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The evaluation of this proof was conducted by the two neurologists from the working team (M. Pardo and M.J. Sobrido).
A final audio proof was conducted by three clinical researchers (native speakers) who independently confirmed that the translated versions retained the original meaning of the English version.
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Proof The proof is conducted by the induction method with respect to the variable k, 1 ≤ k ≤ m − 1.
Numerical simulations and experiments in addition to stability proof are conducted to verify the proposed hybrid-controller dynamic positioning system in varying environmental conditions from calm to extreme seas.
Asymptotic stability proof is conducted with Lyapunov argument for both noise-free and additive noises cases.
In [1] and [9], the proofs are conducted by contradiction to the concavity of solution (also see [4]).
The program operates largely as a black box, that is, the inner working details are hidden from the user; proofs are conducted by rewriting terms that posses recursive definitions, ultimately reducing the conclusion's statement to the T predicate.
Finally, a proof-of-concept validation is conducted using a simulated enterprise network under DDoS attack, which is a typical MSCA variant.
Whereas the extracted interests were enriched and new interests have been discovered, a second proof of concept was conducted specifically to analyze these discovered interests.
Proof of correctness was conducted using the KeY tool (Beckert, Hanle and Schmitt 2007), an interactive theorem proving environment for first-order dynamic logic that allows the user to prove properties of imperative and object-oriented sequential programs.
The proof of concept was conducted at 10 health facilities in Bong and Lofa counties; these counties were selected due to their relatively strong EPI performance.
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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