1995年, 第8卷, 第1期　刊出日期：1995-01-15

  

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  THE RATIONALITY OF THE DISCRETE ORDINATES METHOD FOR TIME DEPENDENT NEUTRON TRANSPORT EQUATION

  LI Xuezhi;ZHU Guangtian;LIANG Benzhong

  Journal of Systems Science and Complexity. 1995, 8(1): 1-003.

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  We know that the discrete ordinates method is an important numerical method for solving transport equation. For the steady state transfer equations, the rationalities of this method have been proved by many authors. But there is no result whether this method is valid for nonsteady state transport equations. In this paper, we solve this problem by means of the theory of integrated semigroups[1-3] which was first considered by W. Arendt[1,2].
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  BOUNDARY LAYER ESTIMATION OF NONLINEAR ELLIPTIC EQUATION

  HE Cheng;ZHANG WeItao

  Journal of Systems Science and Complexity. 1995, 8(1): 4-011.

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  In this paper, we consider the nonlinear elliptic equation... The limit problem is |u|^s=f on \Omega, where 04 ; and s>0, for n\leq 4. Let d(x,\Gamma) be the distance from x to \Omega, let |\Omega| denote the measure of \Omega, and let... When u\in H^2(\Omega)\H_0^2(\Omega), we have the boundary layer estimates for problem... For the nonlinear elliptic singularity perturbation problem of second order, we obtain a similar conclusion.
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  OUTLIERS AND INFLUENTIAL OBSERVATIONS IN A RIDGE MEAN SHIFT REGRESSION

  PAN Jianxin;XIONG Haiyan

  Journal of Systems Science and Complexity. 1995, 8(1): 12-026.

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  In the mean shift regression, it is of interest to detect anomalous observations that provide some large residuals or exert some unduly large influences on the least square analysis when the chosen model is fitted to the data, which are known as outliers or influential observations, respectively. The existence of outliers and influential observations, however, are complicated by the presence of a collinearity, which has great effects on the influences of a set of observations. In this paper, we show that when a ridge mean shift regression is used to mitigate the effects of the collinearity, the influences of some observations can be drastically modified. This is illustrated with an example derived from a set of data given by Mickey, Dunn and Clark[1]. Recommendations are given for obtaining the best use of the procedures.
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  LOCAL INFLUENCE IN DISCRIMINANT ANALYSIS

  WANG Xueren;REN Shiquan;SHI Lei

  Journal of Systems Science and Complexity. 1995, 8(1): 27-036.

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  In this paper, we use the generalized influence function and generalized Cook statistic to study the local influence of small perturbation in discriminant analysis. We give the perturbation theory about Mahalanobis △^2, discriminant means and discriminant function coefficients, and derive the local influence measures for various aspects in discriminant analysis. Finally, an example is used for illustration.
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  ASYMPTOTIC BEHAVIOR OF THE ESTIMATES OF HIGHER ORDER SPECTRA UNDER TRUNCATED WINDOW

  YU Dan

  Journal of Systems Science and Complexity. 1995, 8(1): 37-045.

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  This paper is concerned with the asymptotic behavior of the estimation of higher order spectra of stationary processes. Under suitable conditions, the L_2-consistency, the bias of the estimation and the truncated take optimum weight function are given; and the asymptotic normality result is approved.
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  ON CONVERGENCE AND RATE OF CONVERGENCE OF ALGORITHMS IN THE MOVER-STAYER MODEL

  WANG Dongqian;Lawoko;C. R. O.

  Journal of Systems Science and Complexity. 1995, 8(1): 46-051.

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  The convergence and rate of convergence of an iterative method of Wang and Scott[1] for obtaining maximum likelihood estimates for contingency tables derived from a mover-stayer model are discussed.
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  ON THE BEST UNIFORM CONVERGENCE RATE OF EB ESTIMATORS

  LIANG Hua;YUAN Yahua

  Journal of Systems Science and Complexity. 1995, 8(1): 52-056.

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  In this paper the authors prove that the best uniform convergence rate of EB estimators of the parameter θin uniform distribution family U(0,θ) cannot reach 1 under conditions weaker than Tao Bo's[5].
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  OPTIMAL GLOBAL RATES OF CONVERGENCE OF M-ESTIMATES FOR NONPARAMETRIC REGRESSION

  SHI Peide;LI Guoying

  Journal of Systems Science and Complexity. 1995, 8(1): 57-065.

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  Let (X, Y) be a pair of random variables such that X ranges over [0, 1] and Y is real-valued and let go(X) be the conditional expectation of Y given X. Based on a training sample, the piecewise polynomial estimator of go is obtained via usual M-estimates. It is proved that under certain regularity conditions the piecewise polynomial M-estimator achieves the optimal global rate of convergence of estimators for nonparametric regression.
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  LONG DOMINATING CYCLES IN A KIND OF 2-CONNECTED GRAPHS

  SHEN Ruqun;TIAN Feng;ZHANG Lianzhu

  Journal of Systems Science and Complexity. 1995, 8(1): 66-074.

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  Let G be a connected graph of order of n, and NC2(G) denote min{|N(u) ∪ N(v)| dist(u, v) = 2}, where dist(u, v) is the distance between u and v in G. A cycle C is called a dominating cycle if every component of G\V(C) has order one. In this paper, we prove that if G is a 2-connected graph such that every longest cycle in G is a dominating cycle, then G contains a dominating cycle of length at least min{n, 2NC2(G)} unless G is the Petersen graph or belongs to a family of exceptional graphs.
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  A HOMOCLINIC ORBIT FOR LAGRANGIAN SYSTEMS

  WU Shaoping

  Journal of Systems Science and Complexity. 1995, 8(1): 75-081.

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  We prove the existence of a homoclinic orbit for Lagrangian system (LS) where the Lagrallgian L(t,x,y)=1/2 \sum a_ij(x)y_iy_j-V(t,x). A similar argument to Rabinowitz[5] is used, where a_ij (x) is an identity matrix. Now the differential equation is quasilinear and more estimates are needed to get the uniform bound for the second derivative of periodic sequence {x_k(t)} with period 2kT.
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  STRONG CONSISTENCY OF M-ESTIMATES OF MULTIPLE REGRESSION COEFFICIENTS

  CHEN Xiru;ZHAO Lincheng

  Journal of Systems Science and Complexity. 1995, 8(1): 82-087.

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  In the case where ρ is convex we give a set of sufficient conditions for the strong consistency of M-estimate of multiple regression coefficients.
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  H~∞-IDENTIFICATION OF INFINITE-DIMENSIONAL LINEAR STOCHASTIC SYSTEMS

  WEI Chen;GUO Lei

  Journal of Systems Science and Complexity. 1995, 8(1): 88-096.

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  A method consisting of auto-regressive approximation in system identification and input normal realization truncation in model reduction is proposed for transfer function identification of infinite-dimensional linear stochastic systems. The identified low order transfer function is constructed on basis of the input-output data only, and the estimation error bounds in terms of L∞-norm are also derived.