2003年, 第16卷, 第1期　刊出日期：2003-01-15

  

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  A FRAMEWORK OF FUZZY LANDSCAOE THEORY WITH AN APPLICATION TO ALLIANCE ANALYSIS

  S.Suganuma;V.N.Huynh;Y.Nakamori;S.Y.Wang;K.K.Lai

  Journal of Systems Science and Complexity. 2003, 16(1): 1-012.

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  In this paper, we provide a framework of fuzzy landscape theory and discuss an application to alliance analysis. The fuzzy landscape theory may allow us to analyses a variety of aggregation processes in political, economic, and social problems in a more flexible manner. The simulation results for the problems of the international alignment of the Second World War in Europe and the coalition formation in standard-setting alliances in the case of the UNIX operating system are compared with those given by the original theory.
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  ON A PROBLEM RELATED TO GOLOMB'S CONJECTURES

  Wen Peng ZHANG

  Journal of Systems Science and Complexity. 2003, 16(1): 13-018.

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  The main purpose of this paper is to study a problem related to Golomb's conjectures, and give an interesting asymptotic formula.
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  THE EQUILIBRIA OF THE SIZE STRUCTURED POPULATION MODEL

  Hai Yuan HUANG;Lai Fu LIU

  Journal of Systems Science and Complexity. 2003, 16(1): 19-029.

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  In this paper the existence and stability of the positive equilibrium of the size-structured population model are proved by Rabinowitz's theorem and the local linearization method. The result here shows that near the bifurcating point where a branch of positive equilibria appears, the stability of the positive equilibrium on the branch is dependent on the direction of the bifurcation. The argument for the model of age-structured population is generalized in this paper.
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  THE MODIFIED METHOD OF CHARACTERISTICS WITH FINITE ELEMENT OPERATOR-SPLITTING PROCEDURES FOR COMPRESSIBLE MULTICOMPONENT DISPLACEMENT PROBLEM

  YUAN Yirang

  Journal of Systems Science and Complexity. 2003, 16(1): 30-045.

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  For the three-dimensional compressible multicompouent displacement problem we put forward the modified method of characteristics with finite element operator-splitting procedures and make use of operator-splitting, characteristic method, calculus of variations, energy method, negative norm estimate, two kinds of test functions and the theory of prior estimates and techniques. Optimal order estimates in L~2 norm are derived for the error in the approximate solution. These methods have been successfully used in oil-gas resources estimation, enhanced oil recovery simulation and seawater intrusion numerical simulation.
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  LOCAL STABILITY AND BIFURCATION IN A THREE-UNIT DELAYED NEURAL NETWORK

  Yi Ping LIN;Ji Bin LI;Xiao Hua ZHAO

  Journal of Systems Science and Complexity. 2003, 16(1): 46-052.

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  A system of three-unit networks with coupled cells is investigated.The general formula for bifurcation direction of Hopf bifurcation is calculated and the estimate formula of period of the periodic solution is given.
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  OPTIMAL CONTROL OF GROWTH RATE FOR A CLASS OF POPULATION SYSTEMS

  Zhou Qun WU;Jing Xue YIN;Hang GAO

  Journal of Systems Science and Complexity. 2003, 16(1): 53-066.

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  In this paper, we discuss the optimal control of growth rate for a class of population systems governed by nonlinear degenerate parabolic equations. Given an appropriate cost functional, we prove the existence of the optimal growth rate and give some necessary conditions for optimal growth rate.
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  DECOMPOSITION OF MATRICES INTO COMMUTATORS OF REFLECTIONS

  Hong YOU

  Journal of Systems Science and Complexity. 2003, 16(1): 67-073.

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  <正> Let F be a field and let resA = rank(A - I) for any A in GLnF. We prove that every matrix in SLnF is a product of at most [resA/2] + 2 commutators of reflections for n > 2 except for n = 2 and F = F2.
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  THE MARCINKIEWICZ-ZYGMUND INEQUALITY IN B_α SPACES(I)

  Bao Huai SHENG;San Yang LIU;Guang Rong CHEN

  Journal of Systems Science and Complexity. 2003, 16(1): 74-084.

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  The Marcinkiewicz-Zygmund inequality with derivative for an algebraic polynomial of order ≤ N = (q + 1)n 1 is established in a B_a space. As a corollary, the Marcinkiewicz-Zygmund inequality with derivative for an algebraic polynomial in a particular Orlicz space is obtained.
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  A DYNAMIC OPTIMAL ADVERTISING MODEL FOR NEW PRODUCTS

  Rong DU;Qi Ying HU

  Journal of Systems Science and Complexity. 2003, 16(1): 85-094.

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  Many dynamic optimal control models for advertising make efforts to solve the problem of determining optimal advertising expenditures and other variables of interest; over time for a firm or several competing firms. However, after analyzing the extant literature, one can find that few dynamic optimal advertising models available consider the problem within the product diffusion framework. Furthermore, the established models involving product disillusion are inspired by the Bass model, which has been out of date. This paper poses a dynamic optimal advertising model for new products, which considers the product diffusion based on the relative newly developed generalized version of the Bass model. In this paper, the optimal control model is used to derive the optimal advertising expenditure policy, which gives some implications to advertising practice.
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  A CRITERION FOR DISCRETE SPECTRUM OF A CLASS OF DIFFERENTIAL OPERATORS

  Guang Sheng WEI

  Journal of Systems Science and Complexity. 2003, 16(1): 95-100.

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  In this paper, a sufficient and necessary condition is obtained to ensure that the spectrum of a class of 2n-order weighted differential operators is discrete. The proof is based on the method of certain weighted Sobolev spaces to be compactly embedded in weighted L~2(R).
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  IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT METHODS FOR THE SEMICONDUCTOR DEVICE PROBLEM

  Wei CHEN

  Journal of Systems Science and Complexity. 2003, 16(1): 101-113.

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  The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by the finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The optimal L~2-norm error estimates are derived.
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  PERMANENCE AND PERIODIC SOLUTION IN AN INTEGRODIFFERENTIAL SYSTEM WITH DISCRETE DIFFUSION

  Yan Ni XIAO;Lan Sun CHEN;San Yi TANG

  Journal of Systems Science and Complexity. 2003, 16(1): 114-121.

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  Dynamical characteristics of an iiitegrodLITerential modelling competitive system with diffusion, are investigated. In particular, we derive sufficient conditions for the permanence of species, existence of an attracting periodic solution to the periodic system. The results of Wang Ke in 1994 and 1998 are improved and extended.
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  PACKING A TREE OF ORDER p WITH A (p,p+1)-GRAPH

  Min WANG;Guo Jun LI

  Journal of Systems Science and Complexity. 2003, 16(1): 122-132.

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  Let G_1 and G_2 be two graphs of the same order. If G_1 is isomorphic to a spanning subgraph of the complement of G_2, then we say that G_1 and G_2 are packable. A graph G is called a (p, m)-graph if G has p vertices and m edges. The main purpose of this paper is to present a necessary and sufficient condition for a tree of order p and a (p,p + l)-graph to be packable.
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  ON THE INVARIANT FOR A FAMILY OF DEFORMED HALLEY METHODS

  Zheng Da HUANG;Shi Ming ZHANG

  Journal of Systems Science and Complexity. 2003, 16(1): 133-144.

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  In this paper, an invariant determined by a function used to guarantee the convergence of all members with l ≤ k in the family of deformed Halley iterative methods for solving nonlinear equation in complex field is given. Results include some known ones as this special cases. We get not only the error estimates of the iterative sequences {z_(n,l)} but also those of f(z_(n,l)) for all l ≤ k.