# All Questions

**0**

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2 views

### Existence of minimizer in Sobolev space $H^{1,2}(\Omega)$

I am looking at a functional $$\frac{\int_{\partial \Omega} u^2 \mathrm{dx}}{ \left(\int_{\Omega} u^q \mathrm{dx} \right)^{2/q} }$$
And i want to know if the minimizer exists in the space ...

**5**

votes

**0**answers

22 views

### A linear category with objects of infinite length but which is otherwise finite?

Fix a ground field $k$. By a linear category I will mean an Abelian category which is compatibly enriched over $k$-vector spaces. A linear category is called finite if it satisfies the following four ...

**0**

votes

**0**answers

7 views

### Computing row-sum scaled unsigned Stirling nos. of the 1st kind

As the title suggests, I would like to compute probability vectors with elements proportional to (unsigned) Stirling numbers of the first kind by row. For easy reference, here is the Wiki page.
For ...

**0**

votes

**0**answers

7 views

### Semigroup nilpotents and compostional inversion

The integer coefficients of a general partition formula for the compositional inverse of a function are a refined version of the coefficients of the generating series for the number of nilpotents in a ...

**0**

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**0**answers

23 views

### Is holomorphic 2-form on Moduli of Higgs bundle in Biswas' paper is non-degenerate

In Biswa's paper, Geometry of moduli of higgs bundle, he defined holomorphic 2-form on moduli of stable higgs bundle, using kodaira-spensor map and peterson-weil metric.
I want to know whether this ...

**2**

votes

**0**answers

24 views

### Probability that a sum of intependent random variables hits a point

Let $X_1,\ldots,X_n$ be independent random elements of a normed space $X$. Suppose that $\sup_{x\in X}\mathbb{P}(X_i=x)=p_i$. What is the best known upper bound for
$$\sup_{x\in X} ...

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votes

**0**answers

47 views

### Conjecture Reference Request

If Second Hardy-Littlewood Conjecture is true then we can claim that $\pi(x)-\pi(y)\leq \pi(x-y)$. Thus the conjecture gives an upper bound for the number of primes between $x$ and $y$. I have found ...

**1**

vote

**1**answer

34 views

### a question about minimal non-abelian groups

Let $G$ be a minimal non-abelian group with cyclic Sylow $p$-subgroup $P$ and normal Sylow $q$-subgroup $Q$ , see [ Huppert, Endlich Gruppen I, Aufgaben III, 5.14].
My quesion is, if there is another ...

**7**

votes

**2**answers

173 views

### Is a group uniquely determined by the sets {ab,ba} for each pair of elements a and b?

This is a cross-posted question, originally active here on math.stackexchange.
For a given group $G=(S,\cdot)$ with underlying set $S$, consider the function
$$
F_G:S\times ...

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46 views

### Is the parallelogram rule an axiom or a theorem in euclidean geometry? [on hold]

I am aware of the proof of the rule in inner product spaces. Excluding the geometry of Descartes, is it possible to prove parallelogram rule or is it an axiom?

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vote

**0**answers

19 views

### lower bound of a trace quadratic form

i want to find a lower bound on the following expression:
$tr(AXA^T)$ in terms of $tr(X)$
where A is real $n\times n$ matrix and $X>0$ is positive symmetric. It seems that the following bound is ...

**0**

votes

**1**answer

87 views

### Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?

Given a series with integral coefficiens as following:
$$F(x)=\sum_0^i a_i x^i,\text{where }a_i\in \mathbb{N}\bigcup 0 $$$$\text{and there is a computable function $\psi$ such that } \forall i ...

**2**

votes

**0**answers

40 views

### Does $\mathsf{fReR}_0$ prove the existence of the cartesian product of two sets

$\mathsf{fReR}_0$ is the set-theoretical system whose axioms consist of:
(1) Axiom of extensionality: $\forall z\in x\ (z\in y)\wedge\forall z\in y\ (z\in x)\rightarrow x=y$
(2) Axiom of empty set: ...

**1**

vote

**0**answers

66 views

### Equations over $\mathbb{Z}[[T]]$ vs. equations over $\mathbb{Z}_p$

This question might be deemed totally unanswerable, unless there is an obvious counterexample. Answers to either effect would be welcome.
Question. Let $X$ be a finite-type scheme over ...

**1**

vote

**0**answers

21 views

### Cohomological dimension of transcendental p-adic extensions

Let $k = \mathbb{Q}_p$ for any prime $p$ and set
$L = k(t_1,..,t_n)$.
The u-invariant of a field $u(k)$ is defined by $u(k):=\{ max (\mathrm{rank}(q)) $ | $ q $ is anisotropic over $k\}$.
It is ...

**2**

votes

**1**answer

93 views

### A metric associated with a continuous surjective map $f:X\to Y$

Assume that $f:(X,d_{1})\to (Y,d_{2})$ is a continuous surjective map between compact metric spaces. We define another
metric $d_{f}$ on $Y$ With $$ d_{f}(a,b)=Hd(f^{-1}(x), f^{-1}(y))$$ ...

**2**

votes

**0**answers

73 views

### Characterizing the real analytic Eisenstein series

Consider the classical real analytic Eisenstein series
$$
E(z,s)=\left(\pi^{-s}\Gamma(s)\frac{1}{2}\right)\sum_{(m,n)\neq(0,0)}\frac{y^s}{|mz+n|^{2s}},
$$
where $z=x+iy$. We think of $E(z,s)$ as a ...

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53 views

### Zero-mean assumptions concerning r.d.'s when reading graduate-level probability texts

I'm reading through T. Taos book on random matrices (to be found here), and it is frequent to make without-loss-of-generality certain reductions when proving theorems as for example Hoeffdings ...

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**1**answer

50 views

### Nagakami behavoir

Is the sum of square Nagakami random variables Erlang distributed?
What is the distribution of euclidean norm of complex Nagakami?
Cheers!

**0**

votes

**1**answer

28 views

### Help in finding distribution of the following function of random variable

Let $X_1$ and $X_2$ be independent complex Gaussian random variables, $$X_1 \sim \mathcal{CN}(0,\sigma)$$
$$X_2 \sim \mathcal{CN}(0,\sigma)$$
If $X= aX_1 + bX_2$ where $a,b$ are constants then the ...

**-5**

votes

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44 views

### What is induction to n^(n-1) >= n! for n=9,10 [on hold]

Can somebody help me? How do I prove n^(n-1) >= n! for n=9,10..... by induction?

**4**

votes

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76 views

### A homological criterion for collapsibility?

On page 256 of Kirby and Siebenmann one finds the following lemma (its proof an "elementary exercise", so they only give a hint):
Taking $A$ to be a point and iterating this collapsing lemma, this ...

**5**

votes

**1**answer

221 views

### Parity of primes [duplicate]

While working on a completely different (combinatorial) problem, I ran a simple program to calculate the parity of the first ~50000 primes (number of 1s in their binary representation modulo 2). The ...

**3**

votes

**2**answers

77 views

### Are sums of 0-1 Pareto efficient vectors Pareto efficient?

Does there exist an $m \times n$ matrix $A$ and a vector $x \in \mathbb{R}^m$ such that:
The entries of $A$ are $\in \{0, 1\}$.
For all pairs of columns $u, v$ of $A$ the entries of $u - v$ are ...

**5**

votes

**1**answer

219 views

### Dimension of Hilbert scheme?

I have a subvariety $V \subset X$, and I want to compute the dimension of the connected component of $\textrm{Hilb}(X)$ containing $[V]$.
I can give explicit deformations of $V$ showing that the ...

**3**

votes

**3**answers

131 views

### Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute?

Specifically, are there "nice" (ie, not too obscure or contrived) examples of families of objects, where say for each objects $A,B,C$ in the family, the canonical isomorphism from $A\rightarrow C$ is ...

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vote

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59 views

### Spectral sequence and HOM functor

I work with the category $A-{\rm Mod}$ of left modules over a unital ring $A$, but I could ask the same question for any abelian category with enough projectives. Let $M$ and $N$ be two $A$-modules ...

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**0**answers

26 views

### Number of graphs with n vertices and k edges up to isomorphy [duplicate]

Is there a way to figure out the number of individual graphs with n vertices and k edges up to isomorphy?
I'm particularly looking at graphs with:
n = 25, k = 50
n = 50, k = 170
n = 100, k = 700

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votes

**0**answers

30 views

### Rate of convergence in narrow convergence

Does anyone help me in the following question?
I have a sequence of probability measures $\mu_n$ and know that $\mu_n$ converges narrowly to a probability measure $\mu$. Is there any way to estimate ...

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votes

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10 views

### Bounding a function pointwise from bound on the expectation [migrated]

Suppose we have a Lipschitz continuous positive function with bounded expectation Eg < a. What can be said about the point-wise bound ?

**2**

votes

**0**answers

119 views

### What are the minimal degrees of the real and imaginary part of an algebraic complex number? [on hold]

Let $z=a+bi\in\mathbb C$ with $b\ne0$ be an algebraic complex number of minimal degree $n$. It is obvious that $a=\dfrac {z+\bar{z}}2$ and $b=\dfrac {z-\bar{z}}{2i}$ are also algebraic. For $n=3$, it ...

**1**

vote

**0**answers

68 views

### Finitely co/continuous monad induced by an operad

It is well known that any operad on a nice monoidal category induces a monad.
I was wondering which conditions can be imposed on the operad $T$ (say, in a monoidal closed $\cal V$) so that the ...

**2**

votes

**0**answers

107 views

### What is God's number for the WrapSlide puzzle?

WrapSlide is a slide-puzzle (reminding of Rubik's Cube) consisting of a 6x6 grid of coloured tiles which are separated into four quadrants of 3x3 tiles. When it is unmixed all the tiles in a quadrant ...

**-4**

votes

**0**answers

25 views

### First-order nonlinear ordinary differential eqauation [on hold]

can someone help me to solve this equation? I have been trying a few methods. Thanks.
y'=(y/x)*((xy + 1)/(xy - 1))

**1**

vote

**1**answer

49 views

### Wave equation with linear coefficients

The following pde came up in a physics problem:
$$
(Cy+D)\frac{\partial^2 u}{\partial x^2}-(Ay+B)\frac{\partial u^2}{\partial y^2}-A\frac{\partial u}{\partial y} =f(x,y),
$$
A,B,C,D are fixed ...

**-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

33 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

104 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 ...

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vote

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21 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 ...

**6**

votes

**2**answers

159 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 ...

**0**

votes

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59 views

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

I feel that I should already know the answer to this, but it never sits quite right in my head. Let's look at something relatively concrete.
One way you can look at the moduli of hyperelliptic curves ...

**1**

vote

**1**answer

108 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

41 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 ...

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votes

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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

169 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? ...

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19 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**

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45 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

105 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

35 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

105 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
$$
...