Non-Gaussian statistics, maxwellian derivation and stellar polytropes

In this letter we discuss the Non-gaussian statistics considering two aspects. In the first, we show that the Maxwell's first derivation of the stationary distribution function for a dilute gas can be extended in the context of Kaniadakis statistics. The second one, by investigating the stellar system, we study the Kaniadakis analytical relation between the entropic parameter $\kappa$ and stellar polytrope index $n$. We compare also the Kaniadakis relation $n=n(\kappa)$ with $n=n(q)$ proposed in the Tsallis framework.Comment: 10 pages, 1 figur

The electromagnetic coupling and the dark side of the Universe

We examine the properties of dark energy and dark matter through the study of the variation of the electromagnetic coupling. For concreteness, we consider the unification model of dark energy and dark matter, the generalized Chaplygin gas model (GCG), characterized by the equation of state $p=-\frac{A}{\rho^\alpha}$, where $p$ is the pressure, $\rho$ is the energy density and $A$ and $\alpha$ are positive constants. The coupling of electromagnetism with the GCG's scalar field can give rise to such a variation. We compare our results with experimental data, and find that the degeneracy on parameters $\alpha$ and $A_s$, $A_s \equiv A / \rho_{ch0}^{1+\alpha}$, is considerable.Comment: Revtex 4, 5 pages and 5 figure

String Theory and Cosmology

We discuss the main cosmological implications of considering string-loop effects and a potential for the dilaton in the lowest order string effective action. Our framework is based on the effective model arising from regarding homogeneous and isotropic dilaton, metric and Yang-Mills field configurations. The issues of inflation, entropy crisis and the Polonyi problem as well as the problem of the cosmological constant are discussed.Comment: 7 pages, plain Tex, no figure

Generalized nonuniform dichotomies and local stable manifolds

We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform exponential and polynomial dichotomies as a very particular case. The family of dichotomies considered allow situations for which the classical Lyapunov exponents are zero. Additionally, we give new examples of application of our stable manifold theorem and study the behavior of the dynamics under perturbations.Comment: 18 pages. New version with minor corrections and an additional theorem and an additional exampl