Sentence examples for and prove in a from inspiring English sources

For the proof of these Theorems we need a lemma of independent interest, which we state and prove in a little more general form.

A simple and natural way to unify and prove in a simple manner several metrical fixed point theorems is to consider an implicit contraction type condition instead of the usual explicit contractive conditions.

The purpose of the Doctrine is to prevent innocent patients from having to be arrested and prove in a court of law that they are using cannabis for medical purposes.

The model is tested and proved in a cassava starch factory in Tayninh, Vietnam.

In this way, small but significant metal recovery gains may be measured and proven in a plant trial.

In this paper, we present a generalization of a combinatorial lemma we stated and proved in a recent work.

The character of the solution of the eigenvalue problem of the constrained system is stated and proved in a Theorem.

"When you take something so well established and proven in a global environment like Google and put it out there, it's not just like any open source project invented from scratch when there isn't much known and things are being developed in real time," she said.

and the second and third isomorphism theorem can be formulated and proven in a way very similar to the corresponding statements for groups.

The present study extended previous findings and proved in a one-year long experiment on rats that BD, initiated two weeks after induced myocardial infarction, attenuated LV remodeling and MI expansion, prevented the progressive thinning of LV wall, and actually reduced by 22% the mortality associated with developing chronic heart failure.

Our work lends a theoretical support to such experimentally obtained results and proves, in a generalized way, that it is not the mass of the atoms themselves, but the cumulative effect of hydrophobicity (space-filling nature of hydrophobicity) that governs protein stability.