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.

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.

Characterization of a glucose- and solvent-tolerant extracellular tannase from Aspergillus phoenicis

Tannases have attracted wider attention because of their biotechnological potential, especially enzymes from filamentous fungi and other microorganisms. However, the biodiversity of these microorganisms has been poorly explored, and few strains were identified for tannase production and characterization. This article describes the production, purification and characterization of a glucose- and solvent-tolerant extracellular tannase from Aspergillus phoenicis. High enzymatic levels were obtained in Khanna medium containing tannic acid up to 72 h at 30 °C under 100 rpm. The purified enzyme with 65% of carbohydrate content had an apparent native molecular mass of 218 kDa with subunits of 120 kDa and 93 kDa and was stable at 50 °C for 1 h. Optima of temperature and pH were 60 °C and 5.0-6.5, respectively. The enzyme was not affected significantly by most ions, detergents and organic solvents. While glucose did not affect the tannase activity, the addition of a high concentration of gallic acid did. The Km values were 1.7 mM (tannic acid), 14.3 mM (methyl-gallate) and 0.6 mM (propyl-gallate). The enzyme was able to catalyze the transesterification reaction to produce propyl-gallate. All biochemical properties suggest the biotechnological potential of the glucose- and solvent-tolerant tannase from A. phoenicis. © 2012 Elsevier B.V. All rights reserved.

Effects of dentin dry/moist condition on the immediate adhesive performance of different solvent-based etch-and-rinse adhesivesystems

Purpose: The purpose of this research was to analyze and measure, under optical microscopy, the hybrid layer thickness and resin tags length, as well as the microtensile bond strength of two conventional adhesive systems when applied to dry and moist dentinal substrate. Methods: Thirty-two extracted human molars were randomly distributed into four groups according to the adhesive systems (XP Bond and Prime&Bond 2.1) and moisture condition (dry and moist). In Groups I and II, XP adhesive system was applied on dry and moist dentin, respectively; while Groups III and IV received PB adhesive system, in the same way as was done in Groups I and II, respectively. After adhesive and restorative procedures, all specimens were sectioned along their long axes; one hemi-tooth sample was subjected to the microtensile bond strength test while the other was decalcified and serially sectioned into six micron thick slices and sequentially mounted on glass slides. These sections were stained by the Brown and Brenn method for posterior analysis and measurement of the hybrid layer and resin tags under a light microscope with a micrometric ocular 40/075. Results: Data were analyzed using two-way ANOVA and Tukey's test (α=0.05). For the variable hybrid layer thickness, XP showed no significant differences between dry and moist dentin (5.2 μm and 5.5 μm, respectively), but for PB, hybrid layer was significantly thicker for moist (4.0 μm) than for dry dentin (3.0 μm). For the variable resin tags length XP showed 17.9 μm length for dry dentin and 20.8 μm for moist dentin; PB 11.7 μm for dry and 12.69 μm for moist dentin;there was no significant differences between them, independent of the moisture condition. For the variable microtensile bond strength, XP showed 38.0 MPa for dry dentin and 44.5 MPa for moist dentin; and PB showed 22.7 MPa for dry dentin and 20.8 MPa for dry dentin no significant difference was observed between moist and dry dentin for XP (p=0.2) and PB (p=0.7), but XP was presented significantly higher bond strength values than PB in both moisture conditions (p=0.003 for dry and p=0.002 for moist). Conclusion: The two-step butanol-based etch-and-rinse adhesive XP Bond presented a superior behavior with regard to the hybrid layer thickness, length of resin tags and bond strength to dry and moist dentin substrates when compared with two-step acetone-based adhesive system Prime&Bond2.1. © 2013 Elsevier Ltd.

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.

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.

Influence of solvent on the morphology and photocatalytic properties of ZnS decorated CeO2 nanoparticles

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Vegetable Oil Derived Solvent, and Catalyst Free Click Chemistry'' Thermoplastic Polytriazoles

Azide-alkyne Huisgen click chemistry provides new synthetic routes for making thermoplastic polytriazole polymers-without solvent or catalyst. This method was used to polymerize three diester dialkyne monomers with a lipid derived 18 carbon diazide to produce a series of polymers (labelled C18C18, C18C9, and C18C4 based on monomer chain lengths) free of residual solvent and catalyst. Three diester dialkyne monomers were synthesized with ester chain lengths of 4, 9, and 18 carbons from renewable sources. Significant differences in thermal and mechanical properties were observed between C18C9 and the two other polymers. C18C9 presented a lower melting temperature, higher elongation at break, and reduced Young's modulus compared to C18C4 and C18C18. This was due to the odd-even effect induced by the number of carbon atoms in the monomers which resulted in orientation of the ester linkages of C18C9 in the same direction, thereby reducing hydrogen bonding. The thermoplastic polytriazoles presented are novel polymers derived from vegetable oil with favourable mechanical and thermal properties suitable for a large range of applications where no residual solvent or catalyst can be tolerated. Their added potential biocompatibility and biodegradability make them ideal for applications in the medical and pharmaceutical industries.

Zeros of classical orthogonal polynomials of a discrete variable

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A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula

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Stieltjes functions and discrete classical orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

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

Sieved para-orthogonal polynomials on the unit circle

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Evaluation of solvent effect on the extraction of phenolic compounds and antioxidant capacities from the berries: application of principal component analysis

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