# All Questions

**0**

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4 views

### Algorithm to find the vertices of the equidistant lines between N closed polygonal lines

I have a set $\{C_1, C_2, \ldots, C_N\}$ of $N$ nonintersecting closed polygonal lines on the Euclidean plane. For every point $x \in \mathbb{R}^2$ we say it belongs to a territory serviced by $C_i$ ...

**1**

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5 views

### Minimality of maximal expansions of a hypergraph cover

This is a follow-up question to Maximal expansions of strongly minimal covers of hypergraphs -- for definitions refer to that question.
Does every strongly minimal cover have a maximal expansion that ...

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9 views

### Decomposition of hyperbolic surfaces near cusps into annuli

Let $C=\mathbb{H}/\Gamma$ be a hyperbolic surface and $c$ a cusp of this sruface. In the paper "Billiards and Teichmüller curves on Hilbert modular surfaces" by C. McMullen, it is claimed that near ...

**1**

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9 views

### Sobolev space for Mixed Dirichlet - Neumann boundary condition

Consider the subset $\Omega\subset \mathbb{R}^N$ with boundary $\partial\Omega$ sufficiently regular and let $\Gamma\subset\partial\Omega$ be a $(N-1)$- dimensional submanifold of $\partial\Omega$. ...

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16 views

### Reference request for some “irregularities of distribution” papers

I would like to ask if anyone has access to any of the following papers:
1. J. G. van der Corput, Proc. Kon. Ned. Alcad. v. Wetensch., Amsterdam, 38, 813-821
(1935).
2. J. G. van der Corput, ibid. 38, ...

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19 views

### Lists of sets as objects of ZF axiomatics

I have a naive question about foundations of mathematics. A common opinion of most mathematicians is that the essential part of mathematics can be reduced to ZF(C) axioms. I do not quite understand ...

**-3**

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**0**answers

26 views

### what are the practical applications of sets in our daily life? [on hold]

I don`t know the answer to this question?I know I sound stupid writing something in my own question but the computer was forcing me to write something.

**1**

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29 views

### Examples of toric threefolds

I am looking for examples of smooth projective toric threefolds $\mathbb P_\Delta$ such that the dual polytope of the rational polytope $\Delta$ has only pentagonal faces and hexagonal faces.
I ...

**2**

votes

**1**answer

5 views

### Maximal expansions of strongly minimal covers of hypergraphs

Let $H = (V,E)$ be a hypergraph, that is $V$ is a set and $E \subseteq {\cal P}(V)$. We assume $\bigcup E = V$. Moreover we assume that every $e\in E$ is contained in some maximal member $e'\in E$ ...

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13 views

### Is a toric blow-up in codimension 2 a real toric blow-up?

Let $X, Y$ be toric projective algebraic varieties over $\mathbb{C}$. Suppose that $X$ and $Y$ are $\mathbb{Q}$-factorial and smooth in codimension two (e.g. they have terminal singularities).
Let ...

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19 views

### $A_n \not \rightharpoonup A$ in $L_1[-\pi; \pi] $ ( $A_n$ is partial fourier sum )

Let
\begin{equation*}
(A_n x)(t) = \frac{a_0}{2} + \sum\limits_{k=1}^n a_k cos(kt) + b_k sin(kt), \\
a_k = \frac{1}{\sqrt{\pi}} \int_{-\pi}^{\pi} x(t) cos(kt) dt, \\
b_k = \frac{1}{\sqrt{\pi}} ...

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24 views

### growth series of groups

As I know, in the literature there are formulas for groth series of direct product, free product and free product with amalgamation and graph product of groups.
Is there any formula that gives groth ...

**0**

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**0**answers

13 views

### A constrained positive polynomial

Is there an example of a polynomial $Q(x)\in\Bbb Z_{\geq0}[x]$ with $Q(0)=1$ so that $Q(x)=Q_m(x)Q_+(x)$ where $Q_+(x)\in\Bbb Z_{\geq0}[x]$, $Q_m(x)\in\Bbb Z[x]$ so that $Q_m(x)$ has at least $1$ ...

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20 views

### Finding first integrals

Given a vector field $X \in \mathcal{X}(\Omega)$, a first integral of $X$ is a differentiable mapping $\psi : \Omega \to \mathbb{R}$ such that $\sum_{0}^{n} X_{i}(x)\frac{\partial \psi}{\partial ...

**0**

votes

**1**answer

23 views

### Convergence of measures to an absolutely continuous measure

Suppose that $\{\mu_n\}$ is a sequence of Borel probability measures on a compact metric space $X$ and suppose that $\{\mu_n\}$ converges weakly to a Borel probability measure $\mu$ on $X$. If $\mu$ ...

**3**

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**0**answers

33 views

### Higher-dimensional category theory on objects

I would like to know if there exists a satisfying generalization of higher-dimensional category theory on objects, that doesn't forget the inner structure of objects. Usually, what people do is to ...

**1**

vote

**0**answers

16 views

### Writing a function as a sum of functions of bounded diameter

This problem is distilled from one arising in a study of complex random variables, but I've removed as much baggage as I can without (I hope) making it trivial.
Fix $D>0$. A function $f:\mathbb ...

**1**

vote

**0**answers

61 views

### Correspondence between real forms and real structures on complex Lie groups

I asked this in MSE, but without success, so I hope, it will be suitable here.
E.B.Vinberg and A.L.Onishchik in their book give the following two definitions.
For a complex Lie group $G$ its real ...

**2**

votes

**1**answer

57 views

### For $k>3$ does there exist an odd prime $q_k$ such that $p_k=2^kq_k+1$ is prime and $p_k$ divides $a_k=\dfrac{3^{2^{k-1}}+1}{2}$?

Question: For $k>3$ does there exist an odd prime $q_k$ such that $p_k=2^kq_k+1$ is prime and $p_k$ divides $a_k=\dfrac{3^{2^{k-1}}+1}{2}$?\
If $k=3$ the answer is Yes because for $q_3=5$ we ...

**5**

votes

**1**answer

85 views

### Does the Riemann-Christoffel curvature determine the connection?

I am looking for the integrability condition of the following system of pde:
...

**4**

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**0**answers

68 views

### Representing one diagonal of Pascal's triangle using special sums coming from a different diagonal

Let $m, n$ be any fixed natural numbers. Is it true that infinitely many elements of the sequence $\left(\begin{array}{c}
m+k \\
m \\
\end{array}\right)_{k=1,2,3,...}$ ( as well as of the sequence ...

**7**

votes

**1**answer

54 views

### Does $Add(\kappa,1)^L$ ever collapse cardinals?

In general, we know that adding a subset to a regular cardinal $\kappa$ can collapse cardinals. If, for example, there is $\gamma < \kappa$ with $2^\gamma >\kappa$, then $Add(\kappa,1)$ will ...

**0**

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22 views

### A question and a conjecture on $USp(N)$ group

$USp(N)$ with $N$ an even integer is defined as the group of unitary matrices $M$ that satisfy $M^TJM=J$, where $M^T$ is the transpose of $M$ and $J$ is the anti-symmetric $N$-by-$N$ matrix
...

**0**

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76 views

### Is g( ) rational if it looks that way on a large rational subset?

Let $F$ be any infinite field, $U\subset F^n$ be an open, dense (in Zariski topology) subset,
$x_1,x_2,…,x_n$ be an algebraic independent system of variables over $F$ , $f,f_1,f_2,…,f_n \in ...

**0**

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42 views

### References about identities of Gauss sum

I am reading the paper. In the end of page 10, there are the following identities of Gauss sum.
\begin{align}
& h(b) h(a+b) = q^b h(b) h(a), \\
& h(b) g(a+b) = q^b h(b) g(a), \\
& g(a+b) ...

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21 views

### Sobolev embedding on warped product

Consider the warped product $X = M \times \mathbb{R}$, with the metric $g = dr^2 + \varphi(r) g_M$, where $M$ is a compact manifold. Consider the Sobolev space $H^1(X)$ and let $H^1_{rad}(X)$ denote ...

**3**

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**1**answer

56 views

### Induction and nonstandard halting times of standard machines

For a nonstandard model of enough arithmetic - say, $\mathcal{N}\models I\Sigma_1$ - we can define the set of halting times of standard machines relative to $\mathcal{N}$: ...

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30 views

### Maximum entropy to fit Johnson distribution by moments [migrated]

I am trying to fit a johnson SU distribution to my data with the first 4 moments. To identify the most suitable set of johnson parameters I am trying to maximize the entropy function. However, I see ...

**-3**

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**0**answers

66 views

### Fun math puzzle [on hold]

Have had this math puzzle that I have been unable to solve for a while.
Each leter is a number between 1-9. No letter uses the same number twice (aka if B is 3 D can't be 3 also). The ? mark ...

**7**

votes

**1**answer

76 views

### K-groups of a permutative category - are they finite?

Let $\mathcal C$ be a permutative category, that is a symmetrical monoidal category with strict associativity. One can then define the $K$-groups of $\mathcal C$, for $n >0$ by
$$K_n(\mathcal C) = ...

**1**

vote

**1**answer

96 views

### Explicitly describing the region of the plane “outward of” a simple, open, oriented, cubic curve $c:(0,1)\to\mathbb{R}^2$

Some Context:
I'm working with some data given in the form of Bezier curves. I need to sort these (partially ordered) Bezier curves by "outwardness" (described below) and have come across an ...

**0**

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20 views

### interpolation between Bochner spaces

Is there a reference for the interpolation result stating the existence of an embedding
\begin{equation}
L^2(I;W^{2,p}(\Omega)) \cap H^1(I;L^p(\Omega)) \hookrightarrow ...

**6**

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**0**answers

88 views

### Alexander duality for non-manifolds

Let $X$ be a CW complex and $A$ a subcomplex. I will assume that both are compact, and that $X$ is $n$-dimensional. Furthermore, assume that the local homology of $X$ is that of a manifold in a ...

**-5**

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34 views

### I cannot solve this question! HELP [on hold]

Imagine a 100 storey building. You want to find the highest floor from which an iphone, when dropped, will not break. If an iphone is dropped and does not break, it can be used again with no adverse ...

**4**

votes

**0**answers

97 views

### is there a moduli of stable infinity categories?

I know there exists a moduli (pre-)stack parameterizing (connected) triangulated dg-categories (ie the points of this moduli are not objects of a fixed dg-category, but rather dg-categories ...

**6**

votes

**2**answers

158 views

### What methods do we have to understand the spectrum of matrices with restricted entries?

Consider questions of the form (or the "most probable value of" version of these questions rather than the "largest possible"),
What is the largest possible spectral radius of a $n \times n$ matrix ...

**0**

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**0**answers

26 views

### Non-trivial summand in End(\rho)

Given a finite group representation $\rho:G\to GL_n(\mathbb C)$ one knows that the trivial representation $\mathbb 1$ is contained in $End(\rho)$.
Let $\rho'$ be the other summand, i.e., $\rho'$ is ...

**6**

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**0**answers

41 views

### Prime divisors of the norm of the first coefficient of an elliptic newform at width-1 cusps.

Let $E/\mathbb{Q}$ be an elliptic curve of conductor $N$ and let $f$ be its newform.
Suppose $p \geq 5$ is a prime such that $p^2 \mid N$. We assume $f$ is $p$-minimal, which is equivalent to that the ...

**9**

votes

**1**answer

136 views

### Searching for $C^*$ [on hold]

I am trying to search on MathSciNet for articles which contains $C^*$ in their title (as in $C^*$-algebras) however I can't figure out how to get MathSciNet not to interpret the '*' as a stand in for ...

**6**

votes

**1**answer

183 views

### Are these inequalities for primes equivalent?

Let $p_n$ be the $n$th prime, let $L$ consist of the primes satisfying $p_{n+2} - 2p_{n+1} + p_{n} > 0$, and let $Q$ consist of the primes satisfying $p_{n+1}^2 < p_{n}p_{n+2}.$ Is $L=Q$?
...

**0**

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47 views

### mean value estimate $ \frac{1}{T} \int_0^T | \zeta( \tfrac{1}{2} + it)|^2 \, dt = \log \frac{T}{2\pi } + (2\gamma - 1) + O(T^{\delta})$

I was browsing through the recent paper of Bourgain and Watt on mean value estimates of the Riemann zeta function on the critical line.
$$ \frac{1}{T} \int_0^T | \zeta( \tfrac{1}{2} + it)|^2 \, dt = ...

**2**

votes

**1**answer

57 views

### Defining relations of mapping class group for genus 2 closed surface

We know that mapping class group (MCG) $\Gamma_1$ for genus 1 closed surface
is generated by two elements: $U$ of order 6 and $S$ of order 4.
There is a defining relation that totally fixed the MCG ...

**2**

votes

**0**answers

54 views

### On various “extension closures” and “orthogonals” in triangulated categories

A vague form of my question is the following one: for a class of objects $D$ of a triangulated category $C$ we consider the class $E$ of objects that satisfy $Mor_{C}(d,e)=\{0\}\ \forall d\in D$; ...

**2**

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**0**answers

21 views

### Deriving HJB equation (why $\frac{dZ_t}{dt}=0$?)

I am trying to derive the HJB equation in a stochastic setting. Let
me exemplify my problem with the simplest case where there is no control,
just one state variable. Assume the payoff is given by
$$
...

**2**

votes

**0**answers

89 views

### Primitive elements in a free group

Let $F$ be a free group of rank $\aleph_0$ and let $H$ be a subgroup for which there exists some $a \in F$ such that $\langle H \cup \{a\} \rangle = F$. Must there be some free basis $B$ for $F$ and a ...

**0**

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20 views

### Drawing conclusions from many correlation coefficients [on hold]

I have conducted testing of a search algorithm I have made with test subjects giving a rating of 0-10 for each result. All the results have a calculated rating of 0-100, and the idea is to find a ...

**8**

votes

**0**answers

141 views

### Vector field built from connection and metric

Consider a smooth finite-dimensional manifold $M$ with metric $g$ and connection $\nabla$. For some local coordinate system, denote by $g^{\alpha \beta}$ the inverse of the metric tensor and by ...

**3**

votes

**1**answer

111 views

### Different ways of having infinite global dimension

Is there any ring $R$ of infinite global dimension such that any $R$-module is a retract (i.e. direct summand) of some $\oplus_{i\in I}M_i$ where each $M_i$ has finite projective dimension?
I ask ...

**-1**

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**0**answers

40 views

### Tensor and Hom are bi-adjoint functors for finite dimensional vector spaces? [on hold]

Let $U$, $V$ and $W$ be finite dimensional vector spaces over a field $\mathbb{F}$. It is well known that $U\otimes_\mathbb{F}-$ and $\mathrm{Hom}_\mathbb{F}(U,-)$ are adjoint functors in the sense ...

**1**

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38 views

### Related to derivative of Modified Bessel I function wrt the order

I recently met some problems related to the modified Bessel I funtions. Let $I(\nu,x):=I_\nu(x)$, and $I'_\nu(\nu,x):=\dfrac{\partial}{\partial \nu}I(\nu,x)$.
Using maple, it seems that ...