Sentence examples for is proved by utilizing from inspiring English sources

The fact that symmetry of a spatial parallel mechanism can be directly mapped into the workspace of the end-effector is defined as a strengthened theorem and is proved by utilizing the group theory.

Theorems concerning stationary values of the respective Rayleigh quotients are proved by utilizing the generalized orthogonality relationships for the wet modes of these three kinds of liquid containing tank models.

This is proved by facts.

Theory is proved by simulation.

It is proved by induction.

Lemma 2 is proved by straightforward enumeration.

This is proved by an animal study.

This is proven by many studies [ 21– 21].

was proved by Skof [29].

This study was proved by Institutional Review Board of Qianfoshan Hospital, Shandong University.

This was proved by our statistical analysis.