A functional law of the iterated logarithm for associated sequences

Recently, a functional central limit theorem and a Berry-Essen Theorem have been demonstrated for classes or associated random variables. Using these results, and similar results for multiplicative sequences, we show a functional law of the iterated logarithm for associated sequences satisfying a rate requirement.     

Highly accurate calculation of angular spheroidal functions

A new method for calculating the angular spheroidal functions of the first kind is proposed. The method is partly based on the known representations of these functions; however, some additional structures proposed in this work ensure efficient highly accurate calculation function values at a given point for a wide range of parameters.     

Injective and Epi-Projective Objects in Categories of Convex Spaces

We give a characterization of injective and epi-projective objects in some categories of convex spaces.     

Excess molar volumes of 1-alcohol + aliphatic monoethers at 298.15 K

Excess molar volumes V^E at 298.15 K and atmospheric pressure for 1-propanol and 1-hexanol + butyl methyl ether, + dipropyl ether or + dibutyl ether with a vibrating-tube densimeter. The V^E are negative over the whole mole-fraction range and nearly have been calculated from densities measured symmetrical for all the systems investigated. For each monoether, the V^E decreases as the chain length of the 1-alcohol increases. For each 1-alcohol, the V^E increases as the chain length of the symmetrical di-n-alkyl ethers increases. Moreover, for the butyl methyl ether (an asymmetrical monoether), the V^E is more positive than of the immediately higher symmetrical dipropyl ether. These results, together with previously published excess molar enthalpies H^E, suggest the formation of hydrogen bonds between the functional group (---OH) of the 1-alcohol and the (---O---) atoms of the monoethers.     

Precise Large Deviations for Sums of Negatively Associated Random Variables with Common Dominatedly Varying Tails

In this paper, we obtain results on precise large deviations for non-random and random sums of negatively associated nonnegative random variables with common dominatedly varying tail distribution function. We discover that, under certain conditions, three precise large-deviation prob- abilities with different centering numbers are equivalent to each other. Furthermore, we investigate precise large deviations for sums of negatively associated nonnegative random variables with certain negatively dependent occurrences. The obtained results extend and improve the corresponding results of Ng, Tang, Yan and Yang （J. Appl. Prob., 41, 93-107, 2004）.     

环氧氯丙烷交联季铵化壳聚糖/聚砜复合纳滤膜的制备

将2-羟丙基三甲基氯化铵壳聚糖(HACC)的铸膜液与聚砜超滤膜进行复合,用环氧氯丙烷(ECH)交联,制备了一种新型荷正电复合纳滤膜.结果表明,该类膜呈复合结构,截留分子量为720;20℃时,膜的纯水渗透系数为12.6 L·h-1·m-2·MPa-1,对不同无机盐料液的截留的顺序由高到低为MgCl2,NaCl,KCI,MgSO4,Na2SO4,K2SO4.     

New explicit nonperiodic solutions of the homogeneous wave equation

We exhibit a newansatz for the solution of the homogeneous three-dimensional time-dependent wave equation in spherical coordinates of the form Φ(r,t)=Y(θ, φ)(I(r)+G(g)), whereg ≡ct/r. FunctionG(g) has explicit solution in terms of three independent nonperiodic functionss _ℓ,t _ℓ,u _ℓ (s _ℓ andt _ℓ are related to the associated Legendre functions of the first and second kinds).G(g) is nonperiodic and may be cast as a superposition of incoming and outgoing waves. To obtainG(g), we solved a nonhomogeneous associated Legendre equation (this solution, to our knowledge, is also new).G(g) may prove useful in many microscopic and macroscopic problems, representable by homogeneous wave equations.     

NA样本密度函数估计一致渐近正态性的收敛速度

在平稳NA样本下,讨论了未知密度函数估计的一致渐近正态性.在适当的条件下给出了该密度函数估计一致渐近正态性的收敛速度.这个速度几乎达到n^{-1/6}     

A study of photoelectron spectra in the framework of the semiempirical AM1 method

The characteristics of photoelectron (PE) spectra of 2-phenylpyrroles and biphenyls have been correlated with the UV spectroscopy data for their radical cations. The geometric and electronic structures of the compounds and radical cations have been calculated using the AM1 method. The absorption bands of the radical cations observed in the visible region of spectrum have been found to pertain to the quasi-Koopmans type,i.e., they are realized between the doubly and partially occupied -MO, but their energies differ strongly from those calculated on the basis of PE spectra. This is explained by the distinction between the spatial structure of a molecule and that of the respective radical cation. The second cause of the discrepancy between the data of the two spectral methods consists in orbital — interactions, which are most conspicuous in the case of 4(4)-halogen-substituted compounds.For Part 4 see ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 869–874, May, 1993.     

A mean-field limit for a class of queueing networks

A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limitN is discussed, whereN is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.