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I believe that all of the following are correct. Although many are awkward and could be recast, I was still curious if they were grammatically correct with respect to gerund usage.

1-My not attending the conference offended Larry.
2-He was offended by my not going.
3-His winning the lottery earned him many friends.
4-He was annoyed at John's not showing up for the rehearsal dinner.
5. Pat's smoking a cigarette in the cafeteria raised the ire of many.
6. I was highly annoyed at Pat's smoking in the cafeteria.
7. My winning the championship made many resentful.
8. I was highly annoyed at Pat's smoking a cigar in the cafeteria.

Appteciative and grateful, as always.
Comments  
All fine.

I don't find them especially awkward.
Thank you, Clive.
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I agree that all are fine, but if I may go a bit off topic, all of those verbs would more accurately be termed present participles than gerunds. An even better term, I think, is -ing form.
I agree with you that -ing is a better term.

However, on the question of whether it is an adjective or participle, most writers on grammar consider it to be a gerund or verbal noun. The possessive in front of it does rather tend to confirm that it's more noun-like (gerund) than adjective-like (participle).
fivejedjonThe possessive in front of it does rather tend to confirm that it's more noun-like
To me, it tends to confirm that all of what follows (e.g., smoking a cigar in the cafeteria) is noun-like.
fivejedjonthan adjective-like (participle).
Not all participles are adjective-like. It’s more verbal, hence its direct object (a cigar). Neither adjectives nor nouns take objects.

This is why I prefer the less controversial -ing form. Emotion: smile
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Aspara GusTo me, it tends to confirm that all of what follows (e.g., smoking a cigar in the cafeteria) is noun-like
That's fine, so long as you believe that the underlined part of "The alcoholic old bloke who lives in Prague and smokes too much is an arrogant old ****" is noun-like. In that it is the subject of the verb is, it is noun-like. but that means that it is also gerund-like and pronoun-like.
Aspara Gus Neither adjectives nor nouns take objects.
Quite. That is why many grammarians in the past made the distinction between participles (-ing forms which had some of the properties of both verbs and adjectives) and gerunds (which had some of the properties of both verbs and nouns).
Aspara GusThis is why I prefer the less controversial -ing form.
I have no problem with that.