1996年, 第9卷, 第1期　刊出日期：1996-01-15

  

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  MAXIMUM ENTROPY METHODS FOR CONSTRAINED OPTIMIZATION AND MINIMAX PROBLEMS

  TANG Huanwen;ZHANG Liwei;WANG Xuehua

  Journal of Systems Science and Complexity. 1996, 9(1): 1-004.

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  This paper presents the maximum entropy methods for nonlinearly constrained optumzation and ndulmax problems. Some properties of these method are given. Convergence theorems of the maximum entopy methods for unconstrained minimax problem and equality constrained optidsation problem are proved.
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  PANCONNECTIVITY AND 2-CONNECTED CLAW-FREE GRAPHS

  GAO Jingzhen;ZHU Yongjin

  Journal of Systems Science and Complexity. 1996, 9(1): 5-012.

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  We show that the two distinct venices u and v of a 2-connected claw-free graph G of order n with minimun degree(n- 2)/3 are [7, n]-panconnected whenever both G-u and G-v are 2-connected.
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  ON SUBALGEBRAS OF CHEVALLEY ALGEBRAS CONCERNING SUBFIELDS

  ZHA Jianguo

  Journal of Systems Science and Complexity. 1996, 9(1): 13-019.

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  For any field F of characteristic zero,by g(F) we denote Chevalley algebras of the take of A-G, which are classical simple Lie algebras associated with Cartan matrices. Let X be an algebraically closed field of characteristic zero and k any subfield of K. We attempt to prove a conjugacy theorem: Viewed as Lie algebras over k,any k-subalgebras of g(K),which are isomorphic to g(k), are conjugate under automorphisms of g(X). In the present paper we have proved that the conjugacy theorem is true for Chevalley algebras of the types of A., B2, Cd, E6 and G2.
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  EFFICIENCY OF ESTIMATION OF FIXED POLYNOMIAL EFFECTS IN MIXED MODELS BASED ON PBIB DESIGN

  TAO Jingxuan

  Journal of Systems Science and Complexity. 1996, 9(1): 20-026.

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  In this paper,the main emphasis of the proposed discussion is on the efficiency of estimation of fixed polynomial effects in mired models based on PBIB (partially balanced incomplete block) design. We consider the condition that the design block be orthogonal in the models, and give two criteria for computing the estimator's efficiency based on three classes of estimators used in the eded design model.Lastly we show that the efficiencies of both intra-block estimator and LS estimator equal 1.
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  QUASI-CONCAVE MULTIPLE OBJECTIVE PROGRAMMING WITH CONE STRUCTURE

  HUANG Zhimin;LI Susan X.;Win Quang

  Journal of Systems Science and Complexity. 1996, 9(1): 27-037.

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  In this paper, some basic theory of "cone quasi-concave multiple Objedive programming" is developed. Tall new class of multiple objective programming problems employs ideas of nondorninated solutions associated with dominance cones. Necessary as well as sufficient conditions for optimal solutions to such problems are provided. Aside from these, in order to find a nondominated solution, we peitiou all the objectives into several mutually exclusive subgroups and assume that the weighted sum of the objectives in each subgroup is quasi-concave for the given weights. This is different from the assumption in the exasting multiple objective programming literature that the weighted sum of all the objective functions is quasiconcave.
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  A 2-FACTORIZATION ORTHOGONAL TO A STAR IN A GRAPH

  LIU Guishen

  Journal of Systems Science and Complexity. 1996, 9(1): 38-042.

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  Let G be a graph and let F={F_1,…,F_d}and H be a factorisation and a subgraph of G, respectively. If H exactly has one edge in common with Fi for all i,1 ≤ i ≤ d, then we Say that F is orthogonal to H. In this paper it is proved that if H is a ☆ of a 2d-reghar graph G such that a set of any two edges of H is not a outset of any 4regular subgraph of G, then there is a 2-factorization of -G orthogonal to H. E8pecially, if G is a 2d-regular graph such that any connected 4regular subgraph is 4-edge connected,then for any 4star H, G has a 2-factorisation orthogonal to H.
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  A PROOF OF BROERSMA AND VELDMAN'S CONJECTURES

  HU Zhiquan

  Journal of Systems Science and Complexity. 1996, 9(1): 43-049.

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  Let F be a unique graph with degree sequence(1, 1, 1,3,3, 3). The pendent vertices of F are given by a1, a2 and a3. We say a subgraph H of G satisfies property \phi(u,v) if(N(u) ∩ N(v)) - V(H) ≠ \emptyset. In [1], Broersma and Veldman conjectured that if G is a 2-connected K1,3-be graph and if every induced F of G satisfies (\phi(a1, a2) and \phi(a1, a3)) or (\phi(a1, a2) and \phi(2, Q3)) or (\phi(a1, a3) and \phi(a2, a3)), then G is hamiltonian.In this paper,we show that this conjecture is true. This result generalizes an earlier work of Duffus, Gould and Jacobson. It is (also) applicable to the showing of the hamiltofority of K_{1,3}-free graphs with low edge density and few degrees.
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  A NEW ALGORITHM FOR PURX O-1 LINEAR PROGRAMS WITH INEQUALITY CONSTRAINTS

  CHEN Jianfei;XIA Shaowei

  Journal of Systems Science and Complexity. 1996, 9(1): 50-054.

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  More and more attention has been paid to the HNN algorithm since it used by Hoplield and [1] to solve TSPs in 1985. However,the algorithm can only solve the pure 0-1 linear programs with equality constraints,and many test.[2] showed that it is unreliable.This paper proposes an HNN-type algorithm which can solve some pure 0-1 linear Programs with inequality constraints and gUarantee to find their "near-optimal" solutions. Finally, an example is given.
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  ON THE EXISTENCE OF MEROMORPHIC SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

  YUAN Wenjun

  Journal of Systems Science and Complexity. 1996, 9(1): 55-066.

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  In this paper, we consider the existence of meromorphic solutions of some "non-Malmquist" equations of(1.1). Our sts main results improve and complement the theorems obtained by G. Gundersen and I. Laine[1].
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  A HYBRID POLYNOMIAL ALGORITHM FOR LINEAR PROGRAMMING

  HUANG Saing;Kortanek;K. O.

  Journal of Systems Science and Complexity. 1996, 9(1): 67-075.

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  We propose a "long step" double scaling algorithm. Its local performance has been compared with those of potential-reduction algorithms. On the basis of this analysis, we introduce a polynomial algorithm which combines scaling-steps and potential-reduction steps. The algorithm terminates in O(\sqrt{n}L) iterations.
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  VERTEX-PRIMITIVE 1/2-TRANSITIVE GRAPHS

  DU Shaofei

  Journal of Systems Science and Complexity. 1996, 9(1): 76-082.

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  In this paper,we consider the action of group PSL(2,P)(P≡±1(mod 8))on the set of right cosets of a maximal subgroup isomorphic to S4,and survey the nonself-paired orbitals. Then we find many infinite families of vertex-primitve 1/2-transitive graphs.
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  THE WEAK LAW OF LARGE NUMBERS WHEN EXTREME TERMS ARE EXCLUDED FROM SUMS

  QI Yongcheng

  Journal of Systems Science and Complexity. 1996, 9(1): 83-092.

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  Let {x_n, n\geq 1} be a sequence of i.i.d. random variables and |X_n^(1)|\geq |X_n^(2)|\geq ... \geq |X_n^(n)| be order statistics of |X_1|,|X_2|,...,|X_n|. Set ^{r}S_n=\sum_{i=r+1}^{(1)}X_n^(i) for 0 ≤r≤n-1. Let b_n→\infty, c_n\in R and r=r_n→0. We give the and sufficient conditions when (^{r}S_n-c_n)/b_n couverges to 0 in probability. As a result, we show that Pruitt's conjecture is true.
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  ON THE TOTAL DISTANCE BETWEEN NODES IN TREES

  Moon;J.W.

  Journal of Systems Science and Complexity. 1996, 9(1): 93-096.

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  Zhou G.L. and Shi R. H. proved a lower bound, conjectured by the computer program Grafitti, for the product of the total distance between nodes in a tree T_n and the stun of the reciprocals of the degrees of the nodes of T_n. We establish a stronger version of this inequality that is best possible for all n≥2.