Sentence examples for been provided to demonstrate from inspiring English sources

Numerical results have been provided to demonstrate the procedure.

Two numerical examples have been provided to demonstrate the effectiveness of the proposed method.

Numerical examples have been provided to demonstrate the validity of our results.

Numerical examples have been provided to demonstrate the effectiveness and applicability of the proposed approach.

Numerical results have also been provided to demonstrate the performance of the proposed protocol.

A simple example has been provided to demonstrate the effectiveness and applicability of the proposed testing criteria.

Examples are provided to demonstrate its usefulness.

Examples are provided to demonstrate the results.

Three illustrative examples are provided to demonstrate its applicability.

Finally, two examples are provided to demonstrate the proposed results.

Numerical results are provided to demonstrate the proposed algorithms.