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Questions tagged [reference-request]

This tag is used if a reference is needed in a paper or textbook on a specific result.

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Sufficient condition for the absolute convergence of Fourier series of a function on the adele quotient $\mathbb A_k/k$

Let $G$ be a compact abelian group. The unitary characters of $G$ form an orthonormal basis of $L^2(G)$, so every square integrable function $f: G \rightarrow \mathbb C$ admits a Fourier expansion $$...
3
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1answer
76 views

Partition Calculus and Ramsey theory question

These topics are outside of my area of research, so I am not quite sure where in the literature to find the answers. In what follows, if $X$ is partially ordered and $n$ is a natural number, let $[[...
5
votes
1answer
159 views

Sheaves over a sheaf

Everything I write I mean in the in the sense of Lurie's HTT. Suppose that $ \mathcal{C}$ be a site and let $ F \in Fun( \mathcal{C}^{op} , \mathcal{S})$. Is it always/ever true that $ Sh(\mathcal{C}...
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1answer
98 views

If $p_n(a,b)$ is a rational number (or integer) for 3 consecutive values of $n$ then every $p_n(a,b)$ is

Let $a$ and $b$ be two real numbers and $p_n(x,y)$ the polynomial: $$p_n(x,y)=\sum_{i=0}^{n-1}x^{n-1-i}y^{i},$$ where $n$ is a positive integer. In a previous post I asked if $p_n(a,b)$ was a ...
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1answer
146 views

One particle irreducible Feynman diagrams

In quantum field theory Feynman has invented a diagrammatic method to encode various terms in the Taylor decomposition of integrals of the following form below which I will write in a baby version as ...
9
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0answers
103 views

Quantum Hamiltonian reduction and Quantum Airy structure

I have been reading Kontsevich and Soibelman's "Airy structures and symplectic geometry of topological recursion" (https://arxiv.org/pdf/1701.09137.pdf) and having trouble understanding their Section ...
24
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1answer
576 views

Littlewood’s three precepts of refereeing in mathematics: is it (1) new, (2) correct, (3) interesting?

I have a question regarding Littlewood’s three precepts of refereeing a mathematical paper, namely whether it is (1) new, (2) correct, and (3) interesting. I have found these mentioned in the ...
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0answers
97 views
+300

Continuity of Intersection Pairing on Chow monoids

Let $X$ be a smooth irreducible complex projective variety. As we know, if $\alpha,\beta$ are two cycles intersecting properly in $X$, we can define, via Serre's Intersection Formula, their ...
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0answers
49 views

smoothness of Hurwitz spaces with arbitrary ramification profiles

Fix integers $n\ge 3,d\ge 2$, and partitions $\lambda_1,\ldots,\lambda_n$ of $d$. Let $\mathcal{H}$ be the moduli space of degree $d$ covers $f:C\to\mathbb{P}^1$ that have ramification profiles $\...
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Holomorphic Poisson structures on $C P^{n-1}$ and homogeneous Poisson structures on $C^n$

Is it correct that any holomorphic Poisson structure on $C P^{n-1}$ can be lifted to a homogeneous Poisson structure on $C^n$? By homogeneous I mean a quadratic Poisson structure of the form $\{z_i,...
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1answer
52 views

Name of a function space

For a real function $f$ on $\mathbb{R}$, define $e_n(f)$ to be the infimum of the $L_1$ distance between $f$ and piecewise constant functions on the subdivision of $\mathbb{R}$ into intervals of ...
2
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1answer
96 views

Local Sobolev embedding on complete Riemannian manifold

Let $(M,g)$ be a complete Riemannian $m$-manifold, with bounded geometry and $m\geq2$. Suppose $Ric\geq(n-1)\kappa$. Let $B_p(r)$ be a geodesic open ball. Q Can we find a constant $C=C(\kappa,r,m)$(...
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0answers
42 views

The Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}(\sqrt{-3})$

I'm now on a research about the Iwasawa $\lambda$-invariants of the cyclotomic $\mathbb{Z}_p$-extensions of number fields. And it happens that the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}(\...
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Reference request: Numerical methods for Hamilton-Jacobi-Bellman equations with state constraints

I have two questions on numerical methods for solving Hamilton-Jacobi-Bellman (HJB) equations with state constraints. Consider an optimal control problem given by $$ v(x) = \max_{\{u(t)\}_t} \int_o^\...
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1answer
114 views

Fixed points of the automorphisms of sporadic groups

Sporadic groups have very few outer automorphisms (in fact, $|\mathrm{Out}(G)|\leqslant2$), so it is very natural to ask what are the fixed points subgroups. For a group of Lie type (and a suitable ...
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1answer
236 views

Are there nice isomorphisms $\operatorname{S}^2(k^n)\cong\Lambda^2(k^{n+1})$?

This might be forced to migrate to math.SE but let me still risk it. The spaces $\operatorname{S}^2(k^n)$ and $\Lambda^2(k^{n+1})$ from the title have equal dimensions. Is there a natural isomorphism ...
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0answers
68 views

Power of an integer as a sum of $\binom{n}{n-2}$ integers [on hold]

Consider the following equation $$ y^n=\sum_{k=1}^{\frac{n(n-1)}{2}} x_k, $$ where $x,y,n,x_k\neq 0$ are integers. Although I found a lot of material about how to express an integer as a sum of ...
5
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1answer
172 views

Functional equation for general number fields

When it comes to general number fields beyond $\mathbb{Q}$, the litterature is not so abundant in analytic number theory. For instance over $\mathbb{Q}$, for primitve Dirichlet characters modulo $q$, ...
3
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1answer
547 views

A new generalisation of dimension? part 2

I worked this theory : A new generalization of the dimension? I have a theorem about dimensions which is more general and simple than for matroids. Definition 1: A structure $S$, is a pair $(X, \...
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2answers
157 views

Reference request: Functions of bounded variation in one real variable

Is there a good reference for facts and theorems about BV real valued functions? I’m looking for something with much more than say Stein and Shakarchi 3, or Evans and Gariepy. Thanks!
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+50

Rate of convergence for difference between conditional and marginal probability

Suppose $X\sim \text{Bin}(2n,p)$ and $X_1,X_2\sim\text{Bin}(n,p)$ are independent, with $X_1+X_2=X$. I'm interested in the rate of convergence for the absolute difference $$ \left\vert P(X>c|X_1\...
3
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1answer
232 views

Is it possible to define a linear $A_\infty$-category as a special kind of an $\infty$-category?

A functor $N\colon\mathrm{Cat}_{A_\infty}\longrightarrow\mathrm{Cat}_\infty$ is constructed in a paper [1] by Faonte. This gives a way to get an $\infty$-category by starting with an $A_\infty$-...
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0answers
41 views

Proof that superstable theories with no Vaughtian pairs have no imaginary Vaughtian pairs

In 'Elementary pairs of models' by Bouscaren, she mentions with a remark at the end that if $T$ is a superstable theory then $T$ has a Vaughtian pair if and only if $T^\text{eq}$ has a Vaughtian pair, ...
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0answers
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Quasilinear elliptic problem on fractal domain

Consider the following quasilinear elliptic equation $$\nabla_x (A(x,u(x),\nabla_x u(x))) + f(u,x) = 0 $$ on a bounded domain $\Omega$, augmented with homogeneous Dirichlet boundary data: $$u|_{\...
2
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1answer
59 views

Quasilinear elliptic problem: Ellipticity-type conditions

Consider the following quasilinear elliptic equation $$\nabla_x (A(x,u(x),\nabla_x u(x))) + f(u,x) = 0 $$ on a bounded domain $\Omega$, augmented with homogeneous Dirichlet boundary data: $$u|_{\...
5
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0answers
122 views

Beilinson and Deligne's Motivic Polylogarithm and Zagier Conjecture

Where can I find the preprint Motivic Polylogarithm and Zagier Conjecture by Beilinson and Deligne? I see it referenced in a lot of papers but no one seems to host a copy.
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0answers
113 views

Is there a version of Weyl's law for graph Laplacians?

Is there a version of Weyl's law or a local Weyl's law for eigenvectors of the graph Laplacian? For some context, a colleague in statistics has encountered eigenvectors of the Laplacian for certain ...
9
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3answers
503 views

Reference request for wild 3-manifolds

I’m looking for a text on 3-manifolds that focuses on wild/pathological objects, similar to Bing’s work in the field. I know basic algebraic topology (homotopy, homology, cohomology) and have read ...
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2answers
818 views

A multicategory is a … with one object?

We all know that A monoidal category is a bicategory with one object. How do we fill in the blank in the following sentence? A multicategory is a ... with one object. The answer is fairly ...
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2answers
2k views

Mathematical research in North Korea — reference request

Question: Where can one find information on which areas of mathematics are represented at which of the more than 20 universities in the Democratic People's Republic of Korea (DPRK), and on which ...
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0answers
19 views

Splittings for generic flows on a vector bundle

Question: Consider a smooth vector bundle $\pi:V\to B$ and the space $\mathcal{F}$ of $C^k$ linear flows $\Bbb{R}\times V \to V$ endowed with the strong $C^k$ Whitney topology. Is it true that for all ...
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0answers
25 views

Rotation rates for a linear flow on a vector bundle

The following linear ODE on $\Bbb{C}$ $\dot{z} = (a + i b)z$ has solutions $z(t) = e^{(a+ib)t} z(0)$. Hence the real part $a$ captures expansion rate and the imaginary part $b$ captures rotation ...
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How to show that a continuous family of symmetric matrices is uniformly positive?

My problem : I have a family of $4 \times 4$ symmetric matrices. More precisely consider an interger $d$, a real $\lambda> 0$ and define the family $S_{\lambda}$: $ \{A(\lambda,x_1,x_2) ; (x_1,...
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0answers
28 views

Flat or linkless embeddings of graph with fixed projection

The problem of finding whether a given planar diagram of a graph, with over- and under-crossings, is a linkless embedding or not has unknown complexity (Kawarabayashi et al., 2010). My first question ...
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0answers
66 views

L-functions of tempered automorphic representations

Let $G$ be a reductive group over the adele ring $\mathbb A_F$ of a number field $F$. Let also $r$ be a complex finite dimensional representation of the $L$-group $r:{^LG}\to GL(V)$. It is generally ...
5
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2answers
141 views

Enumeration of lattice paths of a specific type

One of the approaches to "Special" meanders led (in particular) to the following question: What is the number $a_{m,n}(\ell)$ of $\ell$-step paths from $(1,1)$ to $(m,n)$ using the ...
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2answers
259 views

Outer Hodge groups of rationally connected fibrations

I believe the following is true and well known. Theorem (?). Let $X$ and $Y$ be smooth, irreducible, projective varieties over $\mathbb{C}$. Let $$ f\colon X\rightarrow Y $$ be a surjective map with ...
2
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1answer
207 views

Thematic programs for collaborative research (similar to the one in Bonn) [closed]

The Hausdorff Institute in Bonn periodically organizes thematic junior trimester programs, which "give young mathematicians (postdocs, junior faculty) the opportunity to carry out collaborative ...
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Resolvent estimate of compact perturbation of self-adjoint operator

Let $T$ be a selfadjoint operator on Hilbert space $H$. Then we know that there is a resolvent estimation $$\left\lVert (\lambda-T)^{-1}\right\rVert = \frac{1}{dist(\lambda,\sigma(T))}, \ \lambda \in \...
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0answers
106 views

Final step in Coppersmith?

In the final step in Coppersmith technique we have $n$ polynomials (possibly non-homogeneous) in $\mathbb Z[x_1,\dots,x_m]$ where $m\leq n$ and using elimination theory we extract the common integer ...
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83 views

(Semi-)Riemannian geometry for working PDE analysts

What is a good reference on (semi-)Riemannian geometry written for PDE analysts (that is, with main focus on analytical problems and approaches)? The closest thing I know to this, are two books by ...
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Examples of Yang-Baxter monoids

Then we say that an algebra $(X,f,g,\circ,1)$ is a Yang-Baxter monoid if it satisfies the following identities: $(X,\circ,1)$ is a monoid, $f(x,1)=1,f(1,x)=x,g(x,1)=x,g(1,x)=1$ $x\circ y=f(x,y)\circ ...
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1answer
82 views

Analytic approach to geodesic connectedness in Semi-Riemannian manifolds

Can you point out a reference (or references) that deal with analytical methods (rather than methods from differential geometry) for the study of geodesic connectedness on Semi-Riemannian manifolds?
3
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1answer
96 views

What “mild solution” means, and how to find it?

In this paper: Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem Byszewski studied this form of functional-differential nonlocal problem (1)...
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4answers
432 views

How to organize collaborations? Managing communication within the team [closed]

What is an effective tool for managing the communication within a small team of coauthors working on a paper (when face-to-face interaction is not possible)? I've previously used back-and-forth email ...
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0answers
34 views

Anisotropic elliptic problems

Where can I find a reference on the following anisotropic problem? $$(\bullet) \qquad \begin{align*} \nabla_x (A(x) \nabla_x u(x,y)) + \Delta_y(K(y) \ast u(x,y))\end{align*}=0, $$ where $(x,y) \in \...
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1answer
75 views

The definiton of a multiplier on a Banach algebra

Let $A$ be a Banach algebra. Some textbooks define a (left ) multiplier as a map $T:A\rightarrow A$ satisfying $T(ab)=T(a)b$ for all $a,b\in A$ and assume that $A$ needs to be a without order Banach ...
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1answer
58 views

Elliptic interface problem without conditions on the interface

Consider an open domain $U$ split in two non-overlapping subdomains: $U = U_1 \cup U_2$. For a model case, consider a ball split in a smaller ball and an anulus. Consider the following elliptic ...
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1answer
432 views

“Matchmaking website” for project-specific mathematical collaborations [closed]

It seems that even in the age of Internet, most mathematical collaborations are born (and pursued) off-line. However, I wonder if there exists a "matchmaking website" for mathematical ...
6
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1answer
131 views

Anisotropic perimeter and regularity of anisotropic minimal surfaces

1. Introduction. By-now classical results assert that minimal surfaces (in $\mathbb R^n$) are generically "smooth" out of a "small" set. Question. What are the known regularity results for ...