两层密度分层流体毛细重力波三阶Stokes波解

以小振幅波理论为基础,利用摄动方法研究了两层密度成层状态下的毛细重力波,求得了两层密度成层状态下各层流体速度势的三阶解及毛细重力波波面位移的三阶Stokes波解.结果表明:三阶方程的解均受到表面张力的影响.三阶Stokes波解描述了毛细重力波的三阶非线性修正,波速不仅取决于波数和各层流体的厚度,而且还与波幅及表面张力有关.     

S.Earnshow的早期孤立波研究及其重要影响

通过文献考证方法分析考察S.Earnshow 1845年关于孤立波理论的论文.Earnshaw以罗素试验结果为基本假设,建立了一个虽有缺陷但却是Stokes早期有关研究的出发点的非线性理论.Earnshaw的崭新思路昭示了孤立波理论研究的正确方向,并为一般科学理论研究提供了值得借鉴的思想方法.     

有流存在下三层密度分层流体毛细重力波二阶Stokes波解

以小振幅波理论为基础,利用摄动方法研究了有背景流场存在时三层密度分层流体的毛细重力波,给出了三层成层状态下各层流体速度势的二阶渐近解及毛细重力波面位移的二阶Stokes波解.结果表明:一阶解及二阶解除了依赖于各层流体的厚度及密度,也依赖于表面张力和各层流体的背景流场.     

非定常Stokes方程的全离散稳定化有限元格式

本文研究二维非定常Stokes方程全离散稳定化有限元方法.首先给出关于时间向后一步Euler半离散格式,然后直接从该时间半离散格式出发,构造基于两局部高斯积分的稳定化全离散有限元格式,其中空间用P_1—P_1元逼近,证明有限元解的误差估计.本文的研究方法使得理论证明变得更加简便,也是处理非定常Stokes方程的一种新的途径.     

有限水深中的极限非线性波

本文用参数优化方法.计算出有限水深中的极限Stokes波.计算的精度高,效率也高.从而进一步证明了用优化手段求stokes波动解里的待定系数是一个合理的、行之有效的方法.     

半空间MHD方程组弱解的L~2衰减

该文利用Stokes算子的谱表示及能量估计的方法研究半空间MHD方程组初边值问题弱解的L~2衰减.     

两种叠合流体间界面波的非线性调制

本文用多重尺度法研究等深度及固定壁面的两种叠合流体间界面上的重力-表面张力波的缓慢调制,推出第一阶的调制波的演化由非线性Schr?dinger方程所描述,然后讨论了所谓的“Stokes波”的稳定性.     

Stokes型积分-微分方程的Crouzeix-Raviart型非协调三角形各向异性有限元方法

在半离散格式下.研究了Stokes型积分一微分方程的Crouzeix-Raviart型非协调三角形各向异性有限元方法,在不需要传统Ritz-Volterra投影下,通过辅助空间等新的技巧得到了与传统有限元方法相同的误差估计.     

有流存在下两层密度分层流体毛细重力波的三阶Stokes波解

以小振幅波理论为基础,利用奇异摄动方法研究了有背景流存在下两层密度成层状态下的毛细重力波,求得了两层密度成层状态下各层流体速度势的三阶解及毛细重力波波面位移的三阶Stokes波解,并讨论了毛细重力波的kelvin-Helmholtz的不稳定性.结果表明在有流存在的情况下,两层密度成层流体毛细重力波的一阶渐近解、频散关系,二阶渐近解及三阶渐近解不仅依赖于各层流体的厚度和密度,也依赖于表面张力和各层流体的背景流流场;毛细重力波的三阶解描述了背景流场与毛细重力波之问的三阶非线性相互作用.对于给定的波数k(实数)毛细重力波可能出现kelvin-Helmholtz不稳定性.     

在一个半无穷柱体上的非标准Stokes流体方程的二择一问题

考虑了定义在半无限柱体上的非标准Stokes流体方程的初边值问题,其中在柱体的有限端施加非线性边界条件,在柱体的侧面上满足零边界条件.在初始条件中参数的适当范围内,利用微分不等式技术,得到了Stokes流体方程的二择一结果.在衰减的情况下,证明了"全能量"可以由已知数据项控制.     

Study of the 'teaching system' according to systems theory

The traditional triadic 'Teaching System' (the teacher, the student and mathematics) and the new quaternary version (the teacher, the student, mathematics and new technologies), are studied according to Systems Theory. Systems Theory is described and the model of the traditional 'Teaching System' and that of the new system are analysed with the aid of this theory; that is the structure of each system (elements, interactions) and its function are described. Finally, comments are made about the application of the new system on didactic, on the one hand, and the philosophical background of the incorporation of the fourth element (new technologies) in the traditional system, on the other.     

Li'enard型系统全局稳定性的充要条件

本文研究Li'enard型系统x=(h(y)-F(x)), y=-g(x)的全局稳定性问题.利用Filippov变换和一些新的方法建立了系统为全局稳定的系列充要条件.     

Banach空间中关于(H,η)-增生算子的一类新变分包含组问题

In this paper,we first introduce a new class of generalized accretive operators named(H,η)-accretive in Banach space.By studying the properties of(H,η)-accretive,we extend the concept of resolvent operators associated with m-accretive operators to the new(H,η)-accretive operators.In terms of the new resolvent operator technique,we prove the existence and uniqueness of solutions for this new system of variational inclusions.We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.     

Solving soliton equations with self-consistent sources by method of variation of parameters

Starting from the solutions of soliton equations and corresponding eigenfunctions obtained by Darboux transformation, we present a new method to solve soliton equations with self-consistent sources (SESCS) based on method of variation of parameters. The KdV equation with self-consistent sources (KdVSCS) is used as a model to illustrate this new method. In addition, we apply this method to construct some new solutions of the derivative nonlinear Schrödinger equation with self-consistent sources (DNLSSCS) such as phase solution, dark soliton solution, bright soliton solution and breather-type solution.     

Block Transformation of Hybrid Cellular Automata

By introducing a sequence-block transformation and vector-block transformation, we explore the dynamical properties of hybrid cellular automation (HCA) and hybrid cellular automation with memory (HCAM) in the framework of symbolic dynamics. As the local evolution rules of HCA and HCAM are not-uniform, the new uniform cellular automata (CAs) with multiple states are constructed by specifical the block transformations. Furthermore, because the new CA rules are topologically conjugate with the originals, the complex dynamics of the HCA and HCAM rules can be investigated via the new CA rules.     

Liénard型系统全局稳定性的充要条件

本文研究Lienard型系统x=φ（h（y）-F（x））,y=－g（x）的全局稳定性问题．利用Filippov变换和一些新的方法建立了系统为全局稳定的系列充要条件．     

Comparison of V‐cycle multigrid method for cell‐centered finite difference on triangular meshes

We consider a multigrid algorithm (MG) for the cell centered finite difference scheme (CCFD) on general triangular meshes using a new prolongation operator. This prolongation is designed to solve the diffusion equation with strongly discontinuous coefficient as well as with smooth one. We compare our new prolongation with the natural injection and the weighted operator in Kwak, Kwon, and Lee ( 8 ) and the behaviors of these three prolongation are discussed. Numerical experiments show that (i) for smooth problems, the multigrid with our new prolongation is fastest, the next is the weighted prolongation, and the third is the natural injection; and (ii) for nonsmooth problems, our new prolongation is again fastest, the next is the natural injection, and the third is the weighted prolongation. In conclusion, our new prolongation works better than the natural injection and the weighted operator for both smooth and nonsmooth problems. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

小周期型复合材料稳态热传导问题的一种双尺度渐近展开收敛性分析

给出一类具有某种对称性小周期复合材料稳态热传导问题解的渐近表示方法.区别于传统多尺度计算方法,将计算过程中需要求解的关于单胞Q的H_per¹(Q)周期边值问题改为齐次边值问题,这样数值方法求解时协调元空间容易构造;另一方面传统的多尺度渐近解不满足原始问题的边界条件,新构造的渐近形式不仅满足原始问题的物理边界条件,同时保持一定的收敛阶,更能被工程上所接受.     

Q-截集,Q-截云和模糊集的运算

通过引进Q-截集的概念,我们得到了新的分解定理和表现定理。利用Q-截集和随机集落影理论,导出了模糊集的运算、多值蕴涵算子和双蕴涵算子,特别是导出了模糊条件语句的逻辑算子。     

Crowns and centralizers of chief factors of finite groups

We give a new proof of Vaserstein’s Pre-stabilization theorem. This theorem describes GL_n (A) ? E(A) when n is just below the stable range for GL_m (A)/E_m (A) The new proof works only for commutative rings (or ideals in such rings) but it does not need assumptions on Krull dimension, like the old proofs did. All one needs is the relevant stable range con-dition. The new ideas in the proof come from Vaserstein’s recent treatment of the case n = 2. (See preceding paper).