Please capitalize where necessary: in china it is very common with farmers.
A: In China it is very common with farmers.

Please capitalize where necessary: arthur eddington, a leading light in general relativity theory as well as astronomy, was one of those who doubted schwarzschild's discovery.
A: Arthur Eddington, a leading light in general relativity theory as well as astronomy, was one of those who doubted Schwarzschild's discovery.

Please capitalize where necessary: this is known as the theoretical payout percentage.
A: This is known as the theoretical payout percentage.

Please capitalize where necessary: with just a single month left of the danish presidency of the council, the meeting rooms in brussels, luxembourg, strasbourg, copenhagen and horsens hum with intense activity.
A:
With just a single month left of the Danish Presidency of the Council, the meeting rooms in Brussels, Luxembourg, Strasbourg, Copenhagen and Horsens hum with intense activity.