Superfield methods can be used to determine the precise way the self-dual fiveform couples to the metric in the first non-trivial α ′ corrections to type IIB supergravity. We explicitly compute the exact tensor structure of these terms. This requires extensive use of computing algorithms to reduce the complicated expressions that appear to a surprisingly simple form. Along the way we show a new method of computing Schouten identities. With this result we clarify under which conditions one may neglect the five-form higher derivative terms. We comment on corrections to the thermodynamics of charged black holes.

The photonic density of states (PDS) of the eigen polarizations (EPs) in cholesteric liquid crystal (CLC) cells are calculated. The dependences of the PDS on the parameters characterizing absorption, gain and refractive index of the CLC layer surroundings were obtained. We investigated the possibility of connections between the PDS and the density of the light energy accumulated in the medium and showed that these characteristics have analogous spectra and, besides, the influences of the problem parameters on these characteristics also are analogous. It was shown that the decrement of the refractive index of the CLC layer surroundings leads to a sharp increase of the maximum PDS and, consequently, leads to a sharp decrement of the laser excitation threshold. We showed that the subject system can work as a low threshold laser or a multi-position trigger.

An analytical expression is received for the effective interaction potential of a fast charged particle with the ionic crystal CsCl near the direction of axis h100i as a function of the temperature of the medium. By numerical analysis it is shown that the effective potential of axial channeling of positrons along the axis h100i of negatively charged Cl À ions practically doesn't depend on temperature of the media. The wavefunction and the energy spectrum of the localized state are investigated, and the possibility is proved for the formation of metastable, two-dimensional relativistic positron systems or the positron atoms (PA), i.e. the bound state of a positron in the present case with a negatively charged axis of ions. The problem of one-photon decay of PA is investigated. The possibilities of stimulation of resonant transitions between quantum states of PA by the external hypersound are investigated in detail.

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