Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering

We establish high energy $L^2$ estimates for the restriction of the free Green's function to hypersurfaces in $\mathbb{R}^d$. As an application, we estimate the size of a logarithmic resonance free region for scattering by potentials of the form $V\otimes \delta_{\Gamma}$, where $\Gamma \subset \mathbb{R}^d$ is a finite union of compact subsets of embedded hypersurfaces. In odd dimensions we prove a resonance expansion for solutions to the wave equation with such a potential.Comment: 24 page

Relation between number of siblings and adult mortality and stroke risk: 25 year follow up of men in the Collaborative study

<b>Study objective</b>: To investigate the relation between number of siblings, mortality risk, and stroke risk. <b>Design</b>: Prospective cohort study. <b>Setting</b>: 27 workplaces in Scotland. <b>Participants</b>: 5765 employed men aged 35–64 from a variety of different workplaces, screened between 1970 and 1973. <b>Main results</b>: There were strong relationships between number of siblings and socioeconomic variables and also with adult behavioural measures. Men with greater numbers of siblings had an increased risk of dying of all causes, coronary heart disease, lung cancer, stomach cancer, and respiratory disease over a 25 year follow up period. Adjustment for risk factors could explain these associations, excepting stomach cancer mortality. With the definition of stroke as either a hospital admission for stroke or death from stroke, there was a strong relation between number of siblings and haemorrhagic stroke, but not ischaemic stroke. <b>Conclusions</b>: Number of siblings is strongly related to mortality risk, but as it is also related to many risk factors, adjustment for these can generally explain the relation with mortality. The exceptions are stomach cancer mortality and haemorrhagic stroke, which are known to be related to deprivation in childhood, and, in the case of stomach cancer to childhood infection

Decay estimates for variable coefficient wave equations in exterior domains

In this article we consider variable coefficient, time dependent wave equations in exterior domains. We prove localized energy estimates if the domain is star-shaped and global in time Strichartz estimates if the domain is strictly convex.Comment: 15 pages. In the new version, some typos are fixed and a minor correction was made to the proof of Lemma 1

Evaluating distributed cognitive resources for wayfinding in a desktop virtual environment.

As 3D interfaces, and in particular virtual environments, become increasingly realistic there is a need to investigate the location and configuration of information resources, as distributed in the humancomputer system, to support any required activities. It is important for the designer of 3D interfaces to be aware of information resource availability and distribution when considering issues such as cognitive load on the user. This paper explores how a model of distributed resources can support the design of alternative aids to virtual environment wayfinding with varying levels of cognitive load. The wayfinding aids have been implemented and evaluated in a desktop virtual environment

Null form estimates for (1/2,1/2) symbols and local existence for a quasilinear Dirichlet-wave equation

The authors show that bilinear estimates for null forms hold for Dirichlet-wave equations outside of convex obstacle. This generalizes results for the Euclidean case of Klainerman and Machedon, and of Sogge for the variable coefficient boundaryless case. The estimates are used to prove a local existence theorem for semilinear wave equations satisfying the null condition.Comment: To appear in Annales Scientifiques L'Ecole Normale Superieur

Alcohol consumption and use of acute and mental health hospital services in the West of Scotland Collaborative prospective cohort study

<b>Background</b>: Overconsumption of alcohol affects health. Data from men from the West of Scotland Collaborative study were analysed to see how reported alcohol wasrelated to acute and mental health hospital admissions. <b>Methods</b>: Men (N=5772) from a prospective cohort study located in 27 workplaces in West and Central Scotland were screened when aged 35-64 in 1970-3.The number of acute and mental health admissions and bed-days were calculated by alcohol category (none, 1-7,8-14, 15-21, 22-34 and 35 or more units per week) tothe end of 2005. Specific causes were coronary heartdisease (CHD), stroke, respiratory diseases and alcohol related. <b>Results</b>: Men who consumed 22 or more units per week had a 20% higher rate of acute admissions than non drinkers.The number of bed-days were higher for men drinking eight or more units and increased with consumption, with the highest category having a 58% higher rate of bed-days than non-drinkers. Non-drinkers had the highest admissions for CHD. For stroke, drinkers of 15 or more units had higher admissions and higher number of bed-days and these increased with increasing consumption. Respiratory admissions were higher for drinkers of 22 or more units and bed-days were higher for drinkers of 15 or more units. Alcohol-related admissions and number of bed-days generally increased with consumption. Mental health admissions and number of bed-days were raised for drinkers of 22 or more units with a suggestion of a J-shaped relationship. <b>Conclusion</b>: Alcohol consumption has a substantialeffect on acute and mental health admissions and bed-days

A New Approach to Fibrous Composite Laminate Strength Prediction

A method of predicting the strength of cross-plied fibrous composite laminates is based on expressing the classical maximum-shear-stress failure criterion for ductile metals in terms of strains. Starting with such a formulation for classical isotropic materials, the derivation is extended to orthotropic materials having a longitudinal axis of symmetry, to represent the fibers in a unidirectional composite lamina. The only modification needed to represent those same fibers with properties normalized to the lamina rather than fiber is a change in axial modulus. A mirror image is added to the strain-based lamina failure criterion for fiber-dominated failures to reflect the cutoffs due to the presence of orthogonal fibers. It is found that the combined failure envelope is now identical with the well-known maximum-strain failure model in the tension-tension and compression-compression quadrants but is truncated in the shear quadrants. The successive application of this simple failure model for fibers in the 0/90 degree and +/- 45 degree orientations, in turn, is shown to be the necessary and sufficient characterization of the fiber-dominated failures of laminates made from fibers having the same tensile and compressive strengths. When one such strength is greater than the other, the failure envelope is appropriately truncated for the lesser direct strain. The shear-failure cutoffs are now based on the higher axial strain to failure since they occur at lower strains than and are usually not affected by such mechanisms as microbuckling. Premature matrix failures can also be covered by appropriately truncating the fiber failure envelope. Matrix failures are excluded from consideration for conventional fiber/polymer composites but the additional features needed for a more rigorous analysis of exotic materials are covered. The new failure envelope is compared with published biaxial test data. The theory is developed for unnotched laminates but is easily shrunk to incorporate reductions to allow for bolt holes, cutouts, reduced compressive strength after impact, and the like