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

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Transversal theory in ergodic theory

I was taking a glance at the original paper by Donald Ornstein, Bernoulli Shifts with the Same Entropy are Isomorphic, and I came across The Marriage Problem and a paper with the same name by P. ...
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1answer
116 views

Length-preserving Analogue of Riemann's Mapping Theorem

The Riemann mapping theorem (cf e.g. http://en.wikipedia.org/wiki/Riemann_mapping_theorem) essentially guarantees the existence of a biholomorphic mapping of a simply connected, open subset of the ...
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2answers
146 views

Hamilton-Ivey pinching in dimension 4

I've heard it said (e.g., in the accepted answer to this MO question) that a major obstacle to an effective theory of Ricci Flow in dimension 4 is the absence of the Hamilton-Ivey pinching phenomenon. ...
3
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1answer
168 views

Vanishing theorems for pluri-canonical bundle

I would like to know if Grauer-Riemenschneider vanishing theorem is still true in the setting of pluri-canonical bundle, i.e. the power of canonical bundle. Let me recall Grauer-Riemenschneider ...
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2answers
188 views

Inherent ambiguity of the context-sensitive language $L = {a^ib^ic^id^je^jf^j \bigcap a^ib^jc^id^je^if^j} $ or $a^nb^nc^nd^ne^nf^n$

What is the definition of ambiguity of context-sensitive grammar?This is relevant to the definition of inherent ambiguity of context-sensitive language.And any proof for the inherent ambiguity of ...
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0answers
92 views

Bundles over Function Spaces

Is there any reference on bundles over function spaces? In particular, I am interested in Banach-bundles over function spaces like $W^{k,r}(M)$, where $M$ is a Riemannian manifold. Separable ...
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0answers
16 views

Estimating Missing Shortest-Path-Tree Distances from Point Coordinates

Problem: given a finite set of points $\mathcal{P}:=\lbrace p_i\in\mathbb{R}^2 \mid i\in \lbrace 0,...,n\rbrace\wedge i\neq j\Leftrightarrow p_i\neq p_j\rbrace$ a function ...
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2answers
142 views

Visibility spaces and Gromov hyperbolicity

I would like to ask the community for a reference on the following subject: is there some thing as an equivalence between the definitions of Uniform Visibility manifolds and Gromov $\delta$-hyperbolic ...
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3answers
499 views

Is there a “unique” homogeneous contact structure on odd-dimensional spheres?

Let $S^{2n-1}\subset\mathbb{C}^{n}$, and denote by $\langle\,\cdot\,,\,\cdot\,\rangle$ the Hermitian product. Then $$ \mathcal{C}_p:=\{\xi\in T_pS^{2n-1}\mid\langle p,\xi\rangle=0\},\quad p\in ...
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1answer
90 views

maximal chain in (strong) Bruhat order satisfying constraint

Consider the (strong) Bruhat order, $\leq_B$, on the symmetric group $S_n$. Suppose there are permutations $\pi,\sigma∈S_n$ such that $\pi\geq_B \sigma$. Suppose further that they satisfy the ...
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1answer
140 views

Vertices of a polytope as algebra generators

I am wondering if the following kind of objects has some name, or are there any studied examples. I apologize for perhaps too specific definition, this is an adoptation of a situation that arises in ...
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0answers
147 views

Is this function space a “classical” Sobolev space?

I apologise if this is indeed classical but my functional analysis is quite rusty... My work recently led me to the norm: $(\|u\|_p)^p=\int_D (|u|^p+|\Delta u|^p)d\lambda$ where $D$ is the unit disk ...
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3answers
608 views

Number of primitive $n$th roots with positive versus negative real parts

Does anyone know a reference to the following results, which I can prove, but I suspect may be known. Let $R(n)$ denote the number of primitive $n$th roots of unity with positive real part, and $L(n)$ ...
4
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1answer
56 views

Reference: Hardy space regularity of the Jacobian determinant

I'm looking for a reference, expository in nature, for the proof of the following theorem of Coifman, Lions, Meyer and Semmes. Theorem: For all $u\in W^{1,n}(\mathbb{R}^n;\mathbb{R}^n)$, ...
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1answer
65 views

Unitization via “End points compactification”

We know that every compactification of locally compact Hausdorff spaces correspond to a unitization of $C^{*}$ algebras. For example the one point compactification corresponds to the minimal ...
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8answers
4k views

How does one find out what's happening in contemporary mathematics research?

How does one find out what's happening in contemporary mathematics research? EDIT: I should have mentioned that I am looking for open access online sources. It so happens that I have been outside ...
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0answers
71 views

Empty node in cactus construction

Is there a necessary condition for not having empty node in the construction of the cactus of the minimum cuts of a graph? In particular is there a necessary condition for not having empty k-junction ...
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1answer
165 views

Measure Preserving Transformation Induced by a $*$-automorphism on $L^\infty(X,\mu)$

The following excerpt is from Connes' Noncommutative Geometry Let $(X, \mathcal{B}, \mu)$ be a standard Borel space equipped with a probability measure $\mu$, and let $\ T$ be a Borel ...
3
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1answer
233 views

An integral estimate over rotations of the dyadic grid

I'm currently reading the paper Rectifiable Sets and the Traveling Salesman Problem (link) by Peter Jones (Invent. math. 102, 1-15 (1990)), and am having trouble understanding an integral estimate ...
3
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2answers
141 views

Asymptotics of the number of elements in the intersection of two growing sets

Let $[n]:=\{1,\dots,n\}$ and $0\leq p_n\leq n$. Fix any subset $A_n$ of $[n]$ with $p_n$ elements. The number of subsets $B$ of $[n]$ with $p_n$ elements that are disjoint from $A$ is ...
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1answer
91 views

Estimate for the travelling salesman problem for balls inside a grid

This question is probably easy but I only have "tedious case checking" proof strategy in sight, and I'm sure there should be a reference lying around... The question concerns the TSP problem (with ...
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1answer
105 views

How to classify the complex function with same natural boundary in complex plane? [closed]

There are complex functions with the same natural boundaries in the complex plane, but,they are different from each other. For example, there are lots of different lacunary power series with ...
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0answers
51 views

References for LWP of a NLS Equation

I am studying the LWP of $$i \partial_t \psi + \Delta \psi = \left| \psi \right|^{p-1} \psi + \frac{1}{\left| x \right|^2} \psi$$ in $\mathbb{R}^{1+2}$ given appropriate Cauchy data. It will probably ...
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1answer
94 views

Number of Richardson orbits in simple Lie algebras of types $E_n$?

This is a follow-up to my question about nilpotent orbits here asked in connection with an earlier discussion of symplectic resolutions. Leaving aside the connections with algebraic geometry and ...
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0answers
117 views

Dehn functions of Thompson's group $F$

It's well know that the first order Dehn function of $F$ is quadratic. Is a similar result known for its second-order, or even higher-order, Dehn function? The second-order Dehn function of a group ...
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7answers
479 views

Source for roots of matrix polynomials?

A matrix polynomial is a polynomial whose variables are square $n \times n$ matrices, let's say with entries in $\mathbb{C}$, and with coefficients in $\mathbb{C}$. I am seeking a source of results on ...
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1answer
273 views

How to define a generating subset for algebra in a category?

As is well known, the definition of an monoid can be generalised to the notion of a monoid $A$ in a monoidal category $C$ (see the n-lab entry here). What I would like to know is if the notion of ...
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1answer
92 views

Doubling of variables method for parabolic equations

Does anyone have a reference that explains the technique of doubling of variables as introduced by Kruzkov? It seems to be a necessary tool for contraction estimates when we have weak solutions. ...
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1answer
86 views

Getting a comparison principle for parabolic equation when solution is not that smooth

Consider the solution $b(u) \in L^2(0,T;H^1)\cap H^1(0,T;H^{-1})$ with $u \in L^2(0,T;H^1)$ to $$\frac{\partial}{\partial t}b(u) - \Delta u = f$$ where $b$ is continuous, increasing and locally ...
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197 views

Singularities in Yang Mills Flow

In "The Yang Mills flow in four dimensions", M. Struwe proves that this flow converges, up to bubbling phenomena. And he has conjectured that this explosion in finite time should happen as proven for ...
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6answers
383 views

Do you have examples of such “transitive” elements?

(I've asked the same question at the MSE, so far with no answers, so I thought I'd try it here as well. If there's some clash with any site rules, please let me know and I'll abide.) Let $A$ be a set ...
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0answers
57 views

Non-reflexive Orlicz spaces

I am looking for a good reference on Orlicz spaces; I would appreciate any books treating this topic from the Banach-space perspective. For example, I would like to find a reference to the following ...
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0answers
96 views

projecting Laplacian onto tangent and normal bundles of submanifold

If I have a simple linear differential equation involving covariant derivatives such as $\nabla^2 g_{\mu\nu}+ 2g_{\mu\nu}=0$ on a (pseudo-Riemannian) manifold, and I have (say a codimension-2) ...
9
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1answer
159 views

Fixed set of order p automorphism of Bruhat-Tits tree

I would like to know the structure of the fixed set of an order $p$ automorphism [Edit: induced by a matrix in $GL_2(K)$] on the Bruhat-Tits tree for a p-adic field $K$, specifically in the case where ...
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0answers
158 views

In which orders can the numbers of prime factors of consecutive integers be?

Let $\omega(m)$ be the number of distinct prime divisors of a positive integer $m>1$. I am interested in the relative orders in which the numbers $\omega(n+1),...,\omega(n+k)$ can occur. Given ...
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1answer
103 views

Concentration inequalities in $\ell_{\infty}$ for sums of iid random (“nice”) functions?

I'm looking for "tail-bound-like" inequalities that look like this (I state a specific setting but more general settings are interesting): Let $D$ be a distribution on a set of "nice" functions ...
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1answer
274 views

Equivariant motivic sheaves

Thanks to the work of Cisinski-Deglise: http://arxiv.org/abs/0912.2110, we now have a triangulated category of `motivic sheaves' available that admits the standard yoga of the six functors. Is there ...
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2answers
320 views

Euler characteristics with and without compact support of algebraic varieties

Let $X$ be a complex algebraic variety, possibly singular and/or non-compact. It is well known that if $X$ is smooth then its Euler characteristic is equal to its Euler characteristic with compact ...
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1answer
298 views

Elements of the method of forcing in some papers of N. N. Luzin

In the paper Eléments de la méthode de forcing dans quelques travaux de N. N. Lousin. (French) [Elements of the method of forcing in some papers of N. N. Luzin] Amphora, 469–479, Birkhäuser, ...
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0answers
36 views

Relation between Cardinality of Subset Weight-sums and the Weight's Number of Bits in Case of Random Integers

I would like to generate test-instances of "very general" finite, complete, symmetric graphs without self-loops and without parallel edges, which essentially boils down to: the edgeweights should ...
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1answer
172 views

R-linear representations of sl(2,C)

Is there some good reference for the classification of finite-dimensional ${\mathbb R}$-linear (as opposed to ${\mathbb C}$-linear) representations of $\mathfrak{sl}_2{\mathbb C}$? Equivalently, what ...
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1answer
143 views

Mutual information decrease with coarse-graining

Let $X,A,Y,B,C,D$ be random binary variables. $D$ is independent from $X,A,C$ and $C$ is independent from $Y,B,D$. Is it true that: If $I(Y:B|D=0)\leq \epsilon$ then $I(X\oplus Y:A\oplus ...
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1answer
134 views

Homotopy groups of linearization of a space

If $X$ is a pointed space and $A$ is an abelian group, then we can form the space $A[X]$ whose points are finite formal sums $\sum a_i x_i$ with $a_i \in A, x_i \in X$ subject to some natural ...
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458 views

Survey of the history of calculus?

Boyer 1939 is a nice readable survey of the history of the calculus, but it's showing its age. Discussing the notion of instantaneous velocity, he has: Mathematics knows no minimum interval of ...
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418 views

Origin of the term “generic” in set theory

In set theory, in particular the context of forcing, if $M$ is a model of $\sf ZFC$ and $P\in M$ is a partial order, we say that $G\subseteq P$ is a generic filter (or $M$-generic or generic over $M$) ...
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1answer
128 views

$H^s(\mathbb T)$ is a Banach algebra for $s>1/2$

I have not managed to find a reference for the following fact: $H^s(\mathbb T)$ is a Banach algebra for $s>1/2$. In particular, I need reference for the following inequality: $$ \|uv\|_{H^s} ...
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1answer
217 views

Index of congruence modular subgroup of level (1,d)

Let $D = \text{diag}(1,d)\in M_{2}(\mathbb{Z})$ be a $2\times 2$ matrix, where $d$ is an odd integer. We define the subgroup $\Gamma_D\subset M_{4}(\mathbb{Z})$ as: $$\Gamma_D := \left\lbrace R\in ...
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46 views

What are the main open problems in the theory of quasigroups and loops?

What are the main open problems in the theory of quasigroups and loops? A short survey would be welcome. Thanks
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1answer
224 views

Group actions in a homotopy category

Let $M$ be a model category and $G$ a finite group, and equip the category $M^G$ of $G$-objects in $M$ with, say, a projective model structure. Then there is a canonical functor $$\mathrm{Ho}(M^G) ...
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179 views

Localizing 2-categories about a single morphism

This question is a straight-up reference request, but of course I will be grateful for an answer in the event that no references are readily available. Consider a strict $2$-category $\mathbf{C}$ and ...