A Search for Binary Stars at Low Metallicity

We present initial results measuring the companion fraction of metal-poor stars ([Fe/H]$<-$2.0). We are employing the Lick Observatory planet-finding system to make high-precision Doppler observations of these objects. The binary fraction of metal-poor stars provides important constraints on star formation in the early Galaxy (Carney et al. 2003). Although it has been shown that a majority of solar metallicity stars are in binaries, it is not clear if this is the case for metal-poor stars. Is there a metallicity floor below which binary systems do not form or become rare? To test this we are determining binary fractions at metallicities below [Fe/H]$=-2.0$. Our measurments are not as precise as the planet finders', but we are still finding errors of only 50 to 300 m/s, depending on the signal-to-noise of a spectrum and stellar atmosphere of the star. At this precision we can be much more complete than previous studies in our search for stellar companions.Comment: To appear in conference proceedings,"First Stars III", eds. B. O'Shea, A. Heger & T. Abel. 3 pages, 5 figure

Semi-classical Green kernel asymptotics for the Dirac operator

We consider a semi-classical Dirac operator in arbitrary spatial dimensions with a smooth potential whose partial derivatives of any order are bounded by suitable constants. We prove that the distribution kernel of the inverse operator evaluated at two distinct points fulfilling a certain hypothesis can be represented as the product of an exponentially decaying factor involving an associated Agmon distance and some amplitude admitting a complete asymptotic expansion in powers of the semi-classical parameter. Moreover, we find an explicit formula for the leading term in that expansion.Comment: 46 page

Chemical Abundances For Evolved Stars In M5: Lithium Through Thorium

We present analysis of high-resolution spectra of a sample of stars in the globular cluster M5 (NGC 5904). The sample includes stars from the red giant branch (RGB; seven stars), the red horizontal branch (two stars), and the asymptotic giant branch (AGB; eight stars), with effective temperatures ranging from 4000 K to 6100 K. Spectra were obtained with the HIRES spectrometer on the Keck I telescope, with a wavelength coverage from 3700 angstrom to 7950 angstrom for the HB and AGB sample, and 5300 angstrom to 7600 angstrom for the majority of the RGB sample. We find offsets of some abundance ratios between the AGB and the RGB branches. However, these discrepancies appear to be due to analysis effects, and indicate that caution must be exerted when directly comparing abundance ratios between different evolutionary branches. We find the expected signatures of pollution from material enriched in the products of the hot hydrogen burning cycles such as the CNO, Ne-Na, and Mg-Al cycles, but no significant differences within these signatures among the three stellar evolutionary branches especially when considering the analysis offsets. We are also able to measure an assortment of neutron-capture element abundances, from Sr to Th, in the cluster. We find that the neutron-capture signature for all stars is the same, and shows a predominately r-process origin. However, we also see evidence of a small but consistent extra s-process signature that is not tied to the light-element variations, pointing to a pre-enrichment of this material in the protocluster gas.National Science Foundation AST-0802292NSF AST-0406988, AST-0607770, AST-0607482DFGW. M. Keck FoundationAstronom

The C IV Mass Density of the Universe at Redshift 5

In order to search for metals in the Lyman alpha forest at redshifts z > 4, we have obtained spectra of high S/N and resolution of three QSOs at z > 5.4 discovered by the Sloan Digital Sky Survey. These data allow us to probe to metal enrichment of the intergalactic medium at early times with higher sensitivity than previous studies. We find 16 C IV absorption systems with column densities log N(C IV) = 12.50 - 13.98 over a total redshift path Delta X = 3.29. In the redshift interval z = 4.5-5.0, where our statistics are most reliable, we deduce a comoving mass density of C IV ions Omega(C IV) = (4.3 +/- 2.5) x 10(-8) (90% confidence limits) for absorption systems with log N(C IV) > 13.0 (for an Einstein-de Sitter cosmology with h = 0.65). This value of Omega(C IV) is entirely consistent with those measured at z < 4; we confirm the earlier finding by Songaila (2001) that neither the column density distribution of C IV absorbers nor its integral show significant redshift evolution over a period of time which stretches from 1.25 to 4.5 Gyr after the big bang. This somewhat surprising conclusion may be an indication that the intergalactic medium was enriched in metals at redshifts much greater than 5, perhaps by the sources responsible for its reionization. Alternatively, the C IV systems we see may be associated with outflows from massive star-forming galaxies at later times, while the truly intergalactic metals may reside in regions of the Lyman alpha forest of lower density than those probed up to now.Comment: 24 pages including 5 figures. Accepted for publication in the Astrophysical Journal (September 10, 2003 issue

Carbon and Strontium Abundances of Metal-Poor Stars

We present carbon and strontium abundances for 100 metal-poor stars measured from R$\sim$7000 spectra obtained with the Echellette Spectrograph and Imager at the Keck Observatory. Using spectral synthesis of the G-band region, we have derived carbon abundances for stars ranging from [Fe/H]$=-1.3$ to [Fe/H]$=-3.8$. The formal errors are $\sim 0.2$ dex in [C/Fe]. The strontium abundance in these stars was measured using spectral synthesis of the resonance line at 4215 {\AA}. Using these two abundance measurments along with the barium abundances from our previous study of these stars, we show it is possible to identify neutron-capture-rich stars with our spectra. We find, as in other studies, a large scatter in [C/Fe] below [Fe/H]$= -2$. Of the stars with [Fe/H]$<-2$, 9$\pm$4% can be classified as carbon-rich metal-poor stars. The Sr and Ba abundances show that three of the carbon-rich stars are neutron-capture-rich, while two have normal Ba and Sr. This fraction of carbon enhanced stars is consistent with other studies that include this metallicity range.Comment: ApJ, Accepte

Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a `2-encounter'; such configurations are called `Sieber-Richter pairs' in the physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper [13], an inductive argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit

Semiclassical Approach to Chaotic Quantum Transport

We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and other related quantities require trajectory quadruplets; simple diagrammatic rules allow to find the contributions of these pairs and quadruplets. Both pure symmetry classes and the crossover due to an external magnetic field are considered.Comment: 33 pages, 11 figures (appendices B-D not included in journal version

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

Erfahrungen bei der Entwicklung eines Informationssystems auf RDBMS- und 4GL-Basis

Anläßlich der Entwicklung eines großen Informationssystems wurde die Entscheidung getroffen, ein Werkzeug der vierten Generation (4GL) und ein relationales Datenbanksystem (Oracle) zu verwenden. Der Beitrag beschreibt die Erfahrungen, die bei der Datenmodellierung auf Basis des Entity-Relationship-Ansatzes und der Überführung in ein Relationenmodell sowie mit den Oracle-spezifischen 4GL-Werkzeugen und der dadurch ermöglichten Entwicklungsmethodik (Prototyping) gesammelt wurden. Das Informationssystem selbst ist an anderer Stelle beschrieben.<br