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The phrase "after applying the" is correct and usable in written English.
It can be used when discussing the results or outcomes that follow the application of a method, process, or tool.
Example: "After applying the new software update, the system performance improved significantly."
Alternatives: "following the application of" or "subsequent to applying".
Exact(60)
Nominations changed positively after applying the music program.
After applying the glue, wait a few minutes before joining the pieces.
After applying the full thrust, the plane climbed and continued its flight to Greece safely.
After applying the exclusion criteria, a total of 452 neonates remained for analysis.
But dozens of people have reported flipping over the handlebars after applying the brakes.
Rice Yield increased after applying the System of Rice Intensification (SRI).
Although still not extremely accurate, the results are indeed useable after applying the Kalman filter.
After applying the mineral, rice and wheat can be grown in alternating seasons.
After applying the mask to your hair, maximize its benefits by applying heat.
After applying the league's tie-breaking procedure, the Nippon Paper Cranes were ranked first.
Heidenreich put The Undertaker in the casket after applying the cobra clutch.
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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