1995年, 第8卷, 第3期　刊出日期：1995-07-15

  

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  A SUPERLINEAR CONVERGENT FEASIBLE METHOD FOR NONLINEAR PROGRAMMING WITH NONLINEAR CONSTRAINTS

  GAO Ziyou;HE Guoping;LIU Rengkui

  Journal of Systems Science and Complexity. 1995, 8(3): 193-202.

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  A new feasible algorithm is proposed for the minimization of a continuously differentiable function subject to inequality constraints. This algorithm only needs to solve one quadratic programming subproblem at each iteration and can produce feasible successive iterates which have global convergence and local superlinear convergence under some suitable assumptions. Some numerical results are reported.
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  POSITIVE SOLUTIONS FOR DIRICHLET PROBLEMS OF SINGULAR SEMILINEAR ELLIPTIC EQUATIONS

  CUI Shangbin

  Journal of Systems Science and Complexity. 1995, 8(3): 203-208.

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  This paper studies the existence of solutions of the following problem: where Ω is a bounded domain in Rn with smooth boundary, L is a second order uniformly elliptic linear operator, and f(x, u ε) is a C1 function defined on Ω × (0, +∞)×Rn which may be singular both at μ=0 and at x ∈Ω. By using the upper and lower solutions method combined with the domain approximation method, we prove that under certain conditions this problem has at least one solution.
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  MONOTONE COUPLING AND STOCHASTIC ORDERING OF ORDER STATISTICS

  HU Taizhong

  Journal of Systems Science and Complexity. 1995, 8(3): 209-214.

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  Let X_i, Y_j, i, j = 2…, n, be independent nonnegative r.v.'s with X_i～ F_i(t) = 1-exp(-R_i(t)) and Y_j～ G_j(t) = 1- exp(-R(t)), j=1,…, n. Two kinds of models are considered, and the monotone coupling of order statistics X(1),…, X(n) and y(1) ,…, Y(n) is established under certain conditions, that is, it is possible to construct on a common probability space r.v.'s X, K, i= 1,… , n, such that for each i, Y X a.s. and(X,…, X)=d (X_1,…, X_n), (Y,…, Y) =d (Y_1,…, Y_n). The result of Model 1 generalizes the results of Proschan and Sethuraman (1976), Ball (1985) and Barbour et al (1991). We also obtain a result about the stochastic ordering of order statistics. All these results are useful in studying epidemic model and reliability theory.
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  CORRECTION NYSTROM SOLUTIONS OF BIE IN POLYGONAL DOMAIN ON THE PLANE

  SHI Jun;LIN Qun

  Journal of Systems Science and Complexity. 1995, 8(3): 215-223.

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  In this paper, we present a new more efficient Nystrom approximation method for boundary integral equations in a polygonal domain on the plane and show that this is not only a high convergent order and more simple method but also an adaptive one.
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  A LIOUVILLE THEOREM FOR GLOBAL SOLUTIONS OF HOMOGENEOUS CAUCHY PROBLEM OF MRABOLIC EQUATIONS

  MIN Taishan;LIANG Xiting

  Journal of Systems Science and Complexity. 1995, 8(3): 224-227.

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  The Liouville theorem for harmonic functions is extended to the generalized global solutions of homogeneous Cauchy problem of the following parabolic equation u_t- div\underline{A}(x,t,u,\Delta u) + B(x,t,u,\Delta u) = 0 in E^n×(0,∞)where B(x,t,μ,ζ) has superlinear growth with respect to ζ. For the growth order of B with respect to ζfrom the linear arising to the superlinear case the treatment for parabolic equations is different from that for elliptic ones.
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  UNIFORM PERSISTENCE IN DISCRETE SEMIDYNAMICAL SYSTEM AND ITS APPLICATION

  WANG Wendi;MA Zhien

  Journal of Systems Science and Complexity. 1995, 8(3): 228-233.

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  In this paper we consider the uniform persistence of a discrete semidynamical system. We establish the conditions under which the weak persistence implies the uniform persistence. We also apply the theory to a two-dimensional periodic model to obtain its uniform persistence.
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  EXISTENCE OF WEAK SOLUTIONS OF 2-D EULER EQUATIONS WITH INITIAL VORTICITY ω0 ∈L(logL~+)~α(α＞1/2)

  WU Yonghui

  Journal of Systems Science and Complexity. 1995, 8(3): 234-239.

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  In this paper we obtain the existence of global in the weak solution of 2-D inviscid Euler equations with initial vorticity ω0 ∈L(log L)α ∩ L1 (α> i/2) which is of the Zygmund class and contains any space LP ∩ L1 (p>1). At the same time we correct the remark of Professor Chae who claims that ω0 ∈L(log L) is the critical case. Moreover, a counter-example shows that not all approximating solutions of the Euler equations whose vorticities contained in L(log L)α∩ L1 (α< 1/2) tend to a solution of the Euler equation,and in this sense our result is optimistical. The solution is obtained by approximating the Euler equations by Navier-Stokes equations with the same initial data and then making the viscosity vanish.
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  DIAGNOSTICS FOR NONLINEAR REGRESSION MODEL WITH WEIGHTING OR TRANSFORMATION

  SHI Jianqing;WEI Bocheng

  Journal of Systems Science and Complexity. 1995, 8(3): 240-248.

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  In this paper, we propose several diagnostic measures for assessing the influence of an individual case and small perturbations on the transformation power estimator and the variance function estimators in nonlinear regression models with transformation and weighting. A numerical example is presented to illustrate our results.
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  LIMIT THEOREMS FOR SUMS AND MAXIMA OF MIRWISE NEGATIVE QUADRANT DEPENDENT RANDOM VARIABLES

  QI Yongcheng

  Journal of Systems Science and Complexity. 1995, 8(3): 249-253.

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  Consider a sequence of pairwise negative quadrant dependent random variables. This paper studies the almost sure convergence of sequences of partial sums and maxima.
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  GENERALIZED SUBCONVEXLIKE FUNCTIONS AND MULTIPLE OBJECTIVE OPTIMIZATION

  YANG Xinmin

  Journal of Systems Science and Complexity. 1995, 8(3): 254-259.

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  In this paper, we give some equivalent conditions for generalized subconvexlike functions. A Farkas-Minkowski theorem for generalized subconvexlike functions is then proved. These results are used to characterize properly efficient solutions for multiple objective programming problems with generalized subconvexlike functions by associated scalar problems.
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  CONVERGENCY OF THE MAXIMUM OF PERIODOGRAM

  HE Shuyuan

  Journal of Systems Science and Complexity. 1995, 8(3): 260-269.

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  For a linear stationary sequence generated from a martingale difference white noise the uniform log convergency is proved without the aukward condition that the second conditional moment is a constant.
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  A MODIFIED HOMOGENEOUS AND SELF-DUAL LINEAR PROGRAMMING ALGORITHM

  GUO Tiande;WU Shiquan

  Journal of Systems Science and Complexity. 1995, 8(3): 270-277.

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  In this paper,we modify the corrector step of the homogeneous and self-dual linear programming algorithm, proposed by Ye, Todd and Mizuno[1]. The duality gap is reduced by a constant fraction per iteration. It is shown that our modified algorithm retains the O(\sqrt{n}L) iteration complexity and the duality gap converges to zero.
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  CONTINUATION METHOD OF NONLINEAR INTEGRAL EQUATIONS

  YANG Fenghang;SUN Jing

  Journal of Systems Science and Complexity. 1995, 8(3): 278-286.

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  In this paper a continuation method for the Urysohn nonlinear equation is to be established by the use of a homotopy transformation, and the homotopy equation will result in the Cauchy problem of a differentio-integral equation, where the form of the integral equation is linear. Thus this continuation method possesses linearized characteristic and it can be applied to the numerical solution for nonlinear integral equation very conveniently and effectively.
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  A NOTE ON THE PAPER "ON THE CONNECTIVITY OF CAYLEY COLOR GRAPHS"

  MENG Jixiang;HUANG Qiongxiang

  Journal of Systems Science and Complexity. 1995, 8(3): 287-288.

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  In [1], Huang and Liu characterized the Cayley color graphs the connectivity of which attains their regular degrees. Their characterization contains a flaw. This note presents the correct form of the characterization.