Lobatto deferred correction for stiff two-point boundary value problems

An iterated deferred correction algorithm based on Lobatto Runge-Kutta formulae is developed for the efficient numerical solution of nonlinear stiff two-point boundary value problems. An analysis of the stability properties of general deferred correction schemes which are based on implicit Runge-Kutta methods is given and results which are analogous to those obtained for initial value problems are derived. A revised definition of symmetry is presented and this ensures that each deferred correction produces an optimal increase in order. Finally, some numerical results are given to demonstrate the superior performance of Lobatto formulae compared with mono-implicit formulae on stiff two-point boundary value problems. (C) 1998 Elsevier B.V. Ltd. All rights reserved.

Iterated deferred correction for linear two-point boundary value problems

An analysis of iterated deferred correction based on various classes of implicit Runge-Kutta formulae is given. Out of different possibilities considered, it is shown that those based purely on Lobatto formulae have the best stability. The enhanced stability of Lobatto schemes is very important for the efficient integration of excessively stiff boundary value problems and this is demonstrated by means of some numerical results.

Gaussian extended cubature formulae for polyharmonic functions

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses ℳ values of linear functional (integrals over hyperspheres) and is exact for all 2ℳ-harmonic functions, and consequently, for all algebraic polynomials of n variables of degree 4ℳ - 1.

Fluoride concentrations of milk, infant formulae, and soy-based products commercially available in Brazil

To assess the fluoride (F) content in commercially available milk formulae in Brazil and to estimate the F intake in children from this source in the first year of life. Samples of cow's milk (n = 51), infant formulae (n = 15), powdered milk (n = 13), and soy-based products (n = 4) purchased in Araçatuba (Brazil) had their F content measured using an ion-specific electrode, after hexamethyldisiloxane-facilitated diffusion. Powdered milk and infant formulae were reconstituted with deionized water, while ready-to-drink products were analyzed without any dilution. Using average infant body masses and suggested volumes of formula consumption for infants 1-12 months of age, possible F ingestion per body mass was estimated. Data were analyzed by descriptive analysis. Mean F content ranged from 0.02 to 2.52 mg/L in all samples. None of the cow's milk provided F intake higher than 0.07 mg/kg. However, two infant formulae, one powdered milk, and one soy-milk led to a daily F intake above the suggested threshold for fluorosis when reconstituted with deionized water. Assuming reconstitution of products with tap water at 0.7 ppm F, two infant formulae, five powdered milk, and four soymilks led to daily F intake ranging from 0.108 to 0.851 mg/kg. The results suggest that the consumption of some brands of infant formulae, powdered milk, and soy-based milk in the first year of age could increase the risk of dental fluorosis, reinforcing the need for periodic surveillance of the F content of foods and beverages typically consumed by young children.

Ruthenium (II) phosphine/picolinate complexes as antimycobacterial agents

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Ruthenium(II) phosphine/diimine/picolinate complexes: Inorganic compounds as agents against tuberculosis

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

In vitro antibacterial action of Tetraclean, MTAD and five experimental irrigation solutions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Karyotypic evolution trends in Rhamdia quelen (Siluriformes, Heptapteridae) with considerations about the origin and differentiation of its supernumerary chromosomes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mechanisms of karyotype differentiation in Cassidinae sensu lato (Coleoptera, Polyphaga, Chrysomelidae) based on seven species of the Brazilian fauna and an overview of the cytogenetic data

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Cytogenetics of four Omophoita species (Coleoptera, Chrysomelidae, Alticinae): A comparative analysis using mitotic and meiotic cells submitted to the standard staining and C-banding technique

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Empirical diversity indices applied to forest communities in different successional stages

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On a symmetry in strong distributions

A strong Stieltjes distribution d psi(t) is called symmetric if it satisfies the propertyt(omega) d psi(beta(2)/t) = -(beta(2)/t)(omega) d psi(t), for t is an element of (a, b) subset of or equal to (0, infinity), 2 omega is an element of Z, and beta > 0.In this article some consequences of symmetry on the moments, the orthogonal L-polynomials and the quadrature formulae associated with the distribution are given. (C) 1999 Elsevier B.V. B.V. All rights reserved.

INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Convolutions and zeros of orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the relationship between a 2 x 2 matrix and second-order scalar spectral problems for integrable equations

A simple proof is given that a 2 x 2 matrix scheme for an inverse scattering transform method for integrable equations can be converted into the standard form of the second-order scalar spectral problem associated with the same equations. Simple formulae relating these two kinds of representation of integrable equations are established.