1997年, 第10卷, 第2期　刊出日期：1997-04-15

  

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  THE STRICT POSITIVITY IN A NONSTANDARD HULL AND ITS APPLICATIONS TO ECONOMICS

  WU Kangping

  Journal of Systems Science and Complexity. 1997, 10(2): 97-105.

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  The purpose of this paper is to study the strict positivity in a nonstandard hull of an internal normed Riesz space. Several characterizations are obtained for an element of the hull to be strictly positive. Particularly, it is shown that a nonstandard hull of an internal normed Riesz space has strictly positive elements if and only if it has an order unit. This result has an application to the double infillity problem in economics. It follows that the existence of equilibria in a nonstandard double infinity economy is equivalent to the existence of finite equilibria.
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  A METHOD TO APPROXIMATE DISTRIBUTIONS OF RELATED STATISTICS

  SHI Jianqing;ZHENG Zhongguo

  Journal of Systems Science and Complexity. 1997, 10(2): 106-113.

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  In this paper we propose a method to approximate a class of statistics which admit Edgeworth expansions. The accuracy of the approximation is proved to be at the same optimal rate as the well known bootstrap and random weighting. In practice conditional distributions of uni-dimensional statistics constructed by our method can exactly be derived. Meanwhile, our method has a nice model robustness.
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  AN IMPROVEMENT ON JORGENS'S ASYMPTOTIC EXMNSION THEOREM FOR TRANSPORT EQUATION

  SONG Degong;ZHU Guangtian

  Journal of Systems Science and Complexity. 1997, 10(2): 114-119.

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  This paper is devoted to discussing the asymptotic expansion problem for neutron transport in a finite convex medium with energy bounded away from the origin. It is shown that Jorgens's asymptotic expansion theorem holds under the L∞ norms i.e., for every ε > 0, there exist positive constants C_m(ε) and T_m(ε), such that ... for every ψ∈L^2 and t>T_m(ε).
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  CONSTRUCTION OF SAC PERMUTATIONS

  GONG Guang;DAI Zongduo

  Journal of Systems Science and Complexity. 1997, 10(2): 120-128.

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  Nonlinear permutations of GF(2^n) with strong cryptographic properties have important applications in cryptology such as DES-like block ciphers, hush functions and stream ciphers. In paPer [1], we proved that the exponential function can provide a class of permutations satisfying the Strict Avalanche Criterion (SAC permutations) with algebraic nonlinear degree 2. In this paper, we further construct three classes of SAC permutations that are derived from the Dickson polynomials, GMW functions and the exponential functions with maximal algebraic nonlinear degree, respectively.
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  ON A PROPERTY OF SOLUTIONS OF M-MATRIX EQUATIONS

  LI Wen

  Journal of Systems Science and Complexity. 1997, 10(2): 129-132.

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  For M-matrix equations, we provide a necessary and sufficient condition for that the solution of the equations has the property p, which improves and generalizes the corresponding results of [1] and [2].
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  REMARK ON BLOCH FUNCTION AND NORMAL FUNCTION

  XIAO Zhijing

  Journal of Systems Science and Complexity. 1997, 10(2): 133-140.

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  In this paper, we give characterizations for Bloch and normal functions. These caracterizations generalize the results of [1].
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  A HEURISTIC FOR F3/b_i= b/C_{max} AND ITS WORST-CASE ANALYSIS

  HOU Sixiang;DU Donglei

  Journal of Systems Science and Complexity. 1997, 10(2): 141-151.

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  This paper describes a heuristic for solving F3/b_i = b/C_{\max} scheduling problem. This algorithm first uses the Johnson's algorithm solving F2//C_{max}, then, presents revised algorithm to solve F3/b_i = b/C_{max}. Lastly, an O(n log n) time heuristic is presented which generates a schedule with length at most 3/2 times that of an optimal schedule, for even number n\geq 4, and 3/2 + 1/(2n) times that of an optimal schedule, for odd number n \geq 4. These bounds are tight.
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  A SYNTHESIS METHOD FOR TWO-ORDER UNCERTAIN SYSTEMS: AUTO-STABLE REGION APPROACH

  HAN Jingqing;WANG Wei;HUANG Yi

  Journal of Systems Science and Complexity. 1997, 10(2): 152-159.

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  In this paper, the variable structure control method is improved. Based on the existence and the reaching conditions for the auto-stable region of two-order systems, a new synthesis method, auto-stable region approach is presented to construct a global stabilizing feedback law by using a positive definite function and a properly selected saturated function. This new approach is robust with respect to the bounded model uncertainties and is convenient for both analysis and engineering implementation.
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  FRACTIONAL ORDER EVOLUTION EQUATION INTERPOLATING BOTH HEAT AND WAVE EQUATION

  BAI Fengtu;GU Yonggeng;MIAO Changxing

  Journal of Systems Science and Complexity. 1997, 10(2): 160-167.

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  In this paper we consider a class of fractional order evolution equations which interpolates the heat equation and wave equation. By Mittag-Lefflers functions[1] and functions transform the representative formula of solution for fractional evolution equation is obtained. Further we give a theoretical description for fractional evolution equation from the integrated semigroup point of view.
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  A LOGARITHMIC BARRIER NEWTON METHOD FOR SEMIDEFINITE PROGRAMMING

  JIANG Jianmin;SHI Miaogen

  Journal of Systems Science and Complexity. 1997, 10(2): 168-175.

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  In this paper, by analyzing the properties of the central path, we give a logarithmic barrier Newton algorithm for semidefinite programming. It can be seen as an extension of the method for LP problems developed by Rocs and Vial. And also, the algorithm possesses polynomial convergence.
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  LONGEST CYCLES IN 2-CONNECTED CLAW-FREE GRAPHS

  GAO Taiping;LI Hao;WEI Bing

  Journal of Systems Science and Complexity. 1997, 10(2): 176-182.

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  M. Matthews and D. Sumner proved that if G is a 2-connected claw-free graph of order n, then c(G)\geq \min{2δ + 4, n}. In this paper, we prove that if G is a 2-connected claw-free graph on n venices, then c(G) \geq \min{3δ + 2, n} or G belongs to one exceptional class of graphs.
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  OPTIMALITY CONDITIONS FOR NONCONVEX BILEVEL PROGRAMMING PROBLEMS

  LIU Guoshan;HAN Jiye

  Journal of Systems Science and Complexity. 1997, 10(2): 183-192.

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  In this paper, we derive an exact penalty function for nonconvex bilevel programming problem based on its KS form. Based on this exact penalty function a sufficient condition for KS to be partially calm is presented and a necessary optimality condition for nonconvex bilevel programming problems is given. Some existing results about the differentiability of the value function of the lower level programming problem are extended and a sufficient condition for CRCQ to hold for VS form of BLPP with linear lower level programming problem is also given.