Sentence examples for and substituted into from inspiring English sources

Approximate solutions are assumed for the space domain and substituted into the equations of motion.

The extinction at 550 nm is interpolated from lidarderived data and substituted into MODTRAN3 as user-defined 26 layers.

The flow patterns in the reactor were obtained and the mean linear electrolyte velocity was evaluated and substituted into a general mass transport correlation to calculate the mass transport coefficients.

In order to better match the actual force conditions of a satellite formation, a perturbed true anomaly and perturbed argument of perigee are adopted and substituted into the gradient of the J2 disturbance force.

The longitudinal normal stress field is postulated as polynomial and Heaviside step function series and substituted into the infinitesimal equilibrium conditions to develop expressions for the shear and transverse stress fields.

In-plane strain measures of the accelerated plates are obtained from the in-plane equations and substituted into the lateral equations to obtain the linear equations for modal analysis.

and substituting into system (64)–(64).

Then and substituting into (2.3) we have (4.7).

Putting and substituting into (2.10), we obtain (2.22).

By taking the Fourier transforms of (37) and (38), and substituting into (28), we eventually obtain.

The result stated in the lemma follows by using (31) along with the inversion formula (30) and substituting into (32).