Abstract
The Hermite numerical interpolation method used to estimate and predict the radon and radium concentrations, from some of the experimental measurements made on the soil samples of the Bartella region in Iraq. The results obtained from deductible mathematical method were close to real experimental results. Predicted results are in the range of 80.04–4051.59 Bq/m3radon concentrations and 0.322–17.276 Bq/Kgradium concentrations corresponding to 200-10000 tracks of alpha particles. The maximum errors were less than 0.289 and 1.172 percent for radon and radium concentrations, respectively. The effects of radium and radon radiations estimated of soil in the studied area depend on its concentrations, a higher number of alpha particle tracks mean high radiation concentration, the high radiation will cause human health damage. The values are below 370 Bq/Kg the recommended radium concentration permissible values, by the Organization ащк Economic Cooperation and Development (OECD), the studied area is safe from hazards on health of radium and radon exposure from the soil
Highlights
Applied mathematics is one of the important mathematics branches, it solves applied sciences different problems, it deals with all the stages for solving the problems, namely, given a problem, formulate a mathematical model that describes it, through analytical or numerical methods, solve the model, compare the model results with experimental results, in the case that they disagree qualitatively, go back and reformulate the problem [1]
Materials and Methods The Hermite method used to estimate the radiation concentrations in the soil samples of Bartella region located in the Nineveh plain region of Iraq, which its an open plain area, mostly has red soils, where N denotes the radiation emitted alpha particle track counts recorded by a CR-39 nuclear track detector used in measurements the soil sample in the studied area, Rk is the radiation concentration, experimental results taken from [18]
The estimated of radon concentration values are in the range of 80.04–4051.59 Bq/m3 radon concentrations and 0.322–17.276 Bq/Kg radium concentrations corresponding to 200–10000 tracks of alpha particles, The values are below 370 Bq/Kg the recommended radium concentration permissible values of (OECD) [19]
Summary
Applied mathematics is one of the important mathematics branches, it solves applied sciences different problems, it deals with all the stages for solving the problems, namely, given a problem, formulate a mathematical model that describes it, through analytical or numerical methods, solve the model, compare the model results with experimental results, in the case that they disagree qualitatively, go back and reformulate the problem [1]. The numerical Hermite interpolation method used in applied mathematics, which gives values with small amount error from the real values. The method can be used to estimate and predict results close to the experiments from a few sample values when measurements completely are not available for any reason [2]. The Hermite interpolating generated polynomial is related closely to the polynomial of Newton, both from the calculation of divided are derived [3]. Hermite approximations method can be generated from the basis of Newton interpolatory formula of divided difference at x0 , x1,..., xn, that is: n
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