2009年, 第22卷, 第4期　刊出日期：2009-12-25

  

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  A NONLINEAR KREIN RUTMAN THEOREM

  K. C. Chang

  Journal of Systems Science and Complexity. 2009, 22(4): 542-554.

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  A nonlinear version of Krein Rutman Theorem is established. This paper presents a unified proof of the Krein Rutman Theorem for linear operators and for nonlinear operators, and of the Perron-Frobenius theorem for nonnegative matrices and for
  nonnegative tensors.
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  UNIFORM OPTIMAL-ORDER ESTIMATES FOR FINITE ELEMENT METHODS FOR ADVECTION-DIFFUSION EQUATIONS

  Qun LIN;Hong WANG;Shuhua ZHANG

  Journal of Systems Science and Complexity. 2009, 22(4): 555-559.

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  This article summarizes our recent work on uniform error estimates for various finite element methods for time-dependent advection-diffusion equations.
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  MINIMUM HAUSDORFF DISTANCE UNDER RIGID MOTIONS AND COMPARISON OF PROTEIN STRUCTURES

  Banghe LI;Bo LI;Yuefeng SHEN

  Journal of Systems Science and Complexity. 2009, 22(4): 560-586.

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  Hausdorff distance between two compact sets, defined as the maximum distance from a point of one set to another set, has many application in computer science. It is a good measure for the similarity of two sets. This paper proves that the shape distance
  between two compact sets in $R^n$ defined by minimum Hausdorff distance under rigid motions is a distance. The authors introduce similarity comparison problems in protein science, and propose that this measure may have good application to comparison of protein structure as well. For calculation of this distance, the authors
  give one dimensional formulas for problems $(2,n)$, $(3,3)$, and $(3,4)$. These formulas can reduce time needed for solving these problems. The authors did some numerical experiments for $(2,n)$. On these sets of data, this formula can reduce time needed to one fifteenth of the best algorithms known on average. As $n$ increases,
  it would save more time.
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  TWO KINDS OF HARMONIC PROBLEMS IN CONTROL SYSTEMS

  Zhisheng DUAN;Lin HUANG

  Journal of Systems Science and Complexity. 2009, 22(4): 587-596.

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  This paper discusses the harmonic problems in control systems from two aspects: One is the harmonic control among different subsystems, and the other is the harmonic control among multiple inputs. Some intrinsic problems in such systems are discussed. It is pointed out that some subsystems must be unstable to stabilize the whole interconnected system by an example. Especially for discrete-time multi-input systems, a necessary and sufficient condition is presented for the strict decrease of the quadratic optimal performance index with the control input extensions. This shows an essential difference between single-input and multi-input control systems. Finally, some future research directions are discussed in harmonic control of interconnected systems, allocation of multi-control inputs, fault-tolerant control, and fault-diagnosis.
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  SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATION IN R^n

  Xiangqing LIU;Yuxia GUO;Jiaquan LIU

  Journal of Systems Science and Complexity. 2009, 22(4): 597-613.

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  In this paper, the authors study the existence and non-existence of positive solutions for singular $p$-Laplacian equation $-\Delta _pu=f(x)u^{-\alpha}+\lambda g(x)u^\beta$ in $R^N,$ where $N\geq 3, 1<p<N, \lambda>0, 0<\alpha<1, \max(p,2)<\beta+1<p*=\frac{Np}{N-p}.$ We prove that there exists a critical value ${\it \Lambda}$ such that the problem has at least two solutions if $0<\lambda<{\it \Lambda};$ at least one solution if $\lambda={\it \Lambda};$ and no solutions if $\lambda>{\it \Lambda}.$
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  DESIGN OF CONTROL INVARIANT SETS OF PLANAR SYSTEMS

  Daizhan CHENG;Yupeng QIAO;Wei NI

  Journal of Systems Science and Complexity. 2009, 22(4): 614-626.

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  Control invariant sets play a key role in model predictive control. Using Lyapunov function, a technique is proposed to design control invariant sets of planar systems in a precise form. First, it is designed for a linear system in Brunovsky canonical form.
  Then, the result is extended to general linear systems. Finally, the
  nonlinear control systems are considered, and some sufficient conditions and design techniques are also obtained. Numerical examples are presented to illustrate the proposed design methods.
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  A CRITERION FOR TESTING WHETHER A DIFFERENCE IDEAL IS PRIME

  Chunming YUAN;Xiao-Shan GAO

  Journal of Systems Science and Complexity. 2009, 22(4): 627-635.

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  This paper presents a criterion for testing the irreducibility of a polynomial over an algebraic extension field. Using this criterion and the characteristic set method, the authors give a criterion for testing whether certain difference ascending chains are strong irreducible, and as a consequence, whether the saturation ideals of these ascending chains are prime ideals.
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  DID SPECULATIVE ACTIVITIES CONTRIBUTE TO HIGH CRUDE OIL PRICES DURING 1993 TO 2008?

  Xun ZHANG;Kin Keung LAI;Shouyang WANG

  Journal of Systems Science and Complexity. 2009, 22(4): 636-646.

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  By applying two nonlinear Granger causality testing methods and rolling window strategy to explore the relationship between speculative activities and crude oil prices, the unidirectional Granger causality from speculative activities to returns of crude
  oil prices during the high price phase is discovered. It is proved that speculative activities did contribute to high crude oil prices after the Asian financial crisis and OPEC's output cut in 1998. The unidirectional Granger causality from returns of crude oil prices to speculative activities is significant in general. But after 2000, with the sharp rise in crude oil prices, this unidirectional Granger causality became a complex nonlinear relationship, which cannot be detected by any linear Granger causality test.
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  CONTROL AND STABILIZATION OF THE KORTEWEG-DE VRIES EQUATION:RECENT PROGRESSES

  Lionel ROSIER;Bing-Yu ZHANG

  Journal of Systems Science and Complexity. 2009, 22(4): 647-682.

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  The study of the control and stabilization of the KdV equation began with the work of Russell and Zhang in late 1980s. Both exact control and stabilization problems have been intensively studied since then and significant progresses have been made due to many people's hard work and contributions. In this article, the authors intend to give an overall review of the results obtained so far in the study but with an emphasis on its recent progresses. A list of open problems is also provided for further investigation.
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  STABILIZATION OF NONLINEAR TIME-VARYING SYSTEMS: A CONTROL LYAPUNOV FUNCTION APPROACH

  Zhongping JIANG;Yuandan LIN;Yuan WANG

  Journal of Systems Science and Complexity. 2009, 22(4): 683-696.

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  This paper presents a control Lyapunov function approach to the global stabilization problem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws are proposed based on the method of control Lyapunov functions and Sontag's universal formula.
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  AN OVERVIEW OF THE DEVELOPMENT OF LOW GAIN FEEDBACK ANDLOW-AND-HIGH GAIN FEEDBACK

  Zongli LIN

  Journal of Systems Science and Complexity. 2009, 22(4): 697-721.

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  Low gain feedback refers to certain families of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero. Low gain feedback was initially proposed to achieve semi-global stabilization of linear
  systems subject to input saturation. It was then combined with high gain feedback in different ways for solving various control problems. The resulting feedback laws are referred to as low-and-high gain feedback. Since the introduction of low gain
  feedback in the context of semi-global stabilization of linear systems subject to input saturation, there has been effort to develop alternative methods for low gain design, to characterize key features of low gain feedback, and to explore new applications of
  the low gain and low-and-high gain feedback. This paper reviews the developments in low gain and low-and-high gain feedback designs.
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  MULTI-AGENT TRACKING OF A HIGH-DIMENSIONAL ACTIVE LEADERWITH SWITCHING TOPOLOGY

  Yiguang HONG;Xiaoli WANG

  Journal of Systems Science and Complexity. 2009, 22(4): 722-731.

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  This paper considers a multi-agent tracking problem for a high-dimensional active leader and variable interconnection topology. The state of the leader not only keeps changing but also may not be measured. To estimate the state such a leader
  individually, a neighbor-based local controller together with a neighbor-based state-estimation rule is given for each autonomous agent. Then, the authors prove that, with the help of a constructed common Lyapunov function (CLF), each agent can track
  the active leader with unmeasurable states. Finally, the authors explicitly construct a CLF for an active leader with unknown periodic input for illustration.
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  FREQUENTIST MODEL AVERAGING ESTIMATION: A REVIEW

  Haiying WANG;Xinyu ZHANG;Guohua ZOU

  Journal of Systems Science and Complexity. 2009, 22(4): 732-748.

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  In applications, the traditional estimation procedure generally begins with model selection. Once a specific model is selected, subsequent estimation is conducted under the selected model without consideration of the uncertainty from the selection process. This often leads to the underreporting of variability and too optimistic
  confidence sets. Model averaging estimation is an alternative to this procedure, which incorporates model uncertainty into the estimation process. In recent years, there has been a rising interest in model averaging from the frequentist perspective, and
  some important progresses have been made. In this paper, the theory
  and methods on frequentist model averaging estimation are surveyed.
  Some future research topics are also discussed.
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  GLOBAL SMOOTH SOLUTIONS FOR SEMILINEAR SCHR$\ddot{O}$DINGER EQUATIONS WITH BOUNDARY FEEDBACK ON 2-DIMENSIONAL RIEMANNIAN MANIFOLDS

  Li DENG;Pengfei YAO

  Journal of Systems Science and Complexity. 2009, 22(4): 749-776.

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  This paper considers the existence of global smooth solutions of semilinear schr$\ddot{\mbox{o}}$dinger equation with a boundary feedback on 2-dimensional Riemannian manifolds when initial data are small. The authors show that the existence of global solutions depends not only on the boundary feedback, but also on a Riemannian
  metric, given by the coefficient of the principle part and the original metric of the manifold. In particular, the authers prove that the energy of the system decays exponentially.