UNIFORM BOUNDEDNESS AND UNIFORM STABILITY OF A KIND OF DELAY──DIFFERENTIAL EQUATIONS

ＵＮＩＦＯＲＭＢＯＵＮＤＥＤＮＥＳＳＡＮＤＵＮＩＦＯＲＭＳＴＡＢＩＬＩＴＹＯＦＡＫＩＮＤＯＦＤＥＬＡＹ──ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＺｈｅｎｇＢｕｎａｎ（ＧｕａｎｇｘｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐａ...     

GLOBAL STRUCTURE OF THE ORBITS OF A KIND OF N－DIMENSIONAL COMPETITIVE SYSTEMS

ＧＬＯＢＡＬＳＴＲＵＣＴＵＲＥＯＦＴＨＥＯＲＢＩＴＳＯＦＡＫＩＮＤＯＦＮ－ＤＩＭＥＮＳＩＯＮＡＬＣＯＭＰＥＴＩＴＩＶＥＳＹＳＴＥＭＳ￥ＣｈｅｎｇＣｈｕｎ－ｃｈｏｒ，Ｌｉｔｗｉｎ（郑振初）（ＨｏｎｇＫｏｎｇＩｎｓｔｉｔｕｔｅｏｆＥｄｕｃａｔｉｏｎ，香港...     

BOOTSTRAP MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETER IN SPECTRAL DENSITY OF STATIONARY PROCESSES

ＢＯＯＴＳＴＲＡＰ　ＭＡＸＩＭＵＭＬＩＫＥＬＩＨＯＯＤＥＳＴＩＭＡＴＩＯＮＯＦＴＨＥＰＡＲＡＭＥＴＥＲＩＮＳＰＥＣＴＲＡＬＤＥＮＳＩＴＹＯＦＳＴＡＴＩＯＮＡＲＹ　ＰＲＯＣＥＳＳＥＳＹＵＤＡＮ（于丹）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ...     

EXISTENCE OF WEAK SOLUTIONS OF 2－D EULER EQUATIONS WITH INITIAL VORTICITY ω_0∈E（log~＋L）~α（α＞0）

ＥＸＩＳＴＥＮＣＥＯＦＷＥＡＫＳＯＬＵＴＩＯＮＳＯＦ２－ＤＥＵＬＥＲＥＱＵＡＴＩＯＮＳＷＩＴＨＩＮＩＴＩＡＬＶＯＲＴＩＣＩＴＹω＿０∈Ｅ（ｌｏｇ￣＋Ｌ）￣α（α＞０）ＪＩＵＱＵＡＮＳＥＮ（ＩｎｓｔｉｔｕｔｅＯｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔ...     

A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA

ＡＫＥＲＮＥＬＥＳＴＩＭＡＴＯＲＯＦＡＤＥＮＳＩＴＹＦＵＮＣＴＩＯＮＩＮＭＵＬＴＩＶＡＲＩＡＴＥＣＡＳＥＦＲＯＭＲＡＮＤＯＭＬＹＣＥＮＳＯＲＥＤＤＡＴＡ￥ＺｈｏｕＹｏｎｇ（周勇）（ＰｒｏｂａｂｉｌｉｔｙｌａｂｏｒａｔｏｒｙｉｎＩｎｓｔ．ｏｆＡｐｐｌ．...     

ADMISSIBILITY OF LINEAR ESTIMATE OF REGRESSION COEFFICIENTS IN GROWTH CURVE MODEL UNDER MATRIX LOSS

ＡＤＭＩＳＳＩＢＩＬＩＴＹＯＦＬＩＮＥＡＲＥＳＴＩＭＡＴＥＯＦＲＥＧＲＥＳＳＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳＩＮＧＲＯＷＴＨＣＵＲＶＥＭＯＤＥＬＵＮＤＥＲＭＡＴＲＩＸＬＯＳＳＷＡＮＧＸＵＥＲＥＮ（王学仁）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，...     

LIMIT CYCLES AND BIFURCATION CURVES FOR THE QUADRATIC DIFFERENTIAL SYSTEM(III)_(m=0)HAVING THREE ANTI-SADDLES(II)

ＬＩＭＩＴＣＹＣＬＥＳＡＮＤＢＩＦＵＲＣＡＴＩＯＮＣＵＲＶＥＳＦＯＲＴＨＥＱＵＡＤＲＡＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭ（ＩＩ）ｍ＝０ＨＡＶＩＮＧＴＨＲＥＥＡＮＴＩＳＡＤＤＬＥＳ（Ｉ）ＹＥＹＡＮＱＩＡＮＡｂｓｔｒａｃｔＡｓａｃｏｎｔｉ...     

ON THE DIFFERENTIABILITY OF THE PARITY PROGRESSIVE POPULATION SEMIGROUP

ＯＮＴＨＥＤＩＦＦＥＲＥＮＴＩＡＢＩＬＩＴＹＯＦＴＨＥＰＡＲＩＴＹＰＲＯＧＲＥＳＳＩＶＥＰＯＰＵＬＡＴＩＯＮＳＥＭＩＧＲＯＵＰ￥ＳＨＩＤＥＭＩＮＧＡＮＤＹＡＮＧＬＵＳＨＡＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅ...     

A modified Frank-Wolfe algorithm and its convergence properties

ＡＭＯＤＩＦＩＥＤＦＲＡＮＫ－ＷＯＬＦＥＡＬＧＯＲＩＴＨＭＡＮＤＩＴＳＣＯＮＶＥＲＧＥＮＣＥＰＲＯＰＥＲＴＩＥＳＷＵＦＡＮＧ（吴方）ＷＵＳＨＩＱＵＡＮ（吴士泉）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ｔｈｅＣｈｉｎｅｓｅＡｃａｄ...     

A SIMPLE STABILITY CRITERION FOR A SYSTEM OF NEUTRAL DIFFERENTIAL EQUATIONS

ＡＳＩＭＰＬＥＳＴＡＢＩＬＩＴＹＣＲＩＴＥＲＩＯＮＦＯＲＡＳＹＳＴＥＭＯＦＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＹｕＪｉｎｃｈａｎｇ（余晋昌）（ＤｏｎｇｇｕａｎＮｏｒｍａｌＳｃｈｏｏｌ，东莞师范学校，邮编：５１７００）Ａｂｓｔｒａｃ...     

Reliability analysis of a warm standby repairable system with priority in use

In this paper, a warm standby repairable system consisting of two dissimilar units and one repairman is studied. In this system, it is assumed that the working time distributions and the repair time distributions of the two units are both exponential, and unit 1 is given priority in use. After repair, both unit 1 and unit 2 are “as good as new”. Moreover, the transfer switch in the system is unreliable, and the function of the switch is: “as long as the switch fails, the whole system fails immediately”. Under these assumptions, using Markov process theory and the Laplace transform, some important reliability indexes and some steady state system indexes are derived. Finally, a numerical example is given to illustrate the theoretical results of the model.     

Reliability analysis of 1-for-2 shared protection systems with general repair-time distributions

In this paper, we investigate the reliability of a type of 1-for-2 shared protection systems. The 1-for-2 shared protection system is the most basic fault-tolerant configuration with shared backup units. We assume that there are two working units each serving a single user and one shared protection (spare) unit in the system. We also assume that the times to failure and to repair are subject to exponential and general distributions respectively. Under these assumptions, we derive the Laplace transform of the survival function (the cdf that the system will survive beyond a given time) for each user as well as the user-perceived Mean Time to First Failure (MTTFF) by combining the state transition analysis and the supplementary variable method. We also show the effect of the repair-time distribution, the failure rates and the repair rates of the units through the case study of small-sized two enterprises that share one spare device for backup purpose. The analysis reveals what is important and what should be done in order to improve the user-perceived reliability of shared protection systems.     

Bilevel control of degraded machining system with warm standbys, setup and vacation

In this paper, we study (N, L) switch-over policy for machine repair model with warm standbys and two repairmen. The repairman (R₁) turns on for repair only when N-failed units are accumulated and starts repair after a set up time which is assumed to be exponentially distributed. As soon as the system becomes empty, the repairman (R₁) leaves for a vacation and returns back when he finds the number of failed units in the system greater than or equal to a threshold value N. Second repairman (R₂) turns on when there are L(>N) failed units in the system and goes for a vacation if there are less than L failed units. The life time and repair time of failed units are assumed to be exponentially distributed. The steady state queue size distribution is obtained by using recursive method. Expressions for the average number of failed units in the queue and the average waiting time are established.     

Cost-benefit analysis of one-server n-unit adaptive system with slow switch

This paper considers a shared parallel system consisting of n-units supported by single service facility to carry out both installation and repair of a unit. Initially, all the n units share the total load equally and when one or more units fail, they go for repair while the other surviving units share the entire load equally till the failed units are ready for operation after installation. The installation time (switchover time) of a repaired unit is assumed to be non-negligible and random. The system will be down when all the units are non-operative , Assuming that the failure rates are different when the units function under varying loads, the system characteristics, namely, (1) the expected up-time of the system during (0, t], (2) the expected repair time of the units which failed due to varying failure rates during (0, t] and (3) the expected time spent by the units in the installation state during the period (0, t], are obtained by identifying the system at suitable regeneration epochs. The repair time and the switchover time of the units are arbitrarily distributed. The failure rate of unit is assumed to be constant. It depends on the number of surviving units at any instant. The cost-benefit analysis is also carried out using these system characteristics     

Reliability Analysis of a One-Unit System with Unrepairable Spare Units and its Optimization Applications

It is assumed that a unit is either in operation or is in repair. When the main unit is under repair, spare units which cannot be repaired are used. In this system the following quantities are of interest: (i) The time distribution and the mean time to first-system failure, given that the n spare units are provided at time 0. (ii) The probability that the number of the failed spare units are equal to exactly n during the interval (0, t], and its expected number during the interval (0, t]. These quantities are derived by solving the renewal-type equations.Two optimization problems are discussed using the results obtained, viz.: (i) The expected cost of two systems, one with both a main unit and spare units and the other with only spare units is considered. (ii) A preventive maintenance policy of the main unit is considered in order to minimize the expected cost rate. Some policies of the two problems are discussed under suitable conditions. Numerical examples are also presented.     

General analysis of l-out-of-2: f system exposed to cumulative damage processes

This paper presents models in l-out-of-2:F system. In Model 1, one unit is exposed to cumulative damage process and the other unit lias a constant failure rate. In Model 2, the two units are exposed to cumulative damage processes. They have exponential thresholds and exponential inter-damage times. Introducing a repair facility which repairs ail the damages one by one after the system-failure, this paper treats the joint Laplace transforms of the up and the down times. Marginal down time distributions .are calculated when there exists a repair facility for every damage.     

A standby system with two types of repair persons

A continuously monitored one‐unit system, backed by an identical standby unit, is perfectly repaired by an in‐house repair person, if achievable within a random or deterministic patience time (DPT), or else by a visiting expert, who repairs one or all failed units before leaving. We study four models in terms of the limiting availability and limiting profit per unit time, using semi‐Markov processes, when all distributions are exponential. We show that a DPT is preferable to a random patience time, and we characterize conditions under which the expert should repair multiple failed units (rather than only one failed unit) during each visit. We also extend the method when life‐ and repair times are non‐exponential. Copyright © 2009 John Wiley & Sons, Ltd.     

一类具有可修复储备部件的人-机系统解的半离散化

针对一个具有两个运行部件和一个储备部件,考虑系统通常故障的发生,且系统故障修复时间服从一般分布的人-机系统模型,对系统模型中修复率用初等阶梯函数进行逼近,给出了系统的半离散化模型,为进一步数值计算打下理论基础.     

Reliability analysis of a three unit warm standby redundant system with repair

Two-unit warm standby redundant systems have been investigated extensively in the past. The most general model is the one in which both the lifetime and repair time distributions of the units are arbitrary. However the study of standby systems with more than two units, though very important, has received much less attention, possibly because of the built-in difficulties in analyzing them. Such systems have been studied only when either the lifetime or the repair time is exponentially distributed. When both these distributions are general, the problem appears to be intractable even in the case of cold standby systems. The present contribution is an improvement in the state of art in the sense that a three unit warm standby system is shown to be capable of comprehensive analysis. In particular we show that there are imbedded renewal points that render the analysis possible. Using these imbedded renewal points we obtain the reliability and availability functions. Emeritus Deceased 23rd December 2003.     

同时考虑故障相关和变故障率的可修系统可靠性计算

基于Copula相关性理论,考虑可修系统零部件工作寿命、故障部件修复时间之间的正相关性,且将零件工作寿命、修复时间放宽到一般连续分布,而不局限于指数分布.提出微时间差t→t+△t内系统一步状态转移矩阵概念,进而演算出状态转移密度矩阵,经系统状态方程,分别给出了任意时刻t单部件、串联型、二不同单元和一修理工组成的并联可修系统的可用度和稳态可用度计算模型.通过算例,说明该理论方法的可行性.