Spectral and Hodge theory of `Witt' incomplete cusp edge spaces

Incomplete cusp edges model the behavior of the Weil-Petersson metric on the compactified Riemann moduli space near the interior of a divisor. Assuming such a space is Witt, we construct a fundamental solution to the heat equation, and using a precise description of its asymptotic behavior at the singular set, we prove that the Hodge-Laplacian on differential forms is essentially self-adjoint, with discrete spectrum satisfying Weyl asymptotics. We go on to prove bounds on the growth of $L^2$-harmonic forms at the singular set and to prove a Hodge theorem, namely that the space of $L^2$-harmonic forms is naturally isomorphic to the middle-perversity intersection cohomology. Moreover, we develop an asymptotic expansion for the heat trace near $t = 0$

HOUSEHOLD EXPENDITURE ON MEAT VERSUS NONMEAT SOURCES OF PROTEIN IN THE UNITED STATES

Food Consumption/Nutrition/Food Safety,

The origin of the strings in the outer regions of Eta Carinae

The narrow optical filaments (`strings' or `spikes') emerging from the Homunculus of Eta Carinae are modelled as resulting from the passage of ballistic `bullets' of material through the dense circumstellar environment. In this explanation, the string is the decelerating flow of ablated gas from the bullet. An archive HST image and new forbidden line profiles of the most distinct of the strings are presented and discussed in terms of this simple model.Comment: 5 pages, 4 figure

Clumpy Ultracompact HII Regions I: Fully Supersonic Wind-blown Models

We propose that a significant fraction of the ultracompact HII regions found in massive star-forming clouds are the result of the interaction of the wind and ionizing radiation from a young massive star with the clumpy molecular cloud gas in its neighbourhood. Distributed mass loading in the flow allows the compact nebulae to be long-lived. In this paper, we discuss a particularly simple case, in which the flow in the HII region is everywhere supersonic. The line profiles predicted for this model are highly characteristic, for the case of uniform mass loading. We discuss briefly other observational diagnostics of these models.Comment: To appear in Monthly Notices of the Royal Astronomical Society. 5 pages LaTeX (uses mn.sty and epsf.sty macros) + 4 PS figures. Also available via http://axp2.ast.man.ac.uk:8000/Preprints.htm

A high-speed bi-polar outflow from the archetypical pulsating star Mira A

Optical images and high-dispersion spectra have been obtained of the ejected material surrounding the pulsating AGB star Mira A. The two streams of knots on either side of the star, found in far ultra-viollet (FUV) GALEX images, have now been imaged clearly in the light of Halpha. Spatially resolved profiles of the same line reveal that the bulk of these knots form a bi-polar outflow with radial velocity extremes of +- 150 km/s with respect to the central star. The South stream is approaching and the North stream receding from the observer. A displacement away from Mira A between the position of one of the South stream knots in the new Halpha image and its position in the previous Palomar Observatory Sky Survey (POSS I) red plate has been noted. If interpreted as a consequence of expansion proper motions the bipolar outflow is tilted at 69deg +- 2deg to the plane of the sky, has an outflow velocity of 160 +- 10 km/s and is ~1000 y old.Comment: 8 pages, 5 figures. Accepted for pubication by A&

Unified Models of Molecular Emission from Class 0 Protostellar Outflow Sources

Low mass star-forming regions are more complex than the simple spherically symmetric approximation that is often assumed. We apply a more realistic infall/outflow physical model to molecular/continuum observations of three late Class 0 protostellar sources with the aims of (a) proving the applicability of a single physical model for all three sources, and (b) deriving physical parameters for the molecular gas component in each of the sources. We have observed several molecular species in multiple rotational transitions. The observed line profiles were modelled in the context of a dynamical model which incorporates infall and bipolar outflows, using a three dimensional radiative transfer code. This results in constraints on the physical parameters and chemical abundances in each source. Self-consistent fits to each source are obtained. We constrain the characteristics of the molecular gas in the envelopes as well as in the molecular outflows. We find that the molecular gas abundances in the infalling envelope are reduced, presumably due to freeze-out, whilst the abundances in the molecular outflows are enhanced, presumably due to dynamical activity. Despite the fact that the line profiles show significant source-to-source variation, which primarily derives from variations in the outflow viewing angle, the physical parameters of the gas are found to be similar in each core.Comment: MNRAS 12 pages, 16 figure