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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 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
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