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The phrase "obtained by using" is grammatically correct and can be used in written English.
It is typically used to describe how something was acquired or achieved through the use of a specific method or tool. Example: The results of the experiment were obtained by using a microscope to observe the cells.
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In all, he held more than 20 credit cards, which he obtained by using fake driver's licenses and birth certificates.
The discount can be obtained by using the checkout code HANGOVER.
This is obtained by using a vector representation.
where the last equality is obtained by using - ii).
(b) The result obtained by using the GAC model.
Some important results obtained by using modified Nevanlinna counting function.
The data were obtained by using accidental sampling technique.
Periodic solutions are obtained by using linking theorems.
The result is obtained by using standard discrete Gronwall arguments.
Coding is obtained by using a XOR operation.
The energy floor is obtained by using the experimentally determined.
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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