一些极值图问题的谱条件综述（英文）

这篇综述分为两个方面.首先,我们总结了图论中的Turan型问题的谱极值结论的最新进展.更准确地说,关于各种图的邻接谱半径和无符号拉普拉斯谱半径,我们总结了它们的谱版本的Turán型函数.例如,完全图、色数至少为3的一般图、完全二部图、奇圈、偶圈、色临界图和相交三角形图.第二个目标是总结一些最近的关于图性质的谱条件.通过一种统一的方法,基于邻接谱半径和无符号拉普拉斯谱半径,我们给出了一些充分条件,使得该图成为哈密顿图、k-哈密顿图、k-边哈密顿图、可迹图、k-路径可覆盖图、k-连通图、k-边连通图、哈密顿连通图、完美匹配图和β-亏量图.     

含参广义集值强向量平衡问题的稳定性

本文借助集合极限的性质和弱f-性假设证明了含参广义集值强向量平衡问题解集映射的下半连续性,其方法不同于最近文献(Zhao,2016和Meng,2018).此外,建立了含参广义集值强向量平衡问题解集连通性的充分条件,并举例验证了所得结果的正确性.本文得结果推广和改进了已有文献(Gong,2008,Xu,2009,Chen,2010,Xu,2013和Zhao,2013)中相应结果.     

关于子基的连通性的注记

在粗糙集理论研究中,覆盖方法的应用越来越受重视,其中最重要的概念是最近引进的拓扑空间的子集关于子基的内部和闭包以及由它们导入的关于子基的开集、闭集.对由它们导入的拓扑空间关于子基的隔离子集、连通性作进一步研究,所得性质是一般拓扑空间中隔离子集和连通性相应结果的推广.     

基于图像的二维剪纸自动生成方法

中国剪纸的设计极具挑战性, 要求画面简洁、直观, 还需要表达特定的文化内涵, 且整张剪纸须整体连通。提出了一种基于图像的二维剪纸自动生成方法, 能够将任意数码照片自动转化为剪纸图形。首先,利用图像分割方法建立区域连接图; 接着, 基于该连接图对颜色、边界对比度和区域连通性进行数学建模, 并获得优化目标函数; 最后, 通过模拟退火算法求解目标方程, 自动生成保持图像内容的剪纸图形。还开发了连通性后处理和区域指定等用户交互工具, 允许用户在自动生成的剪纸图形中方便地加入个人设计。实验表明, 所生成的剪纸图形画面简洁、整体连通。 本方法在降低剪纸设计难度的同时还可满足个性化的设计需求, 有助于传播和传承我国的民间剪纸艺术。     

Connectivity correlations in three topological spaces of urban bus-transport networks in China

In this paper, an empirical investigation is presented, which focuses on unveiling the universality of connectivity correlations in three spaces （the route space, the stop geographical space and bus-transferring space） of urban bustransport networks （BTNs） in four major cities of China. The underlying features of the connectivity correlations are shown in two statistical ways. One is the correlation between the （weighted） average degree of all the nearest neighbouring vertices with degree k, （Knn^w,（k）） Knn（k）, and k, and the other is the correlations between the assortativity coefficient r and, respectively, the network size N, the network diameter D, the averaged clustering coefficient C, and the averaged distance （l）. The obtained results show qualitatively the same connectivity correlations of all the considered cities under all the three spaces.     

图的直径与Betti亏数

对于任意的正数Ｍ以及正整数ｄ≥４,存在直径为ｄ的ｉ－边连通无环图Ｇ使得ζ（Ｇ）≥Ｍ,其中ζ（Ｇ）是Ｇ的Ｂｅｔｔｉ亏数,ｉ＝１,２,３。     

Connectedness of Cone-Efficient Solution Set for Cone-Quasiconvex Multiobjective Programming in Locally Convex Spaces

This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor multiobjective programming defined by a continuous cone-quasiconvex mapping on a compact convex set ofalternatives.The generalized saddle theorem plays a key role in the proof.     

R（L）弱诱导空间及其连通性

本文研究了R(L)弱诱导空间的性质及其与R(L)底空间在连通性方面的关系.利用文献[4]中I(L)弱诱导空间引入了R(L)弱诱导空间概念,得到了R(L)弱诱导空间的本质刻划定理.它表明:R(L)弱诱导空间是连通的当且仅当其R(L)底空间是连通的.     

<Emphasis Type="Italic">k</Emphasis>-factors in regular graphs

Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular （2n ＋ 1）-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and （or） excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik＇s result and the results obtained by Liu et al. in 1998, and improve Katerinis＇ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.     

A Note on the Connectedness of the Invertible Group of a Nest Algebra

The connectedness of the invertibles question for arbitrary nest has been reduced to the case of the lower triangular operators with respect to a fixed orthonormal basis en for n 1. For each f ∈ H∞, let Tf be the Toeplitz operator. In this paper we prove that Tf can be connected to the identity through a path in the invertible group of the lower triangular operators if f satisfies certain conditions.