1996年, 第9卷, 第3期　刊出日期：1996-07-15

  

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  MINIMUM FILL-IN PROBLEM OF GRAPHS

  YUAN Jinjiang;ZHANG Heping

  Journal of Systems Science and Complexity. 1996, 9(3): 193-197.

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  The computational complexity of the minimum fill-in problem of graphs is discussed in this paper. We prove that this problem is NP-complete even for bipartite graphs and square graphs. A linear time algorithm for outerplane graphs is got. The computational complexity of the minimum fill-in problem of graphs is discussed in this paper. We prove that this problem is NP-complete even for bipartite graphs and square graphs. A linear time algorithm for outerplane graphs is got.
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  QUANTITATIVE PROPERTIES OF GREEN EQUIVALENCES ON SPECIAL MONOIDS

  WU Jinzhao

  Journal of Systems Science and Complexity. 1996, 9(3): 198-204.

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  For the monoids presented by finite special Church-Rosser Thue systems,the number of each kind of Green equivalence classes is either one or infinite, and it is computable in polynomial time. As applications, the regular problem and the existence of non-trivial idempotents for such monoids are decidable in polynomial time. And a result about the descriptive power of finite special Church-Rosser Thue systems is obtained.
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  SMOOTH PL-ESTIMATOR OF DISTRIBUTION FUNCTION UNDER RANDOM TRUNCATION DATA

  ZHOU Yong

  Journal of Systems Science and Complexity. 1996, 9(3): 205-215.

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  For the nonparametric smooth PL-estimator Fn, the smooth PL-process (Fn - F) can be uniformly represented by a smooth empirical process plus a negligible remainder term when the data are subject to random left truncation. The law of the iterated logarithm (LIL) and the weak convergence of the smooth PL-process are established from this representation.
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  AN ELIMINATION METHOD FOR DIFFERENTIAL POLYNOMIAL SYSTEMS I

  WANG Dongming

  Journal of Systems Science and Complexity. 1996, 9(3): 216-228.

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  This is the first in a series of papers describing an elimination method for differential (abbr. d-) polynomial systems. We present two mds algorithms, one with and the other without projection, for decomposing any system of multivariate ordinary d-polynomials over an ordinary d-field of characteristic 0 into d-triangular systems. The second algorithm that computes d-triangular systems possessing certain projection property also yields a quantifier elimination procedure for algebraically closed d-fields. An example is given to illustrate our algorithms with their preliminary implementation in Maple. In the forthcoming papers of this series, we shall present algorithms for irreducible zero decomposition of ordinary d-polynomial systems and zero decomposition of partial d-polynomial systems over d-fields of arbitrary characteristic.
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  EQUILIBRIUM PROBLEMS ON A NETWORK WITH VECTOR-VALUED COST FUNCTIONS

  CHEN Guangya

  Journal of Systems Science and Complexity. 1996, 9(3): 229-235.

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  A kind of equilibrium problems of networks with vector-valued cost functions has proposed. Equivalence between the equilibrium problem of networks and the vector variational inequality is proved.
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  TWO BOUNDARY VALUE PROBLEMS FOR THE REGULAR FUNCTIONS WITH VALUES IN A REAL CLIFFORD ALGEBRA IN THE HYPERBALL

  HUANG Sha

  Journal of Systems Science and Complexity. 1996, 9(3): 236-241.

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  In this paper, introducing the concept of“quasi- permutation”,we solve the sign problem often met with when the operation is carried out in the incommutable Clifford algebra, and using the results in Hua Luogeng and I. N. Vekua famous works, we give the existence and uniqueness theorem of solution of the two problems of Dirichlet's type for the regular functions with values in a 2^{n-1}-dimensional Clifford algebra An(R) in the hyperball and the integral representation of the solution of this problem.
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  NORMAL EULER NUMBERS OF EMBEDDING NONORIENTABLE SURFACES IN 4-MANIFOLDS

  GAO Hongzhu

  Journal of Systems Science and Complexity. 1996, 9(3): 242-251.

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  Let M be a nonorientable surface of genus n. M embeds in a four-manifold N which is not necessarily homologically 1-connected. In the case of M representing zero class in H_2(N,Z_2), restrictions on normal Euler numbers of these embeddings are given.
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  A NOTE ON THE L_p COMPARISON BETWEEN THE BOOTSTRAP AND RANDOM WEIGHTING

  SHI Jian

  Journal of Systems Science and Complexity. 1996, 9(3): 252-258.

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  In the literature of resampling methods, the bootstrap and random weighting are much more studied (the latter is also called Bayesian bootstrap). When they are applied to approximate distributions of pivotal statistics, the strong consistency is often discussed.However, one could not determine which is better becauae both of their accuracies are O (n/(loglogn)1/2). In this note, a comparison between them is investigated under the Lp norm. A result obtained shows that the bootstrap is relatively better.
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  A NEW SUFFICIENT CONDITION FOR THE CONVERGENCE OF THE DFP ALGORITHM WITH WOLFE LINE SEARCH

  XU Dachuan;LIU Guanghui

  Journal of Systems Science and Complexity. 1996, 9(3): 259-269.

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  The DFP algorithm is one of the mest famous numerical algorithms for unconstrained optimization.It is an open problem whether DFP algorithm with inexact line searches is globally convergent. In this paper, we propose a sufficient condition for the convergence of the DFP algorithm with Wolfe line search on uniformly convex objective function.
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  A MULTI-PARAMETER SPLITTING EXTRAPOLATION AND A PARALLEL ALGORITHM FOR PARABOLIC PROBLEM

  LIU Xiaoqi

  Journal of Systems Science and Complexity. 1996, 9(3): 270-277.

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  In this paperl we show that the finite element solution of parabolic equation hasa multi-parameter asymptotic error expansion. From this expansion, a multi-parameter splitting extrapolation method and a Parallel algorithm for solving parabolic equations with higher order accuracy are developed.
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  ON TAKEUCHI EFFICIENCY IN TWO CLASSES OF SINGLE-PARAMETER TWO-SIDED TRUNCATED DISTRIBUTIONS

  LIANG Hua;CHEN Guijing

  Journal of Systems Science and Complexity. 1996, 9(3): 278-282.

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  This paper is concerned with the asymptotic efficiency for two classes oftruncated distributions: f(x;\theta)I_{(\theta\leq x\leq 2\theta)}, and f(x;\theta)I_{(\theta\leq x\leq \theta+1)}. It is shown that the usual estimators of are asymptotically medially unbiased, but noneis asymptotically efficient in the sense of Takeuchi.
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  SELF-ORGANIZING MODELLING IN EXPERIMENTA SYSTEMS ANALYSIS

  J.A.Muller

  Journal of Systems Science and Complexity. 1996, 9(3): 283-287.

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  Several methodological Problems of experimental systems analysis can be overcome by means of parametric and nonparametric selection procedures. Together with theselection of models with optimal complexity and application of optimal clusterizations forstructure analysis the selection of Predictions by means of analogous patterns is considered.