1993年, 第6卷, 第2期　刊出日期：1993-04-15

  

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  ERROR ESTIMATION OF THE APPROXIMATION ALGORITHM FOR THE WINDY POSTMAN PROBLEM

  DU Lingu

  Journal of Systems Science and Complexity. 1993, 6(2): 97-105.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  If we restrict the postman to traversing each edge at most twice in the windy postman problem (WPP), we will get a new problem: 2WPP. An approximation algorithmhas been posed by M. Guan for the WPP. In the present paper, we improve the estimatederror given by M. Guan and show that we can estimate the error for the 2WPP by finding a minimum cost circulation. We also pose a new sufficient condition for the equivalence between WPP and 2WPP, which can be checked in polynomial time steps.
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  ON INADMISSIBILITY OF SOME USUAL ESTIMATORS OF LOSS INCURRED IN ESTIMATING ERROR VARIANCE

  WU Qiguang

  Journal of Systems Science and Complexity. 1993, 6(2): 106-110.

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  Under multivariant normal linear models, it is proved that usual loss estimators based on the uniformly minimum variance unbiased estimator and the best affinely equivariant estimator of error variance are inadmissible with squared error loss.
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  ASYMPTOTIC ANALYSIS OF THE OPTIMAL CONTROL OF AN ELASTODYNAMIC SYSTEM

  ZHANG Weitao;FENG Dexing

  Journal of Systems Science and Complexity. 1993, 6(2): 111-119.

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  Based on the idea of the reduction of optimal control systems in singular perturbations of Lions and a priori estimates in [4], we prove the convergence of the optimal control, state and the cost function between a singular linear elastodynamic systemand a limit system. Our asymptotic analysis is applicable to the optimal control of flexible robotic manipulators.
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  FEEDBACK CONTROL OF A CLASS OF FLEXIBLE SYSTEMS WITH COUPLED BENDING AND TORSIONAL VIBRATIONS

  YU Nairun;WANG Miansen;ZHU Guangtian

  Journal of Systems Science and Complexity. 1993, 6(2): 120-129.

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  In this paper, a class of flexible systems of beams with coupled bending andtorsional vibrations, which has important applications in the dynamics of aircraft is discussed. The existence and uniqueness of the solution for this class of systems are proved, where the spectral analysis method and the unconditional base theory are used, and asufficient condition for the asymptotic stability of the closed-loop system is obtained by means of the (D) class operators theory.
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  VIBRATIONAL SYSTEMS OF A CLASS OF THIN CYLINDRICAL SHELLS

  ZHU Ziqing;CHEN Qinyi;ZIIANG Weiheng

  Journal of Systems Science and Complexity. 1993, 6(2): 130-136.

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  The vibration of thin circular cylindrical shells has been studied extensively. In this paper, the existence and uniqueness of the solution of this system are proved by means of semigroup theory on the Hilbert space, and the eigenvalue problem is discussed. This offers a theoretical basis for solving this kind of engineering problems.
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  IMPROVEMENT ON THE TEST IN THE EXPONENTIAL FAMILY

  ZHENG Zhongguo

  Journal of Systems Science and Complexity. 1993, 6(2): 137-144.

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  Let x_1,…, x_n be the life spans of n items. Suppose that we start the experi-ment at the time t=0 for all the items simultaneuously aud stop the experiment at the time t=r, where r is a stopping time. The observed data set is Z_n=(x_(1),…, x_(k), r(x)), where x_(i)(i=1,…, n) is the order statistic of x_i, i=1,…, n and k=k(x) is the num-ber of the observed data. Suppose that the distribution family of x_i, i=1,…, n is i.i.d.exponential with life expectation θ>0. For testing the hypothesis H_0: θ≤θ_0 against H_1: θ>θ_0, we use the total time of experiment S_r=sub from i=1 to k x_(i) +(n-k)r (x) as the test statistic. We reject H_0 as large value of S_r is observed. In this paper for a given stoppingtime r we construct a stopping time ro so that the resulting test is a best improvement of the one, which is based on r, in the sense that the power functions of the two tests are the same but the test based on r_0 is the one which has the minimnm total experiment time.
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  RELIABILITY BOUNDS IN NWUE CLASS WITH KNOWN MEAN AND VARIANCE

  CHENG Kan;HE Zongfu

  Journal of Systems Science and Complexity. 1993, 6(2): 145-149.

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  Let F∈NWUE with known mean and variance. In this note a simple sharp lower bound of {\overline F}=1-F(t) is given.
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  THE CHARACTERISTIC PAIR AND TRACE EXPRESSION OF LR ARRAYS

  LIN Dongdai

  Journal of Systems Science and Complexity. 1993, 6(2): 150-160.

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  In this paper, the concept of characteristic pair of linear recurring (or LR inshort) arrays is introduced. A decomposition of the linear space consisting of LR arraysand trace expressions of LR arrays is showed.
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  STABILITY AND FEEDBACK CONTROL OF A CLASS OF SECOND-ORDER LINEAR SYSTEMS IN BANACH SPACE

  HE Xiaoliang;WANG Miansen

  Journal of Systems Science and Complexity. 1993, 6(2): 161-174.

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  In this paper. we are concerned with the stability and control problem for a class of second-order linear systems in Banach space. First. a criterion for the exponential stability of a first-order linear system is presented. Then. the exponential stability as wellas some properties of a class of second-order linear systems is proved. At last. the feedback control of this class of systems is investigated.
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  HOMOMORPHISMS OF GENERALIZED DE BRUIJN-GOOD GRAPHS

  LIU Mulan

  Journal of Systems Science and Complexity. 1993, 6(2): 175-178.

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  In the paper the homomorphisms of generalized de Bruijn-Good graphs are described in detail and all homomorphisms of de Bruijn-Good graphs are given as an example.
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  BINDING NUMBER AND MINIMUM DEGREE FOR [a,b]-FACTORS

  CHEN Ciping

  Journal of Systems Science and Complexity. 1993, 6(2): 179-185.

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  We give some sufficient conditions on the binding number and the minimumdegree for a graph to have an [a, b]-factor.
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  AUTOMATED REASONING IN DIFFERENTIAL GEOMETRY AND MECHANICS USING THE CHARACTERISTIC METHOD Ⅳ. Bertrand Curves

  CHOU Shangching;GAO Xiaoshan

  Journal of Systems Science and Complexity. 1993, 6(2): 186-192.

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  This paper reports the study of properties of the curve pairs of the Bertrand types using our automated reasoning program based on Wu's method of mechanical theorem proving for differential geometry. A complete list of results about Bertrand curvesin metric and affine spaces is derived mechanically. The list includes most of the known results of various Bertrand curves. We also derive some new results about Bertrand curves.