综合函数与扩展原理

本文首先对合情扩展映射的公理化条件的完备性与独立性进行讨论,之后给出了扩展原理的一般形式及合情扩展映射的等价定义。最后,利用综合函数,特别是变维综合函数列,给出了扩展原理的一些具体形式     

Lusternik-Schnirelmann 定理的推广

本文根据Brouwer映射度的理论和微分拓扑的基本方法推广了Lusternik_Schnirelmann定理     

双参数变形量子代数SU（1，1）_（q，s）的Nodvik实现和Holstein—Primakoff实现

给出了双参数变形量子代数ＳＵ（１，１）ｑ，ｓ的Ｎｏｄｖｉｋ实现和Ｈｏｌｓｔｅｉｎ－Ｐｒｉｍａｋｏｆｆ实现，并给出了ＳＵ（１，１）ｑ，ｓ，和双参数变形振子的变形映射。     

Pattern recognition display methods for the analysis of computed molecular properties

Summary Pattern recognition methods, particularly the unsupervised learning techniques, are well suited for the preliminary analysis of the large data sets produced by computer chemistry. The use of linear and non-linear display methods for such exploratory analysis are exemplified with the aid of two data sets of biologically active molecules. Advantages and disadvantages of these techniques are discussed.     

Statistics of strange attractors by generalized cell mapping

It is proposed in this paper to use the generalized cell mapping to locate strange attractors of dynamical systems and to determine their statistical properties. The cell-to-cell mapping method is based upon the idea of replacing the state space continuum by a large collection of state space cells and of expressing the evolution of the dynamical system in terms of a cell-to-cell mapping. This leads to a Markov chain which in turn allows us to compute all the statistical properties as well as the invariant distribution. After a general discussion, the method is applied in this paper to strange attractors of a variety of systems governed either by point mappings or by differential equations. The results indicate that it is a viable, effective and attractive method. Some comments on this method in comparison with the method of direct iteration will also be made.     

多圆柱上的完全准凸映射

在C~n中有界凸Reinhardt域上讨论了一类介于凸映射类与星形映射类之间的“完全准凸映射类”.特别地,在C~n中的多圆柱上给出了完全准凸映射的分解定理,得到了多圆柱上判别凸映射的一个改进的充分条件.     

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.