相似椭圆的一组性质

文[1]，文[2]介绍和研究了相似曲线的概念和判定方法,由文[2]得椭圆x^2/α^2＋y^2/b^2=λ^2（0〈λ〈1）与椭圆x^2/α^2＋y^2/b^2=1相似（相似比为λ），本文将给出有关椭圆x^2/α^2＋y^2/b^2=λ^2（0〈λ〈1）与x^2/α^2＋y^2/b^2=1的一组性质。     

用一个含参数的不等式证明一类分式不等式

由不等式（x-λy）^2≥0易推出不等式：x^2/y≥2λx-x^2y（y〉0）（1） 不等式（1）有着很好的结构，用它可以轻松地证明一些分式不等式，下面举例来说明．     

f与f^（k）具有一个CM公共值的亚函数

得到如下结果：设f(z)为非常数亚纯函数，f与f^(k)以1为CM公共值，如果N^-(r，f) N^-(r，1/f^(k))＜λT(r，f)，k=1，0＜λ＜1/6;或3N^-(r，f) N^-(r，1/f^k)＜λT(r，f)，k≥2，0＜λ＜1/3;或N^-(r，1/f) 3N^-(r，1/f^(k))＜λT(r，f)，k≥3，0＜λ＜1/6，则f^(k)-1/(f-1)≡C，其中C为某一非零常数。     

关于一类Müntz有理逼近的点态估计

给定M〉0,设A={λn}∞n=1是一非负实数序列,满足λn＋1-λn≥Mn In n对所有的n≥1成立,本文给出了Müntz系统{x^λn）的有理逼近在区间[0,1]之右端点1处的点态估计．     

一类函数问题的解法探讨

在高三模拟考试中,经常出现下面这类函数题目． 题目 已知函数f（x）=4x-1/x^2＋λ/x．若对任意两个不等的正数a,b,有｜f（a）-f（b）｜〉｜a—b｜恒成立．求λ的取值范围．     

分数次Hardy算子的交换子在变指数Herz-Morrey空间中的有界性

本文主要建立了由分数次Hardy算子与BMO函数生成的交换子从变指数Herz-Morrey空间MK_(q1,p1(·))~(α,λ)(Rn)到MK_(q2,p2(·))~(α,λ)(Rn)的有界性.对n维Hardy算子的交换子也证明了类似的结果.     

修正的Shepard型算子的Lp-逼近

摘要:本文在L_[0.1]~p空间给出了 Durrmeyer型修正的shepard算子D_n(f,x),对 f∈L_[0.1]~p,(p≥1),得到了下列的Jackson型估计:││D)n(f)-f││_p≤ C_(pλω)(f,n~(-1))p,λ≥2, Cω(f,n~(-1)logn)p,λ=2, C_(pλω)(f,n~(-1))p,1<λ<2,     

对称Cantor集自乘积集的Hausdorff中心测度

设Cλ是由迭代函数系统(IFS){f1,f2}生成的对称Cantor集,其中f1(x)=λx, f2(x)=1-λ+λx,0<λ<1/2,x∈[0,1]．在压缩比λ满足一定条件时,本文得到了Cλ与其自身的笛卡尔乘积Cλ×Cλ的Hausdorff中心测度的计算公式．     

一个推广的具有最佳常数的Hardy-Hilbert不等式

本文的目的是建立新的具有最佳常数因子的Hardy-Hilbert不等式的推广式．对二重级数适当配方,利用Hlder不等式及β-函数,得到下面的推广式：∑_(m=1)~∞∑_(n=1)~∞((a_nb_n)/(m~c n~c)■)＜cλ,p(∑n~((P-1)(1-λ))a_n~p)~(1/p)(∑n~((q-1)(1-λ))b_n~q)~(1/q),这里λ＞0,c＞0,p＞1,(1/p) (1/q)=1,a_n≥0,b_n≥0,cλ,p=(1/c)B((λ/cp),(λ/cq)),通过选取两个特殊序列,证明了常数因子cλ,p是最佳的；还给出了它的等价形式,用类似方法给出了重积分形式的Hardy-Hilbert不等式的推广式及其等价形式．     

Hilbert空间中非扩张映象的最近的公共不动点的逼近问题

本文在Hilbert空间的框架下,研究无限族非扩张映象T_1,T_2,…的迭代程序x_n+1=λ_(n+1)y+(1-λ_(n+1))T_(n+1)x_n的收敛性问题．在适当的条件下,证明了该迭代序列收敛于这一非扩张映象族的最近的公共不动点．其结果改进和推广了引文中相应的结果．     

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.     

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.     

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.