In this work, we propose a population dynamics model of the spread of stressful processes in several groups with different characteristics. Such a model is described by a system of nonlinear differential equations. Also, this model provides for the possibility of studying external influences, that is, the effectiveness of actions aimed at increasing the psychological stability of the population. The main objective of the study was to propose algorithms for finding guaranteed predictive estimates of the dynamics of such models. Two scenarios of this challenge are considered: for the case when there are available accurate data on the number of persons under stressful influence in each of the groups during a specific time interval; and for a similar case, but when there is observational data on the dynamics of such individuals. In both cases, we apply the methodology of finding guaranteed predictive estimations of the dynamics within these models. As an example, we consider the special case of the equation of population dynamics without external influence for one group of persons.

The model of nonlinear deformation of a granular composite material of a stochastic structure with physically nonlinear components was constructed. The basis is the stochastic differential equations of the physically nonlinear theory of elasticity by L.P. Khoroshun. The solution to the problem of the stress-strain state and effective deformable properties of the composite material is built using the averaging method. An algorithm for determining the effective properties of granular material with physically nonlinear components has been developed. The solution of nonlinear equations, taking into account their physical nonlinearity, is constructed by the iterative method. The law of the relationship between macrostresses and macrostrains in granular material and the dependence of average strains and stresses in its components on macrostrains has been established. Curves of deformation of the material were constructed for different values of the volume content of its components. The dependence of the effective deformable properties of the granular material on the volume content of the components was studied. The effect of component nonlinearity on the deformation of granular composite material was studied. It was established that the nonlinearity of the components significantly affects the effective deformable properties and the stress-strain state of granular materials.

On September 28, 2023, Mykhailo Moklyachuk, Doctor of Physical and Mathematical Sciences, Professor, Laureate of the State Prize of Ukraine in Education, Honored Worker of Science and Technology of Ukraine, and Academician of the Academy of Sciences of the Higher School of Ukraine, celebrated his 75th birthday. His scientific research is devoted to the study of stationary random processes, functionalities of stationary processes, and random fields.

The article presents modifications for numerical methods for modeling of mass transfer process in porous medium with full saturated zone tracking. The goal of the article is to increase computational efficiency of finding an approximate solution process using division of the area into the two non-intersecting parts: unsaturated zone and zone with full saturation. Numerical methods for solving the one-dimensional Richards-Klute equation with tracking of the full saturated zone have been developed. The cases of monotonic solution and solution with general properties of Richards-Klute equation were considered. A modification of the full saturated zone tracking process using a doubly connected edge list structure have been developed for two-dimensional case. Efficiency increase estimation is proven for one- and two-dimensional cases using probability distibution for a measure of the full saturated zone. A comparative analysis of the proposed modifications was carried out. The results of numerical experiments coincide with the estimates predicted by theory.

The article is devoted to a review of approaches to solving the problem of identifying paraphrases. This problem's relevance and use in tasks such as plagiarism detection, text simplification, and information search are described. Several classes of solutions were considered. The first approach is based on manual rules - it uses manually selected features based on the fundamental properties of paraphrases. The second approach is based on lexical similarity and various databases and ontologies. Machine learning-based approaches are also presented in this paper and describe different architectures that can be used to identify paraphrases. The last approach considered is based on deep learning and modern models of transformers.

This paper investigates the use of fuzzy numbers and the annealing method to improve the results of the traveling salesman problem (TSP) by more accurately representing real-world circumstances, where the value of the objective function represents the subjective perception of the length of the time interval required to travel between cities. TSP is a classic combinatorial optimization problem that involves finding the shortest route between a set of cities. Fuzzy numbers are used to model input inaccuracy and uncertainty, as they allow for a more detailed representation of real-world constraints and factors that may affect the problem. The annealing method is used to optimize the TSP solution by gradually decreasing the temperature of the system, which allows exploring different solutions and avoiding getting stuck in local minima. To demonstrate the effectiveness of this approach, a Python program was developed that was used to compare the results of the TSP problem using crisp and fuzzy numbers using the annealing method. The results show that the use of fuzzy numbers, particularly triangular and parabolic, with the annealing method leads to a significant improvement in the results of the TSP problem compared to the use of crisp numbers, assuming a model is called realistic if it has possible deviations from the expected fixed mean. Computational results of the program are presented and analyzed, demonstrating the potential of this approach for real-world optimization problems involving imprecise or uncertain data and which can be particularly applied to the optimization of processes with subjective time perception.

We consider modeling and geophysical interpretation of the obtained results in the deforming process of the salt structures due to gravitational buoyancy (halokinesis). For solving this geophysical problem, we use variation finite element method of elastic problem resolving with calculation of heterogeneous rocks distribution into considering salt structures. We have defined that salt structures deforming amplitudes mainly depend on linear sizes (length and thickness) of the bottom parts of these structures. Decreasing of these parameters lead to noticeable drop of the press-strain state near the whole region of the salt structure (diapirs). Another hand forms and linear sizes of the top parts of the salt stocks influence only on the deforming of the local regions near these structure elements and don’t essentially influence on the whole region deforming around the stock. Quantity characteristics of linear sizes of the salt diapirs structural elements define the whole picture of the stress-strain state around these objects.

The article is devoted to the analysis of tasks for building a writing assistant, one of the most prominent fields of natural language processing and artificial intelligence in general. Specifically, we explore monolingual local sequence transduction tasks: grammatical and spelling errors correction, text simplification, paraphrase generation. To give a better understanding of the considered tasks, we show examples of expected rewrites. Then we take a deep look at such key aspects as existing publicly available datasets and their training splits, quality metrics for high quality evaluation, and modern solutions based primarily on neural networks. For each task, we analyze its main peculiarities and how they influence the state-of-the-art models. Eventually, we investigate the most eloquent shared features for the whole group of tasks in general and for approaches that provide solutions to them.

We study the Cauchy problem for a parabolic equation on the line driven by a general stochastic measure. Under some assumptions, we prove that the mild solution tends to zero almost surely as the absolute value of the spatial variable tends to infinity.

Trigonometric regression models take a special place among various models of nonlinear regression analysis and signal processing theory. The problem of estimating the parameters of such models is called the problem of detecting hidden periodicities, and it has many applications in natural and technical sciences. The paper is devoted to the study of the problem of detecting hidden periodicities in the case when we observe only one harmonic oscillation with discrete time, where random noise is a local functional of Gaussian random sequence with singular spectrum. In particular, the random sequence in the model can be strongly dependent. For estimation of unknown parameters the periodogram estimator is chosen. Sufficient conditions of the consistency of the amplitude and angular frequency periodogram estimator of the model described above are obtained in the paper. The proof of Lemmas 1 and 2 gave an important asymptotic properties of the random noise functional related to the periodogram estimator which necessary for the proof of the main results. Series expansion of random noise in terms of Hermite polynomials and the Diagram formula are main tools that were used to obtain this lemmas.