Stable singularities of co-rank one quasi homogeneous map germs from (ℂn+1, 0) to (ℂn, 0), n = 2, 3

In this article, we investigate the geometry of quasi homogeneous corank one finitely determined map germs from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. We give a complete description, in terms of the weights and degrees, of the invariants that are associated to all stable singularities which appear in the discriminant of such map germs. The first class of invariants which we study are the isolated singularities, called 0-stable singularities because they are the 0-dimensional singularities. First, we give a formula to compute the number of An points which appear in any stable deformation of a quasi homogeneous co-rank one map germ from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. To get such a formula, we apply the Hilbert's syzygy theorem to determine the graded free resolution given by the syzygy modules of the associated iterated Jacobian ideal. Then we show how to obtain the other 0-stable singularities, these isolated singularities are formed by multiple points and here we use the relation among them and the Fitting ideals of the discriminant. For n = 2, there exists only the germ of double points set and for n = 3 there are the triple points, named points A1,1,1 and the normal crossing between a germ of a cuspidal edge and a germ of a plane, named A2,1. For n = 3, there appear also the one-dimensional singularities, which are of two types: germs of cuspidal edges or germs of double points curves. For these singularities, we show how to compute the polar multiplicities and also the local Euler obstruction at the origin in terms of the weights and degrees. © 2013 Pushpa Publishing House.

Simultaneous linearization of a class of pairs of involutions with normally hyperbolic composition

In this paper we obtain a result on simultaneous linearization for a class of pairs of involutions whose composition is normally hyperbolic. This extends the corresponding result when the composition of the involutions is a hyperbolic germ of diffeomorphism. Inside the class of pairs with normally hyperbolic composition, we obtain a characterization theorem for the composition to be hyperbolic. In addition, related to the class of interest, we present the classification of pairs of linear involutions via linear conjugacy. © 2012 Elsevier Masson SAS.

Comparative cytogenetic analysis of some species of the Dendropsophus microcephalus group (Anura, Hylidae) in the light of phylogenetic inferences

Background: Dendropsophus is a monophyletic anuran genus with a diploid number of 30 chromosomes as an important synapomorphy. However, the internal phylogenetic relationships of this genus are poorly understood. Interestingly, an intriguing interspecific variation in the telocentric chromosome number has been useful in species identification. To address certain uncertainties related to one of the species groups of Dendropsophus, the D. microcephalus group, we carried out a cytogenetic analysis combined with phylogenetic inferences based on mitochondrial sequences, which aimed to aid in the analysis of chromosomal characters. Populations of Dendropsophus nanus, Dendropsophus walfordi, Dendropsophus sanborni, Dendropsophus jimi and Dendropsophus elianeae, ranging from the extreme south to the north of Brazil, were cytogenetically compared. A mitochondrial region of the ribosomal 12S gene from these populations, as well as from 30 other species of Dendropsophus, was used for the phylogenetic inferences. Phylogenetic relationships were inferred using maximum parsimony and Bayesian analyses.Results: The species D. nanus and D. walfordi exhibited identical karyotypes (2n = 30; FN = 52), with four pairs of telocentric chromosomes and a NOR located on metacentric chromosome pair 13. In all of the phylogenetic hypotheses, the paraphyly of D. nanus and D. walfordi was inferred. D. sanborni from Botucatu-SP and Torres-RS showed the same karyotype as D. jimi, with 5 pairs of telocentric chromosomes (2n = 30; FN = 50) and a terminal NOR in the long arm of the telocentric chromosome pair 12. Despite their karyotypic similarity, these species were not found to compose a monophyletic group. Finally, the phylogenetic and cytogenetic analyses did not cluster the specimens of D. elianeae according to their geographical occurrence or recognized morphotypes.Conclusions: We suggest that a taxonomic revision of the taxa D. nanus and D. walfordi is quite necessary. We also observe that the number of telocentric chromosomes is useful to distinguish among valid species in some cases, although it is unchanged in species that are not necessarily closely related phylogenetically. Therefore, inferences based on this chromosomal character must be made with caution; a proper evolutionary analysis of the karyotypic variation in Dendropsophus depends on further characterization of the telocentric chromosomes found in this group. © 2013 Medeiros et al.; licensee BioMed Central Ltd.

Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

Para-orthogonal polynomials derived from orthogonal polynomials on the unit circle are known to have all their zeros on the unit circle. In this note we study the zeros of a family of hypergeometric para-orthogonal polynomials. As tools to study these polynomials, we obtain new results which can be considered as extensions of certain classical results associated with three term recurrence relations and differential equations satisfied by orthogonal polynomials on the real line. One of these results which might be considered as an extension of the classical Sturm comparison theorem, enables us to obtain monotonicity with respect to the parameters for the zeros of these para-orthogonal polynomials. Finally, a monotonicity of the zeros of Meixner-Pollaczek polynomials is proved. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Microsatellite marker-based assessment of the biodiversity of native bioethanol yeast strains

Although many Brazilian sugar mills initiate the fermentation process by inoculating selected commercial Saccharomyces cerevisiae strains, the unsterile conditions of the industrial sugar cane ethanol fermentation process permit the constant entry of native yeast strains. Certain of those native strains are better adapted and tend to predominate over the initial strain, which may cause problems during fermentation. In the industrial fermentation process, yeast cells are often exposed to stressful environmental conditions, including prolonged cell recycling, ethanol toxicity and osmotic, oxidative or temperature stress. Little is known about these S. cerevisiae strains, although recent studies have demonstrated that heterogeneous genome architecture is exhibited by some selected well-adapted Brazilian indigenous yeast strains that display high performance in bioethanol fermentation. In this study, 11 microsatellite markers were used to assess the genetic diversity and population structure of the native autochthonous S. cerevisiae strains in various Brazilian sugar mills. The resulting multilocus data were used to build a similarity-based phenetic tree and to perform a Bayesian population structure analysis. The tree revealed the presence of great genetic diversity among the strains, which were arranged according to the place of origin and the collection year. The population structure analysis revealed genotypic differences among populations; in certain populations, these genotypic differences are combined to yield notably genotypically diverse individuals. The high yeast diversity observed among native S. cerevisiae strains provides new insights on the use of autochthonous high-fitness strains with industrial characteristics as starter cultures at bioethanol plants. © 2013 John Wiley & Sons, Ltd.

Non-Markovian expansion in quantum Brownian motion

We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form. © 2013 Elsevier B.V. All rights reserved.

Teorema de Riemann-Roch e aplicações

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Unidades em corpos abelianos

Pós-graduação em Matemática - IBILCE

Método das aproximações sucessivas e aplicações

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Polinômios ortogonais em várias variáveis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Teorema de Thales: uma conexão entre os aspectos geométrico e algébrico em alguns livros didáticos de matemática

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Criando novos tabuleiros para o jogo Tri-Hex e sua validação didático-pedagógica na formação continuada de professores de matemática: uma contribuição para a geometria das séries finais do ensino fundamental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A investigação do teorema fundamental do cálculo com calculadoras gráficas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A classificação das formas binárias aplicada em máquinas de catástrofes

Pós-graduação em Matemática Universitária - IGCE