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Abstract  

Upper and lower error bounds for an optimal 2-point quadrature rule of open type are derived. These error bounds are sharp. Applications in numerical integration are given

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Abstract  

Standardization methods in activation analysis with charged particles are studied critically. Several approximate standardization methods that do not require knowledge of the excitation function are compared with the “numerical integration method” using excitation function data from the literature. It is shown that these methods yield accurate results if the threshold energy of the considered reaction is high and if sample and standard have a comparable Z value. A method that gives a rapid estimate of the maximum possible error is also presented. It is shown that for the “numerical integration method” the accuracy of the excitation function data has only a small influence on the overall accuracy. The influence of the accuracy of stopping power data and of possible deviations from Bragg's rule for light element standards is also considered.

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Abstract  

The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized in order to obtain approximations with the maximum of accurate.

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Abstract  

A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with several published approximate formulae, this new one is much superior to all other approximations and is the most suitable solution for the evaluation of kinetic parameters from TG experiments.

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