1988年, 第1卷, 第1期　刊出日期：1988-08-15

  

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  A MECHANIZATION METHOD OF GEOMETRY AND ITS APPLICATIONS Ⅲ.MECHANICAL PROVING OF POLYNOMIAL INEQUALITIES AND EQUATION-SOLVING

  Wu Wenjun

  Journal of Systems Science and Complexity. 1988, 1(1): 1-017.

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  This is the third paper of the series entitled “A mechanization method of geometryand its applications”, cf.[WU3—5]. In the present paper it is shown how inequalities can be proved by means of the author's Zero Decomposition Theorem of equations solving Numerous examples are given which deal with definiteness of polynomials, inequalities between symmetric polynomials, trigonometrical inequalities, and geometric inequalities.
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  ON CONNECTIVITIES OF BASE GRAPHS OF SOME MATROIDS

  Liu Guizhen

  Journal of Systems Science and Complexity. 1988, 1(1): 18-021.

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  If a matroid M without loops has basic corank γ_1 and 2-corank γ_2, and G is a base graph of M, then k(G)≥2γ_1+γ_2 where k(G) denotes the connectivity of G.
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  ASYMPTOTIC DECAY OF SOLUTIONS OF A NONLINEAR SCHRODINGER EQUATION IN R~3

  Yao Jingqi

  Journal of Systems Science and Complexity. 1988, 1(1): 22-028.

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  In this paper we consider the following nonlinear Schr\"{o}dinger equation: iu_t+Δu+|u|~2u=0 in R~3×R_+,u(0)=u_0∈H~2(R~3). First we give a sufficient condition on the initial data which guarantees the existence of its global solutions. Then an asymptotic decay result of the solutions is obtained.
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  ON THE DEDEKIND COMPLETION OF ~*R

  Li Banghe;Zhang Jijiang

  Journal of Systems Science and Complexity. 1988, 1(1): 29-039.

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  The Dedekind Completion ~*R of a nonstandard real field ~*R is studied. Topological andalgebraic properties of two subsets of ~*R consisting of additive universal numbers and multiplicative universal numbers respectively are exhibited. From this, we introduce a kind of new non-Archimedean fields, generalizing A.Robinson's ~ρR. We prove that these fields are real closed fields, and study the integer rings, rational fields, fields of algebraic numbers and rings of algebraic integers subordinate tothese fields.
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  A KREIN SPACE APPROACH TO THE OPERATOR VERSION OF CORONA PROBLEM

  Sun Shunhua

  Journal of Systems Science and Complexity. 1988, 1(1): 40-046.

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  A Krein space approach to the operator version of the corona problem (denoted by(CPOV)) for both disk and polydisk is presented in this paper. In the case of polydisk, what we exhibit is only a necessary and sufficient condition for(CPOV) to be solved.
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  THE APPROXIMATION PROBLEM FOR HYPERBOLIC POINTWISE CONTROL SYSTEMS

  Feng Dexing;Ding Zhonghai

  Journal of Systems Science and Complexity. 1988, 1(1): 47-056.

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  The distributed control approximation of pointwise control for the hyperbolic system isconsidered. First, it is, shown that there is a unique solution in C([0,T];L~2(Ω))for the hyperbolic system with pointwise input. Then an approximate technique of the hyperbolic pointwise input system isproposed, and it is proved that the solution of the obtained approximate equation converges in L~2-norm to that of the original pointwise input system. Finally, it is shown that under the quadratic index, the corresponding approximate optimal control is also convergent in L~2-norm.
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  ROBUST STOCHASTIC ADAPTIVE CONTROL FOR NON-MINIMUM PHASE SYSTEMS

  Guo Lei;Chen Hanfu

  Journal of Systems Science and Complexity. 1988, 1(1): 57-071.

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  The adaptive control problem for stochastic systems with unmodelled dynamics is considered. The modelled part of the system is described by an ARMAX model which may not be of minimum phase, while the unmodelled part is dominated by a time-varying quantitydepending upon the systen past input, output and driven noise. The adaptive control law is designed based on a pseudo-linear regression algorithm and a pole-assignment method. Robustness results with regard to stability, performance and convergence are established.
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  A DEFECT CORRECTION METHOD FOR THE EFFECTIVE COMPUTATION OF HIGH-DEGREE FINITE ELEMENT SOLUTIONS

  J. P. Monnet

  Journal of Systems Science and Complexity. 1988, 1(1): 72-093.

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  The high-degree finite element solution of the 2-point boundary value problem: -(p(t)u′(t))′=f(t,u) in (0,1), u(0)=u(1)=0 is considered as a fixed-point of an iterative process using a linear finite element scheme as abasic solver. The rate of contraction is O(h), or O(h~2) if P(t) is piecewise constant in (0,1).
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  THE BASIC THEORY FOR FORMING THE OPTIMUM ARCHITECTURE OF A SYSTEM

  Lin Aizhong

  Journal of Systems Science and Complexity. 1988, 1(1): 94-098.

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  Taking a systen as a 3-tuple, the definition of atomic system and weighted sum are introduced. Though the multistage system analysis, the information passing matrices of all atomic systems(or cells) are obtained and combined, step-by-step, by certain criteria. Also, two methods are used to form the optimum architecture of a system. The semethods can free the system designer from such work as modular dividing and so on.