Sentence examples for globally implies from inspiring English sources

The fact that Φ satisfies the (Delta_{2} -condition globally implies that begin{aligneDelta_{2} -condition quadmbox{in } L^{Phi}(OmegloballyLongleftrimpliesowquad inthatOmega}Phibegin{aligned{n}-u_{n}rightarrowrightarrow0. end{aligned} (2.3).

the origin of system (5) is globally exponentially stable implies that the origin of system (1) is also globally exponentially stable.

(ii) the origin of system (5) is globally exponentially stable implies that the origin of system (1) is also globally exponentially stable.  . the global asymptotic stability of the trivial solution in system (5) implies the same stability of the trivial solution in system (1).

However, Figure 3 and Theorem 2.6 show that the unique positive equilibrium is globally stable, which implies the feedback control variables which make both populations growing unboundedly large now become globally stable.

Therefore, the disease-free equilibrium of model (1) is globally stable, which implies that the disease is extinct from Theorem 3.3.

Existence of the globally stable manifold implies that for any ki 0 there exists a unique pi 0 such that the pair (ki 0, pi 0) is on the globally stable manifold.

A globally shared responsibility implies the acceptance of a shared, not differentiated, value system.

By comparison principle, we conclude that, which implies exists globally.

The correctness preserving refinement of a fully synchronous model onto a globally asynchronous communication media implies that various restrictions be imposed on the synchronous model.

We proved that, if R 0 ≤ 1 holds, then the disease-free equilibrium is globally asymptotically stable, which implies that the disease fades out from the population.

Because the climate system derives all its energy from the Sun, this balance implies that, globally, the amount of incoming solar radiation must on average be equal to the sum of the outgoing reflected solar radiation and the outgoing infrared radiation emitted by the climate system.