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.

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.

Monotonicity of the zeros of orthogonal polynomials through related measures

Relation between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), is well known. We use this relation to study the monotonicity properties of the zeros of generalized orthogonal polynomials. As examples, the Jacobi, Laguerre and Charlier polynomials are considered. (c) 2005 Elsevier B.V. All rights reserved.

On linear combinations of L-orthogonal polynomials associated with distributions belonging to symmetric classes

This paper deals with the classes S-3(omega, beta, b) of strong distribution functions defined on the interval [beta(2)/b, b], 0 < beta < b <= infinity, where 2 omega epsilon Z. The classification is such that the distribution function psi epsilon S-3(omega, beta, b) has a (reciprocal) symmetry, depending on omega, about the point beta. We consider properties of the L-orthogonal polynomials associated with psi epsilon S-3(omega, beta, b). Through linear combination of these polynomials we relate them to the L-orthogonal polynomials associated with some omega epsilon S-3(1/2, beta, b). (c) 2004 Elsevier B.V. All rights reserved.

Another connection between orthogonal polynomials and L-orthogonal polynomials

We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. Examples are given to illustrate the main contribution in this paper. (c) 2006 Elsevier B.V. All rights reserved.

Solvent free esterification reactions using Lewis acids in solid phase catalysis

A clean, efficient and fast method for esterification reactions for sterically (biodiesels) or otherwise inactive (aromatic) precursors was developed, using catalysts supported in a solid phase under solvent free conditions, and whose reactions can be promoted by MW irradiation. (c) 2006 Elsevier B.V. All rights reserved.

Blumenthal's theorem for Laurent orthogonal polynomials

We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).

SILICA MORPHOLOGY CHARACTERIZED BY SEM - THE EFFECTS OF THE SOLVENT TREATMENT AND THE DRYING PROCESS

Scanning electron microscopy (SEM) was used to investigated the effects of volatile solvents (such as water, propanone, ethanol, methanol or ethyl ether), treatment and drying processes, microwave ovens, drying ovens, and vacuum desiccators or freeze driers, on silica morphology. Silica gel was obtained from diluted sodium silicate (1:5 w/w SiO2:H2O). The results showed that the drying process based on freeze drying is more efficient for structural conservation of the precipitate. Treatment with volatile solvents does not change the shape of the aggregates, but has an important role in the determination of aggregate surface roughness.

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.

Chain sequences and symmetric generalized orthogonal polynomials

in this paper, we derive an explicit expression for the parameter sequences of a chain sequence in terms of the corresponding orthogonal polynomials and their associated polynomials. We use this to study the orthogonal polynomials K-n((lambda.,M,k)) associated with the probability measure dphi(lambda,M,k;x), which is the Gegenbauer measure of parameter lambda + 1 with two additional mass points at +/-k. When k = 1 we obtain information on the polynomials K-n((lambda.,M)) which are the symmetric Koornwinder polynomials. Monotonicity properties of the zeros of K-n((lambda,M,k)) in relation to M and k are also given. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Study of the effect of the peptide loading and solvent system in SPPS by HRMAS-NMR

The SPPS methodology has continuously been investigated as a valuable model to monitor the solvation properties of polymeric materials. In this connection, the present work applied HRMAS-NMR spectroscopy to examine the dynamics of an aggregating peptide sequence attached to a resin core with varying peptide loading (up to 80%) and solvent system. Low and high substituted BHAR were used for assembling the VQAAIDYING sequence and some of its minor fragments. The HRMAS-NMR results were in agreement with the swelling of each resin, i.e. there was an improved resolution of resonance peaks in the better solvated conditions. Moreover, the peptide loading and the attached peptide sequence also affected the spectra. Strong peptide chain aggregation was observed mainly in highly peptide loaded resins when solvated in CDCl3. Conversely, due to the better swelling of these highly loaded resins in DMSO, improved NMR spectra were acquired in this polar aprotic solvent, thus enabling the detection of relevant sequence-dependent conformational alterations. The more prominent aggregation was displayed by the VQAAIDYING segment and not by any of its intermediary fragments and these findings were also corroborated by EPR studies of these peptide-resins labelled properly with an amino acid-type spin probe. Copyright (c) 2005 European Peptide Society and John Wiley & Sons, Ltd.

Square-wave voltammetry applied to the analysis of the dye marker, solvent blue 14, in kerosene and fuel alcohol

The purpose of this paper is to develop an electroanalytical method based on square-wave voltammetry (SWV) for the determination of the solvent blue 14 (SB-14) in fuel samples. The electrochemical reduction of SB-14 at glassy carbon electrode in a mixture of Britton-Robinson buffer with N,N-dimethyiformamide (1:1, v/v) presented a well-defined peak at-0.40 V vs. Ag/AgCl. All parameters of the SWV technique were optimized and the electroanalytical method presented a linear response from 1.0 x 10(-6) to 6.0 x 10(-6) mol L-1 (r = 0.998) with a detection limit of 2.90 x 10(-7) mol L-1. The developed method was successfully utilized in the quantification of the dye SB-14 in kerosene and alcohol samples with average recovery from 93.00 to 98.10%.

Evaluation of different solvent on paprika oleoresin extraction

The best solvent for paprika oleoresin extraction was determined by comparison with a commercial oleoresin. Pigment composition was determined by HPLC. The solvent system hexane/acetone/isopropilic alcohol (3:2:1) shown to be the best for extraction of the oleoresin, giving the best yield and colour value and a chromatographic pattern identical to that of the commercial oleoresin.

Effect of Different Solvent Ratios (Water/Ethylene Glycol) on the Growth Process of CaMoO4 Crystals and Their Optical Properties

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