# All Questions

100,158 questions
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### 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}
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### 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 ...
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### 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 ...
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### $(M,g)$ 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $i:A\to B$...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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) ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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....
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### 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 ...
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.
### 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 ...