We show that the class of separable morphisms in the sense of G. Janelidze and W. Tholen in the case of Galois structure of second order coverings of simplicial sets due to R. Brown and G. Janelidze coincides with the class of covering maps of simplicial sets. Introduction Separable morphisms were introduced in [3] by A. Carboni and G. Janelidze for lextensive categories. In the way of [3] one ...

The purpose of this paper is to discuss some recent generalizations of the basic covering radius problem in coding theory. In particular we discuss multiple coverings, multiple coverings of the farthest-o points and weighted coverings.

In this paper we present and describe an improved version of the Zero-Neighbors algorithm, which we call the Zero-Coverings algorithm. We also present a method for finding a smallest subset of codewords ( Zero-Coverings) which need to be stored to perform the Zero-Coverings algorithm. For some short codes, the sizes of Zero-Coverings are obtained by computer searches; for long codes, an asympto...

AIM The aim of the study was to evaluate the ability of in vitro planktonic and immobilized cell models for determining the antimicrobial efficacy of common antimicrobial wound dressings. METHODS AND RESULTS Five strains of Acinetobacter baumannii, Pseudomonas aeruginosa and methicillin resistant Staphylococcus aureus were tested against four antimicrobial wound dressings containing silver, h...

We introduce and study t-coverings in En, i.e., arrangements of proper translates of a convex body K ⊂ En sufficient to cover K. First, we investigate relations between t-coverings of the whole of K and t-coverings of its boundary only. Refining the notion of t-covering in several ways, we then derive, particularly for centrally symmetric convex bodies and n = 2, theorems which are interesting ...

A class of stratified posets I∗ ̺ is investigated and their incidence algebras KI ̺ are studied in connection with a class of non-shurian vector space categories. Under some assumptions on I∗ ̺ we associate with I ∗ ̺ a bound quiver (Q,Ω) in such a way that KI∗ ̺ ≃ K(Q,Ω). We show that the fundamental group of (Q,Ω) is the free group with two free generators if I ̺ is rib-convex. In this case the uni...

We consider hexagonal systems embedded into the 3-dimensional space R3. We define the fundamental group π1(G) of such a system G and show that in case G is a finite hexagonal system with boundary, then π1(G) is a (non-abelian) free group. In this case, the rank of π1(G) equals m(G) − h(G) − n(G) + 1 where n(G) (resp. m(G), h(G)) denotes the number of vertices (resp. edges, hexagons) in G. A hex...

We construct and analyze a family of low-density parity check (LDPC) quantum codes with linear encoding rate, distance scaling as $n^\epsilon $ for notation="LaTeX">$\epsilon > 0$ efficient decoding schemes. The code is based on te...

We apply the methods developed in [Br1] to study holomorphic functions of slow growth on coverings of pseudoconvex domains in Stein manifolds. In particular, we extend and strengthen certain results of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds in the case of coverings of Stein manifolds.

Several isomorphism classes of graph coverings of a graph G have been enumerated by many authors. Kwak and Lee (Canad. J. Math. XLII (1990) 747) enumerated the isomorphism classes of graph bundles and those of n-fold coverings with respect to a group of automorphisms of the base graph G which 9x a spanning tree. Hofmeister (Discrete Math. 98 (1991) 175) independently enumerated the isomorphism ...