Is the sentence below grammatical?
There are a lot of people, with many wearing tuxedos.
There are some cute teenage girls in the club, with many of them being PhD graduates in topological field theory.
I check through my dictionary and don't see a definition of with that makes the above sentence legit.
with wɪð preposition preposition: with
accompanied by (another person or thing). "a nice steak with a bottle of red wine" synonyms: accompanied by, in the company of, escorted by "she's gone out with her boyfriend"
having or possessing (something). "a flower-sprigged blouse with a white collar" wearing or carrying. "a small man with thick glasses"
indicating the instrument used to perform an action. "cut the fish with a knife" indicating the material used for a purpose. "fill the bowl with water"
in opposition to. "a row broke out with another man"
indicating the manner or attitude in which a person does something. "the people shouted with pleasure"
indicating responsibility. "leave it with me"
in relation to. "my father will be angry with me" affected by (a particular fact or condition). "he's in bed with the flu" indicating the cause of (a condition). "he was trembling with fear" because of (something) and as it happens. "wisdom comes with age"
employed by. "she's with the Inland Revenue now" using the services of. "I bank with the TSB"
in the same direction as. "marine mammals generally swim with the current"
indicating separation or removal from something. "to part with one's dearest possessions"
So my questions are:
1] can I use "with" this way?
There are partial differential equations on this paper, with many of them having no real solutions.
2] or with an adjective?
There are deuterium atoms in this jar, with many/some of them ionized.
3] or without "of them"?
There are grey goos everywhere, with many/some consuming the haemocoels of tardigrades.