| 30/2005 |
Isolating blocks for Morse flows Maria Alice Bertolim, Ketty A. de Rezende, O. Manzoli Neto, G. M. Vago We present a constructive general procedure to build Morse flows on n-dimensional isolating blocks respecting given dynamical and homological boundary data recorded in abstract Lyapunov semi-graphs. Moreover, we prove a decomposition theorem for handles which, together with a special class of gluings, insures that this construction not only preserves the given ranks of the homology Conley indices, but it also is optimal in the sense that no other Morse flow can preserve this index with fewer singularities.  rp-2005-30.pdf |
| 29/2005 |
Stability of Periodic Travelling Wave Solutions for the Korteweg - de Vries Equation Lynnyngs Kelly Arruda This paper is concerned with nonlinear stability properties of periodic travelling waves solutions of the classical Korteweg - de Vries equation,\[\label{kdv} u_t+uu_x+u_{xxx}=0, \ \ x,t\in \mathbb R.\]It is shown the existence of a nontrivial smooth curve of periodic travelling wave solutions depending on the classical Jacobian elliptic functions. We find positive cnoidal wave solutions. Then we prove, by using the framework established in \cite{GSS1} by Grillakis, Shatah and Strauss, the nonlinear stability of the cnoidal wave solutions in the space $H^1_{per}([0,L])$. rp-2005-29.pdf |
| 28/2005 |
Haar Wavelets Systems for Hedging Financial Derivatives Pedro J. Catuogno, Sebastian E. Ferrando, Alfredo L. Gonzales We present a new discretization of financial instruments in terms of martingale expansions constructed using Haar wavelets systems. Examples of these systems are constructed which illustrate the discrete, spacewise, nature of the approximations. We emphasize the issue of efficient approximations and remark that expansions on these bases give the pointwise convergence needed in several applications. In particular, we work out the details of an application to hedging an European portfolio of options. We describe natural conditions under which our Haar hedging strategy can be realized by means of a self financing portfolio consisting of binary options. rp-2005-28.pdf |
| 27/2005 |
Spacetime Deformations and Electromagnetism in Material Media Roldão da Rocha Jr., Igor Leite Freire, Márcio A. F. Rosa This paper is intended to investigate the relation between electrodynamics in anisotropic material media and its analogous formulation in an spacetime, with non-null Riemann curvature tensor. After discussing the electromagnetism via chiral differential forms, we point out the optical activity of a given material medium, closely related to topological spin, and the Faraday rotation, associated to topological torsion. Both quantities are defined in terms of the magnetic potential and the electric and magnetic fields and excitations. We revisit some properties of material media and the associated Green dyadics. Some related features of ferrite are also investigated. It is well-known that the constitutive tensor is essentially equivalent to the Riemann curvature tensor. In order to investigate the propagation of electromagnetic waves inmaterial media, we prove that it is analogous to consider the electromagnetic wave propagation in the vacuum, but this time in a curved spacetime, which is obtained by a deformation of the Lorenztian metric of Minkowski spacetime. Spacetime deformations leave invariant the form of Maxwell equations. Also, there exists a close relation between Maxwell equations in curved spacetime and in an anisotropic material medium, indicating that electromagnetism and spacetime properties are deeply related. For instance, the equations of holomorphy in Minkowski spacetime are essentially Maxwell equations in vacuum. Besides, the geometrical aspects of wave propagation can be described by an effective geometry which represents a modification of the Lorentzian metric of Minkowski spacetime, i.e., a kind of spacetime deformation. rp-2005-27.pdf |
| 26/2005 |
Multiplicity of Positive Solutions for a Class of Elliptic Equations in Divergence Form Giovany M. Figueiredo, Marcelo F. Furtado We prove results concerning the existence and multiplicity of positive solutions for the quasilinear equation$$-\text{div}(a(\ep x)|\nabla u|^{p-2}\nabla u) + |u|^{p-2}u = f(u)~~\text{in }\real^N,~~~ u \in W^{1,p}(\real^N),$$where $2 \leq p rp-2005-26.pdf |
| 25/2005 |
Nodal Solutions for a Nonhomogeneous Elliptic Equation with Symmetry Marcelo F. Furtado We consider the semilinear problem $-\Delta u + \lambda u =|u|^{p-2}u + f(u)$ in $\Omega$, $u=0$ on $\partial \Omega$ where $\Omega \subset \mathbb{R}^N$ is a bounded smooth domain, $2 rp-2005-25.pdf |
| 24/2005 |
On the Number of Positive Solutions of a Critical Elliptic Equation in Divergence Form Giovany M. Figueiredo, Marcelo F. Furtado We establish results concerning the existence and multiplicity of positive solutions for the problem $$-\text{div}(a(\varepsilon x)|\nabla u|^{p-2}\nabla u) + |u|^{p-2}u= f(u)+|u|^{p^{*}-2}u~~\text{in }\mathbb{R}^N,~~~ u \inW^{1,p}(\mathbb{R}^N),$$where $2 \leq p rp-2005-24.pdf |
| 23/2005 |
On the Fucík Spetrum for Elliptic Systems Eugenio Massa, Bernhard Ruf We propose an extension of the concept of Fucik spectrum to the case of coupled systems of two elliptic equations, we study its structure and some applications. We show that near a simple eigenvalue of the system, the Fucik spectrum consists (after a suitable reparametrization) of two (maybe coincident) 2-dimensional surfaces. Furthermore, by variational methods, parts of the Fucik spectrum which lie far away from the diagonal (i.e. from the eigenvalues) are found. As application, some existence, non-existence and multiplicity results to systems with eigenvalue crossing ("jumping") nonlinearities are proved. rp-2005-23.pdf |
| 22/2005 |
A New Fatigue Life Model Based on the Family of Skew-elliptical Distributions Filidor E. Vilca-Labra, Víctor Leiva Fatigue is structural damage produced by cyclic stress and tension. An important statistical model for fatigue life is the Birnbaum-Saunders distribution, which was developed to model ruptured lifetimes of metals that had been subjected to fatigue. This model has been previously generalized and in this article we extend it starting from a skew-elliptical distribution. In this work we found the probability density, reliability, and hazard functions; as well as its moments and variation, skewness, and kurtosis coefficients. In addition, some properties of this new distribution were found. rp-2005-22.pdf |
| 21/2005 |
Linear Groups of Isometries with Poset Structures Luciano Panek, Marcelo Firer Let $V$ be an $n$-dimensional vector space over a finite field $\Bbb{F}_{q}$ and $P=\{1,2,\ldots ,n\}$ a poset. We consider on $V$ the poset-metric $d_{P}$. In this paper, we give a completedescription of groups of linear isometries of the metric space $\left(V,d_{P}\right) $, for any poset-metric $d_{P}$. We show that a linear isometry induces an automorphism of order in poset $P$, andconsequently we show the existence of a pair of ordered bases of $V$ relative to which every linear isometry is represented by an $n\times n$ upper triangular matrix. rp-2005-21.pdf |
