We study a mechanism of increasing Hawking radiation from a black hole by using the example of twisted topologically inequivalent configurations (TICs) of a complex scalar field on the Schwarzschild black hole. Physically this increase is tied with the natural presence of Dirac monopoles on black holes. We satisfy both analytical and numerical considerations and find that twisted TICs give the contribution of order 17% to the total luminosity (summed up over all the TICs) of a black hole.

A well known sequential predictor-corrector regularization method for the stable solution of ill-posed Volterra problems is analysed. Under a certain stability assumption wellposedness and convergence results are obtained. Under the additional assumption of smoothness for the exact solution, convergence rates are proved. It is also proved that the stability condition cannot be satisfied for Volterra problems with ν-smoothing kernels, where ν 5. Numerical examples are presented showing the stable and the unstable situations and verifying numerically the convergence rate result.

New losses mechanism in monolayer graphene nanoresonators caused by dissipative intravalley currents stipulated by the synthetic electric fields is considered. These fields are generated by time-dependent gauge fields arising in graphene membrane due to its intrinsic out-of-plain distortions and the influence of the external periodic electromotive force. This losses mechanism accounts for essential part (about 40 percents) of losses in graphene nanoresonator and is specific just for graphene.The ways of the minimization of this kind of dissipation (increase of the quality factor of the electromechanical system) are discussed. It is explained why one can increase quality factor by correctly chosen combination of strains (by strain engineering). Besides, it is shown that quality factor can be increased by switching on a magnetic field perpendicular to graphene membrane.

Bound electron states in impure graphene are considered. Short-range perturbations for defect and impurities of the types "local chemical potential" and "local gap" are taken into account.

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