8,304 research outputs found
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 in the -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
Sharp mixed norm spherical restriction
Let be an integer and let . In this paper
we investigate the sharp form of the mixed norm Fourier extension inequality
\begin{equation*} \big\|\widehat{f\sigma}\big\|_{L^q_{{\rm rad}}L^2_{{\rm
ang}}(\mathbb{R}^d)} \leq {\bf C}_{d,q}\, \|f\|_{L^2(\mathbb{S}^{d-1},{\rm
d}\sigma)}, \end{equation*} established by L. Vega in 1988. Letting
be the set of exponents for which
the constant functions on are the unique extremizers of this
inequality, we show that: (i) contains the even integers and
; (ii) is an open set in the extended topology; (iii)
contains a neighborhood of infinity with
. In low dimensions we
show that . In particular, this breaks for the first time the even
exponent barrier in sharp Fourier restriction theory. The crux of the matter in
our approach is to establish a hierarchy between certain weighted norms of
Bessel functions, a nontrivial question of independent interest within the
theory of special functions.Comment: 21 page
Obtaining pressure versus concentration phase diagrams in spin systems from Monte Carlo simulations
We propose an efficient procedure for determining phase diagrams of systems
that are described by spin models. It consists of combining cluster algorithms
with the method proposed by Sauerwein and de Oliveira where the grand canonical
potential is obtained directly from the Monte Carlo simulation, without the
necessity of performing numerical integrations. The cluster algorithm presented
in this paper eliminates metastability in first order phase transitions
allowing us to locate precisely the first-order transitions lines. We also
produce a different technique for calculating the thermodynamic limit of
quantities such as the magnetization whose infinite volume limit is not
straightforward in first order phase transitions. As an application, we study
the Andelman model for Langmuir monolayers made of chiral molecules that is
equivalent to the Blume-Emery-Griffiths spin-1 model. We have obtained the
phase diagrams in the case where the intermolecular forces favor interactions
between enantiomers of the same type (homochiral interactions). In particular,
we have determined diagrams in the surface pressure versus concentration plane
which are more relevant from the experimental point of view and less usual in
numerical studies
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
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