In this paper we describe six pencils of K3-surfaces which have large Picardnumber (15 ≤ ρ ≤ 20) and contain precisely five singular fibers: four have A-D-E singularities and one is non-reduced. In particular we describe these surfaces as cyclic coverings of the K3-surfaces of [BS]. In many cases using this description and latticetheory we are able to compute the exact Picard-number and to desc...

G: a connected finite simple graph with vertex set V (G) and edge set E(G). Neighborhood N(v) of v : the set of vertices adjacent to v ∈ V (G). A map p : G̃ → G is a covering of G if p : V (G̃) → V (G) is surjective and p|N(ṽ) : N(ṽ) → N(v) is bijective for ∀v ∈ V (G) and ∀ṽ ∈ p−1(v). It is an n-fold covering if p is n-to-one. A covering p : G̃ → G is regular (or, A-covering) if there is a subgrou...

A covering of a multigraph G is a subset of edges which meet ail vertices of G. Partitions of the edges of G into coverings Ci, C2,..., Ck are considered. In particular we examine how close the cardinalities of thèse coverings may be. A resuit concerning matchings is extended to the décomposition into coverings. Finally thèse considérations are generalized to the décompositions of the vertices ...

Abstract. A general greedy approach to construct coverings of compact metric spaces by metric balls is given and analyzed. The analysis is a continuous version of Chvátal’s analysis of the greedy algorithm for the weighted set cover problem. The approach is demonstrated in an exemplary manner to construct efficient coverings of the n-dimensional sphere and n-dimensional Euclidean space to give ...

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence we show that a weakly shod algebra which is not quasi-tilted of canonical type is simply connected if and only if its first Hochschild cohomolog...

A proof of a conjecture for the number of ramified coverings of the sphere by the torus * Abstract An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden, Jackson and Vainshtein for the explicit number of such co...

In this work we deal with coverings and actions of Lie groupgroupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids. Later, we show the equivalence of the category of smooth actions of Lie group-groupoids on Lie groups and the category of smooth coverings of Lie group-groupoids.

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal h $ -subgroup in‎ ‎$g$ if $n_g (h)cap h^gleq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ $mathcal h^ast $-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal h$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎assump...

BACKGROUND Maximal sterile barrier precautions (MSBP) including head coverings and face masks are advocated for use in invasive procedures, including coronary interventions. The rationale for MSBP assumes it is an obligatory measure for infection prevention. However, in many coronary catheterization laboratories, head coverings/face masks are not used in daily practice. This study prospectively...

This paper investigates some possible actions ”à la Johnson” on the set with 2 elements, denoted by E , of Spinstructures which are interpreted as special Z2-coverings of a trivial S−fibration over a non-orientable surface Ng+1. The group acting is first a group of orthogonal isomorphisms of (H1(Ng+1;Z2), ·). A second approach is to consider the subspace of E (with 2 elements) coming from speci...