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This, too, involves a formula that is disputed by some experts.
The secret of the Sugababes' success, if there is one, involves a formula based on such variables as luck, talent, timing, personality, management, image, production and, in particular, some irresistible hit singles (Freak Like Me, Round Round).
The completion of the deal still hinges on Bedoya's ability to obtain a British work permit, an exercise that could derail the deal because it involves a formula that takes into account a player's number of recent appearances for his national team.
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In the presence of expanding rules, such as Lifting, this is not immediately obvious: the transitivity inference from A ⊢ B and B ⊢ C to A ⊢ C involves a 'lemma' formula B which disappears from the conclusion, and there is an infinite number of candidate lemma formulas to consider.
(NB: If you're wondering how exactly we'll be calculating personalized Oculus discounts we can tell you it involves a proprietary formula that Your Club Committee developed based on your lifelong Participation & Attendance Metrics (PAM).
The measurement of internal stresses in coatings through the curvature (or bending) method involves a theoretical formula which connects the internal stress with the experimentally measured sample curvature.
Proof of Theorem 7 The first step involves a combination of formulas (25) and (28) with subsequent derivation of an integral representation for the probability of interest, where the integral over (mathbf {R}_^{1}) is similar to those considered in Vinogradov (2008a, formulas (27) and (32)) and Paris and Vinogradov (2015, formula (3.31)).
The measure passed today, based on an American formula, involves a cumbersome compromise in which both Cambodian and foreign prosecutors and judges would jointly select the defendants and jointly reach their verdicts.
The derived formula involves a harmonic function η and a convenient method for its determination is also shown.
In particular, we prove a variational formula, in K∗(Cr∗, for the index classes associated to 1-parameter family of Dirac operators on a Γ-covering with boundary; this formula involves a noncommutative spectral flow for the boundary family.
Because the state taxes are based on a complicated formula that involves a credit against federal tax liability, the federal government will end up pocketing the money that otherwise would have gone to the states from 2006 through 2011.
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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