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I am confused about when one can omit the article "the"/"a" in front of a noun. Examples are

During (the) observation, it was noticed that ...
The results of (a) quantitative evaluation are listed in table 2.
(A) quantitative analysis shows that ...
(The) execution of the algorithm is very fast.

In all of these, omitting the article feels more natural to me. I tried to verify my gut feeling by comparing the sentences to the rules presented here, but I can't find any rule that justifies the articles' omission.

What is the correct way to formulate the above examples? Is my feeling just wrong? Also, does including/excluding the articles change the sentences' meaning?

Related questions:
https://english.stackexchange.com/questions/239585/why-do-people-omit-the-definite-article
https://english.stackexchange.com/questions/483505/omitting-article-before-evaluation

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    Note that academic writing has its own stylistic conventions, many of which involve distancing the writer from the events being described. Omitting the article to make it sound like they're describing observation in general rather than a specific act of observation is part of the academic style.
    – Canadian Yankee
    Commented Apr 17, 2021 at 13:50

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The phrase "a quantitative analysis" refer to an instance of such analysis. Without the article, you refer to analysis in general, without specifying a particular instance.
Without the article, you could even be referring to the consistent results of many analyses occurring at different times.
If you do use the article "a" or "the", you can probably specify when and where that instance of analysis occurred.

The same distinction applies to the other examples. Sometimes, using an article is just a matter of point of view - you may not wish to refer to a specific analysis, making a more general statement.

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  • So you are saying that none of the 4 sentences would be grammatically incorrect without the article? But whether the article is there or not changes the meaning slightly, as you described?
    – Jaklar
    Commented Apr 19, 2021 at 7:58
  • Yes, that's what I mean.
    – Jack O'Flaherty
    Commented Apr 19, 2021 at 14:45

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