Time delay in the Einstein-Straus solution

We compute the time delay of strong lensing in the framework of the Einstein-Straus solution in presence of a cosmological constant and restrict ourselves to the case of a spatially flat universe. The calculations are done to first order in the ratio of Schwarzschild radius to peri-lens. We apply our results to the lensed quasar SDSS J1004+4112. Our predictions for the time delay between the images C and D of the quasar range from 6 to 13 years and are compatible with the experimental lower bound.     

Multi-Fractal Formalism for Quasi-Self-Similar Functions

The study of multi-fractal functions has proved important in several domains of physics. Some physical phenomena such as fully developed turbulence or diffusion limited aggregates seem to exhibit some sort of self-similarity. The validity of the multi-fractal formalism has been proved to be valid for self-similar functions. But, multi-fractals encountered in physics or image processing are not exactly self-similar. For this reason, we extend the validity of the multi-fractal formalism for a class of some non-self-similar functions. Our functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions. For the computation of their spectrum of singularities, it is unknown how to construct Gibbs measures. However, it suffices to use measures constructed according the Frostman's method. Besides, we compute the box dimension of the graphs.     

Trivalent Cation Substitution Effect into Layered Double Hydroxides Co2Fey Al1−y(OH)6Cl·nH2O: Study of the Local Order: Ionic Conductivity and Magnetic Properties

A series of layered double hydroxide materials of composition Co₂Fe_yAl_1−y(OH)₆Cl·nH₂O (0≤y≤1) was prepared via chimie douce. The crystalline parameter related to the cation to cation distance obeys the expected variation, showing that the substitution is effective over the entire range. Local order around Co and Fe cations is studied by X-ray absorption spectroscopy. Moduli of the Fourier transform at the Fe K-edge are superimposable, in agreement with an ordered model, although present in small domains since no superlattice is depicted. The ionic resistivity of the samples is highly dependent on the water molecule content. The conductivity is found to be thermally assisted, and the variation of the slope in the Arrhenius diagram is explained by a Vogel-Tamman-Fulcher-type behavior. Magnetic susceptibility measurements support the proposed cation composition and indicate the onset of local magnetic order at low temperature (below 10 K). The inter-sheet distance influences the magnetic response at low temperature, showing the presence of weak interactions between lamellae.     

On Dumont's polynomials

We derive two generating functions and an explicit formula for the polynomials {H_n(x)} studied by Dumont.     

Absence of Positive Eigenvalues for the Linearized Elasticity System

In this paper, we prove that the linearized elasticity system has no eigenvalues in two geometric situations: the whole space and a local perturbation of the half-space. We consider the Lamé coefficients and the density varying in an unbounded part of the domain. For the whole space, we use the operations curl and div to reduce our system to a scalar problem and use a limiting absorption principle for the reduced scalar equation given by the partial Fourier transform. For the perturbed half-space, this decompositions being no longer valid, we give an other method based on a pseudo-decomposition using the operations div and curl in the horizontal direction. In contrast to the whole space case, the reduced problems depend strongly on the dual Fourier variable which do not enable us to use same techniques. To study these reduced problems, we use the analytic theory of linear operators.     

Energy decay for the elastic wave equation with a local time-dependent nonlinear damping

In this paper, we shall investigate the decay property of the solutions to the initial-boundary value problem for the elastic wave equation with a local time-dependent nonlinear damping. We give some decay rate of the energy when the damping term is effective only in a neighborhood of a suitable subset of the boundary. The results obtained in this paper extend, in particular, the known results for the scalar wave equation.     

Elaboration and characterisation of a plasticized cellulose triacetate membrane containing trioctylphosphine oxyde (TOPO): Application to the transport of uranium and molybdenum ions

A cellulose triacetate (CTA) membrane containing trioctylphosphine oxyde (TOPO) as carrier and 2-nitrophenyloctyl ether (NPOE) as a plasticizer was prepared. The membrane CTA + NPOE + TOPO was characterised using chemical techniques as well as Fourier Transform InfraRed (FTIR) spectroscopy, X-ray diffraction and Scanning Electron Microscopy (SEM). The CTA membrane is characterised by well-defined pores; these pores are completely filled with the NPOE and carrier. Surfaces of membranes with TOPO are smooth. The systems constituted by the mixture of CTA + NPOE, CTA + NPOE + TOPO do not give any diffraction. This can be due to the absence of crystallization within the membrane. On the other hand, this result should be attributable to the amorphous state of the structure, which permits us to eliminate the mechanism of transfer of the ions by electron jump. A comparative study of transport across a polymer inclusion membrane (PIM) and a supported liquid membrane (SLM) containing the same carrier in chloroform has shown that uranium or molybdenum transport efficiency was increased using PIM instead of SLM. PIM showed higher stability than SLM, the flux of transport remain constant in the former case after 2 weeks.