Sentence examples for proved provided that from inspiring English sources

The existence of a strictly increasing solution (a homoclinic solution) satisfying, is proved provided that has two zeros and a linear behaviour near.

The monotonicity of the tumor growth model is proved providing that the search algorithm finds the optimal solution.

Judge Jameson said he would vary the compensation and costs if evidence could be provided that proved the defendant was in a difficult financial position.

Browder, see [1], proved that is nonempty provided that is, in addition, bounded.

The administration counts all military-age males as possible combatants unless they have information (posthumously provided) that proves them innocent.

According to the law, "the prize can only be paid out if sufficient information is provided that proves without doubt that the claimant is the rightful" winner.

And happily, a handful of wealthy technologists and other private donors have proved willing to provide that support.

It remains to prove (7.2) provided that A is closed.

If (1.12) is not valid, then the existence of both an escape solution and a homoclinic solution is proved in [12], provided that satisfies moreover.

For instance, I have to provide a summary of benefits, and you have to not only provide it, you have to prove you provided it". That was the only example Secor could offer.

We prove that they exist provided that the lengths of the sub-spans are properly chosen.