Search results for "General Mathematics"

Real groups and Sylow 2-subgroups

2016

Abstract If G is a finite real group and P ∈ Syl 2 ( G ) , then P / P ′ is elementary abelian. This confirms a conjecture of Roderick Gow. In fact, we prove a much stronger result that implies Gow's conjecture.

The branch set of a quasiregular mapping between metric manifolds

2016

Abstract In this note, we announce some new results on quantitative countable porosity of the branch set of a quasiregular mapping in very general metric spaces. As applications, we solve a recent conjecture of Fassler et al., an open problem of Heinonen–Rickman, and an open question of Heinonen–Semmes.

A note on the support of block idempotents

1994

Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces

1993

In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Frechet spaces. We give an example of a Frechet-Schwartz space which is not the projective limit of a sequence of superreflex…

Approximate convex hull of affine iterated function system attractors

2012

International audience; In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In additio…

Topological direct sum decompositions of banach spaces

1990

LetY andZ be two closed subspaces of a Banach spaceX such thatY≠lcub;0rcub; andY+Z=X. Then, ifZ is weakly countably determined, there exists a continuous projectionT inX such that ∥T∥=1,T(X)⊃Y, T −1(0)⊂Z and densT(X)=densY. It follows that every Banach spaceX is the topological direct sum of two subspacesX 1 andX 2 such thatX 1 is reflexive and densX 2**=densX**/X.

Some remarks on the category SET(L), part III

2004

This paper considers the category SET(L) of L-subsets of sets with a fixed basis L and is a continuation of our previous investigation of this category. Here we study its general properties (e.g., we derive that the category is a topological construct) as well as some of its special objects and morphisms.

Dichotomies properties on computational complexity of S-packing coloring problems

2015

This work establishes the complexity class of several instances of the S -packing coloring problem: for a graph G , a positive integer k and a nondecreasing list of integers S = ( s 1 , ? , s k ) , G is S -colorable if its vertices can be partitioned into sets S i , i = 1 , ? , k , where each S i is an s i -packing (a set of vertices at pairwise distance greater than s i ). In particular we prove a dichotomy between NP-complete problems and polynomial-time solvable problems for lists of at most four integers.

BLD -mappings in $W^{2,2}$ are locally invertible

2000

We prove that mappings of bounded length distortion are local homeomorphisms if they have L 2 -integrable weak second derivatives.

Generalized Lebesgue points for Sobolev functions

2017

In this article, we show that a function $f\in M^{s,p}(X),$ $0<s\leq 1,$ $0<p<1,$ where $X$ is a doubling metric measure space, has generalized Lebesgue points outside a set of $\mathcal{H}^h$-Hausdorff measure zero for a suitable gauge function $h.$