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THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 1998年第5期16卷 437-444页

作者： (department of mathematics, Peking university, beijing 100871, china) 北京大学数学系北京

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

L~∞ CONVERGENCE OF TRUNC ELEMENT FOR THE BIHARMONIC EQUATION

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Journal of Computational mathematics 1997年第1期15卷 14-22页

作者： M. Wang(department of mathematics, beijing university, beijing, china) 北京大学数学系北京

The paper considers the L∞ convergence for TRUNC finite elements solving the boundary value problems of the biharmonic equation. The nearly optimal L∞ estimates for the error of first order derivatives are *** TRUNC plate element is proposed and developed by Argyris et al.. The numerical experiences show that the element has very good .***,[1l2]. The mathematicalproof of convergence of the TRUNC element is given by Shi Zong-ci in paper [3]. Thispaper will consider the L~∞ convergence for the TRUNC plate element.

关键词：双谐波方程边值问题收敛性有限元法

CONVERGENCE OF THE POINT VORTEX METHODS FOR EULER EQUATION ON HALF PLANE

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Journal of Computational mathematics 1996年第3期14卷 213-222页

作者： P.W. Zhang(department of mathematics, beijing university, beijing, china) 北京大学数学系北京

In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condition.... 详细信息

关键词： Math CONVERGENCE OF THE POINT VORTEX METHODS FOR EULER EQUATION ON HALF PLANE Zhang

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2 1. department of mathematics, beijing Normal university, beijing 100875, china 2. Institute of Applied physics and Computational mathematics, beijing 100080, china department of mathematics Beijing Normal University Beijing China Institute of Applied physics and Computational mathematics Beijing China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS OF SEVERAL VARIABLES

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Acta Mathematica Scientia 2004年第2期24卷 228-234页

作者：马万房艮孙 departmentofmathematics BeijingNormalUniversityBeijing100875China

This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic So... 详细信息

关键词： Integral equations direct methods anisotropic sobolev classes

Effective-Medium Theory for Two-Phase Random Composites with and Interfacial Shell

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Journal of Materials Science & Technology 2000年第4期16卷 367-369页

作者： Qingzhong XUE (department of physics, university of petroleum, Dongying 257062, china) department of physics University of Petroleum Dongying 257062 China

According to the Bruggeman theory and Maxwell-Garnett theory, the effective dielectric constant of a two-phase random composite with an interfacial shell is presented. The nonlinearity of the theory is obvious. Especially, the theory is suited to study the dielectric properties of two-phase random composites with a spherical interfacial shell. The theoretical results on dielectric properties of polystyrene-barium titanate composites with an interfacial shell are in good agreement with experimental data.

关键词： Zhang Effective-Medium Theory for Two-Phase Random Composites with and Interfacial Shell Wang

Wave coupling between the Tianshan orogen and the deformations in its south and north foreland basins in Cenozoic

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Science china Earth Sciences 2008年第S2期51卷 61-69页

作者： CHEN ShuPing1,2,TANG LiangJie & YU YiXin1,2 1 State Key Laboratory of petroleum Resource and Prospecting,china university of petroleum,beijing 102.49,china 2.department of Geoscience,china university of petroleum,beijing 102.49,china State Key Laboratory of petroleum Resource and Prospecting China University of Petroleum Beijing China department of Geoscience China University of Petroleum Beijing China

Attention has been paid to the deformations in the south and north foreland basins of the Tianshan Mountains and their relations to the tectonic movements of the mountains. Based on the seismic data interpretation and field work,the tectonic features,tectonic styles,controlling factors of deformation,deformation time,and their relationships in the three tectonic units were comparably studied. The Ce-nozoic deformations in the two foreland basins were characterized by zonation from south to north,segmentation from west to east,and layering from deep to shallow. The tectonic styles are compres-sive ones,including both basement-involved and cover-detaching. The two foreland basins underwent several times of deformation in Cenozoic and the deformations were transmitted from the Tianshan orogen to the inner basin. The deformation dynamics of the south and north foreland basins of the Tianshan Mountains can be represented by dynamics of orogenic wedges. In terms of the deformations of the wedges with wave-like features,the concept of a wave orogenic wedge was put forward,and a double wave orogenic wedge model was established.

关键词： Tianshan orogen basin-mountain coupling tectonics wave orogenic wedge

THE FUNCTION d_k(n) AT CONSECUTIVE INTEGERS

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Chinese Annals of mathematics,Series B 1999年第4期20卷 473-478页

作者： MENG ZAIZHAO(department of mathematics, Peking university, beijing 100871, china) department of mathematics Peking University Beijing 100871 China

Let dk(n) denote the k-fold iterated divisor function (k ≥ 2). It is proved that for sufficiently large x) dk(n) = dk(n + 1) holds for >> x(log log x)-3 integers n ≤x.

关键词： Divisor function Multiplicative function Congruence

Density-functional formula for strongly correlated systems

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Progress in Natural Science:Materials International 2005年第5期15卷 395-401页

作者： WANG Huaiyu1*, HAN Rushan2 and CHEN Nanxian1(1. department of physics, Tsinghua university, beijing 100084, china 2. department of physics, Peking university, beijing 100871, china) Dept. of Phys. Tsinghua Univ. Beijing 100084 China Dept. of Phys. Peking Univ. Beijing 100871 China

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.

关键词： density-functional theory strongly correlated systems doubly-occupied orbital two-particle wave function self-consistent equations.