Distinguished non-Archimedean representations

For a symmetric space (G,H), one is interested in understanding the vector space of H-invariant linear forms on a representation \pi of G. In particular an important question is whether or not the dimension of this space is bounded by one. We cover the known results for the pair (G=R_{E/F}GL(n),H=GL(n)), and then discuss the corresponding SL(n) case. In this paper, we show that (G=R_{E/F}SL(n),H=SL(n)) is a Gelfand pair when n is odd. When $n$ is even, the space of H-invariant forms on \pi can have dimension more than one even when \pi is supercuspidal. The latter work is joint with Dipendra Prasad

The well-being of carers of older Aboriginal people living in the Kimberley region of remote Western Australia: Empowerment, depression, and carer burden

Objective: To describe demographic features and well-being of carers of Aboriginal Australians aged ≥45 years in remote Western Australia. Method: Carer burden, empowerment, and depression were assessed in 124 Aboriginal carers in four remote Aboriginal communities. Results: Carers were aged 38.8 ± 15.0 years, 73.4% were female, and 75.8% were children or grandchildren of the person cared for. The mean Zarit-6 score was 3.7 ± 3.6. Attending high school (odds ratio [OR] = 0.3; 95% confidence interval [CI] = [0.1, 0.7]) and feeling empowered (OR = 0.2; 95% CI = [0.1, 0.8]) were inversely associated with carer burden; female carers were less likely to feel empowered (OR = 0.4; 95% CI = [0.2, 0.9]); and empowerment was inversely associated with depression (OR = 0.3; 95% CI = [0.1, 0.7]). Discussion: Aboriginal carers in remote communities are relatively young and most are children or grandchildren. Carer burden was lower than anticipated. However, existing tools may not adequately measure Aboriginal perspectives. Education and empowerment are key factors which support programs must consider

RESPOND – A patient-centred programme to prevent secondary falls in older people presenting to the emergency department with a fall: Protocol for a mixed methods programme evaluation.

Background Programme evaluations conducted alongside randomised controlled trials (RCTs) have potential to enhance understanding of trial outcomes. This paper describes a multi-level programme evaluation to be conducted alongside an RCT of a falls prevention programme (RESPOND). Objectives 1) To conduct a process evaluation in order to identify the degree of implementation fidelity and associated barriers and facilitators. 2) To evaluate the primary intended impact of the programme: participation in fall prevention strategies, and the factors influencing participation. 3) To identify the factors influencing RESPOND RCT outcomes: falls, fall injuries and ED re-presentations. Methods/ Design Five hundred and twenty eight community-dwelling adults aged 60–90 years presenting to two EDs with a fall will be recruited and randomly assigned to the intervention or standard care group. All RESPOND participants and RESPOND clinicians will be included in the evaluation. A mixed methods design will be used and a programme logic model will frame the evaluation. Data will be sourced from interviews, focus groups, questionnaires, clinician case notes, recruitment records, participant-completed calendars, hospital administrative datasets, and audio-recordings of intervention contacts. Quantitative data will be analysed via descriptive and inferential statistics and qualitative data will be interpreted using thematic analysis. Discussion The RESPOND programme evaluation will provide information about contextual and influencing factors related to the RCT outcomes. The results will assist researchers, clinicians, and policy makers to make decisions about future falls prevention interventions. Insights gained are likely to be transferable to preventive health programmes for a range of chronic conditions

Liesegang patterns: Effect of dissociation of the invading electrolyte

The effect of dissociation of the invading electrolyte on the formation of Liesegang bands is investigated. We find, using organic compounds with known dissociation constants, that the spacing coefficient, 1+p, that characterizes the position of the n-th band as x_n ~ (1+p)^n, decreases with increasing dissociation constant, K_d. Theoretical arguments are developed to explain these experimental findings and to calculate explicitly the K_d dependence of 1+p.Comment: RevTex, 8 pages, 3 eps figure

Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Moeglin-Waldspurger and Jacquet-Shalika for GL(n).Comment: 49 pages; Appendix by N. Grba

Educators\u27 perspectives about how older hospital patients can engage in a falls prevention education programme: a qualitative process evaluation

Objectives: Falls are the most frequent adverse event reported in hospitals. Patient and staff education delivered by trained educators significantly reduced falls and injurious falls in an older rehabilitation population. The purpose of the study was to explore the educators’ perspectives of delivering the education and to conceptualise how the programme worked to prevent falls among older patients who received the education. Design: A qualitative exploratory study. Methods: Data were gathered from three sources: conducting a focus group and an interview (n=10 educators), written educator notes and reflective researcher field notes based on interactions with the educators during the primary study. The educators delivered the programme on eight rehabilitation wards for periods of between 10 and 40 weeks. They provided older patients with individualised education to engage in falls prevention and provided staff with education to support patient actions. Data were thematically analysed and presented using a conceptual framework. Results: Falls prevention education led to mutual understanding between staff and patients which assisted patients to engage in falls prevention behaviours. Mutual understanding was derived from the following observations: the educators perceived that they could facilitate an effective three-way interaction between staff actions, patient actions and the ward environment which led to behaviour change on the wards. This included engaging with staff and patients, and assisting them to reconcile differing perspectives about falls prevention behaviours. Conclusions: Individualised falls prevention education effectively provides patients who receive it with the capability and motivation to develop and undertake behavioural strategies that reduce their falls, if supported by staff and the ward environment

Antiferromagnetism in the Exact Ground State of the Half Filled Hubbard Model on the Complete-Bipartite Graph

As a prototype model of antiferromagnetism, we propose a repulsive Hubbard Hamiltonian defined on a graph \L={\cal A}\cup{\cal B} with ${\cal A}\cap {\cal B}=\emptyset$ and bonds connecting any element of ${\cal A}$ with all the elements of ${\cal B}$. Since all the hopping matrix elements associated with each bond are equal, the model is invariant under an arbitrary permutation of the ${\cal A}$-sites and/or of the ${\cal B}$-sites. This is the Hubbard model defined on the so called $(N_{A},N_{B})$-complete-bipartite graph, $N_{A}$ ($N_{B}$) being the number of elements in ${\cal A}$ (${\cal B}$). In this paper we analytically find the {\it exact} ground state for $N_{A}=N_{B}=N$ at half filling for any $N$; the repulsion has a maximum at a critical $N$-dependent value of the on-site Hubbard $U$. The wave function and the energy of the unique, singlet ground state assume a particularly elegant form for N \ra \inf. We also calculate the spin-spin correlation function and show that the ground state exhibits an antiferromagnetic order for any non-zero $U$ even in the thermodynamic limit. We are aware of no previous explicit analytic example of an antiferromagnetic ground state in a Hubbard-like model of itinerant electrons. The kinetic term induces non-trivial correlations among the particles and an antiparallel spin configuration in the two sublattices comes to be energetically favoured at zero Temperature. On the other hand, if the thermodynamic limit is taken and then zero Temperature is approached, a paramagnetic behavior results. The thermodynamic limit does not commute with the zero-Temperature limit, and this fact can be made explicit by the analytic solutions.Comment: 19 pages, 5 figures .ep