Higher identities for the ternary commutator

We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc - acb - bac + bca + cab - cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree 7 which alternates in 6 arguments, and no new identities in degree 9. We use the representation theory of the symmetric group to demonstrate the existence of new identities in degree 11. The only irreducible representations of dimension <400 with new identities correspond to partitions 2(5), 1 and 2(4), 1(3) and have dimensions 132 and 165. We construct an explicit new multilinear identity for partition 2(5), 1 and we demonstrate the existence of a new non-multilinear identity in which the underlying variables are permutations of a(2)b(2)c(2)d(2)e(2) f.

Theoretical luminescence spectra in p-type superlattices based on InGaAsN

In this work, we present a theoretical photoluminescence (PL) for p-doped GaAs/InGaAsN nanostructures arrays. We apply a self-consistent method in the framework of the effective mass theory. Solving a full 8 x 8 Kane's Hamiltonian, generalized to treat different materials in conjunction with the Poisson equation, we calculate the optical properties of these systems. The trends in the calculated PL spectra, due to many-body effects within the quasi-two-dimensional hole gas, are analyzed as a function of the acceptor doping concentration and the well width. Effects of temperature in the PL spectra are also investigated. This is the first attempt to show theoretical luminescence spectra for GaAs/InGaAsN nanostructures and can be used as a guide for the design of nanostructured devices such as optoelectronic devices, solar cells, and others.

Atmospheric pollution: influence on hospital admissions in paediatric rheumatic diseases

Objective: To investigate the lag structure effects from exposure to atmospheric pollution in acute outbursts in hospital admissions of paediatric rheumatic diseases (PRDs). Methods: Morbidity data were obtained from the Brazilian Hospital Information System in seven consecutive years, including admissions due to seven PRDs (juvenile idiopathic arthritis, systemic lupus erythematosus, dermatomyositis, Henoch-Schonlein purpura, polyarteritis nodosa, systemic sclerosis and ankylosing spondylitis). Cases with secondary diagnosis of respiratory diseases were excluded. Daily concentrations of inhaled particulate matter (PM10), sulphur dioxide (SO2) nitrogen dioxide (NO2), ozone (O-3) and carbon monoxide (CO) were evaluated. Generalized linear Poisson regression models controlling for short-term trend, seasonality, holidays, temperature and humidity were used. Lag structures and magnitude of air pollutants' effects were adopted to estimate restricted polynomial distributed lag models. Results: The total number of admissions due to acute outbursts PRD was 1,821. The SO2 interquartile range (7.79 mu g/m(3)) was associated with an increase of 1.98% (confidence interval 0.25-3.69) in the number of hospital admissions due to outcome studied after 14 days of exposure. This effect was maintained until day 17. Of note, the other pollutants, with the exception of O-3, showed an increase in the number of hospital admissions from the second week. Conclusion: This study is the first to demonstrate a delayed association between SO2 and PRD outburst, suggesting that oxidative stress reaction could trigger the inflammation of these diseases. Lupus (2012) 21, 526-533.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

A Poisson mixed model with nonnormal random effect distribution

In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration. (C) 2011 Elsevier B.V. All rights reserved.