1988年, 第1卷, 第2期　刊出日期：1988-10-15

  

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  SKIES AND MONADS

  Li Banghe;Zhang Jijiang

  Journal of Systems Science and Complexity. 1988, 1(2): 99-103.

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  In ~*R_+,we define (↑↓)~-equivalence similar to that given by Puritzfor ~*N, and call the (↑↓)~-equivalence classes skies. For x∈~*R_+, let μ(x)be the monad of x defined by Watten-Wattenberg, and let \bar{μ}(x)=sup{|y-z|/y,z∈μ(x)}∈~*R. Then it is proved that x↑↓y iff \bar{μ}(x)=\bar{μ}(y). Furthermore, sup{y/y↑↓x}=\bar{μ}(x)~(-1), and \bar{μ}(x)~2=\bar{μ}(x).
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  SOME PROPERTIES ON PATHS IN MATROID BASE GRAPHS

  Zheng Handing;Liu Guizhen

  Journal of Systems Science and Complexity. 1988, 1(2): 104-108.

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  Let G be the base graph with n vertices of any matroid. It is proved that for any two vertices of G there are at least r internally disjoint shortest paths joining them where r is their distance. Furthermore, for any integer k, r≤k≤n-1, there is a path of length k or k+1 in G joining them. If M is a simple matroid and P=bb_1…b_(r-1)b′is a shortest path in the base graph G of M, then for any integer k, r≤k≤n-1, there is a path of length k between b and b′containing b_1,…,b_(r-1). Therefore the results in [5] are generalized.
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  Lax-Friedrichs Difference Approximations to Isentropic Equations of Gas Dynamics

  Wang Jinghua;Li Xuewu;Huang Jinyang

  Journal of Systems Science and Complexity. 1988, 1(2): 109-118.

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  We are concerned with I.V.P for the isentropic equations of gas dynamics (1) ρ_t+(ρu)_x=0, (ρu)_t+(ρu~2+p)_x=0, (2) (ρ,u)|_(t=0)=(ρ_0(x),u_0(x)), where ρ=(ρ~r)/r, 2
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  LINEARIZATION OF TIME-VARYING AFFINE NONLINEAR SYSTEMS

  Cheng Daizhan;Yun Xiaoping

  Journal of Systems Science and Complexity. 1988, 1(2): 119-130.

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  This paper deals with linearization problems of time-varying affine nonlinear systems using the differential geometric approach. First of all time-varying Lie derivatives are defined and their certain properties are derived. Then necessary and sufficient conditions for state equations' linearization are obtained. Finally the input-output linearization and the full linearization are discussed, and some sufficient conditions are presented.
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  CONVERGENCE RATE OF AN ELS BASED ADAPTIVE TRACKER

  Guo Lei;Chen Hanfu

  Journal of Systems Science and Complexity. 1988, 1(2): 131-138.

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  On the basis of ELS estimate an adaptive tracker is designed and the convergencerates for both performance index and parameter estimate are established.
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  THE DIMENSIONS OF IRREDUCIBLE REPRESENTATIONS OF THE SYMMETRIC GROUP

  Shi He

  Journal of Systems Science and Complexity. 1988, 1(2): 139-147.

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  In this note we derive the demension formula of the irreducible representations of symmetric groups from its defination by using the character formula of the symmetric groupobtained in [7]. Thus we provid a directly proof of the hook formula from the point of view ofthe character of symmetric groups.
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  L_1 DECONVOLUTION FOR A STATIONARY NON-MINIMUM PHASE AR(p) MODEL

  Xu Wenyuan;Jia Peizhang;Lin Yuandan

  Journal of Systems Science and Complexity. 1988, 1(2): 148-158.

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  This paper provides the theoretical fundamentals of L_1 deconvolution for the stationary time series{ y_n}which satisfies a non-minimum phase AR(p) model. An algorithm of the L_1 deconvolution and its convergency are analyzed in detail. Both theoretical analysis and numerical examples show that this kind of deconvolution is especially appropriate for the case of P(x_n=0)≠0, where{x_n} is the system input resulting in {y_n}; and such a case is just interesting in seismic signal processing.
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  THE SOLUTION OF A STATIONARY TRANSPORT EQUATION FOR SPHERES WITH GENERALIZED BOUNDARY CONDITIONS

  Lei Peng;Yang Mingzhu

  Journal of Systems Science and Complexity. 1988, 1(2): 159-163.

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  In this paper the conditions for the stationary transport equation in an inhomogeneous sphere with generalized boundary conditions to get a unique solution, especially a positive solution, are studied. Two estimation formulas for the solution are given.
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  A NEW METHOD FOR SOLVING RICCATI EQUATIONS AND LIAPOUNOFF EQUATIONS

  Chen Wende;Han Jingqing

  Journal of Systems Science and Complexity. 1988, 1(2): 164-171.

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  The present paper gives a new method for solving Riccati equations. Using the Yokoyama canonical form, we transfor the primary Riccati equations, which contain n(n+1)/2 unknown quantities and n(n+1)/2 equations, into other equations which contain only mnunknown quantities and mn equations. Hence the new method simplifies the computation if m<(n+1)/2.
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  AN ALGORITHM FOR DECOMPOSING HIGH DEGREE POLYNOMIALS

  Liu Zhuojun

  Journal of Systems Science and Complexity. 1988, 1(2): 172-176.

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  It is significant in mathematical problems to decompose a polynomial P(x)intoan irreducible representation as follows P(x)=P1(P2(…(Pn(x))…)). In this paper, we present an effective and efficient algorithm to do this work, which has been implemented on computer by using the computer algebraic system SAC-2.
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  T-STATIONARY APPROXIMATION FOR NONSTATIONARY MARKOV DECISION PROGRAMMING

  Wei Liren

  Journal of Systems Science and Complexity. 1988, 1(2): 177-183.

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  The total discounted return v((π,δ)_T,β) which can be obtained by replacing nonstationary v(π,β) by stationary v(δ,β) from stage T on is said to be a T-approximations for nonstationary v(π,β). In this paper, if the bounds on error are given, we can get some results about the determination of both a value T and a T-stationary replacement. Our algorithm canbe regarded as an extension of White's method (1985) of reward revision of stationary version to the nonstationary case.
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  A NOTE ON OPTIMALITY CONDITIONS IN MULTIOBJECTIVE PROGRAMMING

  Wang Shouyang

  Journal of Systems Science and Complexity. 1988, 1(2): 184-190.

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  In this paper we discuss necessary conditions in multiobjective differentiable programming. We first give a counterexample to [1,Theorem 2.1] and then present its correct form with which we can easily establish the generalized Kuhn-Tucker necessary conditions. AKuhn-Tucker type of necessary condition is given, but the proof goes in another line which canexpose something essential to multiobjective optimization. Some remarks are also given, including two interesting problems.
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  A NODAL SUPERCONVERGENCE ARISING FROM COMBINATION OF LINEAR AND BILINEAR ELEMENTS

  Michal Krizek;Lin Qun;Huang Yunqing

  Journal of Systems Science and Complexity. 1988, 1(2): 191-197.

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  We introduce a finite element scheme which yields the O(h~4)-superconvergence at nodes when solving a second order elliptic problem. Finite element functions used are globally continuous and bilinear on every triangle.