Table of Content

    16 October 2008
    Volume 43 Issue 10
    Conjugate vector base algorithm for solving ill-conditioned linear equations
    ZHENG Zhou-shun,HUANG Guang-hui*
    J4. 2008, 43(10):  1-05 .  doi:
    Abstract ( 814 )   PDF (267KB) ( 1160 )   Save
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    The characteristics of the steepest descent method’s small amount of computations and conjugate direction method’s fast convergence combined, a conjugate vector base method for solving ill-conditioned linear equations was proposed. The accurate solution of linear equations could be expressed linearly by the conjugate vector base, and the iterative strategy was used to construct the conjugate vector base groups and the corresponding coefficient. The constructed conjugate vector base groups were proved to be conjugated. Meanwhile, an improved algorithm fitting different required precisions was also given, which can accelerate the iterative convergence. 5000-order Hilbert ill-conditioned linear equations were solved, and the relative error was less than 0.45%. Numerical experiments verified that the method was efficient compared with the efficient methods used commonly nowadays. Numerical experiments results showed that the conjugate vector base method was suited for solving large-scale ill-conditioned linear equations with fast convergence and high precision.

    An inquiry of the model for the tow-echelon supply chain problem
    under stochastic demand
    CUI Yu-quan,WANG Jian-min,RONG Xiao-xia
    J4. 2008, 43(10):  6-11 .  doi:
    Abstract ( 908 )   PDF (265KB) ( 629 )   Save
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    The problem of supply chain management is a hot problem that enterprise departments and commerce departments care about. The central point at issue about supply chain management is how to coordinate the partial and local interests of the member enterprise in the supply chain and the whole interests of the supply chain system, which aims to make the cost of the supply chain system reach the lowest cost. A stochastic supply chain model
    having one supplier and multiple retailers was considered. A general model
    was given under the circumstances that the retailer allowed to be in short supply or not allowed to be in short supply. The conditions were given to supply chain cooperation.

    One direction S-rough sets-based knowledge addition and knowledge battlement recognition
    ZHANG Ling ,QIU Yu-feng ,REN Xue-fang ,
    J4. 2008, 43(10):  12-17 .  doi:
    Abstract ( 879 )   PDF (239KB) ( 1156 )   Save
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    By employing one direction S-rough sets, the concepts of knowledge addition and knowledge battlement generated by knowledge addition were presented, where knowledge battlement has dynamic characteristic. Then rough knowledge battlement generation was given, and the generation principle and the reversion theorem of rough knowledge battlement were proposed. Furthermore, the discernibility metric of rough knowledge battlement was given, and the recognition rule and recognition theorem of rough knowledge battlement were proposed. Finally the applications were given.

    On generalized c-normality of finite groups
    LIU Xiao-lei
    J4. 2008, 43(10):  18-20 .  doi:
    Abstract ( 776 )   PDF (181KB) ( 557 )   Save
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    For a finite group G, a subgroup H is called c-normal in G if there is a normal subgroup K such that G=HK and H∩K≤HG, the largest normal subgroup of G contained in H. c-normality was replaced by c-π-quasinormality or c-sub-normality. The following were showed equivalent. First, there is a solvable maximal subgroup M such that M is c-π-quasi-normal in G.Second, every maximal subgroup with composite index of G is c-π-quasi-normal in G. Third, every maximal subgroup of G is c-subnormal in G. Fourth, G is solvable.

    The inference and forecast of the system S-rough state law
    QIU Yu-feng,ZHANF Ling,
    J4. 2008, 43(10):  21-26 .  doi:
    Abstract ( 838 )   PDF (274KB) ( 777 )   Save
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    First, the concept of the system S-rough state law was proposed, and the S-rough state law generation was given. Then the dynamic inference model of the system S-rough state law was presented on the basis of the logic inference model between interference and system attribute. Second, the dynamic inference and recognition theorems of the S-rough state law was proposed. The forecast model of the S-rough state law and its application were presented based on the above results.

    W-C-tilting modules
    LEI Xue-ping
    J4. 2008, 43(10):  27-30 .  doi:
    Abstract ( 807 )   PDF (170KB) ( 751 )   Save
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    The definition of W-C-tilting modules was given, which is a generalization of the definitions of classical tilting modules and Wakamatsu-tilting modules. Furthermore, the condition of the existence of W-C-tilting modules was given and the properties of W-C-tilting modules were investigated.

    Normal MP-filters and prime filters of an implication lattice
    HU Ming-di,LOU Zhi-gang,
    J4. 2008, 43(10):  31-35 .  doi:
    Abstract ( 754 )   PDF (217KB) ( 558 )   Save
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    The concepts of MP-filters, generated filters, normal MP-filters and prime filters in implication lattice were introduced. Their basic properties were investigated, and the structure of generated filters was obtained. The results show that the normal MP-filters are MP-filters. All the results are the common characters of the corresponding filter theories of R0-algebras or MV-algebras.

    Empirical research on factor allocation in economic growth
    SU Jing,WANG Sha-sha,WANG Qing-xiao
    J4. 2008, 43(10):  36-40 .  doi:
    Abstract ( 820 )   PDF (640KB) ( 707 )   Save
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    Several kinds of production functions were analyzed and a two-level CES model was identified by comparison to be the most appropriate for the economic development of China . Then the economic effect of input elements, especially energy intensity, was studied. Based on the above discussion, a reasonable factor allocation was given to scenario objectives including different economic growths and different energy intensities. From the perspective of optimizing industrial structure, some helpful suggestions were obtained concerning the optimum rate of economic growth and factor allocation under a certain target of energy intensity.

    Analytic solutions of an iterative functional differential equation
    LIU Ling-xia
    J4. 2008, 43(10):  41-45 .  doi:
    Abstract ( 858 )   PDF (212KB) ( 636 )   Save
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    Analytic solutions of an iterative functional differential equation were discussed in a complex field. For constant α given in the Schr〖AKo¨D〗der transformation, besides the case of 0<|α|<1, α is the resonance point, i.e. a root of the unity and those α near resonance point under the Brjuno condition.

    The M/M/1/N queuing system with balking, reneging and multiple working vacations

    ZHAO Xiao-hua,FAN Jian-wu,TIAN Nai-shuo,TIAN Rui-ling
    J4. 2008, 43(10):  46-51 .  doi:
    Abstract ( 1030 )   PDF (561KB) ( 672 )   Save
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    An M/M/1/N queuing system was considered with balking, reneging and multiple working vacations. First, the matrix form solution of steady-state probability was derived by the Markfov process method and the matrix solution method. Some performance measures of the system such as the expected number of customers in the system or in the queue and the average rate of the customer loss were also presented. Finally, the effect of the parameters of the system were investigated by numerical examples, such as the vacation service rate μv and the vacation rate θ on the expected queue length.

    Anti-fuzzy subrings and anti-fuzzy ideals
    ZHU Ling-jiang,WANG Kai-bao,WANG Li,YAO Bing-xue
    J4. 2008, 43(10):  52-55 .  doi:
    Abstract ( 805 )   PDF (178KB) ( 583 )   Save
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    The operation of addition, subtraction and multiplication of fuzzy subsets was given. Equivalent condition and qualities of anti-fuzzy subringswere reduced by the qualities of addition, subtraction and multiplication. The concepts of anti-fuzzy ideals were put forward and the properties were discussed.

    An endogenous growth model of knowledge-based R&D economy
    ZHANG Yan-gang,RONG Xiao-xia,WANG Feng
    J4. 2008, 43(10):  56-59 .  doi:
    Abstract ( 861 )   PDF (261KB) ( 1149 )   Save
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    The element of human capital was introduced into the Romer endogenous growth model, and then technical progress and human capital were considered as endogenous at one time. The optimal balanced growth path of R&D knowledge economy was deduced. Based on the analysis of the optimal path and several factors’ contribution, it was demonstrated that technological advances and human capital play a dominantrole in promoting economic growth. Some policy recommendations were presented.

    Rough data law recognition on the basis of S-rough set theory
    LIU Jiang-chen,CHEN Bao-hui
    J4. 2008, 43(10):  60-66 .  doi:
    Abstract ( 1046 )   PDF (335KB) ( 700 )   Save
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    The concept of rough data was presented by employing S-rough sets having dynamic characteristic and the rough data law generation were given. Based on the concepts above, the generation theorem and the reversion theorem of rough data law, the recognition principle of rough data law and the discernible theorem of rough data law were given. The applications of rough data law were presented.

    The generation of P-rough integrals and their characteristics

    YU Xiu-qing,
    J4. 2008, 43(10):  67-70 .  doi:
    Abstract ( 912 )   PDF (207KB) ( 491 )   Save
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    P-rough integrals are one pair of integrals generated by function double direction S-rough sets. They can extend the study universe of F-rough integrals and -rough integrals. When there are some attributes moving in and out, P-rough integrals changes and have a series of dynamic characteristics. They can generate a P-rough integral chain, P-rough integral ring and P-rough integral ring chain.

    Theoretical and numerical investigation of elastic string with fixed ends

    ZHANG Xing-gang,KONG Wei-shu
    J4. 2008, 43(10):  71-76 .  doi:
    Abstract ( 790 )   PDF (865KB) ( 672 )   Save
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    Free vibration of a string with fixed ends in three-dimension space was studied with the Frenet frame method and Hamilton principles. Based on the Hamilton principle, the nonlinear equation of free vibration of the elastic string was derived. Then, the equilibrium equation of the elastic string and the configuration of balanced string were discussed. Finally, the molecular chain model was established and the molecular dynamics method was used to simulate the process of damped vibration of an elastic string in a gravity field.

    On the adjacent vertex-distinguishing incidence coloring of general Mycielski graphs
    WANG Wen-li,LIU Xi-kui,ZHOU Wei
    J4. 2008, 43(10):  77-79 .  doi:
    Abstract ( 791 )   PDF (187KB) ( 607 )   Save
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    The adjacent vertex-distinguishing incidence coloring is incidence coloring satisfying the sets with different colors of two adjacent vertices.
    The adjacent vertex-distinguishing incidence coloring of path, cycle with 3m
    or 4m vertices and the complete graph's general Mycielski graphs were studied. It exploits the area of the graph coloring for studying the structure of graphs.

    The orbit deflection of the photon in the Reissner-Nordstro¨m metric
    GONG Yan-xiang,LI Feng
    J4. 2008, 43(10):  80-84 .  doi:
    Abstract ( 783 )   PDF (235KB) ( 694 )   Save
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    The post-Newton approximation method was adopted to discuss the orbit deflection of the photon in the Reissner-Nordstr〖AKo¨D]m metric field. The effects of the charge Q on the deflection angle were given. When electricity was equal to zero, the amendments of the first order and the second were in accord with the non charged celestial bodies. This topic is very important to the research of gravitational effects of charged bodies and the singular nature of space-time of black holes.

    The mixed finite element method for the unsteady Stokes equation

    YU Jing-zhi,CHEN Huan-zhen,LIU Xiang-zhong
    J4. 2008, 43(10):  85-90 .  doi:
    Abstract ( 991 )   PDF (212KB) ( 880 )   Save
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    The mixed finite element method for the unsteady Stokes equation was studied. This method is based on using the stream function and vorticity formulation of the unsteady Stokes equation. Error analysis shows that this method is stable and optimal for the stream function and the velocity field in L2 norm.

    A threshold dividend strategy in a risk model with inter-claim-dependent claim sizes
    HUA Zhao-xiu,NIU Ming-fei
    J4. 2008, 43(10):  91-96 .  doi:
    Abstract ( 860 )   PDF (233KB) ( 575 )   Save
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    First, a threshold dividend strategy in a risk model with interclaim-dependent claim sizes was introduced. Then, a nonhomogeneous integro-differential equation for the Gerber-Shiu discounted penalty function in this risk model was derived, and the solution to the Gerber-Shiu discounted penalty function was analyzed. Finally, a homogeneous integro-differential equation for the expected discounted dividend payments before ruin was derived.