In the field of chemical graph theory, a topological index is a real number which is correlated with the various physical properties, biological activities and chemical reactivities of molecular graphs. In recent trends, M-polynomials are used to compute numerous degree-based topological indices. Hex-derived networks have a wide range of applications in pharmaceutical sciences, electronics and communication networks. In this paper, we would like to determine a general form of M-polynomial for the third type of hex-derived network of dimension n and hence generate the related degree-based topological indices. Additionally, we plot the M-polynomial and all the related degree-based topological indices for several n.

The Sturm-Liouville problem is solved for a linear differential second-order equation with generalized boundary conditions of the third kind Generalized boundary conditions consist of a linear combination of the boundary values of a function and its derivative. The coefficients of the linear combination are polynomials of the boundary problem eigenvalue. A method of approximate analytical calculation of boundary problem eigenvalues is proposed The calculation error of an eigenvalue is estimated.

The subject of this paper is the stochastic molecular modelling of the transport coefficients for rarefied gases and gas nanosuspensions. The proposed method is an alternative one to the molecular dynamics method. However, unlike the latter, the phase trajectories of the molecular system are simulated stochastically. Adequate integral characteristics of the studied system are obtained by averaging the calculated data over independent phase trajectories. The efficiency of the proposed algorithm is demonstrated by calculation of the diffusion and viscosity coefficients of several noble and polyatomic gases and rarefied gas nanosuspensions. The modeling accuracy increases when a greater number of molecules and phase trajectories are employed.

Theoretical calculations of optimal control paths minimizing the energy cost of the magnetization reversal in 1D magnetic nanowires are presented. The energy-efficient reversal mechanism is studied as a function of the nanowire length and Gilbert damping parameter. For short nanowires, the optimal reversal mechanism corresponds to a uniform rotation of magnetization. If the length of the wire exceeds a certain critical length defined by the material parameters, switching time and damping, a standing spin wave emerges during magnetization switching. Comparison between the calculated optimal control paths and minimum energy paths reveals that realization of high energy efficiency of switching does not necessarily translate to the minimization of the energy barrier between the target magnetic states.

In this paper, novel gate all-around spin field effect transistors (GAA Spin-FETs) with three different channel materials are proposed and their transport properties are presented. The three channel materials used are Indium Arsenide (InAs), Indium Phosphide (InP) and Aluminum Antimonide (AlSb). Based on the type of semiconducting channel, the results are obtained and a comparison of transport properties among these three FETs is made. The proposed device offers both advantages of reduced power dissipation and compact size. The results reveal that the negative differential resistance (NDR) is observed in all modeled devices and the peak to valley current ratio (PVCR) is different in all structures and is maximum in AlSb based field effect transistor. It is expected that these results will find enormous applications in analog electronics and in the design of oscillators. Additionally, the observed results in this study have great potential for the design of various logic gates and digitals circuits.

We consider optical high harmonic generation in a hydrogen-like atom confined in a spherical cavity caused by interaction with a monochromatic field. The whole system is considered as to be centrally symmetric, i.e., atomic nucleus as fixed at the center of sphere. In such a spherically symmetric atom, the high harmonic generation spectrum is calculated at different values of the oscillation amplitude, frequency of the external field and size of the confining domain.

The general features of nanotechnology processes are summarized. There are three key problems that require theoretical understanding: crystal faceting, crystal shaping and hierarchical organization of matter

The single-phase solid solutions Ba₄Y₃F₁₇:Yb:Eu with fluorite-type structure were synthesized by co-precipitation from aqueous solution technique. The average particle size was approximately 100 nm without agglomeration. The sensitized down-conversion luminescence of Yb³⁺ ions was observed under 296 nm excitation. The quantum yield of Yb³⁺ luminescence was found to reach avalue of 0.4 % for samples with Eu/Yb ratios of 0.1/1.0 and 0.1/10.0.

Cerium dioxide nanoparticles possess unique physical and chemical properties, among which the enzyme-like activity is of particular interest. In particular, they are able to perform the functions of pro- and antioxidant enzymes, such as superoxide dismutase (SOD), catalase, and peroxidase. Due to the advantages associated with pH and temperature stability and low cost, CeO₂ nanoparticles can be considered as promising mimetics of these enzymes. In this paper, the antioxidant activity of a citrate-stabilized colloidal suspension of CeO₂ nanoparticles has been studied using chemiluminometry in model systems generating superoxide anion radical and hydrogen peroxide. In the lucigenin/xanthine/xanthine oxidase system, generating a superoxide anion radical, CeO₂ nanoparticles exhibit antioxidant properties increasing upon conjugation with SOD. When interacting with hydrogen peroxide, CeO₂ nanoparticles exhibit peroxidase-like activity. In the combined ROS generating system, lucigenin/Co(II)/H₂O₂, CeO₂ nanoparticles demonstrated prooxidant activity.

Glasses in the NbO₂F–BaF₂–InF₃ and CdNbOF₅–BaF₂–InF₃ systems have been obtained and investigated by means of IR- and Raman spectroscopy. The analysis of the inelastic light scattering spectra was used to identify the contribution of the photoluminescence in the glasses studied. The contribution of the indium photoluminescence into the inelastic light scattering spectrum of the glasses in the NbO₂F–BaF₂–InF₃ and CdNbOF₅–BaF₂–InF₃ systems has been established by scattering excitation with a laser at a wavelength of 532 nm.

Nanocrystalline Bi₂WO₆ was synthesized by means of hydrothermal treatment. It was shown that the formation rate of bismuth tungstate nanocrystals was determined by the presence of clusters formed at the stage of precipitation and having the same structure as that of Bi₂WO₆, and the morphology of particles formed during hydrothermal treatment depended on the hydrothermal medium’s pH.

Giving professor P.P. Fedorov his due as the leading specialist in fluoride systems and using his theoretical investigations on the topology and geometry of phase diagrams of binary and ternary fluoride systems, as well as experimental results, obtained by colleagues under his leadership, the total geometric description of the systems, forming the LiF–NaF–CaF₂–LaF₃ system, which has considerable promise for the development of fourth generation fuels for nuclear reactors, has been received. For this purpose, three-dimensional computer models of all four ternary systems have been constructed and the T-x-y-z diagram of this fluoride system has been predicted.

Functional nanomaterials based on transition metal oxides are often used for the manufacture of supercapacitors and batteries, due to their special redox properties. The nanosized transition metal oxides used as the electrode material in some cases exhibit abnormally high values of capacitance and energy density. In this regard, it is important to understand what structural features of the nanomaterial determine the electrochemical characteristics of an electronic device. For this purpose, ceria nanorods and nanocubes were specifically synthesized under hydrothermal conditions at elevated pressure (15 MPa), different alkali contents, and two temperature regimes (100 and 180 ^◦C). The obtained CeO₂ nanostructures were characterized using the methods of X-ray diffraction, transmission electron microscopy, and low-temperature nitrogen adsorption. The electrochemical properties of ceria nanostructures were investigated in 1 M Na₂SO₄ water electrolyte. The influence of the structural and surface characteristics of the synthesized nanorods and nanocubes on their charge storage ability is discussed. It was shown that CeO₂ in the form of nanocubes demonstrate higher specific capacitance in comparison with nanorods, which makes them more attractive for application in supercapacitors with neutral electrolytes.