多目标最优化的一种积分型实现算法

在文[1]中给出了求解多目标最优化的一种积分总极值的概念性算法．本文利用数论中的一致分布佳点集列，较为简便的得出了多目标最优化的积分总极值的实现算法和算法终止准则．并经过有关函数数值计算表明该算法是有效的，可用来求解多目标最优化问题的有效解．     

一类二层凸规划的对偶二层规划

本文讨论上层目标函数以下层子系统目标函数的最优值作为反馈的一类二层凸规划的对偶规划问题 ,在构成函数满足凸连续可微等条件的假设下 ,建立了二层凸规划的 Lagrange对偶二层规划 ,并证明了基本对偶定理 .     

On periodic solutions of nonlinear integral equations modelling infectious disease on measure chain

The modelling of the spread of infectious disease is carried out for time t on a measure chain T. Our approach unifies the continuous case and the discrete case . The model is described by the integral equation

where x(t) represents the proportion of the population infected at time t, f(t,x(t)) denotes the proportion of the population newly infected per unit time, and τ is the length of time an individual remains infectious. Using the measure chain calculus, we shall develop criteria for the existence of a nontrivial and nonnegative periodic solution for the modelling equation. The criteria can be implemented numerically, for this we shall give an algorithm as well as illustrative examples.     

AN ALGORITHM FOR JORDAN CANONICAL FORM OF A QUATERNION MATRIX

In this paper, we first introduce a concept of companion vector, and study the Jordan canonical forms of quaternion matrices by using the methods of complex rep resentation and companion vector, not only give out a practical algorithm for Jordan canonical form J of a quaternion matrix A, but also provide a practical algorithm for corresponding nonsingular matrix P with P-1AP = J.     

Nonlinear Filtering for Diffusions in Random Environments

Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X ^W and establish a multiple Wiener integrals representation for the unnormalized pathspace filtering process. Then, we construct a precise nonlinear filtering model for the process X itself and give the corresponding Wiener chaos decomposition.     

On the Nature of Buffering

We state a theorem on the instability of self-similar cycles and tori of a certain type in a system which is a quasinormal form of a boundary-value problem for a nonlinear wave equation in the square.     

Spaces of Densely Continuous Forms, USCO and Minimal USCO Maps

Our paper studies the topology of uniform convergence on compact sets on the space of densely continuous forms (introduced by Hammer and McCoy (1997)), usco and minimal usco maps. We generalize and complete results from Hammer and McCoy (1997) concerning the space D(X,Y) of densely continuous forms from X to Y. Let X be a Hausdorff topological space, (Y,d) be a metric space and D _k (X,Y) the topology of uniform convergence on compact sets on D(X,Y). We prove the following main results: D _k (X,Y) is metrizable iff D _k (X,Y) is first countable iff X is hemicompact. This result gives also a positive answer to question 4.1 of McCoy (1998). If moreover X is a locally compact hemicompact space and (Y,d) is a locally compact complete metric space, then D _k (X,Y) is completely metrizable, thus improving a result from McCoy (1998). We study also the question, suggested by Hammer and McCoy (1998), when two compatible metrics on Y generate the same topologies of uniform convergence on compact sets on D(X,Y). The completeness of the topology of uniform convergence on compact sets on the space of set-valued maps with closed graphs, usco and minimal usco maps is also discussed.     

论光滑粒子流体动力学(SPH)方法

“光滑粒子流体动力学(SPH-SmoothedParticleHydrodynamics)”是近20多年来发展起来的一种新的纯Lagrange方法.SPH是一种质点方法,有点类似质点网格法,但根本的不同点在于SPH方法中计算空间导数时不需要使用任何网格,而被插值公式中的解析微分式子所替代,从而避免了高维拉氏差分网格法中网格缠结和扭曲等最令人头痛的问题.这种方法另一个突出的优点是表现在对缺乏对称性和内含真空的三维系统的计算特别有效.因为利用网格建立的所有传统的差分方法,随着网格数目的增加,到了三维情形变得难以招架,真空区域的网格剖分造成内存储量的大量浪费又实在令人可惜,而SPH恰能克服上述的缺点.本论文重点介绍了该方法的理论基础和SPH执行过程等有关问题.     

A value on ′AN

We prove here the existence of a value (of norm 1) on the spaces N A and even A N, the closure in the variation distance of the linear space spanned by all games f, where is a non-atomic, non-negative finitely additive measure of mass 1 and f a real-valued function on [0,1] which satisfies a much weaker continuity at zero and one. 1991 Mathematics Subject Classification. 90A08, 90A07This research was in part supported by the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Prime Ministers Science Policy Office.     

A NEW FORMULA WITHOUT BOUNDARY INTEGRALS ON A STEIN MANIFOLD

A new Koppelman-Leray-Norguet formula of (p-1,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of (?)-equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals.