| 24/2009 |
On the Problem of Kolmogorov on Homogeneous Manifolds Alexander Kushpel We give the solution of a well-known problem of Kolmogorov on sharp asymptotic of the rates of convergence of Fourier sums on sets of smooth functions on homogeneous manifolds. |
| 23/2009 |
Orthogonal Developments on Compact Symmetric Homogeneous Manifolds of Rank 1 Alexander Kushpel Sharp asymptotic for the norms of Fourier projections on compact homogeneous manifolds of rank 1 are established. These results extend sharp asymptotic estimates found by Fejer in the case of the circle in 1910 and then by Gronwall in 1914 in the case of the 2-dimensional sphere. As an application of these results we give sharp asymptotic for the rate of convergence of Fourier sums on a wide range of sets of multipliers. |
| 22/2009 |
On the Anomalous Diffusion and the Fractional Generalized Langevin Equations R. Figueiredo Camargo, Edmundo Capelas de Oliveira, Jayme Vaz Jr. We introduce the fractional generalized Langevin equation in the absense of a deterministic field, with two deterministic conditions for a particle with unitary mass, i.e., an initial condition and an initial velocity are considered. For a particular correlation function, that characterizes the physical process, and using the methodology of the Laplace transform, we obtain the solution in terms of the three-parameterMittag-Leffler function. As particular cases, some recent resuls are also presented. |
| 21/2009 |
On a General Mittag-Leffler Theorem Ana Luisa Soubhia, R. Figueiredo Camargo, Edmundo Capelas de Oliveira, Jayme Vaz Jr. We present a formal demonstration of a new theorem involving a three-parameter Mittag-Leffler function. As a by product, we recover some known results and we discuss a corollary which appear in a natural way. As an application we obtain the solution of the fractional differential equation associated with a $RLC$ electrical circuit in a closed form, involving the two-parameter Mittag-Leffler function. |
| 20/2009 |
A New Bound on the Multipliers Given by Carathéodory´s Theorem and a Result on the Internal Penalty Method Gabriel Haeser Carathéodory's theorem for cones states that if we have a linear combination of vectors in Rn, we can rewrite this combination using a linearly independent subset. This theorem has been successfully applied in nonlinear optimization in many contexts. In this work we present a new version of this celebrated theorem, in which we prove a bound for the size of the scalars in the linear combination and we provide examples where this bound is useful. We also prove that the convergence property of the internal penalty method cannot be improved.  rp-2009-20.pdf |
| 19/2009 |
On Sequential Optimality Conditions Roberto Andreani, Gabriel Haeser, José Mario Martínez Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Approximate KKT and Approximate Gradient Projection conditions areanalyzed in this work. These conditions are not necessarily equivalent. Implications between different conditions and counter-examples will be shown. Algorithmic consequences will be discussed. rp-2009-19.pdf |
| 18/2009 |
Reversibility and Quasi-Homogeneous Normal Forms of Vector Fields A. Algaba, C. García, Marco A. Teixeira This paper uses tools in Quasi-Homogeneous Normal Form theory to discuss certain aspects of reversible vector fields around an equilibrium point. Our main result provides an algorithm, via Lie Triangle, that detects the non-reversibility of vector fields. As a consequence we answer an intriguing question related to the problems derived from the $16^{\circ}$ Hilbert Problem. That is, it is possible to decide whether a planar center is not reversible. Some of the theory developed is also applied to get further results on nilpotent and degenerate polynomial vector fields. We find several families of nilpotent centers which are non-reversible. rp-2009-18.pdf |
| 17/2009 |
A Caffarelli-Kohn-Nirenberg Type Inequality on Riemannian Manifolds Yuri Bozhkov We establish a generalization to Riemannian manifolds of the Caffarelli-Kohn-Nirenberg inequality. The applied method is based on the use of conformal Killing vector fields and Enzo Mitidieri's approach to Hardy inequalities. |
| 16/2009 |
Reversal Symmetries for Planar Vector Fields A. Algaba, C. García, Marco A. Teixeira In this paper, we formulate a comprehensive study of relevant properties of reversible vector fields. As a consequence, we prove that the reversibility of the first non-zero quasi-homogeneous term, respect to some types, of a vector field is a necessary condition for the reversibility of the vector field. We also provide a straightforward characterization of the reversibility for quasi-homogeneous vector fields. Finally, as an application of our previous results, we analyze some special polynomial and nilpotent systems, including examples which are centers and non-reversible. rp-2009-16.pdf |
| 15/2009 |
Nonlinear Regression Models Based on Scale Mixtures of Skew-Normal Distributions Aldo M. Garay, Víctor H. Lachos, Carlos A. Abanto-Valle An extension of some standard likelihood based procedures to nonlinear regression models under scale mixtures of skew-normal distributions is developed. This novel class of models provides a useful generalization of the symmetrical nonlinear regression models since the error distributions cover both skewness and heavy-tailed distributions such as the skew-t, skew-slash and the skew-contaminated normal distributions. The main advantage of these class of distributions is that they have a nice hierarchical representation which allows easy implementation of inference. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented and the observed information matrix for obtaining the asymptotic covariance matrix is derived analytically. With the aim of identifying atypical observations and/or model misspecification a brief discussion of the standardized residuals is given. Finally, an illustration of the methodology is given considering a data set previously analyzed under skew-normal nonlinear regression models. Our analysis indicates that a skew-t nonlinear regression model with 3 degrees of freedom seems to fit the data better than the skew-normal nonlinear regression model as well as other asymmetrical nonlinear models in the sense of robustness against outlying observations. rp-2009-15.pdf |
