On the Graded Identities for Elementary Gradings in Matrix Algebras over Infinite Fields

We find a basis for the $G$-graded identities of the $n\times n$ matrix algebra $M_n(K)$ over an infinite field $K$ of characteristic $p>0$ with an elementary grading such that the neutral component corresponds to the diagonal of $M_n(K)$

Graded identities of block-triangular matrices

Let $F$ be an infinite field and $UT(d_1,\dots, d_n)$ be the algebra of upper block-triangular matrices over $F$. In this paper we describe a basis for the $G$-graded polynomial identities of $UT(d_1,\dots, d_n)$, with an elementary grading induced by an $n$-tuple of elements of a group $G$ such that the neutral component corresponds to the diagonal of $UT(d_1,\dots,d_n)$. In particular, we prove that the monomial identities of such algebra follow from the ones of degree up to $2n-1$. Our results generalize for infinite fields of arbitrary characteristic, previous results in the literature which were obtained for fields of characteristic zero and for particular $G$-gradings. In the characteristic zero case we also generalize results for the algebra $UT(d_1,\dots, d_n)\otimes C$ with a tensor product grading, where $C$ is a color commutative algebra generating the variety of all color commutative algebras.Comment: 24 pages and 39 references. We have added section 5 in the text about tensor products by color commutative superalgebra

The empirics of the Solow growth model: Long-term evidence

In this paper we reassess the standard Solow growth model, using a dynamic panel data approach. A new methodology is chosen to deal with this problem. First, unit root tests for individual country time series were run. Second, panel data unit root and cointegration tests were performed. Finally, the panel cointegration dynamics is estimated by (DOLS) method. The resulting evidence supports roughly one-third capital share in income, a.Economic growth, panel data, unit root, cointegration and convergence

Estudo de caracterização de adultos idosos dependentes de substâncias

Mestrado em Psicologia - Psicologia Clínica e da SaúdeO principal objetivo da presente dissertação é caracterizar os utentes ativos do CRIA, com 50 anos ou mais, sociodemográficamente; relativamente aos consumos e do ponto de vista clínico, comparando-os consoante o programa de tratamento de manutenção opióide em que se inserem. O crescente envelhecimento da população traz novos desafios, como o envelhecimento da população com perturbações pelo uso de substâncias (EMCDA, 2010). Este grupo tem estado a aumentar e espera-se que continue até pelo menos 2020 (Han, Gfroerer, Colliver, & Penne, 2009). Apesar disso, o desconhecimento do fenómeno é grande e são necessários mais estudos, especialmente devido às vulnerabilidades específicas desta faixa etária. Dos 102 utentes ativos, desta faixa etária, 71 reúnem as condições necessárias para participar no estudo e 42 realizaram a avaliação psicológica. A bateria de avaliação consistiu nos seguintes instrumentos: BSI, MOCA, IAFAI, GDS e WHOQOL-Bref e a análise de dados foi realizada através do SPSS – Versão 20. Foram encontradas diferenças significativas entre os dois programas de tratamento no MOCA, no WHOQOL-Bref (domínio 2 e 4) e no IAFAI (IE). Em todos esses casos o programa de manutenção com metadona obteve piores resultados clínicos que o programa de manutenção com buprenorfina. A amostra global diferiu significativamente da população normal no WHOQOL-Bref (domínio geral), obtendo piores resultados de qualidade de vida; e em alguns domínios do BSI, obtendo melhores resultados de sintomatologia psicológica. Apesar das diferenças encontradas, a amostra encontra-se melhor do que seria de esperar face ao contexto de vida em que se insere.The main goal of this dissertation is to characterize the active patients of the CRIA, with 50 or more years, social and demographically; in respect to their consumption and clinically, comparing them according to the program of opioid maintenance treatment received by them. The growing aging of the general population brings new challenges such as the increase of the age population with substance use disorders (EMCDA, 2010). This group has been increasing and is expected to continue until at least 2020 (Han, Gfroerer, Colliver, & Penne, 2009). Nevertheless, the ignorance of this phenomenon is huge and more studies are largely necessary, especially due to the specific vulnerabilities of this age group. Of the 102 active patients in this age group, 71 meet the necessary conditions for participating in the study and 42 underwent psychological evaluation. The assessment battery consisted of the following instruments: BSI, MOCA, IAFAI, GDS and WHOQOL-Bref and data analysis was performed using SPSS - Version 20. Significant differences between the two treatment programs were found at MOCA, WHOQOL-Bref (domain 2 and 4) and IAFAI (IE). In all these cases the methadone maintenance program got worse clinical outcomes than the buprenorphine maintenance program. The global sample differed significantly from the normal population in the WHOQOL-Bref (general domain), showing worst results of quality of life; and in some domains of the BSI, obtaining better results of psychological symptomatology. Despite those differences the sample is better than expected due the life context in which they are embedded