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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Linear vs smooth actions of finite groups on spheres, euclidean spaces and closed disks

I would like to know examples (with references, if possible) of the following: (1) a finite group $G$ acting effectively and smoothly on a sphere $S^n$ (any $n$) but admitting no effective linear ...
Ignasi Mundet i Riera's user avatar
3 votes
1 answer
186 views

Maximal $\pi/2$-separated subset of the sphere

A subset $A$ of a metric space is called $\varepsilon$-separated if $$dist(x,y)> \varepsilon \mbox{ for all } x\ne y\in A.$$ (Notice that the inequality in my definition is strict.) What is the ...
asv's user avatar
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4 votes
1 answer
149 views

Enumerator Polynomials for Linear Anytime Codes

Let $C = \{c \in \mathbb{F}^n_2 : Hc=0\}$ be a binary linear code where $H \in \mathbb{F}^{k \times n}_2$ is a block lower-triangular matrix of full rank called the parity-check matrix of $C$. Clearly ...
Nikola Kovachki's user avatar
2 votes
1 answer
308 views

How to construct the symmetric power function from a modular form?

I want to understand how we construct from a modular form $f$ its symmetric power function $Sym^rf.$ I read that there is a particular representation that does this but I am not familiar with this ...
Khadija Mbarki's user avatar
10 votes
2 answers
481 views

References on quaternionic geometry

Is there any analog, in the quaternionic setting, of Kahler potentials? In particular I'm interested in a similar construction of the Fubini-Study 2-form on $\mathbb{P}^1(\mathbb{C})$ over the ...
cinzia bisi's user avatar
4 votes
1 answer
188 views

A proof of the Ibragimov-Kara-Mahomed commutation relation

Let $u_a(x),\,a=1,2,\ldots n$ be a $n$-component field in Minkowski spacetime $x^\mu,\,\mu=0,1,2,3$ and let $u_{a,\,\mu}=\frac{du_a}{dx^\mu}$. Let us introduce two operators (we use Einstein ...
Zurab Silagadze's user avatar
16 votes
1 answer
436 views

Types of generating functions (ordinary, exponential, ???) closed under substitution

A nice feature of ordinary and exponential generating functions is that they are closed under substitution: if $F(z)$ and $G(z)$ both have integer coefficients, then $F(G(z))$ also has integer ...
Martin Rubey's user avatar
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8 votes
0 answers
2k views

Possible values of eigenvalues of Hadamard product of Hermitian matrices

One of the most important (and very well-known) result in the study of the spectrum of Hermitian matrices is Horn's conjecture (or theorem?), which provides a complete answer to the following problem: ...
user78370's user avatar
  • 891
1 vote
2 answers
212 views

Completion under weighted limits/colimits

Is there any further reference besides "Basic Concepts of Enriched Categories" (Kelly) for completion under T-(weighted) limits/colimits? (in which T is a set of weights) Thank you in advance
Fernando's user avatar
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3 votes
2 answers
1k views

Propositional logic without negation

As part of a bigger project I am researching a propositional logic, without a negation. And I would like to know, whether this already exists, to avoid double work and have proper references. In this ...
Lucas K.'s user avatar
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3 votes
1 answer
150 views

Regularity of maps in algebraic topology for manifolds

Let $M$ be a $n$ manifold such that $\pi_k(M)$ is non trivial. What can we expect about the regularity of a representant $f:S^k\rightarrow M$ of a non-trivial cycle? For example, if $M$ is a manifold ...
Paul-Benjamin's user avatar
4 votes
0 answers
428 views

Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$?

Let $V$ be a vector space of dimension $>n$, and define the subset $$ K:=\{ ([\omega],v)\mid v\wedge\omega=0 \}\subset\mathbb{P}(\Lambda^nV)\times V\, . $$ Denote also by $\pi:K\longrightarrow \...
Giovanni Moreno's user avatar
2 votes
2 answers
333 views

Composition operators on fractional-order (periodic) Sobolev spaces

(The question was originally posted on MSE.) Preliminaries: We know that the fractional-order Sobolev spaces $\mathrm{H}^s(\mathbb{R})$ and $\mathrm{H}^s(\mathbb{T})$ are closed under multiplication ...
F. H.'s user avatar
  • 63
9 votes
1 answer
812 views

Why is the set-theoretic principle $\diamondsuit$ called $\diamondsuit$?

A shallow answer would just point to theorem 6.2 in Jensen's 1972 paper "The fine structure of the constructible hierarchy", where Jensen introduces this property. Or was this symbol used already ...
Goldstern's user avatar
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1 vote
0 answers
132 views

Monotonic convergence of Newton's method for boundary value problems

I’m interested in solving nonlinear elliptic boundary value problems of the type $$ -a\Delta u + f(u) = 0, $$ $$ u|_\Gamma = u_0 $$ by Newton’s method when its convergence is global and monotonic. ...
jokersobak's user avatar
5 votes
1 answer
180 views

Resource Constrained Routing with Refueling

What are good algorithms (resp. models) for calculating optimal or near optimal routes while taking into account fuel consumption, options for refueling and, limited tank capacity? Especially modeling ...
Manfred Weis's user avatar
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5 votes
1 answer
635 views

Kashiwara's watermelon theorem and Microlocal version of Helgason's (support) and Holmgren's theorems

I would like to find good references for the theorems mentioned above in the title. I am reading chapter VIII of Hörmander's classic, but I wonder whether there is something more up-to-date. My ...
Qwertuy's user avatar
  • 251
2 votes
0 answers
245 views

Reference request: proofs of the theorems in the paper "On the representation of the group GL(n, K) where K is a local field"

In the paper On the representation of the group $GL(n, K)$ where $K$ is a local field by Gelfand and Kazhdan, it is said that the proofs of the theorems in the paper are published in some other papers....
Jianrong Li's user avatar
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3 votes
0 answers
113 views

Reference request concerning PL tangent Stiefel-Whitney classes

I am hoping for a reference for the fact that PL manifolds have tangent Stiefel-Whitney classes. I understand this as follows: they have tangent microbundles, which in turn lead to spherical ...
Tom Goodwillie's user avatar
2 votes
0 answers
413 views

Newer list of open problems in model theory

In the book Model Theory by C. C. Chang and H. J. Keisler, there is a list of open problems in model theory. More exactly, this list is called "Open problems in classical model theory" (on page 597, ...
asdfusername's user avatar
1 vote
1 answer
319 views

A bound on the $\mathrm{L}^p$ norm in terms of the $\mathrm{L}^2$ norm in periodic Sobolev spaces

(The question was originally posted on Math StackExchange.) Preliminaries: Given ${s \geq 0}$, let ${\mathrm{H}_P^s}$ denote the ${\mathrm{L}^2}$-based fractional-order Sobolev space of ${P}$-...
F. H.'s user avatar
  • 63
6 votes
1 answer
478 views

References for Forcing with Side Conditions

I'm looking for some good references about Forcing with Side Conditions, including expository papers that explain the main ideas with some details in order to give me a fairly clear insight of those ...
user avatar
1 vote
1 answer
445 views

Does the Laplacian commutes with elements of the basis of the Lie algebra?

Let $G$ be a compact Lie group with Lie algebra $\mathfrak{g}$. I know that if $g$ is semi-simple then the Laplace-Beltrami operator on $G$ agrees with the Casimir element and therefore commutes with ...
Max Reinhold Jahnke's user avatar
2 votes
1 answer
567 views

On the upper Banach density of the set of positive integers whose base-$b$ representation misses at least one prescribed digit

Let $b$ be a fixed integer $\ge 2$ and $A$ a proper subset of $\{0, \ldots, b-1\}$. Then define $X$ to be the set of all positive integers whose base-$b$ representation consists only of digits from $A$...
Salvo Tringali's user avatar
10 votes
1 answer
542 views

Who was/were the first to note that if $\sum_{x \in X} \frac{1}{x} < \infty$ then the natural density of $X$ is zero?

It is a result of folklore that the natural density of a set $X$ of positive integers such that $\sum_{x \in X} \frac{1}{x} < \infty$ is zero. This is reproved, e.g., in T. Šalát's paper: ...
Salvo Tringali's user avatar
1 vote
1 answer
718 views

Geometric interpretation of Chern classes over flag manifolds

I would like to find that Chern classes of the tautological bundles over a flag manifold are dual to some cells in homology, analogously to what happens for the Grassmanian case. I have not been able ...
Temitope.A's user avatar
4 votes
2 answers
811 views

Künneth formula for Bredon cohomology theory

Let $G$ be a finite group. Let $X$ and $Y$ be two $G$-CW complexes with known integer graded $G$-equivariant Bredon cohomology with constant coefficient systems. Is there any Künneth formula for this ...
Surojit Ghosh's user avatar
0 votes
0 answers
54 views

Differentiation of $(u(t),v(t))_{L^2(\Omega)}$ when $u, v \in H^1(I\times \Omega)$

Let $I=(0,\infty)$. Consider $u, v \in L^2(I;H^1(\Omega))$ with $u_t, v_t \in L^2(I;L^2(\Omega))$ where $\Omega$ is a bounded doamin. Is it true that $$\frac{d}{dt}(u(t),v(t))_{L^2(\Omega)} = (u'(t), ...
JamesCa's user avatar
4 votes
1 answer
259 views

Injectivity of the Funk transform for nonsmooth functions

Let $S^{n-1}$ be the unit sphere in $\mathbb R^n$ and $\Gamma_n$ the collection of great circles on it. Assume $n\geq3$. The Funk transform of a function $f:S^{n-1}\to\mathbb R$ is a map $Ff:\Gamma_n\...
Joonas Ilmavirta's user avatar
11 votes
2 answers
1k views

Concrete examples of covering from the 3-torus to the 3-sphere

There is a two-fold branched covering from 2-torus to the 2-sphere, $T^2 \rightarrow S^2$, whose covering transformation group is generated by the map $x \mapsto -x$ (Note that $T^2$ is an abelian ...
Creg's user avatar
  • 431
16 votes
3 answers
2k views

Your favorite papers on geometric group theory

I would like to improve my "depth of understanding" in geometric group theory. So I am interested in short and accessible papers on subjects related to this field but which are not always ...
2 votes
0 answers
77 views

Maximum cardinality general factor of a graph

Given a graph $G=(V,E)$ and a set of integers $B(v)$ associated to each vertex, a general factor of $G$ is a set of edges $F\subseteq E$ such that the degree of each vertex $v\in V$ in the graph $(V, ...
George Octavian Rabanca's user avatar
2 votes
1 answer
247 views

Well-ordered reference

I'm wondering if there is a standard reference for the following straightforward facts about well-orderings. (They are quite easy to prove, I just need a handy/standard reference.) Let $(S,<)$ be ...
Pace Nielsen's user avatar
7 votes
1 answer
776 views

Infinite-dimensional admissible representations of SL(2,C)

I'm working in my research with the infinite dimensional (admissible) irreducible representations of $\mathrm{SL}(2,\mathbb{C})$ introduced by Harish-Chandra in his paper "Infinite Irreducible ...
Giuseppe Sellaroli's user avatar
1 vote
0 answers
87 views

Reduced products of (abelian and triangulated) categories: references?

For a filter $U$ on a set $X$ and for a family of categories $C_x$ indexed by $X$ I would like to consider the (corresponding categorical version of) reduced product of $C_x$ (for $x\in X$) with ...
Mikhail Bondarko's user avatar
3 votes
0 answers
103 views

Nemytskii/superposition operator without separability of Banach space?

Let $T:[0,1] \times X \to \mathbb{R}$ be a nonlinear map where $X$ is a Banach space. Suppose that $T$ is a Caratheodory map, so that $t \mapsto F(t,x)$ is measurable and $x \mapsto F(t,x)$ is ...
Upin's user avatar
  • 171
3 votes
0 answers
484 views

Riemann-Roch formula for nodal curves

Let $X$ be an irreducible, reduced, projective curve over an algebraically closed field, with at worst nodes as singularities. Let $\mathcal{F}$ be a trivial vector bundle on $X$ of rank $r$. Consider ...
Ron's user avatar
  • 2,116
0 votes
0 answers
117 views

How to solve $\sqrt{-1}\partial\bar{\partial}u=\omega$

I'm looking for references on the study of the equation $\sqrt{-1}\partial\bar{\partial}u=\omega$,especially when $\omega$ is a k\"ahler metric on $\Omega\setminus S$,where $\Omega\subset \mathbb{C}^n$...
whitacre's user avatar
2 votes
1 answer
641 views

Elementary bound on operator norm on symmetric tensors: reference request

My education didn't really cover Tensors very well, so I'm getting stumped by a quite elementary question. Let $T_k$ be a type k symmetric tensor. We can define the "operator norm" (or the induced ...
Guillaume Dehaene's user avatar
0 votes
0 answers
121 views

Bound of Chebyshev function and zeros of zeta function

It is an elementary argument (such as in Multiplicative Number Theory, section 18) that, if the Chebyshev's function $f(x) = \sum_{n \le x} \Lambda(x) = x + O(x^\alpha)$ for some $\alpha < 1$, then ...
Linh Nguyen's user avatar
2 votes
1 answer
146 views

Irreducible unitary representations of semidirect groups of a discrete abelian group by a discrete group

Recently in a paper we get the following result: Let a discrete group $\Gamma$ act on a discrete abelian group $G$ by group automorphisms. Every irreducible unitary representation $\pi$ of $G\rtimes\...
Huichi Huang's user avatar
5 votes
4 answers
620 views

Integrals involving the Tricomi hypergeometric function

I am looking for a reference for the two following equalities involving the Tricomi function $U$ and the Meijer function $G$. I have found these formulas on the website http://functions.wolfram.com/, ...
Stéphane Laurent's user avatar
7 votes
1 answer
196 views

How to prove the existence of the polytope in $\mathbb{R}^d$ with a given number of faces, minimizing the isoperimetric ratio?

This is the isoperimetric type question. We know that in $\mathbb{R}^d$, balls are the sets that minimize the isoperimetric ratio $\frac{S^{d}}{V^{d-1}}$, where $S$ is the surface area and $V$ is the ...
student's user avatar
  • 1,320
4 votes
2 answers
323 views

Non-Forking and Related Concepts

Is the importance of developing forking machinery in the way we set it up, or is it in the fact that it allows us to come up with a notion of independence via the properties of non-forking? I'm ...
user avatar
0 votes
0 answers
406 views

Set as a (strict) infinite-category?

First, let me say that I have no idea if such a post has its place here. However, I believe that the ideas I'm going to present are important. The goal of this thread is three fold: 1) trying to ...
sure's user avatar
  • 438
1 vote
2 answers
359 views

binomial/factorial identity mod p

In trying to determine the spectrum of a well-known ergodic transformation, I came up with the following useful (for me) result. Let $p$ be a prime and $a$ a positive integer. Then for $M$ a positive ...
David Handelman's user avatar
4 votes
0 answers
173 views

Do more generalizations of Schur's inequality exist?

I meet this following problem If $$n\ge 3,\sum_{i=1}^{n}\left(\prod_{j\neq i}(a_{i}-a_{j})\right)\ge 0$$ where $a_{i}$ are real numbers. when $n=3$, it is Schur's inequality so which $n$ such ...
Destiny freedom's user avatar
2 votes
1 answer
280 views

Convergence of weighted double sum of random variables

I'm looking for convergence results of particular weighted sum: $$S_n=\frac{1}{n}\sum_{i=1}^{n}\sum_{j=1}^{n}a_{i,j}X_i X_j.$$ when random variables $X_i$ ar i.i.d. Are there any investigation ...
Tomas's user avatar
  • 267
5 votes
0 answers
270 views

Moore spectra are not E-infinity (oldest known proof)

Fix a prime $p$. Let $M_p(i)$, the $i$-th Moore spectrum at the prime $p$, be the cofiber of the map $$ S^0 \overset{p^i}\longrightarrow S^0 $$ where $S^0$ be the sphere spectrum. In the Mathoverflow ...
Prasit's user avatar
  • 2,013
1 vote
1 answer
113 views

Differences of consecutive ordered fractional parts

Let $r$ and $h$ be a real numbers and $n>0$. Write the fractional parts $\{k*r+h\}$, for $k = 1,2, . . . n$, in increasing order as $$ a_1 < a_2 < \cdots < a_n.$$ Let $D_n$ be the set of ...
Clark Kimberling's user avatar

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