We mention that, in view of the approximation in Theorem 1(b), it is more advantageous to use (h^{-1} ( 2pi n mppi/2 )) as initial guesses for large n.
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.
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).
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).
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.
In view of this, we integrated both approaches by means of a two-cluster approximation (see e.g. [ 27]) to derive the root distribution probabilities from our context-dependent evolutionary model.
Thus in view of these remarks, Rhoades [16 19], Singh, Srivastava [20] have obtained the degree of approximation of functions belonging to various Lipschitz classes using Hausdorff means.
This would then result in a -approximation scheme for MISP of, which, in view of the results in [25], would imply Theorem 5. We next discuss how to construct the graph from in polynomial time.
