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Assuming now that some fluxes in v have been measured (denoted as v m ), while the rest remain unknown (denoted as v u ), equation (13) can be rearranged as follows: (14) As measurements are imprecise in practice, such measurement imprecision can be incorporated as constraints: (15) where e m represents measurements errors and represents the actually measured flux value.
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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