1996年, 第9卷, 第2期　刊出日期：1996-04-15

  

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  GEOMETRIC PROPERTIES OF A CLASS OF CUBICSYSTEM WITH AN INVARIANT LINE

  ZHANG Xingan;LIANG Zhaojun

  Journal of Systems Science and Complexity. 1996, 9(2): 97-100.

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  This paper has obtained that the cubic system ...(1) is topologically equivalent to the general quadratic system. By the use of this property, wecan derive the conditions of a unique limit cycle and the necessary and sufficient conditionsof a centre for the cubic Kolmogorov model (2)...
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  THE OPTIMUM SELECTION FOR A CONTINUOUSTYPE EUCLIDEAN MULTIFACILITY LOCATION

  GAO Chengyun

  Journal of Systems Science and Complexity. 1996, 9(2): 101-106.

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  In this paper we generalize the ordinary discrete type Euclidean multifacility location problem (EMFL) to a continuous type Euclidean multifacility location problem(CEMFL). We propose an algorithm for CEMFL. It is proved that from any initial point, the algorithm generates a sequence of points which converges to the bounded closed convexset of optimal solutions of CEMFL. The algorithm can be used to solve the EMFL problem, and it simplifies the ready-made algorithms for EMFL.
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  SOME RESULTS OF BOUNDARY PROBLEM OFNON-NEWTONIAN FLUIDS

  SHI Xiaoding

  Journal of Systems Science and Complexity. 1996, 9(2): 107-119.

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  In this paper we discuss the first boundary problem of incompressible non-Newtonian fluids. The results of [1] are improved and extended, further we have obtainedsome new conclusions about the characteristics of the solutions when t→∞ and theexistence of periodic solution etc.
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  ON THE ALGEBRAIC VARIETY DECOMPOSITION

  WU Jinzhao

  Journal of Systems Science and Complexity. 1996, 9(2): 120-127.

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  By defining a concept of normal chains, an algorithm to decompose algebraicvarieties is presented, and the applications of this algorithm in solving polynomial equationsand primary decomposition of ideals are discussed.
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  ON THE CONVERGENCE OF CONJUGATEGRADIENT METHODS INVXRIANT TONONLINEAR SCALING

  DENG Naiyang;LI Zhengfeng

  Journal of Systems Science and Complexity. 1996, 9(2): 128-133.

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  In order to construct more efficient methods for unconstrained optimization problems, several authors have considered more general functions than quadratic functionsas a basis for conjugate gradient method in recent years. Although interesting numerical experiments have been obtained by using the new methods, their convergence has remained an open problem even when line searches are exact. Under some assumptions, two global convergence theorems for the extended Fletcher-Reeves and Polak-Ribiere methods proposed in [1] are given in this paper.
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  STABLE POSITIVE PERIODIC SOLUTIONS OF THEPERIODIC COMPETITIVE SYSTEMS

  LI Hua;CHEN Lansun

  Journal of Systems Science and Complexity. 1996, 9(2): 134-139.

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  Consider the general competitive system \dot{u}=uM_1(t;u,v), \dot{v}=vM_2(t;u,v), where \partial M_1/\partial v <0, \partial M_2/\partial u <0, M_i(t+T; u,v) = M_i(t; u, v), i =1, 2. under sonicconditions, it is shown that the system has some positive periodic solutions. The theoremto assess the asymptotic stability and the uniqueness of the periodic solution is obtained byusing the monotonic and strongly concave operator. Some conditions for global asymptoticstability of the periodic solution are also obtained.
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  A GENERALIZED GRADIENT METHOD FORNONLINEAR CONSTRAINTS AND ITS CONVERGENT PROPERTIES

  GAO Ziyou

  Journal of Systems Science and Complexity. 1996, 9(2): 140-144.

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  Although many effective algorithms of the gradient projection type have been proposed for nonlinear programming with nonlinear constraints (see [1-9]), these algorithms must require a regular assumption (i.e. the gradient vectors of the active constraints set at any feasible point are linearly independent). In this paperr a generalized gradient projection method is presented for nonlinear programming with nonlinear constraints under degeneracy. And its convergent properties are discussed.
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  THE GENERALIZED SOLUTIONS OF PBVP FORINTEGRO-DIFFERENTIAL EQUATIONS

  ZHUANG Wan;CHEN Yubo

  Journal of Systems Science and Complexity. 1996, 9(2): 145-150.

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  In this paper, we study the periodic boundary value problems for a class ofnonlinear integro-differential equations of Volterra type with Caratheodory condition. Weobtain an existence result of generalized solutions between generalized upper and lowersolutions, and develop the monotone iterative technique to find generalized extremal solutions as limits of monotone sequences.
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  A SIMPLE ESTIMATOR FOR AN EXPONENTIALTAIL COEFFICIENT

  QI Yongcheng

  Journal of Systems Science and Complexity. 1996, 9(2): 151-156.

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  In this paper a simple estimator for an exponential tail coefficient in risk theoryis constructed. The convergence rate in the weak sense for the estimator is obtained.Additionally, the limit distributions of the estimator are discussed in the paper.
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  ASYMPTOTICALLY EFFICIENT ESTIMATES IN ASYSTEM TREE

  DAI Ming

  Journal of Systems Science and Complexity. 1996, 9(2): 157-163.

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  In this paper, we use the virtual system method to estimate the parametersin a system tree and obtain a series of asymptotically efficient estimates of the interesting parameters. Section 1 is an introduction to the virtual system method, and in Section 2,we extend the virtual system method to estimate the parameters of the last generation subsystems of some subsystem tree. In Section 3, we use the results of Section 2 to some examples. And the proof is in Section 4.
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  SECOND ORDER ASYMPTOTIC EFFICIENCY IN APARTLY AUTOREGRESSIVE MODEL

  LIANG Hua

  Journal of Systems Science and Complexity. 1996, 9(2): 164-170.

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  Consider the model X_t=X_{t-l}β + g(U_t)+ ε_t for t ≥ 1. Here g is an unknownfUnction, β is an unknown parameter to be estimated and εt are i.i.d. with mean 0 andvariance σ^2 and U_t are i.i.d. random variables obeying uniformly on [0, 1]. We constructa class of second order asymptotically efficient estimators based on the LS estimators of β when e is a normal density with mean 0 and variance σ^2.
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  A PROPERTY OF PRODUCTS OF NEWGENERALIZED FUNCTIONS

  LI Yaqing

  Journal of Systems Science and Complexity. 1996, 9(2): 171-174.

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  In this paper, we prove that every distribution on R with compact support isassociated with the product of two elements in new generalized functions G_u(R) associatedwith distribution zero, for any u.
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  THE EXPONENTIAL BOUND OF THE SURVIVALFUNCTION ESTIMAATOR FOR RANDOMLYTRUNCATED AND CENSORED DATA

  ZHU Yujie

  Journal of Systems Science and Complexity. 1996, 9(2): 175-181.

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  A sharp exponential bound for the product-limit estimator of Tsai et al.[1] isobtained when the data are subject to left truncation and right censorship.
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  A NEW GENERALIZATION OF ORE'S THEOREM INVOLVING NEIGHBORHOOD UNIONS

  WANG Diji;LIU Xin

  Journal of Systems Science and Complexity. 1996, 9(2): 182-192.

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  Let G be a 2-connected simple graph of order n. In this paper we prove the following generalization of Ore's theorem: If G is a 2-connected graph such that |N(u) \cup N(v)|+|N(u) \cup N(w)| ≥ n for every triple (u, v, w), where {u, v w} is an independent set, then either G is hamiltonian, or G is the Petersen graph, or G belongs to one of the three families of exceptional graphs of connectivity 2. Our result generalizes three recent theorems: The first one is obtained by Tian[1], the second one by Broersma, Heurel and Veldma.[2] and the third one by Flandrin, Jung and Li[3].