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I think I made a grammatical error by writing "of j-integral" instead of "of the j-integral" in the subtitle of a written work. The subtitle reads "A study of J-integral,..."

Google gives a large number of hits for both phrases:

Google search result:

"of j-integral": 55 600

"of the j-integral": 147 000

Google Scholar search result:

"of j-integral": 9 360

"of the j-integral": 13 300

What is the grammatically correct phrase? Is there any ambiguity?

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    Google Ngram Viewer shows that using 'the' is more popular. Neither is wrong, and the Wikipedia entry uses both. Commented Aug 27, 2022 at 15:42

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It depends on how focused or narrow your study is. If it's specific to describing j-Interval, I would use the article. If it's broader, don't use the article.

When you're referencing something specific --something with a known identity-- you use an article. You use "the" rather than "a" when that something is unique, regardless of whether it's countable.

A Study of the j-Interval

When you use "the", I would expect that your paper has a definition of the j-Interval because it's a specific "thing."

A Study of j-Interval

If you don't use an article, then j-Interval becomes an abstract "thing" that's general in nature and not specific or unique. This allows you to cover topics in your study that are related to j-Interval but not considered to be j-Interval. It's often used in the plural in this case as well.

For example:

A Study of the Electric Vehicle.

Because it's something unique and specific, it more narrowly defines the scope of the study.

A Study of Electric Vehicles.

This allows you to cover a wide variety of topics related to electric vehicles.

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