Nielsen realization for 3-manifolds containing two-sided projective planes

For compact irreducible sufficiently large 3-manifolds containing 2-sided projective planes, we consider the following Realization Problem: Given a finite subgroup of the outer automorphism group of the fundamental group, is there a finite group of homeomorphisms, which induces this subgroup? Received: 16 November 1999; in final form: 18 January 2001 / Published online: 8 November 2002     

Rank-perfect and" weakly rank-perfect graphs

An edge e of a perfect graph G is critical if G−e is imperfect. We would like to decide whether G−e is still “almost perfect” or already “very imperfect”. Via relaxations of the stable set polytope of a graph, we define two superclasses of perfect graphs: rank-perfect and weakly rank-perfect graphs. Membership in those two classes indicates how far an imperfect graph is away from being perfect. We study the cases, when a critical edge is removed from the line graph of a bipartite graph or from the complement of such a graph.     

Stable multi-sets

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets.  For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable multi-sets and conditions for them to be facet defining are determined.  The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets emerge as an important substructure in the design of optical networks. Received: February 14, 2001/Revised version: September 7, 2001     

On a bifurcation governed by hysteresis nonlinearity

We consider autonomous systems with a nonlinear part depending on a parameter and study Hopf bifurcations at infinity. The nonlinear part consists of the nonlinear functional term and the Prandtl--Ishlinskii hysteresis term. The linear part of the system has a special form such that the close-loop system can be considered as a hysteresis perturbation of a quasilinear Hamiltonian system. The Hamiltonian system has a continuum of arbitrarily large cycles for each value of the parameter. We present sufficient conditions for the existence of bifurcation points for the non-Hamiltonian system with hysteresis. These bifurcation points are determined by simple characteristics of the hysteresis nonlinearity.     

V20+离子1s23d-1s2nf的跃迁能和振子强

用全实加关联方法计算了类锂V20+离子1s23d-1s2nf的跃迁能和偶极振子强度.依据量子亏损理论, 确定了1s2nf系列的量子数亏损,用这些作为能量的缓变函数的量子亏损,实现对该Rydberg系列任意高激发态(n≥10)的能量的可靠预言.将这些分立态振子强度与量子亏损理论相结合,得到在电离域附近束缚态间的偶极跃迁振子强度以及束缚态-连续态跃迁的振子强度密度,从而将V20+离子的这一重要光谱特性的理论预言外推到整个能域.     

Fundamental processes in long air gap discharges

The development of atmospheric lightning is initiated and sustained by the formation in virgin air of ‘streamer corona’ and ‘leader’ discharges, very similar to those observed in laboratory long sparks. Therefore, the experimental and theoretical investigations of these laboratory discharges have become of large interest to improve the physical knowledge of the lightning process and to develop self-consistent models that could be applied to new protection concepts.In the present paper the fundamental processes of the subsequent phases of long air gap discharges are analyzed, from the first corona inception and development to the leader channel formation and propagation. For all these processes simulations models are discussed that have been essentially derived and simplified by the authors, in order to develop sequential time-dependent simulation of the laboratory breakdown, with both positive and negative voltages. The possibility of extending these models to the case of natural lightning is discussed in the companion paper, presented in this same volume. To cite this article: I. Gallimberti et al., C. R. Physique 3 (2002) 1335–1359.     

Rehabilitation of the Gauss-Jordan algorithm

Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.     

K(o)the-Bochner空间的凸性

本文利用K(o)the函数空间的性质以及K(o)the函数空间与K(o)the-Bochner空间的关系,讨论了K(o)the-Bochner空间E(X)的凸性,主要结果如下:(a)给出E(X)的端点的充分条件,得到了E(X)严格凸的判据,相应地推广了Lp(μ,X)以及LΦ(X)的结果;(b)讨论了E(X)的弱局部一致凸和局部完全k-凸;(c)刻画了E(X)的强凸,给出了E(X)强凸的充要条件.     

Fibrations of bigroupoids

Using Brown's construction (J. Algebra 15 (1970) 103) of an exact 6-term sequence for a fibration of groupoids we show how an exact 9-term sequence can be associated to a fibration of bigroupoids. Applications to topology and algebra are given.     

研究K4-同胚图K4(α,1,1,δ,ε,η)色性的一个引理

主要介绍了一个引理，这个引理奠定了K4－同胚图K4（α，1，1，δ，ε，η）色性研究的基础。