On the optimal control for variational inequalities

We prove an existence theorem for the optimal control of variational inequalities governed by a pseudomonotone operator: the cost is assumed to be quadratic. Then, we give an extension of the theorem to more general costs (assuming the operator to be monotone); we also give a result on a perturbation problem.This work is an extended part of the author's thesis, written under the direction of Professor T. Zolezzi. This research was partially supported by the Consiglio Nazionale delle Ricerche (CNR), Rome, Italy.     

稀土分量的XRF法分析—熔珠粉末压薄片法

本法用50mg稀土氧化物样品,经四硼酸锂熔融后,粉碎压成薄片,以透空照射法,直接测定15项稀土分量和铀、钍。本法消除基体效应好,制样精度高,测定含量范围宽。     

圆波导劈形端口辐射器的数值分析

 高功率微波运用的圆波导劈形端口辐射器(Vlasov-Nakajima辐射器)的辐射场可视为由平开口圆波导的辐射场和在该辐射场中的劈形圆波导段的散射场叠加而成。运用等效电磁流原理数值求解Kirchhoff-kottler积分获得圆波导TM₀₁模的辐射场,再应用物理光学方法计算劈形段的散射场,并将计算的远场方向图与实验结果比较,获得较满意的一致。     

传输电缆对换能器阻抗特性的影响

本文通过传输线方法讨论了电缆对换能器的影响,随频率增加,电缆对换能器的影响交蛎,主要表现为,最大电导增大,串联谐振率下降,这些都是由于电缆传输系数随频率变化引起的,并且与换能器的阻抗特性有关。     

一种新型的两态叠加多模Schrdinger猫态光场的等阶N次方Y压缩

本文根据量子力学的线性叠加原理,构造了由多模（即q模时目平态的相反态|｛｛－Zj｝〉q及多模虚相干态|｛｛－Zj｝〉q这两者的线性叠加所组成的一种新型的多模Schrodinger猫态光场利用新近建立的多模压缩态理论,研究了态的N次方Y压缩效应,结果发现：①当压缩阶数N＝Zp且p＝2m（m＝1,2,3,…,…）时,态。总是恒处于N－Y最小测不准态;②当压缩阶数N＝2p且p＝2m＋1（m＝0,1,2,3,…,…）时,如果各模的初始相位,态间的初始相位差以及各单模相干态光场的平均光子数之总和等满足一定的量子化条件,则态可呈现出周期性变化的、任意阶的N次方Y压缩效应;③当压缩阶数N＝2P＇＋1时,无论p＇＝2m（m＝0,1,2,…,…）还是p＇＝2m＋1（m＝0,1,2,3,…,……）,只要各模的初始相位满足一定的量子条件,则当两态叠加几率幅满足时,态就恒处于N－Y测不准态,始终不呈现N－Y最小测不准态和N次方Y压缩;而当时,态始终不呈现N－Y测不准态、N－Y最小测不准态和N次方Y压缩效应．     

Reduction of delayed optimal control problems to nondelayed problems

A method is exhibited which transforms a large class of optimal control problems with fixed delays to nondelayed problems, thus permitting classical results to be used in their analysis.     

Remarks on lower semicontinuity and lower closure

In the context of a recent geometric condition of Cesari, used in the reduction of seminormality requirements in lower closure theorems, this paper shows that the existence of a strongly convergent selection from the sequence of orientor fields, under Kuratowski property (K), is adequate to guarantee lower closure theorems. This generalization is justified through examples. Several related remarks are made.This work was done in the framework of Research Project AFOSR-71-2122 at the University of Michigan, Ann Arbor, Michigan. The author wishes to thank Professor L. Cesari for helpful discussions during the writing of this paper.     

Using Fractal Function Auto correlative Method to Confirm Fractal Dimension of Function Graph

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Injection seeding for single-mode operation in an optically pumped high-power D2O laser

Spectrally narrow, pulsed outputs consisting of almost a single mode have been obtained from an optically-pumped high-power (200kW) D₂O laser by adopting the injection seeding method, where single-mode radiation (seed pulse) from a low-power, compact D₂O laser has been injected into the main D₂O laser. Spectrally narrow outputs with high power having spectral widths as narrow as 5 MHz have been obtained, when the seed pulses with frequency tuned to one longitudinal mode of the main D₂O laser have been injected at a time sufficiently before the lasing of the main laser took place. The experimental results have been compared with those of numerical simulation modified to include the injection field with varying injection times.     

Convex duality for finite-fuel problems in singular stochastic control

Upon introducing a finite-fuel constraint in a stochastic control system, the convex duality formulation can be set up to represent the original singular control problem as a minimization problem over the space of vector measures at each level of available fuel. This minimization problem is imbedded tightly into a related weak problem, which is actually a mathematical programming problem over a convex,w*-compact space of vector-valued Radon measures. Then, through the Fenchel duality principle, the dual for the finite-fuel control problems is to seek the maximum of smooth subsolutions to a dynamic programming variational inequality. The approach is basically in the spirit of Fleming and Vermes, and the results of this paper extend those of Vinter and Lewis in deterministic control problems to the finite-fuel problems in singular stochastic control. Meanwhile, we also obtain the characterization of the value function as a solution to the dynamic programming variational inequality in the sense of the Schwartz distribution.The author is much indebted to Professor Wendell H. Fleming for his constant support and many helpful discussions during the preparation of this paper.