近独立子系系统的统计规律(一)——二维系统统计规律的计算机模拟

利用刚球模型,根据力学规律,对二维近独立子系系统粒子的运动进行了计算机模拟;模拟中,在不同时刻对系统中各粒子的能量和速率进行多次测量,并对测量结果进行统计平均,得到了粒子数不同的力学系统中粒子按能量和速率的分布图;根据所得的分布图形曲线,给出了任意数目的粒子系统的统一的分布函数.从而完全证明了少量粒子构成的力学系统,其长时间行为也具有确定的统计规律.     

LF相对乘积空间与近似良紧性

通过引入相对乘积空间证明了近似良紧性关于相对乘积运算而言хоновти乘积定理成立.     

近似锥-次类凸集值优化的严有效性

在Hausdorff局部凸拓扑线性空间中考虑约束集值优化问题(VP)的严有效性.在近似锥-次类凸假设下,利用凸集分离定理,分别得到了Kuhn-Tucker型和Lagrange型最优性条件,建立了与(VP)等价的两种形式的无约束优化.     

Strong Duality for Generalized Convex Optimization Problems

In this paper, strong duality for nearly-convex optimization problems is established. Three kinds of conjugate dual problems are associated to the primal optimization problem: the Lagrange dual, Fenchel dual, and Fenchel-Lagrange dual problems. The main result shows that, under suitable conditions, the optimal objective values of these four problems coincide. The first author was supported in part by Gottlieb Daimler and Karl Benz Stiftung 02-48/99. This research has been performed while the second author visited Chemnitz University of Technology under DAAD (Deutscher Akademischer Austauschdienst) Grant A/02/12866. Communicated by T. Rapcsák     

Convergence of Inexact Mann Iterations Generated by Nearly Nonexpansive Sequences and Applications

The Mann iterates behave well for nonexpansive mappings for any initial guess in the domain. Our aim in this article is to extend this method to a broad class of inexact fixed point algorithms generated by nearly nonexpansive sequences in Banach spaces and to locate the weak limit of the iterates by its initial guesses. Due to the inexactness, our algorithms become e?ciently applicable for a wider class of problems. As applications, we give convergence theorems for finding solutions of variational inclusion problems and constrained multiple-sets split feasibility problems. Our results are significant refinements and improvements of the corresponding results in the literature.     

Near convexity,near smoothness and approximative compactness of half spaces in Banach spaces

The authors discuss the dual relation of nearly very convexity and property WS. By two kinds of near convexities and two kinds of near smoothness, the authors prove a series of characterizations such that every half-space in Banach space X and every weak* half-space in the dual space X* are approximatively weakly compact and approximatively compact. They show a sufficient condition such that a Banach space X is a Asplund space. Using upper semi-continuity of duality mapping, the authors also give two characterizations of property WS and property S.     

边界元法计算近边界点参量的一个通用算法

针对边界元法存在近力界点参量计算的困难,给出了一个通用性方法,将近边界点到边界单元的距离参数通过分部积分变换到积分式之外,从而计算出二维问题近边界点参量的几乎强奇异和超奇异积分,由此,对任何近边界点参量,提出了整套计算方案,算例证明了本法的有效性。     

边界元法中计算几乎奇异积分的一种无奇异算法

边界元法中存在几乎奇异积分的计算困难。引起边界单元上几乎奇异积分的因素是源点到其邻近单元的最小距离δ。本文拓展文[1]的思想,进一步采用分部积分将δ移出奇异积分式中积分核之外,转换后积分核是δ的正则函数。所以几乎强奇异和超奇异积分被化为无奇异的规则积分与解析积分的和,可由通常的Gauss数值积分解。文中应用此正则化技术求解了弹性力学平面问题的近边界点位移和应力。     

非连续边界元积分的精确表达式及相关问题

以二维位势问题边界元分析为例,给出了利用线性非连续边界元离散边界积分方程时系数矩阵积分计算的精确表达式,通过和利用Gauss积分方法计算系数矩阵所得数值结果的比较表明：配位点选择不同对数值计算结果精度影响的主要原因是积分计算的精度,尤其当配位因子选择较大时,存在的准奇异积分（Nearly Singular Integrals)很难利用常规Gauss积分方法准确求得。