Ceiling fan be used to reduce the stratification of warm air in a room by forcing it down to affect both occupants' sensations and thermostat readings, thereby improving climate control energy efficiency. Punkah-type ceiling fans date back to 500 BC, and are native to India. Unlike modern rotary fans, these punkah fans move air by moving to and fro, and were operated manually by cord. The first rotary ceiling fans appeared in the early 1860s and 1870s in the United States. At that time, they were not powered by any form of electric motor. Instead, a stream of running water was used,
Presentation of a group for generators and the Cayley table for relations. The negative solution to the word problem for groups states that there is a finite presentation for which there is no algorithm which, given two words "u", "v", decides whether "u" and "v" describe the same element in the group. This was shown by Pyotr Novikov in 1955 and a different proof was obtained by William Boone in 1958. Suppose "G" has presentation and "H" has presentation with "S" and "T" being disjoint. Then The deficiency of a finite presentation is just and the "deficiency" of a finitely presented group "G", denoted