Practical extensions to a minimum cost flow model for level of repair analysis

The level of repair analysis (LORA) gives answers to three questions that are posed when deciding on how to maintain capital goods: (1) which components to repair upon failure and which to discard, (2) at which locations in the repair network to perform each type of repairs, and (3) at which locations in the network to deploy resources, such as test equipment. The goal is to achieve the lowest possible life cycle costs. Various models exist for the LORA problem. However, they tend to be restrictive in that specific business situations cannot be incorporated, such as having repair equipment with finite capacity or the occurrence of unsuccessful repairs or no-fault-founds. We discuss and model such practically relevant extensions to an existing minimum cost flow formulation for the LORA problem. In an extensive numerical experiment, we show that incorporating the model refinements leads to a substantial change in the costs in general. The repair strategy changes substantially only when incorporating finite resource capacities or a probability of unsuccessful repair that is decreasing with an increasing echelon level.     

An involution on increasing trees

We introduce a method to construct bijections on increasing trees. Using this method, we construct an involution on increasing trees, from which we obtain the equidistribution of the statistics ‘number of odd vertices’ and ‘number of even vertices at odd levels’. As an application, we deduce that the expected value of the number of even vertices is twice the expected value of the number of odd vertices in a random recursive tree of given size.     

Optical and paramagnetic properties of titanium centres in ZnS

ZnS:Ti crystals grown by different methods are investigated at low temperatures (2 K K) by electron paramagnetic resonance (EPR) and optical spectroscopies, mainly with regard to their photoluminescence properties, including excitation and sensitisation spectra. The more familiar lattice-neutral Ti²⁺(d ² ) ion on a cubic site (AN) presents an isotropic EPR signal with g=1.928 observable up to 80 K. Signals of axial PN and AS sites are detected in the same temperature range. This Ti²⁺ ion exhibits the transition in emission, structured by no-phonon lines (NPL) of centres in various environments, with the AN site represented at 3613 cm^-1, and the ³ T ₁ (F) and ³ T ₁ (P) bands in excitation spectra. Substitutional Ti³⁺(d ¹ ) is identified by an anisotropic EPR spectrum at T = 3.5 K, indicating a quasistatic Jahn-Teller effect at the doubly degenerate ² E(D) ground state, while in the first excited vibronic state a quasidynamic JT effect in the strain-split vibronic ² E/² A ₂ manifold is found. A new luminescence band centred at 4500 cm^-1 with NPL structures near 5000 cm^-1 represents AN, PN and AS sites in the transition. Charge-transfer processes are described in a one-particle model, depicting the Ti³⁺/Ti²⁺ donor level at 12 900 cm^-1 below the conduction-band edge. Received: 3 October 1997 / Revised: 17 December 1998 / Accepted: 18 May 1998     

我国某地区居民购买六合彩活动信息的统计分析

本文主要应用统计学方法对由问卷调查所获得的我国某地区居民购买地下六合彩活动的信息进行分析,分别对购买者的结构,经济状况及收益进行分析,指出地下六合彩的本质及这一现象给我们的警示.同时通过分析一个消费者个体的消费模型给出消费者如何理性消费的建议.     

光纤法布里-珀罗(Fabry-Perot)腔液位传感器

提出了一种用于测量液体容器液位高度的新型光纤F-P(Fabry-Perot)腔传感器,它灵敏度高,实现了全光传感和传输,特别适用于一些有害、易燃、易爆液体容器液位的测定.详细分析了该类传感器的传感原理,并给出了传感头参量设计方法.实验结果表明,光纤F-P腔传感器测量液位方法简单,并且可达到相当高的精度.文中分析了实验中的误差,探讨了传感器的稳定性及改进方法,是光纤法布里-珀罗腔传感器实用化的有效尝试.     

Infinite-horizon investment consumption model with a nonterminal bankruptcy

This paper solves a general continuous-time consumption and portfolio decision problem for a single agent for whom there exists, upon bankruptcy, a possibility of recovery from his bankruptcy. The main contribution of the paper is in the modeling of the recovery process. Moreover, it is shown that the model with recovery has a one-to-one correspondence with the model with terminal bankruptcy treated in the literature.This research was supported by Grants SSHRC-410-83-9888 and NSERC-A4619 to the first author and by Grants NSF-DMS-86-01510 and AFOSR-88-0183 to the second author. Comments from E. Presman are gratefully acknowledged.     

General considerations of numerical stability and accuracy in inviscid,compressible flow calculations employing primitive variables

The numerical stability of a number of computation schemes currently used for three-dimensional, inviscid, compressible flow is analysed using one-dimensional Fourier analysis. Whereas Reference 1 analysed schemes which were modified to render them amenable to simple analysis, the present work analyses the stability of schemes as actually used by Highton,³ Ahrabian,¹ Denton² and Spalding.⁶ The use of current values of the variables as they become available is shown to bring a general improvement to stability margin. The manner of damping introduced by the time marching formulation is shown to be deleterious to modifications which reduce truncation error. Staggered grid schemes can be formulated to second order accuracy with better stability margin than the corresponding first order scheme. While unstaggered grid schemes can be formulated to second order error and remain stable, their stability margin becomes very small. Agreement of the theory with numerical experiments continues to be of a high order for both one and three-dimensional disturbances.     

A robust numerical model for premixed flames with high density ratios based on new pressure correction and IMEX schemes

In this study we present a model for the interaction of premixed flames with obstacles in a channel flow. Although the flow equations are solved with Direct Numerical Simulation using a low Mach number approximation, the resolution used in the computation is limited (∼1 mm) hence the inner structure of the flame and the chemical scales are not solved. The species equations are substituted with a source term in the energy equation that simulates a one-step global reaction. A level set method is applied to track the position of the flame and its zero level is used to activate the source term in the energy equation only at the flame front. An immersed boundary method reproduces the geometry of the obstacles. The main contribution of the paper is represented by the proposed numerical approach: an IMEX (implicit–explicit) Runge–Kutta scheme is used for the time integration of the energy equation and a new pressure correction algorithm is introduced for the time integration of the momentum equations. The approach presented here allows to calculate flames which produce high density ratios between burnt and unburnt regions. The model is verified by simulating first simple solutions for one- and two-dimensional flames. At last, the experiments performed by Masri and Ibrahim with square and rectangular bodies are calculated.