Methods Of Mathematical Modeling Research Articles

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.

A novel mathematical-based approach to predict the high-speed deformation behavior of cryodeformed materials with varying stacking fault energies

Cryodeformed (CR) materials have complex microstructures containing nano-twins, dislocation clusters, tangles, and others, depending on the stacking fault energy (SFE). Such unique microstructure makes them suitable for several engineering applications under a high strain rate environment. The high-speed deformation (HSD) behavior of CR materials is difficult to understand due to their complex microstructure. The present work is focused on developing a novel mathematical modeling method to understand the high strain rate deformation of CR materials with varying SFE. The model equation correlates the microstructure-based variables to deformation-based variables like stress, strain, and strain rate. High-speed deformation was conducted using a crossbow test. Transmission electron microscopy (TEM) was conducted on these materials to validate the model output.

АНАЛИЗ АНАЛОГОВЫХ АКТИВНЫХ ЭЛЕКТРОННЫХ СХЕМ НА ОСНОВЕ МЕТОДОВ МОДЕЛИРОВАНИЯ

Various classical methods are often used to analyze analog electronic circuits. It is proposed to use matrix methods of mathematical modeling, which allow using computational tools to obtain fast re-sults with acceptable accuracy. As an example, a scheme of an active second-order electronic filter based on an operational amplifier is proposed

MATHEMATICAL MODELLING OF THE FACTORS OF LAND USE OF THE OBJECTS OF THE NATURE RESERVE FUND OF THE REGIONS

It has been proven that the land use level of the nature reserve fund objects is decreasing, and their condition is being disturbed based on unjustified construction, in particular. In this context, forming a quantitative basis for decision-making through implementing mathematical modelling of the land use factors of the nature reserve fund objects of the regions is particularly relevant. As a result of the generalisation of theoretical approaches, we proposed a definition of ‘land use monitoring of the nature reserve fund objects of the regions’ as a set of legal, constructive, complex, organisational, functional, and instrumental directions aimed at the formation of informational, analytical, and spatial support regarding the state and level of land use of the nature reserve fund objects at the regional level using mathematical modelling methods, which creates a quantitative basis for permanent tracking and control over the use of the nature reserve fund objects. The purpose of the study is to use mathematical modelling tools to establish cause-and-effect relationships between the factors of land use of the nature reserve fund objects of the regions. In this context, the study has solved the following tasks: highlighting the practical aspects of mathematical modelling of the factors of land use of the nature reserve fund objects of the regions; characterisation of the adequacy criteria of the established relationships between the integral indicator of the level of land use of the nature reserve fund objects of the regions and factors using the method of neural networks. The results of mathematical modelling allow for forecasting changes in the integral indicator of the level of land use of the nature reserve fund objects of the regions depending on the relevant factors and for offering scientifically based recommendations for the development and implementation of monitoring of the formation of land use of the nature reserve fund objects of the regions. The conducted analysis of the adequacy of the developed mathematical models of the influence of factors on the integral indicator of the level of land use of the nature reserve fund objects of the regions using the neural network method made it possible to confirm the completeness and reliability of the established relationships based on the low values ​​of the relative error of the test sample. Keywords: land use, objects of the natural reserve fund of the regions, methods, mathematical modelling, monitoring.

Strategic Planning and Ecological Safety Evaluation of University Campuses on Green Marketing Principles

Strategic planning of university campuses (UC) aims to harmonize nature, humans, and architectural complexes, enhancing the positive university image through specialized green and recreation zones. Highly urbanized UC areas, particularly with nearby roads, encounter increased technogenic load and pose additional health hazards. The purpose of the paper is the evaluation of the environmental safety level of the UC recreational territories on the example of campuses of Kyiv universities, located nearby highly loaded roads, using a complex of express methods of analysis, mathematical modeling and criterion-based approach, considering the main green economy principles. The scientific novelty of the paper and the authors’ contribution is in the assessment of the environmental safety level of city-type UC recreational territories being under the significant technogenic load from vehicle emissions. Such express analysis methods as densimetry, viscometry, stalagmometry, conductometry, potentiometry and optical methods, and in particular, refractometric studies have been used to assess the impact of vehicle emissions. The mathematical modeling and computational experiment have been carried out for dispersion fields of the main vehicle emissions pollutants. Ecologically acceptable distances from the road considering the specifics of recreational territory have been determined using the integral index of technogenic load. Propositions for minimizing human health hazards and improving the system of environmental monitoring of such territories have been provided and substantiated. The study also confirms the positive effects of environmental management and green marketing principles synergy, benefiting both nature and humans as well as the university image. Obtained results can be used for the design and reconstruction of UC and their recreational areas, as well as for planning roads located nearby the campuses, improving traffic on them. It is also convenient to foresee the enhancement of the environmental activities in the student research work and create student communities for monitoring the UC environmental state and the development of eco-startup projects.

Enhancing riverine load prediction of anthropogenic pollutants: Harnessing the potential of feed-forward backpropagation (FFBP) artificial neural network (ANN) models

Assessing riverine pollutant loads is a more realistic method for analysing point and non-point anthropogenic pollution sources throughout a watershed. This study compares numerous mathematical modelling strategies for estimating riverine loads based on the chosen water quality parameters: Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD), Suspended Solids (SS), and Ammoniacal Nitrogen (NH3–N). A riverine load model was developed by employing various input variables including river flow and pollutant concentration values collected at several monitoring sites. Among the mathematical modelling methods employed are artificial neural networks with feed-forward backpropagation algorithms and radial basis functions. The classical multiple linear regression (MLR) statistical model was used for the comparison. Four widely used statistical performance assessment metrics were adopted to evaluate the performance of the various developed models: the root mean square error (RMSE), mean absolute error (MAE), mean relative error (MRE), and coefficient of determination (R2). The considerable number of errors (with RMSE, MAE, and MRE) discovered in estimating riverine loads using the multiple linear regression (MLR) statistical model can be attributed to the nonlinear relationship between the independent variables (Q and Cx) and dependent variables (W). The feed-forward neural network model with a backpropagation algorithm and Bayesian regularisation training algorithm outperformed the radial basis neural network. This finding implies that, in addition to suspended sediment loads, riverine loads may be predicted using an artificial neural network using pollutant concentration (Cx) and river discharge (Q) as input variables. Other geographical and temporal fluctuation characteristics that may impact river water quality, on the other hand, may be incorporated as input variables to enhance riverine load prediction. Finally, riverine load analyses were successfully conducted to reduce the riverine load.

Application of a mixed type of optimization in the implementation of pharmaceutical development of a dosage form of eye drops based on oligohexamethyleneguanidine hydrosuccinate

This study focused on the implementation of the stages of pharmaceutical development of a dosage form of eye drops based on the branched oligohexamethylene guanidine hydrosuccinate according to discrete and continuous optimization, followed by risk assessment and process validation. Experimental samples were developed, critical process and quality parameters were identified, technological characteristics were measured, parameters were normalized, a forecast was made, confirmatory experiments were conducted, the optimal composition was identified, risks in the production of eye drops were assessed, and partial validation was performed. During the implementation of the stages of pharmaceutical development of eye drops based on branched oligohexamethylene guanidine hydrosuccinate, three optimization cycles (discrete and continuous) were carried out, and the optimal ratio of active and auxiliary components was justified based on the results (branched oligohexamethylene guanidine hydrosuccinate 0.05%, polyvinyl alcohol 1%, phosphate-buffered saline 20%, sodium chloride 0.45%, and purified water up to 100%). After reviewing the technological process considering risk analysis, critical points were identified, and partial validation was performed, and the positive results verified and confirmed the optimal choice at this stage of pharmaceutical development. In general, a mixed type of optimization (discrete and continuous) can be used to implement pharmaceutical developments of eye drops based on branched oligohexamethylene guanidine hydrosuccinate, which is confirmed by a series of experiments and risk assessment, and the partial validation verified the data obtained. Thus, pharmaceutical development is a complex and time-consuming process, and limited functionality does not always allow quick identification of the optimal composition of a drug. As an effective solution for implementing the stages of pharmaceutical development, mathematical modeling methods and various types of optimization can be applied.

A Novel Mathematical Model and Homotopy Perturbation Method Analyzing the Effects of Saturated Incidence and Treatment Rate on COVID-19 Eradication

A Novel Mathematical Model and Homotopy Perturbation Method Analyzing the Effects of Saturated Incidence and Treatment Rate on COVID-19 Eradication

Methods of mathematical modeling in the management of socio-economic processes: game theory

The possibility of using game theory in the practice of managing socio-economic processes is considered. Examples are given and the possibilities of integrating game theory as a complex of mathematical modeling methods into the daily practice of management are determined.

Тождество теоретического и экспериментального подходов при прототипировании региональных проектов в сфере здравоохранения.

The formalization of processes for finding the parameters of a prototype model of a medical organization implementing a regional project is based on the unity of theoretical and experimental approaches. The purpose of the study was an attempt to create a unified and harmonious theoretical foundation for conducting an experiment in order to find a prototype of a medical organization implementing projects at the regional level. In order to reveal the potential for solving technological problems facing project stakeholders, formalization of approaches was carried out for experimentally finding the parameters of a prototype project for a medical organization implementing a regional project. Materials and methods. The research materials were the works of Russian and foreign scientists related to the issues of mathematical modeling and prototyping. In order to study the research question, more than 30 literature sources were analyzed, directly or indirectly addressing the problems of practical application of object prototyping methods. Methods of system analysis, comparison, systemic and integrated approaches, as well as mathematical modeling methods were used. Results. Complex, multi-level systems when implementing projects in the regions are poorly structured and, accordingly, not fully formalized, so the experimental approach is especially relevant when searching for prototyping tools. The degree of formalization of approaches to searching for a prototype of a project object depends on the completeness (saturation) of processes, their structure and the degree of correlation of process data in a medical organization to process performers, operations, and management objects. Prototyping is designed to optimize the procedures for planning, analyzing and processing the results of research data based on a mathematical foundation. The prototyping technique is primarily aimed at saving resources (labor, financial, time) as much as possible, therefore, justification of the need and mastery of mathematical foundations in formalizing approaches to prototyping is a fundamental factor and the purpose of this discussion. Findings. System analysis using the unity of theoretical and experimental approaches, in the author’s opinion, will allow for a deeper synthesis of knowledge about the potential possibilities for forming decisions through a prototype of a medical organization implementing projects in the healthcare industry.

Toxic heavy metal ions contamination in water and their sustainable reduction by eco-friendly methods: isotherms, thermodynamics and kinetics study

Heavy metal ions can be introduced into the water through several point and non-point sources including leather industry, coal mining, agriculture activity and domestic waste. Regrettably, these toxic heavy metals may pose a threat to both humans and animals, particularly when they infiltrate water and soil. Heavy metal poisoning can lead to many health complications, such as liver and renal dysfunction, dermatological difficulties, and potentially even malignancies. To mitigate the risk of heavy metal ion exposure to humans and animals, it is imperative to extract them from places that have been polluted. Several conventional methods such as ion exchange, reverse osmosis, ultrafiltration, membrane filtration and chemical precipitation have been used for the removal of heavy metal ions. However, these methods have high operation costs and generate secondary pollutants during water treatment. Biosorption is an alternative approach to eliminating heavy metals from water that involves employing eco-friendly and cost-effective biomass. This review is focused on the heavy metal ions contamination in the water, biosorption methods for heavy metal removal and mathematical modeling to explain the behaviour of heavy metal adsorption. This review can be helpful to the researchers to design wastewater treatment plants for sustainable wastewater treatment.

Magnetotelluric Observations in the Caspian Sea

Abstract —To study the geological structure in the search for raw hydrocarbons within the Volga delta and the Caspian Sea, two intersecting profiles of magnetotelluric sounding were performed. The analysis of geoelectric sections based on the one-dimensional inversion of the initial and normalized invariant curves of apparent resistance showed that it is necessary to use methods of three-dimensional mathematical modeling to form reliable geoelectric models. Their initial construction necessary for the three-dimensional interpretation of invariant apparent resistance curves was carried out taking into account their one-dimensional inversion. The resulting model, including the lower structural part, is constructed by the method of interactive matching to the apparent resistance curves of model curves calculated according to the program of three-dimensional mathematical modeling. This approach made it possible to take into account the influence of local galvanic distortions on the apparent resistance curves when evaluating the distribution of electrical conductivity in the lower parts of the subsea deposits. As a result of the integrated interpretation of magnetotelluric data, blocks with increased conductivity have been identified in the subsea deposits of the Northern Caspian Sea, which are most likely associated with high fluid saturation of Cretaceous and Neogene sediments. Their position correlates with the regional discontinuous structures of the region.

Применение концепции общего страхового пространства в ЕАЭС: анализ нормативно-правовой базы и экономических эффектов

The article provides a comprehensive analysis of the concept of creating a common insurance market of the EAEU n and the prospects for its implementation. The reasons for slowing down this integration process are explored, including significant differences in the approaches of the member states to regulating national insurance markets. Special attention is paid to discrepancies in the legislatively established requirements for the minimum authorized capital of insurers, which vary more than 5 times depending on jurisdiction. Authors identify the key negative effects of such fragmentation of regulation on deepening Eurasian economic integration. Basing on comparative legal and statistical analysis, as well as methods of economic and mathematical modeling, options for harmonizing the regulations under consideration are proposed in order to bring together the EAEU countries’ approaches and shape a common competitive insurance market.