1992年, 第5卷, 第2期　刊出日期：1992-05-15

  

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  A NOTE ON THE SPECTRUM OF NEUTRON TRANSPORT OPERATOR IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

  SONG Degong;WANG Miansen;ZHU Guangtian

  Journal of Systems Science and Complexity. 1992, 5(2): 97-107.

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  The spectrum of neutron transport operator A in an arbitrary non-homogeneous slab geometry is discussed in consideration of anisotropic scattering and fission. Under the assumptions that the boundary reflection coefficient function α(v,μ),γ(v,μ) and the scattering-fission kernel k(x,v,v′,μ,μ′)are bounded measurable, and the total collision frequency v∑(x,v) is square integrable, it is shown that A has at most finite spectrum points in any strip {λ=β+i\tau |β_1\le β\le β_2}, where β_2>β_1>-λ~*, with λ~* the essential infimum of v∑(x,v). Fi-nally, the asymptotic expansion of the solution for the time-dependent equation (dN)/(dt)=AN,N(0)=N_0 is given as a corollary.
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  PATHS BETWEEN TWO VERTICES IN A TREE GRAPH

  LIU Guizhen

  Journal of Systems Science and Complexity. 1992, 5(2): 108-110.

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  Let T(G) be the tree graph of a simple graph G. It is proved that if T and T′are two vertices of T(G) such that d_T(G)(T)\le d_T(G}(T′), then there ared_T(G)(T) internally disjoint paths in T(G) joining T and T′.
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  THE OPTIMALITY CONDITIONS OF D-PSEUDOCONVEX PROGRAMMING WITH OPERATOR CONSTRAINTS

  ZHANG Huaxiao;JIN Yuefeng;HE Lunzhi

  Journal of Systems Science and Complexity. 1992, 5(2): 111-120.

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  The problem of D-pseudoconvex programming with operator constraints is discussed in this paper. Some new optimality conditions are presented and an error made by V. Barbu in [4] is pointed out.
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  A REMARK ON PERIODIC SOLUTIONS OF SINGULAR HAMILTONIAN SYSTEMS WITH SUBLINEAR TERMS

  DING Yanheng;LI Shujie

  Journal of Systems Science and Complexity. 1992, 5(2): 121-126.

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  In this paper, we prove the existence of multiple periodic solutions for a class of singular Hamiltonian systems with sublinear terms via variational methods.
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  FINITE ELEMENT APPROXIMATION USING A GRADED MESH ON DOMAINS WITH REENTRANT CORNERS

  CHEN Hongsen;LIN Qun

  Journal of Systems Science and Complexity. 1992, 5(2): 127-140.

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  Finite element approximation of the elliptic operator on a non-convexdomain composed of rectangles is considered using a graded mesh. Some error estimates and error expansion are presented.
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  REMARKS ON THE BINDING NUMBER FOR [a,b]-FACTORS

  CHEN Ciping

  Journal of Systems Science and Complexity. 1992, 5(2): 141-145.

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  We give some answers to the following question: If the binding number of a graph G is more than 1+(a-1)/b, does G have an [a,b]-factor?
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  OPTIMAL AND ROBUST DETECTION OF MULTIVARIATE OUTLIERS FOR ELLIPTICALLY CONTOURED DISTRIBUTION

  WANG Xueren;PAN Jianxin

  Journal of Systems Science and Complexity. 1992, 5(2): 146-163.

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  The outlier problem for a multivariate elliptically contoured distribution's random sample with mean slippage is defined and the likelihood ratio test ofthe null hypothesis, in which there are no outliers, versus the alternative hypothesis, in which some outliers are present, is derived. We show that the testing problem is invariant under a group of affine transformations and obtain the maximal invariance which is equivalent to the likelihood ratio testing statistic. Furthermore, the non-null and null density distribution functions of the likelihood ratio testing statistic are derived. We find that the null density distribution function of the testing statistic is robust and the density distribution function is a monotonical likelihood ratio function of the maximal invariance. Therefore, the likelihood ratiotest is a uniformly most powerful invariant test among the group of affine transfor-mations. In the last section, we give an example of detecting multivariate outliers in elliptically contoured distribution.
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  LOCAL OSCILLATION MODULUS OF THE UNIFORM EMPIRICAL PROCESS

  HONG Shengyan

  Journal of Systems Science and Complexity. 1992, 5(2): 164-179.

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  In this paper, we present a detailed description of the limiting behavior of local oscillation of the uniform empirical process. As an application, we establish the laws of the iterated logarithm for the “naive”estimator and the nearest neighbor estimator of the density function. When compared to those of Hall and Hong, the conditions of the bandwidth imposed here are as weak as possible.
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  A SIMPLIFIED APPROACH TO EMBEDDING PROBLEMS IN NORMAL BORDISM FRAMEWORK

  LI Banghe;LIU Rong;ZHANG Ping

  Journal of Systems Science and Complexity. 1992, 5(2): 180-192.

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  The purpose of this paper is to simplify the computations of the normal bordism groups Ω_i(W_f,M×P~∞;\phi_f) and Ω_i(C_f,\partial W;θ_f) which Salomonsen and Dax introduced respectively to study the existence and isotopy classification of differential embeddings of manifolds in manifolds in the metastable range. A simpler space pair (K_f,M×P~∞)is constructed to replace (W_f,M×P~∞). It is shown that(K_f,M×P~∞) is homotopy equivalent to (W_f,M×P~∞)and homotopy (n-1)-equivalent to (C_f,\partial W). To demonstrate the efficacy of this simplification, the isotopy groups [M~n\subset RP~(n+k)], if n\le 2k-4 and M~n is a closed (n-k+2)-connected manifold, and [M~n\subset L(p;q_1…,q_m)], if 3n\le 4m-2,M~n is a closed (2n-2m+1)-connected manifold and L is a (2m+1)-dimensional lens space, are specifically computed.