ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions.     

Smoothing estimation of rate function for recurrent event data with informative censoring

This paper proposes kernel estimation of the occurrence rate function for recurrent event data with informative censoring. An informative censoring model is considered with assumptions made on the joint distribution of the recurrent event process and the censoring time without modeling the censoring distribution. Under the validity of the informative censoring model, we also show that an estimator based on the assumption of independent censoring becomes inappropriate and is generally asymptotically biased. To investigate the asymptotic properties of the proposed estimator, the explicit form of its asymptotic mean squared risk and the asymptotic normality are derived. Meanwhile, the empirical consistent smoothing estimator for the variance function of the estimator is suggested. The performance of the estimators are also studied through Monte Carlo simulations. An epidemiological example of intravenous drug user data is used to show the influence of informative censoring in the estimation of the occurrence rate functions for inpatient cares over time.     

Mechanisms of n‐butanol formation in butyl acrylate latexes

The mechanisms involved in the formation of n‐butanol during the synthesis of butyl acrylate containing latices were investigated. The experimental results showed that neither the hydrolysis of butyl acrylate nor of the ester bond in the butyl acrylate segments of the polymer played a major role in the formation of n‐butanol, which was mainly generated from the polymer backbone, by transfer reactions to polymer chain followed by cyclization. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5838–5846, 2007     

Theoretical Study on the Long-lived Complexes for the Na＋I2 Collision System

For the Na I2 collision system, theoretical study is performed on the QCISD(T) level by using ab initio method. The ab initio potential energy surfaces are got and on them the long-lived complexes are found and optimized. These results verify the crossed molecule beam experimental phenomenon and the detailed geometry structures are given for the first time. The role of the complexes in the reaction path is also described in detail.     

Ground-state complex formation of perylene with pyromellitic dianhydride studied by static fluorescence quenching

The association of complex formation with static quenching in CT systems was investigated. Evaluation of the data made evident that the inner filter effect must be allowed for. Time-resolved and temperature-dependent stationary measurements of fluorescence led to the separation of dynamic and static quenching components. The static quenching constant is discussed with respect to the equilibrium constant of complex formation determined by absorption spectroscopy.     

Novel pattern formation in the collapse process of floating monolayer at the air-water interface

We have observed a remarkable two-armed spiral in the collapse process of a floating monolayer at the air-water interface by phase contrast microscopy. This demonstrates that the floating monolayer as a form of soft condensed matter reorganizes itself due to a certain kind of macroscopic or collective behavior of molecules as it collapses. This pattern formation is caused by the breakdown of a critical dynamical balance between the deformation of solid domain and the applied surface pressure. The fragility as well as the flexibility of the floating monolayer can be associated with the observed pattern growth. There are also observed interesting, periodically arranged collections of molecules in numerous collapsed regions. Received: 8 July 1997 / Accepted: 4 November 1997     

第I类非自共轭锥上的Gamma函数

本文将Ｇａｍｍａ函数及Ｓｉｅｇｅｌ积分推广到一般的第Ｉ类非自共轭锥上．作为其应用，显式给出了以这些锥为底的管状域（或第一类Ｓｉｅｇｅｌ域）的Ｃａｕｃｈｙ Ｓｚｅｇ¨ｏ核和形式Ｐｏｉｓｏｎ核．     

Energy of formation for and liquid binary alloys

We have investigated the free energy of formation for Ag_xIn_1-x and Ag_xSn_1-x liquid binary alloys at temperatures 1173 and 1250 K, respectively. A microscopic theory based on the first order perturbation has been applied. The interionic interaction and a reference liquid are the fundamental components of the theory. The interionic interaction is described by a local pseudopotential. A liquid of hard spheres (HS) of two different effective diametres and charges is used to describe the reference system. The results of the calculations for energy of formation agree very well with the available experimental data. Our calculations also reveal that a simple perturbative approach along with appropriate effective pair potentials can produce nearly quantitative results for the concerned alloys.     

On Hardy’s Theorem on SU(1, 1)

The classical Hardy theorem asserts that ■ and its Fourier transform ■ can not both be very rapidly decreasing.This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform.However,on SU(1,1)there are infinitely many"good"functions in the sense that ■ and its spherical Fourier transform ■ both have good decay. In this paper,we shall characterize such functions on SU(1,1).