Approximate Solution of Optimization Problems for Infinite-Dimensional Singular Systems

An optimal control problem is considered for a system described by a singular equation of parabolic type. The study bases on a special regularization method. We establish existence of a solution to the regularized problem, as well as the corresponding necessary optimality conditions. The results enable us to find an approximate solution to the original problem even in the absence of solvability.     

Constructive method for solving a linear minimax problem of optimal control

In this paper, we propose a constructive method for solving a linear minimax problem of optimal control. Following the Gabasov-Kirillova approach, we introduce the concept of so-called support control. After establishing an optimality criterion for the support control, we describe a scheme for reducing the initial infinite-dimensional problem to a finite-dimensional one, which can be solved numerically by the methods of linear programming. At the end, we give an illustrative example.     

Regeneration and renovation in queues

Regenerative events for different queueing models are considered. The aim of this paper is to construct these events for continuous-time processes if they are given for the corresponding discrete-time model. The construction uses so-called renovative events revealing the property of the state at timen of the discrete-time model to be independent (in an algebraic sense) of the states referring to epochs not later thann −L (whereL is some constant) given that there are some restrictions on the “governing sequence”. Different types of multi-server and multi-phase queues are considered.     

QSBR Study on the Anaerobic Biodegradation of Chlorophenols

1 INTRODUCTION Chlorophenols (CPs) have been widely applied in such industries[1] as wood preservative, antitrust, bactericide and herbicide since 1930s. Due to the existence of phenol ring structure and chloro-atom, chlorophenols have strong toxicity and high anti- degradation ability. Previous reports show that[2, 3] chlorophenols are difficult to oxidize under aerobic condition, whereas anaerobic biological treatment can effectively reduce the toxicity towards microor- ganism so as to …     

ON THE OPTIMAL POLICY FOR COMBINING HARVESTING OF PREDATOR AND PREY

An optimal policy is sought for maximizing present value from the combined harvest of two ecologically dependent species, which would coexist as predator and prey in the absence of harvesting. Harvest rate for each species is assumed proportional to both stock level and effort. For a large class of biological productivity functions, it is established that the optimal equilibrium point in the phase-plane of stock levels must be a saddle-point. For quadratic productivity functions, a combination of analytical reasoning and numerical experiment is used to show that first and second order necessary conditions for optimality are satisfied by a unique approach to equilibrium, which must therefore be optimal. The corresponding control law is given, and an apparent suggestion of two previous authors concerning the policy is shown to be inappropriate. The optimal policy enables an estimate to be made of the true loss of resource value due to a catastrophic fall in stock level.     

Remarks on a theorem of Burkholder and Gundy

Let (Y _n) be a sequence of i.i.d. random variables with zero mean such thatP(Y ₁0)>0. Consider the random walkS _n=Y₁+...+Y_n and an a.s. finite stopping time with respect to the -fieldsF _n=(Y₁,..., Y_n). In this paper we present a number of remarks on a theorem of Burkholder and Gundy concerning an estimate involvingE(sup _n1|Svn|^p).Dedicated to the memory of Professor József Mogyoródi.     

拟齐次核的 Hilbert 型重积分不等式最佳搭配参数的等价条件及应用*

利用权函数方法, 讨论拟齐次核Hilbert型重积分不等式的最佳搭配参数,得到最佳搭配参数的若干等价条件及不等式最佳常数因子的表达公式. 最后讨论其在奇异积分算子理论中的应用.     

双对称矩阵逆特征值问题解存在的条件

1．引言逆特征值问题在工程中应用广泛，例如逆特征值方法是飞行器设计中的振动设计和振动林制的有力下具．关干研特征相问领的研守己有一ngfRtr的结里【1］．f21．［31分另11就对称拉肚类和一般矩阵类进行了研究，双对称阵在土木工程和振动工程中有实际应用，但其逆特征值问题尚未研究，本文将讨论这个问题．用R"""表示所有nx。阶实矩阵集合，R7""表示其中秩为r的子集；11·1是矩阵的Frobenius范数；A十表示矩阵A的Moors-Penrose广义逆；OR"""表不所有n阶正交阵全体；人表示k阶单位阵；＊＊"""表示n阶实对称阵的全体；战一（ek，ek－1…     

Ordinal algorithms for packing with target center of gravity

The problem of arranging N unit length weights on a line segment of length N, given a target center of gravity on this line segment, is examined under the assumption that the only information we have about the weights is their order, i.e., a ₁ a ₂ ... a _N . Lower bounds on worst case performance of algorithms for this problem are developed, and algorithms (permutations) which come close to achieving these bounds are provided.This work was partially supported under Natural Sciences and Engineering Research Council (NSERC) of Canada research grant number OGP0002507.     

Endogenous cycles with small discounting in multisector optimal growth models: Continuous-time case

This paper discusses the role of the trade-off between the level of discounting and the curvature of preferences and technology in establishing the existence of endogenous cycles. Using the equivalence between the Euler-Lagrange equations and a modified Hamiltonian dynamic system, in a general continuous-time multisector optimal growth model, it is proved that, if the indirect utility function is weakly concave (i.e., concave-, with >0 arbitrarily close to 0), then the discount rate values compatible with endogenous fluctuations are arbitrarily low. We show by numerical simulations that our result explains and generalizes to the multisector case the recent contribution of Benhabib and Rustichini in this field.The author would like to thank P. Cartigny, J. M. Grandmont, P. Michel, and L. Montrucchio for helpful discussions which greatly improved the exposition of the paper. He is also indebted to G. Sorger for a fruitful discussion which clarified some recent contributions. The paper also benefited from comments received during a presentation at the Meeting of the Society for Economic Dynamics and Control, University of California, Los Angeles, California, 1994.