Mathematical Methods Research Articles

Metaphorical meaning dynamics: Identifying patterns in the metaphorical evolution of English words using mathematical modeling techniques

Abstract Conceptual metaphor theory has been criticized due to its emphasis on concepts instead of words and its top-down direction of analysis. In response to these criticisms, this paper employs a new strategy, utilizing established mathematical modeling methods to allow a systematic, quantitative analysis of the entire dataset produced by the Mapping Metaphor project at the University of Glasgow. This dataset consists of 9609 words performing 18916 metaphorical mappings between 414 domains. The data is represented as a network consisting of 414 nodes, the domains, connected by shared words. Words are represented by groups of directed mappings between all domains in which they occur. This is made possible by the use of a directed hypergraph representation, a tool commonly used in discrete mathematics and various areas of computer science but not previously applied to the metaphorical meanings of words. Examining the dataset as a whole, rather than focusing on individual words or metaphors, allows global patterns of behavior to emerge from the data without pre-filtering or selection by the authors. Outcomes of the analysis relating to the distributions of source and target domains within the network, the growth mechanisms at work in the spread of metaphorical meanings and how these relate to existing concepts in CMT are discussed.

Space flight mechanics theoretist and practitioner. On the 100th anniversary of the birth of academician T.M. Eneev

The article presents materials about Academician Timur Magometovich Eneev, an outstanding scientist in the field of space flight mechanics, one of the founders of modern space flight dynamics. His works have made a significant contribution to the achievements of world science. Namely, his contribution to the launch of the first artificial satellite of the Earth, the flight of Yuri Gagarin, to the implementation of flights to the Moon, planets of the Solar system, to the study of small bodies of the Solar system, to the theory of cosmogony, solving problems of genetics is great. The new mathematical methods proposed by T.M. Eneev to solve the problems of space exploration constitute the golden fund of Russian astrodynamics and are successfully used for the implementation of Russian space exploration projects. T.M. Eneev is not only an outstanding scientist, but also a citizen of our Fatherland, who responded to the problems of the formation of science, cosmonautics, cosmogony, biology and other issues of concern to modern society.

Optimization Processes in Automotive Logistic Flow

This paper presents a logistic flow of assembling automotive rear axles. The product is presented in detail starting from the detailed research and analysis of relevant documentation about its functionality, including the manufacturing logistic flow diagram and the required equipment for the product manufacturing and assembly. This study is focused on optimizing the logistic flow for the manufacturing and assembly of automotive rear axles using WITNESS Horizon for system modeling and simulation in order to conduct system diagnostics, identify problems, and find solutions that will facilitate the optimization process. The study included a comprehensive assessment of the logistic flow, highlighting the performance of the equipment involved and identifying potential bottlenecks. Using the results obtained after the simulations, the Simplex linear mathematical method was applied to maximize production efficiency and profitability, considering the suppliers’ capacity constraints and the components’ delivery requirements. The results demonstrated a significantly optimized rear-axle production process, with increased profitability and improved productivity by eliminating identified bottlenecks. This research contributes to a deeper understanding of the complexities within the automotive industry and provides a solid foundation for continuously improving manufacturing and assembly processes.

New Proxy Signature Scheme over Elliptic Curves using Chaotic Maps Applicable during Pandemic COVID-19

Abstract: Digitalization has attracted the world to collect increasing data. Background: Proxy signature is a digital alternative for signing documents in the absence of the original signer. Methods: In this paper, we have used the mathematical methods and concepts of Chaotic maps (CMs) and elliptic curve cryptography. Results: We have proposed a new proxy signature scheme (PSS). Security of our PSS relies on "elliptic curve discrete logarithm (ECDL) and integer factorization (FAC) problems". It requires only low-complexity computation, which increases efficiency. Conclusion: It is the first PSS in such a security setting and can also be assumed to be secure in the post-quantum cryptographic world. It can be highly used digitally during thePandemic conditions like COVID-19.

Research on the Application of Mathematics in Finance

Abstract. Mathematics is a fundamental science and a problem-solving method that plays an important role in revealing the essential laws of the development of certain things. It has rigorous logic, high abstractness, and wide applicability. This brings great difficulties to enterprises, especially high school mathematics because it involves a wide range of knowledge points and complex calculations. Among them, the formation of financial mathematics has greatly promoted the development of China's financial industry. Moreover, in solving financial problems, relevant knowledge and theories of mathematics can be used to analyze and explore financial laws, and the application effect is significant, for example, using deterministic mathematical method and nondeterministic mathematical method to solving question about financial investment and returns; building securities investment portfolio model or asset valuation model to calculating and expressing some economic models. Based on this, this article discusses the application of mathematical knowledge to several financial problems, analyzes the current problems, and looks forward to the future of financial mathematics.

Аналіз результатів анкетування волейболістів-аматорів та здобувачів освіти ЗВО фізичної культури і спорту щодо теоретичної підготовки в навчально-тренувальному процесі волейболістів

The aim of the study is to determine the opinions of amateur volleyball players and students of higher education institutions in the field of physical culture regarding theoretical preparation. Materials and Methods. During the research, the following methods were used: methods of theoretical level of research, methods of empirical level of research and mathematical statistical methods. Our survey aimed to identify the attitudes of amateur volleyball players and students of higher education institutions in physical culture regarding distance teaching of volleyball and theoretical preparation during both online and offline training processes. We proposed 8 specific questions in the survey about the respondents' awareness of theoretical preparation in volleyball, its significance, and the availability of modern forms and methods, as well as their self-assessment of theoretical preparedness, etc. A total of 70 respondents participated in the survey, including: 1 Master of Sports of International Class (1.4%); 1 Master of Sports (1.4%); 6 Candidates for Master of Sports (8.6%); 8 First-Class players (11.4%); 3 Second-Class players (4.3%); and 51 unclassified players (72.9%). Among all respondents, 49 were female (70%) and 21 were male (30%). By age: under 20 years – 17 individuals (24.2%); 20 to 25 years - 24 (34.3%); 25 to 30 years – 18 (25.8%); 30 to 35 years – 7 (10,0%); 35 to 40 years – 3 (4.3%); over 40 years – 1 (1.4%). Additionally, 65 volleyball players live in the city (92.85%), 1 in an urban-type settlement (1.43%), and 4 (5.72%) in rural areas. Among the respondents there were 24 students (34.3%), 40 (57.1%) working volleyball players, and 6 (8.6%) temporarily unemployed. The experience of volleyball training among the respondents varied from 1 to over 20 years: from 0 to 5 years – 19 (27.1%), from 5 to 10 years – 22 individuals (31.4%); from 10 to 15 years – 14 (20%); from 15 to 20 years – 9 (12.85%); over 20 years – 6 (8.6%). The survey was conducted during the "Fit-Mix" park volleyball tournament among amateur teams in Dnipro from March 9 to March 10, 2024, which involved 10 teams. Results. The analysis of the responses from amateur athletes and students of higher education institutions in physical culture to the question "Do you feel the need to acquire theoretical knowledge in volleyball?" indicates that 15 of them (21.4%) do not need theoretical knowledge at all, 14.3% rely on the coach's knowledge, only 8 (11.4%) have a constant need for knowledge about volleyball, and 37 (52.8%) feel the need for theoretical knowledge "from time to time." Conclusions. The research established that our assumption as to the necessity of scientific substantiating the structure and content of theoretical preparation in volleyball is confirmed by the majority of respondents expressing a need for theoretical knowledge. This is a relevant issue which solution will enhance the quality of training for higher education students in the field of physical culture and sports.

Використання теорії невизначеності при дослідженні показників просторового сприйняття в єдиноборствах

Purpose: to study the indicators of spatial perception of martial artists using the provisions of uncertainty theories. Material and Methods. Research methods: analysis and synthesis of scientific and methodological literature, psychophysiological measurements, mathematical and statistical methods using licensed programs RStudio and Numbers. The study was conducted in several stages. At the first stage, taking into account the peculiarities of martial artists' sports activities, a mobile application «Spatial Perception» was developed to assess their spatial perception. At the second stage, the use of the application in the field was tested and the capabilities of the mobile application were expanded in terms of obtaining detailed characteristics of measurements using the provisions of the theory of uncertainty. The study involved junior taekwondo athletes aged 14-17 years (n=25, qualification: 1st category and candidates for master of sports of Ukraine). Results: according to the measurements of the studied martial artists, it can be noted that the highest frequency of reaction time indicators lies within 583 ms (n=291). At the second stage of the test exercise, where the performer needs to react to non-moving 3D figures, there is an increase in the interquartile range by 22 ms and a violation of the symmetry of the data. It was at this stage that the largest value of the standard deviation was noted (SD=172,0 ms). This indicates a high variability of reaction time (V=22,7 %). Also, we can see an increase in reaction time at the fourth stage compared to the result of the third stage by 11,5 ms and an increase in the percentage of errors by 1,4 % (at this stage, the highest percentage of errors was recorded at 8,2 %). Based on the use of membership functions, fuzzy sets were created, which made it possible to evaluate each indicator on a scale from 0 to 1. The analysis of the test exercise performance by martial artists who have the category of KMS (candidate for master of sports) shows that the overall score for the entire test is «Good», the weighting factor is 0,74, which is closer to the «Excellent» score. It should be noted that the highest weighting coefficient was observed in the second stage of the test task. The high weighting factor (0,79) at this stage reflects the ability to quickly recognize 3D shapes in space based on the analysis of individual parts of the shapes. We can also note the low percentage of errors (3 %) at the fourth, most difficult stage. This may indicate the ability to maintain attention on the object and resistance to disturbing visual stimuli. According to the results of the martial artists who have the 1st category, it was noted that they performed the test exercise with a score of «Good» and have a total weighting factor of 0,34. The score at each stage of the test is «Good», but the values of the weighting coefficients are closer to the «Satisfactory» score. The values of the weighting coefficients demonstrate that the level of spatial perception of this group of athletes is below average. It is also worth noting the increase in the percentage of errors, especially at the fourth stage (11,7 %), which indicates a negative impact on the reaction time of additional visual stimuli. The biggest difference between weight coefficients of the studied groups was noted at the second stage and made 49 %, the smallest at the fourth stage – 27 %. Conclusions. The use of fuzzy logic methods is a promising area of activity and finds its application in sports activities. The levels of manifestation of spatial perception by weight coefficients have been determined. Thus, a group of sportsmen with a category of CMS received an overall mark for the whole test «Good»with a weight coefficient of 0,74, and martial artists of the 1st category received an overall mark for the whole test «Good» with a weight coefficient of 0,34. Comparison of results of the estimation of reaction time of martial artists with a category of CMS with sportsmen of the 1st category testifies that there are statistically significant differences between indicators (p<0,05). The use of the theory of uncertainty in the assessment of spatial perception makes it possible to create flexible assessment systems and allows combining different indicators into one complex result.

Why the action?

In this note, I present two variations of the principle of stationary action in order to provide alternative ways for students to think about the action that they may find more intuitive than the traditional approach. These methods involve Lagrange multiplier techniques and are, therefore, best suited for students who are encountering the stationary action principle for a second or third time, perhaps in an advanced undergraduate mathematical methods course or a graduate classical mechanics course.

Artificial neural network-based computational heat transfer analysis of Carreau fluid over a rotating cone

Heat transport in a dynamically rotating cone immersed in a Carreau fluid is the subject of this investigation. The fluid is non-Newtonian, admired for its characteristics, and extensively utilized in numerous industrial domains. The study investigates the interplay between buoyancy and centrifugal forces within an analytical framework. The study employs sophisticated mathematical methods, including similarity transformations, to convert governing partial differential equations into nonlinear ordinary differential equations. These equations are then solved using the shooting method, a numerical technique that solves a boundary value problem by iteratively adjusting the initial conditions until the boundary conditions are satisfied. We employ an artificial neural network algorithm with backpropagation Levenberg–Marquardt scheme to analyze the heat transfer mechanism quantitatively. In conjunction with the shooting mechanism, we will use numerical simulation with an artificial neural network algorithm, namely the backpropagation Levenberg–Marquardt scheme. The results prove the enormous influence of centrifugation and buoyancy on complex fluid dynamics and heat exchange processes. Some critical parameters that govern the convective heat transport process are the Nusselt number, the Reynolds number, the Grashof number, and the fluid and cone rotational velocities. The research validates the requirement of considering non-Newtonian complexity and viscous dissipation when investigating heat transfer dynamics and fluid flow, facilitating more accurate expectations and improved efficiency in various industrial processes.

Application of simplifying jacobian matrix and introducing iterative threshold to improve newton-raphson method in three-phase power flow calculation

Abstract With the expansion of the scale and complexity of the power system, traditional three-phase power flow calculation methods are facing dual challenges of computational efficiency and accuracy. Power flow calculation is a mathematical method for analyzing the power flow of an electrical system. And the Newton-Raphson (NR) method is an effective algorithm for solving nonlinear problems. However, updating the Jacobian matrix in the NR method can take a lot of time. Based on the asymmetry in three-phase power systems and the time-consuming nature of the NR method, an enhanced version of the NR method is proposed in this paper that improves the efficiency of power flow calculations by simplifying the Jacobian matrix and optimizing the iteration speed. Furthermore, in order to minimize the number of iterations in the NR method, it is proposed to use the PO method to determine the ideal iteration threshold.

The true position of the Russian financial market

Subject. The article addresses the true position of the Russian financial market. Objectives. The purpose is to reveal the true position of the Russian financial market in the context of sanctions. Methods. The study rests on the application of general scientific methods, primarily, the analysis and synthesis of data, and special economic and mathematical methods, like correlation and regression analysis. Results. The paper established that the true position of the Russian financial market under sanctions is associated with a focus on capital withdrawal to a greater extent by non-financial organizations, at the expense of domestic borrowings through debt securities, and shifting debt to households. Conclusions. The revealed characteristics of the Russian financial market, describing its true position under the sanctions, enable the expert community to correctly determine its parameters, and the monetary authorities to choose the optimal financial instruments.

Development of an analytical model for assessing the risks of financial and economic activities of State (municipal) institutions based on the pairwise comparison method

Subject. The article considers developing an analytical model to assess the risks of financial and economic activities of State (municipal) institutions. Objectives. The aim is to devise a comprehensive analytical model for assessing the risks of financial and economic activities of State (municipal) institutions, taking into account their specific activities, and assess these risks. Methods. The study employs general and specific scientific methods of cognition (analysis and synthesis, induction and deduction, grouping, comparison, expert assessment, mathematical methods, like the method of analyzing hierarchies, etc.). Results. I designed an analytical (mathematical) model of integral indicator for risk assessment in State (municipal) institutions’ financial and economic activities, offered a scale used to assess such risks. The proposed mathematical model was tested in several State institutions, with the presentation of results. Conclusions. The development of software using intelligent technologies based on the analytical model of integral indicator will enable to more quickly and effectively assess the risks of financial and economic activities of a State (municipal) institution, and track the dynamics of risk changes.

Comparison of deep learning-based models for detection of diseased trees using an image compression algorithm

The object of the research is the application of deep learning algorithms using an improved mathematical lossless image compression method for recognizing and identifying dead trees in aerospace images. The main problem that has been solved is the archiving of images due to their large volume on disk and the possibility of their further processing by deep learning methods such as convolutional and capsule neural networks, which have shown high efficiency and accuracy in image recognition and classification tasks using the proposed new image compression method. The article presents a comparative analysis of the performance of three YOLO (You Only Look Once) models with different types of architectures, such as YOLOv5, YOLOv7 and YOLOv8, to assess the effectiveness of their work for the task of recognizing aerospace tree images obtained from satellites, drones, and aircrafts. Comprehensive analysis of YOLO models presents that model YOLO v8 turned out to be most effective with a positive accuracy of 88.2 %, a recall of 77.4 %, and a mAP50 score of 87.2 %. Moreover, the average detection time was only 0.052 seconds for each image, even though the model size remains very small – 21.5 MB. These results suggest a much better usage of time and precise identification of dead trees, and classified targets with high efficiency. From the research, there is significant prospects of global forest management especially on forest reduction and protection of ecosystems through accurate assessment on the health of forestry. The proposed approach is universal and can be used in real life conditions, providing a good compromise of the speed, accuracy and resources required for forest monitoring and management

Analysis of the third class mechanism using the modeling method in the Mathcad software environment

Purpose. To carry out a kinematic analysis of a flat twelve-link hinged mechanism with three leading links, the basis of which is a structural group of links of the third class of the fourth order with rotational kinematic pairs, which is used in technological equipment. Methodology. The kinematic study of a flat complex mechanism of the third class with three leading links was performed using the mathematical modeling method in the Mathcad software environment. Findings. Using the method of mathematical modeling, the mechanism was presented in the form of free vectors built on its links, for which, taking into account the presence of three leading links, three vector contours were selected, which made it possible to draw up a system of vector equations of their closedness with further solving by a numerical method in the Mathcad software environment. The functions of the rotation angles of the mechanism links, their angular velocities and accelerations were obtained in analytical and graphical form depending on the rotation angle of the first driving crank of the mechanism, the calculation of the angular velocities and accelerations of all the driven links of the mechanism was performed. Originality. A sequence was developed and a kinematic study of a complex planar mechanism of the third class with three leading links was done, the basis of which is a structural group of links of the third class of the fourth order. Schematic modeling of the mechanism with three leading links was performed, a visualization schedule of its kinematic scheme was built, and a valid version of its assembly was obtained from many possible ones, for which the values of kinematic parameters of all its links were determined. Practical value. An analysis of the effect of the kinematic parameters of the three leading links of the third-class mechanism on the movement of the working body of the technological equipment was carried out. From the analysis of the obtained research results for the cycle of the mechanism the reason was found for the incomplete technological stoppage of the link, which should provide the working body of the machine for the required period of time. Recommendations of the elimination were made to identify the deficiency and proposals for the need to improve the drive of this equipment.

Assessment of the efficiency of functioning of the environmental management system of enterprises

Purpose. A multifactor model is developed to assess the efficiency level of an enterprise’s environmental management system, depending on the effectiveness of organizational environmental measures. Methodology. The authors’ method for determining a comprehensive criterion for monitoring the effectiveness of the environmental management system, which characterizes the efficiency of operation and determines the level of environmental safety of enterprises, is proposed and used. To solve the tasks, a complex research method was also used, which included the analysis and generalization of literary and patent sources, and analytical, experimental research using computer and mathematical modeling methods. Findings. According to the studies and calculations of the generalized environmental quality indicator – 0.64, 0.66 and 0.66, the largest negative impact on the environment is caused by the activities of enterprises in the Pecherskyi, Podilskyi, and Solomianskyi districts of Kyiv, respectively. The obtained data testify to the relationship between the effectiveness of the implemented environmental measures (saving and rational use of resources, application of environmental technologies, advanced training, and environmental competence of employees) and the level of efficiency of the environmental management system of enterprises. Originality. As a result of the studies conducted using actual data, a system of indicators of the generalized environmental quality indicator has been proposed for the first time, which allows determining the environmental efficiency and effectiveness of the implemented environmental measures to assess the effectiveness of the functioning of the implemented environmental management system of the enterprise. Practical value. Based on the research results, a technique is proposed to assess the effectiveness of the environmental management system of enterprises by determining a generalized environmental quality indicator in terms of reducing the negative impact of the enterprise’s activities on the environment. Such an assessment system will help the management of the enterprise to promptly introduce corrective actions to improve the efficiency of the environmental management system and increase the level of environmental safety.

Establishing a pattern of change in the quality indicators of Tokaj-type wine materials prepared by different variants

The object of this study is Tokaj-type wine materials made from white and red grape varieties grown in the foothills of the Goy-Gol region and the flat zone of the Samukh region in the Azerbaijan Republic. An important condition for the production of Tokaj wine is the high sugar content in the raw materials. Therefore, fully ripe and slightly withered grape varieties were used to prepare the wine materials. The quality indicators of wine materials prepared in three options were studied. Option 1 – preparation of Tokaj wine material by adding must with pulp from ripe grapes to alcohol; Option 2 – preparation of Tokaj wine material by adding must with pulp from grapes withered on the vine for 10–12 days to alcohol; Option 3 – preparation of Tokaj wine material by adding must with pulp from grapes withered on the vine for 4–5 days to alcohol. The most appropriate options were the first and second, according to which Tokaj wine material is produced by adding must with pulp from grapes ripened and dried on the vine for 4–5 days to alcohol. The content of sugar, volatile acids, titratable acidity, phenolic compounds, methyl alcohol, and the volume percentage of alcohol added to the must were studied in the prepared wine materials. For the preparation of wine material, it is advisable to use the white Rkatsiteli grape variety and the red Cabernet Sauvignon variety grown in the flat zone of the Samukh district. This is due to the fact that in the flat zone, grapes accumulate more sugar, and the volume percentage of alcohol added to the must is less, which is also economically advantageous. During the study, using mathematical and statistical methods, the most appropriate option was determined for the organoleptic indicators of Tokaj wines made from the Rkatsiteli grape variety, which was rated 9.8 points

Development of a mathematical model for managing schedule delays in air traffic operations

The object of this research is delay in air traffic operations. The problem in this research that must be solved is how to reduce the impact of frequent delays which cause time efficiency but cause increased operational costs and make customers dissatisfied with air traffic services and then there is time complexity which is difficult to overcome. The interpretation of this research is to analyze existing problems and then apply mathematical methods so that it is possible to develop a model that is able to dynamically optimize flight rescheduling which can be beneficial for customers in reducing waiting times. This model will consider many important variables in managing delay schedules including real-time weather conditions, aircraft availability, airport capacity so that the results of this model show the ability to reduce the frequency and duration of delays which can increase customer satisfaction. This application shows that the model developed has main characteristics such as flexibility in adjusting schedules in terms of delays and accuracy in predicting potential delays so that the problems analyzed and researched can be resolved effectively and efficiently. This model can predict schedule delays with an accuracy level of 90 % according to predetermined input variables. Then there are quantitative benefits in the form of reducing operational costs for delays, increasing prediction accuracy and optimizing flight schedules. Qualitatively there are benefits in customer satisfaction and faster and more effective decision making. The scope of this research includes managing flight schedules at airports and international hubs. Implementation of this model is important to ensure high operational efficiency and minimize the impact of delays in various operational conditions

Analysis of mathematical methods for describing financial flows: dynamic modeling of an innovative company

Purpose. Development of a dynamic mathematical model of an innovative company operating in accordance with Ukrainian legislation, allowing for the analysis and adjustment of its financial activities. Methodology. When developing a model and description of financial flows, a factor analysis of the necessary indicators of the financial condition of the enterprise in question was carried out, which were used in the calculations of the presented mathematical modeling. A mathematical apparatus has been developed for calculating financial indicators depending on time. Using inductive, deductive and logical methods, an analysis of the financial situation for the year was carried out. Findings. The main methods and tools for describing financial flows have been analyzed. Mathematical modeling of the innovative company is carried out, which allows analyzing the costs of the enterprise and determining the size of its free funds. The calculation of financial indicators of the enterprise, which are demonstrated in the form of tables, is performed and the dynamics is shown in charts and graphs. All calculations were made on the basis of existing Ukrainian legislation using modern information technologies. Originality. A mathematical dynamic model of changes in financial flows at the enterprise has been developed and implemented. The proposed model takes into account various items of expenses and profits in accordance with the state legislation. Calculations allow for dynamic analysis and determination of the impact of various indicators on the financial condition of the enterprise, which allows for faster adoption and implementation of decisions in managing financial flows. This dynamic model is a convenient tool for any enterprise in Ukraine. Practical value. The results that were obtained during the study can become the basis for creating the necessary digital tools for researching, analyzing and adjusting the financial flows of a particular enterprise. Now methods are available that allow analyzing and describing financial flows more accurately and forecasting their changes in the future. The methodology presented allows the creation of dynamic models that can account for complex dependencies between different indicators and forecast the behavior of financial flows in real time. The financial model allows the simulation of cash flows of planned activities and the evaluation of financial planning in advance, taking into account the conducted research. It is straightforward to use and allows the analysis of different scenarios of business development, significantly reducing the time required.

The Perceived Value of Proving in Learning Engineering Mathematics and its Dependence on Motivation and Study Habits

This study reports on engineering students (N=369) from two Swedish universities and focuses on their perceived value of proving in learning engineering mathematics and some factors that may explain the observed variation in the perceived value. Our findings show that there is no significant difference in the perceived value between female and male students. In general, proving is not highly valued, and students are not confident in their skills in proving, except for proving by mathematical induction. However, students’ motivation in mathematics correlates with the perceived value and certain study habits are more regular among those students who appreciate proving as a suitable method for learning mathematics. Examples of such study habits include actively communicating with mathematics course teachers and reading the course textbook both before and after lectures.

Artificial intelligence and classical methods in animal genetics and breeding

The article analyses basic methods of population genetics and animal breeding, as well as mathematical methods of machine learning used in animal breeding. The training of cat boost library models was carried out on the example of two domesticated species – domestic horse (Equus caballus) and reindeer (Rangifer tarandus). Data from microsatellite panels of 16 and 17 loci, respectively, were used to train the model using data on domesticated and wild reindeer, European and Russian horse breeds. The standard indicators: accuracy, precision, recall and f1 were calculated to determine the success of the model. Confusion matrices were constructed. New possibilities of identification of animal breed affiliation were shown.