The accurate estimation of the remaining useful life (RUL) of various components and devices used in complex systems, e.g., airplanes remain to be addressed by scientists and engineers. Currently, there area wide range of innovative proposals put forward that intend on solving this problem. Integrated System Health Management (ISHM) has thus far seen some growth in this sector, as a result of t...

The duality principle for Gabor frames states that a Gabor sequence obtained by a time-frequency lattice is a frame for L(R ) if and only if the associated adjoint Gabor sequence is a Riesz sequence. We prove that this duality principle extends to any dual pairs of projective unitary representations of countable groups. We examine the existence problem of dual pairs and establish some connectio...

We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of Poisson-Lie groups and at the level of braided groups and braided ...

We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of Poisson-Lie groups and at the level of braided groups and braided ...

We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semi-classical level of Poisson-Lie groups and at the level of braided groups and braided...