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Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
On some test ranges, a form is provided for the results, which are then computed as a service to the surveyor. A least squares adjustment provides the best estimate of the calibration values for the instrument, and a report and certificate of calibration may be issued. If the service also tracks each instrument’s calibration history, it is possible to pick up stability problems in oscillators and other problems that may require repair or replacement of the unit.
Effect of correlated hyperfine theory errors in the determination of rotational and vibrational transition frequencies in HD+
Published in Molecular Physics, 2022
Here we propose a pragmatic alternative approach to deal with the issues outlined above. The Monte-Carlo runs developed here provide a means to determine the spread in a way that makes no assumptions regarding the values of whatsoever. As shown above, we were able to quantify the effect of unknown correlation coefficients by computing the mean and standard deviation of all ∼50,000 values of . In addition, we can take advantage of the capability of any least-squares adjustment to provide a (relative) measure – the value – of the compatibility between the measurements and the theoretical model (which now also encompasses the correlation coefficients), in order to get an improved estimate of and its uncertainty. To this end, we use the weights w to calculate means and uncertainties of the weighted results of the Monte-Carlo runs. For example, for the : transition, we earlier found an unweighted mean (standard deviations within parentheses) of kHz relative to , whereas consideration of the weights leads to a compatible but more precise value of kHz. This should be compared with the uncertainty kHz for the uncorrelated scenario (with expansion factor ). Also for the : transition, the weighting reduces the standard deviation significantly, improving the unweighted mean and uncertainty of all values , Hz, to the weighted result Hz. The standard deviation of the weighted result is negligibly small compared to , which equals 17 Hz. The results are summarised in Table 1 for both the : and : transitions.