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25 July 2010, Volume 30 Issue 4 Previous Issue    Next Issue

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A New Blow-up Condition for the Periodic Rod Equation LIU Yong-Ming, ZHOU Yong Acta mathematica scientia,Series A. 2010, 30 (4):  865-872.  Abstract ( 1896 )   RICH HTML PDF (341KB) ( 952 )   Save In this paper, first the authors find optimal constants for a class of Sobolev inequalities by using Fourier expansion. This method is more direct and simple than the usual calculus of variation. Then, they establish a new blow-up condition for the period rod equation by the established inequality. References | Related Articles | Metrics

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Spectra of Compact Weighted Composition Operators on Dirichlet Type Spaces WANG Mao-Fa, LIU Pei-De Acta mathematica scientia,Series A. 2010, 30 (4):  873-883.  Abstract ( 1697 )   RICH HTML PDF (372KB) ( 1500 )   Save In this paper, the authors study the spectra of weighted composition  operators on Dirichlet type spaces Dα(Un) defined on the unit polydisc  {Un) in Cn. Some spectral characterizations of  a class of  compact weighted composition operators on Dα{Un) are obtained, which extend some previous results. References | Related Articles | Metrics

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CBMO Estimates for Commutators of |Integral Operators with Variable Kernel CHEN Dong-Xiang, LIU Shan-Zhen Acta mathematica scientia,Series A. 2010, 30 (4):  884-893.  Abstract ( 1427 )   RICH HTML PDF (265KB) ( 1017 )   Save In this paper, the authors establish the CBMO estimates for the commutators of  integral operators with variable kernel on Herz spaces. References | Related Articles | Metrics

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The Weighted Composition Operators between Little Bloch Type Spaces on the Unit Ball of Cn Strong Approximations of Linear Processes LIU Jing-Cheng, ZHANG Xue-Jun Acta mathematica scientia,Series A. 2010, 30 (4):  894-907.  Abstract ( 1867 )   RICH HTML PDF (343KB) ( 1058 )   Save In  this  paper,   the necessary and sufficient conditions are given for the weighted composition operator Tψ, φ to be bounded or compact from little Bloch type spaces βp0 to βq0 for all 0<p<∞ and 0<q<∞ on the unit ball of Cn. References | Related Articles | Metrics

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The Doubling Property of Markov Measures on Self-similar Sets WANG Xiao-Hua, WEN Zhi-Xiong Acta mathematica scientia,Series A. 2010, 30 (4):  908-914.  Abstract ( 1321 )   RICH HTML PDF (283KB) ( 1093 )   Save The authors study Markov measures on self-similar sets which satisfy the open set condition and study necessary and sufficient conditions for their associated Markov measures to be doubling on its support in this paper. As an application, the authors characterize Markov measures with doubling properties on some self-similar sets. References | Related Articles | Metrics

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The Characterization and Representation of the W-weighted Drazin Inverse of Operators on Hilbert Space ZHONG Jin, LIU Xiao-Ji Acta mathematica scientia,Series A. 2010, 30 (4):  915-921.  Abstract ( 1634 )   RICH HTML PDF (278KB) ( 1133 )   Save In this work the authors study the W-weighted Drazin inverse of operators on Hilbert space. By utilizing the matrix block representation of Hilbert space operators, some characterizations and representations of the W-weighted Drazin inverse are presented, which extend the corresponding results by Wei Y M. References | Related Articles | Metrics

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Weighted End-point Estimates for Commutators of Fractional Integrals on Spaces of Homogeneous Type LIU Zong-Guang, TIAN Mao-Qian Acta mathematica scientia,Series A. 2010, 30 (4):  922-931.  Abstract ( 1586 )   RICH HTML PDF (329KB) ( 1035 )   Save In this paper, it is established that the weighted end-point estimates for the commutator of fractional integrals on the spaces of homogenesous type, i.e., w({x∈X:|[b, Iα]f(x)|>t})≤Cψ(∫X A(||b||* |f(x)|/t Θ(w(x))dμ(x)), where b ∈BMO(X, d, μ), A(t)=tlog(e+t), ψ(t)=[tlog(e+tα]1/1-α, Θ(t)=t1-αlog(e+t-α). References | Related Articles | Metrics

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Global Smooth Solution to the |Landau-Lifshitz-Maxwell Equations LIN Jun-Yu, DING Shi-Jin Acta mathematica scientia,Series A. 2010, 30 (4):  932-944.  Abstract ( 2134 )   RICH HTML PDF (352KB) ( 1230 )   Save The present paper concerns itself with the existence and uniqueness of global smooth solution to the periodic initial value problem of the Landau-Lifshitz equation without Gilbert damping terms but with quasi-static Maxwell equations in one dimension.  To establish the uniform estimates,  the authors use some identities resulting from the fact |Z|=1 and the fact that the vectors {Z, Zx, Z×Zx} form an orthogonal base of the space R3. References | Related Articles | Metrics

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Growth of Solutions of Higher Order Linear Differential Equations with the Coefficient A0 Being Dominant TU Jin, DENG Guan-Tie Acta mathematica scientia,Series A. 2010, 30 (4):  945-952.  Abstract ( 2224 )   RICH HTML PDF (282KB) ( 1198 )   Save In this paper, the authors investigate the growth of solutions of a class of higher order linear homogenous differential equations, where the coefficient A0 is dominating to the growth of solutions of the equations. Two main results are obtained: one is in the complex plane and the other is in the unit disc, which are improvements of some previous results. References | Related Articles | Metrics

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On Generalized Beltrami System GAO Hong-Ya, ZHAO Li-Fang Acta mathematica scientia,Series A. 2010, 30 (4):  953-958.  Abstract ( 1337 )   RICH HTML PDF (306KB) ( 1149 )   Save This paper deals with the generalized Beltrami system Dtf(x)H(x)Df(x)=J(x, f)2/nG(x).                                              (*) A homogeneous elliptic equation of divergence type Div A(x, Df(x))=0 is derived from (*) under the uniformly elliptic conditions on the matrices H(x), G(x) ∈S(n) by using the energy and variational methods. The weak monotonicity properties for the component functions of (*) and a Caccioppoli inequality are also derived. References | Related Articles | Metrics

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Hypersingular Integrals along Hypersurface on Modulation Spaces CHENG Mei-Fang, ZHANG Zhen-Qiu Acta mathematica scientia,Series A. 2010, 30 (4):  959-967.  Abstract ( 1401 )   RICH HTML PDF (351KB) ( 1116 )   Save Let $$Tf(x,x_{n})={\rm p.v.}\int\frac{f(x-y,x_{n}-\gamma(y)){\rm e}^{-2\pi {\rm i}|y|^{-\beta}}\Omega(y)h(y)}{|y|^{n+\alpha-1}}{\rm d}y, ~~~x,y\in{{\Bbb R}}^{n-1}, x_{n}\in{\Bbb R}.$$ The purpose of this paper is to investigate the boundedness of such integral operators  on general modulation spaces. Here the rough kernel $\Omega$ is in the $L^1(S^{n-2})$, $h(y)$ is a bounded radial fuction and $\gamma(y)$ is an appropriate hypersurface. References | Related Articles | Metrics

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The Vertex Arboricity of Integer Distance Graphs G(Dm, k, 2) ZUO Lian-Cui, CUI Yu-Quan, LIU Jia-Zhuang Acta mathematica scientia,Series A. 2010, 30 (4):  968-983.  Abstract ( 1452 )   RICH HTML PDF (395KB) ( 1077 )   Save The vertex arboricity va(G) of a graph G is the minimum number of subsets into which the vertex set V(G) can be partitioned so that each subset induces a subgraph whose connected components are trees. An integer distance graph is a graph G(D) with the set of all  integers as vertex set and two vertices u, v\in Z are adjacent if and only if |u-v in D where the  distance set D is a subset of the positive integers set. Let Dm, k, 2=[1,m]\k, 2k} for m>2k≥2. In this paper, some upper and lower bounds of the vertex arboricity of the integer distance graph G(Dm, k, 2) are obtained. Moreover, va(G(Dm,1, 2))=lm+4/5l  for m≥4 and  va(G(Dm, 2, 2))=lm+1/5l+1 for any positive integer m=10q+j with j =0,1, 2, 3, 5, 6. References | Related Articles | Metrics

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Local Polynomial Estimator of the Regression Function in Autoregressive Models with Errors in Variables YU Zhuo-Xi, WANG De-Hui, SHI Ning-Zhong Acta mathematica scientia,Series A. 2010, 30 (4):  984-999.  Abstract ( 1429 )   RICH HTML PDF (1150KB) ( 924 )   Save In this paper, the authors study the problem of  nonparametric estimation of the autoregression function in autoregressive models with errors-in-variables. With the application of the deconvolution kernel,  the local polynomial estimator of the autoregression function is given. Under some specific conditions, the properties of consistency and asymptotic normality of the estimator can be obtained here. The performance of the method is studied by some simulation experiments. References | Related Articles | Metrics

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Complete Hypersurfaces with Constant Mean Curvature in a Locally Symmetric Riemannian Manifold ZHANG Shi-Cheng, WU Bao-Qiang Acta mathematica scientia,Series A. 2010, 30 (4):  1000-1005.  Abstract ( 1417 )   RICH HTML PDF (241KB) ( 1141 )   Save In this paper, the complete hypersurfaces with constant mean curvature in a locally symmetric manifold are investigatesd,  a characterization of totally umbillic hypersurfaces is obtained, and the corresponding results are generalized. References | Related Articles | Metrics

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Generic Stability of the Solution Set for Symmetric Vector Quasi-equilibrium Problems under the Condition of Cone-convexity CHEN Jian-Chen, GONG Xun-Hua Acta mathematica scientia,Series A. 2010, 30 (4):  1006-1017.  Abstract ( 2078 )   RICH HTML PDF (382KB) ( 1138 )   Save In topological vector spaces, a new existence result on the weakly Pareto solutions for vector quasi-equilibrium problem is obtained by the Ky Fan's section theorem. As an application, a new existence theorem of the weakly Pareto solutions for symmetric vector quasi-equilibrium problem is obtained under the condition that its payoff functions are cone-convex. The theorem, under weaker conditions, solves the second problem proposed by Fu in [1], whether there is a weakly Pareto solution for symmetric vector quasi-equilibrium problem when its payoff functions are cone-convex. At last the authors discuss the generic stability of the solution set for symmetric vector quasi-equilibrium problem under the condition of cone-convexity in normed linear spaces. References | Related Articles | Metrics

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The Lumped Mass Nonconforming Finite Element Approximation for the Nonstationary Navier-Stokes Equations on Anisotropic Meshes SHI Dong-Yang, WANG Hui-Min Acta mathematica scientia,Series A. 2010, 30 (4):  1018-1029.  Abstract ( 1920 )   RICH HTML PDF (403KB) ( 1206 )   Save In this paper, a low order Crouzeix-Raviart type nonconforming triangular element is applied to the nonstationary Navier-Stokes equations. The approximation scheme of the lumped mass finite element methods for the problem is proposed. Without using Ritz-Volterra projection, the error estimates are derived both in the L2-norm and the energy norm for velocity and the L2-norm for pressure on anisotropic meshes through the technique of introducing two auxiliary finite element spaces to the boundary estimate. References | Related Articles | Metrics

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The Order, and |Lower Order of Growth, and the Hyper-order of a Class of Higher Order Linear Differential Equations with Entire CHEN Yu Acta mathematica scientia,Series A. 2010, 30 (4):  1030-1041.  Abstract ( 1975 )   RICH HTML PDF (330KB) ( 1065 )   Save This paper investigates the properties of growth of solutions of a class of higher order linear differential equations with entire coefficients, obtains some precise estimates of the order and lower order of growth and the hyper-order of the solutions of equations f{(k)}+Ak-1(z)eak-1z, f (k-1)+… + A0(z)ea0zf =0 and f (k)+(Ak-1}(z)eak-1z +Dk-1(z)f (k-1)+…+(A0(z)ea0z+D0(z)f =0  when the arguments of aj, 0≤ j ≤ k-1, are  not all equal. References | Related Articles | Metrics

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Estimation in Partially Linear Varying-Coefficient Errors-in-Variables Models with Missing Responses WEI Chuan-Hua Acta mathematica scientia,Series A. 2010, 30 (4):  1042-1054.  Abstract ( 2092 )   RICH HTML PDF (411KB) ( 926 )   Save This paper considers the estimation of partially linear varying-coefficient models, which are useful extensions of varying coefficient models and partially linear models. The author focuses on the case where some covariates are measured with additive errors and the response variable is sometime missing. A class of estimators for the parametric component as well as nonparametric components based on the profile least-squares approach are proposed. The first estimator is constructed by using complete-case observations only, the other two by using simple imputation or replacement techniques respectively to complete the sample. All the proposed estimators for the parametric component are shown to be asymptotically normal, and the estimators of nonparametric component achieve the optimal strong convergence rate of the usual nonparametric regression. For the mean of response variable, two estimators are constructed and their asymptotic normalities are established. Simulation studies are conducted to illustrate the approach. References | Related Articles | Metrics

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Spectrum Analysis of |Transport Operators in the Growing Cell Populations WANG Sheng-Hua, WENG Yun-Fang, YANG Ming-Zhu Acta mathematica scientia,Series A. 2010, 30 (4):  1055-1061.  Abstract ( 1356 )   RICH HTML PDF (286KB) ( 1066 )   Save The objective of this paper is to research the transport equations of Rotenberg's model general boundary condition in the growing cell populations in Lp-space (1≤p <+∞). It is shown the transport operator A generates C0 semigroup and  the existece of the eigenvalue, so it is  obtained that the spectrum of the transport operators only consisting of finitely isolate eigenvalues with finite algebraic multiplicities in the trip Γ. References | Related Articles | Metrics

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Strong Convergence of Implicit Iterative Scheme with Errors for Nonlinear Mappings YANG Li-Ping, XIE Xiang-Sheng Acta mathematica scientia,Series A. 2010, 30 (4):  1062-1070.  Abstract ( 1701 )   RICH HTML PDF (336KB) ( 1140 )   Save Let K be a nonempty closed convex subset of a real uniformly convex Banach space E and Ti: K → K~ (i=1, 2, …, N) be a finite family of total asymptotically nonexpansive mappings. Let the implicit iteration scheme {xn} generated from arbitrary x0∈K by xn=αnxn-1+βnTnk xn+γn un, n≥1, where {αn}, {βn}, {γn} (  [0, 1] and αn+βn+γn=1, {un} is bounded in K. The purpose of this paper is to study several strong convergence of the implicit iteration scheme {xn} under certain conditions. It derives a necessary and sufficient condition for the strong convergence of this iteration scheme to a common fixed point of these mappings. The results of this paper improve and extend the corresponding results of Shahzad and Zegeye, Zhou and Chang, Chang, Tan, Lee and Chan. References | Related Articles | Metrics

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On the Orders of Growth of Meromorphic Solutions of Certain Linear Differential Equations with Meromorphic Coefficients HUANG Zhi-Gang Acta mathematica scientia,Series A. 2010, 30 (4):  1071-1079.  Abstract ( 1529 )   RICH HTML PDF (331KB) ( 1175 )   Save In this paper,  the author investigates the orders of the solutions of the differential equation f (k)+Ak-1f (k-1)}+…+A0f =0,    k≥2  where the coefficients A0, …, Ak-1 are meromorphic functions with at most finitely many poles. Under some conditions, some estimates of the orders of the solutions for the equation are obtained, which are improvements of related results given by Gunderson, Chen and Gao. References | Related Articles | Metrics

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he Inverse Problem of the Identification of the Heat Source for the Poisson Equation YANG Fan, FU Chu-Li Acta mathematica scientia,Series A. 2010, 30 (4):  1080-1087.  Abstract ( 1600 )   RICH HTML PDF (464KB) ( 1091 )   Save This paper discusses the inverse problem of determining a space-wise heat source in the Poisson equation in a half strip domain. This problem is ill-posed, i.e., the solution does not depend continuously on the given data. A regularization solution of the inverse problem is  obtained by the Carasso-Tikhonov regularization method. For the regularization solution, Hölder type stability estimate is obtained between the regularization solution and the exact solution. A numerical example shows that the Carasso-Tikhonov regularization method works effectively for identification the heat source. References | Related Articles | Metrics

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On the Representation |of Linear Isometries between  E(2) Type Real Space LIANG Xiao-Bin, HUANG Shi-Xiang Acta mathematica scientia,Series A. 2010, 30 (4):  1088-1093.  Abstract ( 1286 )   RICH HTML PDF (291KB) ( 1066 )   Save In this paper, the authors give a representation of surjective isometries between the unit spheres of E(2)  type real space if  these isometries can be extended to be real linear isometries on the whole space. References | Related Articles | Metrics

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Existence and Uniqueness of Periodic Solutions for a Class of Neutral |Differential System CHEN Zhi-Bin, HUANG Li-Hong Acta mathematica scientia,Series A. 2010, 30 (4):  1094-1101.  Abstract ( 2194 )   RICH HTML PDF (307KB) ( 1076 )   Save By using the analytical method and utilizing Krasnoselskii fixed point theory, this paper qualitatively and quantitatively studies the existence of periodic solutions for a class of neutral differential systems, and obtains some sufficient conditions of existence and uniqueness of periodic solution for this class of systems. The research method is different from  the commonly used method. The main conclusions obtained are new, and promote the main conclusions in literature. References | Related Articles | Metrics

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On Submanifolds with Constant Scalar Curvature in a Locally Symmetric and Conformally Flat Space SONG Wei-Dong, LIU Min Acta mathematica scientia,Series A. 2010, 30 (4):  1102-1110.  Abstract ( 1405 )   RICH HTML PDF (294KB) ( 1134 )   Save In this paper, the authors discuss the submanifolds with constant scalar curvature in a locally symmetric and conformally flat space, and obtain some intrinsic rigidity theorems. References | Related Articles | Metrics

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The Existence of Solution of Nonlinear Boundary Value Problem Involving the Generalized p-Laplacian Operator in {\boldmath Ls(Ω) WEI Li Acta mathematica scientia,Series A. 2010, 30 (4):  1111-1116.  Abstract ( 1946 )   RICH HTML PDF (325KB) ( 1096 )   Save By using the perturbation results on ranges of nonlinear accretive mappings, the existence of solution of Neumann boundary value problem involving the generalized p-Laplacian operator in Ls(Ω) space is discussed in this paper, where 2 ≤ p ≤ s < + ∞. Some new techniques are used here to prove the main result which can be regarded as a continuation and complement to some of  the previous works. References | Related Articles | Metrics

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A Quadratic Tridiagonal Interpolation DFO Method for Unconstrained Optimization LIU Hao, PAN Ai-Xia, NI Qi Acta mathematica scientia,Series A. 2010, 30 (4):  1117-1125.  Abstract ( 1368 )   RICH HTML PDF (358KB) ( 944 )   Save This paper presents a new derivative free optimization(DFO) method which is based on a quadratic tridiagonal interpolation model. Under mild assumptions, the convergence results of this method are given and proved. Numerical experiments  show that the new method is promising.  References | Related Articles | Metrics

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An Iterative Method for a Kind of |Variational Inequality and Fixed Point Problem of Nonexpansive Mapping   SHANG Mei-Juan, SU Yong-Fu, QIN Xiao-Long Acta mathematica scientia,Series A. 2010, 30 (4):  1126-1137.  Abstract ( 1991 )   RICH HTML PDF (302KB) ( 1043 )   Save In this paper, the authors introduce a new iterative scheme to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a relaxed cocoercive and Lipschitz continuous mapping. The results improve and extend the recent ones announced by many others. References | Related Articles | Metrics

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The Continuity of the Metric Projections on a Close Hyperplane in |Banach Space FANG Hong-Wei, SU Ya-La-Tu Acta mathematica scientia,Series A. 2010, 30 (4):  1138-1143.  Abstract ( 1422 )   RICH HTML PDF (290KB) ( 974 )   Save In this paper,  the authors give a representation of the metric projections on a class of close hyperplanes in a dual space of Banach space  X. For  a  Banach space, some results of continuity of the metric projections on a class of close hyperplanes in  X or X* are obtained. References | Related Articles | Metrics

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Viscosity Approximation Methods for Common Fixed Points of Infinite Nonexpansive Nonself-mappings ZHAO Liang-Cai, ZHANG Shi-Sheng Acta mathematica scientia,Series A. 2010, 30 (4):  1144-1157.  Abstract ( 2360 )   RICH HTML PDF (320KB) ( 1015 )   Save Let E be a real strictly convex and reflexive Banach space with a uniformly Gâteaux differentiable norm and  K be a nonempty closed convex subset of E which is also a sunny nonexpansive retract of E. Let f : K→K be a contractive mapping, P be a sunny nonexpansive retraction of $E$ onto K and {Tn}n=1∞ : K→E be a family of countable infinite nonexpansive nonself-mappings such that the common fixed point set F:=:=∩∞n=1F(Tn)≠Φ and {λn} be a seqence of nonnegative numbers in [0,1]. Consider the following iterative sequence               { xn+1=(1-αn-βn)xn+αn f(yn)+βnWnyn,                  yn=(1-γn-δn)xn+γnWnxn+δnun, n ≥1. where Wn is the W-mapping generated by P, Tn, Tn-1,  …, T1 and λn, λn-1, …, λ1 for n ≥ 1. It is shown that under very mild conditions on the parameters, the sequence {xn} converges strongly to p ∈ F, where p is the unique solution in F to the following variational inequality                  <(I-f)p, j(p-x*)>≤ 0, ∨x* ∈ F. References | Related Articles | Metrics

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The CQ Method for Common |Fixed Point Involving Asymptotically Nonexpansive Semigroups YANG Li, LI Jun Acta mathematica scientia,Series A. 2010, 30 (4):  1158-1165.  Abstract ( 1654 )   RICH HTML PDF (298KB) ( 980 )   Save In this paper, by using the CQ method, the strong convergence of modified Ishikawa iterative sequence involving asymptotically nonexpansive semigroups is proved in Hilbert spaces. These results extend and improve corresponding results of others. References | Related Articles | Metrics

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L2 Decay for Weak Solutions of the MHD Equations in Half Space LIU Ying, LI Jia Acta mathematica scientia,Series A. 2010, 30 (4):  1166-1175.  Abstract ( 2132 )   RICH HTML PDF (291KB) ( 961 )   Save In this paper, the authors mainly study the decay rate for the weak solutions of the initial value and boundary value problem for the incompressible MHD equations in half spaces. The main tool is the spectral representation and the energy estimation. References | Related Articles | Metrics

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Estimation of Unknown Function of |a Class of Integral Inequalities for Discontinuous Function and its Application LUO Ri-Cai, WANG Wu-Sheng, XU Hong-Lei Acta mathematica scientia,Series A. 2010, 30 (4):  1176-1182.  Abstract ( 1722 )   RICH HTML PDF (296KB) ( 1088 )   Save In this paper we give  the estimations of unknown functions of a class of integral  inequalities for discontinuous functions by  techniques  of analysis and mathematical induction. Using our result we can solve  the integral inequality for discontinuous function in[8].  We  apply our result to a class of integral-differential  equations with impulse perturbation for estimation. References | Related Articles | Metrics