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A nonnegative form t on a complex linear space is decomposed with respect to another nonnegative form w: it has a Lebesgue decomposition into an almost dominated form and a singular form.
The present study investigates the influence that polar material response has on the plastic behaviour of thin-walled structures made of ideal fibre-reinforced materials (Spencer, 1972); or, equivalently, on the response of thin-walled fibrous composites within the first branch of the matrix dominated form (MDM) of the bimodal theory of plasticity (Soldatos, 2011, Dvorak and Bahei-El-Din, 1987).
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"There seems to be one dominating form of modern understanding," he wrote.
There were some who doubted he could ever regain his dominating form.
Mauresmo is trying to leave the French Open behind, hoping to recreate the dominating form she had during the spring.
Despite this, they remain the favourites to triumph on Thursday due to their dominating form in Europe this season.
It is rare that a human system develops into a fractal; most become top-heavy, with a few outsize elements dominating form and function.
But it soon became clear that the Red Bull car, little changed from 2012, had returned to its perfect marriage with the Pirelli tires and its dominating form.
In conclusion Mr. Fussell wrote that "there seems to be one dominating form of modern understanding; that it is essentially ironic; and that it originates largely in the application of mind and memory to the events of the Great War".
It did not seem difficult to know for most observers, though, since Red Bull's fortunes turned at the same moment as the tires were changed, when Vettel picked up his dominating form from the previous three seasons.
After consecutive 3-point victories against the Philadelphia Eagles and the Baltimore Ravens, in which their run defense was lacerated and Brady was under unusually stiff pressure, the Patriots returned to their dominating form against the Steelers, the best team remaining on their regular-season schedule and the likely third seed in the American Football Conference playoffs.
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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