Sentence examples for we obtain there from inspiring English sources

The flavours, the colours we obtain there are extraordinary: a range of perfect greens.

Invoking Leray-Schauder's alternative theorem, we obtain there exists x ∈ W 1, 2 ( I, R N ) such that x = L − 1 f ( x ), x is a solution of the problem (3.8).

He added: "We know from the data we obtained there are names of people from more than 170 countries.

However, in the tolerant strains we obtained, there are no significant changes in the expression levels of genes related to fatty acid biosynthesis in comparison with the strain P. In addition to the expression changes common to all tolerant strains as discussed above, there were expression changes specifically occurred in each tolerant strain.

Nevertheless, based on the results we did obtain, there were significant differences between the two groups as described above.

By the Fermat theorem, we obtain that there exists K ∈ ( K m, K M ) such that F ′ ( K ) = 0. □.

We claim that for all By way of contradiction, in view of and for all, we obtain Then there must exist ; for convenience, we can choose such that (2.11).

Since G ( X k ) is closed and by (3.2), we obtain that there exists Y ¯ ∈ X k for which lim n → ∞ G ( Y n ) = lim n → ∞ T ( Y n ) = Z ¯ = G ( Y ¯ ).

Hence, thanks to the contraction mapping principle applied, we obtain that there exists T > 0 such that the integral equation f ( t ) = ∥ u 0 x ∥ L ∞ + c ∫ 0 t [ ε s − r 4 exp ( c ∫ 0 τ f ( s ) d s ) + 1 2 f 2 + 1 ] d τ. has a unique solution f ( t ) ∈ C ( [ 0, T ] ).

In (6.4), using the proof similar to those of Lemma 4.2 and Theorem 4.1, we obtain that there exists subsequences { x k j } and { y k j } of { x k } and { y k }, respectively, such that lim j → ∞ ∥ x k j − y k j ∥ = 0. (6.5).

We can simply reuse the result obtained there if we replace by in (28).