ON THE CONSISTENCY OF TWISTED GENERALIZED WEYL ALGEBRAS

A twisted generalized Weyl algebra A of degree n depends on a. base algebra R, n commuting automorphisms sigma(i) of R, n central elements t(i) of R and on some additional scalar parameters. In a paper by Mazorchuk and Turowska, it is claimed that certain consistency conditions for sigma(i) and t(i) are sufficient for the algebra to be nontrivial. However, in this paper we give all example which shows that this is false. We also correct the statement by finding a new set of consistency conditions and prove that the old and new conditions together are necessary and sufficient for the base algebra R to map injectively into A. In particular they are sufficient for the algebra A to be nontrivial. We speculate that these consistency relations may play a role in other areas of mathematics, analogous to the role played by the Yang-Baxter equation in the theory of integrable systems.

Sets of probability distributions, independence, and convexity

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of "strong independence" (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli's results and recent developments on the axiomatization of non-binary preferences, and its impact on "complete" independence, are described.

The Truncated Inflated Beta Distribution

The study of proportions is a common topic in many fields of study. The standard beta distribution or the inflated beta distribution may be a reasonable choice to fit a proportion in most situations. However, they do not fit well variables that do not assume values in the open interval (0, c), 0 < c < 1. For these variables, the authors introduce the truncated inflated beta distribution (TBEINF). This proposed distribution is a mixture of the beta distribution bounded in the open interval (c, 1) and the trinomial distribution. The authors present the moments of the distribution, its scoring vector, and Fisher information matrix, and discuss estimation of its parameters. The properties of the suggested estimators are studied using Monte Carlo simulation. In addition, the authors present an application of the TBEINF distribution for unemployment insurance data.

A further note on the college admission game

When a stable matching rule is used for a college admission market, questions on incentives facing agents of both sides of the market naturally emerge. This note states and proves four important results which fill a gap in the theory of incentives for the college admission model. Two of them have never been demonstrated but have been used along the years and are responsible for the success that this theory has had in explaining empirical economic phenomena.

Gas-phase reactivity of 2-hydroxy-1,4-naphthoquinones: a computational and mass spectrometry study of lapachol congeners

In order to understand the influence of alkyl side chains on the gas-phase reactivity of 1,4-naphthoquinone derivatives, some 2-hydroxy-1,4-naphthoquinone derivatives have been prepared and studied by electrospray ionization tandem mass spectrometry in combination with computational quantum chemistry calculations. Protonation and deprotonation sites were suggested on the basis of gas-phase basicity, proton affinity, gas-phase acidity (?Gacid), atomic charges and frontier orbital analyses. The nature of the intramolecular interaction as well as of the hydrogen bond in the systems was investigated by the atoms-in-molecules theory and the natural bond orbital analysis. The results were compared with data published for lapachol (2-hydroxy-3-(3-methyl-2-butenyl)-1,4-naphthoquinone). For the protonated molecules, water elimination was verified to occur at lower proportion when compared with side chain elimination, as evidenced in earlier studies on lapachol. The side chain at position C(3) was found to play important roles in the fragmentation mechanisms of these compounds. Copyright (c) 2012 John Wiley & Sons, Ltd.

A ironia na teoria do romance: da exigência normativo-composicional do romance em Goethe ao viver a arte em Novalis

O presente artigo busca explicitar o conceito de ironia na Teoria do romance. A explicitação do conceito de ironia se desdobrará num desenvolvimento duplo: como exigência normativo-composicional e como radicalização subjetiva que excede a normatividade. No primeiro sentido, a ironia configura subjetivamente uma totalidade na obra épica, partindo da sua fragmentação objetiva nas relações sociais modernas. Nessa acepção, a ironia se apresenta como uma manobra subjetiva a serviço da normatividade épica do romance, pois sua finalidade é harmonizar o ideal subjetivo com a objetividade histórica burguesa. Seu paradigma é representado, neste artigo, por Goethe. O outro sentido pelo qual a ironia romântica aparece é demarcado pela forma extremada da subjetividade. Esta, reconhecendo uma impossibilidade de realização de seu ideal harmônico na modernidade, porque o mundo moderno se lhe apresenta como uma efetividade oposta aos anseios subjetivos, refugia-se na própria interioridade e se distancia do mundo presente, buscando refúgio em tempos e lugares mais propícios à realização poética. Novalis é o modelo dessa ironia radicalizada. Essa forma irônica, ao contrário da "cadência irônica" de Goethe, aniquila a forma romance, uma vez que o aspecto subjetivo da pura reflexão, a lírica, se sobrepõe à objetividade histórica presente que o romance também necessariamente deve encerrar.