Sentence examples for said to be persistent from inspiring English sources

System (1.5) is said to be persistent in mean, if.

Definition 4.1 System (1.3) is said to be persistent in the mean, if lim inf t → ∞ 1 t ∫ 0 t I ( r ) d r > 0 a.s.s

(i) The species (X t)) is said to be extinctive if (lim_{trightarrow+infty}X t)=0);   (ii) The species (X t)) is said to be persistent in mean if (lim_{trightarrow+infty}langle X t)rangle_>0).  .

The system (4) is said to be persistent in mean if lim t → ∞ 1 t ∫ 0 t x ( s ) d s > 0, lim t → ∞ 1 t ∫ 0 t y ( s ) d s > 0 a.s.s

The species (X t)) is said to be extinctive if (lim_{trightarrow+infty}X t)=0); The species (X t)) is said to be persistent in mean if (lim_{trightarrow+infty}langle X t)rangle_>0).

The microorganisms (x_{i}(t)) are said to be persistent if there exist positive constants (lambda_{i}) such that (liminf_{trightarrow +infty } x_{i}(t) geq lambda_{i}) ((i=1,2)).

Species (N t)) is said to be stochastically persistent in the mean if ([N]_ > 0).

(2) The population x ( t ) is said to be weakly persistent in the mean if 〈 x 〉 ∗ > 0.   (3) The population x ( t ) is said to be strongly persistent in the mean if 〈 x 〉 ∗ > 0.  .

If (liminf_{trightarrowinfty}frac{1}{t}int_{0}^{t}m(s),ds>0), a.s., then species (m(t)) is said to be strongly persistent in the mean.

The population (x t)) is said to be strongly persistent in the mean if (liminf_{trightarrowinfty} frac{1}{t} int_{0}^{t}x s),ds>0}^{t}x s

If (limsup_{trightarrowinfty}frac{1}{t}int_{0}^{t}m(s),ds>0), a.s., then species (m(t)) is said to be weakly persistent in the mean.