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20 January 2006, Volume 26 Issue 1 Previous Issue    Next Issue

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A NEW APPROXIMATE INERTIAL MANIFOLD AND ASSOCIATED ALGORITHM Li Kaitai; Xu Zhongfeng; Yang Xiaozhong Acta mathematica scientia,Series B. 2006, 26 (1):  1-16.  DOI: 10.1016/S0252-9602(06)60021-0 Abstract ( 1134 )   RICH HTML PDF (188KB) ( 1119 )   Save In this article the authors propose a new approximate inertial manifold(AIM) to the Navier-Stokes equations. The solutions are in the neighborhoods of this AIM with thickness δ=o(h2k+1-ε). The article aims to investigate a two grids finite element approximation based on it and give error estimates of the approximate solution ||(u - u*h* , p - p*h*)|| ≤ C(h2k+1-ε + h*(m+1)), where (h,h*) and (k,m) are coarse and fine meshes and degree of finite element subspaces, respectively. These results are much better than Standard Galerkin(SG) and nonlinear Galerkin (NG) methods. For example, for 2D NS eqs and linear element, let uh, uh, u* be the SG, NG and their approximate solutions respectively, then |u - uh|1≤ Ch, |u - uh|1 ≤ h2, |u -u*|1 ≤ Ch3, and h*≈ h2 for NG, h*≈ h3/2 for theirs. Related Articles | Metrics

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ASYMPTOTIC APPROXIMATION METHOD AND ITS CONVERGENCE ON SEMI-INFINITE PROGRAMMING Wan Zhongping; Wang Xianjia; He Julin; Jia Shihui Acta mathematica scientia,Series B. 2006, 26 (1):  17-24.  DOI: 10.1016/S0252-9602(06)60022-2 Abstract ( 1107 )   RICH HTML PDF (138KB) ( 976 )   Save The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed. Related Articles | Metrics

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METRIZABILITY OF SPACES AND J.NAGATA'S PROBLEM Gao Zhimin Acta mathematica scientia,Series B. 2006, 26 (1):  25-30.  DOI: 10.1016/S0252-9602(06)60023-4 Abstract ( 825 )   RICH HTML PDF (117KB) ( 1133 )   Save In 1988, J.Nagata raised a problem about metrizability. The present article is an attempt to find a solution to the problem. Related Articles | Metrics

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THE MINIMAL OPERATOR AND WEIGHTED INEQUALITIES FOR MARTINGALES Zuo Hongliang; Liu Peide Acta mathematica scientia,Series B. 2006, 26 (1):  31-40.  DOI: 10.1016/S0252-9602(06)60024-6 Abstract ( 1018 )   RICH HTML PDF (154KB) ( 1205 )   Save In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities hold. Related Articles | Metrics

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CRITERIA OF STRONG TRANSIENCE FOR OPERATOR-SELF-SIMILAR MARKOV PROCESSES Wu Chuanju; Zhang Feng; Liu Luqin Acta mathematica scientia,Series B. 2006, 26 (1):  41-48.  DOI: 10.1016/S0252-9602(06)60025-8 Abstract ( 874 )   RICH HTML PDF (138KB) ( 960 )   Save Yamamuro in [1] defines strong and weak transience of Markov processes; gives a criterion for strong transience of Feller processes; and further, discusses strong and weak transience of Ornstein-Uhlenbeck type processes. In this article, the authors weaken the Feller property of the result in [1] to weak Feller property and discuss the strong transience of operator-self-similar Markov processes. Related Articles | Metrics

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PERMANENCE AND PERSISTENCE OF TIME VARYING LOTKA-VOLTERRA SYSTEMS Liu Shaoping; Liao Xiaoxin Acta mathematica scientia,Series B. 2006, 26 (1):  49-58.  DOI: 10.1016/S0252-9602(06)60026-X Abstract ( 944 )   RICH HTML PDF (147KB) ( 1010 )   Save In this article, the permanence and persistence for three classes time varying Lotka-Volterra ecological system are investigated by using Lyapunov stability analysis and constructing the compact set of attraction. Some examples are given to illustrate the theorems. Related Articles | Metrics

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SEMILINEAR HEMIVARIATIONAL INEQUALITIES WITH STRONG RESONANCE AT INFINITY Michael Filippakis; Leszek Gasinski; Nikolaos S. Papageorgiou Acta mathematica scientia,Series B. 2006, 26 (1):  59-73.  DOI: 10.1016/S0252-9602(06)60027-1 Abstract ( 956 )   RICH HTML PDF (186KB) ( 915 )   Save A semilinear elliptic equation with strong resonance at infinity and with a nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and extend results in the literature, two results on existence are obtained. Related Articles | Metrics

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FIXED-DESIGN SEMIPARAMETRIC REGRESSION FOR LINEAR TIME SERIES Hu Shuhe Acta mathematica scientia,Series B. 2006, 26 (1):  74-82.  DOI: 10.1016/S0252-9602(06)60028-3 Abstract ( 842 )   RICH HTML PDF (132KB) ( 1407 )   Save This article studies parametric component and nonparametric component estimators in a semiparametric regression model with linear time series errors; their r-th mean consistency and complete consistency are obtained under suitable conditions. Finally, the author shows that the usual weight functions based on nearest neighbor methods satisfy the designed assumptions imposed. Related Articles | Metrics

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GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA Li Jianquan; Ma Zhien; Zhou Yicang Acta mathematica scientia,Series B. 2006, 26 (1):  83-93.  DOI: 10.1016/S0252-9602(06)60029-5 Abstract ( 1449 )   RICH HTML PDF (171KB) ( 1743 )   Save An SIS epidemic model with a simple vaccination is investigated in this article. The efficiency of vaccine, the disease-related death rate and population dynamics are also considered in this model. The authors find two threshold R0 and Rc (Rc may not exist). There is a unique endemic equilibrium for R0>1 or Rc=R0; there are two endemic equilibria for Rc<R0<1; and there is no endemic equilibrium for R0<Rc<1. When Rc exists, there is a backward bifurcation from the disease-free equilibrium for R0=1. They analyze the stability of equilibria and obtain the globally dynamic behaviors of the model. The results acquired in this article show that an accurate estimation of the efficiency of vaccine is necessary to prevent and controll the spread of disease. Related Articles | Metrics

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NUMERICAL ANALYSIS OF QUASICONFORMAL MAPPINGS BY CIRCLE PACKINGS Lan Shiyi; Dai Daoqing Acta mathematica scientia,Series B. 2006, 26 (1):  94-98.  DOI: 10.1016/S0252-9602(06)60030-1 Abstract ( 1072 )   RICH HTML PDF (133KB) ( 1245 )   Save Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed. Related Articles | Metrics

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OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES Liu Ailian; Wu Hongwu; Zhu Siming; Ronald M. Mathsen Acta mathematica scientia,Series B. 2006, 26 (1):  99-106.  DOI: 10.1016/S0252-9602(06)60031-3 Abstract ( 1079 )   RICH HTML PDF (147KB) ( 1120 )   Save The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set bZ+ of positive integers and for differential equations when the time scale is the set R of real numbers. Related Articles | Metrics

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A RANK THEOREM FOR NONLINEAR SEMI-FREDHOLM OPERATORS BETWEEN TWO BANACH MANIFOLDS Shi Ping; Ma Jipu Acta mathematica scientia,Series B. 2006, 26 (1):  107-114.  DOI: 10.1016/S0252-9602(06)60032-5 Abstract ( 948 )   RICH HTML PDF (126KB) ( 1294 )   Save In this article the concept of local conjugation of a C1 mapping between two Banach manifolds is introduced. Then a rank theorem for nonlinear semi-Fredholm operators between two Banach manifolds and a finite rank theorem are established in global analysis. Related Articles | Metrics

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THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHRODINGER-POISSON EQUATIONS Hao Chengchun Acta mathematica scientia,Series B. 2006, 26 (1):  115-124.  DOI: 10.1016/S0252-9602(06)60033-7 Abstract ( 1261 )   RICH HTML PDF (154KB) ( 1016 )   Save In this article, the author studies the initial-(Dirichlet) boundary problem for a high-field version of the Schrodinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schrodinger equations on the unit cube. A global existence and uniqueness is established for a solution to this problem. Related Articles | Metrics

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EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO CERTAIN QUASILINEAR ELLIPTIC EQUATIONS IN A BALL Wang Quanzhen; Chen Zuchi Acta mathematica scientia,Series B. 2006, 26 (1):  125-133.  DOI: 10.1016/S0252-9602(06)60034-9 Abstract ( 1024 )   RICH HTML PDF (142KB) ( 1082 )   Save By the fixed point theorem on a cone and monotone iterative technique, the existence and multiplicity of the positive radial solutions to a class of quasilinear elliptic equations are considered. Also, using the monotone iteration method the authors deal with the boundary value problem as the nonlinear term f(t,u) increases in u. Related Articles | Metrics

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A WEIGHTED ESTIMATE OF THE HORMANDER MULTIPLIER ON THE HEISENBERG GROUP Liu Mingju; Lu Shanzhen Acta mathematica scientia,Series B. 2006, 26 (1):  134-144.  DOI: 10.1016/S0252-9602(06)60035-0 Abstract ( 1087 )   RICH HTML PDF (170KB) ( 1353 )   Save In this article, the authors prove the weighted boundedness of Hormander-type multiplier on the Heisenberg group. Related Articles | Metrics

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LINEAR SINGULAR INTEGRAL EQUATION ON DOMAINS COMPOSED BY BALLS Huang Yusheng; Lin Liangyu Acta mathematica scientia,Series B. 2006, 26 (1):  145-151.  DOI: 10.1016/S0252-9602(06)60036-2 Abstract ( 1072 )   RICH HTML PDF (149KB) ( 1067 )   Save For domains composed by balls in Cn, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smooth lower dimensional edges on the boundary of the domain. Related Articles | Metrics

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MULTIPLICITY RESULTS FOR THE TWO-POINT BOUNDARY VALUE PROBLEMS AT RESONANCE Su Jiabao; Li Hong Acta mathematica scientia,Series B. 2006, 26 (1):  152-162.  DOI: 10.1016/S0252-9602(06)60037-4 Abstract ( 1086 )   RICH HTML PDF (153KB) ( 1273 )   Save In this article several existence theorems on multiple solutions for the two-point boundary value problem with resonance at both infinity and zero are proved. Related Articles | Metrics

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LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS Jia Yueling; Li Hailiang Acta mathematica scientia,Series B. 2006, 26 (1):  163-178.  DOI: 10.1016/S0252-9602(06)60038-6 Abstract ( 1277 )   RICH HTML PDF (190KB) ( 1403 )   Save A one-dimensional quantum hydrodynamic model (or quantum Euler-Poisson system) for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of the steady-state solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity. Related Articles | Metrics

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THE AVALANCHE DYNAMICS IN RANDOM NEAREST NEIGHBOR MODELS OF EVOLUTION WITH INTERACTION STRENGTH Jia Wu; Fan Wentao Acta mathematica scientia,Series B. 2006, 26 (1):  179-187.  DOI: 10.1016/S0252-9602(06)60039-8 Abstract ( 1029 )   RICH HTML PDF (172KB) ( 1216 )   Save A generalized Bak-Sneppen model (BS model) of biological evolution with interaction strength $\theta$ is introduced in d-dimensional space, where the "nearest neighbors" are chosen among the 2d neighbors of the extremal site, with the probabilities related to the sizes of the fitnesses. Simulations of one- and two-dimensional models are given. For given $\theta>0$, the model can self-organize to a critical state, and the critical threshold fc(\theta)$ decreases as $\theta$ increases. The exact gap equation depending on $\theta$ is presented, which reduces to the gap equation of BS model as $\theta$ tends to infinity. An exact equation for the critical exponent $\gamma(\theta)$ is also obtained. Scaling relations are established among the six critical exponents of the avalanches of the model. Related Articles | Metrics

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ON A LEMMA OF DIPERNA AND CHEN Ding Xiaqi Acta mathematica scientia,Series B. 2006, 26 (1):  188-192.  DOI: 10.1016/S0252-9602(06)60040-4 Abstract ( 943 )   RICH HTML PDF (115KB) ( 990 )   Save This note gives an explicit lower bound of the function $\varphi(t)$ in the lemma of DiPerna and Chen and some remarks. Related Articles | Metrics