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Although there are many solutions for this challenge, there isn't one direct analytic solution[7 9].
Hence, the same observations as presented at the end of the last section prevent a further direct analytic approach to the LDP.
Multiple-scale expansion reduces the problem in the first approximation to low-dimensional vibro-impact system with forcing and damping; the latter problem yields to direct analytic approach.
The goal is to develop direct analytic expressions for estimating the feasibility and efficiency of the method, and guide process design; this is only possible for binary mixtures of silane in the dilute limit which is a somewhat realistic case.
This theory was originally developed as a by-product of the construction of stochastic processes analogous to Brownian motion, but has been given by a direct analytic construction in the work of Kigami.
These studies do not, however, make a direct analytic comparison of visual inspection to a microbiologic comparator for the purposes of determining the accuracy of visual inspection in determining the effectiveness of PDC.
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The third approach that is considered for variance component estimation for MACE is the direct factor analytic approach that will be presented in an upcoming paper.
Pharmaceuticals giant Eli Lilly and Co., for example, is using cloud computing to direct IT analytics power at the right place at the right time.
Those with an iTunes Connect account can also reach the sign-up page using the direct link analytics.itunes.apple.com.com
Direct text-analytic methods such as word frequencies and term frequency-inverse document frequency (tf-idf) scores are limited in the subtlety of their inferences, revealing an incomplete picture of the discursive dynamics within the text.
LH supervised the study and directed the analytic plan and manuscript production.
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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