2004年, 第17卷, 第4期　刊出日期：2004-10-15

  

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  SENSITIVITY ANALYSIS FOR PARAMETERIZED VARIATIONAL INEQUALITY PROBLEMS

  Fei LI

  Journal of Systems Science and Complexity. 2004, 14(4): 445-451.

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  This paper presents sensitivity analysis for parameterized variational inequality problems (VIP). Under appropriate assumption, it is shown that the perturbed solution to parameterized VIP is existent, unique, continuous and differentiable with respect to perturbation parameter. In the case of differentiability, we derive the equations for calculating the derivative of solution variables with respect to the perturbation parameters.
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  GLOBAL SUPERCONVERGENCE ANALYSIS OF WILSON ELEMENT FOR SOBOLEV AND VISCOELASTICITY TYPE EQUATIONS

  Da Yong JIN;Tang LIU;Shu Hua ZHANG

  Journal of Systems Science and Complexity. 2004, 14(4): 452-463.

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  In this paper the Wilson nonconforming finite element is employed to solve Sobolev and viscoelasticity type equations. By means of post-processing technique, global superconvergence estimates are obtained for quasi-uniform rectangular meshes. Finally, an error correction scheme is presented.
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  EXISTENCE OF HAMILTONIAN \mbox{\boldmath$k$}-FACTOR

  Mao Cheng CAI;Qi Zhi FANG;Yan Jun LI

  Journal of Systems Science and Complexity. 2004, 14(4): 464-471.

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  A Hamiltonian $k$-factor is a $k$-factor containing a Hamiltonian cycle. An $n\over 2$-critical graph $G$ is a simple graph of order $n$ which satisfies $\delta(G)\geq n/2$ and $\delta(G-e)
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  KUHN-TUCKER NECESSARY CONDITIONS FOR {\boldmath$(h,\varphi)$}-MULTIOBJECTIVE OPTIMIZATION PROBLEMS

  Yi Hong XU;San Yang LIU

  Journal of Systems Science and Complexity. 2004, 14(4): 472-484.

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  Five kinds of cones are introduced, which are used to establish the constraints qualifications, under which the generalized Kuhn-Tucker necessary conditions are developed for a class of generalized $(h,\varphi)$-differentiable single-objective and multiobjective programming problems by using Motzkin's alternative theorem and Ben-Tal generalized algebraic operations.
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  EXISTENCE OF 0-1 UNIVERSAL MINIMAL TOTAL DOMINATING FUNCTIONS

  Qi Zhi FANG

  Journal of Systems Science and Complexity. 2004, 14(4): 485-491.

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  In this paper, we study the existence of 0-1 universal minimal total dominating functions in a graph. We establish a formulation of linear inequalities to characterize universal minimal total dominating functions and show that for a kind of graphs whose adjacent matrices are balanced, the existence of universal minimal total dominating functions coincides with that of 0-1 ones. It is also proved that for general graphs, the problem of testing the existence of 0-1 universal minimal total dominating functions is ${\cal NP}$-hard.
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  A NEW TEST PROCEDURE FOR NEW BETTER THAN USED IN INCREASING CONVEX ORDERING

  Xiao Hu LI

  Journal of Systems Science and Complexity. 2004, 14(4): 492-499.

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  A new nonparametric procedure is developed to test the exponentiality against the strict NBUC property of a life distribution. The exact null distribution is derived by the theory of sample spacings, and the asymptotic normality is also established by the large sample theory of L-statistics. Finally, the lower and upper tailed probability of the exact null distribution and some numerical simulation results are presented as well.
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  EXISTENCE AND ALGORITHM OF SOLUTIONS FOR GENERALIZED STRONGLY MIXED IMPLICIT QUASI-VARIATIONAL INEQUALITIES

  Lu Chuan ZENG

  Journal of Systems Science and Complexity. 2004, 14(4): 500-510.

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  The purpose of this paper is to introduce and study a new class of generalized strongly mixed implicit quasi-variational inequalities in Hilbert spaces, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case. By applying the auxiliary variational principle technique, the existence of solutions for this class of quasi-variational inequalities is proved. Moreover, a new iterative algorithm for computing approximate solutions is constructed and the convergence criteria for this iterative algorithm are also established.
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  ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

  Jin Hong YOU;Min CHEN;Gemai CHEN

  Journal of Systems Science and Complexity. 2004, 14(4): 511-522.

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  Consider a semiparametric regression model with linear time series errors $Y_k=x'_k\beta+g(t_k)+\varepsilon_k, 1\le k\le n,$ where $Y_k$'s are responses, $x_k=(x_{k1},x_{k2},\cdots,x_{kp})'$ and $t_k\in {\cal T}\subset {\cal R}$ are fixed design points, $\beta=(\beta_1,\beta_2,\cdots,\beta_p)'$ is an unknown parameter vector, $g(\cdot)$ is an unknown bounded real-valued function defined on a compact subset $\cal T$ of the real line ${\cal R}$, and $\varepsilon_k$ is a linear process given by $\varepsilon_k=\sum^{\infty}_{j=0} \psi_je_{k-j},\ \psi_0=1,$ where $\sum^{\infty}_{j=0}|\psi_j|<\infty$, and $e_j,$ $j=0, \pm 1, \pm 2, \cdots$, are i.i.d. random variables. In this paper we establish the asymptotic normality of the least squares estimator of $\beta$, a smooth estimator of $g(\cdot)$, and estimators of the autocovariance and autocorrelation functions of the linear process $\varepsilon_k$.
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  GOAL PROGRAMMING ALGORITHM FOR A TYPE OF LEAST ABSOLUTE VALUE REGRESSION PROBLEM

  Kui Ran SHI;Tiao Jun XIAO;Wei Rong ZHANG

  Journal of Systems Science and Complexity. 2004, 14(4): 523-531.

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  This paper develops goal programming algorithm to solve a type of least absolute value (LAV) problem. Firstly, we simplify the simplex algorithm by proving the existence of solutions of the problem. Then, we present a goal programming algorithm on the basis of the original techniques. Theoretical analysis and numerical results indicate that the new method contains a lower number of deviation variables and consumes less computational time as compared to current LAV methods.
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  VERTEX-DISJOINT QUADRILATERALS IN BIPARTITE GRAPHS

  Jin YAN;Gui Zhen LIU

  Journal of Systems Science and Complexity. 2004, 14(4): 532-537.

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  H. Wang considered the minimum degrees condition that $G$ has large vertex-disjoint cycles in bipartite graphs. Motivated by this, we consider the small vertex-disjoint cycles in bipartite graphs in this paper. We prove the following result: Let $m\geq 3$, $n\geq 2$ and $k\geq 1$ be three integers. Let $G=(V_1,V_2;E)$ be a bipartite graph with $|V_1|=|V_2|=n\geq 2k+1$. If the minimum degree $\delta(G)\geq k +1$ and $\sum\limits_{x\in V(C)}d(x)\geq m(n+1)+1$ for any cycle $C$ of $G$ with length $2m$, then $G$ contains $k$ vertex-disjoint cycles of length 4. Moreover, the degrees condition is sharp.
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  GALERKIN ALTERNATING-DIRECTION METHODS FOR NONRECTANGULAR REGIONS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

  Yi Rang YUAN

  Journal of Systems Science and Complexity. 2004, 14(4): 538-554.

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  For the transient behavior of a semiconductor device, the modified method of characteristics with alternating-direction finite element procedures for nonrectangular region is put forward. Some techniques, such as calculus of variations, isoparametric transformation, patch approximation, operator-splitting, characteristic method, symmetrical reflection, energy method, negative norm estimate and a prior estimates and techniques, are employed. In the nonrectangular region case, optimal order estimates in $L^2$ norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved.
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  THE PERIODIC HOLLING II PREDATOR-PREY MODEL WITH IMPULSIVE EFFECT

  Yu Juan ZHANG;Lan Sun CHEN;Bing LIU

  Journal of Systems Science and Complexity. 2004, 14(4): 555-566.

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  In this paper, a periodic Holling II predator-prey model with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equation, some sufficient conditions are obtained for the linear stability and instability of trivial and semi-trivial periodic solutions. Moreover, we use standard bifurcation theory to show the existence of coexistence states which arise near the semi-trivial periodic solution. As an application, we also examine some special case of the system to confirm our main results.
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  QUANTUM THEORY FOR THE BINOMIAL MODEL IN FINANCE THEORY

  Ze Qian CHEN

  Journal of Systems Science and Complexity. 2004, 14(4): 567-573.

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  In this paper, a quantum model for the binomial market in finance is proposed. We show that its risk-neutral world exhibits an intriguing structure as a disk in the unit ball of \mbox{\boldmath${R}^3$}, whose radius is a function of the risk-free interest rate with two thresholds which prevent arbitrage opportunities from this quantum market. Furthermore, from the quantum mechanical point of view we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering Maxwell-Boltzmann statistics of the system of $N$ distinguishable particles.
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  THE PROBLEM OF ``STRUNG BALLS" IN HIGH DIMENSION

  Wei Nian ZHANG

  Journal of Systems Science and Complexity. 2004, 14(4): 574-577.

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  The problem of ``strung balls", which considers how many circles in a given family of circles can be intersected by a line in a plane, is discussed in ${\mbox{\boldmath${R}$}}^n (n\ge 3)$. Higher dimensional versions of the results given on a plane are obtained.
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  THRESHOLD SCHEMES WITH WEIGHTS

  Liang Liang XIAO;Mu Lan LIU

  Journal of Systems Science and Complexity. 2004, 14(4): 578-581.

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  In this paper, we present the model of threshold schemes with weights as a natural generalization of Shamir's threshold scheme and show how to apply the model to construct secret sharing schemes by two examples.