Molecular programming of organogelators which can accept [60]fullerene by encapsulation

New porphyrin-based gelators bearing eight hydrogen-bond-forming amide groups at their periphery were synthesized. They acted as versatile gelators for aromatic solvents. SEM and TEM observations and X-ray crystallographic analysis established that they tend to aggregate into a two-dimensional sheet-like structure utilizing the intermolecular hydrogen-bonding interaction. In this structure the porphyrin-porphyrin π-π stacking interaction is not involved because of the energetically-predominant hydrogen-bonding interactions, keeping the space distance of 12.9 Å. Very interestingly, when C₆₀ was added, the morphology was transformed to a one-dimensional fibrous structure, which can enjoy a porphyrin-C₆₀-porphyrin interaction. This multicapsular structure having porphyrin-based compartments for hosting C₆₀ was further characterized by XRD, EPR of a Cu(II) analogue, and the theoretical calculation. Thus, this paper presents a new concept, ‘molecular recognition in gel’, which is effective for the weak host-guest interaction.     

An expansion in the exponent for compound binomial approximations

The purpose of this paper is two-fold. First, we introduce a new asymptotic expansion in the exponent for the compound binomial approximation of the generalized Poisson binomial distribution. The dependence of its accuracy on the symmetry and shifting of distributions is investigated. Second, for compound binomial and compound Poisson distributions, we present new smoothness estimates, some of which contain explicit constants. Finally, the ideas used in this paper enable us to prove new precise bounds in the compound Poisson approximation. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 1, pp. 67–110, January–March, 2006.     

Discrete approximation of integral operators

A method to approximate the eigenvalues of linear operators depending on an unknown distribution is introduced and applied to weighted sums of squared normally distributed random variables. This area of application includes the approximation of the asymptotic null distribution of certain degenerated U- and V-statistics.

     

n维广义函数的集值导数

本文将文献［9］中给出的一维广义函数的集值导数的某些结果，推广到n维情形，并给出一些与优化有关的其他结果．     

Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.     

相型同步启动时间的M／M／c排队系统

本文研究带有同步启动时间的Ｍ／Ｍ／ｃ系统，其中启动时间是相型变量，给出了稳态和等待时间分布等结果。     

天然树脂局部结构的径向分布函数研究

本工作用x射线衍射技术分析计算了二种天然树脂的局部结构参数,由测得的衍射强度数据求出了它们的结构因子I(r)和径向分布函数RDF(r),并由此得到了分子链内临近原子和次临近原子平均间距、配位数和短程有序畴。     

A bartlett-type adjustment for the likelihood ratio statistic with an ordered alternative

For testing the equality of normal variances with an increasing alternative, under the null hypothesis the likelihood ratio test statistic is asymptotically distributed as a mixture of chi-squared distributions. In this paper a Bartlett-type adjustment is proposed to improve the approximation of the null distribution of the likelihood ratio test statistic with an ordered alternative.     

UNIQUENESS PROBLEM WITH TRUNCATED MULTIPLICITIES OF MEROMORPHIC MAPPINGS FOR MOVING TARGETS

In this article,two uniqueness theorems of meromorphic mappings on moving targets with truncated multiplicities are proved.