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.

Mathematical tests about the existence and applications of PPS-wavelets in function approximation problems

Neural networks and wavelet transform have been recently seen as attractive tools for developing eficient solutions for many real world problems in function approximation. Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. So, mathematical model is a very important tool to guarantee the development of the neural network area. In this article we will introduce one series of mathematical demonstrations that guarantee the wavelets properties for the PPS functions. As application, we will show the use of PPS-wavelets in pattern recognition problems of handwritten digit through function approximation techniques.

Experimental study of the conventional equation to determine a plate's moment of inertia

In this work, we describe an experimental setup in which an electric current is used to determine the angular velocity attained by a plate rotating around a shaft in response to a torque applied for a given period. Based on this information, we show how the moment of inertia of a plate can be determined using a procedure that differs considerably from the ones most commonly used, which generally involve time measurements. Some experimental results are also presented which allow one to determine parameters such as the exponents and constant of the conventional equation of a plate's moment of inertia.

Experimental study of the moment of inertia of a cone - angular variation and inertia ellipsoid

In this paper, an experimental set-up which differs from the traditional ones is established in order to determine the moment of inertia of a right circular cone. Its angular variation and inertia ellipsoid are determined by means of an experimental study. In addition, a system that allows for the evaluation of the angular acceleration and torque through electric current or frequency measurement is utilized.

Cubic approximation for the transverse displacement in BEM for elastic plates analysis

This work presents an application for the plate analysis formulation by BEM where 3 boundary equations are used, written for the transverse displacement w and the normal and tangential derivatives partial derivativew/partial derivativen and partial derivativew/partial derivatives. In this extension, the transverse displacement w is approximated by a cubic polynomial and, as a consequence, partial derivativew/partial derivatives has a quadratic approximation. This alternative BEM formulation improves the analysis of thin plates, when compared to the formulation using the linear approximation for the displacements, mainly in the obtaining of the bending moments at the boundary of the plate. The implementation of this proposal to the computational codes is simple. (C) 2004 Published by Elsevier Ltd.

Efeito do diclofenaco de sódio na cicatrização da parede abdominal de ratos. Estudo histopatológico, da força de ruptura e do colágeno tecidual

Com o objetivo de estudar os efeitos do diclofenaco sódico sobre a cicatrização da parede abdominal de ratos, foram utilizados 80 animais da linhagem Wistar divididos em dois grupos: Grupo 1: formado por 40 animais submetidos à laparotomia mediana e à injeção intramuscular de soro fisiológico durante quatro dias. Grupo 2: formado por 40 animais submetidos à laparotomia mediana e à injeção intramuscular de diclofenaco sódico durante quatro dias. Animais de ambos os grupos foram analisados no 5°, 7°, 14° e 21° dias de pós-operatório, correspondendo, respectivamente à M1, M2, M3 e M4. em cada momento foram estudados 10 animais e os parâmetros analisados foram a evolução clínica, a força de ruptura, estudo histológico e o conteúdo de colágeno tecidual da parede abdominal. Os animais do grupo tratado apresentaram como complicações, deiscência e/ou hérnia incisional, perda ponderal e taxa de mortalidade, complicações estas não evidenciadas no grupo controle. Observamos também neste grupo, diminuição da força de ruptura no 7° e 14° dia de pós-operatório e diminuição da concentração de colágeno tecidual no 5°, 7° e 14° dia de pós-operatório. Ambos os parâmetros retornaram a valores normais no 21° dia de pós-operatório. Quanto ao estudo histológico, concluímos que a cicatriz da parede abdominal dos animais tratados com D.S. apresentam retardo do processo cicatricial em relação aos seus controles, caracterizado por uma menor fibrogênese, menor densidade de fibras colágenas, além de um número maior de complicações, como microabscessos, em torno dos fios de sutura.

Determination and padronization of normal values of bone mineral density (BMD) of the acessory carpus bone in young Thoroughbred horse using optical densitometry in radiographic image

Em 12 fêmeas e 12 machos da raça Puro Sangue Inglês com idade média de 12 meses, avaliou-se os valores normais da densidade mineral óssea do carpo acessório em milímetros de alumínio (mmAl) até o momento do fechamento completo da epífise distal do rádio, por meio do método de densitometria óptica em imagens radiográficas. A avaliação foi realizada por meio de um programa computacional (software) especialmente desenvolvido para medida de densidade óptica em filmes de raios-X, o qual contém a imagem radiográfica do osso carpo acessório, região de partes moles adjacente ao carpo acessório e os degraus de uma escala de alumínio (phatom), que permitiu a medida de densidade mineral óssea, sendo esta a média aritmética da região de interesse determinada no osso carpo acessório correspondente ao valor em milímetros da escala. Os valores da densidade mineral óssea em mmAl do acessório do carpo em função da idade não apresentaram diferenças entre os sexos (p=0,86) permitindo que uma equação de reta fosse ajustada para ambos os sexos (densidade mineral óssea (DMO) mmAl = 3.109 + 0,056 x idade em meses), na faixa etária estudada.

Ectopic mineralization of articular cartilage in the bullfrog Rana catesbeiana and its possible involvement in bone closure

Mineralization of the articular cartilage is a pathological condition associated with age and certain joint diseases in humans and other mammals. In this work, we describe a physiological process of articular cartilage mineralization in bullfrogs. Articular cartilage of the proximal and distal ends of the femur and of the proximal end of the tibia-fibula was studied in animals of different ages. Mineralization of the articular cartilage was detected in animals at 1 month post-transformation. This mineralization, which appeared before the hypertrophic cartilage showed any calcium deposition, began at a restricted site in the lateral expansion of the cartilage and then progressed to other areas of the epiphyseal cartilage. Mineralized structures were identified by von Kossa's staining and by in vivo incorporation of calcein green. Element analysis showed that calcium crystals consisted of poorly crystalline hydroxyapatite. Mineralized matrix was initially spherical structures that generally coalesced after a certain size to occupy larger areas of the cartilage. Alkaline phosphatase activity was detected at the plasma membrane of nearby chondrocytes and in extracellular matrix. Apoptosis was detected by the TUNEL (TDT-mediated dUTP-biotin nick end-labeling) reaction in some articular chondrocytes from mineralized areas. The area occupied by calcium crystals increased significantly in older animals, especially in areas under compression. Ultrastructural analyses showed clusters of needle-like crystals in the extracellular matrix around the chondrocytes and large blocks of mineralized matrix. In 4-year-old animals, some lamellar bone (containing bone marrow) occurred in the same area as articular cartilage mineralization. These results show that the articular cartilage of R. catesbeiana undergoes precocious and progressive mineralization that is apparently stimulated by compressive forces. We suggest that this mineralization is involved in the closure of bone extremities, since mineralization appears to precede the formation of a rudimentary secondary center of ossification in older animals.

Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters

This work deals with noise removal by the use of an edge preserving method whose parameters are automatically estimated, for any application, by simply providing information about the standard deviation noise level we wish to eliminate. The desired noiseless image u(x), in a Partial Differential Equation based model, can be viewed as the solution of an evolutionary differential equation u t(x) = F(u xx, u x, u, x, t) which means that the true solution will be reached when t ® ¥. In practical applications we should stop the time ''t'' at some moment during this evolutionary process. This work presents a sufficient condition, related to time t and to the standard deviation s of the noise we desire to remove, which gives a constant T such that u(x, T) is a good approximation of u(x). The approach here focused on edge preservation during the noise elimination process as its main characteristic. The balance between edge points and interior points is carried out by a function g which depends on the initial noisy image u(x, t0), the standard deviation of the noise we want to eliminate and a constant k. The k parameter estimation is also presented in this work therefore making, the proposed model automatic. The model's feasibility and the choice of the optimal time scale is evident through out the various experimental results.

Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure

We discuss the q-state Potts models for q less than or equal to 4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions of all critical points, and for the tricritical points when 4 > q greater than or equal to 2. We also note a curious appearance of the extended last line of Freudenthal's magic square in connection with the Potts models. (C) 2003 Elsevier B.V. B.V. All rights reserved.

s-wave approximation for asymmetry in nonmesonic decay of finite hypernuclei

We establish the bridge between the commonly used Nabetani-Ogaito-Sato-Kishimoto (NOSK) formula for the asymmetry parameter a(Lambda) in the Lambda p -> np emission of polarized hypernuclei, and the shell-model (SM) formalism for finite hypernuclei. We demonstrate that the s-wave approximation leads to a SM formula for a(Lambda) that is as simple as the NOSK one and that reproduces the exact results for (5)(Lambda)He and (12)(Lambda)C better than initially expected. The simplicity achieved here is indeed remarkable. The new formalism makes the theoretical evaluation of a(Lambda) more transparent and explains clearly why the one-meson exchange model is unable to account for the experimental data of (5)(Lambda)He.

Low-energy direct muon transfer from H to Ne10+, S16+ and Ar18+ using the two-state close-coupling approximation to the Faddeev-Hahn-type equation

We perform a three-body calculation of direct muon-transfer rates from thermalized muonic hydrogen isotopes to bare nuclei Ne10+, S16+ and Ar18+ employing integro-differential Faddeev-Hahn-type equations in configuration space with a two-state close-coupling approximation scheme. All Coulomb potentials including the strong final-state Coulomb repulsion are treated exactly. A long-range polarization potential is included in the elastic channel to take into account the high polarizability of the muonic hydrogen. The transfer rates so-calculated are in good agreement with recent experiments. We find that the muon is captured predominantly in the n = 6, 9 and 10 states of muonic Ne10+, S16+ and Ar18+, respectively.

Electric charge quantization and the muon anomalous magnetic moment

We investigate some proposals to solve the electric charge quantization puzzle that simultaneously explain the recent measured deviation on the muon anomalous magnetic moment. For this we assess extensions of the electro-weak standard model spanning modifications on the scalar sector only. It is interesting to verify that one can have modest extensions which easily account for the solution for both problems.

Finite-volume form factors in semi-classical approximation

A semi-classical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the spectral representation of correlation functions in a finite volume. Illustrative examples of the applicability of the method are provided by the sine-Gordon and the broken phi(4) theories in 1 + 1 dimensions. (C) 2003 Elsevier B.V. All rights reserved.