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The phrase "a very weak effect" is correct and usable in written English.
It can be used when discussing the impact or influence of something that is minimal or insignificant.
Example: "The new policy had a very weak effect on employee productivity, as most workers continued their previous habits."
Alternatives: "a minimal effect" or "a slight effect".
Exact(22)
On the other hand, extensive investigation of various positions throughout the oven indicated a very weak effect of load position on the thermal response.
In parallel, there is a clear effect of the temperature on crystal nucleation, contrary to a very weak effect of the temperature on crystal growth.
However, Lundqvist (1989,1991) and Lundqvist and Fridman (1996) found that the influence of local and stand-level density had no or only a very weak effect on the growth of small trees in uneven-aged spruce stands in northern and central Sweden, whereas Chrimes and Nilson (2005) reported negative influences which occurred in the very North.
Actually, the composition of the protective coating is the key factor: the best resistance is obtained in the presence of silicate, which plays the role of self-healing agents in corrosive conditions, whereas the incorporation of aluminate in the oxide has a very weak effect on the corrosion resistance of the treated alloy.
It has been found that the reducibility of the MOx/γ-Al2O3 catalysts plays a dominant role in the plasma-catalytic oxidation of acetone, whilst the specific surface area and pore properties of the catalysts have a very weak effect on the performance of the plasma-catalytic reaction.
Quantitative analyses of the pHER2/HER2 ratios indicated that trastuzumab had a very weak effect on HER2 activation.
Similar(38)
Organic matter production also has a positive, but very weak effect on alkalinity, while it strongly decreases DIC [23].
The first group was composed by individuals exhibiting genotype 0 for the N SNPs, i.e., carrying the frequent allele at homozygous state for the N SNPs; this group, theoretically the most frequent group in the study cohort, was set as a reference, and the relating combination of genotypes was considered as the "reference pattern" exhibiting a null or very weak effect on CRC risk.
Is there an explanation for this very weak effect?
Thus, microsatellite selection produced a highly variable and often very weak effect on the values of SFS-based statistics such as D. However, when D was driven negative by microsatellite selection, the decreases were often substantial, expansive, and long ranged.
When the value is small enough ( for both the cylinder--series and rectangular-prism--series building blocks), the blade shape begins to have very weak effect on the system's performance, due to the diminishing role played by the building block's cross-sectional area when compared to its length.
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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