1994年, 第7卷, 第4期　刊出日期：1994-10-15

  

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  AN EXISTENCE THEOREM FOR RADIAL POSITIVE SOLUTIONS OF NONLINEAR DEGENERATE ELLIPTIC EQUATIONS

  LIU Hailiang

  Journal of Systems Science and Complexity. 1994, 7(4): 289-292.

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  We study the existence of positive solutions of nonlinear degenerate elliptic equations with the aid of phase-energy method. The equivalent conditions are given for the existence of positive solutions in an n-ball and in a 1-ball.
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  ON TESTS FOR LOCAL EXTREMUM POINTS IN PROJECTION PURSUIT

  ZHANG Jian;LI Guoying

  Journal of Systems Science and Complexity. 1994, 7(4): 293-301.

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  The local extremum points in the projection pursuit(PP) have played an important role. Many interesting structures are directly related to the local extremum poillts in the PP procedures. Hence, it is very helpful to give some suitable statistical tests to separate the local extremum points from noise. In this paper, a procedure is proposed for constructing tests for the local extremum points of any object function. The asymptotics of these tests are also developed.
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  CRITICAL BIRTH ORDER RATIO CONTROL AND ATTAINABLE SET OF A DISCRETE AGE-DEPENDENT PARITY PSOGRESSION POPULATION SYSTEM

  GUO Baozhu

  Journal of Systems Science and Complexity. 1994, 7(4): 302-311.

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  A colltrolled age-structured difference equation model of population dynamics based on parity progression is discussed. The distribution of the control strategies which guarantee the population to approach a stable state is obtained, and the attainable set at any time of this system is found. Finally, the maximum principle for an optimal control problem with quadratic index is also obtained.
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  SIGN-REVERSAL PROPERTY FOR F-MATRICES AND N-MATRICES

  XU Song

  Journal of Systems Science and Complexity. 1994, 7(4): 312-316.

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  We show that N-matrices and F-matrices introduced by Ky Fan can be characterized in terms of the sign-reversal property. As an application, we obtain a characterization for N-matrices using the linear complementarity problem.
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  SOME NEW CONSTRUCTIONS OF CARTESIAN AUTHENTICATION CODES FROM SYMPLECTIC GEOMETRY

  YOU Hong;GAO You

  Journal of Systems Science and Complexity. 1994, 7(4): 317-327.

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  Two new constructions of Cartesian authentication codes from symplectic geometry are presented and their size parameters are computed.
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  AN EFFICINT IMPLEMENTATION OF MERRILL'S METHOD

  YANG Bing

  Journal of Systems Science and Complexity. 1994, 7(4): 328-336.

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  In this paper a piecewise-linear hometopy algorithm is proposed. The algorithm belongs to the category of Merrill's method. It also may be regarded as a variety of exterior point SUMT. It can be convergent in a finite number of pivoting steps under a nondegeneracy assumption for convex quadratic programming. Some computational results are given to prove that the algorithm is efficient and practical.
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  PERSISTENCE IN A THREE SPECIES LOTKA-VOLTERRA PERIODIC PREDATOR-PREY SYSTEM

  CHEN Lansun;PENG Qiuliang

  Journal of Systems Science and Complexity. 1994, 7(4): 337-343.

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  In this paper we consider the Predator-Prey model for three species in which the right-hand sides are periodic in time. A set of easily verifiable sufficient conditions is obtained for the existence of a globally asymptotically stable positive periodic solution.These conditions also assure that the Predator-Prey system is uniformly persistent. After giving two examples we also introduce a method to determine the upper and lower bounds for the components of the periodic solution.
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  SOME PERFORMANCE MEASURES OF REPAIRABLE TRANSFER LINE WITH GENERAL DISTRIBUTIONS

  LI Wei;CAO Jinhua

  Journal of Systems Science and Complexity. 1994, 7(4): 344-351.

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  In this paper, we consider a transfer line with two unreliable machines and a single storage buffer, in which the second machine's processing time and repair time have general distributions. The compact results of production rate, blocked probability and starved probability are obtained.
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  ROW-ACTION METHODS FOR CONVEX QUADRATIC PROGRAMMING

  GUO Tiande;WU Shiquan

  Journal of Systems Science and Complexity. 1994, 7(4): 352-361.

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  This paper gives new algorithms for convex quadratic programming and linear programming. The algorithms mainly deal with nonconstrained maximization problems with simple concave objective functions. The sparsity of the original problem can be preserved completely.
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  NONSMOOTH MULTIOBJECTIVE PROGRAMMING

  WANG Liancheng;DONG Jiali;LIU Qinghuai

  Journal of Systems Science and Complexity. 1994, 7(4): 362-366.

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  This paper considers the following nonsmooth multiobjective progrmming problem: (P) Weak min f(x) = (f1(x),…, fp(x)),s.t.- g(x) ∈ S, h(x) = 0, where x ∈ R^n, f(x) ∈ R^p, g(x) ∈ R^m, h(x) ∈ R', S\subset R^m is a closed convex cone with interior, and f, g, h satisfy the local Lipschitz condition. The necessary Lagrangian condition is established for a weak minimum of (P), and the proof is different from the proofs given by B.D.Craven, Ying Meiqian and other authors. Necessary conditions of Kuhn-Tucker type are obtained and sufficient conditions are discussed.
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  NONLINEAR FEEDFORWARD SEQUENCES OF m-SEQUENCES (Ⅲ)

  DAI Zongduo;FENG Xuning;LIU Mulan;WAN Zhexian

  Journal of Systems Science and Complexity. 1994, 7(4): 367-370.

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  In this paper, the congruence of feedforward monomial functions is defined, the sufficient and necessary condition on the congruence of non-degenerate monomials is given, and the number of non-equivalent non-degenerate monomials congruent to each others is shown.
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  EXTREME POINT RESULTS FOR STRICT POSITIVE REALNESS OF TRANSFER FUNCTION FAMILIES

  WANG Long;HUANG Lin

  Journal of Systems Science and Complexity. 1994, 7(4): 371-378.

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  Several classical results in systems and control field rely on strict positive realness of suitable transfer functions. Absolute stability of nonlinear systems and convergence analysis of adaptive schemes are typical areas where strict positive realness is a key property. In this paper, invariance of this property for families of perturbed transfer functions is studied. Extreme point results are obtained for strict positive realness of polytopic family, multilinear family, and cascade interval family, etc. The concept of critical venices proves to be an important tool to deal with the robustness of control systems with structured uncertainties.
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  ON THE ISOMORPHISMS OF SMOOTH ALGEBRAIC CURVES (Ⅰ)

  DU Hong

  Journal of Systems Science and Complexity. 1994, 7(4): 379-384.

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  In this paper, I have considered some problems of algebraic curves in some constructive way, especially, I give an algorithm for determining whether two given smooth plane curves are isomorphic and finding all isomorphic maps. I also have given a survey of some miscellaneous results related to the classification of curves. It is clear our method in this paper can be generalized to smooth projective complete intersection varieties.