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The phrase "a weakly positive" is correct and usable in written English.
It can be used in contexts where you want to describe something that has a slight or marginally positive quality or effect.
Example: "The results of the experiment showed a weakly positive correlation between the two variables."
Alternatives: "slightly positive" or "marginally positive".
Exact(54)
After controlling for temperatures in the 18th and 19th centuries, 20th century temperature has either a weakly positive or no effect upon current incomes; this finding survives a host of robustness checks.
Let be a weakly positive linear operator.
Since is a weakly positive linear operator, it follows that and so (3.25).
(1) is the -subdifferential of the convex operator ; (2) is a weakly positive linear operator; (3) is -strictly monotone.
(1) is the Fréchet derivative of the convex operator ; (2) is a weakly positive linear operator; (3) is strictly monotone.
Immunohistochemical examination showed that the tumor cells were strongly positive for CD34, c-kit, and DOG1; a weakly positive for alpha-smooth muscle actin; and negative for S100.
Similar(6)
Staining with the anti-ABCB2 antibody revealed a comparable, weakly positive, cytoplasmatic staining in GLC4 and GLC4-MITO.
This sample showed a very weakly positive signal after MDA treatment, suggesting that the amount of viral NA was close to the assay cut off.
This yielded two positive samples both by neutralisation cytotoxicity assay and VIDAS, and an additional weakly positive result using the VIDAS assay (Table 1).
In the forenoon period of December solstice, a 2 is weakly positive but in the postsunset period, a 2 is clearly positive over Dibrugarh but weakly positive over Okinawa.
A score of 10 or less was considered negative, a score of 11 - 99 weakly positive, a score of 100 - 199 moderately positive, and a score of 200 - 300 strongly positive.
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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