The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship between quantization and phase-space discretization is briefly discussed.

A novel and rational approach based on Lie analysis is proposed to investigate the mechanical behaviour of materials exhibiting experimental master curves. This approach provides a priori two ways of formulating constitutive laws from data as well as the possibility of predicting new master curves and material charts. The first part of the paper is devoted to the presentation of the algorithm. Afterwards, the strategy is applied to the uniaxial creep and rupture behaviour of a Chrome-Molybdene alloy at different temperatures and stress levels.

This is the third part of our series “Quasiclassical and Quantum Systems of Angular Momentum”. In two previous parts we have discussed the methods of group algebras in formulation of quantum mechanics and certain quasiclassical problems. Below we specify to the special case of the group ${\rm SU}(2)$ and its quotient ${\rm SO}(3,\mathbb{R})$, and discuss just our main subject in this series, i.e., angular momentum problems. To be more precise, this is the purely ${\rm SU}(2)$-treatment, so formally this might also apply to isospin. However. it is rather hard to imagine realistic quasiclassical isospin problems.

We consider the recursion operator approach to the soliton equations related to a generalized Zakharov-Shabat auxiliary linear system in pole gauge on the Lie algebra $A_2=\mathfrak{sl}(3,\mathbb{C})$ and show that the recursion operator can be identified with the dual to a Nijenhuis tensor for a Poisson-Nijenhuis structure on the manifold of potentials.