| 39/2006 |
Total Torsion of Curves in Three-Dimensional Riemannian Manifolds Cláudia C. Pansonato, Sueli I. R. Costa A classical result in differential geometry assures that the total torsion of a closed spherical curve in the three-dimensional space vanishes. Besides, if a surface is such that the total torsion vanishes for all closed curves, it is part of a sphere or a plane. We here extend these results to closed curves in three dimensional manifolds with constant curvature. We also extend an interesting companion to the total torsion theorem, which was proved for surfaces in $\mathds{R}^3$ by L. A. Santal\'o, and some results involving the total torsion of lines of curvature. |
| 38/2006 |
Covering Number for Reflections in Trees Marcelo Firer, Humberto L. Talpo We define a reflection in a tree as an involutive automorphism whose set of fixed points is a geodesic and prove that, for the case of a homogeneous tree of even degree, the group of even automorphisms may be covered by at most 11 reflections.  rp-2006-38.pdf |
| 37/2006 |
Martingales on Frame Bundles Pedro J. Catuogno, Simão Stelmastchuk Let $M$ be a smooth manifold endowed with a symmetric connection $\nabla$. There are two important ways of lift the connection $\nabla$ of $M$ to the frame bundle $BM$, the canonical lift $\nabla^c$ and the horizontal lift $\nabla^h$. The aim of this work is determine the $\nabla^c$-martingales and the $\nabla^h$-martingales on $BM$. Our results allow to establish new characterizations of harmonic maps from Riemannian manifolds to frame bundles. Finally, we consider on the associated vector bundles to $BM$ the canonical lift $\nabla^+$ and give a characterization of the $\nabla^+$-martingales. rp-2006-37.pdf |
| 36/2006 |
Frailty Models with Applications in Linkage Analysis Benilton de Sá Carvalho, Hildete P. Pinheiro, Mariza de Andrade The paper presents the Frailty Model using the hazard function in a logistic form. The model developed here is a survival analysis method which aggregates linkage analysis role. The model structure is based on a Cox model extension. The hazard function has a parametric form, the logistic one (Mackenzie, 1996). The censure is defined using the current age and the age at onset , thus if one has the age at onset greater than the current age, then a censured observation is characterized. The additive frailties are constructed from a gamma densities and it incorporates genetic and environmental contributions on the trait of interest.The use of these techniques in a unified way has been shown to be efficient, once the age at onset is usually collected in genetic mapping studies, moreover it is shown to be associated to complex diseases. Then,this is a useful model, which is able to be applied to Cox model situations and genetic mapping cases. The model is adjusted by maximization of retrospective likelihood (Whittemore, 1996), using an iterative algorithm based on the Kuhn-Tucker equations. The proposed model is ascertained by the analysis of simulated data created using G.A.S.P. package and by comparisons with the results from the joint analysis with SAS and GeneHunter softwares. rp-2006-36.pdf |
| 35/2006 |
Os Modelos de Cournot para Duopólio e Cartéis: Uma Revisão R. Aleixo Numa economia de livre concorrência, o preço e a quantidade a ser produzida são estabelecidos pelo jogo da oferta e da procura. Todavia, convém observar que o tipo de economia de livre concorrência (chamada concorrência perfeita) está praticamente desaparecendo. Neste trabalho analisamos duas situações hipotéticas de interação entre duas empresas. Uma estuda um mercado de livre concorrência em que duas empresas decidem simultâneamente que quantidade produzir. O outro estuda o caso em que há uma distorção nesse tipo de mercado que é o caso de um cartel. A teoria dos jogos é a ferramenta utilizada para fazer essas análises. rp-2006-35.pdf |
| 34/2006 |
A Note on a Sum Involving Odd Numbers Edmundo Capelas de Oliveira, H. Germano Pavão We show some results involving summation of series and as a by-product we conclude that the Tren\v{c}evski's claim was wrong. |
| 33/2006 |
Application of Moderate Deviation Techniques to Prove Sinai's Theorem on RWRE Marcelo V. Freire We apply the techniques developed in Comets and Popov (2003) to present a new proof to Sinai’s theorem (Sinai, 1982) on one-dimensional random walk in random environment (RWRE), working in a scale free way to avoid rescaling arguments and splitting the proof in two independent parts: a quenched one, related to the measure $P_\omega$ conditioned on a fixed, typical realization $\omega$ of the environment, and an annealed one, related to the product measure $\mathbb{P}$ of the environment $\omega$. The quenched part still holds even if we use another measure (possibly dependent) for the environment. rp-2006-33.pdf |
| 32/2006 |
Partitions into Parts of the Form nk+mj José Plínio O. Santos, Paulo Mondek In this paper we present new combinatorial interpretations for some identities of the Rogers-Ramanujan type where the parts of the partitions are linear combinations of two parameters. This can be done by the introduction of two parameters k and j in the sum side of the corresponding equation. |
| 31/2006 |
On the Problem of Optimal Reconstruction Alexander Kushpel, Sérgio A. Tozoni We find lower bounds for linear and Alexandrov's cowidths of Sobolev's classes on Compact Riemannian homogeneous manifolds $M^{d}$. Using these results we give an explicit solution of the problem of optimal reconstruction of functions from Sobolev's classes $W^{\gamma}_{p}(M^{d})$ in $L_{q}(M^{d})$, $1 \leq p \leq q \leq \infty$. |
| 30/2006 |
A Numerical Scheme for the Variance of the Solution of the Random Transport Equation Maria Cristina C. Cunha, Fábio A. Dorini We present a numerical scheme, based on Godunov’s method (REA algorithm), for the variance of the solution of the 1D random linear transport equation, with homogeneous random velocity and random initial condition. We obtain the stability conditions of the method and we also show its consistency with a deterministic nonhomogeneous advective-diffusive equation, which means convergency. Numerical results are considered to validate our scheme. rp-2006-30.pdf |
