This inequality is sharp up to a constant (in the Gaussian setting).
The decrease is sharp up to almost 6 g additive and addition of more additive does not change fluid loss volume significantly.
We prove that D2u x0) is negative definite and give a quantitative bound on the spectral gapλmax(D2u x0))≤−c1exp(−c2diaminradfor universalc1,c2>0. This is sharp up to constants.
Gonzalez was sharp breaking up attacks and won most 50/50 balls in his area.
This was sharp, this was grown-up, this was modern.
Alas, the January effect was faithful to its cliché: The run-up was sharp (27% for Nasdaq)—and short-lived.
His disappointment in her was sharp but brief, and bound up with excitement.
The striker's link-up play was sharp, plus he was willing to make intelligent runs into space to receive the ball, and his growing influence was underlined when Ryan Shawcross hacked down the 27-year-old for a deserved booking.
Torres got the 2011 12 season underway in Chelsea's 0 0 draw away against Stoke City on 14 August 2011, in which his "link-up play was sharp, plus he was willing to make intelligent runs into space to receive the ball".
Tom McPhail, the head of retirement policy at the financial advisers Hargreaves Lansdown, said: "We're likely to see more of this kind of announcement in coming months, unless there is sharp pick up in bond yields.
