IN: He restudied and generalised the mathematical theories of Kummer fields and of cyclotomic fields from the standpoint of abelian varieties over algebraic number fields.
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OUT: he restudied and generalised the mathematical theories of kummer fields and of cyclotomic fields from the standpoint of abelian varieties over algebraic number fields.

IN: Google's commitment to the security and privacy of your data is of vital importance, and we are committed to protecting you and your business from any attempts to compromise it.
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OUT: google's commitment to the security and privacy of your data is of vital importance, and we are committed to protecting you and your business from any attempts to compromise it.

IN: 20 km from Copenhagen City Centre
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OUT: 20 km from copenhagen city centre

IN: If the right conditions are in place, the product can harden in just a few seconds.
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OUT:
if the right conditions are in place, the product can harden in just a few seconds.