Sentence examples for presented to demonstrate the validity from inspiring English sources

Examples are presented to demonstrate the validity of the method.

In this section, four numerical examples are presented to demonstrate the validity of the designed method.

Simulation results are presented to demonstrate the validity and feasibility of the proposed approach.

Finally, two numerical examples are presented to demonstrate the validity of the theoretical results.

In this section, one numerical example is presented to demonstrate the validity of the designed method.

Illustrative examples presented to demonstrate the validity and applicability of the algorithms.

Numerical calculations are presented to demonstrate the validity of the first asymptotic approximation.

Numerical examples are presented to demonstrate the validity, functionality and applicability of the proposed methods.

Two illustrative examples are presented to demonstrate the validity of the proposed approaches.

Finally, three numerical examples are presented to demonstrate the validities of the sensitivity analysis and the optimization method.

A concrete example is presented to demonstrate the applicability and validity of the proposed approach.