逆（反）对策问题与“奇门遁甲”预测理论（术）

本文首先提出逆（反）对策这一新问题，给出了数学模型；探讨了“奇门遁甲”预测理论（术）中的数学问题；通过系统分析“专门遁甲”预测过程，可知它的预测过程隐含着一个特殊的逆（反）对策问题；最后指出逆（反）对策问题的广泛存在并给出案例分析．     

A Method for Establishing Optimality Conditions for a Nonsmooth Vector-Valued Minimax Problem

Using a method of uniform approximations, necessary and sufficient conditions for a nonsmooth constrained vector-valued minimax problem are established in terms of Mordukhovich subdifferentials.     

Compactness in fuzzy convergence spaces

Lowen and Lowen [Applications of category theory to fuzzy subsets (Kluwer, 1992) p. 153] and Lowen et al. [Fuzzy Sets and Systems 40 (1991) 347] recently introduced the category FCS of fuzzy convergence spaces, a topological quasitopos which is a supercategory of FTS, the category of fuzzy topological spaces. In this paper, compactness in FCS is examined. Doing so we found that to define compactness as an absolute property we had to generalize the definition of fuzzy convergence space to fuzzy subsets. All basic theorems are proved including the Tychonoff product theorem. Based on the theory developed here, in a following publication, a Richardson compactification for fuzzy convergence spaces will be given.     

周期单元中相对论Boltzmann方程初值问题整体解的存在性

本文证明了周期单元中带有某些硬相互作用的相对论Ｂｏｌｔｚｍａｎｎ方程初值问题在初值满足质量、能量和熵有限的条件下具有一个整体温和解．     

On weak spreadability of distributed-parameter systems and its achievement via linear--quadratic control techniques

In this paper, the concept of weak spreadability is introduced.It constitutes an extension of the idea developed by El Jai& Kassara. In the case of linear distributed systems weconsider quadratic control techniques with a conveniently penalizedcriterion which makes the system weakly spreadable. The approachis outlined for a convection—diffusion system, and theresults of a numerical study are also included to illustratethe main features of the considered problem.     

The Nonexistence of Procedures with Bounded Performance Characteristics in Certain Parametric Inference Problems

This paper gives a condition which implies the nonexistence of parametric statistical procedures with bounded risk or error performance characteristics. Many examples for which such a condition is satisfied are considered.     

Max—min神经网络的一种有效学习算法

本文在Ａ．Ｂｌａｎｃｏ等人的算法的基础上，提出了ｍａｘ－ｍｉｎ神经网络的一种改进了的反馈学习算法，严格证明了该算法的迭代收敛性，理论分析及实例计算结果均表明，本文算法具有算法简单，收敛速度快，输出误差小等显著特点。     

一类经典”秘书问题”的推广

”秘书问题”在最优停时理论的发展中曾起过重要作用 ,实际中的一类问题与”秘书问题”有类似之处 ,但比”秘书问题”更复杂 .本文将经典”秘书问题”进行推广 ,建立了一类比经典”秘书问题”更有实际意义的模型 ,并给出了该类模型的解 .     

A globally convergent Newton method for solving strongly monotone variational inequalities

Variational inequality problems have been used to formulate and study equilibrium problems, which arise in many fields including economics, operations research and regional sciences. For solving variational inequality problems, various iterative methods such as projection methods and the nonlinear Jacobi method have been developed. These methods are convergent to a solution under certain conditions, but their rates of convergence are typically linear. In this paper we propose to modify the Newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length. The purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate. It is then shown that, under the strong monotonicity assumption, the method is globally convergent and, under some additional assumptions, the rate of convergence is quadratic. Limited computational experience indicates the high efficiency of the proposed method.