2009年, 第22卷, 第2期　刊出日期：2009-06-20

  

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  A MULTIYEAR LAGS INPUT-HOLDING-OUTPUT MODEL ON EDUCATION WITH EXCLUDING IDLE CAPITAL

  Xue FU;Xikang CHEN

  Journal of Systems Science and Complexity. 2009, 22(2): 159-170.

  摘要 ( ) PDF全文 ( )   可视化   收藏

  This paper develops a multi-year lag Input-Holding-Output (I-H-O) Model on education with exclusion of the idle capital to address the reasonable education structure in support of a sustainable development strategy in China. First, the model
  considers the multiyear lag of human capital because the lag time of human capital is even longer and more important than that of fixed capital. Second, it considers the idle capital resulting from the output decline in education, for example, student
  decrease in primary school. The new generalized Leonitief dynamic inverse is deduced to obtain a positive solution on education when output declines as well as expands. After compiling the 2000 I-H-O table on education, the authors adopt modifications-by-step method to treat nonlinear coefficients, and calculate education scale, the requirement of human capital, and education expenditure from 2005 to 2020. It is found that structural imbalance of human capital is a serious problem for Chinese economic development.
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  A DIFFERENTIAL GAME MODEL FOR A DEVELOPING AND A DEVELOPEDCOUNTRY

  Rong ZHANG;Xuexiang HUANG

  Journal of Systems Science and Complexity. 2009, 22(2): 171-185.

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  A differential game (DG) model for a developing and a developed country is considered. Each player makes decisions about how much resource to be used to restrict the opponent's development so as to maximize his weighted sum of current
  consumption and final output. Current consumption is assumed to be preferred to final output for both players. The developing country is assumed to have a higher economic growth rate and a higher preference to final output, whereas the developed country is
  assumed to have a higher initial income and a higher efficiency in restricting his opponent. This problem is investigated under three kinds of information structures, i.e., a zerosum, a nonzero-sum, and a Stackelberg game. Open-loop equilibrium solutions are obtained for all the three cases. Economic implications of the
  result are provided.
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  ROBUSTNESS ANALYSIS OF LEADER-FOLLOWER CONSENSUS

  Jinzhi WANG;Ying TAN;Iven MAREELS

  Journal of Systems Science and Complexity. 2009, 22(2): 186-206.

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  In this paper, robustness properties of the leader-follower consensus are considered.
  For simplicity of presentation, the attention is focused on a group of continuous-time first-order dynamic agents with a time-invariant communication topology in the presence of communication errors. In order to evaluate the robustness of leader-follower consensus, two robustness measures are proposed: the $L_2$ gain of the error vector to the state of the network and the worst case $L_2$ gain at a node. Although the $L_2$ gain of the error vector to the state of the network is widely used in robust control design and analysis, the worst case $L_2$ gain at a node is less conservative with respect to the number of nodes in the network. It is thus suggested that the worst case $L_2$ gain at a node is used when the robustness of consensus is considered. Theoretical analysis and simulation results show that these two measures are sensitive to the communication topology. In general, the ``optimal''
  communication topology that can achieve most robust performance with respect to either of the proposed robustness measures is difficult to characterize and/or obtain. When the in-degree of each follower is one, it is shown that both measures reach a
  minimum when the leader can communicate to each node in the network.
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  ROBUST ATTITUDE CONTROL OF A 3DOF HELICOPTER WITH MULTI-OPERATION POINTS

  Yao YU;Yisheng ZHONG

  Journal of Systems Science and Complexity. 2009, 22(2): 207-219.

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  A 3DOF (three degrees of freedom) helicopter attitude control system with multi-operation points is described as a MIMO time-varying uncertain nonlinear system with unknown constant parameters, bounded disturbance and nonlinear uncertainty, and a
  robust output feedback control method based on signal compensation is proposed. A controller designed by this method consists of a nominal controller and a robust compensator. The controller is linear time-invariant and can be realized easily. Robust attitude tracking property of closed-loop system is proven and experimental
  results show that the designed control system can guarantee high precision robust attitude control under multi-operation points.
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  STABILITY RADIUS OF NON-SMOOTH PRITCHARD-SALAMON SYSTEMS ANDTHE ALGEBRAIC RICCATI EQUATION

  Weisheng JIANG;Falun HUANG;Tingyu ZHU

  Journal of Systems Science and Complexity. 2009, 22(2): 220-227.

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  The authors discuss the stability radius of the non-smooth Pritchard-Salamon systems under structured perturbations. A formula for the stability radius in terms of the norm of a certain input-output operator is obtained. Furthermore, the relationship
  between stability radius and the solvability of some type of algebraic Riccati equations is given.
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  OPTIMAL HIERARCHY STRUCTURES FOR MULTI-ATTRIBUTE-CRITERIADECISIONS

  Stan LIPOVETSKY

  Journal of Systems Science and Complexity. 2009, 22(2): 228-242.

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  A problem of a hierarchy structure optimization is considered. Hierarchical structures are widely used in the Analytic Hierarchy Process, conjoint analysis, and various other methods of multiple criteria decision making. The problem consists in finding a structure that needs a minimum number of pair comparisons for a given total number of the alternatives. For an optimal hierarchy, the minimum efforts are needed for eliciting data and synthesizing the local preferences across the hierarchy to get the
  global priorities or utilities. Special estimation techniques are developed and numerical simulations performed. Analytical and numerical results suggest optimal ways of priority evaluations for practical managerial decisions in a complex environment.
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  ON SPECTRUM OF NETWORKS BASED ON MATRIX OF LINK-STATE ANDITS SYMMETRY

  Liuqing XIAO;Shipeng ZHOU

  Journal of Systems Science and Complexity. 2009, 22(2): 243-251.

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  This paper constructs a new spectrum of networks by means of the matrix of link-state of the network, which can reveal the characteristics of the correlation between the degrees of the network. Also, the computation of this spectrum of networks is usually more feasible and more efficient due to the much lower order of its matrix of link-state than its adjacent matrix in practice. Some estimates for the bounds of the key eigenvalues in the spectrum are obtained, the corresponding inequalities are
  presented and proved. For the sake of its application, the authors define spectrum of networks in two ways, and all theorems are given in parallel for both kinds of definition. In addition, the authors find a symmetry in the spectrum, which is relative to the characteristic of structure of its network to some extent.
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  METHOD FOR QUICKLY INFERRING THE MECHANISMS OF LARGE-SCALE COMPLEX NETWORKS BASED ON THE CENSUS OF SUBGRAPH CONCENTRATIONS

  Bo YANG;Xiaorong CHEN

  Journal of Systems Science and Complexity. 2009, 22(2): 252-259.

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  A Mechanism-Inferring method of networks exploited from machine learning theory can effectively evaluate the predicting performance of a network model. The existing method for inferring network mechanisms based on a census of subgraph numbers has some drawbacks, especially the need for a runtime increasing strongly
  with network size and network density. In this paper, an improved method has been proposed by introducing a census algorithm of subgraph concentrations. Network mechanism can be quickly inferred by the new method even though the network has large scale and high density. Therefore, the application perspective of mechanism-inferring method has been extended into the wider fields of large-scale complex networks. By applying the new method to a case of protein interaction network, the authors obtain the same inferring result as the existing method, which approves the
  effectiveness of the method.
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  SEVERAL CRYPTOGRAPHIC APPLICATIONS OF $\Sigma$-PROTOCOL

  Chunming TANG;Zheng-an YAO

  Journal of Systems Science and Complexity. 2009, 22(2): 260-279.

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  ${\it \Sigma}$-protocol has been proved to be a very powerful cryptographic tool and widely used in numerous important cryptographic applications. In this paper, the authors make use of ${\it \Sigma}$-protocol as a main tool to resolve the following
  difficult problems 1--3 and to construct three efficient cryptographic protocols 4--6:\\ 1) How to construct a protocol for proving a secret integer to be a Blum integer with form $PQ$, where $P,Q$ are two different primes and both $\equiv 3({\rm mod}\
  4)$;\\ 2) How to construct a protocol for proving a secret polynomial with exact degree $t-1$ in a $(t,n)$-threshold secret sharing scheme;\\ 3) How to construct witness indistinguishable and witness hiding protocol not from zero-knowledge proof;\\ 4) A
  publicly verifiable secret sharing scheme with information-theoretic security;\\ 5) A delegateable signature scheme under the existence of one-way permutations;\\ 6)
  Non-interactive universal designated verifier signature schemes.
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  SYMMETRY IN WORLD TRADE NETWORK

  Hui WANG;Guangle YAN;Yanghua XIAO

  Journal of Systems Science and Complexity. 2009, 22(2): 280-290.

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  Symmetry of the world trade network provides a novel perspective to understand the world-wide trading system. However, symmetry in the world trade network (WTN) has been rarely studied so far. In this paper, the authors systematically explore the
  symmetry in WTN. The authors construct WTN in 2005 and explore the size and structure of its automorphism group, through which the authors find that WTN is symmetric, particularly, locally symmetric to a certain degree. Furthermore, the authors work out the symmetric motifs of WTN and investigate the structure and function of the symmetric motifs, coming to the conclusion that local symmetry will have great effect on the stability of the WTN and that continuous symmetry-breakings will generate complexity and diversity of the trade network. Finally, utilizing the local
  symmetry of the network, the authors work out the quotient of WTN, which is the structural skeleton dominating stability and evolution of WTN.
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  A SINGLE SERVER RETRIAL QUEUE WITH GENERAL RETRIAL TIMES AND TWO-PHASE SERVICE

  Jinting WANG;Jianghua LI

  Journal of Systems Science and Complexity. 2009, 22(2): 291-302.

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  An $M/G/1$ retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated in this paper. Customers are allowed to balk and renege at particular times. Assume that the customers who find the server busy are queued in the orbit in accordance with an
  FCFS discipline. All customers demand the first ``essential" service, whereas only some of them demand the second ``optional" service, and the second service is multi-optional. During the service, the server is subject to breakdown and repair. Assume
  that the retrial time, the service time, and the repair time of the server are all arbitrarily distributed. By using the supplementary variables method, the authors obtain the steady-state solutions for both queueing and reliability measures
  of interest.
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  TRANSIENT QUEUE SIZE DISTRIBUTION SOLUTION OF GEOM/G/1 QUEUE WITH FEEDBACK--A RECURSIVE METHOD

  Chuanyi LUO;Yinghui TANG;Cailiang LI

  Journal of Systems Science and Complexity. 2009, 22(2): 303-312.

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  This paper considers the ${\rm Geom}/G/1$ queueing model with feedback
  according to a late arrival system with delayed access (LASDA). Using recursive method, this paper studies the transient property of the queue size from the initial state $N(0^+)=i $.~Some new results about the recursive expression of the transient queue size distribution at any epoch ~$n^+ $~and the recursive formulae of the equilibrium distribution are obtained. Furthermore, the recursive formulae of the equilibrium queue size distribution at epoch~$ n^{-}$, and $n$~are obtained, too. The important relations between stationary queue size distributions at different epochs are discovered (being different from the relations given in $M/G/1$ queueing system). The model discussed in this paper can be widely applied in all kinds of communications and computer network.
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  FUZZY EPQ INVENTORY MODELS WITH BACKORDER

  Xiaobin WANG;Wansheng TANG

  Journal of Systems Science and Complexity. 2009, 22(2): 313-323.

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  This paper considers the economic production quantity (EPQ) problem with backorder in which the setup cost, the holding cost and the backorder cost are characterized as fuzzy variables, respectively. Following expected value criterion and chance constrained criterion, a fuzzy expected value model (EVM) and a chance constrained programming (CCP) model are constructed. Then fuzzy simulations are employed to estimate the expected value of fuzzy variable and $\alpha$--level minimal average cost. In order to solve the CCP model, a particle swarm optimization (PSO)
  algorithm based on the fuzzy simulation is designed. Finally, the effectiveness of PSO algorithm based on the fuzzy simulation is illustrated by a numerical example.
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  EXPONENTIAL ESTIMATES FOR STOCHASTIC DELAY EQUATIONS WITHNORM-BOUNDED UNCERTAINTIES

  Hongchu WANG;Shigeng HU

  Journal of Systems Science and Complexity. 2009, 22(2): 324-332.

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  This paper presents the sufficient conditions for the exponential stability of linear or semi-linear stochastic delay equations with time-varying norm bounded parameter uncertainties. Exponential estimates for the solutions are also obtained by using
  a modified Lyapunov-Krasovski functional. These conditions can be tested numerically using interior point algorithms.
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  THREE-STEP ITERATIONS FOR NONEXPANSIVE MAPPINGS ANDINVERSE-STRONGLY MONOTONE MAPPINGS

  Meijuan SHANG;Yongfu SU;Xiaolong QIN

  Journal of Systems Science and Complexity. 2009, 22(2): 333-344.

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  This paper introduces a three-step iteration for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping by viscosity approximation
  methods in a Hilbert space. The authors show that the iterative sequence converges strongly to a common element of the two sets, which solves some variational inequality. Subsequently, the authors consider the problem of finding a common fixed point of a nonexpansive mapping and a strictly pseudo-contractive mapping and
  the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the corresponding results announced by
  Nakajo, Takahashi, and Toyoda.