Sentence examples for sharp criteria from inspiring English sources
There were no sharp criteria for distinguishing the emotions.
They established a spreading vanishing dichotomy, the sharp criteria for spreading and vanishing and estimate of the asymptotic spreading speed.
Lastly, we apply these results to a special situation where two species are competing for the same resources and obtain a sharp criteria in term of certain variable parameters for all kinds of global dynamics.
This section is devoted to the proofs of the spreading-vanishing dichotomy, and the sharp criteria for spreading and vanishing.
Combining Theorems 4.5-4.7 4.5-4.7 derive the sharp criteria for spreading-vanishing for the invasion species.
To carry through this bold program, a sharp criterion of meaningfulness was required.
Moreover, a sharp criterion of weak Poincaré inequalities is presented for Poisson measures on configuration spaces.
Using this result, we derive a sharp criterion for no blow-up.
Moreover, we address a borderline problem in the regularity theory and give a sharp criterion for continuity of the gradient of a solution.
We provide a sharp criterion in term of generalized principal eigenvalues for existence/nonexistence of positive solution of (Pβ) in suitable classes of functions.
