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 ANZIAM JournalJournal Prestige (SJR): 0.216 Number of Followers: 1     Open Access journal ISSN (Print) 1446-1811 - ISSN (Online) 1446-8735 Published by Cambridge University Press  [372 journals]
• ANZ VOLUME 60 ISSUE 2 COVER AND FRONT MATTER

• PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S1446181117000517
Issue No: Vol. 60, No. 2 (2018)

• ANZ VOLUME 60 ISSUE 2 COVER AND BACK MATTER

• PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S1446181117000529
Issue No: Vol. 60, No. 2 (2018)

• THE TWO-TRAIN SEPARATION PROBLEM ON LEVEL TRACK WITH DISCRETE CONTROL

• Authors: PHIL HOWLETT
Pages: 137 - 174
Abstract: When two trains travel along the same track in the same direction, it is a common safety requirement that the trains must be separated by at least two signals. This means that there will always be at least one clear section of track between the two trains. If the safe-separation condition is violated, then the driver of the following train must adopt a revised strategy that will enable the train to stop at the next signal if necessary. One simple way to ensure safe separation is to define a prescribed set of latest allowed section exit times for the leading train and a corresponding prescribed set of earliest allowed section entry times for the following train. We will find strategies that minimize the total tractive energy required for both trains to complete their respective journeys within the overall allowed journey times and subject to the additional prescribed section clearance times. We assume that the drivers use a discrete control mechanism and show that the optimal driving strategy for each train is defined by a sequence of approximate speedholding phases at a uniquely defined optimal driving speed on each section and that the sequence of optimal driving speeds is a decreasing sequence for the leading train and an increasing sequence for the following train. We illustrate our results by finding optimal strategies and associated speed profiles for both trains in some elementary but realistic examples.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S1446181118000214
Issue No: Vol. 60, No. 2 (2018)

• OPTION PRICING UNDER THE KOBOL MODEL

• Authors: WENTING CHEN; SHA LIN
Pages: 175 - 190
Abstract: We consider the pricing of European options under a modified Black–Scholes equation having fractional derivatives in the “spatial” (price) variable. To be specific, the underlying price is assumed to follow a geometric Koponen–Boyarchenko–Levendorski process. This pure jump Lévy process could better capture the real behaviour of market data. Despite many difficulties caused by the “globalness” of the fractional derivatives, we derive an explicit closed-form analytical solution by solving the fractional partial differential equation analytically, using the Fourier transform technique. Based on the newly derived formula, we also examine, in theory, many basic properties of the option price under the current model. On the other hand, for practical purposes, we impose a reliable implementation method for the current formula so that it can be easily used in the trading market. With the numerical results, the impact of different parameters on the option price are also investigated.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S1446181118000196
Issue No: Vol. 60, No. 2 (2018)

• MATHEMATICAL MODELLING OF THE REMOVAL OF ORGANIC MICROPOLLUTANTS IN THE
ACTIVATED SLUDGE PROCESS: A LINEAR BIODEGRADATION MODEL

• Authors: MARK I. NELSON; RUBAYYI T. ALQAHTANI, FAISAL I. HAI
Pages: 191 - 229
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S1446181118000226
Issue No: Vol. 60, No. 2 (2018)

• THE CONTROLLER DESIGN FOR SINGULAR FRACTIONAL-ORDER SYSTEMS WITH
FRACTIONAL ORDER 0 <α< 1

• Authors: T. ZHAN; S. P. MA
Pages: 230 - 248
Abstract: We study the problem of pseudostate and static output feedback stabilization for singular fractional-order linear systems with fractional order $\unicode[STIX]{x1D6FC}$ when \$0
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S1446181118000202
Issue No: Vol. 60, No. 2 (2018)

STRETCHING SHEET

• Authors: S. PANDA; K. K. PATRA, M. SELLIER
Pages: 249 - 268
Abstract: We derive an evolution equation for the free-surface dynamics of a thin film of a second-grade fluid over an unsteady stretching sheet using long-wave theory. For the numerical investigation of the viscoelastic effect on the thin-film dynamics, a finite-volume approach on a uniform grid with implicit flux discretization is applied. The present results are in excellent agreement with results available in the literature for a Newtonian fluid. We observe that the fluid thins faster with the rapid stretching rate of the sheet, but the second-grade parameter delays the thinning behaviour of the liquid film.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S1446181118000251
Issue No: Vol. 60, No. 2 (2018)

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