A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...

The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the deformation of the classical flow by the quantum nonlinearity in the semiclassical limit. The breakdown of the classical trajectories under the quantum nonlin...

In the cone of nonnegative superharmonic functions on a bounded euclidean region Q, quasi-units were introduced as those elements invariant under the infinitesimal generator of the fundamental one-parameter semigroup of operators Sx ( X > 0). All harmonic measures and capacitary potentials are quasi-units, but the latter class has more extensive closure properties. Quasi-units arise naturally u...

BACKGROUND Over the past three decades, a limited range of market like mechanisms have been introduced into the hierarchically structured English National Health Service ('NHS'), which is a nationally tax funded, budget limited healthcare system, with access to care for all, producing structures known as a quasi market. Recently, the Health and Social Care Act 2012 ('HSCA') has been enacted, in...

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.