1989年, 第2卷, 第2期　刊出日期：1989-04-15

  

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  A MECHANIZATION METHOD OF GEOMETRY AND ITS APPLICATIONS Ⅳ.SOME THEOREMS IN PLANAR KINEMATICS

  Wu Wenjun (Wu Wen-tsun)

  Journal of Systems Science and Complexity. 1989, 2(2): 97-109.

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  Let a moving plane MP over a fixed plane FP occupy four different positions. Eachpair of such positions is associated with a center of rotation called pole so that we have a 6-pole configuration. As an illustration of our general method of mechanical theorem proving and discovering, we discuss in the present paper in some derails certain theorems connected with such a configuration.
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  A DOMINANCE APPROACH FOR PLANE PARTITIONS

  Chu Wenchang

  Journal of Systems Science and Complexity. 1989, 2(2): 110-118.

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  By developing the dominance technique of nondecreasing integer sequences into a multifold form, we introduce a new approach for the enumeration of plane partitions, which can be used to generate most of classical theorems in this field. The treatment presented here may be more accessible to readers than the earlier methods of algebra, analysis and algorithm.
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  ITERATIVE METHODS OF OBTAINING ESTIMATES FOR INCOMPLETE CONTINGENCY TABLES

  Wang Dongqian;David J.Scott

  Journal of Systems Science and Complexity. 1989, 2(2): 119-128.

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  An iterative method of De Jong, Greig and Madan(1985)for obtaining maximum likelihood estimates for contingency tables derived from a Mover-Stayer model is considered. It is shown that this method works for other sampling schemes leading to incomplete contingency tables. Moreover, compar-isons indicate that the method is very fast.
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  THE GEOMETRIC PROPERTIES OF THE SET OF LYAPUNOV MATRICES AND THE STABILITY OF THE MATRIX FAMILY

  Zhao Yongdong;Huang Lin

  Journal of Systems Science and Complexity. 1989, 2(2): 129-136.

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  Given a stable matrix A∈C~(n×n), there are some simple simultaneous inequalities whose coefficients rely on A. For \forall P~H=P∈C~(n×n), if P satisfies these inequlities, then PA+A~HP<0. As anapplication of the main results, the stability of the matrix family is treated. Besides, some geometric properties of the set of all the Lyapunov matrices of a given stable matrix are considered.
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  OPTIMAL SWITCHING AND IMPULSE CONTROLS FOR DISTRIBUTED PARAMETER SYSTEMS

  Yong Jiongmin

  Journal of Systems Science and Complexity. 1989, 2(2): 137-160.

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  Optimal switching and impulse controls for a distributed parameter systems are considered. We prove that the value functions u_u(·) of approximating problems approach to the value function u(·) of the original problem, while u_u(·) is the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman system. We also construct an optimal control for the original problem viathe value function u(·).
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  A NEW CHARACTERIZATION OF FIXED MODES FOR DECENTRALIZED CONTROL SYSTEMS

  Chu Delin

  Journal of Systems Science and Complexity. 1989, 2(2): 161-169.

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  In this paper, a study of the characterization of fixed modes in decentralized control is made. A new sufficient and necessary condition for the existence of fixed modes is obtained by means of the generalized eigenvalue theory of matrix pairs, and the computability of the new condition is presented. The results show that fixed modes can be computed in a reliable and efficient manner.
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  CORRELATION PROPERTIES OF DE BRUIJN SEQUENCES

  Zhang Zhaozh;Chen Wende

  Journal of Systems Science and Complexity. 1989, 2(2): 170-183.

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  Several new bounds for the correlation functions of de Bruijn sequences are derived. It is shown that the set of all primitive de Bruijn sequences have the following two properties: 1)for each sequence a in the set with large span n, the magnitude of its auto-correlation function |r_a(k)| is relatively small compared with the peak 2~n for all k≠0 mod 2~n; 2)for each pair of sequences a,b in the set with large span n, the magnitude of their cross-correlation function |r_(ab)(k)| is relatively small compared with the peak 2~n for all k. Some generalizations of the result are also presented.
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  ON A NEW GRADIENT PROJECTION METHOD

  Du Dingzhu;Zhang Xiangsun

  Journal of Systems Science and Complexity. 1989, 2(2): 184-192.

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  In 1983, Du and Sun gave an algorithm which possesses superiorities of both Rosen's gradient projection method and Wolfe's reduced gradient method. However, in order to have theprovable global convergence, the algorithm includes an ε-procedure as one of its parts. In this paper, we delete such a part and prove a convergence theorem.