Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

Modified gravity on the brane and dark energy

We analyze the dynamics of an AdS₅ braneworld with matter fields when gravity is allowed to deviate from the Einstein form on the brane. We consider exact five-dimensional warped solutions which are associated with conformal bulk fields of weight –4 and describe on the brane the following three dynamics: those of inhomogeneous dust, of generalized dark radiation, and of homogeneous polytropic dark energy. We show that, with modified gravity on the brane, the existence of such dynamical geometries requires the presence of non-conformal matter fields confined to the brane.     

Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–StokesNon-blowup at large times and stability for global solutions to the Navier–Stokes equations

Suppose there exists a global solution u to the incompressible Navier–Stokes equations, such that $\text{u∈}\text{C}{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{1/2}}\text{)}$. We prove that its $\text{H}\text{?}{}^{\mathrm{1/2}}$ norm goes to 0 at infinity. We next use this fact to control the $\text{L}{}^2{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{3/2}}\text{)}$ norm of u, and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289–292.     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

Distribution results for lattices in SL(2,ℚ p )

In this paper we study the ergodic properties of the linear action of lattices Γ of SL(2,ℚ_p) on ℚ_p × ℚ_p and distribution results for orbits of Γ. Following Serre, one can define a “geodesic flow” for an associated tree (actually associated to GL(2,ℚ_p)). The approach we use is based on an extension of this approach to “frame flows” which are a natural compact group extension of the geodesic flow.     

Erratum: Synthesis and characterization of diorganotin(IV) complexes of Schiff bases with ONO‐type donors and crystal structure of [N‐(2‐hydroxy‐4‐nitrophenyl)‐3‐ethoxysalicylideneiminato]diphenyltin(IV)

The article referenced above was first published online on 30 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.