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The paper is a review of recent works on superextensions of the model of non-relativistic quantum charged particle moving in a homogeneous magnetic field on the plane R2 (Landau model), and a model of the particle in the field of Dirac monopole on the sphere S2: SU(2)11/(1) (Haldane model). We consider the models on the supersphere Sl/(2|1)/l/(1|1), superflag SU(2|1)/[l/(1)xl/(1)] and their planar limits, based upon a geometric interpretation of these models and their bosonic proptotypes as d=1 analogs of nonlinear sigma models of the Wess-Zumino-Novikov-Witten type.

The quantum equation of relaxation with non-Markovian terms in the approximation of short-time memory is derived. The correlation functions for a single two-level atom and system of two dipole-dipole interaction of atoms in the external regular fields and the contour of the radiation lines are calculated. Accounting Non-Markovian effects leads to a more vivid expression of dipole-dipole interaction.

This article concerns the effect of gravitation field of the spherical electro-magnetic wave (EMW) on its propagation in vacuum. For this it was received a solution of the coupled Maxwell-Einstein equations. The expression for metric is supposed to be just the same as in wellknown Schwarzschild problem for gravitation field at the vicinity of point mass with additional dependence on polar angle 9. The equations for radial and angular parts of EMW fields of ТЕ- and TM-types are received. Their various solutions are Investigated.

The integral and integrodifferential equations for photonic crystal waveguides (fibers) have been obtained both for finite and infinite dimensions of quasiperiodic dielectric coverings. Previously the equations for two-dimensional periodic photonic crystals with magnetodielectric and metallic periodic inclusions have been considered. The corresponding numerical results are presented.

Experimental results suggest that in the Ni/Ba0.8Sr0.2TiO3/MgO structure with linear sizes of 150 ×150 mm can be realized by planar capacitor elements of variability over a range of capacity from 0.02 pF to 3.0 pF, which increased capacity is achieved by increasing the number of electrode sections.

Spheroidal graphite is little-known form of graphite. It is known that its presence affects the properties of gray cast iron post, typical steels. Research evidence that the spheroidal graphite is a unique layered spiral system of micro-and nanostructures, the inhomogeneous phase composition, structure and elemental composition with predominantly periodic alternation of closely spaced layers. Such systems can have properties and their combinations significantly different than the individual micro-and nanoparticles and composites based on them.

The depth of penetration and localization of magnetic microparticles in skin under action of magnetostatic field was studied experimentally. In the study magnetic powder made from intermetallic composition SmCo5 consisting of 37% of samarium and 63% of cobalt was used. Sizes of the particles varied in the range 3–5 μm. As a carrier propylene glycol was used. The experiments were carried out with human skin samples in vitro.

The effect of intravenously injected nanoshells on white outbred male rats with transplanted tumor of kidney cancer was studied. The blood biochemical parameters and morphological changes in the rat internal organs were examined during 24 h after nanoparticle injection. The most pronounced changes were observed 45 min – 2 h after nanoparticle injection and were reversible.

Signal wave parametric gain was calculated in photonic crystal optical fiber. Photonic crystal fiber structure was optimized for broadband parametric gain. It is shown, that gain bandwidth for photonic-crystal fiber optical parametric amplifier could be more than 400 nm. Spectral changings in parametric gain due to modulation of photonic crystal waveguide cross-section was studied.