Sentence examples for and substitute in the from inspiring English sources

In these cases we present all data under the parent category (e.g. quiescent gas) and substitute in the distance from vent data in the subcategory (e.g. quiescent gas from vent).

He featured in qualification matches for the 2007 UEFA European Under-21 Football Championship and appeared as a starter and substitute in the first leg and second leg, respectively, of the team's surprising defeat to Israel in the qualifying playoffs.

Then the production possibilities set will consist of all combinations of fish, F, and coconuts, C, such that F=4L_f \, C=8L_c \, L_f + L_c=12 \, Solve the first two equations and substitute in the third to get, F/4 + C/8=12 \, This equation represents Crusoe's PPF.

The equivalent crack surface stresses are first obtained and substituted in the plane elasticity equations.

We find an equation for the pulse profile A by fitting procedure and substituting in the general equation for the vector potential, Eq. (8).

(42) On the other hand, computing the second-order Taylor coefficient and substituting in the first-order-optimized spectral value in Eq. (42), one finds (C_{4}^{(Omega )}ne0).

Through the monopiles head movements (displacements and rotations), the values of KL, KR and KLR were obtained and substituted in the analytical expression of natural frequency for comparison.

Recalling the model for discharged flow rate, Q in Eq. 9 and substituting in the above equation for discharged flow rate in shallow water: Q c = 0.1225 h o 0.27 g 2.66 sin θ n + n - 1 α 1 / 2 (16).

After conceding an early penalty scored by Antonio Cabrini, Arsenal defender David O'Leary was injured and substituted in the 20th minute, when Juventus striker Roberto Bettega tackled him.

2The value of Vapp can be determined by combining eqs 1 and 2 and substituting in the value for kobs from the chemical-quench experiment (eq 3).

When the glass is exposed to body fluids, initially alkali ions are leached and substituted in the glass structure by H+ or H3O+ cations from the fluid (stage I).