With no established analogues in the current or past global practice, associative data protection remains cautiously perceived by specialists. The time has come to provide an integrated perspective of this method and summarize its numerous and undoubted benefits over competing approaches. In order to demonstrate such benefits, this article overviews the main results of published original research on various aspects of associative data protection. Avoiding exhaustive detail, it focuses, with appropriate references to existing literature, on the principal features of associative data protection: morphology, steganographic strength, cryptographic strength, noise immunity, and volumes of transmitted and stored information. Our central finding is a promising symbiosis of steganography and cryptography. The most notable specific results include the development of a masking algorithm and strategies for associative protection of cartographic scenes and texts, the achievement of a so-called coverage completeness, the discovery of the basic theorem of unambiguous recognition, as well as the estimation of the number of keys, steganographic strength, cryptographic strength, and noise immunity of associative data protection. References are given to the database management systems (DBMSs) already employing associative data protection. The review highlights considerable opportunities for further elaboration of the theory and practice of associative data protection.

The dynamics of regular and stochastic clusters consisting of 16 air bubbles in water near a flat rigid wall under room conditions, as well as with the action they exert on it, was investigated. In the regular cluster, the centers of the equal spherical bubbles were initially located at the nodes of a flat quadratic mesh parallel to the wall. The stochastic clusters were produced from the regular one by the random change in the position or size of the bubbles. The water pressure varied harmonically. The study used a discrete model of the joint bubble dynamics, in which the bubbles are allowed to undergo radial oscillations, translation, and deformations, but not destruction, and proceeded until the destruction began. The dynamics of the bubbles and their action on the wall were analyzed with respect to the amplitude of water pressure oscillations, the distance between the bubbles and the wall, the spacing of the bubbles, the random non-uniformity of the initial size of the bubbles, and the random non-regularity of the initial positions of the bubbles. The pressure on the wall was found to be largely determined by the asynchronous dynamics of the bubbles. Its maximum value was reduced monotonically with a decrease in the amplitude of water pressure oscillations and an increase in the distance between the bubbles and the wall and the spacing of the bubbles.

The construction of systems for online monitoring of the technical state of hydrogen fuel cells by analyzing their electrical fluctuations during operation was explored. A system model of proton-exchange membrane fuel cells that considers the relationships between input and output signals as a source of diagnostic information was described. The results show that only an adapted small-signal system model enables effective online diagnostics. The use of electrical fluctuations for early detection of critical operating modes and taking timely corrective control actions was illustrated by maintaining the water balance in a membrane electrode assembly as an example. The possibility of detecting modes with excessive and insufficient humidification based on the analysis of the spectral characteristics of electrical fluctuations was established. The critical modes and faults of solid polymer fuel cells detectable through electrical fluctuations were examined.

Scientific publications play a crucial role in the exchange of information among scientists. Due to ongoing technological progress and digitalization in all fields, the already large volume of scientific information, both in the form of publications and research data, continues to grow exponentially and demands advanced tools and methods for its efficient and reliable selection, analysis, and structuring. At the same time, new approaches are needed to assess the importance of scientific publications. In this article, in order to obtain a deeper and more objective understanding of the relationships between different publications and to assess their impact within a selected field of study, an innovative approach to ranking scientific publications based on analysis of citation networks was proposed. The approach was successfully applied to analyze the publications of researchers from the Institute of Information Technology and Intelligent Systems of Kazan Federal University, thereby confirming its feasibility and prospects for broader use. All citation metrics were retrieved from the OpenAlex database of scientific literature (https://openalex.org/).

This article reports the results of a multiscale modeling of polymer composite materials (PCMs). It was demonstrated that their mechanical characteristics are determined by the combined contribution of micro-, meso-, and macroscopic strain processes. A multiscale approach to building digital models that account for the structural and mechanical characteristics of the material was introduced and subsequently applied in order to develop a micro-model of a carbon yarn, a meso-model of a PCM based on triaxial woven fabric, and a macro-model of a reflector, enabling prediction of the stressstrain state across different scales. The stress-strain state of the material was evaluated, and the processes of its fracture were analyzed. The stress-strain diagrams were constructed, and the effective mechanical properties of the PCM were identified. The models obtained make it possible to perform virtual tests without resource-intensive experiments and can be employed in the design, adaptation, and optimization of PCMs for solving specific engineering tasks.

A method was proposed for calculating the probability distribution of a discrete random variable (DRV) using a d-ary tree. The tree has n leaves, which is equivalent to the number of elements in the DRV probability distribution, and the remaining vertices represent the DRV generators with the probability distribution including d elements (d-DRV). Variation in the DRV probability distribution by zeroing one of its elements reduces to the recalculation of the d-DRV probability distributions, the number of which increases logarithmically with respect to the value of n.

The problem of linear conjugation for a two-dimensional piecewise analytic vector was reduced to an equivalent problem of fractional linear conjugation, and a connection between their solutions was established. It was shown that, once a particular solution of either problem is known, the canonical system of solutions of the linear conjugation problem can be written in closed form. The relations were specified between the elements of the H¨older matrix-function of the linear conjugation problem under which the fractional linear conjugation problem has a rational solution, thus enabling a closed solution of the linear conjugation problem.

The diffraction of an electromagnetic TE wave on multilayer diffraction gratings with several two-layer lines in the period was investigated. Such optical structures are employed in spectral beam combining. The diffraction problem was solved by a modified method of variable separation, which requires the solution of two one-dimensional boundary value problems for eigenvalues of second-order differential equations on a segment with piecewise constant coefficients. Each of the boundary value problems for eigenvalues reduces to the calculation of a second-order determinant. The proposed method was applied to solve the problem of the electromagnetic TE wave diffraction on multilayer diffraction gratings with several different configurations, as well as to determine their diffraction efficiency. The numerical results were presented. For modeling the diffraction gratings, materials that are commonly used in thin-film coatings were selected. The method can be further developed to model more complex diffraction gratings with multilayer reflective coatings.

A three-particle discrete Schrödinger operator H_µ,γ(K) :≡ H_µ,γ(K), K = (K, K, K) ∈ 𝕋³ , which is associated with a system of three particles (two fermions of mass 1 and one other particle of mass m = 1/γ ,) interacting via pairwise repulsive contact potentials µ > 0 on a three-dimensional lattice ℤ³ , was analyzed. Critical values of mass ratios γs(K) and γas(K) were determined such that the operator H_µ,γ(K) has no eigenvalues if γ ∈ (0, _γs(K)), the operator H_µ,γ(K) has a single eigenvalue if γ ∈ (_γs(K), γas(K)), and the operator H_µ,γ(K) has three eigenvalues lying to the right of the essential spectrum for sufficiently large µ > 0 if γ ∈ (_γas(K), +∞).

The use of the method of Muller boundary integral equations for solving the problem of eigenwaves of weakly guiding dielectric waveguides was justified. A theorem was proved about the spectral equivalence between the original differential problem and the problem for the system of Muller boundary integral equations on the physical sheet of the Riemann surface, where the eigenvalues, the propagation constants of the eigenwaves, are sought. With this aim, the localization regions of the spectra of the original problem and a so-called “turned inside out” problem generating spurious eigenvalues were analyzed. A sufficient condition of equivalence was obtained: the problems are equivalent if the problem turned inside out has only a trivial solution. Consequently, as confirmed by the results of the numerical experiments, only true eigenvalues on the physical sheet of the Riemann surface can be found by using the method of Muller boundary integral equations.

This article is a tribute to the life and scientific legacy of Professor Lubov’ Ivanovna Chibrikova of Kazan University.