Group technology approach to the open shop scheduling problem with batch setup times

This paper studies the problem of scheduling jobs in a two-machine open shop to minimize the makespan. Jobs are grouped into batches and are processed without preemption. A batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. For this NP-hard problem, we propose a linear-time heuristic algorithm that creates a group technology schedule, in which no batch is split into sub-batches. We demonstrate that our heuristic is a -approximation algorithm. Moreover, we show that no group technology algorithm can guarantee a worst-case performance ratio less than 5/4.

The recovery mechanism of platinum group metals from catalytic converters in spent automotive exhaust systems

The recovery of platinum group metals (PGMs) from catalytic converters of spent exhaust systems is considered in this paper. To be cost-effective, recovery processes must be well over 90% efficient and so the optimisation of their operation is vital. Effective optimisation requires a sound understanding of the operation and the underlying process mechanisms. This paper focuses on pyrometallurgical recovery operations used and typified by the Johnson–Matthey process. Analysis of this process reveals that it cannot be simply explained by the gravity model that is normally assumed. The analysis reveals that the affinity of PGM particles for the melted collector metal is a key factor in the behaviour of the process. A rational explanation of the key issues that govern the process behaviour is proposed and shown to be consistent with available operational data. The results generated would be applicable to other similar processes.

Collector-metal behaviour in the recovery of platinum-group metals from catalytic converters

A commercial pyrometallurgical process for the extraction of platinum-group metals (PGM) from a feedstock slag was analysed with the use of a model based on computational fluid dynamics. The results of the modelling indicate that recovery depends on the behaviour of the collector phase. A possible method is proposed for estimation of the rate at which PGM particles in slag are absorbed into an iron collector droplet that falls through it. Nanoscale modelling techniques (for particle migration or capture) are combined with a diffusion-controlled mass-transfer model to determine the iron collector droplet size needed for >95% PGM recovery in a typical process bath (70 mm deep) in a realistic time-scale (<1 h). The results show that an iron droplet having a diameter in the range 0.1–0.3 mm gives good recovery (>90%) within a reasonable time. This finding is compatible with published experimental data. Pyrometallurgical processes similar to that investigated should be applicable to other types of waste that contain low levels of potentially valuable metals.

BSHM meetings: BMS History of Mathematics Splinter Group

Introduction to abstracts from papers given at BMS History of Mathematics Splinter Group, held 17 April 2007, in Swansea.

Muscle activation patterns in shoulder impingement patients

Introduction: Shoulder impingement is one of the most common presentations of shoulder joint problems 1. It appears to be caused by a reduction in the sub-acromial space as the humerus abducts between 60o -120o – the 'painful arc'. Structures between the humeral head and the acromion are thus pinched causing pain and further pathology 2. Shoulder muscle activity can influence this joint space but it is unclear whether this is a cause or effect in impingement patients. This study aimed to observe muscle activation patterns in normal and impingement shoulder patients and determine if there were any significant differences. Method: 19 adult subjects were asked to perform shoulder abduction in their symptomatic arm and non-symptomatic. 10 of these subjects (age 47.9 ± 11.2) were screened for shoulder impingement, and 9 subjects (age 38.9 ± 14.3) had no history of shoulder pathology. Surface EMG was used to collect data for 6 shoulder muscles (Upper, middle and lower trapezius, serratus anterior, infraspinatus, middle deltoids) which was then filtered and fully rectified. Subjects performed 3 smooth unilateral abduction movements at a cadence of 16 beats of a metronome set at 60bpm, and the mean of their results was recorded. T-tests were used to indicate any statistical significance in the data sets. Significance was set at P<0.05. Results: There was a significant difference in muscle activation with serratus anterior in particular showing a very low level of activation throughout the range when compared to normal shoulder activation patterns (<30%). Middle deltoid recruitment was significantly reduced between 60-90o in the impingement group (30:58%).Trends were noted in other muscles with upper trapezius and infraspinatus activating more rapidly and erratically (63:25%; 60:27% respectively), and lower trapezius with less recruitment (13:30%) in the patient group, although these did not quite reach significance. Conclusion: There appears to be some interesting alterations in muscle recruitment patterns in impingement shoulder patients when compared against their own unaffected shoulders and the control group. In particular changes in scapula control (serratus anterior and trapezius) and lateral rotation (infraspinatus), which have direct influence on the sub-acromial space, should be noted. It is still not clear whether these alterations are causative or reactionary, but this finding gives a clear indication to the importance of addressing muscle reeducation as part of a rehabilitation programme in shoulder impingement patients.

Horsham Properties Group Ltd v Clark: possession - mortgagee's right or discretionary remedy?

Comments on the Chancery Division decision in Horsham Properties Group Ltd v Clark on whether a mortgagee's exercise of its contractual right, on the mortgagor falling into arrears, to appoint receivers such that the property could be sold and possession obtained without triggering the court's discretionary powers pursuant to the Administration of Justice Act 1970 s.36 infringed the mortgagor's rights under the European Convention on Human Rights 1950 Protocol 1 art.1. Considers the implications of proposed reforms recasting the mortgagee's right to possession as a discretionary remedy. [From Legal Journals Index]

"Practise what we preach": a social constructivist approach to blended learning

This presentation reports on the formal evaluation, through questionnaires, of a new Level 1 undergraduate course, for 130 student teachers, that uses blended learning. The course design seeks to radicalise the department’s approach to teaching, learning and assessment and use students as change agents. Its structure and content, model social constructivist approaches to learning. Building on the student’s experiences of and, reflections on, previous learning, promotes further learning through the support of “able others” (Vygotsky 1978), facilitating and nurturing a secure community of practice for students new to higher education. The course’s design incorporates individual, paired, small and large group activities and exploits online video, audio and text materials. Course units begin and end with face-to-face tutor-led activities. Online elements, including discussions and formative submissions, are tutor-mediated. Students work together face-to-face and online to read articles, write reflections, develop presentations, research and share experiences and resources. Summative joint assignments and peer assessments emphasise the value of collaboration and teamwork for academic, personal and professional development. Initial informal findings are positive, indicating that students have engaged readily with course content and structure, with few reporting difficulties accessing or using technology. Students have welcomed the opportunity to work together to tackle readings in a new genre, pilot presentation skills and receive and give constructive feedback to peers. Course tutors have indicated that depth and quality of study are evident, with regular online formative submissions enabling tutors to identify and engage directly with student’s needs, provide feedback and develop appropriately designed distance and face-to-face teaching materials. Pastoral tutors have indicated that students have reported non-engagement of peers, leading to the rapid application of academic or personal support. Outcomes of the formal evaluation will inform the development of Level 2 and 3 courses and influence the department’s use of blended learning.