# All Questions

**-2**

votes

**0**answers

33 views

### T is not compact operator [migrated]

I want to show that if $T$ is a bounded operator between two Hilbert spaces and $T$ is not compact then there exists an orthonormal sequence $y_{n}$ and an $R>0$ such that $\forall n\in ...

**-3**

votes

**0**answers

35 views

### Find the integral [on hold]

How can we find the integral of the 1/(1+x^4) in the interval -infinity to +infinity.I tried to find and got it to be pi/sqrt(2). Am I correct? Please help me with an appropriate method. I tried to ...

**3**

votes

**1**answer

114 views

### When are all sums of the elements of a set different?

Consider a set $S = \{x_1, \dots, x_n\} \subset \mathbb{Q}\setminus\{0\}$ and assume that for any $I, J \subset [n]$ with $I \neq J$ we have that
\begin{equation}
\sum_{i \in I} x_i \neq \sum_{j \in ...

**1**

vote

**0**answers

24 views

### Recognizing bridgeless cubic graph with special 2-factor

A 2-factor of graph $G(V, E)$ is a set of vertex-disjoint cycles that cover $V$. It is known that every connected bridgeless cubic graph contains a 2-factor (and a perfect matching).
I conjecture ...

**7**

votes

**2**answers

302 views

### Painting $n$ balls from $2n$ balls red, and guessing which ball is red, game

The game
Lucy has $2n$ distinct white colored balls numbered $1$ through $2n$. Lucy picks $n$ different balls in any way Lucy likes, and paint them red. Lucy then giftwrap all the balls so that it is ...

**2**

votes

**2**answers

194 views

### What is the difference between the moduli space of curves and the moduli space of orbi-curves?

Edit: In my original framing of this question it was not so clear what I was looking for, so this is basically a re-write.
I feel that I should already know the answer to this, but it never sits ...

**1**

vote

**1**answer

119 views

### Does Schur's Lemma hold in this case? Regular representations of $S_n$ over $\mathbb R$

Warning I am a physicist and I am not familiar with a lot of the machinary of representation theory.
I consider the regular representation of $\mathbb S_n$ over reals $\mathbb R$ ($\mathbb R \mathbb ...

**1**

vote

**0**answers

43 views

### Looking for the manuscript “Uniform polytopes” by N. Johnson

The manuscript Uniform Polytopes (1991) by Norman Johnson is cited in the wikipedia page on uniform polytopes (http://en.wikipedia.org/wiki/Uniform_polytope).
Is there an electronic copy of this ...

**0**

votes

**0**answers

12 views

### Functional representation of adapted jointly measurable stochastic processes

It seems like the question stated here in MSE has no answer yet and seems therefore for me to be not of a basic question type. For this reason I move it to MO.
Let $X_t : \Omega \to E, \ t \geq 0$ be ...

**5**

votes

**1**answer

181 views

### Meaning of $g_d^r$ in algebraic geometry

As an editor I often encounter the symbol $g_d^r$ as a noun. I tried googling but I only get papers where the symbol is used without a definition. Can someone supply a reference to a definition? ...

**0**

votes

**0**answers

25 views

### Projective dimension of a sub-ideal

Let $\mathbf{k}$ be a field, and let $S=\mathbf{k}[x_1,x_2,\ldots,x_n]$. Let $I\subset J$ be finitely generated monomial ideals in $S$. Is it true that the projective dimension of $I$ is either ...

**0**

votes

**0**answers

47 views

### K-Permutations with forbidden numbers [on hold]

This question has some references to programming and not as many mathematical terms as you might like, but I think it's more appropriate in a mathematics forum.
Introduction (Skip if you are ...

**6**

votes

**1**answer

112 views

### Which finite p-groups occur as commutators of finite p-groups?

Let $p$ be a prime number. For which finite $p$-groups $H$ there is a finite $p$-group $G$ such that $[G,G] \cong H$?

**-1**

votes

**0**answers

36 views

### maximal abelian subgroup [on hold]

let M(G) denote the set of orders of maximal abelian subgroups of G. If M(G) = M(H), for some group H then what can we say about the prime numbers that divide the order of each group G and H?

**4**

votes

**1**answer

108 views

### “Inverse problem” for the zeta function [duplicate]

Let $C$ be a smooth, projective, geometrically irreducible curve, of genus $g$, over a finite field $\mathbb{F}_q$. By the Weil conjectures, the zeta function has the shape
$$
...

**8**

votes

**1**answer

1k views

### How can I have a copy of this old paper by Frobenius?

How can I have a copy of this old paper and a translation of it?
Frobenius, G. (1902). Uber primitive Gruppen des Grades n und der Klasse n - 1. S. B. Akad. Berlin 1902, 455-459.

**5**

votes

**1**answer

210 views

### What does the sum of the reciprocals of all the highly composite numbers converge to?

I've calculated the sum of the reciprocals of all the $156$ first highly composite numbers up to $10^{18}$:
$\sum \dfrac{1}{HCC(n)} = \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{6} + \dfrac{1}{12} + ...

**12**

votes

**12**answers

1k views

### Obscure Names in Mathematics [on hold]

I recently stumbled over the "Happy Ending Problem" (cf e.g. http://en.wikipedia.org/wiki/Happy_Ending_problem), which made we wonder, if there are other conjectures, theorems or problems, whose names ...

**1**

vote

**0**answers

60 views

### Uniqueness of the maximum derivative of a rational function

This may seem like an elementary question, but bear with me; you'll find that it is actually quite hard. Consider the function
$$f(x)=\frac{a_nx^n}{\sum_{i=0}^n a_ix^i}$$
with all $a_i\geq 0$ and ...

**1**

vote

**2**answers

87 views

### Deformation quantization of a closed Riemann surface with genus >1

Quantization of of an elliptic curve can be done in different ways.
In C^*-algebraic version,
one can start with the C^*-algebra ...

**-3**

votes

**0**answers

47 views

### Proving how many divisors of a prime factorization (including 1 and n) there are [on hold]

I'm trying to figure out this problem but I'm not sure where to start. Could anyone explain to me the question a bit more in depth or give a few hints?
The problem is,
Let n in Z+ with prime ...

**0**

votes

**0**answers

19 views

### Comparing the inverse of a diagonally dominant matrix [migrated]

I have a $d \times d$ matrix $A$ whose entries are bounded (C1): $I - \epsilon X \preceq A \preceq I + \epsilon X$, where $I$ is the identity matrix and $X = 11^\top - I$ is the matrix with ones ...

**-4**

votes

**0**answers

27 views

### How to know which make which surjective and which Tor is correct to represent them surjective for codordism [on hold]

when A connect B through cobordism
A --- cobordism ----B
from view of function, when define surjective
there exist a function g to make f surjective such that g ...

**-2**

votes

**0**answers

101 views

### Is the configuration space of infinite sphere contractible? [on hold]

Let $\Sigma$ be suspension.
Let $S^0$ be $0$-sphere.
Let $\Sigma^\infty S^0$ be the union $\cup_n \Sigma^n S^0$ with respect to the inclusion $\Sigma^kS^0\subset \Sigma^{k+1}S^0$.
Let ...

**22**

votes

**1**answer

535 views

### Making $\mathbb{Q}$-cohomology integral

Let $X$ be an algebraic variety (say, smooth and projective) over $\mathbb{C}$, and fix $$\alpha\in H^i(X^{\text{an}}, \mathbb{Q})$$
with $i>0$.
Does there always exist a variety $Y$ and a ...

**-1**

votes

**0**answers

16 views

### state of art pseudo-boolean optimization solver [on hold]

I am actually constructing engineer application based on pseudo-boolean optimization. I want to ask what is the current status (how many variables, interaction parameters) the solver could generally ...

**0**

votes

**0**answers

170 views

### A problem of a hacked article [on hold]

I am surprised by the fact that a journal published an article that I have in arxiv for a few months. The date of publication is after the date that I have in arxiv. The submission date in the ...

**3**

votes

**2**answers

299 views

### Intuition behind $\zeta(2) = \frac{\pi^2}{6}$ [on hold]

In literature, there are many proofs of the well-known result $$\zeta(2) = \frac{\pi^2}{6}.$$
However, as far as I know, they do not offer an intuitive explanation of why this result should be true. ...

**2**

votes

**3**answers

324 views

### How did the summation operation come into use? [on hold]

So we've been using summations at least since the dawn of calculus. I'm wondering how the process of summing a function came to be known? Are there events that led to the invention of the summation ...

**1**

vote

**1**answer

152 views

### Quotients and radicals

Let $I, J$ be ideals in a commutative ring with identity $R$. Define the quotient ideal $(I : J)$ by $$(I : J)=\{x\in R : xJ\subseteq I\}.$$
Define the radical $r(A)$, of an ideal $A$ of $R$ by
...

**-3**

votes

**0**answers

28 views

### Operations research and Linear Programming [on hold]

I am working on a linear programming maximization problem and need help in understanding how to reformulate this problem so that it has only two functional constraints and all variables have ...

**-1**

votes

**0**answers

73 views

### Combinatorial Proof Problem [on hold]

I'm having trouble solving this because I'm only familiar with algebraic proofs instead of combinatorial.
$$\binom{3n}{3}=n^3+6n\binom{n}{2}+3\binom{n}{3},\quad\text{for }n\ge3.$$

**4**

votes

**0**answers

59 views

### The name for the quotient property

I asked this question on math@stackoverflow and was suggested to ask it here as well.
We call a surjective $f:X\rightarrow Y$ a quotient mapping if it satisfies, for every $U\subset Y$
...

**-1**

votes

**0**answers

62 views

### How to prove that the vertices of a convex hull are only defined by some specific subsets, in this particular case [on hold]

Let $\mathbb{V}$ a vector space of dimension $2^N$, where each vector (of size $N$) is a combination of $0$ and $1$. ex: for $N=2$, $\mathbb{V}$={[0 0],[1 0],[0 1],[1 1]}.
Consider (in ...

**15**

votes

**2**answers

502 views

### Teaching the fundamental group via everyday examples

This is a "prequel" to a similar question about homology. Both questions were inspired by seeing a talk, by Tadashi Tokieda, about the interesting physics that appears in toys.
What stories, ...

**2**

votes

**1**answer

122 views

### Various definitions of the Bruhat decomposition of the affine Grassmannian

Let $G$ be a connected, simply connected, complex, semi-simple group with affine Grassmannian $\mathcal Gr \cong G(\mathbb C[t,t^{-1}])/G(\mathbb C[t])$. Fix a choice of maximal torus $T \subset G$ ...

**3**

votes

**0**answers

60 views

### A problem on chains of squares — can one find an easy combinatorial proof?

Consider the unit square $ S = [0,1] \times [0,1] $. For each $ n \in \mathbb{N} $, we can tessellate $ S $ by the collection
$$
A
= \left\{
\left[ \frac{i}{n},\frac{i + 1}{n} \right] \times
...

**0**

votes

**0**answers

134 views

### Publishing in mathematics [on hold]

I apologize if mathoverflow is not the right place for this question, but I guess it is the only place where I can get an answer.
The question is the following: is publishing a paper in mathematics ...

**-1**

votes

**0**answers

35 views

### Conformal map from a sector of unit disk onto upper half plane [on hold]

How do we construct a conformal map from $\{z=x+iy,x>1/2,|x+iy|<1\}$ onto the upper half plane? My idea is first create a sector sending one of the two intersection points to infinity.Any help ...

**3**

votes

**3**answers

452 views

### What should be considered a finite size of an infinite dimensional space? [on hold]

I've got a map between two infinite dimensional spaces, $f: A\to B$, where $A$ seems "larger" than $B$. For the sake of conversation let's assume that $A$ is the set of smooth maps $\mathbb R^3\to ...

**3**

votes

**1**answer

79 views

### Ising model: probability of a long path of minus under plus boundary conditions

Consider for example the Ising model on a square lattice. Fix zero magnetic field and plus boundary conditions.
Low temperature, one minus spin. With a Peierls argument one can prove that, given a ...

**-2**

votes

**0**answers

89 views

### The field of rational functions on a smooth projective absolutely irreducible curve over a finite field [on hold]

We mean a variety (over "k") of dimension 1 by the curve in the expression "The field of rational functions on a smooth projective absolutely irreducible curve over a finite field k", don't we?

**9**

votes

**2**answers

302 views

### Splitting integers 1, 2, 3, … n to avoid least possible sum

For each positive integer n, partition the integers 1, 2, 3, … 2n into two sets of n integers each. Let g(n) be the least integer such that there is such a partition in neither of whose parts there is ...

**2**

votes

**0**answers

61 views

### What is the significance of the median eigenvalue?

When I look at the spectral density plots of my (usual) laplacian graphs, they spike at the median eigenvalue. But what significance for the graph/matrix (which originates from a network) does the ...

**10**

votes

**2**answers

106 views

### Which real Pin groups agree?

In the Lie theory notes on my website it is claimed (Example 7.3.3.5) that $\mathrm{Pin}(4,0)$ and $\mathrm{Pin}(0,4)$ are not isomorphic. As Nigel Ray pointed out to me, this claim is not quite ...

**0**

votes

**0**answers

49 views

### Generalized weight space

In their paper Lepowsky and Mcmollum sketch theory of weights in a more general setting. Here is their definition of a weight space:
If $A$ is a subset of $\mathfrak g$ and $\lambda$ is a function ...

**0**

votes

**0**answers

42 views

### Green's function of the Ornstein-Uhlenbeck operator

Consider $\mathbb R^d$ with the Gaussian measure $d\gamma(x) = e^{\frac{1}{4}|x|^2}\,dx$. The Ornstein-Uhlenbeck operator $L$ is given by
$$
Lu = \Delta u- \frac{1}{2}x\cdot \nabla u.
$$
Is there a ...

**1**

vote

**0**answers

42 views

### Ozsvath-Szabo orientation convention for Seifert fibred spaces

I am confused by the orientation convention that Ozsvath and Szabo use in On Heegaard Floer homology and Seifert Fibered Surgeries and would appreciate if someone clarifies this for me. On page 15 ...

**0**

votes

**0**answers

42 views

### Which of the following is true? [on hold]

$f(x),g(x)$ are defined on $[-1,1]$, $f'(0),g'(0)$ exist, $f(0)=g(0)$, and $f(x)\ge g(x)$ holds for an open interval containing $0$. Then which of the following is correct:
I, $f(x)$ and $g(x)$ have ...

**2**

votes

**0**answers

56 views

### Hitting time of two dimensional continuous martingale

Let $(\Omega, \mathcal{F}, P)$ be a probability space, on which $\mathcal{F}_t$ is filtration satisfying general conditions. $W_{t}=\left(W_{t}^{1},W_{t}^{2}\right)^{T}$ is a two dimensional Brownian ...