Trivial Jensen measures without regularity

In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point.

National evaluation of NHS genetics service investments: emerging issues from the cancer genetics pilots

In seeking to fulfil the ambition of the 2003 genetics white paper, Our Inheritance, Our Future, to ‘mainstream’ genetic knowledge and practices, the Department of Health provided start-up funding for pilot services in various clinical areas, including seven cancer genetics projects. To help to understand the challenges encountered by such an attempt at reconfiguring the organization and delivery of services in this field, a programme-level evaluation of the genetics projects was commissioned to consider the organizational issues faced. Using a qualitative approach, this research has involved comparative case-study work in 11 of the pilot sites, including four of the seven cancer genetics pilots. In this paper, the researchers present early findings from their work, focusing in particular on the cancer genetics pilots. They consider some of the factors that have influenced how the pilots have sought to address pre-existing sector, organizational and professional boundaries to these new ways of working. The article examines the relationship between these factors and the extent to which pilots have succeeded in setting up boundary-spanning services, dealing with human-resource issues and creating sustainable, ‘mainstreamed’ provision which attracts ongoing funding in a volatile NHS commissioning environment where funding priorities do not always favour preventive, risk-assessment services.

An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.