Zeros of orthogonal polynomials generated by canonical perturbations of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

Smale's Conjecture on Mean Values of Polynomials and Electrostatics

2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.

Futebol como projeto profissional de mulheres : interpretações da busca pela legitimidade = Football as a career project for women : legitimacy search interpretation

Universidade Estadual de Campinas . Faculdade de Educação Física

Revised criteria for the assessment and interpretation of occlusal deviations in the deciduous dentition: a public health perspective

Dados secundários de uma amostra aleatória de pré-escolares brasileiros foram analisados com o objetivo de avaliar a prevalência de desvios oclusais na dentição decídua, que podem adversamente afetar a dentição permanente, com base em critérios revisados. Overjet e overbite apresentaram pontos de corte descritos na literatura para a remoção dos casos de má oclusão leve. Overjet > 3mm e overbite > 3mm afetaram 16% e 7% das crianças, respectivamente. No plano sagital foram consideradas apenas as taxas de desvios bilaterais: relação molar em degrau distal (9,7%) e mesial (6,0%); relação dos caninos Classe 2 (11,0%) e Classe 3 (2,9%). Para os demais desvios não foram relatados na literatura critérios de severidade. Valores brutos de mordida aberta anterior (27,9%); mordida cruzada posterior (11,3%); apinhamento dentário maxilar (7,0%) e mandibular (11,3%) foram registrados. A avaliação da má oclusão na dentição decídua deve considerar a severidade dos desvios para a identificação de casos e não-casos de relevância em saúde pública. Enfatiza-se a necessidade de maior consenso e melhora na interpretação de dados epidemiológicos sobre a má oclusão nesse estágio de desenvolvimento

Interpretation of MINOS data in terms of nonstandard neutrino interactions

The MINOS experiment at Fermilab has recently reported a tension between the oscillation results for neutrinos and antineutrinos. We show that this tension, if it persists, can be understood in the framework of nonstandard neutrino interactions (NSI). While neutral current NSI (nonstandard matter effects) are disfavored by atmospheric neutrinos, a new charged current coupling between tau neutrinos and nucleons can fit the MINOS data without violating other constraints. In particular, we show that loop-level contributions to flavor-violating tau decays are sufficiently suppressed. However, conflicts with existing bounds could arise once the effective theory considered here is embedded into a complete renormalizable model. We predict the future sensitivity of the T2K and NOvA experiments to the NSI parameter region favored by the MINOS fit, and show that both experiments are excellent tools to test the NSI interpretation of the MINOS data.

Information theoretic interpretation of frequency domain connectivity measures

In order to provide adequate multivariate measures of information flow between neural structures, modified expressions of partial directed coherence (PDC) and directed transfer function (DTF), two popular multivariate connectivity measures employed in neuroscience, are introduced and their formal relationship to mutual information rates are proved.

The Reflectance Signature of Canopy Components: Implications for the Interpretation of Remotely Sensed Images

The reflectance signatures of plantation pine canopy and understorey components were measured using a spectro-radiometer. The aim was to establish whether differences observed in the reflectance signature of stressed and unstressed pine needles were consistent with observed differences in the reflectance of multispectral Landsat Thematic Mapper (TM) images of healthy and stressed forest. Because overall scene reflectance includes the contribution of each scene component, needle reflectance may not be representative of canopy reflectance. In this investigation, a limited dataset of reflectance signatures from stressed and unstressed needles confirmed the negative relationship between pine needle health and reflectance which was observed in visible red wavelengths. However, the reflectance contribution from bushes, pine needle litter and bare soil tended to reinforce this relationship suggesting that in this instance, overall scene reflectance is comprised of the proportional reflectance of each scene component. In near infrared wavelengths, differences between healthy and stressed needle reflectance suggested a strong positive relationship between reflectance and tree health. For Landsat TM images, previous research had only observed a weak positive relationship between stand health and near infrared reflectance in these pine canopies. This suggests that for multispectral Landsat TM images, reflectance of near infrared light from pine canopies may be affected by other factors which may include the scattering of light within canopies. These results are seen as promising for the use of hyperspectral images to detect stand health, provided that pixel reflectance is not influenced by other scene components.

Structural interpretation of mutations in phenylalanine hydroxylase protein aids in identifying genotype-phenotype correlations in phenylketonuria

Phenylalanine hydroxylase (PAH) is the enzyme that converts phenylalanine to tyrosine as a rate-limiting step in phenylalanine catabolism and protein and neurotransmitter biosynthesis. Over 300 mutations have been identified in the gene encoding PAH that result in a deficient enzyme activity and lead to the disorders hyperphenylalaninaemia and phenylketonuria. The determination of the crystal structure of PAH now allows the determination of the structural basis of mutations resulting in PAH deficiency. We present an analysis of the structural basis of 120 mutations with a 'classified' biochemical phenotype and/or available in vitro expression data. We find that the mutations can be grouped into five structural categories, based on the distinct expected structural and functional effects of the mutations in each category. Missense mutations and small amino acid deletions are found in three categories:'active site mutations', 'dimer interface mutations', and 'domain structure mutations'. Nonsense mutations and splicing mutations form the category of 'proteins with truncations and large deletions'. The final category, 'fusion proteins', is caused by frameshift mutations. We show that the structural information helps formulate some rules that will help predict the likely effects of unclassified and newly discovered mutations: proteins with truncations and large deletions, fusion proteins and active site mutations generally cause severe phenotypes; domain structure mutations and dimer interface mutations spread over a range of phenotypes, but domain structure mutations in the catalytic domain are more likely to be severe than domain structure mutations in the regulatory domain or dimer interface mutations.

Interpretation of negative values of the interaction parameter in the adsorption equation through the effects of surface layer heterogeneity

The problem of the negative values of the interaction parameter in the equation of Frumkin has been analyzed with respect to the adsorption of nonionic molecules on energetically homogeneous surface. For this purpose, the adsorption states of a homologue series of ethoxylated nonionic surfactants on air/water interface have been determined using four different models and literature data (surface tension isotherms). The results obtained with the Frumkin adsorption isotherm imply repulsion between the adsorbed species (corresponding to negative values of the interaction parameter), while the classical lattice theory for energetically homogeneous surface (e.g., water/air) admits attraction alone. It appears that this serious contradiction can be overcome by assuming heterogeneity in the adsorption layer, that is, effects of partial condensation (formation of aggregates) on the surface. Such a phenomenon is suggested in the Fainerman-Lucassen-Reynders-Miller (FLM) 'Aggregation model'. Despite the limitations of the latter model (e.g., monodispersity of the aggregates), we have been able to estimate the sign and the order of magnitude of Frumkin's interaction parameter and the range of the aggregation numbers of the surface species. (C) 2004 Elsevier B.V All rights reserved.