1991年, 第4卷, 第1期　刊出日期：1991-02-15

  

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  ESTIMATION OF A KIND OF JUMP REGRESSION FUNCTION

  Qiu Peihua

  Journal of Systems Science and Complexity. 1991, 4(1): 1-013.

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  Research on jump regression functions has not been adequate yet According to the information about the number of jumps, their positions and jump magnitudes, jump regression functions can be classified into eight types. This paper deals especially with the second jump regression function. First of all,a concept of trimmed spline estimate is proposed andwith it an L~2-consistent estimate of the smoothing part of the jump regression function is obtained. This along with the L~2-consistent estimate of jump magnitude constitutes an estimate of the second jump regression function. This paper discusses also the case that the jump positions have some indeterminacy. A new criterion is suggested and its unique solution derived. In the end, a few numerical results are given.
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  A POLYNOMIAL ALGORITHM FOR FINDING A BUMP OPTIMAL EXTENSION OF AN ORDERED SET

  Li Weixuan

  Journal of Systems Science and Complexity. 1991, 4(1): 14-019.

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  A polynomial algorithm for finding a linear extension of an ordered set which has the minimum bumps is presented.
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  ADMISSIBILITY OF SIMULTANEOUS ESTIMATION OF SEVERAL LOSSES

  Wu Qiguang

  Journal of Systems Science and Complexity. 1991, 4(1): 20-031.

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  In this paper, admissibility and inadmissibility results of simultaneous estimation of losses of multivariate normal mean estimators are given. Admissible estimators for losses of usual estimators of multivariate gamma parameters, multivariate binomial parameters and Poisson parameters are obtained respectively.
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  CONSTRUCTING THE HAMILTON CYCLE ON γ-ARY DE BRUIJN-GOOD GRAPH——THE γ-ARY DE BRUIJN SEQUENCE

  Yang Junhui

  Journal of Systems Science and Complexity. 1991, 4(1): 32-040.

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  In the paper we use a nonsingular function as an elementary recurring function togenerate a portion graph G(f)on r-ary de Bruijn-good graph, define order function on G(f), construct associated state matrix sets, merge cycles by interchanging successors of associated states to form a full length cycle-the Hamilton cycle on r-ary de Bruijn-good graph(the r-ary de Bruijn sequence).
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  EXTRAPOLATION FOR FINITE ELEMENT METHODS OF THE FIRST KIND FREDHOLM INTEGRAL EQUATIONS

  Zhou Aihui

  Journal of Systems Science and Complexity. 1991, 4(1): 41-050.

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  In this paper,a numerical analysis of finite element methods for Fredholm equations of the first kind, which is based upon regularization, is made. It shows that extrapolation algorithms can accelerate the convergence of approximate solutions.
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  LINEAR COMPLEXITY AND THE MINIMAL POLYNOMIAL OF LINEAR RECURRING SEQUENCES OVER Z/(m)

  Dai Zongduo;Huang Minqiang

  Journal of Systems Science and Complexity. 1991, 4(1): 51-054.

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  In this note we discuss the annihilating properties of sequences over Z/(m). By considering the linear complexity and the annihilator structure, we derive the uniqueness condition for the minimal polynomial, and some related results of decimation sequences.
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  SPANNING TRAILS OF GRAPHS

  Liu Zhenhong;Jin Guoping

  Journal of Systems Science and Complexity. 1991, 4(1): 55-067.

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  Let G be a 2-edge-connected simple graph. We give a sufficient condition in which for any x,y∈V(G), there is an (x,y)-trail which contains every vertex of G(x=y is allowed)except some graphs.
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  A ROBUST DECOMPOSITION OF LINEAR PROGRAMMING USING A GOAL-PARTITIONING METHOD

  Tao Huimin;Zhu Jishan

  Journal of Systems Science and Complexity. 1991, 4(1): 68-077.

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  The Dantzig/Wolfe linear programming decomposition algorithm has had important economic interpretations as well as a widespread impact on solving large scale linear programming problem. In this paper we consider a similar underlying structure, where however there is only one coupling inequality or equation. With this simplification, we demonstrate how to achieve an equitable partition of the overall coupling resource to individual subproblem constraints through a simple iteration procedure which appears to be very efficient.
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  MORSE THEORY UNDER GENERAL BOUNDARY CONDITIONS

  Zhang Gongqing(Kung Ching Chang);Liu Jiaquan

  Journal of Systems Science and Complexity. 1991, 4(1): 78-083.

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  Morse inequalities for Morse functions under general boundary conditions were initially studied by Morse and Van Schaack. It is our purpose to present a natural extension of the theorem due to Morse and Van Schaack with a considerably slmplified proof.
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  THE ASYMPTOTIC BEHAVIOR AND APPLICATIONS OF A CLASS OF PP R-STATISTICS

  Shi Peide

  Journal of Systems Science and Complexity. 1991, 4(1): 84-096.

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  This paper uses R-statistics as projection indices to construct a class of projection pursuit (PP)R-statistics for multivariate two sample tests via PP techniques. Examples are presented as applications to the location and dispersion problems.