Statistical concepts in computational mathematics

For a young science and even for most old ones, the intensity and variety of activities involved in computer science are unsurpassed. In an effort to provide the extremely varied training needed in the field, curriculum planners have tended to slight probability and statistics. Rarely has it been a requisite and only occasionally a desired elective However, not only is an adequate foundation in probability and statistics necessary for such external computer applications as tracking and other data reduction, Monte Carlo techniques, gaming, operations research, traffic analyses, etc., but it also plays an important role in internal applications to computer science and technology This effort in Rand's continuing study of computational mathematics and its applications offers a number of examples in various areas of computational mathematics and computing machine arithmetic-to say nothing of computer design, time sharing, and the like-to support the thesis that probability and statistics should be a requisite, not simply an elective or, even worse, ignored, at any institution offering a program in computer science. Further more, a potentially profitable source of research problems can be found in the interface between probability and statistics and computer science.     

Optimum quantiles for the linear estimation of the parameters of the extreme value distribution in complete and censored samples

The present study is concerned with the determination of a few observations from a sufficiently large complete or censored sample from the extreme value distribution with location and scale parameters μ and σ, respectively, such that the asymptotically best linear unbiased estimators (ABLUE) of the parameters in Ref. [24] yield high efficiencies among other choices of the same number of observations. (All efficiencies considered are relative to the Cramér-Rao lower bounds for regular unbiased estimators.) The study is on the asymptotic theory and under Type II censoring scheme. For the estimation of μ when σ is known, it has been proved that there exists a unique optimum spacing whether the sample is complete, right censored, left censored, or doubly censored. Several tables are prepared to aid in the numerical computation of the estimates as well as to furnish their efficiencies. For the estimation of σ when μ is known, it has been observed that there does not exist a unique optimum spacing. Accordingly we have obtained a spacing based on a complete sample which yields high efficiency. A similar table as above is prepared. When both μ and σ are unknown, we have considered four different spacings based on a complete sample and chosen the one yielding highest efficiency. A table of the efficiencies is also prepared. Finally we apply the above results for the estimation of the scale and/or shape parameters of the Weibull distribution.     

高速核在高温热平衡等离子体中的非平衡弛豫过程对热核反应率参数的影响

高速核入射到高温热平衡等离子体背景中,由于入射核动能远大于背景等离体中带电粒子之平均动能,入射核在与背景等离子体达到热平衡之前,会存在一段逐渐损失能量的非平衡弛豫过程。本文以高速氘核入射到高温氘化锂等离子体为例,在计及氘核的这种非平衡弛豫过程时,给出了一种计算热核反应D(t,n)~4He之反应率参数的方法。氘核在弛豫过程中的能量损失考虑了氘核与各种带电粒子的库仑散射过程,其能量损失率采用快速带电粒子的慢化理论来计算;氘与背景等离子体中的原子核发生的核反应过程,考虑了非平衡状态下束靶机制的D(t,n)~4He反应和热平衡状态下的D(t.n)~4He反应。在暂未考虑核散射的情况下,计算结果表明,当等离子体温度在7.5KeV～20KeV范围内变化时,氘核的非平衡弛豫过程对热平衡状态下D(t,n)~4He反应率参数的修正因子大致在1.0062～1.0943范围内变动,且温度越高,修正因子越小。计算还表明,当温度一定时,修正因子随等离子体中粒子的数密度变化不明显。     

Heuristic modeling of supply availabilities in large networks

The objective of this article is to describe heuristic solutions to the problem of modeling inventories at each node of a large network in the context of a computer simulation model of that network. The heuristic solutions are compared with the mathematical solution which is too unwieldy for use in a simulation model. The Weibull cumulative distribution is used as an approximation for the heuristic models. We question whether the good performance of the Weibull is coincidence or perhaps mathematically justifiable.     

Recent articles on partial backorders: Comment

This note points out the omission of a simple but vital constraint in the recent articles on partial backlogging. Also, a simple intuitive interpretation of the “backorder” inequality of [2], [3], and [4] is provided.     

Inventory management with advance capacity information

An important aspect of supply chain management is dealing with demand and supply uncertainty. The uncertainty of future supply can be reduced if a company is able to obtain advance capacity information (ACI) about future supply/production capacity availability from its supplier. We address a periodic‐review inventory system under stochastic demand and stochastic limited supply, for which ACI is available. We show that the optimal ordering policy is a state‐dependent base‐stock policy characterized by a base‐stock level that is a function of ACI. We establish a link with inventory models that use advance demand information (ADI) by developing a capacitated inventory system with ADI, and we show that equivalence can only be set under a very specific and restrictive assumption, implying that ADI insights will not necessarily hold in the ACI environment. Our numerical results reveal several managerial insights. In particular, we show that ACI is most beneficial when there is sufficient flexibility to react to anticipated demand and supply capacity mismatches. Further, most of the benefits can be achieved with only limited future visibility. We also show that the system parameters affecting the value of ACI interact in a complex way and therefore need to be considered in an integrated manner. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

基于小波分析的柴油机燃油系统故障诊断研究

提出了一种基于小波变换的柴油机燃油系统故障诊断方法。利用夹持在高压油管上的传感器对高压油管外壁弹性变形进行检测,在12150L柴油机喷油泵实验台上进行了大量的实验,对测得的高压油管压力波形进行小波变换,提取反映燃油系统故障状态的特征向量,通过特征参数的变化能有效地诊断燃油系统的各种典型故障。     

不同结构形式气液同轴式喷嘴的流量特性

本文通过实验方法对两种不同结构形式的气液同轴式喷嘴流量特性进行了研究,重点考察了喷嘴内气液相互作用和环境反压的变化对喷嘴流量特性的影响,研究结果表明同轴离心式喷嘴内气液相互作用比同轴直流式喷嘴内气液相互作用要强。对于这两种喷嘴,反压的变化对气相流量的影响规律相同,而对液相流量的影响规律却不同     

三维编织圆管力学性能及火箭级间段模拟结构承载能力研究

对于三维四向（４Ｄ）和五向（５Ｄ）两种编织碳／环氧圆管构件及由其组成的火箭模拟级间段，测试其压缩和扭转力学性能及轴压承载能力。实验表明，５Ｄ材料的压缩性能比４Ｄ材料有较大幅度提高，剪切模量提高幅度不明显。用３—细胞模型和ＦＧＭ模型预测相应的力学性能和压缩强度，并与实验结果进行了比较。结果表明，３—细胞模型的结果与实验结果符合较好，ＦＧＭ模拟预测结果偏低。本文结果为编织结构的设计分析提供了依据。