Sentence examples for using the completeness of from inspiring English sources

By using the completeness of X, there exists (x^in X) such that (x_{n}rightarrow x^) as (nrightarrowinfty).

Using the completeness of (L^{p}_{mathrm{loc}}(mathbb{R}, X)), we denote by (y(t)) the pointwise limit of (y_{i}(t)).

It can be shown that the weighted Orlicz space is also a Banach space by using the completeness of the usual Orlicz space.

Hence, on using the completeness of f ( X ) and assumption (a) (i.e., f ( X ) ⊆ g ( X ) ), there exists u ∈ X such that lim n → ∞ g ( x n + 1 ) = lim n → ∞ f ( x n ) = g ( u ).

The residual disease is classified intraoperatively using the completeness of cytoreduction (CC) score.

Firstly, we point out that Dalal et al. [31] used the completeness of X in their proof but failed to mention the same in the hypotheses.

By using the completeness result of Lemma 8 and the orthogonality relation of Lemma 9, we can easily prove the uniqueness result.

By using the completeness earthquake dataset, the calculated values of b and D C were found to imply variations in seismotectonic stress.

We have x ∈ [ x, → ) ∩ ∩ x ≺ m ( ←, m ], where m ∈ M. Using the external completeness of M, we get M ∩ [ x, → ) ∩ ∩ x ≺ m ( ←, m ] ≠ ∅. It is easy to check that this intersection is reduced to one point. Set M ∩ [ x, → ) ∩ x ≺ m ( ←, m ] = { P ( x ) }. Similarly, let x ∈ C u ( M ).

However, because of the large sample size used and the completeness of the data set, we believe the trends were not altered significantly by this possible limitation.

Newbler assembled consensus EST sequence data was used to assess the completeness of the final assembly using alignment with 90% identity and 85% coverage thresholds.