Clifford 分析中无界域上正则函数带Haseman位移的边值问题

该文在引入修正的Cauchy核的基础上,讨论了Clifford 分析中无界域上正则函数带 Haseman 位移的边值问题. 首先给出了无界域上Cauchy 型积分的Plemelj公式,再利用积分方程方法和压缩不动点定理证明了问题解的存在唯一性.     

Bochner-Martinelli型积分的边界性质

对 Cn中具光滑边界Ω的有界域 D和属于指数α( 0 <α <1 )的 Lipschitz空间 Lip(α,Ω )中的每个函数φ,我们不仅证明了 Bochner- Martinelli型积分Φ ( z) =∫Ωφ(ζ) K(ζ,z)(其中 K(ζ,z)为 Bochner- Martinelli型积分核 )表示的内、外极限值Φ +( t) ,Φ - ( t)属于 Lip(β,Ω ) ( 0 <β <α <1 )而且可分别延拓成 D和 Dc上的指数为β的 Holder连续函数 ,并由此给出了 Bochner- Martinelli变换的 Plemelj跳跃公式 .     

四元数分析中无界域上正则函数的带位移非线性边值问题

讨论了四元数分析中无界域上正则函数的一类带位移非线性边值问题.利用积分方程方法和Schauder不动点理论证明了问题解的存在性,并给出了解的积分表达式.     

具有无界非线性项的广义逐段常变量微分方程拓扑等价函数的正则性

关于微分方程的拓扑等价以及拓扑等价函数的正则性一直是微分方程研究的焦点之一.当非线性项有界时,已经有很多学者证明了微分方程的拓扑等价函数是H?lder正则的.然而,当非线性项无界时,拓扑等价的正则性尚无突破性结果.在无界情形下, Zou和Shi(2017)得到了拓扑线性化的条件.除Zou和Shi(2017)给出的条件外,在附加的一个前提下,本文证明拓扑等价函数的H?lder正则性.事实上,当系统是有界时,系统线性化的条件足以保证其H?lder正则性.但是,当系统是无界时,这个附加条件是必不可少的.本文举例说明这个事实.这是首篇考虑无界系统拓扑等价H?lder正则的文章.     

仿射自同构群和小波变换

令D(Φ,Ω)是第一类典型域的无界实现.它的     

动力系统方法解决无界线性算子方程

针对反问题中出现的第一类算子方程Au=f,其中A是实Hilbert空间H上的一个无界线性算子利用动力系统方法和正则化方法,求解上述问题的正则化问题的解:u'(t)=-A~*(Au(t)-f)利用线性算子半群理论可以得到上述正则化问题的解的半群表示,并证明了当t→∞时,所得的正则化解收敛于原问题的解.     

有界多连通区域数值保角变换的GMRES(m)法北大核心CSCD

求解复杂多连通区域的保角变换函数是困难的.针对这一问题,该文将求解保角变换函数转化为利用模拟电荷法求解一对定义在问题区域上的共轭调和函数,再根据边界条件建立约束方程,并利用GMRES(m)(the generalized minimal residual method)算法求解约束方程,获得了模拟电荷,进而构造了高精度的近似保角变换函数,将有界多连通区域映射为三种无界正则狭缝域.数值实验验证了该文算法的有效性.     

Clifford分析中无界域上Isotonic函数的Plemelj公式

定义了无界域上Isotonic函数的Cauchy型积分和Cauchy主值积分,考虑了其边界性质,得到了无界域上Isotonic函数的Plemelj公式.     

关于域的K_2群的挠

设F是域,记G_n(F)={{a,Φ_n(a))∈K_2(F)|a,Φ_n(a)∈F_~*},这里Φ_n(x)是n次分圆多项式.首先,使用关于数域上的Mordell猜想的Faltings定理证明了若F是数域,n≠1,4,8,12且含有平方因子,则G_n(F)不是K_2(F)的子群;然后,使用Manin,Grauert,Samuel和李克正关于函数域上的Mordell猜想的结果,对代数闭域上的函数域证明了类似的结果.     

PM-空间中扩张型映象的不动点定理

本文中处处假设(E,(?),Δ)是(?)完备的 Menger 空间,t-范数Δ满足(?)Δ(t,t)=1。定义1 设Φ(t)是[0,∞)上的函数,我们称Φ(t)满足条件(Φ_1),如果Φ(t)不减、Φ(0)=0,且(?)Φ~n(t)=∞,(?)t>0;称Φ(t)满足条件(Φ_2),如果Φ(t)严格增、左连续、Φ(0)=0,且(?)Φ~n(t)=∞,(?)t>0,其中Φ~n(t)是Φ(t)的第 n 次迭代。     

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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