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"demonstrate the competence" is correct and usable in written English.
You can use it when expressing the need to showcase a skill or demonstrate expertise in a certain area. For example, "The new employee must demonstrate the competence necessary to perform the job."
Exact(1)
Although additional ecologic studies are needed to confirm a primary vertebrate host for EEEV in Central and South America, our results demonstrate the competence of rats and of sparrows to serve as amplification hosts for NA and SA EEEV.
Similar(59)
However, most of the latently infected people never develop active TB, demonstrating the competence of their immune system to contain the bacilli [2].
This demonstrates the competence of the binding and translocation domains of PE to mediate delivery of the DTA and RTA catalytic domains into cells cytoplasm and, importantly, that NS3 cleavage mediated enhancement in the enzymatic activity of the two zymoxins (as was detected by in-vitro assays) is practically translated to enhancement in cytotoxic activity.
This implication of Ae. aegypti was confirmed by early experimental studies wich demonstrated the competence of this species to transmit ZIKV [ 14, 15].
In these studies, the CXXC-based trapping technique identified both established and novel target proteins, subsequently confirmed by independent techniques, demonstrating the competence of this technique to identify bona fide interaction partners.
Using BSR-Seq of 'green' and 'orange' bulks, derived from a cross between ' Dul' (orange fruit flesh) and ' Tad' (green fruit flesh), we demonstrated the competence of this method to investigate the specific transcriptomic effects of a single mutation, similarly to the accepted use of near-isogenic lines.
3) The solution phase assays especially with a dead mutant as substrate demonstrate the kinetic competence of intermolecular autophosphorylation.
She demonstrated the same competence and cool-headedness on that trip as she did guiding the author and her family down the Middle Fork of the Salmon River during the threat of fire.
X-ray examinations were carried out under full weightbearing conditions, demonstrating the mechanical competence of the formed tissue.
The observed burst-phase rate constant (270 ± 120 s–1) demonstrates the kinetic competence of the protonated His 76 in forming the acyl-enzyme intermediate.
This mass corresponds to the addition of a single sulfur atom to the octanoyl-peptide, demonstrating the catalytic competence of the mercapto-octanoyl intermediate.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com