逆（反）对策问题与“奇门遁甲”预测理论（术）

本文首先提出逆（反）对策这一新问题，给出了数学模型；探讨了“奇门遁甲”预测理论（术）中的数学问题；通过系统分析“专门遁甲”预测过程，可知它的预测过程隐含着一个特殊的逆（反）对策问题；最后指出逆（反）对策问题的广泛存在并给出案例分析．     

Control Policy for a Manufacturing System with Random Yield and Rework

We develop a production policy that controls work-in-process (WIP) levels and satisfies demand in a multistage manufacturing system with significant uncertainty in yield, rework, and demand. The problem addressed in this paper is more general than those in the literature in three aspects: (i) multiple products are processed at multiple workstations, and the capacity of each workstation is limited and shared by multiple operations; (ii) the behavior of a production policy is investigated over an infinite-time horizon, and thus the system stability can be evaluated; (iii) the representation of yield and rework uncertainty is generalized. Generalizing both the system structure and the nature of uncertainty requires a new mathematical development in the theory of infinite-horizon stochastic dynamic programming. The theoretical contributions of this paper are the existence proofs of the optimal stationary control for a stochastic dynamic programming problem and the finite covariances of WIP and production levels under the general expression of uncertainty. We develop a simple and explicit sufficient condition that guarantees the existence of both the optimal stationary control and the system stability. We describe how a production policy can be constructed for the manufacturing system based on the propositions derived.     

Field optimized initial state based control of photodissociation

A new scheme for controlling photodissociation through preparation of a variationally optimized linear superposition of field free vibrational eigenstates is applied for selective control of IBr and HI dissociation. The dependence of photodissociation on various field parameters and initial conditions is examined to investigate the mechanistic basis of selective control. The parametric equations of motion approach for determining vibrational dynamics as a function of field parameters without having to solve the time dependent Schrödinger equation explicitly for each field parameter separately is outlined and its use to identify field characteristics which will provide the requisite population mix represented by the optimal linear superposition of vibrational states is advocated.     

Application of stochastic optimal control to the suboptimal design of thrust-mass profiles

Stochastic optimal control techniques are applied to compare the performance of identical medium-range air-to-air missiles which have different thrust-mass profiles. The measure of the performance is the probability of reaching a lock-on-point with a favorable range of guidance and flight parameters, during a fixed time interval [0,t _f ], given that, during the flight, the trajectories of the missile are subjected to a variety of constraints including dynamic pressure constraints.     

Optimal algebraic multilevel preconditioning for local refinement along a line

The application of some recently proposed algebraic multilevel methods for the solution of two-dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.     

拟线性椭圆变分不等式的障碍最优控制问题

对拟线性椭圆变分不等式的障碍最优控制问题(即以障碍为控制变量)进行了研究．指标泛函为Lagrange型,其中含有控制变量二阶导数的p次幂,这使得最优性条件的推导颇为不易．对所考虑的问题给出了最优控制的存在性定理以及必要条件．     

Long-term optimal operation of series parallel reservoirs for critical period with specified monthly generation and average monthly storage

We present in this paper an efficient approach for solving the problem of planning the long-term (multiyear) operation of a multireservoir hydroelectric power system for the critical period with a monthly variable load. This load is equal to a certain percentage of the total generation at the end of the year, subject to satisfying a number of constraints on the hydrosystem, using the minimum norm formulation.The proposed method is efficient in computing time and in calculating the total expected benefits from the system during the critical period. Numerical results are reported for a real system in operation consisting of two rivers. Each river has two series reservoirs.This work was supported by the Natural Science and Engineering Research Council of Canada, Grant No. A4146.     

On Characterizations of Proper Efficiency for Nonconvex Multiobjective Optimization

In this paper, nonconvex multiobjective optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one scalar optimization problem and the existence of an exact penalty function of a scalar constrained program, respectively. One of the characterizations is applied to derive necessary conditions for a properly efficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints.     

A new method for constructing infinite families of k-tight optimal double loop networks

The double loop network (DLN) is a circulant digraph with n nodes and outdegree 2. DLN has been widely used in the designing of local area networks and distributed systems. In this paper, a new method for constructing infinite families of k-tight optimal DLN is presented. For k = 0,1,…,40, the infinite families of k-tight optimal DLN can be constructed by the new method, where the number nk(t,a) of their nodes is a polynomial of degree 2 in t and contains a parameter a. And a conjecture is proposed.     

An implicit method for linear ill‐posed problems with perturbed operators

An implicit iterative method is applied to solving linear ill‐posed problems with perturbed operators. It is proved that the optimal convergence rate can be obtained after choosing suitable number of iterations. A generalized Morozov's discrepancy principle is proposed for the problems, and then the optimal convergence rate can also be obtained by an a posteriori strategy. The convergence results show that the algorithm is a robust regularization method. Copyright © 2006 John Wiley & Sons, Ltd.