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.

Formation of titania nanotube arrays by anodisation: DOE approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The use of instantaneous phase for improving sparse arrays images

Sparse arrays have pitch larger than half-wavelength (lambda/2) and there is a reduced number of elements in comparison with a full-populated array. Consequently, there is a reduction in cost, data acquisition and processing. However, conventional beamforming techniques result in large side and grating lobes, and consequently in image artifacts. In this work the instantaneous phase of the signals is used in a beamforming technique instead of the instantaneous amplitudes to improve images obtained from sparse arrays configurations. A threshold based on a statistical analysis and the number of signals used for imaging is applied to each pixel, in order to determine if that pixel is related to a defect or not. Three sets of data are used to evaluate the technique, considering medical and non-destructive testing: a simulated point spread function, a medical phantom and an aluminum plate with 2 lambda-, 7 lambda- and lambda-pitch, respectively. The conventional amplitude image is superposed by the image improved by the instantaneous phase, increasing the reflectors detectability and reducing artifacts for all cases, as well as dead zone for the tested plate.

Large-Area Plasmonic Substrate of Silver-Coated Iron Oxide Nanorod Arrays for Plasmon-Enhanced Spectroscopy

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)

Model updating of the non-linear vibrating structures through Volterra series and proper orthogonal decomposition

Classical procedures for model updating in non-linear mechanical systems based on vibration data can fail because the common linear metrics are not sensitive for non-linear behavior caused by gaps, backlash, bolts, joints, materials, etc. Several strategies were proposed in the literature in order to allow a correct representative model of non-linear structures. The present paper evaluates the performance of two approaches based on different objective functions. The first one is a time domain methodology based on the proper orthogonal decomposition constructed from the output time histories. The second approach uses objective functions with multiples convolutions described by the first and second order discrete-time Volterra kernels. In order to discuss the results, a benchmark of a clamped-clamped beam with an pre-applied static load is simulated and updated using proper orthogonal decomposition and Volterra Series. The comparisons and discussions of the results show the practical applicability and drawbacks of both approaches.

Inspeção de materiais compósitos utilizando ondas acústicas guiadas

Pós-graduação em Engenharia Elétrica - FEIS

Para-orthogonal polynomials from constant Verblunsky coefficients

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Highly Sensitive Neurotransmitters Analysis at Platinum-Ultramicroelectrodes Arrays

An easy way to determine norepinephrine (NE) in biological fluid using a platinum ultramicroelectrode array (Pt-UMEAs) is described. Issues related to UME electrode surface treatment and characterizations are also addressed. At optimized experimental conditions the dynamic concentration range was 1.0 to 10.0 mu mol?L-1 with a detection limit of 40.5 nmol?L-1. The repeatability of current responses for injections of 5 mu mol?L-1 NE was evaluated to be 4.0?% (n=10). This approach obtained excellent sensitivity, a reliable calibration profile and stable electrochemical response for norepinephrine detection. The content of NE in urine samples without any preconcentration, purification, or pretreatment step, was successfully analyzed by the standard addition method using the Pt-UMEAs.