可靠度的M-Bayes可信限及其性质

以前作者提出了一种新的参数估计方法-M-Bayes可信限法,并且给出了可靠度的M-Bayes可信下限的估计.给出了另一个可靠度的M-Bayes可信下限的估计,并给出了M-Bayes可信下限的性质一可靠度的两个M-Bayes可信下限与经典置信下限的关系.最后,给出一个例子,从这个例子可以看出本文提出的方法可行且便于应用.     

可靠度的双侧M-Bayes可信限

对二项分布的可靠度,提出了一种新的参数估计方法—双侧M-Bayes可信限法.在无失效数据情形,给出了可靠度的双侧M-Bayes可信的定义、双侧M-Bayes可信的估计,关于双侧M-Bayes可信限的性质提出了一个猜想—可靠度的双侧M-Bayes可信限与双侧经典置信限的关系.最后,给出了一个例子,通过这个例子可以看出双侧M-Bayes可信限优于双侧经典置信限.     

指数分布场合下无失效数据的统计分析

由于产品的可靠性愈来愈高，所以在可靠性寿命试验中，“无失效数据”的现象也愈来愈多．本文根据指数分布的无记忆性，给出可靠度的先验分布，进而在无失效数据的情况下，得到了平均寿命的Bayes估计。     

无失效数据情形可靠性参数的估计和调整

本文在无失效取样情形下,提出了产品可靠性参数的一种估计和调整的方法———加权多层Bayes估计法.在无失效数据情形下失效率的多层Bayes估计和引进失效信息后失效率的多层Bayes估计的基础上,对可靠性参数进行了估计和调整———给出了失效率和可靠度的加权多层Bayes估计.最后,结合发动机的实际问题进行了计算,结果表明本文提出的方法可行且便于应用.     

逐步Ⅰ型混合截尾下指数-威布尔分布竞争失效模型的统计分析（英文）

本文基于指数-威布尔分布研究逐步Ⅰ型混合截尾竞争失效模型的统计推断问题.根据模型假设和竞争失效数据,推导出未知参数和产品可靠度的极大似然估计;考虑极大似然估计的渐近正态性质,计算出观测Fisher信息阵,从而获得未知参数和可靠度的渐近置信区间.由于贝叶斯后验密度函数不具有封闭形式,利用MCMC方法给出未知参数和可靠度的近似贝叶斯估计以及最大后验密度可信区间.最后通过模拟研究对估计方法作出解释并给出数值结果.结果表明极大似然方法和贝叶斯方法可以对逐步Ⅰ型混合截尾竞争失效模型进行统计推断.     

无失效数据失效概率的Bayes估计

本文对无失效数据(ti,ni)在ti 时刻的失效概率pi= P｛T< ti｝的先验密度的核为(1- pi)k时,给出了pi 的Bayes估计和多层Bayes估计,由此可以得到无失效数据可靠度的估计.最后,结合实际问题进行了计算.     

无失效数据的多层Bayes可靠性分析

本文对无失效数据（ti,ni）在时刻ti的失效概率pi＝p｛T＜ti｝的先验分布为不完全Beta分布时，给出了pi的多层Bayes估计，由此可以得到无失效数据可靠度的估计．     

耗损型产品的可靠性评估方法

本文研究耗损型产品可靠度的评定方法 .耗损型产品的可靠度随着每次的使用 ,可靠度会有所降低 .根据多次使用的试验数据 ,推断产品在某次使用之后的可靠度 .这是一个变动母体的统计推断问题 .本文在变动母体的假定下给出了耗损型产品可靠度的置信下限     

无失效数据失效概率的估计

本文对无失效数据(ti,ni),在时刻ti的失效概率pi=p{T＜ti}的先验分布为不完全Beta分布Beta(pi-1,λi;1,b)时,给出了pi的多层Bayes估计,从而可以得到无失效数据可靠度的估计.     

无失效数据的Bayes和多层Bayes分析

本文推广了文献[6]的结果，对指数分布无失效数据的失效率，给出了Bayes估计、Bayes置信上限以及多层Bayes估计，从而可以得到无失效数据可靠度的估计，最后，结合实际问题进行了计算。     

Derivations of Direct Limits of Lie Superalgebras

We describe the derivations of a direct limit 𝔏 of Lie superalgebras 𝔏ⁱ (i ∈ I) in an 𝔏-module 𝔲 as the inverse limit of the derivations of 𝔏ⁱ's in 𝔲. Using this, in case the first cohomology group of each 𝔏ⁱ with coefficients in 𝔲 is zero, we describe the derivations of 𝔏 in 𝔲 as the inverse limit of 𝔲/𝔲𝔏ⁱ (i ∈ I). This then allows us to compute the derivations of direct limits of finite-dimensional basic classical simple Lie superalgebras.     

Some limit analysis in a one-dimensional stationary quantum hydrodynamic model for semiconductors

In this paper, we study the steady-state hydrodynamic equations for isothermal states including the quantum Bohn potential. The one-dimensional equations for the electron current density and the particle density are coupled self-consistently to the Poisson equation for the electric potential. The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations. In a bounded interval supplemented by the proper boundary conditions, we investigate the zero-electron-mass limit, the zero-relaxation-time limit, the Debye-length (quasi-neutral) limit, and some combined limits, respectively. For each limit, we show the strong convergence of the sequence of solutions and give the associated convergence rate.     

Existence and some limits of stationary solutions to a one-dimensional bipolar Euler-Poisson system

In this paper, we study the stationary flow for a one-dimensional isentropic bipolar Euler-Poisson system (hydrodynamic model) for semiconductor devices. This model consists of the continuous equations for the electron and hole densities, and their current densities, coupled the Poisson equation of the electrostatic potential. In a bounded interval supplemented by the proper boundary conditions, we first show the unique existence of stationary solutions of the one-dimensional isentropic hydrodynamic model, based on the Schauder fixed-point principle and the careful energy estimates. Next, we investigate the zero-electron-mass limit, combined zero-electron mass and zero-hole mass limit, the zero-relaxation-time limit and the Debye-length (quasi-neutral) limit, respectively. We also show the strong convergence of the sequence of solutions and give the associated convergence rates.     

ASYMPTOTIC LIMITS OF ONE－DIMENSIONAL HYDRODYNAMIC MODELS FOR PLASMAS AND SEMICONDUCTORS

51. IntroductionIn mathematica1 modeling and numerical simulation for plasmas and semiconductorsdevices, the hydrodynamic model like the Euler-Poisson system is wildly used. Due tothe hyperbolic feature of the Euler equations, the study of weak solutions to the Euler-Poisson system is limited in one space dimension. In such situation, the existence of globalweak solutions can be proved under natural assumptions (see [22, 20, 17, 5, 18]). In aseries of papersl1l'l2'l31l4J l we are interested…     

Semiclassical and relaxation limits of bipolar quantum hydrodynamic model for semiconductors

The global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in R³. We prove that the unique strong solution exists and converges globally in time to the strong solution of classical bipolar hydrodynamical equation in the process of semiclassical limit and that of the classical drift-diffusion system under the combined relaxation and semiclassical limits.     

On the Limiting Proportion of Types

Consider a system into which units of random type enter at fixed points in time. Suppose each unit is endowed with a lifetime whose distribution is specific to its type, during which it is active (present in the system), and after which it is inactive (deleted from the system). Some unit types may tend to remain active for longer periods than others, and thus the limiting proportion of a given type within the active population may differ from the probability that an entering unit is of that type. The relation between the probabilities of types and the limiting proportion of types is shown to depend on the life distributions in a manner determined by the arrival time sequence.     

三元函数的重极限与混合极限

本文引入了三元函数的混合极限概念,对三元函数的混合极限与重极限的区别及联系进行了探讨.结论表明,三元函数的混合极限与重极限之间没有必然的蕴含关系,另一方面,在一定条件下二者也存在着联系.     

On the Continuous Singularity of the Limit Distribution of Products of I.I.D. d×d Stochastic Matrices

This article gives sufficient conditions for the limit distribution of products of i.i.d. d×d random stochastic matrices, d finite and 2, to be continuous singular, when the support of the distribution of the individual random matrices is finite or countably infinite. Proofs are based on applications of the multivariate Central Limit Theorem.     

Asymptotic profile in a one-dimensional steady-state nonisentropic hydrodynamic model for semiconductors

We study the stationary flow for a one-dimensional nonisentropic hydrodynamic model for semiconductor devices. This model consists of the continuous equations for the electron density, the electron current density and electron temperature, coupled the Poisson equation of the electrostatic potential. In a bounded interval supplemented by the proper boundary conditions, we investigate the zero-electron-mass limit, the zero-relaxation-time limit and the Debye-length (quasi-neutral) limit, respectively. We show the strong convergence of the sequence of solutions and give the associated convergence rate.     

基于“以学为中心”的数列极限教学设计研究

本文选取数列极限的定义这一部分内容,基于“以学为中心”教学理念介绍如何设计数列极限定义的教学过程,从九个环节进行设计旨在使学生更好的理解掌握数列极限的本质和内涵,达到以学为中心的教学目标.