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"demonstrate no relation" is correct and can be used in written English.
It is used to describe a lack of connection between two things. For example, "The two statements demonstrate no relation to one another."
Exact(1)
Data obtained in this study demonstrate no relation between genotype and virulence genes repertoire in studied Arcobacter species.
Similar(58)
This was contradictory to other authors [23 25] who reported that ankyloglossia was more common in class III skeletal malocclusion [26, 27] demonstrating no relation between the short lingual frenum and any dental or orthodontic anomalies.
Direct comparison of paired MS13 and MS110 histoscores was performed and demonstrated no relation.
Other factors, such as tumor invasion of blood vessels, lymph nodes or lymphatic ducts, and tumor metastases, also demonstrated no relation with RUNX3 methylation.
It has been presumed that the increased gastric volume leads to regurgitation and aspiration, yet multiple studies have demonstrated no relation between the GRV and the risk of aspiration [ 5, 38].
The expression of p14 ARF and Mdm2 demonstrated no significant relation with p53 levels.
New-onset valvular regurgitation did not demonstrate any relation to clinical or treatment related parameters.
The current study demonstrated that no relation existed between the performance in activities of daily living and the presence of significant valvular heart disease.
We could not demonstrate any relation between cardiovascular disease or the incidence of hypertension in relation to environmental exposure to lead and cadmium (Staessen et al. 2000).
The expression of p21 Cip1 and p27 Kip1 demonstrated no significant differences in relation to the p53 expression in normal, REG, LGD, HGD mucosa.
Here the time step size is controlled to demonstrate the relation between the error function and the spatial sizes.
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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