Numerical method for a class of optimal control problems subject to nonsmooth functional constraints

In this paper, we consider a class of optimal control problems which is governed by nonsmooth functional inequality constraints involving convolution. First, we transform it into an equivalent optimal control problem with smooth functional inequality constraints at the expense of doubling the dimension of the control variables. Then, using the Chebyshev polynomial approximation of the control variables, we obtain an semi-infinite quadratic programming problem. At last, we use the dual parametrization technique to solve the problem.     

气体团簇形成过程的模拟计算

团簇源特性是影响激光与团簇相互作用的一个主要因素,因此团簇源的特性研究是一项非常关键的工作.本文主要从以下两个方面对气体团簇形成过程进行模拟计算:①从流体力学角度出发,讨论气体的密度、压强及温度在喷嘴轴线上的空间分布,结合汽液平衡方程分析团簇开始形成的位置;②采用液滴模型,讨论团簇尺寸随时间的变化.这些结果不仅有利于进一步研究团簇形成过程的特性,而且为激光与团簇相互作用实验的设计提供宝贵的参考.     

p型ZnO薄膜的制备及特性

采用射频磁控溅射在Si片上制备ZnO薄膜，通过离子注入对样品进行N掺杂，在不同温度下进行退火并实现了p型转变.用扫描电子显微镜、X射线衍射和Hall测量对薄膜进行了表征，结果表明薄膜具有良好的表面形貌和高度c轴择优取向，退火后p型ZnO薄膜的最高载流子浓度和最低电阻率分别为1.68×10¹⁶cm^-3和41.5Ω·cm.讨论并分析了退火温度和时间对ZnO薄膜p型转变的影响.     

Hidden Convex Minimization

A class of nonconvex minimization problems can be classified as hidden convex minimization problems. A nonconvex minimization problem is called a hidden convex minimization problem if there exists an equivalent transformation such that the equivalent transformation of it is a convex minimization problem. Sufficient conditions that are independent of transformations are derived in this paper for identifying such a class of seemingly nonconvex minimization problems that are equivalent to convex minimization problems. Thus, a global optimality can be achieved for this class of hidden convex optimization problems by using local search methods. The results presented in this paper extend the reach of convex minimization by identifying its equivalent with a nonconvex representation.     

Optimal value functions of generalized semi-infinite min-max programming on a noncompact set

In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subd-ifferential characterizations of optimal value functions are given. Using these properties, we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.     

没有单调性和紧性的广义向量拟似变分不等式

本文利用极大元定理在非紧拓扑空间设置下证明了没有单调性的广义向量拟似变分不等式解的存在性定理.     

鲁米诺-二甲亚砜-氢氧化钠体系化学发光机理的理论研究

用密度泛函理论(DFT) B3PW91/6-31G**方法研究了鲁米诺-二甲亚砜-氢氧化钠化学发光反应体系中反应物、中间体和产物的分子结构和振动频率, 用B3PW91/6-311＋G(3df,2p)方法获得反应能量以及用时间相关(Time Dependent, TD)的B3PW91/6-311＋G(3df, 2p)方法进行电子激发能态分析. 研究结果支持了下列化学发光反应通道: LH₂(¹A)＋OH^－ →LH₂•OH^－(¹A)→LH^－(¹A)→L^·－(²A)→TS₁(³A)→LO₂^2－(³A)→TS₂(³A)→AP^2－*(?³A)→AP^2－(X³A)＋hν, 最后即AP^2－*回到基态发光; 或AP^2－*(?³A)→AP^2－*(?¹A)→AP^2－(a¹A)＋hν, 即激发态势能面交叉后的单重态跃迁发光. 它们在可见光区域主要有400～460和500～530 nm的强吸收谱带, 与实验结果符合. 研究还表明, 质子化的鲁米诺能量将大幅度降低, 说明酸性溶液导致鲁米诺的反应活性降低, 从理论上解释了鲁米诺化学发光体系的溶液须呈碱性, pH值影响发光反应的实验事实.     

具有变时滞和脉冲效应的Hopfield神经网络的全局指数稳定性

讨论了一类具有变时滞和脉冲效应的Hopfield神经网络模型．利用按段连续的向量Liapunov思想方法,研究了脉冲时滞神经网络的全局指数稳定性．例子及其数值仿真说明了结果的有效性．推广和改进了已有文献的一些结果．     

向量拟平衡问题系统及其应用

引入了向量拟平衡问题系统并证明了其解的存在性定理．作为应用,还得到约束多目标对策和无约束多目标对策弱Pareto平衡的一些存在性结果．