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http://www.physicsforums.com/library.php?do=view_item&itemid=9
Physics Forums Menu Home Action My entries Defined browse Select Select in the list MathematicsPhysics Then Select Select in the list Then Select Select in the list Search perfect numbers Definition/Summary A pe...
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http://math.stackexchange.com/questions/140718/topological-properties-of-a-3-torus?answertab=active
# Topological Properties of a 3-Torus A 3-torus can be constructed by starting with a cube and then conceptually joining the top and bottom, the right and left, and the front and back. In such a space, an object which travels out to the left hand side of the cube instantly reappears at the right hand side (and similar...
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http://mathoverflow.net/questions/81443?sort=oldest
## Fastest Algorithm to Compute the Sum of Primes? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Can anyone help me with references to the current fastest algorithms for counting the exact sum of primes less than some number n? I'm specifically curious about...
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http://math.stackexchange.com/questions/65180/what-is-it-that-makes-this-proof-about-rational-rectangles-work-fundamentally/65182
# What is it that makes this proof about rational rectangles work fundamentally? I saw this problem several years ago, and I discovered a solution to it. I've since learned a somewhat more efficient solution based on the same idea. Call a rectangle in the $(x,y)$ plane rational if it has sides parallel to the axes an...
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http://mathoverflow.net/questions/31065/applications-of-non-reductive-git
## Applications of non-reductive GIT ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Geometric invariant theory works well when the algebraic group $G$ acting on a variety is reductive. There has been recent work by Doran and Kirwan here and here to find a can...
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http://mathhelpforum.com/discrete-math/99145-valid-subsets-reccurence-relation-print.html
# The valid subsets and reccurence relation Printable View • August 24th 2009, 10:36 PM Snowboarder The valid subsets and reccurence relation Hi all. I'm struggling with the one quite hard question for me: Let I_n = {1,2,3,...,n} for n belong to N. A valid subset of I_n does not contain two numbers of the form x, x+...
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http://mathhelpforum.com/pre-calculus/94604-solved-solve-logaritmic-equation-terms-natural-log.html
# Thread: 1. ## [SOLVED] Solve Logaritmic Equation in terms of natural log I need to solve the following equation: 10^(2X+3) = 280 To express in logarithmic, I know I need to do the following: log(10)^280 = 2X+3 At this point I'm not sure where to go. I can move the three over to the left: (log(10)^280) - 3 = 2X...
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http://mathoverflow.net/questions/20919/polish-spaces-in-probability/122393
## Polish spaces in probability ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Probabilist are very often working with Polish spaces, though this is not always very clear where this assumption is needed. question: what can go wrong when doing probability on ...
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http://mathhelpforum.com/discrete-math/118396-cardinality-set-complex-numbers.html
# Thread: 1. ## The cardinality of the set of complex numbers I know $|\mathbb{C}|=|\mathbb{R}|$, but I am not exactly sure how to do a formal proof. I know that every element in $\mathbb{C}$ can be written as $a+bi, \, a,b\in \mathbb{R}$. So every element in $\mathbb{C}$ can be expressed as $(a,b) \in \mathbb{R \tim...
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http://cms.math.ca/Reunions/ete12/abs/cgr.html
Réunion d'été SMC 2012 Hôtels Regina Inn et Ramada (Regina~Saskatchewan), 2 -4 juin 2012 www.smc.math.ca//Reunions/ete12 Géométrie complexe et domaines reliés Org: Tatyana Barron (Western) et Eric Schippers (Manitoba) [PDF] Poincare series map on open Riemann surfaces  [PDF] Poincare series is a classic technique t...
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http://tcsmath.wordpress.com/2010/02/
# tcs math – some mathematics of theoretical computer science ## February 21, 2010 ### The need for non-linear mappings Filed under: Math, Open question — Tags: Dimension reduction, embeddings of finite metric spaces, non-linear mappings — James Lee @ 1:43 pm In the last post, I recalled the problem of dimension re...
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http://mathoverflow.net/questions/26256?sort=newest
## Gauss-Bonnet Theorem for Graphs? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) One can define the Euler characteristic χ for a graph as the number of vertices minus the number of edges. Thus an n-cycle has χ = 0 and K4 has χ = –2. Is there an analog for t...
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http://mathoverflow.net/questions/27220/how-to-solve-a-transcendental-equation
## How to solve a transcendental equation? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) What is the best way to solve an equation of the form $x ^ x = 5$ by hand? I know about approximations using Newton's method etc using a computer, but what I want to kn...
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http://mathhelpforum.com/calculus/161783-sketch-region-integration-change-order-integration.html
# Thread: 1. ## sketch the region of integration and change the order of integration. Heres the problem: HAving a hard time understanding what this question is asking. When they say change the order of integration, it seems like i am supposed to integrate dx with the 4x to 4 bound and integrate dy with the 0 to 1 bo...
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http://math.stackexchange.com/questions/158832/an-upper-bound-for-lambda-a-1
An upper bound for $\|(\lambda-A)^{-1}\|$? Let $A$ be a k-by-k matrix and $\sigma(A)$ its spectrum, or the collection of eigenvalues of $A$. If we know $\lambda\notin\sigma(A)$, then $\lambda$ is at a positive distance to all points in the spectrum since the latter is compact. I wonder whether there is a bound for t...
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http://mathoverflow.net/questions/71514/hausdorff-dimension-of-inverse-images/71520
## Hausdorff dimension of inverse images. ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Let $f: \mathbb{R}^d \to \mathbb{R}$ be a continuous function. Let $t \in (\inf(f), \sup(f))$ and define $C = f^{-1} (t)$. Is it true that the Hausdorff dimension of C is...
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http://mathoverflow.net/revisions/25883/list
Return to Answer 2 added 1039 characters in body Here is a counterexample: A torus embedded in $\mathbb{R}^3$ has a fundamental class in $H_2$, but there are no points with neighborhoods homotopy equivalent to $S^2$. It might be interesting to try to formulate a condition for the homology of pairs $(X,Y)$. Edit: I ...
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http://math.stackexchange.com/questions/252644/evaluate-the-limit-without-lhospitals-rule
# Evaluate the limit without l'Hospital's rule Let $$f(x)=\frac{x}{x}$$ be defined on $\mathbb R\setminus \{0\}$. Show that $$\lim\limits_{x\to 0}f(x) = 1$$ without using l'Hospital's rule. - 3 You do not need any approach... Just tell: how much is $x$ divided by $x$? – Godot Dec 6 '12 at 22:57 ## 3 Answers If $x ...
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http://physics.stackexchange.com/questions/tagged/operators
# Tagged Questions The operators tag has no wiki summary. 2answers 34 views ### Quantum Mechanical Operators in the argument of an exponential In Quantum Optics and Quantum Mechanics, the time evolution operator $$U(t,t_i) = \exp\left[\frac{-i}{\hbar}H(t-t_i)\right]$$ is used quite a lot. Suppose $t_i =0$ for simpl...
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http://regularize.wordpress.com/tag/abstract/
# regularize Trying to keep track of what I stumble upon July 26, 2012 ## Estimating unknown sparsity, sparse signal processing and proximal Newton-type methods Posted by Dirk under Math, Optimization, Signal and image processing, Sparsity | Tags: abstract, arxiv, compressed sensing, papers, sparsity | In this pos...
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http://math.stackexchange.com/questions/19694/what-is-the-most-frequent-number-of-edges-of-voronoi-cells-of-a-large-set-of-ran?answertab=active
# What is the most frequent number of edges of Voronoi cells of a large set of random points? Consider a large set of points with coordinates that are uniformly distributed within a unit-length segment. Consider a Voronoi diagram built on these points. If we consider only non-infinite cells, what would be (if any) the...
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http://mathhelpforum.com/statistics/63364-finding-expected-value-standard-deviation-help-please.html
# Thread: 1. ## Finding Expected Value and Standard deviation...Help please :( The question has a table that contain shows the approximate number of males of Hispanic origin employed in the U.S. in 2005 broken down by age group Age: 15-24.9 25-54.9 55-64.9 Employment (thousands):16,000 13,000 1,600 It then asks tha...
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http://mathoverflow.net/questions/87708/partitions-of-unity
## Partitions of Unity ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Fix a metric $g$ on a smooth, closed manifold $\mathcal{M}$. Take a finite subcover of the manifold from its atlas. Is it true that any smooth partition of unity subordinate to this cover h...
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http://math.stackexchange.com/questions/176329/when-is-a-quasi-projective-variety-affine
# When is a quasi-projective variety affine? By an affine variety I mean a variety that is isomorphic to some irreducible algebraic set in $\mathbb A^n$ and by a quasi-projective variety I mean a locally closed subset of $\mathbb P^n$, with the usual Zariski topology and structure sheaf. (I am not quite familiar with ...
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http://physics.stackexchange.com/questions/16994/total-resistance-of-infinite-resistor-grid/17020
# Total Resistance of Infinite Resistor Grid? The problem of the infinite resistor grid is very common. The solution for the resistance between any 2 nodes in an infinite resistor lattice is all over the internet. My question is somewhat similar but more pragmatic. If we had a grid that was very large but yet finite....
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http://mathoverflow.net/questions/75646?sort=oldest
## “Duals” of Lindenbaum algebras ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) From Wikipedia I learn: The Lindenbaum algebra A of a theory T consists of the equivalence classes of sentences of T. The operations in A are inherited from those in T. If the...
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http://unapologetic.wordpress.com/2012/08/13/ideals-of-lie-algebras/?like=1&source=post_flair&_wpnonce=b0679ce6ea
# The Unapologetic Mathematician ## Ideals of Lie Algebras As we said, a homomorphism of Lie algebras is simply a linear mapping between them that preserves the bracket. I want to check, though, that this behaves in certain nice ways. First off, there is a Lie algebra $0$. That is, the trivial vector space can be gi...
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http://mathhelpforum.com/calculus/167502-telescopic-series.html
# Thread: 1. ## telescopic series sigma k=2 to infinity, 1/k^2-1 how do you break up the k^2-1 into a minus part? i cant do it theres no partial fraction form i can ffind? please help with a little bit 2. Originally Posted by mathcore sigma k=2 to infinity, 1/k^2-1 how do you break up the k^2-1 into a minus part? ...
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http://mathhelpforum.com/calculus/23377-polynomial-roots.html
# Thread: 1. ## Polynomial Roots If A Polynomial Of Degree Greater Than Or Equal To Two With Coefficient From The Set Of Real Numbers Has All Roots In Set Of Real Numbers.then Prove That All The Roots Of Its Derivatives Are Also Real Numbers. 2. Originally Posted by sehrishqau If A Polynomial Of Degree Greater Than ...
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http://math.stackexchange.com/questions/200689/how-to-simplify-log-base-2-and-log-base-4/200692
# how to simplify log base 2 and log base 4 How do I simplify the following expression: $$\log_2(2x+1) - 5\log_4(x^2) + 4\log_2(x)$$ - ## 2 Answers $\log_2(2x+1)-5\log_4x^2+4\log_2x$ $=\log_2(2x+1)+\log_2x^4-5\frac{\log_yx^2}{\log_y4}$ as $\log a+ \log b=\log ab,m\log a=\log a^m$ and $\log_yz=\frac{\log_xz}{\log...
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http://nrich.maths.org/7140
### 14 Divisors What is the smallest number with exactly 14 divisors? ### Summing Consecutive Numbers Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way? ### Rule of Three If it takes four men one ...
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http://mathhelpforum.com/pre-calculus/164319-proving-z-w-z-w.html
# Thread: 1. ## Proving ||z|-|w|| <= |z-w| hi, I stumbled upon a simple demonstration but i can´t solve it: ||z|-|w|| <= |z-w| Can someone help me? Pedro 2. Originally Posted by Pedro hi, I stumbled upon a simple demonstration but i can´t solve it: ||z|-|w|| <= |z-w| Can someone help me? Pedro This is the reve...
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http://math.stackexchange.com/questions/7324/transformation-of-random-variables/7326
# Transformation of Random Variables Suppose $f_{X}(x) = xe^{-x^2/2}$ for $x>0$ and $Y = \ln X$. Find the density function for $Y$. So we want to find $P(Y \leq y)$. This is the same thing as $P(\ln X \leq y)$ or $P(X \leq e^{y})$. Thus $f_{Y}(y) = f_{X}(e^y)$? Or does $f_{Y}(y) = F_{X}(e^y)$ since $P(X \leq x) = F_{X...
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http://mathoverflow.net/questions/1931/bimodules-in-geometry/1943
## Bimodules in geometry ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Grothendieck's approach to algebraic geometry in particular tells us to treat all rings as rings of functions on some sort of space. This can also be applied outside of scheme theory (e.g...
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http://math.stackexchange.com/questions/295959/is-this-sloppy-writing-for-limits?answertab=active
# Is this sloppy writing for limits? Please note that I am not asking you to compute or show me how to do this limit. I am asking how to write out a clean and formal solution that is free of any error, ambiguity, or sloppiness. Given $$\lim\limits_{(x,y) \to (0,0)} \dfrac{3x^2 y}{x^2 + y^2}$$, find its limit So find...
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http://math.stackexchange.com/questions/4406/difference-or-relation-between-inference-reasoning-deduction-and-induction/6536
# Difference or relation between Inference, Reasoning, Deduction, and Induction? What is the precise difference or relation between these terms in logic: Inference, Reasoning, Deduction, and Induction? - This does not appear to be a mathematical question. There are not formal definitions of "inference" and "reasoning...
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http://nrich.maths.org/1310
### Bendy Quad Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load. ### Long Short A quadrilateral inscribed in a unit circle has sides of lengths s1, s2, s3 and s4 where s1 ≤ s2 ≤ s3 ≤ s4. Fi...
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http://physics.stackexchange.com/questions/53558/what-would-happen-if-large-hadron-collider-would-collide-electrons
What would happen if Large Hadron Collider would collide electrons? After some reading about the Large Hadron Collider and it's very impressive instruments to detect and investigate the collision results, there is a remaining question. What would happen if the scientists would use leptons instead of hadrons? Especia...
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http://mathhelpforum.com/calculus/209818-forecast-cubic-spline.html
# Thread: 1. ## Forecast with cubic spline Hi all, I have a simple question: is it possible to make forecast with cubic spline? And, if yes, how? Frecast, for me, meens that I can understend the value of my interpolation function OUTSIDE the data field that I have. Thank you, every help will be appreciated. Igor 2...
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http://www.physicsforums.com/showthread.php?p=4229914
Physics Forums ## singular matrix theory hey guys given $Ax=B$ where A is a square matrix and x and B are vectors, can anyone tell me why a singular matrix (that is, the determinant = 0) implies one of two situations: infinite solutions or zero solutions? a proof would be nice. i read through pauls notes but there w...
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http://unapologetic.wordpress.com/2008/05/02/limits-superior-and-inferior/?like=1&source=post_flair&_wpnonce=2c354f29b9
# The Unapologetic Mathematician ## Limits Superior and Inferior As we look at sequences (and nets) of real numbers (and more general ordered spaces) a little more closely, we’ll occasionally need the finer notion of a “limit superior” (“limit inferior”). This is essentially the largest (smallest) value that a sequen...
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http://mathoverflow.net/questions/27651?sort=newest
## Can SAT be solved in time n^k, for a specific k? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) The P vs NP problem is open. How about the following questions--Can SAT be done in $n^k$ time for some specific $k$? Why do I ask these questions? Ben-David an...
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http://www.physicsforums.com/showthread.php?t=215220
Physics Forums ## Weak force I encountered an argument that says that the weak mediators must be massive because the weak force is short range, by the uncertainty principle. But isn't the uncertainty principle relates the uncertainty in mass, $$\delta m$$ and $$\delta t$$ and not the absolute value of the mass? Phys...
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http://stochastix.wordpress.com/2011/07/18/linear-dynamical-systems-over-finite-rings/
Rod Carvalho Linear dynamical systems over finite rings Consider the following linear dynamical system (example 3.4 in [1]) $\left[\begin{array}{cc} x_1^+\\ x_2^+\end{array}\right] = \left[\begin{array}{cc} 2 & 3\\ 1 & 0\\\end{array}\right] \left[\begin{array}{c} x_1 \\ x_2\\\end{array}\right]$ where the state vect...
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http://en.wikipedia.org/wiki/Peltier_effect
# Thermoelectric effect (Redirected from Peltier effect) This article is about the thermoelectric effect as a physical phenomenon. For applications of the thermoelectric effect, see thermoelectric materials and thermoelectric cooling. Thermoelectric effect Principles • Thermoelectric effect • Seebeck effect • Peltier ...
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http://mathhelpforum.com/differential-geometry/79245-principles-mathematical-analysis-ch2-basic-topology.html
# Thread: 1. ## Principles of Mathematical Analysis - Ch2 Basic Topology Hi, Here I am reading Rudin's Book(3rd). I encountered some problems in Theorem 2.20, page 32. Theorem 2.20 If p is a limit point of a set E, then every neighborhood of p contains infinitely many points of E. By intutition or imagination, I c...
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http://math.stackexchange.com/questions/tagged/complex-geometry+general-topology
# Tagged Questions 1answer 50 views ### Fundamental group of the following disc What is the fundamental group of the following space in $\mathbf C^n$? This is the topological space given by \{(x_1,\ldots,x_n)\in \mathbf C^n-\{0\} : \vert x_1\vert < 1, \ldots, \vert x_n\vert ... 2answers 126 views ### Why is $x^2$ +...
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http://terrytao.wordpress.com/tag/coboundaries/
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 ‘coboundaries’ tag. ## Cohomology for dynamical systems 21 December, 2008 in expository, math.AT, math.DS | Tags: cob...
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http://mathhelpforum.com/calculus/88735-exponential-differentiation.html
# Thread: 1. ## exponential differentiation Hi, I need to show that y=(Ax+B).e^3x is a solution to y''-6y'+9y=0 I'm getting y'=e^3x(3Ax+3B+A) y''=3e^3x(2A+3Ax+3B) When I sub these values back into the condition above its not working out. Thank you 2. Originally Posted by slaypullingcat Hi, I need to show that y=...
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http://mathhelpforum.com/advanced-algebra/87989-group-theory-sylow-theory-simple-groups.html
# Thread: 1. ## Group Theory - Sylow Theory and simple groups I'm unsure on the following points: (i) Prove that if a group G has order $p^nq$, where p and q are prime numbers and $p > q$, then G contains a unique Sylow p-Subgroup. Hence conclude that there are no simple groups of orders 55, 57 or 58. (ii) Prove th...
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http://mathoverflow.net/questions/96661/the-richardson-theorem-and-the-base-identities-problem/96801
## the Richardson theorem and the base identities problem ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) In the fields related to school mathematics there is some acitivity on proving (or disproving) deducibility/decidability for some classes of school identi...
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http://math.stackexchange.com/questions/181293/are-compacta-in-a-complete-infinite-dimensional-normed-space-nowhere-dense
# Are compacta in a complete infinite dimensional normed space nowhere dense? Let $X$ be an infinite dimensional Banach space. I want to show that any compact subset $\varnothing\neq A\subset X$ is nowhere dense. I've been able to prove the statement for $X=(C[0,1],\|\cdot\|_\infty)$ by using an Arzelà-Ascoli argumen...
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http://mathoverflow.net/questions/118208?sort=votes
## Intuitive meaning of Double Commutant Theorem ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Is there any intuitive explanation of the Double Commutant Theorem for Von Neumann Algebras? By intuitive I mean in terms of Quantum Mechanics. For example, dualit...
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http://mathoverflow.net/questions/12461/changing-coordinates-so-that-one-riemannian-metric-matches-another-up-to-second
Changing coordinates so that one Riemannian metric matches another, up to second derivatives Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Let $g$ and $g'$ be two $C^2$-smooth Riemannian metrics defined on neighborhoods $U$ and $U'$ of $0$ in $\mathbb R^2$, resp...
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http://math.stackexchange.com/questions/105668/why-are-modules-called-modules
Why are modules called modules? I know that a module is a generalization of a vector space, but I would like to know why are modules called modules? - 2 – Dylan Moreland Feb 4 '12 at 15:53 1 Answer The name "module" was introduced by Dedekind in his work on ideals and number fields. You can find both his paper (in...
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http://math.stackexchange.com/questions/279569/getting-a-feel-for-the-transformation-a-on-vector-x-which-lies-outside-of-any-ei?answertab=active
# Getting a feel for the transformation A on vector x which lies outside of any eigenspace In one of his videos, after 13:25 Sal starts to talk about the interpretation of the eigenvectors and how they relate to a vector $x$ being transformed by the matrix $A$. He then goes through showing what happens when $x$ would...
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http://mathoverflow.net/questions/78994?sort=oldest
## Where do the real analytic Eisenstein series live? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) In obtaining the spectral decomposition of $L^2(\Gamma \backslash G)$ where $G=SL_2(\mathbb{R})$, and $\Gamma$ is an arithmetic subgroup (I am satisfied with ...
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http://unapologetic.wordpress.com/2008/07/18/unsolvable-inhomogenous-systems/?like=1&_wpnonce=67418a1937
The Unapologetic Mathematician Unsolvable Inhomogenous Systems We know that when an inhomogenous system has a solution, it has a whole family of them. Given a particular solution, it defines a coset of the subspace of the solutions to the associated homogenous system. And that subspace is the kernel of a certain line...
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http://math.stackexchange.com/questions/249181/is-kappa-lambda-2-lambda2-le-kappa-lambda-lambda-infinite-valid-i?answertab=active
# Is $\kappa^\lambda=2^\lambda$($2 \le \kappa<\lambda$,$\lambda$ infinite) valid in set models of ZF? Let $2 \le \kappa<\lambda$(both cardinal numbers), in which $\lambda$ is infinite. Then these formula as follows hold where in ZFC: 1. $\lambda+\kappa=\lambda$ 2. $\lambda\cdot\kappa=\lambda$ 3. $\kappa^\lambda=2^\...
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http://mathoverflow.net/questions/102964/convergence-of-moments-implies-convergence-to-normal-distribution
## Convergence of moments implies convergence to normal distribution ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) I have a sequence ${X_n}$ of random variables supported on the real line, as well as a normally distributed random variable $X$ (whose mean and...
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http://stats.stackexchange.com/questions/5690/how-to-compare-median-survival-between-groups
# How to compare median survival between groups? I'm looking into median survival using Kaplan-Meier in different states for a type of cancer. There are quite big differences between the states. How can i compare the median survival between all the states and determine which ones are significantly different from the m...
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http://physics.stackexchange.com/questions/34573/turning-jupiter-into-a-star?answertab=active
Turning Jupiter into a star So, I've heard from various works of science fiction about the prospect of turning Jupiter into a star. From what I know about the physics of such a task, it would require somehow condensing Jupiter into something quite a bit smaller than it currently is, such that the pressure is sufficien...
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http://physics.stackexchange.com/questions/24380/centripetal-force-of-a-rotating-rigid-body/24383
# Centripetal force of a rotating rigid body? Consider someone pushing a roundabout in a playground. Initially the roundabout is stationary, but when it is pushed, it rotates with increasing rotational speed. The force of the push is balanced by the reaction force exerted by the support at the centre of the roundabou...
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http://terrytao.wordpress.com/tag/lebesgue-dominated-convergence-theorem/
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 ‘Lebesgue dominated convergence theorem’ tag. ## 245A, Notes 3: Integration on abstract measure spaces, and the conver...
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http://alanrendall.wordpress.com/2012/01/
# Hydrobates A mathematician thinks aloud ## Archive for January, 2012 ### Modelling Dictyostelium aggregation, yet again January 29, 2012 In the last post I discussed the second chapter of the book ‘La Vie Oscillatoire’ which is concerned with glycolytic oscillations. The third chapter is on calcium oscillations,...
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http://nrich.maths.org/81/index?nomenu=1
## 'Bean Bags for Bernard's Bag' printed from http://nrich.maths.org/ ### Show menu Some years ago I suddenly had to do some maths with some boys who were a bit turned off about it. If it had been today in England they would have said, "It's not cool!" There were two small PE hoops nearby and some small bean bags. I...
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http://physics.stackexchange.com/tags/potential/new
# Tag Info ## New answers tagged potential 0 ### The potentiality of the electric field Ok, let's consider $\vec{r} \vec{dr}$, it is equal to $|\vec{r}||\vec{dr}|_\vec{r}$ where $|\vec{dr}|_\vec{r}$ is projection of $\vec{dr}$ on $\vec{r}$. If you draw $\vec{r}$ and a small (remember, you need infinitesimal!) $\vec...
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http://www.leancrew.com/all-this/2011/12/omnigraphsketcher-not-yet/
# And now it’s all this ## I just said what I said and it was wrong. Or was taken wrong. « WiFi Woes with Dan Benjamin # OmniGraphSketcher - not yet December 11th, 2011 at 8:50 pm by Dr. Drang The other day I was listening to the latest Mac Power Users podcast, the one with Horace Dediu as guest,1 and I heard Davi...
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http://mathoverflow.net/questions/30742/limit-probability/30753
## Limit probability ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) You start with a bag of N recognizable balls. You pick them one by one and replace them until they have all been picked up at least once. So when you stop the ball you pick has not been picke...
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http://math.stackexchange.com/questions/208075/extracting-an-almost-independent-large-subset-from-a-pairwise-independent-set?answertab=votes
# Extracting an (almost) independent large subset from a pairwise independent set of Bernoulli variables Let $n>1$, and let $X_1,X_2, \ldots ,X_n$ be non-constant random variables with values in $\lbrace 0,1 \rbrace$. Let us say that a subset of variables $X_{i_1},X_{i_2}, \ldots,X_{i_d}$ is complete if the vector $\o...
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http://mathhelpforum.com/pre-calculus/130855-geometrical-properties-ellipses.html
# Thread: 1. ## Geometrical Properties of Ellipses Hi. 1. If M and M' are the points where the tangent at P on the ellipse meets the tangents at the ends of the major axis, then MM' subtends a right angle at either focus. Show that the line y = mx + c touches the ellipse x^2/a^2 + y^2/b^2 = 1 when c = +/- sqrt[a^2m^...
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http://physics.stackexchange.com/questions/2175/is-it-possible-for-information-to-be-transmitted-faster-than-light-by-using-a-ri/13299
# Is it possible for information to be transmitted faster than light by using a rigid pole? Is it possible for information (like 1 and 0s) to be transmitted faster than light? For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them starts pulling and pushing on ...
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http://mathoverflow.net/questions/73785?sort=newest
Drawing natural numbers without replacement. Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Suppose we start with an initial probability distribution on $\mathbb{N}$ that gives positive probability to each $n$. Let's call this random variable $X_1$ so we have $P(...
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http://mathhelpforum.com/calculus/189517-finding-region-positive-negative-regions.html
# Thread: 1. ## Finding region positive/negative regions. Hi there. I am given these functions and I want to find out in which areas they are positive or negative. x^y - 1 |x+y| - |x-y| so the way i tried the first one is i set the function x^y-1 = c and take c = 0, simplifying i get y log (x) = 0. What do i do n...
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http://mathhelpforum.com/calculus/212103-asymptotic-analysis-wkb-approx.html
# Thread: 1. ## Asymptotic analysis to the WKB approx Hi i have the WKB approx of: $u_{+} = \sqrt{1-\frac{bm}{f}}e^{i\int f_{k} dt} + \sqrt{1+\frac{bm}{f}}e^{-i\int f_{k} dt}$ to the differential equation: $\frac{d^{2}u_{+}}{dt^2} + [f_{k}^{2} + i(\frac{d(bm)}{dt})]u_{+} =0$ This equation can be written as: $\frac{...
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http://math.stackexchange.com/questions/tagged/exponentiation+roots
Tagged Questions 1answer 194 views Why use radical notation instead of rational exponents? I'm helping my younger sister for her math class. She has recently been taught integer exponents, and has starteed studying radicals (mainly square roots). The next topic will be rational exponents, ... 3answers 324 views How...
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http://mathoverflow.net/questions/7650/generalizations-of-planar-graphs/57849
## Generalizations of Planar Graphs ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) This is a follow up to Harrison's question: why planar graphs are so exceptional. I would like to ask about (and collect answers to) various notions, in graph theory and beyond...
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http://physics.stackexchange.com/questions/916/imagine-a-long-bar-floating-in-space-what-force-does-it-exert-on-itself-in-the/960
# Problem If you had a long bar floating in space, what would be the compressive force at the centre of the bar, due to the self-weight of both ends? Diagram - what is the force at point X in the middle of the bar?: ````<----------------------L--------------------->, total mass M =======================X============...
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http://crypto.stackexchange.com/questions/1247/101-advanced-access-content-system-aacs-and-subset-difference-techniques-for/1256
# 101: Advanced Access Content System (AACS) and Subset Difference techniques for Broadcast Encryption I'm trying to get a grasp on AACS and Subset Difference for a project I'm working on and am having a hard time coming up with a technically valid layman explanation, let alone implementation. Is it fair to say that ...
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http://mathhelpforum.com/calculators/86272-should-i-upgrade-83-89-next-semester-print.html
Should I upgrade from an 83 to an 89 for next semester? Printable View • April 28th 2009, 12:37 PM sinewave85 Should I upgrade from an 83 to an 89 for next semester? Right now I have a Ti 83 that I have had since eighth grade. At this point (wrapping up my first semester of Calculus) I use it infrequently -- mostly t...
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http://math.stackexchange.com/questions/174779/if-phi-in-c1-c-mathbb-r-then-lim-n-int-mathbb-r-frac-sinnxx-p
# If $\phi \in C^1_c(\mathbb R)$ then $\lim_n \int_\mathbb R \frac{\sin(nx)}{x}\phi(x)\,dx = \pi\phi(0)$. Let $\phi \in C^1_c(\mathbb R)$. Prove that $$\lim_{n \to +\infty} \int_\mathbb R \frac{\sin(nx)}{x}\phi(x) \, dx = \pi\phi(0).$$ Unfortunately, I didn't manage to give a complete proof. First of all, I fixed $\v...
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http://physics.stackexchange.com/tags/subatomic/hot?filter=all
# Tag Info ## Hot answers tagged subatomic 39 ### What does it mean for two objects to “touch”? Wow, this one has been over-answered already, I know... but it is such a fun question! So, here's an answer that hasn't been, um, "touched" on yet... :) You sir, whatever your age may be (anyone with kids will know what ...
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http://mathhelpforum.com/algebra/9994-show-inequality-x-2-a.html
# Thread: 1. ## Show Inequality X^2 > a If a > 0, show that the solution set of the inequality x^2 > a consists of all numbers x for which -(sqrt{a}) < a (sqrt{a}). Okay...what exactly is the question asking in simple math terms? I don't follow the logic behind this sort of reasoning. 2. Originally Posted by symme...
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http://medlibrary.org/medwiki/Gelfand%E2%80%93Naimark%E2%80%93Segal_construction
Gelfand–Naimark–Segal construction Welcome to MedLibrary.org. For best results, we recommend beginning with the navigation links at the top of the page, which can guide you through our collection of over 14,000 medication labels and package inserts. For additional information on other topics which are not covered by o...
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http://physicspages.com/2011/07/07/doppler-effect/
Notes on topics in science ## Doppler effect Required math:vectors, algebra Required physics: basics of relativity The world line of a photon is a null line, so any vector tangent to a photon’s world line is a null vector. This means in particular that a four-velocity cannot be defined for a photon, since all four-...
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http://mathoverflow.net/revisions/73658/list
## Return to Answer 1 [made Community Wiki] I was trying to write this as a comment, but the place is too small. According to the intro of http://www.jstor.org/stable/1428226, the perimeter of the typical cell is in $\mathbb{R}^2$: $4/\sqrt{\lambda}$ ($\lambda$: intensity of the Poisson point process). It means that...
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http://math.stackexchange.com/questions/97309/legendre-symbol-and-from-mathbbz-p-mathbbz?answertab=active
# Legendre symbol and from $\mathbb{Z}/p\mathbb{Z}$ Let's define map $$\Phi:\mathbb{Z}/p\mathbb{Z}\to\mathbb{Z}/p\mathbb{Z}$$ as $$\Phi(x) = x^{(p-1)/2}.$$ It's easy to proof that $$\Phi(x) = 1,~~~\text{iff}~~~x = b^2~~~\text{for some}~~~b\in\mathbb{Z}/p\mathbb{Z}$$ and $$\Phi(0) = 0.$$ And consider Legendre symbol $$...
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http://mathhelpforum.com/algebra/191018-reciprocal-quadratic-function.html
# Thread: 1. ## Reciprocal of a Quadratic Function Say you have a function f(x)=1/(x^2+6x+11). Would you have to complete the square to figure out the vertex of the parabola in the denominator(then sub in the x-value in the function to figure out the vertex in the rational function), or is there an easier way to draw...
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http://mathematica.stackexchange.com/questions/tagged/diophantine-equations?sort=votes&pagesize=15
# Tagged Questions Questions on the use of Mathematica to find integer/rational solutions to equations. 6answers 395 views ### How to find lattice points on a line segment? How do I find points on the line segment joining {-4, 11} and {16, -1} whose coordinates are positive integers? 2answers 227 views ### Is ther...
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http://mathoverflow.net/questions/17803?sort=oldest
## What is the infinite-dimensional-manifold structure on the space of smooth paths mod thin homotopy? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) This question is motivated by the recent paper An invitation to higher gauge theory by Baez and Huerta, and t...
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http://math.stackexchange.com/questions/257946/how-to-solve-x1-2-x1-3-0/257948
# How to solve $x^{1/2}-x^{1/3} = 0$ How can I solve the following equation? I really can't figure out how to solve it: $x^{1/2}-x^{1/3} = 0$ Thank you. - 2 Please, try to make the title of your question more informative. E.g., Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question abo...
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http://mathoverflow.net/questions/10123?sort=newest
## presentation for GL(n,K) ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) let $K$ be a field, $n \geq 1$. denote $E_{i,j}$ the elementary matrix having $1$ on the diagonale and in the entry $(i,j)$, and $E_i(a)$ the elementary matrix $diag(1,...,a,...,1)$. y...
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http://pediaview.com/openpedia/Ising_model
# Ising model Statistical mechanics • NVE Microcanonical • NVT Canonical • µVT Grand canonical • NPH Isoenthalpic–isobaric • NPT Isothermal–isobaric • µVT Open statistical Models • Debye • Einstein • Ising Scientists The Ising model (; German: ), named after the physicist Ernst Ising, is a mathematical model of ferro...
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http://mathoverflow.net/questions/41416?sort=newest
## Glueing triangulated categories ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Hello! Given a triangulated category, one can look for semiorthogonal decompositions into (simpler?) triangulated subcategories. I'd like to know if there's a way to attack th...
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http://mathoverflow.net/questions/56378/semisimplicity-of-etale-cohomology-representations
## Semisimplicity of étale cohomology representations ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Let $K$ be a number field and $G=Gal(\overline{K}/K)$ the absolute Galois group of $K$. Let $\ell$ be a prime number. Let $A/K$ be an abelian variety. Then t...
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http://mathoverflow.net/questions/76126/lifting-the-isomorphisms-between-abelian-schemes-over-pd-thickenings/76132
## lifting the isomorphisms between abelian schemes over PD thickenings ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Assume that X and Y are abelian schemes (or even abelian varieties) over a base T. If $\ S --> T$ is a PD nilpotent thickening (i.e. the ide...
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http://physics.stackexchange.com/questions/56239/when-i-ride-my-bike-does-half-of-the-energy-go-into-the-earth/56244
# When I ride my bike, does half of the energy go into the earth? When I ride my bike, does half of the energy go into the earth because of Newton's third law? Does the energy in the earth transfer into heat upon my brakes when I utilize them? If the earth was 2000 times less massive than it is, and I applied the sam...
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http://mathoverflow.net/questions/39960/geodesic-metrics-that-admit-dilatation-at-each-point
## Geodesic metrics that admit dilatation at each point ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Consider the class of geodesic metrics $g$ on manifolds, that have the following property: for each point $x$ there exists a neighbourhood $U_x$ and a smoot...
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http://cms.math.ca/Reunions/hiver12/abs/mpr
Réunion d'hiver SMC 2012 Fairmont Le Reine Elizabeth (Montréal), 7 - 10 décembre 2012 Physique mathématique - matrices aléatoires et systèmes intégrables Org: Marco Bertola et Dmitry Korotkin (Concordia) [PDF] MARCO BERTOLA, Concordia University Universality in Unitary Random matrix models  [PDF] It is very well kn...
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http://physics.stackexchange.com/questions/tagged/waves+wavelength
# Tagged Questions 2answers 135 views ### De Broglie wavelength, frequency and velocity - interpretation Two fundamental equations regarding wave-particle duality are: $$\lambda = \frac{h}{p}, \\ \nu = E/h .$$ We talk about de Broglie wavelength, is it meaningful to talk about de Broglie frequency ... 1answer 212 vi...
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