Noncommutative Black Holes and the Singularity Problem

A phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model is considered to study the interior of a Schwarzschild black hole. Due to the divergence of the probability of finding the black hole at the singularity from a canonical noncommutativity, one considers a non-canonical noncommutativity. It is shown that this more involved type of noncommutativity removes the problem of the singularity in a Schwarzschild black hole.Comment: Based on a talk by CB at ERE2010, Granada, Spain, 6th-10th September 201

Quantum mechanics of a constrained particle and the problem of prescribed geometry-induced potential

The experimental techniques have evolved to a stage where various examples of nanostructures with non-trivial shapes have been synthesized, turning the dynamics of a constrained particle and the link with geometry into a realistic and important topic of research. Some decades ago, a formalism to deduce a meaningful Hamiltonian for the confinement was devised, showing that a geometry-induced potential (GIP) acts upon the dynamics. In this work we study the problem of prescribed GIP for curves and surfaces in Euclidean space $\mathbb{R}^3$, i.e., how to find a curved region with a potential given {\it a priori}. The problem for curves is easily solved by integrating Frenet equations, while the problem for surfaces involves a non-linear 2nd order partial differential equation (PDE). Here, we explore the GIP for surfaces invariant by a 1-parameter group of isometries of $\mathbb{R}^3$, which turns the PDE into an ordinary differential equation (ODE) and leads to cylindrical, revolution, and helicoidal surfaces. Helicoidal surfaces are particularly important, since they are natural candidates to establish a link between chirality and the GIP. Finally, for the family of helicoidal minimal surfaces, we prove the existence of geometry-induced bound and localized states and the possibility of controlling the change in the distribution of the probability density when the surface is subjected to an extra charge.Comment: 21 pages (21 pages also in the published version), 2 figures. This arXiv version is similar to the published one in all its relevant aspect

Vacuum decay in an interacting multiverse

We examine a new multiverse scenario in which the component universes interact. We focus our attention to the process of "true" vacuum nucleation in the false vacuum within one single element of the multiverse. It is shown that the interactions lead to a collective behaviour that might lead, under specific conditions, to a pre-inflationary phase and ensued distinguishable imprints in the comic microwave background radiation.Comment: 9 pages, 5 figure

Plagiarism phenomenon in European countries: results from GENIUS Project

The present study aims to explore 170 teachers and 334 secondary school student's perceptions on plagiarism of seven European countries. Results indicate that both know that plagiarism is illegal; attribute plagiarism to the easiness on contents access on Internet but while teachers tend to attribute causes to student's lack of skills, students highlight the pressure to get good grades, laziness and poor management as well as the expectation that won’t be caught. To prevent plagiarism while teachers suggest to promote student's skills, students focus on pedagogical issues. Similarities and differences are explored as well as the possible effects and implications.info:eu-repo/semantics/publishedVersio

Discrete-Time Fractional Variational Problems

We introduce a discrete-time fractional calculus of variations on the time scale $h\mathbb{Z}$, $h > 0$. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of the discrete-derivatives are integer values, and that they converge to the fractional continuous-time solutions when $h$ tends to zero. Our Legendre type condition is useful to eliminate false candidates identified via the Euler-Lagrange fractional equation.Comment: Submitted 24/Nov/2009; Revised 16/Mar/2010; Accepted 3/May/2010; for publication in Signal Processing