数学物理学报(英文版)

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A NEW APPROXIMATE INERTIAL MANIFOLD AND ASSOCIATED ALGORITHM

李开泰; 徐忠锋; 杨晓忠

数学物理学报(英文版). 2006 (1): 1-16. DOI: 10.1016/S0252-9602(06)60021-0

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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(h^2k+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(h^2k+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 u_h, u^h, u* be the SG, NG and their approximate solutions respectively, then |u - u_h|₁≤ Ch, |u - u^h|₁ ≤ h², |u -u^*|₁ ≤ Ch³, and h^*≈ h² for NG, h^*_≈ h^3/2 for theirs.

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ASYMPTOTIC APPROXIMATION METHOD AND ITS CONVERGENCE ON SEMI-INFINITE PROGRAMMING

万仲平; 王先甲; 何炬林; 贾世会

数学物理学报(英文版). 2006 (1): 17-24. DOI: 10.1016/S0252-9602(06)60022-2

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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.

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METRIZABILITY OF SPACES AND J.NAGATA'S PROBLEM

高智民

数学物理学报(英文版). 2006 (1): 25-30. DOI: 10.1016/S0252-9602(06)60023-4

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In 1988, J.Nagata raised a problem about metrizability. The present article is an attempt to find a solution to the problem.

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THE MINIMAL OPERATOR AND WEIGHTED INEQUALITIES FOR MARTINGALES

左红亮; 刘培德

数学物理学报(英文版). 2006 (1): 31-40. DOI: 10.1016/S0252-9602(06)60024-6

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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.

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CRITERIA OF STRONG TRANSIENCE FOR OPERATOR-SELF-SIMILAR MARKOV PROCESSES

吴传菊; 张峰; 刘禄勤

数学物理学报(英文版). 2006 (1): 41-48. DOI: 10.1016/S0252-9602(06)60025-8

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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.

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PERMANENCE AND PERSISTENCE OF TIME VARYING LOTKA-VOLTERRA SYSTEMS

刘少平; 廖晓昕

数学物理学报(英文版). 2006 (1): 49-58. DOI: 10.1016/S0252-9602(06)60026-X

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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.

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SEMILINEAR HEMIVARIATIONAL INEQUALITIES WITH STRONG RESONANCE AT INFINITY

Michael Filippakis; Leszek Gasinski; Nikolaos S. Papageorgiou

数学物理学报(英文版). 2006 (1): 59-73. DOI: 10.1016/S0252-9602(06)60027-1

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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.

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FIXED-DESIGN SEMIPARAMETRIC REGRESSION FOR LINEAR TIME SERIES

胡舒合

数学物理学报(英文版). 2006 (1): 74-82. DOI: 10.1016/S0252-9602(06)60028-3

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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.

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GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA

李建全; 马知恩; 周义仓

数学物理学报(英文版). 2006 (1): 83-93. DOI: 10.1016/S0252-9602(06)60029-5

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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 R_c (R_c may not exist). There is a unique endemic equilibrium for R₀>1 or R_c=R₀; there are two endemic equilibria for R_c<R₀<1; and there is no endemic equilibrium for R₀<R_c<1. When R_c 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.

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NUMERICAL ANALYSIS OF QUASICONFORMAL MAPPINGS BY CIRCLE PACKINGS

蓝师义; 戴道清

数学物理学报(英文版). 2006 (1): 94-98. DOI: 10.1016/S0252-9602(06)60030-1

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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.

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OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES

刘爱莲; 吴洪武; 朱思铭; Ronald M. Mathsen

数学物理学报(英文版). 2006 (1): 99-106. DOI: 10.1016/S0252-9602(06)60031-3

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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.

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A RANK THEOREM FOR NONLINEAR SEMI-FREDHOLM OPERATORS BETWEEN TWO BANACH MANIFOLDS

史平; 马吉溥

数学物理学报(英文版). 2006 (1): 107-114. DOI: 10.1016/S0252-9602(06)60032-5

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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.

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THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHRODINGER-POISSON EQUATIONS

郝成春

数学物理学报(英文版). 2006 (1): 115-124. DOI: 10.1016/S0252-9602(06)60033-7

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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.

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EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO CERTAIN QUASILINEAR ELLIPTIC EQUATIONS IN A BALL

汪全珍; 陈祖墀

数学物理学报(英文版). 2006 (1): 125-133. DOI: 10.1016/S0252-9602(06)60034-9

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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.

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A WEIGHTED ESTIMATE OF THE HORMANDER MULTIPLIER ON THE HEISENBERG GROUP

刘明菊; 陆善镇

数学物理学报(英文版). 2006 (1): 134-144. DOI: 10.1016/S0252-9602(06)60035-0

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In this article, the authors prove the weighted boundedness of Hormander-type multiplier on the Heisenberg group.

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LINEAR SINGULAR INTEGRAL EQUATION ON DOMAINS COMPOSED BY BALLS

黄玉笙; 林良裕

数学物理学报(英文版). 2006 (1): 145-151. DOI: 10.1016/S0252-9602(06)60036-2

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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.

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MULTIPLICITY RESULTS FOR THE TWO-POINT BOUNDARY VALUE PROBLEMS AT RESONANCE

苏加宝; 李红

数学物理学报(英文版). 2006 (1): 152-162. DOI: 10.1016/S0252-9602(06)60037-4

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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.

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LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

贾月玲; 李海梁

数学物理学报(英文版). 2006 (1): 163-178. DOI: 10.1016/S0252-9602(06)60038-6

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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.

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THE AVALANCHE DYNAMICS IN RANDOM NEAREST NEIGHBOR MODELS OF EVOLUTION WITH INTERACTION STRENGTH

贾武; 范文涛

数学物理学报(英文版). 2006 (1): 179-187. DOI: 10.1016/S0252-9602(06)60039-8

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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 f_c(\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.

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ON A LEMMA OF DIPERNA AND CHEN

丁夏畦

数学物理学报(英文版). 2006 (1): 188-192. DOI: 10.1016/S0252-9602(06)60040-4

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This note gives an explicit lower bound of the function $\varphi(t)$ in the lemma of DiPerna and Chen and some remarks.

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