A database of number fields

We describe an online database of number fields which accompanies this paper The database centers on complete lists of number fields with prescribed invariants. Our description here focuses on summarizing tables and connections to theoretical issues of current interest.Comment: 25 pages, 1 figur

Competition and Post-Transplant Outcomes in Cadaveric Liver Transplantation under the MELD Scoring System

Previous researchers have modelled the decision to accept a donor organ for transplantation as a Markov decision problem, the solution to which is often a control-limit optimal policy: accept any organ whose match quality exceeds some health-dependent threshold; otherwise, wait for another. When competing transplant centers vie for the same organs, the decision rule changes relative to no competition; the relative size of competing centers affects the decision rules as well. Using center-specific graft and patient survival-rate data for cadaveric adult livers in the United States, we have found empirical evidence supporting these predictions.liver transplantation, competition, optimal stopping

Number Fields Ramified at One Prime

For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q)≅G and disc(K)=±pa for some a. We study the existence of G-p fields for fixed G and varying p

Nonic 3-adic Fields

We compute all nonic extensions of Q3 and find that there are 795 of them up to isomorphism. We describe how to compute the associated Galois group of such a field, and also the slopes measuring wild ramification. We present summarizing tables and a sample application to number fields

Sustainability Reporting Practices In Portugal: Greenwashing Or Triple Bottom Line?

This paper examines the status of sustainability reporting in Portugal.  The Global Reporting Initiative’s (GRI) guidelines for sustainability reporting is an initiative that attempts to create a paradigm of triple bottom line reporting that encompasses the economic, environmental, and social performance of business. Measurement and reporting of environmental and social aspects are in their infancy compared to financial/economic reporting. The objective of the GRI’s framework is to elevate environmental and social reporting to the level of financial reporting by developing reporting principles and information qualities similar to those used in corporate financial reporting. In the post-Enron corporate reporting environment, such credibility may be tarnished and lead stakeholders to suspect corporations of greenwashing their reputations by issuing reports that are environmental window dressing.Currently 860 companies in a variety of industries worldwide are voluntarily listed as using the guidelines on the GRI’s web site; however, only five are from Portugal. Two of the five companies are GRI organizational stakeholders and one is listed as reporting 'in accordance' with the guidelines. Content analysis will be used to examine both the quantity and quality of information in the GRI reports of Portuguese companies. An additional issue regarding the transparency and credibility of the information provided is whether the reports have been verified (a more generic term than audit used for a similar assurance-type service relative to GRI Reports). The results of the content analysis will be used to shed some light on whether the companies generating these reports are bridging or widening the sustainability reporting expectations gap between companies and stakeholders

A Database of Local Fields

We describe our online database of finite extensions of Qp, and how it can be used to facilitate local analysis of number fields

Mixed Degree Number Field Computations

We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the 25 octic fields with Galois group PSL₂(7) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group 2³:GL₃(2) of smallest absolute discriminant

The Tame-Wild Principle for Discriminant Relations for Number Fields

Consider tuples ( K1 , … , Kr ) of separable algebras over a common local or global number field F1, with the Ki related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants of Ki ∕ F . We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification