All Questions

-1
votes
0answers
56 views

Spectrum of non compact operator is 0 [migrated]

Can you please help me to give an example of non compact operator which spectrum is {0}
1
vote
0answers
48 views

What is known about the combinatorics of the hyperplane arrangement spanned by cyclic polytopes?

Let $1\leq d$ be an integer. Consider the $d$-dimensional moment curve $\mu\colon \mathbb R\to \mathbb R^d$ given by $t\mapsto (t,t^2,\dots, t^d)$. Given a finite subset $S\subset \mathbb R$ of ...
1
vote
1answer
82 views

Linear operator on polynomials and invariant sets of roots

Let $T:\mathbb{C}_n[x] \to \mathbb{C}_n[x]$ be a linear map from the vector space of polynomials of degree $n$ to itself. Let $S \subset \mathbb{C}$ be a set with at least $3$ points, such that for ...
2
votes
1answer
94 views

$(M,g)$ is complete iff $(\tilde{M},\tilde{g})$ is complete (non-Riemannian version)

I'm not sure if this question is too low level for Math Overflow (so feel free to move this to SE if you think it is). Inspired by this and this question I'm wondering if the following statement is ...
1
vote
1answer
47 views

Approximate $\log \mathbb E_P[\exp(th(x)]$ for a function $h$ which is lipschitz and has finite moments of order 1 and 2 w.r.t $P$

Let $P$ be a probability measure on a space $\mathcal X$ and $h: \mathcal X \rightarrow \mathbb R$ is measurable function with finite moments of order 1 and 2. I'm interested in approximating the ...
1
vote
0answers
93 views

Closed symplectic manifold with Euler characteristic 2

I am working about an article. In this article, author said that if close symplectic manifold $M$ has two fixed points implies that either $M$ is 2-sphere or $\dim M=6$. The closed symplectic manifold ...
22
votes
2answers
1k views

Is every commutative ring a limit of noetherian rings?

Edit of Feb. 14, 2019. After Laurent Moret-Bailly's accepted answer, only Questions 4 and 5 remain open. I don't care that much about Question 4, but I'm very curious about Question 5, which is Do ...
3
votes
2answers
129 views

Rigid space, but with homeomorphic neighborhoods

What is an example of a topological space $(X,\tau)$ on more than one point, with the following properties? the only homeomorphism from $X$ to itself is the identity, and given $x,y\in X$ there are ...
1
vote
0answers
54 views

inequality for the difference between largest eigenvalues of an irreducible matrix $A$ and a matrix $B$ with all the entries non-negative

I found an inequality for the difference between largest eigenvalues of an irreducible matrix $A$ and a matrix $B$ with all the entries non-negative (with the assumption that its largest eigenvalue is ...
7
votes
2answers
127 views

The degree of the hypersurface of pfaffian cubic fourfolds

Let $\Pi:=\mathbb{P}(H^0(\mathbb{P}^5,\mathcal{O}_{\mathbb{P}}(3)))$ be the space of cubic fourfolds in $\mathbb{P}^5$. It is well-known that those cubics which are pfaffian, i.e. defined by the ...
4
votes
1answer
134 views

Morphism of sites and abelian sheaf cohomology

Let $f : \mathcal{C}\to\mathcal{D}$ be a morphism of sites (see the Stacks Project) with induced morphism of topoi $$(f^{-1}, f_*) : Sh(\mathcal{D})\to Sh(\mathcal{C}).$$ By assumption, $f^{-1}$ is ...
2
votes
1answer
86 views

Does such a parametric distribution family exist that is “closed” with respect to addition and multiplication simultaneously?

Dear mathoverflow community, I tried to find such a parametric distribution family that "forms a semiring", but I failed. For example, it is common knowledge that Gaussian distribution family forms ...
3
votes
0answers
89 views

A concept weaker than geodesibility of flows which is possibly useful in limit cycle theory

The main objective of this post is to apply the Gauss Bonnet Theorem to count the number of limit cycles of a polynomial vector field as described in this MO post and its linked MO posts But in this ...
5
votes
0answers
124 views

closest area of research to transcendental number theory or/and algebraic independence theory?

My primary interests are transcendental number theory and algebraic independence theory, especially the Euler's constant. There is no person working on these areas in the university that I want to ...
5
votes
0answers
60 views

Compact Generation of Co-Module Categories

Let $\mathcal{C}$ be a compactly generated stable $\infty$-category, linear over a field of characteristic $0$ (i.e., so that it is in particular a dg-category). Let $A$ be a co-monad acting on $\...
-1
votes
0answers
41 views

Reducing Kernel Hilbert Space: Reproducing property [closed]

If the inner product between tho functions is the integral over R of f(x)g(x)dx and it's equal to f(x), how whould g(x) be in order to satisfy this equality?
0
votes
1answer
52 views

$\overline{conv}(C)$, where $C = \{ e _{1}, \cdots e _{n} \}$, $e _{i} \in \ell ^{p, \infty}$ is diametral

Let $C = \{ e _{1}, \cdots e _{n} \}$, where each $e _{i}$ are unit vectors in $\ell ^{p, \infty}$, and $1 < p < \infty$. I want prove that $\overline{conv}(C)$ is diametral. My doubt is: $\...
0
votes
0answers
113 views

Approximation in the circle method

I am interested in the circle method and I am currently working on Vaughan's book. Let $f$ be the generating function $f$ of the squares, that is to say the power series sum of $z^{m^2}$. One of the ...
3
votes
1answer
136 views

Cofibrations of functors

Let $\cal M$ and $\cal N$ be model categories, $S,T:\cal M\to N$ functors, and $\alpha:S\to T$ a natural transformation. Say that $\alpha$ is a <blank> cofibration if for any cofibration $i:A\to B$...
0
votes
0answers
31 views

Nonlinear norm-preserving mapping [closed]

Mazur–Ulam theorem states that every surjective norm-preserving mapping is an affine mapping. But what I'm confusing is that which condition fails on an example $y:= \frac{||x||}{||Ax||}Ax$ for a ...
1
vote
0answers
48 views

anomalous primes and CM elliptic curves

Let $E$ be an elliptic curve defined over a number field $F$ and suppose $E$ has CM by $\mathcal{O}_K$ where $K$ is an imaginary quadratic field. What can we say about the non-anomalous primes of such ...
2
votes
0answers
130 views

Schemes obtained replacing variables by $n \times n$ matrices?

Let $k$ be an algebraically closed field and $n \geq 1$ be an integer. Choose a polynomial $f \in k[x_1,\dots,x_m]$ and place the variables in a fixed order (i.e we choose a preimage of $f$ inside $k\...
-4
votes
1answer
44 views

Two notions of boundedness in metrizable topological vector space

In a metrizable topological vector space X with the metric d, a subset A is said to be bounded if it can be absorbed by any neighbourhood of 0 and a subset A is said to be d-bounded if its diameter ...
5
votes
0answers
311 views
+50

Are nearby points in an algebraic curve necessarily connected?

I would like a result of the following form: For every algebraic curve $C$ in $\mathbb{R}\mathbf{P}^{n-1}$, there exists an explicit and easy-to-compute $\epsilon=\epsilon(C)>0$ such that ...
3
votes
0answers
33 views

Rings with only finitely many indecomposable reflexive modules

Let $R$ be a ring. Recall that a module $M$ is called reflexive in case the natural evaluation map $M \rightarrow M^{**}$ (with $M^{*}=Hom_R(M,R)$) is an isomorphism. A module is reflexive if and only ...
-3
votes
0answers
32 views

Joint probability distribution for X, Y and X, Z [closed]

I have this exercise from lecture notes. I found the answer, but I don't really get it. Is it right? Exercise: Let $X$ be a random variable such that $\mathbb{P}(X = 0) = 1 - p$ and $\mathbb{P}(X = 1)...
2
votes
2answers
112 views

Construction of Fano threefold of degree $5$ and its defining equations

The Fano threefold $X$ of index $2$, degree $5$ and Picard number $1$ is known to be a general codimension $3$ linear section of the $Pl\ddot{u}cker$ embedding of Gr(2,5). My first question: what ...
19
votes
1answer
346 views

The Euler-Mascheroni constant and entropy

I would like to know if I have discovered or merely rediscovered the following pretty fact. A partition of $[0,1]$ into intervals of lengths $p_{i, i=1\ldots n}$ induces a probability distribution ...
3
votes
1answer
141 views

How to construct groups and large dimension representations? How about faithful ones?

Below I am referring to complex representations. We know that if $G$ is a finite group with $m=(G:Z(G))$, then every irreducible representation has size at most $\sqrt{m}$. One cannot hope for this ...
0
votes
1answer
80 views

Requirement that source and target maps are surjective submersions

Definition I am aware of for Lie groupoid is that (among other things) the source and target maps $s,t:\mathcal{G}_1\rightarrow \mathcal{G}_0$ are submersions. On page 9 of Du Li's thesis Higher ...
3
votes
0answers
54 views

Laplacian variational problem with asymptotically quadratic term

Consider the functional $$J= \int_\Omega |\nabla u|^2 - \int_\Omega F(u),$$ where $\Omega$ is a bounded smooth domain. The problem has been solved for example if $F$ is (1) subquadratic, or (2) ...
4
votes
0answers
148 views

Regular functions vs holomorphic functions

Let $X$ be an affine smooth variety over the complex numbers, $X^{an}$ its associated smooth complex analytic space, and $\mathcal{O}$, resp. $\mathcal{O}^{an}$ the respective structure sheaves. Is ...
1
vote
1answer
69 views

Does the following percolation model have a name?

Consider the following model for percolation in an infinite graph: each vertex has a certain region (set of vertices) associated with it, which at the beginning contains only the vertex itself, and ...
1
vote
0answers
117 views

Where can I find a copy of this paper of Chowla and Vijayaraghavan?

Does anyone know where I can find a copy of Chowla and Vijayaraghavan's paper, ''On the largest prime divisors of numbers''? The relevant literature say it was published in the Journal of the Indian ...
2
votes
1answer
91 views

Finding all $d$-dimensional indecomposable representations

Given a connected quiver algebra $A$ over a finite field $K$. Question : Is there an effective/quick method to obtain all $d$-dimensional indecomposable representations for a fixed $d$ with a ...
-7
votes
0answers
133 views

Grothendieck, Sphere, Cylinder [closed]

Archimedes' theorem relating the surface areas and volumes of the sphere and cylinder is well known. I'm wondering if scheme theory (specifically etale cohomology of schemes) may be useful to gain ...
7
votes
1answer
183 views

Twisted spin bordism invariants in 5 dimensions

[Note]: My question will be a bit long. So, first, thank you for your careful reading, generous comments, helps and answers, in advance! The spin $G$-bordism invariant can be twisted in the way that ...
5
votes
0answers
226 views

Geometric bang-bang theorem for nonlinear optimal control

The classical bang-bang theorem is usually stated for linear systems (e.g. Control Theory from the Geometric Viewpoint by Agrachev-Sachkov, p. 209). Sussman proved a nice generalization for systems ...
8
votes
3answers
408 views

SL(2, C)-representation of a knot

When studying knot theory I often encounter $SL(2, \mathbb{C})$-representation of knots (of the knot group) or the $SL(2, \mathbb{C})$ character variety of a knot group. But I just don't seem to ...
2
votes
1answer
171 views

Termination of “unpacking” abbreviations

It is a normal practice to use a minimal set of operators in logical systems and construe the other operators as abbreviations. Let's look at the propositional logic: If $\mathcal{V}$ denotes the ...
9
votes
0answers
147 views

How small may the discriminant of an $S_d$-field be?

In every degree $d$, the Galois closure of the typical number field has the maximal possible Galois group $S_d$. Denote by $f(d)$ the least absolute value of a discriminant of an $S_d$-field of degree ...
1
vote
1answer
122 views

Why is this series summable?

Let $\delta, \epsilon \in \mathbb{R}$, $\delta >0$, $\epsilon >0$. Let $\{ a_k\}^\infty$,$\{ b_k\}^\infty$ be sequences of positive integers such that $\lim \sup_{k \rightarrow \infty} \frac{...
5
votes
1answer
91 views

Hessian formula for the sub manifold distance

I am working on some problems involving foliations and group actions and would be very nice to consider the second derivatives for the distance function of an orbit or a leaf. So my question is: does ...
5
votes
0answers
60 views

Alexander-Whitney for cyclic objects

What is known about the extension of the AW map from simplicial to cyclic Abelian groups? Homological perturbation theory implies there is an A infinity-like sequence of maps, but is it known ...
3
votes
1answer
63 views

Existence of Laurent series with zeroes at $𝑒^2𝑛$ (𝑛∈ℕ0 ) and even faster coefficient decay

This is an extension of an earlier question of mine which corresponds to the case $A = 1$. Precisely, my question is as follows: Given $A > 0$ fixed but arbitrary, is there a non-trivial ...
1
vote
1answer
59 views

Expectation of random variables coincides

Let $Y_1:=(X_i)_{i \in \mathbb Z}$ be a family of random variables that are identically distributed but not necessarily independent. We can then also define the shifted sequence $Y_2:=(X_{i+1})_{i \...
0
votes
0answers
19 views

Transforming an ODE into a hypergeometric ODE

I have seen numerous times the statement that any 2nd order ODE with three regular singular points can be converted into a hypergeometric ODE by a change of variables. See for instance https://en....
0
votes
0answers
83 views

A conjecture stronger than Gauss' triangular number theorem

A subset $A$ of $\mathbb N=\{0,1,2,\ldots\}$ is called an asymptotic additive basis of order $3$ if any sufficiently large integer can be written as the sum of three elements of $A$. I have ...
0
votes
0answers
38 views

Is there a general way to solve these equations? [on hold]

The equations are: $$n_x=x+a_x\cos{(b_xt)}+c_x\cos{(d_xt)}+e_x\cos{(f_xt)}$$ and $$n_y=y+a_y\sin{(b_yt)}+c_y\sin{(d_yt)}+e_y\sin{(f_yt)}$$ where all the values except $t$ are known. Thanks.
4
votes
1answer
144 views

Graphs that are not $\mathbb{R}^2$-realizable

We say that a finite, simple, undirected graph $G=(V,E)$ is $\mathbb{R}^2$-realizable if there is an injective map $\varphi:V\to \mathbb{R}^2$ such that for $v\neq w \in V$ we have $\{v,w\} \in E$ if ...

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