's comments. I am ready for more comments
Smaurer1 11:03, 12 June 2010 (UTC) I've gone through the latest version now.
The demonstration and movie showing that the 2nd differences are 8 is lovely. If... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/cp-violation?sort=unanswered&pagesize=15 | # Tagged Questions
is a property of a system or theory where the combined charge conjugation (replacing particles with their anti-particles) and parity (reversing the sign of every vector, equivalent to reflecting the system through the origin) operations yield non-equivalent results. Only the weak interaction is 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": 6, "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/116719/localization-of-a-pure-injective-module-is-pure-injective/117547 | ## Localization of a pure-injective module is pure-injective?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi,
is there some work on localization of pure-injective modules? Is a localization of a pure-injective module pure-injective?
By localization I mea... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 67, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://polymathprojects.org/2011/02/05/polymath6-improving-the-bounds-for-roths-theorem/?like=1&source=post_flair&_wpnonce=104f7cb3e5 | # The polymath blog
## February 5, 2011
### Polymath6: improving the bounds for Roth’s theorem
Filed under: polymath proposals — gowers @ 12:03 pm
For the time being this is an almost empty post, the main purpose of which is to provide a space for mathematical comments connected with the project of assessing whethe... | {"extraction_info": {"found_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": 174, "mimetex.cgi": 0, "/images/m... |
http://enc.tfode.com/Least_squares | Least squares - 2 results found: Wikipedia, twitter
Pronunciation -
Also found in
Dictionary: English
Encyclopedia: Deutsch
English Wikipedia
# Least squares
Regression analysis
Models
Estimation
Background
The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 57, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/102440-approximate-numbers-rounding-print.html | # Approximate numbers and rounding
Printable View
• September 15th 2009, 02:20 PM
redshirt
Approximate numbers and rounding
I hope this is the proper spot for this! I did a little bit of searching and couldn't quite find what I was looking for, so here goes (it's more of a procedure question than a specific problem):... | {"extraction_info": {"found_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://math.stackexchange.com/questions/210642/probability-of-finding-a-fit-for-bin-packing?answertab=votes | # Probability of finding a fit for bin packing
Given that I know the total available space for a set of bins, and the number of bins, I'm trying to determine how likely it is that an item of size $n$ will fit into one of the bins.
As an example, I figured that if I need to fit a size 4 item and I have 4 bins, then as... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-topics/181708-projectiles-print.html | # projectiles
Printable View
• May 26th 2011, 07:36 AM
Duke
projectiles
A Rocket R is fired from ground with inital speed s to the horizontal at an angle $\alpha$. There is a resistive force F=-mkv where m is the mass and v is the vector (v1,v2) and K is a constant. Show the equations of motion are
$d/dt(v1)+kv1=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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://oumathclub.wordpress.com/tag/obama/ | # Why Math Research Is Practical
Posted on April 30, 2009 by
We’ve discussed a few modern areas of research in mathematics: the search for a combinatorial proof of the density Hales-Jewett theorem lead by Timothy Gowers and some of the open questions about the number $\pi$. A fair question is why should people spen... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/212845-factorising-over-complex-numbers.html | # Thread:
1. ## factorising over complex numbers:
Factorize: $3iu^2+26iu+4u^2+3i-4$ over complex numbers, where $i$ represents the imaginary unit.
Thanks
2. ## Re: factorising over complex numbers:
$\displaystyle \begin{align*} 3i\,u^2 + 26i\,u + 4u^2 + 3i - 4 &= \left( 4 + 3i \right) u^2 + 26i\,u + 3i - 4 \\ &= \... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/2326/brute-forcing-cardan-grille?answertab=oldest | Brute forcing Cardan grille
Having a "rotating" square Cardan Grill with sides long n cells, how could i determinate the cost of a brute-force attack? How many configurations should be considered to perform an exhaustive search?
EDIT FOR MORE DETAIL:
This was an exam question so these are all the information given 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": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/68058-solving-trig-identities.html | # Thread:
1. ## Solving Trig Identities??
For my homework tonight, there is this one problem that is supposed to be easy but i can't figure it out.
Solve for exact solutions in the interval [0degrees, 360degrees)
[ means include, & ) means exclude
2sinx -1= cscx
I am supposed to find the degree value for x. and i 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 27, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cdsmith.wordpress.com/2009/06/15/thoughts-on-an-associative-metric-for-the-non-negative-reals/?like=1&_wpnonce=24a0599870 | software, programming languages, and other ideas
June 15, 2009 / cdsmith
A recent reddit post posed the question of whether there exists an associative metric on the non-negative reals. I didn’t see it until after most people moved on, so I’m posting my thoughts on the subject here. It is likely that none of 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": 0, "wp_latex": 71, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/4162-roots-equation.html | # Thread:
1. ## Roots of equation
How many negative roots has the equation
$x^6 - bx^5 - 2ax^3 - cx + a^2=0, b\geq0, c\geq0?$
Keep Smiling
Malay
2. Since $f(-x)=x^{6}+bx^{5}+2ax^{3}+cx+a^{2}$ has no variation in signs, there are no negative roots.
It's been awhile since I thought about Descartes rule. Isn't that 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 20, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/tagged/differential-equations | # Tagged Questions
The differential-equations tag has no wiki summary.
1answer
243 views
### Connections between random walk and heat equation (Material for ~)
I am preparing an undergraduate lecture in quantitative finance and I am looking for material that combines the topics: random walk and heat equation The ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/99150/testing-isomorphism-of-finitely-generated-algebras | ## Testing isomorphism of finitely generated algebras
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $A=\mathbf{Q}[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over the rational numbers. Let $B=\mathbf{Q}[f_1,\ldots,f_r]$ and $C=\mathbf{Q}[g_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": 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/117904/elementary-examples-of-the-weil-conjectures | ## Elementary examples of the Weil conjectures
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I'm looking for examples of the Weil conjectures---specifically rationality of the zeta function---that can be appreciated with minimal background in algebraic geome... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 63, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/22911-minimum-value.html | # Thread:
1. ## the minimum value
Find the minimum value of the function
$f(x)=|1001+1000x+999x^2+...+2x^{999}+x^{1000}|$.
2. This problem only works for even degree exponents, it is hard to state the details in general so I will do it for special cases to show how to proceede. Let $f_n(x) = x^n + 2x^{n-1}+...+nx+(... | {"extraction_info": {"found_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": 28, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4254730 | Physics Forums
Mentor
## Number of pairings in a set of n objects
This isn't homework, just a combinatorics problem I came across. However, it is a textbook-style problem. So I'm compromising and posting in the math forums, but using the HH template. I asked a mentor and he said it was acceptable.
1. The problem st... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 16, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/172080/int-0-infty-frac-sin2n1xx-mathrm-dx-evaluate-integral | # $\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral
Here is a fun integral I am trying to evaluate:
$$\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \ dx=\frac{\pi \binom{2n}{n}}{2^{2n+1}}.$$
I thought about integrating by parts $2n$ times and then using the binomial theorem for $\sin(x)$, that 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": 20, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.aps.org/articles/large_image/f1/10.1103/Physics.4.82 | (a) APS/Alan Stonebraker; (b) Y. Zhang et al. [7]
Figure 1: (a) The magnetic dipole field produced by an electron spin. Note that the magnetic field experienced by the nuclear spin has a transverse component along the $x$-axis, even though the electron spin is aligned with the external field along the $z$-axis. Theref... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "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/mat... |
http://asmeurersympy.wordpress.com/2010/06/11/ | # Aaron Meurer's SymPy Blog
My blog on my work on SymPy and other fun stuff.
## Integration of rational functions
June 11, 2010
So for this week’s blog post I will try to explain how the general algorithm for integrating rational functions works. Recall that a rational function is the quotient of two polynomials. 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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 76, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-challenge-problems/3359-rubik-s-cube-riddle.html | # Thread:
1. ## Rubik's Cube Riddle
Anyone who has ever played with a rubik's cube knows that it is possible to only complete 1 of the 6 sides.
Anyone who has ever played with a rubik's cube knows that it is NOT possible to only complete x of the 6 sides.
find x
(I am proud of this one I made it up last night!)
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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/209365-change-variables-needed-print.html | # Change of variables needed?
Printable View
• December 8th 2012, 01:26 PM
cubejunkies
Change of variables needed?
Let there be a surface bounded below by the cone ${ z }^{ 2 }={ x }^{ 2 }+{ y }^{ 2 }$ and above by $1={ x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }$. Calculate the flux through this surface due to a vector field ... | {"extraction_info": {"found_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://calculus7.org/2012/01/31/another-orthonormal-basis-hermite-functions/ | being boring
## Another orthonormal basis: Hermite functions
Posted on 2012-01-31 by
This is an orthonormal basis for $L^2(\mathbb R)$. Since the measure of $\mathbb R$ is infinite, functions will have to decay at infinity in order to be in $L^2$. The Hermite functions are
$\displaystyle \Phi_n(x)=(2^n n! \sqrt{\pi}... | {"extraction_info": {"found_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": 53, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/109480?sort=votes | ## The highest root of an ADE quiver
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $\Gamma$ be a finite subgroup of $SL_2({\mathbb C})$, and $Q$ the set of its irreducible representations. McKay makes $Q$ into a directed graph by having $V \to W$ if $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": 50, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showpost.php?p=2763391&postcount=2 | View Single Post
Mentor The rest-mass energy of the Z is about 91 GeV = 91000 MeV. If you can find a $\beta^{-}$ emitter and a $\beta^{+}$ emitter with decay energies that add to give 91000 MeV, I will be very surprised. Beta decay energies are generally only a few MeV. I don't know what the maximum is, but I'd be su... | {"extraction_info": {"found_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://mathoverflow.net/questions/16243/tetrahedra-with-prescribed-face-angles | ## Tetrahedra with prescribed face angles
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am looking for an analogue for the following 2 dimensional fact:
Given 3 angles $\alpha,\beta,\gamma\in (0;\pi)$ there is always a triangle with these prescribed angle... | {"extraction_info": {"found_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://math.stackexchange.com/questions/138056/is-the-right-shift-operator-bounded | # Is the right shift operator bounded?
I was reading my lecture notes for functional analysis when I came across the following statement:
Let $(e_{n})$ be a total orthonormal sequence in a separable Hilbert space H. The right shift operator, defined as the linear operator $T: H\rightarrow{}H$ such that $Te_{n} = e_{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": 40, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/18363/how-to-evaluate-the-sum-over-a-hyperplane | # How to evaluate the sum over a hyperplane
I have difficulties in evaluating the following expression:
$$\sum_{\small n_1+...+n_{k}=m-k}\; \prod_{i=1}^{k}\frac{1}{(n_i+1)(n_i+2)}$$
I have tried the function `RootSum`, but it doesn't work and gives the following warning:
````RootSum[Sum[Subscript[n, j], {j, 1, 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": 32, "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/64510/classes-of-metric-spaces-with-additional-structure/64570 | ## Classes of metric spaces with additional structure [closed]
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As is often the case in mathematics there is an option of studying a more general topic but this comes with a price of losing some interesting proper... | {"extraction_info": {"found_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/65227/square-root-of-a-matrix/65257 | # Square root of a matrix
Under what conditions does a matrix $A$ have a square root? I saw somewhere that this is true for Hermitian positive definite matrices(whose definition I just looked up).
Moreover, is it possible that for some subspace $X \subset M_n(\mathbb R)$ of $n\times n$ matrices over $\mathbb R$, 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": 102, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathematica.stackexchange.com/questions/11342/union-and-intersection-of-intervals/11343 | # Union and Intersection of intervals
I have two sets $A = \{1 \leq x \leq 5\}$ and $B = \{5 \leq x \leq 8\}$. Now I want to find the `Union` and `Intersection` of $A$ and $B$.
I tried `Union[A, B]`, I got `{1 <= x <= 5, 5 <= x <= 8}` and for `Intersection[A, B]`, I got `{}`. The correct answer for $A \cup B$ 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": 10, "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/2011/04/06/derivatives-in-coordinates/?like=1&source=post_flair&_wpnonce=a832ba55c5 | # The Unapologetic Mathematician
## Derivatives in Coordinates
Let’s take the derivative and see what it looks like in terms of coordinates. Say we have a smooth manifold $M$ and a smooth map $f:U\to N$ from an open subset of $M$ to another smooth manifold $N$. If $p\in U$ is any point, we define the derivative $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": 0, "wp_latex": 34, "mimetex.cgi": 0, "/images/ma... |
http://scicomp.stackexchange.com/questions/3564/affecting-the-rank-of-a-gram-matrix-by-configuration-shift | # Affecting the rank of a Gram matrix by configuration shift
Let certain configuration of $n$ points exist in $d-$dimensional space, $X\in\mathbb{R}^{n\times d}$, $d<<n$. Also, let the corresponding Gram matrix be defined as $G=XX^T$.
Since $X$ exists in Euclidean space, rank of $G$ is, $rank(G)=rank(X)=d$. Now, supp... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 60, "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/307988/cleaning-a-signal-and-computing-period | # Cleaning a signal and computing period
I am working with a signal which is a periodic square signal with some kind of noise and some outliers. I would like to know which is the best solution in order to get the period and clean the outliers that can be seen in the image:
The final goal is to binarize the signal.
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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/tagged/pairings | # Tagged Questions
Pairing-based cryptography uses bilinear maps to create a gap group that allows efficient constructions of certain primitives.
learn more… | top users | synonyms
1answer
55 views
### Exponentiation In PBC library
I need to compute a function $h^l$, where h is an element of G2 and l is a rational... | {"extraction_info": {"found_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/52397?sort=newest | ## Are there (-2)-curves on an Enriques surface?
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Let $X$ be an Enriques surface. A $(-2)$-curve is an irriducible rational curve on X such that $C^2 = -2$. By Proposition [VIII,16.1] from Barth-Peters-Van de Ven,... | {"extraction_info": {"found_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://math.stackexchange.com/questions/251558/original-papers-on-the-subject-of-group-actions/251564 | # Original papers on the subject of group actions
Does anyone if there are any original paper(s) that first introduced the notion of group action or permutation representation, and who the author(s) were? Any references I have found so far on e.g. Wikipedia are for current textbooks.
I am interested to find out the 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": 7, "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/59413/convergence-of-eigenvectors/59542 | ## Convergence of eigenvectors
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Let $T$ be a compact operator on $l^2$. Let $T_n$ be finite rank operators and $T_n \to T$ in the operator norm. Is it true that the eigenvalues and eigenvectors of $T_n$ converge 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": 21, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/85268-exponentials-i-need-help.html | # Thread:
1. ## exponentials....i need help
I have two problems I am stuck on. I missed lecture and need help with both
1. 256^x=4
2. 1/9x=6561
Thanks to anyone who can help me. Leilani
2. Originally Posted by leilani
I have two problems I am stuck on. I missed lecture and need help with both
1. 256^x=4
2. 1/9x=6... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 21, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/61802/projecting-the-unit-cube-onto-a-very-special-subspace | ## Projecting the unit cube onto a (very special) subspace
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Let $n>1$ be an integer, and $a>1$ a real number. Consider the subspace `$L<R^{2^n}$` generated by the $n$ possible tensor products of the $n-1$ copies 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": 50, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/general-relativity+black-holes | # Tagged Questions
1answer
9 views
### Can we build a synthetic event horizon?
If we imagine ourselves to be a civilization capable of manipulating very heavy masses in arbitrary spatial and momentum configurations (because we have access to large amounts of motive force, for ...
0answers
51 views
### Gravitational... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/105304/criteria-for-irreducibility-of-polynomial/105323 | ## Criteria for irreducibility of polynomial
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If $f, g\in \mathbb C[a,b]$ are polynomials in two variables, are there easy criteria that allow to see if $f(x,y)-g(t,z)\in \mathbb C[x,y,t,z]$ is irreducible?
Thank... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 89, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-challenge-problems/117052-i-identity.html | Thread:
1. i identity
Demonstrate that $\arccos^i(\cosh1) = e^{-\frac{\pi}{2}}$
I am not a mathematician so sorry if this is not very challenging. Basically I just found this identity to be interesting and wonder how obvious/obscure it is to real mathematicians.
2. Note that $cosh(1)=cos(i)$
$cos^{-1}(cos(i))=i$
... | {"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": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/73145?sort=newest | ## “Measuring” how far is one Banach space from being surjectively isometric to another
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Bonjour/bonsoir à toutes et à tous.
Assume that `$\mathbf{V} \equiv (V, \|\cdot\|_V)$` and `$\mathbf{W} \equiv (W, \|\cdot\... | {"extraction_info": {"found_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://math.stackexchange.com/questions/20685/in-differential-calculus-why-is-dy-dx-written-as-d-dx-y | # In differential calculus, why is dy/dx written as d/dx ( y)?
In differential calculus, We know that dy/dx is the ratio of between the rate of change in y and the rate of change in x. In other words, the rate of change in y with respect to x.
Then, why is dy/dx written as d/dx ( y)?
That is, why and how d/dx is con... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/19/hows-the-energy-of-particle-collisions-calculated | # How's the energy of particle collisions calculated?
Physicist ofter refer to the energy of collisions between different particles. My questions is how is that energy calculated? Is that kinetic energy?
Also, related to this question, I know that the aim is to have higher and higher energy collisions (e.g to test fo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/349/solution | ### Dodecawhat
Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.
# Platonic Planet
##### Stage: 4 Challenge Level:
Elijah sent us a clear explanation of how he tackled this problem... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/4944/regime-switching-in-mean-reverting-stochastic-process/4949 | # Regime switching in mean reverting stochastic process
Let you have a mean reverting stochastic process with a statistically significant autocorrelation coefficient; let it looks like you can well model it using an $ARMA(p,q)$.
This time series could be described by a mean reverting stochastic process like
$dS=k(\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": 22, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/38118/parallel-lines-on-residual-vs-fitted-plot | Parallel lines on residual vs fitted plot
I have a multiple regression problem, which I tried to solve using simple multiple regression:
````model1 <- lm(Y ~ X1 + X2 + X3 + X4 + X5, data=data)
````
This seems to be explaining the 85% of variance (according to R-squared) which seems pretty good.
However what worries... | {"extraction_info": {"found_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://mathhelpforum.com/discrete-math/200926-help-modular-arithmetic-print.html | # Help with modular arithmetic
Printable View
• July 12th 2012, 08:23 PM
joatmon
Help with modular arithmetic
I'm doing some self-study in cryptography and have come across something that I don't understand. Hoping somebody can help me with the gap in my knowledge.
I'm trying to follow an algorithm to compute expone... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/109339?sort=oldest | ## Commuting Linear Operators In Hilbert Spaces
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Let $V$ be a finite dimensional vector space over the complex field $\mathbb C$. Let $L:V\rightarrow V$ be a linear operator. Using the matrix of $L$ and the Jordan... | {"extraction_info": {"found_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://math.stackexchange.com/questions/tagged/pigeonhole-principle?sort=unanswered&pagesize=15 | # Tagged Questions
Questions involving the pigeonhole principle in Combinatorial Analysis.
1answer
52 views
### Consider a set A of 100, 000 arbitrary integers. Prove that there is some subset of 22 integers that end in the same last three digits.
Consider a set A of 100, 000 arbitrary integers. Prove that there 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": 4, "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/24468/rotational-kinetic-energy-during-vertical-circular-motion-of-a-particle/24476 | # Rotational kinetic energy during vertical circular motion of a particle
Why is it not necessary to take into account rotational kinetic energy when using the Law of Conservation of Mechanical Energy to solve vertical circular motion problems? After all, the particle is rotating about the centre of the circle and doe... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/54569/question-about-proper-time-in-general-relativity?answertab=oldest | # Question about proper time in general relativity
I think I may have some fundamental misunderstanding about what $dt, dx$ are in general relativity.
As I understand it, in special relativity, $ds^2=dt^2-dx^2$, we call this the length because it is a quantity that is invariant under Lorentz boosts. If a ball is movi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 57, "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/14866?sort=votes | ## slice=ribbon generalization to higher genus + potential counterexamples to slice=ribbon.
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I have two questions about the slice=ribbon conjecture.
(1) If a knot $K \hookrightarrow S^3$ has smooth slice genus $g... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/127986-limit-problem.html | # Thread:
1. ## A Limit Problem
Dear friends,
I need help in showing the following.
$\lim_{\substack{\lambda\in\mathbb{R}\\ \lambda\to0}}\bigg(\frac{1}{\lambda}\log|1+z\lambd a|\bigg)=\mathrm{Re}(z)$
Thanks!
bkarpuz
2. Originally Posted by bkarpuz
Dear friends,
I need help in showing the following.
$\lim_{\lambd... | {"extraction_info": {"found_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": 27, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/80323/list | Return to Question
2 added 5 characters in body
I am sorry if the answer to my question is well-known. I am quite new in this topic, so it will be also nice to have a reference, if it exists.
I was wondered if there exists a nice closed formula for a logarithm of an arbitrary hypergeometric series in term the terms ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/159410/purpose-of-linear-algebra/159427 | # Purpose of Linear Algebra
How much emphasizes should be on proof on a first course in Linear Algebra? I sometimes feel that they (proofs) crowd out a coherent vision for linear algebra. However I also think a central theme of a Linear Algebra course is to learn reasoning even though it does not always succeed. The 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/218553/extension-of-a-smooth-function-on-a-set-of-manifold | # Extension of a smooth function on a set of manifold
I encountered the following proposition:
If a function is smooth on an arbitrary set $S\in M$, where $M$ is a smooth manifold, then it has a smooth extension to an open set containing $S$.
It seems the proof needs the partition of unit, but I don't think this pro... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/53861/would-a-laser-with-four-possible-energy-levels-be-better-than-three?answertab=votes | # Would a laser with four possible energy levels be better than three?
I'm wondering about achieving population inversion for a laser. I learned that without an active medium, it's not possible to create a laser with only two energy levels, but it would be possible with three. What is the advantage of having four leve... | {"extraction_info": {"found_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/kinematics+suvat-equations | # Tagged Questions
1answer
45 views
### Projectile's angle in midflight
For a missile travelling from (0,0) at angle $\theta$ (to the horizontal) and initial velocity $u$, the y (vertical) position at time t is given by $s_{y} = u\sin (\theta) t - 0.5gt^{2}$ and the x ...
2answers
90 views
### Doubt in Kinematics
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Unrestricted_grammar | # Unrestricted grammar
In formal language theory, an unrestricted grammar is a formal grammar on which no restrictions are made on the left and right sides of the grammar's productions. This is the most general class of grammars in the Chomsky–Schützenberger hierarchy, and can generate arbitrary recursively enumerable... | {"extraction_info": {"found_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://mathoverflow.net/questions/55824/is-there-any-efficient-way-to-compute-the-follow-matrix-equations-easily/55827 | ## is there any efficient way to compute the follow matrix equations easily
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Let $A$ and $D$ are $n\times n$ diagnal matrices, and $B$ is an $n\times n$ orthogonal matrix. Is there any efficient way to compute 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": 50, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/500/finite-groups-with-the-same-character-table/502 | ## Finite groups with the same character table
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Say I have two finite groups G and H which aren't isomorphic but have the same character table (for example, the quaternion group and the symmetries of the square). ... | {"extraction_info": {"found_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/3122/showing-frac1x-left-frac1x-right-is-riemann-integrable | # Showing $\frac{1}{x}-\left[\frac{1}{x}\right]$ is Riemann Integrable
Some days ago as i had asked as to how to test the Riemann Integrability of the function. Now i was recently given this question about proving that the given function is Riemann Integrable.
How can i show that this function is Riemann Integrable 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": 26, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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