关于n平面线性相干光处理系统的讨论(Ⅰ)

讨论n平面线性相干光处理系统(简称n平面线性系统)的一般性质。在两个特例情况下,借助于傅里叶变换的相似性定理和空间频率的标度变换,可以证明:n平面线性系统的(n—1)个间距参数{z_i}_n-1不是实质性参数。利用所得结果,演示了相干光成象和空域中的频率的标度变换,说明理论结果是有效的。 关键词：     

半线性系统Robin问题的奇摄动

本文利用微分不等式的方法和技巧,研究半线性系统Robin问题的奇摄动,对它的近似解作出了估计,且得到包括边界层在内的任意次近似的一致有效的渐近展开式。     

关于一篇论文的注记

文[1]讨论3维Lotka-Volterra合作系统的全局稳定性,其中定理2给出:系统唯一的正平衡点渐近稳定的充要条件是线性变分阵B的行列式小于零.此定理的充分条件是成立的,但必要条件未必成立.当平衡点渐近稳定时,B的特征根未必均具负实部,因此未必│B│<0.因为当B具有一零特征根或一对纯虚特征根而其它特征根具负实部(相应于Liapunov稳定性的第一、第二临界情形)时,对应的非线性系统仍可以是渐近稳定的.特别要提的是文[1]中的定理3:存在实对角正定阵C使CA A~TC=-I的充要条件是│A│<0(等价于A的特征根均是负实部).此定理仅对一般的正定阵C成立,而对于对角正定阵C一般是不成立的,而在文[1]中是根本不成立的。现简析如下.设C=diag(C_1,C_2,C_3)>0,则     

求解一类复对称线性系统的改进的SNS和SSS迭代法

本文在Bai的基础上提出改进的斜正规分裂(MSNS)和斜尺度化分裂(MSSS)迭代法,用以求解一类应用广泛的复对称线性系统,并证实MSNS和MSSS迭代法是无条件收敛的.通过利用一些Krylov子空间方法,本文给出相对应的非精确版本的MSNS(MSSS)方法.数值实验说明了所给方法的有效性.     

A NEW PRECONDITIONING STRATEGY FOR SOLVING A CLASS OF TIME-DEPENDENT PDE-CONSTRAINED OPTIMIZATION PROBLEMS

In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distributed control problem involving the heat equation with two different functions. First a natural order-reduction is performed, and then the reduced- order linear system of equations is solved by the preconditioned MINRES algorithm with a new preconditioning techniques. The spectral properties of the preconditioned matrix are analyzed. Numerical results demonstrate that the preconditioning strategy for solving the large sparse systems discretized from the time-dependent problems is more effective for a wide range of mesh sizes and the value of the regularization parameter.     

含有一个控制的拟线性抛物系统的能控性

该文讨论了一类拟线性抛物系统的全局零能控性和逼近能控性. 文中首先给出并证明了相应的线性系统的Carleman不等式,再由Carleman不等式去证明观测不等式, 最后利用Kakutani不动点定理证明非线性系统的全局零能控性和逼近能控性.     

A NEW ALGORITHM FOR COMPUTING LARGEST REAL PART EIGENVALUE OF MATRICES：COLLATZ ＆ PERRON-FROBERNIUS＇ APPROACH

This paper describes a new method and algorithm for the numerical solution of eigenvalues with the largest real part of positive matrices.The method is based on a numerical implementation of Collatz’s eigenvalue inclusion theorem for non-negative irreducible matrices.Eigenvalues are analyzed for the studies of the stability of linear systems.Finally, a numerical discussion is given to derive the required number of mathematical operations of the new algorithm. Comparisons between the new algorithm and several well known ones, such as Power, and QR methods, are discussed.     

人造量子系统的理论研究与代数动力学

从控制与利用微观系统的量子工程的观点,讨论了人造量子系统的基本物理问题。针对人造量子系统中的一大类———非自治量子系统的求解问题,提出了代数动力学理论方法。运用代数动力学,对人造量子系统进行了理论研究;对可积的非自治系统,详细介绍了线性系统和非线性可积系统的求解问题;对不可积系统,用代数动力学观点研究了量子规则运动和无规运动的特征,它们之间的过渡,以及它们对时间有关外场的不同响应。     

STABILIZATION OF MARKOVIAN JUMP LINEAR SYSTEMS VIA RANDOM COMMUNICATION TIME DELAYED AND IMPULSIVE CONTROLLERS

This paper deals with the stabilization problems for a networked control system via time-delayed and impulsive controllers. The random communication delays in the model signal are modeled as a Markov chain. First, we introduce a hybrid controller with delay and impulses for the networked control systems. Then, some sufficient conditions are proposed for the design of a hybrid controller such that the closed-loop system is stochastically stable.     

Theory and Applications of Discontinuous State Feedback Generating Chaos for Linear Systems

We investigate a kind of chaos generating technique on a type of n-dimensional linear differential systems by adding feedback control items under a discontinuous state. This method is checked with some examples of numeric simulation. A constructive theorem is proposed for generalized synchronization related to the above chaotic system.