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"under the operation" is a correct and usable phrase in written English.
It is typically used to describe an action or process that is being carried out by something or someone. Example: The patient was placed under the operation of a skilled surgeon. In this sentence, "under the operation" means that the patient is being operated on by the surgeon. Another example could be: The factory was shut down for repairs under the operation of the maintenance team. In this case, "under the operation" implies that the maintenance team is carrying out the process of repairing the factory.
Exact(53)
Open image in new window Figure 4 Inner working of method under the operation of different operators.
The group, operating under the Operation Africa banner, with the hashtag #OpAfrica, says it is targeting those who "enable and perpetuate corruption on the African continent", and those responsible for child abuse and child labour.
The conventional CCHP systems often operate at part load and cause power surplus under the operation mode of power following thermal load.
High-profile figures unconnected to Savile, including publicist Max Clifford and DJ Dave Lee Travis, have been convicted for sex crimes under the operation.
Then he realized he was abandoning an infant to a vehicle under the operation of a man kneading tinctures of a patently illicit substance into his face.
The Tex Beneke Orchestra, now under the operation of Jim Snodgrass, still tours and performs, and is based in Southern California.
Similar(7)
A subalgebra of an algebra is a set of elements of the algebra closed under the operations of the algebra.
They are also applicable to many nonnumeric domains such as the subsets of a given set under the operations of union and intersection, the words over a given alphabet under the operations of concatenation and reversal, the permutations of a given set under the operations of composition and inverse, etc.
It is straightforward to see that this collection is the least collection containing the closed sets and closed under the operations of complementation and countable union.
Notice that the sets (mathcal{K}(Y)) and (mathcal{K}_{C}(Y)) are closed under the operations of addition and scalar multiplication.
From entering the harbour to leaving with the ships under tow, the operation had taken 30 minutes, without any losses to the raiding party.
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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