1,459 research outputs found
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 yields exactly the Gorenstein
projective modules. Specifically, given an exact sequence of Gorenstein
projective -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 -module , 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.
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
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