Sentence examples for proved in the context of from inspiring English sources

In 1922, S Banach proved in the context of metric spaces his celebrated fixed point result.

The following results are proved in the context of spaces of homogeneous type in [13, 14] and [10].

The main result is a generalization of a theorem previously proved in the context of isodual codes.

On the basis of the inequality presented in Theorem 6, the well-known Markov inequality and the Chebyshev inequality in probability theory are proved in the context of fuzzy rough theory as follows, which can be seen as special cases of Theorem 6.

Furthermore, the Vpx part within the HA-Vpr/Vpx fusion protein was still functional in terms of enabling efficient transduction of monocytes, as proven in the context of the PBj4xko-EGFP vector.

The underlying premise – namely that all humans are possessed of dignity in virtue of a special relationship to a God – is, however, incapable of being used as a basis of public policy proven in the context of a democratic, multicultural and multi-faith society that must cleave to the strictures of public reason in ethical deliberation.

Several decades ago, the beneficial effects of goal-directed therapy, which include decompressive laparotomy (DL) and open abdomen procedures in cases of intra-abdominal hypertension (IAH) in children, were proven in the context of closures of abdominal wall defects and large-for-size organ transplantations.

Chen and Yang [28] proved that in the context of nonnegative toll schemes and/or toll-cum-rebate schemes for Pareto-efficient control, the TSS always has a solution.

The innovative strategies indeed proved significant in the context of current Philippine education, UN priority directions, and priorities of other development and donor agencies working for the country.

Spreading project activities over a relatively long period of time enabled the engagement and support of senior management as part of the process which proved beneficial in the context of this project in securing structural changes to service delivery.

Overall, although we do not know to what extent the research priorities identified apply to other fields of practice, we consider that this method proved appropriate in the context of the current study.