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Table of Content

      
    16 April 2008
    Volume 43 Issue 4
    Articles
    Existence of solutions to differential system on the non-cylindrical domain in Banach spaces
    LIU Xin-min,CUI Yu-jun*
    J4. 2008, 43(4):  1-05 .  doi:
    Abstract ( 906 )   PDF (220KB) ( 874 )   Save
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    The existence of solutions for the following differential system (IVP;τ,z0) z′=x′ y′=f1(t,x,y) f2(t,x,y)=f(t,z), (t,z)∈Ω, z(τ)=x(τ) y(τ)=z0=x0 y0 in Banach space was investigated, where f1 and f2 respectively meet noncompact condition and dissipative condition. The results extend and improve some known results.
    Jordan ideals in triangular algebras of type II1 hyper-finite factors
    JI Pei-sheng,QI Wei-qing,LIU Zhong-yan
    J4. 2008, 43(4):  6-08 .  doi:
    Abstract ( 849 )   PDF (174KB) ( 891 )   Save
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    It was shown that every weakly closed Jordan ideal in triangular algebra of the type II1 hyper-finte factor is an associative ideal.
    The absolute exponential stability of BAM neural networks with variable coefficients and mixed delays
    KAO Yong-gui,GAO Cun-chen,MENG Bo
    J4. 2008, 43(4):  9-13 .  doi:
    Abstract ( 1434 )   PDF (229KB) ( 996 )   Save
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    The absolute exponential stability for BAM neural networks with continuously distributed signal transmission delays along the axon of a neuron was investigated, using the Brouwer fixed point theorem and inequality techniques. Some novel criteria were obtained for checking the equilibrium point, in which the activation functions only need to be partially Lipschitz continuous, but not to be bounded or differentiable. An example shows the effectiveness of the results.
    Rough similarity degree of an information vector and its knowledge mining
    HAO Xiu-mei,DU Ying-ling,REN Xue-fang
    J4. 2008, 43(4):  14-16 .  doi:
    Abstract ( 916 )   PDF (195KB) ( 909 )   Save
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    By using the concepts of rough information matrix and similarity degree, the concept of rough similarity degree of a rough information vector was proposed.The characteristics of a rough similarity degree and a rough similarity degree matrix were discussed, and the generation of a rough similarity degree matrix and important theorems were given.
    Descriptions of the pre-R0 separation axiom in fuzzifying topological space
    LI Ning
    J4. 2008, 43(4):  17-20 .  doi:
    Abstract ( 983 )   PDF (174KB) ( 859 )   Save
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    The definition of the pre-R0 separation axiom was introduced. Descriptions of the pre-R0 separation axiom based on the pre-closure, the pre-θ closure and the pre-kernel in fuzzifying topology were discussed.
    Dynamic inference and recognition of S-rough sets knowledge
    REN Xue-fang,DU Ying-ling,QIU Yu-feng
    J4. 2008, 43(4):  21-27 .  doi:
    Abstract ( 959 )   PDF (281KB) ( 1033 )   Save
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    When the knowledge system was interfered dynamically by some exterior attributes, a logic inference structure for system interferes was constructed and the issue of dynamic inference and recognition of knowledge was proposed by using the propositional logic model of symbolic logic. Then, the theorem of inference and recognition of knowledge, the theorem of inference and recognition of S-rough sets, and the principle of inference and recognition of knowledge were given. Finally, the application of dynamic inference and recognition of knowledge in the issue of dynamic recognition of knowledge was presented.
    Measurement of F-rough integrals and recognition of the medicinal effect
    YU Xiu-qing,REN Xue-fang
    J4. 2008, 43(4):  28-32 .  doi:
    Abstract ( 1018 )   PDF (231KB) ( 1009 )   Save
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    F-rough integrals were defined on the basis of function one direction S-rough sets. Using F-rough integrals, the concepts of shrinkage measurement and shrinkage rate were given. By shrinkage measurement and shrinkage rate, the changing extent can be expressed with numbers. The shrinkage measurement and the shrinkage rate can also be used to compare treatment effects of different medicines or different dosages of the same medicine to the same pathological changes in the medicinal field.
    F-knowledge and its hiding-dependence characteristics
    SU Shao-qing,LIU Ruo-hui,CAI Cheng-wen
    J4. 2008, 43(4):  33-37 .  doi:
    Abstract ( 1253 )   PDF (230KB) ( 706 )   Save
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    S-rough sets (singular rough sets) have three forms: one direction S-rough sets (one direction singular rough sets), the dual of one direction S-rough sets (dual of one direction singular rough sets), and two direction S-rough sets(two direction singular rough sets). S-rough sets have dynamic characteristics, genetic characteristics, memorial characteristics and hiding characteristics. By using S-rough sets, the concepts of f-hiding knowledge, F-hiding knowledge, hiding degree and dependence degree were presented, hiding theorem and dependence theorem of hiding knowledge were proposed, and the applications of hiding knowledge were given.
    The uniqueness of meromorphic functions with finite non-integer (lower) order
    CHEN Gui-ling,ZHANG Xiao-bin
    J4. 2008, 43(4):  38-41 .  doi:
    Abstract ( 969 )   PDF (174KB) ( 717 )   Save
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    The four-valued theorem of Nevanlinna for meromorphic functions of finite non-integer order was studied, which is a generalization and improvement of H.X.Yi,Weichuan Lin etc.
    The *-coparacompactness in L-bitopological spaces
    LIU Hong-ping,MENG Guang-wu
    J4. 2008, 43(4):  42-46 .  doi:
    Abstract ( 999 )   PDF (239KB) ( 846 )   Save
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    The *-coparacompactness was introduced in L-bitopological spaces. The results show that the *-coparacompactness is a extension of B-cocompactness, and it has some good properties. For instance, it is hereditary with respect to biclosed subsets and is preserved under strong bihomeomorphisms. With specifical conditions, the Cartesian product of a B-cocompact set and a *-coparacompact set is a *-coparacompact set. It was also proved that a *-coparacompact and bi-T2 space is both a bi-regular and a coregular space.
    A computational method for the nonlinear BBM equation
    ZUO Jin-ming
    J4. 2008, 43(4):  47-50 .  doi:
    Abstract ( 978 )   PDF (454KB) ( 912 )   Save
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    A computational method based on a linearized implicit scheme was proposed for the solution of the BBM equation.An important advantage to be gained from the linearized implicit method is unconditional stablility. Numerical results portraying a single line-soliton solution and the interaction of two-line solitions were reported for the BBM equation. The results show that the method has good stability and accuracy.
    A two-grid algorithm for a finite difference solution of semi-linear elliptic equations
    LIU Wei, RUI Hong-xing
    J4. 2008, 43(4):  51-54 .  doi:
    Abstract ( 1205 )   PDF (474KB) ( 886 )   Save
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    An efficient two-grid algorithm was presented for the approximation of semi-linear elliptic equations using the finite difference method. The solution of a nonlinear system in fine space was reduced to the solution of one small system in coarse space and two linear systems on the fine space. A remarkable fact is that any order accuracy of approximation in coarse grid size can be obtained if other iterations are performed similarly to last step of the algorithm. The numerical results confirm that the algorithm obtains a decrease in the amount of computing time without sacrificing the order of accuracy of the fine grid solution.
    H#-abundant semi-groups
    DING Yue
    J4. 2008, 43(4):  55-57 .  doi:
    Abstract ( 844 )   PDF (176KB) ( 1096 )   Save
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    The usural Green relations and *-Green relations were generalized to #-Green relations, and the semi-lattice decomposition of H#-abundant semi-groups was given.
    Robust resilient H∞ control for interval singular systems with time-varying delays
    ZHANG Wei,JU Pei-jun*
    J4. 2008, 43(4):  58-61 .  doi:
    Abstract ( 943 )   PDF (245KB) ( 741 )   Save
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    The problem of robust resilient H∞ control of interval singular systems with time-varying delays was discussed. Using the equivalent form of interval matrix, the interval singular systems were converted to a class of uncertain singular systems with time-varying delays. A sufficient condition for the solvability of the robust resilient H∞ control in term of a matrix inequality and cone complementarity. Numerical examples were proposed to illustrate the effectiveness of the result.
    The strong law of large numbers for the sum of partial sums of identically distributed NA sequences
    YU Shi-hang
    J4. 2008, 43(4):  62-66 .  doi:
    Abstract ( 1051 )   PDF (198KB) ( 888 )   Save
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    The strong law of large numbers for the sum of partial sum of identically distributed NA sequences was studied. The strong law of large numbers was established by giving some egenvalent conditions, and similar results to the I.I.D case were then obtained.
    1-resonance of a class of Fullerene graphs
    QI Zhong-bin,ZHANG He-ping
    J4. 2008, 43(4):  67-72 .  doi:
    Abstract ( 972 )   PDF (305KB) ( 917 )   Save
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    A plane graph with 1 hexagonal inner face and 6 pentagonal inner faces was denoted by R(0), where these pentagonal faces can form a ring chain, and are adjacent to the hexagonal face. The construction and a classification of the Fullerene graphs containing R(0) were given. Further, it was proved that every Fullerene graph with R(0) as its subgraph is 1-resonant.
    The parallel row action method with the greedy method for the system of linear equations
    ZENG Xian-wen,LI An-zhi
    J4. 2008, 43(4):  73-75 .  doi:
    Abstract ( 1137 )   PDF (221KB) ( 1090 )   Save
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    The Gram-Schmidt’s orthogonalization, row action method with the greedy method and dividing-conquering strategy were used to put forth a parallel numerical method of solving an arbitrary system of linear algebraic equations. It was proved that this method is convergent to the arbitrary consistent system of linear algebraic equations. Its computational complexity and numerical stability were analyzed, and its application prospects in the study of a message passing parallel algorithm for a system of linear algebraic equations were discussed.
    Strongly order continuity and pseudo-S-property of generalized fuzzy valued Choquet integrals
    LI Yan-hong,WANG Gui-jun
    J4. 2008, 43(4):  76-80 .  doi:
    Abstract ( 969 )   PDF (218KB) ( 743 )   Save
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    In general fuzzy measure spaces, aimed at giving generalized fuzzy valued Choquet integrals, these kind of integrals were completely regarded as a set function taken fuzzy numbers in measurable spaces. Then, when the fuzzy measure satisfied the strongly order continuity and pseudo-S-property, the heredity of the fuzzy valued Choquet integrals was researched.
    Global exponential stability for static neural network models with time-varying delays and Markovian jumping parameters
    WANG Shun-kang,WANG Lin-shan
    J4. 2008, 43(4):  81-84 .  doi:
    Abstract ( 1133 )   PDF (221KB) ( 834 )   Save
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    By using the Lyapunov-Krasovskii functional theory and the linear matrix inequality (LMI) approach, the global exponential stability of static neural network models with time-varying delays and Markovian jumping parameters was studied. A criterion of the global exponential stability was derived.
    The complex modulus and the complex compliance for higher-order fractional constitutive models of visco-elastic materials
    LIU Jia-guo
    J4. 2008, 43(4):  85-88 .  doi:
    Abstract ( 1089 )   PDF (436KB) ( 881 )   Save
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    By the theory of fractional calculus (FC) based higher-order fractional constitutive models of visco-elastic materials, the complex modulus of FVMP model and complex compliance of FVMS model were discussed.The theory curves were also given. The results are significant in guilding dynamical tests on viscoelastic materials.
    Implementation, comparison and improvement of the methods of characteristic set, Grbner bases and well-behaved bases
    LI Zhao-li,FENG Xiao*
    J4. 2008, 43(4):  89-96 .  doi:
    Abstract ( 976 )   PDF (258KB) ( 717 )   Save
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    The algorithmization of the methods of well-behaved bases and differential characteristic sets was given. Some experiments were put forth to give the comparison of the methods of well-behaved bases and Gro¨bner bases. For computing differential characteristic sets, the method can improve the algorithm for computing the passive auto-reduced sets by detecting unnecessary computations in the process.