We show how ideas originating in the theory of dynamical systems inspire a new approach to numerical integration of functions. Any Lebesgue integral can be approximated by a sequence of integrals with respect to equidistributions, i.e. evenly weighted discrete probability measures concentrated on an equidistributed set. We prove that, in the case where the integrand is real analytic, suitable l...

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...

2. Write a Matlab script of no more than 10 lines to calculate the Newton-Cotes quadrature weights wj , j = 1, 2, . . . , n, n + 1; go to the end of this handout for more details about wj . For uniformity, we require that the script starts with the four lines n=2; h=1/n; nodes=(0:h:1)’; f=eye(n+1); where the j-th column of the matrix f are needed for the Lagrange interpolation in order to find ...

The main purpose of this paper is to examine the effectiveness of the Quarter-Sweep Gauss-Seidel (QSGS) method in solving the dense linear systems generated from the discretization of the linear Fredholm integral equations of the second kind. In addition, the applications of the various orders of closed Newton-Cotes quadrature discretization schemes will be investigated in order to form linear ...

and hosti 013.02.0 Abstract A numerical method based on an NM-set of general, hybrid of block-pulse function and Taylor series (HBT), is proposed to approximate the solution of nonlinear Volterra–Fredholm integral equations. The properties of HBT are first presented. Also, the operational matrix of integration together with Newton-Cotes nodes are utilized to reduce the computation of nonlinear ...

The exact order of deterministic, stochastic and average error bounds of multidimensional quadrature formulas for anisotropic Sobolev class W r pðIÞ; Nikolskii class H pðIÞ and their periodic analogue is obtained. It is proved that if p41; then the stochastic and average error bounds are essentially smaller than the deterministic error bounds. Nonlinear methods, adaptive methods, or even method...