On the spectrum of stochastic perturbations of the shift and Julia sets

We extend the Killeen-Taylor study in \cite{KT} by investigating in different Banach spaces ($\ell^\alpha(\N), c_0(\N),c_c(\N)$) the point, continuous and residual spectra of stochastic perturbations of the shift operator associated to the stochastic adding machine in base 2 and in Fibonacci base. For the base 2, the spectra are connected to the Julia set of a quadratic map. In the Fibonacci case, the spectra involve the Julia set of an endomorphism of \C^2.Comment: 24 pages, 8 figures and 10 reference

A class of cubic Rauzy Fractals

In this paper, we study arithmetical and topological properties for a class of Rauzy fractals ${\mathcal R}_a$ given by the polynomial $x^3- ax^2+x-1$ where $a \geq 2$ is an integer. In particular, we prove the number of neighbors of ${\mathcal R}_a$ in the periodic tiling is equal to $8$. We also give explicitly an automaton that generates the boundary of ${\mathcal R}_a$. As a consequence, we prove that ${\mathcal R}_2$ is homeomorphic to a topological disk

General Stability in Viscoelasticity

In this chapter, we consider a problem which describes the motion of a viscoelastic body and investigate the effect of the dissipation induced by the viscoelastic (integral) term on the solution. Precisely, we show that, under reasonable conditions on the relaxation function, the system stabilizes to a stationary state. We also obtain a general decay estimate from which the usual exponential and polynomial decay rates are only special cases

Grande tache pigmentée pileuse révélant une forme familiale de la maladie de Von Recklinghausen

La neurofibromatose de type 1 (NF1) ou maladie de Von Recklinghausen appartient au groupe de maladies appelées phacomatoses. C'est une affection autosomique dominante relativement rare. La NF1 est caractérisée par une extrême variabilité clinique que l'on retrouve également au sein d'une même famille. Le tableau clinique de la NF1 associe, le plus souvent, de multiples taches café au lait, des lentigines axillaires ou inguinales, des neurofibromes cutanés et des nodules de Lisch. Les difficultés d'apprentissage sont fréquentes et peuvent être graves dans certaines formes cliniques. Il est important de détecter précocement les neurofibromes plexiformes, les gliomes intracérébraux, les tumeurs des gaines nerveuses, les anomalies vasculaires et les dysplasies osseuses. L'évolution est imprévisible ce qui rend le pronostic incertain par une éventuelle survenue dedégénérescence malignes. Nous rapportons ici l'observation d'une grande tache cutanée pigmentée pilleuse de découverte fortuite qui nous a révélé deux cas familiaux de neurofibromatose 1 d'expression différente

Nonlinear optical mechanism of forming periodical nanostructures in large bandgap dielectrics

Nonlinear excitation mechanisms of plasmons and their influence on femtosecond-laser induced sub-wavelength ripple generation on dielectric and semiconducting transparent materials are discussed. The agreement of theoretical and experimental data indicates the relevance of the model

Blowup of solutions of a nonlinear wave equation

We establish a blowup result to an initial boundary value problem for the nonlinear wave equation utt−M(‖B1/2u‖ 2) Bu+kut=|u| p−2, x∈Ω, t>0