Sentence examples for deduce estimates from inspiring English sources

Now, arguing as in Theorem 3.4, we easily deduce estimates (23) and (24).

where are given in (1.21) and (1.22), we deduce estimate (1.16) from condition (1.26) below given directly in the terms of matrix.

Thus taking into account (29), Corollary 5.2 in [11] and a well-known interpolation inequality (see Theorem 4.14 in [16]), we easily deduce estimate (28).

We then deduce Strichartz estimates for these equations.

To deduce these estimates we used only the strong ellipticity assumptions for the thermoelastic coefficients.

Our next goal is to deduce the estimates of (mathbb{G}(t)).

Then by Lemmas 3.3 and 3.7 we can deduce the estimates of ∫ 0 T ∥ y ( U h ) − Y h ∥ ∗ 2. □.

In order to deduce some estimates for the σ constant, we evaluate the series gamma biggl(frac{1}{2} biggr)=sum _{k=1}^{infty}frac{1}{2^{k-1}} biggl( frac{1}{k}-lnfrac{k+1}{k} biggr).

Before stating our main result, we first deduce certain estimates on (ϕ t, x), ψ t, x)) based on the assumption (1.16).

In the previous section, when we employ the Gronwall's inequality to deduce the estimates for higher regularity, it holds only with (C=C(T)).

To this end, we need to deduce certain estimates on composite functions and to do so, we need the following result whose proof can be found in the proof of Theorem 4.3 of [5].