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We also provide natural sharp condition to recover exactly the spectrum of the unit sphere.
This year, she is in sharp condition again; in last Sunday's victory in a 10-kilometer road race in Charleston, S.C., she ran a 31:531
In particular, we give a sharp condition for the discreteness of the spectrum of H beyond which we find dense pure point spectrum.
It was an encouraging performance, and Jim Conway, who trains Chateaugay, deserves full marks for bringing him back to the races in such sharp condition after all the ankle trouble that plagued him.
Kenig, F. Merle, Global well-posedness, scattering and blow-up for the energy critical focusing non-linear wave equation, preprint], where a sharp condition on the smallness of the initial data is given.
We formulate here, among others, a sharp condition for its asymptotic stability.
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We find sharp conditions for the stability and instability of solitary waves.
In this paper we improve their results and obtain sharp conditions under which the Koplienko Neidhardt trace formulae hold.
We present here essentially sharp conditions under which the DAD problem (k, α, β) has a solution.
As a byproduct, we obtain sharp conditions for the twisted convolution to be bounded on Wiener amalgam spaces.
We provide sharp conditions for the autonomous structure to break up and give way to a bewildering diversity of nonautonomous bifurcations.
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CEO of Professional Science Editing for Scientists @ prosciediting.com