Field Of Mathematical Modeling Research Articles

A systematic literature review of soft set theory

AbstractSoft set theory, initially introduced through the seminal article “Soft set theory—First results” in 1999, has gained considerable attention in the field of mathematical modeling and decision-making. Despite its growing prominence, a comprehensive survey of soft set theory, encompassing its foundational concepts, developments, and applications, is notably absent in the existing literature. We aim to bridge this gap. This survey delves into the basic elements of the theory, including the notion of a soft set, the operations on soft sets, and their semantic interpretations. It describes various generalizations and modifications of soft set theory, such as N-soft sets, fuzzy soft sets, and bipolar soft sets, highlighting their specific characteristics. Furthermore, this work outlines the fundamentals of various extensions of mathematical structures from the perspective of soft set theory. Particularly, we present basic results of soft topology and other algebraic structures such as soft algebras and $$\sigma$$ σ -algebras. This article examines a selection of notable applications of soft set theory in different fields, including medicine and economics, underscoring its versatile nature. The survey concludes with a discussion on the challenges and future directions in soft set theory, emphasizing the need for further research to enhance its theoretical foundations and broaden its practical applications. Overall, this survey of soft set theory serves as a valuable resource for practitioners, researchers, and students interested in understanding and utilizing this flexible mathematical framework for tackling uncertainty in decision-making processes.

Application Strategies of Computer Technology in the Field of Mathematical Modeling

The era of big data has arrived in society, and the technology behind com-puter networks has not only raised the general level of people's living stand-ards but is also making steady headway in the direction of artificial intelli-gence. The most important theoretical basis for it is mathematics. The pro-cess of abstracting and synthesizing the laws of reality through the use of mathematical techniques is known as mathematical modeling. The applica-tion of mathematical modeling in the natural sciences seeks to approach a problem with more precision by employing mathematical rigor and a mathe-matical language that is systematically complete. At this point in time, the progression of mathematical modeling just can't happen without the assis-tance of advances in computer technology. The significance of computer technology in mathematical modeling is demonstrated by a detailed examina-tion of the formula underlying the computer technology model. After con-ducting research on the results of the mathematical modeling competition held over the course of several years, utilizing the artificial neural network (ANN) algorithm to analyze the data, and coming to the conclusion that the implementation of computer technology plays a role in the dissemination of mathematical modeling, we say that computer technology has a part to play in the dissemination of mathematical modeling.

Reaction–Diffusion Equations in Mathematical Models Arising in Epidemiology

The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-19 pandemic modeling. Most of our attention is given to the studies in which not only results of numerical simulations are presented but analytical results as well. In particular, traveling fronts (waves), exact solutions, and the estimation of key epidemic parameters of the epidemic models with governing PDEs (typically reaction–diffusion equations) are discussed. The review may serve as a valuable resource for researchers and practitioners in the field of mathematical modeling in epidemiology.

Analisis Bibliometrik Trend Penelitian Pemodelan Matematis Menggunakan Database Google Scholar, Publish or Perish, dan Vosviewer

This study aims to identify the topic of the study of mathematical modeling by highlighting publications on Google Scholar from 1951 to 2022. This study uses the Google Scholar citation database for 71 years to collect articles. The keyword used in this research is "mathematical modeling" with a filter of English documents. Simple statistical methods were used, and bibliometric analysis was performed using Publish or Perish and Vos-viewer software. This study visualizes the co-occurrence patterns of keywords and citations. This study reveals a significant research trend in the field of mathematical modeling from 71 years ago. Based on the visualization of the large cluster network map which includes mathematical modeling concepts, it is known that the health sector is dominant as the background for its presence. Study of the topic of mathematical modeling still revolves around theoretical developments, economics, industry and environment. However, there has been no study of mathematical modeling in the social and cultural fields. Moreover, by using the bibliometric method to re-identify keywords that are in accordance with the development of problem solving through mathematical models

“Digital Core” Technology and Supercomputer Computing

This article is focused on the modeling of multiphase hydrodynamic flows within “digital core” technology for the needs of the oil and gas industry. The essence of this technology is direct numerical simulation of the flows on the scale of the pore space of oil and gas reservoir rocks with direct resolution of the structure of this space and the dynamics of interphase boundaries. The importance of the development of high-performance computing facilities (supercomputers) for the successful implementation of this technology is emphasized. Work carried out by the Keldysh Institute of Applied Mathematics, RAS, in the field of mathematical models, computational algorithms, and their software implementation is described.

Modelagem matemática, professor mediador-orientador e construtivismo: entrelaçamentos discursivos na constituição da figura docente

ABSTRACT The purpose of this article is to discuss the few conditions that made it possible for the emergence of the statement “the teacher, while developing Modeling activities, is no longer the transmitter but a mediator-mentor in the process of teaching” in the field of Mathematical Modeling from the perspective of Mathematical Education. We make use of the concepts, discourse, enunciate and statement from Michel Foucault's line of thought. The analytical material from which the aforementioned enunciate emerged encompasses theses and dissertations defended in the period between 1987 and 2016, which report, describe, or discuss the development of Modeling activities in the classroom of basic education. The analysis made it evident that the constructivist discourse did not consist only of a possibility for the emergence of the statement mediator-teacher, but also of the crystallization of this teaching representation as a pedagogic truth in the field of Mathematical Modeling.

Mathematical modeling in the agro-industrial complex: basic problems and models construction

Currently, information technologies have been tightly integrated into agriculture. Since no computer calculations are possible without a powerful mathematical apparatus, the question arises about the possibility of modeling the processes occurring in agriculture with the help of modern achievements of science and technology. The present study is devoted to the existing methods of mathematical modeling in agriculture in relation to the applied aspects of agriculture. The aim of the research is to develop a critical approach to modern developments in the field of mathematical modeling and their place in agriculture. It is shown that the introduction of mathematical models based on modern scientific knowledge contributes to the optimization of agricultural processes and increasing the efficiency of any farm. Based on statistical studies, it is shown that among all branches of agriculture, mathematical methods are most often used in economic calculations, least of all, in calculations related to farm modeling. This is explained both by the complexity of modeling all processes occurring within a single farm, and by the loss of accuracy, which increases with the complexity of the system model.

Self-purification processes of natural water and their laboratory model

In this work, the processes of self-purification of natural water masses have been studied, and the possibility of laboratory modeling based on the obtained coefficient of the rate of self-purification of water K from pollutants has been investigated. The correlation between the phenol content and the physical factors of the selected sample was investigated. The calculation of the rate coefficient of self-purification of river water from a contaminant is carried out. The physico-chemical composition of surface waters directly depends on the hydrological regime of the river, which means that the model of self-purification processes can be applied under certain parameters of the studied rivers. On the model obtained during these works, various studies of the correlation of the physico-chemical composition of water from various hydrological parameters can be carried out. The basis of this study was the work of Soviet scientists in the field of mathematical modeling of physico-chemical processes in the natural environment of surface waters.

Research Project DN 12/11/December 2017-January 2022 financed by the National Science Fund at the Ministry of Education and Science: "Stochastic and Simulation Models in medicine, social sciences and dynamic systems"

The project "Stochastics and Simulations Models in the Medicine, Social Sciences and Dynamical Systems" is focused on the stochastics models and their application in the field of medicine, insurance, astrophysics and some simulation models applicable in social sciences and thermohydraulic processes. There are six work packages included in the research. The introduced models had been adapted to real data by three PhD students, two post-doctoral students and four Bulgarian scientists which are leaders in the field of mathematical modelling. The participants' research results are published in eight scientific papers with impact factor and thirty-six papers with impact rang. The results are approbated in more than twenty prestigious international conferences. As a good result of the participation three PhD scientific degrees and two scientific positions have been acquired.

Цифровые двойники в педагогическом моделировании

The article deals with the possibilities of using modern digital technologies in pedagogical activity on the example of digital twins. The change in the nomenclature of the scientific pedagogical specialty affects the approaches to the implementation of research. At the same time, education should be guided by trends and opportunities offered to society by scientific and technological progress. The digital technology proposed for study is actively used in industry and in the analysis of the behavior of social systems. A digital twin is a digital copy of a living or inanimate physical entity. In the hypothesis under consideration, the pedagogical model will be imitative, and its digital copy will be ontological. Based on the ontological model, we formulate the elements of the system, set mathematical parameters for it and translate it into machine language, prolong the model in time and space and get the result. The form of designing a digital twin of a pedagogical model is presented and described. Research in the field of mathematical modeling and synergetics served as the basis for building a hypothesis. A new approach to pedagogical modeling can serve as a basis for improving vocational education and designing the future professional activities of students.

In the Lab: Research and Development in the Field of (Renewable) Gas Processing Technology at DBI Group

DBI Group’s field of activity covers the complete process development of chemical processes, starting with the process balancing and testing of catalysts including the determination of catalyst-specific reaction kinetics, up to lifetime investigations, ageing tests and other reaction engineering investigations. With the data obtained, complex mathematical models can be generated which can be used for the design of reactors or the optimisation of operating regimes. In addition, the company also applies its know-how in the field of mathematical models in application-oriented simulations of thermal processing plants, heat exchangers and gas treatment plants. On the basis of these models, it designs demonstration plants which provide important design fundamentals and technical-scientific correlations for large-scale applications.

Cognitive approach in the implementation of local geodynamic monitoring

International practice shows that the most effective way to reduce the socio-economic consequences of natural and man-made emergencies is to prevent them. This prevention is based on constant monitoring of industrial facilities and provides information support for the procedures of decision-making to prevent such emergencies. Far years, higher requirements are placed on systems for monitoring, modeling, forecasting and managing emergencies. One of the possible solutions is the cognitive modeling – an approach based on new opportunities in the field of mathematical modeling, information technologies and telecommunications.

Analytical model for estimating the production and composition of gas resulted through gasification

For the modelling of gasification processes, several models have been developed over the years. It is remarked that gasification calculation models of very high complexity entail some complications. Therefore, simpler mathematical representations of gasification characteristics and process behavior are required as a first step in addressing such systems. The preliminary calculation simplicity is needed form two perspectives: First – the pre-sizing of gasification installations, and second – the estimation of experimental or functional results. For this kind of topics, an adequate simplified model should be defined. Further, to validate the results it will be necessary to use complex calculation models. The model proposed in this paper addresses gasification with distributive air in the air distribution current, considering general concurrent flow of air fuel. Previous successful investigations, conducted by the present research team, are taken into account within model definition stages. Thus, the work presented here provides useful advances in the field of mathematical modeling of gasification processes. The originality of the model consists in its easy computational accessibility, which allows the approach of technological optimizations, such as the variation of excess air and fuel composition.

Analytical review of modern studies of changes in the biotic components of the carbon cycle

The research on changes in the spatial-temporal dynamics of carbon in natural ecosystems on land is explored. The works of Russian and foreign authors on the analysis of the depositing ability of the cover are presented. Works on biomass reserves and primary production of biogeocenoses, research in the field of mathematical modeling of the carbon cycle in terrestrial ecosystems using remote sensing data are described. The article discusses modern approaches to mathematical modeling of productive processes and biological cycles of elements in plant ecosystems. The contribution of Russian and foreign authors to the spatial-temporal dynamics of carbon is analyzed. The research data in the assessment of the sequestration capacity of plant ecosystems, as the role of an ecosystem function, performing the function of a climatic ensemble of the state of the atmosphere is given. The various modeling-based methods for assessing and forecasting carbon stocks in forests, which have received international recognition, are presented, and the role of climate in managed forests in mitigating changes and predicting their carbon storage potential for the period up to 2050 under different forest management scenarios is examined. Among them: ISIS IIASA (Austria), EFIMOD + ROMUL (Russia), ROBUL (Russia), Information System for Determination and Mapping of Carbon Deposition by Forests (Russia, UGFTU), CBM-CFS3 (Canadian Forest Service), FORCARB2 (US Forest Service). The works based on the spatial model of the carbon cycle in the atmosphere - plant - soil system (A.M. Tarko) of the Computing Center of the Russian Academy of Sciences, used to assess the absorption potential in various regions of the world, are outlined.

Improvement of Bachelors' Professional Mathematical Competence in the Field of Modeling for Oil and Gas industry

<p>The study is devoted to improving the professional training of students in the field of mathematical modeling in the oil and gas industry. Deeper integration into the training of modern statistical methods and models is used to improve the educational efficiency and develop mathematical models of technological processes of the oil and gas industry. To test the proposed models, a pedagogical experiment with 189 students aged 19 to 21 is performed. The research is based on the November Institute of Oil and Gas in the Yamalo-Nenets Autonomous District. The outcomes of training under the new program are evaluated at three levels of competency formation in accordance with the university’s assessment systems. This approach ensures a level playing field for all respondents. The relevance of improving the competence of students in the field of mathematics is proved through the increase in grades at all three levels of competency formation.</p><p>The study describes in detail the system of profile differentiation of the mathematical training, which is based on a modular competency approach and compares various approaches and methods of professional competence formation among oil and gas workers.</p>

A generalized delta derivative on time scale with applications

Inspired by a well‐known “Hilger‐derivative” on time scale introduced by Stephan Hilger, we introduce a new derivative on the time scale, called “black delta (or in notation )‐derivative.” It is an adaptive unified approach of derivative of continuous and discrete calculus. Several important nontrivial results concerning this derivative are obtained. Also, a necessary and sufficient condition for the existence of this new derivative and its connection with Hilger‐derivative are discussed. In addition, a new general a‐exponential function (for fixed a ≥ 1) is introduced to obtain the unique solution of the initial value problem on time scales with this derivative. Furthermore, a relation between the a‐exponential function with the existing exponential function on the time scale is obtained. We elucidate the results by considering some interesting examples. We expect that this derivative will be applicable for future investigations on various studies in the field of mathematical modeling, engineering applications.

Mathematical modelling competence. Selected current research developments

Current research areas in the field of mathematical modelling are identified on the basis of specific research and development projects. Modelling cycles are an important theoretical basis for this. The measurement of students modelling competence as well as that of competence for teaching mathematical modelling with the help of written tests are key components. The investigation of different mathematical modelling tools, such as the use of technology in larger control group studies, and the evaluation of seminars in teacher education, are current lines of research in the field of modelling in mathematics education. Technology use in mathematical modelling is given special consideration. Overall, selected studies from Germany are used as examples to provide insight into the current research landscape.

Workshop on Incorporating Wildlife Compartments in FMD Simulation Modelling

An expert meeting, held in 2019, was organised between EFSA and FAO with the objective to discuss the integration of a wildlife compartment in the current EuFMDis model. Experts in the field of mathematical modelling, animal disease spread models, virology, veterinary epidemiology and animal health discussed i) features and structure of the current EuFMDis model ii) EFSA's models used on spread of animal diseases and simulation modelling iii) ENETWILD project and interface between domestic populations (e.g. pigs) and wildlife (e.g. wild boar) iv) available data sources for simulating spread and control of FMD in different wildlife species and iv) EFSA's SIGMA project (standardised data collection). It was concluded that the addition of a wildlife spread component in the EuFMDis is a priority in order to evaluate contingency plans associated with wildlife. Two scenarios were proposed, and key issues were identified to integrate the wildlife spread component in the EuFMDis model. It was concluded that control measures may be parametrised for FMD and maybe for other diseases, but available data are limited.

Computer Simulation of a Group of Mobile Robots in Special Software Tools

The problem of controlling a group of special robots for application in the high-risk conditions (for example, for fire extinguishing, search for hazardous substances, or elimination of consequences of emergencies) is solved. According to the task, robots operate in the industrial and urban environment, i.e., the movement of robots is planar. Various strategies of group interaction between robots are analyzed; a literature review is conducted. Due to the task specifics, a decentralized management strategy has been selected. For solving the problem, a movement algorithm of a group of mobile robots with a subsequent visual check of the resulting algorithm operation is proposed. Implementation of the algorithm’s work is performed in the MATLAB environment. For preliminary algorithm verification and modeling of various dangerous cases, a model of robot group using the Mobile Robotics Simulation Toolbox of MATLAB was made. For a more detailed and accurate analysis of the real robot’s behavior, a model in the ROS package has been developed. That model interacts with the developed algorithm through the ROS Toolbox package of MATLAB. This software can be used for the training of engineering staff in the field of mathematical modeling, group control, and multi-agent systems. As a result of verification, the program and the model successfully solve the task. Yet, the model in the ROS package requires greater computational power because of the large number of complex calculations.

ИНФОРМАЦИОННО-ЭКОНОМИЧЕСКИЙ ПОДХОД ДЛЯ ОЦЕНКИ НЕФТЕГАЗОВЫХ ИНВЕСТИЦИОННЫХ ПРОЕКТОВ

A modern assessment of the technical and economic efficiency of the oil and gas project involves the construction of a specific economic and mathematical calculation model, as well as an analysis of project criteria based on a set of predicted technological indicators for the formations and the field as a whole. An automated system developed for this purpose served as the basis for theoretical and applied research in the field of mathematical modeling and modern digital technologies.