2
votes
0answers
20 views

Can a nowhere differentiable function preserve measurability?

I want to know whether a continuous nowhere differentiable function $f: \mathbf{R} \to \mathbf{R}$ can map Lebesgue measurable sets to Lebesgue measurable sets. More generally I'm interested to know ...
0
votes
0answers
7 views

Ddifference between deduct and deduce [on hold]

In the context of logic, the term "deduction" was used as a way of thinking. I think, apparently, the verb of "deduction" should be "deduct", hence it is natural and reasonable to use the term ...
1
vote
0answers
41 views

$\Bbb A^1$-Localisation of Schemes, and $\Bbb A^1$-Rigid Schemes

Question 1: Are there some publications or preprints that provide $\Bbb A^1$-fibrant replacements of certain classes of (smooth) schemes? Of course, smooth schemes that are $\Bbb A^1$-fibrant are ...
2
votes
0answers
43 views

Dessin d'enfant and moduli space of bordered/punctured hyperbolic Riemann surfaces

Belyi's theorem states that if a Riemann surface could be defined as an algebraic curve over an algebraic number field, then this Riemann surface could be described by a Dessin d'enfant. I have two ...
0
votes
0answers
41 views

“Sheaf” on the nerve of a category

So I have the nerve of a category and want to communicate information about the sets at each level in the simplicial set (nerve). Is there a way to regard the nerve as a category itself? Then one ...
7
votes
2answers
183 views

Homotopy groups of Moore spaces

Is there anything known about the homotopy groups of the Moore spaces $M(\mathbb Z_m,n)$ if $m\neq 2$ and $n \geq 2$?
0
votes
1answer
18 views

Convergence of unitary products on a Hilbert space

First: I'm sorry for the basic question--I can move it to Math SE if necessary... Let $X$ be a Hilbert space and suppose $\{U_k\}_k$ is a sequence of unitary operators on $X$. Let $||\cdot||$ be the ...
-1
votes
1answer
65 views

Normalization of complete intersection

Let A be an integral complete local ring over a field which is complete intersection. Let B be a normalization of A. Q. Is B gorenstein? I guess that even the normalization of gorenstein local ...
-1
votes
0answers
23 views

Condition to be Fourier coefficients for an periodic function

It is well known that a periodic function $f(t)$ satisfying Dirichlet conditions has its unique Fourier series representation. Inversely, I wonder what conditions is needed for sequence $\{c_n\}_{n ...
-4
votes
0answers
40 views

Probability problem - no idea where to start [on hold]

I have been working on this question for a few days and I am completely lost on how to solve it. Any suggestions, comments, hints are greatly appreciated. Participants are competing in a ...
0
votes
0answers
64 views

Is the category Cat complete? [on hold]

Let $Cat$ denote the 2-category of small categories. Is $Cat$ complete? That is, given a diagram $\phi:J\rightarrow Cat$, does the limit over the diagram exist in $Cat$?
0
votes
0answers
29 views

Groebner basis of algebraic system of polynomials [on hold]

I have 8 polynomials with 8 unknowns as {p,L,x1,x2,y1,y2,z1,z2}, and the remaining are all known coefficients. The polynomials are as follows: f1=h1*p - L*(h1*xb*y2 - h2*x1*y1 - h3*x2*y1) + h4; ...
0
votes
0answers
28 views

Arnold chord conjecture

Recently I've started learning about the Arnold conjecture for the number of Reeb chords on a Legendrian submanifold of a contact manifold. It says that under some conditions, the number of Reeb ...
0
votes
0answers
38 views

Number of solutions to a modular congruence

What methods are there for determining the number of solutions to modular congruences of the form $a^m \equiv b^n k \pmod{p}$ with $1 \leq a,b \leq p-1$ where $p$ is a prime? In the case $m,n$ ...
-2
votes
0answers
50 views

Could it be possible to check if Pi is a normal number? [on hold]

So currently we don't know if Pi is a normal number and if it really contains all finite number sequences. Is it possible that we will know this in the future? Can we be sure one day?
9
votes
1answer
152 views

Digital physics and “Gandy-like” machines

Various physicists, famously John Wheeler, have asserted that physical information is the central object of study in physics, in the sense that an object or concept is "physically meaningful" if it ...
2
votes
0answers
96 views

Show that $SL_2(\mathbb{F}_p)$ is quasi-random

Terry Tao gives this oblique definition of quasirandom group in his notes 3 $G$ is quasi-random (of order $D$) if all non-trivial unitary representations $\rho: G \to U(H)$ have dimension at ...
7
votes
1answer
558 views

Should I quit the PhD? [on hold]

I am not sure whether this is the right place to post this question. I am at the end of my seventh year. I won't have funding neither from my department nor from my advisor next year and I do not ...
1
vote
2answers
40 views

What does the existence of self complemented elements tell us about a complete lattice?

Let $L$ be a complete lattice with an involution operation $*$ (a unary operation such that for any $x, y \in L$, $x \leq y$ implies $x^{*} \geq y^{*}$). Now, suppose that there is an element of $L$ ...
-3
votes
0answers
85 views

Math notation with no possible syntax errors [on hold]

It surely is possible for e.g. simple integer arithmetic to invent a notation where every statement is syntactical correct, just enumerate them - "#" means "0=0", "##" "0=1", maybe "#...#" (239 of ...
0
votes
0answers
57 views

Taylor-Series e^e^x [on hold]

I'm new to the whole topic of Taylor-Series and I am trying to figure out the Taylor-Series of $e^{e^x}$. I got the derivatives but that doesn't help right now. I think I need the n-th derivative, ...
3
votes
2answers
163 views

Relation of these two Dirichlet $L$-functions

Let $\chi$ and $\psi$ be two quadratic Dirichlet characters and let $L(s,\chi)$ and $L(s,\psi)$ their associated Dirichlet $L$-functions. Is there a realtion between these two Dirichlet ...
0
votes
0answers
58 views

Free Symmetric Operads

In the definition of operads, if we restrict our attention to S-modules where the action by the symmetric groups is free, then the free operads have still an underling "free S-module"? Even the ...
3
votes
1answer
174 views

Number of prime divisors of p^2-1 for a prime p

Let $n$ be an integer and $n=p_1^{a_1}\dots p_s^{a_s}$ be its factorization into primes. Denote by $\Omega(n)$ the sum of $a_i$. Does there exist a constant $k$ such that there are infinitely many ...
-2
votes
0answers
29 views

Expected number of tree component should be less than equal to zero in random graph [on hold]

In Erdos-Renyi random graph $G(n,p(n))$, set $p(n) ≥ (\frac{\ln n}{10n})$. We want to show that expected number of tree component on 11 vertices with this probability $p(n) ≥ (\frac{\ln n}{10n})$ ...
9
votes
0answers
93 views

List of Applications of the $\partial\overline{\partial}$-lemma

Quoting from Huybrecht's book Complex Geometry on the $\partial\overline{\partial}$-lemma for Kaehler manifolds: Although it looks like a rather innocent technical statement, it is crucial for ...
-1
votes
1answer
112 views

Invariance of the fiber-dimension of a finite map

Let $A\subseteq B$ be commutative Noetherian rings such that $A$ is a regular ring, i.e., $A_{\mathfrak{m}}$ is a regular local ring for all maximal ideals $\mathfrak{m}$ of $A$ and $B$ is a finite ...
0
votes
0answers
17 views

Is the Lopatinski-Shapiro condition invariant under diffeomorphism?

If a PDE (eg. the heat equation with Robin BCs, or the elliptic version) on a bounded smooth domain $U$ satisfies the Lopatinski-Shapiro condition (for a definition see eg. Wloka), and if $T:U \to W$ ...
5
votes
2answers
238 views

Kazhdan's property (T) vs. residual finiteness

I have asked this question already on mathstackexchange but got no answer (see http://math.stackexchange.com/questions/1795795/kazhdans-property-t-vs-residual-finiteness) and it was suggested that I ...
3
votes
2answers
86 views

Cube Lemma on a cofibrantly generated (almost) model category

Suppose I have a complete and cocomplete category $\mathscr{C}$ with two sets of maps $I,J$ that are the candidates for generating (trivial) cofibrations on a model structure on $\mathscr{C}$. The ...
1
vote
1answer
113 views

Interpreting peano arithmetic without parameters

I will accept an answer in the form of references to the literature about my question as well as any other information. I am quite ignorant of the area and that will be clear from my question. I ...
11
votes
1answer
162 views

Does a Kähler manifold always admit a complete Kähler metric?

Every smooth manifold admits a complete Riemannian metric. In fact, every Riemannian metric is conformal to a complete Riemannian metric, see this note. What about in the Kähler case? Does a ...
3
votes
0answers
69 views

Deformation quantization of Poisson bracket without star-product

Kontsevich's formality theorem implies in particular that star-products on a $C^\infty$-manifold $M$, $$f\star g = fg + \sum_{k\geq1} \hbar^k B_k(f,g),\qquad f,g\in C^\infty(M),$$ where $B_k$ are ...
1
vote
1answer
70 views

Ask for a special function related to the error function

I am wondering whether anyone knows the following integration has a named special function or a reference $$ F_{a,b}(z) :=\frac{2}{\sqrt{\pi}} \int_0^z \text{erf}(a+b y)\: e^{-y^2} \text{d}y $$ for ...
5
votes
1answer
156 views

Is this weak form of $V=L$ (in)consistent with large cardinals?

I have been considering a (definability-free) weak form of the constructibility axiom, which is intended to capture the coarse structure of the constructible hierarchy. This means that this weak form ...
0
votes
0answers
24 views

max min of ratio of quadratic forms

Consider the optimization over two vectors $x$ and $y$ $$\max_{x,y} \min\left(\frac{x^TAx}{y^TAy},\frac{y^TBy}{x^TBx}\right)$$ for two positive definite matrices $A$ and $B$. This problem can be ...
-3
votes
0answers
109 views

Detecting Bijection between two Permutation Set [on hold]

Let, $L$ is a set of $n$ labels / colors (repetition of label/color is possible). Assume, there is a function $f$, that maps labels of $L$ to itself. this mapping is bijective. Let, $\beta$ is a set ...
1
vote
0answers
32 views

Continuously variable *space*

I'm trying to understand formally how and why a fiber bundle with fiber $F$ should be thought of as a gluing of homeomorphic copies of $F$ which varies continuously. I do not understand how this is ...
5
votes
0answers
44 views

Calculation of characteristic strip, solutions of a geometric PDE [on hold]

Say I have a family of spheres of radius $1$ with centers in the $xy$-plane$$u = G(x, y, \lambda, \mu) = \sqrt{1 - (x - \lambda)^2 - (y - \mu)^2}.$$I've found that $u_x = -(x - \lambda)u^{-1}$ and ...
1
vote
1answer
60 views

Convexity of truncated expectation

Let $k, n$ be two positive integers with $k \leq n$, and let $P = \{ (x_1, \dots, x_n) \in [0, 1]^n : \sum_i x_i = k \}$. Given $x = (x_1, x_2, \dots, x_n) \in P$, let $X_i$ be the random variable ...
0
votes
0answers
143 views

Warren's Theorem

At the end of page 12 in this document Noga Alon mentions Warren's Theorem on sign patterns: tau.ac.il/~nogaa/PDFS/tools1.pdf Does anyone know of an intuitive explanation of the proof of it ? Also, ...
4
votes
1answer
249 views

The Hypercomplex Structure of $SU(3)$

(A) In this really stylish answer it is shown that one can define a family of complex structures $J_{\lambda}$ on the Lie group SU(3), dependent on the parameter $\lambda \in {\mathbb C}\backslash ...
1
vote
0answers
73 views

A probability question related to combinatoric problem

I am trying to solve a combinatoric problem. The problem is the following: There are A,B,C three types of people. There are totally N people arriving sequentially and make a choice between two boxes X ...
5
votes
1answer
95 views

Interior periodic points of area preserving homeomorphisms of a pair of pants

A celebrated result of Franks shows that any area preserving homeomorphism of the closed annulus $A$ with at least one periodic point (possibly along the boundary) has infinitely many interior ...
5
votes
1answer
193 views
+50

Any similar Lagrange's identity inequality

we know Lagrange's identity $$(a^2_{1}+a^2_{2}+a^2_{3})(b^2_{1}+b^2_{2}+b^2_{3})=(a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3})^2+\sum_{i=1}^{2}\sum_{j=i+1}^{3}(a_{i}b_{j}-a_{j}b_{i})^2$$ then we have ...
7
votes
2answers
148 views

Is there a rate of convergence for Donsker's theorem?

For the standard CLT, one can easily estimate a rate of convergence if you assume that the random variables have a little more than two moments. Let $S_n$ be the centered-scaled sum of $n$ iid ...
5
votes
1answer
116 views

Can samples be compressed?

The Fisher information of a random variable $Y$ about a parameter $\theta$ upon which the probability of $Y$ depends is: $\mathcal{I}_Y(\theta)= -E\left[\left.\strut \frac{\partial^2}{\partial ...
1
vote
0answers
58 views

Finding the infimum using a piecewise isometry

Given a finite set of unit circles in the plane such that the area of their union $U$ is $S$, what is the largest possible bound $kS$ for some constant $k$ such that there exists a subset of ...
117
votes
81answers
94k views

Do good math jokes exist? [closed]

Have a good joke? Share. I know this is subjective, but the principle "should be of interest to mathematicians" trumps. (I hope.)
15
votes
3answers
368 views

Evaluating an infinite sum related to $\sinh$

How can we show the following equation $$\sum_{n\text{ odd}}\frac1{n\sinh(n\pi)}=\frac{\mathrm{ln}2}8\;?$$ I found it in a physics book(David J. Griffiths,'Introduction to electrodynamics',in ...

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