1991年, 第4卷, 第4期　刊出日期：1991-11-15

  

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  ASYMPTOTIC THEORIES FOR THE ROBUST PP ESTIMATORS OF THE PRINCIPAL COMPONENTS AND DISPERSION MATRIX Ⅲ.BOOTSTRAP CONFIDENCE SETS,BOOTSTRAP TESTS

  Zhang Jian

  Journal of Systems Science and Complexity. 1991, 4(4): 289-301.

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  In this paper the bootstrap theories, which are based on the author's former paper, of M-typ eprincipal components and dispersion matrices and M-type PP tests for multivariate locationand scale are obtained. The bootstrap confidence sets for the principal components, dispersion matrices and correlation matrices are also constructed.
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  A CRYPTOGRAPHIC STUDY ON S—BOXES OF DES TYPE Ⅱ AN ENTROPY LEAKAGE ANALYSIS FOR THE KEY

  Zeng Kencheng;Dai Zongduo;Yang Junhui

  Journal of Systems Science and Complexity. 1991, 4(4): 302-308.

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  The concept of key-entropy drop in an S-box is introduced. It is established that the output functions of the permutations composing an S-box belong to three patterns of key-entropy drop. An analysis of the distribution of the key-entropy drop patterns in the 8 S-boxes in the DES has been made.
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  PURE JUMP SHOCK MODELS IN DISCRETE TIME CASE

  Cheng Shixue

  Journal of Systems Science and Complexity. 1991, 4(4): 309-320.

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  In this paper the bootstrap theories, which are based on the author's former paper, of M-typ eprincipal components and dispersion matrices and M-type PP tests for multivariate locationand scale are obtained. The bootstrap confidence sets for the principal components, dispersion matrices and correlation matrices are also constructed.
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  EXISTENCE OF THE VALUE FOR A DIFFERENTIAL GAME WITH SWITCHING STRATEGIES IN A BANACH SPACE

  Yong Jiongmin

  Journal of Systems Science and Complexity. 1991, 4(4): 321-340.

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  A two-player zero-sum differential game in some Banach space is studied. Positive switching costs are associated with each player. By regularizing the game and combining thenotion of viscosity solutions for Isaacs-Bellman equation, we obtain the existence of the Elliot-Kalton value of the game under suitable conditions.
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  PARALLEL ALGORITHMS FOR VARIATIONAL INEQUALITIES BASED ON DOMAIN DECOMPOSITION

  Lü Tao;Chin-Bo Liem;Tsi-Min Shih

  Journal of Systems Science and Complexity. 1991, 4(4): 341-348.

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  We present two parallel algorithms based on the domain decomposition methodfor solving a variational inequality over a closed convex cone. First, construct an opencovering {Ω_i} of the original domain Ω∶Ω=\cap_{i=1}^m \Omega_i, where Ω_i,i=1,…,m, are overlapping. i.e. for each Ω_i there exists at least one Ω_j(j≠i) such that Ω_i∩Ω_i≠φ. Choosing an initial guess u~0 for the solution u, we solve parallelly the inequality in each subdomain Ω_i(i=1,…,m) to obtain m corrections. Take an appropriate average of these m corrections as a correctionover Ω and hence obtain a new approximation to u. In this paper we discuss the convergenceof the continuous problem and also the corresponding discrete problem which is obtained by the finite element method.
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  THE POLE ASSIGNMENT OF LINEAR SYSTEMS

  Shi He

  Journal of Systems Science and Complexity. 1991, 4(4): 349-361.

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  In this paper the pole assignment problem of a time invariant linear control system issolved by using the Wu Elimination Method. In general, the questions are classified into (i)the poleassignment by using state feedback, (ii)the pole assignment by using output feedback, (iii)the pole assignment via dynamic compensator. The key point of all these problems is to solve a certaincorresponding system of polynomial equations. Based on algebraic geometry, the Wu method provides a mechanical algorithm for solving the system of polynomial equations. Therefore, a unified definite algorithm for solving all these problems is given in this paper. During the procedure of elimination, the unknowns are automatically separated into parameters and apparent variables. Thus, the freedom of the corresponding feedback can be defined as the number of parameters. Meanwhile, the explicit expressions of the apparent variables depending on the parameters are obtained.
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  PACKING AND COVERING WITH ARBORESCENCES

  Cai Maocheng

  Journal of Systems Science and Complexity. 1991, 4(4): 362-367.

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  The aim of this note is to exhibit some recent results on packing and covering with arborescences.
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  ENUMERATION OF LINEAR RECURRING m-ARRAYS

  Liu Mulan;Lin Dongdai

  Journal of Systems Science and Complexity. 1991, 4(4): 368-373.

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  In this paper we prove that the number of translation equivalence classes of linear recurring m-arrays over F_q with period (r,s) is(φ(rs))/(log_q(rs+1)), where φ is Euler function.
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  FORBIDDEN SUBGRAPHS,DEGREES,NEIGHBORHOOD UNIONS AND CIRCUMFERENCES OF GRAPHS

  Tian Feng

  Journal of Systems Science and Complexity. 1991, 4(4): 374-382.

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  Combining forbidden subgraphs with degree restrictions and neighborhood union restrictions, respectively, we prove the following results: (1) Let G be a 2-connected graph of order n, and 3≤c≤n. If for each induced subgraph L of order four of G, |V_1(L)∩S_c|≥2 if L≌K_(1,3), and |V(L)∩S_c|≥1 if L≌P_4, then the circumference of G is at least c, where V_1(L) is the set of vertices with degree 1 of L, S_c is the set of vertices with degree at least c/2 of G and P_4 is a path of order 4. (2) Let G be a 2-connected graph of order n, and n≥s+2. If for each induced subgraph L of G isomorphic to K_(1,3) or P_4, d_L(u,v)=2 \Rightarrow |N(u)∪N(v)|≥s, then the circumferencec (G) of G is at least s+2. Moreover, if n≥s+3 and s is odd, then c(G)≥s+3.