Application Of Mean Value Theorem Research Articles

Application of mean value theorem of integrals in the efficiency callibration technology of radioactive xeon sample

The radioxenon from environmental samples is usually measured by the HPGe detector. The relative measurement method is used in the analysis process. However, the half-life of radioactive isotopes of xenon is too short to be used as a standard, so the calibration of the HPGe detector is difficult. In order to resolve this problem, the mixed disk sources are used to simulate the efficiencies of four radioactive xenon isotopes, and the mean value theorem of integrals is adopted, thereby improving the accuracy and simplifying the process. The samples are obtained by the xenon system under environment of high activity of radon, then the γ spectrum with regions of interest for 133Xe are obtained by the sample measurement. The activity of 133Xe is given by using the detection efficiency of disk source at a certain source-detector distance. The detection efficiency simulated by disk source is consistent with the detection efficiency of gas cell. Therefore, the simulated technology of disk source and mean value theorem of integrals are identified to be correct and effective.

On the application of mean value theorem to reaction kinetics over inhomogeneous surfaces

The application of a common mean-value theorem for the description of kinetics of heterogeneous catalytic reactions over inhomogeneous surfaces is discussed. Being mathematically correct for integration of multiple integrals, the mean value theorem can provide a correct value of reaction rate for a particular set of parameters, but physical reasons of its application are doubtful, as it obviously contradicts the kinetic regularities. As an example, the kinetics of a two-step sequence on an inhomogeneous surface is discussed.