1998年, 第11卷, 第4期　刊出日期：1998-10-15

  

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  A NEIGHBORHOOD UNION CONDITION FOR PANCYCLIC GRAPHS

  LI Xiangwen;WEI Bing

  Journal of Systems Science and Complexity. 1998, 11(4): 289-298.

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  Let C be a 2-connected graph on n\geq 31 venices. G is called pancyclic if itcontains a cycle of length for every l such that 3\leq l \leq n. In this paper we shall prove that if |N(u)\cup N(v)| \geq (2n - 3)/3 for any nonadjacent pair u,v \in V(G), then G is pancyclic.
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  GLOBALLY TOPOLOGICAL EQUIVALENCE OF NONAUTONOMOUS SYSTEMS

  CHEN Mingwei;ZHENG Zuohuan

  Journal of Systems Science and Complexity. 1998, 11(4): 299-304.

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  The definition of the globally topological equivalence of nonautonomous systems is introduced, and some sufficiency theorems about the globally topological equivalence of two systems are given.
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  THE IRREGULAR OBLIQUE DERIVATIVE PROBLEM FOR NONLINEAR ELLIPTIC SYSTEMS OF SECOND ORDER

  WEN Guochun;ZHAO Chun

  Journal of Systems Science and Complexity. 1998, 11(4): 305-313.

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  This paper deals with the irregular oblique derivative boundary value problemfor nonlinear elliptic systems of second order equations in multiply connected domains.Firstly the well-posedness of the irregUlar oblique derivative problem and an a priori estimate of solutions for the modified boundary value problem are given, afterwards the existence of solutions for the modified boundary value problem is proved by using theabove estimates of solutions and the Schauder fixed-point theorem. Finally the solvability conditions of the original boundary value problem can be derived.
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  LONG DOMINATING CYCLES IN GRAPHS

  SUN Zhiren

  Journal of Systems Science and Complexity. 1998, 11(4): 314-320.

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  Let G be a connected graph of order n, and NC2(G) denote min{|N(u)\cup (v) |: dist(u,v) = 2}, where dist(u,v) is the distance between u and v in G. A cycle C in Gis called a dominatiny cycle, if V(G)\V(C) is an independent set in G. In this paper, weprove that if G contains a domillating cycle and 2, then G contains a dominating cycleof length at least min{n, 2NC2(G) - 2}, which proves partially a conjecture of R. Shenand F. Tian. And we give a class of graphs that show the result is sharp.
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  A NEW METHOD FOR FINDING MAJOR EFFICIENT SOLUTIONS AND MAJOR OPTIMAL SOLUTIONS OF DISCRETE MULTIOBJECTIVE PROGRAMMING

  CHEN Zhanfeng;XU Duan

  Journal of Systems Science and Complexity. 1998, 11(4): 321-326.

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  Major efficiency is an efficiency theory of multiobjective programming, whichis based on the law of majority. For the case that the feasible region is a finite set, paper [3] gave a comparison-number method for finding major efficient solutions and major optimalsolutions.This paper represents a new method to solve the same problem. The new method isbased on a concept of efficient equivalence point set. We give the definition of efficient equivalence point set, discuss the relationship between it and major efficiency, and present a new approach to find major efficient (optimal) solutions.
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  CONTINUOUS-TIME KIEFER-WOLFOWITZ ALGORITHM WITH RANDOMIZED DIFFERENCES

  CHEN Hanfu;WANG Qian

  Journal of Systems Science and Complexity. 1998, 11(4): 327-341.

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  A continuous-time Kiefer-Wolfowitz algorithm with randomized differences andwith truncations at randomly varying bounds is proposed. It is shown that the algorithmconverges to the desired value almost surely under mild conditions. The rate of convergenceand the asymptotic normality of the algorithm are also established.
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  EFFECTS OF TOXICANTS ON CHEMTAT MODEL WITH TIME VARIABLE NUTRIENT INPUT AND WASHOUT

  MA Zhien;GUO Sangang;P. Fergola;C. Tenneriello

  Journal of Systems Science and Complexity. 1998, 11(4): 342-350.

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  The influence of toxicants on the competition of n populations for time variable nutriellt input rate and time variable washout rate in a chemostat model is investigated. After proving some qualitative properties of the solutions, the threshold between persistence and extinction of the populations has been obtained.
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  A VARIATION OF GOLDFARB'S METHOD FOR LINEARLY CONSTRAINED OPTIMIZATION PROBLEMS AND ITS SUPERLINEAR CONVERGENCE RATE

  SHI Zhenjun;ZHANG Yuzhong;LI Qun

  Journal of Systems Science and Complexity. 1998, 11(4): 351-358.

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  This paper presents a variant algorithm of Goldfarb's method for linearly constrained optimization problems. In the variant algorithm, we introduce a concept called conjugate projection, which differs from orthogonal projection. The variant algorithm has global convergence, superlinear convergence rate.
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  SENSITIVITY ANALYSIS IN BILEVEL LINEAR PROGRAMMING

  JIA Fuchen;YANG Fengmei;WANG Shouyang

  Journal of Systems Science and Complexity. 1998, 11(4): 359-366.

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  In this paper, we study sensitivity analysis of bilevel linear programming. Twocases of the leader's objective function and the right-hand side of the constraints including parameters are discussed separately. We presellt a necessary and sufficient optimality condition for an optimal solution to a bilevel linear programming problem and its equivalent expression in nonconvex quadratic programming. The necessary and sufficient conditionsare proposed to guarantee that the current optimal solution or the corresponding basis remains optimal when the parameters vary. An algorithm is also proposed to determinethe set of the parameters which leaves the current optimal solution optimal or -optimal.
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  INVENTORY ANALYSIS OF AN UNRELIABLE PRODUCTION-INVENTORY SYSTEM

  LIU Bin;CAO Jinhu

  Journal of Systems Science and Complexity. 1998, 11(4): 367-374.

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  This paper deals with a production-inventory system in which there are amachine consisting of multiple unreliable units and a storage facility of fixed capacity. Theproduct produced is stored in the storage facility. The demand process for product is acompound Poisson process. We assume that the demand-size distributions are arbitrary, and the unsatisfied demand is backlogged rather than lost. Our main results are to provean existence theorem on stationary distribution of the slack capacity and to derive an expression of its stationary distribution function.
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  A NONMONOTONE TRUST REGION TECHNIQUE FOR UNCONSTRAINED OPTIMIZAfION PROBLEMS

  ZHU Detong

  Journal of Systems Science and Complexity. 1998, 11(4): 375-382.

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  Trust region methods with nonmonotone technique for unconstrained opti-mization problems are presented and analyzed. The convergence results are demonstratedfor the proposed algorithms even if the conditions are mild.