三阶非线性特征值问题解的存在性

利用锥不动点指数研究了三阶非线性特征值问题u+ρ3u=λg(t)f(u),00.     

Some remarks and problems on complex homogeneous domains Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

We discuss some problems on rigidity of canonical realizations of complex homogeneous domains at Cn     

The Fermat rule for multifunctions on Banach spaces

Using variational analysis, we study vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In particular, in terms of the coderivatives, we present Fermat’s rules as necessary conditions for an optimal solution of the above problems. As applications, we also provide some necessary conditions (in terms of Clarke’s normal cones or the limiting normal cones) for Pareto efficient points.This research was supported by a postdoctoral fellowship scheme (CUHK) and an Earmarked Grant from the Research Grant Council of Hong Kong. Research of the first author was also supported by the National Natural Science Foundation of P. R. China (Grant No. 10361008) and the Natural Science Foundation of Yunnan Province, P. R. China (Grant No. 2003A002M).     

Two classes of merit functions for the second-order cone complementarity problem

Recently Tseng (Math Program 83:159–185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204–225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related properties. In this paper, we extend this class of merit functions to the second-order cone complementarity problem (SOCCP) and show analogous properties as in NCP and SDCP cases. In addition, we study another class of merit functions which are based on a slight modification of the aforementioned class of merit functions. Both classes of merit functions provide an error bound for the SOCCP and have bounded level sets.Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author’s work is partially supported by National Science Council of Taiwan.     

移相式干涉仪在锥体棱镜角度测试中的应用

为了实时、高精度地测试光学零件，对移相式数字波面干涉仪在锥体棱镜角度测试中的应用进行了研究。通过锥体棱镜二面角偏差计算方法得到了二面角偏差和干涉波面之间的关系，分析了干涉波面的形状与锥体棱镜综合误差的关系，编写了锥体棱镜角度和综合误差测试程序，并且在移相式数字波面干涉仪和ZYGO干涉仪上分别对锥体棱镜进行测试，给出了2者的比较测试结果。结果表明，移相式数字波面干涉仪测量锥体棱镜二面角偏差的误差在0.3″范围内，RMS值的测量误差在λ/50内；提出的方法可实现检测过程的自动化。     

Subdifferentials of Distance Functions, Approximations and Enlargements

In this work, we study some subdifferentials of the distance function to a nonempty nonconvex closed subset of a general Banach space. We relate them to the normal cone of the enlargements of the set which can be considered as regularizations of the set.     

一类泛函微分方程周期正解的存在性

本文研究了一类带参数的高维泛函微分程(1.1)的周期正解的存在性.利用一个著名的不动点指标定理,获得了该方程周期正解的存在性、多重性和不存在性.     

自反Banach空间中锥拟凸映射多目标最优化问题锥有效解集的弱连通性

本文在自反Banach空间中引进了锥弱连续映射和点集的弱连通概念．在讨论锥弱连续和锥拟凸映射以及锥最小上界的几个性质的基础上,证明了当象集为锥凸集时定义在自反Ba- nach空间中的有界闭凸集上的锥弱连续和锥拟凸映射多目标最优化问题的锥有效解集是弱连通的．     

二阶测度链上Sturm-Liouville型边值问题的多个正解存在性

本文讨论一类二阶测度链上Sturm-Liouville型边值问题X~△△ f(t,x(σ(t))=0,t∈[t_1,t_2],αx(t_1)—βx~△(t_1)=0,γx(σ(t_2)) δx~△(σ(t_2))=0,其中f_1,t_2](?),(?)是测度链．在适当的条件下,通过运用Leggett-Williams不动点定理,得到了三个正解的存在性．     

Normal Characterization of the Main Classes of Quasiconvex Functions

In this article we explore the concept of the normal cone to the sublevel sets (or strict sublevel sets) of a function. By slightly modifying the original definition of Borde and Crouzeix, we obtain here a new (but strongly related to the already existent) notion of a normal operator. This technique turns out to be appropriate in Quasiconvex Analysis since it allows us to reveal characterizations of the various classes of quasiconvex functions in terms of the generalized quasimonotonicity of their `normal' multifunctions.