Generic Well-Posedness of Constrained Variational Problems Without Convexity Assumptions

In our previous work, a generic well-posedness result (with respect to variations of the integrand of the integral functional) without the convexity condition was established for a class of optimal control problems satisfying the Cesari growth condition. In this paper, we extend this generic well-posedness result to classes of constrained variational problems in which the values at the endpoints and constraint maps are also subject to variations.     

晶体微观结构的数值计算

晶体微观结构是晶体材料在特定物理条件下其多个能量极小平衔态在空间形成的某种微尺度的规则分布．几何非线性的连续介质力学理论可以用能量极小化原理来解释晶体微观结构的形成，并用Young测度来刻画平衡态各变体在空间的概率分布．定性的理解与定量地分析和计算晶体材料的微观结构对于发展和改进高级晶体功能材料，如形状记忆合金、铁电体、磁至伸缩材料等，有重要的意义．本文回顾了近年来晶体微观结构数值计算方面的最新进展．介绍了计算晶体微观结构的几种数值方法及有关的数值分析结果。     

美式期权定价中非局部问题的有限元方法

在本文中 ,我们关心的是美式期权的有限元方法 .首先 ,根据 [4 ]我们对所讨论的问题引进一个新奇的实用的方法 ,它涉及到对原问题重新形成准确的数学公式 ,使得数值解的计算可以在非常小的区域上进行 ,从而该算法计算速度快精度高 .进而 ,我们利用超逼近分析技术得到了有限元解关于 L2 -模的最优估计 .     

广义集值强非线性拟变分不等式

本文引入并研究一类新的广义集值强非线性拟变分不等式,讨论这类广义集值强非线性拟变分不等式解的存在性以及由算法所构造的迭代序列的收敛性.我们的结果改进和发展了Noor,Siddiqi和Ansari等人近期的一些主要结果.     

Formulation,Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems

In this paper, we present a unified treatment and analysis of a dynamic traffic network model with elastic demands formulated and studied as a projected dynamical system. We propose a travel route choice adjustment process that satisfies the projected dynamical system. Under certain conditions, stability and asymptotical stability of the equilibrium patterns are then derived. Finally, two discrete-time algorithms, the Euler method and the Heun method, are proposed for the computation of the solutions, and convergence results established. The convergence results depend crucially on stability analysis. The performance of the algorithms is then illustrated on several transportation networks.     

Asymptotic Expansions of Posterior Distributions in Nonregular Cases

We study the asymptotic behaviour of the posterior distributions for a one-parameter family of discontinuous densities. It is shown that a suitably centered and normalized posterior converges almost surely to an exponential limit in the total variation norm. Further, asymptotic expansions for the density, distribution function, moments and quantiles of the posterior are also obtained. It is to be noted that, in view of the results of Ghosh et al. (1994, Statistical Decision Theory and Related Topics V, 183-199, Springer, New York) and Ghosal et al. (1995, Ann. Statist., 23, 2145-2152), the nonregular cases considered here are essentially the only ones for which the posterior distributions converge. The results obtained here are also supported by a simulation experiment.     

Necessary conditions and non-existence results for autonomous nonconvex variational problems

Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained.     

广义分解定理与两个不等式

本文给出了Banach空间广义分解定理的一个初等证明,并利用它来证明两个对称不等式.这是首次在Banach空间获得这样的不等式.     

高功率微波高斯馈源口面场分析

 用波导本征模展开方法对用于高功率微波发射系统的方角锥高斯馈源口面场进行分析，提出结合馈源远场辐射特性和避免高功率击穿折衷选定相应的高斯模注腰半径，进而确定多个波导模幅值，从而为运用模匹配或耦合波理论设计高斯馈源提供依据。