一个非线性扩散系统解的存在性及线性系统的最优控制

讨论关于生物种群的一个非线性扩散系统和线性系统的一些问题,得到了非线性扩散系统弱解的存在性;线性系统最优繁殖率的存在性和关于边界扰动的最优解的存在唯一性。     

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。     

拟线性常微分方程组边值问题的奇摄动

本文研究拟线性常微分方程组边值问题x′=f(t,x,y,ε),εy″=g(t,x,y,ε)y′+h(t,x,y,ε), x(0,ε)=A(ε),y(0,ε)=B(ε),y(1,ε)=C(ε)的奇摄动.其中x,f,y,h,A,B和C均属于Rn和g是对角矩阵.在适当的假设下,利用对角化技巧和微分不等式理论获得了解的存在和它的按分量逐个一致有效的估计.     

求多变量线性系统的逆向系统的一种新方法

对多变量线性系统,本文给出了求其逆向系统的一种新方法,这种方法将逆向系统计算中高阶矩阵的求逆转化为通过初等变换求低阶矩阵的规范型,比以往的方法更加简单有效且易于编程计算。本文结合系统的可观测空间与不可观测空间的情况,给出了一种特定的等价变换,得到了比通常更低阶的逆向系统。     

Stochastic resonance in linear system driven by multiplicative noise and additive quadratic noise

In this paper the stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative noise and additive quadratic noise. The exact expressions are obtained for the first two moments and the correlation function by using linear response and the properties of the dichotomous noise. SR phenomenon exhibits in the linear system. There are three different forms of SR: the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the effect of the asymmetry of the multiplicative noise on the signal-to-noise ratio (SNR) is different from that of the additive noise and the effect of multiplicative noise and additive noise on SNR is different.     

New scheme of anticipating synchronization for arbitrary anticipation time and its application to long-term prediction of chaotic states

How to predict the dynamics of nonlinear chaotic systems is still a challenging subject with important real-life applications. The present paper deals with this important yet difficult problem via a new scheme of anticipating synchronization. A global, robust, analytical and delay-independent sufficient condition is obtained to guarantee the existence of anticipating synchronization manifold theoretically in the framework of the Krasovskii-Lyapunov theory. Different from ＇traditional techniques （or regimes）＇ proposed in the previous literature, the present scheme guarantees that the receiver system can synchronize with the future state of a transmitter system for an arbitrarily long anticipation time, which allows one to predict the dynamics of chaotic transmitter at any point of time if necessary. Also it is simple to implement in practice. A classical chaotic system is employed to demonstrate the application of the proposed scheme to the long-term prediction of chaotic states.[第一段]     

ON CONTRACTION AND SEMI-CONTRACTION FACTORS OF GSOR METHOD FOR AUGMENTED LINEAR SYSTEMS

The generalized successive overrelaxation （GSOR） method was presented and studied by Bai, Parlett and Wang [Numer. Math. 102（2005）, pp.1-38] for solving the augmented system of linear equations, and the optimal iteration parameters and the corresponding optimal convergence factor were exactly obtained. In this paper, we further estimate the contraction and the semi-contraction factors of the GSOR method. The motivation of the study is that the convergence speed of an iteration method is actually decided by the contraction factor but not by the spectral radius in finite-step iteration computations. For the nonsingular augmented linear system, under some restrictions we obtain the contraction domain of the parameters involved, which guarantees that the contraction factor of the GSOR method is less than one. For the singular but consistent augmented linear system, we also obtain the semi-contraction domain of the parameters in a similar fashion. Finally, we use two numerical examples to verify the theoretical results and the effectiveness of the GSOR method.     

求解Hubbard线性系统的快速稳定算法

求解Hubbard线性系统是材料物理中DQMC/HQMC模型的核心问题之一,本文讨论了Hubbard矩阵的结构,然后给出了当能量参数U=O的情况下快速稳定求解Hubbard线性系统的算法.数值实验说明了方法的有效性.     

Modified iterative method for augmented system

The successive overrelaxation-like(SOR-like) method with the real parameters ω is considered for solving the augmented system. The new method is called the modified SOR-like(MSOR-like) method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like(Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel Scientific Computations, 7(4), 453–462(1999)) and the modified symmetric SOR-like(MSSOR-like) methods(Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems.     

A Linear System Arising from a Polynomial Problem and Its Applications

A linear system arising from a polynomial problem in the approximation theory is studied, and the necessary and sufficient conditions for existence and uniqueness of its solutions are presented. Together with a class of determinant identities, the resulting theory is used to determine the unique solution to the polynomial problem. Some homogeneous polynomial identities as well as results on the structure of related polynomial ideals are just by-products.