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The phrase "a function of the magnitude" is correct and usable in written English.
It can be used in contexts involving mathematics, science, or engineering to describe how one variable depends on the size or extent of another variable.
Example: "The pressure exerted by the gas is a function of the magnitude of the temperature and volume."
Alternatives: "dependent on the size" or "related to the extent".
Exact(30)
The LUT expresses the desired parameterb as a function of the magnitude and phase of the diffuse component R ik.
Fig. 4. Photometric uncertainties as a function of the magnitude at each IRC band for sources with full color information.
The amount of stiffness reduction was observed to be a function of the magnitude of the fatigue loading applied to the specimen.
The amount of stiffness reduction was observed to be a function of the magnitude of applied fatigue loading on the specimen.
Figure 4 shows the mean weight of earthquakes with magnitude M > m in R over the period 2000 2009, as a function of the magnitude threshold m.
The misfit stresses at the length-scale of grain families, measured by neutron diffraction, were shown to be a function of the magnitude of the tensile pre-strain.
Similar(29)
The range of beneficial tax levels can, therefore, be identified as a function of the possible magnitude of future shocks in transportation costs.
(3) The occurrence probability of ESF is characterized by a continuous probability distribution as a function of the PRE magnitude.
Figure 8 shows the mean damage degrees obtained using the two methodologies as a function of the earthquake magnitude.
Note that ε is a function of the fading magnitude |h|, signal-to-noise ratio SNR, and blocklength m.
The risk is a function of the probability, magnitude, and other characteristics of an event and the consequences of the event.
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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