Asymptotics in the Baum—Katz formula for random fields

In 1996, D. Deng established an analog of the Baum—Katz theorem on the convergence rate in the law of large numbers for multi-indexed random variables. The series describing the convergence rate depends, in a natural way, on the parameter characterizing the excess of the normalized sums over some level. In this paper, we find the precise asymptotics of the sum of this series with respect to the above-mentioned parameter. Thus, a generalization of a recent result due to A. Gut and A. Spataru is obtained.     

单位球上全纯函数空间的系数乘子

本文给出了C^n中超球B上Hardy空间H^p,Bergman空间Lα^p,Bloch空间β，Besov空间Bp及Lipschitz空间Ak^p之间的系数乘子。     

新课标体系下高师本科数学分析教学所面临的问题和所采取的措施

从三个方面讨论了在高中新课标体系下高师本科数学分析教学所面临的问题,并结合作者的实际教学经验给出了一些具有实际操作意义的解决措施和办法.     

About Regularity of Collections of Sets

The paper continues investigations of stationarity and regularity properties of collections of sets in normed spaces. It contains a summary of different characterizations (both primal and dual) of regularity and a list of sufficient conditions for a collection of sets to be regular.     

响应变量随机缺失下的半参变系数模型的均值估计

在响应变量随机缺失时,研究了半参数变系数模型响应变量均值的借补估计.首先利用完整个体估计模型中的参数与非参数部分,然后再用借补方法与加权借补方法估计响应变量的均值.最后求出了估计的渐近偏差与渐近方差,研究了所得到的估计的渐近性质,并进行模拟比较.     

单轴晶体内表面入射e光线的双反射

基于光线遵从的Fermat原理,从几何学的角度讨论和分析了在单轴晶体中入射的e光线在界面上的双反射,得到了确定光线反射方向的一般公式,并对几种特殊情况进行了讨论.指出了上述结果与由电磁波的边界条件计算所得结果是一致的.     

Electronic spectra of cationic forms of meso-tetrapropylporphin in a nanoporous silicate gel matrix

We have studied the fluorescence and fluorescence excitation spectra at 300 K, 77 K, and 4.2 K for silicate gel matrices colored with meso-tetrapropylporphin by impregnation of the matrix with a solution of the pigment. Comparison of the data obtained with the absorption spectra in acidified solutions and analysis of the low-temperature fine-structure vibronic spectra, and also taking into account data obtained earlier for octaethylporphin in a xerogel showed formation of two cationic forms of meso-tetrapropylporphin in the gel matrix: the short-wavelength form has a dicationic structure, while the long-wavelength form has a monocationic structure. We have traced out the correlations of the vibrational structure in the spectra of the dicationic form with data for the porphin dication, and we have drawn a number of conclusions concerning the normal vibrational modes that are active in the vibronic fluorescence and absorption spectra of the studied cationic forms. Using the AM1 semiempirical quantum chemical method, we optimized the geometry of the mesotetrapropylporphin dication: the most stable of the possible conformers is the dication structure with saddleshaped macrocycle nonplanarity. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 453–461, July–August, 2006.     

Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains

We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso(D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F). In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN, F)) and Iso(D(VN,F))(0), where G(0) is the unit connected component of the Lie group G.     

On uniformly Gâteaux smooth norms and normal structure

It is shown that every separable Banach space admits an equivalent norm that is uniformly Gâteaux smooth and yet lacks asymptotic normal structure.

     

The twist coefficient of periodic solutions of a time-dependent Newton's equation

This paper gives sufficient conditions for the existence of periodic solutions of twist type of a time-dependent differential equation of the second order. The concept of periodic solution of twist type is defined in terms of the corresponding Birkhoff normal form and, in particular, implies that the solution is Lyapunov stable. Some applications to nonlocal problems are given.