-3
votes
0answers
25 views

Is a vector space with two identical vectors a vector space with one or two vectors? [on hold]

I'm new this, and cannot find any answers by searching. If a vector space has 2 identical vectors, in particular the zero vector, is it a vector space with 2 vectors or since they are linearly ...
2
votes
1answer
21 views

Regularized sums of Mobius sequence

Do $\lim_{s \rightarrow \infty} \sum_{n \geq 1} \mu(n) e^{-n/s}$ and $\lim_{s \rightarrow \infty} \sum_{n \geq 1} \mu(n) e^{-n^2/s^2}$ both equal $-2$? Experimentally this seems plausible (up through ...
0
votes
0answers
38 views

Does SL(3,q) have a subgroup of order $q^3.(q^3-1)$

Let $q=p^n$ for $p>3$.I want to know whether the group $G_2(q)$ has a subgroup of order $q^3.(q^3-1)$. First I look the paper of Peter Kleidman. In this paper Kleidman determined all maximal ...
0
votes
0answers
21 views

Help in finding the distribution and pdf

Considering a set of $n$ points that are $d$ dimensional and are independently and uniformly distributed on a surface. The points are homogeneous poisson point process. Considering nearest neighbor ...
0
votes
0answers
12 views

exit time of a non degenerate diffusion

Let $n, d \geq 1$, $b : \mathbb{R}^n \to \mathbb{R}^n$ and $\sigma: \mathbb{R}^n \to \mathbb{R}^{n \times d}$ two Lipschitz functions. We assume that \begin{equation} \exists \mu >0, \xi^T ...
0
votes
0answers
26 views

Non Normal operator

Standard example for non normal operator is the shift operator. It is continous but the image of the left shift is not dense. Can we have an example of a non normal operator $A$ which is continuous ...
2
votes
0answers
76 views

Group laws in class field theory

In the case of quadratic number field one can construct its maximal abelian extension using torsion points of an elliptic curve with complex multiplication by this field. In the case of local field, ...
1
vote
1answer
49 views

Questions about a possible way of representing construcive ordinal numbers

Let $K$ be the set of all total recursive functions of non-negative integers having only non-negative integers as values. Let $L$ be any well-ordered subset of $K$ in which the ordering $<$ is ...
0
votes
0answers
21 views

Can the GUE be thought of as a uniform point in a high-dimensional polytope

I have thought about this question for a long time and could only find partial answers. The Gaussian Unitary Ensemble (or GUE) is the eigenvalues of a random Hermitian matrix with complex Gaussian ...
2
votes
1answer
89 views

What is the growth of the rank of a power of a finite simple group?

Which asymptotic bounds (upper and lower) are known for $s_n$ - the minimal number of generators of $S^n$ where $S$ is a nonabelian finite simple group?
4
votes
1answer
147 views

Adding sets not containing arithmetic progressions of length three by forcing

Consider the following forcing notion: conditions in $\mathbb{P}$ are pairs $(s, N),$ where: 1) $s\in 2^{<\omega}$, 2) $N\in \mathbb{N}$, 3) (by identifying $s$ with a subset of $lh(s)$) $s$ ...
0
votes
0answers
34 views

separating parameters in generalized quadratic Gauss sum

The normalized generalized quadratic Gauss sum is defined by $$ G(a,b,c)=\frac{1}{c}\sum_{n=1}^ce\left(\frac{an^2+bn}{c}\right) $$ where $e(x)=\exp(2\pi ix)$. Under what conditions on $c$ can we ...
1
vote
0answers
40 views

Tree property and singular strong limit cardinals

I heard that the following theorem is proved recently by Foreman-Magidor, which answers a famous old open question: Theorem. It is consistent, relative to the existence of large cardinals, that ...
-2
votes
0answers
32 views

When is a word metric on a CAT(-1) group a bounded distance from some CAT(-k) metric?

Let $\Gamma$ be a group admitting a discrete and cocompact action on a CAT(-1) space. Let $d$ a word metric on $\Gamma$ coming from some finite set of generators. My question is: Does there exist a ...
6
votes
0answers
76 views

Solving a set of equations in a finite symmetric group

A standard way to find solutions to a finite set of equations in a finite symmetric group ${\rm S}_n$ is to take the equations as relators of a finitely presented group, to use the low index subgroups ...
1
vote
2answers
176 views

Tensor calculus on the frame bundle

Let $M$ be a manifold and let $g$ be a tensor on it, say for example a metric $g\in\Gamma(T^{\ast}M\otimes T^{\ast}M)$. I know how to perform any computation on $g$. For instance, taking its ...
2
votes
0answers
81 views

Application of Stickelberger's Theorem to Quadratic field

I am trying to understand a proof of the Kronecker-Weber Theorem by Franz Lemmermeyer,[http://arxiv.org/pdf/1108.5671.pdf] in which he uses Stickelberger's Theorem applied to Kummer extensions. I can ...
1
vote
1answer
118 views

About direct limit of groups

Let $G_i$ be sequence of groups for $i\in \mathbb N$ and Let $\phi_i$ be a monomorphism from $G_i$ to $G_{i+1}$. Let $\Sigma$ be the direcet limits of $G_i$ under the embeddings of $\phi_i$. Let ...
-1
votes
0answers
38 views

Minimum rank non-negative matrix summations

Given matrix $M\in\Bbb Z_{\geq0,\leq b}^{n\times n}$ of rank $r$. What is minimum $k$ such that $$\mathscr{A}[b,k]=\{Q\in\Bbb R_{\geq0,\leq b}^{n\times n}:\mathsf{rank}(Q)\leq k\}$$ contains $R,S$ ...
0
votes
0answers
29 views

Integral Transform with associated Legendre Function of second kind as kernel

In my research the following equation appeared: $$\frac{1}{4\pi}\int_{0}^{1}\frac{t^{s-1}(1-t)^{s-1}}{(\rho-t)^s}dt=\int_0^{\infty} f(a) Q^{i\sqrt{a}}_{s-1}(2\rho-1) da,$$ where $\rho,s>1$, ...
-5
votes
0answers
51 views

I don't get how -6cos3xsin3x becomes -3sin6x in the later part [on hold]

y = cos²3x dy/dx = 2cosx(-sin3x)(3) = -6cos3xsin3x = -3sin6x I found this answer key in my guidebook but I can't find any trigonometric function's or differentiation formula ...
0
votes
0answers
24 views

Unimodular triangulation and affine toric variety

Let $\mathcal{K}$ be a $pointed$ rational cone in $\mathbb{R}^d$ with extremal rays generated by $r_1,r_2,\dots, r_m\in \mathbb{Z}^d$. Here, pointed means that all $r_i$ lie strictly on one side of ...
1
vote
0answers
100 views

Sum-epimorphisms and prod-monomorphisms

        Sum-epimorphisms A longer time ago I have introduced the bi-onto maps for the topological category. Let me formulate here its general categorical definition: ...
4
votes
1answer
77 views

Convex hull of the union of two parameterized curves in $\mathbb{R}^3$

My goal is to find a way to calculate the convex hull of the union of some parameterized curves. For instance, I had to calculate the convex hull of $A=\{(-4k,k^2+2,2k^2-2k)|k\ge 2\}\cup ...
0
votes
0answers
56 views

Alternating quotients of (2,3,7;10)

It was shown that the only quotient of the group $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{10} \rangle$ of the form PSL(2, q) is PSL(2, 41). That lead me to consider other families of simple ...
0
votes
0answers
20 views

Is it possible (or even valid) to obtain an eigensystem from a set of recursive equations? [on hold]

Let us start with the Golden Ratio, which is the number $\varphi \approx 1.6180339887\cdots$, and it can be defined in several ways, one of them is through a recurrent process involving the Fibonacci ...
-6
votes
0answers
33 views

formula for turning star reviews into upvotes [on hold]

I want to turn reviews of up to 5 stars and the number of reviews into upvotes. Whats a good algorithm for doing this? A venue with 10 reviews total with a 5 star average rating should obviously get ...
2
votes
0answers
65 views

For which quiver varieties is Kirwan surjectivity known?

The cohomology of Nakajima quiver varieties is a quite interesting object. It's equipped with some natural classes given by the Chern classes of the tautological bundles associated to the spaces in ...
4
votes
1answer
207 views

Is the ring of invariants Noetherian?

Let $R$ be a complete regular local ring whose residue field is perfect. Suppose that a finite group $G$ acts on $R$ by ring automorphisms in such a way that the induced action on the residue field is ...
7
votes
0answers
172 views

Can an abelian variety/Q have no points over Q_sol?

Let $A/\mathbb{Q}$ be an abelian variety. Must there be a finite solvable extension $K/\mathbb{Q}$ such that $A(K)$ is nontrivial? This follows from the conjecture that the maximal ...
1
vote
0answers
35 views

Probability of non-negative matrix relaxation

Given matrix $M\in\Bbb\{0,1\}^{n\times n}$, take $\mathscr{M}[M]=\{Q\in R_{\geq0}^{n\times n}:Q[ij]>0\iff M[ij]=1\}$. Does ...
5
votes
0answers
52 views

flatness and derived completion

Let $A$ be a local ring of maximal ideal $\mathfrak{m}$. Let $\hat{A}$ be its completion. If $A$ is noetherian , then we know that $A\rightarrow\hat{A}$ is faithfully flat. If $A$ is not noetherian, ...
8
votes
2answers
343 views

Non-Forcing and Independence

I asked this question about two weeks ago on MSE and haven't gotten an answer, so I thought I would post the question here. Do there exists sentences which are independent of ZFC, cannot be shown to ...
1
vote
0answers
36 views

Relative nonarchimedean disks and annuli

Let $A$ be a Huber (i.e. f-adic) ring, meaning a topological ring with an open subring $A_0$ which is adic and has finitely generated ideal of definition. Is there a good notion of closed disk of ...
-3
votes
0answers
52 views

What does this graph notation mean? E\S [on hold]

I am studying graph theory right now but I am confused what E\S means where both E and S are sets of edges. What does the "\" indicate?
2
votes
1answer
95 views

Unitary representation with fixed Casimir

Let $G$ be a connected reductive real Lie group with Lie algebra $\mathfrak{g}$. We denote by $\widehat{G}_u$ the unitary dual, that is the set of isomorphism classes of unitary reprensentation of ...
0
votes
1answer
92 views

Properties of Integral Closure [on hold]

Definition(Integral closure): Let $R$ be a ring and $I$ an ideal of $R$. An element $x$ is said to be integral over $I$ if $x$ satisfies a monic equation $x^n + i_1x^{n−1} + ··· + i_n = 0$ such ...
1
vote
1answer
77 views

Are there compact Riemannian manifolds whith Q-curvature negative?

Are there known examples of compact Riemannian manifolds with Q-curvature negative?
5
votes
0answers
113 views

3D models of the unfoldings of the hypercube?

There are (apparently) 261 distinct unfoldings of the 4D hypercube, a.k.a., the tesseract, into 3D.1 These unfoldings (or "nets") are analogous to the 11 unfoldings of the 3D cube into the plane.2 ...
-2
votes
0answers
82 views

Lie algebra and Lie groups [on hold]

A complex Lie algebra $L$ has a representation on $Der(L)$ by just putting $x.D=-ad_{Dx}$. For semisimple Lie algebras, by Weyl's theorem, $Der(L)$ decomposes into irreducible subspaces $D_i$. Then my ...
-2
votes
0answers
28 views

Population and date values [on hold]

Use the population data values below. North= 18,200 South=12,900 East=17,600 West=13,300 If there are 26 representatives for all districts how many ...
-2
votes
1answer
88 views

Combinatorical meaning of such expression [on hold]

Any combinatorical meaning or interpretation of $$1^{\alpha_1}2^{\alpha_2}3^{\alpha_3}...s^{\alpha_s}\alpha_1!\alpha_2!...\alpha_s!$$ for partition ...
0
votes
1answer
73 views

Completeness of a set of propositional formulas [on hold]

A set $\sum$ of formulas in propositional logic is complete if for each propositional formula $\phi$ either $\sum \vdash \phi$ or $\sum \vdash \neg \phi$. Clearly every inconsistent set of formulas ...
2
votes
1answer
61 views

Classification of ergodic measures for circle expanding maps

Let us consider the classical self-covering of the circle $S^1=\mathbb{R}/\mathbb{Z}$ given by $$\times_d(x) = dx \mod 1$$ where the degree $d$ is any integer greater than $1$. There are a wealth of ...
0
votes
1answer
66 views

Totally non fixed point property

Edit: According to the comment of Pietro Majer, I revise the question Is there a non singleton compact connected Hausdorff topological space $X$ for which the following property hold?: "Constant ...
3
votes
0answers
129 views

Reference for Arakelov's theorem: $K^2_f=0$ iff $f$ is locally trivial

Let $f:X\longrightarrow B$ be a family of curves, with $f$ relatively minimal, over a fixed curve $B$ ($B$ is projective, irreducible and smooth). The fibration $f$ is said locally trivial if all ...
5
votes
0answers
61 views

A jump operator for Borel equivalence relations

It is well-known that with respect to Borel reducibility the class of Borel equivalence relations on a standard Borel space does not admit a maximal element. We can use the well-known Friedman-Staley ...
8
votes
1answer
187 views

Translates of meager sets

Does there exist a meager set of reals M such that every meager set can be covered by countably many translates of M? This is the category analogue of the following.
-1
votes
0answers
52 views

Name and theorems of transitive/Galois groups of quadratic (even) and cubic power polynomials: cyclic group extensions [on hold]

What is the transitive group details of a polynomial where only the third power terms occur? That is ${x}^{3n}+{a}_{n−1}{x}^{3(n−1)}+\cdots+{a}_{1}{x}^{3}+{a}_{0}$. I need the basic theorems that ...
2
votes
2answers
146 views

boundary homomorphism in the homotopy exact seqeunce of principal $SO(9)$ bundle over $S^8$

Consider principal $SO(9)$ bundles over $S^8$.They are in 1-1 correspondence with $$[S^8,BSO(9)]\cong \pi_7(SO(9))\cong \mathbb{Z}$$ Now pick up one such bundle $\xi$,we have the long exact sequence ...

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