Methods Of Mathematical Modeling Research Articles

Предел передаваемой мощности в системе тягового электроснабжения

Objective: the concept of the limit of power flow is widely used in general industrial power engineering to compare different ways of amplifying an electric network. In this paper, it is proposed to use it to evaluate the operation of traction networks of railways. Setting the traction power load is used in several simulation development of an express methodology for comparing various ways to enhance traction power supply is an urgent task. Methods: the paper uses mathematical modeling methods based on the theory of electrical circuits. The MATLAB software package was used as a modeling tool. Results: expressions are obtained for calculating the maximum transmitted power depending on the length of the substation zone. The dependence of the transmitted power on the minimum voltage on the current collector, the equivalent resistance of traction substations for DC sections, is analyzed. For alternating current sections, the dependence of the transmitted power on the power factor of the traction load is analyzed. The conclusion is made about the relevance of increasing the power factor of an alternating current electric rolling stock. Practical importance: the proposed technique will allow you to quickly assess the effect of using various methods of strengthening the traction power supply system.

Biologically Active Terpenoids Ligularia Macrophylla (Ledeb.) DC. аnd Technology of New Drug Substance

The article presents the results of a chemical study of Ligularia macrophylla (Ledeb.) DC. The essential oil was isolated by hydrodistillation using a Clevenger apparatus and microwave extraction using a NEOS installation. Using mass spectrometry, 52 components were identified in the essential oil isolated by hydrodistillation; 63 components were identified in the essential oil isolated by microwave extraction. The main components of the essential oil are Δ3-carene, β-bisabolene, β-myrcene. It was revealed that the substance obtained from the essential oil of Ligularia macrophylla (Ledeb.) DC. has anti-inflammatory and antimicrobial activity. For the first time, the optimal technological parameters for alcohol extraction of Ligularia macrophylla (Ledeb.) DC roots were determined using the method of mathematical modeling, providing a quantitative yield of the sesquiterpene lactone furanoeremophilan-14β,6α-olide, which has anti-inflammatory activity.

TO HIGHLY PRODUCTIVE SYNTHESIS OF ALUMINUM NANOPARTICLES IN PLASMA FLOW AT ATMOSPHERIC PRESSURE

Purpose. To study the highly productive evaporation of aluminum micron powder in an atmospheric pressure plasma jet for the synthesis of nanoaluminum. Using special plasma technology, nanoparticles can be produced by rapid melting and evaporation of the initial micrometer particles and their subsequent re-nucleation. Research methods. Methods of mathematical and computer modeling of subsonic plasma turbulent jets at atmospheric pressure and experimental studies of two-phase processes during thermal plasma treatment using an arc plasma torch. Results. Based on computer modeling, a special reactor system was designed and developed, which includes a plasma-jet reactor with an electric arc plasma torch for the synthesis of aluminum nanoparticles. Numerical modeling makes it possible to determine the position of the melting point, evaporation and crushing of a molten particle, the evolution of the fractional composition of the dispersed phase, and find the speed and temperature of the particle in the area from its melting point to the crushing point. An experimental test of the operation of the reactor system was carried out using arc plasma torches with a power of 30 and 150 kW. It has been shown that intensifying the fragmentation of dispersed raw materials in a plasma jet can be useful in technologies for producing nanomaterials. The consequence of the fragmentation process is the redistribution of the fractional composition of the powder along the plasma jet and the accompanying changes in the dynamics of movement, heating and evaporation of particles. It has been determined that when the temperature of the largest aluminum particles reaches 2500 C, the total amount of evaporated mass is theoretically equal to 100%. The main parameters influencing the behavior of particles in a plasma jet are particle diameter, powder injection rate, flow rate, temperature and composition of the plasma gas. Taking these parameters into account will allow the process to operate at increased productivity. Scientific novelty. A mathematical description of the process of fragmentation a polydisperse powder, based on a continuum approach, has been obtained, which makes it possible to determine the position of the crushing point of a molten particle, the fractional composition of the dispersed phase, and find the speed and temperature of the particle in the area from its melting point to the point of crushing and evaporation. It was shown for the first time that it is possible to carry out a process in which complete evaporation of a molten drop is achieved due to the high enthalpy of the plasma before the end of mixing with steam. Practical value. A special reactor system has been designed and developed, which includes a plasma-jet reactor with an electric arc plasmatron for the synthesis of aluminum nanoparticles. The operating parameters of the reactor system have been determined, which will allow the synthesis of aluminum nanoparticles to be carried out with high productivity.

ИСПОЛЬЗОВАНИЕ МАТЕМАТИЧЕСКОГО МОДЕЛИРОВАНИЯ ДЛЯ МНОГОПАРАМЕТРИЧЕСКОГО АНАЛИЗА ЭЛЕКТРОННЫХ СХЕМ С ЛИНЕЙНЫМ АКТИВНЫМ УСТРОЙСТВОМ

It is proposed to use matrix methods for mathematical modeling of the operation of electronic analog linear devices. They allow using computational tools to obtain results with high calculation speed and acceptable accuracy. For example, a scheme of an active second-order electronic filter based on an operational amplifier is proposed. A multiparametric analysis of the transfer function based on the primary parameters of the electronic circuit is proposed. The proposed method for analyzing linear active electronic circuits based on the conduction matrix can significantly reduce the calculation time and significantly simplify the forms of writing analytical expressions. The calculation results are com-pared with the results obtained in a specialized program for modeling electronic circuits OrCAD PSpice. For example, the transfer function is analyzed according to the following parameters: sensi-tivity, statistical synthesis, optimization of tolerances

Статистическая оценка влияния антироссийских санкций на динамику развития российской промышленности

The relevance of the study is due to the unprecedented number of economic sanctions imposed on the Russian economy since 2014. In this paper we will assess the impact of economic sanctions on the development of key sectors of the Russian industry: machine-building complex, food industry and extraction of fuel and energy minerals. The dynamics of the development of the analyzed branches of the Russian industry in the 13-year time interval was multidirectional. High utilization of production capacities and support of national production by the weak national currency were counteracted by negative factors associated with the coronavirus pandemic and sectoral sanctions against the Russian economy. The study verifies the hypothesis of the negative impact of economic sanctions on the development of Russian industry using economic and mathematical modeling methods. The results of the study showed the existence of a relationship between the number of anti-Russian sanctions and the dynamics of development of two branches of the Russian industry: food and machine-building. For the mining industry the correlation coefficient was insignificant.

Метод визначення вібраційних характеристик промислового обладнання в частотній та часовій областях

This paper proposes hardware and software solutions and a data processing method for vibration diagnostics of industrial equipment, which uses discrete Fourier transform and Allan dispersion to increase the accuracy and stability of measurement processes and result processing. The object of this study is the use of vibration diagnostic methods to implement the concept of maintenance of industrial equipment based on monitoring its current and future condition. The subject of this research is the hardware and software solutions for vibration diagnostics systems and methods for processing measurement results. The purpose of this work is to develop a new resource-saving IoT-oriented wireless solution for vibration diagnostics, where the contact method and MEMS accelerometers are used to measure vibration parameters and to evaluate the effectiveness of new methods and algorithms for processing experimental data. The task: justify the need to find new hardware and software solutions and methods of processing the obtained results for the implementation of the service concept based on the tracking of vibration indicators of technical equipment; provide basic hardware and software solutions for the implementation of the cloud platform of vibration diagnostics; develop methods of processing results; check the developed methods and algorithms using mathematical modeling methods and in an on-site experiment; compare the effectiveness of own and competitive solutions; draw conclusions and formulate a plan for further research. Conclusions. It has been proven that the combination of known analysis methods in the time and frequency domains with multi-level processing gives better results than analogous methods. The developed hardware and software tools and the method of processing measurement results effectively implement the contact method of vibration measurement, which provides the possibility of tracking the state of technical equipment. The developed equipment for the calibration of vibration acceleration sensors can reduce accelerometer errors. Further areas of research are the search for the optimal distribution of calculations on IoT levels, reducing the computational complexity of algorithms, increasing the time of continuous autonomous operation of the lower-level microcontroller, creating micro services for time-series analysis, and researching the dependence of the technical state of the equipment on the calculated Allan deviation.

Algorithm of Development for Stabilization of Socio-Ecological Situation in Karakalpakstan

The relevance of developing a scientific framework for stabilizing the socio-ecological situation of the Republic of Karakalpakstan is determined by the need to address the environmental, social and economic challenges faced by the region. It is designed to improve the population’s quality of life, sustainable development and balanced interaction with the environment. The purpose of the research was to establish the relationship between social and environmental factors, to establish a mathematical model based on them, which will enable predicting future development and establishing a set of recommendations to improve the situation in the Republic of Karakalpakstan. The methods of theoretical analysis and mathematical modelling were used. The research outlines modern ideas about modelling the dynamics of socio-ecological processes in the example of the Republic of Karakalpakstan. It is established that the Republic has several problems, the solution of which should be started shortly. Considerable attention is paid to the setting of tasks and using for this purpose methods of system analysis of socio-ecological factors. In this work, the analysis of factors affecting the social and environmental environment of the Republic of Karakalpakstan using regression analysis is considered. The parameters of the developed mathematical model and their adequacy are determined. The developed mathematical model will allow identification of the social and ecological situation of the republic. At the end of the work, ten priority points for the next 5-10 years to improve the socio-ecological situation were presented. The practical value of the results is implemented in promoting the identification of new powerful reserves for further improvement of the management of social processes. This approach allows for increasing the national economic efficiency of the region and ensuring a balance between economic, social and environmental aspects of development, which is an essential step towards a sustainable future.

Modeling of Non-Stationary Mass Transfer Process in Groundwater

Purpose. Infiltration of contaminated water and accidental spills of chemically hazardous substances into groundwater lead to the formation of large zones of man-made pollution in aquifers. Therefore, it is important to develop protection systems against groundwater pollution. To analyze the effectiveness of such protection systems at the design stage, it is necessary to have scientifically based information on the dynamics of changes in groundwater contamination zones. Such information can be obtained using the method of mathematical modeling. The study aims to create a numerical model for calculating the non-stationary process of geomigration when using chemical protection of groundwater from pollution. Methodology. To describe the dynamics of groundwater flows, two filtration equations are considered, which allow mathematical modeling of the filtration process both for solving planned problems and for solving problems of specialized filtration. A two-dimensional geomigration equation was used to analyze changes in groundwater quality. This equation takes into account the convective transfer of impurities in the filtration flow, dispersion, and the intensity of impurity infiltration into the groundwater flow. This equation is also used to calculate the movement of the neutralizer in groundwater. The numerical integration of the filtration equation was performed using finite difference methods. An implicit splitting scheme was used to numerically integrate the geomigration equation. Findings. A fast-applicable numerical model for calculating groundwater dynamics has been built. The model is also a platform for solving another important task – the calculation of geomigration processes. A numerical model for calculating the unsteady-state geomigration process is proposed, which makes it possible to assess not only the process of formation of contamination zones in the groundwater flow, but also to determine the effectiveness of the method of neutralizing the impurities in the groundwater flow. Originality. Effective numerical models for rapid assessment of changes in groundwater dynamics and quality under the influence of anthropogenic sources have been developed. These models take into account a set of important physical factors that affect the process of geomigration and the process of neutralizing the impurity in the groundwater flow. Practical value. A computer program has been developed that allows determining the effectiveness of the process of neutralizing an aggressive impurity in groundwater by a computational experiment to protect it from anthropogenic pollution.

Digital Visualization of Environmental Risk Indicators in the Territory of the Urban Industrial Zone

This study focused on predicting the spatial distribution of environmental risk indicators using mathematical modeling methods including machine learning. The northern industrial zone of Pavlodar City in Kazakhstan was used as a model territory for the case. Nine models based on the methods kNN, gradient boosting, artificial neural networks, Kriging, and multilevel b-spline interpolation were employed to analyze pollution data and assess their effectiveness in predicting pollution levels. Each model tackled the problem as a regression task, aiming to estimate the pollution load index (PLI) values for specific locations. It was revealed that the maximum PLI values were mainly located to the southwest of the TPPs over some distance from their territories according to the average wind rose for Pavlodar City. Another area of high PLI was located in the northern part of the studied region, near the Hg-accumulating ponds. The high PLI level is generally attributed to the high concentration of Hg. Each studied method of interpolation can be used for spatial distribution analysis; however, a comparison with the scientific literature revealed that Kriging and MLBS interpolation can be used without extra calculations to produce non-linear, empirically consistent, and smooth maps.

Mathematical modeling methods in assessing the prospects of export development in the Republic of Tatarstan of the Russian Federation

In the conditions of instability of the Russian economy, Russian regions have faced the problem of finding new directions of foreign economic development. Mathematical modeling methods, considering the distance between partner regions and their economies volumes, can be effective tools for solving the problem. The article touches upon the modeling foreign trade relations issues in the Republic of Tatarstan on the gravity models’ basis. The purpose of the study is to identify potential trade partners and assess the prospects for the export relations development in the Republic of Tatarstan. The structure, dynamics, and main directions of exports of the constituent entity have been analyzed. Potential trade partners of the Republic of Tatarstan among the Commonwealth of Independent States countries have been identified using the classical gravity model based on assessing the internal regional product and the distance among the regions. The prospects of foreign trade relations with Belarus and the Republic of Uzbekistan have been assessed. Based on J. Tinbergen’s gravity model models of interaction among the regions have been built and forecast values of export volumes for the short term calculated. It was revealed that the Republic of Azerbaijan can become a potential partner for the Republic of Tatarstan. The analysis of the forecast data on the domestic regional product of the Republic of Tatarstan and the gross domestic product of Azerbaijan in 2023 suggests that the exports volume between these entities is expectedly high.

ОБОСНОВАНИЕ КОНСТРУКЦИИ КРЫТОГО ГРУЗОВОГО ВАГОНА С УВЕЛИЧЕННЫМ ОБЪЕМОМ ГРУЗОВОГО ПОМЕЩЕНИЯ

The market of covered freight cars, as well as existing designs of this car type of domestic and foreign production is analyzed. Promising trends of making innovative designs of freight cars for the transportation of piece and container goods are found out. The original design of a covered freight car with an increased body space due to the use of the space between trucks is proposed. To reduce the complexity of loading and unloading operations, sliding sections of the side walls and roof are provided in the car design. To confirm the compliance of the proposed design with the requirements of regulatory and technical documents, the car was entered into the dimension, checking for automatic coupling at the junction of a straight line and a curve, passage in the coupling of an s-shaped curve and coupling of a straight line and a curve, and a single car along a circular curve of a small radius, as well as passing without self-decoupling of the hump of the sorting slide, the ramp exit of the train ferry. A safety assessment is carried out with regard to rolling the wheel onto the rail and overturning the car in curves. The car dynamic characteristics are found out by mathematical modeling methods. The assessment of the strength of the body load-bearing structure, lifting mechanisms of the floor sections, sliding sections of the roof and side walls is performed using the finite element method implemented in the environment of a specialized software package. The results obtained as a result of calculations and computer modeling confirmed the operability and safety of the proposed design of a covered freight car with an increased loading space.

COMPARATIVE ANALYSIS OF SPECTRAL ANOMALIES DETECTION METHODS ON IMAGES FROM ON-BOARD REMOTE SENSING SYSTEMS

The subject matter of the article is methods of detecting spectral anomalies on images from remote sensing systems. The goal is to conduct a comparative analysis of methods for detecting spectral anomalies on images from remote sensing systems. The tasks are: analysis of the main methods of detecting spectral anomalies on images from remote sensing systems; processing of images from remote sensing systems using basic methods of detecting spectral anomalies; comparative assessment of the quality of methods for detecting spectral anomalies on images from remote monitoring systems. The methods used are: methods of digital image processing, mathematical apparatus of matrix theory, methods of mathematical modeling, methods of optimization theory, analytical and empirical methods of image comparison. The following results are obtained. The main methods of detecting spectral anomalies on images from remote sensing systems were analyzed. Processing of images from remote sensing systems using the basic methods of detecting spectral anomalies was carried out. A comparative assessment of the quality of methods for detecting spectral anomalies on images from remote monitoring systems was carried out. Conclusions. The spectral difference of the considered methods is revealed by the value of information indicators - Euclidean distance, Mahalanobis distance, brightness contrast, and Kullback-Leibler information divergence. Mathematical modeling of the considered methods of detecting spectral anomalies of images with a relatively “simple” and complicated background was carried out. It was established that when searching for a spectral anomaly on an image with a complicated background, the method based on the Kullback-Leibler divergence can be more effective than the other considered methods, but is not optimal. When determining several areas of the image with high divergence indicators, they should be additionally investigated using the specified methods in order to more accurately determine the position of the spectral anomaly.

Protein content prediction of rice grains based on hyperspectral imaging

This study utilized hyperspectral imaging technology combined with mathematical modeling methods to predict the protein content of rice grains. Firstly, the Kjeldahl method was used to determine the protein content of rice grains, and different preprocessing techniques were applied to the spectral information. Then, a prediction model for rice grain protein content was developed by combining the spectral data with the protein content. After performing multiplicative scatter correction (MSC) preprocessing and selecting feature wavelengths based on successive projections algorithm (SPA), the multivariate linear regression (MLR) model showed the best prediction performance, with a calibration set R2C of 0.9393, a validation set R2V of 0.8998, an RMSEV of 0.1725, and an RPD of 3.16. Finally, the quantitative protein content model was mapped pixel by pixel to visualize the distribution of rice protein, providing possibilities for non-destructive protein content detection.

MODELING OF GROUND WATER DYNAMICS AND ITS POLLUTION

Problem statement. Large accumulators of liquid waste (e.g., mine water ponds, tailing ponds, etc.) are long-term sources that change the hydrological regime. A negative consequence of this process is flooding of the territory. In addition, the infiltration of contaminated water from such hazardous sources changes the quality of groundwater. Therefore, it is important to analyze the impact of such anthropogenic sources on the process of flooding and deterioration of groundwater quality. To solve this problem, it is very important to use the method of mathematical modeling as an effective mean of researching problems of this class, since the use of physical modeling is practically impossible within the scope of problems of this class. The purpose of the article. Development of numerical models for predicting changes in the hydrological regime (flooding of the territory) and groundwater quality under the influence of anthropogenic pollution sources. Methodology. To assess the dynamics of changes in the hydrological regime, a two-dimensional equation of filtration of a non-pressure groundwater flow is used. A two-dimensional geomigration equation (planned model) is used to analyze changes in groundwater quality during infiltration of contaminated water from the settling pond. This equation takes into account the convective transfer of contaminants in the filtration flow, dispersion, and the intensity of contaminant infiltration into the groundwater flow. The method of total approximation is used for numerical integration of the filtration equation. For the numerical integration of the geomigration equation, an implicit splitting scheme is used. Scientific novelty. Effective numerical models for rapid assessment of changes in groundwater dynamics and quality under the influence of anthropogenic sources that change the hydrological regime are proposed. The constructed numerical models take into account a set of important physical factors that affect the process of geomigration and flooding of the territory, namely: filtration coefficient, variable depth of free-flowing groundwater, dispersion, intensity of the source of impurity emission into the groundwater flow. This makes it possible to obtain a comprehensive assessment of the process of flooding and groundwater pollution.. Practical significance. A computer code has been created that allows practical usage of the developed numerical models. This code is an effective tool for theoretical study of non-stationary processes of territory flooding and anthropogenic groundwater pollution. Conclusions. A numerical model for calculating groundwater dynamics has been developed. The model allows to predict the level of groundwater rise under the influence of a man-made source of wastewater infiltration from a settling pond. A numerical model for calculating the process of geomigration from an anthropogenic source of emissions has been developed. The model makes it possible to predict the dynamics of contamination zone formation in a non-pressure groundwater flow. The developed numerical models take into account the most important parameters that affect the formation of flooding zones and groundwater contamination.

Research of the regulator of an expander-generator unit

The relevance of research is determined by the tasks of increasing the efficiency of alternative and renewable energy power plants. The purpose of the work is to develop a method of coordinating the settings of the automatic excitation regulators and the speed of rotation of the rotor of the generator from the vortex installation of the expander-generator unit, which is part of the autonomous power consumption network. To achieve the goal, the methods of mathematical modelling in the MATLAB environment, physical modelling, processing of experimental data, theory of automatic control, theory of magnetic field, theory of electric machines, programming of microprocessor devices were used. Considering the need to expand the base of alternative energy sources, the task of controlling the energy plant for the utilization of excess pressure of gas transportation networks was considered. The study of the regulator of the expander-generator unit was based on a model reflecting the interaction of mechanical and electrical processes. A set of nonlinear differential equations corresponded to the description of these processes. Accurate consideration of nonlinearities of the considered control object complicates the implementation of the corresponding microprocessor control systems. Modelling is aimed at achieving a compromise between the required accuracy of object control and the possibilities of simplifying the object control structure. The use of experimental and datasheet data of the devices made it possible to evaluate the dynamics of turbine rotation and voltage generation, forming the factors for the untying of the control circuits. The use of MATLAB with the Lookup Table option made it possible to perform a multi-point linearization of the nonlinear description of the process, speeding up the modelling and adjustment of the regulator. This is important to incoordinate the settings of the frequency control loops and the output voltage, given the trade-off between the speed of the regulator and the minimization of oscillations in the generation frequency. Based on the obtained results, a regulator of the expander-generator unit was developed, which ensures the stabilization of the initial parameters of the unit under the conditions of electrical load disturbances. In practice, the obtained data can be used in the integration of renewable energy sources into the general energy system through the optimization of the operation of generators

DESIGN OF MECHANICAL PROPERTIES OF WIND FABRIC

In the article, among the main properties of the fabric, the fiber composition of the hemlock thread, the thickness of the hemlock thread, and changes in the density of the hemlock thread in the fabric are analyzed as factors affecting it. Using mathematical modeling methods, regression equations were obtained to calculate the tensile strength of the tissue. The coefficients of the regression equation were tested by Student's and the equation by Fisher's test. Cotton and polyester fibers were used as the fiber content of the hemp yarns used in weaving. 100 percent polyester yarn used as a yarn of 3 different linear densities has been found to have little effect on strength and elongation at break, and strength compared to cotton yarn.

Analysis of torsional properties of a rubber rope as a composite material in multilayer winding

Purpose. The main purpose of this study is to analyse the results of a theoretical study on the effect of the longitudinal stiffness of the rope on the mechanism of deformation of the winding body as a composite material on the basis of experimental data. The methods. The methodology is based on the analysis of scientific papers by leading experts in the field of mechanical engineering specialising in the development of hoisting machines with rubber-rope cables. The development of the model of torsional stiffness of the winding body of reel hoists was based on mathematical and physical modelling methods, including methods of planning a multifactorial experiment and statistical processing of experimental data. Findings. When solving the problem of determining the stiffness of the body of a rubber-rope winding, the physical model of its spool body was presented in the form of a rubber-metal hinge. After processing the results of the experiment to determine the parameters of the winding body, an analytical expression was obtained to calculate the torsional stiffness of the winding body of a rubber-rope cable. The originality. The regularities of the influence of the parameters of a rubber rope on the torsional stiffness of its winding body have been established. The stiffness of the winding body depends on its outer diameter quadratically, while the local stiffness is weak. With a small number of turns, the stiffness of the homogeneous body exceeds the local stiffness, but the total pliability is low. The risk of dynamic effects in a spool hoist during braking increases with a large number of turns, when the homogeneous body stiffness is much lower than the local stiffness. The total torsional stiffness of the winding body can be determined by the proposed formula with sufficient accuracy for dynamic analysis. Practical implementation. The developed mathematical model for determining the torsional stiffness of a rubber rope winding makes it possible to find such values of the parameters of a spool hoist that will avoid the danger of dynamic effects during emergency and operational braking of the device caused by the torsional stiffness of the winding body.

A descriptive and prescriptive analysis of rail service subsidies in the China–Europe freight transportation market

This study delivers a descriptive and prescriptive analysis of rail service subsidies for China Railway Express (CRE) in the China-Europe freight transportation market. The analysis is conducted by advanced mathematical modeling and programming methods. Specifically, we implemented a multicommodity multimodal freight transportation network equilibrium model that can be used for predicting the commodity-specific mode-route cargo flow pattern and hence for assessing the effectiveness and limitations of the current CRE subsidy scheme. To properly quantify the impact of subsidies on individual shippers’ decision making, the model explicitly characterizes individual shippers’ mode-route choice behavior and takes into account shipping cost, transit time, capacity-induced congestion surcharge, and unobserved transportation impedances as shippers’ disutility. The solution of the network equilibrium model resorts to a disaggregate simplicial decomposition algorithm within the well-known Lagrangian relaxation framework. A bi-level network-based subsidy optimization model is constructed, in which the upper level aims at minimizing the sum of revenue loss and congestion charge, and the lower level is the aforementioned freight transportation network equilibrium model. A tabu search procedure is proposed and implemented to derive the solution of the bi-level model. The above models and algorithms are then applied to the China-Europe containerized freight transportation network, which comprises all China-Europe liner shipping lines, all CRE service lines, and the highway networks in China and Europe. The evaluation and optimization results show that the current subsidy scheme creates an imbalanced capacity utilization pattern across CRE service lines while an optimized line-specific subsidy solution can yield noteworthy improvements in the service utilization and economic efficiency of CRE.

Applications of mathematical modeling methods for optimizing the contents of composite coatings for the protection against high precision laser-guided weapons

Applications of mathematical modeling methods for optimizing the contents of composite coatings for the protection against high precision laser-guided weapons

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.