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

Finally some benchmark data sets are applied to demonstrate the validity and efficiency of this method.

Finally, several numerical examples are analyzed to demonstrate the validity and capability of proposed computational algorithm.

To demonstrate the validity and accuracy of the technique developed, several numerical examples are illustrated.

A frame structure is used to demonstrate the validity and versatility of the method.

Numerical examples are presented to demonstrate the validity and the accuracy of the proposed method.

Several cases are solved to demonstrate the validity and performance of the proposed analytical method.

Finally, two simulation examples are given to demonstrate the validity and effectiveness of the proposed approach.

Numerical results are presented to demonstrate the validity and good performance of our proposed algorithm.

Several numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.

An illustrative design example is used to demonstrate the validity and applicability of the proposed approach.

Numerical examples will be given to demonstrate the validity and applicability of the present problem statement.