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ON THE GENERAL k-TH KLOOSTERMAN SUMS AND ITS FOURTH POWER MEAN

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Chinese Annals of Mathematics,Series B 2004年第1期25卷 97-102页

作者： LIUHONGYAN ZHANGWENPENG departmentofmathematics NorthwestUniversityXi＇an710069China departmentofmathematics NorthwestUniversityXi＇an710069China.

The main purpose of this paper is to study the asymptotic property of the fourth power mean of the general k-th Kloosterman sums, and give an interesting asymptotic formula.

关键词：广义k阶KLOOSTERMAN和幂平均渐近公式 Dirichlet特征

3D couette flow of dusty fluid with transpiration cooling

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第2期8卷 313-322页

作者： GOVINDARAJAN A. RAMAMURTHY V. SUNDARAMMAL K. departmentofmathematics SRMUniversity Kattankulathur603203India

The couette dusty flow between two horizontal parallel porous flat plates with transverse sinusoidal injection of the dusty fluid at the stationary plate and its corresponding removal by constant suction through the plate in uniform motion was analyzed. Due to this type of injection velocity the dusty flow becomes 3D. Perturbation method is used to obtain the expressions for the velocity and temperature fields of both the fluid and dust. It was found that the velocity profiles of both the fluid and dust in the main flow direction decrease with the increase of the mass concentration of the dust particles, and those in cross flow direction increase with an increase in the mass concentration of the dust particles up to the middle of the channel and thereafter decrease with increase in mass concentration of the dust particles. The skin friction components Tx and Tz in the main flow and transverse directions respectively increase with an increase in the mass concentration of the dust particles (or) injection parameter. The heat transfer coefficient decreases with the increase of the injection parameter and increases with the increase in the mass concentration of the dust particles.

关键词：粉尘颗粒物摩擦力多相流流体力学

ON THE ERROR ESTIMATES FOR THE ROTATIONAL PRESSURE-CORRECTION PROJECTION SPECTRALMETHODS FOR THE UNSTEADY STOKES EQUATIONS

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Journal of Computational Mathematics 2005年第3期23卷 285-304页

作者： Feng-huiHuang departmentofmathematics XiamenUniversityXiamen361005China

This paper provides an analysis of the rotational form of the pressure-correction methods by spectral approximations for the unsteady Stokes equations. Error estimates in finite time for the fully discrete case are given. Numerical experiences using both spectral and spectral element methods are carried out to confirm the theoretical results.

关键词： Stokes equations Projection methods Spectral methods

GENERALIZED LAGUERRE APPROXIMATION AND ITS APPLICATIONS TO EXTERIOR PROBLEMS

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Journal of Computational Mathematics 2005年第2期23卷 113-130页

作者： Ben-yuGuo JieShen Cheng-longXu departmentofmathematics ShanghaiNormalUniversityandDivisionofComputationalScienceofE-instituteofShanghaiUniversitiesShanghai200233China departmentofmathematics PurdueUniversityUSA DepartmentofAppliedMathematics TongjiUniversityShanghai200092China

Approximations using the generalized Laguerre polynomials are investigated in this paper. Error estimates for various orthogonal projections are established. These estimates generalize and improve previously published results on the Laguerre approximations. As an example of applications, a mixed Laguerre-Fourier spectral method for the Helmholtz equation in an exterior domain is analyzed and implemented. The proposed method enjoys optimal error estimates, and with suitable basis functions, leads to a sparse and symmetric linear system.

关键词： Generalized Laguerre polynomials Exterior problems Mixed Laguerre-Fourier spectral method

MAXIMUM GENUS,INDEPENDENCE NUMBER AND GIRTH

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Chinese Annals of Mathematics,Series B 2000年第1期21卷 77-82页

作者： HUANGYUANQIU LIUYANPEI departmentofmathematics NormalUniversityofHunanChangsha410081China. departmentofmathematics NorthernJiaotongUniversityBeijing100044China.

It is known (for example see [2]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, the authors establish an upper bound on the Betti deficiency in terms of the independence number as well as the girth of a graph, and thus use the formulation in [2] to translate this result to lower bound on the maximum genus. Meantime it is shown that both of the bounds are best possible.

关键词：围长极大亏格独立数图形

ASYMPTOTIC STABILITY OF RUNGE-KUTTA METHODS FOR THE PANTOGRAPH EQUATIONS

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Journal of Computational Mathematics 2004年第4期22卷 523-534页

作者： Jing-junZhao Wan-rongCao Ming-zhuLiu departmentofmathematics HarbinInstituteofTechnologyHarbin150001China)

This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay.{x′(t)+Bxd(t)+Cx′(qt)+Dx(qt)=0,t>0,x(0)=X0,}where B, C, D∈C^d×d, q∈(0, 1), and B is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient conditions for the asymptotic stability of the zero solution. Furthermore, we focus on the asymptotic stability behavior of Runge-Kutta method with variable stepsize. It is proved that a Lstable Runge-Kutta method can preserve the above-mentioned stability properties.

关键词： Neutral delay differential equations

ON THE EXISTENCE OF POSITIVESOLUTIONS OF AN ELLIPTICBOUNDARY VALUE PROBLEMON THE EXISTENCE OF POSITIVESOLUTIONS OF AN ELLIPTICBOUNDARY VALUE PROBLEM

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Chinese Annals of Mathematics,Series B 2000年第4期21卷 499-510页

作者： LIUZHAOLI LIFUYI departmentofmathematics ShandongUniversityJinan250100China. departmentofmathematics ShanxiUniversityTaiyuan030006China.

Using variational method, the authors get an existence result for positive solutions of a superlinear elliptic boundary value problem without assuming the P.S. condition. To prove the results in this paper, the author... 详细信息

关键词：存在性正解椭圆边界值问题变分法

AN IMPLICIT SCHEME FOR INCOMPRESSIBLE LBGK MODEL

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Journal of Hydrodynamics 2005年第3期17卷 330-337页

作者： DURui SHIBao-chang WANGGuang-chao LIUHong-juan departmentofmathematics HuazhongUniversityofScienceandTechnologyWuhan430074China departmentofmathematics HuazhongUniversityofScienceandStateKeyLaboratoryofCoalCombustionHuazhongUniversity430074China／／TechnologyWuhan430074ChinaofScienceandTechnologyWuhan

In this paper, an implicit scheme (also called the θ method) was proposed for the Lattice Bhatager-Gross-Krook (LBGK) model simulating incompressible flows. The new parameter θ made the model more flexible. Through the Chapman-Enskog procedure the impressible Navie-Stokes equations could be recovered with the coupled kinetic viscosity. Boundary conditions were treated briefly and it kept the numerical accuracy of the Lattice Boltzmann Method (LBM). The two-dimensional Poiseuille flow was simulated with different values of the parameters. It is found that the numerical accuracy and stability of the implicit scheme can be improved if some adaptable parameters are chosen.

关键词： Lattice Boltzmann Method (LBM) implicit scheme θ-Lattice Bhatager-Gross-Krook (LBGK) model Poiseuille flow

Multi-linear Variable Separation Approach to Solve a （2＋1）-Dimensional Generalization of Nonlinear Schrodinger System

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Communications in Theoretical Physics 2005年第6期43卷 965-968页

作者： SHENShou-Feng ZHANGJun PANZu-Liang departmentofmathematics ZhejiangUniversityofTechnologyHangzhou310014China departmentofmathematics ZhejiangUniversityHangzhou310027China

By using a Backlund transformation and the multi-linear variable separation approach, we find a new generalsolution ofa (2+1)-dimensional generalization of the nonlinear Schrodinger system. The new 'universal' formula... 详细信息

关键词：相干结构非线性施荣丁格尔函数偏微分方程变量分离路径