-7
votes
0answers
7 views

bamwar3강남오피funexcitinggood

남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1 ...
9
votes
1answer
153 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 ...
-1
votes
0answers
29 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.
7
votes
1answer
302 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 ...
0
votes
1answer
103 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
72 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 ...
3
votes
0answers
40 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 ...
0
votes
0answers
63 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 ...
1
vote
3answers
124 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
54 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
75 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 $$\sum_{a<n\le b}\{f(n)\}=\frac{1}{2}(b-a)+O(\lambda^{1/3}(b-a)+\lambda^{-1/2}).$$ ...
3
votes
1answer
184 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
49 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
33 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
69 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
6 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
40 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
207 views

Beginners Guide to Cartan for Beginners

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. In particular, I am seeking ...
-3
votes
0answers
94 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
31 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
59 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
24 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
67 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
63 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
71 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
146 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
125 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
43 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
61 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
32 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
39 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
50 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 ...
0
votes
0answers
36 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
139 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
70 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)?
5
votes
1answer
123 views

When is $\vartheta(x)>x$? [Skewes number analog]

Let $\vartheta(x)=\sum_{p\le x}\log p$. What is known about the first time $\vartheta(x)>x?$ Bays & Hudson give good upper bounds (slightly improved by Chao & Plymen) on the first crossing ...
0
votes
0answers
98 views

Understanding the homotopy category of chain complexes [on hold]

In the definition of the Homotopy category of chain complexes http://en.wikipedia.org/wiki/Homotopy_category_of_chain_complexes , One defines maps between chain complexes in a certain way that I ...
0
votes
0answers
88 views

Shimura reciprocity law

I have spent quite some time understanding class fields generated by Kummer extensions and class fields generated by modular forms. Now, I am turning the notch of sophistication a bit to study class ...
0
votes
1answer
105 views

On understanding Orlov's LG B model

I try to read Orlov's papers on Landau-Ginzburg model, but I am quite puzzled,there are several questions: 1 the method of truncation is used frequently,(that is: using a bounded above complex $Q$ ...
-2
votes
0answers
63 views

Handwaving explanation of “unit root” sought [on hold]

I am struggling to get my head around the concept of "unit root" in relation to time series. And it would be a great help if someone could give me a two or three sentence handwaving explanation of the ...
-4
votes
0answers
35 views

Weak convergence in Lp [on hold]

Got a little problem with this ex. I could use some help. Let $U := \Pi_{i=1}^d(a_i, b_i) \subset \mathbb{R}$ ($a_i < b_i$ for each $i$) and let $f \in L^p(U)$ for some $1<p<+\infty$. Let us ...
0
votes
0answers
73 views

A consequenc of a Lie group act on a Riemannian manifold by isometry

I am learning differential geometry for using this topic in my research. I am stuck to prove following Result which I got in a article. Formulation: Let $ f: [0, 1]\rightarrow \mathbb{R}^2$ be a ...
1
vote
1answer
42 views

An optimization problem in complex space

Consider the following optimization problem $$ \min \| \textbf{Ax-B}\| $$ $$ s.t.|x_i|=1,i=1,...,n $$ where $\textbf{x}\in \mathbb{C}^{n}$ is the optimization varaible, $x_i$ is the $i$-th ...
1
vote
1answer
315 views

Numerical evidence and argument against Littlewood conjecture

This is joint work with someone. We got numerical evidence and argument against Littlewood conjecture, though mistakes are certainly possible. Littlewood conjecture states that for any two real ...
2
votes
2answers
87 views

Uniformly bounded operator family and pointwise convergence

Let $1 \leq p < \infty$ be fixed and let $\Omega \subseteq \mathbb{R}^n$ be open. Let $(Q_n)_{n \in \mathbb{N}}$ be a uniformly bounded family of operators on $L^p(\Omega)$, i.e. there exists ...
3
votes
1answer
89 views

Classify set theories whose transitive models sharing the same sets of ordinals are equal

This question is a follow-up from my recent question, Classifying set theories whose standard models sharing the same ordinals are equal Let's say that a (recursively axiomatizable) set theory $T$ ...
4
votes
2answers
152 views

“All retracts are closed” as separation axiom

The starting point of this question is the fact that any retract of a $T_2$-space is closed. Let's say a topological space $(X,\tau)$ is $T_{\textrm{rc}}$ if all retracts of $X$ are closed. All ...
1
vote
0answers
65 views

Lefschetz fixed notation

If $f\colon X\to X$ is a self-map of a nice space with isolated fixed points, then the Lefschetz fixed point theorem relates a global number to local numbers. Some write: $L(f)=\sum_{x\in ...

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