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The first variations of state variables due to a change of the design variable are investigated.
roughly speaking, we should have begin{aligned} frac{delta F}{delta varrho } varrho ^tau _{k+1})+frac{varphi }{tau }=const end{aligned} (4.11)(where the reasons for having a constant instead of 0 is the fact that, in the space of probability measures, only zero-mean densities are considered as admissible perturbations, and the first variations are always defined up to additive constants).
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Stalling tactics dominate the first variation.
Dena Abergel had clarity and energy in the first variation.
Neither dancer overcame the difficulties, though, of the first variation.
In particular it is shown that the first variation vanishes and the second variation is nonpositively definite.
The first variation was danced by David Blumenfeld at the matinee and Ben Griffiths in the evening.
(the trailing backslash in the first variation is the shell line continuation character).
The long-limbed Ashley Laracey danced the first variation like a flowing dream, with Erica Pereira standing out for the piquancy of her second variation.
A fidgety flurry of semi-quavers in the first variation causes one of the dancers to develop a twitch.
From the first variation, he smothered the gorgeous tune in filigree, apparently harking back to those pianistic showpieces of yore.
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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