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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?
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.
