凹面光栅型波长解复用器的标量波动分析

利用标量波动衍射理论，通过对光栅槽面的数值积分，计算了罗兰圆型集成二维凹面光栅像点的光强分布。给出了光线追变法难以得到的光栅槽面沿光栅圆不同方位刻划所引起的成像点对于光栅方程计算位置的偏离；在对色散和分辩力的分析上，获得了与光线追迹法很好的一致性；分析了光栅的槽面波、光源的模场宽度以及因工艺产生的槽面圆角对光栅成像的影响；最后给出了光栅的波像差和光线像差的计算。     

A parallel algorithm for constrained concave quadratic global minimization

The global minimization of large-scale concave quadratic problems over a bounded polyhedral set using a parallel branch and bound approach is considered. The objective function consists of both a concave part (nonlinear variables) and a strictly linear part, which are coupled by the linear constraints. These large-scale problems are characterized by having the number of linear variables much greater than the number of nonlinear variables. A linear underestimating function to the concave part of the objective is easily constructed and minimized over the feasible domain to get both upper and lower bounds on the global minimum function value. At each minor iteration of the algorithm, the feasible domain is divided into subregions and linear underestimating problems over each subregion are solved in parallel. Branch and bound techniques can then be used to eliminate parts of the feasible domain from consideration and improve the upper and lower bounds. It is shown that the algorithm guarantees that a solution is obtained to within any specified tolerance in a finite number of steps. Computational results are presented for problems with 25 and 50 nonlinear variables and up to 400 linear variables. These results were obtained on a four processor CRAY2 using both sequential and parallel implementations of the algorithm. The average parallel solution time was approximately 15 seconds for problems with 400 linear variables and a relative tolerance of 0.001. For a relative tolerance of 0.1, the average computation time appears to increase only linearly with the number of linear variables.     

The Minimum Concave Cost Network Flow Problem with fixed numbers of sources and nonlinear arc costs

We prove that the Minimum Concave Cost Network Flow Problem with fixed numbers of sources and nonlinear arc costs can be solved by an algorithm requiring a number of elementary operations and a number of evaluations of the nonlinear cost functions which are both bounded by polynomials inr, n, m, wherer is the number of nodes,n is the number of arcs andm the number of sinks in the network.On leave from Institute of Mathematics, P.O. Box 631, Bo Ho, Hanoi, Vietnam.     

Some Classes of Life Distributions Characterized by Concave Ordering

1.IntroductionandDefintionsInreliabilitytheory,maintenancetheory,biometricsandeconometrics,variousclassesoflifedistributionsbasedondifferentconceptsofagingareveryuseful.Recently,anumberofclassesoflifedistributionshavebeenintroducedbymeansofdifferentapproachestocharacterizingagingproperty.Oneoftheseapproachesisbasedonthefactthatmanyclassesoflifedistributionmaybecharacterizedbyvariousstochasticorderings,see,e.g.[if.[2],[3]and[4],etc.LetFbethedistributionfunctionofanon-negativerandomvariableXre…     

Smooth representation of a parametric polyhedral convex set with application to sensitivity in optimization

We show in this paper that if a polyhedral convex set is defined by a parametric linear system with smooth entries, then it possesses local smooth representation almost everywhere. This result is then applied to study the differentiability of the solutions and the marginal functions of several classes of parametric optimization problems.

     

凹角型区域椭圆边值问题的自然边界归化

In this paper, the natural boundary reduction for some elliptic boundary value problems with concave angle domains and their natural boundary methods are investigated. The natural integral equations and the Poisson integral formulae are given. The finite element methods of the natural integral equations are discussed in details. The convergences of the approximate solutions and their error estimates are obtained. Finally, some numerical examples are presented to show that our methods are effective.     

Algorithms for optimization problems with exclusion constraints

This paper proposes algorithms for minimizing a continuously differentiable functionf(x): ⁿ subject to the constraint thatx does not lie in specified bounded subsets of ⁿ . Such problems arise in a variety of applications, such as tolerance design of electronic circuits and obstacle avoidance in the selection of trajectories for robot arms. Such constraints have the form . The function is not continuously differentiable. Algorithms based on the use of generalized gradients have considerable disadvantages because of the local concavity of at points where the set {j|g ^j (x)=(x)} has more than one element. Algorithms which avoid these disadvantrages are presented, and their convergence is established.This research was sponsored in part by the National Science Foundation under Grant ECS-81-21149, the Air Force Office of Scientific Research (AFSC), United States Air Force under Contract F49620-79-C-0178, the Office of Naval Research under Grant N00014-83-K-0602, the Air Force Office of Scientific Research under Grant AFOSR-83-0361, and the Semiconductor Research Consortium under Grant SRC-82-11-008.     

Linear system model for planar concave grating demultiplexer

A linear system model for planar concave grating demultiplexer is developed based on the scalar diffraction theory. With this model the system can be simulated by using Fourier transform. Many device performances such as dispersion features, N × N interconnection, channel uniformity, insertion loss, crosstalk can be estimated or optimized. Furthermore, the behavior of aberration is included in the generalized model.