1997年, 第10卷, 第4期　刊出日期：1997-10-15

  

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  THE CONVERGENCE OF BROYDEN ALGORITHMS WITHOUT CONVEXITY ASSUMPTION

  PU Dingguo

  Journal of Systems Science and Complexity. 1997, 10(4): 289-298.

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  In this paper we discuss the convergence of the Broyden algorithms without convexity and exact line search assumptions. We proved that if the objective function is suitably smooth and the algorithm produces a convergent point sequence, then the limit point of the sequence is a critical point of the objective function.
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  EQUIVILENT CONDITIONS FOR THE FINITENESS OF GAUGE

  YIN Chuancun;JIANG Zhaolin

  Journal of Systems Science and Complexity. 1997, 10(4): 299-308.

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  Some equivalent conditions for the finiteness of gauge on a class of unbounded domains in R^d are given.
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  ON THE CRITERIA AND ENUMERATION OF BOOLEAN FUNCTIONS USED IN STREAM CIPHERS

  WANG Jianyu

  Journal of Systems Science and Complexity. 1997, 10(4): 309-314.

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  In this paper, we discuss the criteria of boolean functions used in stream ciphers, and enumerate boolean functions which satisfy some criteria.
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  NECESSARY CONDITIONS FOR MAJOR OPTIMAL SOLUTIONS AND MAJOR EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING

  HU Yuda;MENG Zhiqing

  Journal of Systems Science and Complexity. 1997, 10(4): 315-319.

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  In this papers the Fritz John conditions and Kuhn-Tucker conditions for majoroptimal solutions and major efficient solutions of multiobjective programming are givenand proved.
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  NONLINEAR GALERKIN METHOD FOR STEADY NONLINEAR DIFFERENTIAL EQUATIONS

  HE Yinnian;LI Kaitai

  Journal of Systems Science and Complexity. 1997, 10(4): 320-328.

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  A nonlinear Galerkin method using spectral expansions is presented for the steady nonlinear partial differential equations. We prove the existence, uniqueness and convergence of the numerical solution corresponding to this method. Compared with the usual Galerkin method, the nonlinear Galerkin method is simpler under the same convergence accuracy.
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  SUPER HYPERBOLIC TYPE KAC-MOODY LIE ALGEBRA

  CHEN Hongji;LIU Bin

  Journal of Systems Science and Complexity. 1997, 10(4): 329-332.

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  In this paper we give the definition of super hyperbolic type Kac-MoodyLie algebra and discuss its imaginary roots systems. Finally, we give the necessary and sufficient condition for Cartan matrices to be of super hyperbolic type.
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  EQUIVALENT CONDITIONS FOR THE UNIFORMCONTINUITY OF DUALITY MAPPING

  WANG Qi

  Journal of Systems Science and Complexity. 1997, 10(4): 333-336.

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  For a duality mapping F(x), this paper gives equivalent conditions for F(x) being single-valued and uniformly continuous, or uniformly lower semi-continuous, or for existence a uniformly continuous support functions.
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  THE HOPF BIFURCATION DIRECTION OF A FOUR DIMENSIONAL ELECTRONIC NEURAL NETWORK SYSTEM

  LIN Yiping;LI Jibin;CAO Jinde

  Journal of Systems Science and Complexity. 1997, 10(4): 337-343.

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  In this paper we give an applicable parameter formula about the bifurcationand stability of periodic solution for a four-dimensional differential system. By using thisresult in a simple electronic neural network system, we obtain a strict condition of the existence of periodic solution.
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  DETERMINATION OF THE SIGN OF DIVERGENCE OF A QUADRATIC SYSTEM AT CRITICAL POINTS

  ZHANG Xiang

  Journal of Systems Science and Complexity. 1997, 10(4): 344-355.

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  In this paper we completely solve the problem on the determination of the signof divergence of a quadratic system at critical points.
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  THE ASCENDING SUBGRAPH DECOMPOSITION OF K_n-H_{2n-1}

  MA Kejie;ZHANG Yuzhong

  Journal of Systems Science and Complexity. 1997, 10(4): 356-360.

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  A conjecture concerning a new kind of subgraph decomposition, the ascending subgraph decomposition, was proposed by Alavi Y. et al., as follows: Every graph ofpositive size has an ascending subgraph decomposition. In this paper it is proved thatG = K_n- H_{2n-1} has an ascending subgraph decomposition, where H_{2n-1} is any graphwith at most n venices and at most 2n - 1 edges (n \geq 6).
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  QUENCHING PHENOMENA FOR SYSTEMS OF SEMILINEAR PARABOLIC EQUATIONS I

  DAI Qiuyi;GU Yonggeng

  Journal of Systems Science and Complexity. 1997, 10(4): 361-371.

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  Initial-boundary value problems for a class of systems of semilinear parabolicequations with singular terms are investigated, conditions for the existence and nonexistence of the global solutions to the above problems are given, and upper bounds of the quenching time and the critical length are obtained.
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  THE SPLITTING EXTRAPOLATION FOR FINITE ELEMENT METHOD

  LÜTao;FENG Yong

  Journal of Systems Science and Complexity. 1997, 10(4): 372-382.

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  A new splitting extrapolation based on multivariate asymptotic expansionsof finite elemellt eraes for differellt mesh parameters is described. By means of splittingextrapolation, a far 3 scale problem is decomposed into many subproblems, which can besolved in parallel. 111 this paper) we prove that the splitting extrapolation algorithm possesses a high order accuracy and the computation is almost independent of the dimension ofthe problem. Moreover, an extrapolation algorithm at global fine grid points is presented,several numerical examples including interface problems are discussed.