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Table of Content

      
    24 December 2007
    Volume 42 Issue 12
    Articles
    Stability analysis for some classes of time-delay nonlinear Hamiltonian systems
    SUN Wei-wei,WANG Yu-zhen
    J4. 2007, 42(12):  1-09 .  doi:
    Abstract ( 939 )   PDF (223KB) ( 983 )   Save
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    The stability of Hamiltonian systems with time delay was investigated. Using the technique of the Lyapunov direct method and the dissipative structural properties of Hamiltonian systems, some sufficient conditions are derived for the stability of several classes of time-delay Hamiltonian systems. First, the stability is studied for the system with delay only in the Hamiltonian function, with which the stability of a class of time-delay nonlinear systems is also investigated by Hamiltonian realization. Second, the robust stability is considered for a class of time-delay Hamiltonian systems which possesse time-invariant uncertainties belonging to some convex bounded polytypic domain. Finally, several illustrative examples are studied by using the proposed results. Examples show that the results are very practicable in analyzing the stability of some classes of time-delay nonlinear systems.
    Positive solutions of nonlinear second-order Neumann boundary value problems with a variable coefficient
    YAO Qing-liu
    J4. 2007, 42(12):  10-14 .  doi:
    Abstract ( 1110 )   PDF (238KB) ( 1183 )   Save
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    Neumann boundary value problems describe many physical phenomena whose gradients are zero at boundary points. The positive solutions of nonlinear second-order Neumann boundary value problem u″(t)+k(t)u(t)=f(t,u(t)), 0≤t≤1, u′(0)=u′(1)=0 with function coefficient k(t)were studied by applying the fixed-point index theorem of cones. The main results show that the problem has n positive solutions provided growth rates of nonlinear term on some bounded sets are appropriate, where n is an arbitrary natural number.
    Eigen-problem and singular value decomposition of the generalized symmetric matrix
    JIA Zhi-gang,ZHAO Jian-li,ZHANG Feng-xia
    J4. 2007, 42(12):  15-18 .  doi:
    Abstract ( 1589 )   PDF (207KB) ( 1362 )   Save
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    For every singular Hermitian matrix A, there exists a k-th unit matrix R such that A is k degree R-symmetric. Suppose that a k-th unit matrix R is given for a k-degree R-symmetric matrix A. It presents the properties of its eigen-pairs, the explicit expression of its characteristic polynomial, and its singular value decomposition. Moreover, an eigen-problem of A can be reduced to multi eigen-problems of matrices of small dimensions by applying its structure.
    Perfect sorting by reversals and deletions
    ZHANG Hai-yan,LI Guo-jun
    J4. 2007, 42(12):  19-23 .  doi:
    Abstract ( 1063 )   PDF (227KB) ( 1150 )   Save
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    The problem of perfect sorting by reversals and deletions was considered, and one kind of polynomial algorithm was given.
    Two biometric identities based signature schemes
    LIU Xiao-dong,JIANG Ya-li,LI Da-xing
    J4. 2007, 42(12):  24-28 .  doi:
    Abstract ( 1207 )   PDF (205KB) ( 1226 )   Save
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    In the first scheme, the signer's public key was constructed from his biometric data. The verifier performed verification successfully by asking signer to show his biometric data, which makes the verifying operation more visible and convenient. In the second scheme, since the private key of the signer was constructed from the biometric data of the signer, it does not need to be placed in hardware, and therefore there is no worry about the loss and inconvenience caused by the fault of the hardware. These two schemes were constructed from the fuzzy extractor method proposed by Dodis, Liu scheme and classical BLS short signature scheme. Finally, two possible attacks on the schemes mentioned above were described and the ways to combat them were suggested.
    Many-valued filter and its application
    LI Ling-qiang,QIU Jin
    J4. 2007, 42(12):  29-32 .  doi:
    Abstract ( 1086 )   PDF (198KB) ( 1221 )   Save
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    A basic question in fuzzy set theory was studied: what is a many-valued filter on a set X? A new answer was presented by interpreting the axioms (three logical formulas) for classical filter theory in the fuzzy setting, which made use of the intrinsic fuzzy partial order on the fuzzy power set of X. The many valued filter theory was applied to characterize one of the many-valued topological theory —strong Ω-topology.
    A model based on the grey relation grade for multi-objective decision-making and its application
    LI Xiu-hong
    J4. 2007, 42(12):  33-36 .  doi:
    Abstract ( 1200 )   PDF (241KB) ( 1549 )   Save
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    Based on the grey relation grade theory, a multi-objective decision-making model was built by using the targets grey relation grade to determine the weights of the indicators and taking the weighted grey relation degree of alternatives as the evaluation criteria. Finally, an example was given to show its practicability and effectiveness.
    Uniqueness of an invariant probability for non-degenerate Markov-Feller operators
    GUO Xin-wei
    J4. 2007, 42(12):  37-41 .  doi:
    Abstract ( 931 )   PDF (191KB) ( 976 )   Save
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    The ergodicity of non-degenerate Markov-Feller operators on locally compact separable metric space was discussed and the necessary and sufficient condition for the existence of the unique invariant probability was given.
    Pre-continuity mapping in I-fuzzy topological space
    LI Ning
    J4. 2007, 42(12):  42-45 .  doi:
    Abstract ( 950 )   PDF (177KB) ( 884 )   Save
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    The concepts of the pre-open operator and pre-quasi-coincident neighborhood system in I-fuzzy topological space were given. The properties of the pre-continuity mapping of I-fuzzy topological space were studied.
    Sorting circular binary strings with length weighted transpositions
    QI Xing-qin,CAO Jing,ZHANG Chen
    J4. 2007, 42(12):  46-48 .  doi:
    Abstract ( 1335 )   PDF (193KB) ( 1119 )   Save
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    The problem of sorting circular binary strings with length-weighted transpositions was considered, i.e. the cost of a transposition is f(l)=lα,0≤α<1, where l is the length of the transposition. An O(logn)approximation algorithm is given for sorting a circular binary string with the minimum cost, where n is the length of the circular string. The result has direct applications in computational biology in the field of comparative genomics.
    H∞ tracking control for a class of uncertain nonlinear systems with time-delay by using multi-model switching
    QIAN Cheng-shan,WU Qing-xian,JIANG Chang-sheng,FANG Wei
    J4. 2007, 42(12):  49-54 .  doi:
    Abstract ( 1166 )   PDF (298KB) ( 914 )   Save
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    The design of H∞ tracking control for a class of uncertain nonlinear systems with time-delay was given using multi-model switching in the presence of uncertainty and disturbance. First, T-S models with time-delay were employed to model the uncertain nonlinear system with time-delay. The inputspace was divided into multiple regions. Local T-S models and controllers were designed in each region, such that the approach precision improves as the fuzzy domain decreases under constant fuzzy rules. Then, on the condition that the uncertain is gain bounded, a sufficient condition is presented for the existence of the controller, which satisfies the closedloop stability and the performance of H∞ tracking. By solving a family of linear matrix inequalities, the H∞ tracking control law was obtained. Based on Lyapunov theory, it was proven that the closed-loop system has exponential stability. Finally, a region controller, which was chosen according to the selected variables by the multiple-model switching control, was switched to the whole controller and that other controllers did not operate. The approach and control of the entire nonlinear system was therefore established.
    Pre-derived operators, pre-difference derived operators and pre-topologies
    YANG Xiao-fei,LI Sheng-gang*
    J4. 2007, 42(12):  55-57 .  doi:
    Abstract ( 1031 )   PDF (186KB) ( 849 )   Save
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    The concepts of pre-derived operator and pre-difference derived operator were introduced. It was proved that, for a given set X, appropriate order relations≤can be defined on PD(X) (the set of all pre-derived operators on X) and PDD(X) (the set of all pre-difference derived operators on X), respectively, such that both (PD(X), ≤) and (PDD(X), ≤) are complete lattices which are isomorphic to (PT(X))(the set of all pre-topologies on the set X).
    Forward-backward doubly stochastic differential equations under local Lipschitz condition
    ZHU Qing-feng,SHI Yu-feng
    J4. 2007, 42(12):  58-62 .  doi:
    Abstract ( 1161 )   PDF (225KB) ( 905 )   Save
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    The existence and uniqueness for the solution of forward-backward doubly stochastic differential equations were obtained under local Lipschitz condition, where the time duration could be arbitrarily given.
    Correlation analysis of the Shanghai-Shenzhen stock index based on Gaussian Copula and t-Copula
    YANG Xing-min,LIU Bao-dong*,LI Juan
    J4. 2007, 42(12):  63-68 .  doi:
    Abstract ( 1275 )   PDF (217KB) ( 1105 )   Save
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    Gaussian Copula and t-Copula density functions were discussed according to the Shanghai-Shenzhen stock index, and a correlation model was provided. The parameter of this model was estimated by the two-step estimating method and the relative index was given. Finally, the difference between Copula correlation structures was compared by the Monte Carlo method.
    A unicity theorem on the entire function and its linear differential polynomials
    CAO Yin-hong,GAO Rui
    J4. 2007, 42(12):  69-72 .  doi:
    Abstract ( 1167 )   PDF (188KB) ( 933 )   Save
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    By employing the auxiliary functions constructed by P. Li and C. C. Yang, a unicity theorem on the entire function in the open complex plane and its generated linear differential polynomials sharing two distinct finite values was proved, which can extend and generalize many previous results.
    Path factor in a quasi-claw-free graph
    GENG Jian-yan,YAN Jin,GAO Yun-shu
    J4. 2007, 42(12):  73-76 .  doi:
    Abstract ( 1468 )   PDF (196KB) ( 828 )   Save
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    It was proved that if G is a quasi-claw-free graph with a minimum degree at least d, then it has a path factor such that the order of each path is at least d+1.
    α-Embedding of rough both-branch fuzzy sets
    LIU Ruo-Hui,LIU Bao-Cang
    J4. 2007, 42(12):  77-81 .  doi:
    Abstract ( 1076 )   PDF (210KB) ( 1037 )   Save
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    The concept of the rough both-branch and the concept of α-embedding of rough both-branch were presented based on rough sets and both-branch fuzzy sets. The α-embedding union-decomposition and α-embedding intersection-decomposition of rough both-branch fuzzy sets were discussed.
    Existence of an analytic solution for a first order iterative functional differential equation
    LIU Ling-xia
    J4. 2007, 42(12):  82-86 .  doi:
    Abstract ( 1101 )   PDF (209KB) ( 1143 )   Save
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    The existence of an analytic solution was discussed for a first order iterative functional differential equation x′(z)=1/x(az+bx(z)), z∈C (Ⅰ) in a complex field. In previous work[6], the eigen-value of the linearization was required to fulfill that α is not on the unit circle or lies on the circle with the Diophantine condition. Results of the analytic solution were obtained in the case that α was the unit root and the case that α is near resonance under the Brjuno condition.
    PS-property of Malcev-Neumann rings
    ZHAO Ren-yu
    J4. 2007, 42(12):  87-89 .  doi:
    Abstract ( 1118 )   PDF (176KB) ( 747 )   Save
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    Let R be a ring,G a group and σ a map from G into the group of  automorphisms of R. It was shown that if R is a reduced right  the PS ring G is an ordered group and σ is weakly rigid,  then the Malcev-Neumann ring R*((G)) is a right PS-ring. It was  also shown that, under the same conditions, the sub-ring R*(G) of R*((G)) is also a right PS ring.
    Condition number of the quasi-maximal solution to a matrix equation X+A*X-pA=I when p>0
    LI Jing,ZHANG Yu-hai
    J4. 2007, 42(12):  90-94 .  doi:
    Abstract ( 1414 )   PDF (199KB) ( 1037 )   Save
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    Consider the nonlinear matrix equation X+A*X-pA=I(p>0), where A is n×n complex matrix and A* denotes the conjugate transpose of a matrix A.The explicit expressions of the condition number of the quasi-maximal solution were obtained.
    Local S*-compactness of L-topological spaces
    HAN Hong-xia
    J4. 2007, 42(12):  95-98 .  doi:
    Abstract ( 1093 )   PDF (184KB) ( 1046 )   Save
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    The notion of local S*-compactness of L-topological spaces was introduced. It was proved that the local S*-compactness is an L-good extension, which is inherited by a closed subspace, multiplicative, and invariable under the continuous open subjective Zadeh function.
    γ-compactness in L-topological spaces
    YAN Biao,HE Chun-hua, MENG Guang-wu, MENG Han
    J4. 2007, 42(12):  99-103 .  doi:
    Abstract ( 1086 )   PDF (205KB) ( 942 )   Save
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    In L-topological spaces, γ-open L-sets were introduced and the definition of γ-compactness was presented by inequality, where L was a complete DeMorgan algebra. This definition does not rely on the structure of basic lattice L and no distributivity was required in L. It was characterized by means of γ-closed L-sets and their inequality. The further characterizations of γ-compactness were discussed when L is a completely distributive DeMorgan algebra.
    Finite time control of an uncertain linear singular system with a time-varying disturbance
    LI Cui-cui,SHEN Yan-jun*,ZHU Lin
    J4. 2007, 42(12):  104-109 .  doi:
    Abstract ( 1047 )   PDF (260KB) ( 861 )   Save
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    The finite time control problem was studied based on the state-feedback control for an uncertain linear singular system with exogenous disturbance, of which the state matrix and input matrix have norm-bounded uncertainties. By the Lyapunov functional method and linear matrix inequality (LMI) technique, the sufficient conditions of finite time boundedness (FTB) for the singular system via state feedback controller were provided. Then, the conditions were reduced to feasibility problems involving linear matrix inequalities (LMIs). Finally, a numerical example was given to illustrate the validity of this proposed method.
    Global bifurcation of a predator-prey system incorporating a prey refuge
    ZHANG Li-na,LI Yan-ling,XIE Yu-long
    J4. 2007, 42(12):  110-115 .  doi:
    Abstract ( 1130 )   PDF (259KB) ( 1248 )   Save
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    A predator-prey system between two species with Holling type Ⅲ functional response incorporating a prey refuge was discussed. The existence of positive steady-state solutions was derived mainly through the global bifurcation and the maximum principle of elliptic equations. In a one dimensional case, a detailed description for the global bifurcation of the set of the non-constant steady states was given.
    Cardinal functions in L-fuzzy order-preserving spaces
    CHEN Bin
    J4. 2007, 42(12):  116-119 .  doi:
    Abstract ( 1337 )   PDF (210KB) ( 1072 )   Save
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    Cardinal functions were used to study the properties of L-fuzzy order-preserving spaces. The efinitions of ω-weight, ω-character and ω-density in L-fuzzy order-preserving spaces were given and their basic properties were studied. Some theorems mentioned in this paper were generalizations of S.L.Chen's in 2004.
    An O(h4) accurate new alternating segment explicit-implicit schemes for a parabolic problem
    ZHANG Shou-hui,WANG Wen-qia
    J4. 2007, 42(12):  120-126 .  doi:
    Abstract ( 1026 )   PDF (373KB) ( 837 )   Save
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    A high accurate new alternating segment explicit-implicit(nASE-I) scheme for a parabolic problem was given. This scheme can be used in parallel computation, which was proved to be unconditionally stable. The spatial accuracy rate is O(h4), which was proved to be highly accurate by numerical experiments.