I noticed that the most expressions ... of... use the zero article after of, like in the following examples:

'a generation of users'
'the most basic of mathematical sums'
'a a future individual incapable of independent human thought'

Which is the explanation for the use of 'the' after 'of' in the sentences below:

'Please watch the cabin attendant as she demonstrates the use of the oxygen mask.'
'The Call of the Wild.'

Is there a rule for using the definite article in such cases?

What is the difference between the following sentences:

'It is a software for monitoring the activity of users on a PC.'
'permits to control the activity of the users.'

Both examples are to be found on the internet using Google.

Thanks in advance
No rule except that of placing an article before singular countable nouns.

Your first 3 examples-- 'users', 'sums', and 'thought' are either plural countables or noncount.
Your 'oxygen mask' is a singular countable noun.

A generation of users.
A generation of discontent.
A generation of the computer.

The most basic of mathematical sums.
The most basic of advice.
The most basic chapter of the book.

Incapable of thought.
Incapable of errors.
Incapable of a lie.

The use of the oxygen mask.
The use of oxygen masks.
The use of air transportation.
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Hello Mr. Micawber,

Thank you for the tip about uncountable and plural countables nouns after of.
So the expression 'the activity of users' is correct, and 'the activity of the users' is not because the article has to be placed before singular countable nouns.
What do you think about the example I found in an on line dictionary:
'the wilds of the northern steppes.'
'An uninhabited or uncultivated region. Often used in the plural: the wilds of the northern steppes.'

Best regards
Alex RO
The rule is that the singular countable must have an article, demonstrative or possessive adjective. Plurals are not limited by this, and can take either the definite or zero article. These are correct:

The activity of a user
The activity of the user
The activity of that user
The activity of its user

The activity of users
The activity of the/those/its users

I just have few questions here. Starting with this.

How do they differ?

1. The activity of users

2. The activity of the users

When would they use "the" in front of the word "users"?

How about these sentences:

1. I am sending memos to all the people I know.

I am sending the memos to all the people I know.

2. Please give assignments to all the students here.

Please give the assignments to all the students here.

I don't the overall concept governing this area of grammar is specific vs. non-specific but perhaps, you can shed some enlightening force on this.
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