Diffusion limits for shortest remaining processing time queues

We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length process. These results allow us to make some observations on the queue length optimality of SRPT. In particular, they provide the sharpest illustration of the well-known tension between queue length optimality and quality of service for this policy.Comment: 19 pages; revised, fixed typos. To appear in Stochastic System

Rational points in the moduli space of genus two

We build a database of genus 2 curves defined over $\mathbb Q$ which contains all curves with minimal absolute height $h \leq 5$, all curves with moduli height $\mathfrak h \leq 20$, and all curves with extra automorphisms in standard form $y^2=f(x^2)$ defined over $\mathbb Q$ with height $h \leq 101$. For each isomorphism class in the database, an equation over its minimal field of definition is provided, the automorphism group of the curve, Clebsch and Igusa invariants. The distribution of rational points in the moduli space $\mathcal M_2$ for which the field of moduli is a field of definition is discussed and some open problems are presented

Metal abundances in PG1159 stars from Chandra and FUSE spectroscopy

We investigate FUSE spectra of three PG1159 stars and do not find any evidence for iron lines. From a comparison with NLTE models we conclude a deficiency of 1-1.5 dex. We speculate that iron was transformed into heavier elements. A soft X-ray Chandra spectrum of the unique H- and He-deficient star H1504+65 is analyzed. We find high neon and magnesium abundances and confirm that H1504+65 is the bare core of either a C-O or a O-Ne-Mg white dwarf.Comment: To be published in: Proceedings 13th European Workshop on White Dwarfs, NATO Science Series, 4 pages, 1 figur

FUSE Spectroscopy of the Two Prototype White Dwarfs With Signatures of a Super-hot Wind

The O VIII phenomenon describes the occurrence of ultra-high ionization absorption lines of the CNO elements (e.g. O VIII, N VII, C VI, and even Ne X) in the optical spectra hot of DO WDs

Iron abundance in the prototype PG1159 star, GW Vir pulsator PG1159-035, and related objects

We performed an iron abundance determination of the hot, hydrogen deficient post-AGB star PG1159-035, which is the prototype of the PG1159 spectral class and the GW Vir pulsators, and of two related objects (PG1520+525, PG1144+005), based on the first detection of Fe VIII lines in stellar photospheres. In another PG1159 star, PG1424+535, we detect Fe VII lines. In all four stars, each within Teff = 110,000 - 150,000 K, we find a solar iron abundance. This result agrees with our recent abundance analysis of the hottest PG1159 stars (Teff = 150,000 - 200,000 K) that exhibit Fe X lines. On the whole, we find that the PG1159 stars are not significantly iron deficient, in contrast to previous notions.Comment: Accepted for publication in A&