Orthogonal polynomials on the unit circle and their derivatives

We characterize the sequences of orthogonal polynomials on the unit circle whose derivatives are also orthogonal polynomials on the unit circle. Some relations for the sequences of derivatives of orthogonal polynomials are provided. Finally, we pose some problems about orthogonality-preserving maps and differential equations for orthogonal polynomials on the unit circle.     

Quadratic decomposition of symmetric semi-classical polynomial sequences of even class: an example from the case s = 2

In the present work, we deal with the quadratic decomposition of symmetric semi-classical polynomial sequences of even class. An example from class 2 is settled. We give an integral representation of the considered symmetric form.     

The connection between self‐associated two‐dimensional vector functionals and third degree forms

We deal with the 2‐orthogonal, 2‐symmetric self‐associated sequence (2‐orthogonal Tchebychev polynomials) and its cubic components. We prove that all the forms (linear functionals) arising are third degree forms. Therefore, an introduction to third degree forms is provided. We look for the connection between these components which are 2‐orthogonal with respect to the functional vector ^t(w₀{^μ},w₁ ^μ) and orthogonal sequences with respect to w₀ ^μ, μ=0,1,2. Associated forms w₀ ^μ)¹) and their inverse w₀ ^μ)^-1 are also studied through the symmetrized w₀}₀ ^μ, μ=0,1,2. Further, we give integral representations for some of these forms. This revised version was published online in June 2006 with corrections to the Cover Date.     

Effect of CeO2 buffer layer thickness on the structures and properties of YBCO coated conductors

Biaxially textured YBa₂Cu₃O_7−x (YBCO) films were grown on inclined-substrate-deposited (ISD) MgO-textured metal substrates by pulsed laser deposition. CeO₂ was deposited as a buffer layer prior to YBCO growth. CeO₂ layers of different thickness were prepared to evaluate the thickness dependence of the YBCO films. The biaxial alignment features of the films were examined by X-ray diffraction 2θ-scans, pole-figure, ?-scans and rocking curves of Ω angles. The significant influence of the CeO₂ thickness on the structure and properties of the YBCO films were demonstrated and the optimal thickness was found to be about 10 nm. High values of T_c = 91 K and J_c = 5.5 × 10⁵ A/cm² were obtained on YBCO films with optimal CeO₂ thickness at 77 K in zero field. The possible mechanisms responsible for the dependence of the structure and the properties of the YBCO films on the thickness of the CeO₂ buffer layers are discussed.     

Le serie lineari speciali sulle curve trigonali

Sunto Introdotto, per le curve trigonali di dato genere. un altro carattere invariante per trasformazioni birazionali della curva (carattere che qui vien chiamatola specie della curva stessa), si procede alla determinazione delle serie lineari speciali complete su ogni curva trigonale di generep e di speciem, precisandone la dimensione. In fine. come applicazione. si determinano le curve trigonali. di dato genere e di data specie, appartenenti ad unS _r e aventi il minimo ordine. Ricevuta in Redazione nel gennaio del 1945.     

The symmetric D ω -semi-classical orthogonal polynomials of class one

We give the system of Laguerre–Freud equations associated with the D _ω -semi-classical functionals of class one, where D _ω is the divided difference operator. This system is solved in the symmetric case. There are essentially two canonical cases. The corresponding integral representations are given.     

Room temperature 2 μm Tm,Ho : YLF laser

We present the results obtained with a Tm,Ho : YLF crystal, grown in the new crystals growth facility realized in the Dipartimento di Fisica of the Università di Pisa. The 2 μm laser performance has been studied for three different pump sources, a Ti : Sapphire, a diode—tuned at 792.7 nm—and a Co : MgF₂ laser, tuned at 1.682 μm.