Sentence examples for using the above relations from inspiring English sources

Then using the above relations and the Eqs.

Therefore, using the above relations, we obtain (2.18).

Finally, application of inequality (4.2) using the above relations leads to the claimed result.

Finally, since equalities, hold, we can apply inequality (4.2), using the above relations to get the required inequality.

Using the above relations, we can get the theoretical fittings for the experimental relationships between Vreset, Ireset, and Ron through choosing appropriate parameters of Treset and RTH,⟂.

Moreover, it is clear that ∫ - ∞ ∞ ( 1 + t x 1 ) - 1 d x 1 = O t - 1 2. Thus from (24) by using the above relations and Young's inequality we obtain the desired estimate T 1 * f L 2 ( B 0 ; H ) ≤ C t - 1 ∫ ∫ 1 + t ( x 1 - y 1 ) 2 f ( y 1, ⋅ ) L 2 d y 1 d x 1 ≤ C t - 3 / 2 f L 2 ( R n ; H ).

Using the above relation and Eq. (28), we find.

Using the above relation, we may estimate the electron carrier density.

Using the above relation in a recursive way, we obtain (3.34).

Using the above relation in a recursive way as well as the same argument of Proposition 3.2, we have (344).

The supernatant was separated by centrifugation and the content of chromate was measured by UV visible spectrometry and the uptake amount was deduced using the above relation.