Sentence examples for deduce the estimates from inspiring English sources

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

Then the following a posteriori error estimate holds: ∥ ξ z n − 1 ∥ ∗ ⪯ η z, n, where η z, n 2 = ∑ K ∈ T h α K 2 ∥ R K, z n ∥ 0, K 2 + ∑ E ∈ E h ε − 1 2 α E ∥ ε R E, z n ∥ 0, E 2 + ∑ E ∈ E h α E 2 h E ∥ R E, z n ∥ 0, E 2. In the following we shall deduce the estimates of ρ y and ρ z.

By a similar argument, we deduce the estimate δΩ (γw) ≍ |γw||θ - θ k | and so.

end{aligned} Combining these inequalities and using again Theorem 16, we deduce the estimate asserted.

(4.31) Inserting this into (4.30) and choosing ε sufficiently small, we deduce the estimate (4.23).

From (3.21), converting back to the x-variables ( z = T ( x ) ), we easily deduce the estimate (3.9).

As for the first term, by the continuity of and (4.5), the facts that and that is increasing, we deduce the estimate.

For example, from Weil's classical work [7] one can deduce the estimate | C ( m, 0, 2, χ ; p ) | ≤ 2 ⋅ p 1 2. for ( m, p ) = 1.

If f ( x ) is not a perfect q th power modp, then from Weil's classical work (see [10]), we can deduce the estimate ∑ x = N + 1 N + M χ ( f ( x ) ) ≪ p 1 2 ln p, where '≪' constant depends only on the degree of f ( x ).