非线性抛物型偏积分微分方程的H1-Galerkin 混合有限元方法

收稿给出一类非线性抛物型偏积分微分方程的H1-Galerkin混合有限元方法.给出了一维空间的半离散、全离散格式及最优阶误差估计,并将该方法推广到二维和三维空间.     

两类非线性双曲型方程组有限元方法的误差估计

对两类非线性双曲型方程组给出了全离散有限元逼近格式,并得到最优H^1模和L^2模误差估计。     

一类三维变动区域上的非线性抛物型方程之全离散有限元形式

1 引言 1986年,L.Cermak和M.Zlamal研究了半导体器件中杂质的重新分布,对具有活动边界的二维非线性扩散问题。给出在时间方向上是一阶精度的全离散有限元格式。证明了格式最优的H~1模和次最优的L~2模估计。1989年.P.Lesaint和R.Touzani对一维变动区域上的热传导方程。经过坐标变换,给出了在固定区域上的全离散有限元格式和最优的L~2模估计。1990年,梁国平和陈志明利用时空有限元,给出了变动区域上线性抛物型的方程的全离散变网格有限元格式。证明了最优的L~2收敛性。本文考虑了一类具有活动边界的三维     

带广义边界条件的四阶抛物型方程的混合间断时空有限元法

构造具有广义边界条件的四阶线性抛物型方程的混合间断时空有限元格式,利用混合有限元方法将高阶方程降阶,利用空间连续而时间允许间断的时空有限元方法离散方程,证明了离散解的存在唯一性,稳定性和收敛性,并给出数值算例验证了方法的有效性.     

一类非线性对流占优抛物型方程组的特征交替方向有限元方法

对一类非线性对流占优抛物型方程组建立时间离散的Patch逼近特征交替方向有限元格式 ,并给出了最优阶的L2 和H1模误差估计 .     

几乎不可压线弹性问题的新的Uzawa型自适应有限元方法

本文针对几乎不可压线弹性问题设计新的Uzawa型自适应有限元方法,该方法可克服"闭锁"现象·通过引入"压力"变量将弹性问题转化为一个鞍点系统,对该系统将Uzawa型迭代法和自适应有限元方法相结合,建立了Uzawa型自适应有限元方法,并给出了该算法的收敛性.该算法采用低阶协调有限元通近空间变量,选取的有限元空间对无需满足离散的BB条件.最后,数值算例验证了理论结果的正确性.     

双曲型方程的一类各向异性非协调有限元逼近

在各向异性条件下,讨论了双曲型方程的一类非协调有限元逼近,给出了半离散格式下的最优误差估计.同时通过新的技巧和精细估计得到了一些超逼近性质和超收敛结果.     

离散哈密顿系统极限圆型及非极限圆型的判定

讨论了高阶离散哈密顿系统的亏指数问题,得到了该系统是极限圆型的充要条件,并且在此基础上给出了半退化型和Dirac型离散哈密顿系统是非极限圆型的判别准则.     

常用离散型随机变量的高阶原点矩

对离散型随机变量的高阶矩进行了研究,给出了几类离散型随机变量的高阶原点矩的统一递推公式,得到了离散型随机变量的高阶原点矩的形式特征.     

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.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

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.     

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.     

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.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

正~~     

An alternative mathematical algorithm for the photo- and videokeratoscope

Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography.