广义凸性条件下一类多目标分式规划问题的最优性条件和对偶

本文在广义凸性条件下讨论了一类带扰动的多目标分式规划问题的最优性条件和对偶．将这类多目标分式规划问题转化为多目标规划问题,我们给出了原问题的最优性充分条件,并得到了弱对偶和强对偶结果．     

锥约束向量最优化问题的弱有效解的一些充分条件

本文在实赋范线性空间中,利用几类广义凸性概念,获得了一类锥约束向量最优化问题的弱有效解的一些充分条件．     

Banach空间若干凸性及相互关系

概述了Banach空间一致凸、(弱)局一致凸、中点局一致凸、(局)各向一致凸、(弱)紧局一致凸、强凸、非常凸、严格凸等凸性概念，讨论了它们之间的相互关系，并给出了它们等价的一些条件．     

函数凸性的一个充分必要条件

文章得到拓扑线性空间X上广义实值函数f的凸性的一个新的充分必要条件：对于任意x,h∈X,实函数φ（x,h,t）=f（x＋th）-f（x）/t关于t在R／{0}上单增。     

Convexity in scientific collaboration networks

Convexity in a network (graph) has been recently defined as a property of each of its subgraphs to include all shortest paths between the nodes of that subgraph. It can be measured on the scale [0, 1] with 1 being assigned to fully convex networks. The largest convex component of a graph that emerges after the removal of the least number of edges is called a convex skeleton. It is basically a tree of cliques, which has been shown to have many interesting features. In this article the notions of convexity and convex skeletons in the context of scientific collaboration networks are discussed. More specifically, we analyze the co-authorship networks of Slovenian researchers in computer science, physics, sociology, mathematics, and economics and extract convex skeletons from them. We then compare these convex skeletons with the residual graphs (remainders) in terms of collaboration frequency distributions by various parameters such as the publication year and type, co-authors’ birth year, status, gender, discipline, etc. We also show the top-ranked scientists by four basic centrality measures as calculated on the original networks and their skeletons and conclude that convex skeletons may help detect influential scholars that are hardly identifiable in the original collaboration network. As their inherent feature, convex skeletons retain the properties of collaboration networks. These include high-level structural properties but also the fact that the same authors are highlighted by centrality measures. Moreover, the most important ties and thus the most important collaborations are retained in the skeletons.     

一类具有样条和逼进性质的n次代数曲线

在平面上,将形如（1－u）l1l2－ul0~2=0的二次曲线族中的l0~2换成l0~n,得到一类形如（1－u）l1l2－ul0~n=0的n次代数曲线,文章通过对此类曲线正则性、凸性的研究,给出了此类曲线在插值和逼进等方面的应用．