It is shown that an eigenvalue of the Laplacian exists below the continuous spectrum for a system of threedimensional quantum waveguides laterally coupled via a small window and placed in a transverse electric field, and the estimation for the eigenvalue is obtained. A field induced shift of the eigenvalue is estimated by using a variation.

In this paper we consider the spectral problem for two kinds of chains of weakly coupled conglobate resonators: a direct one and one with a kink. Equations for spectrum of these chains are derived by using of the theory of self-adjoint extensions of symmetric operators, Bloch's theory and approach of the transfer-matrices. The paper shows that the system of direct-type chain of weakly coupled conglobate resonators has a continious energy spectrum with a band structure. And for the chain with a kink we prove the existence of point spectrum.

Metamaterials are artificially created structures owning electromagnetic characteristics typical of traditional materials. The most promising metamaterials are hyperbolic media. Such systems are uniaxial materials with different signs of major components of the dielectric constant. Successful realization of such materials in optical frequency range is a metal nanowire medium formed in porous dielectric matrices by filling them with metal. The review considers the creation processes of dielectrics matrices with an ordered structure based on Al2O3 fabricated by means of anodization and filling of these matrices with various metals by electrochemical methods.

The single-particle potentials for the different adsorbents with spherical and cylindrical geometry were obtained. A comparative analysis of these potentials was performed. Limitations relating the implementation of the proposed model potentials were discussed.

The role of excitonic interaction between chromophores in a molecule of NADN at its excitation is determined. The data obtained are indicative of the presence of nonradiative singlet-singlet energy transfer in a molecule of NADH.

A modification of the method of statistical regularization to restore the volume distribution function of the particle radius of gyration given by small-angle X-ray scattering indicatrix is developed. The criteria to select grid nodes along the radius of gyration together with the choice of the optimal value of the regularization parameter is described.

The effectiveness of the method is confirmed in tests of the particle distribution of the three shapes with symmetrical cross-section (ellipsoid, rectangular parallelepiped, right cylinder) and anisometry in the range 0,5…2. Integral ambiguity of reconstruction of the distribution function does not exceeds 4%.

The method of calculating the specific surface area on the basis of the reconstructed distribution function is represented. The obtained specific surface depends weakly on the assumed anisometry and is depends strongly on different proposed forms of the particles.

We discuss an analytical model that describes polarization distortion of an optical signal that appears during its propagation in a fiber optics line. The model is applied for illustrating the principles of weak signal distortion compensation in different types of quantum cryptography systems.

Usually, atom-like functions of s-, p- and d-type (linear combinations of atom-like orbitals – LCAO method) are used for study of electronic structure of molecules, crystals end nanoobjects. It is necessary to enlarge the basis by including atom-like functions of f-type for more precise calculations and for study of compounds with heavy atoms. Taking into account the spin-orbit interaction, the basis ought be composed by the products of coordinate and spin functions (or spinors). Symmetrized combinations of s-, p-, d-, f-type functions are built and presented in this article (with and without spin multiplier) by means of compact tables. The symmetrization is made according to irreducible representations of usual and double point groups with axes up to six order.

The theory of X-ray scattering from the multilayers with rough interfaces is developed. Both kinematic (Born) and dynamic (the distorted wave Born) approaches are considered. Modeling of x-ray specular scattering for the superlattices with different periods as well as amplitudes and correlation lengths of interface roughness are performed.The results of calculations in different approximations are compared with experiment.

The transformations of structures in the nanocomposite ZrO2 - amorphous Al2O3 in the process of heat treatment were investigated. It is shown that melting of non-autonomous phase is the key process leading to starting of active transformations in the structure of the composite.