1993年, 第6卷, 第4期　刊出日期：1993-10-15

  

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  PP K-MEAN CLUSTERING

  ZHANG Dixin;ZHU Lixing

  Journal of Systems Science and Complexity. 1993, 6(4): 289-295.

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  In this paper, we propose a dimension-reducing, K-mean clustering procedureby Projection Pursuit (PP) technique so as to explore the clustering structure of data in high-dimensional space in terms of low-dimensional projective points of data, and we obtainthe a.s. consistence of the estimates of the cluster centers and projection orientations.
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  SYSTEM MODELING AND OPTIMIZATION OF A PORT SYSTEM WITH DIFFERENT SHIP'S KINDS

  YUE Wuyi;GU Jifa;NIE Jiayu;Hu Pingxian

  Journal of Systems Science and Complexity. 1993, 6(4): 296-311.

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  The analysis and evaluation of an actual port system containing R differentship's kinds and N subsystems each of which consists of M.(i=1, 2,…, N) ports arederived. The external arrivals of ships to the system come from R different Poisson sources and the interarrivals to the queue of each port of a subsystem are determined according tocondition probabilities. Each port has multiple berths whose service times are distributed according to Erlang probability distribution functions. Each port of a subsystem has Rinfinite capacity buffers for storing ships interarrived. This method provides a good approximation procedure for obtaining system perfor-mance measures such as waiting times of ships, average queue lengths, etc. Optimum portcapacity can thus be evaluated by using this analysis. A simulation is also presented to test this approximate analysis, and a good agreement is observed. This model shall be used in the planning of several actual port systems. Through the application of this model, it is possible to analyze and evaluate performances of the systems.
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  SYNTHESIS AND ANALYSIS OF A FEEDBACK CONTROL SYSTEM

  ZHOU Rongxing

  Journal of Systems Science and Complexity. 1993, 6(4): 312-319.

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  In this paper, supposing that the received signals at the input are of the formv(t)=s_1[t, x_1(t)]s_2[t, x_2(t)]+n(t) where s_i are FM signals (i=1, 2), a novel cross-coupled phase-locked loop (CCPLL(M)) and its mathematical model are obtained. The global qualitative structural analysis of the mathematical model of the first-order loop, the acquisition region and synchronization region of the first-order loop, and the synchronization region of the second-order loop are obtained.
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  ANALYSIS OF BOUNDARY LAYER SINGULARITY OF A HYPERBOLIC EQUATION

  ZHANG Weitao;FENG Dexing

  Journal of Systems Science and Complexity. 1993, 6(4): 320-330.

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  Using the interpolation theory of a family of linear operators and the Sobolev spaces, we introduce a quantity J_∈~4(λ) which depicts the shape of the boundary layer, andthen analyze the boundary singularty of J_∈~4(λ). Our result shows that the thickness of the boundary layer (or the regular region of J_∈~4(λ)) is intrinsically related to the reciprocal ofthe order of the equation; the loss of boundary conditions between the singular solution andthe limit solution does not influence the thickness of the boundary layer, but it influences the process of increasing singularity of J_∈~4(λ); the more the loss of boundary conditions, thesmaller the region of increasing singularity. Finally, we give a definition of a neighborhood of sudden change and propose an open problem regarding this neighborhood.
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  INTERPOLATED FINITE ELEMENT METHODS FOR SECOND ORDER HYPERBOLIC EQUATIONS AND THEIR GLOBAL SUPERCONVERGENCE

  LIN Qun;WANG Hong;LIN Tao

  Journal of Systems Science and Complexity. 1993, 6(4): 331-340.

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  We develop the interpolated finite element method to solve second-order hyperbolic equations. The standard linear finite element solution is used to generate a newsolution by quadratic interpolation over adjacent elements. We prove that this interpolated finite element solution has superconvergence. This method can easily be applied to generating more accurate gradient either locally or globally, depending on the applications. This method is also completely vectorizable and parallelizable to take the advantages ofmodern computer structures. Several numerical examples are presented to confirm our theoretical analysis.
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  MODELLING AND STABILITY ANALYSIS OF POPULATION GROWTH WITH SPATIAL DIFFUSION

  W.L.CHAN;FENG Dexing

  Journal of Systems Science and Complexity. 1993, 6(4): 341-352.

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  In recent years, population growth models with spatial diffusion have been extensively studied by many authors (for example, see [1-5]). In this paper, a population growth model is considered with a discrete age-dependence and spatial diffusion, and is investigated in a semigroup framework. The spectral properties of the population oper-ator are given. On the basis of such spectral consideration, the asymptotic behaviour of the semigroup generated by the population operator is obtained. Finally, a nonlinear population growth model is considered and its stability is analyzed.
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  AN INFORMATION THEORETICAL APPROACH TO NEURAL NETWORKS

  Caro Lucas

  Journal of Systems Science and Complexity. 1993, 6(4): 353-372.

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  The purpose of this paper is to present a unified theory of several differentneural networks that have been proposed for solving various computation, pattern recog-nition, imaging, optimization, and other problems. The functioning of these networks is characterized by Lyapunov energy functions. The relationship between the deterministic and stochastic neural networks is examined. The simulated annealing methods for finding the global optimum of an objective function as well as their generalization by injecting noise into deterministic neural networks are discussed. A statistical interpretation of the dynamic evolution of the different neural networks is presented. The problem of training different neural networks is investigated in this general framework. It is shown how this approach can be used not only for analyzing various neural networks, but also for the choice of the proper neural network for solving any given problem and the design of a training algorithm for the particular neural network.
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  ON NICE SEQUENCES CONCERNING HAMILTONICITY OF GRAPHS

  LIU Yiping;WU Zhengsheng

  Journal of Systems Science and Complexity. 1993, 6(4): 373-375.

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  In the paper, the (k-1)-traceable-nice ((k-1)-T-nice) and k-homogeneously-traceable-nice (k-HT-nice) sequence are defined similarly to the definition of k-Hamilton-nice (k-H-nice) and (k+1)-Hamilton-connected-nice ((k+1)-HC-nice) sequence. The relationships among these four nice sequences are discussed. The main results are as follows: Let_η=(a_1, a_2,…, a_(k+1) be a non-negative rational sequence, k≥2. (1) If η is(k+1)-HC-nice and a_(k+1)=2, then η is k-HT-nice, (2) If η is k-HT-nice and a_(k+1)=2,then η is (k-1)-T-nice, (3) If η is k-H-nice, then η is k-HT-nice. Meanwhile, four unsolved problems on these topics are proposed.
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  EDGE RECONSTRUCTION OF PLANAR GRAPHS WITH MINIMUM DEGREE AT LEAST THREE-(Ⅰ)

  FAN Hongbing

  Journal of Systems Science and Complexity. 1993, 6(4): 376-382.

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  The object of this series of papers is to show that every planar graph of minimum degree at least 3 is edge reconstructible. In this paper, we prove that such agraph with connectivity 2 is edge reconstructible.