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3
votes
0answers
108 views

Is there some sort of formula for $t(S_n)$?

Let $G$ be a finite group. Define $t(G)$ as the minimal number, such that $\forall X \subset G$ if $|X| > t(G)$ and $\langle X \rangle = G$, then $XXX = G$. Is there some sort of formula for $t(S_n)...
0
votes
1answer
123 views

Factorize a morphism into a morphism locally of finite type and a quasi-compact morphism

Does there exist a scheme not admitting a morphism locally of finite type to a quasi-compact scheme? The reason I am asking this is that being locally of finite type and being quasi-compact are ...
2
votes
0answers
39 views

Hadamard $\ell_p$ sum of two symmetric positive semidefinite matrices: follow-up

I asked the following question here: "Does there exist $p>1$ such that for all $n\geq 2$, if $(a_{ij})$ and $(b_{ij})$ are symmetric positive semidefinite $n\times n$ matrices and $a_{ij}, b_{ij}\...
-1
votes
1answer
89 views

Balls into bins with random number of balls

In the classical balls into bins we throw $m$ balls into $n$ bins. We throw the balls independently of each other and the probability of choosing the bins is uniform. For $n=m$ it is known that the ...
-2
votes
1answer
33 views

Dividing exponential scale into 7 bands [on hold]

So what I was (incorrectly) doing is to put a song in Matlab and divide it to 7 frequency bands. I was doing that by finding the biggest and smallest fundamental frequencies and then calculating (Fmax-...
3
votes
0answers
115 views

Universal closure of schemes à la Nagata

Nagata compactification theorem is the following fundamental result: Let $S$ be a qcqs scheme. Let $X$ be a separated $S$-scheme of finite type. Then there exists a proper $S$-scheme $\overline{X}$ ...
-3
votes
0answers
138 views

Glue DVR to itself, get a separated non-affine scheme

Here is what seems to be a fun little exercise in algebraic geometry. Take a DVR $R$ and automorphism of $Frac(R)$; glue $Spec(R)$ to itself via this automorphism. Can the glued scheme be separated ...
0
votes
0answers
27 views

Neumann equation on manifold with edge or corner

Let $(M,g)$ be a compact Riemannian manifold with boudnary and corner, i.e. locally mdoelled in $[0,\infty)^1\times \mathbb R^{n-1}$ or $[0,\infty)^k\times \mathbb R^{n-k}$, where $n=\dim(M)$. ...
-2
votes
0answers
25 views

How do I calculate the percentile of a discrete distribution? [on hold]

I have a discrete distribution based on the table below. If I am always drawing $N$ numbers $x_1, x_2, ..., x_n$, multiplying them by $n_1, n_2, ..., n_N$ and summing it up, is it possible to get a ...
11
votes
3answers
1k views

Are L-functions uniquely determined by their values at negative integers?

Are L-functions uniquely determined by their values at negative integers? In another words, is there a sequence of integers $a_1, a_2, a_3, \cdots$ such that the corresponding L-function $$L_{\{a_n\}...
0
votes
0answers
60 views

Can 3 points forming a right angle spherical triangle make a right angle chord triangle? [on hold]

I am trying to determine, and perhaps provide proof, that there are no three arbitrary points on a sphere that can form a right angle triangle both spherically and plenarily at the same time.
1
vote
0answers
62 views

A mathematical area capable of describing nonstationary game-like problem [on hold]

Here is my definition of the problem that I am trying to model: Let's have two agents and an environment. Each agent can do two types of actions. They are either supporting the environment or don't. ...
1
vote
0answers
58 views

Defining pull-back of Chow groups under a morphism of special type

Let $X$ be a normal complex projective variety (not necessarily smooth), and let $Y$ be a smooth complex projective variety. Let $Z\subset X$ be a smooth closed subvariety. Let $\pi : Y\rightarrow X$...
12
votes
2answers
401 views

Possible isometry groups of open manifolds

Consider a non-compact manifold $M$. Does there always exist a Riemannian metric on $M$ such that the isometry group is non-compact?
4
votes
2answers
277 views

Representation theory of inner forms

I once heard something like "inner forms of reductive groups have the same representation theory". Is this assertion misguided? If this assertion is not misguided, then is there a precise ...
4
votes
1answer
132 views

Exponential objects in the category of measurable spaces

Let $\text{Meas}$ be the category of measurable spaces with measurable functions as morphisms. Does $\text{Meas}$ have exponential objects?
0
votes
0answers
68 views

Express $\zeta(n)$, in particular the Apéry's constant, in terms of series involving Gregory coefficients or the Schröder's integral

The idea and motivation of this post is to know if it is possible to express integer arguments of the Riemann zeta function $\zeta(n)$, in particular $\zeta(3)$, in terms of series involving the so-...
1
vote
0answers
85 views

Quadrilateral fundamental domain

Let P be a hyperbolic quadrilateral. Poincare polygon theorem provides sufficient condition for P to be a fundamental domain of some Fuchsian group in term of its inner angles. I find the angle sum ...
4
votes
1answer
270 views

Why does $\sqrt 5$ occur in manageable situations of these scenarios?

Banach-Mazur distance between $P_5$ and $P_3$ is $d(P_5,P_3)=1+\frac{\sqrt5}2$ where $P_n$ is regular polygon in $n$ sides https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7968198&tag=...
2
votes
1answer
70 views

Gaussian null coordinates

I find it hard to find information on the so-called "Gaussian null coordinates", which Wikipedia says is used to describe "near horizon geometries". Can someone provide a reference where I can read ...
1
vote
0answers
89 views

Does $\Sigma$ generate the variety of all groups?

Suppose $FT$ is the class of all isomorphism classes of finite T-groups (a T-group is a group, where all subnormal subgroups are normal). Define, $\Sigma$ as the set of all functions $f$ from $FT$ to $...
2
votes
0answers
40 views

Example Petrov Classification

I would like to calculate the Petrov type for a specific spacetime, unfortunately I am not able to find a step by step algorithm or example for the process, either using null-tetrad, nor calculating ...
1
vote
1answer
98 views

On the number of involutions in some groups

How many involutions are there in $O_7(11)$ and $PSp_6(11)$ respectively? (Note that the sizes of the two groups mentioned here are the same.)
-1
votes
0answers
58 views

Points on an Elliptic Curve, how to interpret $(x(2P):z(2P))$?

This is from J.S. Milne's book 'Elliptic Curves'- With $E(\mathbb{Q}) : Y^2Z = X^3 +aX Z^2+bZ^3$ and given a point on $P =(x,y)$ on it's Weierstrass equation dehomogenized $E: y^2= x^3+ax+b$ where $a,...
7
votes
0answers
195 views

Triangle $X'\to X\to X''\to\Sigma X'$ splits if $X\simeq X'\oplus X''$?

Given a commutative ring $R$ and a distinguished triangle $X'\to X\to X''\xrightarrow e\Sigma X'$ in the derived category $D(R)$, where $X',X,X''$ are perfect complexes. If we have an equivalence $X\...
2
votes
1answer
68 views

Products of functions in fractional-order Sobolev spaces

It is well known that $\|fg\|_s \lesssim \|f\|_{s_1} \|g\|_{s_2}$ for functions $f: {\mathbb R}^n \rightarrow {\mathbb R}$ under certain conditions on $s$, $s_1$, $s_2$ (i.e. $s_1$, $s_2 \geq s$ and $...
-1
votes
0answers
116 views

Norm of a Riemannian metric

I'm writing a thesis and I need to be able to say when two Riemannian metrics are close. I was reading a paper and there the definition was assumed to be known, so I guessed it had to be something ...
2
votes
0answers
134 views

Brauer Group of a nodal curve

What is known about the Brauer Group of a Nodal curve (complete integral curve) over $k$ with singularity as ordinary double point? Is it trivial if $k$ algebraically closed?
1
vote
0answers
67 views

Notation/definition for the state of a FIFO queue [on hold]

A first-in first-out queue is filled up by tokens $t \in T$. The state of the queue $q \in Q$ is being changed by two operations, \begin{equation} \mathrm{push} : Q \times T \rightarrow Q \end{...
-1
votes
0answers
20 views

Ideas for basic models of periodic variables? [on hold]

I would like to come up with a basic model for a real variable which I expect to be some kind of addition of periodic phenomena. Let's make this more concrete. For example, I want to model the ...
1
vote
1answer
72 views

Monomials in products in power series ring on several variables

Let $A \colon= K[[X_1,\ldots,X_m,Y_1,\ldots,Y_n]]$ be a power series ring over a field $K$ in $m + n$ variables and ${\frak m}$ be the unique maximal ideal of $A$. For arbitrary two elements $\alpha ...
2
votes
0answers
46 views

The graph polynomial of the Total Graph of a Graph

Consider the Total Graph ($T(G)$) of a graph $G$ with vertex set $V$ edge set $E=\{(u,v)\}$ with Line graph $L(G)$ and subdivision graph $S(G)$ (formed by putting a vertex in each edge of the original ...
7
votes
0answers
105 views
+100

Variously pointed closed sets

A tree $A\subseteq \omega^{<\omega}$ - possibly with dead ends - is pointed iff every path $p\in[A]$ has $p\ge_TA$. This lifts to two distinct notions of pointedness for closed sets in Baire space: ...
0
votes
0answers
55 views

What is the geometric or dynamic meaning of a global attractor with an infinite fractal dimension?

In Efendiev-Ôtani's article: Infinite-dimensional attractors for parabolic equations with p-Laplacian in heterogeneous medium (Ann.I. H. Poincaré, AN 28,2011), is obtained that the fractal dimension ...
2
votes
0answers
85 views

Mod $2$ of $\#PM(G)$ for arbitrary G?

Permanent mod $2$ of biadjacency gives polynomial time algorithm of $\#PM(G)\mod 2$ of perfect matchings of bipartite graph. Is there a similar efficient strategy for general graphs?
3
votes
1answer
128 views

Mapping Problems to Boolean Formulas for SAT Solvers

I came across Marijn Heule and Oliver Kullmann's paper on recent techniques in highly efficient SAT solvers. In particular they describe the Pythagorian Triple Problem, which they solved using that ...
0
votes
0answers
56 views

Spectra of one dimensional Schrodinger operators [on hold]

I am trying to understand how to compute the spectra of one-dimensional Schrödinger operators $$ \mathcal{L}:=-\partial_x^2+V, $$ where $V$ is a bounded function in the whole line. I am particularly ...
4
votes
2answers
532 views

A DVR algebra with weird automorphisms

Denote by $k$ an algebraically closed field. Can one produce a DVR $A$ over $k$ such that the fraction field of $A$ has an automomorphism not preserving $A$ no non-trivial field extension of $k$ maps,...
5
votes
0answers
101 views

Weyl Group Action on Littelmann Paths

In his paper "Paths and Root Operators in Representation Theory," Littelmann gives an action of the Weyl group on the set of integral paths via $$ \tilde{s}_\alpha(\pi):= \begin{cases} f^n_\alpha(\pi)...
12
votes
1answer
307 views

Legendary extra parameters to simplify a counting problem

I am reading Proofs and Confirmations, the history behind the alternating sign matrix conjecture, regarding counting $n \times n$ alternating sign matrices. In the introduction, it is written that ...
-1
votes
0answers
45 views

Bounds on the moment of a matrix

Let $A$ be a positive semidefinite matrix. Are there any bounds known for the $q$-th moment of the $p$-th Schatten norm of matrix $A$? Here, $1 \leq p,q \leq \infty$.
4
votes
1answer
82 views

Minimal assumptions such that the solution of Poisson equation is $C^2$

Take a weak solution $u$ of the Poisson equation on $\mathbb{R}^d$ $$ \Delta u = f $$ By standard elliptic regularity theory we have (for some $\alpha\in (0,1]$) $f\in C^{0, \alpha}_{\text{loc}}(\...
-1
votes
0answers
30 views

Buildup a model from samples [on hold]

Assuming I have an historical data of a stock, and I want to build up a model that can generate the same behavior of this stock randomly. what are the parameters I should implement in the model (mean, ...
0
votes
0answers
57 views

Given a composite norm what polygon describes its unit ball?

Note: This is very similar to this question of mine on Math.Se, which hasn't received any answers yet. It is known, that for any centrally symmetric convex polygon $A$ there exists a norm $\| \cdot \|...
2
votes
0answers
255 views

Morphisms of smooth varieties

Let $f:X\rightarrow Y$ be a surjective morphism of varieties (integral separated schemes of finite type over an algebraically closed field) such that $Y$ is smooth projective and all the fibers are ...
3
votes
1answer
148 views

Hadamard $\ell_p$ sum of two symmetric positive semidefinite matrices

Does there exist $p>1$ such that for all $n\geq 2$, if $(a_{ij})$ and $(b_{ij})$ are symmetric positive semidefinite $n\times n$ matrices and $a_{ij}, b_{ij}\geq 0$ then $\bigl(\|(a_{ij},b_{ij})\|...
-1
votes
1answer
126 views

Denominator approximation sequence of a real number

For any positive integer $[n]$, let $[n]=\{1,\ldots,n\}$. Let $r\in\mathbb{R}$. We define for every positive integer $n\in\mathbb{N}$ the minimal difference from a rational with denominator $\leq n$ ...
5
votes
1answer
105 views

Is the conformal compactification of $M \setminus \{ p \}$ unique?

Let $(M,c)$ be a compact conformal manifold and $p \in M$. $M$ is a conformal compactification of $M \setminus \{ p \}$, because the embedding $M \setminus \{p\} \hookrightarrow M$ is an isometry. ...
0
votes
1answer
133 views

Localization and containment in commutative ring

Let $R$ be a commutative ring with identity and $x, y $ be fixed elements of $R$ such that for each maximal ideal $m$ of $R$ we have $\langle \frac{x}{1_m}\rangle\subseteq\langle \frac{y}{1_m}\rangle$ ...
1
vote
0answers
107 views

Exact sequence of normal cones

Suppose that we have a sequence $i: X \hookrightarrow Y$, $j: Y \hookrightarrow Z$ of closed embeddings of varieties such that $i$ is regular. In this case, do we have an exact sequence of cones of ...

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