Sentence examples for are given to validate from inspiring English sources

Lastly, numerical results are given to validate the present method.

Numerical examples are given to validate the proposed approach.

The simulation results are given to validate the analytical results.

Simulation results are given to validate the derived properties.

Simulation examples are given to validate the results.

Finally, numerical examples are given to validate the theoretical results.

Numerical simulation is given to validate the proposed theoretical result.

An example is given to validate the theoretical results.

An example is given to validate the proposed methods.

Finally, an illustrative example is given to validate the effectiveness of the proposed design methods.

Some numerical simulations have been given to validate the performance of the encryption scheme.