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.

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.

Orthogonal polynomials on the unit circle and chain sequences

Szego{double acute} has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1,1] by the transformation 2x=z+z-1. In the 80's and 90's Delsarte and Genin showed that real orthogonal polynomials on the unit circle can be mapped to symmetric orthogonal polynomials on the interval [-1,1] using the transformation 2x=z1/2+z-1/2. We extend the results of Delsarte and Genin to all orthogonal polynomials on the unit circle. The transformation maps to functions on [-1,1] that can be seen as extensions of symmetric orthogonal polynomials on [-1,1] satisfying a three-term recurrence formula with real coefficients {cn} and {dn}, where {dn} is also a positive chain sequence. Via the results established, we obtain a characterization for a point w(|w|=1) to be a pure point of the measure involved. We also give a characterization for orthogonal polynomials on the unit circle in terms of the two sequences {cn} and {dn}. © 2013 Elsevier Inc.

Interlacing of zeros of orthogonal polynomials under modification of the measure

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (x), where c and d are outside (a, b) We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. © 2013 Elsevier Inc.

Influence of the sodium content on the reactivity of carbon anodes

Spent anodes, denominated butts in the aluminum industry, are recycled as part of the raw material used to produce new anodes. The fragmentation of the butt generates some sodium-rich powder, which is captured and included in the recycled material. This paper evaluates the influence of sodium content on anode reactivity. Six formulations with 0 to 25% butt powder were used. An average increase of 48 ppm of sodium from one to another formulation caused average increments of 3.38 and 2.72% for air and CO2 reactivity, respectively. The quality-related figures varied from 1.34 to 1.12 for CO2 and from 1.10 to 0.62 for air, showing quality loss in higher sodium content and higher impact on air reactivity. The Fischer formula predicted a carbon specific consumption of - 48.47 kg.t-1 Al for baked carbon anodes with 127 ppm to 367 ppm of sodium content, showing that the sodium can cause relevant carbon losses and increase costs of the aluminum production.

Serological cross-reactivity of Trypanosoma cruzi, Ehrlichia canis, Toxoplasma gondii, Neospora caninum and Babesia canis to Leishmania infantum chagasi tests in dogs

Introduction: The aim of this study was to evaluate the serological cross-reactivity between Leishmania sp. and other canine pathogens. Methods: Positive serum samples for Ehrlichia canis, Babesia canis, Toxoplasma gondii, Neospora caninum and Trypanosoma cruzi were tested using three serological methods enzyme linked immunosorbent assay (ELISA), indirect immunofluorescent antibody test (IFAT) and Kalazar Detect™, for canine visceral leishmaniasis. Results: Of the 57 dog samples tested, 24 (42.1%) tested positive using one of the three serological methods: 10/57 (17.5%) for ELISA, 11/57 (19.3%) for IFAT and 3/57 (5.3%) for Kalazar Detect™. Conclusions: Our results demonstrated that the presence of other infectious agents may lead to cross-reactivity on leishmaniasis serological tests.

Determination of reactivity rates of silicate particle-size fractions

The efficiency of sources used for soil acidity correction depends on reactivity rate (RR) and neutralization power (NP), indicated by effective calcium carbonate (ECC). Few studies establish relative efficiency of reactivity (RER) for silicate particle-size fractions, therefore, the RER applied for lime are used. This study aimed to evaluate the reactivity of silicate materials affected by particle size throughout incubation periods in comparison to lime, and to calculate the RER for silicate particle-size fractions. Six correction sources were evaluated: three slags from distinct origins, dolomitic and calcitic lime separated into four particle-size fractions (2, 0.84, 0.30 and <0.30-mm sieves), and wollastonite, as an additional treatment. The treatments were applied to three soils with different texture classes. The dose of neutralizing material (calcium and magnesium oxides) was applied at equal quantities, and the only variation was the particle-size material. After a 90-day incubation period, the RER was calculated for each particle-size fraction, as well as the RR and ECC of each source. The neutralization of soil acidity of the same particle-size fraction for different sources showed distinct solubility and a distinct reaction between silicates and lime. The RER for slag were higher than the limits established by Brazilian legislation, indicating that the method used for limes should not be used for the slags studied here.

Vitamin D Induces Increased Systolic Arterial Pressure via Vascular Reactivity and Mechanical Properties

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

Reactivity of IgE to the allergen hyaluronidase from Polybia paulista (Hymenoptera, Vespidae) venom

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

Zeros of classical orthogonal polynomials of a discrete variable

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stieltjes functions and discrete classical orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

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

Sieved para-orthogonal polynomials on the unit circle

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

New method to assess the pozzolanic reactivity of mineral admixtures by means of pH and electrical conductivity measurements in lime:pozzolan suspensions

A very simple method based on electrical conductivity and pH measurements was proposed for assessing reactivity of pozzolans. Calcium hydroxide: pozzolan water suspensions were monitored by means of measurements of electrical conductivity and pH values. In these suspensions, Ca(OH)(2) in solid state was initially present, being them, thus, saturated in this reagent. Three testing temperatures were selected (40, 50 and 60 degrees C). In the experiments carried out, calcium hydroxide was suspended in deionized water for yielding a lime saturated suspension. The addition of siliceous pozzolan (two types of rice husk ash RHA and two types of densified silica fume DSF were tested) to the saturated lime suspension can produce the unsaturation of the system, depending on the testing time, testing temperature and reactivity of pozzolan. When unsaturation was reached, the loss of electrical conductivity was higher than 30% and the variation of pH was higher than 0.15 units. These threshold values were selected for characterizing the reactivity of pozzolans by means of a proposed template, classifying the pozzolan in three different reactivity levels.