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Existence of $G$-map between finite $G$-simplicial complex

Let $X, Y$ be finite free $G$- simplicial complex. What kind of properties are necessary for existence a $G$-map,i.e, a continuous map which preserves $G$-action, from $X$ to $Y$? Does existence of ...
MathFun's user avatar
  • 233
4 votes
2 answers
424 views

A homeomorphism between the unit interval $[0,1]$ and a linearly independent subset of a Hilbert space

Let $H$ be a infinite dimensional, separable Hilbert space over $\mathbb{C}$ Let $B$ a subset of $H$ such that $B$ is linearly independent and such that exists a homeomorphism $f : [0,1] \to B$ ...
Matey Math's user avatar
1 vote
1 answer
155 views

Are there polygonal tilings with infinitely many positions, each (or at least one) occurring infinitely often?

My recent question about polygonal tilings where tiles can occur in infinitely many positions has been answered by two nice constructions (besides Jan Kyncl's answer, there is the Conway tessellation ...
Wolfgang's user avatar
  • 13.2k
2 votes
0 answers
228 views

Question about the term $\sum_{ \rho} \frac{X^{\rho}}{\rho}$ in the explicit formula of $\sum_{n \leq X} \Lambda(n) \chi(n)$

Let $\Lambda$ be the von Mangoldt function and $\chi$ a primitive character mod $q$, then we have the explicit formula $$ \sum_{n \leq X} \Lambda(n) \chi(n) = \delta_{\chi} X - \sum_{ |Im \ \rho| \leq ...
Johnny T.'s user avatar
  • 3,547
1 vote
1 answer
221 views

A double sequence in a Banach space

Let $V$ be a infinite dimensional Banach space over $\mathbb{C}$ Let $\{a_{m,n} \cdot v_{m,n}\}_{m,n \in \mathbb{N}}$ be a double sequence with $a_{m,n} \in \mathbb{C}$ and $v_{m,n} \in V$ such that: ...
Matey Math's user avatar
6 votes
0 answers
210 views

Reconstruct orthogonal from an orthostochastic matrix

Given an $n \times n$ orthostochastic matrix $\mathbf{A}$, i.e., there exists an orthogonal matrix $\mathbf{O}$ with $A_{ij} = O_{ij}^2$ for all $1\leq i,j \leq n$. What is the fastest way to find $\...
Jiro's user avatar
  • 909
2 votes
2 answers
223 views

A Characterization of the traces of functions in $W^{1,2}$

I have a question about the traces of functions in $W^{1,2}$. Let $D$ be a connected open subset of $\mathbb{R}^d$.We denote $W^{1,2}(D)$ by \begin{align*} W^{1,2}(D)=\{f \in L^{2}(D,dx) \mid \...
sharpe's user avatar
  • 701
-2 votes
1 answer
74 views

Matching and minimal degree

Let $n\in\mathbb{N}$ be a positive integer and let $G =(V,E)$ be a connected simple undirected graph with $|V| = 2n$. Is it true that if for the minimal degree $\delta(G)$ we have $\delta(G) \geq n$, ...
Dominic van der Zypen's user avatar
6 votes
1 answer
316 views

The Euclidean norm and $k$ largest elements

This is not a homework problem, although I fear it may turn out to be at that level. For any nonnegative $x\in\mathbb{R}^n$, let $f_k(x)$ be the sum of the $k$ largest values in $x$, and define $$f(x)...
Tom Solberg's user avatar
  • 3,929
9 votes
1 answer
279 views

Essential maps of spectra which are null when localized at any prime

There are maps of spaces which are not null-homotopic, but when localized at any prime become null. I don't know explicit constructions of any, but an example is given in Section 6 of Chapter 25 of ...
Jonathan Beardsley's user avatar
12 votes
0 answers
802 views

Number field analog of Artin-Tate $\Rightarrow$ BSD?

What is the difference between the alternating product of the Hasse-Weil $L$-functions of the generic fiber of an arithmetic scheme $X\to\text{Spec}(\mathbf{Z})$ and the zeta function of $X$? (each ...
user avatar
14 votes
2 answers
825 views

Automorphism of $\mathbb{P}_A^n$

Let $k$ be a field. The proof that $Aut(\mathbb{P}_k^n)=PGL(n+1:k)$ relies on the fact for any automorphism $\alpha$ of $\mathbb{P}_k^n$, $\alpha^*(\mathcal{O}_{\mathbb{P}_k^n}(1)) = \mathcal{O}_{\...
user's user avatar
  • 719
9 votes
0 answers
617 views

Hartshorne's Conjectures about Algebraic Bundles?

In 1978 Hartshorne published a list of 26 open problems about algebraic bundles on projective spaces [Hart], proceeding from an Oxford conference organized by Atiyah. I understand that many of these ...
user avatar
4 votes
1 answer
444 views

Is there a measure on the sphere with positive Fourier transform?

Is it possible to have an even probability measure $\mu$ (that is $\mu(A)=\mu(-A)$ for any set $A\subset \mathbb{R}^d$) supported on the unit sphere $S^{d-1}$ such that its Fourier Transform $$ \...
Felipe Ferreira's user avatar
2 votes
1 answer
97 views

Reflexive modules up to multiplicity

Call an indecomposable module $M$ over a ring $A$ (restrict to finite dimensional algebras if you like or if it helps) $n$-almost reflexive in case $M^{**} \cong nM$, when $(-)^{*}=Hom_A(-,A)$ and $nM$...
Mare's user avatar
  • 25.8k
1 vote
0 answers
51 views

A Pathwise Optimization Problem

Suppose $X$ is a nonnegative semimartingale that is progressively measurable with respect to a given filtration $\{\mathcal F_t\}_{t\ge 0}$. Let $c:\mathbb R_+ \mapsto \mathbb R_+$ be a strictly ...
epsilon's user avatar
  • 622
10 votes
1 answer
374 views

How many positions of a tiling polygon can occur simultaneousy?

Let $T$ be a polygon which tiles the plane. For an instance of $T$ (mirrored or not), call the set of its translates a position of $T$. My question: How many different positions can occur in ...
Wolfgang's user avatar
  • 13.2k
5 votes
0 answers
478 views

Poincaré duality for motivic cohomology

Is Poincaré duality for étale motivic cohomology known for projective regular (not necessarily smooth, just regular) schemes over Dedekind rings? More precisely, two questions. Let $f: \mathcal{X}\to\...
user avatar
1 vote
0 answers
18 views

Empirical approaches to validate observational bounds on minimum gap between least eigenvalues of $n \times n$ correlation matrix and its submatrices

Let $\Sigma$ be an $n \times n$ correlation matrix whose least eigenvalue is denoted by $\lambda$. $\Sigma_i'$ be an $(n-1) \times (n-1)$ submatrix of $\Sigma$ obtained by eliminating the $i$-th row ...
Saurabh Agrawal's user avatar
8 votes
0 answers
258 views

Shift on trivalent directed tree, operator and von Neumann algebra

Let $\mathcal{T}$ be the trivalent directed tree, with two parents and one child for each vertex (see below). Let $\mathcal{V}$ be the set of vertices of $\mathcal{T}$ and $H$ be the Hilbert space $\...
Sebastien Palcoux's user avatar
2 votes
0 answers
87 views

Functional equation involving integrals and exponential

Can we find on $\mathbb{R}^+$ a real positive function $f(x)$ (in $C^{\infty}$) such that: $$\int_0^{\infty} f(x) e^{\lambda \int_1^{x} f(t)^2 dt} dx=0$$ where $\lambda$ is a complex number (with $0&...
Bertrand's user avatar
  • 1,121
1 vote
2 answers
194 views

Isolated periodic trajectories of Hamiltonian systems

Is there any example of an autonomous Hamiltonian system with a periodic trajectory isolated in the whole phase space? The Poincar\'e map of such a trajectory within its energy level should be very ...
V.V.Veskatov's user avatar
0 votes
0 answers
219 views

Angle between two vectors in a Minkowski (Finsler) space

Given a Minkowski (or Finsler) space $(V,F)$, I am wondering how to define the angle between two vectors $w$ and $v$. I first thought it must be as $$\cos\theta(w,v)=\frac{g_w(w,v)}{\sqrt{g_w(w,w)g_w(...
Majid's user avatar
  • 227
7 votes
1 answer
235 views

Independent/Easy fraction of sentences over PA

Let $S(n)$ be the set of all sentences over PA of length at most $n$ (counting the quantifier symbols, boolean connectives, arithmetic operations and constants, and counting each variable as length $1$...
user21820's user avatar
  • 2,734
2 votes
0 answers
125 views

Computing the $K$-theory of the free inverse semigroup $C^*$-algebra

A typical example where I know the $K$-theory of the quotient, and wonder if this could help to compute the $K$-theory of the extension. (Or other way round: knowing one part out of three ones.) I ...
hänsel's user avatar
  • 665
5 votes
2 answers
374 views

Can the relative degree and ramification index can be read off the characteristic polynomial?

Let $L/K$ be a Galois extension of global fields with Galois group $G$. Assume that for a prime $p$ of $K$ we are given the datum $(L_{p}(s,\rho))_{\rho}$, where $\rho$ varies over the irreducible ...
Lior Bary-Soroker's user avatar
2 votes
0 answers
70 views

Convergence of empirical measure in case of proliferation

I am currently working on the theory of mean field limits of interacting particles. Here are two slides of a talk from an Italian researcher: I don't understand why he calls $u(t,x)$ a time dependent ...
Jack_Stiller10's user avatar
5 votes
1 answer
154 views

A regular first countable space of cellularity at most $2^\omega$

Let $X$ be a regular first countable space of cellularity at most $2^\omega$. Is it true that the cardinality of $X$ is at most $2^\omega$? A cellular family is a family of pairwise disjoint non-...
Paul's user avatar
  • 601
7 votes
1 answer
330 views

Crafting Suspension Spectra

There is a theorem by Hopkins and Smith which states that for every $n > 0$ there is an ideal $I_n = (v_0^{k_0}, \dots, v_n^{k_n})$ such that there exist a spectrum $X_n$ with the following ...
Alfred's user avatar
  • 879
3 votes
0 answers
164 views

Characterisation of reflexive modules for general rings

A module $M$ over a general ring A is called reflexive in case the canonical evaluation map $e_M: M \rightarrow M^{**}$ is an isomorphism, when $(-)^{*}:=Hom_A(-,A)$. Is $M$ reflexive iff $M \cong M^{*...
Mare's user avatar
  • 25.8k
2 votes
0 answers
142 views

Any proved connection between Roth theorem and hartmanis stearns conjecture?

Roth theorem classifies numbers into two classes, one is rational and transcendental, another is irrational algebraic numbers, by the number of solutions to the inequality (finite or infinite), and ...
XL _At_Here_There's user avatar
9 votes
3 answers
1k views

Does there exist a notion of discrete riemannian metric on graph?

I would like to know if there is any notion of a discrete Riemannian metric on graphs. C. Mercat has worked on discrete Riemann Surfaces, but that's not exactly what I am working on. To be more ...
Laurent.C's user avatar
4 votes
1 answer
320 views

Decompostion of hook schur function in terms of cauchy product of holonomic functions

Let $s_{\lambda}$ denote the schur function and $\lambda$ is the partion of an integer. The schur function written in power sum symmetric basis apper as following. $\chi$ denote the character. \begin{...
GGT's user avatar
  • 685
-1 votes
1 answer
117 views

Hierarchies of Operator Norms [closed]

Given some linear operator $T: V \mapsto W$, we can talk about the operator norm between the spaces V and W, i.e. $$ \| T \|_{V \mapsto W} \ = \ \sup_{g} \| Tg \|_W \ , \quad \mbox{ with } \| g \|_V \...
Atransportconfusion's user avatar
3 votes
1 answer
1k views

Completing the square of a matrix expression

Let $A,C\in\mathbb{R}^{m\times n}$, $n\ge m$, $B\in\mathbb{R}^{n\times m}$, and $P$ be a real positive definite $m\times m$ matrix. Denote by $\mathcal{S}^n$ the space of $n\times n$ real symmetric ...
Ludwig's user avatar
  • 2,682
6 votes
0 answers
328 views

Current state of Serre's Motives conjectures in Seattle

It would be worth if we have a current state of the conjectures of Propriétés conjecturales des groupes de Galois motiviques et des représentations l-adiques. J P Serre. In Motives, Seattle And ...
Jean's user avatar
  • 61
10 votes
0 answers
193 views

A theorem of Gugenheim on twisted tensor products

Suppose $A$ is a DGA algebra and $C$ a DGA coalgebra. An $(A,C)$-bimodule is an object $M$ that is both a right $A$-module and a left $C$-comodule in the evident compatible way. An $(A,C)$-bundle is ...
Pedro's user avatar
  • 1,534
3 votes
0 answers
128 views

Improving prime number generation probability?

Deterministic generation of primes in polynomial time is unknown. Is there a way to probablistically in $O(n^c)$ time bound for some $c>0$ generate polynomially $\Omega(n^c)$ many integers in $[0,...
Turbo's user avatar
  • 13.7k
5 votes
1 answer
273 views

Factorization of Gabriel-Zisman localization construction?

My question concerns whether the Gabriel-Zisman localization construction $S^{-1}$ for categories admits a known factorization into a pair of commuting constructions $S^l$ and $S^r$. The localization ...
Ben Cooper's user avatar
4 votes
0 answers
165 views

A forcing which can build weird models of $\neg$ADS

There is a class of forcing notions I've been playing around with recently. They have a couple nice properties, and all have the same theme, but I've found them difficult to analyze beyond the basics. ...
Noah Schweber's user avatar
3 votes
1 answer
192 views

Why are supplemented line bundles the correct generalization of "lines"?

Originally I had asked this on mathstack exchange but seems possibly appropriate for overflow as well. Let $k$ be a field. For the vector space $k^d$, a line in $k^d$ is a one dimensional subspace ...
Yuugi's user avatar
  • 255
2 votes
1 answer
512 views

Characterisation of reflexive modules

Let $A$ be a semiperfect noetherian ring. A module $M$ is called reflexive in case the canonical map $f_M: M^{**} \cong M$ is an isomorphism, when $(-)^{*}:=Hom_A(-,A)$. This is equivalent to say that ...
Mare's user avatar
  • 25.8k
6 votes
0 answers
365 views

K-theory of the infinite dimensional projective space

What is the $K$-theory of the category of coherent sheaves on the infinite (countable) dimensional projective space over a field? As far as I know, $K$-theory is oriented; hence this theory should be "...
Mikhail Bondarko's user avatar
5 votes
0 answers
125 views

Volumes of Hecke operators

Let $G=GL(2, F)$ and $K$ a maximal compact subgroup. Unramified Hecke operators are defined by the action of the double cosets $$T(n) = \bigcup_{\substack{ad=n, a>0 \\ a|d}} K \left( \begin{array}{...
Wolker's user avatar
  • 541
3 votes
2 answers
206 views

(How) do Better TSP Heuristics help in Answering the $NP=P$ Question?

This question is motivated by my impression, that finding better heuristics for the TSP problem (or any other $NP$-complete problem) is "only" of practical interest, but doesn't provide any progress ...
Manfred Weis's user avatar
  • 12.6k
11 votes
0 answers
244 views

Poset of nonvanishing minors of a matrix

This question was posed on MSE here three days ago, but hasn't gotten any answers or suggestions. I hope it's okay to ask it on MO, but if I should wait a little longer, please just let me know. Say $...
Zach Teitler's user avatar
  • 6,197
3 votes
0 answers
435 views

"Frobenius Descent"

The following proposition is there in Pink's lecture notes on finite group schemes. Let $k$ be an algebraically closed field of characteristic $p$. The category of finite length $W(k)$-modules $N$ ...
Shubhodip Mondal's user avatar
4 votes
0 answers
105 views

Valued fields with quantifier elimination in the Macintyre language

For which fields $k$ of characteristic $p$ does the Witt construction of a discretely valued field $W(k)$ of characteristic $0$ with residue field $k$ eliminate quantifiers in the language of rings ...
Alex Mennen's user avatar
  • 2,090
1 vote
1 answer
351 views

Are $\| \Delta u \|_{L^p(\Bbb R^d)} + \| u \|_{L^p(\Bbb R^d)}$ and $\| u \|_{W^{2,p}(\Bbb R^d)}$ equivalent norms?

Is it true that $$\| \Delta u \|_{L^p(\Bbb R^d)} + \| u \|_{L^p(\Bbb R^d)}\quad\text{and}\quad\| u \|_{W^{2,p}(\Bbb R^d)}$$ are equivalent norms? This results is pretty easy and straightforward for $...
Guy Fsone's user avatar
  • 1,033
5 votes
0 answers
244 views

A conjecture in rate distortion theory and stochastic filtering

Let $(X_t)_{t\in T}$ be a stationary random process with known and fixed law $P_X$ describing a dynamic source. This source is to be encoded real-time by an encoder $e$ into an encoded message $E_t$ ...
S.Surace's user avatar
  • 1,675

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