1992年, 第5卷, 第4期　刊出日期：1992-11-15

  

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  ON LOCAL STABILIZATION OF NONLINEAR CONTROL SYSTEMS

  ZHENG Yufan

  Journal of Systems Science and Complexity. 1992, 5(4): 289-298.

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  Based on the notion of maximal absolute observability and its normalforms, a new method for studying the local stabilization for a kind of nonlinearcontrol systems is established. Different from the previous results given by Byrnes-Isitori and others, this new method can deal with more general systems, and has much simpler way to prove the stabilization conditions and to design the feedback laws.
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  QUALITATIVE ANALYSIS FOR A THIRD-ORDER DIFFERENTIAL EQUATION IN A MODEL OF CHEMICAL SYSTEMS

  LIU Zhenrong;JING Zhujun

  Journal of Systems Science and Complexity. 1992, 5(4): 299-311.

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  In this paper a mathematical model of chemical systems is investigated. We present the conditions for the existence and local stability of the steady states and the periodic solution of the Hopf type. Specifically, we show by using an ana-lytical method that there may exist two or four Hopf bifurcation points separated at a finite distance from each other; at the same time, a technique for studying the Hopf bifurcation value is given.
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  A REMARK ABOUT TARTAR'S LEMMA

  ZHANG Weitao;FENG Dexing

  Journal of Systems Science and Complexity. 1992, 5(4): 312-315.

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  Let \partial Ω=Γ=Γ_1+Γ_2 (see Fig.1), meas(Γ_1)>0, V={v|v∈H~1(Ω),v|Γ_1=0}, and V_0={ω|Δω=h in Ω,ω|Γ=0,\forall h∈V}. Let V_0′=the dual space of V_0,a(u,v)=∫_Ω▽u·▽Δvdx, and F(v)=∫_Ω fvdx+∫_(Γ_2)g1Δvds-∫_Γg2\partial v/{\partial \nu}ds, f∈V′_0,g1∈H~(-(1/2))(Γ_2), g2∈H~(-(3/2))(Γ). Consider the variational problem: find u ∈ V such that a(u,v)=F(v),\forall v∈V_0. (1)Using Tartar's lemma, we prove that for problem (1) there exists a unique u∈V satisfying.
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  APPLICATIONS OF INTEGRATED SEMIGROUPS TO HIGHER ORDER ABSTRACT CAUCHY PROBLEMS

  ZHENG Quan

  Journal of Systems Science and Complexity. 1992, 5(4): 316-327.

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  This paper is concerned with applications of integrated semigroups to the following Cauchy problem: (ACP_n) x~(n)(t)=sum from i=0 to n-1 B_ix~(i)(t),x~(i)(0)=x_i,0\le i\le n-1 where B_i (0\le i\le n-1) are closed linear operators on a Banach space X. Auniqueness theorem, a condition of the solvability, a condition of the exponential well-posedness, and some results for the special case that B_(n-1) is bounded and D(B_(n-2))\subset D(B_i)(0\le i\le n-3) are obtained.
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  THE NP-HARDNESS OF THE SINGLE MACHINE COMMON DUE DATE WEIGHTED TARDINESS PROBLEM

  YUAN Jinjiang

  Journal of Systems Science and Complexity. 1992, 5(4): 328-333.

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  In this paper we prove that the single machine common due date weighted tardiness problem is NP-hard.
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  ATOMIC DECOMPOSITION AND FREE INTERPOLATION IN A~1(φ)

  XIAO Jie

  Journal of Systems Science and Complexity. 1992, 5(4): 334-339.

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  Let φ be a normal function on [0,1] and A~1(φ)the Bergman space with weight φ(|z|)/(1-|z|~2). An atomic decomposition theorem for A~1(φ)is obtained, and a necessary and nearly-sufficient condition is given to make a sequence of points interpolate for A~1(φ).
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  MARKOV DECISION PROGRAMMING-THE FIRST PASSAGE MODEL WITH DENUMERABLE STATE SPACE

  LIU Jianyong;LIU Ke

  Journal of Systems Science and Complexity. 1992, 5(4): 340-351.

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  In this paper, we discuss MDP with discrete time parameter-the first passage model with denumerable state space. Under assumption A in this paper, we prove that an ε(>0)-optimal stationary policy exists. To find an ε-optimal stationary policy, an algorithm of policy improvement iteration and a method of successive approximations are given.
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  A HIGH ACCURACY ANALYSIS OF THE MIXED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATIONS

  CHEN Hongsen;LIN Qun

  Journal of Systems Science and Complexity. 1992, 5(4): 352-364.

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  In this paper, the linear mixed finite element method is considered for the biharmonic Dirichlet boundary value problem. Almost optimal error estimates, superconvergence estimates and the derivative error expansion are obtained.
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  STRONG UNIFORM CONSISTENCY RATES FOR CONDITIONAL FUNCTION ESTIMATORS WITH $\varphi$-MIXING SAMPLE

  HU Shuhe

  Journal of Systems Science and Complexity. 1992, 5(4): 365-382.

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  Strong uniform consistency rates are given for kernel type estimators of the conditional function with \varphi-mixing sample. Especially, for nonparametrice stimators of kernel density, the regression function when Y is bounded, conditionaldf's,L-smoothing and M-smoothing,we obtain the same rate O((n/log n)~(-1/3)) as in the i.i.d. sample established by Hardle, Janssen and Serfling.