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Effective properties for an isotropic matrix reinforced by congruent cylinders or patterns are estimated within a mean field approximation context.
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A more realistic aim is therefore to identify a model that provides an acceptable approximation, in the context of the application in which it is used.
In this paper, we consider the acoustic cloaking based on singular transformations and its approximation in the context of scattering problems in R3.
Hence, this motivates the use of the new APP approximation in the context of EM channel estimation for trellis-coded modulation.
For the first time in the literature, the beam-shape coefficients for ordinary Bessel beams were numerically evaluated using the integral localized approximation in the context of the generalized Lorenz-Mie theory.
Two families of high-order locally conservative schemes matching this discretized skew-symmetric form are considered and rewritten in terms of telescopic fluxes for both finite difference and finite volume approximations in the context of compressible flows.
Listening tests were conducted to validate the use of linear approximations in this context.
We will show the definition of contexts of a collection of concepts and successively the definitions of lower and upper approximations through a context.
The main reason for this significant difference is hence likely the more accurate approximation of the context-dependent Markov substitution process by allowing the ancestral sequences to change in between the internal speciation nodes (which is also responsible for the small differences in model estimates).
Given that this approach does not lead to significantly different parameter estimates, the increased log Bayes factor can be attributed to the more accurate approximation of the context-dependent Markov substitution process by allowing the ancestral sequences to change in between the internal speciation nodes [ 17].
Back-propagation neural networks (BPN) have been extensively used as global approximation tools in the context of approximate optimization.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com