Global bifurcation for monotone fronts of elliptic equations

In this paper, we present two results on global continuation of monotone front-type solutions to elliptic PDEs posed on infinite cylinders. This is done under quite general assumptions, and in particular applies even to fully nonlinear equations as well as quasilinear problems with transmission boundary conditions. Our approach is rooted in the analytic global bifurcation theory of Dancer and Buffoni--Toland, but extending it to unbounded domains requires contending with new potential limiting behavior relating to loss of compactness. We obtain an exhaustive set of alternatives for the global behavior of the solution curve that is sharp, with each possibility having a direct analogue in the bifurcation theory of second-order ODEs. As a major application of the general theory, we construct global families of internal hydrodynamic bores. These are traveling front solutions of the full two-phase Euler equation in two dimensions. The fluids are confined to a channel that is bounded above and below by rigid walls, with incompressible and irrotational flow in each layer. Small-amplitude fronts for this system have been obtained by several authors. We give the first large-amplitude result in the form of continuous curves of elevation and depression bores. Following the elevation curve to its extreme, we find waves whose interfaces either overturn (develop a vertical tangent) or become exceptionally singular in that the flow in both layers degenerates at a single point on the boundary. For the curve of depression waves, we prove that either the interface overturns or it comes into contact with the upper wall.Comment: 60 pages, 6 figure

Policy and practice change at local, regional and international levels: impacts from Born in Bradford

YesBorn in Bradford is a prospective pregnancy and birth cohort in the UKs 6th largest city. Between 2007 and 2011 12,453 women (13,776 pregnancies), 3,448 of their partners and 13,818 babies were recruited. Half of families are in the poorest fifth of deprivation for England and Wales, and 45% are of Pakistani origin. Recruitment was in one Metropolitan District. This allows consideration of the impact of local circumstances, including service provision and policy choices, and engagement with the local community to implement evidence based responses to study findings. The introduction of a large study into a local health economy contributed to organizational changes including the development of a paperless maternity data system and better links between primary, secondary, and child health services. Embedding research in practice can lead to improved quality of routine data collected, for example on infant growth, and make routine data available for research, enhancing its cost effectiveness. Early adoption of research findings locally includes the introduction of routine vitamin D supplementation and an oral glucose tolerance test for all pregnant women. Findings that consanguinity was associated with a doubling of risk for congenital anomaly and that 30% of all anomalies in children of Pakistani origin could be attributed to consanguinity reinforced local commitment to community education about genetics and targeted genetic counselling. These findings also led to the establishment of a regional congenital anomalies register. In partnership with the European ESCAPE consortium (14 cohorts in 12 countries) a significant association was found between fetal growth and air pollution. The European Environmental Agency Director stated that this evidence is sufficient to trigger changes in EU regulations. Some findings can be quickly embedded in local provision, some have a resonance that prompts regional changes, some are generated with collaborators and can lead to policy change at international level

Characteristic Timing

We use differences between the attributes of stock issuers and repurchasers to forecast characteristic-related stock returns. For example, we show that large firms underperform following years when issuing firms are large relative to repurchasing firms. Our approach is useful for forecasting returns to portfolios based on book-to-market (HML), size (SMB), price, distress, payout policy, profitability, and industry. We consider interpretations of these results based on both time-varying risk premia and mispricing. Our results are primarily consistent with the view that firms issue and repurchase shares to exploit time-varying characteristic mispricing.