Absolute continuity and spectral concentration for slowly decaying potentials

We consider the spectral function $\rho(\mu)$ $(\mu \geq 0)$ for the Sturm-Liouville equation $y^{''}+(\lambda-q)y =0$ on $[0,\infty)$ with the boundary condition $y(0)=0$ and where $q$ has slow decay $O(x^{-\alpha})$ $(a>0)$ as $x\to \infty$. We develop our previous methods of locating spectral concentration for $q$ with rapid exponential decay (JCAM 81 (1997) 333-348) to deal with the new theoretical and computational complexities which arise for slow decay

Extensions of a New Algorithm for the Numerical Solution of Linear Differential Systems on an Infinite Interval

This paper is part of a series of papers in which the asymptotic theory and appropriate symbolic computer code are developed to compute the asymptotic expansion of the solution of an n-th order ordinary differential equation. The paper examines the situation when the matrix that appears in the Levinson expansion has a double eigenvalue. Application is made to a fourth-order ODE with known special function solution

Alcohol and healthy ageing: a challenge for alcohol policy

Objectives: This paper presents findings of a qualitative study of older people's use of alcohol during retirement and identifies ways that an improved understanding of older people's drinking can inform policy approaches to alcohol and active and healthy ageing. Study design: Qualitative semi-structured interviews conducted with a self-selecting sample of retired people. Methods: Participants were recruited from three geographical locations in the West of Scotland. A quota sampling design was used to ensure a broad spread of participants in terms of socio-economic position, age and gender. In total 40 participants were interviewed and the data analysed thematically using Braun and Clarke's (2006) approach. Results: Amongst those who used alcohol, it was most often framed in terms of pleasure, relaxation, socialising and as a way to mark the passage of time. Alcohol was often associated with social occasions and interactions both in private and in public spaces. There were also many examples of the use of imposed routines to limit alcohol use and of a decreasing volume of alcohol being consumed as participants aged. This suggests that older people are often active in constructing what they regard as ‘healthier’ routines around alcohol use. However, processes and circumstances associated with ageing can lead to risk of social isolation and/or increased alcohol consumption. Such processes include retirement from paid work and other ‘biographical disruptions’ such as caring for a partner, bereavement and/or loss of social networks. Conclusions: These findings highlight processes that can result in changes in drinking habits and routines. Whilst these processes can be associated with a reduction or cessation of alcohol use as people age, they can also be associated with increased risk of harmful alcohol consumption. Fractured or disrupted routines, particularly those associated with bereavement or the burden of caring responsibilities, through increasing the risk of loneliness and isolation, can construct increased risk of harmful alcohol consumption. These findings reframe the pathway of risk between ageing and alcohol-related harm by highlighting the vulnerability to harmful drinking practices brought by fracture or sudden change of routine. The findings point to a role for public health in supporting the reconstruction of routines that provide structure and meaning and can be used to actively manage the benefits and harms associated with drinking

Results of cross-faculty 'capstone' assessments involving nursing and performing arts students

This article describes how ‘capstone’ assessments were created to provide two different student groups, nursing and performing arts students, with a lived experience of learning together about their own fields of practice. Capstone assessments combine ‘live’ human simulation with self‑reflection and peer review. A capstone assessment is the integration of a body of relatively fragmented knowledge and learning to form a unified whole and can be used as a transitional assessment and a bridging experience to connect knowledge between modules or courses. The capstone assessments involved two faculties and four modules, three nursing and one performing arts. Case studies were designed to represent real-life situations that students were likely to encounter during their careers, either playing a patient as an actor or performing a caring role as a nurse. Assessments for the capstone simulation were formative, and involved the students engaging in self-reflection and peer review. Videos were available to enhance the self-reflection and peer-review process. Evaluation was undertaken through verbal feedback during debrief, written feedback, video footage and nursing student and acting student peer review. The experience of capstone assessments for two diverse student groups provided valuable learning from their own and from a different group outside their subject area