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http://mathoverflow.net/questions/9786?sort=votes
## Use of the word “data” not in the statistical sense [closed] ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Occasionally I see the use of the word "data" in definitions. For instance, one definition of an exact sequence starts off by saying, "An exact sequ...
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http://math.stackexchange.com/questions/126013/taxicab-distance-city-block-distance-manhattan-distance?answertab=oldest
# Taxicab distance , city block distance, Manhattan distance Is defined in Wikipedia http://en.wikipedia.org/wiki/Taxicab_geometry But I saw it as another way of calculating it for vectors and similar $$d = \mathrm{num}_1 + \mathrm{num}_2 - 2 \times \mathrm{intersect}$$ • $d$= distance • $\mathrm{num}_1$ = number o...
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http://www.physicsforums.com/showthread.php?t=148460
Physics Forums ## Canonical transformation 1. The problem statement, all variables and given/known data Consider a canonical transformation with generating function $$F_2 (q,P) = qP + \epsilon G_2 (q,P)$$, where $$\epsilon$$ is a small parameter. Write down the explicit form of the transformation. Neglecting terms...
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http://math.stackexchange.com/questions/tagged/powers+inequality
# Tagged Questions 2answers 103 views ### pow$(X,Y)$ $>$ pow$(Y,X)$, if $X<Y$. How can we proof following? if $X < Y$, then: $X^{Y} > Y^{X}$ , Where X, and Y are integers. Also $X,Y > 1$. Except a special case $2^{3} < 3^{2}$. I think for other ... 1answer 63 views ### Summation of powers inequality Can anyone pro...
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http://math.stackexchange.com/questions/178214/a-group-of-order-108-has-a-proper-normal-subgroup-of-order-geq-6
# A group of order $108$ has a proper normal subgroup of order $\geq 6$. Problem: Let $G$ be a group of order $108 = 2^23^3$. Prove that $G$ has a proper normal subgroup of order $n \geq 6$. My attempt: From the Sylow theorems, if $n_3$ and $n_2$ denote the number of subgroups of order $27$ and $4$, respectively, in ...
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http://medlibrary.org/medwiki/Signal-to-noise_ratio
# Signal-to-noise ratio 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 our database...
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http://www.physicsforums.com/showthread.php?t=112649
Physics Forums perfect square hi I am wondering whether there is any systematic way to determine for what values of x this function is a perfect square : f(x) = square root ( x!+1) thanks for any advice. Roger PhysOrg.com science news on PhysOrg.com >> Front-row seats to climate change>> Attacking MRSA with met...
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http://www.physicsforums.com/showthread.php?p=2765255
Physics Forums Thread Closed Page 1 of 2 1 2 > ## Does this reasoning ever reach infinity? 0<1<2<3<4<5 Does this reasoning ever reach infinity? 0<1<2<3<4<5..... What does it mean? Thanks! PhysOrg.com science news on PhysOrg.com >> Front-row seats to climate change>> Attacking MRSA with metals from antiba...
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http://mathoverflow.net/questions/87860/example-of-a-compact-kahler-manifold-with-non-finitely-generated-canonical-ring
## Example of a compact Kähler manifold with non-finitely generated canonical ring? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) A celebrated recent theorem of Birkar-Cascini-Hacon-McKernan and Siu says that the canonical ring $R(X)=\oplus_{m\geq 0}H^0(X,mK...
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http://mathhelpforum.com/math-topics/111630-physics-3-a.html
# Thread: 1. ## physics 3 1.A spring has a length of L cm when a force of W N is applied to stretch it. When the force is increased to 6W N, the length of the spring increases to 2L cm. Find the percentage increase in the length of the spring from its original length when a force of W N is applied to stretch it. 2. ...
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http://physics.stackexchange.com/questions/13917/reflection-at-speed-of-light/13919
Reflection At Speed of Light I have looked online to no avail. There is two competing answers and I am curious to know which one is right. Someone asked me this question. If you are traveling at the speed of light can you see your reflection in a mirror in front of you? My answer to the question is no, I would figur...
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http://en.wikipedia.org/wiki/Product_type
# Product type In programming languages and type theory, a product of types is another, compounded, type in a structure. The "operands" of the product are types, and the structure of a product type is determined by the fixed order of the operands in the product. An instance of a product type retains the fixed order, b...
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http://math.stackexchange.com/questions/13054/how-to-show-eee79-is-not-an-integer/14885
# How to show $e^{e^{e^{79}}}$ is not an integer In this question, I needed to assume in my answer that $e^{e^{e^{79}}}$ is not an integer. Is there some standard result in number theory that applies to situations like this? Much later addendum: when I asked this, I didn't expect it to be an open question. If it is o...
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http://math.stackexchange.com/questions/160998/finding-a-solution-of-a-heat-equation
# finding a solution of a heat equation Let $f\in C^0(\mathbb R^n)\cap L^\infty(\mathbb R^n)$ and $\alpha\in\mathbb R$. How can you find a solution $u$ of $$\begin{cases}\frac{\partial u}{\partial t}(x,t)-\Delta u(x,t)&=&-\alpha\cdot u(x,t) &\text{ in }]0,\infty[\times\mathbb R^n\\ \space\space\space\space\space\space...
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http://mathoverflow.net/questions/90197?sort=newest
## Transpose of unbounded operators between Banach spaces. ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Let $X$ and $Y$ be Banach spaces, and let $L : X \rightarrow Y$ be a unbounded operator with dense domain $\operatorname{dom}(L)$. We can then talk about...
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http://mathoverflow.net/questions/83965/interesting-applications-of-the-classical-stokes-theorem/84002
## Interesting Applications of the Classical Stokes Theorem? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) When students learn multivariable calculus they're typically barraged with a collection of examples of the type "given surface X with boundary curve Y,...
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http://math.stackexchange.com/questions/152703/godels-incompleteness-theorem-diagonal-lemma
# Gödel's Incompleteness Theorem - Diagonal Lemma In proving Gödel's incompleteness theorem, why does he needed the Diagonal Lemma or the Fixed Point Theorem for building a formula $\phi$ that spoke about itself? Can't this formula be built this way: Diagonal Function. Let $D(x, y)$ be the diagonal function, such tha...
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http://mathhelpforum.com/advanced-algebra/75293-find-subspaces-show-linear-transformation-permutes-subspace.html
Thread: 1. Find the subspaces and show a linear transformation permutes subspace Let $V = K^2$ be a vector space over a field finite field K, in which |K| = 4. Show that V has exactly five 1-dimensional subspaces, say $U_1,...,U_5$ and that a non-singular linear transformation of V permutes these five subspaces. 2. ...
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http://mathhelpforum.com/pre-calculus/896-math-quiz-question-help.html
# Thread: 1. ## Math Quiz question help ok, since my teacher isnt doing a very good job at explaining this we need to know for quizzes, I was wondering if you guys can help me. here are some of the questions om stuck on 1.Find the limit if it exists Lim log (x-4) x->4 5 2.Find the derivatives g(x)=ax+b/cx+d, whe...
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http://mathoverflow.net/questions/124919/angles-of-a-triangle-in-hilbert-spaces-and-in-metric-spaces
## Angles of a triangle, in Hilbert spaces and in metric spaces ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) http://mathoverflow.net/questions/124899/solid-angles-of-a-tetrahedron Does the statement "the side opposite the largest angle has the largest len...
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http://cstheory.stackexchange.com/questions/16582/l-0-estimation-not-in-a-stream
# $L_0$ estimation, not in a stream What is the current state of the art for $L_0$ estimation when not in a stream? I assume that the total number of (not necessarily distinct) objects is very large so you can only see a sample of them. I found http://en.wikipedia.org/wiki/Good%E2%80%93Turing_frequency_estimation but...
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http://mathoverflow.net/questions/93958?sort=newest
## Simple Equivariant homology [no borel-Moore] ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Hey. I'm working with Bredon's equivariant cohomology. At some point I need to compute the $4$th equivariant cohomology group of $S^1 \x D^3$ relatively to its boun...
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http://mathhelpforum.com/advanced-algebra/50009-need-help-permutation-proof.html
# Thread: 1. ## need help in this permutation proof Can anyone help me in this proof ? If A and B are in S_n, then $ABA^{-1}$ is the permutation that has the same cycle structure as B and that is obtained by applying A to the symbols in B. 2. Hello, Prove it when the length of A is 2 and the B is cyclic: A=(i j), ...
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http://mathoverflow.net/questions/60655/subspaces-of-a-subfactor/60661
## Subspaces of a Subfactor ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Is the following true? Let $\mathcal N \subset \mathcal M$ be a subfactor. There is a bijective correspondence between the ultraweakly closed subspaces of $\mathcal M$ that are bimodu...
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http://mathoverflow.net/questions/37239/dense-cyclic-subgroup/37241
## Dense cyclic subgroup ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Does anyone know a continuous group (not necessarily locally compact) with dense cyclic subgroup other than a torus? - Anything procyclic. Someone below already listed the $p$-adic inte...
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http://mathhelpforum.com/calculus/37236-stationary-points-revisited.html
# Thread: 1. ## stationary points revisited I have this function and I am looking for the stationary points: $<br /> f(x,y) = x^4 + 2x^2y^2 + y^4 + 2x^2 - 2y^2 + 6<br />$ I have the two partial derivatives: $<br /> 4x(x^2 + y^2 + 1) = 0, (E.1)<br />$ $<br /> 4y(y^2 + x^2 - 1) = 0, (E.2)<br />$ I have already foun...
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http://mathhelpforum.com/calculus/51598-lebesgue-integration.html
# Thread: 1. ## Lebesgue Integration Let $(S,\Sigma,\mu)$ be a measure space. Prove that if $f$ is a Lebesgue integrable function, then for each $\varepsilon > 0$ there exists a $\delta > 0$ such that $\int_A \mid f \mid \mathrm{d} \mu$ for each $A \in \Sigma$ with $\mu(A) < \delta$. 2. Originally Posted by syme.gab...
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http://mathhelpforum.com/geometry/106639-left-right-coordinate-space.html
# Thread: 1. ## left or right in coordinate space Hi all. Im new to the forum, and came across it on the hunt for some maths brains better than mine. I'm a hobbyist programmer and have hit a barrier. Eternally grateful if you can help. In the diagram there are two points creating a line in a coordinate space. This i...
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http://mathoverflow.net/questions/55014?sort=votes
some questions on Riemann surface Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) There are several puzzling questions on Riemann surface for me: Q.1 Definition of Riemann surface can be given in at least two ways: Def.1) it is a complex one dimensional manifold; ...
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http://math.stackexchange.com/questions/88503/computing-the-minimal-polynomial-of-an-invertible-matrix-whose-minimal-and-chara?answertab=active
# Computing the minimal polynomial of an invertible matrix whose minimal and characteristic polynomial coincide Let $M$ be an invertible $n \times n$ matrix whose minimal polynomial $q_M$ and characteristic polynomial are equal. Suppose as well that the $M$ has entries in an algebraically closed field. How do we show...
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http://mathoverflow.net/questions/107437/eigenvalues-of-a-special-block-matrix-associated-with-strongly-connected-graph/107555
Definition Let $G=(V,E,A)$ be a strongly connected directed graph, where $V={1,2,...,n}$ denotes the vertex set, $E$ is the edge set, and $A$ is the associated adjacency matrix with $0-1$ weighting, that is $a_{i,j}=1$ if $(j,i)\in E$, and $a_{i,j}=0$ otherwise. $B$ and $D$ are two diagonal matrices, where $b_{ii}=\s...
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http://dsp.stackexchange.com/questions/tagged/fft
# Tagged Questions The fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse. 1answer 46 views ### frequency domain phase shift While going through FFT I came to know that, shifting of phase in frequency domain results on shifting of time in time domain. Ac...
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http://mathhelpforum.com/discrete-math/173047-prove-equal-powers-probably-fairly-primitive-print.html
# Prove equal powers (probably fairly primitive) Printable View • March 1st 2011, 06:06 AM Pranas Prove equal powers (probably fairly primitive) Hello. My discrete mathematics course has just started, so I'm not very good even at probably fairly easy things: Prove if $\displaystyle \[G = A \times B\]$ is a bijectio...
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http://stats.stackexchange.com/questions/10021/new-mean-calculation-in-multivariate-gaussian
# New mean calculation in multivariate gaussian Given a Gaussian distribution $N(\mu_1,\sigma_1^2)$, i would like to choose another mean $\mu_2$ which is $2\sigma_1$ away from $\mu_1$. In this case our new mean $\mu_2=\mu_1\pm 2\sigma_1$. How do we calculate the new mean($\mu_2$) in multivariate case? I mean to say,...
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http://physics.stackexchange.com/questions/50153/eutectic-systems-behavior-near-100-0-composition-and-low-temperature/51167
# Eutectic systems behavior near 100%-0% composition and low temperature I can't understand why in this phase diagram , in the area where the system is approaching the 100% $\alpha$ or 100% $\beta$ composition, the state is just a pure solid. I mean, where does the other component go? If I am interpreting it right, ...
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http://mathoverflow.net/questions/19648/method-of-moments-and-laplace-transform-from-shepp-and-lloyd/19737
method of moments and Laplace transform from Shepp and Lloyd Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Again from the Shepp and Lloyd paper "ordered cycle lengths in a random permutation", I found this puzzling equality. This one might require access to the ...
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http://physics.stackexchange.com/questions/22664/what-are-the-physycal-meaning-of-universal-constants-such-as-the-magnetic-elect/22672
# What are the physycal meaning of universal constants such as the magnetic, electric and gravitational constants? I know that: $G=6.67300 × 10^{-11}\dfrac{Nm^2}{kg^2}$(Gravitational constant) $K_e=9×10^9\dfrac{Nm^2}{C^2}$(Electric constant or Coloumb's constant) $k_m=1×10^{-7}\dfrac{Ns^2}{C^2}$(Magnetic constant) ...
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http://math.stackexchange.com/questions/296796/existence-and-uniqueness-theorem/296807
# Existence and Uniqueness Theorem I had a question about how to do one of these problems. So here's the question: Given this equation $y'=\frac{-\cos(t)y(t)}{(t+2)(t-1)}+t$, find if the initial conditions $y(0)=10, y(2)=-1, y(-10)=5$ exist. So I think the first step is just to take the partial derivative with respec...
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http://math.stackexchange.com/questions/165883/what-should-i-call-this-commutative-monoid-of-order-three
# What should I call this commutative monoid of order three? I'm looking for a name for the monoid given by the following table: $$\begin{array}{c|ccc}&1&a&b\\ \hline 1&1&a&b\\ a&a&1&b\\ b&b&b&b \end{array}$$ Is there a name that would be understandable to an undergraduate student who hasn't read anything about semi...
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http://math.stackexchange.com/questions/180915/is-the-green-tao-primes-theorem-true-or-pseudo-true/180916
Is the Green-Tao primes theorem true or pseudo-true? [closed] The Green-Tao primes theorem "The primes contain arbitrarily long arithmetic progressions" Ann Math 2008, is certainly a tour de force and extremely technical. The authors point out that they have taken precautions to not use Axiom of Choice. Choice is men...
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http://math.stackexchange.com/questions/139897/fourier-transform-of-sinx-sinx/139961
Fourier transform of Sin(x + Sin(x)) Does anybody happen to know what the Fourier transform of $f(x) = \sin(x + \sin(x))$ is? More generally, what is the Fourier transform of $g(x) = \sin(\phi_1 x + \mu \sin(\phi_2 x))$? ($\phi_1$, $\phi_2$ and $\mu$ are constants.) I'm pretty sure I saw these written down somewhere...
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http://mathhelpforum.com/calculus/146875-finding-parametrizattion-line-integral.html
# Thread: 1. ## Finding parametrizattion for a Line Integral I've been asked to evaluate the line integral $\int (10x^4 - 2xy^3)dx - 3x^2y^2dy$ Over the curve $x^4 - 6xy^3 - 4y^2 = 0$ Between the points (0,0) and (2,1). What I'm trying to do is finding a parametrization x(t) from the given curve and then put tha...
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http://mathhelpforum.com/calculus/27343-determing-range-values-x-y.html
# Thread: 1. ## Determing range of values of x & y Hi If real variables x and y are related by the equation: ln(3-y) = 3ln(2x+1)-x then how do i: a). determine the range of values of x and y for which expressions on each side of equation are defined, and b). find y explicitly as a function of x, that is, express...
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http://math.stackexchange.com/questions/207379/proving-the-limit-of-an-improper-integral-of-a-sequence-of-functions?answertab=votes
# Proving the limit of an improper integral of a sequence of functions. I was trying to prove that the following limit $$\lim_{n\to\infty}\int^{\infty}_{1}\frac{\sin{x}}{x^{n+1}}\mathrm{d}x$$ is equal to $0$. I believe that the easiest option in similar cases - and the only one I know... - is proving that that $f_{n...
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http://mathhelpforum.com/calculus/159792-tough-max-min-problem-print.html
# Tough Max/Min Problem Printable View • October 15th 2010, 10:09 PM Em Yeu Anh Tough Max/Min Problem Let $F(x,y) = 2(1-x)^{\frac{1}{2}}+(x+y)^2+x-2y$ be a function that is bounded by $x=-3, y(t)=t^2, x(t)=2t+t^2$ I am to find the absolute max/min values. Completely lost! This is significantly more difficult that any...
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http://physics.stackexchange.com/questions/12353/dalemberts-principle-and-the-term-containing-the-reversed-effective-force/12355
D'Alembert's Principle and the term containing the reversed effective force For our Classical Mechanics class, I'm reading Chapter 1 of Goldstein, et al. Now I come across Eq. (1.50). To put it in context: $$\begin{align*} \sum_i{\dot{\mathbf{p}_i} \cdot \delta\mathbf{r}_i}&=\sum_i{m_i\ddot{\mathbf{r}}_i \cdot \delta...
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http://mathoverflow.net/revisions/41172/list
## Return to Answer 3 added 423 characters in body; added 1 characters in body; edited body; edited body This is all best explaied by working with groupoids in schemes. By this, I mean, groupoid objects in the category of schemes over $S$. A groupoid object $\mathcal G$ consists of two schemes $\mathcal G_0$ (the obj...
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http://math.stackexchange.com/questions/227263/inverse-functions-in-real-analysis
# inverse functions in real analysis Can anyone help me with this? Spose $I$ is a closed interval from $0$ to $1$ and let $f$ go from $I$ to $R$ be defined by $f(x) = x$ for $x$ rational, and $f(x) = 1-x$ for $x$ irrational. Show that $f$ is injective on $I$ and that $f(f(x)) = x$ for all $x \in I$. Show that $f$ is ...
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http://mathhelpforum.com/calculus/142763-l-hopital-s-questions.html
# Thread: 1. ## L'Hopital's Questions Hi I need some help on the following questions: 1) Use L'Hopital's rule to obtain: $\lim_{x \to 0} \frac{e^{x}-x-1}{3x^2}$ $f'(x) = \frac{3x^{2}*(e^{x}-1)-(e^{x}-x-1)*6x^2}{9x^4}$ $f'(x) = \frac{3x^{2}e^{x} - 6xe^{x}+3x^2+6x}{9x^4}$ $f'(x) = \frac{3x(xe^{x} - 2e^{x} +3x+2}{9x...
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http://mathhelpforum.com/pre-calculus/86514-inverse-function.html
# Thread: 1. ## Inverse Function Is the inverse of f(x) = 9-2x^2 f-1(x) = -sqrt( (9/2) - (x/2) ) Thanks, D. 2. Originally Posted by dboyd435 Is the inverse of f(x) = 9-2x^2 f-1(x) = -sqrt( (9/2) - (x/2) ) Thanks, D. The working in your post is correct except I do not see why you can't have a plus or minus infront ...
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http://mathoverflow.net/questions/81265/getting-b-t-from-its-local-times-lx-t
## Getting $B_t$ from its local times $L^x_t$ ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Hi Given a Brownian Motion $B_t$ is it possible to reconstruct it from the knowledge of the local times $L^x_t$ ? Using occupation time formula this would mean solv...
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http://mathoverflow.net/questions/19014/finding-questions-between-functional-analysis-and-set-theory/23880
## Finding questions between functional analysis and set theory ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Are there some good questions on functional analysis whose solution depends on tools in set theory? My major is mathematical logic, I think tools in...
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http://physics.stackexchange.com/questions/19254/violation-of-conservation-of-energy-and-potential-energy-between-objects
# Violation of conservation of energy and potential energy between objects I would like to clarify my question. I have numbered them to be independent questions 1. For any conservative fields, $\vec{F} = -\nabla U$. Which means the restoring force is opposite to the increasing values of the potential energy. If it so...
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http://physics.stackexchange.com/questions/38237/is-there-a-time-delay-during-tunnelling/45815
# Is there a time delay during tunnelling? A particle hitting a square potential barrier can tunnel through it to get to the other side and carry on. Is there a time delay in this process? - ## 2 Answers There is a roughly constant time delay during tunnelling that is roughly proportional to $\hbar$ over the barrie...
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http://mathhelpforum.com/number-theory/178840-inverse-2-mod-108-quadratic-equation.html
# Thread: 1. ## Inverse of 2 mod 108 and the quadratic equation This is actually related to a problem in this thread, but is so much more basic I didn't want to interrupt any discussion that the original thread might generate. The problem is to solve $x^2 + 3x - 22 \equiv 0~\text{mod(108)}$ Since the details of sol...
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http://math.stackexchange.com/questions/48230/investigations-about-the-trace-form
# Investigations about the trace form Let us (again) consider the bilinear form $\beta(A,B)=\operatorname{Tr}(AB)$ for $A,B \in \mathbb{F}^{n,n}$ (quadratic matrices over a field $\mathbb{F}$). I am interested in finding the biggest subspace $U \subset \mathbb{F}^{n,n}$ such that for all $A \in U: \beta(A,A)=\operator...
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http://mathoverflow.net/questions/46794?sort=oldest
## Generalization of the Structure theorem for artinian rings? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Let $A$ be a commutative ring with identity. If $A$ is a ring with only a finite set of prime ideals $p_1...p_n$ and moreover $\prod_{i=1}^n p_i^{k_i...
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http://math.stackexchange.com/questions/194409/interpolation-error-for-the-exponential-function
# Interpolation error for the exponential function I'm studiyng for my exam of scientific computing, specifically to the subject of interpolation techniques, I'm stuck with this problem: How many equally spaced nodes must be taken to interpolate the function $f(x) = \exp(x)$ on the interval $[-1,1]$, so that the inte...
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http://mathoverflow.net/questions/62302/examples-of-amenable-groups-other-than-z-n/62333
## Examples of Amenable Groups other than Z_n ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) I'm reading about amenable groups. What are explicit examples of nonabelian discrete amenable groups other than finite groups? Perhaps a group presentation or matrix ...
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http://mathoverflow.net/questions/26304/is-there-a-definition-of-analogue-weyl-group-for-lie-super-algebra/26332
## Is there a definition of analogue Weyl group for Lie super algebra? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) I heard from some people working in Lie super algebra that there was no proper definition for Weyl group of Lie super algebra. I do not know ...
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http://stats.stackexchange.com/questions/4446/sum-of-squares-two-ways-how-are-they-connected?answertab=votes
# Sum of squares two ways, how are they connected? The standard sum of squares as I know it is: Σ (X-m)2 where m is the mean. I ran into a different one which can be written two ways: Σ(X2) - (ΣX)2/n = Σ(X2) - m ΣX I believe the latter is called the "correction term for the mean" (e.g. here). My algebra seems to b...
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http://physics.stackexchange.com/questions/tagged/geodesics
# Tagged Questions For questions involving consideration of the shortest (or longest) path between two points in a curved space (e.g. a straight line between two points on the surface of a sphere such as the earth). 1answer 76 views ### Killing vector argument gone awry? What has gone wrong with this argument?! The...
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http://physics.stackexchange.com/questions/18395/simple-description-of-exchange-interaction/18528
# Simple description of exchange interaction? What is a simple bare-bones description of exchange interaction between two electrons? For instance, it seems to me that the only necessary ingredients are the Coulomb interaction and the requirement that the total wavefunction be antisymmetric. - 1 Your intuition is co...
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http://www.physicsforums.com/showthread.php?s=10ca930c2e49cc6d79006fce8f40692e&p=4322219
Physics Forums ## Colour Octet States Hey, I'm having an issue seeing how these octet states are reproduced via SU(3) transformations, in my notes it is written: "Now, the remaining 8 states in (25) mix into each other under SU(3) transformations. For example just interchange two labels such as R<->B and you'll see...
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http://mathhelpforum.com/differential-geometry/83047-intermediate-value-theorem-application.html
Thread: 1. Intermediate Value theorem application Let p(x) be an odd-degree polynomial function. Prove that p(x)=0 has at least one real solution 2. Not sure if there is a formal proof of this, but one can see that as $x \to \infty$ then $p(x) \to \infty$ and as $x \to -\infty$ then $p(x) \to -\infty$. (assuming lea...
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http://mathoverflow.net/questions/62577/
## Rate of decay of variance for a tensor product Markov process (100 pt bounty for good answer by 1800 EST Fri) ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Let $Q$ be the generator of a well-behaved (not necessarily reversible) Markov process $X$ on `$[n]...
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http://lembolies.com/energy
# Energy Research Materials This page contains a list of latest news about Energy which has been collected from credible news resources: CNN, Forbes, Bloomberg, TIME Magazine, FoxNews, BBC, New York Times, CBS, Sky News, Reuters, World Magazine, etc. Apart from News, you can also use the tabs to browse Energy images,...
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http://physics.stackexchange.com/questions/46180/can-a-deformable-object-swim-in-curved-space-time
# Can a deformable object “swim” in curved space-time? [duplicate] Possible Duplicate: Swimming in Spacetime - apparent conserved quantity violation It is well known that a deformable object can perform a finite rotation in space by performing deformations - without violating the law of conservation of angular moment...
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http://mathoverflow.net/revisions/118451/list
Return to Answer 1 [made Community Wiki] As a set theorist, I feel some obligation to offer an answer here. First, the difficulties students may have in proving set theoretic containments like the one you mention above or in constructing $\epsilon$-$\delta$ proofs is not a matter of them struggling with set theory bu...
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http://physics.stackexchange.com/questions/30435/when-does-the-norm-of-quasi-eigenvectors-matter-in-calculations-for-which-phy
# When does the “norm of quasi-eigenvectors” matter in calculations? For which physical results are these even used? Which physical system in nonrelativistic quantum mechanics is actually described by a model, where the norm of the "position eigenstate" (i.e. the delta distribution as limit of vectors in the Hilbert s...
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http://mathoverflow.net/revisions/43153/list
## Return to Answer 2 deleted 10 characters in body Dear Tim: I am not sure perhaps I understand misunderstood your question. , but I think any reasonably technical field has a few examples. I heard algebraic geometry is such a field, so I looked up a couple of sources and found these tworight away: 1) Let $f: R\to ...
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http://mathoverflow.net/questions/83977/second-conjugate-operators-to-operators-on-c-0
## Second conjugate operators to operators on $c_0$ ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) I posted my question at MS but unfortunately it is still without a response, so let me ask it here. We can think about a bounded operator $T\colon c_0\to c_0$ ...
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http://physics.stackexchange.com/questions/32502/can-quantum-mechanics-really-be-the-same-as-underlying-deterministic-theory
# Can quantum mechanics really be the same as underlying deterministic theory? I am perplexed by recent papers by 't Hooft giving an explicit construction for an underlying deterministic theory based on integers that is indistinguishable from quantum mechanics at experimentally accessible scales. Does it mean that it ...
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http://mathhelpforum.com/geometry/2566-test-4-14-geometry-picture-included-please-help-asap-please-print.html
# Test on 4/14. Geometry. Picture included Please help ASAP please Printable View • April 13th 2006, 04:49 PM AirForceOne http://img.photobucket.com/albums/v2...e/441fd7bf.gif The ones I know are know are correct but no well understood: a) 1:1 because both triangles have the same base? So 16:16 = 1:1 right? b) same...
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http://mathoverflow.net/questions/71877/on-a-claim-of-ramanujan-in-his-lost-notebook/71922
## On a claim of Ramanujan in his “Lost Notebook”. ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) As I was flipping through the scanned version of Ramanujan's "Lost Notebook" in our library, I came across a result which caught my attention. And as any excited...
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http://mathoverflow.net/questions/74119?sort=votes
## What are categorical models of W-types in intensional type theory? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) I'm familiar with container functors and older work by Dybjer on categorical models for W-types in the extensional theory, but I was looking f...
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http://mathoverflow.net/questions/92061?sort=newest
## Square of a continuous map ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Recently a student asked me the following (elementary looking) question : If $T$ is an invertible linear transformation of some finite-dimensional space $E$ into itself which factor...
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http://mathoverflow.net/questions/107804/a-continuous-linear-functional-on-l-inftyr-that-vanishes-on-cr
## A continuous linear functional on $L^\infty(R)$ that vanishes on $C(R)$. ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) Intuitively, I want to construct the functional F in this way: $$F(f)=\lim_{x\rightarrow 0+}f(x)-\lim_{x\rightarrow 0-}f(x)$$ for $f\i...
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http://physics.stackexchange.com/questions/tagged/black-holes
Tagged Questions A black hole is a volume from which photons, or any matter, can not escape. More formally, the coordinate speed of light at the event horizon - the boundary of a black hole - is zero, as measured by a sufficiently separated observer. 0answers 51 views Entanglement and Black holes If you have two en...
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http://math.stackexchange.com/questions/91141/terminology-for-properties-of-functions
# Terminology for properties of functions. So I was wondering, is there a name for a function whose output is always less than or equal to its input ($f(x)≤x$)? I know there is a name for functions that satisfy $x_1<x_2\rightarrow f(x_1)<f(x_2)$ (monotonic) so I figured there would be a name for $f(x)≤x$. Does anyone ...
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http://mathoverflow.net/questions/12147/how-can-i-tell-if-y-is-a-function-of-x-in-a-random-sample
## How can I tell if y is a function of x in a random sample? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) I have some data and believe that a given metric is a function of another metric. I have the values of both metrics and many different sets of these v...
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http://math.stackexchange.com/questions/187794/why-did-my-friend-lose-all-his-money/187808
# Why did my friend lose all his money? Not sure if this is a question for math.se or stats.se, but here we go: Our MUD (Multi-User-Dungeon, a sort of textbased world of warcraft) has a casino where players can play a simple roulette. My friend has devised this algorithm, which he himself calls genius: • Bet 1 gold...
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http://math.stackexchange.com/questions/34101/conditional-expectation-ea-mid-b-b-and-eb-mid-a-a-implies-a-b
# Conditional expectation: $E[A \mid B] = B$ and $E[B \mid A] = A$ implies $A = B$ Given two $L^1$ random variables $A$, $B$ satisfying $E[A \mid B] = B$, $E[B \mid A] = A$. The claim is that $A = B$. So is this easy? I don't really see it.. If $A$ and $B$ are in $L^2$ it's clear, for then $E[AB] = E[A^2] = E[B^2]$, t...
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http://mathematica.stackexchange.com/questions/tagged/distributions+random
# Tagged Questions 1answer 98 views ### Safe values of $\mu$ and $\sigma$ when randomly sampling from a Log-Normal Distribution? I believe I'm obtaining overflow errors when randomly sampling from a log-normal distribution with the command: RandomVariate[LogNormalDistribution[μ, σ], 1] ... 1answer 143 views ### Cal...
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http://physics.stackexchange.com/questions/41174/does-every-wavenumber-of-ir-result-in-a-different-kind-of-vibration?answertab=oldest
# Does every wavenumber of IR result in a different kind of vibration? Does every wavenumber of IR result in a different kind of vibration? If that is true, what if a molecule absorb 2 different wavenumbers (which cause different rocking and symmetrical stretching for example ) in the same time? - ## 1 Answer In mo...
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http://math.stackexchange.com/questions/35561/visualizing-operators-on-mathbbcn?answertab=votes
# Visualizing Operators on $\mathbb{C}^n$ I am trying to get some better intuition about operators on complex inner product spaces. When we identify $\mathbb{C}^n$ with $\mathbb{R}^{2n}$, is there a nice geometric interpretation for the resulting operators on $\mathbb{R}^{2n}$? Ideally, this characterization would giv...
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http://stats.stackexchange.com/questions/40343/calculating-the-probability-of-the-nth-sample-in-the-birthday-problem-w-o-knowin
# Calculating the probability of the Nth sample in the birthday problem w/o knowing the previous samples If we draw two random variates from a discrete uniform distribution $[1, D]$, the probability that the samples are distinct is $(D-1)/D$. Explanations of the birthday problem state that if we sample a third time, t...
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http://stats.stackexchange.com/questions/30171/boosted-ar-for-time-series-forecasting
# Boosted AR for time series forecasting? I have time series data recorded at multiple locations, stored in a matrix $Y$. I have fit a Vector Autoregressive Model to it which forecasts the data pretty well on a test set. However, if I plot the residuals there is definitely some time series structure left; ideally the ...
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http://mathhelpforum.com/calculus/197465-dot-vs-cross.html
# Thread: 1. ## dot vs. cross What is the purpose of the dot product as opposed to the purpose of the cross product? 2. ## Re: dot vs. cross Originally Posted by delgeezee What is the purpose of the dot product as opposed to the purpose of the cross product? the result of a dot product of two vectors is a scalar .....
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http://math.stackexchange.com/questions/142821/matrix-for-rotation-around-a-vector
# Matrix for rotation around a vector I'm trying to figure out the general form for the matrix (let's say in $\mathbb R^3$ for simplicity) of a rotation of $\theta$ around an arbitrary vector $v$ passing through the origin (look towards the origin and rotate counterclockwise). This is inspired by a similar problem whi...
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http://math.stackexchange.com/questions/152462/inverse-of-transformation-matrix/152479
# Inverse of transformation matrix I am preparing for a computer 3D graphics test and have a sample question which I am unable to solve. The question is as follows: For the following 3D transfromation matrix M, find its inverse. Note that M is a composite matrix built from fundamental geometric affine transformation...
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http://mathhelpforum.com/statistics/191052-finding-probability-function-r-remainder-when-divided-distribution.html
# Thread: 1. ## Finding a probability function R (the remainder when divided by a distribution) Hi everyone, I am really unsure of how to do this question. Let X have a geometric distribution with f(x) = p(1-p)^x for x = 0,1,2,.... Find the probability function of R, the remainder when X is divided by 4. I don't kn...
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http://math.stackexchange.com/questions/40930/what-is-the-name-for-the-archetypical-example-of-a-test-function-varphix-e
# What is the name for the archetypical example of a test function, $\varphi(x)=e^{1/(x^2-1)}$? $$\varphi(x)=e^{1/(x^2-1)}$$ This function (on the interval $\quad]\!-1,1[ \,\,\,$, outside of it simply $\equiv0$) is used as the typical example of a test function / bump function, I have so far seen it it every book that...
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http://en.wikipedia.org/wiki/Gas_constant
# Gas constant Values of R [1] Units (V P T −1 n−1) 8.3144621(75)[2] J K−1 mol−1 5.189×1019 eV K−1 mol−1 0.08205746(14) L atm K−1 mol−1 1.9858775(34) cal K−1 mol−1 1.9858775(34)×10−3 kcal K−1 mol−1 8.3144621(75)×107 erg K−1 mol−1 8.3144621(75) L kPa K−1 mol−1 8.3144621(75)×103 cm3 kPa K−1 mol−1 8.3144621(75) m3 Pa K−1...
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http://mathoverflow.net/revisions/19470/list
Return to Answer 2 added 1 characters in body I feel it's more informative to have the thought process that leads to the example rather than just be told some magic formula that works, however simple that formula might be. Here is a way of explaining it. We'll decide that our function is going to be discontinuous at...
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http://mathhelpforum.com/calculus/2382-derivative-invert-tan.html
# Thread: 1. ## Derivative of invert tan? I read from the rules that the derivative of (tan^-1)x is (1/x^2+1), but I cannot figure out why and I can't find any explantations on the web. Anyone have any ideas? Thank you. 2. Originally Posted by tttcomrader I read from the rules that the derivative of (tan^-1)x is (...
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http://mathoverflow.net/questions/22583/why-torsion-is-important-in-cohomology/22640
## Why torsion is important in (co)homology ? ### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points) I've once been told that "torsion in homology and cohomology is regarded by topologists as a very deep and important phenomenon". I presume an analogous statement cou...
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http://math.stackexchange.com/questions/184285/i2-does-not-retract-into-comb-space
$I^2$ does not retract into comb space In Hatcher's book on Algebraic Topology in Chapter 0 (where the Homotopy Extension Property is discussed) the claim is being made that there is no retraction of $I^2$ into $I \times \{0\} \cup A \times I$ where $A = \{0, 1, \frac 12 , \frac 13, \ldots \}$. However I couldn't come...
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http://mathhelpforum.com/advanced-algebra/140799-hermitian-positive-definite-matrix-invertibility-print.html
# Hermitian positive definite matrix and invertibility Printable View • April 22nd 2010, 04:15 PM math8 Hermitian positive definite matrix and invertibility Suppose A is a Hermitian positive definite matrix split into $A = C + C^{*} + D$ where $D$ is also Hermitian positive definite. We show that $B=C+ \omega ^{-1} D...
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http://math.stackexchange.com/questions/54292/find-the-isomorphism-between-two-table-representations-of-the-same-finite-field
# Find the isomorphism between two table representations of the same finite field I am given two multiplication and addition tables for a finite field (i.e. the tables are for different naming of the elements of the field) and I want to find the isomorphism between the two representations. One idea is to map a primiti...
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