0
votes
0answers
4 views

question about Baer sum of extensions

Let $E_1$ and $E_2$ be extensions of $\mu_p$ by $\mathbb{Z}/{p\mathbb{Z}}$. Assume that $E$ contains $E_1$ and $E_2$ both, and $E_1 \cap E_2 = \mathbb{Z}/{p\mathbb{Z}}$. Then, does $E$ contain their ...
0
votes
0answers
21 views

A 5 element lattice which does not generate any finite abelian group

Let $(G,+)$ be a finite abelian group. If $A\subseteq G$ is a generator for $G$ then $G$ is the the set of all arbitrary sums of elements of $A$. I'm thinking about limiting the sums by a ...
0
votes
0answers
35 views

Is there any progress on Problem 13 (from Schoen and Yau)?

This is closed related to the question asked here. I wonder if there is any progress on Problem 13 from the "Problem Section" in Schoen and Yau, page 281, problem 13, which asks: Let $M_1$ and $M_2$ ...
2
votes
0answers
32 views

Real points of zero-dimensional real algebraic varieties

There have been a number of discussions of zeros of random polynomials here (the most recent being: Why do roots of polynomials tend to have absolute value close to 1?). Here is a closely related ...
0
votes
0answers
12 views

Classification properties of fusion rings

Fusion rings have so many classification properties (I checked the literature a bit) that my head hurts. For practical reasons I define the following three new properties (which might coincide with ...
-3
votes
0answers
15 views

Does $(n + 2)$ have a multiplicative inverse mod $(n - 1)$ over $GF(5)$? [on hold]

I have been stuck on understanding this for hours. The reason I am confused is that I thought over $GF(k)$, only constants have inverses. Also, how would one go about applying EGDC to figure this out? ...
0
votes
0answers
38 views

Closure in Hilbertspace

I know that i asked this question already on stackexchange.com (http://math.stackexchange.com/questions/983377/closure-in-a-hilbertspace) Define for a pure contraction $S$ (remember: $\|S\|\leq1$ and ...
6
votes
0answers
62 views

Mixed Hodge structure on configuration spaces

Let $X$ be a smooth complex projective variety. Let $F(X,n)$ be the configuration space parametrizing $n$ distinct ordered points in $X$. The cohomology groups $H^k(F(X,n),\mathbf Q)$ carry a mixed ...
0
votes
0answers
22 views

Estimation of growth rate of spectral radius

I have following problem: Let the spectral radius of $S=(a_{ij})_{n\times n}$ be $\lambda>1$, where each $a_{i,j}$ is a positive integer, then we have that $$\lim_{k\to ...
1
vote
0answers
39 views

Chances for a cosine polynomial to be positive at a point

Let $k_1,\ldots,k_n$ be distinct integers. Let $s_n(t)=\cos (k_1t)+\cdots+\cos (k_nt)$ be a trigonometric sum. Consider any interval $I\subset [-\pi,\pi)$ of length $\delta=\delta(n)$. Let $\,U$ be a ...
1
vote
0answers
18 views

How to define Product of Conditional Measures?

I have been wondering how to define the product of conditional measures as defined by Renyi-Popper. I spell the details below. If $(X,\Sigma)$ is a measurable space, then the function $\mu : ...
0
votes
0answers
27 views

Number of maximal chains in Bruhat order

Is there a formula for the number of maximal chains between two permutation in the (strong) Bruhat order?
4
votes
0answers
40 views

Picard scheme of varieties over imperfect fields

Let $k$ be a field and $X$ a proper $k$-scheme. It is a theorem of Murre and Oort that the Picard functor is representable by a $k$-group scheme $\operatorname{Pic}_{X/k}$ which is locally of finite ...
-2
votes
0answers
28 views

Wielandt's exercise on regular groups [on hold]

Assume that the intransitive group $G$ has degree $n$ and minimal degree $n-1$. If no transitive constituent of $G$ has degree $1$, then they all are faithful and all except one are regular. Any ...
2
votes
0answers
23 views

Reference for existence results for 2D forced viscous Burgers equation

I am looking for results concering the following parabolic PDE $$u\cdot\nabla u + \Delta u = F(x),$$ where $$u\colon\Omega\to\mathbb{R}^2,$$ and $\Omega\subset\mathbb{R}^2$ is a 2D domain (bounded or ...
1
vote
2answers
89 views

Calculating Exterior Distance from Measurements of Inner Geometry

Gauss has proven in his famous Theorema Egregium, that it is possible, to calculate the gaussian curvature from measuring angles and distances on the surface, irrespective of how the surface is ...
1
vote
1answer
33 views

Integrals involving trigonometric functions and polynomes

Let $P(x)$ be a real polynome. Specify all such $P(x)$ that one of the next integrals converge: $$ \int_0^{\infty} sin(P(x))dx, \int_0^{\infty} cos(P(x))dx ? $$ Among special cases are such ...
1
vote
1answer
49 views

On the Saito Kurokawa representation

I know Saito-Kurokawa(SK) representation is the famous non-tempered representation of $SO(5)$. But since the tempered or non-tempered terms are concerned with local phenomenon, I am wondering that ...
1
vote
0answers
46 views

A number array related to colored necklaces and the primes

I stumbled upon entry OEIS-A208535 on the enumeration of certain kinds of colored necklaces and noticed that the integers for the odd prime rows of the table there seem to be given by the Moreau ...
2
votes
0answers
34 views

Reference request: Invariant sets of dynamical systems

(I should preface this with the disclaimer that this is a slightly elaborated version of a question that I posted onto math se recently to which I received no responses, and have since deleted the ...
-1
votes
1answer
38 views

differential Proper Maps [on hold]

If $K$ is a subset of $M$ we write $M_{K}(M,M)$ for the set of diffferential maps of $M$ into $M$ with support in $K$.If $K$ is compact,then $M_{K}(M,M)$ consists of maps for which the preimages of ...
0
votes
0answers
17 views

Questions about some special tensor transformation

Suppose tensor $U_{i\alpha\beta}$ with dimension $M*N*N$ satisfy following condition: $$U_{i\beta\alpha}=W^1_{\alpha\alpha'}W^2_{\beta\beta'}U_{i\alpha'\beta'}$$ where $W^1$ and $W^2$ are $N*N$ ...
-4
votes
0answers
46 views

Lemma on Polish Spaces [on hold]

I asked the following question on StackExchange earlier, but received no replies yet. Let $(X_1,\Sigma_1,\mu_1)$ and $(X_2,\Sigma_2,\mu_2)$ be probability spaces. Suppose the following conditions ...
1
vote
0answers
21 views

Anti-Invariant Polynomials of the Dihedral group

I'm interested in the one-dimensional irreducible representations of $D_{2n}$ acting on $\mathbb{R}[x,y]$. I have found that the trivial representations for an algebra freely generated by $x^2+y^2$ ...
0
votes
0answers
49 views

How to prove $\lim _{ \delta\rightarrow {0}^{+}}\int_{a}^{b} F_{\delta}(x)dx=0 ? $ [on hold]

This question comes from http://math.stackexchange.com/questions/982231/a-function-fx-that-riemann-integrable-on-a-b Define a function $f(x)$ that Riemann integrable on $[a,b]$. Let ...
2
votes
0answers
37 views

Invariant Theory over finite adeles

Classical invariant theory, among the other things, classifies polynomial functions over a vector space $V$ endowed with a quadratic form $Q$ which are invariant under the action of $SO(V,Q)$. I am ...
-2
votes
0answers
33 views

estimate angle between two lines y = 1000x and y = 999x [on hold]

How to estimate the angle between line y = 1000 x and y = 999 x? I use the calculator and get 10^(-6) but how to approximate it by hand. Does it relate to Taylor Expansion?
19
votes
3answers
541 views

Why is it so hard to compute $\pi_n(S^n)$?

Of course it isn't really that hard - nowhere near as hard as $\pi_k(S^n)$ for $k>n$, for instance. The hardness that I'm referring to is based on the observation that apparently nobody knows how ...
3
votes
0answers
35 views

The 4-th generator of $K_1$ group for 3-dimensional NC tori algebra

An $n$-dimensional NC torus algebra $A_\theta^{(n)}$ is defined for any antisymmetric $n\times n$ matrix $\theta$ of real numbers as the universal $C^*$-algebra, generated by unitaries ...
0
votes
0answers
56 views

The behavior of series involving special subsets of the prime numbers

It is well known that the series $\sum_{p\in \mathbb{P}} \frac{1}{p}$ diverges where $\mathbb{P}$ denotes the set of primes. Brun proved that $\sum_{p\in \mathbb{P_2}} \frac{1}{p}$ converges where $ ...
7
votes
1answer
138 views

A curious Gauss-Sum type identity

Let $q=e^{2\pi i/m}$, $a\in\mathbb{R}$ and $1\leq j\leq m-1$. I would like to prove that: $$(a-1)\sum_{n=0}^{m-1} q^n\frac{\prod_{k=0}^{j-2} (q^{n+k+1}-a)}{\prod_{k=0}^{j} (aq^{n+k}-1)}=0.$$ For ...
-8
votes
0answers
84 views

Is there a site where I should post questions about mathematics for which I seek a solution? [on hold]

Is there a site where I should post questions about mathematics for which I seek a solution, without risk that it will be closed for not being "research level"?
0
votes
0answers
18 views

Is there effective algorithm for finding “minimal discovery time” for large graphs?

Consider a large, probably sparse graph with Markovian random walkers on it. Define discovery time as time to first reach a vertex by random walk from uniform start. Are there effective ways to find ...
0
votes
0answers
24 views

Isotropic correlation function for a vector valued random field

I'm having trouble with some of the implications of the following theorem. Let $\mathbf{T} (\mathbf{x})$ be a mean-square continuous vector valued random field on $\mathbb{R}^3$ satisfying conditions ...
6
votes
0answers
78 views

What is known about the chromatic number for minimum-distance graphs in higher dimensions?

For a set of points in $\mathbb{R}^d$ with minimum distance $a$, the minimum-distance graph connect two points iff they are at distance $a$. We can also view it as the tangency graph for a set of ...
-5
votes
0answers
78 views

Which univariate function satisfies $e^{g(x)} + e^{-g(x)} = \alpha x$ for $x>0$ and some constant $\alpha>0$? [on hold]

Which univariate function $x \mapsto g(x)$ satisfies $$e^{g(x)} + e^{-g(x)} = \alpha x$$ for $x>0$ and some constant $\alpha>0$? How can it be computed? What does it look like? How can it be ...
-2
votes
0answers
67 views

toledo's lecture on cartwirght-steger surface [on hold]

I am interested in Toledo's lecture given in IAS workshop. I want to find some related reference about his lecture. While actually i am not able to find much. Is someone also interested in this and ...
0
votes
0answers
79 views

A probability application question

Suppose there are two possible states $H$ and $L$, with prior probability $p$ and $1-p$ respectively. There are infinite rounds with a discount factor $ d$. In round 1, you could choose a value ...
1
vote
0answers
23 views

About the $C^{1,1} $regularity of the boundary of a set

I am studying a paper that uses the following property : Consider $U$ and $V$ open, bounded and convex domains in $R^n$ with $U \supset \overline{V}$ and suppose that $min_{y \in V} |x - y| = \lambda ...
2
votes
1answer
102 views

Quantitative stability: Hausdorff distance between subdifferentials

Suppose I have two convex functions $f$ and $g$ mapping $\mathbb{R}^{n}\to\mathbb{R}$ (so they are 'more' than proper). Suppose $\|f-g\|_{\infty}<\epsilon$, the sup-norm. In particular, the ...
0
votes
1answer
99 views

Which $\frak{sl}_2$-Representations Arise From Hermitian Metrics

Recal that $\frak{sl}_2$ is the Lie algebra with basis elements $e,f,h$, and bracket $$ [e,f] = h, ~~~ [h,e] = 2e, ~~~ [h,f] = -2f. $$ For $M$ a $2n$-complex manifold, the Lefschetz identities tell us ...
3
votes
0answers
119 views

Monte Carlo variant of Hilbert's Tenth Problem

Let $k \in \mathbb{N}$. Given an algorithm $\mathcal{A}$ which takes as argument a polynomial $P \in \mathbb{Z}[x_1,\dots,x_k]$ and either returns true or false, we say that $\mathcal{A}$ works for ...
0
votes
0answers
65 views

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 ...
-2
votes
0answers
40 views

identity of equation [on hold]

We have the equation ($\partial_{\mu}\partial_{\nu}$-$\eta_{\mu\nu}\Box$)$\phi=0$, where $\phi$ is a scalar field, $\Box=\partial_{\mu}\partial^{\mu}$ is a standart Dalamber operator, $\eta_{\mu\nu}$ ...
-3
votes
0answers
241 views

College - Ecuation to solve in 3 variables (p,q,r) in [1,2] [on hold]

This is the image containing the ecuation
1
vote
1answer
37 views

orthonormal basis or Parseval frame for Sobolev spaces

Consider the uni-variate Sobolev space of order $m$: $$ \mathcal{W}_2^m=\{ f:[0,1] \rightarrow \mathbb{R}|f,f^{(1)},\dots ,f^{(m-1)}\, \text{are absolutely continuous and}\, f^{(m)}\in L^2\}.$$ It is ...
0
votes
0answers
68 views

Calculation in From Seiberg Witten to pseudo-holomorphic curve

I am reading the Taubes's paper: From From Seiberg Witten to pseudo-holomorphic curve. I don't know how to get the result (2.17) \begin{eqnarray*} ...
6
votes
0answers
114 views

scheme of commuting matrices

Let $k$ be any field. Let $r$ and $n$ be two positive integers. Consider the functor $F$ from the category of $k$-schemes to the category of sets which sends a $k$-scheme $T$ to the set of matrices ...
1
vote
0answers
27 views

Properties of solutions of Parabolic type equations

Assume $u\in C([0,1],L^{2})$ satisfies the following Schrodinger equation $$ \partial_t u=i(\Delta u+Vu), \text{in} ~\mathbb{R}^n\times[0,1],\\ u(0)=u_{0}. $$ with $V=V_1(x)+V_2(x,t)$, where $V_{1}$ ...
0
votes
2answers
73 views

Motivation for weak solution of a PDE (initial condition)

The following question came to me when reading the famous paper of ALT and LUCKHAUS: "Quasilinear elliptic-parabolic differential equations" When looking at a (nonlinear degenerate) PDE like $$ ...

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