On approximate calculations

The ability to undertake approximate calcutations and to get a “rough feel” for data is an important skill which must not be overlooked.

A polynomial algorithm for the three-machine open shop with a bottleneck machine

The paper considers the three‐machine open shop scheduling problem to minimize themakespan. It is assumed that each job consists of at most two operations, one of which is tobe processed on the bottleneck machine, the same for all jobs. A new lower bound on theoptimal makespan is derived, and a linear‐time algorithm for finding an optimalnon‐preemptive schedule is presented.

Exploring genetic alternative concepts for FUELGEN

This paper describes new crossover operators and mutation strategies for the FUELGEN system, a genetic algorithm which designs fuel loading patterns for nuclear power reactors. The new components are applications of new ideas from recent research in genetic algorithms. They are designed to improve the performance of FUELGEN by using information in the problem as yet not made explicit in the genetic algorithm's representation. The paper introduces new developments in genetic algorithm design and explains how they motivate the proposed new components.

Scheduling three-operation jobs in a two-machine flow shop to minimize makespan

This paper considers a variant of the classical problem of minimizing makespan in a two-machine flow shop. In this variant, each job has three operations, where the first operation must be performed on the first machine, the second operation can be performed on either machine but cannot be preempted, and the third operation must be performed on the second machine. The NP-hard nature of the problem motivates the design and analysis of approximation algorithms. It is shown that a schedule in which the operations are sequenced arbitrarily, but without inserted machine idle time, has a worst-case performance ratio of 2. Also, an algorithm that constructs four schedules and selects the best is shown to have a worst-case performance ratio of 3/2. A polynomial time approximation scheme (PTAS) is also presented.

[BSHM meetings] Topics in the history of financial mathematics: early commerce to chaos in modern stock markets

This account provides an overview of the study day, entitled 'Topics in the History of Financial Mathematics: Early commerce to chaos in modern stock markets,' held by the British Society for the History of Mathematics jointly with Gresham College, at Gresham College, London on 25th April 2008. The series of talks explored the development of mathematics and mathematical techniques in a commercial and financial context.

The impact on students of coursework assessment deadlines and penalties

The use by students of an e-learning system that enhances traditional learning in a large university computing school where there are clear assessment deadlines and severe penalties for late submission of coursework is examined to assess the impact of changes to the deadline model on the way students use the system and on the results they achieve. It is demonstrated that the grade a student achieves is partly dependent on the time before the deadline when the work is completed - in general, students who submit earlier gain higher grades. Possible reasons for this are explored. Analysis of the data from a range of different implementations of deadline policies is presented. Suggestions are made on how to minimise any possible negative impact of the assessment policy on the student's overall learning.

Contractual termination of leases: lessons from the Commonwealth: Pt. 2

This, the second part of a three-part article on contractual termination of leases, considers the extent to which English courts have allowed the contract law principles of frustration and acceptance of a repudiatory breach to be applied to leaseholds. Distinguishes cases involving a repudiatory breach by a landlord from those where the tenant is the one in breach.

Spaces of observation and obscurity: cinematic prisons of light and dark

In The Eye of Power, Foucault delineated the key concerns surrounding hospital architecture in the latter half of the eighteenth century as being the ‘visibility of bodies, individuals and things'. As such, the ‘new form of hospital' that came to be developed ‘was at once the effect and support of a new type of gaze'. This was a gaze that was not simply concerned with ways of minimising overcrowding or cross-contamination. Rather, this was a surveillance intended to produce knowledge about the pathological bodies contained within the hospital walls. This would then allow for their appropriate classification. Foucault went on to describe how these principles came to be applied to the architecture of prisons. This was exemplified for him in the distinct shape of Bentham's panopticon. This circular design, which has subsequently become an often misused synonym for a contemporary culture of surveillance, was premised on a binary of the seen and the not-seen. An individual observer could stand at the central point of the circle and observe the cells (and their occupants) on the perimeter whilst themselves remaining unseen. The panopticon in its purest form was never constructed, yet it conveys the significance of the production of knowledge through observation that became central to institutional design at this time and modern thought more broadly. What is curious though is that whilst the aim of those late eighteenth century buildings was to produce wellventilated spaces suffused with light, this provoked an interest in its opposite. The gothic movement in literature that was developing in parallel conversely took a ‘fantasy world of stone walls, darkness, hideouts and dungeons…' as its landscape (Vidler, 1992: 162). Curiously, despite these modern developments in prison design, the façade took on these characteristics. The gothic imagination came to describe that unseen world that lay behind the outer wall. This is what Evans refers to as an architectural ‘hoax'. The façade was taken to represent the world within the prison walls and it was the façade that came to inform the popular imagination about what occurred behind it. The rational, modern principles ordering the prison became conflated with the meanings projected by and onto the façade. This confusion of meanings have then been repeated and reenforced in the subsequent representations of the prison. This is of paramount importance since it is the cinematic and televisual representation of the prison, as I argue here and elsewhere, that maintain this erroneous set of meanings, this ‘hoax'.

Synthesis and spectroscopic investigation of iron(III) complexes of N'-(thioaroyl)pyridine-2-carbohydrazides

A new series of iron(III) complexes [Fe(L(1))(HL(1))], [Fe(L(1)) Cl]; [H2L(1) = N'-(2-methoxythiobenzoyl)pyridine-2-carbohydrazide], [Fe(L(2))(acac)], [Fe(HL(2))2 Cl]; [H2L(2) = N'-(4-methoxythiobenzoyl)pyridine-2-carbohydrazide] and [Fe(L(3)) (acac)]; [H2L(3) = N'-(2-hydroxythiobenzoyl)pyridine-2-carbohydrazide] were prepared by stirring/refluxing/mixing the respective ligand with FeCl3/Fe(acac)3 in chloroform/methanol. All the compounds were characterized by elemental analyses, magnetic susceptibility, IR, UV and Mossbauer spectral data. The complexes high/low spin state and have tetrahedral/octahedral geometry.