# All Questions

**3**

votes

**0**answers

10 views

### Singularities of Pfaffian hypersurfaces

Let $X\subset\mathbb{P}^4$ be an hypersurface of degree six given by the Pfaffian of a $6\times 6$ matrix $M$ whose entries are quadratic forms in the homogeneous coordinates of $\mathbb{P}^4$. I am ...

**2**

votes

**1**answer

24 views

### Is every closed curve in 3D a geodesic on a genus-0 surface?

Let $\gamma$ be a smooth, closed, unknotted curve embedded in $\mathbb{R}^3$.
Q. Does there always exist a smooth, embedded, genus-zero surface
$S \subset \mathbb{R}^3$
such that $\gamma$ is a ...

**0**

votes

**0**answers

4 views

### Link Between Birkhoff Ergodic Theorem and Strong LLN for Harris Recurrent Markov chain

Is it possible to derive strong law of large numbers for a Harris recurrent stationary Markov chain form Birkhoff Ergodic Theorem? As I know that there is a link between SLLN for iid sample and ...

**0**

votes

**0**answers

4 views

### Any reference in absorbing boundary conditions for non-abelian gauge fields?

Is there any paper on absorbing boundary conditions for non-abelian gauge fields?
Currently I only saw some on elastic wave equations and some on EM fields.

**0**

votes

**0**answers

4 views

### A nullspace identity for operator exponentials

Let $X$ be a complex Banach space. Does validity of
$$
\mbox{ker}\left(e^{2\pi \imath \, T} - 1\right) = \sum\nolimits_{k\in \mathbb{Z}} \mbox{ker} (T-k) \quad \forall \, T \in B(X,X)
$$
imply that ...

**3**

votes

**0**answers

13 views

### divisibility by Bernoulli numbers of discriminant of Hecke algebra over the space of modular forms of level 1

For the space of modular forms and the space of cusp forms (here I only care about the level $1$ case), we have the action by Hecke algebras. Therefore, we can calculate the discriminant of this ...

**0**

votes

**0**answers

10 views

### Estimation of connection ignoring the inverse parallel transport in manifolds open in Euclidean space

Let $(M,g)$ be a Riemannian manifold, with parallel transport $P_{t_1,t_2}$ from time $t_1$ to time $t_2$. We know that, along a curve $c$:
$$ \nabla_{c} V(t)= lim_{h\to 0} ...

**1**

vote

**0**answers

26 views

### Euclidean minimum spanning trees intersecting each unit square

The recent question "Euclidean Minimum Spanning Trees Restricted to One Vertex Per Grid Cell" can be restated in terms of "minimum spanning trees intersecting each (closed) lattice square of an ...

**-2**

votes

**0**answers

38 views

### For natural numbers 1 to n, is the square of their sum equal to the sum of their cubes? [on hold]

I've had this rolling around my head for over a decade now. It first occurred to me in high school. I never knew where to ask, but I thought this might be a good place.
Given a sequence of natural ...

**1**

vote

**1**answer

15 views

### Efficient algorithm for finding normals of a high dimensional convex hull with few facets

I am looking for the most efficient algorithm to use to, given a set of points in $d$ dimensional space, find the normals of the convex hull of these points, given that I know that the number of ...

**-2**

votes

**0**answers

88 views

### Are there “adelic” L-functions?

Following Tom163's answer to this question, I would like to know whether L-functions defined through adelic representations (as defined in https://projecteuclid.org/euclid.em/1317758108) have been ...

**-1**

votes

**1**answer

47 views

### Exponential map and convergence

I posted this question on Math Stack Exchange, but nobody answered so I decided to ask this question here.
Suppose that $M$ is smooth compact manifold and let $y \to x$. Let also $f \in C^{\infty}(M)$ ...

**7**

votes

**1**answer

91 views

### The multiplication on $THH$ of finite fields

Let $k$ be a finite field, $THH(k)$ its topological Hochschild homology spectrum. For essentially formal reasons, we know that it's an $E_\infty$-algebra over the Eilenberg-Mac Lane spectrum $Hk$, and ...

**1**

vote

**1**answer

27 views

### Morphisms $P \to M$ in the derived category of a dg-category, if $P$ is h-projective

Let $\mathbf A$ be a dg-category. Denote by $\mathsf{C}_{\mathrm{dg}}(\mathbf A)$ the dg-category of right $\mathbf A$-modules, and by $\mathsf{C}(\mathbf A) = Z^0(\mathsf{C}_{\mathrm{dg}}(\mathbf ...

**-4**

votes

**0**answers

32 views

### Periodicity of any fermat number modulo a prime [on hold]

It's simple to prove the recursive formula for Fermat numbers $F_n$ :
$F_{n+1} = ( F_n - 1 )^2 +1 $. From this , if one define the sequence $a_n = F_n \pmod p$ , where
$p$ is a odd prime , there's a ...

**0**

votes

**1**answer

52 views

### Is the space of smooth maps $C^{\infty}(M,N)$ with the Whitney $C^{\infty}$ topology locally compact, if $M$ is compact

The title says it all:
Let $M$ be a compact manifold and $N$ a (possible non compact) manifold. Equip the space of smooth functions $C^{\infty}(M,N)$ with the Whitney $C^{\infty}$ topology. (The ...

**0**

votes

**0**answers

16 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

**0**answers

13 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, ...

**1**

vote

**2**answers

36 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

**0**answers

114 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 ...

**23**

votes

**3**answers

523 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 ...

**2**

votes

**2**answers

122 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!

**-2**

votes

**0**answers

60 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

**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 ...

**-2**

votes

**1**answer

51 views

### How does deletion-contraction affect chromatic number? Can it increase chromatic number? [on hold]

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 ...

**3**

votes

**3**answers

260 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

19 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

18 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

13 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

33 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

28 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

**0**answers

29 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

56 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

**2**answers

122 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

12 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

**0**answers

29 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

**0**answers

41 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

51 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

32 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

38 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

39 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 $\mu$ ...

**4**

votes

**1**answer

129 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

23 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 ...

**2**

votes

**0**answers

95 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 ...

**3**

votes

**2**answers

160 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

122 views

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

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

**4**

votes

**0**answers

91 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

89 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

**0**answers

32 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
...