# All Questions

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### Wave equation with linear coefficients

The following pde came up in a physics problem: $$(Cy+D)\frac{\partial^2 u}{\partial x^2}-(Ay+B)\frac{\partial u^2}{\partial y^2}-A\frac{\partial u}{\partial y} =f(x,y),$$ A,B,C,D are fixed ...
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### Looking for the manuscript “Uniform polytopes” by N. Johnson

The manuscript Uniform Polytopes (1991) by Norman Johnson is cited in the wikipedia page on uniform polytopes (http://en.wikipedia.org/wiki/Uniform_polytope). Is there an electronic copy of this ...
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### Functional representation of adapted jointly measurable stochastic processes

It seems like the question stated here in MSE has no answer yet and seems therefore for me to be not of a basic question type. For this reason I move it to MO. Let $X_t : \Omega \to E, \ t \geq 0$ be ...
1answer
181 views

### Meaning of $g_d^r$ in algebraic geometry

As an editor I often encounter the symbol $g_d^r$ as a noun. I tried googling but I only get papers where the symbol is used without a definition. Can someone supply a reference to a definition? ...
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### Projective dimension of a sub-ideal

Let $\mathbf{k}$ be a field, and let $S=\mathbf{k}[x_1,x_2,\ldots,x_n]$. Let $I\subset J$ be finitely generated monomial ideals in $S$. Is it true that the projective dimension of $I$ is either ...
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### K-Permutations with forbidden numbers [on hold]

This question has some references to programming and not as many mathematical terms as you might like, but I think it's more appropriate in a mathematics forum. Introduction (Skip if you are ...
1answer
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### Which finite p-groups occur as commutators of finite p-groups?

Let $p$ be a prime number. For which finite $p$-groups $H$ there is a finite $p$-group $G$ such that $[G,G] \cong H$?
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### maximal abelian subgroup [on hold]

let M(G) denote the set of orders of maximal abelian subgroups of G. If M(G) = M(H), for some group H then what can we say about the prime numbers that divide the order of each group G and H?
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### Publishing in mathematics [on hold]

I apologize if mathoverflow is not the right place for this question, but I guess it is the only place where I can get an answer. The question is the following: is publishing a paper in mathematics ...
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35 views

### Conformal map from a sector of unit disk onto upper half plane [on hold]

How do we construct a conformal map from $\{z=x+iy,x>1/2,|x+iy|<1\}$ onto the upper half plane? My idea is first create a sector sending one of the two intersection points to infinity.Any help ...
3answers
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I've got a map between two infinite dimensional spaces, $f: A\to B$, where $A$ seems "larger" than $B$. For the sake of conversation let's assume that $A$ is the set of smooth maps $\mathbb R^3\to ... 1answer 81 views ### Ising model: probability of a long path of minus under plus boundary conditions Consider for example the Ising model on a square lattice. Fix zero magnetic field and plus boundary conditions. Low temperature, one minus spin. With a Peierls argument one can prove that, given a ... 0answers 89 views ### The field of rational functions on a smooth projective absolutely irreducible curve over a finite field [on hold] We mean a variety (over "k") of dimension 1 by the curve in the expression "The field of rational functions on a smooth projective absolutely irreducible curve over a finite field k", don't we? 2answers 304 views ### Splitting integers 1, 2, 3, … n to avoid least possible sum For each positive integer n, partition the integers 1, 2, 3, … 2n into two sets of n integers each. Let g(n) be the least integer such that there is such a partition in neither of whose parts there is ... 0answers 61 views ### What is the significance of the median eigenvalue? When I look at the spectral density plots of my (usual) laplacian graphs, they spike at the median eigenvalue. But what significance for the graph/matrix (which originates from a network) does the ... 2answers 108 views ### Which real Pin groups agree? In the Lie theory notes on my website it is claimed (Example 7.3.3.5) that$\mathrm{Pin}(4,0)$and$\mathrm{Pin}(0,4)$are not isomorphic. As Nigel Ray pointed out to me, this claim is not quite ... 0answers 49 views ### Generalized weight space In their paper Lepowsky and Mcmollum sketch theory of weights in a more general setting. Here is their definition of a weight space: If$A$is a subset of$\mathfrak g$and$\lambda$is a function ... 0answers 42 views ### Green's function of the Ornstein-Uhlenbeck operator Consider$\mathbb R^d$with the Gaussian measure$d\gamma(x) = e^{\frac{1}{4}|x|^2}\,dx$. The Ornstein-Uhlenbeck operator$L$is given by $$Lu = \Delta u- \frac{1}{2}x\cdot \nabla u.$$ Is there a ... 0answers 42 views ### Ozsvath-Szabo orientation convention for Seifert fibred spaces I am confused by the orientation convention that Ozsvath and Szabo use in On Heegaard Floer homology and Seifert Fibered Surgeries and would appreciate if someone clarifies this for me. On page 15 ... 0answers 42 views ### Which of the following is true? [on hold]$f(x),g(x)$are defined on$[-1,1]$,$f'(0),g'(0)$exist,$f(0)=g(0)$, and$f(x)\ge g(x)$holds for an open interval containing$0$. Then which of the following is correct: I,$f(x)$and$g(x)\$ have ...

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