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The definition of these spaces is based on a regularity property for the critical Sobolev spaces Ws,p(Rn), where sp= n, obtained by J. Bourgain, H. Brezis, New estimates for the Laplacian, the div curl, and related Hodge systems, C. R. Math.
Survival in these circumstances obviously depends on a regularity of precipitation.
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Burials there took on a grim regularity in October, when more than 100 Americans were killed in Iraq and Afghanistan.
Burials at Arlington National Cemetery took on a grim regularity in October, when at least 103 American troops were killed in Iraq and Afghanistan.
McMahon's cooperation ebbed, but Meltzer's coverage of these dramas was inexhaustible, as it was for entries that took on a morbid regularity: eulogies for deceased wrestlers, many of whom were younger than 50, and many of whom Meltzer had counted as friends.
Of the central characters, one is an out and out cad (he cheats on his wife with a regularity that would test the bounds of scheduling and stamina).
Tom Harrison is not a household name just yet but the England and Wales Cricket Board's new chief executive has been sending forlorn employees on their way with a regularity that Lord Sugar might envy.
The comic also appears on television panel shows with a regularity that threatens to put Jimmy Carr in the shade, and next weekend her TV show is up for a Bafta award.
Using a simple reformulation and shortest path problem duality as in Vohra (2011) we transform the initial non-convex pricing problem of the monopolist into an equivalent optimization problem yielding a closed-form pricing formula under a regularity assumption on the probability distribution of buyer types.
Other garments add atmosphere: the skillfully diaphanous angels' robes, bordered in a white-on-black-on red geometric pattern, have a regularity that is as reassuring as the asymmetry of the tormentors' bright clothes is not.
In fact, despite we collected data about people with different incomes and working habits, their movements are concentrated around a radius of about 100 kilometers showing also a regularity on the number of places visited during the week.
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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