Sentence examples for using the computations of from inspiring English sources

Thus, for each t ∈ J, by using the computations of Step 2, we have that ∥ A x ∥ ≤ ρ.

Using the computations of the second step above we have begin{aligned} |u| le& (Lambda_{1}+Lambda_{2}+Lambda_{3}+ Lambda_{4}) bigl[|p_{1}|psi _{1}bigl Vert u Vert bigr)+|p_{2}|psi_{2}bigl Vert uVert bigr) &+ |p_{3}|psi_{3}bigl Vert uVert bigr)+ |p_{4}|psi_{4}bigl Vert uVert bigr) bigr], end{aligned} which implies that frac{|u|}{ sum_{i=1}^{4}Lambda_{i}|p_{i}|psi_{i}(|u| )}le1.

For the sparse solution, we used a reimplementation of Hunt and Szymanski's [ 17] algorithm that was presented by Gusfield in [ 18] using the computation of a LIS (Longest Increasing Subsequence).

For instance, if the full matrix is used, the computation of in (8) involves full matrices, and therefore the computational complexity would be at least.

For this purpose, we use the computation of two scenic properties that are obtained independently, but with both representing a moving object at this position.

We used the computation of the F st that accounts for differences in sample size (The International HapMap Consortium, 2005).

Using the standard computation of Calculus of Variation of with respect to, we can get its Euler-Lagrange equation: (31).

The gPROMS ModelBuilder was used in the computations of generic cases.

Fig. 2 Seismic velocity structure used for the computations of the Green's functions.

The first group was used for the computations of Odds ratios and coefficients, the second for validation of the model.

Four relaxation frequencies as 0.02, 0.2, 2.0 and 20.0 Hz were used for the computations of the unrelaxed moduli.