Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces. (C) 2002 Elsevier Science B.V. All rights reserved.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Simulations of thermal Bose fields in the classical limit

We demonstrate that the time-dependent projected Gross-Pitaevskii equation (GPE) derived earlier [M. J. Davis, R. J. Ballagh, and K. Burnett, J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. Contrary to the often held belief that the GPE is valid only at zero temperature, we find that this equation will evolve randomized initial wave functions to a state describing thermal equilibrium. In the case of small interaction strengths or low temperatures, our numerical results can be compared to the predictions of Bogoliubov theory and its perturbative extensions. This demonstrates the validity of the GPE in these limits and allows us to assign a temperature to the simulations unambiguously. However, the GPE method is nonperturbative, and we believe it can be used to describe the thermal properties of a Bose gas even when Bogoliubov theory fails. We suggest a different technique to measure the temperature of our simulations in these circumstances. Using this approach we determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. Interesting behavior near the critical point is observed and discussed.

Expert review of an approach to functional capacity evaluation

Functional capacity evaluation (FCE) is a widely used tool in work rehabilitation, despite the limited examination of the soundness of its measurement properties. This paper outlines the development of a new approach to FCE, the GAPP FCE, and reports on the findings of an expert review of aspects of its content validity and technical adequacy and how it meets established test criteria. Five expert occupational therapists reviewed the materials of the GAPP FCE then completed a questionnaire related to the content validity, technical adequacy and safety, reliability, validity, practicality and utility of the GAPP FCE. The experts gave support to most aspects of these criteria. The main issue identified by the review was related to interpretation and extrapolation of the FCE results for return to work. This and other issues are discussed in relation to recent developments in FCE and plans for future development of the GAPP FCE.

Patients' interactions with health providers - A linguistic category model approach

Two studies investigated interactions between health providers and patients, using Semin and Fiedler's linguistic category model. In Study 1 the linguistic category model was used to examine perceptions of the levels of linguistic intergroup bias in descriptions of conversations with health professionals in hospitals. Results indicated a favourable linguistic bias toward health professionals in satisfactory conversations but low levels of linguistic intergroup bias in unsatisfactory conversations. In Study 2, the language of patients and health professionals in videotaped interactions was examined for levels of linguistic intergroup bias. Interpersonally salient interactions showed less linguistic intergroup bias than did intergroup ones. Results also indicate that health professionals have high levels of control in all types of medical encounters with patients. Nevertheless, the extent to which patients are able to interact with health professionals as individuals, rather than only as professionals is a key determinant of satisfaction with the interaction.

The Building Partnerships Program: An Approach to Community-based Learning for Medical Students in Australia

The Building Partnerships Program at the University of Queensland, Australia seeks to address the dual challenge of preparing doctors who are responsive to the community while providing a meaningful context for social sciences learning. Through partnerships with a diverse range of community agencies, the program offers students opportunities to gain non-clinical perspectives on health and illness through structured learning activities including: family visits; community agency visits and attachments; and interview training. Students learn first-hand about psychosocial influences on health and how people manage health problems on a day-to-day basis. They also gain insights into the work of community agencies and how they as future doctors might work in partnership with them to enhance patient care. We outline the main components of the program, identify challenges and successes from student and community agency perspectives, and consider areas that invite further development.