1996年, 第9卷, 第4期　刊出日期：1996-10-15

  

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  APPROXIMATION OF SOLUTION OF RELAXED DIFFERENTIAL INCLUSION ON COMPACT SET

  SONG Wen

  Journal of Systems Science and Complexity. 1996, 9(4): 289-294.

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  In this papert we discuss the uniform approximation problem of the relaxedsolution for defferential inclusion in Banach space. Under some conditions, we obtain theexistence theorem of approximation solution. This paper extends the similar result of Ornelas[1], which is discussed in finite dimensional space.
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  HAMILTONICITY IN 2-CONNECTED {K_(1,3) F}-FREE GRAPHS

  LI Guojun;LIU Zhenhong

  Journal of Systems Science and Complexity. 1996, 9(4): 295-305.

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  Let F be a graph consisting of a triangle with a pendant leaf dangling from each vertex. A graph is {K_{1,3}, F}-free if it contains no induced subgraph isomorphic to K_{1,3} or F. We give a stronger structural characterisation of {K_{1,3}, F}-free graph with which we obtain a more general result than that in [1] as follows: Given any two venices in a 2-connected {K_{1,3}, F}-free graph, if there exists a shortest path between them containing no 2-cutset of the graph, then the graph has a Hamilton path cormecting these two venices.
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  EXISTENCE OF SOLUTIONS FOR A CLASS OF SYSTEMS GOVERNED BY NONLINEAR DIFFERENTIAL INCLUSIONS

  XIANG Xiaoling;WANG Yuandi;AHMED N. U.

  Journal of Systems Science and Complexity. 1996, 9(4): 306-312.

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  In this article we discuss the existence of solutions for a class of controlled systems governed by nonlinear differential inclusion where principal operator A is a nonlinear monotone operator. Using Galerkin approach and selection theorem we prove the existence of W_{pq}-solution.
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  A METHOD FOR MECHANICAL GEOMETRY THEOREM PROVING

  WU Jinzhao;TAN Hongyan

  Journal of Systems Science and Complexity. 1996, 9(4): 313-319.

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  A method for mechanical geometry theorem proving is presented. By using this method, if the ascending chains derived via Wu-Ritt's well ordering algorithm satisfy a condition, all the irreducible characteristic sets we need can be obtained at the same time, and the general case can be reduced to this special case. Thus whether a geometry theorem is generally true can be decided.
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  A CONNECTED GRAPH IS PATH-POSITIVE IFF ITS SPECTRAL RADIUS IS AT LEAST TWO

  SHI Ronghua

  Journal of Systems Science and Complexity. 1996, 9(4): 320-325.

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  The main purpose of this paper is to prove that a connected graph is pathpositive if and only if its spectral radius is at least two.
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  DESIGN OF NONLINEAR OBSERVERS

  ZHENG Yufan;CHEN Shuzhong

  Journal of Systems Science and Complexity. 1996, 9(4): 326-333.

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  The design of observers for nonlinear controlled systems presented in this paperconsists of two stages. In the first stage, the nonlinear controlled system is transformed intoan observability canonical form by mealls of a generalized state transformation, in whichthe control variables (inputs) are parameterized, and then the system is control-free. Inthe second stage, an observer is designed for a control-free system. Form the mathematicalpoint of view the method given in this paper is valid for any observable nonlinear controlled(analytic) system, but from the engineering point of view the design for nonlinear observeris constrained by the choice of input variables. By several examples it is demonstrated how to design the observers practically.
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  THE OPTIMAL CONTROL OF AGE-DEPENDENT POPULATION DYNAMICS BASED ON PARITY PROGRESSION

  GUO Baozhu;WU Guofu

  Journal of Systems Science and Complexity. 1996, 9(4): 334-344.

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  The optimal control problem for an age-dependent population dynamics basedon parity ratio progression is considered. The functional analytie approach of Dubovitskiiand Milyutin is adopted in the investigation. Maximum principles for problems with fixedtime and free end condition, free final time are developed.
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  STRONG APPROXIMATION FOR PERTURBED EMPIRICAL PROCESSES

  ZHOU Yong

  Journal of Systems Science and Complexity. 1996, 9(4): 345-353.

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  Strong approximations for the perturbed (kernel-smoothing) empirical processare obtained under weak conditions. From these results we can obtain the law of iteratedlogarithm and asymptotic normality for the perturbed empirical process.
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  1/2-TRANSITIVE GRAPHS ASSOCIATED WITH LINEAR GROUPS

  DU Shaofei

  Journal of Systems Science and Complexity. 1996, 9(4): 354-357.

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  In this paper, we consider the action of G= PSL(n,p) (n \geq 3, p is an odd prime, and (n, p-1)= 1) on the set of frames of the projective space PG(n - 1, p) over thefield GF(P), and survey the non-self-paired orbitals of G. Then we find an infinite family of vertex-primitive 1/2-transitive graphs. In addition, we get a method of computing the suborbits of PSL(n,p) acting on the frame-set of PG(n-1,p).
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  THE SPACE-TIME INTEGRALITY FOR SOLUTIONS OF SOME HIGHER EVOLUTION

  MIAO Changxing

  Journal of Systems Science and Complexity. 1996, 9(4): 358-368.

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  In this paper we establish the space-time integrality for solutions of some higherorder evolution equations in Besov space, by devoted to the technology of determined indexand functional analysis.
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  POPOV METHOD FOR ROBUST ANALYSIS AND ROBUST SYNTHESIS OF MIMO LINEAR SYSTEMS WITH MRAMETRIC UNCERTAINTIES

  HUANG Yi;TIAN Yuping;FENG Chunbo

  Journal of Systems Science and Complexity. 1996, 9(4): 369-375.

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  The paper discusses the problem of robust analysis and robust synthesis forMIMO linear systems with parametric uncertainties by using Popov method. First, thefamous Popov criterion is recasted as a convex optimization problem and a new method forcalculating Popov multiplier is provided so that Popov criterion can be effectively used foranalyzing MIMO systems. Then the method of using Popov criterion to analyze parametricuncertainties is studied. Compared with other ones, this method is less conserVative andmuch quicker. At last, a direct search method is adopted to design robust controller baizedon Popov criterion.
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  REMARKS ON DIFFUSIVITY VERSUS ABSORPTION THROUGH THE BOUNDARY

  WU Yonghui;DU Jun

  Journal of Systems Science and Complexity. 1996, 9(4): 376-382.

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  In this paper we solve an open problem of [1], and prove that in the criticalcase m = 2α- 1 > 1, the solution of problem (D) exists globally. Moreover, \forall u_0\in C^{2+\gamma}(\overline\Omega) with u_0(x)>0 on \overline{\Omega}, there exist positive constants C and K which depend only on |u_0|_{L^\infty} such that u(x, t) \leq C exp(m^{-1}k\alpha t).