并行计算的带有高阶导数的块隐式单步法

本文讨论了一类并行计算常微分方程初值问题的带有高阶导数项的块隐式单步方法,这种方法可以在 K 台处理机上并行进行数值处理.本文对方法的一般性质及方法收敛的条件进行了讨沦,得到方法的阶数为2l,并且指出适 l≤4时方法是 A-稳定的,最后给出了一个数值例子.     

一类求解常微分方程数值解的块方法

本文讨论了一类并行计算常微分方程初值问题的带有高阶导数的块隐式混合单步方法，这种方法可以在Ｋ台处理机上并行进行数值计算，本文对方法的一般性质及收敛性进行了讨论，得知该方法的阶数为２ｌ＋１，并且指出当ｌ＝１，２时，方法是Ａ－稳定的，最后给出了一个数值例子。     

带有高阶导数的块隐式混合单步法

本文讨论了一类求解常微分方程初值问题的带有高阶导数项的块隐式混合单步方法,首先讨论了这类方法的一些一般性质,得到了方法收敛的一些条件,然后指出方法所能达到的阶数为(ι+1)(k+1);最后推导出方法是A-稳定的条件:并给出了几个数值例子。     

多导块方法的稳定性分析

文[1]中提出了一种使用高阶导数的块隐式单步法,并在文末留下一个问题:即对给定的方法中使用的最高阶导数阶数l≥1,为使该方法是A-稳定的,块的大小k应满足什么条件?本文将彻底地解答这个问题.首先,我们给出稳定函数ξk(h)=P(h)/Q(h)中多项式P(h)及Q(h)的系数的显式表达式,并证明P(-h)=Q(h);另外,我们使用计算机符号运算及对角Pade'逼近公式,对任意的l≥1,给出了为使方法A-稳定时块的大小k应满足的条件.     

带有高阶导数的块隐式单步并行算法

1 引 言 随着科学技术的发展,各种类型的并行处理计算机已大量出现,为了提高这些机器的实际效率,需要构造与其相适应的并行算法。对于常微分方程初值问题,本文构造了一类带有高阶导数的块隐式单步并行计算公式,该方法可以在多台处理机上进行并行计算,而且具有良好的数值稳定性。本文将给出方法的构造,并且对其收敛性、精度及数值稳定性进行讨论。 2 方法的构造与精度 考虑常微分方程初值问题:     

一类块隐式混合单步并行计算方法

本文讨论了一类解常微分方程初值问题的块隐式混合单步并行算法，这种算法的块数为K，精度阶为2d＋2，可在S台处理机上进行并行计算，其中K＝S·d．本文讨论了方法的一般性质，给出了方法的稳定性定理，最后给出了一个数值例子．     

齐次Moran集的Bouligand维数

设m({nk}k≥1,{Ck}k≥1是由{nk}k≥1,{Ck}k≥1所确定的齐次Moran集类，其中{nk}k≥1是正整数序列，{Ck}k≥1是正实数列。本文确定了m中元素的上（下）Bouligand维数的最大、小值之间的数s，存在m中的元素使其上（下）Bouligand维数值为s。还讨论了齐次Cantor集与偏齐次Cantor集的Bouligand维数存在性之间的关系。     

奇异k紧整数的无限族

设n，s1，s2是3个正整数，使得s1〈s2〈n，gcd（n．s1，s2）=1，G（n；s1，s2）是n个结点的步长为s1和s2的双环网，d（n；s1，s2）是其直径．设d（n）=min{d（n；s1，s2）│s1〈s2〈n}，d1（n）=min{d（n；1，s）│1〈s〈n}．已知d1（n）≥d（n）≥[√3n]-2=lb（n）．若d（n；s1，s2）=d（n）=lb（n）＋k，k≥0，则称双环网G（n；s1，s2）是k紧优双环网．若d1（n）〉d（n）=lb（n）＋k，则n称为奇异k紧整数．本文给出构造奇异k紧整数无限族的方法，并对于k=1，2．…，20．构造出这样的无限族．     

f^（k）（1≤k≤n-1）与原函数f和最高阶导数f^（n）之间的一个不等式

证明了f^（k）（1≤k≤n-1）与原函数f和最高阶导数^（n）之间的一个不等式关系．     

递归序列与高阶项式

引　　言关于递归序列与Euler-Bernoulli数和多项式、递归序列与高阶Euler-Bernoulli数和多项式的关系问题的研究一直是国内外许多学者感兴趣的课题,并有了许多研究成果(见[1]～[7]).本文首先对Euler-Bernoulli数和多项式、高阶Euler-Bernoulli数和多项式进行推广,提出高阶多元Euler数和多项式、高阶多元Bernoulli数和多项式的定义,然后讨论它们与递归序列的关系,文中得出的结果是P.F.Byrd[1],R.P.Kelisky[2]和Zhangzhizheng[3]的相应结果的推广和深化.2　定义和引理定义2.1　k阶s元Euler数E(k)v1…vs和k阶s元Bernoulli数B(k)v1…v…     

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.     

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

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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.     

A note on Sobolev orthogonality for Laguerre matrix polynomials

Let {Ln(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0, ∞) by Ln(A,λ)(x)=n!/(-λ)n∑nk=0(-λ)κ/k!(n-1)! (A I)n[(A I)k]-1 xk,where A ∈ Cr×r. It is known that {Ln(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) ＞ - 1 for every z ∈σ(A).In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln(A,λ) (x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case.     

CONTENTS OF VOLUME 30

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