求解非线性中立型延迟微分方程一类线性多步方法的收敛性

本文致力于带有Lagrang插值的一类线性多步法求解非线性中立型延迟微分方程的误差分析.证明了一个p′阶的线性多步方法配上一个q阶的Lagrang插值导致一个minf[p′,q 1]阶的E-(或EB-)收敛的非线性中立型延迟微分方程数值方法.     

非线性中立型延迟积分微分方程单支方法的收敛性

获得了求解非线性中立型延迟积分微分方程单支方法的收敛性结果.证明了当且仅当相应的常微分方程方法是A-稳定的且经典相容阶为p（p=1,2）时,单支方法是p阶E（或EB）-收敛的.数值实验结果验证了所获理论的正确性.     

Cn中多圆柱上广义Bloch空间的点乘子

讨论了Cn(n>1)中多圆柱上广义Bloch空间βp上的点乘子,根据p、q的不同情况得到βp空间到βq空间所有的点乘子,得到(1)当p<1时M(βp)=βp;(2)当p≥1时M(βp)=c;(3)当p>q时M(βp,βq)={0};(4)当p<q<1时M(βp,βq)=βq;(5)当p<1≤q时M(βp,βq)=Jp,q∩βq;(6)当1≤p<q时M(βp,βq)=c.     

一类三阶拟线性微分方程非振动解的渐近性

主要讨论的是一类三阶拟线性微分方程(p(t)|u″|~(α-1)u″)′+q(t)|u|~(β-1)u=0其中α0,β0,p(t)和q(t)是定义在区间[a,∞)上的连续函数,且满足当t≥a时p(t)0,q(t)0.当t→∞时此方程满足∫_a~∞1/((p(t))~(1/α))dt=∞的特殊非振动解存在的充分必要条件.     

中立型延迟微分方程一般线性方法的非线性稳定性

本文研究一类非线性中立型延迟微分方程一般线性方法的数值稳定性.证明了一般线性方法为(k,p,O)-代数稳定时,在一定的约束条件下,其数值解保持微分方程理论解的稳定性质,特别是证明了在约束网格情形代数靛的-般线性方法能无条件保持解析解的稳定性.     

带逐段常变量的二阶中立型延迟微分方程的概周期解

本文讨论了带逐段常变量的二阶中立型延迟微分方程(x(t)+px(t-1))″=qx(2[(t+1)/2])+f(t)的概周期解的存在性,此处[.]表示取整函数,p,q是非零实数,|p|=1,q≠-4,f(t)是一个概周期函数.     

Bargmann系统与耦合Harry-Dym方程解的对合表示

在位势与特征函数确定的约束下,耦合 Harry-Dym 方程 Lax 对的空间部分非线性化为一个完全可积的系统{R~(2N),dpΛdq,H=1/2〈Λ~2q,q〉〈Λq,q〉~(-2)+1/2〈p,p〉-1/2α〈q,q〉},而时间部分的非线性化导出它的 N-对合系{F_m}.约束映射将相容系统(H)、(F_m)的对合解映成 m 阶耦合 Harry-Dym 方程的解.一个 Neumann 系统和定态 Harry-Dym 方程之间的关系被讨论.系统{R~(2N),dpΛdq,(?)=1/2〈p,p〉-1/2〈Λq,q〉~(-1)-1/2α〈q,q〉}证明是完全可积的.     

非线性中立型随机延迟微分方程随机θ方法的稳定性

本文研究非线性中立型随机延迟微分方程随机θ方法的均方稳定性.在方程解析解均方稳定的条件下,证明了如下结论:当θ∈[0,1/2)时,随机θ方法对于适当小的时间步长是均方稳定的;当θ∈[1/2,1]时,随机θ方法对于任意步长都是均方稳定的.数值结果验证了所获结论的正确性.     

一类带调和势的非线性Schrdinger方程在R~N中的整体解存在的门槛

本文考虑一类带调和势的非线性 Schrdinger 方程 it=-△ |x|~2-μ||~(p-1)-λ||~(q-1),x∈R~N,t≥0, 其中μ＞0,λ＞0．当 N=1,2时,1＜p＜q＜∞；当 N≥3时,1＜p＜q＜(N 2)/(N-2)．运用精巧的变分方法、势井方法和凸方法,得到了方程的整体解和爆破解存在的门槛．进一步回答了：当 q＞p＞1 4/N 时,方程的 Cauchy 问题的初值小到什么程度,其整体解存在?     

加权Herz型Hardy空间上的Littlewood-Paley g函数

研究了Littlewood-Paley g函数gψ(f)(x)在加权Herz型Hardy空间上的性质,得到了如下结果,若ω1,ω2∈A1,则当n(1-1/q)≤α≤n(1-1/q) ε时,gψ为HK^a,p q(ω1,ω2)到K^a,p q(ω1,ω2)上的有界算子,当α＝n(1-1/) ω时,gψ为HK^a,p q(ω1,ω2）到WK^a,p q(ω1,ω2)上的有界算子。     

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.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

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.     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.