1989年, 第2卷, 第3期　刊出日期：1989-07-15

  

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  ON(η,d)-CONTRACTIBLE ORBITS OF VECTOR FIELDS

  Liao Shantao

  Journal of Systems Science and Complexity. 1989, 2(3): 193-227.

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  Let \mathcal{X} be the linear space of all C~1 vector fields X on a compact n-dimensional C~∞ Riemann manifold(n≥2), endowed with the C~1 norm ‖X‖_1. Write θ(X) for the numberof contractible periodic orbits of X∈\mathcal{X}, which may be finite or infinite. Let \mathcal{X}~* be the set of all X∈\mathcal{X} possessing the property that X has a neighbourhood \mathcal{V} such that every Y∈\mathcal{V} has only a finite number of singularities and at most a countable number of periodic orbits. In this paper, it is shown that any given S∈\mathcal{X}^* has a neighbourhood \mathcal{W} in \mathcal{X} together with a number λ=λ(\mathcal{W})>0 such that θ(X)≤λ for all X∈\mathcal{W}.
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  THE POSITIVITY OF THE CHERN CHARACTERS OF A HYPERSURFACE WITH SINGULARITIES

  Shi He

  Journal of Systems Science and Complexity. 1989, 2(3): 228-235.

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  The Chern characters of a hypersurface with singularities are appropriate combinations of Ehresmann characters of this hypersurface. The Chern characters are usual Chern numbers when the hypersurface is smooth. Some sorts of inequalities for these Chern characters of an n-dimensional hypersurface are derived.
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  THE MINIMAL CHARACTERISTIC BASIS OF A POLYNOMIAL IDEAL

  Gao Xiaoshan

  Journal of Systems Science and Complexity. 1989, 2(3): 236-242.

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  The concept of minimal characteristic basis(abbr. char basis) of a polynomial ideal is presened to give the uniqueness of the char basis of an ideal. For the prime ideal, we give an algorithmto construct the minimal char basis from generators of the given ideal.
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  D-CONTROLLABILITY AND CONTROL OF MULTIPARAMETER AND MULTIPLE TIME-SCALE SINGULARLY PERTURBED SYSTEMS

  Xu Kekang;Wang Zhenquan

  Journal of Systems Science and Complexity. 1989, 2(3): 243-251.

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  Concepts of D-controllability and strong D-controllability are introduced, in terms of which the controllability of multiparameter and multiple timescale singularly perturbed systems is investigated, even regardless of the relative magnitudes of the singular perturbation parameters.
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  RELATIVE FAILURE RATE AND ITS TEST

  Chen Keiwei;Zheng Zhongguo

  Journal of Systems Science and Complexity. 1989, 2(3): 252-256.

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  In this paper we develop scale and location invariant tests using U statistic forconstant relative failure rate against monotone relative failure rate. Monotone power andasymptotic normality of the test statistic are obtained. Some examples are presented, including tests for exponentiality. Weibull distribution and the two-sample problem.
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  EXACT CONTROLLABILITY OF A CLASS OF DISTRIBUTED PARAMETER SYSTEMS

  Ding Zhonghai;Feng Dexing

  Journal of Systems Science and Complexity. 1989, 2(3): 257-265.

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  The exact controllability of a class of distributed parameter systems governedby Petrowsky equations is considered. On the basis of the Hilbert Uniqueness Methodproposed by J.L.Lions, it is found that the Petrowsky systems with Dirichlet boundarycontrol are exactly controllable.
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  A FAST PROCEDURE OF VARIABLE SELECTION IN LINEAR REGRESSION MODEL

  An Baiqing

  Journal of Systems Science and Complexity. 1989, 2(3): 266-274.

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  In many situations, we are interested in selection of important variables whichare adequate for prediction under a linear regression model. In this paper, a fast selection procedure is proposed and is proved to be strongly consistent. Also, the convergence rate of misjudgement probability is given.
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  FINITE ELEMENT ERROR EXPANSION FOR NONUNIFORM QUADRILATERAL MESHES

  Lin Qun

  Journal of Systems Science and Complexity. 1989, 2(3): 275-282.

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  An error expansion for isoparametric bilinear finite element approximation is established with some kind of nonuniform quadrilateral mesh constructed in the following way: We first decompose the considered polygonal domain into several fixed convex macro-quadrilaterals and then link up some equi-proportionate points of the opposite edges in eachmacro-quadrilateral and form a quadrilateral mesh which may not be uniform and so is useful in the adaptive refinement.
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  A NEW SUFFICIENT CONDITION FOR S-CIRCUITS IN GRAPHS

  Zang Wenan;Tian Feng

  Journal of Systems Science and Complexity. 1989, 2(3): 283-288.

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  In [1], P.Paulraja posed the following problem: Let G be a 2-connected graph such that δ(G)≥3, where δ(G)denotes the minimum degree of G. If each edge of G lies on either a cycle of length 3 or a cycle of length 4, is it true that G has a spanning Eulerian subgraph? A related case in which δ(G)≥4 is settled affairmatively in this paper.