Sentence examples for approximation demonstrated from inspiring English sources
Using orbital-free framework, a simple numerical optimization of the density functional for ground state electronic energy is described for any type of functional approximation, demonstrated via the example of linear combinations of homogeneous functionals of the density.
The logarithmic transformation of several data values (HGF, white blood cell counts (WBC), and lactate dehydrogenase (LDH)) allowed Gaussian approximation (demonstrated by the Kolmogorov -Smirnov and Shapiro-Wilk tests).
We used non-parametric Mann-Whitney U tests to compare scores on the MVQOLI subscales by diagnosis (cancer vs. HIV), as the Kolmogorov-Smirnov test (with Lilliefors approximation) demonstrated that the distribution of scores was skewed for all subscales, and we treated the groups as independent samples given our attempt to minimise site effects.
A comparison with an estimation technique based on the finite-difference approximation demonstrates advantages of the ML estimator.
The local Nusselt number distribution also highlights the inaccuracies arising from the use of incompressible approximation demonstrating that it remains invalid for such scenarios.
A simple model of spherical parabolic quantum dot within effective-mass approximation demonstrates that the coupling strengths of the dots are adjustable by applying a lateral field.
See the Materials and methods for a quasi-steady state approximation demonstrating this effect of GTP-Cdc42 on the Bem1-GEF dwell time.
See the Materials and methods for a quasi-steady state approximation demonstrating how Cdc42 dwell time is related to GEF activity.
By selecting relatively limited Legendre Gauss Lobatto and Gauss Radau collocation nodes, we are able to get very accurate approximations, demonstrating the utility and high accuracy of the new approach over other numerical methods.
The accuracy of each approximation is demonstrated.
Engineering features and small errors of the approximation are demonstrated.
