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The phrase "further determined" is correct and commonly used in written English.
It is typically used to add emphasis or expand upon a previous statement or decision. Example: After careful consideration, the committee further determined that the proposed changes would not be in the best interest of the company's employees.
Exact(60)
We further determined whether CBX6 directly targets BST2.
The trial court further determined that APTC satisfied this test.
We further determined the overall genomic organization of BmChi-h.
The IC50 values and inhibition constants were further determined.
Morphology was further determined using scanning electron microscopy.
We further determined the mechanism by which JMJD2B promotes PPARγ2 expression.
We further determined whether altered MMP activity was explained by amount of MMP protein.
Oocyte quality was further determined by spindle morphology and chromosome alignment (Fig. 3a).
We further determined the crystal structure of JMJ13 in peptide-free and H3K27me3 peptide-bound forms.
Cell viability was further determined using the CCK-8 assay (Supplementary Fig. S1c).
The court below further determined that the jury instructions comported with this legal standard.
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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