Numerical comparison of methods for solving second-order ordinary initial value problems

In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm of a special second-order ordinary initial value problems. The ADM does not require discretization and consequently of massive computations. This paper is particularly concerned with the ADM and the results obtained are compared with previously known results using the Quintic C²-spline integration methods. The numerical results demonstrate that the ADM is relatively accurate and easily implemented.     

A Note on the Indirect Controls for a Coupled System of Wave Equations

By a procedure of successive projections, the authors decompose a coupled system of wave equations into a sequence of sub-systems. Then, they can clarify the indirect controls and the total number of controls. Moreover, the authors give a uniqueness theorem of solution to the system of wave equations under Kalman’s rank condition.     

Second Order Optimality Conditions for Problems with Continuously Differentiable Data

In this note, by making use of the concept of unbounded approximate Hessian matrices, we present second order optimality conditions for a constrained mathematical programming problem with data whose gradient map is continuous, but not necessarily locally Lipschitz.     

Approximate controllability for a class of hemivariational inequalities

In this paper, we deal with the approximate controllability for control systems described by a class of hemivariational inequalities. Firstly, we introduce the concept of mild solutions for hemivariational inequalities. Then the approximate controllability is formulated and proved by utilizing a fixed-point theorem of multivalued maps and properties of generalized Clarke subdifferential.     

作用模糊子集推理方法的研究与应用

针对实用模糊控制过程,提出作用模糊子集和作用模糊控制规则的概念;根据模糊逻辑推理中真值的产生、传递和接收机理,提出作用模糊子集推理方法;比较分析了作用模糊子集推理方法与CRI法的推理结果;利用该推理方法实现了试验室温度模糊控制试验。     

Lukasiewicz n值命题逻辑中命题的真度理论

利用势为 n的均匀概率空间的无穷乘积在 Lukasiewicz n值命题逻辑中引入了公式的真度概念,当3≤n≤17时证明了全体公式的真度值之集在[0,1]上是稠密的,并给出了公式真度的表达通式;利用真度定义了公式间的相似度,进而导出了全体公式集上的一种伪距离,为n值Lukasiewicz命题逻辑系统的近似推理理论提供了一种可能的框架。     

时滞惯性流形及近似时滞惯性流形族

时滞惯性流形是对耗散系统惯性流形、近似惯性流形的最新发展,它基于对 大小涡分量间相互作用更细致的观察,即改变了惯性流形和近似惯性流形方法中大小 涡分量间相互作用为瞬时行为的隐含假定,而认为这种作用与系统的历史相关的．本 文结出了一类耗散系统时滞惯性流形的存在性证明,由于其存在性不需要“谱间隔条 件”保证,因而时滞惯性流形是广泛存在的．随后我们引出了一类离散的时滞惯性流 形,并在此基础上构造了一种近似时滞惯性流形族,分别给出了它们近似时滞惯性流 形的误差估计,结果显示这种新方法为构造稳定和高精度的算法提供了可能．     

基于可靠度的结构优化的序列近似规划算法

基于可靠度的优化的最直观解法是把可靠度和优化的各自算法搭配一起形成嵌套两层次迭代。为改善其收敛性提高计算效率,人们提出了功能测度法、半无限规划法、单层次算法等多种改进方法。本文对传统结构优化界的经典序列近似规划法改造并扩展应用于求解基于可靠度的结构优化问题,构造该问题的序列近似规划模型和求解过程;其核心思想是在每个近似规划子问题中采用近似可靠度指标对设计变量的线性近似,在优化迭代过程中同步更新设计变量和随机空间中的近似验算点坐标,以达到可靠度分析和优化迭代同步收敛的目标。为了算法的实施,还推导出近似可靠度指标的半解析灵敏度计算公式,编制了程序,最终实现与通用软件的连接。论文用算例证实算法的有效性。