# All Questions

**0**

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4 views

### On the induced norms of stochastic operator and its adjoint operator

The background: when studying the paper published in Automatica named '$H_{\infty}$ control and filtering of discrete-time stochastic systems with multiplicative noise' (volume 37, pp. 409-417), I ...

**0**

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**0**answers

6 views

### Truncated Robbins-Monro

I'm reading Han-Fu Chen's book "Stochastic Approximation and Its Applications", and in Chapter 1, he's got a statement of a theorem and proof on a truncated Robbins-Monro algorithm. In this version, ...

**0**

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**0**answers

10 views

### Distinct 2D RCFTs with the same underlying MTC

A 2d rational conformal field theory (RCFT) gives rise to a modular tensor category (MTC) equipped with a Frobenius algebra object (see, for example, http://arxiv.org/abs/hep-th/0204148).
Is there an ...

**-1**

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**0**answers

65 views

### A not-so-weak Goldbach's conjecture

While Goldbach's conjecture (every even integer greater than 2 can be expressed as the sum of two primes) remains open, one can weaken the question by asking whether every (even,odd) integer can be ...

**16**

votes

**2**answers

216 views

### How did Cole factor $2^{67}-1$ in 1903

I just heard a This American Life episode which recounted the famous anecdote about Frank Nelson Cole factoring $N:=2^{67}-1$ as $193707721 \times 761838257287$. There doesn't seem to be a historical ...

**1**

vote

**1**answer

53 views

### $\mathcal S'(\mathbb R^d)$ is separable

I Think the statement is true, but I struggle to find a reference for the fact that the space of tempered distributions equipped with the weak-* topology is separable.
Thank you for your help!

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votes

**0**answers

41 views

### Understanding Mathematics [on hold]

I don't feel like I understand mathematics until I have an idea of how it was discovered or derived because otherwise it doesn't make sense and it takes along time to do that does that happen to ...

**-3**

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**0**answers

12 views

### Descrition of clipping algorithm in Murta's gpc [on hold]

I have searched but failed to get a algorithmic description of the algorithm used by Alan murta in general polygon clipper.It is NOT vatti,for sure.
Unfortunately old versions of his code are also ...

**-1**

votes

**1**answer

35 views

### How does deletion-contraction affect chromatic number? Can it increase chromatic number?

Question: In graph theory, contracting an edge or deleting an edge are basic operations in many topics such as graph minors or Wagner's theorem on planar graphs. And I'm interested in how these ...

**2**

votes

**3**answers

151 views

### what is exactly the difference between the Selberg class and the set of Artin L-functions?

The question is in the title: from what I read in the answer to another question, Artin L-functions are conjecturally cuspidal automorphic L-functions for some algebraic group that can be transfered ...

**-4**

votes

**0**answers

17 views

### Iterative methods for linear algebra, Convergence and divergence of a 5 x 5 system [on hold]

I have one question.
it states that
"solve a system A(5*5) . X(5*5) = B(5*1) such that jacobi method diverges but gauss seidal converges. Also, solve a system A(5*5) . X(5*5) = B(5*1) such that gauss ...

**1**

vote

**1**answer

16 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 piecewise linear curves on the Euclidean plane. For every point $x \in \mathbb{R}^2$ we say it belongs to a territory serviced by ...

**1**

vote

**0**answers

12 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 ...

**0**

votes

**0**answers

26 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 ...

**3**

votes

**0**answers

24 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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**0**answers

25 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, ...

**0**

votes

**0**answers

21 views

### Lists of sets as objects of ZF axiomatics [migrated]

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 ...

**-5**

votes

**0**answers

50 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.

**2**

votes

**1**answer

81 views

### Examples of toric threefolds

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

**2**

votes

**1**answer

11 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 $e'\in E$ ...

**0**

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**0**answers

26 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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**0**answers

40 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}} ...

**0**

votes

**0**answers

45 views

### growth series of groups [on hold]

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**

votes

**0**answers

29 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]\mbox{ so that }Q_m(x)\mbox{ has at ...

**0**

votes

**0**answers

36 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

37 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**

votes

**1**answer

99 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

21 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

84 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

**2**answers

111 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 ...

**6**

votes

**1**answer

107 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

81 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 ...

**8**

votes

**1**answer

78 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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**0**answers

25 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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**0**answers

88 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 ...

**1**

vote

**1**answer

80 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) ...

**1**

vote

**0**answers

31 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 ...

**4**

votes

**1**answer

88 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 $\mathcal{N}$: ...

**0**

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**0**answers

31 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**

votes

**0**answers

73 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

106 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

149 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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**0**answers

25 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 ...

**7**

votes

**0**answers

108 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**

votes

**0**answers

38 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

143 views

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

I know there exists a groupoid-valued prestack 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

167 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**

votes

**0**answers

30 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**

votes

**0**answers

44 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 ...

**7**

votes

**1**answer

144 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 ...