On the other hand, beyond a certain degree of super-directivity, the FE beam patterns may suffer from excessive degradation in view of the approximations inherent in (11).
In view of the universal approximation properties of PWA system maps [6, 7], these systems yield a nonlinear black-box structure.
Here we provide a comparison of some of these methods in view of the function approximation problem considered.
However, in view of the unavoidable approximations made in constructing the generalised curves of the MW and FW series, the additional error should be negligible.
The Wentzel−Kramers−Brillouin approximation is employed to solve the Bernoulli−Euler equation for the layer with perfectly smooth periodic corrugation, and the results are discussed in view of existence of pass and stop bands and in view of the levels of approximation used in alternative asymptotic methods.
This is probably a reasonable approximation in view of the quite fuzzy interface between the nematic and isotropic regions, as evidenced from microscopy images.
In view of the last equation and uniform sprinkling, implying that the expected number of nodes dN in spacetime volume dV is dN = δ dV, the temporal node density ρ(t) at time is where the last approximation holds for.
end{aligned} (3.25) In view of (3.25), using the approximation properties of (P_{h}) and (P_{k}) in Lemma 1, we get (3.20).
In view of this, such approximations should be used with care, and in any case we have provided an exact approach (strictly, more nearly exact, from replicate simulations).
Noteworthy, the bottommost hierarchical level of VFE in NP-biased composites comprising inter-crystalline interactions is composed of vacancy-type defects (multi-vacancies) in "pure" A and B components and inter-crystalline TJ of irregular shape in view of rather non-spherical approximation validated for such crystallites.
