The aim of the present work is to show that results obtained earlier on approximation distributions sums independent summands by infinitely divisible laws may be transferred estimation closeness convex polyhedra.

We consider a transport equation by gradient vector field with small viscous perturbation -εΔ g . study uniform observability (resp. controllability) properties in the (singular) vanishing viscosity limit ε→0 + , that is, possibility of having uniformly bounded observation constant control cost). prove series examples general, minimal time for may be much larger than needed ε=0. also two times ...

We show that recent results on adiabatic theory for interacting gapped many-body systems finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem automorphism group describing infinite volume dynamics quasi-local algebra of observables. The key assumption is existence sequence Hamiltonians, which generates same Our also holds certai...