半导体问题的向后差分配置法及误差分析

Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.     

ALTERNATING-DIRECTION MULTISTEP PRECONDITIONED ITERATIVE METHODS FOR SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION

The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. Electric potential equation is approximated by mixed finite element method, concentration and heat-conduction equations are approximated by Galerkin alternating-direction multistep methods. Error estimates of optimal order in L2 are demonstrated.     

On the Blaschke isoparametric hypersurfaces in the unit sphere

Given an immersed submanifold x ： M^M → S^n in the unit sphere S^n without umbilics, a Blaschke eigenvalue of x is by definition an eigenvalue of the Blaschke tensor of x. x is called Blaschke isoparametric if its Mobius form vanishes identically and all of its Blaschke eigenvalues are constant. Then the classification of Blaschke isoparametric hypersurfaces is natural and interesting in the MSbius geometry of submanifolds. When n = 4, the corresponding classification theorem was given by the authors. In this paper, we are able to complete the corresponding classification for n = 5. In particular, we shall prove that all the Blaschke isoparametric hypersurfaces in S^5 with more than two distinct Blaschke eigenvalues are necessarily Mobius isoparametric.     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE NONLINEAR HEAT-CONDUCTION EQUATION AND ITS APPLICATION

1 IntroductionIn the heat-conduction equationp is the density,c is the specific heat,k is the thermal conductivityLet u = w -- wco be therelative temperature, where woo is the environmental temperature. In many cases, the thermalconductivity k is dependent of the temperature,forrexample, the heat-conduction of electron iuthe plasma body and the radiation heat-conduction in the high temperature,k(u) = uoum--' (m > 1).Assume that p, c are constants, then the equation (1.1) can be written asWe c…     

AN A.D.I.GALERKIN METHOD FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION USING PATCH APPROXIMATION

An A. D. I. Galerkin scheme for three-dimensional nonlinear parabolic integro-differen-tial equation is studied. By using alternating-direction, the three-dimensional problem is reduced to a family of single space variable problems, the calculation is simplified; by using a local approxima-tion of the coefficients based on patches of finite elements, the coefficient matrix is updated at each time step; by using Ritz-Volterra projection, integration by part and other techniques, the influence coming from the integral term is treated; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity is treated. For both Galerkin and A. D. I. Galerkin schemes the con-vergence properties are rigorously demonstrated, the optimal H~1-norm and L~2-norm estimates are obtained.     

TRAVELING WAVE SOLUTIONS AND THEIR STABILITY OF NONLINEAR SCHRDINGER EQUATION WITH WEAK DISSIPATION

In this paper,several new constant-amplitude and variable-amplitude wave solutions(namely,traveling wave solutions) of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique.     

Bohr Inequality for Multiple Op erators

An absolute value equation is established for linear combinations of two operators. When the parameters take special values, the parallelogram law of operator type is given. In addition, the operator equation in literature [3] and its equivalent deformation are obtained. Based on the equivalent deformation of the operator equation and using the properties of conjugate number as well as the operator, an absolute value identity of multiple operators is given by means of mathematical induction. As Corollaries, Bohr inequalities are extended to multiple operators and some related inequalities are reduced to, such as inequalities in [2] and [3].     

Definite Conditions and Asymptotic Solution of One Nonlinear Partial Differential Equation in Morphogenesis

One reaction-diffusion equationhas been presented in the study of Morphogenesis.In this paper,reasonable de-finite conditions of the equation are proposed and the asymptotic form of itssolution is obtained by using perturbation method.So the existence of solution ofthis probtem is solved.     

Analysis of an Implicit Finite Difference Scheme for Time Fractional Diffusion Equation

Time fractional diffusion equation is usually used to describe the problems involving non-Markovian random walks. This kind of equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α∈(0, 1). In this paper, an implicit finite difference scheme for solving the time fractional diffusion equation with source term is presented and analyzed, where the fractional derivative is described in the Caputo sense. Stability and convergence of this scheme are rigorously established by a Fourier analysis. And using numerical experiments illustrates the accuracy and effectiveness of the scheme mentioned in this paper.     

The existence of Silnikov''''s orbits in one coupled Duffing equation

The existence of Silnikov's orbits in one coupled Duffing equation is discussed by using the fiber structure of invariant manifold and high-dimensional Melnikov's method. Example and numerical simulation results are also given to demonstrate the theoretical analysis.     

热传导方程的小波解法

本文利用微分算子的小波表示，讨论一维热传导方程初值问题的Daubechies小波解，给出此问题的显式离散格式。由于小波在时间和频率上的局部性，此方法特别适用于有奇异解的热传导方程，逼近精度高，而且没有发生解的振荡现象。     

单位球面S~6中的Blaschke等参超曲面

单位球面中的一个无脐点浸入子流形称为Blaschke等参子流形如果它的Mbius形式恒为零并且所有的Blaschke特征值均为常数.维数m4的Blaschke等参超曲面已经有了完全的分类.截止目前,Mbius等参超曲面的所有已知例子都是Blaschke等参的.另一方面,确实存在许多不是Mbius等参的Blaschke等参超曲面,它们都具有不超过两个的不同Blaschke特征值.在已有分类定理的基础上,本文对于5维Blaschke等参超曲面进行了完全的分类.特别地,我们证明了S6中具有多于两个不同Blaschke特征值的Blaschke等参超曲面一定是Mbius等参的,给出了此前一个问题的部分解答.     

Non-linear seismic response of concrete gravity dams to near-fault ground motions including dam-water-sediment-foundation interaction

This study focuses on non-linear seismic response of a concrete gravity dam subjected to near-fault and far-fault ground motions including dam-water-sediment-foundation rock interaction. The elasto-plastic behavior of the dam concrete is idealized using Drucker–Prager yield criterion based on associated flow rule assumption. Water in the reservoir is represented by 9-noded isoparametric quadrilateral fluid finite elements while the dam, the foundation rock and the sediment layer are modeled by using 8-noded isoparametric quadrilateral solid finite elements. The program NONSAP modified for elasto-plastic analysis of fluid-structure systems using the Lagrangian fluid finite element is employed in the response calculations. The fluid element includes the effects of surface waves and sloshing behavior of fluids. Non-linear seismic analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. The results obtained from linear and non-linear analyses are compared with each other.     

R~6中的Laguerre等参超曲面的分类

若超曲面的Laguerre形式为零且Laguerre第二基本形式的特征值(称为Laguerre主曲率)为常数,则称超曲面为Laguerre等参超曲面.对R~6中的Laguerre等参超曲面进行了研究,得到了分类定理.     

复射影空间的等参子流形

本文给出了复射影空间Ｐ＿ｎ（Ｃ）上的等参映射定义，并证明了等参映射ｆ在Ｈｏｐｆ主丛π：Ｓ￣（２ｎ＋１）→Ｐ＿ｎ（Ｃ）下的水平提升为Ｓ￣（２ｎ＋１）的等参映射。同时，利用对称空间的表示给出了Ｐ＿ｎ（Ｃ）上等参子流形的例子．     

一组适合于带纵向裂纹柱体圣维南扭转的等参数元素

本文给出一组新的适合于带纵向裂纹柱体圣维南扭转的等参数元素,它们分别是八结点等参数元素、在裂纹尖端具有r-1/2奇异性的“1/4”八结点等参数元素及八结点过渡元素.利用这些元素,对含有径向纵裂纹的圆柱体进行了圣维南扭转计算.计算结果表明,本文给出的等参数元素有较高的精度、较好的收敛性及快的收敛速度,同时还具有程序简单、省机时等优点,所以特别适合于实际的工程计算.     

Gradient map of isoparametric polynomial and its application to Ginzburg-Landau system

In this note, we study properties of the gradient map of the isoparametric polynomial. For a given isoparametric hypersurface in sphere, we calculate explicitly the gradient map of its isoparametric polynomial which turns out many interesting phenomenons and applications. We find that it should map not only the focal submanifolds to focal submanifolds, isoparametric hypersurfaces to isoparametric hypersurfaces, but also map isoparametric hypersurfaces to focal submanifolds. In particular, it turns out to be a homogeneous polynomial automorphism on certain isoparametric hypersurface. As an immediate consequence, we get the Brouwer degree of the gradient map which was firstly obtained by Peng and Tang with moving frame method. Following Farina's construction, another immediate consequence is a counterexample of the Brézis question about the symmetry for the Ginzburg-Landau system in dimension 6, which gives a partial answer toward the Open problem 2 raised by Farina.