Sentence examples for were proved using from inspiring English sources

Differences among groups were proved using two-tailed, unpaired Student's t test with Welch's correction.

It should be noted that these inequalities were proved using the variation of some functions and their derivatives, meanwhile, some of the above inequalities were improved using Taylor's expansions of inverse trigonometric functions.

The pioneering paper for the heat diffusion in a two-component domain with similar jump conditions on the interface is due to Auriault and Ene [6] (see also [7], where the results were proved using asymptotic expansions).

Structure validity and prognostic validity were proved using the linear regression through the origin method.

The direct antiangiogenic activity were proven using the rat aortic assay, The anti-HUVEC proliferation, migration assay and CAM assay.

Unconditional stability is proved using Von-Neumann approach.

Stability is proved using a Lyapunov approach.

Prior bounds are proved using Lyapunov function.

The stability analysis is proved using Lyapunov functions.

The stability of the drive is proved using Lyapunov criteria.

The stability of system is proved using Lyapunov theory.