The unique map of an exponential Lie - Algebra is a diffeomorphism between the Lie - Algebra and the nilpotent - associated , simply associated lie group .
The unique map of an exponential Lie algebra is a diffeomorphism between the Lie algebra and the nilpotent associated connected , simply-connected Lie group .

Are these two sentences paraphrases of each other?
yes

The House Democratic Caucus nominates and elects the Democratic Party leadership in the United States House of Representatives .
The House Democratic Caucus nominates and elects the Democratic Party leadership in the House of Representatives of the United States .

Are these two sentences paraphrases of each other?
yes

Vohma is a village in Laaneranna Parish , Estonia , in western Parnu County .
Vohma is a village in the parish Laaneranna , Estonia , in western Parnu County .

Are these two sentences paraphrases of each other?
yes

A second portion is exposed to a universal allergy such as pokeweed to serve as a positive control .
A second portion is exposed to a universal allergen , such as Pokeweed , to serve as a positive control .

Are these two sentences paraphrases of each other?
yes