Exact(1)
The same implies for movies with numbers in the beginning of their title.
Similar(7)
"Proponents" implies "for"; make it "proponents of".
Since ({x_{n}}) is monotone increasing and the order interval ([x_{k},rightarrow)) is closed and convex, we conclude that (omega_{i} in[x_{k},rightarrow)) for (i = 1,2). Hence ({x_{n}} subset leftarrow, omega_{i}]) for (i = 1,2), holds which implies for the same reason (omega_{j} in(leftarrow, omega_{i}]) for (i,j = 1,2).
Using the same symmetry argument from Equations 9– 11, implies for the FI: (18) J (Ω, ρ, H C P ) (x ) ≈ J (Ω, ρ, H C P ) (0 ) ≈ M vol (V 0 ) ∫ V 0 J Ω H C P (c ) d c.
In short: same likelihoods implies same theory.
Historical data imply for the same period a phase of economic and social decline which involved the whole Empire.
Prediction within the same cross implies training and validating within, for example, F2 individuals or doubled haploids or advanced inbred lines (that is, F6) derived from one cross for which phenotyping in multi-environment trials is more expensive than genotyping.
Repeatedly measured P-ADL functioning for the same individuals implies dependency in data.
Related(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