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.

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

∗ Partially supported by Grant MM-428/94 of MESC.

Para-orthogonal polynomials from constant Verblunsky coefficients

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Szegö polynomials: quadrature rules on the unit circle and on [-1, 1]

We consider some of the relations that exist between real Szegö polynomials and certain para-orthogonal polynomials defined on the unit circle, which are again related to certain orthogonal polynomials on [-1, 1] through the transformation x = (z1/2+z1/2)/2. Using these relations we study the interpolatory quadrature rule based on the zeros of polynomials which are linear combinations of the orthogonal polynomials on [-1, 1]. In the case of any symmetric quadrature rule on [-1, 1], its associated quadrature rule on the unit circle is also given.

The unit ball of the complex P(3H)

Let H be a two-dimensional complex Hilbert space and P(3H) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, P(3H), from which we deduce that the unit sphere of P(3H) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of P(3H) remains extreme as considered as an element of L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H) and give a characterization of its smooth points.

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.

On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball

2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32

Effect of the Edge Type and Strain on the Structural, Electronic and Magnetic Properties of the BNRs

We present the effect of edge structures on the edge energy and stress of BN nanoribbons. Ab initio density functional calculations show that the armchair edge is lower in energy than the zigzag edge by 0.43 eV/angstrom. Both types of the edges are under the compressive stress. The zigzag edges are mechanically more stable than the armchair edges. Based on the calculated edge energies, the equilibrium shape of the BN flakes are found to be regular hexagonal, and dominated by the armchair edges. The zigzag ribbons are found to be half-metallic, whereas the armchair ribbons are semiconducting.

Impact of wide bandgap p-type nc-Si on the performance of a-Si solar cells

This paper reports the impact of a wide bandgap p-type hydrogenated nanocrystalline silicon (nc-Si:H) on the performances of hydrogenated amorphous silicon (a-Si:H) based solar cells. The player consists of nanometer-sized Si crystallites and has a wide effective bandgap determined mainly by the quantum size-confinement effect (QSE). By incorporation of this p-layer into the devices we have obtained high performances of a-Si:H top solar cells with V-infinity=1.045 V and FF=70.3 %, and much improved mid and bottom a-SiGe:H cells, deposited on stainless steel (SS) substrate. The effects of the band-edge mismatch at the p/i-interface on the I-V characteristics of the solar cells arc discussed on the bases of the density-functional approach and the AMPS model.

Impact of wide bandgap p-type nc-Si on the performance of a-Si solar cells

This paper reports the impact of a wide bandgap p-type hydrogenated nanocrystalline silicon (nc-Si:H) on the performances of hydrogenated amorphous silicon (a-Si:H) based solar cells. The player consists of nanometer-sized Si crystallites and has a wide effective bandgap determined mainly by the quantum size-confinement effect (QSE). By incorporation of this p-layer into the devices we have obtained high performances of a-Si:H top solar cells with V-infinity=1.045 V and FF=70.3 %, and much improved mid and bottom a-SiGe:H cells, deposited on stainless steel (SS) substrate. The effects of the band-edge mismatch at the p/i-interface on the I-V characteristics of the solar cells arc discussed on the bases of the density-functional approach and the AMPS model.

Feature tracking on the unit-sphere

Techniques used in a previous study of the objective identification and tracking of meteorological features in model data are extended to the unit sphere. An alternative feature detection scheme is described based on cubic interpolation for the sphere and local maximization. The extension of the tracking technique, used in the previous study, to the unit sphere is described. An example of the application of these techniques to a global relative vorticity field from a model integration are presented and discussed.

Effect of cultivar type and ripening on the polyphenol content of date palm fruit

Date palm (Pheonix dactylifera) fruit contains an array of polyphenols, although how these levels alter with cultivar type and fruit ripening is unclear. Utilizing HPLC and LC-ESI-MS/MS, this study define and quantify an array of hydroxybenzoic acids, hydroxycinnamic acids, and flavonoids in three common cultivars of dates (Ajwa, Barni, and Khalas) at the main ripening stages (kimri, khalal, rutab, and tamr). Polyphenols were at highest concentration at earlier stages of ripening, with concentrations reducing with ripening. The khalal stage of the Ajwa cultivar contained significantly higher (P < 0.001) levels of polyphenols than measured in the Barni and Khalas dates at the same degree of ripening. Furthermore, the Ajwa cultivar was the only one to contain significant quantities of anthocyanidins, in particular at the khalal stage. These data suggest dates are a significant source of polyphenols, especially if the earlier edible ripening stages are consumed or utilized as food ingredients.

SYMMETRICAL ORTHOGONAL POLYNOMIALS AND THE ASSOCIATED ORTHOGONAL L-POLYNOMIALS

We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx(2))(1 - x(2))(-1/2), k > 0.