Table of Content

    16 August 2008
    Volume 43 Issue 8

    A class of parallel finite difference methods for solving a two-dimensional diffusion equation

    XU Qiu-yan
    J4. 2008, 43(8):  1-05 .  doi:
    Abstract ( 1126 )   PDF (630KB) ( 1188 )   Save
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    A class of simple and practical parallel finite difference methods for solving a two-dimensional diffusion equation were introduced. Based on the skew direction difference operator[1], the implicit skew difference schemes were constructed, and the boundary condition was unified, to solve the diffusion equation. Although the schemes are implicit, this kind of algorithms can be computed explicitly with the boundary conditions. In this way, both the stability and accuracy of the implicit schemes were kept, and the complexity of calculation decreased. An example was presented to illustrate the usefulness of these parallel methods.

    A least-squares mixed finite element procedure with the method of
    characteristics for convection-dominated diffusion equations

    GUO Hui
    J4. 2008, 43(8):  6-10 .  doi:
    Abstract ( 1027 )   PDF (241KB) ( 818 )   Save
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    A least-squares mixed finite element procedure with the method of characteristics for convection-dominated diffusion equations was presented. By properly selecting the least-squares functional, the procedure can be split into two independent sub-procedures. The solution u and the flux σ can be directly obtained. Moreover the method permits the use of large steps. The optimal convergence analysis was established.

    A 2-approximation algorithm for an embedded hypergraph in a weighted cycle

    YANG Zhao-xia
    J4. 2008, 43(8):  11-13 .  doi:
    Abstract ( 988 )   PDF (194KB) ( 940 )   Save
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    The problem of hypergraph embedding in a weighted cycle (HEWC) is to embed the hyperedges of a hypergraph as the paths in a weighted cycle, such that the maximum congestion of any weighted link in the cycle is minimized. A simple version of this problem is graph embedding in a weighted cycle(GEWC) that embeds the edges of a normal graph as the paths in a weighted cycle. The HEWC problem was formulated as an integer linear program, and an approximation solution was obtained by using LP-relation and rounding heuristic. Then, a linear time approximation algorithm was developed, which also provided a solution with the same worst case approximation bounds as LP-approximation.

    The extremal Hosoya index of the trees with a given diameter
    YE Cheng-fu,YIN Jian
    J4. 2008, 43(8):  14-18 .  doi:
    Abstract ( 998 )   PDF (214KB) ( 1006 )   Save
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    The Hosoya index of graph G is defined as the total number of the independent edge sets. Let τn,d denote trees having n vertices and having the diameter with the minimal length as d. The trees with the second and the third minimal Hosoya index of τn,d were characterized.

    Strategic multi-brand retailer response to the asymmetric supply chain channel
    LU Yuan-yuan ,
    J4. 2008, 43(8):  19-23 .  doi:
    Abstract ( 872 )   PDF (272KB) ( 958 )   Save
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    In a supply chain system formed by one retailer and two different brandmanufactures, a Stackelberg game model was presented to illustrate a strategic retailer response to the asymmetric margin channel profit in an asymmetric channel. The retailer can make use of joint advertising and promotion for the general brand, which has high-quality and low-cost to gain more profits. In addition, this strategy can enhance the bargaining ability of the retailer, which can use it as a strategic weapon to elicit concessions from a well-known brand manufacturer.

    On the vertex-distinguishing chromatic number of Pm∨Cn

    LI Jing-wen ,XU Bao-gen,LI Mu-chun ,ZHANG Zhong-fu ,ZHAO Chuan-cheng ,REN Zhi-guo

    J4. 2008, 43(8):  24-27 .  doi:
    Abstract ( 1463 )   PDF (187KB) ( 959 )   Save
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    The vertex-distinguishing edge coloring of join-graph of path and cycle was discussed, and the chromatic number of Pm∨Cn.

    Co-*n-module over ring homomorphism
    XING Jian-min
    J4. 2008, 43(8):  28-30 .  doi:
    Abstract ( 846 )   PDF (154KB) ( 887 )   Save
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    A co-*n-module was defined. The conditions under which a left co-*n-module A〖KG*2]U lifts to a left R co-*n-module HomA(ARR,AU) over a ring homomorphism between ring A and R were given.

    Clumping effect in a host—parasitoid interaction model
    LIU Hua ,LIU Zhi-guang ,SU Min ,LI Zi-zhen ,
    J4. 2008, 43(8):  31-34 .  doi:
    Abstract ( 1189 )   PDF (728KB) ( 838 )   Save
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    Through computer simulation, the effect of parasitoid aggregation attacks on a host in a host—parasitoid model was qualitatively investigated. The results indicate that parasitoid aggregation may be a strong stabilizing factor and the clumping effect is favorable to the coexistence of the populations.

    Construction of regular semigroups with orthodox transversals
    YUAN Zhi-ling
    J4. 2008, 43(8):  35-37 .  doi:
    Abstract ( 766 )   PDF (159KB) ( 818 )   Save
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    The construction theorem of regular semigroups with orthodox transversals was given by a simpler formal set (R,L).

    *-Nearly paracompactness in L-topological spaces
    LIU Hong-ping,MENG Guang-wu
    J4. 2008, 43(8):  38-41 .  doi:
    Abstract ( 821 )   PDF (225KB) ( 989 )   Save
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    With α-regular closed remote family, a new paracompactness called *-nearly paracompactness in L-topological spaces was introduced, and was characterized by means of semi-interior. It was proved that *-nearly paracompactness has many properties,such as that it has L-good extension,hereditary with respect to regular closed subsets and weakly in homeomorphic invariant property. Also, the semi-regularization space of *-nearly paracompactness was discussed, the importantproperties of *-nearly paracompactness in induced space were also obtained.

    Characterization and perturbation of the generalized Drazin inverse for Banach space operators
    WANG Qiao,LIU Xiao-ji*
    J4. 2008, 43(8):  42-45 .  doi:
    Abstract ( 1026 )   PDF (177KB) ( 672 )   Save
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    The generalized Drazin inverse of Banach space operators was studied. Some characterizations of the generalized Drazin inverse were obtained, and the perturbation bound of operators with equal spectral projection related to their generalized Drazin inverse was estimated.

    The Constructions of the minimum l-defeasible set
    ZHOU Jing-zhi
    J4. 2008, 43(8):  46-50 .  doi:
    Abstract ( 947 )   PDF (216KB) ( 680 )   Save
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    To maximize the squared error-correction radius (SECR) of a Chase-like decoding algorithm, the constructions for the l-defeasible set were given according to the definition of the l-defeasibleset and somedecision conditions, by investigating the center vectors of spheres of radius l which cover all the vectors of length 2l+2, namely the search centers of Chase-like decoding algorithms.

    Identities and application of the rank of a class of matrices polynomials

    HU Fu-gao,ZENG Yu-e
    J4. 2008, 43(8):  51-54 .  doi:
    Abstract ( 1034 )   PDF (204KB) ( 833 )   Save
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    A sufficient condition about the Frobenius inequality of the rank of a matrix, when it is equivalent, was given. Based on this, some identities of the rank of a class of matrix polynomials were obtained. Using these identities, some relevant conclusions in the recent literature were generalized and some errors were also found and corrected.

    Element transfer-based dynamic inference and recognition of S-rough set knowledge
    REN Xue-fang,ZHANG Ling
    J4. 2008, 43(8):  55-61 .  doi:
    Abstract ( 990 )   PDF (280KB) ( 852 )   Save
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    By using the model of propositional logic of symbolic logic, the expression of logic inference for system interferes and relation factors were given. Then the expressions of logic inference for system knowledge and logic inference for S-rough sets were given under the condition that the knowledge system wasinterfered with by exterior factors. Finally, the dynamic inference and recognition theorem of knowledge, and the dynamic inference and recognition theorem of S-roughsets were given. The problem of dynamic interference and recognition of knowledge for S-rough sets were solved when a system was interfered with by element interference.

    Extremum in the Schrodinger variational principle
    CHEN Gang
    J4. 2008, 43(8):  62-64 .  doi:
    Abstract ( 830 )   PDF (182KB) ( 790 )   Save
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    Some references indicated that the extremum in the Schrodinger variational principle is a minimum. It was shown that the extremum corresponding to the ground state is indeed a minimum, while the extremum corresponding to the excited states are not a minimum, unless the wave-function used in variation is orthogonal to all the lower energy state wave-functions.

    Induced L-smooth topological space
    HU Xiao-nan,MENG Guang-wu
    J4. 2008, 43(8):  64-68 .  doi:
    Abstract ( 952 )   PDF (168KB) ( 944 )   Save
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    The concepts of L-fuzzifying topological space and generated L-smooth topological space were introduced, the connection between (X,τ)and its corresponding generated space (LX,ω(τ)) was studyed. Also, the properties of operators ω and the concepts of induced L-smooth topological space, weakly induced L-smooth topological space and stratified L-smooth topological space were given.

    The dimension of the principle indecomposable module for the finite group of type C2
    YU Gui-hai,QU Hui
    J4. 2008, 43(8):  69-71 .  doi:
    Abstract ( 795 )   PDF (183KB) ( 751 )   Save
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    Let G be a simply-connected semisimple algebraic group over an algebraic closed field K, Fn be the n-th Frobenius morphism of G. Denoted by G(n), the finite group consisting of fixed points under Fn in G. The dimension of the principle indecomposable module for G(n)=Sp(4,5n was calculated.

    Construction of a parametric cubic curve with quadratic precision

    ZHANG Fan,PAN Jing-chang
    J4. 2008, 43(8):  72-76 .  doi:
    Abstract ( 951 )   PDF (237KB) ( 817 )   Save
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    A method for constructing a parametric cubic curve to interpolate a set of distinct data points was presented. Unlike existing methods, this method includes the determination of knots in the process of constructing a parametric curve, and the new method can construct an interpolation curve without the process of determining knots. Between each pair of data points, a cubic Hermite interpolation curve segment was constructed by the new method, and all the curve segments are put together to form the whole interpolation curve. Hence, the key of this new method is to compute the derivative vector at each data point. For each data point, this newmethod constructs a quadratic polynomial curve using five or four data points,
    and th
    e derivative vector at each data point was computed by the quadratic polynomial curve. The constructed cubic polynomial curve has the precision of the quadratic polynomial. Experiments for testing the efficiency of the new method with the existing ones were included, and comparison results show that the curves by this new method have better precision.

    An F-model generated by function one-direction S-rough sets
    ZHANG Ling ,REN Xue-fang
    J4. 2008, 43(8):  77-81 .  doi:
    Abstract ( 920 )   PDF (245KB) ( 792 )   Save
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    By employing function one-direction S-rough sets, the generation method 〖JP2〗and correlative concepts of f-model and f-t order one-direction dynamic model of R-function equivalence class [u(x)], and the generation method and the correlative concepts of F-model and F-one-direction dynamic model were proposed. Then the order relation theorem and the dynamic separation theorem of F-one direction dynamic model were presented. The dynamic characteristic of F-model depends on the attribute augment to the attribute set α. The generation principle of F-model and its application were given on the basis of the above research.

    Gauge transformation for a kind of soliton hierarchy
    WANG Yan ,ZHANG Yi-ning ,DU Dian-lou
    J4. 2008, 43(8):  82-89 .  doi:
    Abstract ( 767 )   PDF (179KB) ( 589 )   Save
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    Based on a 2×2 eigenvalue problem, a new 1+1 dimensional soliton hierarchy was presented. By choosing some special values of parameters in
    the hierarchy, the hierarchies of the TD, generalized TD, the C-KdV and general
    ized C-KdV were obtained. Furthermore, a gauge transformation for this 2×2 eigenvalue problem was given, and through this transformation, the 2×2 hierarchy was gauged equivalent to the AKNS hierarchy, and also, the generalized Miura transformation between the potential functions of the two hierarchies was also given.

    The researches on gracefilness of two kinds of unconnected graphs
    WEI Li-xia,YAN Shou-feng,ZHANG Kun-long
    J4. 2008, 43(8):  90-96 .  doi:
    Abstract ( 1025 )   PDF (184KB) ( 569 )   Save
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    Two kinds of unconnected graphs (K2〖TX-〗∨Cn)∪[DD(]3[]i=1[DD)]St(mi) and (K2〖TX-〗∨C2n+k)∪St(m)∪G(k)n-1(k=1,2) were presented, and following results were proved: for natural number n, m, m1, m2, m3, let s=〖JB([〗〖SX(〗n〖〗2〖SX)〗〖JB)]〗, n≥9, m1≥s+2, then graph (K2〖TX-〗∨Cn)∪[DD(]3[]i=1[DD)]St(mi) is a graceful graph; for k=1,2, let n, m≥3, and let G(k)n-1 be a k-graceful graph with n-1 edges, then graph (K2〖TX-〗∨C2n+k)∪St(m)∪G(k)n-1 is a graceful graph. Where K2 bea complete graph with 2 vertices, K2〖TX-〗 is the complement of graph K2, graph K2〖TX-〗∨Cn is the join graph of K2〖TX-〗 and n-cycle Cn, St(m) isa star tree with m+1 vertices.