On a generalized Laguerre operational matrix of fractional integration

A new operationalmatrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived.The fractional integration is described in the Riemann-Liouville sense.This operational matrix is applied together with generalized Laguerre tau method for solving general linearmultitermfractional differential equations (FDEs).Themethod has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposedmethod is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.

Approximating fractional derivatives through the generalized mean

This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm.

Modelling the Contribution of 40K, 232Th and 226Ra to Radiation Dose and Risk from Airborne Discharges of Coal-Fired Power Plants

Coal contains trace elements and naturally occurring radionuclides such as 40K, 232Th, 238U. When coal is burned, minerals, including most of the radionuclides, do not burn and concentrate in the ash several times in comparison with their content in coal. Usually, a small fraction of the fly ash produced (2-5%) is released into the atmosphere. The activities released depend on many factors (concentration in coal, ash content and inorganic matter of the coal, combustion temperature, ratio between bottom and fly ash, filtering system). Therefore, marked differences should be expected between the by-products produced and the amount of activity discharged (per unit of energy produced) from different coal-fired power plants. In fact, the effects of these releases on the environment due to ground deposition have been received some attention but the results from these studies are not unanimous and cannot be understood as a generic conclusion for all coal-fired power plants. In this study, the dispersion modelling of natural radionuclides was carried out to assess the impact of continuous atmospheric releases from a selected coal plant. The natural radioactivity of the coal and the fly ash were measured and the dispersion was modelled by a Gaussian plume estimating the activity concentration at different heights up to a distance of 20 km in several wind directions. External and internal doses (inhalation and ingestion) and the resulting risk were calculated for the population living within 20 km from the coal plant. In average, the effective dose is lower than the ICRP’s limit and the risk is lower than the U.S. EPA’s limit. Therefore, in this situation, the considered exposure does not pose any risk. However, when considering the dispersion in the prevailing wind direction, these values are significant due to an increase of 232Th and 226Ra concentrations in 75% and 44%, respectively.