We use the atomistic-continuum equivalence model for the sp 2 carbon-carbon bonds to extract the equivalent isotropic mechanical properties (Young's modulus and Poisson's ratio) as a functions of the thickness d of the C-C bond [13, 14].
This equivalence model can be effectively used to support interactive processes and performance measures designed to establish future performance goals while taking into account the preferences of decision makers (DMs).
The process for examining the applicability of the energy equivalence model is difficult and appears logically inappropriate (for discussion see [9]).
The burst pressure (BP mmHg) was calculated from the rupture test; using the same equivalence model used for the compliance, the pressure was derived from the ultimate tensile stress and the diameter was derived from the ultimate strain.
Similarly, variance component estimation by REML and Bayesian methods are unaffected by the allele coding due to equivalence of models with the marker-based models.
The dynamical equivalence between models of this sort, where populations experience exponential growth asymptotically approaching a threshold, and those models used in neural networks of excitation/inhibition between neurons is well recognised ([ 64] and refs. within).
The notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation.
It is necessary to re-run that comparison and therefore we will include the SNB model and the Zayatz equivalence class model in our evaluation.
In more complex situations, such as the longitudinal data we are studying, the same equivalence between model descriptions exist and we use both model formulations for the NLMMs and SEMs that follow.
Basic concepts in equivalence checking, model checking, and theorem proving also are reviewed in the chapter.
