# All Questions

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Given a series with integral coefficiens as following: $$F(x)=\sum_0^i a_i x^i,\text{where }a_i\in \mathbb{N}\bigcup 0$$$$\text{and there is a computable function \psi such that } \forall i ... 1answer 48 views ### Are sums of 0-1 Pareto efficient vectors Pareto efficient? Does there exist an m \times n matrix A and a vector x \in \mathbb{R}^m such that: The entries of A are \in \{0, 1\}. For all pairs of columns u, v of A the entries of u - v are ... 2answers 61 views ### Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute? Specifically, are there "nice" (ie, not too obscure or contrived) examples of families of objects, where say for each objects A,B,C in the family, the canonical isomorphism from A\rightarrow C is ... 0answers 12 views ### Does \mathsf{fReR}_0 prove the existence of the cartesian product of two sets \mathsf{fReR}_0 is a set-theoretical system whose axioms consist of: (1) Axiom of extensionality: \forall z\in x\ (z\in y)\wedge\forall z\in y\ (z\in x)\rightarrow x=y (2) Axiom of empty set: ... 0answers 55 views ### Characterizing the real analytic Eisenstein series Consider the classical real analytic Eisenstein series$$ E(z,s)=\left(\pi^{-s}\Gamma(s)\frac{1}{2}\right)\sum_{(m,n)\neq(0,0)}\frac{y^s}{|mz+n|^{2s}}, $$where z=x+iy. We think of E(z,s) as a ... 0answers 21 views ### Equations over \mathbb{Z}[[T]] vs. equations over \mathbb{Z}_p This question might be deemed totally unanswerable, unless there is an obvious counterexample. Answers to either effect would be welcome. Question. Let X be a finite-type scheme over ... 1answer 68 views ### u-Invariants of p-adic function fields In his Paper "Fields of u-invariant 9" Oleg Izhboldin points out that for a algebraic closed, finitely generated field k we have u(k)= 2^{cd(k)}. In particular we have ... 0answers 11 views ### Cohomological dimension of transcendental p-adic extensions Let k = \mathbb{Q}_p for any prime p and set L = k(t_1,..,t_n). The u-invariant of a field u(k) is defined by u(k):=\{ max (\mathrm{rank}(q))  |  q  is anisotropic over k\}. It is ... 0answers 128 views ### On the ratio of Gilbreath sequences Definitions: let n \in \mathbb{N}_{>0} \cup \{ \infty \} and let E_n be the set of sequences (d_i)_{i=1}^n such that d_1=1, d_i is an even integer (for i > 1) and 0<d_i \le i. ... 1answer 266 views ### Beurling density and interpolation Let \Lambda=\{\lambda_n\}_1^\infty a set of points on the real line. We denote by \bar{n}(r) the largest number of points in any interval [x,x+r], r>0. Define the upper uniform density ... 13answers 1k views ### Obscure Names in Mathematics [on hold] I recently stumbled over the "Happy Ending Problem" (cf e.g. http://en.wikipedia.org/wiki/Happy_Ending_problem), which made we wonder, if there are other conjectures, theorems or problems, whose names ... 1answer 67 views ### A metric associated with a continuous surjective map f:X\to Y Assume that f:(X,d_{1})\to (Y,d_{2}) is a continuous surjective map between compact metric spaces. We define another metric d_{f} on Y With$$ d_{f}(a,b)=Hd(f^{-1}(x), f^{-1}(y))$$... 1answer 112 views ### Weinstein's local classification of Lagrangian foliations In the paper "Symplectic manifolds and their Lagrangian submanifolds", Weinstein showed that locally all the Lagrangian foliations are symplectomorhic to the fiber foliation of a cotangent bundle. I ... 1answer 43 views ### Nagakami behavoir Is the sum of square Nagakami random variables Erlang distributed? What is the distribution of euclidean norm of complex Nagakami? Cheers! 2answers 94 views +100 ### Projection formula for smooth representations of locally profinite groups Let G be a locally profinite (i.e., locally compact, Hausdorff, and totally disconnected) topological group, H \le G a closed subgroup, (\pi, V) a smooth representation of G, and (\sigma, W) ... 0answers 228 views ### A metric on S^{2} [on hold] Let p:S^{3}\to S^{2} be the Hopf fibration p(z,w)= (\parallel z\parallel^{2}-\parallel w\parallel^{2},\;2z\bar{w}). Define a metric on S^{2} as follows:$$d(x,y)=Hd(p^{-1}(x), ...
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I'm reading through T. Taos book on random matrices (to be found here), and it is frequent to make without-loss-of-generality certain reductions when proving theorems as for example Hoeffdings ...
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### An easy proof that S(n) does not embed into A(n+1)?

Rotman's book An Introduction to the Theory of Groups (Fourth Edition) asks, on page 22, Exercise 2.8, to show that S(n) cannot be embedded in A(n+1), where S(n) = the symmetric group on n elements, ...
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### How can I have a copy of this old paper by Frobenius?

How can I have a copy of this old paper and a translation of it? Frobenius, G. (1902). Uber primitive Gruppen des Grades n und der Klasse n - 1. S. B. Akad. Berlin 1902, 455-459.
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### Help in finding distribution of the following function of random variable

Let $X_1$ and $X_2$ be independent complex Gaussian random variables, $$X_1 \sim \mathcal{CN}(0,\sigma)$$ $$X_2 \sim \mathcal{CN}(0,\sigma)$$ If $X= aX_1 + bX_2$ where $a,b$ are constants then the ...
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### What is induction to n^(n-1) >= n! for n=9,10 [on hold]

Can somebody help me? How do I prove n^(n-1) >= n! for n=9,10..... by induction?
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### Can (how) one distinguish germs of continuous functions by a countable set of params?

Continuous functions can be distinguished by their values at say rational points of [0 1]. Germs of analytic functions can be distinguished by derivatives at a point. So in both cases we see ...
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### Dimension of Hilbert scheme?

I have a subvariety $V \subset X$, and I want to compute the dimension of the connected component of $\textrm{Hilb}(X)$ containing $[V]$. I can give explicit deformations of $V$ showing that the ...
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### Making $\mathbb{Q}$-cohomology integral

Let $X$ be an algebraic variety (say, smooth and projective) over $\mathbb{C}$, and fix $$\alpha\in H^i(X^{\text{an}}, \mathbb{Q})$$ with $i>0$. Does there always exist a variety $Y$ and a ...
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