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    25 December 2009, Volume 29 Issue 6 Previous Issue    Next Issue
    Articles
    Weighted Adjust LS Estimation |in EV Model with Missing Data
    ZHANG Juan, CUI Heng-Jian
    Acta mathematica scientia,Series A. 2009, 29 (6):  1465-1476. 
    Abstract ( 1799 )   RICH HTML PDF (398KB) ( 1308 )   Save

    The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of
    Rubin (1976) is considered in this paper. The weighted adjust LS parameter estimation based on inverse probability is proposed. It is shown that the estimators have consistency and asymptotic normality.
    Simulations are shown that our estimators perform well.

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    Invertibility of Differences of Two Generalized |Idempotent Operators
    DENG Chun-Yuan
    Acta mathematica scientia,Series A. 2009, 29 (6):  1477-1486. 
    Abstract ( 1404 )   RICH HTML PDF (264KB) ( 1180 )   Save

    Let P and Q be two idempotents on a Hilbert space H. The  set ω(P) of generalized idempotent operators with respect to P is defined by ω(P)={AB(H): A2=α A+β P, AP=PA=AP2=P, for some α, β ∈C}. In this note, the author proves that the invertibility of A-B is completely determined by the invertibility of  P-Q,  and R(AB) is closed if and only if  R(PQ) is closed for arbitrary A ∈ω(P) and B ∈ω(Q) such that A2=α A + β P, B2=mB+nQ, where β n ≠ 0, α and m are arbitrary.

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    An Almost Sure Central Limit Theorem for Weighted Sums under Association
    ZHANG Yong, DONG Zhi-Shan, ZHAO Shi-Shun
    Acta mathematica scientia,Series A. 2009, 29 (6):  1487-1491. 
    Abstract ( 1609 )   RICH HTML PDF (265KB) ( 1148 )   Save

    In this paper, the authors prove an almost sure central limit theorem for weighted sums of negatively or positively associated random variables without  stationary assumption. This extends the earlier work on an associated random variables.

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    Existence of Solution for a |Singular Biharmonic Equation Involving Critical Exponent
    PENG Yan-Fang, ZHANG Zheng-Jie
    Acta mathematica scientia,Series A. 2009, 29 (6):  1492-1499. 
    Abstract ( 1365 )   RICH HTML PDF (294KB) ( 1101 )   Save

    In this paper, the authors present a result on existence to the following singular biharmonic equation involving
    singular terms
    {?2u-μ/|x|α μ λg(x)μ+k(x)|μ|q-2 μ+|μ|2*-2 μ,      x ∈ Ω,  
      μ ∈D02,2(Ω),                                                        x ∈∂Ω,

    where Ω is a bounded domain containing origin, Ω ( RN, N ≥ 5, 0 ≤ α, s < 4,2 < q < 2^*(s) = 2(N-s)/N-4}, and g(x), k(x) are nonnegative functions, the existence of solution is shown by variational method, the acquired function for the imbedding mapping D2,2(RN) → L2*(RN) plays an important role in the discussion.

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    Atomic Decomposition of Herz-type Besov and Triebel-Lizorkin Spaces
    XU Jing-Shi
    Acta mathematica scientia,Series A. 2009, 29 (6):  1500-1507. 
    Abstract ( 1628 )   RICH HTML PDF (280KB) ( 1180 )   Save

    The atomic decomposition of Herz-type Besov and Triebel-Lizorkin spaces is given.

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    Boundedness of Commutators Related to Marcinkiewicz Integrals with Variable Kernels in Herz-type Hardy Spaces
    TAO Xiang-Xin, WEI Rui-Ying
    Acta mathematica scientia,Series A. 2009, 29 (6):  1508-1517. 
    Abstract ( 1932 )   RICH HTML PDF (329KB) ( 1177 )   Save

    The authors of this article are interested in the commutator μΩ, b generated by a function b ∈Lipβ (Rn)(0 < β ≤ 1) and the Marcinkiewicz integrals μΩ with variable kernel Ω ∈L(Rn) ×Lr(Sn-1) (r ≥ 1). The boundedness results for μΩ, b in the homogeneous Herz-type Hardy spaces are obtained. Moreover, The same results are shown for the commutator μρΩ, b related to the parametric Marcinkiewicz integral μρΩ.

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    The State Representation Theorem of a Class of Effect Algebras
    LUO Lai-Zhen, LI Rong-Lu
    Acta mathematica scientia,Series A. 2009, 29 (6):  1518-1522. 
    Abstract ( 1500 )   RICH HTML PDF (257KB) ( 1177 )   Save

    In 1994, Foulis and Bennett introduced effect algebra to represent the unsharp quantum logic structure.  In this
    paper, using the direct construction method, the authors present a state representation theorem of a class of effect algebras. That is, if Ω is a compact Hausdorff topological space, E(Ω)= {f: f ∈C(Ω, 0 ≤ f ≤ 1, then φ is a state of the effect algebra (E(Ω), Ο, 0, 1) if there exists a unique regular Borel probability measure μ on Ω such that for each f (E(Ω), Ο, 0, 1), φ (f) = ∫ Ω dμ.

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    On the Unique Continuation Property for a Nonlinear Dispersive System
    FU Ying, MA Yi-Chen, QU Chang-Zheng
    Acta mathematica scientia,Series A. 2009, 29 (6):  1523-1536. 
    Abstract ( 1210 )   RICH HTML PDF (340KB) ( 1200 )   Save

    It is proved that, if a sufficiently smooth solution $(u,v)=(u(x,t),v(x,t))$ to the initial value problem associated with the dispersive coupled system
    {∂ u+∂3x u+∂ x(up vp+1)=0,
     ∂v+∂3x v+∂x(up+1vp)=0,        x ∈R, t ≥ 0
    is supported on a half line at two different instants of time then u ≡ 0, v ≡ 0.

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    On the Borel Direction Dealing with Multiple Values of Algebroidal Functions and Their Derivatives
    LIU Hui-Fang, SUN Dao-Chun
    Acta mathematica scientia,Series A. 2009, 29 (6):  1537-1546. 
    Abstract ( 1589 )   RICH HTML PDF (310KB) ( 1326 )   Save

    In this paper, for algebroidal functions with finite and positive order, the existence domain of the Borel direction dealing with multiple values is investigated. Some methods to find the common Borel direction dealing with multiple values of algebroidal functions and their derivatives are obtained.

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    Inverse Problems for Generalized Reflexive Matrices on a Linear Manifold
    YUAN Yong-Xin, DAI Hua
    Acta mathematica scientia,Series A. 2009, 29 (6):  1547-1560. 
    Abstract ( 2073 )   RICH HTML PDF (344KB) ( 1235 )   Save

    Let R ∈Cm×m and SCn×n be nontrivial unitary involutions, i.e., RH=R=R-1 ≠ ± Im and SH=S=S-1 ≠ ± In. Cm×n is said to be a generalized reflexive matrixif RAS=A.  This paper is concerned with the inverse problem for generalized reflexive matrices on a linear manifold and the optimal approximation to a given matrix. The general expression of the solutions of the problem is presented. Sufficient and necessary conditions for equations AX2=Z2, Y2H A=W2H having a common generalized reflexive matrix solution on the linear manifold are derived. The expression of the solution for relevant optimal approximation problem is given.

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    Existence of Solution to Some Othmer-Stevens Chemotaxis System with Reaction Term
    LI Jun-Feng, LIU Wei-An
    Acta mathematica scientia,Series A. 2009, 29 (6):  1561-1571. 
    Abstract ( 1791 )   RICH HTML PDF (363KB) ( 1092 )   Save

    In this paper, the authors study an initial-boundary value problem of Othmer-Stevens chemotaxis system with reaction term in the master equation

    {∂u/∂t=D∨(u ∨ln u/Φ(x, t, w))+ f(x, t, u),
     

     ∂w/∂t=g(x, t, u, w),

     u∨ln u/Φ(x, t, w) ?n=0.
    They prove that there exists a unique solution if the boundary ∂Ω ∈C2+β, the functions Φ(x, t, w), f(x, t, u) and g(x, t, u, w) are  sufficiently smooth.

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    Ore Extensions of Quasitriangular Hopf Algebras
    WANG Zhi-Hua, LI Li-Bin
    Acta mathematica scientia,Series A. 2009, 29 (6):  1572-1579. 
    Abstract ( 1630 )   RICH HTML PDF (286KB) ( 1105 )   Save

    In this paper, a certain Ore extensions of quasitriangular Hopf algebras are considered. And the necessary and
    sufficient conditions for the Ore extensions of quasitriangular Hopf algebras to be quasitriangular with the same R-structures are also given. Finally, as an application, the Ore extensions of Sweedler Hopf algebra and Lusztig small quantum group are discussed.

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    Weighted Hardy and BMO Spaces Associated with Semigroup with Non-smooth Kernel
    XU Ming
    Acta mathematica scientia,Series A. 2009, 29 (6):  1580-1589. 
    Abstract ( 1594 )   RICH HTML PDF (300KB) ( 1278 )   Save

    In the paper the author gives weighted Hardy spaces and BMO spaces associated with semigroup with non-smooth kernel, then gives their properties and duality arguments.

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    The |Covering Numbers for |Some Periodic Reproducing Kernel Spaces
    SHENG Bao-Huai
    Acta mathematica scientia,Series A. 2009, 29 (6):  1590-1600. 
    Abstract ( 1770 )   RICH HTML PDF (340KB) ( 1213 )   Save

    A kind of method of estimating the norm of the inverse of the periodic Mercer kernel matrices is proposed with discrete Fourier transforms,with which a general way of estimating the upper and lower bounds of the covering
    number for periodic reproducing kernel  Hilbert spaces is provided. In particular,the lower and upper bounds of the covering number for two special periodic  reproduced kernel spaces are compared.

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    Loewner Chains and the Generalized Roper-Suffridge Extension Operator
    FENG Shu-Xia, LIU Xiao-Song, XU Qing-Hua
    Acta mathematica scientia,Series A. 2009, 29 (6):  1601-1612. 
    Abstract ( 2067 )   RICH HTML PDF (363KB) ( 1217 )   Save

    In this paper, the authors give the characterization of almost spirallike mappings of type β and order α on the unit ball B in finite dimensional complex Banach space from the Loewner chains point of view, and prove that the generalized Roper-Suffridge extension operator can be embedded in a Loewner chain on a bounded convex circular domain.

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    Multiple Periodic Solutions for a Delayed Stage-Structure Predator-Prey Systems |with Harvesting Rate and Diffusion
    QIN Fa-Jin
    Acta mathematica scientia,Series A. 2009, 29 (6):  1613-1622. 
    Abstract ( 1559 )   RICH HTML PDF (371KB) ( 1199 )   Save

    In this paper, the author studies the existence of periodic solutions for a delayed stage-structure predator-prey
    system with harvesting rate and diffusion. By developing some technique of analysis and using continuation theorem based on coincidence degree, some sufficient conditions are derived, under which this system has at least four positive periodic solutions.

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    (Cα)-summability of Character System of p}-series Field in Kaczmarz Rearrangement
    ZHANG Chuan-Zhou, ZHANG Xue-Ying
    Acta mathematica scientia,Series A. 2009, 29 (6):  1623-1633. 
    Abstract ( 1704 )   RICH HTML PDF (302KB) ( 1230 )   Save

    Let Gp be the p-series field. G.Gát and K.Nagy[8] have shown that the maximal operator of the (C,1) means of the character system of the p-series filed in the Kaczmarz rearrangement is of type (q,q) for all 1<q ≤ ∞ and of weak type (1,1). In the present work the authors  extend these results to the (C, α) means where 0 < α ≤ 1 and prove
    its maximal operator σ~α: Hp → Lp is bounded for all 1/(α+1) < p ≤ 1. By means of interpolation and duality argument, this theorem can be extended to Hardy-Lorentz spaces. As a consequence, the $(C,\alpha)$ means of an integrable function f converge to f a.e..

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    Composition Operators Between H and Generally Weighted Bloch Spaces in Polydisk
    LI Hai-Ying, LIU Pei-De
    Acta mathematica scientia,Series A. 2009, 29 (6):  1634-1641. 
    Abstract ( 1500 )   RICH HTML PDF (287KB) ( 1125 )   Save

    Let φ be a holomorphic self-map of the open unit polydisk Un in Cn and α > 0. In this article, the boundedness and compactness of composition operator Cφ between H and generally weighted Bloch space Bαlog in polydisk are investigated.

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    On Singular Directions of |Meromorphic Algebroidal Functions
    ZHANG Hong-Shen
    Acta mathematica scientia,Series A. 2009, 29 (6):  1642-1650. 
    Abstract ( 1749 )   RICH HTML PDF (275KB) ( 1938 )   Save

    Let w(z) be a meromorphic algebroidal   function  for |z|<+∞. If limr →∞lg T(r, w)/lg r =0,  limr →∞lg T(r, w)/lg lg r =+∞, then there exists a direction arg z=θ0 such that, for any N>0, ∑i1/(lg|zi(a; ?(θ0δ))|)N=+∞, with 2 v possible exceptions for a. If limr →∞T(r, w)/lgKr =+∞,  limr →∞lg T(r, w)/lg lg r =M, then there exists a direction arg z=θ0 such that ∑1/lg|zi(a; ?(θ0δ))|)σ=∞ (σ=M-2 or σ=M-2-ε), with 2 v possible exceptions for a. For meromorphic functions, these singular directions have not been studied yet.

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    On Some Explicit Blow-up Solutions to |3D Incompressible Magneto-hydrodynamic Equations
    LI Feng-Ping, YUAN Bao-Quan
    Acta mathematica scientia,Series A. 2009, 29 (6):  1651-1656. 
    Abstract ( 1524 )   RICH HTML PDF (268KB) ( 1219 )   Save

    This paper gives some explicit blow-up solutions in the form of separate variables and some explicit self-similar blow-up solutions to the
    3-dimensional incompressible magneto-hydrodynamic equations.

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    A Jump-diffusion Risk Model with Dependence |between Claim Sizes and Claim Intervals
    ZHAO Xiang-Hua, YIN Chuan-Cun
    Acta mathematica scientia,Series A. 2009, 29 (6):  1657-1664. 
    Abstract ( 1386 )   RICH HTML PDF (306KB) ( 1211 )   Save

    Using Laplace transform, the paper studies the joint distribution of the time of ruin, the surplus prior to ruin and the deficit at ruin for the jump-diffusion model with a dependent setting, where the claim inter-occurrence times depend on the previous claim size. Exact analytical expressions for the Laplace transform of the joint distribution are derived. The asymptotic behavior of the joint distribution as the initial capital tends to infinity is discussed.

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    Uniform Blow-up Properties for a Degenerate Parabolic System with Nonlocal Sources
    JIANG Liang-Jun, LI Hui-Ling
    Acta mathematica scientia,Series A. 2009, 29 (6):  1665-1678. 
    Abstract ( 2077 )   RICH HTML PDF (347KB) ( 1109 )   Save

    This paper deals with the blow-up properties of positive solutions to degenerate parabolic systems with nonlocal sources, subject to null Dirichlet boundary conditions. Under appropriate hypotheses, the authors establish the local existence of the solution and the finite time blow-up. Moreover, they obtain a necessary condition for which the two components of the solution blow up simultaneously, and then establish the uniform blow-up profiles in the interior.

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    Exponential Inequalities for Negatively Associated Random Variables
    XING Guo-Dong, YANG Shan-Chao
    Acta mathematica scientia,Series A. 2009, 29 (6):  1679-1688. 
    Abstract ( 1897 )   RICH HTML PDF (327KB) ( 1258 )   Save

    The authors show some exponential inequalities for negatively associated random variables. These inequalities improve the rresponding results which Jabbari and Azarnoosh (2007) and Oliveira (2005) got. As an application, the authors obtain the rate of convergence n-1/2(log log n)1/2(log n)2 for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Jabbari and Azarnoosh (2007) only got n-1/3(log n)5/3 for the case mentioned above.

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    Almost Sure Central Limit Theorem for the Product of Partial Sums
    TAN Zhong-Quan, PENG Zuo-Xiang
    Acta mathematica scientia,Series A. 2009, 29 (6):  1689-1698. 
    Abstract ( 1721 )   RICH HTML PDF (311KB) ( 1156 )   Save

    Let {Xn, n ≥ 1} be a sequence of i.i.d positive random variables with E(X1)=u >0, Var(X1)=σ2 and E|X1|3<∞, Sn=∑Nk=1Xk. Denote γ=σ/u the coefficient of variation.
     The authors give an unbounded measurable function g to satisfy the almost sure central limit theorem, i.e.,
     limN→∞1/logN∑Nn=11/n g((∏nk=1Sk/n!un )1/γ√n )=∫0g(x)dF(x), a.s.,
    where F(•) is the distribution function of the random variable e√2 ξ and ξ is a standard normal random variable.

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    Quantization of Block Type Algebras
    LI Jun-Bo, SU Yu-Cai
    Acta mathematica scientia,Series A. 2009, 29 (6):  1699-1703. 
    Abstract ( 1256 )   RICH HTML PDF (224KB) ( 1364 )   Save

    The authors quantize a family of Block type algebras, whose Lie bialgebra structures were investigated in a recent paper [1] by the authors.

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    On the Numerical Solution of the Direct Acoustic Scattering Problem for an Impedance Boundary
    WANG Lian-Tang, YANG A-Li, GUAN Jin-You, WANG Qing-Yun, ZHANG Mei-Dong
    Acta mathematica scientia,Series A. 2009, 29 (6):  1704-1713. 
    Abstract ( 1760 )   RICH HTML PDF (333KB) ( 1187 )   Save

    In this paper, the authors describe a fully discrete method for the numerical solution of the hyper-singular integral equation arising from the combined single and double layer potential approach for the solution of the exterior impedance boundary problem to the two-dimensional Helmholtz equation in smooth domains. The equation contains a hyper-singular operator. The authors develop an error analysis in a H\"{o}lder space setting with point-wise estimates and prove an exponential convergence rate for analytic boundaries and boundary data. Finally the numerical example is given to show the validity of the method.

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    Meromorphic Functions that Share Three Weighted Values
    CHEN Jun-Fan, LIN Wei-Chuan, Chen-Sheng-Jiang
    Acta mathematica scientia,Series A. 2009, 29 (6):  1714-1723. 
    Abstract ( 1675 )   RICH HTML PDF (288KB) ( 1201 )   Save

    Using the idea of weighted sharing of values, the authors deal with the problem of uniqueness of meromorphic functions that share three values. The results in this paper improve all theorems given by Alzahary and Yi in J. Math. Anal. Appl. 295 (2004) 247--257.

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    Almost Periodic Solutions to a Class of Generalized Liénard Equations
    LI Li-Jie, YANG Qi-Gui
    Acta mathematica scientia,Series A. 2009, 29 (6):  1724-1731. 
    Abstract ( 1591 )   RICH HTML PDF (320KB) ( 1207 )   Save

    This paper investigates bounded solutions or the existence of almost  periodic solutions of the following Liénard system: x'=φ(y)-F(x), y'=-g(x)+p(t). The authors obtain some results that the ultimate boundedness with respect to part of the solution implies the existence of an almost periodic solution by using Amerio's results. The results are the natural generalization of the main result by Cieutat[1].

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    Properties of the Solution in Generalized Minty Vector Variational-like Inequalities
    XIAO Gang, LIU San-Yang
    Acta mathematica scientia,Series A. 2009, 29 (6):  1732-1742. 
    Abstract ( 1812 )   RICH HTML PDF (305KB) ( 1142 )   Save

    Generalized Minty vector variational-like inequalities as being of lower Dini directional derivative type are studied in topological vector  spaces, which include Minty variational inequalities, Minty  variational-like inequalities and Minty vector variational inequalities as being of differential type. Some relations between solutions of Minty vector
    variational-like inequalities and solutions of vector optimization problems, as well as radial decrease properties of functions, are investigated. Moreover, the affine solution sets of Minty  vector variational-like inequalities  are
    presented. As consequences, some recent known results in literature are obtained in the special case.

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    Propagation of Conormal Singularities for Semilinear Elastic Dynamical System
    LEI Yuan-Ming, LIU Zi-Shan
    Acta mathematica scientia,Series A. 2009, 29 (6):  1743-1749. 
    Abstract ( 1896 )   RICH HTML PDF (375KB) ( 1192 )   Save

    The propagation of initial singularities for a semilinear elastic dynamic system is discussed. First, construct conormal distribution spaces for the system and discuss its character. Then study decomposition, as Stokes-Helmholtz decomposition in elastodynamics, of functions in the spaces. Lastly, prove, if initial dates are 
    bounded and have conormal singularities in zeros,  then initial problems have  bounded solutions with conormal
    singularities only in two characteristic surfaces of the system, and have higher regularities.

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    The Stability of Aleksandrov-Fenchel Inequality for Polars of Mixed Projection Bodies |and Mixed Intersection Bodies
    MA Tong-Yi
    Acta mathematica scientia,Series A. 2009, 29 (6):  1750-1764. 
    Abstract ( 1620 )   RICH HTML PDF (409KB) ( 1130 )   Save

    A metric method for homothetic deviation of m(m ≥ 2) geometirc bodies(star bodies or convex bodies) is provided. By the metric mthod, and utilizing a refinement of Hölder inequality the author establishes a stablity version of Aleksandrov-Fenchel inequality for polars of mixed projection bodies and mixed intersection bodies.

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    The Density of the Common Value-points of Two Algebroidal Functions and the Uniqueness Theorems
    CHAI Fu-Jie
    Acta mathematica scientia,Series A. 2009, 29 (6):  1765-1770. 
    Abstract ( 1762 )   RICH HTML PDF (254KB) ( 1102 )   Save

    In This paper, the author investigates the density of the common points of two algebroidal functions  by using the Sun Dao-chun's definition of the addition of algebroidal functions, and extends several uniqueness theorems of meromorphic functions to algebroidal functions.

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    A Forward and Backward Diffusion Model for Gray Level Image Restoration
    KONG Ling-Hai, HUAN Zhong-Dan
    Acta mathematica scientia,Series A. 2009, 29 (6):  1771-1784. 
    Abstract ( 2817 )   RICH HTML PDF (541KB) ( 1468 )   Save

    In this paper, a spacially adaptive smoothing and enhancing partial differential equation for image restoation,
     is presented, which is  coupled with time-delay regularization. In order to reverse the process of image degradation, a newly defined shock filter for edge enhancement is incorporated with a level set motion based equation for noise removal. The balance between the two processes is achieved by an edge discrimination function, which is coupled with time-delay regularization, for distinguishing boundary areas and homogeneous regions in  given images. The proposed model is well-posed in terms of viscosity solutions: the existence and
    uniqueness of periodic viscosity solution to the initial value problem of the equation is established. Numerical examples of some kinds of images are presented for illuminaating the efficiency of the proposed model.

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