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Discover LudwigExact(46)
where a(n) and ({hat a(n)}) are real and estimated amplitudes respectively.
where A(n) is the mixing matrix or the array steering matrix for the n th snapshot.
Relevant examples are repeated below as 45, where a transported theme/causand is advanced as the trigger, and as 46, where a(n) beneficiary/instrument is advanced as the trigger.
Here, "movement" is defined as M n) = 1 – Intersect(A(n), A(n+1))/Union(A(n), A(n+1)), where A(n) is denoted as the animal area at previous frame n.
where a n = m !
where a n is defined in (2.3).
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Now, conjugation by y sends x to ( x^a), where ((a,n) = 1), and we have also ( a^m equiv 1 ( mod n)).
We consider a cognitive relay system where a N-antenna cognitive relay forwards message transmitted by a cognitive source to K cognitive destinations.
The base case corresponds to the first depth level, where a n-input A-operation can form a constant with at most n non-zero digits.
where { a n } is a sequence in ( 0, 1 ).
where { a n } and { b n } are the sequences in ( 0, 1 ).
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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