| 24/2002 |
Finite Energy Superluminal Solutions of Maxwell Equations Edmundo Capelas de Oliveira, Waldyr A. Rodrigues Jr. We exhibit exact finite energy superluminal solutions of Maxwell equations in vacuum and discuss the physical meaning of these solutions.  rp-2002-24.pdf |
| 23/2002 |
Thoughtful comments on `Bessel beams and signal propagation' Edmundo Capelas de Oliveira, Waldyr A. Rodrigues Jr., Dario S. Thober, Ademir L. Xavier Jr. In this paper we present thoughtful comments on the paper `Bessel beams and signal propagation' showing that the main claims of that paper are wrong. Moreover, we take the opportunity to show the non trivial and indeed surprising result that a scalar pulse (i.e., a wave train of compact support in the time domain) that is solution of the homogeneous wave equation (vector ($\vec{E},\vec{B}$ pulse that is solution of Maxwell equations) is such that its wave front in some cases does travel with speed greater than $c$, the speed of light . In order for a pulse to posses a front that travels with speed $c$, an additional condition must be satisfied, namely the pulse must have finite energy. When this condition is fulfilled the pulse still can show peaks propagating with superluminal (or subluminal) velocities, but now its wave front travels at speed $c$. These results are important because they explain several experimental results obtained in recent experiments, where superluminal velocities have been observed, without implying in any breakdown of the Principle of Relativity. rp-2002-23.pdf |
| 22/2002 |
Causal explanation for observed superluminal behavior of microwave propagation in free space Waldyr A. Rodrigues Jr., Dario S. Thober, Ademir L. Xavier Jr. In this paper we present a theoretical analysis of an experiment by Mugnai and collaborators where superluminal behavior was observed in the propagation of microwaves. We suggest that what was observed can be well approximated by the motion of a superluminal X wave. Furthermore the experimental results are also explained by the so called scissor effect which occurs with the convergence of pairs of signals coming from opposite points of an annular region of the mirror and forming an interference peak on the intersection axis traveling at superluminal speed. We clarify some misunderstandings concerning this kind of electromagnetic wave propagation in vacuum. rp-2002-22.pdf |
| 21/2002 |
Adaptive wavelet representation and differentiation of block-structured grids M. O.Domingues, Sônia M. Gomes, L. M. A. Diaz This paper considers an adaptive finite difference scheme for the numerical solution of evolution partial differential equations. The computational domain is formed by non-overlapping blocks. Each block is a uniform grid, but step size may change from one block to another. The blocks are not predetermined, but they are dynamically constructed according to the refinement needs of the numerical solution. The decision over whether a block should be refined or unrefined is taken by looking at the magnitude of wavelet coefficients of the numerical solution on such block. The main objective of this paper is to establish a general framework for the construction and operation on such adaptive block-grids in 2D. The algorithms and data structure are formulated by using abstract concepts borrowed from quaternary trees. This procedure helps the understanding of the method and its computational implementation. The ability of the method is demonstrated by solving some typical test problems. rp-2002-21.pdf |
| 20/2002 |
Connected components of open semigroups in semi-simple Lie groups Osvaldo G. do Rocio, Luiz A. B. San Martin This paper studies connected components of open subsemigroups of non-compact semi-simple Lie groups through the control sets in the flag manifolds and their coverings. A method for computing the number of components we call recurrent, which includes the semigroup components, is developed and it is proved that the union of this set of components is a subsemigroup. The idea of mid-reversibility comes up to show that an open semigroup has just one semigroup component if the identity belongs to its closure. A necessary and sufficient condition for mid-reversibility is proved showing that e.g. in a complex group any open semigroup is mid-reversible. rp-2002-20.pdf |
| 19/2002 |
Poincaré - Hopf Inequalities Maria Alice Bertolim, Margarida P. Melo, Ketty A. de Rezende In this article the main theorem establishes the necessity and sufficiency of the Poincar\'{e}-Hopf inequalities in order for the Morse inequalities to hold under the hypothesis that the flow and the reverse flow satisfy the Conley index duality condition on components of the chain recurrent set. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described. rp-2002-19.pdf |
| 18/2002 |
Perfect simulation for a continuous one-dimensional loss network Nancy L. Garcia, Nevena Marić Sufficient conditions for ergodicity of a one-dimensional loss networks on R with length distribution G and cable capacity C are found. These processes are spatial birth-and-death processes with an invariant measure which is absolutely continuous with respect to a Poisson process and we implement the perfect simulation scheme based on the clan of ancestors introduced by Fernández, Ferrari and Garcia (2002) to obtain perfect samples viewed in a nite window of the in nite-volume invariant measure. Moreover, by a better understanding of the simulation process it is possible to get a better condition for ergodicity. rp-2002-18.pdf |
| 17/2002 |
Convolution of Robust Functions Heriberto Román-Flores, Rodney C. Bassanezi, Laécio C. Barros Recently Zheng [1,2], in the setting of global optimization, introduced the concepts of robust set and robust function as a generalization of open set and upper semicontinuous (u.s.c) function, respectively. The aims of this paper are to study the structure of robust sets defined on a normed space $X$ as well as to extend some multivalued convergence results obtained by the author in [3,4] and Greco et al. [6] for semicontinuous functions to the class of robust functions. More precisely, we introduce the concepts of level-convergence and epigraphic convergence on $\mathcal{R}(X)$ the space of nonnegative robust functions on a normed space $X$ and, on one hand, we study its properties and relationships, and on the other, we present some results on level-approximation and epi-approximation of functions by using convolution of robust functions. rp-2002-17.pdf |
| 16/2002 |
Cotype and absolutely summing homogeneous polynomials in Lp spaces Daniel Pellegrino In this paper we lift to homogeneous polynomials and multilinear mappings a linear result due to Lindenstrauss and Pe{\l}czy\'{n}ski for absolutely summing mappings. We explore the notion of cotype to obtain stronger results and provide various examples of situations in which we have the space of absolutely summing polynomials different from the whole space. Among other consequences, these results enable us to obtain answers to some open questions about absolutely summing polynomials and multilinear mappings on $\mathcal{L}_{\infty}$ spaces. rp-2002-16.pdf |
| 15/2002 |
Cotype and non linear absolutely summing mappings Daniel Pellegrino In this paper we study absolutely summing mappings on Banach spaces by exploring the cotype of their domains and ranges. It is proved that every $n$-linear mapping from $\mathcal{L}_{\infty}$-spaces into $\mathbb{K}$ is $(2;2,...,2,\infty)$-summing and also shown that every $n$-linear mapping from $\mathcal{L}_{\infty}$-spaces into $F$ is $(q;2,...,2)$-summing whenever $F$ has cotype $q$. We also give new examples of analytic summing mappings and polynomial and multilinear versions of a linear Extrapolation Theorem. rp-2002-15.pdf |
