关于修正的功的互等定理的讨论

以线弹性直梁系统为例,对Betti-Maxwell功的互等定理与修正的功的互等定理进行了比较研究.研究发现处于真实状态的两个不同的直梁系统均可等效地转化为同一直梁受两组不同外力作用的系统,进而揭示了修正的功的互等定理中"两个不相同的线弹性体"即为位移和力的边界条件相互等效的同一个结构.所以,"修正的功的互等定理"实际上仍是Betti-Maxwell功的互等定理的另一种表现形式.     

“一言堂”变为“一起议”:集体备课方式的进阶思考——以“比较二次函数值的大小问题”为例

<正>集体备课作为学校最基本的教研模式与载体,是实现高质量备课的路径之一.传统集体备课的主要形式：主备或老教师的“一言堂”,言完即收场.一是缺乏教材解读过程中的异质交流;二是缺少适切班情、学情的不同教学方案的个性研磨等.如何改变现状? 可从以下三点入手：一是让不同层次的教师抱团,把个体备课变为差异性共同体备课,让教师之间的交流成为一种必然;二是把主备说课变为差异性共同体之间的对话,形成互辩互证、互学互鉴的氛围; 三是让教学设计先求同,再求异,     

关于求解弹性力学平面问题的功的互等定理法

本文推广功的互等定理法于求解具有复杂边界条件矩形板的弹性力学平面问题.首先,我们给出了作为基本系统的四边固定矩形板平面问题的基本解,然后基于在具有复杂边界条件的实际系统与基本系统之间应用功的互等定理,从而求得实际系统的位移表达式.当只存在位移边界条件时,用功的互等定理法求得的位移表达式就是真实的.但是在另一些情况下,当有静力边界条件或混合边界条件时,所求得的位移是容许的.为求得真实位移.必须应用最小势能原理.一些计算表明.对于求解具有复杂边界条件的矩形板弹性力学平面问题,功的互等定理法是一简便通用的方法.显然,这是一个新方法.     

修如新模型中备件量的计算及其置信上限的Fiducial推断

本文研究了在修如新模型下, 对预定贮存期为$T$同时开始贮存的$N$个系统, 给出在$P_0$可修复率下所需备件数的计算公式; 针对贮存寿命服从威布尔分布的系统, 利用枢轴量, 在$P_0$可修复率和预定贮存期为$T$的条件下, 给出$N$个系统所需备件数的置信上限的定义; 并基于系统寿命试验的完全样本, 利用Fiducial方法得出备件数置信上限的计算方法.     

过抽样四相混沌序列的构成及其扩频应用

结合Chebyshev源映射和通信原理中抽样理论,产生了过抽样混沌映射(OSCM),证明了OSCM也具备混沌特性.并提出利用最大平衡差函数考察序列平衡性.通过和源映射序列广义相关函数的对比,分析了自相关、互相关旁瓣的最大值和平均值,进而分析了四相OSCM序列的相关性.仿真结果表明:针对现行移动通信扩频系统地址码,四相ChebyshevOSCM序列具有良好的自相关和互相关性,可以增强系统的保密性和提升系统容量,是CDMA移动通信扩频系统地址码的优选方案之一.     

浅谈假设检验中原假设和备择假设的建立

建立原假设和备择假设是进行假设检验的第一步.如何设立假设检验中的原假设和备择假设,是学生和初学者普遍困扰的问题.而根据奈曼—皮尔逊准则,原假设和备择假设的地位不对等.本文对如何建立假设检验中的原假设和备择假设进行了讨论,给出了几个建立原假设和备择假设的原则.     

应用功的互等定理法求立方体的位移解

本文推广功的互等定理法于求解弹性力学空间问题.首先,我们给出作为基本系统的六面固定的立方体的基本解,然后在受单位集中载荷作用的基本系统与已知表面位移的实际系统之间应用功的互等定理,从而求得实际系统的位移解.     

基于有限域上奇异线性空间的码本的新构造

码本广泛应用于码分多址系统用于区分不同用户发出的信号.基于有限域上奇异线性空间构造了一类新的码本.运用奇异线性空间的计数定理,得到了码本的参数,计算了码本的最大互相关振幅,并且给出了最大互相关振幅渐近达到Welch界的条件,证明了所构造的码本是渐近最优码本.     

模糊有穷自动机的互模拟关系

互模拟是离散事件系统中的一个等价关系,它已经应用到概率、随机和加权自动机中.本文给出模糊有穷自动机(FFA)前向互模拟关系和后向互模拟关系的定义,并给出它们的一些性质,证明前向和后向互模拟关系对于模糊有穷自动机(FFA)的一些运算(并,连接,交)和模糊正则语言的表现定理是封闭的.另外文中还给出一个可在有限步计算极大前向互模拟关系的算法,最后指出前向和后向互模拟之间的区别.     

多元分布下单边备择假设的两步检验

x~2检验是熟知的拟合优度检验.它适用于任意的备择假设,尤其是适用于一般的备择假设"H_0不真"的情况.但是,当备择假设是一个单边假设时,x~2检验没有用到单边假设所提供的信息.因此,一个充分利用单边备择假设信息的检验是有可能优于传统的x~2检验的.本文就是利用单边备择假设的信息给出了一个两步检验,并通过一个例子,详细介绍了两步检验法的实施,说明了其应用.     

Synthesis and analysis of temporal fault trees with PANDORA: The time of Priority AND gates

Classical Fault Tree Analysis (FTA) can determine the effects of combinations of failure events on a system but cannot capture the significance of the temporal order of events, which may be critical. In this paper, we propose an extension based on formal definition and use of Priority AND gates that enables representation of event sequences and analysis of temporal relationships in FTA. In addition, we show how this type of temporal analysis can be used in conjunction with a recently proposed method for automated fault tree synthesis to allow accurate failure analyses of system models to be carried out efficiently. The approach is demonstrated on a generic system with a shared backup component. The paper tentatively concludes that this type of temporal FTA can provide a more precise and ultimately more correct insight into the failure behaviour of a system.     

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.     

A server backup model with Markovian arrivals and phase type services

We consider a finite capacity queueing system with one main server who is supported by a backup server. We assume Markovian arrivals, phase type services, and a threshold-type server backup policy with two pre-determined lower and upper thresholds. A request for a backup server is made whenever the buffer size (number of customers in the queue) hits the upper threshold and the backup server is released from the system when the buffer size drops to the lower threshold or fewer at a service completion of the backup server. The request time for the backup server is assumed to be exponentially distributed. For this queuing model we perform the steady state analysis and derive a number of performance measures. We show that the busy periods of the main and backup servers, the waiting times in the queue and in the system, are of phase type. We develop a cost model to obtain the optimal threshold values and study the impact of fixed and variable costs for the backup server on the optimal server backup decisions. We show that the impact of standard deviations of the interarrival and service time distributions on the server backup decisions is quite different for small and large values of the arrival rates. In addition, the pattern of use of the backup server is very different when the arrivals are positively correlated compared to mutually independent arrivals.     

An analysis of p-median location problem: Effects of backup service level and demand assignment policy

Any solution to facility location problems will consider determining the best suitable locations with respect to certain criteria. Among different types of location problems, involving emergency service system (ESSs) are one of the most widely studied in the literature, and solutions to these problems will mostly aim to minimize the mean response time to demands. In practice, however, a demand may not be served from its nearest facility if that facility is engaged in serving other demands. This makes it a requirement to assign backup services so as to improve response time and service quality. The level of backup service is a key, strategic-level planning factor, and must be taken into consideration carefully. Moreover, in emergency service operations conducted in congested demand regions, demand assignment policy is another important factor that affects the system performance. Models failing to adopt sufficient levels of backup service and realistic demand assignment policies may significantly deteriorate the system performance.Considering the classic p-median problem (pMP) location model, this paper investigates the effects of backup service level, demand assignment policy, demand density, and number of facilities and their locations on the solution performance in terms of multiple metrics. For this purpose, we adopt a combined optimization and simulation approach. We will first modify the classic pMP to account for distances to backup services. Next, we employ a discrete event simulation to evaluate the performance of location schemes obtained from the deterministic mathematical model. Our results provide insights for decision-makers while planning ESS operations.     

An economical backup strategy for floppy disks

A variety of data files are preserved on floppy disks. Document files created using a word processor as well as a personal computer are, for instance, stored on floppy disks. Nevertheless, such flies are occasionally lost due to human errors, the life of the floppy disk and a failure of hardware devices, which are comprised in a word processor or a personal computer. This is called a floppy disk failure. One of the simplest methods for protecting us from such serious losses is to backup files on another floppy disk periodically. Frequent backup operations would spend considerable cost in operations themselves although they could reduce the loss at a floppy disk failure. On the contrary, rare backup operations would make the loss at a floppy disk failure very large although they could considerably save cost in backup operations. These observations reveal the significance of determining an adequate backup timing of files.The present study considers an economical backup strategy for floppy disks, which suggests backing up files when each 1/N of the total memory of a floppy disk is consumed. The long-run average cost of the proposed backup strategy is formulated as an objective function. It is shown that there always exists an economical integer N* that minimizes the long-run average cost. Numerical examples are also presented.     

Analysis of the BMAP/PH/N queueing system with backup servers

We consider a novel multi-server queueing system that is potentially useful for optimizing real-world systems, in which the objectives of high performance and low power consumption are conflicting. The queueing model is formulated and investigated under the assumption that an arrival flow is defined by a batch Markovian arrival process and random values characterizing customer processing have the phase-type distribution. If the service time of some customer by a server exceeds a certain random bound, this server receives help from a so-called backup server from a finite pool of backup servers. The behavior of the system is described by a quite complicated multi-dimensional continuous-time Markov chain that is successfully analyzed in this paper. Examples of the potential use of the obtained results in managerial decisions are presented.     

The capacitated maximal covering location problem with backup service

The maximal covering location problem has been shown to be a useful tool in siting emergency services. In this paper we expand the model along two dimensions — workload capacities on facilities and the allocation of multiple levels of backup or prioritized service for all demand points. In emergency service facility location decisions such as ambulance sitting, when all of a facility's resources are needed to meet each call for service and the demand cannot be queued, the need for a backup unit may be required. This need is especially significant in areas of high demand. These areas also will often result in excessive workload for some facilities. Effective siting decisions, therefore, must address both the need for a backup response facility for each demand point and a reasonable limit on each facility's workload. In this paper, we develop a model which captures these concerns as well as present an efficient solution procedure using Lagrangian relaxation. Results of extensive computational experiments are presented to demonstrate the viability of the approach.     

Nonlinear dynamic analysis of a complex dual rotor-bearing system based on a novel model reduction method

In this paper, a dynamic model of a complex dual rotor-bearing system of an aero-engine is established based on the finite element method with three types of beam elements (rigid disc, cylindrical beam element and conical beam element), as well as taking into account the nonlinearities of all of the supporting rolling element bearings. To rapidly and accurately analyze dynamic behaviors of the complex dual rotor-bearing system, a two-level model order reduction (MOR) method is proposed by combining component mode synthesis (CMS) method and proper orthogonal decomposition (POD) technique. The first-level reduced-order model (ROM) of the dual rotors is obtained by CMS method with a high precision for the original system. Then, the POD method is applied to second-level model order reduction to further decrease the degrees of freedom (DOFs) of first-level ROM. Second-level ROM with mode expansion and direct second-level ROM are obtained, and the nonlinear displacement responses of the two ROMs are compared with the first-level ROM. The numerical results demonstrate that the proposed method has a higher computational efficiency and accuracy in terms of mode expansion than the direct model reduction by using POD method. In addition, the nonlinear vibration responses of the dual rotor-bearing system are studied by this second-level ROM in the case of different clearances of the inter-shaft bearing. The results indicate that the dynamic characteristics of the dual rotor-bearing system are very complicated for a large clearance.     

Price-only contracts with backup supply

This paper studies a supply chain in which a manufacturer holds backup supply with extra cost to satisfy demand unmet by a retailer. We provide a simple threshold condition for when the manufacturer should hold backup supply. We also study how the backup supply affects the supply chain performance.     

Two-sided model order reduction for two-directional difference system

This paper defines a two-directional difference system and constructs the projection matrix. Then the original system is projected into the smaller system, and we discuss its moment-matching properties. Next we define the dual system, and discuss the dual relation between the dual system and the original system. Then we can construct the projection matrix with the above mentioned dual relation, and project the dual system into the respectively smaller system, hence derive the moment-matching properties. Finally synthesizing the above two moment-matching properties we obtain the main results that the number of moments matched is twice as much as the number of the generating terms of the constructed projection subspace. We apply this result to the two-sided model order reduction for parameter time delay system, and obtain the result that the reduced system can preserve twice moments as the number of the generating terms of the constructed projection subspace. Finally we derive an algorithm to compute the basis of the subspace involved in the reduction process.