1990年, 第3卷, 第1期　刊出日期：1990-02-15

  

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  AN APPROACH TO RESOLVE CONFLICTS BY TRADE-OFF ANALYSIS

  Wang Shouyang

  Journal of Systems Science and Complexity. 1990, 1(1): 1-015.

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  In this paper we propose an approach to resolve the conflicts in which more thantwo parties are allowable. It is a refinement and extension of Lootsma's pairwise comparison method for resolution of conflicts. The trade-offs of benefits and costs are judged in verbalterms which are subsequently converted into numerical values on a discrete geometric scale. Three schemes are suggested for supporting a mediator to recommend an appropriate dealto all the parties. We also present a procedure to estimate the trade-offs of the composite deals. The approach is illustrated via the example of a market scramble.
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  ON CLASSIFICATION OF HIGHER ORDER IMMERSIONS OF MANIFOLDS

  Li Guisong

  Journal of Systems Science and Complexity. 1990, 1(1): 16-024.

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  Denote by V_f~p the set of homotopy classes of codimensiom m framings of the p thorder stable normal bundle of a map f:M~n→N~(v(n,p)+m). Where 3≤m=n-1 or m=n-2 but n=0,1 mod 4. We determine in this paper the set V_f~p and then the set of p-homotopy classes of p-immersions homotopic to f for some special cases.
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  ON THE EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS OF VOLTERRA INTEGRAL DIFFERENTIAL EQUATIONS

  Wang Ke

  Journal of Systems Science and Complexity. 1990, 1(1): 25-035.

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  In this paper, we use the contraction principle and the Leray-Schauder principle to deal with the existence of periodic solutions of the Volterra integral differential equation. Some new existence criteria and unique existence criteria are obtained.
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  OPTIMAL ASSEMBLY BY MONOTONIC PROPERTY

  Du Dingzhu;F.K.Hwang

  Journal of Systems Science and Complexity. 1990, 1(1): 36-045.

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  Consider a system containing a type of n devices. Each device consists of mparts. Given mn parts for n devices with different working probabilities, how do we groupthem into n devices such that the system is most reliable. A monotonic grouping means that the best parts are put together, then the best remaining parts are put together, etc. A sufficient and necessary condition for such grouping being optimal will be given in this paper. As an application, we show that the monotonic grouping is optimal for the two-stagek-out-of-n system. When m=2, we also study the grouping that the best pairs to the worst, the second best pairs to the second worst, etc., associated with a redundant device problem.
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  APPROXIMATE OPTIMAL BIRTH CONTROL OF POTULATION SYSTEMS

  W.L.Ohan;Guo Baozhu

  Journal of Systems Science and Complexity. 1990, 1(1): 46-052.

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  We consider optimal birth control for the McKendrick equation of population dynamics. It consists of optimizing a system described by a first order partial differential equationwith nonlocal bilinear boundary control. Approximate minimum principles are obtained using Ekeland's variational principle.
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  A NEW APPROACH ON IDENTIFICATION OF BOUNDARY PARAMETER FOR A TWODIMENSIONAL DIFFUSION SYSTEM

  Hu Shunju;Wang Guoli

  Journal of Systems Science and Complexity. 1990, 1(1): 53-075.

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  This paper presents a new approach of the boundary parameter identification of adiffusion system. The system model is governed by a two-dimensional parabolic problem, which involves an unknown boundary parameter. Identifiability of the boundary parameter and the new approach are discussed briefly, which show that the new approach can overcome not only the ill-posedness of the nonlinear output least square method but also the difficulty of numerical computation of the nonlinear output least square estimate due to the existence of the local minima of the performance functional, Finally, some numerical examples are given.
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  A NEW PROOF OF THE HADAMARD MONODROMY THEOREM AND THE PERRIODIC SOLUTION FOR A CLASS OF O.D.E. SYSTEMS AT RESONANCE

  Li Shujie;Feng Dexing

  Journal of Systems Science and Complexity. 1990, 1(1): 76-082.

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  Early in 1904, Hadamard [1] showed the scale implicit function theorem of finite dimensions. Then it was generalized to infinite dimensions. In this paper a new proof of this theorem is given and the unique existence of the periodic solutions for aclass of ordinary differential equation systems at resonance is obtained.
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  SEVERAL RESULTS ON ESTIMATION OF PARAMETERS UNDER MATRIX LOSS FUNCTION

  Wu Qiguang

  Journal of Systems Science and Complexity. 1990, 1(1): 83-096.

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  In this paper, the definitions of Bayes estimator, minimax estimator, minimumrisk equivariant estimator and admissible estimator under the general matrix loss functionare given. Several results on estimation of parameters with the ordinary loss function are extended to the case of the matrix loss function.