强一致收敛与动力性质

一般,许多动力性质(如:拓扑传递、拓扑混合等)不能被一致收敛性所遗传.本文引入强一致收敛性的概念,并说明紧致度量空间上映射的一些动力性质被强一致收敛性所保持.     

概率度量空间的拓扑结构和度量化问题及其应用

本文研究了概率度量空间的拓扑结构和度量化的问題,得到了一种充分条件,给出其具体度量函数的形式,并由此得到了概率度量空间中的Ekeland变分原理和Caristi定理,以及概率度量空间和非阿基米德概率度量空间中映象的不动点定理。     

Banach空间中伪单调变分不等式的严格可行性

证明了在无限维的Banach空间中,当假设映射是紧场和伪单调时,变分不等式的解集非空有界等价于它的严格可行性,将文献(Facchinei F, Pang J S. Finite-dimensional Variational Inequalities and Complementarity Problems[M]. New York:Springer-Verlag,2003.)中定理2.4.4从有限维欧氏空间推广到了无限维的Banach空间.     

拓扑系统的分离性

拓扑系统是目前最广泛的拓扑研究对象之一，它以点集拓扑空间，Locale的空间化，模糊拓扑空间与拓扑分子格为特例，它可以用来研究 计算机程序语言的指称语义的Domain理论。作者从拓扑学的角度研究了拓扑系统的分离性，得到了关于拓扑系统分离性刻画的几个定理。     

A survey of social network and information dissemination analysis

In recent years, with the rapid growth of social network services （SNS）, social networks pervade nearly every aspect of our daily lives. Social networks are influ- encing today＇s societal and cultural issues, and changing the way of people seeing themselves. To fully understand the running mechanisms of social networks, in this paper, we aim at series of high knitted and important elements of online social networks. We mainly focus on 3 important but also open research problems, they are （1） structural properties and evolving laws, （2） social crowds and their interaction behaviors and （3） information and its diffusion. In this paper, we review the related work on the 3 prob- lems. Then, we briefly introduce some interesting research directions and our progress on these research problems.     

拓扑矢量空间中的随机混合似变分不等式(英)

本文在Ｈａｕｓｄｏｒｆ拓扑矢量空间和Ｂａｎａｃｈ空间内研究了一类随机混合似变分不等式．由应用Ｔａｒａｆｄａｒ和Ｙｕａｎ的随机极小极大不等式，随机混合似变分不等式随机解的几个存在唯一性定理被证明．由使用辅助问题技巧，对在Ｂａｎａｃｈ空间内计算随机混合似变分不等式的近似解，作者建议和分析了一个十分一般的算法．最后收敛性准则也被讨论．这些定理和算法推广了许多已知结果．     

Orlicz空间L~(*)在~(△)拓扑下局部有界的一个必要条件

在[1]中，作者对（L*，△）中某些性质作了深入的讨论，本文在[1]的基础上，对线性拓扑空间（L*，△）的局部有界性进行了研究，得到了一个必要条件．     

A novel topological index for the studies on structure-properties of alkanes

A novel topological index derived from eccentric connectivity index has been proposed. The new topological index and eccentric connectivity index were correlated with eight physical properties such as the boiling point, critical temperature, critical pressure, critical volume, evaporation heat, density, heat capacity, surface tension, and three thermodynamic properties such as standard enthalpy, standard entropy and standard formation free energy of alkanes. A series of empiric equations for calculating the properties were obtained. Correlation coefficients of nine properties were more than 0.99. Regression analysis and calculation results indicated that the topological indices were well correlated with the physico-chemical properties of alkanes, and the novel topological index was far superior to eccentric connectivity index in the correlation. Foundation item: Supported by the Natural Science Fund of Hubei Educational Committee (99A088) Biography: Ni Cai-hua (1956-), male, Professor, research direction: organic chemistry and Polymer.     

蛋白质拓扑结构预测的进一步讨论

利用信息论方法，找到了与蛋白质拓扑结构相关性较好的一些二级结构参数，确定了预测蛋白质拓扑结构的最佳参数、对α类，β类，α／β类蛋白制定了简洁的预测规则；对结果进行了讨论。     

关于G_δ对角线的拓扑性质

本文讨论了一种较之G_δ对角线更为一般的拓扑性质(称为0-G_δ对角线),分别改进了R.Blair(1977年)、J.Chaber(1976年)、Ginsburg & Woods(1977年)、D.Lutzer(1969年)、H.W.Martin(1975年)等的结果。一系列例子表明这种推广是十分有意义的。