右半平面解析的Laplace-Stieltjes变换的广义级与型

给出右半平面解析的Laplace-Stieltjes变换的广义级与广义型的定义,研究了最大模M_u(σ,F)=sup{|∫_0~x e~(-(σ+it)y)dv(y)|:x∈(0,+∞),t∈R},最大项μ(σ,F)=max_(n∈N){A_n~*e~(-λnσ)},最大项指标v(σ,F)=max_k{λ_k|μ(σ,F)=A_k~*e~(-λkσ)}及其系数之间的关系,推广了Dirichlet级数的相关结果.     

线性模型中均值向量的LSE和BLUE的偏差估计

对于线性模型 Y=Xβ+e,E(e)=0,cov(e)=σ~2∑,∑≥0μ=Xβ的LSE和BLUE分别为■=X(X′X)-X′Y和μ~*=X(X′T-X)-X′T-Y,其中T=∑+XUX′,U是对称阵且使Rank(T)=Rank(∑X)和T≥0,本文证明了‖■-μ~*‖_2≤(λ_r-λ_ζ)/(2(λ+λ_k)~(1/2))‖Y-■‖_2这里λ_4=ch_4(T),i=1,2,…,n,λ_1≥…≥λ_n≥0。k=Rank(X),‖a‖_2=(a′a)~(1/2),并且给出了‖cov(■)-cov(μ~*)‖_s‖PT~2P-(PTP)~2‖_s和‖(cov+(μ~*))~(1/2)cov(■)(cov+(μ~*))~(1/2)‖s的上界,这里‖A‖_s=(tr(A′A)~(3/2))~(■),s≥1。     

三元四次对称不等式的统一加强

在文 [1 ]中 ,笔者给出了三元四次对称不等式λ( ∑x) 4 μ∑ ( yz) 2 υ∑x .∏x k( ∑x) 2 ∑yz≥ 0　 ( x,y,z >0 )成立的一个充要条件 .它等价于下面的命题　记σ1=x y z,σ2 =xy yz zx,σ3 =xyz,则F( x,y,z)≡λ0 σ41 λ1σ21σ2 λ2 σ22 - ( 2 7λ0 9λ1 3λ2 )σ1σ3 ≡λ0 σ1(σ3 1- 2 7σ3 ) λ1σ1(σ1σ2 - 9σ3 ) λ2 (σ22 - 3σ1σ3 )≥ 0 ( 1 )对任意 x,y,z >0成立的充要条件是λ0 ≥ 0 ,λ1≥ - 5λ0 ,1 6λ0 4λ1 λ2 ≥ 0( 2 .1 )或λ0 >0 ,λ1<- 5λ0 ,λ0 λ2 ≥ ( 3λ0 λ1) 2( 2 .2 )本文进而…     

一类时标动态方程属于极限圆型的判定

本文在时间刻度T上定义新的L2(T)空间,利用Weyl圆理论研究了二阶动态方程Ly=-[p(t)y△]△+q(t)yσ=λyσ,(其中p(t)∈Cˊrd,q(t)∈Crd,q(t)>0,λ∈C0)的极限点型与极限圆型的分类问题.并在此基础上研究了方程Ly=λyσ的有界扰动问题,得到了扰动状态下极限圆型的不变性准则.     

三个共轴等离心率椭圆的有趣性质

我们知道,椭圆x2/a2＋y2/b2=λ1（λ1〉0）与椭圆x2/a2＋y2/b2=λ2（λ2〉0,λ2≠λ1）有相同的对称轴（x轴和y轴）和相等的离心率e=（（2a-b2）/a）~（1/2）,下面我们给出关联三个共轴等离心率椭圆的两个有趣性质.定理1给定两个共轴等离心率椭圆C1：     

变量分离型积分因子存在定理及应用

给出了变量分离型积分因子μ(x,y)=p(x)q(y)的定义,得到了微分方程M(x,y)dx+N(x,y)dy=0存在变量分离型积分因子μ(x,y)=p(x)q(y)的充要条件和计算积分因子的公式.     

三个共轴等离心率椭圆的有趣性质

我们知道,椭圆x2/a2+y2/b2=λ1（λ1>0）与椭圆x2/a2+y2/b2=λ2（λ2>0,λ2≠λ1）有相同的对称轴（x轴和y轴）和相等的离心率e=（（2a-b2）/a）^1/2,下面我们给出关联三个共轴等离心率椭圆的两个有趣性质.定理1给定两个共轴等离心率椭圆C1:     

变系数EV模型基于核估计的误差方差估计

在利用核函数法和广义最小二乘法讨论变系数EV模型系数参数估计的基础上给出了其误差方差σ2的一种估计量(σ)2n,证明了所定义的估计量(σ)2n有很好的大样本性质.     

相似椭圆的性质再探

由文[1]的定义,我们把椭圆E1:x2/a2+y2/b2=1(a>b>0)和E2:x2/a2+y2/b2=λ(λ>0,λ≠1)称为相似椭圆(可以证明:两相似椭圆有相同的离心率),文[2],[3],[4]给出了相似椭圆的一些性质,本文再给出相似椭圆的若干性质.     

Jacobi矩阵的逆特征问题

本文研究了两个Jacobi矩阵的逆特征问题：I给定实数λ,μ(λ＞μ）和n维非零实向量x，y，求n阶Jacobi矩阵J,使Jx=λx，Jy=μy,且λ＞λ2（J）＞…＞λi-1（J）＞μ＞λi＋1（J）…＞λn（J），或λi（J）＞λ2（J）＞…＞λi－1（J）＞λ＞λi＋1（J）＞…＞λn-1（J）＞μ·II给定实数λ，μ（λ＞μ）和n维非零实向量x，y，求n阶Jacobi矩阵J，使Jx＝λx，Jy＝μy，且λ1（J）＞λ2（J）＞…＞λi－1（J）＞λ＞μ＞λi＋2（J）＞…＞λn（J）．文中给出了问题I；II有唯一解的充要条件，并给出了解的表达式．     

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.     

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.