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http://math.stackexchange.com/questions/tagged/discrete-mathematics?sort=votes&pagesize=15 | Tagged Questions
Questions on discrete mathematics generally: "the study of mathematical structures that are fundamentally discrete rather than continuous"
1answer
6k views
How many fours are needed to represent numbers up to $N$?
The goal of the four fours puzzle is to represent each natural number using four copi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 124, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/trigonometry/4888-trig-help.html | # Thread:
1. ## Trig help!
Hey guys im abit confused with the different quadrants of the trig ratios thing.
I know all trig ratios are positive in 1st quadrant, then sine, tan, cosine only. However, why does:
cos x= -5/11 (solve for x if 0<x<180)
= 117 degrees?
I thought only sine could be positive when greater 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": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cstheory.stackexchange.com/questions/9497/pseudo-random-function-families-whose-instances-have-full-domain/9514 | # Pseudo-Random Function families whose instances have full domain
The GGM construction gives (PRF) pseudo-random function families whose instance's input's are binary strings of a single length.
I've convinced myself that one could get a PRF family whose instances have domain of all finite binary strings by taking 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": 66, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cs.stackexchange.com/questions/6773/finding-negative-cycles-for-cycle-canceling-algorithm | # Finding negative cycles for cycle-canceling algorithm
I am implementing the cycle-canceling algorithm to find an optimal solution for the min-cost flow problem. By finding and removing negative cost cycles in the residual network, the total cost is lowered in each round. To find a negative cycle I am using the bellm... | {"extraction_info": {"found_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://mathoverflow.net/questions/30191/software-for-tree-decompositions/31545 | Software for Tree-Decompositions
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Does anybody know about software that exactly calculates the tree-width of a given graph and outputs a tree-decomposition? I am only interested in tree-decompositions of reasonbly sma... | {"extraction_info": {"found_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://catalog.flatworldknowledge.com/bookhub/reader/2992?e=coopermicro-ch06_s02 | # Microeconomics: Theory Through Applications, v. 1.0
by Russell Cooper and A. Andrew John
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 lets you take notes, highlight im... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 9, "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://mathoverflow.net/questions/26207?sort=newest | ## How can we explicitly find the maximum eigenvalue of a tridiagonal matrix?
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I just came across a matrix of the form ```$A:=\begin{pmatrix}
0&-\frac{c_0}{b_0}&0&\cdots&0\\-\frac{a_1}{b_1}&0&-\frac{c_1}{b_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": 19, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikibooks.org/wiki/Engineering_Acoustics/Piezoelectric_Transducers | # Engineering Acoustics/Piezoelectric Transducers
Authors · Print · License Edit this template Part 1: Lumped Acoustical Systems – 1.1 – 1.2 – 1.3 – 1.4 – 1.5 – 1.6 – 1.7 – 1.8 – 1.9 – 1.10 – 1.11 Part 2: One-Dimensional Wave Motion – 2.1 – 2.2 – 2.3 Part 3: Applications – 3.1 – 3.2 – 3.3 – 3.4 – 3.5 – 3.6 – 3.7 – 3.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/216816/combinatorial-identity-related-to-the-volume-of-a-ball-in-mathbbr2k1 | # Combinatorial identity related to the volume of a ball in $\mathbb{R}^{2k+1}$
Calculating the volume of a ball in $\mathbb{R}^{2k+1}$ in two different ways gives us the following formula:
$$\sum_{i=0}^k {k \choose i} \frac{(-1)^i}{2i+1} = \frac{(k!)^2 2^{2k}}{(2k+1)!}$$
Is there a more direct way to prove this ide... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/32368/hamiltonian-mechanics-and-special-relativity/32375 | # Hamiltonian mechanics and special relativity?
Is there a relativistic version of Hamiltonian mechanics? If so, how is it formulated (what are the main equations and the form of Hamiltonian)? Is it a common framework, if not then why?
It would be nice also to provide an example --- a simple system with its Hamiltoni... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/rocket+momentum | # Tagged Questions
3answers
247 views
### Conservation of Energy in Different Frames of Reference
Say I have a bucket of fuel that can produce 150J of energy by combustion. No matter what frame of reference an observer or the bucket of fuel is in, since the configuration of molecules stay the ...
3answers
415 views
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/114131-maximum-volume.html | # Thread:
1. ## Maximum Volume
A hemisphere of radius 7 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the center of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume.
I have no clue how to go ab... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.ateacher.org/blog/?cat=1 | # Divide By Zero
Do the impossible
Archive | everything else
October 27, 2010
## Juice Mixing
You have two glasses with an equal amount of juice in them. One has apple juice, the other: orange juice. You take some amount from the apple juice and put it into the
orange juice glass, then mix it up real nice. Then 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": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://reference.iucr.org/dictionary/Incommensurate_magnetic_structure | # Incommensurate magnetic structure
### From Online Dictionary of Crystallography
Structure magnétique incommensurable (Fr.)
## Definition
An incommensurate magnetic structure is a structure in which the magnetic moments are ordered, but without periodicity that is commensurate with that of the nuclear structure 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": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/301/is-sha-512-bijective-when-hashing-a-single-512-bit-block | # Is SHA-512 bijective when hashing a single 512-bit block?
It's been said that CRC-64 is bijective for a 64-bit block.
It the corresponding statement true for SHA-2?
-
## 2 Answers
It would be very freakish if it turned out to be true. It is not an expected property of SHA-512 to have such bijectivity. It would 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": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/252425/convergence-of-infinite-potence-tower | # Convergence of (infinite) potence tower?
Let $(a_n)_{n\in\mathbb{N}}$ be a series in $\mathbb{C}$ or $\mathbb{R}$. Which contraints must $(a_n)$ match to make $b_n := a_1^{a_2^{...^{a_n}}}$ converge for $n\rightarrow\infty$?
For constant series with $e^{-e}<a_n<e^{1/e}$, the series $b_n$ converges; So I guess serie... | {"extraction_info": {"found_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://mathhelpforum.com/differential-equations/212280-differential-equation-problem.html | # Thread:
1. ## Differential equation problem
Hello,
I'm trying to find the integration factor $\lambda(x,y)$ of this differential equation: $(siny-3x^2cosy)cosydx+xdy=0$, with exception that $\lambda$ being a function, dependent in only one variable, x or y.
Any ideas on solving this equation?
Thanks
2. ## Re: 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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/271688/projective-geometry-hyperplane?answertab=votes | # projective geometry hyperplane
For $j=0,\ldots,n$ consider the affine hyperplane $A_j:=e_j+\langle e_0,\ldots,e_{j-1},e_{j+1},\ldots,e_n\rangle$ in $\mathbb K^{n+1}$ and the associated embedding $\tau_j:\mathbb K^n\rightarrow\mathbb KP^n, \tau_j(x_1,\ldots,x_n):=[x_1:\ldots:x_j:1:x_{j+1}:\ldots:x_n]$, where $e_j\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": 26, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/185535-pigeon-hole-principle-2-a.html | # Thread:
1. ## Pigeon-hole Principle (2)
(a) Let n >= 2. We select n + 1 different integers from the set {1, 2, ..., 2n}. Is it true that there will always be two among the selected integers so that one of them is equal to twice the other?
(b) Is it true that there will always be two among the selected integers so t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 41, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/106147/is-partial-x-a-sphere-for-x-a-complete-cat0-space | ## Is $\partial X$ a sphere for $X$ a complete CAT$(0)$ space?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $X$ be a complete CAT$(0)$ metric space, and $\partial X$ its boundary. One way to define $\partial X$ is as the equivalence class of geodesic ra... | {"extraction_info": {"found_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://mathinsight.org/prototypes_more_serious_questions_taylor_polynomials_refresher | # Math Insight
• Top
• In threads
When printing from Firefox, select the SVG renderer in the MathJax contextual menu (right click any math equation) for better printing results
### Prototypes: More serious questions about Taylor polynomials
Beyond just writing out Taylor expansions, we could actually use them to app... | {"extraction_info": {"found_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/260597/linear-transformation?answertab=active | # Linear transformation
Let $T:\mathbb R^7 \longrightarrow \mathbb R^7$ be the linear transformation given by $$T(x_1, x_2, x_3, x_4 ,x_5, x_6, x_7) = (x_7, x_6, x_5 ,x_4 ,x_3 ,x_2 ,x_1)$$ Which of the following statements are true?
a. Determinant of $T$ is $1$
b. Basis of $\mathbb R^7$ w.r.t. $T$ is a diagonal matr... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/214/would-it-help-if-you-jump-inside-a-free-falling-elevator | # Would it help if you jump inside a free falling elevator?
Imagine you're trapped inside a free falling elevator. Would you decrease your impact impulse by jumping during the fall? When?
-
Your actual, literal answer to your actual question is "Yes, you would decrease your impact impulse". Your relevant answer is gi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 20, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/business-math/64875-need-help.html | # Thread:
1. ## Business Calculus - Need help! :(
I've no idea is it the right section to post this,
But I had some problems dealing with this problem.
Total costs
Market price
Tax (per unit produced)
Find:
1. Quantity to produce to maximise profits
2. What should t be, so as to maximise tax revenue?
* * * * * *... | {"extraction_info": {"found_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://scicomp.stackexchange.com/questions/5328/complex-least-squares-problem | # Complex least-squares problem
Having a matrix $\mathbf{A} \in \mathcal{C}^{m\times n}$ I solve following least-squares problem $$Re(\mathbf{A}^H \mathbf{A})x=Re(\mathbf{A}^H\mathbf{b}).$$ If the matrix $\mathbf{A}$ was a real matrix, the solution to the equation above could have been written as $$\mathbf{x} = \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": 15, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/97387-difficult-differential-equation-system.html | # Thread:
1. ## Difficult Differential Equation System
The following is a model for HIV.
Infected cells = T
Concentration of viral particles = C
$\dot{T} = 0.06V - \frac{T}{2} , \dot{V} = 100T - cV$
where $c > 0$ is the rate constant for viral clearance.
1) Show that there are 2 possible types of critical points 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/319?sort=newest | ## Spectrum of the Grothendieck ring of varieties
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Here's a problem that may ultimately require just simple algebraic-geometry skills to be solved, or perhaps it's very deep and will never be solved at all. From t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/67611/self-dual-representations | self-dual representations
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Let $V$ be a finite-dimensional irreducible representation (complex or $\ell$-adic) of a group $G$ (compact Lie group or algebraic group etc.). Does there always exist a linear character $\r... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "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/2011/11/30/homotopies-as-2-morphisms/?like=1&source=post_flair&_wpnonce=5d5a17dad5 | # The Unapologetic Mathematician
## Homotopies as 2-Morphisms
Last time, while talking about homotopies as morphisms I said that I didn’t want to get too deeply into the reparameterization thing because it could get too complicated. But since when would I, of all people, shy away from 2-categories? In case it wasn’t ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 32, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/16830/list | Return to Answer
1 [made Community Wiki]
In question #14739, I asked whether the product of two ideals of a commutative ring $R$ could be defined lattice-theoretically the same way the sum and intersection can. Bjorn Poonen gave a great counterexample that shows the answer is no! This supports a point fpqc had been 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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/26861?sort=votes | ## Explicit ordering on set with larger cardinality than R
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Is it possible to construct (without using Axoim of Choice) a totally ordered set S with cardinality larger than $\mathbb{R}$?
Motivation: A total 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": 171, "mathjax_display_tex": 0, "mathjax_asciimath": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/269439/how-to-simplify-this-equality-factorials/269445 | # How to simplify this equality (factorials)?
This was in one of the examples of the textbook, but I couldn't figure out how they solved it. They say they multiply the left hand side by $\frac{n!}{n!}$ to get the right hand side:
$$\frac{2^n \cdot (2n-3)!!}{n!} = 2\frac{(2n-2)!}{n!(n-1)!}$$
The double factorial stan... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/90136-problem-idempotent-matrix.html | Thread:
1. Problem of Idempotent matrix
Assume $A$ is idempotent matrix of order n,in other words: $A^2 = E_{n}$,and $det(A) > 0$.show that: $det(A + E_{n}) \not=0$
2. Originally Posted by Xingyuan
Assume $A$ is idempotent matrix of order n,in other words: $A^2 = E_{n}$,and $det(A) > 0$.show that: $det(A + E_{n}) \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": 40, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/3251/is-mac-better-than-digital-signature | # Is MAC better than digital signature?
MACs differ from digital signatures in the sense that MAC values are both generated and verified using a shares secret key. Does this in any way put MAC on a disadvantage as compared to digital signatures? How is one of them better than the other?
-
## 1 Answer
Was, as you st... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/27255/instanton-moduli-space-with-a-surface-operator?answertab=oldest | # Instanton Moduli Space with a Surface Operator
I would like to understand the mathematical language which is relevant to instanton moduli space with a surface operator.
Alday and Tachikawa stated in 1005.4469 that the following moduli spaces are isomorphic.
1. the moduli space of ASD connections on $\mathbb{R}^4$ ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 40, "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/67091-optimization-problem.html | # Thread:
1. ## Optimization Problem
Find the larger of two numbers whose sum is 30 for which the sum of their squares is a minimum.
2. Let the first number $x_1$ and the second number $x_2$.
Then $f\left( {x_1 ,x_2 } \right) = x_1^2 + x_2^2 \to \min$ and $x_1+x_2=30\Rightarrow$.
$\Rightarrow x_2=30-x_1\Rightarrow... | {"extraction_info": {"found_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/22352/can-there-be-such-a-thing-as-a-classification-of-classification-theorems | # Can there be such a thing as a classification of classification theorems?
Can there be such a thing as a classification of classification theorems?
-
7
Sure. Every classification theorem is of the form "every P is of the form Q, R, S, T..." for some P, Q, R, S, T.... – Qiaochu Yuan Feb 16 '11 at 13:32
But I mean 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": 14, "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/535/why-does-kinetic-energy-increase-quadratically-not-linearly-with-speed/538 | # Why does kinetic energy increase quadratically, not linearly, with speed?
As Wikipedia says:
[...] the kinetic energy of a non-rotating object of mass $m$ traveling at a speed $v$ is $mv^2/2$.
Why does this not increase linearly with speed? Why does it take so much more energy to go from 1 m/s to 2 m/s than it doe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 75, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/22910?sort=newest | ## Exactness of 2nd-Order Differential Equations via Differential Forms
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
This (probably very elementary) question came up the last time I taught differential equations, and I've been toying with it for a while wit... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/48024-determine-number-terminates-base-m-but-will-not-terminate-base-n.html | Thread:
1. Determine that a number terminates in base m but will not terminate in base n?
Is there a way to determine that for some number $a$ in base m that it will or will not have a terminating equivalent number $b$ in base n?
For example, when converting number 0.315 in base 10 to base 2, we get the base 2 numbe... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/27785/what-compactifications-of-the-poincare-group-have-been-studied | # what compactifications of the Poincare group have been studied?
as we know the Poincare group is non-compact. Poincare invariance have been observed in velocities and energies up to $10^{20}$ eV in cosmic rays. The other day i was thinking in how $SU(2)$ homeomorphism in $SO(3)$ imposes a double cover, and i keep wo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "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/120374-find-maximum-size-cylinder-fits-sphere.html | # Thread:
1. ## Find maximum size of Cylinder that fits in sphere
I'm kinda stuck on this.
I need to find the maximum size of a Cylinder that fits in sphere of radius 1.
Ive come up with the following, .. am I on the right track so far?
Volume of Cylinder = Pi(r^2)h = Pi(r^2)(sqrt(1^2 - r^2))
Volume of Sphere = 4/... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/48411/are-there-any-abelian-2-groups-with-complete-holomorphs-other-than-c2-2-and-c/48431 | ## Are there any abelian 2 groups with Complete Holomorphs Other than $C^2_2$ and $C^4_2$?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The title says it. I'm reviewing some group theory concepts I haven't touched in quite a while, since I don't teach abstr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 35, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/177488/computing-the-volume-of-a-set-efficiently?answertab=oldest | # Computing the volume of a set efficiently
Given a set of vectors $\mathbf v_i$ for $i=1,\dots,k$, $\mathbf v_i \in \{0,1\}^n$, is that possible to efficiently find the volume of the set,
$$\left\{\mathbf x \in [0,1]^n:\mathbf x \le \sum_{i=1}^k \alpha_i\mathbf v_i\ \text{for some $\alpha_i$}\right\},$$ such 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": 20, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/129945-need-demonstrate-slope-strictly-positive.html | # Thread:
1. ## Need to demonstrate that the slope is strictly positive
If I have a multivariable equation whose slope is always positive, say $f(x,y,z)=x^2+y^2+z^2$ how do I demonstrate that the slope is always positive?
I imagine this involves partial derivatives but need some guidance.
Thanks
2. Originally Post... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/30366/why-wet-is-dark/30436 | # Why wet is dark?
When something gets wet, it usually appears darker. This can be observed with soil, sand, cloth, paper, concrete, bricks ...
What is the reason for this? How does water soaking into the material change its optical properties?
-
## 3 Answers
When you look at a surface like sand, bricks, etc, 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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/933/when-is-an-asymmetric-scheme-considered-broken | # When is an asymmetric scheme considered broken?
Does the following quote imply that valid encrypted data can be created and decrypted by someone other than the owner of a private key:
An asymmetric encryption scheme is considered to be broken if an attacker can decrypt a given ciphertext, even if he can convince 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": 10, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/55250/how-to-tell-if-a-complex-exponential-blows-up?answertab=votes | # How to tell if a complex exponential blows up
I'm following Griffiths' Introduction to Quantum Mechanics, where he's discussing the general solution to the delta-function potential problem. The solution he refers to is $$\psi(x)=Ae^{ikx}+Be^{-ikx}$$
Now, he says that neither of the the terms blows up. The case he 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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/72059/matrix-inversion-lemma-with-pseudoinverses | ## Matrix inversion lemma with pseudoinverses
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The utility of the Matrix Inversion Lemma has been well-exploited for several questions on MO. Thus, with some positive hope, I'd like to field a question of my own.
... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-applied-math/175637-game-theory-hotelling-game-3-players.html | # Thread:
1. ## Game Theory: Hotelling game with 3 players
Hi,
The problem is relatively well-known. IN its basic form there are two firms competing either on location or on some product characteristic. They can each choose a number in [0;1] and the consumers are uniformly distributed along [0;1]. Each consumer buys ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/41054/pade-approximation-usability-in-iterative-algorithms/41085 | ## Padé approximation - usability in iterative algorithms
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Firstly, I have to say that I don't understand Padé approximation well.
But I discovered that, it is more precise than Taylor series.
I have to create app... | {"extraction_info": {"found_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://math.stackexchange.com/questions/181023/balanced-tree-number-of-nodes | # Balanced tree number of nodes
This should be a simple one but maybe I'm dumb or maybe I'm just tired, but how to prove that
$$n = 1 + 2^1 + 2^2 + \cdots + 2^h$$
is equal to
$$n = 2^{h+1} - 1$$
?
-
2
Find $2n - n$. Solve for $n$. – ladaghini Aug 10 '12 at 13:06
2
multiply the first expression by $(2 - 1)$ and ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/6171/why-is-feed-forward-mechanism-used-in-hash-functions/6172 | # Why is feed-forward mechanism used in hash functions?
The compression function of SHA-1 when used in Davies-Meyer mode adds its input to the chaining values at the final step. For the first message block, the IV is used as the input and in the next step, the previous block's output (as specified by Merkle-Damgard) 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": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/211979-question-intervals.html | # Thread:
1. ## Question on intervals
My question is:
i) Is the following statement true or false, and explain why: "If a is less than or equal to b, then (-infinity, a) is a subset of (-infinity, b)".
I drew a diagram which showed that this was true, but how would you go about proving it formally?
Any help 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/2280/note | nrich enriching mathematicsSkip over navigation
### Cuisenaire Rods
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
### Making Boxes
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/45854?sort=newest | ## Explicit Coquasi-Triangular Quantised Coordinate Algebra of a Complex Semi-Simple Lie Group?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $SL_q(N)$ be usual quantised coordinate algebra of the special linear group. As is well-known, this is co-quasi-... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/145421-finding-limit-finding-maclaurin-series.html | # Thread:
1. ## Finding a limit. Finding Maclaurin series.
How can these problems be worked out?
1) lim as x goes to 0 of (1/x - 1/sinx)
2) find the 1st 4 derivatives of y= ln(1+sinx) and the Mclaurin series up to the term containing x^4
I know some calculus, but I need help with this. Thank you.
2. Originally 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 31, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/287676/stabilizer-of-a-4-by-4-skew-symmetric-matrix-by-orthogonal-matrix?answertab=votes | # Stabilizer of a 4 by 4 skew symmetric matrix by orthogonal matrix
Matrices are over the field of complex numbers, and $X^t$ means transpose of a matrix $X$.
Consider the group action of $O(4)=\{P\mid PP^t=I\}$ on $SK(4)=\{M\mid M^t=-M\}$ by $(P,M) \rightarrow PMP^t$. Does anyone know what is the stabilizer of a gen... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 61, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/29651/is-it-possible-to-estimate-the-odds-of-winning-a-multi-entry-contest-when-i-don | # Is it possible to estimate the odds of winning a multi-entry contest, when I don't know the breakdown of entries?
Suppose I am entered into a contest, with the following rules:
• Every person may get up to 6 entries
• All the entries will be pooled, and 25% of the entries will be selected to be winners, with a maxi... | {"extraction_info": {"found_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://math.stackexchange.com/questions/84435/why-is-the-mollified-process-a-semimartingale | # Why is the mollified process a semimartingale?
Let $X_t$ be a continuous adapted stochastic process and let $X_t^n$ be the mollified process defined by $$X_t^n= n \int\limits_{(t-\frac{1}{n})^{+}}^{t} X_s \,ds$$ Prove that $X_t^n$ is a semimartingale.
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## 1 Answer
At fixed $n$,and for $t>\frac{1}{n}$ it is clear... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/124159/find-root-of-non-continuous-function-using-a-numerical-method/124167 | # Find root of non-continuous function using a numerical method
Given the formula (source) $$M = P \times \frac{J}{1 - (1 + J)^{-N}}$$ Assume $P$ and $J$ remain constant. I want to be able to find $N$ for given $M.$
Could you please give an example of a numeric method (like secant to solve the same)? [My] problem 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": 11, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/10.4153/CMB-2011-066-2 | Canadian Mathematical Society
www.cms.math.ca
| | | | |
|----------|----|-----------|----|
| | | | | | |
| Site map | | | CMS store | |
location: Publications → journals → CMB
Abstract view
# Limit Sets of Typical Homeomorphisms
Read article
[PDF: 145KB]
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": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/relativity+time | Tagged Questions
1answer
85 views
How much time has passed for Voyager I since it left the Earth, 34 years ago?
34 years have passed since Voyager I took off and it's just crossing the solar system, being approximately at 16.4 light-hours away. How much time have passed for itself, though?
1answer
97 views
How do 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": 6, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/290939/polar-decomposition-for-non-square-matrices?answertab=active | # polar decomposition for non square matrices
I know that for a square complex matrix $A\in\mathbb{C}^{n\times n}$ there exist matrices $O$ and $P$ in $\mathbb{C}^{n\times n}$ with $O$ unitary and $P$ hermitian positive semidefinite such that $A=OP$. The proof starts with applying the spectral theorem to the matrix $A... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/76798?sort=votes | A question about J.H. Conway’s SURREAL NUMBERS
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My quesion is: What set theory are the mathematicians who are developing the theory of these numbers working in-or are they, in fact, working outside any of the standard... | {"extraction_info": {"found_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://mark.reid.name/blog/prediction-with-expert-advice-as-online-convex-optimisation.html | Prediction with Expert Advice as Online Convex Optimisation
I have been working with Bob Williamson and Tim Van Erven recently to better understand the notion of mixability in what is known as the Prediction With Expert Advice (PWEA) setting for online learning. I was curious as to how this setting relates to 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": 74, "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/64249?sort=votes | ## Automorphism groups and etale topological stacks
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Recall that an etale topological stack is a stack $\mathscr{X}$ over the category of topological spaces (and open covers) which admits a representable local hom... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/87106/when-finitely-generated-free-algebras-are-finite | ## When finitely generated free algebras are finite
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The variety (in the sense of universal algebra) of Boolean algebras, for example, has the property that finitely generated free algebras have finite cardinality... | {"extraction_info": {"found_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": 9, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/2317/changing-variables-algebraically?answertab=oldest | # Changing variables algebraically
Suppose one has two functions, $y(x)$ and $z(x)$, and one seeks to obtain $y(z)$ by substituting $x(z)$ into $y(x)$. Can this be done in a single step? Or must $z(x)$ first be inverted independently? For the sake of illustration, suppose the functions consist of transcendental 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": 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/37070?sort=votes | ## Why can’t proofs have infinitely many steps?
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I recently saw the proof of the finite axiom of choice from the ZF axioms. The basic idea of the proof is as follows (I'll cover the case where we're choosing from ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/tagged/lie-algebroids | ## Tagged Questions
1answer
362 views
### What’s an example of a commutative algebra over $\mathbb Q$ that fails to satisfy this version of the “PBW theorem”
In a recent question, I recalled the notion of differential operator, polyderivation, and principal symbol for a commutative algebra $A$ over some fixed commut... | {"extraction_info": {"found_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://mathoverflow.net/questions/81079/primes-of-the-form-x2ny2mz2-and-congruences/81124 | ## Primes of the form $x^2+ny^2+mz^2$ and congruences.
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This is a sequel of this question where I asked for which positive integer $n$ the set of primes of the former $x^2+ny^2$ was defined by congruences (a set o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 64, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/32149/fatous-lemma-and-the-bounded-convergence-theorem | ## Fatou’s Lemma and the bounded convergence theorem. [closed]
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I have been studying measure theory of late, and i was stuck up in these two things.
BOUNDED CONVERGENCE THEOREM: It states that $f_n$ is a sequence... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/647/digital-signature-algorithm-signature-creation | # Digital Signature Algorithm signature creation
I was studying DSS from "Cryptography and Network Security" by William Stallings. What puzzled me was the DSS approach figure described in the text. It says it uses Public and Private Keys for creating signature.
But the algorithm for creating signature in DSA doesn'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": 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/118383/convergence-of-sum-limits-n-1-infty-left-dfrac-1-cdot3-cdots-2n-1 | # convergence of $\sum \limits_{n=1}^{\infty }\left\{ \dfrac {1\cdot3 \cdots (2n-1)} {2\cdot 4\cdots (2n)}\cdot \dfrac {4n+3} {2n+2}\right\} ^{2}$
I am investigating the convergence of $$\begin{split}\sum _{n=1}^{\infty }\left\{ \dfrac {1\cdot 3\cdots (2n-1)} {2\cdot 4\cdots (2n)}\cdot \dfrac {4n+3} {2n+2}\right\} ^{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": 11, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/antimatter | # Tagged Questions
The antimatter tag has no wiki summary.
1answer
33 views
### Would an antimatter beam create multiple matter-antimatter explosions?
To expand upon the question - in an atmosphere, would a beam of pure antimatter (disregarding technical difficulties creating such a beam or passing it through a med... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/3525/when-are-probability-distributions-completely-determined-by-their-moments/4787 | ## When are probability distributions completely determined by their moments?
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If two different probability distributions have identical moments, are they equal? I suspect not, but I would guess they are "mostly" ... | {"extraction_info": {"found_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/trigonometry/33472-trig-equations-multiple-trig-functions-cont.html | Thread:
1. Trig Equations with Multiple Trig Functions cont.
Find, to the nearest tenth of a degree, all values of x in the interval 0≤x≤360 that satisfy the equation.
tan x=cos x
also solve for x in the interval 0≤x≤2π
cos ½x= cos x
2. Originally Posted by ~berserk
tan x=cos x
$\frac{sin x}{cos x} = cos x$
$sin... | {"extraction_info": {"found_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/math-topics/49330-define-rational-function.html | # Thread:
1. ## Define rational function
From graph of the rational function, you must define $a, b, c, d$ in $f(x)=\frac{ax+b}{cx+d}$.
(I'm assuming both x-axis and y-axis are crossed at $-\frac{1}{2}$)
I start with this set-up: $\frac{b}{d}=-\frac{1}{2}$ (because of $f(0)=-\frac{1}{2}$)
$\frac{a}{c}=2$ (asymptote)... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2009/10/08/cauchys-invariant-rule/?like=1&_wpnonce=401286028f | # The Unapologetic Mathematician
## Cauchy’s Invariant Rule
An immediate corollary of the chain rule is another piece of “syntactic sugar”.
If we have functions $g:X\rightarrow\mathbb{R}^n$ and $f:Y\rightarrow\mathbb{R}^p$ for some open regions $X\subseteq\mathbb{R}^m$ and $Y\subseteq\mathbb{R}^n$ so that 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 62, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/30338/what-is-the-relation-between-physicists-functional-derivatives-and-frechet-der/30339 | # What is the relation between (physicists) functional derivatives and Fréchet derivatives
I´m wondering how can one get to the definition of Functional Derivative found on most Quantum Field Theory books:
$$\frac{\delta F[f(x)]}{\delta f(y) } = \lim_{\epsilon \rightarrow 0} \frac{F[f(x)+\epsilon \delta(x-y)]-F[f(x)]... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 42, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://jdh.hamkins.org/about/ | # About
My main research interest lies in mathematical and philosophical logic, particularly set theory, with a focus on the mathematics and philosophy of the infinite. I have worked particularly with forcing and large cardinals, those strong axioms of infinity, and have been particularly interested in the interaction... | {"extraction_info": {"found_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://mathematica.stackexchange.com/questions/tagged/polynomials+algebraic-manipulation | Tagged Questions
0answers
57 views
Apart may use Padé method: what's that?
How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart ...
7answers
215 views
Defining a function that completes the square given a quadratic polynomial expression
How can I write a function that would co... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/8709/does-mass-affect-speed-of-orbit-at-a-certain-distance?answertab=oldest | Does mass affect speed of orbit at a certain distance?
Does the mass of both the parent object, and the child object affect the speed at which the child object orbits the parent object?
I though it didn't (something like T^2 = R^3) until I saw an planet on the iphone exoplanet app, that is closer to it's star than 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": 15, "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/280079/sum-of-two-squares-modulo | # Sum of two squares modulo
In the following all variables are non-negative integers.
It is well known (Fermat) that a number $a$ is a sum of two squares $a = x^2 + y^2$ if and only if the prime factors of $a$ of the form $p = 4k+3$ occurs to an even power. Example: $$7^2 \times 5 = 245 = 7^2 + 14^2 \ .$$
I want to ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/159021-perpendicular-bisector-print.html | # Perpendicular bisector
Printable View
• October 10th 2010, 04:47 AM
Greener
Perpendicular bisector
The main help i need is with this question:
1)****The perpendicular bisector of a straight line joining the points (3,2) and (5,6) meets the x axis at A and the y at B. Prove that the distance AB is equal to 6root5.
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/63898/isolated-conics-on-a-del-pezzo-surface/63901 | ## Isolated conics on a del Pezzo surface
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Is there anything known about isolated conics in a del Pezzo surface: their number, arrangement, and the corresponding elements of the class group of surface's minimal de... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 50, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/29577-concavity-points-inflection.html | # Thread:
1. ## Concavity / Points of Inflection
I am stuck on this problem, and I am thinking that I am not getting the derivatives (1st and 2nd) correct. Here is the problem:
F(X)= 2X(X+4)^3
I know I have to get the first and second deriviative's but don't I need to cube the inside function first and then distrib... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/182428/proving-that-22n-5-is-always-composite-by-working-modulo-3?answertab=votes | # Proving that $2^{2^n} + 5$ is always composite by working modulo 3
By working modulo 3, prove that $2^{2^n} + 5$ is always composite for every positive integer n.
No need for a formal proof by induction, just the basic idea will be great.
-
2
– Martin Sleziak Aug 14 '12 at 13:03
## 5 Answers
Obviously $2^2 \equ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 60, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/35600/what-are-your-favorite-puzzles-toys-for-introducing-new-mathematical-concepts-to/35638 | ## What are your favorite puzzles/toys for introducing new mathematical concepts to students?
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We all know that the Rubik's Cube provides a nice concrete introduction to group theory. I'm wondering what other simi... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/21925/what-is-the-proper-way-to-connect-two-light-bulbs-in-a-circuit-in-series-or-par?answertab=votes | # what is the proper way to connect two light bulbs in a circuit? in series or parallel?
What is the proper way to connect two light bulbs in a circuit? in series or in parallel and why?
My thought is that it's better to hook them in parallel, since if we take into account Ohm's Law, the sum of their resistance will ... | {"extraction_info": {"found_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/number-theory/40924-simple-congruence.html | Thread:
1. Simple congruence
Does $\frac{2^x-1}{3}=n$, n natural, have odd solutions in the naturals for x? How do you know (does Euler's theorem tell me this)?
2. Originally Posted by sleepingcat
Does $\frac{2^n-1}{3}$ have odd solutions in the naturals? How do you know?
All odd natural numbers (n) can be written $... | {"extraction_info": {"found_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/102696?sort=votes | ## Realizing not-quite-barycentric subdivision of a polytope
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Given a poset $S$, one can form a new poset $I(S)$ whose elements are intervals in $S$ (i.e. either $\emptyset$ or $[a,b]$ for some $a\leq b\in S$) wit... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 40, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/243899/any-forest-on-5-or-more-vertices-contains-an-independent-set-of-size-3?answertab=oldest | # Any forest on 5 or more vertices contains an independent set of size 3.
I am looking for a short proof of this fact. This is clearly true by drawing these trees, but I am having trouble putting it into writing. Somehow I need to select 3 of the 5 vertices and show that there must be a $3$-cycle or an independent set... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/165402/solving-y-frac1x-y-1-frac-cot-xx-y-0-by-rank-reduction | # Solving $y'' - \frac{1}{x} y' + (1+\frac{\cot x}{x}) y = 0$ by rank reduction
With the substitution $$y(x) = \sin x \int u(x) \, dx\tag{*}$$ I managed to get to$$u'(x) = \left(\frac{1}{x}-2\cot x\right)u(x)$$ Solving which gave me $$u(x) = C_1 \frac{x}{\sin^2 x}$$ Inserting that back into $(*)$ $$y(x) = (\sin x) C_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": 11, "mathjax_display_tex": 15, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/trigonometry/111224-solving-x-trig-function.html | # Thread:
1. ## Solving for x with a trig function
How do I solve for x when f = 4(-cos^2(x) + sin^2(x) + sin(x))?
I can regroup the function in various ways, and I factored out the 4 already, but I don't know how get the function so that I can solve for x... If you get me started on the right path, or hint at an id... | {"extraction_info": {"found_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://m-phi.blogspot.co.uk/2013/01/are-there-causally-active-mixed.html | # M-Phi
A blog dedicated to mathematical philosophy.
## Saturday, 5 January 2013
### Are there causally active mixed mathematical objects?
At the heart of the indispensability arguments against nominalism lie mixed mathematical objects - henceforth MMOs. A simple example of an MMO is the set of US presidents. Or 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": 56, "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/15/what-experiment-would-disprove-string-theory/19086 | # What experiment would disprove string theory?
I know that there's big controversy between two groups of physicists:
1. those who support string theory (most of them, I think)
2. and those who oppose it.
One of the arguments of the second group is that there's no way to disprove the correctness of the string theory... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/20142/find-the-unit-vector-of-a-three-dimensional-vector?answertab=oldest | # Find the Unit Vector of a Three Dimensional Vector
How can I find the unit vector of a three dimensional vector? For example, I have a problem that I am working on that tells me that I have a vector $\hat{r}$ that is a unit vector, and I am told to prove this fact:
$\hat{r} = \frac{2}{3}\hat{i} - \frac{1}{3}\hat{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": 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/1963/how-large-should-a-diffie-hellman-p-be/1964 | # How large should a Diffie-Hellman p be?
In a Diffie-Hellman exchange, the parties need to agree on a prime `p` and a base `g` in order to continue. Assuming some application that's going to want to initiate handshakes with some large portion of its users, each of which only need to be realistically secure for a few ... | {"extraction_info": {"found_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... |
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