0
votes
0answers
5 views

Is there a Riemann existence theorem for orbifolds?

For smooth algebraic varieties $X$ over $\mathbb{C}$, the Riemann existence theorem establishes an equivalence of categories between the category of finite etale covers of $X$ and finite unramified ...
1
vote
0answers
5 views

Floquet-Bloch solutions of the quasiperiodic Schrödinger equation

I am concerned about the Schrödinger equation $-x''(t)+q(\omega t)x(t)=Ex(t).$ Here, the potential $q$ is real and quasiperiodic with frequency vector $\omega$. Equivalently, we may formulate this ...
0
votes
0answers
5 views

how to efficiently compute the mean function for non-homogeneous poisson process?

Suppose that I know all intensity functions lambda(t) during given period [0,t], how can I compute the mean function m(t) for non-homogeneous Poisson process? Basically, m(t) in the integral of ...
1
vote
0answers
17 views

Intersection of ordinary subspaces at different primes

Choose two distinct primes $\ell$ and $\ell'$, and embeddings $\iota_\ell : \overline{\mathbb Q} \to \overline{\mathbb Q_\ell}$, $\iota_{\ell'} : \overline{\mathbb Q} \to \overline{\mathbb ...
0
votes
0answers
42 views

Strong Morita equivalence and representation theory

In the context of pure algebra we say that two algebras (in general: rings) $A,B$ are Morita equivalence when there are bimodules $_AP_B,_BQ_A$ such that $P \otimes_B Q \cong _AA_A$ and $Q \otimes_A P ...
3
votes
0answers
25 views

Eigenvectors of a symmetric positive definite Toeplitz matrix

I wish to efficiently compute the eigenvectors of an n x n symmetric positive definite Toeplitz matrix K. A full eigendecomposition would be even better. Although I assumed this would be a well ...
1
vote
1answer
126 views

How many k-subsets of the integers {1,…,n} sum to N?

Given the set of integers $S = \{1,..n\}$, how many subsets of $S$ with $k$ elements sum to $N\in \mathbb Z$?
7
votes
3answers
172 views

Complete resolutions of GCH

Let's say that a "complete resolution of GCH" is a definable class function $F: \operatorname{Ord}\longrightarrow \operatorname{ Ord}$ such that $2^{\aleph_\alpha} = \aleph_{F(\alpha)}$ for all ...
1
vote
1answer
48 views

Simple Isogeny Question

I'm looking for a reference of an isogeny fact that I've used many times but am having a hard time proving formally. One can define the degree of an isogeny as the degree of extension fields of the ...
-4
votes
0answers
32 views

transition matrix [on hold]

Gene mutation. Suppose a gene in a chromosome is of type $A$ or type $B$. Assume that the probability that a gene of type $A$ will mutate of type $B$ in one generation is $10-4$ and that a gene of ...
11
votes
1answer
108 views

Nonperiodic points of homeomorphisms of a ball

Suppose $B$ is a $d$-dimensional ball (for some $d \geq 1$) and $T$ is a homeomorphism from $B$ to itself. Suppose also that $T$ is not of finite order (that is, for no $n \geq 1$ is it the case that ...
0
votes
0answers
29 views

Does an arbitrary product of $f$ and $f^\dagger$ belong to a universal enveloping algebra of the Heisenberg algebra?

The Heisenberg algebra is essentially the canonical commutation relations (CCR) for bosons $[f,f^\dagger]=1$. $f$ is called an annihilation operator in physics ($f^\dagger$ creation operator). ...
2
votes
0answers
23 views

Existence of solution to weak form of linear equation with boundary integral (parabolic PDE)

Let $W(0,T) := \{ u \in L^2(0,T;H^{\frac 12}(\partial\Omega)) \mid u_t \in L^2(0,T;H^{-\frac{1}{2}}(\partial\Omega))\}$. Let $\gamma$ and $\xi$ denote the trace map and its right inverse. Does there ...
3
votes
1answer
182 views

Example of a Frobenius algebra that is not projective over a Frobenius subalgebra

I'd like to know an example of a Frobenius algebra $A$, with a subalgebra $B$ that is itself a Frobenius algebra, such that $A$ is not projective as a left $B$-module. I don't require any ...
12
votes
1answer
801 views

The letters of the word “ART”

Are there only a finite number of connected topological spaces $X$ (up to homeomorphism) with the property that $X$ has an open subset $U$ such that $U$ and $X-U$ are homeomorphic to $\mathbb{R}$? I ...
-2
votes
0answers
38 views

Linear algebra over principal rings 1 [on hold]

If N is a left-idea of ring R and R is a left R-module, then submodule N is a direct sum if and only if N has a right unit.
11
votes
1answer
695 views

Joyal's letter to Grothendieck

Mostly out of curiosity: Where do I find Joyal's letter to Grothendieck in which he defines a model structure on simplicial sheaves? The question was already asked in this MO post, but that ...
-1
votes
1answer
143 views

journal to submit mathematic books' review

it has been asked to me to write a review on a book about the history of mathematics in Italy between the two world wars. The book is a non-technical one. I would like to know which journal accepts ...
0
votes
0answers
104 views

On matrix rank inequality

Let $A$ be a $\{0,1\}$ square matrix. Let $J$ be all $1$ matrix. Let $\bar{A}=J-A$. Is it possible for $rk_+(A)\geq c\cdot rk_+(\bar{A})^d-1$ and $rk_+(\bar{A})\geq c\cdot rk_+({A})^d-1$ for some ...
5
votes
1answer
128 views

Can ergodic theory help to prove ergodicity of general Markov chain?

I am a beginner in ergodic theory. I have read some lecture notes(such as this and this) about it in hope that I could find something which helps to prove the ergodicity of some Markov chain taking ...
1
vote
0answers
93 views

Real algebraic solution

Suppose a system of polynomial equations with rational coefficients has a real solution. Does necessarily there exists a real solution with algebraic coordinates? What about the simplest case of one ...
3
votes
3answers
174 views

Injective map between two schemes

Assuem we have a finite surjective map between two irreducible, separated schemes, $f:X \rightarrow Y$, and for a dense open $U \subset Y$ and for any $y \in U$, $|X_y| =1$, then can we say $f$ is ...
1
vote
1answer
68 views

Dual connections for Information Geometry

In information Geometry, there is a definition of dual connection, which is: two affine connections $\nabla$ and $\nabla^*$ are called dual if they satisfied ...
-2
votes
1answer
103 views

Prove that $\sum_{a<n\le b}\{f(n)\}=\frac{1}{2}(b-a)+O(\lambda^{1/3}(b-a)+\lambda^{-1/2})$ [on hold]

Let $a,b\in\mathbb{Z}$, and $f\in C^2([a,b])$ such that $|f''(t)|\asymp \lambda$ for $a\le t\le b$. Prove that $$\sum_{a<n\le b}\{f(n)\}=\frac{1}{2}(b-a)+O(\lambda^{1/3}(b-a)+\lambda^{-1/2}).$$ ...
4
votes
1answer
241 views

Results about moduli of surfaces

There are early successes of the moduli theory - the construction and compactification of the moduli spaces of curves $\overline{\mathcal{M}}_g$ . I want to study about the moduli of algebraic ...
-2
votes
0answers
53 views

Finding an example for [on hold]

Let $\varphi$ be a periodic function s.t. at zero and every integer points it is equal to 1. Moreover it's equal to one in at least one point between each integer. Can we have two distinct density ...
2
votes
0answers
60 views

invariant measures of the expanding maps on the circle

I would be very happy to know about original references for the following results; For the expanding map $x \mapsto mx$ on the circle, (with $m$ some integer greater than 1) (1) There exist ...
2
votes
1answer
78 views

How to construct a graph with arbitrarily large girth and large chromatic number? [on hold]

Erdos theorem says it is possible and it is not so easy. What is the general procedure to construct graphs like Grötzsch graph?
0
votes
0answers
7 views

Looking to derive bound for modulus of harmonic eigenfunction on weighted graph

We have a homogeneous graph $G = (V,E)$ with a function $f:V\rightarrow \mathbb{R}$. We define the following modulus: $\displaystyle \omega(s) = \sup\{f(x)-f(y) \ | \ |x-y|=s \}$ and wish to lower ...
-4
votes
0answers
42 views

Height of a tripod [on hold]

I am trying to determine the height of a tripod when the length on the tripod's legs (81") and the distance between the ends that touch the ground are 57" apart. My thought process so far: When the ...
4
votes
1answer
333 views

Beginners Guide to Cartan for Beginners [on hold]

I am working through parts of Cartan For Beginners by Ivey and Landsberg. Thankfully some exercises have solutions, but, we would benefit from some additional guidance. Question: I am seeking ...
-3
votes
0answers
102 views

Cylinder in a topological space? [on hold]

There is a notion of path in a topological space $X$, namely a continuous function f with domain X and codomain the interval $[0, 1]$. Given that, in a Quillen model category, the dual of a path ...
0
votes
0answers
33 views

Is the blowing up the rectifiable set cone?

Let $M$ be a rectifiable set in $\mathbb{R}^N$. For any point $p\in M$, is the following true?: $\lambda_i M$ subconverges to a cone in $p$ for $\lambda_i\to\infty$, i.e. $(\lambda_i M)\cap B(p,R)$ ...
-2
votes
0answers
45 views

Proof of Kolomogrov-Sinai Theorem [on hold]

I've seen reference to the result, but have not been able to actually locate a proof of said theorem. If anybody here could point me that way, then I'd greatly appreciate it.
-3
votes
0answers
63 views

Isoceles Triangles on a Grid Proof [on hold]

Given: A Finite Set of Unit Squares on a Large Grid. If we were to choose one of those sets of unit squares, we see that the squares of the set are tiled with isosceles right triangles, each with a ...
-2
votes
0answers
25 views

Transformation Matrix Problem [on hold]

Can anyone break down this Transformation Matrix process for me after the characteristic polynomial? http://i.stack.imgur.com/xdvyp.png
0
votes
1answer
72 views

Inverting using the Lambert $W$ function

I apoligise if this question is too elementary for this site but I believe that it may possibly lead to more interesting questions. Given an expression, say $$x(t)= (t^2 - ...
0
votes
0answers
71 views

Pathological behavior of Lie algebra under a map of abelian schemes

I am trying to understand Example 7.5/9 from the book "Neron models". There one has a discrete valuation ring $R'$ that is the localization of $\mathbb{Z}[\zeta_p]$ at $p$, so that the absolute ...
7
votes
0answers
99 views

Preserving Jonsson cardinals

I am (still) interested in trying to characterize and describe forcings that preserve Jonsson cardinals. A cardinal $\kappa$ is a Jonsson cardinal if there is no Jonsson algebra on $\kappa$, i.e. ...
6
votes
1answer
157 views

Diagonalization of the matrix $(1/(i+j+\rm{const}))_{i,j}$

Consider the following infinite matrix: $A_{i,j}=\frac1{i+j+\gamma}$, $0\leq i,j<\infty$, $\gamma>0$ is a constant. Is it known how to diagonalize $A$, or, say, calculate $(I+tA)^{-1}$ for ...
3
votes
1answer
133 views

Is there a “natural” bijection between models of $ZFC$ and $ZF\neg C$?

I'm quite confident that there is the same number of models of $ZFC$ and of $ZF\neg C$, which means that there would exist a bijection between the former and the latter, by definition. However, I was ...
1
vote
1answer
50 views

Image of (right) inverse trace map $\xi\colon H^{\frac 12}(\partial\Omega) \to H^1(\Omega)$ dense in $H^1(\Omega)$?

Let $\gamma\colon H^1(\Omega) \to H^{\frac 12}(\partial\Omega)$ be the linear trace map which has a right continuous inverse $\xi\colon H^{\frac 12}(\partial\Omega) \to H^1(\Omega)$. Is the image of ...
2
votes
1answer
76 views

Hopf structures on “pictorial” descriptions of permutations

There is a well-known Hopf structure on permutations, due to Malvenuto and Reutenauer. Here, the F basis elements are permutations in one-line notation, the product of two permutations is their ...
1
vote
0answers
35 views

Reducing enumeration of reduced words in general Coxeter groups to another #P-complete problem

There is a polynomial time algorithm that takes as inputs a Coxeter system $(W,S)$ with $S$ finite (but with $W$ not necessarily finite), say encoded as a Coxeter matrix, as well as two reduced words ...
2
votes
0answers
41 views

Application of Egorov's Theorem for Pseudodifferential Operators

Let $\;P_{0} \in OPS^{m}_{1,0}(\mathbb{R}^{n} \; \times \; \mathbb{R}^{n})\;$, $\;A \in OPS^{1}(\mathbb{R}^{n} \; \times \; \mathbb{R}^{n})$ and $S(t)$ the solution operator of the scalar hyperbolic ...
0
votes
1answer
53 views

contracting homotopy on simplicial sets

Let $X$ be a topological space and let $PX$ be its space of paths. Let $I=[0,1]$ with coordinate $s$. There is an homotopy $$ F\: : \: I\times PM\to PM $$ Defined by $F(s,y)(t):=y(st)$. This map is an ...
-2
votes
0answers
27 views

Solving nonlinear system of ODEs

I have the following system of differential equations: $$ \begin{cases} \frac{dx}{dt} = (1 - y) x - 0.4 xu \\ \frac{dy}{dt} = (x - 1)y - 0.2yu \\ \psi_1' = - \frac{dH}{dx} = (-1 + 0.4u)\psi_1 + y ...
2
votes
0answers
63 views

Is there any study about positive definiteness of some matrix space whose matrices don't have to be positive-definite?

--Updated description-- I'm trying to investigate the stability of tensegrity structures, and this question is related to the second order test. Suppose there is a vector space ...
4
votes
1answer
145 views

Which criteria for “uniformly splitting” polynomials?

Let $P(x)$ be an irreducible monic polynomial of degree $\ge4$ with integer coefficients. We all know that over a finite field $\mathbb F_p$, $P$ will often split, and I am interested in polynomials ...
0
votes
1answer
74 views

References: Solutions of the Bethe Ansatz Equations [on hold]

Could someone show me good references to find solutions of the Bethe Ansatz Equations, for simple cases (using algebraic geometry or others interfaces with mathematics)?

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