8/2018 |
Estimates for Entropy Numbers of Sets of Smooth Functions on the Torus Td R. L. B. Stabile, S. A. Tozoni In this paper, we investigate entropy numbers of multiplier operators of functions defined on the d-dimensional torus. In the first part, upper and lower bounds are established for entropy numbers of general multiplier operators bounded from Lp to Lq. In the second part, we apply these results to study entropy numbers of sets of finitely differentiable functions, in particular Sobolev classes, and sets of infinitely differentiable and analytic functions, on the d-dimensional torus. We prove that, the estimates for the entropy numbers are order sharp in various important situations. rp-2018-08.pdf |

7/2018 |
A log Birnbaum-Saunders regression model based on the skew-normal distribution under the centred parameterization Nathalia L. Chaves, Caio L. N. Azevedo, Filidor Vilca-Labra, Juvêncio S. Nobre In this paper, we introduce a new regression model for positive and skewed data, a log Birnbaum-Saunders model based on the centred skew-normal distribution, and we present a several inference tools for this model. Initially, we developed a new version of skew-sinh-normal distribution and we describe some of its properties. For the proposed regression model, we carry out, through of the expectation conditional maximization (ECM) algorithm, the parameter estimation, model fit assessment, model comparison and residual analysis. Finally, our model accommodates more suitably the asymmetry of the data, compared with the usual log Birnbaum-Saunders model, which is illustrated through real data analysis. rp-2018-07.pdf |

6/2018 |
A new Birnbaum-Saunders model based on the skew-normal distribution under the centred parameterization Nathalia L. Chaves, Caio L. N. Azevedo, Filidor Vilca-Labra, Juvêncio S. Nobre In this paper we introduce a new distribution for positive and skewed data by combining the Birnbaum-Saunders (BS) distribution and the centred skew-normal distribution. Several of its properties are developed. Our model accommodates both positively and negatively skewed positive data. Also, we show that our model circumvents some problems related to another BS distribution, based on the skew-normal distribution under the direct parameterization, previously presented in the literature. We developed both maximum likelihood (ML) and Bayesian estimation procedures, comparing them through a suitable simulation study. The convergence of the expectation conditional maximization (ECM) (for ML inference) and MCMC algorithms (for Bayesian inference) were veried and several factors of interest were compared in the parameter recovery study. In general, as the sample size increases, the results indicated that the Bayesian approach provided the most accurate estimates. Finally, our model accommodates the asymmetry of the data, compared with the usual BS model, which is illustrated through real data analysis. rp-2018-06.pdf |

5/2018 |
Optimal Approximation by sk-Splines on the Torus J. G. Oliveira, S. A. Tozoni Fixed a continuous kernel rp-2018-5.pdf |

4/2018 |
On the Ree Curve Saeed Tafazolian, Fernando Torres We point out a characterization of the Ree curve which involves the number of rational points, the genus, and the shape of two elements of the Weierstrass semigroup at a rational point. rp-2018-042018.pdf |

3/2018 |
Limit Cycles Bifurcating From Discontinuous Polynomial Pertubations of Higher Dimensional Linear Differential Systems Jaume Llibre, Douglas D. Novaes, Iris O. Zeli We study the periodic solutions bifurcating from periodic orbits of linear differential systems x0 = Mx, when they are perturbed inside a class of discontinuous piecewise polynomial differential systems with two zones. More precisely, we study the periodic solutions of the differential system x0 = Mx + "F n 1 (x) + "2Fn2 (x); rp-2018-03.pdf |

2/2018 |
Normal Forms of Bireversible Vector Fields P. H. Baptistelli, M. Manoel, I.O. Zeli In this paper we adapt the method of [P. H. Baptistelli, M. Manoel and I. O. Zeli. Normal form theory for reversible equivariant vector elds. Bull. Braz. Math. Soc., New Series 47 (2016), no. 3, 935-954] to obtain normal forms of a class of smooth bireversible vector elds. These are vector elds reversible under the action of two linear involution and whose linearization has a nilpotent part and a semisimple part with purely imaginary eigenvalues. We show that these can be put formally in normal form preserving the reversing symmetries and their linearization. The approach we use is based on an algebraic structure of the set of this type of vector elds. Although this can lead to extensive rp-2018-02.pdf |

1/2018 |
The Generic Unfolding of a Codimension-Two Connection to a Two-Fold Singularity of Planar Filippov Systems Douglas D. Novaes, Marco A. Teixeira, Iris O. Zeli Generic bifurcation theory was classically well developed for smooth differential systems, establishing results for k-parameter families of planar vector rp-2018-01.pdf |

16/2017 |
An Alphabetical Approach to Nivat´s Conjecture Colle, C. F., Garibaldi, E. Abstract rp-2017-16.pdf |

15/2017 |
On Maximal Curves Related to Chebyshev Polynomials Ahmad Kazemifard, Saeed Tafazolian, Fernando Torres We study maximal curves arising from Chebyshev polynomials, where in particular some results from Garcia-Stichtenoth [4] are revisited and generalized. rp-2017-15.pdf |

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