Locally Farkas-Minkowski linear inequality systems

This paper introduces thelocally Farkas-Minkowski (LFM) linear inequality systems in a finite dimensional Euclidean space. These systems are those ones that satisfy that any consequence of the system that is active at some solution point is also a consequence of some finite subsystem. This class includes the Farkas-Minkowski systems and verifies most of the properties that these systems possess. Moreover, it contains the locally polyhedral systems, which are the natural external representation of quasi-polyhedral sets. TheLFM systems appear to be the natural external representation of closed convex sets. A characterization based on their properties under the union of systems is provided. In linear semi-infinite programming, theLFM property is the more general constraint qualification such that the Karush-Kuhn-Tucker condition characterizes the optimal points. Furthermore, the pair of Haar dual problems has no duality gap.     

A note on the compactness of the index set in convex optimization. Application to metric regularity

We consider the linear quadratic optimal control problem in the infinite time horizon case for a class of discrete-time systems controlled by a continuous inputs. We show that, under certain hypothesis, the Hilbert uniqueness method can be used to determine the optimal control.     

Isolated efficiency in nonsmooth semi-infinite multi-objective programming

ABSTRACT

In this paper, isolated efficient solutions of a given nonsmooth Multi-Objective Semi-Infinite Programming problem (MOSIP) are studied. Two new Data Qualifications (DQs) are introduced and it is shown that these DQs are, to a large extent, weaker than already known Constraint Qualifications (CQs). The relationships between isolated efficiency and some relevant notions existing in the literature, including robustness, are established. Various necessary and sufficient conditions for characterizing isolated efficient solutions of a general problem are derived. It is done invoking the tangent cones, the normal cones, the generalized directional derivatives, and some gap functions. Using these characterizations, the (strongly) perturbed Karush-Kuhn-Tucker (KKT) optimality conditions for MOSIP are analyzed. Furthermore, it is shown that each isolated efficient solution is a Geoffrion properly efficient solution under appropriate assumptions. Moreover, Kuhn-Tucker (KT) and Klinger properly efficient solutions for a nonsmooth MOSIP are defined and it is proved that each isolated efficient solution is a KT properly efficient solution in general, and a Klinger properly efficient solution under a DQ. Finally, in the last section, the largest isolated efficiency constant for a given isolated efficient solution is determined.     

Modified Derivative Scalar Coupling Model in Semi-infinite Nuclear Matter

Semi-infinite nuclear matter has been investigated in relativistic Thomas-Fermi and Hartree approximations based on the modified derivative scalar coupling model. Our results show that the spin-orbit potential has been improved by the tensor coupling. However, the surface tension and the surface thickness become considerably small with increasing of the tensor coupling constant. The effects of the σ-meson mass on the spin-orbit potential, on the surface tension, and on the surface thickness have also been discussed.     

垂直与水平渗透作用下潜水非稳定渗流运动规律

对河渠边界控制的半无限含水层,建立垂向入渗与河渠水平渗透共同作用下的潜水非稳定渗流模型;利用Boussinesq第一线性化方法,通过Laplace变换,给出模型的解析解. 证明相关经典公式与模型特定解之间的转换关系,分析经典公式适用范围．根据模型解,逐一定量研究下述变量,如垂向入渗强度、河渠水位变动幅度、含水层结构参数如给水度和导压系数、计算点与边界之间的距离,对渗流过程的影响．这些变量的变化,对潜水位获最大上升速度的时间产生延迟效应;论证一些变量间产生等效延迟效应的条件．根据解的数学特征,讨论其对应的物理意义和潜水位变动规律．     

杆式射流侵彻半无限靶的理论分析

 理论分析高速杆式射流侵彻半无限靶过程时,考虑速度梯度对聚能射流的影响,将射流进行分段计算,得到了射流拉伸后实际碰靶时的微元长度和直径变化。采用伯努利方程和静力学方法,通过对射流形状和速度分布作线性近似,理论分析了高速杆式射流侵彻半无限靶的过程,得到了靶体中的侵彻深度和侵彻孔径与射流长度、速度及直径之间的关系。将模拟结果与实验结果进行对比,结果表明理论分析结果与侵彻实验结果符合较好。     

一类非光滑多目标半无限规划的最优性条件

利用K-方向导数,给出了一类存在性更为广泛的广义凸函数.即广义一致K-（F,α,ρ,d）-I型凸函数,进而讨论了涉及这些新广义凸性的一类多目标半无限规划的最优性条件。     

THE METHOD OF WEIGHTED DIFFERENCE FOR SINGULAR PERTURBATION PROBLEM

In this paper, we introduce a new difference approximation to the first order derivative u′and give a class of uniformly convergent difference schemes.     

半无限晶体中慢速运动的表面极化子

本文研究电子与体纵光学声子耦合弱、与表面光学声子耦合强的半无限晶体中的表面极化子的性质.采用改进了的线性组合算符法和微扰法导出了半无限晶体中的慢速运动极化子的有效哈密顿量.在计及电子在反冲效应中发射和吸收的不同波矢的声子之间的相互作用时,讨论了对有效哈密顿量,诱生势和有效质量的影响.对AgBr晶体进行了数值计算,结果表明反冲效应中发射和吸收的不同波矢的声子之间的相互作用对有效质量和诱生势的影响随耦合常数αt的增加而增加,对有效质量的影响随坐标z的增加而减小的更多,对诱生势的影响随z的增加而增加的更多.