Methods Of Mathematical Modeling Research Articles

Mathematical modeling and analysis of export trends for certain pharmaceutical groups

Background. The analysis of the exports of medicines of the Russian Federation (RF) by group 30 (pharmaceutical products) of the commodity nomenclature of foreign economic activity of the Eurasian Economic Union (equal to Harmonized System Code 30, HS 30) is an important task for determining the economic potential of the country in the pharmaceutical industry.Objective: building an export regression model. Development of an alternative mathematical model of pharmaceutical products’ export, suitable for making the forecast.Material and methods. Statistical data on HS 30 exports from 2010 to 2021 were taken from an open source: The International Trade Center (Trade Map). Data for 2022 and later for the Russian Federation are not available in open sources. Registration on the website is not required to collect statistics on export and import volumes based on annual data. The well-known statistical methods and methods of mathematical modeling were used. An alternative approach to regression analysis was developed. Technical data analysis was performed using MAPLE (Watcom Products Inc., Canada) and R (Bell Laboratories, USA) software.Results. Two models were constructed: Model I – a differential model based on cumulative data by year, and Model II – a model of standard regression analysis, the input parameters of which were quarterly export data, and the influencing parameters were a certain group of factors. Model I allowed considering the dynamics of changes in pharmaceutical exports over time (dynamic factors and nonlinear interactions). Model II, in turn, made it possible to determine the dependence of the volume of pharmaceutical exports on various economic indicators, such as gross domestic product, the volume of government procurement, and measures of protectionism. The relative error of Model I does not exceed 10%, which makes it suitable for forecasting.Conclusion. The construction and analysis of specified models help to provide main information about the trends in pharmaceutical product exports in the RF and assess its potential in the global market. The obtained results can be useful for developing strategies of the pharmaceutical industry development, making management decisions and forecasting future exports.

ПОРІВНЯЛЬНИЙ АНАЛІЗ МАЛОГАБАРИТНИХ ВИСОКОШВИДКІСНИХ СИНХРОННИХ МАГНІТОЕЛЕКТРИЧНИХ ДВИГУНІВ

Using the methods of mathematical modeling, a comparative analysis of the characteristics of three variants of small-sized high-speed synchronous magneto-electric motors (SMD) with permanent magnets on the rotor, which are intended for driving the propeller of quadcopter-type aircraft, was investigated and carried out. Namely: SMD with external grooved stator and internal rotor; SMD with internal grooved stator and external rotor; SMD with internal clear-pole stator and external rotor. On the example of an aircraft with a total mass of 4 kg, a comparative analysis of the amount of power developed by the specified engine variants under the same operating conditions: the same overall dimensions, rotor speed, current in the stator winding and volume of permanent magnets was carried out. An assessment of the magnitude of electromagnetic moment pul-sations is given. It was established that although an SMD with an internal clear-pole stator is the most technologically simple, but under the same other conditions, it is inferior in power to an SMD with an internal slotted stator and an external rotor. References 7, Figures 4.

Automatic Patient Injection Robot With 6 Degrees of Freedom by 3D Simulation Using Webots Software

The manipulator robot is one of the most widely used robots in the industry. The movement of the robot manipulator in this sector is a mechanical system that requires a mathematical modeling method to represent its geometric aspects and manipulate its dynamic parts. One of the most critical industries is healthcare. In this paper, a simulation is carried out on one of the factors, namely patient injection. The research results from this simulation used Webots software and was successfully simulated using a 6-degree-of-freedom robot. The positions simulated in several movements include: gripper position opens to take the needle, gripper closes to take the needle, the needle is held and directed to the patient, the needle is inserted into the patient area and pulled out again, returning to its initial position by placing the needle. However, this simulation does not add a needle so that only the 3D simulated robot movement can move by entering the expected position value to inject the patient according to the target.

ОЦІНЮВАННЯ РІВНЯ ЕКОЛОГІЧНОЇ ЕФЕКТИВНОСТІ МІЖНАРОДНИХ АЕРОПОРТІВ

Introduction. The importance of ensuring environmental efficiency at enterprises in the transport and logistics sector is growing. The requirements for tools that are designed to ensure the implementation of this process in airports are constantly growing, which requires their constant addition and improvement. It is obvious that environmental monitoring is becoming an integral part of ensuring the strategic development of the airport and is defined by government institutions, investors and all stakeholders as mandatory. Problem Statement. International airports that are interested in their own development should try to implement the best quality tools to improve environmental efficiency. One of them is to be an adequate criterion-based assessment according to the relevant schemes and plans, which will become part of the airport's strategy for the coming decades. Purpose. Based on the defined criteria for assessing the environmental performance of international airports, to finalize and clarify the importance coefficients of these criteria, as well as to propose an effective scheme for implementing environmental measures at international airports, supporting it with appropriate calculations. Materials and Methods. The article uses expert assessment methods to clarify the importance coefficients of the criteria for assessing the environmental performance of international airports, as well as mathematical modelling methods to assess the effectiveness of environmental management. In addition, the methodological basis for ensuring environmental monitoring at airports was analyzed, and it was found that the most active researchers, in solving the tasks, used factor analysis methods and a number of mathematical modelling methods. Results. The use of the refined coefficients of the criteria importance for assessing the environmental performance of international airports proposed in this paper allowed us to assess the effectiveness of environmental management for a number of European airports and to assert that the level of environmental performance is above average, but each of them, based on a review of the proposed criteria, can refine their environmental plans for the future by minimizing emissions.

ДИНАМІЧНІ ВИПРОБУВАННЯ МОСТІВ. ЗАГАЛЬНИЙ ОГЛЯД МЕТОДІВ

Introduction. This article deals with the issue of relevance of dynamic testing of bridges in Ukraine, an overview of dynamic testing methods and the prospects for the development of this type of bridge testing. Problem statement. Monitoring the technical condition of bridges is an urgent problem for maintenance services and requires the use of the most advanced methods to quickly identify possible defects and damage in their structures. Dynamic testing is one of such methods, the development and implementation of which requires joint efforts of engineers and the scientific community. Objective. The main purpose of the article is to evaluate and analyze existing approaches to dynamic testing of bridges to diagnose their condition. This study aims to highlight the need to apply these methods to improve the reliability and safety of bridges, as well as to improve strategies for the maintenance and repair of bridge structures. Materials and methods. The material for the article is the experience of performing dynamic tests of bridges in Ukraine, including an example of testing a 420-meter-long reinforced concrete road bridge located in the Western Ukraine. The following research methods were used: analysis of data from scientific sources, analysis of regulatory documents, practical results of using the «Spectrum» software package, mathematical modeling, and general methods of theoretical research.

Complex fracture description and quasi-elastic energy development mathematical model for shale oil reservoirs

Reservoir numerical simulation is an important tool and method for the reasonable and efficient development of shale reservoirs. Accurate description of three-dimensional fractures in shale reservoir development is a necessary and sufficient condition to improve the accuracy and robustness of shale reservoir numerical simulation. This paper achieves precise characterization of complex fracture shapes and oil, gas and water flow by establishing an embedded discrete fracture model based on a non-structural network, which has advantages in the fine characterization of complex morphological fractures in the reservoir and the grid division of the reservoir. In the large matrix solution method, the Newton-Raphson method is used to linearize the nonlinear equations, the Jacobian matrix is ​​constructed, the ILU method is used for preprocessing, the conjugate gradient method is used to solve the linear equations, and the shale oil quasi-elasticity is established A fully implicit solution method for mathematical models of energy development.

Research on Multi-Objective Optimization of Heliostat Field Based on DELSOL3 Layout

With the intensification of global climate change, it is urgent to reduce greenhouse gas emissions and protect the environment. To address this issue, it is crucial to develop the new energy industry and increase the proportion of clean energy. Tower solar power, as an innovative and environmentally friendly technology with low carbon emissions, has great potential and broad prospects. This study determines the position of the absorption tower, heliostat size, and installation height. By utilizing the ground coordinates of the heliostats and given formulas, parameters such as average optical efficiency, cosine efficiency, shadow blocking efficiency, and cut-off efficiency are calculated. The focus is on power loss caused by shading, so a shadow blocking model is constructed by using differential methods. The heliostat plane is divided into equal sections, and it is determined whether the transformed coordinates of the mirror plane are within the grid. The effective blocked area is then calculated to obtain the shadow blocking efficiency. To improve the efficiency and reduce costs of solar thermal power plants, the standard radial staggered layout in DELSOL3 empirical layout is adopted. A multi-objective optimization model is established with heliostat size and height as variables. The optimal solution for the average output thermal power per unit mirror area is obtained through genetic algorithms. Through mathematical modeling and solution methods, this study provides theoretical basis for the application of tower solar power.

Mathematical Modelling and Optimisation in Multibeam Bathymetry: A Study of Coverage Width, Overlap Rate and Course Optimisation

This paper focuses on the field of multibeam bathymetry, firstly, a two-dimensional mathematical model with coverage width, overlap rate, and seawater depth as the objectives is established by using the trigonometric properties, the terrain slope factor and the effect of different survey line distances from the centre on multibeam bathymetry. Matlab software was used to solve the model, and the expressions for the coverage width and the overlap rate of adjacent strips were obtained. Secondly, for the multibeam bathymetry along a certain direction, based on the three-dimensional geometric seawater depth model, the coverage width model corresponding to different survey line directions was obtained by using the classification discussion method. Finally, through the optimisation model and traversal algorithm, the optimisation model that meets the requirement of the overlap rate of adjacent strips is established with the objective of minimising the total routes, and solved by the cyclic traversal idea. This study provides a comprehensive mathematical model and optimisation method for multibeam bathymetry, and lays a theoretical foundation for practical applications in related fields.

A systematic review of optimization methods for recovery planning in cyber–physical infrastructure networks: Current state and future trends

Cyber–Physical Systems are increasingly complex and frequently integrated into modern societies via critical infrastructure systems, products, and services. Consequently, there is a need for reliable functionality of these complex systems under various scenarios, from physical failures due to aging to cyber attacks. However, the development of effective strategies to restore disrupted cyber–physical infrastructure systems continues to be a major challenge. Even though there have been an increasing number of papers evaluating recovery planning in cyber–physical infrastructures networks, a comprehensive literature review focusing on mathematical modeling and optimization methods is still lacking. Thus, this study critically analyzes the literature on optimization techniques for recovery planning of cyber–physical infrastructure networks after a disruption, to synthesize key findings on the current methods in this domain. A total of 152 relevant research papers are reviewed following an extensive assessment of all major scientific databases. The main mathematical modeling practices and optimization methods are identified for both deterministic and stochastic formulations, categorizing them based on the solution approach (exact, heuristic, metaheuristic), objective function, and network size. Having identified the gaps, a set of future trends for both the methodology and application of optimization algorithms is presented. Overall, there is a need to shift toward scalable optimization solution algorithms, empowered by data-driven methods and machine learning algorithms, to provide reliable and computationally efficient decision-support systems for decision-makers and practitioners.

Обеспечение канцерогенной безопасности копченой рыбной продукции

The purpose of the study is to develop recommendations for rational smoke generation parameters that ensure the quality and environmental safety of smoked fish products. Objectives: to establish the influence of smoke generation parameters on the assessment of the carcinogenicity of smoked products; to evaluate the quality and safety of smoked products produced under optimal smoke generation parameters; to develop recommendations to ensure the quality and safety of smoked fish products. Research was carried out at the department of Management of Technical Systems at the Federal State Budgetary Educational Institution of Higher Education Dalrybvtuz (Vladivostok, Primorsky Region). The object of the study is the process of smoke generation. Analytical, physical and chemical methods, and mathematical modeling methods were used. To prepare smoke-drying smoke samples, 10 kg of alder sawdust with a moisture content of 30–35 % was prepared. Hot smoked smelt samples were obtained under optimal smoke generation conditions. The overall organoleptic index was 5. The content of individual polyaromatic hydrocarbons was: chrysene – 71 ng/kg; benz(a)anthracene – 70 ng/kg; benz(b)fluoranthene – 602 ng/kg; benz(a)pyrene – 64 ng/kg; benz(e)pyrene – 667 ng/kg; dibenz(a,c)anthracene – 57 ng/kg; dibenz(a,h)anthracene – 69 ng/kg, which corresponds to a generalized quality index of 0.99 (very good). During the study, the influence of smoke generation parameters on the assessment of the carcinogenicity of smoked fish products was established, and the dependence of the content of individual polyaromatic hydrocarbons on the excess air coefficient in the smoke generation zone was confirmed. Optimal smoke generation modes: smoke generation temperature 475 °C, excess air coefficient – 0.4. Rational smoke generation parameters: smoke generation temperature 450–500 °C, excess air coefficient – 0.3–0.6.

A simplified mathematical modeling approach for thermal runaway of Li(Ni0.8Co0.1Mn0.1)O2 pouch cells based on thermal runaway experimental data

Currently, the numerical modeling methods used to characterize the thermal runaway and propagation mechanisms in NCM811 pouch batteries still face numerous challenges. This is primarily due to the uncertainties in thermal runaway reactions and the immense computational demands encountered when modeling begins at the granular level of the cell. To address this issue, this study designed a series of experiments for an NCM811 pouch battery. By employing experimental data, reasonable assumptions were made regarding the combined effects of solid-state thermal conduction, electrochemical heating, and fluid-solid heat transfer through gas jet streams. A simplified thermal runaway mathematical modeling method based on experimental data was proposed, effectively tackling the problem. This framework was then applied to thermal runaway experiments on a single NCM811 battery used in this study, providing essential input parameters for three-dimensional numerical modeling of modules composed of multiple batteries in multiphysics simulation software. The simulation results derived from the proposed method were in good agreement with experimental data. This study can characterize the thermal runaway and thermal propagation characteristics of battery modules using single-cell thermal runaway experiments. Moreover, the proposed modeling approach not only predicted the experimental outcomes of the NCM811 pouch battery with reasonable accuracy but also provided smoother data, elucidating the highly fluctuating trends observed in experimental data. This method also offers guidance for designing fire prevention and smoke exhaust systems for battery packs. This study presents a novel approach for the mathematical modeling of thermal runaway and thermal propagation in battery modules using NCM811 pouch batteries, contributing to the ongoing development of lithium-ion battery module design.

Preface

The 2023 International Conference on Applied Mathematics and Digital Simulation (AMDS 2023) was held successfully on 28-29 December 2023 in Beijing, China. The contributions are the results of submissions from the conference participants, who provide readers with a broader view of mathematical, statistical and computational science methods, ideas and tools.There are 92 participants in AMDS 2023, in which the program includes 6 keynote reports (35-45 minutes), 48 oral presentations (15 mins+3 Q&A) included in four sessions (Mathematics and Computational Theory, Mathematical Modelling and Machine Learning Methods Statistics Modelling and Data Analysis, and Fluid Dynamics and Mechanics), 15 E-posts and 23 listeners. The point of the conference emphasizes the development of theories and applications and promotes interdisciplinary endeavors among mathematicians, statisticians, scientists, engineers and researchers from other related disciplines.This volume comprises selected papers from the AMDS2023 conference. Accepted manuscripts were peer-reviewed by 2 to 4 reviewers in a double-blind review process. A total of 48 reviewers participated in this conference and provided their professional comments to authors to ensure the quality of the manuscripts. There are six topic partitions, including Mathematics and Computational Theory, Statistics Modelling and Data Analysis, Mathematical Modelling and Machine Learning Methods, Fluid Dynamics and Mechanics, Mathematical Modelling in Physics and Control and Automation, which constitutes an up-to-date account of principles, techniques, and tools for mathematical simulation and modelling in a wide range of research fields.We would like to thank the authors of all papers and participants; the members of the Scientific Committee who assisted with the review of the papers submitted and presented at the conference; the four session chairs: Prof. Yichuan Zhao, Prof. Quanxin Zhu, Prof. P.M. Siva Raja, Prof. Rao Li; the six keynote speakers: Prof. Alexander G. Ramm, Prof. Ovidiu Radulescu, Prof. Hajime Urakawa, Prof. Yanjun Liu, Prof. Grienggrai Rajchakit and Prof. Oscar Eduardo Ruiz Salguero; the organzier and sponsors: the Hubei Mengshun Exhibition Service Center, the Research Center for Stochastic Configuration Machines (SCM), the National Laboratory for Scientific Computing (LNCC); the publisher: IOP Publishing Ltd agrees to publish the AMDS 2023 proceedings. We are grateful for your attendance and contribution to a successful AMDS 2023.Organizing Cmmittee of AMDS 2023Jiang Zhu (Advisory Chair)National Laboratory for Scientific Computing-LNCC, BraziList of Conference Committees are available in this Pdf.

Development and key technologies for architectural design and technical solutions of CIM platform: A review

The integration of building information modeling (BIM), geographic information systems (GIS), 5G, IOT, cloud computing, big data, artificial intelligence, and other technologies in urban management has become a new and rapidly developing trend in recent years. However, most of the existing research on the construction of city information modeling (CIM) platforms based on the integration of BIM and GIS technologies focuses on integration technologies, and there is a lack of theories, methods, and standards for further data analysis and mathematical modeling. This paper analyzes and summarizes the actual situation of the application of recent research papers in the BIM field and the application of CIM platform pilot projects, reviews the application of BIM and GIS technologies in smart cities, and discusses future trends. For example, the construction of a basic platform for smart cities requires the establishment of a three-dimensional visual CIM platform with functions such as the planning review, architectural design plan review, construction drawing review, completion acceptance filing. A smart city is built by analyzing the cyber security risks faced during the construction. The technical, management, and operational measures of the security system provide guidance and reference for the secure construction of smart cities. This involves promoting the reform of the construction work system driven by data resources obtained from government information, and the establishment a new digital government construction management system through the “separation of management and transportation.” These analyses highlight the evolution of the CIM platform construction. The results indicate that the use of key technology integration in the construction of a CIM platform requires a system theory that goes beyond integration technology and mathematical modeling methods for a detailed application. It involves analyzing the deep integration of key technologies and business processes in the CIM platform.

Three-dimensional density model of the mantle beneath the Ukrainian shield

Purpose. Mantle density models are key tools for understanding the fundamental geological and physical processes occurring within the Earth and are essential to our scientific and applied understanding of the planet. Methodology. The tasks were solved by a complex research method, including analysis and generalization of literary and patent sources, analytical, experimental studies, using computer and mathematical modelling methods. Findings. One-dimensional models simplify the mantle density distribution by assuming that it is uniform only in the vertical direction. This limitation does not allow for horizontal variations in mantle density, which may be important on a regional scale. 3D models are more complex and require more data and computational resources, so their use may be limited. In this study, we present a quasi-three-dimensional model of mantle density beneath the Ukrainian Shield. This 3D model is obtained using a basic set of one-dimensional seismic tomographic velocity models calculated for 21 mantle domains in the depth range from 50 to 2,600 km. The process of converting the P-wave velocity model into a density model includes the following stages: 1) determining seismic boundaries in the mantle based on P-wave velocity curves for each mantle domain; 2) creating a synthetic mantle model beneath the Ukrainian Shield for the P,S-wave velocity curves; 3) solving the Adams-Williamson equation for each domain, considering polynomial corrections to extract heterogeneities during its solution; 4) analysing existing models by comparing the calculated gravitational potential at the central point of the Ukrainian Shield as the standard reference for selecting one of 5 reference models. Here, we focus on the final stages of constructing the mantle density model by: 1) balancing the mass of the upper and lower mantle for each domain when determining density using the Adams-Williamson equation and introducing polynomial corrections; 2) calculating densities for each of the 21 mantle domains and their 3D integration. Originality. The obtained mantle-density model of the Ukrainian Shield aligns well with the division of the mantle into three main layers: lithosphere, upper mantle, and lower mantle. Each of the mantle’s structural layers has its representation pattern in density heterogeneities. Anomalies of decreased density in the lithosphere of the Ukrainian Shield correlate with thermal anomalies, whereas anomalies of increased density correspond to tectonic zones dividing its megablocks. Practical value. Regions of increased density gradient are associated with mantle thrust faults, which in some cases can be boundaries between different petrological formations and serve as channels for magma ascent into the Earth’s crust at certain stages of geological development of the Ukrainian shield and, in turn, be sources of minerals.

Container technology for transporting rock masses in quarries

Container technology for transporting rock masses in quarries

Optimization of coagulation wastewater treatment of leather industry

The object of the study was the process of coagulation treatment of wastewater of leather industry enterprises. The treatment of samples of real wastewater from a leather production was investigated. Such wastewater is characterized by high concentrations of pollutants of varying degrees of dispersion, which is due to the use of a large number of various chemicals in the leather production process. During technological operations related to the skinning and processing of skins, these substances enter the wastewater, which is discharged into the sewer. A peculiarity of leather production wastewater is large fluctuations in composition and volume, high concentrations of pollutants, and an increased content of suspended solids. Such waters have certain toxicity. The existing methods of wastewater treatment of leather industry enterprises do not provide the necessary treatment efficiency, do not allow to create a closed circulation of water at enterprises, to use or regenerate valuable components of wastewater, and to ensure their economically feasible disposal. Therefore, the research is aimed at improving the process of coagulation wastewater treatment of leather factories using mathematical modeling and optimization methods. This will make it possible to modernize existing wastewater treatment schemes. The experiments were carried out on the Niva Jar-test laboratory unit, which allows simultaneous examination of 6 samples. Samples of wastewater from leather production after the fattening-filling and dyeing stages were studied. The effectiveness of the coagulation process was determined by the degree of wastewater treatment. The factors were analyzed and the intervals of variation of factors that have a significant impact on the process of coagulation treatment of wastewater from leather factories were established. An experiment plan was drawn up and implemented in order to study the effect of coagulants based on aluminum and ferrum, as well as flocculants on the quality of wastewater treatment. The choice of quality indicators of the coagulation process is substantiated. A statistical analysis of the results of experimental studies was performed, a correlational analysis of the interdependence of parameters and indicators of the quality of the coagulation process was performed. Aluminum-based coagulant has been found to be more effective than iron-based coagulant. The results of mathematical modeling were used to determine the optimal parameters of the coagulation process: pH 10, coagulant dose – 2.5 g/dm3, flocculant dose – 100 mg/dm3.

ДВА СПОСОБА МОДЕЛИРОВАНИЯ РИСКА ПРОГРЕССИРУЮЩЕГО АТЕРОСКЛЕРОЗА

Background. Relevance Progressive atherosclerosis has attracted researchers for the last decade due to the fact that it is associated with unfavorable clinical outcomes. Application of modern methods of mathematical modeling will allow to identify patients with such extreme risk of cardiovascular events and optimize their management. Purpose of the study. To develop a mathematical model of the risk of progressive atherosclerosis using the free cross-platform visual programming system Orange and to compare it with the method of nonlinear regression model of logistic type implemented in C++ programming language. Materials and Methods. Female and male patients diagnosed with coronary heart disease (CHD) were included in the study, 100 of them had signs of progressive course of atherosclerosis, 102 - its spontaneous course. Risk models were built using the free cross-platform visual programming system Orange, SPSS 22.0 package, and C++ console. Results and conclusion. The author's proposed approaches to assess the risk of progressive atherosclerosis using regression analysis and machine learning have good prognostic accuracy; both methods are recommended by the authors for application in practice.

Mathematical modeling of minimization of electricity consumption by industrial enterprises with continuous production

Relevance. Determined by the importance of minimizing electrical power consumption in industrial enterprises with continuous production, considering the specific characteristics of their technological processes and the requirements to maintain the output volume of their products. Aim. To solve the task of minimizing electrical power consumption based on a mathematical model and gradient method under optimal planning of the production volume of the industrial enterprises with continuous production; to develop a mathematical model for optimal distribution of production over a time cycle (month, quarter, year) across departments, taking into account both simple and functional constraints, derived from the condition of ensuring minimal electrical power consumption in industrial enterprises with continuous production. Methods. When developing the mathematical model for ensuring minimal electrical power consumption while preserving the production volume, classic Lagrange optimization methods were used. To ensure sufficient calculation accuracy, iterative methods were also applied. For the task under consideration, a calculation error margin of ε=0,1 was assumed and established. It is known that the choice of calculation error margin depends on the specifics of the problem at hand and the decision-maker. To verify the adequacy of the developed model, the method of finding the relative extremum of a function of several variables was used. Results. The use of the mathematical model, which takes into account the nature of the technological process and boundary conditions in both simple and integral forms, demonstrated the feasibility of optimal planning of electrical power consumption by the enterprise. The effectiveness of the developed approaches was verified using a metallurgical enterprise as an example of an industrial enterprise with continuous production, in solving the task of minimizing electrical power consumption for products produced during the reporting period. The use of the proposed model allowed for a reduction in annual electrical power consumption by 2.5% while maintaining the same production volume. One of the classic optimization methods – the method of finding the relative extremum of functions of several variables – showed almost identical results upon verification. This serves as further evidence of the adequacy of the proposed model.

Development of Solutions Based on Computer Simulation for Quantitative SPECT/CT

Purpose: In modern nuclear medicine, an ordered subset expectation maximization (OSEM) iterative algorithm is used to obtain images by single photon emission computed tomography (SPECT) method. At the same time, the problem of choosing the stopping iteration number at which the solution will be as close as possible to the exact value has not been solved. The purpose of this work is to study the problem of stopping the OSEM algorithm. Material and methods: The studies were carried out using the method of mathematical modeling based on the software package “Virtual Platform for Simulation Testing of the SPECT/CT Method”. Computer experiments simulated SPECT/CT with 99mTc phosphotech of a patient with metastatic lesion of the posterior segment of the third rib. The stopping criterion of the iterative OSEM algorithm was studied to obtain a solution that is quantitatively closest to the exact value of the accumulated activity at the tumor. Results: In computer modeling experiments, the tumor dependent Pearson chi-square test was shown to provide a solution that should give correct values for the SUVmean score. However, further research is needed on this important problem to determine how strongly the number of iterations depends on the size of the tumor and the amount of activity accumulated in it. Conclusion: Based on the results obtained, we can conclude that in the SPECT method, in order to move to accurate quantitative estimates of the accumulated activity in the tumor, it is necessary to develop a tumor-oriented stopping criterion for iterative algorithm. If there are several tumors, the stopping iteration numbers for them may differ. Further research on this important issue is planned.

METHODOLOGY OF STEP-BY-STEP DESIGN OF INVESTMENT PROJECT PORTFOLIO

Project portfolio management is an important stage in the project life cycle. The project portfolio selection phase is the most important in the portfolio life cycle. Until now, the optimal solution to the problem of this phase has not been found. A methodology for step-by-step design of a portfolio of investment projects is proposed. The first is the formation of a portfolio of projects based on mathematical programming and modeling methods. The second is the evaluation of the effectiveness of the selected projects by the method of analysis of hierarchies. The third is the distribution of investors' funds between the projects of the project portfolio on the basis of playing with nature. The evaluation of the effectiveness of the three projects was carried out by the method of analysis of hierarchies, and the criteria are the following performance indicators: the indicator of scientific and technical efficiency, the economic indicator, the social indicator and the indicator of ensuring information security. Each criterion has four subcriteria. The results of the calculation determine the effectiveness of projects, which allows resources to be allocated between projects.