The L2L^2 essential spectrum of the 2D Euler operator

Even in two dimensions, the spectrum of the linearized Euler operator is notoriously hard to compute. In this paper we give a new geometric calculation of the essential spectrum for 2D flows. This generalizes existing results---which are only available when the flow has arbitrarily long periodic orbits---and clarifies the role of individual streamlines in generating essential spectra.Comment: 14 pages; hypotheses of the main theorem clarifie

Serological survey of anti-group A rotavirus IgM in UK adults

Rotaviral associated disease of infants in the UK is seasonal and infection in adults not uncommon but the relationship between these has been little explored. Adult sera collected monthly for one year from routine hospital samples were screened for the presence of anti-group A rotavirus immunoglobulin M class antibodies as a marker of recent infection. Anti-rotavirus IgM was seen in all age groups throughout the year with little obvious seasonal variation in the distribution of antibody levels. IgM concentrations and the proportion seropositive above a threshold both increased with age with high concentrations consistently observed in the elderly. Results suggest either high infection rates of rotavirus in adults, irrespective of seasonal disease incidence in infants, IgM persistence or IgM cross-reactivity. These results support recent evidence of differences between infant and adult rotavirus epidemiology and highlight the need for more extensive surveys to investigate age and time related infection and transmission of rotavirus

Blowup solutions of Jang's equation near a spacetime singularity

We study Jang's equation on a one-parameter family of asymptotically flat, spherically symmetric Cauchy hypersurfaces in the maximally extended Schwarzschild spacetime. The hypersurfaces contain apparent horizons and are parametrized by their proximity to the singularity at $r = 0$. We show that on those hypersurfaces sufficiently close to the singularity, every radial solution to Jang's equation blows up. The proof depends only on the geometry in an arbitrarily small neighborhood of the singularity, suggesting that Jang's equation is in fact detecting the singularity. We comment on possible applications to the weak cosmic censorship conjecture.Comment: 18 pages, 1 figure; second version has expanded Introduction, and new description of blowup solutions in Section

The jaw is a second-class lever in Pedetes capensis (Rodentia: Pedetidae)

The mammalian jaw is often modelled as a third-class lever for the purposes of biomechanical analyses, owing to the position of the resultant muscle force between the jaw joint and the teeth. However, it has been proposed that in some rodents the jaws operate as a second-class lever during distal molar bites, owing to the rostral position of the masticatory musculature. In particular, the infraorbital portion of the zygomatico-mandibularis (IOZM) has been suggested to be of major importance in converting the masticatory system from a third-class to a second-class lever. The presence of the IOZM is diagnostic of the hystricomorph rodents, and is particularly well-developed in Pedetes capensis, the South African springhare. In this study, finite element analysis (FEA) was used to assess the lever mechanics of the springhare masticatory system, and to determine the function of the IOZM. An FE model of the skull of P. capensis was constructed and loaded with all masticatory muscles, and then solved for biting at each tooth in turn. Further load cases were created in which each masticatory muscle was removed in turn. The analyses showed that the mechanical advantage of the springhare jaws was above one at all molar bites and very close to one during the premolar bite. Removing the IOZM or masseter caused a drop in mechanical advantage at all bites, but affected strain patterns and cranial deformation very little. Removing the ZM had only a small effect on mechanical advantage, but produced a substantial reduction in strain and deformation across the skull. It was concluded that the masticatory system of P. capensis acts as a second class lever during bites along almost the entire cheek tooth row. The IOZM is clearly a major contributor to this effect, but the masseter also has a part to play. The benefit of the IOZM is that it adds force without substantially contributing to strain or deformation of the skull. This may help explain why the hystricomorphous morphology has evolved multiple times independently within Rodentia