A system of parallel chain-type macromolecules (linear polymers) is considered. The spectrum of an electron in such a system is described. Waveguide bands are shown to be present, ensuring conductivity. Consideration is undertaken within the framework of a zero-range potentials model based on the theory of self-adjoint extensions of symmetric operators. Possible applications also discussed. 

In this paper the existence and uniqueness of positive fixed points operator for a nonlinear integral operator are discussed. We prove the existence of a finite number of positive solutions for the Hammerstein type of integral equation. Obtained results are applied to the study of Gibbs measures for models on a Cayley tree. 

The absorption and scattering efficiency factors for cobalt nanoparticles over wavelengths ranging from 400 – 1200 nm were calculated. The maximum values and corresponding radii of the absorption efficiency were shown to be dependent upon the incident light wavelength. The highest scattering factor values in the studied spectral range were between 2.2 and 2.4. If the absorptivity of the matrix increases, absorption of the light by cobalt nanoparticles begins to dominate over scattering process. The obtained results allow us to predict the optical properties for composite materials based on a transparent matrix with cobalt nanoparticles, which is essential for the accurate modeling of such systems’ behavior under laser irradiation. 

An explicitly solvable model for periodic chain of coupled disks in orthogonal magnetic field is considered. The spectrum for the Hamiltonian is compared with the spectrum for the corresponding chain of circles. These models are used for the comparison of the bulk and edge states. It is found that for some range of the magnetic field values the lowest band for the circles system lies below the spectrum for the corresponding disks system, i.e. the edge band is below and is separated from the lowest bulk band. 

In this paper, we report the effect of deposition time on the properties of zinc sulfide thin films. The ZnS thin films have been grown on amorphous glass substrates and at various deposition periods ranging from 30 to 120 min by chemical bath deposition technique. Other parameters, such as reactant concentration, solution pH, and bath temperature were kept constant for the all depositions. Morphological characterizations of the surface were studied using the atomic force microscopy (AFM). The AFM images confirmed that the grain size of ZnS increased with increased deposition time. Average diameter of nanoparticles was between 60 and 90 nm, while the roughness ranged from 6 to 11 nm. Optical properties, which were determined from UV–VIS spectrophotometry, were obtained by analyzing the measured absorbance and transmittance spectrum. The zinc sulfide thin films show high transmittance in the visible region and the ZnS band gap value was estimated to be in range of 3.99 – 4.05 eV. 

 Binary CuxZr1−x (x = 0.46, 0.50, 0.58, 0.62) alloy systems were developed using a conventional melting route. Molecular dynamics (MD) simulations have been carried out using the embedded atom method (EAM) potentials. Radial distribution function (RDF) and Voronoi calculations have been conceded for amorphous structure verification. The reduced glass transition temperature (Trg) has been determined in order to predict the glass forming ability (GFA) of these alloys. Tl is found to be a better substitute for Tm and the simulated Trg values are seen to be in good agreement with the experimental results in limits of 0.8 – 5.4 %. 

In this article, the exact solutions of equations of motion for a charged particle in a frequency-modulated wave are presented. We performed an analysis of the results for the motion of a charged particle in the field of frequencymodulated electromagnetic waves. A point of interest was a solution for the equations of the motion for a charged particle in the field of a plane electromagnetic wave. We investigated the interaction of high intensity laser pulses with solid targets in relation to the practical development of multi-frequency lasers and laser modulation technology. This study was undertaken because of the wide practical application of high-temperature plasma formed on the surface of the target and the search for new modes of laser plasma interaction 

Three-dimensional Stokes equations with variable viscosity in cylindrical coordinates are considered. This case is natural for flow through a nanotube in biological applications. We obtain exact particular solutions – a benchmark for numerical approache. 

In this paper, we apply results of analysis of the Raman spectrum from an amorphous carbon film modified with iron (a − C : F e) which leads to construction of clusters containing fragments of graphene and a layer of iron atoms. Such clusters may be candidates for the role of microwave radiation absorbers. For the Raman experiments we performed deposition of a thin film of a − C : F e. Details of the film deposition process, together with the corresponding Raman experiments are presented in this paper. Comparison with a literature model was performed for the intensity ratio of the maxima for specific Raman bands, using the letter D to represent “disorder” and the letter G to represent “graphite”. Comparison gives evidence for the existence of nanosize fragments of graphene embedded in an amorphous matrix of the a − C : F e film. The diameter of the fragments is predicted to attain a value of about 1.2 nm. Moreover, in a comparison with experimental data for defective graphite, the position of the maximum of the D band for a−C : F e appeared to be red shifted. This could support the proposition that damping of Raman-active oscillations occurs by an electron gas in fragments of graphene after introduction of iron, e.g. after intercalation. On the basis of these estimates, we modeled a symmetrical polycyclic aromatic hydrocarbon having a similar size and converted it into fragment of a graphene plane by removal of hydrogen atoms occupying the edge states. To preserve symmetry, we placed atoms of iron on top of the fragment, situating them exactly above the centers of hexagons at a certain distance and placed another fragment of graphene on the top of the iron atoms, symmetrically. For a distance of 2.52 ˚Abetween the centers of the hexagon and the iron atom, distortions of carbon-carbon valence bonds and angles were found to be minimal, as shown through optimization of the system’s geometry using the Avogadro molecular editor. This result supports an hypothesis of graphene fragments during the growth of an amorphous carbon film modified by simultaneous addition of a dopant metal such as iron. This example may illustrate the stability of a two-dimensional electron gas confined between the fragments. 

We consider the generation of entangled biphoton states with orbital-angular-momentum in triangular quadratic waveguide arrays with twisted geometry. For this purpose, we derive the Shrodinger equation for ¨ biphoton wave function and equation for pump field profile. We describe numerically the process of biphoton generation through spontaneous four-wave mixing. We suggest that biphoton correlations can be controlled by the amount of twist and pump field profile. 

Processes occurring during the thermal treatment of nanocrystalline zirconium dioxide are reviewed. Changes in the dimensions and structure of ZrO2 that occur depend upon the calcination conditions used. 

Cryometry investigations of the C60(OH)24±2 – H2O and C70[=C(COOH)2]3 – H2O binary systems were conducted over the 0.1 – 10 g concentration range of fullerenols per 1 dm3 of solutions. The decreases of the temperatures at the onset of H2O – ice crystallization were determined. Excess functions of aqueous solutions – water and fullerenols (trismalonates) activities and activity coefficients and excess Gibbs energy of the solutions were calculated. All solutions demonstrated huge deviations from those of ideal solutions. The last fact, to our opinion, is caused by a very specific – hierarchical type of association of fullerenols (trismalonates) solution components, which was proved by the results of visible light scattering analysis.

Cryometry investigation of C60(C6H12NaN4O2)8H8 - H2O solutions was made over concentrations ranging from 0.1 – 10 g of fullerene-arginine adduct per 1 dm3 . Freezing point depression was measured for these aqueous solutions. Excess functions for water and fullerene-arginine adduct activities, activity coefficients and excess Gibbs energy of the solutions were calculated. All solutions demonstrate huge deviations from ideality. The last fact, to our opinion, is caused by the very specific – hierarchical type of association of fullerene-arginine adducts in aqueous solution components, which is proved by the results of our visible light scattering analysis. 

The properties of emulsions stabilized by complexes of silica particles with hexylamine are analyzed. It is shown that water-in-oil emulsions were obtained only if the hexylamine volume fraction was greater than that of the silica (Aerosil) volume fraction in the aqueous phase. So, in the case of water-in-oil emulsions, hexylamine is a completely equivalent co-stabilizer together with silica, rather than just a solid surface modifier. It is assumed that at high concentrations this short-chain surfactant, together with silica, forms hybrid organic-inorganic particles that are attached at the oil/water interface and promotes the formation of oil droplets in the water.