Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

Ag/InP Schottky结热退化机理的研究

Ag/InP Schottky结是制作TE场助光电阴极的关键,本文利用Auger分析技术,详细地研究了热处理对Ag/InPSchottky结界面特性的影响。实验结果表明高温长时间热处理会导致严重界面相互扩散,同时使Schottky结的势垒高度降低,理想因子增大,泡利负电性理论很好地解释了扩散效应。势垒高度的降低及理想因子的增大也是由界面互扩散造成的,这种扩散导致界面特性由Schotthy特性向欧姆性质转化。为防止界面互扩散及Schottky结特性的退化,可选用负电性小的金属制作Schottky结,并在工艺上尽量减少热处理的温度和时间。     

A Lot-sizing Model for Just-in-time Manufacturing

We consider the problem of determining lot sizes of multiple items that are manufactured by a single capacitated facility. The manufacturing facility may represent a bottleneck processing activity on the shop floor or a storeroom that provides components to the shop floor. Items flow from the facility to a downstream facility, where they are assembled according to a specified mix. Just-in-time (JIT) manufacturing requires a balanced flow of items, in the proper mix, between successive facilities. Our model determines lot sizes of the various items based on available capacity and four attributes of each item: demand rate, holding cost, set-up time and processing time. Holding costs for each item accrue until the appropriate mix of items is available for shipment downstream. We develop a lot-sizing heuristic that minimizes total holding cost per time unit over all items, subject to capacity availability and the required mix of items.     

Developing and Maintaining an Equity Index Fund

An index fund is a portfolio of shares designed to replicate the investment performance of a market index. The index represents the behaviour of the market as a whole. This paper describes the selection of an index fund which minimizes expected tracking error. Using a multivariate model of returns on shares, a development of a univariate model by Taylor, the selection problem is formulated as a quadratic programme. The effects of various constraints on tracking error are demonstrated. Several policies for the readjustment of a fund are examined in the context of the differing objectives of fund managers. As a general rule, regular readjustment is shown to be a more expensive policy than irregular updating.     

Scheduling Parts in a Combined Production-transportation Work Cell

This paper is concerned with a combined production-transportation scheduling problem. The problem comprises a simple, two-machine, automated manufacturing cell, which either stands alone or is a subunit of a complete flexible manufacturing system. The cell consists of two machines in series with a dedicated part-handling device such as a crane or robotic arm for transferring parts from the first machine to the second. The loading of a new piece on the first machine and the ejection of a finished piece from the second machine are performed by dedicated automated mechanisms. The introduction of parts into the system is done n at a time, whereby the parts are reshuffled into a sequence that minimizes completion time. All processing and transfer times are considered deterministic—a reasonable assumption for a cell comprising a robotic transfer device and two CNC machining units. What complicates the problem is the assumption of a non-negligible time for the transfer device to return (empty) from the second machine to the first. The operation is a generalization of a two-machine flowshop problem, and is formulated as a specially structured, asymmetric travelling salesman problem. An approximate polynomial time 0(n log n) algorithm is proffered. The procedure incorporates a lower bound using the Gilmore–Gomory algorithm for the no-wait, two-machine flowshop problem.     

A posteriori error estimates for optimal control problems governed by parabolic equations

Summary. In this paper, we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation. We obtain a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive finite element approximation schemes for the control problem. Received July 7, 2000 / Revised version received January 22, 2001 / Published online January 30, 2002 RID="*" ID="*" Supported by EPSRC research grant GR/R31980     

Positive solutions of singular boundary value problem of negative exponent Emden—Fowler equation

This paper investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar to standard Emden-Fowler equation. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as well as C¹[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem.     

Lower Bounds for the Height and Size of the Ideal Class Group in CM-Fields

 We prove that, under the assumption of the Generalized Riemann Hypothesis, the exponent of the ideal class group of a CM-field goes to infinity with its absolute discriminant. This gives a positive answer to a question raised by Louboutin and Okazaki [4]. Received September 10, 2001; in revised form April 5, 2002