This article investigates small oscillations of a vortex ring with zero thickness that evolves under the Local Induction Equation (LIE). We deduce differential equation describes dynamics these oscillations. suggest new approach to Hamiltonian description this dynamic system. is based on extension set dynamical variables by adding circulation ? as variable. The constructed theory invariant tran...

We prove a quantitative stability result for the Heisenberg–Pauli–Weyl inequality. This leads to next, and next-to-next order correction terms in

A careful study of the physical properties of a family of coherent states on the circle, introduced some years ago by deBì evre and González in [DG 92], is carried out. They were obtained from the Weyl–Heisenberg coherent states in L 2 (R) by means of the Weil– Brezin–Zak transformation, they are labeled by the points of the cylinder S 1 × R, and they provide a realization of L 2 (S 1) by entir...

Using coherent states of the Weyl-Heisenberg algebra hN , extended Voros products and Moyal brakets are derived. The covariance of Voros product under canonical transformations is discussed. Star product related to BarutGirardello coherent states of the Lie algebra su(1, 1) is also considered. The star eigenvalue problem of singular harmonic osillator is investigated.