| 50/2003 |
On Factorization of Schatten Class Type Mappings Cristiane de Andrade Mendes We present some results on factorization of multilinear mappings and polynomials of Schatten class type $\mathcal{S}_2$ through infinite dimensional Banach spaces, $\mathcal{L}_1 $ and $\mathcal{L}_{\infty}$ spaces. We conclude this work with a factorization result for holomorphic mappings of Schatten class type $\mathcal{S}_2$.  rp-2003-50.pdf |
| 49/2003 |
The Performance of a Reversible Jump Markov Chain Monte Carlo Algorithm for DNA Sequences Alignment Luis J. Álvarez, Nancy L. Garcia, Eliane R. Rodrigues Assume that K independent copies are made from a common prototype DNA sequence whose length is considered to be a random variable. In this paper the problem of aligning these copies and therefore the problem of estimating the prototype sequence that produced the copies is addressed. A hidden Markov chain is used to model the copying procedure and a reversible jump Markov chain Monte Carlo algorithm is used to sample the parameters of the model from their posterior distribution. Using the sample obtained, the Bayesian model selection may be made and the prototype sequence may be selected using the maximum a posteriori estimate. A prior distribution for the prototype DNA sequence that incorporates a correlation among neighbouring bases is also considered. Additionally, an analysis of the performance of the algorithm is presented when different scenarios are taken into account. rp-2003-49.pdf |
| 48/2003 |
On Zeeman Topology in Kaluza-Klein and Gauge Theories Ivan Struchiner, Márcio A. F. Rosa E. C. Zeeman [1] has criticized the fact that in all articles and books until that moment (1967) the topology employed to work with the Minkowski space was the Euclidean one. He has proposed a new topology, wich was generalized for more general space-times by Goebel [2]. In the Zeeman and Goebel topologies for the space-time, the unique continuous curves arepolygonals composed by time-like straight lines and geodesics respectively. In his paper, Goebel proposes a topology for which the continuous curves are polygonals composed by motions of charged particles. Here we obtain in a very simple way a generalization of this topology, valid for any gauge fields, by employing the projection theorem of Kaluza-Klein theories (page144 of Bleecker [3] ). This approach relates Zeeman topologies and Kaluza-Klein, therefore Gauge Theories, what brings insights and points in the direction of a completely geometric theory. rp-2003-48.pdf |
| 47/2003 |
A equação de Dirac no espaço-tempo de Robertson-Walker D. Gomes, Edmundo Capelas de Oliveira rp-2003-47.pdf |
| 46/2003 |
Invariant nearly-Kähler structures Luiz A. B. San Martin, Rita de Cássia de J. Silva This paper considers invariant almost Hermitian structures on a flag manifold $G/P=U/K$ where $G$ is a complex semi-simple Lie group, $P$ is a parabolic subgroup of $G$, $U$ is a compact real form of $G$ and $K=U\cap P$ is the centralizer of a torus. The main result shows that there are nearly-K\"{a}hler structures in $G/P$ which are not K\"{a}hler if and only if $G/P$ has height three. This proves for the flag manifolds a conjecture by J.A. Wolf and A. Gray. rp-2003-46.pdf |
| 45/2003 |
On the classification of second order partial differential equations in two independent variables revisited Silke Humbert, Edmundo Capelas de Oliveira We present and discuss the classification of second order partial differential equations in two independent variables. We focus our attention on the case of non-constant coefficients, where the so-called partial differential equations of mixed type can appear. As an application we discuss a partial differential equation of mixed type associated with projective relativity. rp-2003-45.pdf |
| 44/2003 |
On the Sonine-Bessel integral representation R. Aleixo de Carvalho , Edmundo Capelas de Oliveira Using an integral representation for the first kind Hankel (Hankel-Bessel) function we obtain the so-called Basset formula, an integral representation for the second kind modified Bessel function. Using the Sonine-Bessel integral representation we obtain the Fourier cosine integral transform of the zero order Bessel function. As an application we present the calculation of the Green's function associated with a second order partial differential equation , particularly a wave equation for a lossy two-dimensional medium. This application is associated to the transient electromagnetic field radiated by a pulsed source in the presence of dispersive media, which is of great importance in the theory of geophysical prospecting, lightning studies rp-2003-44.pdf |
| 43/2003 |
On a real integral: particular case Edmundo Capelas de Oliveira, Ary O. Chiacchio, R. Figueiredo Camargo Using two convenient contours of integration in the complex plane we calculate a real integral, depending on two parameters. Several particular cases are discussed. As a by product we determine in a closed form a sum involving a product of trigonometric and hyperbolic functions. Particular cases are also presented. rp-2003-43.pdf |
| 42/2003 |
Positive and Multiple Solutions for Quasilinear Problem Francisco O. V. de Paiva In this paper we establish the existence of positive and multiple solutions for the quasilinear elliptic problem\begin{eqnarray*}\begin{array}{ccl}-\Delta_p u = g(x,u) & {\rm in} & \Omega\\ u = 0 & {\rm on} & \partial \Omega,\end{array}\end{eqnarray*}where $\Omega \subset \mathbb{R}^N$ is an open bounded domain with smooth boundary $\partial \Omega$, $g:\Omega\times\mathbb{R}\to \mathbb{R}$ is a Carath\'eodory function such that $g(x,0)=0$ and which is asymptotically linear. We suppose that $g(x,t)/t$ tends to an $L^r$-function, $r>N/p$ if $1N$, which can change sign. We consider both cases, resonant and nonresonant. rp-2003-42.pdf |
| 41/2003 |
Uma Estratégia de Geração de Colunas para o Problema de Empacotamento Bidimensional Clovis Perin, Valéria de Podestá Gomes rp-2003-41.pdf |
