Exact solutions of Brans-Dicke cosmology with decaying vacuum density

We investigate cosmological solutions of Brans-Dicke theory with both the vacuum energy density and the gravitational constant decaying linearly with the Hubble parameter. A particular class of them, with constant deceleration factor, sheds light on the cosmological constant problems, leading to a presently small vacuum term, and to a constant ratio between the vacuum and matter energy densities. By fixing the only free parameter of these solutions, we obtain cosmological parameters in accordance with observations of both the relative matter density and the universe age. In addition, we have three other solutions, with Brans-Dicke parameter w = -1 and negative cosmological term, two of them with a future singularity of big-rip type. Although interesting from the theoretical point of view, two of them are not in agreement with the observed universe. The third one leads, in the limit of large times, to a constant relative matter density, being also a possible solution to the cosmic coincidence problem.Comment: Minor changes, references added. Version accepted for publication in Classical and Quantum Gravit

Exact solutions of Brans-Dicke cosmology and the cosmic coincidence problem

We present some cosmological solutions of Brans-Dicke theory, characterized by a decaying vacuum energy density and by a constant relative matter density. With these features, they shed light on the cosmological constant problems, leading to a presently small vacuum term, and to a constant ratio between the vacuum and matter energy densities. By fixing the only free parameter of our solutions, we obtain cosmological parameters in accordance with observations of the relative matter density, the universe age and redshift-distance relations.Comment: To appear in Brazilian Journal of Physics (proceedings of the conference 100 Years of Relativity, Sao Paulo, August 2005

Bandlimited approximations to the truncated Gaussian and applications

In this paper we extend the theory of optimal approximations of functions $f: \R \to \R$ in the $L^1(\R)$-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd Gaussians using explicit integral representations and fine properties of truncated theta functions obtained via the maximum principle for the heat operator. As applications, we recover most of the previously known examples in the literature and further extend the class of truncated and odd functions for which this extremal problem can be solved, by integration on the free parameter and the use of tempered distribution arguments. This is the counterpart of the work \cite{CLV}, where the case of even functions is treated.Comment: to appear in Const. Appro

Decifrando o genoma.

Os genes, unidades biologicas que determinam as caracteristicas de um organismo, estao contidos em moleculas de DNA presentes no nucleo das celulas. Portanto, o estudo do DNA e de fundamental importancia para o entendimento de como as caracteristicas de um organismo sao formadas. Com o grande avanco alcancado pelas tecnicas de Biologia molecular nas ultimas decadas, hoje, somos capazes de isolar e sequenciar moleculas de DNA de maneira rotineira. A partir da otimizacao das tecnicas de sequenciamento, surgiram programas com o objetivo de sequenciar genomas inteiros. atualmente, estao depositados em bancos de dados mais de 3 milhoes de sequencias de DNA e, grande parte delas ainda nao tem sua funcao conhecida. O processo de caracterizacao da funcao genica envolve um volume muito maior de pesquisas e conhecimentos do que as etapas de isolamento e sequenciamento. A funcao de um gene pode ser desvendada por meio de tecnicas de genetica direta ou reversa. Descrevem-se algumas das metodologias usadas para a caracterizacao da funcao genica, bem como o potencial dos programas de sequenciamento de genomas

On Useful Conformal Tranformations In General Relativity

Local conformal transformations are known as a useful tool in various applications of the gravitational theory, especially in cosmology. We describe some new aspects of these transformations, in particular using them for derivation of Einstein equations for the cosmological and Schwarzschild metrics. Furthermore, the conformal transformation is applied for the dimensional reduction of the Gauss-Bonnet topological invariant in $d=4$ to the spaces of lower dimensions.Comment: 17 pages, LaTeX. The paper is intended mainly for pedagogical purposes and represents a collection of exercises concerning local conformal transformations and dimensional reduction. To be published in "Gravitation and Cosmology

Equality of opportunity and educational achievement in Portugal

Portugal has one of the highest levels of income inequality in Europe, and low wages and unemployment are concentrated among low skill individuals. Education is an important determinant of inequality. However, there are large differences in the educational attainment of different individuals in the population, and the sources of these differences emerge early in the life-cycle when families play a central role in individual development. We estimate that most of the variance of school achievement at age 15 is explained by family characteristics. Observed school inputs explain very little of adolescent performance. Children from highly educated parents benefit of rich cultural environments in the home and become highly educated adults. Education policy needs to be innovative: (1) it needs to explicitly recognize the fundamental long run role of families on child development; (2) it needs to acknowledge the failure of traditional input based policies