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Question 1.

I found the following example sentence in Longman Dictionary of Contemporary English: She was finally evicted in April for non-payment of rent.

Is it optional to put "the" between "for" and "non-payment"?

She was finally evicted in April for the non-payment of rent.

Question 2

According to a Japanese website for English learning, the following sentences are both acceptable and there is no difference in meaning between them.

The closure of a factory causes hardship to everyone involved.

Closure of a factory causes hardship to everyone involved.

But the definite article before "closure" is required in the following case.

The closure of that factory caused hardship to all of them.

Wrong: Closure of that factory caused hardship to all of them.

Does it mean that "the" is required before "closure of that factory" because the sentence mentions "that factory" (not just any factory)?
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Comments  
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Question 1.

Is it optional to put "the" between "for" and "non-payment"?-- Yes but the omission is more usual. It is the name of a social breach: he was arrested for murder.

Question 2
Does it mean that "the" is required before "closure of that factory" because the sentence mentions "that factory" (not just any factory)?-- The Japanese website (of course) is wrong. All 4 are acceptable and the members of each pair carry the same meaning.
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Mister MicawberThe Japanese website (of course) is wrong. All 4 are acceptable and the members of each pair carry the same meaning.
According to Longman Dictionary of Contemporary English,

The is
used before nouns referring to actions and changes when they are followed by 'of':
the growth of the steel industry
the arrival of our guests

You mean it is quite okay to say, for example, "I would like to report growth of the steel industry," or "I heard that arrival of our quests has been postponed."?
Students: Are you brave enough to let our tutors analyse your pronunciation?
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Not at all; I only said that those 4 sentences were all correct. I think that, as with most grammar books, Longman has oversimplified.
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Thank you, but I'm a little confused.

Mr. Micawber, I suppose you live in Japan. Probably you realize that the English definite and indefinite articles are very difficult to Japanese people

Let me propose the following hypothesis:

Hypothesis

Closure of a factory causes hardship to everyone involved.” is okay, because we can use the ing-form "Closing" instead.
Closing of a factory causes hardship to everyone involved.
"She was finally evicted in April for non-payment of rent." is okay, because we can use the ing-form instead.
She was finally evicted in April for not paying rent.

If this hypothesis is correct, "the" is optional in the following case.

What do you think of the liberalization of rice imports?/What do you think of liberalization of rice imports?
Because we can say, "What do you think of liberalizing rice imports?"

May I have your opinion?
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It doesn't work for your other sentences (which require 'the'), even though conversion to the gerund is possible here, too:

"I would like to report growing of the steel industry," or "I heard that arriving of our quests has been postponed".
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Mister MicawberIt doesn't work for your other sentences (which require 'the'), even though conversion to the gerund is possible here, too:

"I would like to report growing of the steel industry," or "I heard that arriving of our quests has been postponed".
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Thank you!
Very helpful.
Mister MicawberIt doesn't work for your other sentences (which require 'the'), even though conversion to the gerund is possible here, too:
May I confirm one more thing?

Do you mean #1 below is okay but #2 is not okay?

1. Closing of a factory causes hardship to everyone involved.
2. The closing of a factory causes hardship to everyone involved.
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Both are fine.
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