"by an application of" is correct and can be used in written English.
You can use it when referring to something being caused or determined by a particular process or method. For example: "The success of the experiment was determined by an application of the scientific method."
Many smaller drums have laced and wedged heads, the skin being further tensed by an application of tuning paste.
"To me the best skin care regime for a baby with sensitive skin is plenty of hydration, a bath a day, followed immediately by an application of plain old petroleum jelly," said Dr. Siegfried.
This week, she said, she will also give "superamped facials" to a few awards-goers; the facials involve an acid peel or microdermabrasion to exfoliate the top layer of skin cells, followed by an application of a moisturizing serum.
Bill Frisell, the most widely imitated guitarist to emerge in jazz since the beginning of the 1980's, was once drawn to vaulting, heavily electrified sounds, with notes rounded into massive bubbles by an application of the volume pedal.
While he was self-deprecating about that success, Heinlein was never shy about his conviction that most social problems could be solved by an application of scientifically informed reason -- if only the irrational fools in power could be forced to step aside.
By an application of (3.6) we derive (3.9).
Now the result follows by an application of Hopf's lemma.
Rather, the doctrine is supported by an application of the latest scientific thinking.
With the assumption of (g=I), the corollary follows by an application of Theorem 3.1.
The proof is then completed by an application of Theorem 3.1.
The proof of the theorem follows now by an application of Lemma 2.1.
