Viscosity solutions of fully nonlinear parabolic systems

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128.     

Eu3+、Tb3+与1-乙酰乙酰吲哚、1,10-邻菲啰啉二元、三元体系在溶液中荧光光谱研究

观察了以不同比例溶解在乙醇中的Eu3+、Tb3+、1-乙酰乙酰吲哚(HL)和1,10-邻菲啉(Phen)的荧光光谱.结果表明HL能有效地把吸收的能量传递给Tb3+,而不能有效地传递给Eu3+.讨论了HL和Phen对Eu3+、Tb3+的配位作用及其对Eu3+或Tb3+所组成的三元体系中敏化发光性能的影响.     

水溶液中新型氨羧螯合剂对Eu3+、Tb3+离子的敏化发光性能研究

研究了四种新型氨羧螯合剂在水溶液中自身的荧光及对Eu3+、Tb3+离子的敏化发光性能.考察了浓度、pH值对荧光强度的影响.     

C60/PMMA复合材料的反饱和吸收与光限幅特性研究

本文报导C₆₀/PMMA复合材料的制备方法,并采用调QNd:YAG倍频脉冲激光照射C₆₀/PMMA夏合材料,研究了其反饱和吸收与光限幅将性。在线性透射率为46%条件下,光限幅阈值能量密度为65mJ/cm²,材料破坏能量密度阈值为600mJ/cm².与C₆₀甲苯溶液相比具有一定的优点。     

Eu~（3＋）、Tb~（3＋）与1－乙酰乙酰吲哚、1，10－邻菲啰啉二元、三元体系在溶液中荧光光谱研究

观察了以不同比例溶解在乙醇中的ＥＵ（３＋）、Ｔｂ（３＋）、１－乙酰乙酰吲哚（ＨＬ）和１，１０－邻菲啉（Ｐｈｅｎ）的荧光光谱．结果表明ＨＬ能有效地把吸收的能量传递给Ｔｂ（３＋），而不能有效地传递给Ｅｕ（３＋）．讨论了ＨＬ和Ｐｈｅｎ对Ｅｕ（３＋）、Ｔｂ（３＋）的配位作用及其对Ｅｕ（３＋）或Ｔｂ（３＋）所组成的三元体系中敏化发光性能的影响．     

Near-Optimal Controls of Discrete-Time Dynamic Systems Driven by Singularly-Perturbed Markov Chains

This work is devoted to near-optimal controls of large-scale discrete-time nonlinear dynamic systems driven by Markov chains; the underlying problem is to minimize an expected cost function. Our main goal is to reduce the complexity of the underlying systems. To achieve this goal, discrete-time control models under singularly-perturbed Markov chains are introduced. Using a relaxed control representation, our effort is devoted to finding near-optimal controls. Lumping the states in each irreducible class into a single state gives rise to a limit system. Applying near-optimal controls of the limit system to the original system, near-optimal controls of the original system are derived.     

Analysis of dispersion characteristics of groove guides with mode-matching method

Groove guide is widely recognized as one of the most promising millimeter wave transmission structures. In this paper, the mode-matching method is used to analyse the dispersion characteristics of single and asymmetrical double groove guides, and the unified formulae of Nth-order approximation dispersion equations are presented. Based on this analysis, a general program for calculating the dispersion characteristrics of single and asymmetrical double groove guides has been completed. Some comparisons between the results obtained by present method and published data show that very good agreement has been seen. The effectiveness and the reliability of the given formulae and program are thus verified.     

Near optimality of stochastic control in systems with unknown parameter processes

Stochastic control for systems with an unknown parameter is considered in this paper. The underlying problem is to minimize a functional subject to a system described by a singularly perturbed differential equation with an unknown parameter process driven by fast fluctuating random disturbances. This problem arises in the context of stochastic adaptive control, adaptive signal processing, and failure-prone manufacturing systems. Due to the nature of the wide-bandwidth noise processes, identifying the parameter process for eacht is very hard since the driving noise changes very rapidly. An alternative approach is used, and an auxiliary control problem is introduced to overcome the difficulties. By means of weak convergence methods and comparison control techniques, nearly optimal controls are obtained.This research was supported in part by the National Science Foundation under Grant DMS-9022139 and DMS-9224372.     

Using stochastic optimization to determine threshold values for the control of unreliable manufacturing systems

A manufacturing system with two tandem machines producing one part type is considered in this work. The machines are unreliable, each having two states, up and down. Both surplus controls and Kanban systems are considered. Algorithms for approximating the optimal threshold values are developed. First, perturbation analysis techniques are employed to obtain consistent gradient estimates based on a single simulation run. Then, iterative algorithms of the stochastic optimization type are constructed. It is shown that the algorithms converge to the optimal threshold values in an appropriate sense. Numerical examples are provided to demonstrate the performance of the algorithms.The research of these authors was supported in part by grants from URIF, MRCO, National Science Foundation, and Wayne State University. The authors would like to thank Dr. X. R. Cao, Digital Equipment Corporation, for the valuable initial discussion and Dr. X. Y. Zhou, University of Toronto, for his helpful comments.     

间二甲苯分子在不同外电场下结构和解离特性研究

间二甲苯是挥发性有机物(VOCs, Volatile Organic Compounds)的关键活性成分,研究其在外电场下的性质十分重要.采用密度泛函理论(DFT),在B3LYP/6-311G++基组水平上对间二甲苯分子进行优化,从分子结构研究了不同外电场(-0.025 a.u.～0.025 a.u.)作用下,间二甲苯分子的总能量,键长,电偶极矩,前线轨道,红外光谱和解离势能面.计算结果表明,沿两甲基中C原子连线方向的电场(-0.025 a.u.～0.025 a.u.)增加时,分子总能量和能隙先增大后减小,电偶极矩先减小后增加.通过计算发现外电场对间二甲苯分子不同键长和不同振动模式的红外光谱的影响均有所不同.间二甲苯分子的解离特性表现为:沿两甲基中C原子连线方向施加强度超过0.047 a. u.的电场时,位于电场增加方向的甲基与苯环之间起连接作用的C-C键断裂.以上计算结果可为利用电场降解间二甲苯提供重要理论参考.