关于整值随机序列滑动平均的若干小偏差定理

研究任意整值随机序列部分和滑动平均的小偏差定理，在适当的条件下，有：limNinfh^-2(n)^N h(N)∑i=N Xi≥α(γ(ω)),limNsuph^-1(N)^N h(N)∑i=N Xi≤β(γ(ω))     

量测误差为 ARMA 过程的随机逼近

为了求回归方程 h(x)=0的根 x~0,根据对回归函数 h(·)的量测,在 i 时刻对x~0的估计为 x_i,在 i+1时刻对回归函数在 x_i 处进行量测,但量测量 y_(i+1)带有误差ε_i:y_(i+1)=h(x_i)+ε_i,而误差是相关的,构成一个 ARMA 过程:ε_(n+1)+D_1ε_n+…+D_dε_(n-d+1)=ω_(n+1)(x_n,ω)+C_1ω_n(x_(n-1),ω)+…+C_rω_(n-r+1)(x_(n-r),ω),其中 ω_(i+1)(x_i,ω)是一个鞅差序列,熟知的定理讨论的是 d=0,r=0的特例,并要求 ω_(i+1)(x_i,ω)相互独立.本文给出一个随机逼近算法,并给出条件,当 n→∞时,x_n(?)x~0 a.s..这个结果对d=0,r=0的特例,和熟知的事实相比,不仅在噪声的性质上,而且对 h(·)及E‖ω_(n+1)(x,ω)‖~2的控制函数,y_(i+1)和 x_i 的维数差别等方面都减弱了条件.     

θ-型Calderón-Zygmund算子多线性交换子的加权估计

讨论了θ-型Calderón-Zygmund算子T与b=(b_1,b_2,…,b_m)(b_j∈Osc_(exp L~Tj),1≤j≤m)生成的多线性交换子(?)的加权估计.当0相似文献   

关于■敛散性的定理

本文讨论了非负Jacobi矩阵和逐次松弛矩阵(0<ω≤1),证明了它们同时敛散,推广了[1]中的Stein-Rosenberg定理,揭示了ρ(ω)和ρ(B)之间的关系,并给出了估计谱半径ρ(ω)上下界的两组不等式。     

Marcinkiewicz积分交换子的加权有界性(英文)

本文应用加权Hardy空间H_ω~p(R~n)上的原子分解理论,研究了由函数b∈Λβ(R~n)(0<β≤1)与Marcinkiewicz积分μ_Ω生成的交换子μ_Ω~b的有界性;证明了μ_Ω~b是从L~q(ω~q)到L~q(ω~q)有界的,从L~1(|x|γ(n-β)/n)到弱L(n/n-β)(|x|~γ)有界的,且从H~p(ω~p)到L~q(ω~q)有界的,这里1/p-1/q=β/n.     

线性模型中最小二乘估计的强收敛速度问题

本文减弱了陈桂景文章中(1981)关于误差序列{e_i,i≥1}的收敛系统的重要条件,所得的最小二乘估计的强收敛速度仍然和陈桂景文中的速度相同.从这个结果,可得关于有γ-阶矩存在(0≤r<2)的i.i.d误差序列的重要推论,其结果在某种意义下达到最优的情形.     

有序Banach空间中非线性二阶周期边值问题的正解

讨论了有序Banach空间E中的非线性二阶周期边值问题-u″(t)+bu′(t)+cu(t)=f(t,u(t)),0≤t ≤ ω,u(0)=u(ω),u′(0)=u′(ω)正解的存在性,其中b,c∈R且c＞0,f:[0,ω]×P→P连续,P为E中的正元锥.本文通过新的非紧性测度的估计技巧与凝聚映射的不动点指数理论,获得了该问题正解的存在性结果.     

平稳弱相关过程积分的收敛性

Lei g(x,ω) be a stationary weakly conelated process, G(t, x) be the Green's function and G(x) be a function with a smooth one-order derivative. Define stochastic processes ξ(t,ω)=∫₀¹G(t,x)g(x,ω)dx (0≤t≤1) and η(t,ω)=∫₀^tG(x)g(x,ω)dx (0≤t≤T) In this paper we give the strong approximations of random variables ξ(t) and η(t) to normal variables, and also give a weakly in variance principle for process η(·).     

变量核奇异积分和分数次微分加权范不等式

用T和D~γ(0≤γ≤1)分别表示变量核奇异积分和分数次微分算子.T~*和T~#分别为T的共轭算子及拟共轭算子.利用球调和多项式展式,本文得到了TD~γ-D~γT和(T~*-T~#)D~γ在B_ω~(q,λ)(R~n)上的有界性.同时也得到了变量核奇异积分的积T_1T_2和拟积T_1■T_2的加权范不等式.     

k—full整数的分布（Ⅱ）

设k≥2是固定整数。自然数n称为k-full,如果对n的任一素因子p,均有p~k|n。以A_k(x)表示不超过x的k-full整数的个数,则可将A_k(x)写成如下形式: 这里γ_(i,k)(0≤i≤k-1)是非零常数,△_k(x)A_k(x)之误差项,本文在Riemann猜想成立的假设下证明了下结面论: 定理设。若Riemann猜想成立,则有:对k≥10成立。对2≤k≤9则得到了关于△_k(t)dt之渐近估计,其误差项为O(x_k~(a′+2))(ε>0)。     

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.