Then the image of formula _ 31 is not real-valued , but nevertheless it is a subset of formula _ 1085 Thus , the character of the representation is real .
Then the image of Formula 31 is not really valuable , but nevertheless it is a subset of Formula 1085 , so the character of the representation is real .

Are these two sentences paraphrases of each other?
yes

Coronets and supporters were also reserved for the nobility , but were formally used by a number of others without any protests from the public authorities .
The Coronets and the supporters were formally reserved for the nobility , but were also used by a number of others without protests from the public authorities .

Are these two sentences paraphrases of each other?
no

He is a specialist in Baroque music and contemporary music .
He is specialist in contemporary music and baroque music .

Are these two sentences paraphrases of each other?
yes

Alzheimer was known for having a variety of medical interests including early diseases of the brain , vascular dementia , brain tumors , forensic psychiatry and epilepsy .
Alzheimer 's was known for a variety of medical interests , including vascular diseases of the brain , early dementia , brain tumors , forensic psychiatry , and epilepsy .

Are these two sentences paraphrases of each other?
no