Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Effect of enzymatic treatment on the cross-flow microfiltration of acai pulp: Analysis of the fouling and recovery of phytochemicals

This study aimed to investigate the effects of pectinase enzyme treatment of acai pulp on cross-flow microfiltration (CFMF) performance and on phytochemical and functional characteristics of their compounds. Analyses of fouling mechanisms were carried out through resistance in series and blocking in law models. The enzymatic treatment was conducted using Ultrazym(R) AFPL (Novozymes A/S) at 500 mg kg(-1) of acai pulp for 30 min at 35 degrees C. Before microfiltrations, untreated and enzyme-treated acai pulps were previously diluted in distilled water (1:3; w/v). CFMFs were conducted using commercial alpha-alumina (alpha-Al2O3) ceramic membranes (Andritz AG, Austria) of 0.2 mu m and 0.8 mu m pore sizes, and 0.0047 m(2) of filtration area. The microfiltration unit was operated in batch mode for 120 min at 25 degrees C and the fluid-dynamic conditions were transmembrane pressure of Delta P = 100 kPa and cross-flow velocity of 3 m s(-1) in turbulent flow. The highest values of permeate flux and accumulated permeate volume were obtained using enzyme-treated pulp and 0.2 mu m pore size membranes with steady flux values exceeding 100 L h(-1) m(-2). For the 0.8 mu m pore size membrane, the estimated total resistance after the microfiltration of enzyme-treated acai pulp was 21% lower than the untreated pulp, and for the 0.2 mu m pore size membrane, it was 18%. Cake filtration was the dominant mechanism in the early stages of most of the CFMF processes. After approximately 20 min, however, intermediate pore blocking and complete pore blocking contributed to the overall fouling mechanisms. The reduction of the antioxidant capacity of the permeates obtained after microfiltration of the enzyme-treated pulp was higher (p < 0.01) than that obtained using untreated pulp. For total polyphenols, on the contrary, the permeates obtained after microfiltration of the enzyme-treated pulp showed a lower mean reduction (p < 0.01) than those from the untreated pulp. The results show that the enzymatic treatment had a positive effect on the CFMF process of acai pulp. (C) 2012 Elsevier Ltd. All rights reserved.

O livro didático no ensino do direito

Esse trabalho tem por objetivo a análise de livros didáticos jurídicos na perspectiva da história dos direitos europeu e brasileiro, tendo como referencial teórico o texto de Alain Choppin sobre as funções do livro didático. Foram analisados livros didáticos jurídicos produzidos desde a Antiguidade até os dias atuais, assim como importantes mudanças legislativas ocorridas em Portugal no século XVIII e no Brasil no século XIX. Seus autores são, em sua maioria, professores universitários, para que seus textos servissem de fonte de argumentos de autoridade na prática. Ao lado dos manuais, sempre foi recorrente o uso de apostilas elaboradas pelos professores ou pelos próprios alunos, a partir das anotações das aulas. Nos últimos tempos, os manuais sofrem a concorrência dos resumos voltados para concursos públicos e dos “cadernos” distribuídos pelos alunos pela Internet. As principais conclusões foram as de que os livros didáticos jurídicos são importantes para o aprendizado do Direito.