In March 1833 , Pekin was renamed Redford and the southern half was on April 1 , Dearborn Township .
In March 1833 , Dearborn Township was renamed Redford and the southern half became Pekin on April 1st .

Are these two sentences paraphrases of each other?
no

A closely related formulation of Hamiltonian mechanics is classical mechanics .
A closely related formulation of the classical mechanics is Hamiltonian mechanics .

Are these two sentences paraphrases of each other?
no

The affine scaling direction can be used to choose a heuristic to adaptively define the centering parameter as
The affine scaling direction can be used to create a heuristic to adaptively define the centering parameter as

Are these two sentences paraphrases of each other?
yes

He married Lady Florence Jane Taylour , daughter of Thomas Taylour , 3rd Marquess of Headfort and Amelia Thompson , on 5 August 1875 .
He married Lady Florence Jane Taylour , the daughter of Thomas Taylour , 3rd Marquess of Headfort and Amelia Thompson , on 5 August 1875 .

Are these two sentences paraphrases of each other?
yes