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

Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold

We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our main result, we develop the Melnikov functions for a class of nonsmooth differential systems, which generalizes, up to order 2, some previous results in the literature. Whereas the first order Melnikov function for the nonsmooth case remains the same as for the smooth one (i.e. the first order averaged function) the second order Melnikov function for the nonsmooth case is different from the smooth one (i.e. the second order averaged function). We show that, in this case, a new term depending on the jump of discontinuity and on the geometry of the switching manifold is added to the second order averaged function

Parâmetros físicos e químicos da laranja pera na região de Manaus, AM.

bitstream/item/32012/1/CPATU-BP109.pd

Nutrientes nos solos de floresta primária e pastagem de Brachiaria humidicola na Amazônia Central.

bitstream/item/31994/1/CPATU-BP98.pd

Effects of Dry‐Season Irrigation on Leaf Physiology and Biomass Allocation in Tropical Lianas and Trees

Lianas are more abundant in seasonal forests than in wetter forests and are thought to perform better than trees when light is abundant and water is limited. We tested the hypothesis that lianas perform better than trees during seasonal drought using a common garden experiment with 12 taxonomically diverse species (six liana and six tree species) in 12 replicated plots. We irrigated six of the plots during the dry season for four years, while the remaining six control plots received only ambient rainfall. In year 5, we measured stem diameters for all individuals and harvested above‐ and belowground biomass for a subset of individuals to quantify absolute growth and biomass allocation to roots, stems, and leaves, as well as total root length and maximum rooting depth. We also measured rate of photosynthesis, intrinsic water use efficiency (iWUE), pre‐dawn and midday water potential, and a set of functional and hydraulic traits. During the peak of the dry season, lianas in control plots had 54% higher predawn leaf water potentials (ΨPD), and 45% higher photosynthetic rates than trees in control plots. By contrast, during the peak of the wet season, these physiological differences between lianas and trees become less pronounced and, in some cases, even disappeared. Trees had higher specific leaf area (SLA) than lianas; however, no other functional trait differed between growth forms. Trees responded to the irrigation treatment with 15% larger diameters and 119% greater biomass than trees in control plots. Liana growth, however, did not respond to irrigation; liana diameter and biomass were similar in control and irrigation plots, suggesting that lianas were far less limited by soil moisture than were trees. Contrary to previous hypotheses, lianas did not have deeper roots than trees; however, lianas had longer roots per stem diameter than did trees. Our results support the hypothesis that lianas perform better and experience less physiological stress than trees during seasonal drought, suggesting clear differences between growth forms in response to altered rainfall regimes. Ultimately, better dry‐season performance may explain why liana abundance peaks in seasonal forests compared to trees, which peak in abundance in less seasonal, wetter forests

Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line

Altres ajuts: acords transformatius de la UABIn this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. In this class and considering a degenerated Hopf bifurcation near families of centers we obtain again at least five limit cycles but now from infinity, which is of monodromic type, and with simpler computations. The proof uses a partial classification of the center problem when both systems are of center type

Orbitally symmetric systems with applications to planar centers

We present a generalization of the most usual symmetries in differential equations known as the time-reversibility and the equivariance ones. We check that the typical properties are also valid for the new definition that unifies both. With it, we are able to present new families of planar polynomial vector fields having equilibrium points of center type. Moreover, we provide the highest lower bound for the local cyclicity of an equilibrium point of polynomial vector fields of degree 6, M(6) ≥ 48