The concept of configuration of groups which is defined in terms of finite partitions and finite strings of elements of the group is presented by Rosenblatt and Willis. To each set of configurations, a finite system of equations known as configuration equations, is associated. Rosenblatt and Willis proved that a discrete group G is amenable if and only if every possible instance of its configur...

In its weak form, the Banach-Tarski paradox states that for any ball in R, it is possible to partition the ball into finitely many pieces, reassemble them using rotations only, producing two new balls of the exact size as the original ball. In its strong form, the paradox states that for any two bounded sets A,B ∈ R with non-empty interior, it is possible to partition A, move the pieces around,...

There is considerable evidence to support the hypothesis of relationship between paradoxical sleep (PS) and learning–memory processing. It has been suggested that PS is important in memory retention at the specific time course called PS windows (PSW). The time of PSWs occurrence and duration of these PSWs following the training sessions and, the neurochemical nature of PSWs has not been well kn...