Quasifractional Approximants in the Theory of Composite Materials

We study the effective heat conductivity of regular arrays of perfectly conducting spheres embedded in a matrix with unit conductivity. Quasifractional approximants allow us to derive an approximate analytical solution, valid for all values of the spheres volume fraction [0, _max] (_max is the maximum volume fraction of a spheres). As a starting point we use a perturbation approach for 0 and an asymptotic solution for _max. Three different spatial arrangements of the spheres, simple cubic, body centred and face centred cubic arrays, are considered. Results obtained give a good agreement with numerical data.     

Asymptotic Behavior of Loss Probability in GI/M/1/K Queue as K Tends to Infinity

We obtain an asymptotic behavior of the loss probability for the GI/M/1/K queue as K for cases of <1, >1 and =1.     

一类非线性微分方程周期解的研究

本文研究了一类最普遍的四阶非线性非自治系统的周期解的存在唯一性与渐近稳定性。我们采用了类比缓交系数的方法,作出了相应的Liapunov函数,对缓交系数作了较为精确的估计,得到了存在唯一渐近稳定的周期解的充分条件。     

CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS

ＣＯＮＶＥＲＧＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳ　ＦＯＲＲＬＣ－ＮＯＮＬＩＮＥＡＲＮＥＴＷＯＲＫＳＷＩＴＨＴＩＭＥ－ＶＡＲＹＩＮＧＥＬＥＭＥＮＴＳ￥ＪｉａｎｇＪｉｊａ（蒋断发）（Ｄａｐｔ．ｏｆＭａｔｈ．，ＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃ...     

Third order efficiency implies fourth order efficiency: A resolution of the conjecture of J. K. Ghosh

Under suitable regularity conditions, it is shown that a third order asymptotically efficient estimator is fourth order asymptotically efficient in some class of estimators in the sense that the estimator has the most concentration probability in any symmetric interval around the true parameter up to the fourth order in the class. This is a resolution of the conjecture by Ghosh (1994, Higher Order Asymptotics, Institute of Mathematical Statistics, Hayward, California). It is also shown that the bias-adjusted maximum likelihood estimator is fourth order asymptotically efficient in the class.     

Robust Tracking and Model Following Control with Zero Tracking Error for Uncertain Dynamical Systems

The problem of robust tracking and model following for a class of linear dynamical systems with time-varying uncertain parameters and disturbances is considered. A class of continuous (nonlinear) state feedback controllers is proposed for robust tracking of dynamical signals. The proposed robust tracking controllers can guarantee that the tracking error decreases asymptotically to zero in the presence of uncertain parameters and disturbances. A procedure for designing such a zero tracking state feedback controller is also introduced. Finally, a numerical example is given to demonstrate the validity of the results.     

MOMENT GENERATING FUNCTIONS OF RANDOM VARIABLES AND ASYMPTOTIC BEHAVIOUR FOR GENERALIZED FELLER OPERATORS

1. Introduction and NotationsThe generalized Feller operators which include many famous operators, such ajsBernstein, Szasz-Mirakjan, BaskakoV, Meyer--K5nig and Zeller operators, can be constructed by making use of the probabilistic method. In the paper [1][2], Xu JihuaPr(--lvjdetl a general scheme f(,r its construction, and Zhao Jillghui showed that theFeller type operators are of good approximations f'or unbounded functions.Our purpose is to present representation of moment generating …     

Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship

Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.     

一类二元相关威布尔分布的可靠性问题

本文考虑生存函数为${\ol{F}(x_{1},x_{2})}=\exp\{-[(x_{1}^{1/\alpha}/\theta_{1})^{1/\delta}+(x_{2}^{1/\alpha}/\theta_{2})^{1/\delta}]^{\delta}\},\;x_{i}>0,\;\alpha>0$, $1\geq\delta>0,\;\theta_{i}>0\;(i=1,2)$的二元威布尔分布的两种可靠性问题, 提出可靠度$\pr$的估计并讨论了它们的渐近性, 最后还作了模拟计算.     

具有局部阻尼的热弹性问题的渐近行为和指数稳定性

一个关于具有局部阻尼的半线性热弹性问题,是材料科学中最重要的数学模型之一．这个问题的解的存在性和齐次问题解的指数衰竭于零的性质被得到了．进而,也得到了对非齐次问题吸收集的存在性．结果显示了所研究的系统是渐近稳定的．