For scalar fluctuations , formula _ 9 is referred to as the scalar spectral index , with formula _ 10 corresponding to scale invariant fluctuations .
For scalar fluctuations , Formula 9 is referred to as a scalar spectral index , with the formula 10 corresponding to scaleninvariant fluctuations .

Are these two sentences paraphrases of each other?
yes

In return , Grimoald granted him his daughter in marriage and gave him the duchy of Spoleto after the death of Atto .
In return , Grimoald granted him his daughter in marriage and , after the death of Atto , gave him the duchy of Spoleto .

Are these two sentences paraphrases of each other?
yes

Pearland ISD serves most of the city of Silverlake , the city of Pearland , and unincorporated areas in Brazoria County ( including Brookside Village ) .
Pearland ISD serves most of the city of Silverlake , the city of Pearland and unregistered territories in Brazoria County ( including Brookside Village ) .

Are these two sentences paraphrases of each other?
yes

Bartosism is not a theoretically manifested and well-structured philosophy but a definite way of life .
Bartosism is not a theoretically manifested and well-structured philosophy , but rather a particular way of life .

Are these two sentences paraphrases of each other?
yes