Vanishing of cohomology groups of random simplicial complexes

We consider k‐dimensional random simplicial complexes generated from the binomial random (k + 1)‐uniform hypergraph by taking the downward‐closure. For 1 ≤ j ≤ k ? 1, we determine when all cohomology groups with coefficients in from dimension one up to j vanish and the zero‐th cohomology group is isomorphic to . This property is not deterministically monotone for this model, but nevertheless we show that it has a single sharp threshold. Moreover we prove a hitting time result, relating the vanishing of these cohomology groups to the disappearance of the last minimal obstruction. We also study the asymptotic distribution of the dimension of the j‐th cohomology group inside the critical window. As a corollary, we deduce a hitting time result for a different model of random simplicial complexes introduced by Linial and Meshulam, previously only known for dimension two.     

锥—连续凸映射的严有效解连通性

本文介绍了严有效解的概念,并在[1]工作的基础上进一步研究了锥连续拟凸映射的严有效的连通性。     

闭集空间的某些拓扑性质

证明紧致度量空间的具有Hausdorff度量的闭集空间的紧致性与连通性，并给出连通的紧致度量空间的连通分支与相应的闭集空间的连通分支之间关系的一个条件．     

Remark on the Connectedness of Space in the Experimental Devices of Aharonov-Bohm Effect

This article shows that in Aharonov-Bohm (AB) effect arrangements, the electron wave propagation spaceis doubly connected for two real coherent sources, and simply connected under certain condition for two virtual coherentsources, and all known AB experiments belong to the latter case. By the Feynman path integral method, we show thatin the former case there is no AB effect, whereas in the latter case there is.     

超拓扑空间的分离性、紧致性及连通性

本文引进了超空间上的超拓扑结构，证明了超拓扑空间的拓扑性质及其与一般拓补空间的关系。     

New Saddle Point Theorem Beyond Topological Vector Spaces

The purpose of this note is to prove a new topological saddle-point theorem, which in turn includes classical saddle-point theorems such as the Sion minimax theorem and others in topological vector spaces as special cases.     

Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems

In this paper, we introduce the concepts of globally efficient solution and cone-Benson efficient solution for a vector equilibrium problem; we give some scalarization results for Henig efficient solution sets, globally efficient solution sets, weak efficient solution sets, and cone-Benson efficient solution sets in locally convex spaces. Using the scalarization results, we show the connectedness and path connectedness of weak efficient solution sets and various proper efficient solution sets of vector equilibrium problem. This research was partially supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jinxing Province, China.     

一类二层多目标规划的若干性质

本文对于下层为线性多目标规划的二层规划问题,在约束域非空有界的条件下证明了可行集的弱拟凸性、连通性,为算法设计提供了理论依据．     

关于子基的连通性

覆盖方法在粗糙集理论研究中的应用越来越受到重视,而其中最重要的两个概念是最近引入的拓扑空间的子集关于子基的内部和闭包.本文研究由它们导出的关于子基的连通性的概念,它比一般拓扑学中的连通性的概念弱,但具有许多类似的性质,这些性质事实上也是连通性相应结果的推广.