局部误差的有界约束非线性方程组的非单调信赖域算法

本文提供了在没有非奇异假设的条件下,求解有界约束半光滑方程组的投影信赖域算法.基于一个正则化子问题,求得类牛顿步,进而求得投影牛顿步.在合理的假设条件下,证明了算法不仅具有整体收敛性而且保持超线性收敛速率.     

Controlling Chaotic Behavior in a Bose-Einstein Condensate with Linear Feedback

The spatial structure of a Bose-Einstein condensate （BEC） loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative.     

时变观测算子族的无限时容许性

对Hilbert空间中的无界时变观测算子族引入无限时容许性概念,并利用发展半群理论,给出无界时变观测算子族的无限时容许性刻画.最后,对一类具混合边界条件的非自治系统,构造了一类无限时容许观测算子族.     

中立型延迟微分方程一般线性方法的非线性稳定性

本文研究一类非线性中立型延迟微分方程一般线性方法的数值稳定性.证明了一般线性方法为(k,p,O)-代数稳定时,在一定的约束条件下,其数值解保持微分方程理论解的稳定性质,特别是证明了在约束网格情形代数靛的-般线性方法能无条件保持解析解的稳定性.     

GLOBAL EXISTENCE AND EXTINCTION FOR A DEGENERATE NONLINEAR DIFFUSION PROBLEM WITH NONLINEAR GRADIENT TERM AND ABSORPTION

Existence and extinction in finite time of global weak solutions for the problem （P） are proved.     

REPELLERS FOR MULTIFUNCTIONS OF SEMI-BORNOLOGICAL SPACES

In this article the notion of repeller for multifunctions from the viewpoints of semi-bornologicul spaces is considered. The concept of lower semi-continuous multifunctions is extended by the use of semi-bornological spaces. Semi-bornological vector spaces are studied. The notion of conjugacy for semi-bornological multifunctions is considered. The persistence of repeller under conjugate relation is proved.     

线性空间偶的运动公式

本文研究了线性空间偶的运动公式．利用活动标架法．在获得相交线性空间偶的运动密度公式的基础上，得到一系列有关相交线性空间偶的运动公式．     

一类三阶微分方程边值问题的单调迭代法

用单调迭代法研究一类三阶微分方程边值问题解的存在性,不仅证明了该问题解的存在性,而且得到了其迭代格式.     

具有两参数的椭圆型方程Robin问题解的渐近性态

讨论了一类具有双参数的椭圆型方程边值问题.引入伸长变量,构造了问题的形式渐近解.利用微分不等式理论,证明了边值问题渐近解的存在性和一致有效性.由解的结构指出,在两参数一定的情况下,相应问题的解只具有二个边界层.