Geometric Difference of Multivalued Maps

An analog of the finite-dimensional theorem about the upper semicontinuity of the geometric difference of continuous multivalued maps for separable Banach spaces is obtained. Sufficient conditions for the continuity of the geometric difference of multivalued maps in finite-dimensional spaces without the nonempty interior condition are obtained. Examples that demonstrate the unimprovability of these results are given.     

小扰动下奇异闭轨附近后继函数的光滑性

扰动系统在奇异闭轨附近的后继函数对于判断奇异闭轨分支出极限环的个数、极限环的稳定性和相对位置具有极其重要的作用。通过对Dulac映射及正则映射的光滑性的研究得到结论:具有奇异闭轨的Ck系统在小扰动下奇异闭轨附近的的后继函数为Ck-1的。所得结果简洁,可为以后相关研究工     

Maps Interchanging f-Structures and their Harmonicity

We study some remarkable classes of metric f-structures on differentiable manifolds (namely, almost Hermitian, almost contact, almost S-structures and K-structures). We state and prove the necessary condition(s) for the existence of maps commuting such structures. The paper contains several new results, of geometric significance, on CR-integrable manifolds and the harmonicity of such maps.     

On the Stability of the Feasible Set in Linear Optimization

This paper deals with the stability of two families of linear optimization problems, each one formed by the dual problems to the members of the other family. We characterize the problems of these families that are stable in the sense that they remain consistent (inconsistent) under sufficiently small arbitrary perturbations of all the data. This characterization is established in terms of the lower semicontinuity property of the feasible set mapping and the boundedness of the optimal set of the corresponding coupled problem. Other continuity properties of the feasible set mapping are also derived. This stability theory extends some well-known theorems of Williams and Robinson on the stability of ordinary linear programming problems to linear optimization problems with infinitely many variables or constraints.     

Complete Distributivity of Lattice Ordered Groups and of Vector Lattices

In this paper we investigate the possibility of a regular embedding of a lattice ordered group into a completely distributive vector lattice.     

Existence of a Solution and Variational Principles for Vector Equilibrium Problems

In this paper, we prove an existence result for a solution to the vector equilibrium problems. Then, we establish variational principles, that is, vector optimization formulations of set-valued maps for vector equilibrium problems. A perturbation function     

Multiplicities of fixed points of holomorphic maps in several complex variables

Let Δ^υ be the unit ball in ℂ^υ with center 0 (the origin of υ) and let F:Δ^υ→ℂ^υbe a holomorphic map withF(0) = 0. This paper is to study the fixed point multiplicities at the origin 0 of the iteratesF ⁱ =F∘⋯∘F (i times),i = 1,2,.... This problem is easy when υ = 1, but it is very complicated when υ > 1. We will study this problem generally.     

A description of Kac-systems of multiplicative unitary operators

Let V be a multiplicative unitary operator on a separable Hilbert spaceH, then there are two subalgebras ofB( H) denoted byA( V) and ?( V), respectively, which correspond to V. If V satisfiesV ² =I, then we will obtain the necessary and sufficient condition of Baaj and Skandalis’ main theorem, i.e.V has a Kac-system if and only if the linear closed space of the product of the above two algebras is the compact operator space; with this condition the above algebras are also quantum groups.     

集值映射向量优化问题的锥弱有效解的镇定性和稳定性(英文)

本文研究了集值映射向量优化问题的锥弱有效解的镇定性和稳定性,我们引进了集值映射向量优化问题的镇定性和稳定性的定义,并证明了集值映射向量优化问题的镇定性和稳定性的一些主要定理.     

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.