Questions tagged [reference-request]
This tag is used if a reference is needed in a paper or textbook on a specific result.
14,581
questions
2
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0
answers
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How to write BRST-BV for dg-Lie?
The usual BRST-BV implements a Lie algebra and its module in terms of ghosts, etc.
Where is there written a corresponding formula incorporating the differential of
a dg Lie algebra and module?
- 3,850
4
votes
1
answer
1k
views
Compact radial Sobolev embedding $H^1_{rad}\hookrightarrow L^p$
I want to show:
Let $N\geq 2$ and $2< q <2^\ast$. Then the embedding \begin{align}
H^1_{\text{rad}}(\mathbb{R}^N)\hookrightarrow L^q(\mathbb{R}^N)
\end{align}
is compact.
I was able to show ...
- 439
5
votes
2
answers
883
views
Stirling numbers of the second kind with maximum part size
The stirling number of the second kind $S(n,k)$ counts the number of partitions of the set $[n]$ into $k$ non-empty parts. I found a definition for the numbers called the $r$-associated stirling ...
- 1,825
1
vote
0
answers
157
views
Kwantitatieve Methoden [closed]
I'm looking for one article (Eilers P. H. C., 1987, Asymmetric least squares: New faces of a scatterplot. Kwantitatieve methoden 8, 45-64) and since I was not able to find it for some time, I'm asking ...
- 151
7
votes
1
answer
571
views
Alternate proof of Morley's theorem?
I'm trying to understand the result given in the first box at slide 45 of this talk. Specifically:
1) What is the source cited? I have not been able to find any article by Keisler, Chudnovsky and/or ...
- 187
4
votes
0
answers
131
views
Improvements of the Reidemeister-Schreier index formula for particular classes of groups
I have a couple of questions regarding possible improvements of the Reidemeister-Schreier index formula: let $G$ be a $d$-generated group and let $H$ be a subgroup of $G$, then
$$d(H) \le (d-1) \...
- 116
7
votes
2
answers
1k
views
Primitive recursive arithmetic via universal algebra
From the Wikipedia article on Primitive recursive arithmetic:
"Primitive recursive arithmetic, or PRA, is a quantifier-free formalization of the natural numbers. It was first proposed by Skolem[1] ...
- 437
7
votes
3
answers
904
views
Survey of Engineering Problems for Mathematicians [closed]
I am looking for survey-books on open math (esp. probability) problems from engineering fields but phrased in mathematical language.
There are hundreds of specialized math-engineering books out there,...
- 651
1
vote
0
answers
118
views
Fractional Poincare inequality on closed manifold
Let $u \in H^{\frac 12}(M)$ on a compact closed Riemannian manifold. Can someone refer me to a source where the inequality
$$\lVert u - \bar u \rVert_{L^{2^*}} \leq C|u|_{H^{\frac 12}}$$
is proved, or ...
- 11
4
votes
1
answer
248
views
Explicit bounds for transfer results in algebraic geometry
Assume you have an ideal $I\subseteq\mathbb{Z}[X_1,\ldots,X_n]$ of the polynomial ring in $n$ variables over the integers. For any field $\Bbbk$, I can consider the ideal $I(\Bbbk):=I\otimes_{\mathbb{...
- 4,822
2
votes
0
answers
186
views
Examples of Geometric Constructions in Higher Dimensions
The classical problem of geometric construction seems to be restricted to planar Euclidean Geometry with straight edge and compass as the only admissible "construction-tools".
I would like to know,...
- 12.7k
2
votes
1
answer
400
views
Hodge structure of relative cohomology groups
I need a hint or a good reference for definition of mixed Hodge structure on the relative cohomology groups ($\mathrm{H}^*(X,Y)$, $Y\subset X$ a closed subvariety of a comolex quasiprojective variety $...
- 4,454
2
votes
1
answer
181
views
On a tower of strongly normal extensions
Where I could see the following statement?
Let $K\subset L\subset M$ be a tower of the strongly normal extensions of differential fields. If $M$ is weakly normal over $K$, then $M$ is strongly ...
- 21
3
votes
1
answer
311
views
Was $\Sigma x$ used as quantifier?
Kurt Gödel in 1931 used $x\Pi a$ where we in contemporary notation would use $(\forall x) A$ or $(x)A$, and $Ex a$ where we would use $(\exists x) A$. I believe that I remember that $\Sigma xA$ has ...
- 3,292
2
votes
0
answers
251
views
Uniqueness of analytic center manifold
In a book, i have read a remark which says that the center manifold of an equilibrium point of a differential equation is not unique in general but is unique in the class of analytic manifold. The ...
- 21
1
vote
0
answers
99
views
Summing a function at integer points
For a real function $f$ defined on the reals, and real $y$, define the 2-way infinite sum
$$ F_f(y) = \sum_{i\in\mathbb Z} f(y+i). $$
If $F_f(y)$ is defined for all $y$, it is periodic of period 1.
...
- 37.2k
2
votes
0
answers
290
views
Is this approach to the combinatorics of knots well known?
I am teaching a course on knots for the first time, and this led me to play with an approach which I have not seen in the literature. I would be surprised if no one had used it before, so I am ...
- 55k
2
votes
1
answer
629
views
Boundary energy estimate of wave equations
Let $D$ be the unit disk in $\mathbb{R}^{n}$, we consider the $n$ dimension wave equation defined on $D$,
$$\square u=F$$
where $\square=\partial_{t}^{2}-\triangle$ is the standard wave operator in $\...
- 81
6
votes
2
answers
1k
views
Line bundles over Kähler–Hodge manifolds
A Kähler–Hodge manifold $M$ can be defined as a Kähler manifold whose Kähler form $\omega$ is integral, namely $\omega\in H^{2}(M,\mathbb{Z})$. It is known then that there always exists a Hermitian ...
- 3,064
1
vote
0
answers
133
views
Reference Request: Category of explicit maps between primitive recursive sets?
[Edited]
Let $\mathsf{PR}$ be the category defined as follows:
Choose a specific presentation of Primitive Recursive Arithmetic, that is, with a specific set of terms for primitive recursive ...
- 437
0
votes
0
answers
57
views
References for symmetric α-stable process (SSP) for $a>2$
Many properties of Brownian motion have been extended to SSP's for $0\leq \alpha\leq 2$ and so it is quite easy to find literature on them. However, I am currently studying the SSP for $\alpha>2$ ...
- 651
1
vote
1
answer
469
views
Wong-Zakai smooth approximation in probabilty for stochastic differential equations
I'm looking for a result of the form: Let $B_\epsilon$ denote a "natural" smooth $\epsilon$-approximation to an $n$-dimensional Brownian motion $B$ (e.g. by mollification or simply piecewise linear) ...
- 111
11
votes
0
answers
620
views
Pairing of cohomology and homology Künneth formulas
Let $k$ be a field, and let $X$ and $Y$ be CW-complexes of finite type (although the question makes sense for $k$ a ring and for more general chain complexes of finitely generated free abelian groups)....
- 35k
3
votes
2
answers
740
views
orbits of linear algebraic group $G({\Bbb Q}_p)$ acting on subgroups of ${\Bbb Q}_p^n$
Let $G\subseteq GL(n)$ be a linear algebraic group, and let $G({\Bbb Q}_p)\subseteq GL(V)$ act on a ${\Bbb Q}_p$-vector space V of finite dimension.
Consider the action of $G$ on abelian subgroups $L\...
- 1,299
2
votes
2
answers
541
views
Upper bounds on the edge clique cover number on special graph classes
An edge clique cover of an undirected graph $G$ is a set of cliques of $G$ such that every edge of $G$ is an edge in at least one clique in the set. The edge clique cover number $\theta(G)$ is the ...
- 717
7
votes
2
answers
901
views
Concise mathematical definition of the fusion product on the Verlinde ring?
The Verlinde ring of a (let us say) simply connected simple compact Lie group has as underlying additive group the Grothendieck group of representations of the central extension $\widehat{LG}$ of the ...
- 33.9k
23
votes
2
answers
1k
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fake $S^{2k}\times S^{2k}$
Let $X$ be a fixed closed manifold,$S(X)$ the structure set and $Aut(X)$ the group of self homotopy equivalence of $X$.
surgery theory tells us that $\mathcal{M}(X):=S(X)/Aut(X)$ is in bijection ...
- 593
1
vote
0
answers
173
views
Property theories
Property theory is, as I have understood it, first of all characterized by an attempt to approach naive comprehension type-freely and without committing to extensionality.
There is e.g. the work of ...
- 3,292
1
vote
1
answer
184
views
What is the fractional derivative smoothness of functions from the Zygmund class?
Let $\Lambda([0,1])$ be the Zygmund class of continuous on $[0,1]$ functions for which $$\sup h^{-1}|f(x+2h)-2f(x+h)+f(x)|<\infty.$$ What would be the exact smoothness class for the fractional ...
- 2,645
1
vote
1
answer
290
views
Explicit deformations of pseudo representations
Let $G$ be a group (which I will be glad to consider to be the absolute Galois group of a $p$-adic field, and so satisfies Mazur's finiteness condition which appears in his paper Deforming Galois ...
- 113
1
vote
0
answers
66
views
Quotient groups of "Abelian-times-compact", what are they called?
In what I am doing now this class of groups appears all the way: (Hausdorff) quotient groups of $A\times K$, where $A$ are locally compact abelian groups, and $K$ compact groups.
I wonder, if this ...
- 7,274
9
votes
3
answers
2k
views
Need examples of homotopy orbit and fixed points
I am no expert in equivariant homotopy theory. Let's say, I am planing to give a talk on homotopy fixed points and orbits. My audience will be graduate students who are doing algebraic topology or ...
- 2,013
7
votes
1
answer
291
views
Symmetric L-groups of integral group ring of finite cyclic groups
Where can i find the results about $L^{\ast}(\mathbb{Z}\pi)$ for $\pi$ a finite cyclic group?
- 593
2
votes
0
answers
895
views
Cubic fourfold and K3 surface: geometric constructions of Hodge isometry
Hodge structure on K3 surface (the middle line of Hodge diamond is 1 20 1) is similar to the Hodge structure of cubic fourfold (the middle line of Hodge diamond of primitive cohomology is 0 1 20 1 0). ...
- 600
1
vote
0
answers
74
views
Equivalent of Lauricella $F_D$ on an elliptic curve?
Lauricella's hypergeometric function $F_D$ is related to (weighted) configurations of points on $\mathbb{P}^1$. I am looking for generalizations to weighted point configurations on an elliptic curve. ...
- 111
2
votes
1
answer
498
views
What are some good references on the Galois theory, factorization, or minimality of differential equations?
Let $\lambda$ be a nonzero complex number and let $u(x)$ be some smooth function $\mathbb{R}\to\mathbb{C}$, not identically zero. I want to prove that if $u$ satisfies $$u'' + \lambda u'+ \lambda^2 u =...
- 123
5
votes
1
answer
622
views
Localization principle in supersymmetry
In $\S$ 9.3 of the book "Mirror symmetry" (Vafa, Zaslow eds.) the authors formulate the following general localization principle for computation of integrals with respect to both even and odd ...
- 21.1k
2
votes
0
answers
88
views
explicit matrices for Weil ($p^2$ dimensional) representation of $Sp(4,\mathbb{F}_p)$, $p>3$
I am looking for more-or-less explicit matrices for the $p^2$ dimensional Weil representation of $Sp(4,\mathbb{F}_p)$, suitable for computer implementation. Ideally, I would like the images of the ...
- 1,629
6
votes
1
answer
1k
views
Structure of symplectic group over finite fields
We are working over the finite field $\mathbb{F}_{q}$ of odd prime characteristic $p$ and of cardinality $q$ some power of $p$. We recall the symplectic group $Sp(4,\mathbb{F}_{q})$ as the group of ...
- 85
13
votes
4
answers
843
views
The groupoid of algebraic expressions and proofs
Fix a set of variables $V$, and suppose we're given a presentation of a monosorted algebraic theory, with variable symbols taken from $V$. For the sake of example, suppose the presentation consists of ...
- 3,693
2
votes
0
answers
723
views
Reference: Continuity of Eigenvectors [closed]
I am looking for an appropriate reference for the following fact. I already posted on math.stackexchange, but got no answer.
For each $X \in \mathbb{R}^{n \times n}_{\text{sym}}$ (symmetric matrix),...
- 1,474
3
votes
2
answers
891
views
Positive definiteness of infinite tridiagonal matrices
I am interested in the following problem: I have an infinite symmetric tridiagonal matrix
$$
A=
\begin{bmatrix}
a_1 & b_1 & & & \\
b_1 & a_2 & b_2 & & \...
- 682
5
votes
2
answers
190
views
Accuracy of the formulas for angles between almost colinear vectors
Assume $x$ and $y$ are two vectors in $\mathbb{R}^3$ and we want to compute the acute angle $\alpha\in(0,\pi/2]$ between these two (noncolinear) vectors. There are (at least) two possibilities:
In ...
- 215
11
votes
2
answers
2k
views
Banach-Zarecki theorem - who was Zarecki?
I'm writing a paper for real analysis seminar, a paper about Banach-Zarecki theorem and I need some information about the authors.
Stefan Banach - there is no problem to find information about him.
...
- 111
7
votes
1
answer
410
views
Fractal dimension of scaling limits of discrete structures
Let $S$ be the set of positive integers whose base-three expansion contains only the digits 0 and 2. The discrete set $S$ in a sense has (negative) fractal dimension $(\log 1/2)/(\log 3)$, since if ...
- 19.4k
2
votes
1
answer
315
views
Reference request: Research done on whether the Euler prime can be the largest factor of an odd perfect number
(Note: This was cross-posted from MSE.) I posted the following reference request in MSE three (3) days ago, but was unable to elicit any responses. I am cross-posting it to MO, hoping that it is ...
- 1,008
8
votes
1
answer
871
views
Weisinger's thesis
I am currently reading Atkin and Li's paper on Twists of newforms and Atkin-Lehner pseudo eigenvalues and one of the references there is to Weisinger's thesis:
Weisinger J., Some results on classical ...
- 363
1
vote
0
answers
321
views
Occupancy problem with limited capacity and two types of balls [closed]
I am considering the following problem that I suspect to be standard.
One has a set of $N$ balls composed of a fraction $\alpha$ of red balls and $(1-\alpha)$ of black balls (we assume $\alpha N$ is ...
- 19
10
votes
2
answers
2k
views
A result attributed to Whitney
One of the basic results of real analysis says that any closed subset of a smooth ($C^\infty$) manifold $M$ is the set of zeros of some map $\lambda\in C^\infty(M;[0,1])$. This result (or some ...
- 717
6
votes
1
answer
330
views
What is known about the boundary between Richardson's theorem and the Tarski-Seidenberg theorem?
Tarski proved that equalities and inequalities in can be decided over $\mathbb{R}[x].$ Richardson proved that adding composition with the sine and exponential functions caused the problem to become ...
- 8,984