Sentence examples for by substituting the solution from inspiring English sources

Because direct solution of (1) is computationally intractable, to quantify the amount of sub-optimality, we calculate an upper bound (denoted in Figure3 as Upperbound) by substituting the solution of DIS NC into (4).

Finally, by substituting the solution for λ in Eq. (46), we find the explicit formula of the required parabola:.

These knockdown-to-knockdown influences, m 12 and m 21, are: (4) m 12 = δ 1 1 + δ 2, m 21 = δ 2 1 + δ 1 By substituting the solution of Equation 3 into Equation 4 we obtain the influence coefficients m i j as a function of the regression parameters.

end{aligned} (3.16) By substituting the solutions (3.12)–(3.16) inside (3.1), we obtain an approximate formula for the membrane potentials of the neural network.

The residual is calculated by substituting the numerical solution into the differential equation, (3.7). Figure 2 Problem (1. 9a - 1.9b): The numerical solution, the error estimate, and the residual for, and.

The resulting equations are put into a state-space representation and the frequency values are finally obtained by substituting the general solution of the state equation into the set of boundary conditions and solving the related homogeneous system.

According to Lubinski's analysis, a system of linear equations in the form of (mathbf{MX} = 0) is obtained by substituting the general solution Eq. (2) into boundary conditions at the top and bottom ends of the drill string.

So, one can obtain the full set of exact solutions of NLEEs by substituting the various solutions of elliptic like equations into original NLEEs.

Finally, by solving (23)[17] and substituting the solution into (22), the CDF (i.e., outage probability) of the random variable γj,k is obtained as F γ j, k ( x ) = 1 - 2 2 α 1 α 2 x exp ( - Zx ) K 1 2 2 α 1 α 2 x. (24).

Without loss of generality, assuming that (c=1) and substituting the solution of the spectral problem (6) given by Eqs.

The buckling mode shapes are obtained by substituting the nontrivial coefficient solutions into the mode shape solutions of the subproblems, followed by superposition.