[Introduction to] The Cauchy Transform

The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an in-depth treatment of Clark measures.https://scholarship.richmond.edu/bookshelf/1094/thumbnail.jp

The Backward Shift on the Space of Chauchy Transforms

This note examines the subspaces of the space of Cauchy transforms of measures on the unit circle that are invariant under the backward shift operator f --\u3e z-1 (f—f (0)). We examine this question when the space of Cauchy transforms is endowed with both the norm and weak* topologies

Exploring the Structure of Distant Galaxies with Adaptive Optics on the Keck-II Telescope

We report on the first observation of cosmologically distant field galaxies with an high order Adaptive Optics (AO) system on an 8-10 meter class telescope. Two galaxies were observed at 1.6 microns at an angular resolution as high as 50 milliarcsec using the AO system on the Keck-II telescope. Radial profiles of both objects are consistent with those of local spiral galaxies and are decomposed into a classic exponential disk and a central bulge. A star-forming cluster or companion galaxy as well as a compact core are detected in one of the galaxies at a redshift of 0.37+/-0.05. We discuss possible explanations for the core including a small bulge, a nuclear starburst, or an active nucleus. The same galaxy shows a peak disk surface brightness that is brighter than local disks of comparable size. These observations demonstrate the power of AO to reveal details of the morphology of distant faint galaxies and to explore galaxy evolution.Comment: 5 pages, Latex, 3 figures. Accepted for publication in P.A.S.

Reducing drug related deaths : a pre-implementation assessment of knowledge,barriers and enablers for naloxone distribution through general practice

Peer reviewedPublisher PD

Spectroscopy of High-Redshift Supernovae from the ESSENCE Project: The First Four Years

We present the results of spectroscopic observations from the ESSENCE high-redshift supernova (SN) survey during its first four years of operation. This sample includes spectra of all SNe Ia whose light curves were presented by Miknaitis et al. (2007) and used in the cosmological analyses of Davis et al. (2007) and Wood-Vasey et al. (2007). The sample represents 273 hours of spectroscopic observations with 6.5 - 10-m-class telescopes of objects detected and selected for spectroscopy by the ESSENCE team. We present 174 spectra of 156 objects. Combining this sample with that of Matheson et al. (2005), we have a total sample of 329 spectra of 274 objects. From this, we are able to spectroscopically classify 118 Type Ia SNe. As the survey has matured, the efficiency of classifying SNe Ia has remained constant while we have observed both higher-redshift SNe Ia and SNe Ia farther from maximum brightness. Examining the subsample of SNe Ia with host-galaxy redshifts shows that redshifts derived from only the SN Ia spectra are consistent with redshifts found from host-galaxy spectra. Moreover, the phases derived from only the SN Ia spectra are consistent with those derived from light-curve fits. By comparing our spectra to local templates, we find that the rate of objects similar to the overluminous SN 1991T and the underluminous SN 1991bg in our sample are consistent with that of the local sample. We do note, however, that we detect no object spectroscopically or photometrically similar to SN 1991bg. Although systematic effects could reduce the high-redshift rate we expect based on the low-redshift surveys, it is possible that SN 1991bg-like SNe Ia are less prevalent at high redshift.Comment: 21 pages, 17 figures, accepted to A

The Type Ic Hypernova SN 2003dh/GRB 030329

The spectra of SN 2003dh, identified in the afterglow of GRB030329, are modeled using radiation transport codes. It is shown that SN 2003dh had a high explosion kinetic energy ($\sim 4 \times 10^{52}$ erg in spherical symmetry), making it one of the most powerful hypernovae observed so far, and supporting the case for association between hypernovae and Gamma Ray Bursts. However, the light curve derived from fitting the spectra suggests that SN 2003dh was not as bright as SN 1998bw, ejecting only \sim 0.35\Msun of \Nifs. The spectra of SN 2003dh resemble those of SN 1998bw around maximum, but later they look more like those of the less energetic hypernova SN 1997ef. The spectra and the inferred light curve can be modeled adopting a density distribution similar to that used for SN 1998bw at $v > 25,000$\kms but more like that of SN 1997ef at lower velocities. The mass of the ejecta is \sim 8\Msun, somewhat less than in the other two hypernovae. The progenitor must have been a massive star (M \sim 35-40\Msun), as for other hypernovae. The need to combine different one-dimensional explosion models strongly indicates that SN 2003dh was an asymmetric explosion.Comment: 11 pages, 1 table and 5 figures. To appear in the Astrophysical Journal (Letters). Revised version taking referee's comments into account, minor change

Low Carbon Abundance in Type Ia Supernovae

We investigate the quantity and composition of unburned material in the outer layers of three normal Type Ia supernovae (SNe Ia): 2000dn, 2002cr and 20 04bw. Pristine matter from a white dwarf progenitor is expected to be a mixture of oxygen and carbon in approximately equal abundance. Using near-infrared (NIR, 0.7-2.5 microns) spectra, we find that oxygen is abundant while carbon is severely depleted with low upper limits in the outer third of the ejected mass. Strong features from the OI line at rest wavelength = 0.7773 microns are observed through a wide range of expansion velocities approx. 9,000 - 18,000 km/s. This large velocity domain corresponds to a physical region of the supernova with a large radial depth. We show that the ionization of C and O will be substantially the same in this region. CI lines in the NIR are expected to be 7-50 times stronger than those from OI but there is only marginal evidence of CI in the spectra and none of CII. We deduce that for these three normal SNe Ia, oxygen is more abundant than carbon by factors of 100 - 1,000. MgII is also detected in a velocity range similar to that of OI. The presence of O and Mg combined with the absence of C indicates that for these SNe Ia, nuclear burning has reached all but the extreme outer layers; any unburned material must have expansion velocities greater than 18,000 km/s. This result favors deflagration to detonation transition (DD) models over pure deflagration models for SNe Ia.Comment: accepted for publication in Ap