Boundary Harnack Principle for fractional powers of Laplacian on the Sierpinski carpet

We prove the Boundary Harnack Principle related to fractional powers of Laplacian for some natural regions in the two-dimensional Sierpinski carpet. This is a natual application of a probabilistic method based on the Ikeda-Watanabe formul

On measures driven by Markov chains

We study measures on $[0,1]$ which are driven by a finite Markov chain and which generalize the famous Bernoulli products. We propose a hands-on approach to determine the structure function $\tau$ and to prove that the multifractal formalism is satisfied. Formulas for the dimension of the measures and for the Hausdorff dimension of their supports are also provided

Poisson kernel of half spaces in real hyperbolic spaces

International audienceWe provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space \H^n. This enables us to find asymptotic properties of the kernel. We also show convergence to the Poisson kernel of the whole space \H^n. For n=3, 4 or 6 we compute explicit formulas for the Poisson kernel itself

Poincaré Inequality and Hajlasz-Sobolev spaces on nested fractals

Given a nondegenerate harmonic structure, we prove a Poincaré-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajlasz-Sobolev spaces on nested fractals. In particular, we describe how the "weak"-type gradient on nested fractals relates to the upper gradient defined in the context of general metric spaces

Objetos metálicos de la Edad del Bronce de Chipre - metal procedente de Anatolia y el Mediterráneo Occidental

Hundreds of Bronze Age metal artefacts excavated on archaeological sites in Cyprus have been analysed for their lead isotope and elemental composition in the Isotrace Laboratory, University of Oxford, in the years 1982-2002. In parallel, but in particular after 1995, hundreds of samples of minerals and slags collected from the mines and smelting sites around the Troodos Mountains were also analysed. Most of the results were published in various articles over the years, but the interpretation of some of the lead isotope data needs a current revision in view of new research conducted in Spain, Sardinia and southern France. It has been known that the lead isotope data for metal artefacts from the Cypriot Bronze Age sites shows that not all of the copper is consistent with origin from the Cypriot ores. In addition, the lead and silver artefacts found there must have been imported, because there are no lead or silver ores on Cyprus. The re-evaluation of the data shows that about 11 % of the analysed metal artefacts are consistent with the origin from the deposits in the Aegean and Turkey, while about 14 % with sources in the Western Mediterranean. This paper discusses in detail the current interpretation of the research into the sources of imported metal found in the Bronze Age context on Cyprus.Cientos de objetos de metal de la Edad del Bronce excavados en yacimientos de Chipre han sido analizados para conocer su composición elemental y sus isótopos de plomo en el Isotrace Laboratory de la Universidad de Oxford entre los años 1982 y 2002. Especialmente con posterioridad a 1995 cientos de muestras de minerales y escorias recogidas de minas y sitios de reducción de minerales localizadas en el entorno de las montañas de Troodos también fueron analizadas. La mayoría de los resultados fueron publicados en varios artículos a lo largo del tiempo, pero la interpretación de algunos análisis de isótopos de plomo necesitan de una revisión a la vista de las nuevas investigaciones realizadas en España, Cerdeña y Sur de Francia. Es sabido que los datos de isótopos de plomo de objetos metálicos de yacimientos chipriotas de la Edad del Bronce muestran que no todo el cobre es consistente con un origen de minerales de Chipre. Además, los objetos de plomo y plata debieron ser importados debido a que no existen minerales de plomo o plata en la isla. La re-evaluación de los datos muestra que alrededor del 11 % de los objetos de metal analizados son consistentes con un origen en los depósitos del Egeo y Turquía, mientras que un 14 % lo son con minerales del Mediterráneo Occidental. Este artículo discute en detalle la interpretación actual de la investigación sobre el metal importado recuperado en contextos de la Edad del Bronce en Chipre

Spectral properties of the Cauchy process

We study the spectral properties of the transition semigroup of the killed one-dimensional Cauchy process on the half-line (0,infty) and the interval (-1,1). This process is related to the square root of one-dimensional Laplacian A = -sqrt(-d^2/dx^2) with a Dirichlet exterior condition (on a complement of a domain), and to a mixed Steklov problem in the half-plane. For the half-line, an explicit formula for generalized eigenfunctions psi_lambda of A is derived, and then used to construct spectral representation of A. Explicit formulas for the transition density of the killed Cauchy process in the half-line (or the heat kernel of A in (0,infty)), and for the distribution of the first exit time from the half-line follow. The formula for psi_lambda is also used to construct approximations to eigenfunctions of A in the interval. For the eigenvalues lambda_n of A in the interval the asymptotic formula lambda_n = n pi/2 - pi/8 + O(1/n) is derived, and all eigenvalues lambda_n are proved to be simple. Finally, efficient numerical methods of estimation of eigenvalues lambda_n are applied to obtain lower and upper numerical bounds for the first few eigenvalues up to 9th decimal point.Comment: 37 pages, 1 figur