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http://physics.stackexchange.com/questions/16943/what-are-the-final-particles-emitted-from-an-evaporating-black-hole | # What are the final particles emitted from an evaporating black hole?
Hawking radiation predicts that black holes can slowly evaporate through the effective emission of a particle. This particle is a real particle, as in, it is not a black hole itself. I'll write this (a bit tongue-in-cheek) as follows, with $A$ bein... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/115706/how-to-solve-a-system-of-linear-equations-without-storing-the-matrix/115716 | ## How to solve a system of linear equations without storing the matrix?
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I have a procedurally defined Hermitian matrix $M$, i.e. I can get any matrix element by calling a black box function (e.g. a library funct... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bbms/1337864268 | ### Petrov-Galerkin method with cubic B-splines for solving the MEW
equation
Turabi Geyikli and S. Battal Gazi Karakoç
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 19, Number 2 (2012), 215-227.
#### Abstract
In the present paper, we introduce a numerical solution algorithm based on a Petrov-Galerkin 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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.reference.com/browse/wiki/Boyer-Lindquist_coordinates | Definitions
# Boyer-Lindquist coordinates
A generalization of the coordinates used for the metric of a Schwarzschild black hole that can be used to express the metric of a Kerr black hole.
The coordinate transformation from Boyer-Lindquist coordinates r, $theta$, $phi$ to cartesian coordinates x, y, z is given by
$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "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://mathoverflow.net/questions/70952/smooth-real-analytic-interpolation-of-monotonic-sequence/108611 | smooth/real analytic interpolation of monotonic sequence
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Let $x_n$ be a increasing sequence of negative real numbers that converge to $0$. Let $f$ be a function defined on $x_n$ such that $f(x_n)$ is a increasing seq... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 55, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/4023/using-pairings-to-verify-an-extended-euclidean-relation-without-leaking-the-valu?answertab=active | # Using pairings to verify an extended euclidean relation without leaking the values?
Let $P_i(x)$ be polynomials $i=1,...,n$, $s$ some value, and $g$ a generator of a group $G$ where the discrete logarithm is hard.
Assume a prover wants to convince a verifier having access to the values $g^{P_i(s)}$ that it knows po... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://catalog.flatworldknowledge.com/bookhub/reader/21?e=rittenberg-ch06_s02 | Please wait while we create your MIYO...
# Principles of Microeconomics, v. 1.0
by Libby Rittenberg and Timothy Tregarthen
Study Aids:
Click the Study Aids tab at the bottom of the book to access your Study Aids (usually practice quizzes and flash cards).
Study Pass:
Study Pass is our latest digital product 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": 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-statistics/158665-conditinal-probability-numbers-selected-random.html | # Thread:
1. ## Conditinal Probability with numbers selected at random
Suppose that three numbers are selected one by one, at random, and without replacement from the set of numbers {1, 2, 3, ... n}. What is the probability that the third number falls between the first two if the first is smaller than the second?
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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/63974/is-every-homology-theory-given-by-a-spectrum/63975 | ## Is every homology theory given by a spectrum?
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Let $E$ be a spectrum. For any CW complex $X$, define $h_*=\pi_i(E\wedge X)$. Then we know that $h_*$ form a homology theory. In other words, there functors satisf... | {"extraction_info": {"found_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://mathoverflow.net/revisions/5457/list | ## Return to Question
Post Made Community Wiki by Harry Gindi
2 edited tags
1
# $\omega$-topos theory?
I've been reading through Lurie's book on higher topos theory, where he develops the theory of $(\infty,1)$-toposes, which leads me to the following question: Is there any sort of higher topos theory on the more 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": 3, "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/showpost.php?p=3656415&postcount=2 | View Single Post
Recognitions:
Homework Help
Hi Ad123q!
Quote by Ad123q Hi, Was wondering if anyone could give me a hand. I need to prove that the Cayley Transform operator given by U=(A-i)(A+i)^-1 is UNITARY, ie that UU*=U*U=I where U* is the adjoint of U (I am given also that A=A* in the set of bou... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-algebra/108622-boolean-ring.html | # Thread:
1. ## Boolean Ring
For the case a^2 = a (a belongs to R), I already showed that a+a = 0 for all a in R
What can you say a ring in which for all a in R, a^3 = a and more generally, for all a in R, a^n = a where n >= 4?
2. Originally Posted by knguyen2005
For the case a^2 = a (a belongs to R), I already sho... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-algebra/178019-consistency-matrix.html | # Thread:
1. ## Consistency of a matrix
Hi guys,
My problem states:
Let $A$ be an augmented matrix of size m x m+1 (that is to say, the coefficient matrix of the system is square and of size m x m), and $A$ has all non-zero entires. Prove or disprove that this system is consistent and, in fact, has one and only 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": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/27896/differential-equations | # Differential Equations
How would I solve these differential equations? Thanks so much for the help!
$$P'_0(t) = \alpha P_1(t) - \beta P_0(t)$$ $$P'_1(t) = \beta P_0(t) - \alpha P_1(t)$$
We also know $P_0(t)+P_1(t)=1$
-
## 3 Answers
Note that from the equation you have $$P'_0(t) = \alpha P_1(t) - \beta P_0(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": 11, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/10217/list | ## Return to Answer
3 added 2 characters in body
Let $K$ be a number field and $F$ a polynomial with coefficients in $K$. Class field theory shows that the following properties of $F$ are equivalent:
(1) There is subgroup $H$ of a generalized ideal class group $C_{\mathfrak m}$ (of some appropriately chosen conducto... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 77, "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/275522/dual-notion-of-free-module | # Dual notion of free module
I was just introduced to the notion of projective module (through Matsumura, Commutative ring theory), and there it is said that the reason that there is no easy description for injective modules (along the lines of "projective modules are direct summands of injective modules") is that 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": 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/differential-geometry/160019-limits-function-complex-numbers.html | Thread:
1. Limits of Function with complex numbers
I am studying for an exam and came across this excercise...
Let $f: D\rightarrow C$
(complex numbers). Suppose a is a limit point of D. If $f(x)\rightarrow b$ as $x\rightarrow a$, then $Re(f(x))\rightarrow Re(b)$ as $x\rightarrow a$.
So we have that if $0<|x-a|<\del... | {"extraction_info": {"found_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://nrich.maths.org/2127/index?nomenu=1 | ## 'A Mixed-up Clock' printed from http://nrich.maths.org/
### Show menu
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from the ten statements below?
Here is a clock-face with letters to mark the position of the numbers so that the statements are... | {"extraction_info": {"found_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://cs.stackexchange.com/questions/20/evaluating-the-average-time-complexity-of-a-given-bubblesort-algorithm | # Evaluating the average time complexity of a given bubblesort algorithm.
Considering this pseudo-code of a bubblesort:
````FOR i := 0 TO arraylength(list) STEP 1
switched := false
FOR j := 0 TO arraylength(list)-(i+1) STEP 1
IF list[j] > list[j + 1] THEN
switch(list,j,j+1)
s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 39, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/105612?sort=votes | ## The distance between the centroid of $P$ points and the centroid of a subset of the points
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Imagine I have an $(p_1, ..., p_N) \in P$ points, on a two-dimensional plane, patterned in a rectangular or hexagonal ... | {"extraction_info": {"found_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/207294/ordinary-differential-equation-strategy?answertab=oldest | Ordinary Differential Equation Strategy
In one of the examples in the Differential Equations for Dummies Workbook (Holzner), you are asked to use an integrating factor to solve $$\frac{dy}{dx} +2y =4$$
My question is, is this the most efficient way to solve it? Can't I also solve it by separating the $y$, turning 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": 19, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/36071/how-to-make-the-projected-image-smaller-by-adding-one-ore-more-lenses-in-front-o | # How to make the projected image smaller by adding one ore more lenses in front of the built in projector lense?
I have a projector that creates a large image, even if the distance to the screen is short. The device is very small, approximateley 10x10 cm if you look from above. The height is only 3 cm.
I could remov... | {"extraction_info": {"found_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://mathoverflow.net/questions/69576/sum-of-squares-modulo-a-prime/69577 | ## Sum of squares modulo a prime
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What is the probability that the sum of squares of n randomly chosen numbers from $Z_p$ is a quadratic residue mod p?
That is, let $a_1$,..$a_n$ be chosen at random. Then how oft... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 97, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Mole_fraction | # Mole fraction
In chemistry, the mole fraction $x_i$ is defined as the amount of a constituent $n_i$ divided by the total amount of all constituents in a mixture $n_{tot}$:[1]
$x_i = \frac{n_i}{n_{tot}}$
The sum of all the mole fractions is equal to 1:
$\sum_{i=1}^{N} n_i = n_{tot} ; \; \sum_{i=1}^{N} x_i = 1$
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": 27, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/9096 | # Some Thoughts on Teaching about Area
##### Stage: 3, 4 and 5
Article by Alison Kiddle
One of the most common problems that arises when secondary school students work on problems about area is the confusion between area and perimeter. Looking at a common textbook treatment of area and permiter suggests why this 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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://terrytao.wordpress.com/2012/11/14/expanding-polynomials-over-finite-fields-of-large-characteristic-and-a-regularity-lemma-for-definable-sets/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets
14 November, 2012 in math.AG, math.CO, paper | Tags: algebraic regularity le... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 219, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/algebra/134225-inequality-problem.html | # Thread:
1. ## inequality problem
The real number c is positive and the real numbers a and b are such that $ab > 0$ and $a > b$. How can I disprove the case $a - c < b + c$ for all such a, b, and c? (The case $\frac{c}{a} < \frac{c}{b}$ works). When I tried it, I can't seem to get numbers that disprove it??
2. Orig... | {"extraction_info": {"found_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": 18, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/33906/the-relationship-between-the-number-of-support-vectors-and-the-number-of-feature | # The relationship between the number of support vectors and the number of features
I ran an SVM against a given data set, and made the following observation: If I change the number of features for building the classifier, the number of resulting support vectors will also be changed.
I would like to know how to expla... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikisource.org/wiki/Attempt_of_a_Theory_of_Electrical_and_Optical_Phenomena_in_Moving_Bodies/Introduction | # Attempt of a Theory of Electrical and Optical Phenomena in Moving Bodies/Introduction
From Wikisource
by Hendrik Lorentz Introduction
Hendrik Lorentz
## Introduction
§ 1. The question as to whether the aether shares the motion of ponderable bodies or not, has still found no answer that satisfies all physicists. ... | {"extraction_info": {"found_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": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/105955/please-check-the-solution-of-my-ode | # Please Check The Solution of my ODE
hey guys just need to know if my differential equation is right
the question is
b)$$\frac{dy}{dx} = x + 6y.$$
the question is :Find the general solutions to the following differential equations. Sketch at least 4 solution curves for each.
the answer that i have found is $$y=\s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 17, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2007/06/14/pushouts-and-pullbacks/?like=1&source=post_flair&_wpnonce=bbf4ba6a50 | # The Unapologetic Mathematician
## Pushouts and pullbacks
If we have two sets $X$ and $Y$ we can take their union $X\cup Y$: the set of all elements in at least one of the two. We can also characterize this in categorical terms without reference to elements.
One thing we can see right off is that $X$ and $Y$ are bo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 87, "mimetex.cgi": 0, "/images/ma... |
http://wiki.math.toronto.edu/DispersiveWiki/index.php/NLS_wellposedness | # NLS wellposedness
### From DispersiveWiki
In order to establish the well-posedness of the NLS in Hs one needs the non-linearity to have at least s degrees of regularity; in other words, we usually assume
p is an odd integer, or p > [s] + 1.
With this assumption, one has LWP for $s \ge 0, s_c\,$, CaWe1990; see als... | {"extraction_info": {"found_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://mathhelpforum.com/algebra/92445-help-factorising.html | Thread:
1. Help with factorising
I am need of help please!
We have just started doing factorising in math and I am stumped by the following:
21a^2y^3q-14y^4q^3+7y^2q
I need to factorise this, I understand that I have to take out the common factors but don't know where to start!
Thanks in advance!
2. $21a^2y^3q-14y... | {"extraction_info": {"found_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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/42594-linear-independence-zero-vector.html | # Thread:
1. ## linear independence and the zero vector
how would i prove that for a vector space V, a subset of V that contains the zero vector is linearly dependent?
2. Isn't any vector space containing the zero vector linearly dependent or am I misreading this?
Consider the nonempty set $S = \{\bold{v}_{1}, \bol... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/81680/recovering-a-matrix-instead-of-a-vector/81689 | Recovering a matrix instead of a vector
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It is known that given corrupt measurements $y = Af+e$ one can recover an input vector $f \in \textbf{R}^n$ exactly by solving a convex optimization problem. What if $f$ is ins... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=1374456 | Physics Forums
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## Very simple QFT questions
I have some extremely basic questions in QFT.
First, P&S discuss causality in QFT in the first chapter of the book and, after showing that $<0| \phi(x)\phi(y)|0>$ 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": 4, "mathjax_display_tex": 15, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/4202/how-does-interpolation-really-work/4204 | # How does Interpolation really work?
I'm looking for some explanation or advice, not help in solving something. Recently I finished my program and my supervisor said "Ok, now it's time for your first paper: write a scientific text about how your program works". If I understand him correctly it means I have to describ... | {"extraction_info": {"found_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/55029/ramified-extension-in-number-theory | # Ramified extension in number theory
Assume that $K$ is a complete field under a discrete valuation with Dedekind ring $A$ and maximal ideal $\mathfrak p$ and $A\diagup\mathfrak p$ is perfect. Let $e$ be a positive integer not divisible by $E$. Let $E$ be a finite extension of $K$, $\pi_0$ a prime element in $\mathfr... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/48469?sort=oldest | ## Sequential sampling of Gaussian and von Mises-Fisher Random Variable
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I don't find any article discussing this problem, so I dare to ask it.
Suppose we are dealing with a data $x_0 \in \mathbb{R}$ and a functi... | {"extraction_info": {"found_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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/26860-difference-equations-again-d.html | # Thread:
1. ## Difference Equations.. Again :D
Given that the following sequence, Q_{n} , satisfies a homogeneous second order difference equation with constant coefficients find Q_{n} :
$Q_{1} = 1, Q_{2} = 3, Q_{3} = 4, Q_{4} = 7, Q_{5} = 11, Q_{6} = 18, ...$
I reckon that it would have to start with $AQ_{n} + BQ... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/45095-extremes-f-x.html | # Thread:
1. ## Extremes of f"(x)
Assuming the second derivative f"(x)>0 of a convex function f(x) exists over an interval (a,b).
Is it correct saying that the extremes (min, max, relative or absolute) of f"(x) always occur at the same ordinates where the extremes* of f(x) occur?
(*) Not necessarily of the same typ... | {"extraction_info": {"found_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://theoreticalatlas.wordpress.com/2007/09/25/coming-attractions/ | # Theoretical Atlas
He had bought a large map representing the sea, / Without the least vestige of land: / And the crew were much pleased when they found it to be / A map they could all understand.
September 25, 2007
## Coming Attractions
Posted by Jeffrey Morton under category theory, groupoids, higher dimensional... | {"extraction_info": {"found_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": 17, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/tagged/copula | # Tagged Questions
The copula tag has no wiki summary.
0answers
61 views
### Estimation of ranks of log-returns via copula
I have successfully chosen and estimate a copula for the ranks of the log-returns of my actions. My question is, since I have worked with the ranks instead of directly the log-returns (in order... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "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/Abundant_number | # Abundant number
In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/86877-show-qualities-related-law.html | # Thread:
1. ## Show that the qualities are related by the law?
I am studying analytical methods as part of my course and i have just enjoyed Pascals triangle and got my head round binomial theorem :-)
Can any one help me with the question below a bit lost!!
Atmospheric pressure(p) is measured at varying altitudes (... | {"extraction_info": {"found_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://alanrendall.wordpress.com/2009/07/24/metabolic-networks/ | # Hydrobates
A mathematician thinks aloud
## Metabolic networks
The processes of life involve systems of coupled chemical reactions. Often these are assumed to be homogeneous in space so that the concentrations of the substances involved are functions of time alone. The dynamics of these quantities are described by ... | {"extraction_info": {"found_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": 35, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/110810?sort=votes | ## Dual (/reduction?) graph of a curve
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This might be a bit of a broad question, or maybe even questions.
Recently I have learned about the connection between algebraic geometry and graph theory, via the dual gra... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 66, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Sample_size_determination | # Sample size determination
Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size... | {"extraction_info": {"found_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": 23, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/162088/a-linear-differential-equation?answertab=active | # A linear differential equation
Find the general solution to: $$x'' + 2c \; x' + \left( \frac{2}{\cosh^2 t} - 1\right)x =0$$ where $c$ is a constant.
-
In order to get the best possible answers, it is helpful if you say what your thoughts on the problem are so far; this will prevent people from telling you things yo... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/138243/how-to-prove-coshx-ge-1-without-the-cosh2x-sinh2x-1-identity/138263 | How to prove $\cosh(x) \ge 1$ without the $\cosh^2x-\sinh^2x=1$ identity
I think it's pretty easy question, maybe even dumb one, but still I can't find a nice way to solve it.
How do you prove that $\forall x . \cosh(x) \ge 1$ , without using the identity: $\cosh^2x-\sinh^2x=1$, and not without using derivatives.
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": 33, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/3382/stock-price-behavior-and-garch/3399 | # Stock Price Behavior and GARCH
In my (limited) understanding, the behavior of a stock price can be modeled using Geometric Brownian Motion (GBM). According to the Hull book I'm currently reading, the discrete-time version of this model is as follows:
$$\Delta S = \mu S \Delta t + \sigma S \varepsilon \sqrt{\Delta 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": 32, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?s=c3532470767de9361c8fcded6eceaf91&p=4152334 | Physics Forums
## Electric field of a line charge with the divergence theorem
Hi,
on page 63 of David J. Griffiths' "Introduction to Electrodynamics" he calculates the electric field at a point z above a line charge (with a finite length L) using the electric field in integral form.
$E_z = \frac{1}{4 \pi \epsilon_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": 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/122870/about-the-boundedness-of-a-multiplication-operator/122885 | ## About the boundedness of a multiplication operator.
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Let be $f$ a $2\pi-$periodic function and $\hat{f}(k)=\frac{1}{2\pi}\int_0^{2\pi}f(x)e^{-ikx}dx$. Consider the operator: \begin{equation} Tf(x)=\sum_{k\in\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": 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/statistics/195815-probability-prizes.html | # Thread:
1. ## Probability for prizes!
Hi all,
Could someone help me with a problem please?
I have 32 rounds and in each round there are 6 possible outcomes. Could someone please give the basic working of the probability of getting i.e. 5 out of 32 correct, or 10 out of 32 correct. Or even 5-9 out of 32, or 10-14 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://dsp.stackexchange.com/questions/270/what-is-the-relation-between-the-psds-of-filter-input-and-output-called-r-y | # What is the relation between the PSDs of filter input and output called? $R_Y = |H|^2R_X$
If a wide-sense stationary signal X is fed to an LTI filter with the transfer function H, the power spectral density (PSD) of the output Y can be expressed as:
$R_Y(f) = |H(f)|^2R_X(f)$
where $R_X$ denotes the PSD of X.
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": 22, "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/198269/vector-valued-function | # Vector valued function
How can I determine if a function lies within the span of a vector valued function?
For an example does $\begin{bmatrix} 2\\ 1\end{bmatrix}$ lie in the span of:
$$a(x) = \begin{bmatrix} 1\\ x\end{bmatrix}$$ $$b(x) = \begin{bmatrix} x\\ 1\end{bmatrix}$$ $$c(x) = \begin{bmatrix} x\\ 2x\end{bma... | {"extraction_info": {"found_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": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/85593/decompose-tensor-product-of-type-g-2-lie-algebras/86137 | ## Decompose tensor product of type $G_2$ Lie algebras.
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Let $G$ be a semisimple Lie algebra over $\mathbb{C}$. Let $V(\lambda)$ be the irreducible highest weight module for $G$ with highest weight $\lambda$. 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": 68, "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/161725-evaluate-line-integral.html | Thread:
1. Evaluate Line Integral
Q: Evaluate $\int_{\gamma} y^2 e^{2\sin{x}} \cos{x} dx + ye^{2\sin{x}} dy$ where $\gamma$ is the arc of the curve $y = \cos{x}$ from the point $(0,1)$ to the point $(\frac{\pi}{2},0)$.
A: We know that the integral is exact, meaning that we can choose any path from $(0,1)$ to $(\frac... | {"extraction_info": {"found_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": 35, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/210769-hausdorff-spaces-convergence-print.html | # Hausdorff spaces and convergence
Printable View
• January 4th 2013, 12:57 PM
Impo
Hausdorff spaces and convergence
Hi Everyone,
I'm new here and I'm dealing with some topology questions.
Suppose that (X,T) is a C1 space then the following statements are equivalent:
(1) (X,T) is a hausdorff space
(2) Every converg... | {"extraction_info": {"found_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": 72, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4033953 | Physics Forums
## noise term η(t) in Langevin equation
Langevin equation describes the brown motion. But I don't understand the nose term η(t) in the equation. What's the relationship between η(t) and the force proportional to the velocity due to stoke's law? I mean they both belong to the force between the collision... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.openwetware.org/wiki/Physics307L:People/Josey/Final_Draft | # Physics307L:People/Josey/Final Draft
### From OpenWetWare
Steve Koch 21:29, 14 December 2010 (EST):Overall, excellent report!
## Measuring and Predicting Background Radiation Using Poisson Statistics
Author: Brian P. Josey
Experimentalists: Brian P Josey and Kirstin G G Harriger
Junior Lab, Department of Physic... | {"extraction_info": {"found_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://cs.stackexchange.com/questions/7055/how-does-this-algorithm-for-verifying-if-a-string-is-0n1n-work | # How does this algorithm for verifying if a string is $0^n1^n$ work?
I have found an efficient algorithm for verifying if a string $\omega$ is of the form $0^n1^n$, where $n \in \mathbb{N}$.
1. Scan across $\omega$. If a 1 appears before a 0, then reject.
2. Repeat so long as some 0s and some 1s remain on the tape.
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/43366/tricky-integral/43368 | Tricky Integral
Can one show that
$$\int_{0}^{\infty} \! \frac {1}{1+x^{2}} \frac {x^{a}-x^{b}}{(1+x^{a})(1+x^{b})}~\mathrm{d}x=0 ~~~~~~~~ \forall ~a,b~\in \mathbb{R}.$$
Any hints?
-
is it $x^{x^{b}}$ – user9413 Jun 5 '11 at 11:06
@Chandru: No, it is just $(1+x^b)$. – night owl Jun 5 '11 at 11:27
@Rasholnikov: Rig... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/45884/conjugate-variables-noethers-theorem-and-qm/45890 | # Conjugate Variables, Noether's Theorem and QM
What is the underlying reason that the same pairs of conjugate variables (e.g. energy & time, momentum & position) are related in Noether's theorem (e.g. time symmetry implies energy conservation) and likewise in QM (e.g. $\Delta E \Delta t \ge \hbar$)?
-
– Qmechanic♦ ... | {"extraction_info": {"found_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/106130/counting-functions-or-asymptotic-densities-for-subsets-of-k-almost-primes | # Counting Functions or Asymptotic Densities for Subsets of k-almost Primes
This question is an extension of this question. There the asymptotic density of k-almost primes was asked.
By subsets I mean the following: Let $\lambda$ be a partition of $k$ and $P_{\lambda}=\{ \prod p_m^{\lambda_m} \; |\; p_m\neq p_k \}$. ... | {"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": 30, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/48511-elliptic-integral-sqrt-cosx.html | # Thread:
1. ## elliptic integral of SQRT(cosx)
hey..we are studying elliptic integrals in my class and I did some additional research online....where i came across the formula for the integral of SQRT(cosx) = 2E (1/2 *x, SQRT(2)). I couldn't figure out how to get there myself...would someone mind writing out the 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/69411/bound-on-the-real-part-of-roots-of-a-polynomial | ## Bound on the real part of roots of a polynomial
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi,
I'm not sure if you can help me with this, but I'm currently looking for an upper bound on the real part of the roots of a polynomial with real coefficients... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/2774/rotate-a-long-bar-in-space-and-get-close-to-or-even-beyond-the-speed-of-light | # Rotate a long bar in space and get close to (or even beyond) the speed of light $c$
Imagine a bar
spinning like a helicopter propeller,
At $\omega$ rad/s because the extremes of the bar goes at speed
$$V = \omega * r$$
then we can reach near $c$ (speed of light) applying some finite amount of energy just doing
... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://sbseminar.wordpress.com/requests/ | ## Requests
This is a page where anyone can suggest topics on which they would like to see us (and perhaps others) blog. We make no promises about following through on suggestions, but will make a good faith effort.
## Comments»
1. Nathan Dunfield - June 14, 2008
How about a discussion of long-distance collaboratio... | {"extraction_info": {"found_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://mathhelpforum.com/math-challenge-problems/94180-find-out-fallacy.html | # Thread:
1. ## Find out fallacy
FInd out fallcy in the proof. This "proof" will attempt to show that all people in Canada are the same age, by showing by induction that the following statement (which we'll call "S(n)" for short) is true for all natural numbers n:
Statement S(n): In any group of n people, everyone 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": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/229676/lim-limits-n-to-infty-fracnn1n-with-sandwich-rule?answertab=oldest | $\lim\limits_{n\to\infty}\frac{n^{n+1}}{n!}$ with sandwich rule
Determine the result of
$$\lim\limits_{n\to\infty}\frac{n^{n+1}}{n!}.$$
I would like to use the sandwich rule for limits to find two sequences which define lower and upper bounds to determine the appropriate limit which is obviously $+\infty$.
By now 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": 4, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2011/04/13/cotangent-vectors-differentials-and-the-cotangent-bundle/?like=1&source=post_flair&_wpnonce=78d053c4d8 | # The Unapologetic Mathematician
## Cotangent Vectors, Differentials, and the Cotangent Bundle
There’s another construct in differential topology and geometry that isn’t quite so obvious as a tangent vector, but which is every bit as useful: a cotangent vector. A cotangent vector $\lambda$ at a point $p\in M$ is just... | {"extraction_info": {"found_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": 57, "mimetex.cgi": 0, "/images/ma... |
http://en.m.wikipedia.org/wiki/Gravitation | # Gravitation
"Gravity" redirects here. For other uses, see Gravity (disambiguation).
"Law of Gravity" and "Laws of Gravity" redirect here. For other uses, see Law of Gravity (disambiguation).
Hammer and Feather Drop - Apollo 15 astronaut David Scott on the Moon recreating Galileo's famous gravity experiment. (1.38 MB... | {"extraction_info": {"found_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": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/170203/nth-derivative-of-tanm-x?answertab=oldest | # Nth derivative of $\tan^m x$
$m$ is positive integer,
$n$ is non-negative integer.
$$f_n(x)=\frac {d^n}{dx^n} (\tan ^m(x))$$
$P_n(x)=f_n(\arctan(x))$
I would like to find the polynomials that are defined as above
$P_0(x)=x^m$
$P_1(x)=mx^{m+1}+mx^{m-1}$
$P_2(x)=m(m+1)x^{m+2}+2m^2x^{m}+m(m-1)x^{m-2}$
$P_3(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": 33, "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/47214?sort=votes | ## How To Present Mathematics To Non-Mathematicians?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
(Added an epilogue)
I started a job as a TA, and it requires me to take a five sessions workshop about better teaching in which we have to present a 10 minute... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 39, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/21136-airline-probability.html | # Thread:
1. ## airline probability
airline passengers arrive randomly and independently at the passenger screening facility at an airport. The mean arrival rate is 10 passengers per minute. What is the probability of no arrivals in a 15 second period.
2. Originally Posted by dclift
airline passengers arrive randoml... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=497780 | Physics Forums
Recognitions:
Gold Member
Science Advisor
## Why using quantum group SUq(2) instead of SU(2) makes sense?
Increasingly QG is being done with a q-deformed symmetry group: replacing SU(2) by
the quantum group SUq(2). What do you see as the intuitive basis for this?
One intuitive justification is 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": 2, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://gilkalai.wordpress.com/2009/08/01/test-your-intuition-8/?like=1&source=post_flair&_wpnonce=c1ce40f6e1 | Gil Kalai’s blog
## Test Your Intuition (8)
Posted on August 1, 2009 by
Consider all planar sets A with constant width 1. Namely, in every direction, the distance between the two parallel lines that touch A from both sides is 1. We already know that there exists such sets other than the circle of radius 1/2.
Among... | {"extraction_info": {"found_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": 8, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/62340/propositions-equivalent-to-the-completeness-of-the-real-numbers | ## Propositions equivalent to the completeness of the real numbers
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Can anyone point me to a reasonably comprehensive article (or book chapter) explaining which basic theorems of calculus are equivalent to the com... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/5449/combinatorial-results-without-known-combinatorial-proofs/5451 | ## Combinatorial results without known combinatorial proofs
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Stanley likes to keep a list of combinatorial results for which there is no known combinatorial proof. For example, until recently I believe the explici... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 46, "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/246590/evaluate-mathop-lim-limits-x-to-infty-left-int-limits-0-pi-6 | # Evaluate $\mathop {\lim }\limits_{x \to \infty } {\left( {\int\limits_0^{\pi /6} {{{(\sin t)}^x}dt} } \right)^{1/x}}$
It is given that the following limit $\mathop {\lim }\limits_{x \to \infty } {\left( {\int\limits_0^{\pi /6} {{{(\sin t)}^x}dt} } \right)^{1/x}}$ exists. Evaluate the limit.
I've tried tackling this... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/hydrogen+homework | # Tagged Questions
1answer
83 views
### Finding the wavelength of an electron in its ground state?
To find the wavelength of an electron in its ground state in a hydrogen atom, would I or could I do the following? Use the ground state energy (-13.6eV) in $E^2 = m^2c^4 + p^2c^2$ Solve for $p$ Use ...
2answers
174 vie... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/7317/understanding-black-scholes | # Understanding Black-Scholes
Assume I have only basic math knowledge, what specific areas of math would I need to learn in order to understand the following webpage:
Black-Scholes
Many thanks.
-
1
How "basic" are we talking? Certainly you would have to know PDEs and stochastic calculus to grok Black-Scholes. – J.... | {"extraction_info": {"found_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/265105/how-can-i-find-maximum-and-and-minimum-values-of-fx-y-xye-xy | # How can I find maximum and and minimum values of $f(x,y)=xye^{-(x+y)}$?
How can I find maximum and and minimum values of $f(x,y)=xye^{-(x+y)}$ in the region $(x-1)^2+(y-1)^2 \leq4$ ?
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## 3 Answers
First look for critical points of $f$ in the interior $(x-1)^2 + (y-1)^2 < 4$. Do this by comparing the partial deri... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 114, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://physics.stackexchange.com/questions/57165/question-about-the-linearity-of-wave-functions/57166 | # Question about the linearity of wave functions
For piece-wise constant potential, the potential energy is constant so the time dependent wave function can take the form $\psi(x,t)=C_1e^{i(kx- \omega t)}+C_2e^{i(-kx-\omega t)}$ where $k=\frac{p}{h}=\frac{\sqrt{2mE}}{h}$ and $E$ is just the difference between the ener... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "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/18762/locality-in-quantum-mechanics?answertab=active | # Locality in Quantum Mechanics
We speak of locality or non-locality of an equation in QM, depending on whether it has no differential operators of order higher than two.
My question is, how could one tell from looking at the concrete solutions of the equation whether the equ. was local or not...or, to put it another... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/17425/list | ## Return to Question
Suppose I have a small category $\mathcal{C}$ which is fibered over some category $\mathcal{I}$ in the categorical sense. That is, there is a functor $\pi : \mathcal{C} \rightarrow \mathcal{I}$ which is a fibration of categories. (One way to say this, I guess, is that $\mathcal{C}$ has a factoriz... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "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/tagged/disorder+linear-algebra | # Tagged Questions
0answers
28 views
### Random quantum systems with asymmetric Lifshitz tails?
For a quantum mechanical system with a periodic Hamiltonian (Schrödinger operator) $H$, let $N(E)$ be its integrated density of states, i.e. the fraction of eigenvalues in the spectrum $\sigma(H)$ ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "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/2011/02/01/the-branching-rule-part-4/?like=1&source=post_flair&_wpnonce=5092e672ce | The Unapologetic Mathematician
The Branching Rule, Part 4
What? More!?
Well, we got the idea to look for the branching rule by trying to categorify a certain combinatorial relation. So let’s take the flip side of the branching rule and decategorify it to see what it says!
Strictly speaking, decategorification means... | {"extraction_info": {"found_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": 13, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/20858/graph-for-fx-sin-x-cos-x | # Graph for $f(x)=\sin x\cos x$
Okay, so in my math homework I'm supposed to draw a graph of the following function: $$f(x)=\sin x \cos x.$$ I have the solution in the textbook, but I just can't figure out how they got to that. So, if someone could please post (a slightly more detailed) explanation for this, it would ... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathforum.org/mathimages/index.php?title=Solving_Triangles&diff=20913&oldid=20906 | # Solving Triangles
### 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": 54, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/43833/a-markov-process-which-is-not-a-strong-markov-process/43841 | ## A Markov process which is not a strong markov process?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Can anyone give an example of a Markov process which is not a strong Markov process? The Markov property and strong Markov property are typically introduc... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/143584/related-rates-with-a-cylinder | # Related rates with a cylinder
A cylindrical tank with radius 5m is being filled with water at a rate of $3m^3/min$ How fast is the height of the water increasing?
I know that $$dv/dt = 3$$
And that $$v= \pi r^2 h$$
So I want to find the derivative of h
$$h= \frac {v}{ \pi r^2}$$
$$h' = \frac{3 \pi * 25}{ (\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": 17, "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/221028/permutations-and-the-binomial-coefficient | # permutations and the binomial coefficient
I have seen several times the use of "n choose k" in the left side of the permutations formula.
However, this expression is usually referred to be used with combinations.
Not that this change when or how using "permutations" or "subsets" according to the context.
But I wonde... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Grashof_number | # Grashof number
The Grashof number $\mathrm{Gr}$ is a dimensionless number in fluid dynamics and heat transfer which approximates the ratio of the buoyancy to viscous force acting on a fluid. It frequently arises in the study of situations involving natural convection. It is named after the German engineer Franz Gras... | {"extraction_info": {"found_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": 81, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/14509/various-concepts-of-closure-or-completion-in-mathematics/14511 | ## Various concepts of “closure” or “completion” in mathematics
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Out of idle curiosity, I'm wondering about all the various idempotent constructions we have in mathematics (they seem to be generally referred to 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": 16, "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/2008/08/12/additive-functions/?like=1&source=post_flair&_wpnonce=3fdfac1636 | # The Unapologetic Mathematician
## Additive Functions
I’ve got internet access again, but I’m busy with a few things today, like assembling my furniture. Luckily, Tim Gowers has a post on “How to use Zorn’s lemma”. His example is the construction of additive (not linear) functions from $\mathbb{R}$ to itself.
In pr... | {"extraction_info": {"found_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": 7, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/32055/when-can-we-factor-out-the-time-dimension/32058 | ## When can we factor out the time dimension?
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First of all, my knowledge of both GR and differential geometry is quite weak, so forgive me if the physics here doesn't make much sense.
Let $(M, g)$ be a smooth, 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": 65, "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/254138/how-to-find-the-maximum-number-of-vertices-in-a-tree-with-respect-to-maximum-pat | How to find the maximum number of vertices in a tree with respect to maximum path length and maximum degree value
Given a tree, find the maximum number of vertices $v$ in that tree using the maximum path length $p$ and a maximum degree that applies to all vertices $d$.
Assuming that I drew my test tree correctly, 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": 18, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/tag/margulis-lemma/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Tag Archive
You are currently browsing the tag archive for the ‘Margulis lemma’ tag.
## 254A, Notes 9: Applications of the structural theory of approximate groups
13 November, 2011... | {"extraction_info": {"found_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": 41, "mimetex.cgi": 0, "/images/ma... |
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