Here we present a detailed statement about solving of spectral and transport problems for quantum graphs. The practical prescriptions for finding the energy of pi-electrons and current-voltage characteristics for aromatic at the disposal of models of quantum graphs are suggested. We propose an algorithm increasing the precision of numerical solution and discuss the facilities for parallel computations. Here we also suggest the method of inverse problem solution which plays an important role in engineering.

   It has been considered the possibilities of the experimental setup for temporary registration form of pulsed THz radiation reflected from objects (THz reflectometer) for pulsed terahertz imaging reflectometry and tomography, the visualization of internal objects structures which are transparent in the THz frequency range. It has been received two- and three-dimensional topograms test object and defined resolution limit of the method. It has been found that the space-time registration form of the reflected pulses can effectively generate topograms of surfaces with relief depth ranging from 1 to 1000 microns.

   This paper considers the functionality of FDTD (Finite difference time-domain) method for parallel computing; the main difficulties that arise in its practical use are listed; a comparison with other numerical methods of electromagnetic phenomena simulation is made. The requirements to performance balance of supercomputer node, at which effective implementation of the parallel version of FDTD method is possible, are specified. The need for computing at exaflops scale for solving the tasks of integral nanophotonics is shown, an approach to solving such problems is proposed.

   The coherence excitation of the atomic states in the presence of strong magnetic field can lead to the appearance of the dark states.

   Comparison of the computer simulation of spall fracture and real experiments is presented. Simulation using particle dynamic method with Morse potential is carried out. The dependences of the spall fracture parameters on the dimensionless parameter k which characterize the width of the potential well is obtained. The values of the parameter k that allow one to describe the results of real experiments for some metals are presented.

   Optical properties of spatially ordered nanocomposites consisting of spherical dielectric nanoparticles have been investigated. We proposed an analytical solution allowing us to use simple Airy formulas (“imaginary boundary” method) to describe interaction of a light with an ordered nanostructure without averaging of optical constants over the volume. We show the good agreement with strict numerical simulations’ results.

   The results of synthesis and physicochemical analysis of ceramic and composite materials based on calcium phosphates are presented. The structure and properties of the materials by techniques such as X-ray powder diffraction, scanning electron microscopy and microindentation was characterized. Influence of parameters of ultrasonic, hydrothermal and thermal treatment on the properties of the synthesis products was investigated. The values of linear shrinkage, water absorption and porosity of ceramic samples were determined. The possibility of obtaining promising for use nanoceramics containing phase double phosphates of calcium and alkali metal, which has an unusual microstructure and high degree of resorption was shown.

   It is reported about results of the study of processes of nucleation at the synthesis of binary compounds A2B6 from vapor phase on the substrate cooled by liquid nitrogen. It is presented curves of condensation, electron diffraction patterns, microphotographs of the surface and distribution functions of group of islands - nucleation centers on the earlier stages of growth of nano-sized system. The results are rationalized in frame of model of the type of Stranskoi-Krastanov one, modified for excess chemical energy.

   Film nanostructured materials and powders-xerogels of sols based on the system Y-Fe-Si-O were obtained by sol-gel method. Investigations of the properties of nanocomposite materials by atomic force microscopy, X-ray diffraction and thermal desorption of nitrogen were carried out.

   Reactions of barium nitrate water solutions with hydrofluoric acid were studied. Barium hydrofluoride BaF₂.HF is the product of reaction at any ratio and concentrations of initial solutions. Barium fluoride BaF₂ is formed under using of NH₄F as precipitate agent and as a result of interaction of BaCO₃ with HF solution. SEM and XRD analysis were used for characterization of phase composition and morphology of particles.

   The possibility of the formation of thermally stable of pseudo cubic-ZrO2 nanocrystals in combination with the thermally expanded graphite is shown.