Search results for "Combinatorics"

A quasiconformal composition problem for the Q-spaces

2017

Given a quasiconformal mapping $f:\mathbb R^n\to\mathbb R^n$ with $n\ge2$, we show that (un-)boundedness of the composition operator ${\bf C}_f$ on the spaces $Q_{\alpha}(\mathbb R^n)$ depends on the index $\alpha$ and the degeneracy set of the Jacobian $J_f$. We establish sharp results in terms of the index $\alpha$ and the local/global self-similar Minkowski dimension of the degeneracy set of $J_f$. This gives a solution to [Problem 8.4, 3] and also reveals a completely new phenomenon, which is totally different from the known results for Sobolev, BMO, Triebel-Lizorkin and Besov spaces. Consequently, Tukia-V\"ais\"al\"a's quasiconformal extension $f:\mathbb R^n\to\mathbb R^n$ of an arbitr…

Structure of eigenvectors of random regular digraphs

2018

Let $d$ and $n$ be integers satisfying $C\leq d\leq \exp(c\sqrt{\ln n})$ for some universal constants $c, C>0$, and let $z\in \mathbb{C}$. Denote by $M$ the adjacency matrix of a random $d$-regular directed graph on $n$ vertices. In this paper, we study the structure of the kernel of submatrices of $M-z\,{\rm Id}$, formed by removing a subset of rows. We show that with large probability the kernel consists of two non-intersecting types of vectors, which we call very steep and gradual with many levels. As a corollary, we show, in particular, that every eigenvector of $M$, except for constant multiples of $(1,1,\dots,1)$, possesses a weak delocalization property: its level sets have cardin…

Homogeneous actions on the random graph

2018

We show that any free product of two countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite group, admit such an action and we extend our results to groups acting on trees. Finally, we show the ubiquity of finitely generated free dense subgroups of the automorphism group of the Random Graph whose action on it have all orbits infinite.

Maintaining Dynamic Minimum Spanning Trees: An Experimental Study

2010

AbstractWe report our findings on an extensive empirical study on the performance of several algorithms for maintaining minimum spanning trees in dynamic graphs. In particular, we have implemented and tested several variants of the polylogarithmic algorithm by Holm et al., sparsification on top of Frederickson’s algorithm, and other (less sophisticated) dynamic algorithms. In our experiments, we considered as test sets several random, semi-random and worst-case inputs previously considered in the literature together with inputs arising from real-world applications (e.g., a graph of the Internet Autonomous Systems).

Periodic Classification of Local Anaesthetics (Procaine Analogues)

2006

Algorithms for classification are proposed based on criteria (information entropyand its production). The feasibility of replacing a given anaesthetic by similar ones in thecomposition of a complex drug is studied. Some local anaesthetics currently in use areclassified using characteristic chemical properties of different portions of their molecules.Many classification algorithms are based on information entropy. When applying theseprocedures to sets of moderate size, an excessive number of results appear compatible withdata, and this number suffers a combinatorial explosion. However, after the equipartitionconjecture, one has a selection criterion between different variants resulting fromc…

Fields of values of odd-degree irreducible characters

2019

Abstract In this paper we clarify the quadratic irrationalities that can be admitted by an odd-degree complex irreducible character χ of an arbitrary finite group. Write Q ( χ ) to denote the field generated over the rational numbers by the values of χ, and let d > 1 be a square-free integer. We prove that if Q ( χ ) = Q ( d ) then d ≡ 1 (mod 4) and if Q ( χ ) = Q ( − d ) , then d ≡ 3 (mod 4). This follows from the main result of this paper: either i ∈ Q ( χ ) or Q ( χ ) ⊆ Q ( exp ⁡ ( 2 π i / m ) ) for some odd integer m ≥ 1 .

Inequalities for Information Potentials and Entropies

2020

We consider a probability distribution p0(x),p1(x),&hellip

Radical Rings with Soluble Adjoint Groups

2002

Abstract An associative ring R , not necessarily with an identity, is called radical if it coincides with its Jacobson radical, which means that the set of all elements of R forms a group denoted by R ∘ under the circle operation r  ∘  s  =  r  +  s  +  rs on R . It is proved that every radical ring R whose adjoint group R ∘ is soluble must be Lie-soluble. Moreover, if the commutator factor group of R ∘ has finite torsion-free rank, then R is locally nilpotent.

2020

Abstract We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees.

Classification criteria for regular trees

2021

Esitämme säännöllisten puiden parabolisuudelle yhtäpitäviä ehtoja. We give characterizations for the parabolicity of regular trees. peerReviewed