On the Local Uniqueness of Solutions of Variational Inequalities Under H-Differentiability

In this paper, we give some sufficient conditions for the local uniqueness of solutions to nonsmooth variational inequalities where the underlying functions are H-differentiable and the underlying set is a closed convex set/polyhedral set/box/polyhedral cone. We show how the solution of a linearized variational inequality is related to the solution of the variational inequality. These results extend/unify various similar results proved for C ¹ and locally Lipschitzian variational inequality problems. When specialized to the nonlinear complementarity problem, our results extend/unify those of C ² and C ¹ nonlinear complementarity problems.     

体操课教学训练过程最优化的探索

本文作者应用教学教育过程最优化的理论与方法，指导体操教学训练。经过多年的探索，实践证明要提高教学训练的效益和质量，就应发挥教学系统的整体功能，选择最佳教学方法，突出教学重点，抓住关键环节。     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

关于一类二次哈密尔顿系统在二次扰动下的极限环个数问题

本文研究了一类具有两个鞍点和一个中心的通用二次哈密尔顿向量场在二次扰动下的三参数开折，证明极限环的最小上界为２。     

Equivalence of variational inequality problems to unconstrained minimization

In this paper we propose a class of merit functions for variational inequality problems (VI). Through these merit functions, the variational inequality problem is cast as unconstrained minimization problem. We estimate the growth rate of these merit functions and give conditions under which the stationary points of these functions are the solutions of VI. This work was supported by the state key project “Scientific and Engineering Computing”.     

一类资源分配问题的最优化方法的研究

建立了树型生产系统的一类资源分配问题的数学模型和计算法,并给出一般网络简化为树型网络的树化变换。然后建立了一般生产系统资源分配问题的网络优化算法。     

理性看待特许经营

目前，国内许多企业为了在较短的时间内迅速扩大规模，纷纷采取特许经营模式，有些已经取得了较大的进展，但其中也不乏盲目跟刚才是，文章从国内特许经营存在的问题入手，指出了特许经营中的陷阱及对策。     

高师田径教学存在的问题与改革对策

以中小学体育与健康课程的变革为依托 ,阐述了目前高师田径教学存在的问题 ,并提出了一些相应的改革对策     

地下洞室形状优化设计

洞室开挖会使围岩周边产生应力集中 ,产生拉应力与压应力。围岩出现拉应力对洞室稳定十分不利 ,通常通过改变洞室形状和轴比来消除围岩中的拉应力。本文提出一种使洞室拉应力σθ=0 ,而压应力最小的确定洞室最优几何形状的方法。     

城市土地规划的优化方法研究

以多目标决策理论、组合优化理论以及预测科学技术为依据 ,首先建立了土地功能配置模型 ,帮助规划师对各种不同功能土地的片面布置进行分析 ,从而找到最合理的城市土地布局 ;然后以遗传算法作为优化工具 ,对建立的模型进行了优化。