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Little-Parks Oscillations in Hybrid Ferromagnet-Superconductor Systems

On the basis of of linearized Usadel equations we consider superconductivity nucleation in multiply connected mesoscopic superconductor/ferromagnet hybrids such as thin-walled superconducting cylinders placed in electrical contact with a ferromagnetic metal. We study the interplay between the oscillations of $T_c$ due to the Little--Parks effect and the oscillations due to the exchange field. We demonstrate that the exchange field provokes the switching between the superconducting states with different vorticities and this may result in the increase the critical temperature of the superconducting transition in the magnetic field. Moreover we analyse the influence of the S/F transparency on the realisation of the states with higher vorticities.