Sentence examples for exists provided from inspiring English sources

An endemic equilibrium (E^(S^, V^,I^)) exists provided that (R_{v} >1).

It has been shown that an endemic equilibrium exists provided that (R_{v}>1).

We also observe that the inverse of in the ML estimator (16) exists provided that is full rank and.

Therefore our first task here is to prove that at least one escape solution of (1.1), (1.11) exists, provided (1.3)–(1.10, (1.10), and (1.13).

Then, for any (omegain operatorname{Fix}(T)), (lim_{n rightarrowinfty} |x_{n}-omega|) exists provided (x_{1}) and ω are comparable.

In case (i), a closed real loop exists provided than the fluid-to-solid density ratio is smaller than a certain critical value, estimated here in a simple explicit form.

The situation on the ground, as it exists, provides sufficient motivation to all well-meaning donors to come and do a decent part".

In other words, according to these criteria, a notch root radius different from zero exists, providing a minimum fracture load.

Theists, however, have often contended that there are a variety of arguments that, even if they do not prove that God exists, provide positive evidence.

And even when the infrastructure that allows interdisciplinary research to take place exists, providing training for the next generation of scientists doesn't happen automatically.

At present a large network of neutron monitors exists, providing the studies of cosmic ray variations related to the interplanetary conditions and geomagnetic activity.