2005年, 第18卷, 第3期　刊出日期：2005-07-15

  

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  MAXIMUM PRINCIPLE FOR THE OPTIMAL CONTROL OF AN ABLATION-TRANSPIRATION COOLING SYSTEM

  SUN Bing;GUO Baozhu

  Journal of Systems Science and Complexity. 2005, 18(3): 285-301.

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  This paper is concerned with an optimal control problem of an ablation-transpiration cooling control system with Stefan-Signorini boundary condition. The existence of weak solution of the system is considered. The Dubovitskii and Milyutin approach is adopted in the investigation of the Pontryagin's maximum principle of the system. The optimality necessary condition is presented for the problem with fixed final horizon and phase constraints.
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  ROBUST STABILITY WITH GUARANTEEING COST FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR PERTURBATION

  JIA Xinchun;ZHENG Nanning;LIU Yuehu

  Journal of Systems Science and Complexity. 2005, 18(3): 302-308.

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  The problems of robust stability and robust stability with a guaranteeing cost for discrete time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in an LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. Two examples are used to illustrate the efficiency of the results.
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  COMPARING THE INDEPENDENCE OF DIFFERENT RANDOM NUMBER GENERATORS

  WANG Dongqian

  Journal of Systems Science and Complexity. 2005, 18(3): 309-318.

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  Pseudo-random number generators have always been important in experimental design, computer simulation, cryptography and statistical analysis. This paper presents a method of comparing the degree of independence exhibited by various random number generators, a procedure, based on consideration of the largest (in modulus) non-unit eigenvalue of the observed Markov transition matrix, is used to assess the `randomness' of a random number generator.
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  ASYMPTOTIC PROPERTY OF THE TIME-DEPENDENT SOLUTION OF A RELIABILITY MODEL

  Geni Gupur;GUO Baozhu

  Journal of Systems Science and Complexity. 2005, 18(3): 319-339.

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  We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction $C_0$-semigroup $T(t),$ and prove that $T(t)$ is a quasi-compact operator. Next we verify that $0$ is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.
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  GRAPHS WHOSE CIRCULAR CLIQUE NUMBER EQUAL THE CLIQUE NUMBER

  XU Baogang;ZHOU Xinghe

  Journal of Systems Science and Complexity. 2005, 18(3): 340-346.

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  The circular clique number of a graph $G$ is the maximum fractional ${k/d}$ such that $G_{d}^{k}$ admits a homomorphism to $G$. In this paper, we give some sufficient conditions for graphs whose circular clique number equal the clique number, we also characterize the $K_{1,3}$-free graphs and planar graphs with the desired property.
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  LIMIT THEOREMS AND OPTIMAL DESIGN WITH ADAPTIVE URN MODELS

  CHEN Guijing;ZHU Chunhua

  Journal of Systems Science and Complexity. 2005, 18(3): 347-360.

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  In this paper we study urn model, using some available estimates of successes probabilities, and adding particle parameter, we establish adaptive models. We obtain some strong convergence theorems, rates of convergence, asymptotic normality of components in the urn, and estimates. With these asymptotical results, we show that the adaptive designs given in this paper are asymptotically optimal designs.
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  ON APPROXIMATION BY SPHERICAL ZONAL TRANSLATION NETWORKS BASED ON BOCHNER-RIESZ MEANS

  SHENG Baohuai;LI Hongtao

  Journal of Systems Science and Complexity. 2005, 18(3): 361-374.

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  A sequence of spherical zonal translation networks based on the Bochner-Riesz means of spherical harmonics and the Riesz means of Jacobi polynomials is introduced, and its degree of approximation is achieved. The results obtained in the present paper actually imply that the approximation of zonal translation networks is convergent if the action functions have certain smoothness.
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  THE UNIVERSAL GROEBNER BASIS UNDER COMPOSITION

  LIU Jinwang;HOU Jinjun;PENG Zhenyun;CAO Wensheng

  Journal of Systems Science and Complexity. 2005, 18(3): 375-382.

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  Composition is the operation of replacing variables in a polynomial with other polynomials. The main question in this paper is: when does composition commute with universal Groebner basis computation? We prove that this happens iff the composition is single variable. This has a natural application in the computation of universal Groebner bases of composed polynomials.
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  MINIMAL INVERSION AND ITS ALGORITHMS OF DISCRETE-TIME NONLINEAR SYSTEMS

  ZHENG Yufan

  Journal of Systems Science and Complexity. 2005, 18(3): 383-395.

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  The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.
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  GLOBAL ATTRACTIVITY OF POPULATION MODELS WITH DELAYS AND DIFFUSION

  QIU Zhipeng

  Journal of Systems Science and Complexity. 2005, 18(3): 396-403.

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  In this paper, the asymptotic behavior of three types of population models with delays and diffusion is studied. The first represents one species growth in the patch ${\it\Omega}$ and periodic environment and with delays recruitment, the second models a single species dispersal among the $m$ patches of a heterogeneous environment, and the third models the spread of bacterial infections. Sufficient conditions for the global attractivity of periodic solution are obtained by the method of monotone theory and strongly concave operators. Some earlier results are extended to population models with delays and diffusion.
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  CATALAN NUMBERS, DYCK LANGUAGE AND TIME SERIES OF ELEMENTARY CELLULAR AUTOMATON OF RULE 56

  QIN Dakang;XIE Huimin

  Journal of Systems Science and Complexity. 2005, 18(3): 404-418.

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  A new approach to study the evolution complexity of cellular automata is proposed and explained thoroughly by an example of elementary cellular automaton of rule 56. Using the tools of distinct excluded blocks, computational search and symbolic dynamics, the mathematical structure underlying the time series generated from the elementary cellular automaton of rule 56 is analyzed and its complexity is determined, in which the Dyck language and Catalan numbers emerge naturally.
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  STABILIZATION OF NONUNIFORM TIMOSHENKO BEAM WITH COUPLED LOCALLY DISTRIBUTED FEEDBACKS

  YAN Qingxu;HOU S. H.;HUANG G.D.;WAN Li

  Journal of Systems Science and Complexity. 2005, 18(3): 419-428.

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  The stabilization problem of a nonuniform Timoshenko beam system with coupled locally distributed feedback controls is studied. First, by proving the uniqueness of the solution to the related ordinary differential equations, we establish the asymptotic decay of the energy corresponding to the closed loop system. Then, by virtue of piecewise multiplier method, we prove the exponential decay of the closed loop system.