用区域分解法求不可压N-S方程的差分解

§1.引言 对不可压小粘性流的数值解,[1]和[2]用奇异摄动观点提出了一个区域分解法.从常微分方程(组)的奇异摄动问题出发,解分解为外部解加边界修正解(以下简称为修正解).外部解的边界条件有:给定(原边界条件)、待定(用原边界条件和修正解)和延拓类.修正解的边界条件有:给定(用原边界条件和外部解延拓)渐近(在边界层外缘)和待定     

具有球对称结构的相对论欧拉方程组稳态解的存在性

对于等温气体,作者将考虑具有球对称结构的相对论欧拉方程组经典稳态解(定理1.1)和弱稳态解(定理1.2)的存在性.通过求解两个常微分方程以及比较马赫数M和1的关系,定理1.1证明了相对论欧拉方程组经典稳态解的存在性.在一个C~(2,α),α∈(0,1)稳态背景解的扰动下,定理1.2将证明高维球对称跨音速(双曲-椭圆)解的存在性.     

Riccati方法与微分方程的渐近积分

考虑二阶常微分方程x″ f(t)x=0,t≥a,(1)假设应用Riccati方法得到方程(1)的主解(principal solution)的一个渐近积分并研究其副解(nonprincipal solutions)的三种不同的渐近性质.主要结果如下:定理1 若(Ⅰ)成立,则方程(1)有解x_1满足及另一解x_2满足x_2(t)=t[1 o(1)]. 反之,若方程(1)有解x(t)→1,t→∞,则(Ⅰ)成立. 定理2 设(Ⅰ)成立.(i)若(Ⅱ)成立,则方程(1)有解x_2使x_2’(t)=1 [tF(t) G(t)][1 o(1)] o(1). (ii) 反之,若方程(1)有解x使x’→1,t→∞,则(Ⅱ)成立. 定理3 若(Ⅲ)和(Ⅳ)成立,则方程(1)有解x_1满足(2)及解x_2满足     

TLS问题和LS问题解加权残量的比较

总体最小二乘(TLS)问题和最小二乘(LS)问题解残量的比较已有多篇文献予以探讨.本文对TLS问题和LS问题解的加权残量进行了比较. 导出了TLS解、改进的LS解及普通LS解加权残量之间的误差界. 从而进一步完善了已有的相关结果.     

一类广义Liénard系统解的有界性

研究了一类广义 Liénard系统dxdt=p(y) -F(x) ,　 dydt=-g(x) (E)解的有界性 .首先获得了系统 (E)存在无界解的两个新的充分条件 ,然后获得系统 (E)所有解正向有界的若干充分条件和充要条件 ,所获结果改进和扩展了文 [1 -2 ]中的相应结果 .     

一类反应扩散方程的行波解

1　引　　言由于反应扩散方程涉及的大量问题来自物理学、化学、生物学和人口动力学中众多的数学模型,因而有广阔的实际背景.其行波解引起了人们的兴趣,行波解是某个常微分方程的解,对某些传播速度,利用几何方法可以建立其解的存在性(见[1][2][3]).在文[4]中J.Canosa讨论了Fisher方程ut=2u2x+u(1-u)(1)行波解的存在性、逼近解和误差估计.所谓方程(1)的行波解是指形为u(x,t)=u(x-ct)=u(z)的解.众所周知,行波解u(x,t)=u(x-ct)=u(z)是方程(1)的行波解的充要条件是d2udz2+cdudz+u(1-u)=0(2)若u(z)是单调有界且不恒为常数,则u(z)叫做(1)的波前…     

一阶脉冲微分方程的周期解(英文)

本文在Banach空间PC(J)上研究了一阶脉冲微分方程的周期解.利用迭代分析法得到了一阶脉冲微分方程周期解的存在唯一性和其解在Banach空间PC(J)上的范数估计.     

N维非线性时滞分数阶微分方程初值问题的全局解

微分方程初值问题全局解的存在性是研究李雅普诺夫意义下稳定性的先决条件。该文旨在研究初值问题(1.10)-(1.11)全局解的存在性.首先得到了初值问题(1.10)-(1.11)局部解的存在性,推广了文献[14]的结果;然后基于得到的延拓定理,证明了初值问题(1.10)-(1.11)全局解的存在性和唯一性.     

复合系统双荷子解的存在性

用不定变分法研究了由Georgi-Glashow(GG)模型和SO(3)规范Skyrme模型所构成的复合(简记为GGS)模型,证明了其既带电荷又带磁荷的类粒子稳态解——双荷子解的存在性.该解是依赖于两个物理参数的径向对称解.最后,给出了解在无穷远处的渐近估计.     

中细柔性圆环壳整体弯曲的一般解及在波纹管计算中的应用(Ⅳ)——U型波纹管的计算

(Ⅳ)是(Ⅰ)的具体应用,讨论了U型波纹管的角向刚度和相应的应力分布.将波纹管的凸面、凹面和环板分开处理,分别应用一般解(Ⅰ)和由其退化而成的环板一般解,使连接点满足表面应力和子午转角连续性条件.所得结果与细环壳解、美国膨胀节制造商协会标准(EJMA)、实验及有限元法进行了分析比较.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by