The purpose of this paper is to reduce the complexity computing components integral Fm-transform, m≥0, whose analytic expressions include definite integrals. We propose use nontrivial quadrature rules with nonuniformly distributed integration points instead widely used Newton–Cotes formulas. As weight function that determines orthogonality, we choose generating fuzzy partition associated Fm-tra...

It is well-known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial pn(x) interlace with the zeros of pn(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of k-th, 1 ≤ k ≤ n − 1, zeros of the associated polynomial and the derivative of an orthogonal...

This chapter describes the adverse health effects associated with exposure to respirable coal mine dust. Epidemiological studies of underground and surface coal miners in the United States and other countries are discussed. Also discussed are animal studies that add to our understanding of particle deposition and retention in the lungs and associated disease responses. This chapter emphasizes s...

Newton-Cotes quadrature rules are based on polynomial interpolation in a set of equidistant points. They are very useful in applications where sampled function values are only available on a regular grid. Yet, these rules rapidly become unstable for high orders. In this paper we review two techniques to construct stable high-order quadrature rules using equidistant quadrature points. The stabil...

This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.

A decrease in arterial oxygen saturation (Sao2) has been observed to follow intravenous aminophylline administration in patients with chronic pulmonary disease (Halmagyi and Cotes, 1959). The decrease in Sao2 occurred 40 minutes or more after the injection in a group of patients who had shown an increase in maximum breathing capacity (M.B.C.) in response to the drug. The onset of symptomatic re...

This paper presents a framework for the calculation of functional requirements at several stages of the product life cycle. It uses the TTRS/MGRE concept for the determination of dimension chains. The geometry of the assembly is represented using a parametric model constituted of points and vectors. Finally, it also integrates the calculation of part deformation due to changing operating condit...

In many applications of ageand size-structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Si...