摘要:This article deals with the Riemann-Hilbert problem for degenerate elliptic complex equations of first order in multiply connected domains. Firstly the representation of solutions of the boundary value problem for the equations is given, and then the uniqueness and existence of solutions for the problem are proved.%讨论一阶退化椭圆型复方程在多连通区域上的Riemann-Hilbert 边值问题.文中先给出这种边值问题的表示式,然后证明上述边值问题解的存在性和唯一性.
摘要:对称性是图作为网络模型的重要性质.而网络设计者关注较多的是那些同距离有关的对称性.这是因为路径问题是网络研究的核心问题.BSn,ECn和FCn是三类常用于互联网络的Cayley图.1993年,lakshmivarahan等人提出了一些公开问题.其中包括BSn,ECn和FCn的距离正则性.在本文中,对于BSn,ECn和FCn我分别定义了一些参数称为"改良的交叉数".并且证明了这三类图的确具有依赖于距离的对称性.这说明在这三类图中寻找一个不依赖于点的路径是可行的.%Symmetry properties are of vital importance for graphs used as interconnection network models. Among which network designers pay much attention on those properties relative to distance because routing is the core of networks. BSn, ECn and FCn are three classes of Cayley graphs which are mostly used in interconnection networks. In 1993, Lakshmivarahan et al. asked some problems including the distance regularity of BSn, ECn and FCn. In this paper, some parameters called modified intersection numbers of BSn, ECn and FCn are defined and these three graphs do have the symmetry properties relying on distances are proved,which shows that it is possible to find a routing not depending on vertices in these three kinds of graphs.
摘要:许多作者提出和讨论了二阶退化椭圆型方程的一些边值问题,如Dirichlet边值问题和混合边值问题.本文讨论高维区域中退化秩为0的二阶椭圆型方程的一些边值问题,这些问题包括上述问题作为特殊情况.先给出这些问题的提法,然后使用列紧性原理和极值原理证明了上述二阶椭圆型方程边值解的存在性和唯一性.%Many authors posed and discussed some boundary value problems,mainly the Dirichlet problem and mixed boundary value problem for second order elliptic equations with parabolic degeneracy.In this paper some boundary value problems for the degenerate elliptic equations of second order are discussed in a high dimensional domain,which include the above problems as a special case.Fristly the boundary value problems for the equations is formulated,and then by using the compactness principle, the existence of solutions for the above problems is proved.