CERTAIN ASYMPTOTIC EXPANSIONS FOR LAGUERRE POLYNOMIALS AND CHARLIER POLYNOMIALS

Here proposed are certain asymptotic expansion formulas for Ln(w-1)(λz) and Cn(ω)(λz) in whichO(λ) and n = 0(λ1/2 )(λ→∞) , z being x complex number. Also presented are certain estimates for the remainders(error bounds) of the asymptotic expansions within the regions D1( - ∞相似文献   

平面上具有有界Fréchet导数的调和映照单叶半径的精确估计

给定单位圆盘D={z||z|1}上调和映照f(z)=h(z)+g(z),其中h(z)和g(z)为D上的解析函数,满足f(0)=0,λf(0)=1,ΛfΛ.通过引入复参数λ,|λ|=1,本文研究调和映照Fλ(z)=h(z)+λg(z)和解析函数Gλ(z)=h(z)+λg(z)的性质,得到Fλ(z)和Gλ(z)单叶半径的精确估计.作为应用,本文得到单位圆盘D上某些K-拟正则调和映照Bloch常数的更好估计,改进和推广由Chen等人所得的相应结果.     

任意阶Laplace算子的特征值估计

设D为n维Euclid空间Rn的一个有界区域,且0＜λ1≤λ2≤…≤λk≤…是l阶Laplace算子的Dirichlet问题{(-△)lu=λu, 在D中,u=(e)u/(e)n=…=(e)l-1u/(e)nl-1=0,在(e)D上的特征值.得到了该问题用其前k个特征值来估计第(k+1)个特征值λk+1的不等式k∑i=1(λk+1-λi)≤1/n(4l(n+2l-2)]1/2{k∑i=1(λk+1-λi)1/2λil-1/lk∑i=1(λk+1-λi)1/2λi1/l}1/2,此不等式不依赖于区域D.对l≥3,上述不等式比所有已知的结果都要好.陈庆民与杨洪苍考虑了l=2的情形.我们的结果是他们结果的自然推广.当l=1时,我们的不等式蕴含杨洪苍不等式的弱形式.文中还给出了陈和杨的一个断言的直接证明.     

Completely Settling of the Multiplier Conjecture for the Csse of n＝3pr

A k-subset D of a group G of order v (1相似文献   

多项式矩阵互质的结式定理

一、问题的提出 在多变量控制系统理论的线性定常系统的微分算符描述中,系统 P(D)Z=Q(D)u y=R(D)u (1)的能控、能观的充分必要条件,分别为多项式矩阵P(λ)、Q(λ)的左互质与P(λ)、R(λ)的右互质。 结合系统理论,Rosenbrock、Wolovich等讨论了两多项式矩阵互质的充分必要条     

量子群Uq(D4)上不可约模的Grobner-Shirshov对

首先,利用量子群Uq (D4)的已知的Grobner-Shirshov基和Chibrikov的双自由模方法来计算量子群Uq(D4)上不可约模Vq(λ)的一个Grobner-Shirshov对,然后在Uq(D4)的适当形式U'q(D4)中取q=1得到D4型单李代数的泛包络代数U(D4)上不可约模V(λ)的一个Grobner-Shirshov对.     

关于Cn空间有界域的一个解析不变量

The main results of the present paper are: For any bounded D in space Cⁿ, there is an analytic invariant λ(D)(≤1). If D is a transitive domain, then λ(D)<1 and k₀(D)=(λ(D))/(1-λ(D)), where k₀(D) is the Schwarz constant of domain D (cf[1]). And we have discussed the Characteristic properties of λ(D).     

加法与乘法逆特征值问题的可解性

1.引言 本文讨论如下代数特征值反问题可解的充分条件: 问题A(加法逆特征值问题)。给定一Hermite矩阵A=(a_(ij))_(n×n)及n个实数λ_1,…,λ_n,求一实对角阵D=diag(c_1…,c_n),使得A+D的特征值为λ_1,…,λ_n。 问题M(乘法逆特征值问题)。给定一正定Hermite矩阵A=(a_(ij))_(n×n)和n个正实数     

John圆的可分解性质和拟圆的一个充要条件

证明D-R2是John圆当且仅当D具有John可分解性质;D-R2是拟圆当且仅当对于任意的z1,z2∈D,存在常数c≥1,使得1cλD(z1,z2)≤λD*(z1,z2)≤cλD(z1,z2).     

有向图的谱半径的二次度形式的上界

1 预备知识设D=D(V,E)为n 阶有向图(V 为顶点集,E 为弧集),其邻接矩阵A=A(D)= (α_(uv))_(n×n)的所有特征根:λ_1,λ2,…,λ_n 被称为有向图D 的邻接谱,简称谱.称(?){|λ_i|} 为D 的谱半径,记作ρ,ρ(D)或ρ(A).用d~-(u)和d~ (u)分别表示D 中顶点u 的入度和出度. 记V~-(u)={v}(v,u)∈E},V (u)={v|(u,v)∈E}.m~-(u)=1/((d~(u))(?)d~-(v), 称为D 中顶点u 的平均二次入度,m~ (u)=1/((d (u))(?)d~ (v),称为顶点u 的平均二次出度.其它有关术语可参考[1,2].     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the comparison between the APV and the NPV computed via the WACC

The valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of the APV is available. The paper shows that the APV can be interpreted as the arbitrage free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation, generally different from the APV, allows for arbitrage. We provide various conditions which completely characterize the sign of the error as a functions of all the variables entering the model.     

用常微分方程模型分析预防和隔离措施对SARS发病率的影响

通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 .     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

On the Gap in the Spectrum of the Translations

The spectrum of the translations in local quantum field theory will be analyzed in order to show that in a positive energy representation without vacuum vector and with lowest mass m₁ there is no gap in the spectrum which is larger than 2m₁. In particular in a zero mass representation there is no hole at all. These results are obtained with methods of analytic functions of several complex variables.     

From the subalgebras of the square to the discriminator

Presented by A. F. Pixley.     

On the Decomposition of the Riesz Operator and the Expansion of the Riesz Semigroup

For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues denote by E(λ_i; T) the eigen-projection corresponding to an eigenvalue λ_i. In this paper we will show that if the operator sequence is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators T_p and T_r: T = T_p + T_r, where T_p is the weak limit of T_n and T_r is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t ≥ τ. As an application, we consider the solution of transport equation on a bounded convex body.