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which is in turn equivalent to (16).
which is in turn equivalent to the fixed point equation.
This turns out to be equivalent to the NP-hard problem of computing the intersection number of G, thus in turn equivalent to the clique cover problem.
The FP equation is, in turn, equivalent to a Langevin equation, which is used to reconstruct the data, i.e. generate the time series that mimic, in a statistical sense, the original data.
end{aligned} (7.2)But this is in turn equivalent to the following extension problem: for a given (zin D) find (fin mathcal O(D)) such that (f z)=1) and begin{aligned} int _D|f z)|^2dlambda le frac{pi }{c_D z)^2}.
This equation is in turn equivalent to the following: - γ δ a R z 2 + O a 2 ( R z 2 ) 2 - γ + 2 π j = γ δ a ( R z 2 ) 1 - 2 γ + O a 2 ( R z 2 ) 2 - 3 γ, Open image in new window.
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Note that by Lemma 1.11, (1.33) and (1.37), the inequality on the left in (1.39) is equivalent to (Psi (H,Y) le Psi _D H,Y)), which in turn is equivalent under the Legendre transform to (D_D(X||Y) le D(X||Y)).
Since all norms on are equivalent, the limit in (d) can be relative to any norm on, so that (d) is equivalent to all the entries of converge to zero as, which in turn is equivalent to for all.
This is equivalent to a reduction of 39.0 deaths per 1000 households of average size who remediate, which in turn is equivalent to 516.9 life years gained, or 212.0 discounted QALYs gained.
Deletion of C4 and C6 hydroxyacyl CoA is equivalent to reducing the number of reactions in the linkage class to which they belong, which in turn is equivalent to replacing the enzymes crotonase and M/SCHAD with a single enzyme CRMS.
In turn, owners' equivalent rent has risen too, even though homeowners have seen no change in the actual costs of owning their house.
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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