The Q-D algorithm for transforming series expansions into a corresponding continued fraction: an extension to cope with zero coefficients

An algorithm for deriving a continued fraction that corresponds to two series expansions simultaneously, when there are zero coefficients in one or both series, is given. It is based on using the Q-D algorithm to derive the corresponding fraction for two related series, and then transforming it into the required continued fraction. Two examples are given. (C) 2003 Elsevier B.V. All rights reserved.

Some Extensions of M-Fractions Related to Strong Stieltjes Distributions

The purpose of this paper is to show the symmetric relations that appear between the coefficients of some even and odd extensions of the M-fractions related to a certain kind of symmetric strong Stieltjes distribution.

SZEGO POLYNOMIALS FROM HYPERGEOMETRIC FUNCTIONS

Szego polynomials with respect to the weight function w(theta) = e(eta theta)[sin(theta/2)](2 lambda), where eta, lambda is an element of R and lambda > -1/2 are considered. Many of the basic relations associated with these polynomials are given explicitly. Two sequences of para-orthogonal polynomials with explicit relations are also given.

BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Generating Birth and Death Processes

Associated with an ordered sequence of an even number 2N of positive real numbers is a birth and death process (BDP) on {0, 1, 2,..., N} having these real numbers as its birth and death rates. We generate another birth and death process from this BDP on {0, 1, 2,..., 2N}. This can be further iterated. We illustrate with an example from tan(kz). In BDP, the decay parameter, viz., the largest non-zero eigenvalue is important in the study of convergence to stationarity. In this article, the smallest eigenvalue is found to be useful.

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.

Chebyshev-Laurent polynomials and weighted approximation

Let (a, b) subset of (0, infinity) and for any positive integer n, let S-n be the Chebyshev space in [a, b] defined by S-n:= span{x(-n/2+k),k= 0,...,n}. The unique (up to a constant factor) function tau(n) is an element of S-n, which satisfies the orthogonality relation S(a)(b)tau(n)(x)q(x) (x(b - x)(x - a))(-1/2) dx = 0 for any q is an element of Sn-1, is said to be the orthogonal Chebyshev S-n-polynomials. This paper is an attempt to exibit some interesting properties of the orthogonal Chebyshev S-n-polynomials and to demonstrate their importance to the problem of approximation by S-n-polynomials. A simple proof of a Jackson-type theorem is given and the Lagrange interpolation problem by functions from S-n is discussed. It is shown also that tau(n) obeys an extremal property in L-q, 1 less than or equal to q less than or equal to infinity. Natural analogues of some inequalities for algebraic polynomials, which we expect to hold for the S-n-pelynomials, are conjectured.

Frações contínuas que correspondem a séries de potências em dois pontos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Polinômios de Szegö e análise de frequência

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Polinômios ortogonais e análise de freqüência

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Antibacterial and antiparasitic effects of Bothrops marajoensis venom and its fractions: Phospholipase A(2) and L-amino acid oxidase

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Organic matter fractions and soil fertility under the influence of liming, vermicompost and cattle manure

Os efeitos do vermicomposto de esterco de curral associado à calagem em atributos da fertilidade do solo foram avaliados através de experimento em vasos empregando um Latossolo Vermelho, distrófico, textura média. Cinco doses do vermicomposto (equivalentes a 0; 28; 42; 56 e 70 t ha-1, peso seco) e cinco doses de calcário (visando elevar a saturação por bases a: 20; 30; 40; 50 e 60%) foram combinadas em esquema fatorial, sendo as amostras de solo incubadas por 180 dias. Para comparação entre o vermicomposto e o esterco de curral, amostras do mesmo solo receberam o equivalente a 70 t ha-1 do esterco de curral que originou o vermicomposto e as cinco doses de calcário listadas anteriormente. Através do cálculo do Índice de Eficiência Agronômica, foi verificado que o potencial de fornecimento de K e de Mg pelo esterco é maior do que o do vermicomposto, e que o de P, é semelhante. O vermicomposto aumentou os teores de Ca2+ e de matéria orgânica (MO), os valores de pH em CaCl2 e a CTC a pH 7. Com o aumento das doses de vermicomposto houve diminuição do C-ácidos húmicos e aumento do C-humina e com a calagem o C-total não aumentou mas houve diminuição do C-ácidos húmicos.

The status of soil phosphate fractions and the ability of fungi to dissolve hardly soluble phosphates

Brazilian soils predominantly consist of iron and aluminum oxides and have a low phosphorus content. The present study was carried out in order to assess the status of phosphate fractions in pasture, forest and agricultural soils and the ability of soil fungi to solubilize iron and aluminum phosphates. The abundance of P fractions in the soils studied occurred in the following order: Fe-P > reductant-soluble Fe-P > occluded Fe-P > occluded Al-P > Al-P > Ca-P. of the 481 fungi isolated, 33 showed the ability to solubilize the inorganic phosphates in culture. of these, 14 were considered to be high or very high solubilizers based on a solubilization capacity > 1000 mu g PO43- ml(-1). Isolate F-111 was the only one that dissolved all the insoluble phosphates used. Nine isolates solubilized both Al-P and Ca-P, and four other isolates only solubilized Ca-P. The highest number of isolates with high solubilization capacity were detected in pasture soil, followed by tropical rain forest and forest patch soils. Pasture soil presented both the largest contents of insoluble phosphates and the largest number of fungal isolates with phosphate-solubilizing ability. The range and size of P fractions influenced the number of fungi and their ability to solubilize hardly soluble phosphates. (c) 2004 Elsevier B.V. All rights reserved.