0
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
0answers
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
2answers
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
1answer
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!
0
votes
0answers
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
votes
0answers
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
1answer
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
3answers
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
0answers
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
1answer
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
0answers
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
0answers
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
0answers
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 $\partial\Omega$. ...
0
votes
0answers
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
0answers
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
0answers
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
1answer
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
1answer
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
votes
0answers
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 ...
0
votes
0answers
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
0answers
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
0answers
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
0answers
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
1answer
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
1answer
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
0answers
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
0answers
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
2answers
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
1answer
107 views

Does the Riemann-Christoffel curvature determine the connection?

I am looking for the integrability condition of the following system of pde: ...
4
votes
0answers
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
1answer
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
votes
0answers
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
votes
0answers
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
1answer
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
0answers
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
1answer
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
votes
0answers
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
0answers
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
1answer
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
1answer
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
votes
0answers
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
0answers
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
0answers
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
0answers
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
2answers
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
0answers
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
0answers
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
1answer
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 ...

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