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The phrase "depending on the variations" is correct and usable in written English.
It can be used when discussing how something may change or be influenced by different factors or conditions.
Example: "The outcome of the experiment will vary depending on the variations in temperature and pressure."
Alternatives: "contingent upon the variations" or "based on the variations".
Exact(7)
Therefore, we want to analyze the channel capacity depending on the variations of the correlation matrix.
The speeds are varied depending on the variations in the path and on the posture of the robot.
It should be noted that the concrete properties will be different depending on the variations of each of the concrete trucks.
Depending on the variations of the geometrical offset along the glaciers, a post-processing step can be necessary to deduce the offsets only due to the glacier movement.
The data indicated that the metabolic responses to H2O2 challenge were uniquely different depending on the variations of temperature and pH.
On the moving glaciers, the measured offset is the sum of the displacement offset and the geometrical offset which has not been compensated for at step 1. Depending on the variations of the geometrical offset along the glaciers, a post-processing step can be necessary to deduce the offsets only due to the glacier movement.
Similar(53)
Both involve shrinking and expanding the city in a kind of land swap with the Palestinians, by which Jewish settlements in the West Bank that abut the city would be added to a reconfigured Jewish Jerusalem, while Palestinian neighborhoods would be given to the Palestinians -- in full or in part, depending on the variation.
This process resulted in obvious structural transformation depending on the variation of volume and the surface height of photoresists [26].
Also, depending on the variation of the methanol concentration, the IR loss and Faradaic impedance is measured via impedance analysis.
The results showed that this controller could adjust the welding current accurately and promptly depending on the variation of the arc sound signal.
It is done periodically depending on the variation of the PA parameters due to thermal effects (which usually vary slowly with the time).
More suggestions(16)
depending on the variants
depending on the substitutes
depending on the variances
depending on the interpretations
depending on the varied
depending on the variability
depending on the discrepancy
depending on the alternative
depends on the variations
depending on the changes
dependent on variations
depending on the variables
depending on variability
information on the variations
depending on divergence
depending on individual variations
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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