Sentence examples for using the proposed expressions from inspiring English sources

The validation was performed in two steps: (1) The changes in pullout force with the modified earth pressure coefficient were calculated numerically as well as using the proposed expressions; (2) a case study is presented where the pipe response measured during centrifuge experiments is compared with the pullout force calculated using the proposed method.

The location of prying force can be determined using the proposed expressions (Eqs. 2, 3).

Open image in new window Fig. 11 Calculated pullout force using the proposed expression.

Experimental results obtained in bubble column and airlift contactors (external-loop and concentric-tube) of pilot-plant scale (ca. 50L liquid capacity), with water and 0.15 kmol m−3 NaCl solution as liquid media, were used to test the proposed expressions.

The material savings resulting from using the proposed design expression are also illustrated.

Secondly, the tension stiffening behaviour was investigated using the proposed analytical expression of the tension stiffening contribution in the cracking range.

Firstly, the work presents the validity of the model described in the above sections, and secondly the tension stiffening behaviour was investigated using the proposed analytical expression of the tension stiffening contribution in the cracking range.

And then, an equivalent damping ratio model suitable for flexure-shear critical RC columns is proposed by using the proposed hysteretic loop expression based on the Jacobsen's approach.

The lowest equal error rates of identical twins recognition that are achieved using the proposed method are 2.07% for natural expression, 0.0% for smiling expression, and 2.2% for controlled illumination compared to 4.5, 4.2, and 4.7% equal error rates of the best state-of-the-art algorithm under the same conditions.

Another important problem approached and solved by using the proposed PSO method is related to the expressions of reaction kinetics.

A case study [10] that involves centrifuge tests and numerical analysis performed on a rigid pipe buried in dense sand and subjected to relative axial movement is used to further validate the proposed expression.