| 42/2005 |
Influence Diagnostics in the Capital Asset Pricing Model Under Elliptical Distributions Manuel Galea, José A. Díaz-García, Filidor E. Vilca-Labra In this paper we consider the Capital Asset Pricing Model under Elliptical (symmetric) Distributions. This class of distributions, which contain the normal distribution, t, contaminated normal and power exponential, among others, offers a more flexible framework for modelling asset prices or returns. In order to analyze the sensibility to possible outliers and/or atypical returns of the maximum likelihoodestimators, the local influence method was implemented. The results are illustrated by using a set of shares from companies who trade in the Chilean Stock Market. Our main conclusion is that symmetric distributions having heavier tails than those of the normal distribution, especially the t distribution with small degrees of freedom, show a better fit and allow the reduction of the influence of atypical returns in the maximum likelihood estimators.  rp-2005-42.pdf |
| 41/2005 |
Lie Algebras with Complex Structures Having Nilpotent Eigenspaces Edson Carlos Licurgo Santos, Luiz A. B. San Martin Let $ g $ be a Lie algebra with an integrable complex structure $J$. The eigenspaces of $J$ are complex subalgebras of ${g}^{C}$ isomorphic to the algebra $({g},[*]_{J}) $. We consider here the case where these subalgebras are nilpotent and prove that the original Lie algebra $(g,[,])$ must be solvable. We consider also the $6$-dimensional case and determine explicitly the possible nilpotent * Lie algebras. Finally we produce several examples illustrating different situations, in particular we show that for each given $s$ there exists $g$ with complex structure $J$ such that its *-algebra is $s$-step nilpotent. Similar examples of hipercomplex structures are also built. rp-2005-41.pdf |
| 40/2005 |
Perturbative Self-Interacting Scalar Field Theory: A Differential Equation Approach Roldão da Rocha Jr., Edmundo Capelas de Oliveira, C. H. Coimbra-Araújo We revisit the investigation about the partition function related to a $\phi^4$-scalar field theory on a $n$-dimensional Minkowski spacetime, which is shown to be a self-interacting scalar field theory at least in 4-dimensional Minkowski spacetime. After rederiving the analytical calculation of the perturbative expansion coefficients and also the approximate values for suitable limits using Stirling's formul\ae, which consists of Witten's proposed questions, solved by P. Deligne, D. Freed, L. Jeffrey, and S. Wu, we investigate a spherically symmetric scalar field in a $n$-dimensional Minkowski spacetime. For the first perturbative expansion coefficient it is shown how it can be derived a modified Bessel equation (MBE), which solutions are investigated in one, four, and eleven-dimensional Minkowski spacetime. The solutions of MBE are the first expansion coefficient of the series associated with the partition function of $\phi^4$-scalar field theory. rp-2005-40.pdf |
| 39/2005 |
Sufficient Conditions for Regularity and Uniqueness of a 3D Nematic Liquid Crystal Model Francisco Guillén-Gonzáles, Marko A. Rodríguez-Bellido, Marko A. Rojas Medar rp-2005-39.pdf |
| 38/2005 |
Tightness and Efficiency of Irreducible Automorphisms of Handlebodies Leonardo Navarro Carvalho Among (isotopy classes of) automorphisms of handlebodies those called irreducible (or generic) are the most interesting, analogues of pseudo-Anosov automorphisms of surfaces. We consider the problem of isotoping an irreducible automorphism so that it is most efficient (has minimal growth rate) in its isotopy class. We describe a property, called tightness, of certain invariant laminations, which we conjecture characterizes this efficiency. We obtain partial results towards proving the conjecture. For example, we prove it for genus two handlebodies. We also show that tightness always implies efficiency.In addition, partly in order to provide counterexamples in our study of properties of invariant laminations, we develop a method for generating a class of irreducible automorphisms of handlebodies. rp-2005-38.pdf |
| 37/2005 |
Dispersão de Poluentes em Sistemas Estuarinos: Modelo Matemático, Aproximação Numérica e Simulações João Frederico C. A. Meyer, Geraldo L. Diniz rp-2005-37.pdf |
| 36/2005 |
Inference in the Grubbs Model Under Elliptical Distributions Filidor E. Vilca-Labra, Manuel Galea In this paper we consider estimation and hypotheses testing in the Grubbs model under elliptical distributions. Thus is, we assume that the measurements obtained follow a multivariate elliptical distribution. Wald type statistics are considered which are asymptotically distributed according to the chi-square distribution. The statistics are based on maximum likelihood estimator, in sample mean and sample covariance. matrix.Mathematics Subject Classifications (2000): rp-2005-36.pdf |
| 35/2005 |
Nonsmooth Continuous-Time Multiobjective Optimization Problems L. Batista dos Santos, Adilson J. Vieira-Brandão, R. Osuna-Gómez, Marko A. Rojas-Medar We discuss necessary and sufficient conditions of optimality for nonsmooth continuous-time multiobjective optimization problems under generalized convexity assumptions. rp-2005-35.pdf |
| 34/2005 |
Semigroups in Symmetric Lie Groups Laércio J. dos Santos, Luiz A. B. San Martin Let $G$ be a connected noncompact semi-simple real Lie group, $\tau $ an involutive automorphism of $G,$ and $L$ a subgroup of $G$ such that $G_{0}^{\tau }\subset L\subset G^{\tau }.$ In this article we give conditions on $x\in G$ such that the semigroup generated by the coset $Lx$ has nonempty interior in $G$. As a consequence we prove that for several $\tau $ the fixed point group $G^{\tau }$ is a maximal semigroup. rp-2005-34.pdf |
| 33/2005 |
Invariant Cones and Convex Sets for Bilinear Control Systems and Parabolic Type of Semigroups Osvaldo G. do Rocio, Luiz A. B. San Martin, Alexandre J. Santana This paper studies invariant cones for bilinear control systems, and relates them to the controllability of the system. The full picture is provided by the parabolic type of a semigroup. rp-2005-33.pdf |
