Geodesics on the Ellipsoid and Monodromy

The equations for geodesic flow on the ellipsoid are well known, and were first solved by Jacobi in 1838 by separating the variables of the Hamilton-Jacobi equation. In 1979 Moser investigated the case of the general ellipsoid with distinct semi-axes and described a set of integrals which weren't know classically. After reviewing the properties of geodesic flow on the three dimensional ellipsoid with distinct semi-axes, we investigate the three dimensional ellipsoid with the two middle semi-axes being equal, corresponding to a Hamiltonian invariant under rotations. The system is Liouville-integrable and thus the invariant manifolds corresponding to regular points of the energy momentum map are 3-dimensional tori. An analysis of the critical points of the energy momentum maps gives the bifurcation diagram. We find the fibres of the critical values of the energy momentum map, and carry out an analysis of the action variables. We show that the obstruction to the existence of single valued globally smooth action variables is monodromy.Comment: 24 pages, 7 figure

Factors affecting recruitment into General Practice : a double binary choice approach

Recruitment to General Practice (GP) is currently low in many countries. Here we focus on two binary choices for junior doctors: first, whether to apply to GP; second, whether to accept a GP training place if offered. Previous attitudinal studies have indicated factors claimed to affect recruitment. The current study goes further by quantifying the relative impact of different factors on the propensity of candidates to apply to GP and accept a training place. An online questionnaire was sent to candidates applying to United Kingdom (UK) specialty training in 2015. Descriptive statistics and a path analysis evaluated the importance of various factors on GP applications. Our results were synthesised with an analysis of data from the online applications portal. With 3838 candidates responding to the survey, the path analysis showed that personality and previous GP experiences were strongly associated with the decision to apply. There was some evidence that it was easier to enter GP than other specialties; in terms of deciding whether to accept, the evidence suggests GP was a backup plan for around 9% of candidates who accepted a GP post. Our results indicate that recruitment initiatives should focus on candidates who apply to GP but not as first choice or consider GP but do not apply, particularly by providing substantial experience of GP and accentuating the positives of the specialty such as work-life balance and the intellectual challenge of working with patients in primary care. Acceptance of a GP place may also depend on competition for places in other specialties

Revenue Management: A Real Options Approach

Revenue management is the process of actively managing inventory or capacity to maximize revenues. The active management typically occurs through managerial levers such as price, promotion, or availability. We present a novel real options approach to revenue management that is specifically suited to the car rental business. We illustrate the concept with actual car rental data. The model produces minimally acceptable prices and inventory release quantities (number of cars available for rent at a given price) as a function of remaining time and available inventory. The pricing and inventory release recommendations of the developed model confirm earlier empirical analysis that suggested current practices discount too deeply early in the booking cycle

Developing and evaluating interventions for women firesetters in high secure mental healthcare

Purpose The purpose of this paper is to discuss the implementation and evaluation of interventions for women firesetters in high secure mental healthcare at the UK’s National Women’s Service. Design/methodology/approach Two types of Arson treatment programmes for women, one delivered to individuals, the other within a group context, were developed, delivered and evaluated. The evaluation incorporated qualitative and quantitative data, including psychometric measures. Qualitative data were analysed using thematic analysis. Findings The evaluation evidenced very high engagement with and attendance at treatment programmes, and several post-treatment gains. Participants’ ratings of programmes and qualitative feedback were similarly very positive. The study demonstrated that engaging women firesetters in their treatment is paramount and can be facilitated by consistent boundaries around therapy provision balanced with sensitivity, empathy and flexibility; providing interactive and varied teaching methods; ongoing service user involvement and recognising participants’ achievements; employing a mixed cognitive analytic therapy and cognitive behavioural therapy therapeutic approach; having input from fire service staff; and maintaining organisational support for firesetting interventions. Practical implications In all, 12 key recommendations are made for clinicians considering offering treatment programmes for women firesetters. Originality/value Amid few published papers on treating women firesetters this paper guides forensic clinicians in establishing and delivering interventions for women firesetters