Sentence examples for substituted back from inspiring English sources

the updated B automatically satisfies the solenoidal condition, and it is then substituted back into Eq. (23).

end{aligned} (17 The obtained contrained forces (due to the inputs in the system) can be substituted back onto the equations of motion (12).

To evaluate the curve, the observed responses for the individual standards were substituted back into the equation in order to calculate the predicted concentrations based on the calibration curve.

Values of the local parameter, L, for each family were then substituted back into Eq. (1) in order to calculate Wood Density Index (i.e. D BH for a 20-year-old tree).

The updated Lagrange multipliers μ [s+1] and λ [s+1] are then substituted back into (26) to obtain the new power allocation ({tilde {mathbf {P}}_{n}}^{k}}^{[s+1]}), and the resulting rate allocation (tilde {R}_{n,l}^{k}}^{[s+1]}) is obtained from ({tilde {mathbf {P}}_{n}}^{k}}^{[s+1]}) using (4).

If Equation 10 is substituted back into Equation 6, the relation between the log-spectrum vectors in the noisy training and test speech can be obtained as follows: y Te = y Tr + G y Tr, n, n Tr = y Tr + log i + exp n - y Tr - exp n Tr - y Tr (11).

"We don't have any problem substituting back and forth," Jones said.

Substituting back into (31), the linear MMSE estimator of can be rewritten as (34).

Our obtained solutions are verified by substituting back into their corresponding equations.

The optimal borrowing of the fund from each agent ( {A}_i^{ast } ) is obtained by substituting back X* into (A17).

Substituting back in (17), the dual function is Θ = - λ P ̌ + ∑ k = 1 K μ k d ˇ k + ∑ n = 1 N min s f n, s (37).