Eigenvalues homogenization for the fractional p−p-Laplacian operator

In this work we study the homogenization for eigenvalues of the fractional $p-$Laplace in a bounded domain both with Dirichlet and Neumann conditions. We obtain the convergence of eigenvalues and the explicit order of the convergence rates.Comment: 12 page

Complete Genome Sequence of Staphylococcus epidermidis ATCC 12228 Chromosome and Plasmids Generated by Long-Read Sequencing

Staphylococcus epidermidis ATCC 12228 was sequenced using a long-read method to generate a complete genome sequence, including some plasmid sequences. Some differences from the previously generated short-read sequence of this nonpathogenic and non-biofilm-forming strain were noted. The assembly size was 2,570,371 bp with a total G+C% content of 32.08%

Relevance of nonadiabatic effects in TiOCl

We analyze the effect of the phonon dynamics on a recently proposed model for the uniform-incommensurate transition seen in TiOX compounds. The study is based on a recently developed formalism for nonadiabatic spin-Peierls systems based on bosonization and a mean field RPA approximation for the interchain coupling. To reproduce the measured low temperature spin gap, a spin-phonon coupling quite bigger than the one predicted from an adiabatic approach is required. This high value is compatible with the renormalization of the phonons in the high temperature phase seen in inelastic x-ray experiments. Our theory accounts for the temperature of the incommensurate transition and the value of the incommensurate wave vector at the transition point.Comment: 4 pages, 2 figure

From Entropic Dynamics to Quantum Theory

Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration space and the corresponding probability distributions constitute a statistical manifold. The dynamics follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. A welcome feature is that the entropic dynamics notion of time incorporates a natural distinction between past and future. The statistical manifold is assumed to be a dynamical entity: its curved and evolving geometry determines the evolution of the particles which, in their turn, react back and determine the evolution of the geometry. Imposing that the dynamics conserve energy leads to the Schroedinger equation and to a natural explanation of its linearity, its unitarity, and of the role of complex numbers. The phase of the wave function is explained as a feature of purely statistical origin. There is a quantum analogue to the gravitational equivalence principle.Comment: Extended and corrected version of a paper presented at MaxEnt 2009, the 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 5-10, 2009, Oxford, Mississippi, USA). In version v3 I corrected a mistake and considerably simplified the argument. The overall conclusions remain unchange