We consider a model operator (Hamiltonian) H associated with a system of three particles on a d-dimensional lattice that interact via non-local potentials. Here the kernel of non-local interaction operators has rank n with n ≥ 3. We obtain an analog of the Faddeev equation for the eigenfunctions of H and describe the spectrum of H. It is shown that the essential spectrum of H consists the union of at most n + 1 bounded closed intervals. We estimate the lower bound of the essential spectrum of H for the case d = 1.

Electron-electron interactions in a single highly doped heterojunction are considered, taking into account both intra- and intersubband transitions. Expressions are derived for the time of electron-electron interaction, matrix elements of the full screening potential and dynamic dielectric function in a 2D electron system with the fine structure of the energy spectrum, and for the electron density spatial distribution. The theoretical dependences τ th ee (T, ns) provide a good description of the experimental times of Landau levels collisional broadening τ exp q (T, ns).

We propose three algorithms that can fairly accurately estimate the degree of convergence to the limit cycle using time-series generated by systems that converge to a quasi-periodic oscillation and consider their applicability ranges. As a proof-of-concept, a trivial two-dimensional case is studied. A practically important three-dimensional case is considered. Generalization of the algorithm to the space of any number of dimensions is presented. An example of these algorithms was used for estimating the Van-der-Pol system convergence.

This article contains a comparison of three data analysis methods’ informativity: wavelet transform, Fourier transform and short-time Fourier transform. This work contains an attempt to find the most sensitive method for the detection of quasiharmonic components in experimental data that have pronounced non-stationary behavior.

Results of high-frequency near-field sounding, IR-spectroscopy and NMR analysis of water, and also model harmonic signal were used as non-stationary processes for analysis.

The investigation of second-harmonic generation in a one-dimensional photonic crystal was carried out. The calculation of the χ (2) – grating recording in a periodic system consisted of air and glass layers and secondharmonic generation in it was performed. The frequency conversion efficiency at different wavelengths of the first harmonic was estimated.

The analytical expression for the absorption coefficient of the electromagnetic radiation by electrons a quantum wire is obtained. We used the first-order perturbation theory. The cases of linear and circular polarization of the electromagnetic wave are investigated. The resonance character of the absorption is shown and resonant frequencies are found.

An algorithm for the approximation of relationship pluralities is set by linear combinations of functions with unknown coefficients, which in part coincides in all relationship pluralities having been built using ordinary least squares. Examples of the algorithm’s realization, when finding particular solutions plurality of linear nonhomogeneous differential equations, have been given.

Essential viscosity variation creates additional difficulties for numerical investigation of flows through nanotubes and nanochannels. Benchmark solutions of the Stokes and continuity equations with variable viscosity are suggested. This is useful for testing of numerical algorithms applied to this problem.

Fluid flow in a nanotube, caused by a moving soliton-like perturbation of its wall, is considered. We use a crystallite model for nanotube flow. A picture of the flow is described. The formula for crystallite velocity is derived, allowing one to find fluid flux through a nanotube.

Feasible nucleation in condensed media by the aggregation mechanism of small metastable crystalline clusters is demonstrated. The presence of the stable small clusters in the initial phases makes the homogeneous and heterogeneous nucleation processes more similar.

This study summarizes the results for the investigation of the process of gallium arsenide thermal oxidation processes activated by the coaction of the oxides in Sb2O3+Bi2O3, Sb2O3+PbO and PbO+Bi2O3 binary compositions was studied. The analysis of the character and nature of nonlinear effect of various compositions of chemostimulators on the GaAs-supported oxide layer thickness grown on the GaAs surface was performed. It is shown that the actual oxide layer thickness is different from the additive value. The main patterns of the impact for binary compositions of p-element oxides of p-elements on thermal oxidation of gallium arsenide determined by physico-chemical nature of chemostimulators, the nature of their interaction and the method of administration in the system were described.

The volume Properties of water soluble tris-malonate of light fullerene — C60[=C(COOH)2]3 were investigated with the help of quartz pycnometers at 25 ◦C, including the concentration dependence of density, average molar volume of the solutions and partial molar volumes of C60[=C(COOH)2]3 and H2O. Concentration dependence of the refraction index in water solutions of C60[=C(COOH)2]3 was also determined with the help of refractometer, specific and molar refraction of the components were calculated with the help of the rules of the additive refraction of solution components.

The poly-thermal solubility of the tris-malonate C60[=C(COOH)2]3 – H2O binary system was investigated from 20 – 80 ◦C with the help of the method of isotherm saturation in ampoules. Concentration of tris-malonate C60[=C(COOH)2]3 in solutions was determined by light absorption at 330 nm. A diagram of the solubility is non-monotonic, consisting of 2 branches, which correspond to 2 different crystal-hydrates of C60[=C(COOH)2]3 and one non-variant point, corresponding to the saturation both crystal-hydrates. Complex thermal analysis of C60[=C(COOH)2]3 crystal hydrates, in equilibrium with a saturated aqueous solution at room temperature, was performed from 20 – 600 ◦C. Consecutive effects of the losses of C=O and C=O + H2O were determined.

Herein, we report the effect of calcination on the structural and optical properties of nanocrystalline NiO. NiO nanoparticles were synthesized by chemical precipitation method using nickel nitrate hexahydrate and ammonium carbonate. Thermogravimetric analysis was done to determine the thermal behavior of the precursor. The samples were characterized by X-ray diffraction (XRD), energy dispersive X-ray analysis (EDAX), high resolution transmission electron microscopy (HRTEM), Fourier transform infrared spectroscopy (FTIR), UV-visible and photoluminescence (PL) spectroscopy. Crystallite size and lattice strain on peak broadening of NiO nanoparticles have been studied using Williamson–Hall (WH) analysis. Significant modifications were observed in the crystallite size, absorption spectra and photoluminescence intensity due to calcination. The desired structural and optical properties of NiO nanoparticle make it as a promising material for optoelectronic applications.