1989年, 第2卷, 第1期　刊出日期：1989-01-15

  

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  GENERIC POINTS IN ALGEBRAIC GEOMETRY AND LOEB MEASURES

  Li Banghe

  Journal of Systems Science and Complexity. 1989, 2(1): 1-003.

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  For any irreducible complex projective variety A, we prove that in the nonstandard extension ~*A of A in a polysaturated model, the set of points which are not generic points of A has Loeb measure zero. This is similar to the Sard theorem asserting that the critical values of a smooth maphave Lebesgue measure zero.
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  THE EQUALITIES OF THE CHERN CLASSES

  Shi He

  Journal of Systems Science and Complexity. 1989, 2(1): 4-013.

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  In this paper we generalize the results of [1] and prove that, for any given 4≤k≤n, the Chern classes of hypersurface V_n corresponding to the partitions of k also satisfy some equalities. Furthermore, we obtain the equalities of Chern classes concretely for k=4,5,6.
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  ASYMPTOTIC BEHAVIOR OF THE SOLUTION FOR THE NEUTRON TRANSPORT EQUATION IN A SLAB WITH GENERALIZED REFLECTING BOUNDARY CONDITIONS

  Xu Jianguo;Wang Miansen;Zhu Guangtian

  Journal of Systems Science and Complexity. 1989, 2(1): 14-021.

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  This paper discusses the neutron transport equation in a slab with generalized reflecting boundary conditions. By means of the positive C_0-semigroup theory, we have proved that this problem has a unique nonnegative solution and found the spectral property of the corresponding transport operator. Finally we give the asymptotic behavior of the solution for this equation.
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  BIPANCYCLISM IN HAMILTONIAN BIPARTITE GRAPHS

  Tian Feng;Zang Wenan

  Journal of Systems Science and Complexity. 1989, 2(1): 22-031.

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  It is shown that if G is a hamiltonian bipartite graph on 2n vertices and δ(G)>2n/5+2, where n≥60, then G is bipancyclic.
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  THE MORSE INDEX OF A SADDLE POINT

  Liu Jiaquan

  Journal of Systems Science and Complexity. 1989, 2(1): 32-039.

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  This paper is devoted to clarifying the relationship between the classical Morse theory and the Mountain Pass Lemma via the local linking concept. It is shown that for a C~1-function f with alocal linking, the m-th critical group is nontrivial, where m is the Morse index. Combined with the behavior of f at infinity, this result can be used to offer the existence of nontrivial critical points.
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  STOCHASTIC ADAPTIVE CONTROL FOR SYSTEMS WITH NOISE BEING AN ARMA PROCESS

  Chen Hanfu(Han-Fu Chen);Zhang Jifeng

  Journal of Systems Science and Complexity. 1989, 2(1): 40-053.

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  Stochastic adaptive control is considered for the discrete-time multi-input and multi-output system of multi-delay with noise expressed by an ARMA process. The CARIMA model is a special case of the system in question. The optimal adaptive control law is given and it is shown thata quadratic cost function is minimized and the closed-loop system is stable. Further, when the systemis of minimum phase, the convergence rates of parameter estimates and of the cost-function are alsoderived.
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  FINITE ELEMENT EXPANSION FOR VARIABLE COEFFICIENT ELLIPTIC PROBLEMS

  Ding Yanheng;Lin Qun

  Journal of Systems Science and Complexity. 1989, 2(1): 54-069.

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  The Ritz projections of the elliptic problem -\partial_i (a_(ij)(\partial _ju)+c_0u=f in Ω, u=0 on \partial Ω, and the quasilinear eiliptic problem -\partial (a_i(x,Du))+a_0(x,Du)=0 in Ω, u=0 on \partial Ω with linear finite elements admit an asymptotic error expansion, respectively, for certain classes of“uniform” meshes. This provides the theoretical justification for the use of Richardson extrapolation for increasing the accuracy of the scheme from O(h~2) to O(h~4 |ln h|).
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  COMPUTATIONAL COMPLEXITY OF INTEGRATION AND DIFFERENTIATION OF CONVEX FUNCTIONS

  Du Dingzhu;Ker-I Ko

  Journal of Systems Science and Complexity. 1989, 2(1): 70-079.

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  In this paper, we study the computational complexity of the integrals and the derivatives ofconvex functions defined on the interval [0,1].
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  ALL ADMISSIBLE LINEAR ESTIMATES OF REGRESSION COEFFICIENTS UNDER MATRIX LOSS

  Wu Qiguang;Chen Jianbao

  Journal of Systems Science and Complexity. 1989, 2(1): 80-091.

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  The necessary and sufficient conditions for a linear estimator of a linear estimable function of regression coefficients in a general fixed effects linear model with the assumptions of normality to beadmissible in the class of all estimators under matrix liss function are given. For a general random effects or mixted effects linear model the necessary and sufficient conditions are obtained too.
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  THE SOLUTION OF A PARAMETERIC EQUATION ARISING IN TRANSPORT THEORY

  Yang Bin;Yang Mingzhu

  Journal of Systems Science and Complexity. 1989, 2(1): 92-096.

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  This paper deals with the solution of a neutron transport equation with parameter δ. Using the theory of functional analysis, we discuss the distribution of the parameters which make the equationhave a non-zero solution, and obtain a necessary and sufficient condition for the existence of the control critical eigenvalue δ_0 which possesses a physical meaning.