Aim. The work aims to develop a physico-mathematical model that links the physical and technical characteristics of a display – namely spatial resolution, refresh rate, color gamut, and image output latency, taking into account material parameters – with the productivity of a teacher who checks digital educational materials using AI tools for compliance with the requirements of the Federal State Educational Standards (FSES).

Methodology. The starting point was the well-studied limitations of the human visual system: the angular resolution of the eye, the critical flicker fusion frequency, and thresholds for color discrimination. Based on this data, the authors determined which display parameter values should be considered minimally acceptable and which should be considered desirable. Next, an efficiency objective function W_disp was introduced, comprising three components: time spent, number of errors made, and subjectively perceived workload (according to the NASA TLX methodology). In addition, a review was carried out of publications on how pixel density, frame refresh rate, and color accuracy affect the user's cognitive load.

Results. Based on physiological limitations of vision, the following set of display parameters is justified for AI monitoring tasks: pixel density of about 300 PPI, refresh rate of 120 Hz, sRGB color space coverage of at least 99%, and response time not exceeding 8 ms. The form of the efficiency objective function is formulated. Calculations show that when working on a display with the above characteristics, the value of W_disp is approximately 30–35% higher than when using a standard office monitor.

Research implications. The proposed model makes it possible to translate display equipment requirements into quantitative indicators, which is especially relevant for educational institutions where AI monitoring systems are already being implemented or are planned for implementation. The findings can be applied in two directions: first, in developing standards for equipping schools with technical means, and second, in compiling methodological materials and recommendations addressed directly to practicing teachers. It is shown what physical properties of the material affect the parameters of the information display device.

Aim. To examine the rheological behavior of a thermotropic liquid-crystalline polymer (LC-5000) in the linear viscoelasticity region.

Methodology. Experimental data were approximated using the equations of a structural rheological model.

Results. The relationship between the coefficients of the rheological equations and the temperature and phase state of the polymer was demonstrated.

Research implications. Equations are proposed that can approximate experimental data on the frequency dependences of the storage and loss modulus and describe a specific structural state of the liquid crystalline polymer melt.

Aim. Solving the problem of the distribution of the temperature field over the thickness of a thin metal layer with boundary conditions of the first kind due to the release of Joule heat during the passage of an electric current, taking into account the coefficients of specularity of the conductor surfaces.

Methodology. The paper presents a mathematical description of the temperature field distribution inside a thin metal layer based on a kinetic approach.

Results. The variation of the specularity coefficients when electrons are reflected from the surfaces of a thin metal layer in the case of a high-frequency current passing through it causes uneven heating of the layer, which differs significantly from the classical results.

Research implications. The theoretical and practical significance lies in calculating the temperature conditions of integrated circuits during their operation.

Aim. To develop and test a numerical method for analyzing optical distortions arising from light propagation through a gas flow with a spatially inhomogeneous refractive index.

Methodology. Numerical simulation of light ray propagation in a gradient medium was performed using the ray tracing method in the ANSYS Zemax OpticStudio software environment. The refractive index distribution was defined by a parametric function. The ray coordinates after passing through the gas flow model were exported and processed in an external Python program to construct displacement fields similar to those used in schlieren methods.

Results. The simulation of light propagation through a thermal plume model was carried out, and the dependences of image displacement on the initial ray coordinates were obtained. The agreement between the numerical simulation results and experimental data is shown. It is established that the observed scatter of points is due to the statistical nature of ray tracing and aberrations of the optical system.

Research implications. The proposed approach allows taking into account the real parameters of the optical recording system and simulating arbitrary refractive index distributions. The method can be used for interpreting data from schlieren experiments and solving inverse problems of reconstructing gas flow parameters. 

Aim. The purpose of this work is to evaluate the results of a Navier–Stokes–Fourier model with an artificially introduced stagnation point to describe flow around a sharp edge at moderate supersonic Mach numbers.

Methodology. This paper utilizes the Navier–Stokes–Fourier equation system with artificial viscosity. The applied model features an artificially introduced stagnation point. A numerical method for solving these differential equations using an upwind scheme was used to implement the model.

Results. Calculated results for Mach numbers of 2 and 3 with different stagnation point coefficient beta in range from 0.1 to 0.2.

Research implications. The obtained results confirm the applicability of this model to calculating the density and normal stresses in flow around sharp edges. The model can be used to calculate the edges of nose cones of aircrafts, air intakes, and other similar surfaces of advanced aircraft in the fields of aerospace engineering.

Aim: to formulate the principle of selecting correct physical and mathematical models based on systems of partial differential equations.

Methodology. The procedure for selecting correct models consists of a comparative analysis of the relationships between the total differentials from the convective part of the system equations and the eigenvalues of their Jacobian matrix. There total differential method and finite differences method are used in this paper.

Results. With increasing number of moment equations in finite closed systems as the Grad 10 moment or 13-moment systems, there may be several characteristics sound velocities, not equal acoustic sound velocity. This results in the appearance of a subshock within the shock wave profile. Solutions to the Grad equations lose stability already at M=1.65. Equations of the Navier – Stokes are acoustic compatibility.

Research implications. The principle proposed in this paper allows for the elimination of mathematically incorrect models at the initial stages of their development.

Aim. The aim of the work is to find conditions under which the Tricomi equation has exact solutions and to find these solutions.

Methodology. We consider the Dirichlet – Neumann problem for a multidimensional generalization of the Tricomi equation in an infinite domain bounded by two hyperplanes. Using the Fourier transform, it is shown that this problem in the domain of ellipticity of the equation has a unique solution in the class of functions of slow growth.

Results. It is shown that when the right-hand sides of the equation and boundary conditions are polyharmonic functions (specifically, polynomials), exact solutions to the problem exist. An algorithm for obtaining the solution is presented.

Research implications consist of finding the conditions for the existence of exact solutions to the problem and finding the exact solutions themselves, which can be used to test the accuracy of approximate methods.

Aim. Defining the transformation of a set of functions of two real variables based on the concept of a directional derivative, representing methods for applying the transformation to explore functions and their approximation, constructing numerical methods and determining the transformation for functions of more variables.

Methodology. Analysis of the theory of sets and their mappings, including mappings of a set of functions, the use of relevant sections of the theory of mathematical analysis, including the transformation of functions and the expansion of non-periodic and periodic functions into series, the theory of constructing numerical methods for approximating functions.

Results. The transformation of functions of two real variables is defined, methods of applying the transformation to study functions in the vicinity of a given point and expansion of functions into special functional series are described, centrifugally periodic functions of two variables are defined, numerical methods for approximating functions of two variables are constructed, and transformation of functions of a larger number of variables is defined.

Research implications. The presented transformation of functions of several variables is an element of the further development of the theory of functions and functional analysis; the described methods of its use expand the directions for research of this theory, including the area of expansion of functions of several variables into functional series. The theoretical results obtained can be used in applied problems of mathematical modeling, including the use of centrifugally periodic functions for modeling wave processes (in seismology, explosion physics and other fields), in approximating functions using the presented numerical methods, and in the development of new numerical methods.

This addendum provides funding and acknowledgement details that were inadvertently omitted from the original publication: Sunegin, D. E. & Belyaev, V. V. (2026). Jahn–Teller effect as a controlling parameter of structural and electronic properties. In: Bulletin of the Federal State University of Education. Series: Physics and Mathematics, 1, pp. 6–15. DOI: 10.18384/2949-5067-2026-1-6-15.