SZEGO and PARA-ORTHOGONAL POLYNOMIALS on THE REAL LINE: ZEROS and CANONICAL SPECTRAL TRANSFORMATIONS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Szego{double acute} and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations

We study polynomials which satisfy the same recurrence relation as the Szego{double acute} polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szego{double acute} polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szego{double acute} polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szego{double acute} polynomials and polynomials arising from canonical spectral transformations are obtained. © 2012 American Mathematical Society.

On the Apterous Line of the Termite Velocitermes heteropterus (Isoptera: Termitidae): Developmental Pathways and Cellulose Digestion

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

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.

On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line

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

Real orthogonal polynomials in frequency analysis

We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel numbers of polynomials orthogonal on the real line. This leads to a simple and fast algorithm for the estimation of frequencies. We also provide a new method, faster than the Levinson algorithm, for the determination of the reflection coefficients of the corresponding real Szego polynomials from the given moments.

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Polinômios ortogonais de Laurent na reta real e no círculo unitário

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On perturbed Szego recurrences

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Another connection between orthogonal polynomials and L-orthogonal polynomials

We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. Examples are given to illustrate the main contribution in this paper. (c) 2006 Elsevier B.V. All rights reserved.

Behavior of overhead transmission line parameters on the presence of ground-wires

Initially this paper shows the ground wire reduction process for generic multiphase transmission lines and after, the ground wire reduction process for a specilic 440-kV three-phase overhead transmission line. Following this, the influence of the ground wire reduction process considering two situations is shown: first, considering frequency independence and second, when these parameters are considered as frequency dependent. This paper presents analytical results for generic multiphase transmission lines. For a specific 440-kV three-phase overhead transmission line, analytical and graphic results are shown considering real data for every frequency between 10 Hz and 1 MHz.

APPLICATION of THE HAZARD ANALYSIS and CRITICAL CONTROL POINT (HACCP) SYSTEM on THE MUSHROOM PROCESSING LINE FOR FRESH CONSUMPTION

The Hazard Analysis and Critical Control Point (HACCP) is a preventive system that intends to guarantee the safety and harmlessness of food. It improves the quality of products as it eliminates possible defects during the process, and saves costs by practically eliminating final product inspection. This work describes the typical hazards encountered on the mushroom processing line for fresh consumption. Throughout the process, only the reception stage of mushrooms has been considered a critical control point (CCP). The main hazards at this stage were: the presence of unauthorised phytosanitary products; larger doses of such products than those permitted; the presence of pathogenic bacteria or thermo-stable enterotoxins. Putting into practice such knowledge would provide any industry that processes mushrooms for fresh consumption with a self-control HACCP-based system for its own productions.

The Effect of a Supragingival Plaque-Control Regimen on the Subgingival Microbiota in Smokers and Never-Smokers: Evaluation by Real-Time Polymerase Chain Reaction

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the relationship between a 2 x 2 matrix and second-order scalar spectral problems for integrable equations

A simple proof is given that a 2 x 2 matrix scheme for an inverse scattering transform method for integrable equations can be converted into the standard form of the second-order scalar spectral problem associated with the same equations. Simple formulae relating these two kinds of representation of integrable equations are established.

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.