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Table of Content

      
    24 February 2007
    Volume 42 Issue 2
    Articles
    The quadratic Waring-Goldbach problem
    LIU Jian-ya and ZHAN Tao
    J4. 2007, 42(2):  1-18 .  doi:
    Abstract ( 1783 )   PDF (442KB) ( 1658 )   Save
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    The purpose of this paper is to briefly survey the recent progress towards the quadratic Waring-Goldbach problem. Contents of the paper are as follows: the Waring-Goldbach problem, the circle method, Hua's theorem with five almost equal prime variables, treatment of the enlarged major arcs, the major arcs in the representation by four squares of primes, mean-value estimates for Dirichlet polynomials, the minor arcs and exceptional set in the representation by four squares of primes, estimates of exponential sums over primes, sieve methods in the representation by four squares of primes, Lagrange's theorem with almost prime variables, the Linnik-Gallagher problem, new results for Hua's theorem with five almost equal prime variables, sums of three squares of almost primes, Sarnak's conjecture and ternary quadratic forms.
    Distribution of limit cycles for a class of higherdegree degenerate planar polynomial systems of codimension two
    LI Zong-cheng,
    J4. 2007, 42(2):  19-27 .  doi:
    Abstract ( 1157 )   PDF (329KB) ( 1052 )   Save
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    Distribution of limit cycles for a class of higher-degenerate planar polynomial systems of codimension two is discussed. It is proved that the system has at most three limit cycles. If they exist, then there will be only seven distinct relative locations.
    Overlapping domain decomposition parallel finite difference algorithm of wave equation
    TIAN Min and YANG Dan-ping
    J4. 2007, 42(2):  28-38 .  doi:
    Abstract ( 1263 )   PDF (329KB) ( 1331 )   Save
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    An efficient parallel finite difference scheme based upon overlapping domain decomposition is proposed for solving wave equation. The algorithm is based upon the domain decomposition method and the modification of classical parallel subspace correction method. The provement of optimal convergent rate shows that only one or two iterations are needed at each time step. Numerical experiments confirm the theoretical analysis.
    Global asymptotic robust stability of interval cellular neural networks with S-type distributed delays
    ZHANG Ruo-jun and WANG Lin-shan
    J4. 2007, 42(2):  39-42 .  doi:
    Abstract ( 1145 )   PDF (197KB) ( 1071 )   Save
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    The global asymptotic robust stability of interval cellular neural networks with S-type distributed delays is investigated.The convenient criteria and an example are presented.
    Proof of a class of matrix rank identities
    WANG Ting-ming,LI Bo-tang
    J4. 2007, 42(2):  43-45 .  doi:
    Abstract ( 1517 )   PDF (158KB) ( 1045 )   Save
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    By using Jordan canonical form of matrix, it is proved that when k1,k2,…ktsatisfy the related conditions of characteristic root of matrix A,the speculation of a class of matrix rank identities is tenable. The identity of related matrix rank is also extended.
    Three-channel transmission scheduling in WDM star single-hop networks
    DAI Zhen-xiang,LI Shu-guang,and QI Xing-qin
    J4. 2007, 42(2):  46-50 .  doi:
    Abstract ( 1080 )   PDF (249KB) ( 1122 )   Save
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    The problem of scheduling packet transmissions in WDM star single-hop networks with tunable transmitters and fixedtuned receivers is considered. It is NP-complete for any fixed m≥2, where m is the number of available channels. By a rigorous analysis, the worstcase performance ratio of the currently approximation Rnown as the best algorithm for this problem is reduced to 7/4 for three channels. An example is presented to show that this result is best possible.
    Different game models for two-stage supply chain
    JIANG Peng-fei,SHA Ya-jun and HU Fa-sheng
    J4. 2007, 42(2):  51-55 .  doi:
    Abstract ( 1359 )   PDF (253KB) ( 1886 )   Save
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    The payoffs of manufacturer and retailer under two different bargaining game models, principal-agent game and cooperative game, are studied. The conclusion is suggested that both the players will obtain more profit by cooperating, and the consumers can also get benefit at the same time. In the cooperative game model, the K-S solution is improved and a new method of allocating total profit based on the player's distributions is introduced. The equilibrium of this game becomes more reasonable which having good directive meaning for the corporation of manufacturers lieing at the supply chain.
    On the coloring of C-hypergraphs with minimum connected pair graphs
    DIAO Ke-feng and ZHAO Ping
    J4. 2007, 42(2):  56-58 .  doi:
    Abstract ( 1180 )   PDF (197KB) ( 1113 )   Save
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    The upper (lower) chromatic number X(H) of a mixed hypergraph H=(A,B,C) is the maximum (minimum) number of colors that can be assigned to the vertices of H in such a way that each C-edgecontains a monochromatic pair of vertices and each D-edge has two vertices colored differently. The upper (lower) chromatic number of a mixed hypergraph is colosely related to the number of edges, and the number of edges is colosely related to the connectness of the pair graphs of its vertices. In this paper we diascuss the relationship between the coloring and the connectess of the pair graphs of its vertices of a C-hypergraph, and we prove that for any positive integer n(≥3), there exists a 3-uniform C-hypergraph with upper chromatic number n and minimum connectedpair graphs.
    Computational formulae of generalized m-th-order Bell numbers and generalized m-order orderd Bell numbers
    LI Zhi-rong
    J4. 2007, 42(2):  59-63 .  doi:
    Abstract ( 917 )   PDF (185KB) ( 1056 )   Save
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    By using the method of generating function and the technique of calculating,computational fomular of generalized m-th-order Bellnumbers and ggeneralized m-th-order orderd Bell numbers are given by the first kind of Stirling numbers and the second kind of Stirling numbers.In addition,their recurrence formulae are given.
    An IM-shared unique image set for meromorphic functions with 10 elements
    BAI Xiao-tian and HAN Qi
    J4. 2007, 42(2):  64-67 .  doi:
    Abstract ( 1296 )   PDF (199KB) ( 943 )   Save
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    For any two nonconstant meromorphic functions f and g on C with Θ(∞, f & g)>6/7, there exists a set S∈C consisting of 10 elements, such that the condition Ē(S,f)=Ē(S,g) implies f≡g
    Continuous dependence of the solution of multidimensional reflected backward stochastic differential equations on the parameters
    XIAO Hua
    J4. 2007, 42(2):  68-71 .  doi:
    Abstract ( 1221 )   PDF (200KB) ( 1062 )   Save
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    The prior estimates of multi-dimensional reflected backward stochastic differential squations are studied.It is proved that solution has dependence on the parameters of the equations.
    The interior and exterior product and similarity measurement of both-branch fuzzy sets
    LI Cheng-dong and WEI Rong
    J4. 2007, 13(2):  72-76 .  doi:
    Abstract ( 1180 )   PDF (213KB) ( 1253 )   Save
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    Based on the concept of both-branch fuzzy sets, the concepts and properties of the interior and exterior product of both-branch fuzzy sets are proposed, which are the general extension of the concepts of the interior and exterior product of one-branch fuzzy set. Based on the concepts of the interior and exterior product, the concept of similarity measurement of both-branch fuzzy sets is also proposed, and several formulae of similarity measurement are put forward.
    Random characteristics of assistant sets
    LIU Bao-cang,LU Chang-jing and SHI Kai-quan
    J4. 2007, 42(2):  77-82 .  doi:
    Abstract ( 1059 )   PDF (224KB) ( 1333 )   Save
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    By using theory of S-rough sets and random characteristics of element transference, the concept of reliability of element transference and reliability function are presented. The concepts of random assistant sets are presented. The random assistant sets (α,β)-generation and random assistant sets (α,β)-strong random generation are given. The generation characteristics of random assistant sets are discussed.
    On problems of Suryanarayana
    DONG Xin-mei
    J4. 2007, 42(2):  83-86 .  doi:
    Abstract ( 1211 )   PDF (167KB) ( 1242 )   Save
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    Two problems of Suryanarayana have been studied. The first problem is solved by using elementary methods. An asymptotic formula for an arithmetical function is obtained and the result of QIU Zhuo-ming as improved by the application of the other problem.
    Existence of analytic invariant curves for a planar mapping near resonance
    LIU Ling-xia
    J4. 2007, 42(2):  87-91 .  doi:
    Abstract ( 887 )   PDF (205KB) ( 1116 )   Save
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    The existence of analytic invariant curves is discussed for the paanar mapping F(x,y)=(x+y,y+G(x)+H(x+y)),x∈C in complex field.
    Properties of maximal mathematical expectation
    SHI Heng-lu,DENG Wei and QI Lu
    J4. 2007, 42(2):  92-94 .  doi:
    Abstract ( 1612 )   PDF (190KB) ( 1303 )   Save
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    Maximal mathematical expectation is nonlinear as well as g-expectation. There are some connections between these two nonlinear expectations. Some special useful properties are obtained by the definition of maximal mathematical expectation or via g-expectation.