Companion orthogonal polynomials: some applications

In this paper the recurrence relations of symmetric orthogonal polynomials whose measures are related to each other in a certain way are considered. Many of the relations satisfied by the coefficients of the recurrence relations are exposed. The results are applied to obtain, for example, information regarding certain Sobolev orthogonal polynomials and regarding the measures of certain orthogonal polynomial sequences with twin periodic recurrence coefficients. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

A note on the controllability for the wave equation in nonsmooth plane domains

We study exact boundary controllability for a two-dimensional wave equation in a region which is an angular sector of a circle or an angular sector of an annular region. The control, of Neumann type, acts on the curved part of the boundary, while in the straight part we impose homogeneous Dirichlet boundary condition. The initial state has finite energy and the control is square integrable. (c) 2005 Elsevier B.V. All rights reserved.

Effect of niobia on the crystal structure and dielectric characteristics of Pb(Zr0.45Ti0.55)O-3 prepared from polymeric precursor

The influence of niobia addition on the phase formation and dielectric properties of Pb(Zr0.45Ti0.55)O-3 powder prepared from polymeric precursor was analyzed. The weight fraction and unit-cell volume of the tetragonal phase decreased, and the mass fraction of the rhombohedral phase increased, with increasing niobia concentration. The rhombohedral unit-cell volume increased up to 5 mol% of added Nb and then decreased. Small amounts of pyrochlore and tetragonal zirconia phases were observed in PZT powder with more than 10 mol% Nb. These results were interpreted as an indication that the Nb ion was substituted for the zirconium ion in the tetragonal phase. For sintered PZT samples at 1100 degrees C, no free-zirconia phase was observed. The dielectric constant increased with the niobia addition up to 5 mol% and decreased for higher concentrations. The Curie temperature decreased with niobia addition up to 10 mol% before the formation of pyrochlore phase. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Companion orthogonal polynomials

We give some properties relating the recurrence relations of orthogonal polynomials associated with any two symmetric distributions d phi(1)(x) and d phi(2)(x) such that d phi(2)(x) = (I + kx(2))d phi(1)(x). AS applications of these properties, recurrence relations for many interesting systems of orthogonal polynomials are obtained.

Geometrical Lagrangian for a supersymmetric Yang-Mills theory on the group manifold

Perhaps one of the main features of Einstein's General Theory of Relativity is that spacetime is not flat itself but curved. Nowadays, however, many of the unifying theories like superstrings on even alternative gravity theories such as teleparalell geometric theories assume flat spacetime for their calculations. This article, an extended account of an earlier author's contribution, it is assumed a curved group manifold as a geometrical background from which a Lagrangian for a supersymmetric N = 2, d = 5 Yang-Mills - SYM, N = 2, d = 5 - is built up. The spacetime is a hypersurface embedded in this geometrical scenario, and the geometrical action here obtained can be readily coupled to the five-dimensional supergravity action. The essential idea that underlies this work has its roots in the Einstein-Cartan formulation of gravity and in the 'group manifold approach to gravity and supergravity theories'. The group SYM, N = 2, d = 5, turns out to be the direct product of supergravity and a general gauge group g: G = g circle times <(SU(2, 2/1))over bar>.

Influence of the network former on the properties of magnesium spinels

Undoped and/or doped with 1 mol% of Co2+ Mg2TiO4 and Mg2SnO4 powders were synthesized by the polymeric precursor method. The influence of the network former (Sn4+ or Ti4+) on the thermal, structural and optical properties was investigated. The recorded mass losses are due to the escape of water and adsorbed gases and to the elimination of the organic matter. Mg2TiO4 crystallizes at lower temperatures and also presents more ordered structure with a smaller unit call and having more intense green color than Mg2SnO4 has.

Zeros of orthogonal polynomials generated by canonical perturbations of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

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

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

First principles calculations on the origin of violet-blue and green light photoluminescence emission in SrZrO3 and SrTiO3 perovskites

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

On the two point Padé table for a distribution

Some additional recurrence relations for the denominator polynomials of two point Padé approximants are derived. An example in which the coefficients of one of the two series, from which the Padé approximants are derived, are moments of a distribution is considered. For this example, properties of the denominator polynomials, and their zeros, are described.

Effectiveness of six different disinfectants on removing five microbial species and effects on the topographic characteristics of acrylic resin

Purpose: The aim of this study was to evaluate the effectiveness of disinfectant solutions (1% sodium hypochlorite, 2% chlorhexidine digluconate, 2% glutaraldehyde, 100% vinegar, tabs of sodium perborate-based denture cleanser, and 3.8% sodium perborate) in the disinfection of acrylic resin specimens (n = 10/group) contaminated in vitro by Candida albicans, Streptococcus mutans, S. aureus, Escherichia coli, or Bacillus subtilis as measured by residual colony-forming unit (CFU). In a separate experiment, acrylic resin was treated with disinfectants to monitor potential effects on surface roughness, Ra (μm), which might facilitate microbial adherence. Materials and Methods: Three hundred fifty acrylic resin specimens contaminated in vitro with 1×10 6 cells/ml suspensions of standard strains of the cited microorganisms were immersed in the disinfectants for 10 minutes; the control group was not submitted to any disinfection process. Final counts of microorganisms per ml were performed by plating method for the evaluation of microbial level reduction. Results were compared statistically by ANOVA and Tukey's test (p ≤ 0.05). In a parallel study aiming to evaluate the effect of the tested disinfectant on resin surface, 60 specimens were analyzed in a digital rugosimeter before and after ten cycles of 10-minute immersion in the disinfectants. Measurements of superficial roughness, Ra (μm), were compared statistically by paired t-test (p ≤ 0.05). Results: The results showed that 1% sodium hypochlorite, 2% glutaraldehyde, and 2% chlorhexidine digluconate were most effective against the analyzed microorganisms, followed by 100% vinegar, 3.8% sodium perborate, and tabs of sodium perborate-based denture cleanser. Superficial roughness of the specimens was higher after disinfection cycles with 3.8% sodium perborate (p = 0.03) and lower after the cycles with 2% chlorhexidine digluconate (p = 0.04). Conclusion: Within the limits of this experiment, it could be concluded that 1% sodium hypochlorite, 2% glutaraldehyde, 2% chlorexidine, 100% vinegar, and 3.8% sodium perborate are valid alternatives for the disinfection of acrylic resin. © 2008 by The American College of Prosthodontists.

Effect of radiotherapy on the radiopacity and flexural strength of a composite resin.

The aim of this study was to evaluate the effect of radiotherapy on the radiopacity and flexural strength of composite resin. Forty Z250 composite resin specimens were polymerized using a halogen light-curing unit and divided into 5 groups, in accordance with the radiotherapy dose: G1- without irradiation, G2- 30 Gy, G3- 40 Gy, G4- 50 Gy and GS- 60 Gy Digital images were obtained using a GE 100 X-ray. Radiopacity values were obtained with the Digora digital imaging system and the flexural strength was evaluated with an EMIC universal testing machine. Data were submitted to ANOVA and Tukey 's test. G1 presented the highest radiopacity value, followed by G3, G5, G4 and G2. For flexural strength, G1 presented the lowest value, followed by G2, G5, G3 and G4. Differences were no significant (p>0.05). The commonly used dosage of radiotherapy treatment, did not cause alteration in the radiopacity and flexural strength of resin-based composites.

Zeros of Jacobi-Sobolev orthogonal polynomials following non-coherent pair of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The effects of exposure time on the surface microhardness of three dual-cured dental resin cements

This study evaluated the exposure time of light-curing of the polymers used for cementation on microhardness test in different storage times. The polymers (specifically called resin cements) were RelyX ARC, RelyX U100, and SET. Five specimens of each group were prepared and photo-polymerized with exposure times of 20 s and 180 s, using a LED polymerization unit with wavelength of 440 ~ 480 nm and light output was consistently 1,500 mW/cm2. The Vickers hardness test was performed in a MMT-3 Microhardness Tester. Data were submitted to ANOVA and Tukey's test (α = 0.05). The values of RelyX ARC showed statistically significant difference to groups with light exposure when considering only chemical cure (p < 0.05). The groups with light exposure (20 s and 180 s) showed no significant difference between them (p > 0.05). The RelyX U100 cured only chemically showed statistically significant difference between 48 h and 7 days (p < 0.05). The SET resin cement showed no significant difference to groups without light exposure for all storage times (p > 0.05). The values of hardening of the dual-cured resin cements improved after setting by light and chemical activation demonstrating the importance of light curing. © 2011 by the authors.