具有三次代数曲线解的五次系统的极限环

本文利用Maple软件强大的符号计算能力,得到了以 y=ax~3+bx~2+cx+d 为解的平面五次多项式系统的特征,由此证明了该系统在奇点的邻域内可以存在极限环。     

Limit Theorems for Semi-Markov Queues and Their Applications

We begin by definition of semi-Markov flow and discussion of its properties. Asymptotic behavior of multi-server and single-server queueing systems is studied under assumption of time-compression or service time growth. The results obtained are used for calculation of large systems reliability. Statistical estimates of parameters involved are also provided.     

Applications of quadrivariate exponential distribution to a three-unit warm standby system with dependent structure

Two-unit warm standby systems have been elaborately dealt within the literature. However, the study of standby systems with more than two units, though very relevant in state-of-the-art practical situations, has received little attention because of mathematical intricacies involved in analyzing them. Also, such systems have been studied assuming: (i) the lifetime or repair time of the units to be exponential, or (ii) the lifetime and repair time to be independent. The present contribution is an improvement in the state-of-the-art in the sense that three-unit warm standby system with dependent structure is shown to be capable of comprehensive analysis.     

The effect of autocorrelation on the ewma maxmin tolerance limits

Amin et al. (1999) developed an exponentially weighted moving average (EWMA) control chart, based on the smallest and largest observations in each sample. The resulting plot of the extremes suggests that the MaxMin EWMA may also be viewed as smoothed tolerance limits. Tolerance limits are limits that include a specific proportion of the population at a given confidence level. In the context of process control, they are used to make sure that production will not be outside specifications. Amin and Li (2000) provided the coverages of the MaxMin EWMA tolerance limits for independent data. In this article, it is shown how autocorrelation affects the confidence level of MaxMin tolerance limits, for a specified level of coverage of the population, and modified smoothed tolerance limits are suggested for autocorrelated processes.     

Central Limit Theorem approximations for the number of runs in Markov-dependent binary sequences

We consider Markov-dependent binary sequences and study various types of success runs (overlapping, non-overlapping, exact, etc.) by examining additive functionals based on state visits and transitions in an appropriate Markov chain. We establish a multivariate Central Limit Theorem for the number of these types of runs and obtain its covariance matrix by means of the recurrent potential matrix of the Markov chain. Explicit expressions for the covariance matrix are given in the Bernoulli and a simple Markov-dependent case by expressing the recurrent potential matrix in terms of the stationary distribution and the mean transition times in the chain. We also obtain a multivariate Central Limit Theorem for the joint number of non-overlapping runs of various sizes and give its covariance matrix in explicit form for Markov dependent trials.     

双曲率面光线追迹公式及应用

本文提出了用牛顿迭代法计算光线与双曲率面的交点,并给出了具体的计算公式。文中还认为可以利用双曲率面来描述存在着局部变形的球面光学零件,为制定光学零件的公差提供了依据。     

可数集类的共性集

讨论了有限集类在增补集合的情况下同阶共性集的相互联系，有限集类的共性集与可数集类的共性集之间的极限关系，得出了可数事件的共性事件概率公式．     

改进的L1范数故障诊断方法

本文提出一种线性模拟容差电路故障诊断方法——改进的L_1范数方法。此方法首先运用蒙特卡诺容差分析方法,建立线性模拟容差电路模型,然后通过求解L_1范数优化诊断方程,以诊断故障元件,并在优化求解过程中作了线性化处理。     

追诉时效延长制度探讨

新旧刑法均有关于追诉时效的规定 ,但在追诉时效延长方面规定却有不同。本文认为追诉时效延长制度应当有三种情况 ;同时对这一制度的可能产生歧义的地方进行了理论上的辨析。     

On Max-Multiscaling Distributions as Extended Max-Semistable Ones

Abstract

We introduce max-multiscaling distributions as solutions to a functional equation which, in a natural way, extends the one fulfilled by max-semistable distributions. We establish that strictly max-multiscaling distributions are products of at most two max-semistable distributions. Next, we show how to obtain these solutions as limit laws of normalized maximum of suitable independent sequences of random variables when sample size has geometric growth.