1990年, 第3卷, 第4期　刊出日期：1990-11-15

  

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  LONGEST CYCLES IN REGULAR 3—CONNECTED GRAPHS

  Yu Zhengguang;Zhu Yongjin;Liu Zhenhong

  Journal of Systems Science and Complexity. 1990, 1(4): 289-297.

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  It is proved that for k≥71, the circumference c(G)of a 3-connected k-regular graphG on n vertices is at least min{|G|,3k+5}. This result is essentially best possible.
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  HEURISTIC SUPERVISION OF DISCRETE EVENT SYSTEMS

  Li Yonghua;Gao Weibing

  Journal of Systems Science and Complexity. 1990, 1(4): 298-307.

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  Results on supervisory control of discrete event processes are mainly concerned with designing a controller such that the closed loop system generates a language L which coincides with the target language.In this paper we consider supervisory control problem for a class of discrete event processes when the design target is that a certain set of language patterns can not occur in the closed loop language.A heuristic supervisor is constructed via the heuristic search method developed in AI. This scheme requires only the information about thecontrollability of the event symbol set. It is capable of designing a modular heuristic supervisor when there are many such forbidden strings. Effectiveness of such a supervisor is proved forsystems with perfect and partial observation.
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  Q-ANALOG OF LI SHAN-LAN IDENTITY

  Guan Aiwen;Shi He

  Journal of Systems Science and Complexity. 1990, 1(4): 308-326.

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  The expansions of the higher power of Gaussian polynomial are studied in this paper. And an elementary proof of the Q-analog Li Shan-lan identity is provided.
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  QUADRATURE AND EXTRAPOLATION FOR THE VARIABLE COEFFICIENT ELLIPTIC EIGENVALUE PROBLEM

  Ding Yanheng;Lin Qun

  Journal of Systems Science and Complexity. 1990, 1(4): 327-336.

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  For the variable coefficient elliptic eigenvalue problem on a smooth domain or aconvex polygonal domain,a numerical quadrature scheme over triangles is used for computing the coefficient of the resulting linear finite element system. The effect of numerical integrationis studied. The corresponding discrete eigenvalue with linear finite elements is shown to admit asymptotic error expansions for certain classes of“uniform”meshes. Hence, the Richardson extrapolation increases the accuracy of the scheme from second to fourth order.
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  CORRECTED PROOF OF A THEOREM CONCERNING A CONJECTURE OF SINGH

  Chen Xiru;Tao Bo

  Journal of Systems Science and Complexity. 1990, 1(4): 337-340.

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  A theorem concerning a conjecture of Singh is formulated in [2]. But the argument in [2] contains a serious gap which is in fact the essential point of the proof. A correct proof is presented here.
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  THE UNBIASED ESTIMATION THEORY FOR EXPONENTIAL FAMILY

  Chen Hongjian

  Journal of Systems Science and Complexity. 1990, 1(4): 341-355.

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  In this paper, the necessary and sufficient conditions for a function of the parameterin a one-parameter natural exponential family(NEF) to have an unbiased estimator with finite variance are obtained. The recursive formulae of the Fisher information matrices of any order for a one-parameter NEF and a one-parameter regular exponential family(REF)arederived respectively. The expression of the UMVUE for an estimable function of the parameterin a one-parameter NEF or a one-parameter REF is given.
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  A LAW OF THE ITERATED LOGARITHM FOR RANDOM WINDOW-WIDTH KERNEL ESTIMATOR OF A NONPARAMETRIC REGRESSION FUNCTION

  Hong Shengyan

  Journal of Systems Science and Complexity. 1990, 1(4): 356-363.

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  In this paper we study the estimation of the regression function. We establish a law ofthe iterated logarithm for the random window-width kernel estimator and, as an application, for a nearest neighbor estimator. These results give sharp pointwise rates of strong consistency of these estimators.
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  A MODEL FOR MEDIUM-OR LONG-TERM PLANNING

  Deng Shuhui;Yang Shetang

  Journal of Systems Science and Complexity. 1990, 1(4): 364-374.

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  The PDAS(Production Distribution Area,Spatial)is an efficient method for optimalanalysis of the existing industrial production spatial distribution. As the main problem formedium- and long-term programming of the industrial production level isproject investment analysis, incorporation of project investment into PDAS to evaluate the project investment comprehensively over the whole planned period will be an ideal approach. This, however, changes the linear programming problem into a mixed integer programming problem with constraints which include a step function. To simplify the algorithm, in light of large scale system decomposition,a model and an algorithm with coordinative running of schedulingand distribution optimization are proposed. The new version of PDAS, named PDAS-D, will have more practical use in decision support analysis for the medium-and long-termproduction spatial distribution and optimal adjustment of industrial structure by means of project investment.
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  STATE FEEDBACK STABILIZATION OF PLANE SYSTEMS

  Cheng Daizhan

  Journal of Systems Science and Complexity. 1990, 1(4): 375-380.

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  The problem of state feedback stabilization of control systems is tackled in this paper. The stabilizability of the plane control systems with critical spectrum is considered, By using therecently developed center manifold method combined with Liapunov second method, it is shownthat in all critical cases the above mentioned systems are state feedback stabilizable.
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  WHAT CAN A PRODUCT OF DISTRIBUTION ZERO AND ITSELF BE?

  Li Yaqing

  Journal of Systems Science and Complexity. 1990, 1(4): 381-383.

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  In this paper, it is proved that, given any standard locally Lebesgue integrable function F(x) on R, there exist nonstandard representations f_1(x) and f_2(x) of the distribution zero,suchthat, for any φ∈\mathcal{D},integral from R F(x)φ(x)dx-integral from ~*R f_1(x)f_2(x)φ(x)dx=an infinitesimal.