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The effect of mean stress on the fatigue limit of the cracked specimen was formulated, and fatigue tests were performed on a magnesium alloy to check the approximation errors, which were found to be almost within 10%.
All approximations are of restricted use and can be applied only for a limited number of reactions and it is desirable to check the approximation with the aid of a numerical solution before it is used for mass transfer calculations.
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Checking the approximation results for errors [removed edges violating Condition (4 ], we saw that the simplified algorithm introduced no errors in any of the five networks indicating that the simplified algorithm delivers reasonable approximations in realistic gene regulatory networks.
Moreover, a novel exchange method is designed to enumerate all permutations of alternatives for checking the approximation-consistency. By considering the randomness exhibited in pairwisely comparing alternatives, a method of obtaining the interval weight vector is given.
To test explanation (1) we performed parametric bootstrapping to check the chi-square approximation to the likelihood ratio statistic (see Materials and Methods).
We compared the results of the MOS scheme with results obtained from exact enumeration to check that the approximation scheme produces good statistics, for details see SI text S1 and Figs.
This development involved experimenters and theoreticians working in harness; the results of specially revealing experiments served to check the validity of approximations without which the calculations would have required excessive computing time.
In order to check the accuracy of the approximations used in the analysis, a simulation was built with the above parameter setting.
To check the convergence of numerical approximations, we plot the curves from different starting points at the time (t=0) in the same graph.
In addition, for short sequences, the Gaussian assumption is not well satisfied and we have checked that the approximation is very pessimistic.
We would like to check the validity of the mean-field approximation in two extreme cases: in the limits of the infinitely fast and infinitely slow switching.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com