The author is very grateful to Dr. A. B. for Lemma  1 which was  jointly obtained with him.

The author acknowledges the efforts of the anonymous referees in providing thoughtful and insightful reports.

Their reports have improved the quality of the presentation significantly.

We thank Professor A.B. for his valuable comments and suggestions.

We thank the referee for many helpful comments regarding the presentation

The author is greatly indebted to ... for pointing out a mistake in

We gratefully acknowledge the comments of anonymous referees, whose careful scrutiny helped improve this paper considerably.