1. Introduction. The richness of the theory of functions over the complex field makes it natural to look for a similar theory for the only other non-trivial real asso-ciative division algebra, namely the quaternions. Such a theory exists and is quite far-reaching, yet it seems to be little known. It was not developed until nearly a century after Hamilton's discovery of quaternions. Hamilton him...

Generating-line method, which is based on the generating process of spherical involute curve, is a new processing theory of cutting ideal spherical involute gears. Based on the principle of the new method, this paper expands the traditional geometrical relationship into the cutting geometry of generating-line method, and proposes the base-cone parameters with their formulas to provide necessary...

A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization traditional and complex based on quaternions. The novelty that the range membership function set quaternions with modulus less than or equal to one, which real imaginary parts can be used for four different features. discussion made intuitive interpretation quaternion-valued grades possible a...

The second quantization of the quaternionic fermionic field is undertaken using real Hilbert space approach to quantum mechanics ([Formula: see text]QM). solution responds an open problem theory, and launches basis development interaction theory.