In the article, the author considers an analog circuit (analog computer) in which the dynamics of voltage changes is described by the Chua system. The initial states (setting the initial voltages) are found which bring the circuit to the limit mode of operation (a hidden attractor): a stable limit cycle with a frequency of $\approx0.5$ Hz. In this case, the received signals have a shape close to a harmonic signal. The developed oscillation generator circuit contains seven operational amplifiers, does not have a memristor which significantly reduces the cost of assembly, inductors which eliminates the problems of their manufacture, and gyrators. The values of the resistance and capacitance ratings corresponding to the considered system parameters are deter-mined. One of the inverters of the circuit based on the operational amplifier models the nonlinearity of the stop type, present in the Chua system, periodically entering saturation states. After assembling the device, the output signals of the circuit corresponding to the phase coordinates of the Chua system are recorded in the text file in time steps using a digital oscilloscope. The parameters of the mathematical model in the computer program developed by the author are identified, the adequacy of the model is checked by the coefficient of determination and the Fisher criterion. Also, by numerically investigating the Poisson stability of the found mode in the Chua system, the period and frequency of the obtained cycle are determined, and a comparison is made with the frequency given by the digital oscilloscope.

When modeling social processes and phenomena, it is often necessary to process data related to categorized features, identify cause-and-effect relationships between such data, and determine the most significant indicators. A study of existing approaches to analyzing dependencies between categorized variables revealed several problems when applying these methods to multidimensional categorized data (tensors). Therefore, this article proposes an approach to studying dependencies between such variables using multidimensional component analysis. This approach involves applying tensor unfolding matrices obtained for each of its axes (categorized features). The method allows for the construction of integral characteristics (components) based on the elements of the original tensor, the formation of component loading matrices, and the calculation of the tensor core, which has fewer gradations of categorized features (lower number of dimensions in the tensor axes) than the original tensor. The article proposes a method for ranking the gradations of categorized variables by the degree of cumulative influence of component loadings, based on the calculation of vector norms. The described approach to studying dependencies between multidimensional categorized variables is demonstrated using a three-dimensional tensor with the shape (4;10;10) and categorized features: nosology group, field of activity, and group of professionally significant qualities. The algorithm for analyzing multidimensional categorized data using multidimensional component analysis, discussed in this article, is intended to be incorporated as an analytical tool into the regional information and analytical portal "PERSPEKTIVA-PRO." This tool can be used to develop a digital support trajectory for people with disabilities and special needs, taking into account their personal and variable characteristics.

This paper proposes a systematic approach to developing combinatorial generation algorithms for sets of discrete structures whose cardinality is determined by the coefficients of algebraic generating functions and their powers. The study is based on the relationship between operations on generating functions and combinatorial sets. It uses the mathematical apparatus of AND/OR trees as a foundation, which allows combining combinatorial generation algorithms for simple substructures into complex combinatorial objects. The main theoretical result of the work is the derivation of new efficient recurrence formulas for calculating the values of the coefficients of algebraic generating functions and their powers with polynomial computational complexity $O((n_1 + \ldots + n_m + m) \cdot n^2)$ for time and $O(n^2)$ for memory. Based on proven theorems on recurrence formulas, the proposed approach enables the construction of algorithms with polynomial computational complexity estimates, making them applicable to solving practical problems in applied discrete mathematics and theoretical computer science. Moreover, the use of coefficients of generating function powers expands the generation capabilities, since it allows us to construct not only objects of the original combinatorial set associated with the generating function, but also tuples of such objects. Validation of the proposed approach is demonstrated using examples of deriving recurrence formulas and generation algorithms based on them for classical numerical sequences, such as the Fibonacci, Pell, Catalan, Motzkin, and Schroder numbers. The proposed approach opens up new possibilities for solving problems of optimization, modeling, and coding complex discrete structures, for example, in fields such as bioinformatics and cryptography.

The task of automated morpheme segmentation for morphologically rich but low-resource languages, such as Belarusian, remains insufficiently studied. This paper presents the first large-scale comparative study on the effectiveness of modern neural network approaches to morpheme segmentation using Belarusian language data. We compared three approaches that have demonstrated high quality for other languages: algorithms based on convolutional neural networks (CNNs), algorithms based on LSTM networks, and fine-tuning of BERT-like models. Due to the limited availability of monolingual Belarusian models, we also included larger Russian and multilingual models in the comparison. The experiments were conducted on the openly available Slounik dataset using two strategies for splitting the data into training and test sets. In the first case, the split was random; in the second, words were split by their roots to ensure that words with the same root did not appear in both the training and test sets simultaneously. An ensemble of LSTM networks achieved the best performance in the experiments, with a word accuracy of 91.42% on the random split and 73.89% on the root-based split. Comparable results were demonstrated by fine-tuned multilingual and Russian BERT-like models, highlighting the potential of applying large models, including those trained on closely related and higher-resource languages, to this task. An analysis of the errors confirmed that, as with other Slavic languages, the majority of inaccuracies are related to the identification of root boundaries.

Artificial intelligence (AI) models can fully or partially automate the assessment of student assignments, making assessment methods more accurate and objective. The performance of such models depends not only on the underlying algorithms and training data but also on the effectiveness of the queries they formulate. The aim of the work is to investigate the possibility of using open artificial intelligence models to evaluate students' answers for compliance with the teacher's standard answer, as well as to increase the quality of problem solving using prompt engineering. The method for determining this quality was selected by statistical characteristics of the results of classifying answer texts into four categories: correct, partially correct, incorrect, inappropriate to the topic of the question, by GAI models using the following prompt options: simple prompt, role-playing prompt, "chain of thoughts" prompt, prompt generated by artificial intelligence. Models available for open use were selected for the study: ChatGPT o3-mini, DeepSeek V3, Mistral-Small-3.1-24B-Instruct-2503-IQ4_XS and Grok 3. Testing of the models was carried out on a corpus of student texts collected by teachers of Demidov Yaroslavl State University, from 507 answers to 8 questions. The best quality of answer assessment was shown by the ChatGPT o3-mini model. with the prompt it generated. The accuracy rate was 0.82, the mean square error (MSE) was 0.2, and the F-score reached 0.8, demonstrating the potential of GAI as not only an assessment tool but also a means of automatically generating instructions. The Fleiss coefficient was used to assess the consistency of the model's responses across 10 identical queries. For this model-prompt pair, it ranged from 0.48 for complex questions to 0.69 for simple questions.