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Do you still use such constructions as:
-The morning being cold, Nick put on his overcoat.
-The rain having stopped, they went on with their work. ???

I come across such expressions very seldom, so I decided to find out whether they're still used or not.
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Yes, still very much in use, Red, but often considered awkward in style (at least by me), and I might emend them to:

'The morning was cold, so Nick put on his overcoat.'
'The rain stopped and they went on with their work.'
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The above-mentioned sentences sounded strange to me, that's why I decided to ask you. They're presumably considered akward in style by common people but when it comes to writers...
I am not from among the hoi polloi. English is my business.