1995年, 第8卷, 第2期　刊出日期：1995-04-15

  

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  PARALLEL COMPUTATION AND DOMAIN DECOMPOSITION FOR A CLASS OF HYPERBOLIC PROBLEMS

  LIN Qun;YAN Ningning;ZHOU Aihui

  Journal of Systems Science and Complexity. 1995, 8(2): 97-101.

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  It is shown in this paper that convection problems can be in parallel computed by using finite element methods, of which the error estimates are presented.
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  DYNAMICAL BEHAVIORS OF A FOUR-DIMENSIONAL SYSTEM IN INFECTIOUS DISEASE

  LIN Yiping;JING Zhujun

  Journal of Systems Science and Complexity. 1995, 8(2): 102-115.

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  In this paper a mathematical model of a four-dimensional system in infectious disease with 16 parameters is investigated, the bifUrcation of equilibria depending on one parameter is given, and the conditions of local stability of equilibria and the existence of Hopf bifurcation are studied.
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  OPTIMALITY CONDITIONS AND DUALITY THEOREMS IN NONCONICAL MULTIOBJECTIVE PROGRAMMING

  LI Yuanxi

  Journal of Systems Science and Complexity. 1995, 8(2): 116-120.

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  This paper is concerned with the nonconical multiobjective programming proly fern. By virtue of the derivate of a binary relation, the sufficient and necessary optimality conditions are presented, and the duality theorems (weak and strong) are proved.
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  GLOBAL CONVERGENCE OF UNCONSTRAINED MINIMIZATION METHODS WITH A GENERALIZED BACKTRACKING LINESEARCH PROCEDURE

  LIU Guanghui;HAN Jiye

  Journal of Systems Science and Complexity. 1995, 8(2): 121-127.

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  This paper presents a generalized backtracking linesearch procedure, which includes the backtracking linesearch and many other linesearches. Under very mild conditions we show the global convergence of the well-known BFGS algorithm with the generalized backtracking linesearch.
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  ON ASYMPTOTICALLY MEDIAL UNBIASED ESTIMATORS IN TRVNCATED-TYPE DISTRIBUTION FAMILIES

  LIANG Hua

  Journal of Systems Science and Complexity. 1995, 8(2): 128-133.

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  In this paper, the author constructs asymptotically medial unbiased estimators for two classes of truncated-type distributions.
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  POLYTOPIC PERTURBATION BOUND FOR STABILITY OF POLYNOMIALS

  AN Senjian;WANG Enping

  Journal of Systems Science and Complexity. 1995, 8(2): 134-143.

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  The presence of uncertain parameters in the state space or frequency domain description of a time-invariant system manifests itself as variability in the coefficients of the characteristic polynomial.In this paper, a new approach is proposed to analyze the stability robustness of Hurwitz polynomials with polytopic uncertainties in the coefficient space. This method is very simple and the perturbation bounds can be calculated easily on computer. From this result, the largest polytope in the coefficient space can be found such that the perturbed polynomial remains stable.
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  A k-HAMILTON-NICE SEQUENCE

  LIU Yiping;TIAN Feng;WU Zhengsheng

  Journal of Systems Science and Complexity. 1995, 8(2): 144-151.

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  Let G be a simple finite graph, I_{k+1} (G) the set of independent sets of cardinality (k + 1) of G. If Y ∈I_{k+1}(G), define S_i(Y)={v|N(v)\cap Y| = i}, s_i(Y) =|S_i(Y)|for each i ∈ {0, 1, 2,...,k+1}. In this paper we prove that, if k ≥ 2 and G is a k-connected　graph of order n such that Σ_{i=1}~k {k+i-2}/{k-1}s_i(Y) + 2s_{k+1}(Y) > n - 1 for each Y ∈ I_{k+1}(G),then G is hamiltonian. This theorem generalizes several well-known sufficient conditions for graphs to be hamiltonian.
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  ON THE ISOMORPHISMS OF COMPLETE INTERSECTION VARIETIES

  DU Hong

  Journal of Systems Science and Complexity. 1995, 8(2): 152-156.

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  In this paper,I have given an effective algorithm basing grobner basis method for deciding whether two given smooth varieties are isomorphic. This algorithm can also be used to find isomorphisms between two given smooth complete intersection varieties. some miscellaneous results related isomorphisms between complete intersection satisfying some condition are also given, and these results can sometimes give more efficient algorithm for deciding isomorphisms.
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  OUTLIER SCORE TEST IN A GROWTH CURVE MODEL

  FEI Yu

  Journal of Systems Science and Complexity. 1995, 8(2): 157-165.

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  Score test statistic has been successfully used to solve many problems in the regression model.In this paper,we use the method to study the problem of local influence of a covariance perturbation in a growth curve model. First, we establish the score test function of the growth curve model with a variance enlargement under Rao's Simple Structure (Abbr.: RSS).Second, we discuss similar problems of the model with a general covariance structure (Abbr.: GCS). Furthermore, we give an approach to detecting one outlier or some outliers. The numerical example analysed at the end shows that our results are very useful in practice.
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  CONTINUOUS-TIME STOCHASTIC ADAPTIVE CONTROL STABILIZING THE SYSTEM AND MINIMIZING THE QUADRATIC LOSS FUNCTION

  CHEN Hanfu

  Journal of Systems Science and Complexity. 1995, 8(2): 166-181.

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  For the completely observed colltinuous-time stochastic system (A, B, C)an adaptive control based on the ELS estimation algorithm is designed so that the quadratic loss function is minimized and the unknown coefficients are consistently estimated.The conditions imposed on the system are as follows: Span(B)\subset Span(C) and (A, B, D) is controllable and observable with D^\tau D = Q_1, where Q_1 is the weighting matrix for states in the loss function.
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  METRICS,PROBABILISTIC METRICS AND RANDOM METRICS

  GUO Tiexin

  Journal of Systems Science and Complexity. 1995, 8(2): 182-186.

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  First, this paper gives a precise representation of the diagonal section of the largest weak t-norm of a probabilistic metric space, which makes the important YouZhu theorems in the theory of probabilistic metric spaces obvious. Then it shows that probabilistic metric space-system is equivalent to ordinary metric space-system in the sense of isometrical isomorphism, and random metric space-system is distinct essentially from both probabilistic metric space-system and ordinay metric space-system.
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  ROBUST NONPARAMETRIC REGRESSION BASED ON L_1-NORM AND B-SPLINES

  SHI Peide;ZHANG Zhengjun

  Journal of Systems Science and Complexity. 1995, 8(2): 187-192.

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  This paper deals with L1-norm estimators for nonparametric regression models,where the unknown regression functions are approximated by using B-spline functions.With a potential use of the generalized Akaike information criterion (GAIC) a stepwise forward/backward strategy of selecting the B-spline knots is proposed. A procedure for calculating the L1-norm estimators is presellted via the linear programming technique. The numerical performance of the proposed estimator is compared with that of smoothing spline estimators (SSE) and TURBO based on a simulation experiment. The simulation results indicate that when error distribution is normal or of double exponential power,TURBO, SSE and L1 estimator behave similarly. However, when error distribution is contaminated normal, the performance of L1 estimator is superior to that of TURBO and SSE. When the spline knots are deterministically given, the large sample properties of the L1-norm estimator are discussed.