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.

A hybrid image restoration algorithm based on Projections onto Convex Sets and Harmony Search

Image restoration is a research field that attempts to recover a blurred and noisy image. Since it can be modeled as a linear system, we propose in this paper to use the meta-heuristics optimization algorithm Harmony Search (HS) to find out near-optimal solutions in a Projections Onto Convex Sets-based formulation to solve this problem. The experiments using HS and four of its variants have shown that we can obtain near-optimal and faster restored images than other evolutionary optimization approach. © 2013 IEEE.

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.

Demographic projections for Latin American countries

Includes bibliography

Situación demográfica de América Latina evaluada en 1983: estimaciones para 1960-1980 y proyecciones para 1980-2025 = Demographic situation of Latin America as evaluated in 1983: estimates for 1960-1980 and projections for 1980-2025

Incluye Bibliografía

Algunas estimaciones y proyecciones de población para el Caribe angloparlante = Some population estimates and projections for the English-speaking Caribbean

Incluye Bibliografía

Reunión Microcomputación y Sistemas de Información Documentales en América Latina: Problemas, Experiencias y Proyecciones = Meeting Microcomputers and Bibliographic Information Systems in Latin America: Problems, Experiences and Projections

Contiene objetivos, conclusiones y recomendaciones de la Reunion sobre Microcomputacion y Sistemas de Informacion Documentales en America Latina: Problemas, Experiencias y Proyecciones. Incluye ademas, lista de participantes y de siglas de instituciones, redes de informacion y paquetes de programas; resumenes de trabajos presentados; caracteristicas de paquetes de programas revisados y lista de documentos presentados.

Desarrollo económico: una evaluación y proyecciones 1985-1995 = Economic development: an appraisal, and projections 1985-1995

Incluye Bibliografía

Report on ECLAC/CELADE Regional Training Seminar on Population Projections

Informe del Seminario que tuvo por objetivo principal fortalecer las capacidades de los estadisticos y planificadores de los gobiernos para llevar a cabo proyecciones de poblacion.

Population projections for eight Caribbean countries 1980-2015

Includes bibliography

Preliminary report on population projections (1980-2015) for nine Caribbean countries

Includes bibliography

Approaches and methodologies used in the preparation of economic projections in Caribbean countries: difficulties and suggestions for improvement

Includes bibliography

Export commodity price projections: a study of autoregressive-moving average projections methods: preliminary version

Includes bibliography