By Masayoshi Hata

This detailed quantity offers a fruitful and lovely mathematical international hidden in Caianiello's neuronic equations, which describe the instant habit of a version of a mind or pondering computing device. The distinctive research from a standpoint of "dynamical systems", even in one neuron case, permits us to procure amazingly solid rational approximations to the Hecke-Mahler sequence with variables. a few fascinating numerical purposes of our rational approximations also are discussed.

This publication is essentially self-contained and plenty of themes required in it are defined from the start. each one bankruptcy includes a variety of instructive and more often than not unique workouts at a number of levels.

Readership: Graduates and researchers drawn to dynamical platforms, Farey sequence, Hecke Mahler sequence, Diophantine approximation (irrationality measures, transcendental numbers).