2005年, 第18卷, 第4期　刊出日期：2005-10-15

  

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  A NEWTON MULTIGRID METHOD FOR QUASILINEAR PARABOLIC EQUATIONS

  YU Xijun

  Journal of Systems Science and Complexity. 2005, 18(4): 429-438.

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  A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is $O(NN_k)$ similar to multigrid method for linear parabolic problems.
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  ROBUST KALMAN FILTERING FOR SYSTEMS UNDER NORM BOUNDED UNCERTAINTIES IN ALL SYSTEM MATRICES AND ERROR COVARIANCE CONSTRAINTS

  XIA Yuanqing;HAN Jinqing

  Journal of Systems Science and Complexity. 2005, 18(4): 439-445.

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  This paper concerns robust Kalman filtering for systems under norm bounded uncertainties in all the system matrices and error covariance constraints. Sufficient conditions are given for the existence of such filters in terms of Riccati equations. The solutions to the conditions can be used to design the filters. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed design procedure.
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  ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL

  CUI Hengjian

  Journal of Systems Science and Complexity. 2005, 18(4): 446-455.

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  This paper addresses estimation and its asymptotics of mean transformation $\theta=E[h(X)]$ of a random variable $X$ based on $n$ iid. observations from errors-in-variables model $ Y=X+~v $, where $v$ is a measurement error with a known distribution and $h(\cdot)$ is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.
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  SERVICE LEVEL EVALUATION OF AN ASSEMBLY-TO-ORDER SYSTEM

  WANG Haiwen;CHEN Rongqiu;WU Jibing

  Journal of Systems Science and Complexity. 2005, 18(4): 456-463.

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  An assembly-to-order system, which at the end the buffer distinguishes its assembly stages of the system from the downstream systems, is considered in this paper. The system produces semi-finished products for the downstream system and starts from a basic subassembly, and at each stage a component is assembled into the corresponding subassembly. The basic subassembly, components and buffer all follow a periodic-review, order up-to-level inventory policy. The buffer holds the semi-finished products to serve the specific demand from the downstream system. The service level of the system is determined by aggregate effects of the components held at stockpiles before the buffer and the basic subassembly. In order to measure the service level of the system, some notations and assumptions are made, on which the closed form expression of the service level of the system is achieved.
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  EXTINCTION AND WAVEFRONT IN AN AGE-STRUCTURED POPULATION MODEL ON INFINITE PATCHES WITH DISTRIBUTED MATURATION DELAY

  LING Jiaoxiu;WENG Peixuan

  Journal of Systems Science and Complexity. 2005, 18(4): 464-477.

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  In this paper, we derive a lattice model for a single species on infinite patches of one-dimensional space with that the maturation could occur at any age. The formulation involves a distribution of possible ages of maturation and a probability density function on which ecological assumptions are made. The following results are obtained: the existence and isotropy of the unique nonnegative solution for initial value problem, the extinction of the species provided with the non-existence of positive equilibria, and the existence of wavefronts with the wave speed $c>c_*$.
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  THE SUPERCONVERGENCE ANALYSIS OF AN ANISOTROPIC FINITE ELEMENT

  SHI Dongyang;ZHU Huiqing

  Journal of Systems Science and Complexity. 2005, 18(4): 478-487.

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  This paper deals with the high accuracy analysis of bilinear finite element on the class of anisotropic rectangular meshes. The inverse inequalities on anisotropic meshes are established. The superclose and the superconvergence are obtained for the second order elliptic problem. A numerical test is given, which coincides with our theoretical analysis.
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  ALMOST PERIODIC SOLUTION FOR A CLASS OF LOTKA-VOLTERRA TYPE $N$-SPECIES ECOLOGICAL SYSTEMS WITH TIME DELAY

  MENG Xinzhu

  Journal of Systems Science and Complexity. 2005, 18(4): 488-497.

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  The uniform permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type $N$-species competitive systems with diffusion and delays are investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and new sufficient conditions are obtained for the global asymptotic stability of the unique positive almost periodic solution of the system.
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  PARAMETER-UNIFORM FINITE DIFFERENCE SCHEME FOR A SYSTEM OF COUPLED SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS

  CEN Zhongdi

  Journal of Systems Science and Complexity. 2005, 18(4): 498-510.

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  A coupled system of singularly perturbed convection-diffusion equations is considered. The leading term of each equation is multiplied by a small positive parameter, but these parameters may have different magnitudes. The solutions to the system have boundary layers that overlap and interact. The structure of these layers is analyzed, and this leads to the construction of a piecewise-uniform mesh that is a variant of the usual Shishkin mesh. On this mesh an upwind difference scheme is proved to be almost first-order accurate, uniformly in both small parameters. We present the results of numerical experiments to confirm our theoretical results.
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  THE EXISTENCE OF SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEMS INVOLVING THE $p$-LAPLACIAN OPERATOR IN $L^{s}$-SPACES

  WEI Li;ZHOU Haiyun

  Journal of Systems Science and Complexity. 2005, 18(4): 511-521.

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  By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution $u \in L^{s}({\it\Omega})$ of nonlinear boundary value problems involving the $p$-Laplacian operator, where $2 \leq s < +\infty $, and $ \frac{2N}{N+1}< p\leq 2$ for $N(\geq 1)$ which denotes the dimension of $R^{N}.$ To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.
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  DIVERGENCE RATE OF STATE OF AR SYSTEMS WITH UNSTABLE UNIT ROOTS

  CAO Xianbing;HUANG Xiankai

  Journal of Systems Science and Complexity. 2005, 18(4): 522-528.

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  The order of weighted sum of noise sequence for stochastic system is estimated by using limit theory in probability. Then the divergence rates of state of unstable AR system driven by noise of martingale difference sequence are established.
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  DOMAIN DECOMPOSITION WITH NON-MATCHING GRIDS FOR COUPLING OF FEM AND NATURAL BEM

  YANG Ju'e;HU Qiya;YU Dehao

  Journal of Systems Science and Complexity. 2005, 18(4): 529-542.

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  In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method (FEM) and natural boundary element method(BEM). We first derive the optimal energy error estimate of the nonconforming approximation generated by this method. Then we apply a Dirichlet-Neumann(D-N) alternating algorithm to solve the coupled discrete system. It will be shown that such iterative method possesses the optimal convergence. The numerical experiments testify our theoretical results.
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  EQUILIBRIUM ALGORITHMS WITH NONMONOTONE LINE SEARCH TECHNIQUE FOR SOLVING THE TRAFFIC ASSIGNMENT PROBLEMS

  ZHAO Hui;GAO Ziyou

  Journal of Systems Science and Complexity. 2005, 18(4): 543-555.

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  This paper presents a unified framework of the nonmonotone convex combination algorithms (such as Frank-Wolfe Algorithm) for solving the traffic assignment problems. Global convergence results are established under mild conditions. The line search procedure used in our algorithm includes the nonmonotone Armijo rule, the nonmonotone Goldstein rule and the nonmonotone Wolfe rule as special cases. So, the new algorithm can be viewed as a generalization of the regular convex combination algorithm.
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  A MATHEMATICAL PROGRAMMING MODEL FOR THE COEXISTENCE OF COMPETITIONS AND COOPERATIONS PROBLEMS

  MENG Zhiqing;HU Qiying;DANG Changyan

  Journal of Systems Science and Complexity. 2005, 18(4): 556-563.

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  We study in this paper a mathematical programming model for the coexistence of competitions and cooperations problems. We introduce a new solution concept, $s$-optimal solution for the problem, which always exists under compact and continuous conditions. It is shown that an $s$-optimal solution can be obtained by solving a nonlinear programming problem. Some examples are given to explain how to compute an $s$-optimal solution.
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  MINIMALLY $( n, \lambda )$-CONNECTED GRAPHS OF LOW ORDER AND MAXIMAL SIZE

  XU Liqiong;GUO Xiaofeng

  Journal of Systems Science and Complexity. 2005, 18(4): 564-569.

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  A. Kaneko and K. Ota proved that for a minimally $(n, \lambda)$-connected graph $G$, if $|G|=p \geq 3n - 1$, then $e(G)\leq n\lambda (|G| - n)$; and if $e(G) = n\lambda (|G| - n)$, then $G$ is isomorphic to the graph $K_{n, p - n}^\lambda$ which is obtained from the complete bipartite graph $K_{n, p - n}$ by replacing each edge with $\lambda$ multiple edges; if $3n - 1\geq |G| \geq n + 1$, then $e(G) \leq \lambda (|G| + n)^2 /8$. In this paper, we determine all the minimally $(n, \lambda)$-connected graphs with order $p$ and the maximum size $\lambda (p + n)^2 /8$ for $3n - 1\geq p \geq n + 1$ for $3n-1\geq p\geq n+1$.