Sentence examples for taking the solutions of from inspiring English sources

Therefore, applying Theorem 2.4 part (d) as in the proof of Theorem 2.1, and taking the solutions of (2.15) as values for parameters, we obtain that there exist positive profiles f i (i = 1, 2,..., k) solving (2.16) and satisfying (2.14).

(II) If α i < 0 and α i + β i > 0 (i = 1, 2,..., k), we can apply Theorem 2.4 part (c) as in the proof of Theorem 2.1 and taking the solutions of (2.15) as the parameters, we obtain that there exist compactly supports profiles f i (i = 1, 2,..., k) solving (2.16) and satisfying the boundary conditions (2.14).  .

The idea is to run a distributed optimization routine, taking the solution of (14) as the starting point, to solve for (6).

Step2: Take the solutions of (3) in the more general form: u ξ = a 0 + ∑ i = 1 m a i G ξ G ′ ξ i + b i G ξ G ′ ξ - i Open image in new window (4).

We suppose that (u^{0}_{1}(ageq00), (ageq0) is known, we take the solution of (2.7) as history function for (2.8) and we obtain nonnegative solutions if (u^{0}_{1}(a)) is not known.

We take the solution of reduced equations (B) of case (5) of Table 2 in the form F ( xi ) =sum_{i=1}^{m}a_{i} varphi^{i}, qquad H ( xi ) =sum_{i=1}^{m}b_{i} varphi^{i}, (31) where (varphi =varphi ( xi ) ) is a solution of the Riccati equation varphi '=q+varphi^{2}.

We take the solution of the u0 and u1 equations to have the form (41) u 0 = A ^ cos ⁡ σ, (42) u 1 = m 1 sin 2 σ + m 2 sin 2 σ + m 3, where A = A ^ ϵ from (29) and (31).

If no censoring takes place, the solutions of (2) simplify to the well-known standard equations for the empirical mean and standard deviation of log10 D i,j.

Proof Firstly, we take the solution ω ( t ) of Eq. (3) and make an appropriate substitution for the variable x.

According to the discrepancy principle, we will take the solution (xi _{max}) of the equation rho xi_{max})=taudelta (3.5) to be the regularization parameter, where (tau>1) is a constant.

Take the solution and allow a couple of drops on each side of the swab.