一类具有不定奇性的二阶微分方程周期正解的存在性

本文研究了一类具有不定奇性的二阶微分方程x″-(α(t))/(x~(μ(t)))=h(t)周期正解的存在性问题,其中μ∈(0,1]为常数,α(t)和h(t)是T-周期的函数:α,h∈L~1([0,T],R),而且α(t)在t∈[0,T]上是可变号的.     

周期演化域上一个禽流感模型的动力学分析

本文研究了周期演化区域上一个禽流感模型.首先假设区域的增长为各向同性,将模型转换为固定区域上的反应扩散问题.然后利用相关的特征值问题和上下解方法得出模型解的渐近性态.研究结果表明,周期性区域的演化对疾病的传播与抑制取决于区域的周期演化速率ρ(t)的积分平均值-(ρ-2)=1/T∫T01/ρ2(t)dt.若-(ρ-2)＞...     

系统的最佳随机维护策略

系统进行有计划的预防性维护时,要求设计一个具有周期T的维护时间表.有一个重要的问题就是这种维护时间表是否具有最佳周期.本文给出最佳随机维护策略问题有解存在的必要条件,并得到结论:当失效时刻Y服从指数分布时,对维护次数N的任意概率分布,最佳随机维护策略问题都无解.     

具有变量时滞的周期微分系统的周期解

本文考虑周期微分系统x(t) =A(t,x(t- r1(t) ) ) x(t) + f (t,x (t- r2 (t) ) )的 T-周期解的存在性问题 ,其中 (t,x)∈R× Rn,A(t,x)是 n× n连续矩阵函数 ,f(t,x)是 n维连续向量函数 ,时滞 ri(t) (i=1,2 )是连续函数 ,且 A(t+ T,x) =A(t,x) ,f(t+ T,x) =f(t,x) ,ri(t+ T) =ri(t) (i=1,2 ) ,常数T>0 .本文利用不动点方法 ,建立了保证系统存在 T-周期解的充分条件 ,推广了文 [1- 3]的相关结果 .     

一类推广的干摩擦问题周期解的存在性

为了得到干摩擦问题存在周期解的判断方法,利用微分包含理论对系统+k~2x+μSngp(t)+T(t)a.e.进行了讨论.在周期外力p(t)周期等于固有周期2π/R的情形下得到了周期解存在的充要条件,在周期外力p(t)周期不等于固有周期整数倍2nπ/R的情形下得到了周期解存在的充分条件.     

具时滞的高维周期系统周期解的存在性与唯一性

本文考虑了具时滞的高维周期系统x’(t)=A(t,x(t))x(t)+f(t,x(t-r)),其中(t,x)∈R×R~n,A(t,x)是n×n连续矩阵,f(t,x)是n维连续向量,且A(t+T,x)=A(T,x),f(t十T,x)=f(t,x).利用不动点方法,建立了保证其T周期解的存在性及唯一性的充分条件.所得结果推广、改进了文[1-3]的主要结果.     

周期函数基本结果概览北大核心

1基本定义为简单起见,我们不妨设所考虑的函数f(t)定义在整个数轴R=(-∞,+∞)上.定义1(周期函数)若实数T≠0使得f(t+T)=f(t)对一切t∈R恒成立,则称T是f的一个周期,并称f是周期为T的周期函数.注1设函数f的定义域是R的某个子集D,若对任意t∈D有t±T∈D且f(t+T)=f(t),则称f是D上的周期函数.     

高校应用数学学报第18卷(2003年)B辑(英文版)第4期目次和提要

非线性微分方程的正周期解刘玉记　葛渭高 (北京理工大学 )研究一阶非线性微分方程 x′( t) =-δ( t) x( t) + f ( t,x( t) )的正周期解的存在性 ,其中δ( t)是非负周期为 T的周期函数 ,f ( t,x)连续且关于 t的周期为 T,这里 T >0 .获得了该方程存在两个正周期解的充分条件 .用例子说明了定理的实用性 .具超前变元的二阶微分方程三点边值问题的正解朱立斐　李永昆 (云南大学数学系 )用 Krasnoselskii不动点定理获得如下具超前变元的二阶微分方程u″( t) +λa( t) f ( u( h( t) ) ) =0 ,　 t∈ ( 0 ,1) ,u( 0 ) =0 ,　αu(η) =u( 1)三点边…     

二阶哈密尔顿系统的对称扰动(英文)

我们研究二阶Hamiltonian系统-ü=▽F1(t,u)+ε▽F2(t,u)a.e.t∈[0,T]的多重周期解,其中ε是一个参数,T0.F1(F2)∶R×RN→R关于t是T周期的,▽F1(t,x)关于x是奇的;并且Fi(t,x)(i=1,2)对所有x∈RN关于t是可测的,对几乎所有t∈[0,T]关于x是连续可微的,而且存在a∈C(R+,R+),b∈L+(0,T;R+)使得|Fi(t,x)|≤a(|x|)b(t),|▽Fi(t,x)|≤a(|x|)b(t)对所有x∈RN及几乎所有t∈[0,T]成立.我们对F1施加适当的条件,能够证明对任意的j∈N存在εj0使得|ε|≤εj,则上述问题至少有j个不同的周期解.     

关于函数周期性的一些讨论

设Q表示有理数集 ,R表示实数集 ,C表示复数集 .函数f(t) :R →C称为是T周期的 ,是指存在常数T>0 ,使f(t +T) =f(t) , t∈R .最小的周期T >0 ,称为f(t)的基本周期 .众所周知 ,Dirichlet函数 (它不连续 )和常函数是周期函数 ,但它们没有基本周期 .那么会问什么样的函数会有基本周期呢 ?我们有命题 1　如果f(t)是非常数的连续周期函数 ,则它有基本周期 .证明　用反证法 .若f(t)不存在最小的正周期 ,则存在单调减少的正序列 {kn},kn → 0 ,满足f(t+kn) =f(t) ,t∈R .于是f(t+mkn) =f(t) , t∈R和对任何整数m ,n .设t0 是任何实数 .对任何n…     

Unrelated parallel-machine scheduling with deterioration effects and deteriorating multi-maintenance activities for minimizing the total completion time

This paper investigates scheduling problems with simultaneous considerations of deterioration effects and deteriorating multi-maintenance activities on unrelated parallel machines. We examine two models of scheduling with the deterioration effect, namely the job-dependent and position-dependent deterioration model and the time-dependent deterioration model. We assume that each machine may be subject to several maintenance activities over the scheduling horizon, and the duration of maintenance on a machine depends on its running time. Moreover, due to the restriction of the budget of maintenance, the upper bound of the total maintenance frequencies on all the machines is assumed to be known in advance. The objective is to find jointly the optimal maintenance frequencies, the optimal maintenance positions, and the optimal job sequences such that the total completion time is minimized. If the number of machines is fixed, we introduce polynomial time solutions for all the versions of the problem under study.     

Contribution of simulation to the optimization of maintenance strategies for a randomly failing production system

This paper compares two strategies for operating a production system composed of two machines working in parallel and a downstream inventory supplying an assembly line. The two machines, which are prone to random failures, undergo preventive and corrective maintenance operations. These operations with a random duration make the machines unavailable. Moreover, during regular subcontracting operations, one of these machines becomes unavailable to supply the downstream inventory. In the first strategy it is assumed that the periodicity of preventive maintenance operations and the production rate of each machine are independent. The second strategy suggests an interaction between the periods of unavailability and the production rates of the two machines in order to minimize production losses during these periods. A simulation model for each strategy is developed so as to be able to compare them and to simultaneously determine the timing of preventive maintenance on each machine considering the total average cost per time unit as the performance criterion. The second strategy is then considered, and a multi-criteria analysis is adopted to reach the best cost-availability compromise.     

Two-machine flowshop scheduling with availability constraints

The majority of the scheduling literature carries a common assumption that machines are available all the time. However, this availability assumption may not be true in real industry settings, since a machine may become unavailable during certain periods of time when, for instance, a machine breakdown or a preventive maintenance activity is scheduled. Although the problem is realistic and important, it is relatively new and unstudied. In this paper, we study the two-machine flowshop problem under the assumption that the unavailable time is known in advance. We assume that if a job cannot be finished before the next down period of a machine then the job will have to partially restart when the machine has become available again. We call our model semiresumable. Our model contains two important special cases: resumable where the job can be continued without any penalty and nonresumable where the job needs to totally restart. We study the problem where an availability constraint is imposed only on one machine as well as on both machines. We provide complexity analysis, develop a pseudo-polynomial dynamic programming algorithm to solve the problem optimally and also propose heuristic algorithms with an error bound analysis.     

Determining Economic Maintenance Frequency for a Family of Machines

This paper deals with the problem of determining economic maintenance frequency for a group of machines. The operating cost for each machine is assumed to increase with time since the last maintenance work carried out on the machine. The cost of carrying out maintenance work is known and assumed constant. A fixed cost is incurred whenever maintenance work is carried out, and this fixed cost is assumed to be independent of the number of machines on which maintenance work is carried out. The total cost of the system is given by the sum of maintenance and operating costs for all the machines. A heuristic method is proposed for determining the economic maintenance frequency of each machine. An example is given to illustrate the method.     

带两个服务等级的三台机最优在线算法

研究了带服务等级约束的三台平行机在线排序问题.每台机器和每个工件的服务等级为1或者2,工件只能在等级不高于它的机器上加工,即等级为1的工件只能在等级为1的机器上加工,等级为2的工件可在所有机器上加工.每个工件的加工时间为一个单位,目标是极小化所有工件的总完工时间.考虑两种情形:当一台机器等级为1,两台机器等级为2时,给出了竞争比为17/14的最优在线算法;当两台机器等级为1,一台机器等级为2时,给出了竞争比为43/36的最优在线算法.     

Complexity results and approximation algorithms for the two machine no-wait flow-shop with limited machine availability

The scheduling problems studied in this paper concern a two-machine no-wait flow shop problem with limited machine availability. In this model, we assume that machines may not always be available, for example because of preventive maintenance. We only consider the deterministic case where the unavailable periods are known in advance. The objective function considered is the maximum completion time (C_max). We prove that the problem is NP-hard even if only one non-availability period occurs on one of machines, and NP-hard in the strong sense for arbitrary numbers of non-availability periods. We also provide heuristic algorithms with error bounding analysis.     

Efficiency and production rate of a transfer line with two machines and a finite storage buffer

A markov model for a transfer line with two unreliable machines separated by a finite storage size buffer is introduced. Service time distribution for the two machines is Erlang whereas failure and repair times are assumed to be exponential random variables. The paper presents an efficient method to solve analytically the steady state probabilities of the system. This method is independent of the buffer size. We also include in the paper a study of the behavior of some systems performance measures such as the efficiency of the two machines and the production rate of the system.     

Parallel machines scheduling with a deteriorating maintenance activity

In this paper, we consider parallel identical machines scheduling problems with a deteriorating maintenance activity. In this model, each machine has a deteriorating maintenance activity, that is, delaying the maintenance increases the time required to perform it. We need to make a decision on when to schedule the deteriorating maintenance activities and the sequence of jobs to minimize total completion time. We provide a polynomial time algorithm to solve the total completion time minimization problem.     

具有时间与位置相关的两类平行机排序问题

研究带有维修时间限制的时间和位置效应平行机排序问题,涉及同型机和非同类机两种机器类型.工件的实际加工时间同时受到位置效应和时间效应影响,且机器具有维修限制.目标函数由机器负载,总完工时间与总等待时间组成.非同类机情形下,通过将排序问题转化为指派问题,给出多项式时间算法,其算法的时间复杂度为O（n^k+2/（k-1）!）.同型机情形下通过转化目标函数,使用匹配算法得出排序问题的多项式时间解,其时间复杂度为O（（2n+m+n log n）n^k-1/（k-1）!）.     

平行机上带有前瞻区间的不相容工件组在线排序问题

研究当不相容工件组的个数与机器数相等时,具有前瞻区间的单位工件平行机无界平行分批在线排序问题.工件按时在线到达, 目标是最小化 最大完工时间. 具有前瞻区间是指在时刻t, 在线算法能预见到时间区间(t,t+\beta) 内到达的所有工件的信息.不可相容的工件组是指属于不同组的工件不能被安排在同一批中加工. \beta\geq 1 时, 提供了一个最优的在线算法; 当0\leq \beta < 1时, 提供了一个竞争比为1+\alpha 的最好可能的在线算法, 其中\alpha是方程\alpha^{2}+(1+\beta) \alpha+\beta-1=0的一个正根.最后, 给出了当\beta =0 时稠密算法竞争比的下界,并提供了达到该下界的最好可能的稠密算法.