On the icosahedron: from two to three dimensions

In his famous book, Felix Klein describes a complex variable for the quotients of the ordinary sphere by the finite groups of rotations and in particular for the most complex situation of the quotient by the symmetry group of the icosahedron. The purpose of this work and its sequels is to obtain similar results for the quotients of the three--dimensional sphere. Various properties of the group $SU(2)$ and of its representations are used to obtain explicit expressions for coordinates and the relations they satisfy.Comment: 8 page

Optimality and strong stability of control systems

Optimality and strong stability of control syste

Applications of Liapunov Stability Theory to Control Systems

Applications of Liapunov stability theory to control system

A Report on Session 12 IFAC Congress, 1966 (engeneering Philosophy of Optimization in the Problemof Analytical Design of Optima Controllers)

Summaries and abstracts on theory, design, optimization, and stability problems of nonlinear control system

An invariance principle in the theory of stability

Invariance principle in Liapunovs stability theor

Spinodal instability growth in new stochastic approaches

Are spinodal instabilities the leading mechanism in the fragmentation of a fermionic system? Numerous experimental indications suggest such a scenario and stimulated much effort in giving a suitable description, without being finalised in a dedicated transport model. On the one hand, the bulk character of spinodal behaviour requires an accurate treatment of the one-body dynamics, in presence of mechanical instabilities. On the other hand, pure mean-field implementations do not apply to situations where instabilities, bifurcations and chaos are present. The evolution of instabilities should be treated in a large-amplitude framework requiring fluctuations of Langevin type. We present new stochastic approaches constructed by requiring a thorough description of the mean-field response in presence of instabilities. Their particular relevance is an improved description of the spinodal fragmentation mechanism at the threshold, where the instability growth is frustrated by the mean-field resilience.Comment: Conf. proc. IWM2014-EC, Catania, 6-9 May 201