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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  

The235U fission neutron spectrum averaged cross section for the50Ti(n,)47Ca reaction was experimentally determined by irradiation of titanium with reactor neutrons. A value of (9.7±1.1) b was found for this cross section, using (307±11) b for the48Ti(n,p)48Sc spectrum-averaged cross section that was used as a standard. The50Ti(n,)47Ca spectrum-averaged cross section was also semiempirically evaluated by numerically integrating, through the ENDF/B-V representation of the235U fission neutron spectrum, the available experimental differential cross section data.

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