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Table of Content

    06 July 2001, Volume 21 Issue 3 Previous Issue    Next Issue
    Articles
    ENUMERATING ROOTED EULERIAN PLANAR MAPS
    CAI Jun-Liang, HAO Rong-Xia, LIU Yan-Pei
    Acta mathematica scientia,Series B. 2001, 21 (3):  289-294. 
    Abstract ( 686 )   RICH HTML PDF (99KB) ( 1129 )   Save

    This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as two parameters. It is also an answer to open problem 7.1 in [1]. Meanwhile, the case of three variables can be derived by using Lagrangian inversion.

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    SOME NEW RESULTS ON WAITING TIME AND BUSY TIME IN M/G/1 QUEUE
    TANG Ying-Hui
    Acta mathematica scientia,Series B. 2001, 21 (3):  295-301. 
    Abstract ( 592 )   RICH HTML PDF (110KB) ( 928 )   Save

    This paper considers an M/G/1 queue with Poisson rate  > 0 and service time distribution G(t) which is supposed to have finite mean 1/μ. The following questions are first studied: (a) The closed bounds of the probability that waiting time is more than a fixed value; (b)The total busy time of the server, which including the distribution,probability that are more than a fixed value during a given time interval (0, t], and the expected value. Some new and important results are obtained by theories of the classes of life distributions and renewal process.

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    A NEW EXTENSION OF THE HIGH-ORDER VIRASORO ALGEBRA
    WANG Hong, XU Zhao-Xin, ZHA Chao-Zheng
    Acta mathematica scientia,Series B. 2001, 21 (3):  302-306. 
    Abstract ( 642 )   RICH HTML PDF (98KB) ( 847 )   Save

    This paper investigates the high order differential neighbourhoods of holomor-phic mappings from S1×S1 to a vector space and gives a new extension of the high-order Virasoro algebra.

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    NORMAL THEOREMS ON SEVERAL COMPLEX VARIABLES
    SUN Dao-Chun
    Acta mathematica scientia,Series B. 2001, 21 (3):  307-315. 
    Abstract ( 656 )   RICH HTML PDF (134KB) ( 834 )   Save

    For general quasimeromorphic mappings of several complex variables, their normal theorems are studied by the method of covering surface, and some important theorems on normality are obtained.

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    ORTHOGONAL (g, f)-FACTORIZATIONS OF BIPARTITE GRAPHS
    LIU Gui-Zhen, DONG He-Nian
    Acta mathematica scientia,Series B. 2001, 21 (3):  316-322. 
    Abstract ( 684 )   RICH HTML PDF (116KB) ( 1021 )   Save

    Let G be a bipartite graph with vertex set V (G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V (G) such that g(x)  f(x) for every vertex x of V (G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x)  dH(x)  f(x) for each x 2 V (H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2, · · · , Fm} and H be a factorization and a subgraph of G, respectively. If Fi, 1  i  m, has exactly one edge in common with H, then it is said that F is orthogonal to H. It is proved that every bipartite
    (mg+m−1,mf −m+1)-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if k 2  g(x) for all x 2 V (G). Furthermore, it is showed that the results in this paper are best possible.

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    TAYLOR SERIES AND ORTHOGONALITY OF THE OCTONION ANALYTIC FUNCTIONS
    LI Xing-Min, PENG Li-Zhong
    Acta mathematica scientia,Series B. 2001, 21 (3):  323-330. 
    Abstract ( 715 )   RICH HTML PDF (126KB) ( 2075 )   Save

    The Taylor series of the Octonion analytic function is given. And the orthogonal formula for the Octonion analytic functions is also obtained.

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    A THEOREM ON THE CONVERGENCE OF SUMS OF INDEPENDENT RANDOM VARIABLES
    KONG Fan-Chao, TANG Qi-He
    Acta mathematica scientia,Series B. 2001, 21 (3):  331-338. 
    Abstract ( 905 )   RICH HTML PDF (117KB) ( 1097 )   Save

    Let 1 Pn=1 Xn be a series of independent random variables with at least one non-degenerate Xn, and let Fn be the distribution function of its partial sums Sn =n Pk=1 Xk. Motivated by Hildebrand’s work in [1], the authors investigate the a.s. convergence of 1 Pn=1 Xn under a hypothesis that 1
    Pn=1 (Xn, cn) = 1 whenever 1 Pn=1 cn diverges, where the notation (X, c) denotes the L´evy distance between the random variable X and the
    constant c. The principal result of this paper shows that the hypothesis is the condition under which the convergence of Fn(x0) with the limit value 0 < L0 < 1, together with the essential convergence of 1 Pn=1 Xn, is both sufficient and necessary in order for the series 1 Pn=1 Xn to a.s. converge. oreover, if the essential convergence of 1 Pn=1 Xn is strengthened to lisup n!1 P(|Sn| < K) = 1 for some K > 0, the hypothesis is already equivalent to the a.s. convergence of 1 Pn=1 Xn. Here they have not only founded a very general limit theorem, but improved the related result in Hildebrand[1] as well.

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    CONTINUITY FOR MAXIMAL COMMUTATORS OF BOCHNER-RIESZ OPERATORS WITH BMO FUNCTIONS
    JIANG Yin-Sheng, TANG Lin, YANG Da-Chun
    Acta mathematica scientia,Series B. 2001, 21 (3):  339-349. 
    Abstract ( 939 )   RICH HTML PDF (153KB) ( 1136 )   Save

    Let p 2 (n/(n + 1), 1]. The authors investigate the (Hp b (Rn),Lp(Rn))-type and (Hp,1 b (Rn),Lp,1(Rn))-type continuities for the maximal operators associated with the commutators of Bochner-Riesz operators with BMO(Rn) functions, where Hp b (Rn) and Hp,1 b (Rn) are, respectively, the variants of the standard Hardy spaces and the standard weak Hardy spaces.

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    THE GEOMETRY OF HYPERSURFACES IN A KAEHLER MANIFOLD
    ZHONG Tong-De
    Acta mathematica scientia,Series B. 2001, 21 (3):  350-362. 
    Abstract ( 1016 )   RICH HTML PDF (145KB) ( 916 )   Save

    The geometry of hypersurfaces of a Kaehler manifold are studied. Some well-known formulas and thorems in theory of surfaces of Euclidean 3-space are generalized to the hypersurfaces in a Kaehler manifold, such as Gauss’s formulae, second fundamental form, the equation of Gauss and Codazzi and so forth.

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    ON THE DISTRIBUTION OF VALUES AND DEFICIENT FUNCTION OF A GENERAL RANDOM INTEGRAL FUNCTION
    TIAN Fan-Ji
    Acta mathematica scientia,Series B. 2001, 21 (3):  363-368. 
    Abstract ( 784 )   RICH HTML PDF (106KB) ( 889 )   Save

    Under suitable conditions on {Xn}, the author obtains the important results: it is almost sure that the random integral function f! =1P n=0 Xnzn (of finite positive order) has no deficient function, and any direction is a Borel direction (without finite exceptional value) of f!.

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    MULTIFRACTAL DECOMPOSITION OF CERTAIN RECURSIVE SETS WITHOUT THE OPEN SET CONDITION
    GUO Hong-Wen, DENG Ai-Jiao
    Acta mathematica scientia,Series B. 2001, 21 (3):  369-374. 
    Abstract ( 660 )   RICH HTML PDF (108KB) ( 998 )   Save

    The open set condition is the weakest condition hitherto in multifractal decomposition on the recursive sets. This paper deals with certain recursive fractals which have no relevence to the separation condition and gives their multifractal decomposition.

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    SOME PROPERTIES OF ROSEN’S MLE FOR GENERAL DISTRIBUTIONS
    CUI Heng-Jian, CHEN Qiu-Hua
    Acta mathematica scientia,Series B. 2001, 21 (3):  375-382. 
    Abstract ( 718 )   RICH HTML PDF (123KB) ( 838 )   Save

    Von Rosen (1989) proposed the MLE of parameters in multivariate linear normal model MLNM(Pm i=1 AiBiCi). This paper discusses some roperties of Rosen’s MLE for general distributions which includs invariant, equivariant, strong consistency and asymptotic normality. Furthermore, we can construct the consistent confidence region for the parameter of experctation in MLNM( Pm i=1 AiBiCi) and obtain asymptotic distrib- ution and consistent confidence region of the linear discrimination function for canonical correlation by Kahtri (1988).

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    ON HYPER-ORDER OF MEROMORPHIC SOLUTIONS OF FIRST-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS
    LI Ye-Zhou, FENG Shao-Ji
    Acta mathematica scientia,Series B. 2001, 21 (3):  383-390. 
    Abstract ( 839 )   RICH HTML PDF (127KB) ( 1000 )   Save

    The authors give a precise estimate of the hyper-order of meromorphic solu-tions of general first-order algebraic differential equations.

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    THE EXISTENCE AND UNIQUENESS OF SOLUTION FOR A CLASS OF STOCHASTIC FUNCTIONAL EQUATIONS ON S.P. SPACE
    LIU Kun-Hui, QIN Ming-Da, LU Chuan-Lai
    Acta mathematica scientia,Series B. 2001, 21 (3):  391-400. 
    Abstract ( 652 )   RICH HTML PDF (136KB) ( 1138 )   Save

    This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X = (X), where
    : B ! B and B is a Banach spaceconsisted of all left-continuous, (Ft)-adapted processes. Also, the main result is applied tosome S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the existence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.

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    EMBEDDING THEOREM OF FILTERED LIE SUPERALGEBRAS
    ZHANG Yong-Zheng, SHEN Guang-Ning
    Acta mathematica scientia,Series B. 2001, 21 (3):  401-411. 
    Abstract ( 550 )   RICH HTML PDF (136KB) ( 871 )   Save

    The homomorphic realization of Lie superalgebras and the embedding theorem of filtered Lie superalgebras are given and proved.

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    SOME PRIMITIVE POLYNOMIALS OVER FINITE FIELDS
    Seunghwan Chang, June Bok Lee
    Acta mathematica scientia,Series B. 2001, 21 (3):  412-416. 
    Abstract ( 974 )   RICH HTML PDF (104KB) ( 1266 )   Save

    This paper proves that if qn is large enough, for each element a and primitive element b of Fq, there exists a primitive polynomial of degree n  5 over the finite field Fq having a as the coefficient of xn−1 and b as the constant term. This proves that if qn is large enough, for each element a 2 Fq, there exists a primitive polynomial of degree n  5 over Fq having a as the coefficient of x.

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    POINTWISE ESTIMATE OF SOLUTIONS OF ISENTROPIC NAVIER-STOKES EQUATIONS IN EVEN SPACE-DIMENSIONS
    XU Hong-Mei, WANG Wei-Ke
    Acta mathematica scientia,Series B. 2001, 21 (3):  417-427. 
    Abstract ( 747 )   RICH HTML PDF (144KB) ( 1097 )   Save

    This paper is concerned with the dissipation of solutions of the isentropic Navier-Stokes equations in even and bigger than two multi-dimensions. Pointwise estimates of the time-asymptotic shape of the solutions are obtained and the generalized Huygan’s principle is exhibited. The approch of the paper is based on the detailed analysis of the Green function of linearized system. This is used to study the coupling of nonlinear diffusion waves.

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    A CAPACITY EXPANSION PROBLEM WITH BUDGET CONSTRAINT AND BOTTLENECK LIMITATION
    YANG Chao, LIU Jing-Lin
    Acta mathematica scientia,Series B. 2001, 21 (3):  428-432. 
    Abstract ( 1025 )   RICH HTML PDF (101KB) ( 1256 )   Save

    This paper considers a capacity expansion problem with budget constraint. Suppose each edge in the network has two attributes: capacity and the degree of difficulty.The difficulty degree of a tree T is the maximum degree of difficulty of all edges in the tree and the cost for coping with the difficulty in a tree is a nondecreasing function about the difficulty degree of the tree. The authors need to increase capacities of some edges so that there is a spanning tree whose capacity can be increased to the maximum extent, meanwhile the total cost for increasing capacity as well as overcoming the difficulty in the spanning tree does not exceed a given budget D. Suppose the cost for increasing capacity on each edge is a linear function about the increment of capacity, they transform this problem into solving some hybrid parametric spanning tree problems[1] and propose a strongly polynomial algorithm.

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