Aim is to development of a reproducible and mild method for cleaning and activating the surface oftransparent conductive electrodes (ITO, FTO) that enables high surface energy while preserving the substrate’s morphology and electrophysical properties for their subsequent application in organic
optoelectronics.

   Methodology. A new cleaning protocol was developed based on treating surfaces in a boiling ammonia–peroxide solution followed by activation in an ozone chamber. To evaluate the method’s effectiveness, contact angle measurements were performed followed by surface energy calculations, as well as analysis of surface morphology and its electrophysical characteristics.

   Results. It is shown that the developed protocol enables achieving surface energy values of up to ~70 mJ/m², indicating a significant increase in hydrophilicity and a high degree of cleaning. It has been established that the method does not lead to degradation of the conductive layers, preserving their initial morphology and electrical conductivity, unlike traditional acid-based approaches.

   Research implications. The high surface energy achieved through ammonia–peroxide solution treatment combined with ozone activation contributes to improved adhesion and uniformity of organic layer deposition, which is critically important for enhancing the efficiency and stability of
OLEDs, OPVs, and other hybrid devices.

   Aim. Verification of local similarity method for calculating the aerodynamics of aircraft at low supersonic speeds.

   Methodology. The primary criterion for developing this method is minimal computation time. The method is based on the hypothesis of locality, i. e. aerodynamic characteristics of each surface element are calculated independently. The proposed technique for aerodynamics calculation is a combination of well-known methods widely-used in supersonic flow around a thin plate and a flexible mechanism for their application taking into account the curvature of the aircraft surface.

   Results. The technique proposed has been verified on s cone, a slender body of revolution and a thin straight wing. The verification has been carried by comparing with numerical simulation results and existing techniques of aerodynamics calculation. Good agreement between the aerodynamic coefficient values and the numerical calculation results was demonstrated.

   Research implications. The technique considered is supposed to be used to make preliminary assessment of the aerodynamics of an aircraft at low supersonic flight speeds, followed by their refinement using more accurate methods.

   Aim is to identify the features of the dynamic behavior of hexagonal graphene and graphene oxide nanoparticles in solution and at the surface of deoxyribonucleic acid (DNA) complexes with the DNA-binding protein Dps.

   Methodology. Based on quantum chemical calculations, the structures, partial charges, and other parameters of molecular dynamics force fields for hexagonal graphene nanoparticles with varying numbers of oxygen-containing groups were determined. Using the all-atom approximation, molecular dynamics simulations were performed to obtain the dynamics of graphene nanoparticles in solution and at the surface of bacterial biopolymers.

   Results. Graphene and graphene oxide nanoparticles have been shown to form clusters in solution and at the surface of proteins and DNA. Graphene nanoparticles can influence the dynamics of DNA and the DNA-binding protein Dps, leading to changes in the structure of DNA-protein complexes.

   Research implications. The obtained data are of practical interest to researchers studying the structure of biological molecules and their complexes exposed to graphene nanoparticles (graphene, graphene oxide, and reduced graphene oxide). These data can also be used to create nanomaterials with tailored properties that combine nano-biointerfaces.

   Aim. The investigation into the applicability of classical macroscopic approximations to obtain the nonequilibrium local distribution function inside the structure of a strong shock wave.

   Methodology. This paper examines the capability of various macroscopic models (the Navier – Stokes – Fourier equations, the Burnett equations, and the original and regularized 13-moment Grad equations) to approximate a nonequilibrium molecular velocity distribution function.

   Results. The locally reconstructed distribution functions obtained from the flow macro-parameters for the considered models are compared with each other and with a benchmark solution at different locations within the structure of a planar shock wave. The benchmark solution is provided by the Direct Simulation Monte Carlo (DSMC) method, which supplies the flow macro-parameters required for the reconstruction of the distribution function.

   Research implications. All considered models predict the distribution function rather poorly in the supersonic part of the shock-wave structure, where strong oscillations and nonphysical negative values are observed.

   Aim. Development of low-cost flexible Optically Rewritable E-paper using nanotechnology to address the challenge of aligning liquid crystals on plastic substrates.

   Methodology. The approach is based on nanosized azo-dye photoaligning layers, which enable high-quality liquid crystal alignment on flexible plastics without the high-temperature processes required by conventional methods.

   Results. The fabricated E-paper demonstrates fast response (<2 s), low writing energy (<1 J/cm²), and over 1000 rewrite cycles. The device is mechanically robust, complex driving electronics is not needed.

   Research implications. This technology enables a mass production of low-cost, durable flexible displays for applications like price tags, advertising and smart cards, positioning optically rewritable E-paper as a strong competitor in the E-paper market.

   Aim. The aim of this study is demonstration of the process of transitioning the use of digital capabilities in teaching mathematical disciplines from automation systems to intelligent assistants capable of interacting with students in a dialog mode.

   Methodology. The analysis of scientific and educational literature devoted to the use of artificial intelligence in education, in particular the didactic aspects of integrating neural networks and assessing the effectiveness of their use in education. Modeling and designing a neural network model for student learning for automatic generation of assignments, explanations of problem solutions, and feedback organization.

   Results. A variant of a neural network learning model for generating learning tasks, developing explanation techniques and implementing feedback is proposed using the example of studying the Taylor formula and its applications in a course on mathematical analysis by first-year university students.

   Research implications. The practical significance lies in the development of methodological recommendations for teachers on organizing the procedure for interaction between students and an intelligent tutor in the course of independent learning activities to master the content of sections and topics of mathematical disciplines that cause the greatest frequency of difficulties in understanding the essence and significance of mathematical content.

   Aim. The purpose of this paper is to prove theorems on the existence, nonexistence, and divisibility of power sequences.

   The power sequences considered in this paper consist of elements that generalize the properties of well-known Diophantine equations, such as the unsolvable equation in Fermat's Last Theorem or the equation relating the lengths of the sides of a right triangle using the Pythagorean theorem.

   Methodology. In this work, the methods of elementary number theory were mainly used. In this work, the methods of elementary number theory were mainly used.

   Results. The result of the work is completely proven theorems on sequences generalizing Diophantine equations of high degrees.

   Research implications. The theoretical significance of this study lies in its generalization of the concept of Diophantine equations to a set of sequences. The work is purely theoretical in nature.

   This work is a brief summary of one of the sections of a lecture course on the history of quantum theory that is being developed by the author. 

   The relevance of this topic is determined by the applications that quantum mechanics has received over the past decade, such as the need to create quantum computers and develop quantum communication systems based on the phenomenon of quantum entanglement of bound states. 

   Without a deep understanding of quantum theory, it is impossible to create quantum computers and quantum communication systems. The need to create such a course is dictated by the fact that students often experience difficulties when studying quantum theory, and for a deeper understanding of quantum mechanics, the author suggests that students simultaneously read a course on the history of quantum theory. An additional argument for creating such a course is that many subtle issues of the interpretation of quantum mechanics cannot be understood without having knowledge of at least a basic course on the history of quantum theory.