# All Questions

0answers
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### bamwar3강남오피funexcitinggood

남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1bamwar3강남오피#1 ...
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 ...
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.
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 $$\sum_{a<n\le b}\{f(n)\}=\frac{1}{2}(b-a)+O(\lambda^{1/3}(b-a)+\lambda^{-1/2}).$$ ...
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 ...
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 ...
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 ...
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?
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 ...
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 ...
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 ...
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 ...
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. $(\lambda_i M)\cap B(p,R)$ ...
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.
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 ...
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
1answer
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### 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 ...
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 ...
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)?
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 ...
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 ...
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 ...
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 $Q$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 $T$ ...
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 ...
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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