1. For all '' z '' < 1 . Since the left hand side is a harmonic function , the maximum principle implies the inequality is strict .
2. For all '' z '' 1 Since the left side is a harmonic function , the maximum principle implies that inequality is strict .

no

1. Vinac District is one of thirty-three districts of the Lima Region in the Yauyos Province of Peru .
2. District Vinac is one of thirty-three districts in the Lima region in the province of Yauyos in Peru .

yes

1. For many centuries it was a royal peculiar , independent royal , and from 1480 a chapel of the Diocese of Lichfield and even the Province of Canterbury .
2. For many centuries it was a royal , independent royal royal and from 1480 a chapel of the diocese of Lichfield and even the province of Canterbury .
yes