函数的振动熵

本文定义了振动函数与函数的振动熵。对函数的振动性质进行了初步的讨论。振动熵是对函数振动程度的度量(振动愈剧烈振动熵的值愈大)。导数是振动熵的特例。     

二阶线性时滞微分方程的广义振动性

本文主要研究了二阶线性时滞微分方程的广义振动性和广义非振动性,给出了方程广义振动和广义非振动的一些判定定理,同时给出了一类方程广义非振动的充要条件.     

脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.     

高阶线性时滞微分方程的广义振动性

该文考虑了一类高阶线性常系数时滞微分方程 y( n) (t) py′(t) qy(t-τ) =0的广义振动性和广义非振动性 ,给出了一些该类方程广义振动和广义非振动的判定定理 .文中的定理 4还给出了一类非振动但广义振动的方程的判别法则     

具有振动系数时滞差分方程解的振动性

本文研究了一类具振动系数时滞差分方程解的振动性,给出了一个新的振动准则,改进了已有文献中许多相关的结果．     

高阶泛函微分方程的振动性质*

本文借助于Lebesgue测度等工具研究了一类高阶非线性泛函微分方程的振动性质.文中指出.在一定条件下,方程的非振动解仅有两类,而且给出了每一类非振动解存在的必要条件,同时也建立了方程振动的若干充分判据.     

一类具多滞量的二阶中立型差分方程的振动定理

研究了一类具有多个滞量的变系数的二阶中立型差分方程的振动性,给出了该类方程振动及差分算子振动的充分条件。     

二阶中立型差分方程的振动性

研究了一类变系数的二阶中立型时滞差分方程的振动性,得到了该类方程振动及解的一阶差分振动的充分条件。     

三阶非线性泛函微分方程振动的比较准则

本文利用比较法,与一阶时滞微分方程的振动性相比较,研究一类三阶非线性泛函微分方程的振动性,建立该类方程振动的新比较振动准则.本文结果推广和改进了最近文献中的一些新结果.     

时滞抛物方程组振动的充要条件

本文研究了一类时滞抛物微分方程组在齐次Neumann边界条件下解的振动性,用平均值技巧和Green公式把时滞抛物方程组的振动问题转化为泛函微分方程组的振动问题,获得了判别其所有解振动的一个易于验证的充要条件,并举出实例对主要结果进行阐明.     

拟阵的可去圈

本首先用拟阵语言将图论的新概念定义成了拟阵的新概念，然后用拟阵语言将Goddyn和Heuevl所得的图论上的新结果平移成了拟阵的新结果，最后用拟阵的方法对它们给出了新的证明。     

Nontrivial solutions for resonant cooperative elliptic systems via computations of the critical groups

In this paper, we consider a class of resonant cooperative elliptic systems. Based on some new results concerning the computations of the critical groups and the Morse theory, we establish some new results about the existence and multiplicity of solutions under new classes of conditions. It turns out that our main results sharply improve some known results in the literature.     

FC-空间上的连续选择和邻近选择定理

给出了-些从仿紧拓扑空间到FC-空间的新的连续选择;也给出了-些从仿紧拓扑空间到局部FC-一致空间的新的邻近选择.这些结果改进且推广了-些近来的结论.     

Fixed Point Theorems and a New System of Multivalued Generalized Order Complementarity Problems*

Some new fixed point and coupled fixed point theorems for multivalued increasing type mappings are obtained and a new system of multivalued generalized order complementarity problems is introduced in this paper. In terms of new fixed point and coupled fixed point theorems, we give some existance results of solutions for this new system of multivalued generalized order complementarity problems. The results presented in this paper extend and improve the corresponding results announced by Isac and Kostreva.     

An adaptive trust region method and its convergence

In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved. Numerical results indicate that the new method is very efficient.     

近于凸函数新子类的偏差定理和卷积性质

引进了近于凸函数的新子类.利用从属关系得到了偏差定理和卷积性质.所得结果推广了一些作者的相关结果,并得到有趣的新结果.     

Existence results for equilibrium problems with applications to evolution equations

In this paper, we consider evolution equations with time-dependent pseudomonotone and quasimonotone operators by a new approach based on equilibrium problems theory. We establish new existence results for equilibrium problems associated to pseudomonotone and quasimonotone bifunctions in the topological sense. The results obtained are then applied to derive existence of solutions for evolution equations. The approach is new and leads to improve and unify most of the results obtained in this direction.     

Banach空间上Ptolemy常数的计算

利用绝对正规范数生成凸函数的关系,给出了加权平均范数空间上Ptolemy常数的取值,解决了一些文献的遗留问题,并在一些具体的空间上给出了Ptolemy常数的新结果.     

Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations

We obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton-Jacobi-Bellman equations by introducing a new notion of consistency. Our results are robust and general - they improve and extend earlier results by Krylov, Barles, and Jakobsen. We apply our general results to various schemes including Crank-Nicholson type finite difference schemes, splitting methods, and the classical approximation by piecewise constant controls. In the first two cases our results are new, and in the last two cases the results are obtained by a new method which we develop here.

     

Projection algorithms for solving a system of general variational inequalities

In this paper, we introduce and consider a new system of general variational inequalities involving four different operators. Using the projection operator technique, we suggest and analyze some new explicit iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of variational inequalities involving three operators, variational inequalities and related optimization problems as special cases, results obtained in this paper continue to hold for these problems. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities.