Vector-valued non-homogeneous Tb theorem on metric measure spaces

We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem which is quite general with respect to both of them.Comment: 31 page

Pairing in a three component Fermi gas

We consider pairing in a three-component gas of degenerate fermions. In particular, we solve the finite temperature mean-field theory of an interacting gas for a system where both interaction strengths and fermion masses can be unequal. At zero temperature we find a a possibility of a quantum phase transition between states associated with pairing between different pairs of fermions. On the other hand, finite temperature behavior of the three-component system reveals some qualitative differences from the two-component gas: for a range of parameters it is possible to have two different critical temperatures. The lower one corresponds to a transition between different pairing channels, while the higher one corresponds to the usual superfluid-normal transition. We discuss how these phase transitions could be observed in ultracold gases of fermionic atoms.Comment: 10 pages, 3 figure

Neighbourhoods and self rated health: a comparison of public sector employees in London and Helsinki

Study objective: Mortality and morbidity vary across neighbourhoods and larger residential areas. Effects of area deprivation on health may vary across countries, because of greater spatial separation of people occupying high and low socioeconomic positions and differences in the provision of local services and facilities. Neighbourhood variations in health and the contribution of residents' characteristics and neighbourhood indicators were compared in London and Helsinki, two settings where inequality and welfare policies differ.Design: Data from two cohorts were used to investigate associations between self rated health and neighbourhood indicators using a multilevel approach.Setting: London and Helsinki.Participants: From the Whitehall II study (London, aged 39-63) and the Helsinki health study (aged 40-60).Main results: Socioeconomic segregation was higher in London than in Helsinki. Age and sex adjusted differences in self rated health between neighbourhoods were also greater in London. Independent of individual socioeconomic position, neighbourhood unemployment, proportion of residents in manual occupations, and proportion of single households were associated with health. In pooled data, residence in a neighbourhood with highest unemployment was associated with an odds ratio of less than good self rated health of 1.51 (95% CI 1.30 to 1.75). High rates of single parenthood were associated with health in London but not in Helsinki.Conclusions: Neighbourhood socioeconomic context was associated with health in both countries, with some evidence of greater neighbourhood effects in London. Greater socioeconomic segregation in London may have emergent effects at the neighbourhood level. Local and national social policies may reduce, or restrict, inequality and segregation between areas