Sentence examples for been proved by using from inspiring English sources

Best proximity point theorems for weakly contractive and weakly Kannan mappings, generalized best proximity point theorems for generalized contractions, and best proximity points for proximal cyclic contraction mappings have been proved by using this new method.

An aberrant presence of miR-21 in the blood vessel wall after balloon damage has been proved by using microarray and Northern blot analysis as well as qRT PCR method [ 30].

The evaluation of the endocrine activity in wastewater samples could already been proven by using these assays[75 78].

It has been proven by using band-corrected pseudopotential density functional theory that the ZnO/ZnS hetero-nanostructure can induce new interface state and related photoluminescence [17].

Stability and robustness are proved by using Lyapunov's method.

This result is proved by using the implicit function theorem.

The asymptotic stability of the closed-loop MRR system is proved by using the Lyapunov theory.

Then, the stability of controlled system is proved by using Lyapunov's direct method.

The global stability and the convergence of the designed controller are proved by using Lyapunov method.

The convergence of the identification error is proved by using the Lyapunov theory.

The asymptotic stability of the control system is proved by using Lyapunov theory.