Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the zeros of a class of generalized hypergeometric polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Lê–Greuel type formula for the Euler obstruction and applications

The Euler obstruction of a function f can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we establish several Lê–Greuel type formulas for germs f:(X,0)→(C,0) and g:(X,0)→(C,0). We give applications when g is a generic linear form and when f and g have isolated singularities.

Horospheres in hyperbolic geometry

In this paper we investigate the role of horospheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combinations” of support maps or curves. Finally we obtain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.

Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Chebyshev-type quadrature formulas for new weight classes

We give Chebyshev-type quadrature formulas for certain new weight classes. These formulas are of highest possible degree when the number of nodes is a power of 2. We also describe the nodes in a constructive way, which is important for applications. One of our motivations to consider these type of problems is the Faraday cage phenomenon for discrete charges as discussed by J. Korevaar and his colleagues.

Study of sunless tanning formulas using molted snake skin as an alternative membrane model

Sunless tanning formulas have become increasingly popular in recent years for their ability to give people convincing tans without the dangers of skin cancer. Most sunless tanners currently on the market contain dihydroxyacetone (DHA), a keto sugar with three carbons. The temporary pigment provided by these formulasis designed to resemble a UV-induced tan. This study evaluated the effectiveness of carbomer gels and cold process self emulsifying bases on skin pigmentation, using different concentrations of a chemical system composed of DHA and N-acetyl tyrosine, which are found in moulted snake skins and their effectiveness was tested by Mexameter (R) MX 18. Eight different sunless tanning formulas were developed, four of which were gels and four of which were emulsions (base, base plus 4.0%, 5.0% and 6.0% (w/w) of a system of DHA and N-acetyl tyrosine). Tests to determine the extent of artificial tanning were done by applying 30 mg cm(-2) of each formula onto standard sizes of moulted snake skin (2.0 cm x 3.0 cm). A Mexameter (R) MX 18 was used to evaluate the extent of coloration in the moulted snake skin at T(0) (before the application) and after 24, 48, 72, 168, 192 and 216 h. The moulted snake skins can be used as an alternative membrane model for in vitro sunless tanning efficacy tests due to their similarity to the human stratum corneum. The DHA concentration was found to influence the initiation of the pigmentation in both sunless tanning systems (emulsion and gel) as well as the time required to increases by a given amount on the tanning index. In the emulsion system, the DHA concentration also influenced the final value on the tanning index. The type of system (emulsion or gel) has no influence on the final value in the tanning index after 216 h for samples with the same DHA concentration.

Tea consumption and incidence of type 2 diabetes in Europe: the EPIC-InterAct case-cohort study.

BACKGROUND In previous meta-analyses, tea consumption has been associated with lower incidence of type 2 diabetes. It is unclear, however, if tea is associated inversely over the entire range of intake. Therefore, we investigated the association between tea consumption and incidence of type 2 diabetes in a European population. METHODOLOGY/PRINCIPAL FINDINGS The EPIC-InterAct case-cohort study was conducted in 26 centers in 8 European countries and consists of a total of 12,403 incident type 2 diabetes cases and a stratified subcohort of 16,835 individuals from a total cohort of 340,234 participants with 3.99 million person-years of follow-up. Country-specific Hazard Ratios (HR) for incidence of type 2 diabetes were obtained after adjustment for lifestyle and dietary factors using a Cox regression adapted for a case-cohort design. Subsequently, country-specific HR were combined using a random effects meta-analysis. Tea consumption was studied as categorical variable (0, >0-<1, 1-<4, ≥ 4 cups/day). The dose-response of the association was further explored by restricted cubic spline regression. Country specific medians of tea consumption ranged from 0 cups/day in Spain to 4 cups/day in United Kingdom. Tea consumption was associated inversely with incidence of type 2 diabetes; the HR was 0.84 [95%CI 0.71, 1.00] when participants who drank ≥ 4 cups of tea per day were compared with non-drinkers (p(linear trend) = 0.04). Incidence of type 2 diabetes already tended to be lower with tea consumption of 1-<4 cups/day (HR = 0.93 [95%CI 0.81, 1.05]). Spline regression did not suggest a non-linear association (p(non-linearity) = 0.20). CONCLUSIONS/SIGNIFICANCE A linear inverse association was observed between tea consumption and incidence of type 2 diabetes. People who drink at least 4 cups of tea per day may have a 16% lower risk of developing type 2 diabetes than non-tea drinkers.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Composition and structural formulas of ODP Site 200-1224 Eocene ferrobasalt minerals

The ~46-m.y.-old igneous basement cored during Leg 200 in the North Pacific represents one of the few cross sections of Pacific oceanic crust with a total penetration into basalt of >100 m. The rocks, emplaced during the Eocene at a fast-spreading rate (~14 cm/yr; full rate) are strongly differentiated tholeiitic basalts (ferrobasalts) with 7-4.5 wt% MgO, relatively high TiO2 (2-3.5 wt%), and total iron as Fe2O3 (9.1-16.8 wt%). The differentiated character of these lavas is related to unusually large amounts of crystallization differentiation of plagioclase, clinopyroxene, and olivine. The lithostratigraphy of the basement (cored to ~170 meters below seafloor) is divided into three units. The deepest unit (lithologic Unit 3), is a succession of lava flows of no more that a few meters thickness each. The intermediate unit (lithologic Unit 2) is represented by intermixed thin flows and pillows, whereas the shallowest unit (lithologic Unit 1), comprises two massive flows. The rocks range from aphyric to sparsely clinopyroxene-plagioclase-phyric (phenocryst content = <3 vol%) and from holocrystalline to hypohyaline. Chilled margins of pillow fragments show holohyaline to sparsely vitrophyric textures. Site 1224 oxide minerals present a type of alteration not previously seen, where titanomagnetite is only partially destroyed and the pure magnetite component is partially removed from the mineral, leaving, in the most extreme case, a nearly pure ulvöspinel residuum. As a result of this dissolution, iron, mainly in the oxidized state, is added to the circulating solvent fluids. This means that a considerable metal source can result from low-temperature reactions throughout the upper ocean crust. The coarsest-grained lithologic Unit 1 rocks have interstitial myrmekitic intergrowths of quartz and sodic plagioclase (~An12), roughly similar in mineralogy and bulk composition to tonalite/trondhjemite veinlets in abyssal gabbros from the southwest Indian Ocean and Hess Deep, eastern equatorial Pacific. Based on idiomorphic relationships and projections into the simplified Q-Ab-Or-H2O granite ternary system, the myrmekitic intergrowths formed at the same time as, or just after, the oxide minerals coprecipitated and at low water vapor pressure (~0.5 kbar). Their compositions correspond to SiO2-oligoclase intergrowths that are considerably less potassic than dacitic glasses that erupt, although rarely, along the East Pacific Rise or that have been produced experimentally by partial melting of gabbro. Based on the crystallization history and comparison to experimental data, the original interstitial siliceous liquids resulted from late-stage immiscible separation of siliceous and iron-rich liquids. The rare andesitic lavas found along the East Pacific Rise may be hybrid rocks formed by mixing of these immiscible siliceous melts with basaltic magma.

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros.

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.

Computing with noise: phase transitions in Boolean formulas

Computing circuits composed of noisy logical gates and their ability to represent arbitrary Boolean functions with a given level of error are investigated within a statistical mechanics setting. Existing bounds on their performance are straightforwardly retrieved, generalized, and identified as the corresponding typical-case phase transitions. Results on error rates, function depth, and sensitivity, and their dependence on the gate-type and noise model used are also obtained.

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas

2010 Mathematics Subject Classification: Primary 65D30, 32A35, Secondary 41A55.