An Euler characteristic for modules of finite {G}-dimension

We extend Auslander and Buchsbaum's Euler characteristic from the category of finitely generated modules of finite projective dimension to the category of modules of finite G-dimension using Avramov and Martsinkovsky's notion of relative Betti numbers. We prove analogues of some properties of the classical invariant and provide examples showing that other properties do not translate to the new context. One unexpected property is in the characterization of the extremal behavior of this invariant: the vanishing of the Euler characteristic of a module M of finite G-dimension implies the finiteness of the projective dimension of M. We include two applications of the Euler characteristic as well as several explicit calculations.Comment: 20 pages, uses xypic, minor changes to final version, to appear in Math. Scan

Stability of Gorenstein Categories

We show that an iteration of the procedure used to define the Gorenstein projective modules over a commutative ring $R$ yields exactly the Gorenstein projective modules. Specifically, given an exact sequence of Gorenstein projective $R$-modules G=...\xra{\partial^G_2}G_1\xra{\partial^G_1}G_0\xra{\partial^G_0} ... such that the complexes \Hom_R(G,H) and \Hom_R(H,G) are exact for each Gorenstein projective $R$-module $H$, the module \coker(\partial^G_1) is Gorenstein projective. The proof of this result hinges upon our analysis of Gorenstein subcategories of abelian categories.Comment: 21 pages, uses XY-pic. Version 2 contains corrected proofs of Lemma 2.1 and Theorem 4.

Something Like an Aubade

Pages 105-10

A Structured Methodology for Systematically Describing Health Informatics Hazards

This research establishes a framework which uses simple language constructs, recognising the socio-technical context in which they exist to establish hazard descriptions that capture and reflect the harm-scenario, relative to the carepathway and focus on the credible patient harm outcome

Autonomy versus futility? Barriers to good clinical practice in end-of-life care: a Queensland case

Findings from a Queensland coronial inquest highlight the complex clinical, ethical and legal issues that arise in end-of-life care when clinicians and family members disagree about a diagnosis of clinical futility. The tension between the law and best medical practice is highlighted in this case, as doctors are compelled to seek family consent to not commence a futile intervention. Good communication between doctors and families, as well as community and professional education, is essential to resolve tensions that can arise when there is disagreement about treatment at the end of life

Particle Astrophysics and Cosmology: Cosmic Laboratories for New Physics (Summary of the Snowmass 2001 P4 Working Group)

The past few years have seen dramatic breakthroughs and spectacular and puzzling discoveries in astrophysics and cosmology. In many cases, the new observations can only be explained with the introduction of new fundamental physics. Here we summarize some of these recent advances. We then describe several problem in astrophysics and cosmology, ripe for major advances, whose resolution will likely require new physics.Comment: 27 pages, 14 figure

Simulation of Reduction of Cr(VI) by Fe(II) Produced Electrochemically in a Parallel-Plate Electrochemical Reactor

A model is presented for the reduction of hexavalent chromium in a parallel-plate electrochemical reactor via a homogenous reaction between Cr(VI) and Fe(II) generated at the iron anode. The effects of the space velocity of the feed solution, the concentration of supporting electrolyte, the distance between the electrodes, and the cell potential on conversion of Cr(VI) to Cr(III), are discussed. This study indicates that for reduction of Cr(VI) using Fe(II), the space velocity must be maintained below 0.02s−1 or the system becomes limited by the rate of reduction of Cr(VI) by Fe(II). Increasing the current density by increasing the cell potential, increasing the amount of supporting electrolyte, and decreasing the distance between the electrodes increases single pass conversion of Cr(VI) to Cr(III); however, increasing the current density also increases the specific energy required by the system