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The phrase "a small influence of" is correct and usable in written English.
It can be used when discussing the impact or effect of something that is minor or limited in scope.
Example: "The study revealed a small influence of environmental factors on the participants' behavior."
Alternatives: "a slight impact from" or "a minor effect of".
Exact(17)
Therefore, taking intermittency into account only demonstrates a small influence of the reserve margins of the entire power system and the total generation costs.
The Ic-o WFJs exhibited significant recovery; a small influence of the FRP viscoelastic properties on recovery and a constant damage rate were observed.
Conversely, reduced imperfection amplitudes reported in the literature are found to lead to well documented failure mechanisms and to a small influence of the buckling mode interaction.
On the basis of a duplex layer structure for the anodic layer, the results show only a small influence of the nature of the cations in those process concerning the inner barrier layer specifically.
The application of the ultimate failure load prediction method showed a small influence of the adhesive layer thickness on the joint strength although the influence of the fillet radius was seen to be much higher.
A small influence of differences in volume of the QC sample was observed mainly on strip 1.
Similar(43)
We therefore also expect productivity to have a small influence on the probability of being served by these types.
This distance has a small influence on the accuracy of the proposed methods, all analytical CDF fit well with the CDF obtained by simulations.
Step-length and step-length noise have a small influence on the value of the objective function reached (see figures 5A and 5B).
Genetic variants that putatively affect bone maintenance and/or loss in adults appear to have a small influence on the rate of bone acquisition through adolescence.
Here again, the parameter has a small influence on the globally good accuracy of the methods.
More suggestions(14)
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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