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http://mathoverflow.net/revisions/59980/list | ## Return to Answer
Every torsion-free abelian group of cardinality at most $2^\omega$ is isomorphic to a subgroup of the reals. (To see this, note that any such group can be embedded in a divisible torsion-free group of the same cardinality, i.e., a vector space over $\mathbb Q$, which can therefore in turn be embedd... | {"extraction_info": {"found_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/114021/cardinality-of-the-power-set-of-natural-numbers | Cardinality of the power set of natural numbers
I was reading an article on infinite sets and I came across a proof about how the power set of natural numbers has a greater cardinality than the set of natural numbers. I know that both given that proof and the proof of Cantor's theorem, that it must be true. So, my que... | {"extraction_info": {"found_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/15031/is-the-massive-calogero-moser-system-still-integrable/15335 | ## Is the ‘massive’ Calogero-Moser system still integrable?
### Background
The (rational) Calogero-Moser system is the dynamical system which describes the evolution of $n$ particles on the line $\mathbb{C}$ which repel each other with force proportional to the cube of their distance. If the particles have (distinct!... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 78, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/8314/maximum-time-difference-between-clocks-in-a-gravity-field/8330 | # Maximum time difference between clocks in a gravity field
From Surely you must be joking, Mr Feynman.
You blast off in a rocket which has a clock on board, and there's a clock on the ground. The idea is that you have to be back when the clock on the ground says one hour has passed. Now you want it so that when you ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/44096-tangent-circle.html | # Thread:
1. ## Tangent of a Circle
The question is
Find the equation of the tangent and normal to the circle x^2 + y^2 = 13 at the point t(-2,3)
I was thinking about this question and would the tangent be perpendicular to the straight line joining the (-2,3) and Origin?
2. Originally Posted by immunofort
The ques... | {"extraction_info": {"found_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/19107?sort=oldest | ## a question about flatness
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In the book "étale cohomology" by Milne, proposition 2.5 at p.9, it said :
Let $B$ be a flat $A-$algebra where $A$ and $B$ are noetherian rings, and consider $b \in B$. If the image ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/201205/inclusion-exclusion-and-lcm/206228 | # Inclusion Exclusion and lcm
I would like to show that for any positive integers $d_1, \dots, d_r$ one has $$\sum_{i=1}^r (-1)^{i+1}\biggl( \sum_{1\leq k_1 < \dots < k_i \leq r} \gcd(d_{k_1}, \dots , d_{k_i})\biggr) ~\leq~ \prod_{i=1}^r\biggl( \prod_{1\leq k_1 < \dots < k_i \leq r} \gcd(d_{k_1}, \dots , d_{k_i}) \big... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://johncarlosbaez.wordpress.com/2011/12/22/quantropy/ | Azimuth
Quantropy (Part 1)
I wish you all happy holidays! My wife Lisa and I are going to Bangkok on Christmas Eve, and thence to Luang Prabang, a town in Laos where the Nam Khan river joins the Mekong. We’ll return to Singapore on the 30th. See you then! And in the meantime, here’s a little present—something to mull... | {"extraction_info": {"found_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": 392, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/86803-need-some-help-method.html | # Thread:
1. ## Need some help with the method
I've got an equation: 4x^3 - 24x^2 + 45 x - 23
A tangent is drawn at point P. (1,2)
dy/dx = 12x^2 - 48x +45
At f´(1) = 12 -48 + 45 = 9
2 = 9(1) +c
y = 9x - 7
Show that the x coordinate of point q is 4.
9x-7 = 4x^3 - 24x^2 + 45 x - 23
0 = 4x^3 - 24x^2 + 36 x - 16
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Scalar_potential | # Scalar potential
This article is about a general description of a function used in mathematics and physics to describe conservative fields. For the scalar potential of electromagnetism, see electric potential. For all other uses, see potential.
Scalar potential, simply stated, describes the situation where the diff... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/44541/thermal-expansion-of-sphere | # Thermal expansion of Sphere
How would one go about writing an expression of the expansion of the volume of a sphere of a given material? I noticed a few sources give it as
$\Delta V= 3\gamma V\Delta T$
where V is the initial volume; $\gamma$ is the expansivity coefficient and $\Delta T$ is change in temperature of ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/53130-solved-i-need-help-proving-cross-product-2-countable-sets-countable.html | # Thread:
1. ## [SOLVED] I need help proving that the cross product of 2 countable sets is countable.
Statement to prove:
If A and B are countable sets, prove A x B is countable.
My work so far:
I've thought of 2 ways to approach proving this.
(1) I read that "Every subset of a countable set is again countable."
So ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/312107/find-point-x-such-that-line-through-plane-e-and-sphere-s-meet-at-0-0-1 | # Find point $X$ such that line through plane $E$ and sphere $S$ meet at $(0,0,1)$ (stereographic projection)
Find the point $X$ such that the line going through the plane $E$ and sphere $S$ meet at the point $(0,0,1)$ (stereographic projection).
Let $S$ denote the unit sphere
$$S = \{(x,y,z) \in \mathbb{R}^3 \mid 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": 62, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/statistics/99691-probability-rolling-die.html | Thread:
1. Probability--Rolling a die
This probably should be very easy but i am not good at probability.
Given a fair die, what is the probability of rolling at least 2 sixes if the die is rolled 12 times.
I have tried a little bit, and this is what I have.
First of all, i know the universe is equal to 6^12. And ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/204787-calculate-volume-using-method-cylindrical-shells-urgent.html | 1Thanks
• 1 Post By skeeter
# Thread:
1. ## Calculate Volume using the Method of Cylindrical Shells - Urgent
Here are some things I have done. I already found the volume since the other part of the question said to use the method of discs/washers. It is 54.0633 cubic units (correct answer).
I found by trial and err... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/4862/interference-of-polarized-light | # Interference of polarized light
Does polarized light interfere?
-
4
Yes, it does. Could you be more specific, why do you think it would not? – gigacyan Feb 9 '11 at 14:11
Question is unclear but can be useful. Don't think need to close -- just downvote. – Kostya Feb 10 '11 at 9:36
3
@Kostya: the problem is, if 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": 16, "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/45483?sort=oldest | ## Word maps on compact Lie groups
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $w=w(a,b)$ be a non-trivial word in the free group $F_2 = \langle a,b \rangle$ and $w_G \colon G \times G \to G$ be the induced word map for some compact Lie group $G$.
Mur... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 58, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/121510/list | ## Return to Answer
2 added 9 characters in body
The situation as I see it is as follows:
The first definition you give is the natural one. It implies that D-modules on the $X$ are given by sheaves of modules for the sheaf of algebras $f_\ast D_X$ on $Y$. However, I am curious if there are actually any interesting 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": 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/revisions/21004/list | ## Return to Answer
2 added 48 characters in body
Edit[ The following is wrong ~ see comments]
I don't think so.
Suppose $f$ to be surjective. Let $x\mapsto 0$ and $y\mapsto 1$. Now consider two distinct paths $\gamma,\eta:[0,1]\to\mathbb Q\times\mathbb Q$ from $x$ to $y$. Since $f$ is continuous it maps these path... | {"extraction_info": {"found_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://mathhelpforum.com/math-puzzles/156259-number-theory-puzzle.html | # Thread:
1. ## A number theory puzzle
I give you 7x - 17y = 1. Now give me back how many solution pairs (in natural numbers) there are for the equation? For example (5,2) and (22,9) are solutions (if you can't figure this one out in a week, I'll drop a hint and if you still can't solve it after another week, then 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://mathematica.stackexchange.com/questions/tagged/summation?sort=unanswered | # Tagged Questions
The summation tag has no wiki summary.
I am trying to get something in the form of a $\Sigma (\dots) * \alpha_i = (\dots)$ from the output of the code below. The thing is that I cannot figure out how to tell Mathematica to "collapse" down ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/36136-isosceles-triangle-angle-area-triangle-inscribed-circle.html | # Thread:
1. ## Isosceles triangle, angle, area of triangle inscribed in a circle!
An isosceles triangle is inscribed in a circle of radius R. Determine the value of theta that maximizes the area of the triangle given that theta is the angle contained between the two equal sides.
2. Originally Posted by rawrzjaja
A... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/80367/primes-and-ackermanns-function/80445 | ## Primes and Ackermann’s function
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
If $A(m,n)$ is Ackermann's function, and $c$ is a fixed integer, are there any heuristics/conjectures/obvious things that can be said about primes of the form $A(m,n)+c$, $m \ge... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 47, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/45936/modal-logic-satisfiability | ## Modal logic - satisfiability
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi there,
Assuming X and Y are modal formulae and diamond X is satisfiable and diamond Y is satisfiable, how would one show that they X AND Y is satisfiable?
I don't think it req... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/95092/linear-characterization-of-inverse-of-stieltjes-matrix/95098 | ## Linear characterization of inverse of Stieltjes matrix
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Is there a linear characterization of being the inverse of a Stieltjes matrix? In other words, if $A$ is a $n \times n$ matrix over the reals, is there 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": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/83420?sort=oldest | ## algorithms for comparing two simplicial complexes
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Given a set $A$ of subsets of ${1, \ldots n}$ which is closed under taking subsets, let $X(A)$ be the corresponding simplicial complex, i.e. simplices of $X(A)... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "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/103355-subset-u-subset-not-subspace-superset.html | # Thread:
1. ## subset U subset is NOT subspace of Superset?
Hello,
I have an assignment due tomorrow, and Im stuck at this problem:
Let V be a vector space over any field F, and W1 and W2 be two subspaces of V.
b) Give examples for V, W1, W2 such that W1 U W2 is NOT a subspace of V.
Any ideas?
2. In $\mathbb{R}^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://blog.pwnthesat.com/2011/03/plugging-in-ftw.html | ### Plugging In FTW
OK, so you know how I'm always saying that the SAT is not a math test? This is one of the primary reasons why. On the SAT, it's often completely unnecessary to do the math that's been so carefully laid out before you. A lot of the time (and on a lot of the most otherwise onerous problems), all you ... | {"extraction_info": {"found_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://sagemath.org/doc/thematic_tutorials/numtheory_rsa.html | # Number Theory and the RSA Public Key Cryptosystem¶
Author: Minh Van Nguyen <nguyenminh2@gmail.com>
This tutorial uses Sage to study elementary number theory and the RSA public key cryptosystem. A number of Sage commands will be presented that help us to perform basic number theoretic operations such as greatest 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": 7, "mathjax_display_tex": 101, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/tagged/torque?sort=unanswered&pagesize=50 | # Tagged Questions
The torque tag has no wiki summary.
2answers
91 views
### Thrust center in space
I have this dilemma: Suppose you have a space ship somewhere in deep space, where there is no drag force or substantial gravity. If the ship has a single engine situated in such a way that the center ...
1answer
106 ... | {"extraction_info": {"found_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/showthread.php?p=4027917 | Physics Forums
Page 1 of 3 1 2 3 >
## Rolling friction on ice...
Hello Forum,
Consider a rigid disk that is rotating on a surface. If the surface is elastic but not symmetric, the rotating disk will eventually slow down.
If the surface was perfectly and symmetrically elastic the object will continue to rotat... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2011/09/30/inner-products-of-vector-fields/?like=1&source=post_flair&_wpnonce=d91e0e6d9a | # The Unapologetic Mathematician
## Inner Products of Vector Fields
Now that we can define the inner product of two vectors using a metric $g$, we want to generalize this to apply to vector fields.
This should be pretty straightforward: if $v$ and $w$ are vector fields on an open region $U$ it gives us vectors $v_p$... | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 50, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/tag/homogenisation/ | 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 ‘homogenisation’ tag.
## Localisation and compactness properties of the Navier-Stokes global regularity problem
4 Aug... | {"extraction_info": {"found_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": 91, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/15729-leslie-matrix.html | Thread:
1. (Leslie) Matrix
I'm having difficulty trying to prove this theorem for my REU research.
I won't go into the full details of the thing I'm trying to prove as it's quite complicated. However, I am trying to solve the inverse of the following n x n matrix:
Code:
```1 0 0 0 0 ...
-s_1 1 . . . . . . .
. . 1 ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/243344/integrating-an-n-th-degree-polynomial/249947 | # Integrating an n-th degree polynomial
Integrating a polynomial over a fixed interval is usually very straightforward. However, I can't seem to get very far with an $n$-th degree polynomial:
$$\int_a^b \bigg(\sum_{i=0}^n q_i\,x^{n-i}\bigg)dx = \bigg[\sum_{i=0}^n \frac{q_i}{1+n-i}\,x^{1+n-i}\bigg]_a^b \\ = \bigg(\sum... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/157002-help-solving-linear-eq-print.html | # Help Solving Linear Eq
Printable View
• September 21st 2010, 05:43 PM
quarinteen
Help Solving Linear Eq
I need help and instructions for solving this problem. If you could list the steps so I understand it would be appreciated.
-7/8c +5.6 = -5/8c - 3.3
• September 21st 2010, 07:16 PM
quarinteen
ok i got that one n... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/153436/open-sets-of-symplectic-manifolds/153449 | # Open sets of symplectic manifolds
Suppose I have a symplectic manifold $(\mathcal{M}, \omega)$. Does it hold that any open subset of $(\mathcal{M}, \omega)$ is a symplectic submanifold?
The statement trivially holds for smooth manifold but in the symplectic setting I am not sure.
-
## 1 Answer
It trivially holds... | {"extraction_info": {"found_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://mathhelpforum.com/math-topics/55289-find-number-elements-intersection-3-sets.html | # Thread:
1. ## Find the number of elements in the intersection of 3 sets
Let A={ $n \in N$ | 5 divides n}
B={ $n \in N$| both n and $\frac {n}{5}$ contain only odd digits}
and C={ $n \in N$ | both n and $\frac {n}{5}$ contain exactly 2006 digits} where N
denotes the set of all natural numbers.
Find the number of ele... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/6435/cosmic-ray-hazards/6437 | # Cosmic ray hazards
The Pierre Auger Observatory site mentions the detection of a 3E20 eV (48 J) cosmic ray whose energy, well above the GZK cutoff, was based on an analysis of its atmospheric shower. This was equivalent to the kinetic energy of a baseball with a speed of 79.5 m/s or 177 mph. Of course, cosmic rays 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": 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/199018/transversal-intersection/199024 | # Transversal intersection.
In my textbook, it says: "Consider two curves in the plane, one of which is the x-axis, the other being the graph of a function $f(x)$. The two curves intersect transversally at a point x if $f(x)=0$ (the intersection condition), and $f'(x)\neq0$ (transversality)." I know that: "Two submani... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/87676/probability-from-other-probability?answertab=oldest | # Probability from other probability [closed]
Let $m$, $n$ be very big natural numbers, s.t. $m\leq n$. Let $L\geq 1$ and $Ln\ge 1$. Let also $t>0$, $C>0$ and for some random variable $x$ the following is true: $P(x^2\geq Ln )\geq \frac{C}{(Ln)^t}$.
Show: if $t\geq 4$, then $\frac{n}{2}P(x^2\geq Ln )\leq \frac{1}{m}$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "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/25430?sort=votes | ## Can Goodstein’s theorem been proven with first order PA + Constructive Omega Rule?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am trying to understand transfinite induction and Gentzen's theories.
But I was wondering, if there is any connection with ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/53016/does-f-1x-yf-2x-y-imply-y-1y-2-for-solutions-to-the-integral-equation/116354 | ## Does $f_1(x,y)<f_2(x,y)$ imply $y_1<y_2$ for solutions to the integral equation $y_k'=f_k(x,y_k)$?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Suppose for two given functions $f_1,f_2 \colon \mathbb{R}^2 \to \mathbb{R}$ there exist unique solutions $y_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": 40, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/134739-lie-group-frame-bundle.html | # Thread:
1. ## Lie group and the frame bundle
I am working in a (psuedo) Riemannian manifold with the fibres of orthonormal frame based on some Lie group. From the Levi-Civita connection, I can separate the tangent space of the frame bundle into horizontal and vertical bits, i.e.
$T(\mathbb{O}M)=H(\mathbb{O}M)\oplus... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-statistics/183035-covariance-functions-random-variable.html | # Thread:
1. ## Covariance of functions of a random variable
Let X be a random variable in the range (0,1), i.e. P(X)=0 for X<=0 or X>=1. Is there a way to prove that Cov(X,X/(1-X)) > 0 ? Is it true for any pdf f(X) whose support is in (0,1)?
2. ## Re: Covariance of functions of a random variable
Wow, this took me ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/geometry/199772-regular-polygon-formula-print.html | Regular polygon formula
Printable View
• June 7th 2012, 01:24 PM
Alex3914425
Regular polygon formula
Hello geniuses,
Recently, when making some calculations for people, I came across what I hope is a new formula. I have done some googling and I can't find it anywhere.
Could you take a look at this and tell me if it ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.cs.purdue.edu/homes/dgleich/nmcomp/lectures/lecture-0.html | # Basic Notation
$\newcommand{\mat}[1]{\boldsymbol{#1}} \renewcommand{\vec}[1]{\boldsymbol{\mathrm{#1}}} \newcommand{\vecalt}[1]{\boldsymbol{#1}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\normof}[1]{\|#1\|} \newcommand{\onormof}[2]{\|#1\|_{#2}} \newcommand{\itr}[2]{#1^{(#2)}} \newcommand{\itn}[1]{^{(#1)}} \new... | {"extraction_info": {"found_math": true, "script_math_tex": 34, "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": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/43530/item-information-in-irt-with-item-covariates-linear-logistic-test-model | # Item information in IRT with item covariates (linear logistic test model)
Short question: How does the calculation and interpretation of IRT item information and test information change in the presence of item properties?
Long question: There's a variation on IRT called the linear logistic test model (LLTM):
$logi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/18638/model-selection-logistic-regression | # Model Selection: Logistic Regression
Suppose we have $n$ covariates $x_1, \dots, x_n$ and a binary outcome variable $y$. Some of these covariates are categorical with multiple levels. Others are continuous. How would you choose the "best" model? In other words, how do you choose which covariates to include in the mo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/F-test | # F-test
An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled. Exact F-tes... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-algebra/49116-system-equation-condition.html | # Thread:
1. ## System of equation, condition of a
For which values of $a$ the following system of equations has a unique solution? Infinite solutions?
$\left[ \begin{array}{ccc}x-y+z=2 \\ ax-y+z=2 \\ 2x-2y +(2-a)z=4a \end{array} \right]$.
I've solve the system via matrices and got that $\left[ \begin{array}{ccc}x=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": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/149833/is-critical-haudorff-measure-a-frostman-measure?answertab=active | # Is critical Haudorff measure a Frostman measure?
Let $K$ be a compact set in $\mathbb{R}^d$ of Hausdorff dimension $\alpha<d$, $H_\alpha(\cdot)$ the $\alpha$-dimensional Hausdorff measure. If $0<H_\alpha(K)<\infty$, is it necessarily true that $H_\alpha(K\cap B)\lesssim r(B)^\alpha$ for any open ball $B$? Here $r(B)... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "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?t=472029 | Physics Forums
Page 1 of 3 1 2 3 >
## Simple dipstick problem
1. The problem statement, all variables and given/known data
I have a problem involving a dipstick, a cone and a cylinder. Basically I want to make a dipstick for a cone and cylinder which shows the volume of remaining fluid in the containers.
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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.mathscoop.com/calculus/infinite-sequences-and-series/nth-term-test.php | The Nth Term Test is often called the "Divergence Test"
It can only prove that a series diverges.
This test does not verify that a series converges.
# The Formula
$$\sum\limits_{n=1}^{\infty}a_{n} \text{ diverges if } \lim\limits_{n\rightarrow\infty}a_{n} \text{ fails to exists or does not equal zero.}$$
Note: If the... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 19, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/tagged/manifold | ## Tagged Questions
0answers
1 views
### Lipschitz map of the ellipse
Is there a L-Lipschitz homeomorphism of the Elipse $x^2/4+y^2=1$ onto the unit circle $x^2+y^2=1$ such that $L<1$?
5answers
648 views
+100
### Another colored balls puzzle (part II)
The same colleague as in http://mathoverflow.net/questions/1304... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/181720/proof-of-non-ordering-of-complex-field/181732 | # Proof of Non-Ordering of Complex Field
Let $\mathcal F$ be a field. Suppose that there is a set $P \subset \mathcal F$ which satisfies the following properties:
• For each $x \in \mathcal F$, exactly one of the following statements holds: $x \in P$, $-x \in P$, $x =0$.
• For $x,y \in P$, $xy \in P$ and $x+y \in P$... | {"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": 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/algebra/67370-geometric-arithmetic-sequence.html | # Thread:
1. ## Geometric and Arithmetic Sequence
Hi im a bit confused about these questions here. I do not know where to start, but much help is appreciated.
Question 1
In an arithmetic sequence t4 + t5 + t6 = 300 and t15 + t16 + t17 = 201
Find t18
Question 2
In a geometric sequence t1 + t2 + t3 = 21 and t4 + t5... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2009/11/11/the-jacobian/?like=1&_wpnonce=67418a1937 | # The Unapologetic Mathematician
## The Jacobian
Now that we’ve used exterior algebras to come to terms with parallelepipeds and their transformations, let’s come back to apply these ideas to the calculus.
We’ll focus on a differentiable function $f:X\rightarrow\mathbb{R}^n$, where $X$ is itself some open region 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 41, "mimetex.cgi": 0, "/images/ma... |
http://conservapedia.com/Cosecant | # Cosecant
### From Conservapedia
The cosecant is a trigonometric function describing the ratio of the hypotenuse to the opposite side in a right triangle. It is often abbreviated as cosec or cose.
$\csc \theta = \sec \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\sin \theta}\,$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2008/07/21/the-sum-of-subspaces/?like=1&source=post_flair&_wpnonce=d0199d491e | # The Unapologetic Mathematician
## The Sum of Subspaces
We know what the direct sum of two vector spaces is. That we define abstractly and without reference to the internal structure of each space. It’s sort of like the disjoint union of sets, and in fact the basis for a direct sum is the disjoint union of bases for... | {"extraction_info": {"found_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": 64, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/1924/what-are-some-reasonable-sounding-statements-that-are-independent-of-zfc/6594 | What are some reasonable-sounding statements that are independent of ZFC?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Every now and then, somebody will tell me about a question. When I start thinking about it, they say, "actually, it's undecidable in ZFC."
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": 52, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2009/12/16/iterated-integrals-i/?like=1&source=post_flair&_wpnonce=18b5244a97 | # The Unapologetic Mathematician
## Iterated Integrals I
We may remember from a multivariable calculus class that we can evaluate multiple integrals by using iterated integrals. For example, if $f:R\rightarrow\mathbb{R}^{\geq0}$ is a continuous, nonnegative function on a two-dimensional rectangle $R=[a,b]\times[c,d]$... | {"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": 0, "wp_latex": 33, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/88090/list | ## Return to Question
2 added 5 characters in body
I am trying to understand the topology (in terms of homology groups) of the free loop space $\Lambda M$ of nice spaces (Complete Riemannian connected finite dimensional manifolds $M$). I see the free loop space (of H^1 loops) as a Hilbert manifold, cf. Klingenbergs b... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "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-math-topics/123008-infinity.html | # Thread:
1. ## Infinity
I understand how the set of transcendental numbers is greater than the set of algebraic numbers (Aleph II vs Aleph I). Can someone explain why the set of functions (Aleph III) is greater than the set of transcendental numbers?
2. Originally Posted by wonderboy1953
I understand how the set of... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 25, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.haskell.org/haskellwiki/index.php?title=Power_function&oldid=19570 | Power function
From HaskellWiki
Revision as of 13:44, 26 February 2008 by Rk (Talk | contribs)
1 Question
Why are there several notions of power in Haskell, namely
(^)
,
(^^)
,
(**)
?
2 Answer
The reason is that there is no definition for the power function which covers all exotic choices for bases and exponent... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/116894/list | ## Return to Question
2 added 2 characters in body
Let $G$ be a compact Lie group, let $T$ be a maximal torus, and let $W$ be the Weyl group. My main question is as follows:
• How does one prove that `$H^\ast(BG,\mathbb{Q})$` is isomorphic to the $W$-invariant part of $H^\ast(BT,\mathbb{Q}) \cong \mathbb{Q}[[x_1, \l... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/5619/public-key-cryptography-public-key-encrypts-and-cannot-decrypt?answertab=oldest | # Public key cryptography - public key encrypts and cannot decrypt?
I understand the basics behind public key cryptography, in that each party has two keys - the public one encrypts, and the private one decrypts. What I cannot figure out is, How does the public key encrypt and not decrypt, but yet the private key can ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "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/90884-can-someone-help-me-function.html | Thread:
1. Can someone help me with this function
Hi can anyone help me out with how to find the stationary points of this functions:
y = x/x^2+1
Thanks I am completely at a loss
2. Originally Posted by Emililypad
Hi can anyone help me out with how to find the stationary points of this functions:
y = x/x^2+1
Tha... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.aps.org/articles/print/v2/103 | # Viewpoint: The super cool atom thermometer
, JILA, NIST, and University of Colorado, Department of Physics, University of Colorado, Boulder, CO 80309, USA
Published December 7, 2009 | Physics 2, 103 (2009) | DOI: 10.1103/Physics.2.103
A new method of thermometry for ultracold atoms in optical lattices has the p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 33, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/38433/energy-is-quantized | # Energy is quantized
How can energy be quantized if we can have energy be measured like in 1.56364, 5.7535, 6423.654 kilo joules, with decimals? Thanks
Also isnt it quantization means energy is represented in bit quantities meaning you can not divide, lets say 1 bit of energy
-
## 3 Answers
As far as the first pa... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2008/02/25/indefinite-integration/?like=1&source=post_flair&_wpnonce=78d053c4d8 | # The Unapologetic Mathematician
## Indefinite Integration
Since we’ve established the connection between integration and antidifferentiation, we’ll be concerned mostly with antiderivatives more directly than derivatives. So, it’s useful to have some simple notation for antiderivatives.
That’s pretty much what the “... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 8, "mimetex.cgi": 0, "/images/mat... |
http://motls.blogspot.com/2013/01/quantum-physics-doesnt-depend-on.html?showComment=1358364357245 | # The Reference Frame
## Wednesday, January 16, 2013
... /////
### Quantum physics doesn't depend on definitions of observers
Lots of people who are trying to understand quantum mechanics but who don't really want to listen constantly ask the same question:
What is an observer really?
This question is usually enca... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/1061/why-does-gps-depend-on-relativity/1063 | # Why does GPS depend on relativity?
I am reading A Brief History of Time by Stephen Hawking, and in it he mentions that without compensating for relativity, GPS devices would be out by miles. Why is this? (I am not sure which relativity he means as I am several chapters ahead now and the question just came to me.)
-... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.reference.com/browse/Position+Operator | Definitions
Nearby Words
# Position operator
In quantum mechanics, the position operator corresponds to the position observable of a particle. Consider, for example, the case of a spinless particle moving on a line. The state space for such a particle is L2(R), the Hilbert space of complex-valued and square-integrabl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 10, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2011/07/16/the-exterior-derivative-is-a-derivation/?like=1&source=post_flair&_wpnonce=c1c9c39881 | # The Unapologetic Mathematician
## The Exterior Derivative is a Derivation
To further make our case that the exterior derivative deserves its name, I say it’s a derivation of the algebra $\Omega(M)$. But since it takes $k$-forms and sends them to $k+1$-forms, it has degree one instead of zero like the Lie derivative... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 19, "mimetex.cgi": 0, "/images/ma... |
http://alanrendall.wordpress.com/2012/02/25/entrainment-by-oscillations/ | Hydrobates
A mathematician thinks aloud
Entrainment by oscillations
In the book of Goldbeter which I have mentioned in several recent posts a concept which occurs repeatedly is that of entrainment. While looking for some more information about this topic I found a paper of Russo, di Bernardo and Sontag (PloS Computa... | {"extraction_info": {"found_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": 5, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/51204/photoionization-equation | # Photoionization equation
I really need help understanding this equation ,i am new to quantum mechanics and i cant understand the math, so i need every single symbol to be explained or given a value if it is a constant , ( lets say X is Hydrogen)
-
1
What is the formula supposed to describe? What are the quantities... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/103810?sort=votes | ## Reference for subsemigroups of $\mathbb{N}^n$
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
A well known result about the natural numbers $\mathbb{N}$ says that for any finite subset $A \subset \mathbb{N}$ there exists $R \ge 0$ such that if $n$ is in the... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "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/252/the-many-body-problem?answertab=oldest | # The Many Body problem
(This is a simple question, with likely a rather involved answer.)
What are the primary obstacles to solve the many-body problem in quantum mechanics?
Specifically, if we have a Hamiltonian for a number of interdependent particles, why is solving for the time-independent wavefunction so hard?... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/100573/extending-psc-metrics | ## Extending psc metrics
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $S^1$ denote the circle with the non-trivial spin structure, i.e. $0\neq[S^1]\in\Omega^{Spin}_1$. Considering characteristic numbers it is easy so see that $S^1\times\mathbb{H}P^3$ 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": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/tagged/gaga | ## Tagged Questions
1answer
159 views
### algebraic de Rham cohomology of singular varieties
Hi, Is there a simple example of an (affine) algebraic variety $X$ over $\mathbb C$ where the $H^*_{dR}(X/\mathbb C) = H^*(\Omega^\bullet_{A/\mathbb C})$ differs from the singular …
0answers
126 views
### How do fibers of 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": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/278864/a-family-of-functions | # A family of functions
Does there exist an infinite family of functions which satisfy
$|f^\prime(x)|=1$ and $f(1)=f(-1)=0$?
where a) $f\colon \mathbb{R}\to \mathbb{R}$ b) $f$ is a complex function defined on some open neighbourhood of the closed unit disc in the plane.
-
3
$|f'(x)| = 1$ everywhere? At one point? ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/175880-disproving-existance-limit-infinity.html | # Thread:
1. ## Disproving the existance of a limit at infinity
Hello
I'm given the function x*sin(x), and asked whether it has a limit of some sort as x goes to negative infinity. In other words does it converge to a number or go off to positive infinity or negative infinity.
Based on the graph of the function my ... | {"extraction_info": {"found_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/calculus/174700-find-area-petal-sketch.html | # Thread:
1. ## Find the area of a petal sketch.
Find the area of a petal sketch.
1) r= 4 sin(2theta)
2) r= 4sin(theta)
3) Compare and contrast conjecture.
Please please please help me with this calculus problem. I am so lost in my class. step by step work would be greatly appreciated. The work does not have to be 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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/92781/total-variation-distance-is-often-too-strong-to-be-useful?answertab=votes | Total Variation distance is often too strong to be useful.
While reading lecture notes on Stein's method, there's one example that I cannot prove myself.
For iid random variables $X_1, ..., X_n$ where $\Pr(X_i=1) = \Pr(X_i=-1) = 1/2$, define $S_n=\frac{1}{\sqrt{n}}\sum_{i=1}^n X_i$. Then $S_n$ converges to normal dis... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/119348/convexity-of-a-certain-set-of-covariance-matrices | ## Convexity of a Certain Set of Covariance Matrices
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hello,
My question is about a certain set of matrices being convex or not. I'll start with some preliminaries in order to define myself properly. Let $X_1,U,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": 20, "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/127723/convex-combination-in-compact-convex-sets/127762 | # Convex combination in compact convex sets.
Let's $K\subset\mathbb{R}^n$ compact. If $K$ is convex then who to prove that any point of $K$ is convex combination of one or two extremal points of $K$?
Intuitively, for any closed ball that is true.
-
3
It won't be "one or two". Think of a simplex. In ${\mathbb R}^n$ ... | {"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": 36, "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/24028?sort=votes | ## What is the difference between the biconditional iff. and equality = ?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hello,
I've been used to writing logical transformations using equality, but the other day it struck me that perhaps I should be using 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": 68, "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/144818/interesting-determinant | # Interesting Determinant
Let $x_1,x_2,\ldots,x_n$ be $n$ real numbers that satisfy $x_1<x_2<\cdots<x_n$. Define \begin{equation*} A=% \begin{bmatrix} 0 & x_{2}-x_{1} & \cdots & x_{n-1}-x_{1} & x_{n}-x_{1} \\ x_{2}-x_{1} & 0 & \cdots & x_{n-1}-x_{2} & x_{n}-x_{2} \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ x_{n-1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 53, "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/1438/reciprocal-lattices/1449 | # Reciprocal Lattices
Is there an easy way to understand and/or visualize the reciprocal lattice of a two or three dimensional solid-state lattice? What is the significance of the reciprocal lattice, and why do solid state physicists express things in terms of the reciprocal lattice rather than the real-space lattice?... | {"extraction_info": {"found_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/differential-geometry/154240-critique-my-proof.html | # Thread:
1. ## [Solved] ....
Claim: The series $\sum_{n=1}^{ \infty} \frac{2}{n^2 + n}$ converges.
By definition:
The series $\sum_{n=1}^{ \infty} \frac{2}{n^2 + n} = \sum_{n=1}^{ \infty} a_n$ converges if and only if for every $\epsilon > 0$, there exists some $N \in \mathbb{N}$ such that for all $n, m$ with $n > ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/262973/legendre-polynomials-triple-product/262983 | # Legendre Polynomials Triple Product
I have to solve the following integral:
\begin{align} \int_{-1}^{1} \left(x^2 -1\right)^3 P_k(x)\,P_l(x)\, P_m(x) \;dx \end{align} where $P_{k,l,m}$ are Legendre Polynomials
The triple product \begin{align} \int_{-1}^{1} P_k(x)\,P_l(x)\, P_m(x) \;dx = 2 \begin{pmatrix} k & l & m... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "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/2268/supermassive-black-holes-with-the-density-of-the-universe?answertab=active | # Supermassive black holes with the density of the Universe
This question was inspired by the answer to the question "If the universe were compressed into a super massive black hole, how big would it be"
Assume that we have a matter with a uniform density $\rho$. Some mass of this matter may forms a black hole with 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://mathoverflow.net/questions/115940?sort=votes | ## For finite group G and field k of char=p, if P,P′ are projective k[G]-modules with [P]=[P′], is it true that P=P′ ?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
That is: is it true that if projective k[G]-modules have same composition factors then they 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": 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/199456/matrix-of-linear-transformation-range-of-transformation?answertab=votes | # Matrix of linear transformation (range of transformation)
I'm doing a bit of homework and want to check if I'm doing it right. The question is as follows:
Let $T: P_2(\mathbb{R}) \rightarrow P_3(\mathbb{R})$ be defined by $T(p)(x) = (x-1)p(x)$
We're then asked to compute the matrix of $T$ with respect to the stand... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 31, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/dice+probability-distributions | # Tagged Questions
4answers
46 views
### Probability of $X$ out of $N$ dice landing on $M$
The problem is as follows: We have $N$ dice and we throw them on a table. What is the probability that $M$ will fall $X$ times? Specific example: We have $10$ dice and we throw them on a table. What ...
1answer
66 views
### D... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/139123-group-order-p-2-q-2-solvable.html | # Thread:
1. ## Group of order p^2*q^2 is solvable?
Hi! Im having an exam in group theory in few days. Ive lost some of my solutions and cant proof this by myself.
There was also a specific example regarding group of order 36=2^2*3^2. With number of sylow 2-subgroups or 3-subgroups being one its simple. But I dont k... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/On_the_Equilibrium_of_Heterogeneous_Substances | # On the Equilibrium of Heterogeneous Substances
In the history of thermodynamics, On the Equilibrium of Heterogeneous Substances is a 300-page paper written by American mathematical-engineer Willard Gibbs. It is one of the founding papers in thermodynamics, along with German physicist Hermann von Helmholtz's 1882 pap... | {"extraction_info": {"found_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://electronics.stackexchange.com/questions/30053/why-voltage-lags-by-90-from-magnetic-flux | Why voltage lags by 90° from magnetic flux?
I was not sure if I should write it here or on Physics board, but I will give a try.
As I understood current (generally emf) can be generated in a system by varying magnetic flux.
For example, let's take AC generator. A loop of wire rotates between N and S magnets.
$\Phi =... | {"extraction_info": {"found_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/106706/approximation-of-a-non-holomorphic-function-closed | ## Approximation of a non-holomorphic function [closed]
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Hi,
I am unfortunately very new to analysis and this may be a simple question-- if so, please forgive my ignorance.
The function $f(z) = z\bar{z}$ is not ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
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