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Even using a limited number of contours provides a useful approximation to the 3D face surface.
Classical mechanics emerges as a useful approximation to the more fundamental quantum mechanics under suitable conditions.
Hence classical physics seems merely to be a useful approximation to a world which is quantum mechanical on all scales.
The ratio of persons in the dependent age groups to those of the working age groups provides a useful approximation to economic dependency burden.
In addition we derive a useful approximation to our method which results in a simple equation capturing the relation between monitoring and epidemic dynamics.
It can exactly transform a SH-wave propagation problem posed for a medium with spherical symmetry into a problem posed for a plane-stratified medium and give a useful approximation to a P-SV problem in a spherically symmetric medium.
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A very useful approximation to this relation is established through numerical experiments which is exact for all practical purposes.
The Taylor series of ln z provides a particularly useful approximation to ln(1+z) when z is small, |z| < 1, since then : \ln (1+z) = z - \frac{z^2}{2} +\frac{z^3}{3}\approx\approx z.
Therefore, the application of the reference ratio method results in a useful approximation, at best.
Many would defend utility theory (as well as other aspects of their standard model of behaviour) as a useful approximation, pointing out that exceptions to approximations can always be found.
The C + NVC model with the incorporation of Wu et al. (2009) outputs was adapted for use in this paper, it was shown to give a useful approximation of the difference between scenarios, and could be further utilised with specific wildfire management data (i.e. pre-suppression efforts–such as prescribed burning) if and where available.
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CEO of Professional Science Editing for Scientists @ prosciediting.com