Weak KKM theorems in generalized finitely continuous space with applications

Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.     

Green's functions for anisotropic piezoelectric bimaterials with a slipping interface

An explicit full-field expression of the Green's functions for anisotropic piezoelectric bimaterials with a slipping interface is derived. When the electro-elastic singularity reduces to a pure dislocation in displacement and electric potential, interaction energy between the dislocation and the bimaterials is obtained explicitly while the generalized force on the dislocation is given in a real form which is also valid for degenerate materials. The investigation demonstrates that the boundary conditions at the slipping interface between two piezoelectric materials will exert a prominent influence on the mobility of the dislocation. Project supported by the National Natural Science Foundation of China (No. 59635140).     

Some new integral inequalities for conjugate A-harmonic tensors

A new kind of weight-Ar^λ3 （λ1, λ2, Ω）-weight is used to prove the local and global integral inequalities for conjugate A-harmonic tensors, which can be regarded as generalizations of the classical results. Some applications of the above results to quasiregular mappings are given.     

Critical values of set-valued maps with stratifiable graphs. Extensions of Sard and Smale-Sard theorems

We prove three theorems extending Sard's theorem and its infinite dimensional extension due to Smale to set-valued mappings with stratifiable graphs. The very concept of a critical value comes from (nonsmooth) variational analysis and turns out to be perfectly compatible with the natural condition defining ``good' stratifications (e.g., Whitney stratification in the finite dimensional case).

     

Building confidence in models for multiple audiences: The modelling cascade

This paper reports on a model building process developed to enable multiple audiences, particularly non-experts, to appreciate the validity of the models being built and their outcomes. The process is a four stage reversible cascade. This cascade provides a structured, auditable/transparent, formalized process from “real world” interviews generating a rich qualitative model through two intermediate steps before arriving at a quantitative simulation model. There are a number of advantages of the cascade process including; achieving comprehensiveness, developing organizational learning, testing the veracity of multiple perspectives, modeling transparency, achieving common understanding across many audiences and promoting confidence building in the models. The paper, based on extensive work with organizations, discusses both the cascade process and its inherent benefits.     

On Ekeland's Variational Principle for Set-Valued Mappings

In this paper,we derive a general vector Ekeland variational principle for set-valued mappings,which has a closed relation to εk~O-efficient points of set-valued optimization problems.The main result presentedin this paper is a generalization of the corresponding result in[3].     

Gap functions for a system of generalized vector quasi-equilibrium problems with set-valued mappings

In this paper, some gap functions for three classes of a system of generalized vector quasi-equilibrium problems with set-valued mappings (for short, SGVQEP) are investigated by virtue of the nonlinear scalarization function of Chen, Yang and Yu. Three examples are then provided to demonstrate these gap functions. Also, some gap functions for three classes of generalized finite dimensional vector equilibrium problems (GFVEP) are derived without using the nonlinear scalarization function method. Furthermore, a set-valued function is obtained as a gap function for one of (GFVEP) under certain assumptions.      

关于全纯函数的正规定则

研究涉及微分多项式与公共值的全纯函数族的正规性问题.设F为区域D内的全纯函数族,n 1为任一正整数,b为有限常数,如果对F中任意两个函数f与g,fn(f-1)f′与gn(g-1)g′在D内都以b为公共值,则F在D内正规.此结果对亚纯函数不成立.     

中微子质量矩阵和中微子转换矩阵间的一种可能的关系

我们探讨了以ν_e,ν_μ,ν_τ为基的, 具有一种新的对称性的中微子质量矩阵M. 首先在没有T(时间)破坏的前提下, 假定该质量矩阵具有一个简单的三参数形式. 这一矩阵确定了3种中微子的质量m₁, m₂, m₃以及使M对角化的转换矩阵U. 因为无T破坏的U给出3个可测量参数s₁₂, s₂₃, s₁₃, 我们的形式用3个参数表示6个可测量的物理量, 其结果与实验数据符合得很好. 更精确的测量将对模型给出严格的检验, 并确定这3个参数的值. 本文还推广讨论了包含T破坏的情况.