The horizon problem for prevalent surfaces

We investigate the box dimensions of the horizon of a fractal surface defined by a function $f \in C[0,1]^2$. In particular we show that a prevalent surface satisfies the `horizon property', namely that the box dimension of the horizon is one less than that of the surface. Since a prevalent surface has box dimension 3, this does not give us any information about the horizon of surfaces of dimension strictly less than 3. To examine this situation we introduce spaces of functions with surfaces of upper box dimension at most \alpha, for \alpha $\in$ [2,3). In this setting the behaviour of the horizon is more subtle. We construct a prevalent subset of these spaces where the lower box dimension of the horizon lies between the dimension of the surface minus one and 2. We show that in the sense of prevalence these bounds are as tight as possible if the spaces are defined purely in terms of dimension. However, if we work in Lipschitz spaces, the horizon property does indeed hold for prevalent functions. Along the way, we obtain a range of properties of box dimensions of sums of functions

Continuum of cardiac care

Ohio Valley Medical Center is 453-bed acute care hospital in Wheeling, West Virginia. The hospital is centrally located in the Upper Ohio Valley and provides tertiary care services to a patient population in excess of 150,000. The hospital provides the full array of cardiac services with the exception of open heart surgery and coronary angioplasty. The hospital must determine the need and financial viability to institute these services. The financial stability of the organization and the health care needs of the patient population depend on the continuum of cardiac care. The researcher established need through a recognized methodology. Need was well documented and financial viability was proven. Alternatives to the establishment of an open heart surgery and coronary angioplasty program at Ohio Valley Medical Center are provided. All documentation was in order with established protocols set forth by the state of West Virginia. The researcher recommended the development of the program after certificate of need approval from the state of West Virginia and provided alternative solutions if the certificate of need was not granted

High velocity clouds in the Galactic All Sky Survey I. Catalogue

We present a catalogue of high-velocity clouds (HVCs) from the Galactic All Sky Survey (GASS) of southern-sky neutral hydrogen, which has 57 mK sensitivity and 1 km/s velocity resolution and was obtained with the Parkes Telescope. Our catalogue has been derived from the stray-radiation corrected second release of GASS. We describe the data and our method of identifying HVCs and analyse the overall properties of the GASS population. We catalogue a total of 1693 HVCs at declinations < 0 deg, including 1111 positive velocity HVCs and 582 negative velocity HVCs. Our catalogue also includes 295 anomalous velocity clouds (AVCs). The cloud line-widths of our HVC population have a median FWHM of ~19 km/s, which is lower than found in previous surveys. The completeness of our catalogue is above 95% based on comparison with the HIPASS catalogue of HVCs, upon which we improve with an order of magnitude in spectral resolution. We find 758 new HVCs and AVCs with no HIPASS counterpart. The GASS catalogue will shed an unprecedented light on the distribution and kinematic structure of southern-sky HVCs, as well as delve further into the cloud populations that make up the anomalous velocity gas of the Milky Way.Comment: 21 pages, 14 figures, accepted for publication in ApJ

Measuring the atomic composition of planetary building blocks

Volatile molecules are critical to terrestrial planetary habitability, yet difficult to observe directly where planets form at the midplanes of protoplanetary disks. It is unclear whether the inner 1 AU of disks are volatile-poor or if this region is resupplied with ice-rich dust from colder disk regions. Dust traps at radial pressure maxima bounding disk gaps can cut off the inner disk from such volatile reservoirs. However, the trap retention efficiency and atomic composition of trapped dust have not been measured. We present a new technique to measure the absolute atomic abundances in gas accreting onto T Tauri stars and infer the bulk atomic composition and distribution of midplane solids retained in the disk around the young star TW Hya. We identify line emission from gas-phase material inside the dust sublimation rim of TW Hya. Gaussian decomposition of the strongest H Paschen lines isolates the inner disk hydrogen emission. We measure several key elemental abundances, relative to hydrogen, using a chemical photoionization model and infer dust retention in the disk. With a 1D transport model, we determine approximate radial locations and retention efficiencies of dust traps for different elements. Volatile and refractory elements are depleted from TW Hya's hot gas by factors of ~10^2 and up to 10^5, respectively. Dust traps beyond the CO and N2 snowline cumulatively sequester 96% of the total dust, while the trap at 2 AU retains 3% of the initial dust mass. The high depletions of Si, Mg, and Ca are explained by a third trap at 0.3 AU. TW Hya has a significant volatile reservoir rich in C- and N-ices in its outer ring structure. However, the lack of C resupply may leave the terrestrial planet-forming region dry and carbon-poor. Any planets that form within the silicate dust trap at 0.3 AU may resemble Earth in terms of the degree of their volatile depletion.Comment: Accepted for publication in A&A Letters. 6 pages, 3 figures, plus appendice