Mathematical Methods Research Articles

Large-scale optimization of nonconvex MINLP refinery scheduling

Modeling and optimization of large-scale refinery scheduling problems is challenging because of their complexity and size. Herein, we propose a mathematical model to represent such problems more accurately and realistically, and a state-of-the-art optimization framework for its solution. The framework leverages the use of mathematical optimization and algorithmic methods by combining modeling approaches (process design, model decompositions), solving strategies (rescheduling, heuristics), and machine learning regression (surrogate models). An industrial-size refinery scheduling problem (2 blenders, 4 feed tanks, distillation network with 5 towers, processing network with FCC, hydrotreaters, debutanizers, superfractionator, catalytic reformer) is formulated as a hierarchical nonconvex mixed-integer nonlinear programming (MINLP) model and is successfully optimized, providing higher profitability and more efficient scheduling operations considering 12 feedstocks, 10 products and multiple scenarios for time horizon and step. Results highlight the importance of tuning scheduling parameters and employing an enhanced computer-aided framework to enable the solution of industrial refinery scheduling operations.

Using the State Space Method for Calculating Electromechanical Transients

The state space method is widely used for the analysis and synthesis of automatic control systems in a wide variety of industries. It was revealed that the analysis of electromechanical processes in electrical systems is associated with the solution of a system of nonlinear differential equations by very laborious mathematical methods. It is shown how to represent a system of differential equations describing electromechanical transients in synchronous machines in d, q, 0 – coordinates, in matrix form. An algorithm for calculating electromechanical transients by the state space method is considered. The transit matrix of states is represented by a decomposition formula, the terms of which are determined by matrices with constant elements. Comparison with known numerical calculation methods allows us to conclude that the state space method is a fairly effective way to analyze electromechanical transients in synchronous machines.

An Analytic Model for COVID-19 Cases in Iran and Its Neighbors Using Deep Learning and Time Series Methods

Since the pandemic of the coronavirus (COVID-19) in 2019, it has rapidly become a major global health concern. Various mutations and rapid spread of the virus, a lack of specific treatment, and limited hospital facilities highlight the importance of anticipation, risk analysis, and timely treatment. The use of mathematical models, artificial intelligence, and simulation methods are effective tools in predicting the spread and providing effective solutions to prevent virus transmission. Analysis and forecasting require an integrated model to cover different aspects of the problem and use different methods to obtain appropriate results. In this research, a proposed model for analysis and prediction of COVID-19 cases in Iran and neighboring countries is presented. The performance of mathematical and deep learning models in the proposed model has been evaluated using data from Johns Hopkins University from January 29, 2020, to April 30, 2021. Evaluation of the predictive outcomes of daily cases was performed using RMSE criteria. Then, the effect of the trend of cases in neighboring countries of Iran on the rate of new cases in this country has been studied. These models can help governments predict the number of infections to provide the necessary solutions and prevent a new wave of the virus.

WAYS OF STRENGTHENING THE FINANCIAL STABILITY OF SMALL ENTERPRISES IN AZERBAIJAN

Topicality. In recent years, mechanisms to support and encourage small businesses have been widely used to promote the positive impact of income distribution on the development of a competitive economy, poverty reduction and rapid response to changing market conditions. Aim and tasks. The primary aim of this research is to investigate and enhance the financial stability of small enterprises in Azerbaijan, emphasizing their crucial role in the country's economic development. The research evaluates the profitability and management efficiency of small enterprises through indicators such as general profitability, net profitability, net return on equity, and total profitability of production funds. Materials and methods. Data Collection, literature review, mathematical analysis methods were used in the study. There are methods of financial planning aimed at studying its object, and the preparation of this financial plan is carried out by various methods. Among them, we can show methods on the coefficient, methods on the norm, and also methods on the balance. As a result of determining financial ratios, financial risks can be analyzed and eliminated. To achieve stability, it is necessary to analyze financial ratios, which are relative indicators of the financial condition of the enterprise. These coefficients are calculated as the ratio of absolute indicators or their complex. The analysis of financial ratios is carried out by comparing their values for periods (report and base). Research results. While each enterprise demonstrates its unique financial performance, "Karmen LLC" appears to exhibit promising signs of stability with positive profitability, reasonable liquidity, and efficient management. However, continuous monitoring and strategic planning are necessary for sustaining and enhancing their financial health and market stability. Conclusion. The financial analysis of "Karmen LLC", "Azdad 2020 LLC", "Karvan L LLC", and "NEON LLC" highlights variations in their financial stability, profitability, and management efficiency. While "Karmen LLC" and "Azdad 2020 LLC" demonstrate stronger financial positions and profitability, "Karvan L LLC" and "NEON LLC" face challenges such as lower liquidity and profitability. Further research should focus on industry benchmarking, trend analysis, and qualitative assessments to provide a more comprehensive understanding of their financial performance and prospects. These insights will be crucial for informed decision-making and strategic planning in the competitive business landscape.

Comparative study of silver-blood-based three binary nanofluids and thermal enhancement in a PTSC

This paper studies the similarity of silver-blood-based Carreau–Maxwell, Carreau–Oldroyd-B and Carreau–Jeffrey binary nanofluids on the parabolic trough solar collector. By the energy equations, Joule heating effects and nonlinear thermal radiation were integrated. The velocity slip condition by the solid–liquid interface was again worked out. In this model, magnetic field aspects and viscous dissipation were again taken into account. The converted construction was modeled into ordinary differential methods with the help of appropriate comparison applications. This governing relation on current flow problem was given graphically and determined mathematically by applying made-up MATLAB computational tool with the aid of renowned mathematical shooting methods bvp4c (Lobatto’s IIIa Formulae). This mathematical outcomes are given in tabular and graphical models. It was observed that the nonlinear thermal radiation aggregates the temperature profile. This skin friction was improved for greater values of magnetic parameter by 6.16%. Moreover, the local Nusselt number was reduced about developing values of radiation parameter into 71.78%. Moreover, these Casson–Jeffrey and Casson–Maxwell nanofluid models are more efficient than the Casson–Oldroyd-B nanofluid models.

Development of the composіtіon and technology of the herbal mixture with the cerebroprotectіve actіon

Aіm. To determine the prospects for using the plant raw material for the creation of herbal medicines with the cerebroprotective effect, as well as to develop the composition and technology of a new medicine of natural origin. Materіals and methods. The study objects were black horehound (Ballota nigra L.) herb, white dead nettle (Lamium album L.) herb, and Austrian wormwood (Artemisia austriaca) herb. Experimental studies were conducted using modern physical, physicochemical, pharmacotechnological, and mathematical methods of analysis. Results and dіscussіon. Based on the analysis of scientific sources on the situation with cerebrovascular diseases (CVD) and the range of drugs for their treatment, it has been proven that to improve the quality of therapy, it is rational to conduct a complex pharmacotherapy with the use of herbal medicines. We have proposed a new drug with the cerebroprotective action based on the plant raw material. The medicinal product was obtained in the form of the herbal mixture, which included black horehound herb, white dead nettle herb, and Austrian wormwood herb. The rational technology of the drug has been theoretically and experimentally substantiated. A block diagram of the herbal mixture has been developed, and the critical parameters of its production have been determined. The pharmacotechnological studies of the plant raw material and the drug obtained have been conducted. Conclusіons. Based on the results of the work conducted, the data scientific sources on the spread of CVD have been analyzed and summarized; the expediency of using the plant raw material in medicines for a complex pharmacotherapy of CVD has been proven; the composition and technology of the drug from black horehound herb, white dead nettle herb, and Austrian wormwood herb in the form of the herbal mixture with the cerebroprotective action for internal use have been developed.

Оптимізація будівельних конструкцій

In the field of the theory of calculation of building structures, there is a constant refinement of the actual operation of these structures, i.e. design schemes are created that most accurately correspond to actual operating conditions. Creating optimal structures is a very urgent task facing designers. Therefore, it is quite natural to try to solve this problem using mathematical programming methods, which involve: selecting dependent and independent variables, constructing mathematical models and establishing criteria for the effectiveness of the selected model. In this case, the model should be a function that fairly accurately describes the research being carried out using mathematical apparatus (various types of functions, equations, systems of equations and inequalities, etc.). In mathematical programming, any set of independent (controlled) variables is called a solution. Optimal solutions are those that, for one reason or another, are preferable to others. The preference (effectiveness) of the study is quantified by the numerical value of the objective function. “Solution Search” is an add-in for Microsoft Excel that is used to solve optimization problems. Simply put, with the Solver add-in, you can determine the maximum or minimum value of one cell by changing other cells. Most often, this add-in is used to find optimal solutions to problems economically. There are not enough results of using this approach for calculating building structures in the public domain. Therefore, it is quite logical to try to use this add-on in problems of optimization of building structures. In this work, an attempt was made to use mathematical programming methods and this add-on to optimize the geometric dimensions of the structure, when the numerical value of the bending moment in a specific section was chosen as an optimization criterion.

Inflation targeting regime in the Russian economy

Subject. This article discusses the issues related to the inflation targeting regime in the Russian economy. Objectives. The article aims to assess the impact of the inflation targeting regime on the Russian economy. Methods. For the study, I used analysis and synthesis, special economic and mathematical methods, correlation and regression analysis, and the graphical method. Results. The article covers the impact of the inflation targeting regime on the Russian economy in the context of numerous aspects and positions. It reveals that the inflation targeting regime for the Russian economy causes the depreciation of ruble liabilities, increasing the requirements for guarantees of their high profitability. Conclusions. The impact of the inflation targeting regime on the Russian economy, which is ultimately expressed in the depreciation of ruble liabilities and the devaluation of the ruble, in the context of a decrease in the gold content of the average monthly nominal accrued wages of employees in a full range of organizations, informs the authorities about the possibilities of stimulating the growth and development of the Russian economy.

Fractional order model of MRSA bacterial infection with real data fitting: Computational Analysis and Modeling

Bacterial infections in the health-care sector and social environments have been linked to the Methicillin-Resistant Staphylococcus aureus (MRSA) infection, a type of bacteria that has remained an international health risk since the 1960s. From mild colonization to a deadly invasive disease with an elevated mortality rate, the illness can present in many different forms. A fractional-order dynamic model of MRSA infection developed using real data for computational and modeling analysis on the north side of Cyprus is presented in this paper. Initially, we tested that the suggested model had a positively invariant region, bounded solutions, and uniqueness for the biological feasibility of the model. We study the equilibria of the model and assess the expression for the most significant threshold parameter, called the basic reproduction number (ℛ0). The reproductive number’s parameters are also subjected to sensitivity analysis through mathematical methods and simulations. Additionally, utilizing the power law kernel and the fixed-point approach, the existence, uniqueness, and generalized Ulam–Hyers–Rassias stability are presented. Chaos Control was used to regulate the linear responses approach to bring the system to stabilize according to its points of equilibrium, taking into account a fractional-order system with a managed design where solutions are bound in the feasible domain. Finally, numerical simulations demonstrating the effects of different parameters on MRSA infection are used to investigate the impact of the fractional operator on the generalized form of the power law kernel through a two-step Newton polynomial method. The impact of fractional orders is emphasized in the study so that the numerical solutions support the importance of these orders on MRSA infection. With the application of fractional order, the significance of cognizant antibiotic usage for MRSA infection is verified.

Оцінювання тенденцій фінансового результату збутової діяльності виробничого підприємства

The article discusses the main principles of forming the financial result of the sales activity of the business entity. At the same time, the main attention is focused on the evaluation of the trends of changes in the gross profit of the manufacturing enterprise. The main factors influencing its change under martial law are outlined. It has been proven that timely monitoring of the results of sales activity requires the use of economic and mathematical methods and models for estimating gross profit. The means of econometric modeling provide for the selection of the most significant factors of its change, assessment of the density and closeness of the connection, the share of influence of the selected factors on the performance indicator, modeling and further forecasting of the gross profit. The trends of changes in the result of the sales activity of the manufacturing enterprise over the last fifteen years were analyzed. The main problems have been identified and the ways to overcome problematic areas of sales activities have been outlined. It is substantiated that in order to overcome the mentioned troubles, it is necessary to apply the correlation-regression analysis of the gross profit of the manufacturing enterprise. At the same time, the most influential factors of its change were chosen: the volume of sales of the main type of products, the cost of goods and retained earnings (uncovered loss). The result of the conducted research is the construction of multifactorial econometric models of the formation of the gross profit of the manufacturing enterprise. It was established that all these models are adequate according to the coefficient of determination and Fisher's test. Therefore, gross profit forecasting for the next two years was carried out based on them. The forecasting process was carried out on the basis of the assumption of a one percent change in the selected factors and on the basis of the trends existing at the production enterprise. The forecasting results are of a recommendatory nature and can be applied in accordance with changing business conditions. Forecasting changes in factors, using the TREND function, leads to a rapid increase in gross profit. Applying an expert assessment of changes in factors proves a more optimistic prediction of the size of the gross profit of the manufacturing enterprise. The work offers several possible options for changing the result of sales activities in accordance with the dynamics of changes in the selected factors. The relevance of the provided information will allow not only to evaluate the existing trends regarding changes in gross profit, but also to choose the best result depending on the dynamism of the internal and external environment of the production enterprise.

The current state of the dairy cattle industry in the region

Subject. The article is devoted to dairy cattle breeding being an important industry in the agro-food complex of the country that occupies a high share in the structure of gross agricultural output. Objectives. The purpose is to analyze the development of dairy cattle breeding in the Russian Federation, the Nizhny Novgorod Oblast, and Knyagininsky District. Methods. We employed economic, statistical, and mathematical research methods. Results. The study provides the analysis of dairy cattle breeding development in the Russian Federation, the Nizhny Novgorod Oblast, and the Knyagininsky District, reveals the interrelation of factors influencing the development of dairy cattle breeding in the Knyagininsky District. We determined reasons for a decline in the number of animals and the growth factors of cow milk yield. The paper offers the application of State support for the development of dairy production. Conclusions. Currently, it is possible to ensure the growth of milk volumes only on the basis of innovation-oriented development of dairy cattle breeding, which includes the introduction of technical, technological, organizational, and economic innovations, optimal combination of megafarms, dairy complexes, medium and small dairy farms, an increase in the genetic potential of the dairy herd, optimization of fodder base, improvement of the system of relations between the subjects of the milk and food subcomplex of the agro-industrial complex. It is crucial to provide State support for the development of dairy cattle breeding in the Nizhny Novgorod Oblast.

Process approach to managing a site 
 Railroad repair system

Aim. This study aims to develop a scientific and practical tool for assessing the influence of the effectiveness of the district system of modernizing and current maintenance of railway tracks.
 Methods. To evaluate the process of introducing modern breakthrough technologies in terms of determining the time costs of work and the degree of their modification, the mathematical modeling method of business processes is used.
 Results. A model of the organization of the mechanized process of capital overhaul of the track was developed, and the economic efficiency of using satellite navigation during capital overhaul of the track was calculated.
 Conclusion. The introduction of digital technologies to control the depth of the ballast prism cutout during the operation of gravel-cleaning machines relative to the adjacent track successfully replaces the labor process of measuring with a horizontal rail with a leveling under the inner thread of the repaired track, excludes technological stops of machines, and reduces the time of work of machines and personnel and operational costs.

СОЗДАНИЕ ИНФОРМАЦИОННОЙ БАЗЫ ДАННЫХ ПО КАЧЕСТВЕННЫМ ПОКАЗАТЕЛЯМ ВИНОГРАДА НА ФОНЕ КОМПЛЕКСА АГРОКЛИМАТИЧЕСКИХ ПАРАМЕТРОВ И ИНДЕКСОВ, ХАРАКТЕРИЗУЮЩИХ ТЕПЛООБЕСПЕЧЕННОСТЬ ТЕРРИТОРИИ, ПРИМЕНЯЕМЫХ ДЛЯ ВЫДЕЛЕНИЯ ТЕРРУАРОВ КРЫМА

Climate is one of the main factors determining the possibility of grape cultivating and influencing its growth and development. Climatic factors have a huge impact on obtaining high-quality products of grape processing. In the process of work, in order to create an informational database, the archival data on the content of sugars and titratable acids in grapes from the vineyards of Crimea were collected and systematized. According to the criteria necessary for this study, we have selected the information on 8 varieties from the Steppe zone for 11 years, 1 variety from the Piedmont zone for 3 years, and 4 varieties from the South Coast zone for 6 years. By collecting and nonlinear interpolating of long-term observations from Crimean weather stations using geoinformation and mathematical modeling methods, the values of agroclimatic factors were calculated for each selected vineyard on the dates of determining the quality indicators of grapes during their ripening at the location points of the vineyards. For this purpose, 10 agroclimatic indicators characterizing the heat supply were selected. Based on the research results, basic principles for creating an informational database of agroecological resources and quality composition of grapes were developed. Informational database can be further modified and extended with various agroclimatic indicators. Subsequently, the accumulated array of database information will be used to identify patterns reflecting the influence of agroecological conditions on the formation of grape quality parameters for various types of production, which will serve as a basis for establishing viticultural and winemaking terroirs. Key words: CLIMATIC FACTORS, ZONES OF THE CRIMEAN PENINSULA, HEAT SUPPLY INDICATORS, GEOINFORMATION MODELING, MASS CONCENTRATION OF SUGARS, MASS CONCENTRATION OF TITRATABLE ACIDS

Математичне моделювання динамічних впливів на будівельні конструкції

The solution of the problem of mathematical modeling of dynamic influences on building structures is considered in general and in connection with important scientific and practical tasks. In modern conditions, special attention should be paid to the problems of taking into account dynamic influences, parameters of load-bearing structures of buildings that affect their structural reliability and safety. For many years, information about catastrophic destruction of buildings and structures has been appearing more often, which are the result not only of errors that arose during the construction of facilities, but also due to dynamic influences that arose during their operation. A buildable technical system will be used in advance with the technical parameters set, which is responsible for the control of the process of the preparation of structures, the installation of the equipment, during the operation and operation. The development will be carried out and the sporud will be constantly used to promote the development of future technologies, the development and the establishment of the future, as well as the development of dynamic developments in the future. In particular, it is important to understand the development of the engineering and geological minds of the spores, as they have known the front deformation of the non-essential axis of the runt foundations. Various methods are used for structural dynamics, such as modal analysis, response spectrum analysis, time analysis, and finite element analysis. These methods include mathematical modeling, numerical simulation, and computational methods to predict the behavior and response of a structure under dynamic load conditions. Knowing the frequency and form of the structure, it is possible to estimate the dynamic reaction of the design to the application. For the purpose of including the transfer of the world, the destruction of internal forces in the real parts of the construction. Analyses of the response to the additional assessment of the characteristics of the construction, the identification of critical areas and the re-conversion, which the project is able to meet the criteria.

A robust numerical method based on deep learning operator for solving the 2D acoustic wave equation

The numerical solution of wave equations plays a crucial role in computational geophysics problems, which forms the foundation of inverse problems and directly impact the high-precision imaging results of earth models. However, common numerical methods often lead to signifcant computational and storage requirements. Due to the heavy reliance on forward modeling methods in inversion techniques, particularly full waveform inversion, enhancing the computational efficiency and reducing storage demands of traditional numerical methods becomes a key issue in computational geophysics. In this paper, we present the deep Lax-Wendroff correction method (DeepLWC), a deep learning-based numerical format for solving two#xD; dimensional (2D) hyperbolic wave equations. DeepLWC combines the advantages of the traditional numerical schemes with a deep neural network. We provide a detailed comparison of this method with representative traditional Lax-Wendroff correction (LWC) method. Our numerical results indicate that the DeepLWC signifcantly improves calculation speed (by more than ten times) and reduces storage space by over 10000 times compared to traditional numerical methods. In contrast to the more popular Physics Informed Neural Network (PINN) method, DeepLWC maximizes the advantages of traditional mathematical methods in solving PDEs and employs a new sampling approach, leading to improved accuracy and faster computations. It is particularly worth pointing that, DeepLWC introduces a novel research paradigm for numerical equation-solving, which can be combined with various traditional numerical methods, enabling acceleration and reduction in storage requirements of conventional approaches.

Issues of Interaction Between Operational and Strategic Management of an Enterprise in a Market Environment

Main problem: One of the priority directions for improving the management system at the enterprise is the organization of effective interaction between strategic and operational management through the formation of a mechanism for their interaction, orienting operational management to achieve strategic goals and objectives. In market conditions, issues of interaction between strategic and operational production management are particularly relevant, allowing solving complex economic problems of the enterprise related to the rational use of resources involved in production, reducing production costs, improving the quality of products, optimizing production potential in order to increase the efficiency of the entire enterprise as a whole and its structural divisions. The role of the mechanism of interaction between strategic and operational production management also lies in the possibility of coordinating those final strategic goals that the enterprise strives for with the actual internal production capabilities. The purpose of this article is to study the issues of interaction between operational and strategic management of an enterprise in a market environment. The theory and modern practice of production management in a competitive environment show that the implementation of operational production management is a natural stage in the implementation of strategic management, therefore, there is a close relationship between them, which manifests itself in their interaction. Methods: The methods of analysis and generalization, the method of systematic and comparative analysis, structural and functional method, economic and mathematical methods, graphical and tabular method were used in the work. Results and their significance: the authors consider the theoretical aspects of the relationship between strategic and operational production management at an enterprise in a competitive environment. There is a low level of compliance of operational tasks of production with the strategic goals of development of domestic enterprises and the special role of information systems designed to link operational and strategic management tasks together. Accordingly, the key aspects of information technology implementation are investigated, including the need for employee training, strategic communications planning, information flow management and the use of data analytics. Examples of successful application of information technologies in various industries and organizations are given.

Demystifying math myths: Examining rules that expire

AbstractIn our mathematics methods courses for elementary preservice teachers, we work to uncover and confront students' understandings as well as misconceptions about important mathematical topics. Karp and colleagues' (Teaching Children Mathematics, 21(1), 18–25) “13 Rules That Expire” article has been a useful resource for us to highlight and challenge students' mathematical misconceptions. In this article, we share the components of an iteratively developed assignment focused on the 13 rules article. We detail how students explored the “lives” of these rules and investigated alternatives to pervasive mathematics shortcuts and tricks. We posit that our intentionally designed assignment provides an opportunity for students to think critically about their views, beliefs, and misconceptions, which encourages a mindset for preservice teachers to consider the kinds of mathematical misconceptions they will encounter in their classroom teaching. We anticipate that sharing this developed assignment with other mathematics teacher educators could provide opportunities for additional adaptations in unique contexts and continued improvements to support future teachers.

Cascade-Forward, Multi-Parameter Artificial Neural Networks for Predicting the Energy Efficiency of Photovoltaic Modules in Temperate Climate

Solar energy is a promising and efficient source of electricity in countries with stable and high sunshine duration. However, in less favorable conditions, for example in continental, temperate climates, the process requires optimization to be cost-effective. This cannot be done without the support of appropriate mathematical and numerical methods. This work presents a procedure for the construction and optimization of an artificial neural network (ANN), along with an example of its practical application under the conditions mentioned above. In the study, data gathered from a photovoltaic system in 457 consecutive days were utilized. The data includes measurements of generated power, as well as meteorological records. The cascade-forward ANN was trained with a resilient backpropagation procedure and sum squared error as a performance function. The final ANN has two hidden layers with nine and six nodes. This resulted in a relative error of 10.78% and R2 of 0.92–0.97 depending on the data sample. The case study was used to present an example of the potential application of the tool. This approach proved the real benefits of the optimization of energy consumption.

Comparison between mathematical methods to estimate blood glucose levels from ECG signals

Diabetes mellitus, known as diabetes, is a chronic disease that affects the control of blood glucose concentration levels, it is a disease that mostly affects adults (type 2 diabetes), but it can also occur in children (type 1 or childhood diabetes), as well as in pregnant women (gestational diabetes). Diabetes is one of the diseases with the highest prevalence and high mortality worldwide. Diabetes has no cure, but continuous monitoring to maintain blood glucose levels in normal ranges reduces the possibility of suffering from gastrointestinal problems, vision loss, limb amputations (such as diabetic foot) and damage to vital organs such as the heart and kidneys, among other associated complications. This article compares the results in glucose estimation by using a linear, quadratic and cubic regression considering the electrical characteristics generated in the cardiac conduction (HR, HRV, T-wave peak, and QT interval) recorded on a single-lead electrocardiogram (VII), used as a non-invasive blood glucose estimation model. The best estimate was obtained using a cubic regression. The validation was performed using the Clarke grid having 77.78 % of data in the A zone and 22.22 % in the B zone and a Pearson correlation value of 0.94103 in the cubic regression.

The use of geometric morphometry and traditional methods to analyze intraspecific variability of the first lower molar (m1) of Alexandromys fortis (Arvicolinae) in island and continental populations of Primorye, Russia

The complexity of the structure of the dental surface of the first lower molar (m1) of mainland and island populations of the reed vole Alexandromys fortis (Büchner, 1889) was assessed using two different methods. Using the traditional approach and methods of geometric morphometry (GM), the morphological variability of the anteroconid m1 of this species of the mainland (the south of Primorsky Krai) and the islands of the Peter the Great Gulf was analyzed. The traditional approach was based on describing the folding of the occlusal surface using three features: 1) folding of the lingual side of the anterior unpaired anteroconid loop (AC); 2) the shape of the labial side of the AC; 3) the shape of the fourth lingual reentrant angle. On the mainland part of the species' range, the highest occurrence was shown by morphotype III-C-a, which also predominated in the Late Pleistocene samples of the species in Primorye. The research revealed increased morphotypic diversity in island populations of the reed vole, which is probably due to the phenotypic and genotypic characteristics of the founders of island populations, as well as inbreeding, which can cause the release of hidden diversity and an increase in the number of rare morphotypes. The most numerous morphotype on the De Livrona – Durnovo Islands was II-C-a, rare for the mainland. In general, the most complex forms are present on the islands. Using a geometric morphometry approach, the anteroconid was divided into two separately studied structures: the anterior unpaired loop of the anteroconid (AC) and the base of the anteroconid (AB). The distribution of AC configurations in the space of the two principal components took on an arcuate shape, revealing a “forbidden zone.” The main changes occur on the lingual side of the AC. Regression analysis showed a direct relationship between the length of the contour (mm) and the complication of the shape of the anterior unpaired loop. The base of the anteroconid (AC) also undergoes transformation: it either stretches or contracts, while if the anterior unpaired loop of the anteroconid (AB) is more complex, then simplification and compression of its base is observed (negative regression). Analysis of the results of using two approaches, traditional and GM methods, in the analysis of the variability of the anteroconid section m1 of A. fortis showed extreme subjectivity in the use of the first one and the wide possibilities of the second one for identifying different aspects of molare transformation using mathematical methods.