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One of Labour's immediate problems in Scotland was that the SNP proved sharper at articulating its policies and in presenting itself to the left of Labour.
Allen hit nine 3-pointers, tying a playoff record, as the Bucks proved sharper from 3-point range (13 of 19, 68 percent) than from the field over all (37 of 77, 48percentt).
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When two proven sharp-shooters meet in sudden-death circumstances both understand that only one can be left standing.
Richard Fahey also has prospects in the other Group race on the opening day, through Supplicant, but the downhill five furlongs in the Molecomb Stakes could prove sharp enough for a colt who should stay a mile in time.
Any book whose acknowledgments begin "I am extremely grateful to Her Majesty the Queen" would seem to promise pretty rarefied reading, but Juliet Nicolson's brief new social study of England in the summer of 1911 proves sharp and rangy, making room for the lower orders along with the royals and the gentry.
We prove sharp nonexistence results.
We prove sharp large time Gaussian upper bounds.
We prove sharp Lp→Lq estimates for averaging operators along general polynomial curves in two and three dimensions.
The results are applied in proving sharp embedding assertions in some limiting situations.
We prove sharp quantitative isoperimetric inequalities for John domains in Rn.
We prove sharp Lp − Lq estimates for the convolution operators defined through μ.
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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