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

learn more… | top users | synonyms

3
votes
1answer
91 views

Tiling with restricted overlap

Non-overlapping tilings of regions is a well-studied topic. I wonder if the following variant has been considered: A tile can be partitioned into several regions, where such regions from different ...
2
votes
0answers
91 views

Reference request for the relation of Ext groups and bar construction

I need a reference for the description of Ext groups in mixed categories (i.e. abelian categories with a weight filtration and semisimple graded quotients) by using the bar complex, as mentioned in ...
2
votes
1answer
96 views

Legendre transform and Lipschitz approximation

Let $(X,d)$ be a compact metric space and $f:X \to \mathbb{R}$ a real valued continuous function. Let us agree that a modulus of continuity means concave, nondecreasing, uniformly continuous function ...
0
votes
0answers
19 views

Interesting properties of complex Gateaux derivatives

The complex Gateaux derivatives are for $\psi=\psi_{1}+i\psi_{2}$ and functional F $dF(\psi,\xi)=d_{\psi_{1}}F(\psi_{1},\xi_{1}-id_{\psi_{2}}F(\psi_{2},\xi_{2}$ and ...
2
votes
0answers
41 views

Reference for exercises with solutions for affine Lie algebras

I am doing self-study of affine Lie algebras, and while I have all recommended reference material, I find it hard to prepare for the exam. It was quite easy to study finite-dimensional simple Lie ...
-1
votes
0answers
22 views

Ky Fan norms and nuclear norm [on hold]

Ky Fan norms and the nuclear norm seem to be very relevant to my research so I would like to be familiar with what is already known. Can anybody recommend a reference discussing any aspects of these ...
7
votes
0answers
154 views

Open problems in Berkovich geometry

I would like to know if there is a state of the art recent reference on non-archimedean analytic spaces mentioning/listing open problems, conjectures, unresolved questions in the theory (*). I have ...
2
votes
1answer
70 views

Is a matrix element of a norm continuous representation always a trigonometric polynomial?

I asked a similar question for the case of compact groups not long ago in math.stackexchange. Now I understand that the answer was "yes", and I want to modify that question. This is also related to my ...
6
votes
1answer
107 views

Trigonometric polynomials on non-compact and non-abelian groups

I asked this initially in math.stackexchange, but it disappeared almost immediately, so I hope it will be proper to aks this here. Hewitt and Ross define trigonometric polynomial on a locally compact ...
7
votes
2answers
157 views

Recent trends in effective analysis

The references listed at http://en.wikipedia.org/wiki/Computable_analysis have all been published 30-15 years ago. Are the approaches which these references expose still up-to-date and relevant to the ...
0
votes
0answers
182 views

Can mathematics get from other sciences what it got from physics? [on hold]

Throughout history, physics has been an unparalleled source of '' inspiration'' for discovering/inventing mathematical ideas, which is due to its ability to describe the physical world. But can this ...
3
votes
3answers
229 views

Survey papers of results (relevant to mathematics) produced during research on the relationship between mathematics and music theory

It is well-known that there is a relationship between music and mathematics, and there are many references that explore this topic (for example, Benson's book). However, I would like to ask if there ...
7
votes
1answer
134 views

A question on the twistor space of a manifold

Let $M$ be either (a) self-dual conformal 4-manifold, or (b) hypercomplex $4n$-manifold. In either case one can construct the twistor space $Z$ (in the case (b) $Z=\mathbb{C}\mathbb{P}^1\times M$ as a ...
2
votes
0answers
78 views

Isomorphic subcategories of directed graphs and presets

For the purposes of this post, a digraph (directed graph) has neither loops nor multiple parallel edges, and a preset is an ordered pair consisting of a set $S$ and a preorder (viz., a reflexive and ...
0
votes
1answer
49 views

Are Carnot groups (as Carnot Caratheodory metric spaces) doubling?

I need to use the Lebesgue differentiation theorem for doubling metric measure spaces and was wondering if Carnot groups are doubling. If yes, is there any reference you can point me to? Thank you.
9
votes
2answers
580 views

nonstandard models and mathematical theorems

Is there a first order statement about the natural numbers (not nonstandard analysis) such that the truth of the statement is easier to see in a nonstandard model? In other words, do nonstandard ...
3
votes
1answer
155 views

Special linear groups over function fields

Let $p$ be a prime number, and let $q$ be a finite power of $p$. Denote by $F_q$ the unique field with $q$ elements. What is known about the structure and properties of $\mathrm{SL}_2(F_q[t])$ as ...
4
votes
0answers
90 views

Characterizations of an exotic measure on the open sets in the circle $S^{1}$

Suppose that $U\subseteq S^{1}$ is open where $S^{1}=\{z\in\mathbb{Z}:|z|=1\}$. Then define $\mu_{n}(U)=\max_{t\in S^{1}}\frac{1}{n}\cdot|\{k\in\{1,...,n\}|t\cdot e^{\frac{2\pi ik}{n}}\in U\}|$. ...
7
votes
0answers
68 views

Approximate singular value decomposition in Banach spaces

I am interested in generalisations to Banach spaces of the following construction, which relates to the singular value decomposition of a finite-dimensional linear map. If $V$, $W$ are ...
0
votes
0answers
193 views

“Bridging the gap” to research level linear algebra [on hold]

I would like to ask if there exist reference books to "bridge the gap" between the material presented in Lang's Linear Algebra and current research in linear algebra. Put another way, what is the ...
2
votes
1answer
325 views

Do hom-sets really live in the category Set?

This isn't really a research-level question (sorry!), but I asked on math.se (link), and though the question was upvoted a few times, I didn't get any answers. So since there may well be more ...
1
vote
0answers
52 views

Invariance of the Noether charge

The paper http://epubs.siam.org/doi/abs/10.1137/1023098 (Generalizations of Noether’s Theorem in Classical Mechanics, by Willy Sarlet and Frans Cantrijn) mentions "an interesting property of the ...
4
votes
0answers
278 views

Consequences of ZF+“all subsets of reals are Lebesgue measurable”

(I'm not sure if this is entirely suitable here so feel free to close it if it's not.) The statement "there is a Lebesgue measure on $\mathbb{R}$($2^\omega$)" means: there is a total $\sigma$-additive ...
0
votes
1answer
127 views

A question on the Lebesgue differentiation theorem

In the paper [Jessen, B., Marcinkiewicz, J., and Zygmund, A. Note on the differentiability of multiple integrals. Fundamenta Mathematicae 25.1 (1935): 217-234] it is considered the limit $$ ...
0
votes
0answers
30 views

Regularity of solutions of strongly elliptic system: how smooth must the boundary be?

Let $\Omega \subset \mathbb{R}^d$ be a bounded domain with the boundary of class $C^{1,1}$. Let $A$ be a selfadjoint operator acting in $L^2(\Omega;\mathbb{C}^n)$. The operator $A$ is given by the ...
6
votes
1answer
391 views

An old paper of S.Chowla on unit equations

It is referenced that in Chowla, S., Proof of a conjecture of Julia Robinson, Norske Vid. Selsk. Forh. (Trondheim) 34, 100–101 (1961), it is shown that the equation $\epsilon_1 + \epsilon_2 = 1$ ...
2
votes
0answers
47 views

Nonattacking configurations of k bishops on an m by n rectangular board

The number of ways to place k bishops in a nonattacking configuration on an n by n square board is a well known result and can for example be found in ...
3
votes
1answer
126 views

Polynomial that is symmetric in some variables

I would like to construct (or determine the existence/inexistence) of a polynomial $p(x_1,...,x_k, y_1,...,y_n)$ satisfying the following properties: $p$ is symmetric with relation to the variables ...
1
vote
1answer
74 views

Computation Complexity for Golden Section method

I need to provide computational complexity for the algorithms in my work. One of the algorithms I have used is Golden Section method for line search. I took a look at "Nonlinear Programming" book by ...
2
votes
1answer
162 views

Lusternik-Schnirelmann Theorem

In various paper i found this: But i don't find this theorem of Lusternik-Schnirelmann, have you an idea where i can find this theorem, the condition? Thank you.
1
vote
1answer
127 views

A weak analytic version of the valuative criterion of properness

EDIT: Let $f\colon X\to Y$ be a morphism of complex analytic spaces (not necessarily smooth or reduced). Assume that (a) $f$ is injective on points; (b) $f$ is local imbedding near each point $x\in ...
6
votes
0answers
152 views

What is a good introduction to cluster algebras from surfaces?

What is a good reference for cluster algebras from surfaces, with a view to their connection to Teichmuller theory? In my view, that means it should start off with unpunctured surfaces (and in ...
1
vote
0answers
84 views

Stack of curves and universal deformations

I've just started studying algebraic stacks and I have a very basic question. I've learned the notion of Deligne Mumford stack and I've seen as the stack of stable curves $\overline{\mathcal{M}_g}$ ...
6
votes
2answers
243 views

Is every $S^3$ block bundle over $S^4$ a fiber bundle?

I am interested in the difference between block bundle and fiber bundle. Let $K$ be a simplicial complex and $p: E\to |K|$ be a continuous map. A block diffeomorphism of $\Delta^p\times M$ is a ...
1
vote
0answers
32 views

Rook Polynomials of Skew-Ferrers Boards

What are some known method for calculating the rook polynomials of skew Ferrers boards? Currently all I have been able to find is the following paper Bruhat intervals as rooks on skew Ferrers boards ...
1
vote
1answer
66 views

Convex subcomplexes of CAT(0) cubical complexes

Is the following statement true? If so, can anyone provide a reference? Let $X$ be a CAT(0) cubical complex, and let $Y$ be a connected subcomplex of $X$. Then the following are equivalent: ...
7
votes
2answers
276 views

Ring of differential operators of a quotient ring

All rings are assumed to have unity. Let $k$ be a field. Recall the definition of Grothendieck's ring of ($k$-linear) differential operators $D(R;k)$ of a commutative $k$-algebra $R$: ...
2
votes
0answers
78 views

Under what conditions do time averages of ergodic transformations satisfy a central limit theorem?

Let $(X, \mu)$ be a probability space and $T:X\rightarrow X $ an ergodic transformation, i.e. $T$ is measure preserving and the only $T$ invariant subspaces have either measure $0$ or measure $1$ ...
1
vote
3answers
282 views

What are Carnot groups?

I'm trying to learn the Pansu differentiability theorem and I need to know what Carnot groups are. Can someone please explain what Carnot groups are? An introductory reference would be greatly ...
5
votes
0answers
149 views

Core model for supercompact cardinals and iteration trees

I have a few somehow related questions: Question 1. What do we expect for an inner model $\mathcal{K}$ to be a core model for a supercompact cardinal? What properties should it have, and what ...
5
votes
1answer
343 views

Why is this group called “The Holomorph of a group”

Many years ago I found in google the notation "Holomorph of group". It is the semi direct product of $G$ with $Aut(G)$. Why is the term "Holomorph" used here, while it is usually used for complex ...
2
votes
1answer
126 views

Survey on functional equations and inequalities

Where can I find a comprehensive survey monograph on functional equations and inequalities from sketch to current research trends with some focus on applications (both inside and outside mathematics)? ...
6
votes
0answers
180 views

Does anyone know this determinant?

The following determinant arises in a combinatorial enumeration problem. I wonder if anyone has seen it before in any context or knows how to evaluate it. I tried computing it for small $n$ but didn't ...
4
votes
2answers
262 views

Has this construction, which builds a symmetric multicategory from a commutative monoid, been described or studied anywhere, and if so, where?

Whenever $R$ is a commutative ring, write $R[x^{(n)}]$ for the set of all $p \in R[x]$ such that $p$ is a monic polynomial of degree $n$. Then $R[x^{(n)}]$ is not closed under sums, nor does it ...
5
votes
2answers
215 views

Embedding $G$ in a $Z(G)$ extension of $\operatorname{Aut}G$

This question follows up a question I asked on math.SE. This is a refinement and a reference request. For what groups $G$ does there exist a $Z(G)$-extension of $\operatorname{Aut}G$ (call it ...
0
votes
0answers
123 views

What is the state of the art of visualizing bifurcations for “difficult” dynamical systems?

This question is related to my other recent question on MO (although I am not confident that the dynamical system described in that other question is actually "difficult," in the sense that I will ...
-1
votes
0answers
36 views

representing quasicrystal as tilings and appearing frequencies of each tile

Quasicrystal can be fully represented either using projection method or tilings with constraints. For the latter, is there some sort of study on the "appearing frequency" of each tile or even ...
5
votes
2answers
298 views

TM and abstract algebra

Usually, during lectures Turing Machines are firstly introduced from an informal point of view (for example, in this way: http://en.wikipedia.org/wiki/Turing_machine#Informal_description) and then ...
5
votes
1answer
195 views

Is there a standard name for this poset

I've run into the following poset and I would expect it has a standard name. Let $n\geq k\geq 0$. Then $P_{n,k}$ consists of all $k$-element subsets of $\{1,\ldots,n\}$ ordered by $X\leq Y$ if ...
2
votes
1answer
104 views

Ergodicity for the mean of a linear process without finite second moment

Suppose that $\{X_k:k\in\mathbb Z\}$ is a linear process, i.e. a sequence of random variables such that $$ X_k=\sum_{j=0}^\infty\psi_j\varepsilon_{k-j} $$ for each $k\in\mathbb Z$, where ...