Sentence examples for sharp conditions from inspiring English sources

Moreover, Faria [35] gave some sharp conditions on the general Lotka Volterra systems with delays.

The main results are Theorems 1 and 2, where we obtain sharp conditions for the solvability.

We find sharp conditions for the stability and instability of solitary waves.

In [7] the authors provide sharp conditions on the triple (Omega, rho ) and C for the validity of (2).

Weinstein [8] and Zhang [9] obtained the sharp conditions of global existence for critical and supercritical nonlinearity.

In this paper we improve their results and obtain sharp conditions under which the Koplienko Neidhardt trace formulae hold.

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

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.

We formulate here, among others, a sharp condition for its asymptotic stability.

We also provide natural sharp condition to recover exactly the spectrum of the unit sphere.

An example is also worked out to verify that the global attractivity condition is a sharp condition.