# All Questions

**-3**

votes

**0**answers

22 views

### What is the single and double derivative of following equation? [on hold]

d/dt(e^ (-0.06 pi t))(sin(2t-pi))
using product rule fine the double and single derivative.please help me to solve this?

**0**

votes

**0**answers

14 views

### A simple group that its order divide order of an alternating group

Let $G$ be a simple group such that
1) $|G|\mid|\mathrm{Allt}_{p}|$
2) $p\mid |
G|$, and $p>13$.
3) $G$ hasn't any elements of order $rp$ for every prime number $r$.
My question: (without ...

**4**

votes

**0**answers

92 views

### Pros and cons of Stacks Project as a reference compared with EGA/SGA

I would like to know pros and cons of Stacks Project compared with EGA and SGA and whether it serves as a nice alternative to them. Since I haven't read both of these texts, my attempt to compare the ...

**3**

votes

**0**answers

36 views

### Non-orientable $6$-manifold with $H_4(M)=\mathbb{Z}/2$?

Does there exist a smooth, closed, non-orientable $6$-manifold $M$ such that $H_4(M;\mathbb{Z})=\mathbb{Z}/2$?

**1**

vote

**0**answers

23 views

### A subgroup of corank 1 in a free group contains a primitive element?

Let $F$ be the free group on $\{x_i\}_{i=1}^\infty$, and let $H \leq F$ be a subgroup with $\langle H \cup \{x_1\} \rangle = F$. Must there be a free basis $B$ of $F$ for which $B \cap H \neq ...

**0**

votes

**0**answers

28 views

### Which automorphisms on $H_{1}(M^{3})$ are induced by homotopy equivalences?

Let $M^{3}$ be a closed orientable 3-manifold, and $\phi:H_{1}(M;\mathbb{Z})\to H_{1}(M;\mathbb{Z})$ be an automorphism of abelian groups.
My question is: Is there any characterization of $\phi$ ...

**0**

votes

**0**answers

6 views

### Is there some kind of lower bound for estimation error of the estimation of (near) low-rank matrices in high-dimension?

I'm reading S.Negahban and M.J.Wainright's paper, ESTIMATION OF (NEAR) LOW-RANK MATRICES WITH NOISE AND HIGH-DIMENSIONAL SCALING. In the paper, they give a upper bound for estimation error of the ...

**0**

votes

**0**answers

11 views

### Painleve test of a new PDE hierarchies

This PDE hierarchies is :
$$u_t=\sum_{i=0}^{N}c_iu^iu_x-\frac{1}{2}\sum_{i=0}^N(c_iu^i)_{xxx}$$
so far, I have proved that this equation hierarchies has Resonaces at:$$j=2N+2,4N+2$$,according to ...

**0**

votes

**0**answers

24 views

### Lie algebra structure on $\chi^{\infty}(\mathbb{R}^{2})$

In this question $\chi^{\infty}(\mathbb{R}^{2})$ or $\chi^{\infty}(S^{2})$ is the space of all smooth vector fields on the plane or sphere. A limit cycle for a vector field $X$ is an isolated closed ...

**2**

votes

**0**answers

25 views

### Conditions for a set being closed under taking complement of a ball twice

Given a subset $S$ of a finite metric space $F$ with a distance function $d(,)$ and a number $\delta$ let $N_\delta(S) = \{x \in F| d(x,S)\ge \delta\}$. Is there a characterization of conditions ...

**0**

votes

**0**answers

36 views

### A question on the Frechet derivative

Suppose the derivative of a functional is given by $\int_{\Omega}(\vec{v}.\nabla u)|\nabla u|^{p-2} \phi=\int_{\Omega}\nabla.(u\vec{v})|\nabla u|^{p-2} \phi$ for $\phi\in W_0^{1,p}(\Omega)$ where the ...

**-1**

votes

**0**answers

18 views

### Implementation of almost integer to cryptography [on hold]

Can there be any implementation of almost integers to create intractable problems relevant to public key cryptography?

**0**

votes

**0**answers

18 views

### Preimage of singular points of smooth map between vector space and $SU(n)$

(Moved from Math SE as no answer was forthcomming: http://math.stackexchange.com/q/1294521/161684)
Given a smooth ($C^{\infty}$) map $\phi: V \rightarrow SU(n)$ (which is taken to be surjective) ...

**-2**

votes

**0**answers

19 views

### Matrix decomposition ( Kronecker product decomposition) [on hold]

How to solve the following matrix equation: $Q = A \bigotimes B$ (Given $Q$)?
Can we prove that if $Q \in \mathbb{R}^{n^2\times n^2}$ and $Q$ is symmetric, there always exist $A,B$ such that $Q = A ...

**0**

votes

**1**answer

25 views

### solution uniqueness of non-linear Fredholm equations

the equation is
$F(x)=G(\int k(x,y)f(y)dy)$ $(*)$
where $f(x)=dF(x)/dx$ is the unknown and it's required to be non-negative. With integral by parts we'll have the form of a non-linear Fredholm ...

**5**

votes

**1**answer

63 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 ...

**8**

votes

**2**answers

176 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

12 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

7 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

16 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 ...

**4**

votes

**0**answers

28 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

24 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} ...

**2**

votes

**0**answers

39 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

54 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 ...

**2**

votes

**1**answer

24 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 ...

**-3**

votes

**0**answers

122 views

### Are there “adelic” L-functions? [on hold]

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

54 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 $f \in C^{\infty}(M)$ ...

**8**

votes

**1**answer

115 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 ...

**2**

votes

**1**answer

38 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

36 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

60 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

17 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

15 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, ...

**2**

votes

**2**answers

53 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

120 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 ...

**28**

votes

**3**answers

631 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 ...

**3**

votes

**2**answers

130 views

### $\mathcal S'(\mathbb R^d)$ is separable [on hold]

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

62 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 ...

**-4**

votes

**0**answers

56 views

### How is this convex set compact as well? [on hold]

Given $\epsilon\in(0,1)$, supposing we have a collection $\mathscr{C}(\epsilon)$ of multilinear polynomials in $\Bbb R[x_1,\dots,x_n]$ that on $\{0,1\}^n$ is in range $[-\epsilon,\epsilon]$ on $S_0$ ...

**-2**

votes

**1**answer

52 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 ...

**4**

votes

**3**answers

274 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 ...

**2**

votes

**1**answer

20 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 ...

**2**

votes

**0**answers

14 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

38 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 ...

**4**

votes

**0**answers

34 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

30 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

60 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.