Current bibliographic databases incorporate vast volumes of information, thus necessitating the identification of a “core” subset to evaluate the highest-quality research outputs. The Hirsch index, an objective bibliometric indicator utilized in gauging an author’s performance and impact, can be calculated for both the entire database or its core content. This study introduces a novel quality index for measuring the publishing activity of individual authors and institutions, which is defined as the ratio between the Hirsch index values for the entire database and its core. The approach enables multiple comparisons: between authors, departments, universities, and even the roles of specific authors within institutions in terms of their publishing activity. Its application was demonstrated through a case study of Samara National Research University. Based on the results obtained, strategic recommendations to improve the quality of the university’s publishing activity were outlined.

   A model of nondeterministic ordered binary decision diagrams (NOBDDs) was analyzed. A method for proving a lower bound on the complexity of quantum NOBDDs was developed. Two functions were introduced: one function has linear complexity in the quantum NOBDD but constant complexity in the classical NOBDD, while the other function demonstrates the same complexity in both quantum and classical NOBDD models. The relationships among the complexity classes specific to the OBDD model were described.

   Using a commonly agreed definition of the journal impact factor, its various applications in the mathematical modeling of scientific research were investigated. Special attention was paid to the impact factor’s properties related to the disciplinary structure of science, the limitations of source data in existing databases, statistical reliability, the relevance of document types, and the effect of outliers. The potential bias resulting from journal self-citation practices was discussed.

   A satellite moving along a circular Keplerian orbit in near-Earth space was explored, focusing on its attitude stabilization in the orbital coordinate system using the intrinsic magnetic and Lorentz force moments. Fluctuations in geomagnetic induction that occur as the satellite orbits cause the coefficients in the dynamical equations governing the satellite’s attitude motion to vary over time. The results show that, although the linearized system of differential equations of the satellite’s motion is non-stationary, it can be reduced to a stationary system of higher order, which holds even for high-precision multipole models of the geomagnetic field. Thus, a control law design was proposed to stabilize the satellite. The controllability of the system was analyzed, and an optimal stabilization algorithm based on the LQR method was developed. The effectiveness of the proposed approach was validated by computer modeling.

   A computer model of a two-stage system for locating faults by analyzing reflected signals was developed. The simulation results for power transmission lines with varying numbers of branches extending from the main line were discussed. The relationship between fault location efficiency and the network bit error rate was analyzed. The dependence of diagnostic reliability on the number of branches and fault types was examined.

   This article introduces FAST-GM (Formal Approach to Spatio-Temporal Game Modeling), a new unified approach to formal modeling of game entities and their interactions that integrates temporal and probabilistic dimensions, thus offering a comprehensive framework for capturing the dynamics of game systems. Built upon the principles of extended temporal logic and probability theory, FAST-GM accurately describes complex game mechanics and how they evolve. A formal definition of game entities was considered. Their states and interactions were explored. The methods for integrating temporal and probabilistic elements into gameplay were discussed. The applicability of FAST-GM for game balancing, formal verification of game scenarios, and automated generation of test cases was analyzed. Its scalability and adaptability in various game genres were assessed. The results obtained show that FAST-GM should advance the formal modeling of game systems, equipping developers with a powerful toolset for analysis, verification, and optimization of game mechanics throughout the process of creating a video game.

   This article presents a mathematical model of heat and mass transfer in anisotropic heat-protective composite materials (HPCM) during phase transformations of HPCM binders with the formation of a porous coke residue and pyrolysis gases filtering through the residue to the outer boundary. Using known binder decomposition and nonlinear filtration laws for random HPCMs, the model determines the velocity and coordinates of the two-dimensional HPCM binder decomposition zone, as well as the two-dimensional regions of the porous-gas residue and the initial phase, which are unsteadily separated by a moving zone of binder decomposition. In the newly formed porous-gas region, a two-dimensional unsteady problem of anisotropic heat conduction was solved taking into account nonlinear anisotropic gas filtering. In the initial region unaffected by the binder decomposition, a two-dimensional unsteady problem of anisotropic heat conduction was solved. The mass and linear velocities of the binder decomposition (pyrolysis) zone were calculated from Stefan conditions for heat flow and temperature continuity. The complex model was solved by the previously developed effective and absolutely stable method of alternating directions with extrapolation. New results were
obtained and discussed.

   A general solution is constructed for the distribution of stresses within a thin, hyperbolic elastic-plastic disk subjected to external and internal pressures while in a steady-state temperature field and under plane stress conditions. The pressures applied to the disk are assumed not to induce any plastic flow at the initial, uniformly distributed temperature. The disk is loaded by increasing the temperature of its inner radius. The temperature of the outer radius is kept constant. Elastic and temperature strains are related to stresses by the Duhamel–Neumann law. In the plastic region, the von Mises yield criterion is valid. The tensile yield stress is taken as constant. The boundary value problem is statically determinate. Therefore, the plastic flow rule is not required to determine the stress field. The final part of the general solution depends on the parameters classifying the boundary value problem, including whether the plastic flow initiates at the inner or outer radius of the disk. The solution is presented in dimensionless form. The loading parameter comprises the inner surface temperature of the disk, the coefficient of linear thermal expansion, the initial temperature of the disk, the dimensionless inner radius of the disk, the yield stress under uniaxial tension, and Young’s modulus. The general solution is obtained for both cases (for a plastic region appearing at the inner or outer radius of the disk). A specific numerical solution is constructed for a disk subjected to external pressure and a steady-state temperature field. The temperature of the inner radius at which the plastic region first appears is calculated. As it increases, the plastic region extends. At a certain temperature value, another plastic region appears near the outer radius of the disk. This value is determined as part of solving the boundary value problem. The influence of the parameters classifying the boundary value problem on the development of the plastic region and the stress distribution along the radius of the disk is shown. The qualitative differences between the new and existing solutions for a disk of constant thickness under the action of a uniform temperature field are discussed.

   The progress in developing an effective automatic knowledge control system is directly associated with creating and implementing a software module for grading answers to test questions formulated in natural language. Previously, an experimental prototype of such a system was designed, and a study was performed where short answers to basic question types provided by students were examined via a pragmatically oriented question-answer text processing algorithm, considering its outputs and exposing flaws. This article introduces the next iteration of the algorithm tailored to handle more complex question types that requires the identification of relations such as “Definition” and “Description.” The key features of the enhanced algorithm were outlined, with a particular focus on the problem of segmenting answers into meaningful chunks, a task for which processing methods have already been found. The results of an experiment based on the developed prototype with obtaining answers from students and a thorough analysis of the instances of the system’s incorrect behavior were discussed.

   The catalytic activity coefficient and emissivity of the surface of thin-walled oxidation- and erosion-resistant coatings for high-speed aircraft were determined experimentally and theoretically. The coating was applied as an aerosol mixture to a carbon-carbon composite substrate, and the resulting sample was subjected to fully dissociated air to measure heat fluxes to the sample surface and its enthalpy. Using established relationships between total convective-diffusive heat fluxes, stagnation enthalpy, and the heterogeneous recombination coefficient of oxygen and nitrogen atoms into molecules, the catalytic activity coefficient and surface emissivity were calculated based on the Stefan–Boltzmann law utilizing the measured enthalpy (and temperature) of the wall. The experiments were performed on five coating types containing silicon, titanium, molybdenum, and boron. The findings were summarized in a table showing how the recombination coefficient and emissivity depend on heat fluxes and wall temperature.

   A method was outlined for determining the coefficient of third-kind boundary conditions of the piezoconductivity problem in an oil reservoir, particularly on its external contour, which has, as a rule, no specific hydrodynamic properties and is set to reduce computational costs. The coefficient was determined using an integral balance model of an interaction between the oil deposit and the outer region of the reservoir. The optimization problem of approximating the average reservoir pressure to the values obtained from the well pressure measurements was solved. Assuming the homogeneity of the reservoir, the applicability of the algorithm was assessed under various geometries of the external contour, well placements, and operating conditions. The stability of the algorithm for solving the inverse problem was analyzed against pressure measurement errors. The proposed approach offers a relatively simple algorithm for defining the boundary conditions of a reservoir flow model, which enables a good approximation of the hydrodynamic interaction of the reservoir with its outer region. However, due to uncertainties in the initial data for regions distant from the well-drilled area of the reservoir, significant difficulties remain in calibrating the model.

   Using a three-dimensional topographic map of a typical microdistrict in Kazan, multipath radio wave propagation in mobile radio communication systems was modeled by the method of ray tracing. An ensemble of 4000 radio links, each 200 m long, was generated and randomly positioned on the map. The wave propagation scenarios included both line-of-sight and non-line-of-sight conditions of visibility between transmitters and receivers. A quantitative analysis of the contribution made by multiply scattered waves to the channel impulse response was performed. The results show that single-scattering approximation is generally sufficient for 200-m line-of-sight links. However, in the non-line-of-sight scenario, it is necessary to also account for waves scattered two or three times.

   A method was proposed for solving the traveling salesman problem (TSP) using N -complex Markov chains (N -MC), the state sequence of which simulates a path through N points, each visited only once. Transition probabilities from each point to one of the next l points were set, where l < N. The complexity of implementing all stages of the method, depending on the values of N and l, was analyzed. Estimates of the complexity of the N -MC generator were obtained based on the composition of a finite deterministic automaton and a probabilistic memoryless automaton. The complexity of the N -MC generator is characterized by the volume of input sets, internal states, and outputs, as well as the amount of memory required to implement the transition and output functions of the automata. The delay time of the N -MC generator operation was also estimated. The probability of generating valid paths, i. e., those resolving TSP, and the memory requirements for storing valid paths were calculated.

   The necessary and sufficient conditions for stochasticity and bistochasticity of positive operators were analyzed. Key criteria for stochasticity of continuous positive operators in Rm were proved. The necessary and sufficient condition for these operators to be referred to as bistochastic was established.