In the case of both MacLehose et al. and Chu et al., the authors had a range of prior validity studies with validated biomarkers to inform the sensitivity analysis and potentially allow estimation of a central, posterior OR.
The use of linearisation of nonlinear dynamic systems to obtain a linear model, with a limited range of validity, which facilitates theoretical analysis is a very common approach in engineering fields such as systems and control theory, electrical circuit theory (small signal analysis), rotating machinery and vibrational analysis.
This approximate description of the gene pool of the whole population, which accelerates our simulations, is appropriate if subpopulations are strongly dominated by single clones; see Appendix A and Discussion for an explicit range of validity.
Incorporating this effect, the stopping number of an electron is given by a complicated expression that involves a different arrangement of the parameters found in the stopping number of heavy charged particles; i.e., This stopping-power formula has a wide range of validity, from approximately a few hundred electron volts to a few million electron volts in materials of low atomic number.
The two relaxation times (TRT) collision scheme with the specific eigenvalue combination fixed to a constant value within a typical range of validity is employed for solving the present problems.
So this means that their prediction of a geometric series of periods, even in one dimension, has a limited range of validity.
So this means that the prediction of a geometric series of periods is based on a tenuous analysis with an uncertain range of validity.
The JKR theory and the DMT theory each have a certain range of validity [5].
Furthermore, the current micro and macro models have a limited range of validity and also require significant computational resources and high expertise.
However, for ice covered waters such tools are hardly available and are either costly as ice model tests or have a limited range of validity, such as semi-empirical formulas.
