1992年, 第5卷, 第1期　刊出日期：1992-02-15

  

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  ESTIMATING THE NONCENTRALITY PARAMETER OF A t-DISTRIBUTION

  Andrew L.Rukhin

  Journal of Systems Science and Complexity. 1992, 5(1): 1-008.

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  Inadmissibility of a traditional class of noncentrality parameter estimators under quadratic loss is established. The result is heuristically motivatedby the form of generalized Bayes estimators and is proved via unbiased estimators of the risk function and a solution to an integro-differential inequality.
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  CHARACTERIZATIONS OF PROPER EFFICIENT SOLUTIONS IN TERMS OF SADDLE POINTS AND DUALITY

  LI Shizheng

  Journal of Systems Science and Complexity. 1992, 5(1): 9-018.

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  In this paper we characterize the proper efficient solution of a multiobjective programming problem (P) in terms of the saddle point criterion of a new problem(S)and establish a pair of dual problems (S_α) and (D_α) in order todecide the proper efficient solution by the strong duality. We also give method of characterization in terms of the saddle point criterion of(P). Finally, we prove that every efficient solution of the matrix linear programming problem is a proper efficient solution.
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  A CLASS OF TESTS USING L STATISTIC FOR CONSTANT RELATIVE FAILURE RATE AGAINST MONOTONE RELATIVE FAILURE RATE

  K.W.Chen;ZHENG Zhongguo

  Journal of Systems Science and Complexity. 1992, 5(1): 19-026.

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  In this paper we develop tests using L-statistic for constant relative failure rate against monotone relative failure rate. Scale invariance, monotonepower and locally asymptotic power results are obtained. Some examples are presented.
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  A CRYPTOGRAPHIC STUDY ON S-BOXES OF DES TYPE Ⅲ

  YANG Junhui;DAI Zongduo;ZENG Kencheng

  Journal of Systems Science and Complexity. 1992, 5(1): 27-032.

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  The so-called selected permutations on the set of the first 16 non-negative integers are classified under the action of a certain motion group. A data-base consisted of the class representatives has been provided.
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  THE EXTRAPOLATION METHOD FOR A CLASS OF NON-SMOOTH FREDHOLM INTEGRAL EQUATIONS

  SHI Jun

  Journal of Systems Science and Complexity. 1992, 5(1): 33-041.

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  For a class of non-smooth Fredholm integral equations we prove that Richardson extrapolation method can be used to increase accuracy for finite element methods. On the basis of local refinement mesh, a superconvergence result is shown. Our theory also covers a class of non-smooth Wiener-Hopf equations and an application includes the calculation in certain linear elastic fracture problems.
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  ON ROBUST STABILITY OF POLYNOMIALS AND RELATED TOPICS

  HUANG Lin;WANG Long;Hollot;C.V.

  Journal of Systems Science and Complexity. 1992, 5(1): 42-054.

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  Complex polynomials are of significance in engineering applications. This paper addresses the robust stability of such polynomials. We first systematically discuss the alternative pair of polynomials and obtain some fundamental results. The geometric characterizations of the family of stable complex polynomials are investigated. Some connections with Sturm chains and conditions for theconvex combination of polynomials to be aperiodic are established.
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  ASYMPTOTIC PROPERTIES OF L_1-NORM KERNEL ESTIMATOR OF THE CONDITIONAL MEDIAN

  HONG Shengyan

  Journal of Systems Science and Complexity. 1992, 5(1): 55-069.

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  Let (X,Y) be a pair of R~d×R~1-valued random variables. In thispaper we investigate the asymptotic properties of the L_1-norm kernel estimator of the conditional median function of Y on X. Under appropriate regularity conditions, asymptotic normality and the optimal rates of convergence n~((-1)/(2+d)) and (n~(-1)log n)~(1/(2+d)) in the L~q(1\le q<∞)-and L~∞-norms restricted to a compactset, respectively, are obtained. Our study shows that this estimator and the well-known Nadaraya-Watson's kernel estimator of the conditional mean function of Yon X have the same asymptotic properties.
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  SYNTHESES OF ARRAYS

  LIN Dongdai;LIU Mulan

  Journal of Systems Science and Complexity. 1992, 5(1): 70-080.

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  In this paper, we present an algorithm to find a shortest linear recurring relation generating a given finite array.
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  A NOTE ON THE PAPER“A NEW SUFFICIENT CONDITION FOR HAMILTONIAN GRAPHS”

  TIAN Feng

  Journal of Systems Science and Complexity. 1992, 5(1): 81-083.

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  We prove that if G is a graph of order n and connectivity k, and there exists some t,t\le k, such that for every independent set S={x_0,x_1,…x_t} of cardinality t+1, we have sum from i=0 to t |N(S/{x_i}|>t(n-1), then G is Hamiltonian.
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  APPROXIMATE SUBDIFFERENTIALS AND NONSMOOTH ANALYSIS FINITE DIMENSIONS

  WANG Yuntong

  Journal of Systems Science and Complexity. 1992, 5(1): 84-96.

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  Ioffe's approximate subdifferentials are reviewed and some of his results are generalized. An extension of the calculus of the approximate subdifferentials for the sums to any finite number of functions is provided along with a generalization of the Dubovitzkii-Milyutin theorem. The presentation also indicates some of the limitations of nonsmooth analysis and optimization. Restriction to the class of function which is suitable for most of the purposes in nonsmooth optimization is suggested.