Sentence examples for established the result from inspiring English sources

This established the result.

In 1962, Rakotch [29] extended the Banach contraction principle with replacing the contraction constant c in (1.1) by a contraction function γ and established the result later.

It is worth noting that these steps only need to be run once for one population beforehand, and after sig-mers are selected and their connections with transcripts are established, the result can be repeatedly used on quantifying the transcriptome of many samples.

In 1492 Nicholas, the fifth Pope, established 'The Doctrine of Discovery' which established the resulting protocols of death and enslavement when discoverer's traveled and encountered non-Christians.

Once the open reading frames of relevant gene entries were established, the resulting protein sequences were analysed in various ways.

(The Supreme Court prevented the country from definitively establishing the result of the 2000 election).

Proof The reasoning in Theorem 2.2 establishes the result.

To establish the result, we need the following hypotheses.

To establish the result, we need the following lemma.

Using similar arguments to Theorem 4.1, we establish the result.

The key step in establishing the result of Theorem 2.2 is the following lemma.