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The phrase "a specific case of our" is correct and usable in written English.
You can use it when referring to a particular instance or example that falls under a broader category or concept that belongs to a group or organization.
Example: "This is a specific case of our ongoing research into climate change impacts."
Alternatives: "a particular instance of our" or "an example of our".
Exact(2)
A specific case of our main result is the following theorem.
It is also shown that the existing biquaternion multiple signal classification (BQ-MUSIC) estimator is a specific case of our BB-MUSIC ones.
Similar(58)
However, as already said in the introduction, our work considers a specific case of WSCs based on multiple collaborating processes.
A multi-casing structure in a wellbore in the formation belongs to a specific case of an inhomogeneous body.
The hierarchy is a specific case of entity-relation graph using a containment relation.
Then we can get a specific case of system (2).
It is a specific case of a generalized case where more than one feature occur.
Obviously, an ordinary fixed-rate loan is a specific case of this type.
As DCF is a specific case of EDCA, the totality of argument is reserved.
The last one is called pesticide DRASTIC index and represents a specific case of DRASTIC index.
This is a specific case of the general image stitching problem.
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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