Sentence examples for a sharp criterion from inspiring English sources

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.

In order to show the results of the spreading-vanishing dichotomy, the eigenvalue problems associated with model (1.3) are given in Section 3, and a sharp criterion for spreading and vanishing is established in Section 4.

A sharp criterion for the transition from a dimerized state to a long-range ordered state can be inferred from Figure 2(b), where the energy of the lowest singlet and the lowest triplet excitation is plotted.

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.

To understand the effects of the advection rate α and the expansion capacity μ on the dynamics of this model, we derive a spreading-vanishing dichotomy and obtain the sharp criterion for the spreading and vanishing by choosing α and μ as variable parameters.

Bartu A, Sharp J, Ludlow J, Doherty DA.

They established a spreading vanishing dichotomy, the sharp criteria for spreading and vanishing and estimate of the asymptotic spreading speed.

These criteria are widely used and do not consider the positivity to Sm antigen as an exclusion criterion like the Sharp criteria do [ 3, 37].