Carathéodory's method for a class of second order differential equations on the half-line

The method of equivalent variational methods, originally due to Carathéodory for free problems in the calculus of variations is extended to investigate boundary value problems for a class of second order differential equations on the half-line. Some applications are presented to illustrate the potential of this method.     

Parameter determination of a thermal desorption model

A new method for the analysis of thermal desorption spectra is presented, based on the experimental peak maximum functions for temperatureT _m(β) and pressureP _m(β) and a rigorous mathematical treatment. The resonant heating rate β_r is determined, satisfyingT _m(β_r)=T _r, whereT _r is the resonant temperature defined byA exp(−E _d/(RT _r))=1. Desorption energyE _d and frequency factorA can be determined simultaneously with relatively high robustness towards statistical experimental errors as demonstrated by computer-simulated thermal desorption spectra.     

Large Sample Properties of Mixture Models with Covariates for Competing Risks

We study the large-sample properties of a class of parametric mixture models with covariates for competing risks. The models allow general distributions for the survival times and incorporate the idea of long-term survivors. Asymptotic results are obtained under a commonly assumed independent censoring mechanism and some modest regularity conditions on the survival distributions. The existence, consistency, and asymptotic normality of maximum likelihood estimators for the parameters of the model are rigorously derived under general sufficient conditions. Specific conditions for particular models can be derived from the general conditions for ready check. In addition, a likelihood-ratio statistic is proposed to test various hypotheses of practical interest, and its asymptotic distribution is provided.     

K2O-ZnO-Al2O3-B2O3-SiO2系掺Cr3+透明莫来石微晶玻璃的研究

采用了X射线衍射、透射电镜和吸收光谱及荧光光谱技术研究了K2O－ZnO-Al2O3-B2O3－SiO2系掺Cr^3 玻璃的析晶性能和光谱。研究结果表明：在K2O－Al2O3-B2O3-SiO2系掺Cr^3 玻璃的基础上引入ZnO后，析晶性能明显改善；析晶温度降低，析出的纳米莫来石微晶均匀、规则；微晶玻璃的发光强度明显增强。     

Use of a long-spacer-side-chain liquid crystalline polysiloxane containing a crown ether as a stationary phase for capillary gas chromatography

A new kind of side chain liquid crystalline polysiloxane containing a crown ether with a longer spacer (PSC-11) has been prepared and coated on a fused silica capillary column. The main chroma-tographic characteristics including efficiency, polarity, and selectivity have been examined. The phase exhibits the retention properties of both liquid crystal and crown ether stationary phases and possesses higher efficiency and better selectivity than PSC-3, which has a shorter spacer between the main polysiloxane chain and liquid crystalline side chain.     

几类数列通项的矩阵求法

本利用矩阵给出了几类数列的通项公式的求法，把数列通项公式的求法转化为矩阵幂的计算，思路简单、计算简便，并能判别其敛散性。     

THE ASYMPTOTIC SOLUTION FOR A CLASS OF SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR SINGULAR EQUATION

The singularly perturbed boundary value problem for a class of semilinearsingular equation is considered. Using a simple and special method the asym-ptotic behavior of solution is studied.     

具有位相型修理的离散时间可修排队系统

本文研究了具有一般独立输入，位相型修理的离散时间可修排队系统，假定服务台对顾客的服务时间和服务台寿命服从几何分布，运用矩阵解析方法我们给出系统嵌入在到达时刻的稳态队长分布和等待时间分布，并证明这些分布均为离散位相型分布．我们也得到在广义服务时间内服务台发生故障次数的分布，证明它服从一个修正的几何分布．我们对离散时间可修排队与连续时间可修排队进行了比较，说明这两种排队系统在一些性能指标方面的区别之处．最后我们通过一些数值例子说明在这类系统中顾客的到达过程、服务时间和服务台的故障率之间的关系．