某个非紧集上的拓扑压的变分原理

任给一个遍历测度,我们考虑在该测度下Brin-Katok定理和Birkhoff遍历定理成立的点所组成的集合.我们证明了测度理论压等于这个集合上的拓扑压.     

广义射影神经网络的指数稳定性

研究了一类广义射影神经网络,分析了它的稳定性和收敛性.当映射和非对称时,分别定义了恰当的能量函数,在适当的条件下证明了该网络的全局收敛性和指数稳定性.与已有结果相比,文中的稳定性条件并不需要映射的可微性及映射和的对称性.理论分析和数值实例表明所得结果适用于非单调问题,而且给定的条件易于验证.由于该网络可求解一大类优化和平衡问题,因此文中结论具有一定的理论价值和实际意义.     

一般非线性变分不等式组的两步投影算法

对一类新的包含两个不同非线性算子的一般变分不等式组进行了研究；利用投影技巧，给出了一个求解这种一般变分不等式组的显式两步迭代算法；证明了该算法在适当的条件下收敛；所得的结果改进了该领域内的一些最新结果．     

迈克尔逊干涉仪测角度改变量

讨论了迈克尔逊干涉仪补偿板的作用和补偿板角度改变量的测量方法。补偿板的转动会引起光程差的变化，产生干涉条纹数目的变化。通过测量条纹的改变数目，算出补偿板的角度改变量。文中所述方法新颖，精确度较高。     

Cell evolutionary algorithm: a new optimization method on ground-state energy of the atomic

The purpose of this paper is to present a new general approach to solve ground-state energies of the double-electron systems in a uniform magnetic field, in which the basic element of evolution is the set in the solution space, rather than the point. The paper defines the Cell Evolutionary Algorithm, which implements such a view of the evolution mechanism. First, the optimal set in which the optimal solution may be obtained. Then this approach applies the embedded search method to get the optimal solution. We tested this approach on the atomic structure, and the results show that it can improve not only the efficiency but also the accuracy of the calculations as it relates to this specific problem. Foundation item: Supported by the opening Foundation of state key Laboratory of Magnetic Resonance and Atomic and Molecular physics, Wuhan Institute of physics, Chinese Academy of Science (981510) Biography: Liu Lian-jun(1946-), female, Associate professor, research direction: atom and molecular physics.     

带误差项的广义集值变分包含

研究了一类新的广义集值变分包含：０∈Ｎ（ｗ，ｙ）＋Ａ（ｚ，ｕ）在实Ｈｉｌｂｅｒｔ空间，利用极大单调算子的性质，建立了广义集值变分包含和不动点问题的等价性，利用这种等价性，建立了一些摄动迭代算法，并证明了近似解序列强收敛于精确解。     

A Combined Feasible-Nonfeasible Point Continuation Method for Strongly Monotone Variational Inequalities

IntroductionWeconsidertilefollowingvariationalinequalityproblelll(VIPforshort)wllicllistofillfiavectorx*eXsuchthatVIP(X,F)F(X*)"(X~X.)Z0VXEX.(1)wiler(iF:R;;-R"isagivenfllllctiollandXCRniscalls(1tilefeasiblesetofVIP(X.F)ItiswellknownthatVIPisaveryilnportalltrcsearcllareasillceit11dsllumerousapl)licatiollsinbothmatllelllaticsitselfalldecollonlics.Mailysocialalldeconomiclllodels,collvexluathelnaticalprogranullillgsandsooncanbecollsideredasspecialcasesofVIP,tile"lorecollcreteapplicit…     

波浪计算中的一个局部变分法

本文提出了一个改进的局部变分法以计算波浪绕流问题，和已有的局部变分法相比，不增加新的未知量且易于编制计算机程序．