Application Of Mathematical Methods Research Articles

Margarita Vladimirovna Zhilinskaya — pediatrician and scientist (on the 100th anniversary of her birth)

The article is devoted to the life and scientific career of Margarita Vladimirovna Zhilinskaya, Doctor of Medical Sciences, Professor, head of the first department of computer diagnostics in pediatrics in Russia and the USSR created in 1970 on her initiative. For 5 years before that, she was the Chief Freelance Pediatrician of the Ministry of Health of the RSFSR. The new area of activity was a continuation of research on the application of mathematical methods in clinical work. The department actively developed and implemented methods for planning research, assessing the informativeness of signs, multiple connections of signs in the analysis of the pathogenesis of diseases, for which the method of correlation pleiades was developed. The main paradigm in as early as the beginning of the department’s activity was a comprehensive quantitative assessment of the conditions of the child’s organism, mathematical analysis of risk factors and the formation of risk groups for diseases in children on this basis. At the same time, computer programs were created for differential diagnosis and evaluation of treatment effectiveness. Employees of the department conducted comprehensive research in the field of developing computer systems for rapid and in-depth analysis of infant mortality. For the first time, a mathematical apparatus was implemented to quantify the contribution of qualitative characteristics to the outcome of the disease. Research conducted under the scientific guidance of M.V. Zhilinskaya in 1970–1979 laid the ground for the subsequent creation of an automated system for clinical examination of pediatric population and numerous systems for disease diagnosing.

Analysis of mathematical methods for diagnosis of breast diseases

This paper analyzes the diagnosis of breast diseases is a critical aspect of modern healthcare, as early detection can greatly improve patient outcomes. Mathematical methods have increasingly been utilized in recent years as a means of aiding in the diagnosis of breast diseases. This abstract provides an analysis of the various mathematical methods that have been developed and applied to this important area of medical research. The methods include but are not limited to artificial intelligence (AI), machine learning, and statistical modeling. The strengths and limitations of these approaches are examined, as well as their potential impact on clinical practice. Furthermore, the abstract will discuss the current state of research in this field and offer insights into future directions for the development and application of mathematical methods in the diagnosis of breast diseases. Keywords: mathematical methods, breast diseases (BD), mastopathy, fibroadenoma, risk factors, X-ray devices, ultrasound examination (USE).

Трансдисциплинарный подход к изучению музыкальных явлений: теория информации и её воздействие на различные области музыкознания

At the present time, the application of mathematical methods in musicology, as well as the examination of the entailing facts of indeterminacy in the system of musical thinking are some of the most actively developing directions in the sphere of humanitarian disciplines, becoming important tools of cognition and interpretation of the semantic structures of all temporal arts, including the art of music. This article presents a continuation of the multicomponent complex research carried out by its authors, aimed at identifying the issues related to the use of a transdisciplinary approach, comprising an effectual foundation for a qualitative and quantitative evaluation of musical phenomena with the use of the resources of present-day musical computer technology, including the factors of indeterminacy in music researched with the aid of these technologies. Special attention in the article is devoted to the mathematical theory of information and its impact on various spheres of musicology. Musical computer technology, the use of which stipulates the possibilities of creation of new technological and experimental-practical means of music studies, may also be used upon the construction of music theory systems applicable to the sphere of musical education. It becomes an active instrument of research devoted to the problem range of trans-disciplinarity as a principle of organization of academic knowledge, presuming the interaction of many directions of scholarly research upon the solution of complex problems of musicology. The present-day level of development of musical computer technology makes it possible to examine use as an effective basis fo the creation of multicomponent complexes of hardware-software programs, which may be applied in the process of construction of intellectual systems of analysis and cataloguing of the music of the peoples of Russia and the whole world. The authors of the article illuminate the project of development of a Russian Electronic Musical Instrument undertaken by the associates of the scholarly-methodological laboratory “Musical computer technology” of the Herzen State Pedagogical University of Russia, relying on materials created with the participation of specialists who possess various methods and tools of a transdisciplinary approach towards the study of musical phenomena and endowed with the experience of developing contemporary musically directed programmatic means in both the sphere of the technology of their application for carrying out scholarly research and in the process of the realization of new professional directions in musical education.

MATHEMATICAL METHODS IN CYBER SECURITY: CLUSTER ANALYSIS AND ITS APPLICATION IN INFORMATION AND CYBERNETIC SECURITY

The huge number of information threats and their complexity prompts research and modeling of new methodologies and information protection systems. The development and improvement of information and cyber security systems includes the creation and processing of mathematical models using information technologies. This article is a follow-up study on the application of mathematical methods and technologies in cyber security, namely: methods of cluster analysis. The modern development of computer technology and the growth of their power have contributed to the wide implementation of Data Mining algorithms for processing large volumes of information in various fields of society and science, in particular in the field of cyber security. Cluster analysis allows the set to be divided into subsets, so that the elements of each subset are similar to each other, and the elements of different subsets are the most different. This provides an opportunity to eliminate the shortcomings of the qualitative approach in assessing information risks. The paper reviews scientific sources regarding the applied aspect of the application of clustering methods in security systems, because timely forecasting of possible incidents allows you to manage information risks and make effective decisions to ensure confidentiality, availability and integrity of information. The stages of the clustering procedure are characterized, the issues of choosing the distance measure and the similarity measure for the objects under study are highlighted. The comparative characteristics of the most popular methods of cluster analysis are presented: the “nearest neighbor” algorithm, “k-means”, “fuzzy c-means”, “cosine similarity”, their advantages and disadvantages are defined. This study can be useful and used in the educational process of students of the specialty 125 “Cyber security and information protection”.

Inovatyvių analitinių ir statistinių technologijų, kaip kovos su korupcija priemonės, įgyvendinimo kryptys

Relevance of the topic. The article sets out to explore the potential of innovative analytical and statistical technologies in monitoring, detecting, and counteracting corruption within state systems. The central objective is to clarify key concepts, determine the nature and content of these technologies, and analyse their applications in anti-corruption efforts. The research methodology combines the scrutiny of official documents, legislations, public authority websites, and software providers with a focus on their anti-corruption capabilities. The study reveals that analytical and statistical technologies constitute a specific form of information technology, embodied in functional information systems that fulfil organisational objectives and assist in decision-making processes. They assist primarily in the identification and prediction of probable cases of corruption or fraudulent activities, utilising mathematical methods and advanced analytical algorithms. Key areas where these technologies can significantly contribute include data collection and processing, communication and office processes, general management processes, decision-making processes, and expert systems development. The problem. Corruption remains one of the largest socio-economic issues affecting a country’s development and undermining citizens’ trust in governing structures. Innovative analytical and statistical technologies such as artificial intelligence, machine learning, big data analysis, and others, hold the potential to provide effective monitoring and detection of corrupt schemes. The purpose of this article is to determine the directions for implementing innovative analytical and statistical technologies as a tool for monitoring, detecting and counteracting corruption in the state. Research object: Application of innovative analytical and statistical technologies in the fight against corruption. The results. Innovative analytical and statistical technology is a type of information technology, which is embodied in the form of a functional information system aimed to fulfil organisational objectives and assist in decision-making processes. These technologies are considered essential tools for countering corruption at the state level, primarily by identifying and predicting probable cases. The application of mathematical methods and advanced analytical and statistical algorithms can reveal inconsistencies and potential corruption or fraudulent activities. Counteracting corruption has also benefitted from advancements in information technologies. Currently, efforts to counter corruption focus on digital government services, crowdsourcing platforms, transparency portals, big data, and artificial intelligence. In this context, there are five key areas where analytical and statistical technologies can contribute: data collection and processing, communication and office processes, general management processes, decision-making processes, and the development of expert systems. Keywords: corruption counteraction, artificial intelligence, machine learning, information

Mathematical Modeling in Development and Improvement of Methodological Basics of Criminology

The article deals with the application of mathematical methods in criminological research and the applicable significance of these processes, which is, in general, developed scientific problems, requiring reassessment in modern conditions of development of mathematical modeling theory and information technologies, the technologization of science and the state of criminological theory. The scientific approaches announced today on the use of mathematics as the language of social sciences and their basic methodology need to be analyzed. Criminometrics is assessed ambiguously, the integrated industry has not received significant development and testing of findings directly in the criminological context. Certain studies on the measurement of crime dynamics, the degree of interaction of criminologically significant processes represent to a greater extent the application of mathematical modelling methods. Other methods of econometrics in solving private or group scientific problems are not used in practical crime prevention. The measurement of the level of statistically significant relationships having criminological significance is carried out mainly by area specialists in the sphere of econometric and mathematical knowledge application that is logical from the methodology viewpoint, since the system analyst able to apply an econometric approach is the presence of specific training. There are no interdisciplinary studies using the integrative criminological and mathematical potential of these sciences.

The modern mathematical models in economics and finance

With this article, we open a new section in this journal: the application of mathematical methods in economics and finance. A few topics we would like to discuss to get started are corporate finance, investments, business valuation, taxation, and ratings. We describe shortly mathematical models in these areas. In the field of corporate finance, we discuss the foundations of two main theories of capital structure, the Modigliani-Miller and the modern theory of Brusov-Filatova-Orekhova (BFO theory). We compare them and describe the differences between them and their results. In the field of investments, we describe two modern investment models: (1) with debt repayment at the end of the project and (2) with uniform debt repayment and discuss their properties and applications. In business valuation, we discuss the problems that exist in this area and ways to solve them. In rating methodology, a new approach is devoted to the rating of non–financial issuers, as well as to long–term and arbitrary duration project rating. The key factors of a new approach are the adequate use of discounting of financial flows virtually not used in existing rating methodologies, and the incorporation of rating parameters (financial "ratios") into the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory). This article is devoted to the analysis of the theoretical mathematical methods and models based on first principles. The novelty of this consideration is due to the fact that we are considering and discussing recently developed mathematical models in economics and finance.

Affordable and Easy Data Exploration of NIR Spectra Using Chemometric Techniques

The pharmaceutical industry relies heavily on analytical techniques for identifying and characterizing drug compounds. In this experiment, undergraduate pharmacy students explored the applications of near-infrared spectroscopy for pharmaceutical analysis and its potential for identifying patterns and relationships among pharmaceutical samples. In addition, they were introduced to the chemometrics field using classical pretreatment and data exploration methods. To reduce the need for expensive instrumental equipment, we have developed a small and affordable device based on the DLP NIRscan Nano EVM by Texas Instruments using free software solutions and a 3D-printed case for Raspberry Pi single-board computers. The goal of the experiment was to guide students through all the necessary steps for measuring and analyzing samples using NIR spectroscopy and to encourage their learning through the application of mathematical methods in a defined laboratory setting.

Comparison Of Euler Method And Runge Kutta Method In Estimation Of The Number Of Population In Aceh Province

Residents are people who are in an area and are controlled by applicable rules and interact with each other Residents are people who are in an area and are bound by applicable rules and interact with each other continuously or continuously. If population growth increases, this will cause many problems, including: poverty levels, unemployment, school dropout rates and increasing crime rates in each region. In anticipating the problem of increasing the population of Aceh Province, information about the population is needed. Therefore, this study will discuss several applications of mathematical methods in estimating the population of Aceh Province in the coming year using the Euler method and the Runge Kutta method of order 4. The results of the estimation of the population of Aceh Province using the Runge Kutta method are 5.030.503 inhabitants in 2021, 5.076.307 in 2022 and 5.122.486 in 2023 The estimation results using the Euler method are 5.026.162 in 2021, 5.071.745 in 2022 and 5.117.700 in 2022. The conclusion in this study is that estimation using the Runge Kutta method is a method that is better applied than the method Euler on the problem of estimating the population of Aceh Province. This is because the error value of the Runge Kutta method is smaller than the Euler method with an error value of about 0.04%. Key words : Runge Kutta, Euler, Population.

Application of mathematical methods and machine learning algorithms for classification of X-ray images

The relevance of the topic, in particular, if to take one of the information flows, whether it is the action of a human factor or a specific object, then it is true that special processing of the machine learning language and automatic information output significantly optimize human life. With the help of neural networks and their chest radiography is one of the most accessible radiological studies for screening and diagnosis of many lung diseases a special machine learning language is to study the flow of information about it and the same object in real time using neural networks. The article describes the terminology of the problem of X-ray recognition using machine learning methods and algorithms, examines the relevance of the problem, and analyzes the current state of the problem in the field of X-ray recognition. The aspects of the problem being solved, identified during the analysis, in the form of solved problems, approaches, methods, information technologies used, tools and software solutions to the problem are noted The paper is devoted to the description of a modified method of fuzzy clustering of halftone images, which at each iteration performs a dynamic transformation of the source data based on a singular decomposition with automatic selection of the most significant columns of the matrix of left singular vectors. The results of experimental studies were obtained by processing X-ray images. As a result of testing a neural network model, in the output layer of which a sigmoidal activation function was used to activate neurons, and an algorithm was used as an optimization method, the best values of accuracy and completeness were obtained: accuracy – 94.2 During testing, the neural network showed an accuracy of pneumonia recognition equal to 94,27 %

Evaluating Impact with All Rigor Possible. Applicability of Mathematical Methods in Measuring Social Impact (Exemplified by the Health Insurance Subsidy Program)

Increasing incomes, improving the education system, reducing morbidity are important areas of impact investment. Whether these changes will actually be achieved is the key question for an investor deciding on a social technology or project to invest in. However, the leaders of social projects and programs often focus on measuring the immediate outputs rather than on assessing whether projects and programs have had the expected impact. In this article, we would like to highlight the experience of evaluating the impact of the Health Insurance Subsidy Program (HISP) and describe approaches that can be used to address this and other similar problems.

About Modeling Digital Twins of a Social Group

The object of the study is mathematical modeling methods. The subject of the study is the application of mathematical methods in modeling digital twins of a social group. The aim of the work is to model the digital counterparts of a social group. A digital double is a digital copy of a physical object or process, with the right approach, it helps to improve the main and auxiliary business processes. This concept is part of the fourth industrial revolution and is designed to help detect problems faster, find out what will happen to the original in different conditions and, as a result, produce better products. In this article, some applied aspects are considered, the main provisions of the mathematical theory of digital twins of social groups are presented. To solve the problem of creating a digital double of a social group (students) as one of the tools, the authors proposed to use the technologies of population algorithms. The novelty of the research consists in the application of the swarm part algorithm for modeling digital twins of a social group. The particle swarm method was chosen as a research tool. As the social group under study finds the optimal position in space, so the element of the digital twin of the particle swarm model based on them can search in space, in particular, the extremes of functions. Which, for example, is applicable to finding the minimum of the loss function in machine learning. A graphical simulation in the Java Script language was performed using the three library.js. Data processing was performed using the C# Job System, which provides parallelization of computing processes and is integrated into the Entity Component System. A program was implemented that simulates the activity of a student group as one of the constituent elements of a digital twin of a social group. Swarm algorithms are promising in the field of practical application. On their basis, it is possible not only to solve the problems of digital twins, but also to manage groups of robots, robotic systems and complexes.

Determination of Technological Parameters of Fiber Separation Device from Cotton Waste

This article examines the technological parameters of the device for the separation of fibers suitable for spinning by processing fibrous waste from the technological processes of ginneries. Technological processes in the cotton ginning industry include a complex of physical and mechanical advantages, the successful study of which is possible only with the use of modern achievements in science and technology. Therefore, it is advisable to conduct scientific research based on mathematical modeling. To justify the effective operation of the selected design of the cotton fiber separation device, it is necessary to select its optimal technological parameters. Improving the efficiency of the process of separation of spinning fibers from the composition of fibrous waste depends directly on technological parameters. The application of mathematical methods in the planning and conduct of research allows for determining the individual effects of the interaction of several factors that characterize the combined parameters of the optimization parameters, in contrast to traditional computational methods of research. As a result, it will be possible to obtain a mathematical model of the object understudy in a relatively small number of tests, which will simultaneously serve to obtain optimal solutions.

MODERN PROBLEMS OF APPLYING MATHEMATICAL METHODS IN THE ASPECT OF ECONOMICS

The penetration of the mathematical apparatus into the economy created the basis for the development of methods of economic analysis, econometrics, mathematical programming, economic statistics, etc. Today, the interpenetration of different branches of knowledge continues, in particular, the application of mathematical methods in the natural and social sciences and in the economic sphere. Among mathematical methods of data processing are polynomial, linear, quadratic, trigonometric, exponential and combined dependencies, differential and algebraic equations. The statistical processing of data from the evaluation of the structure and dynamics of the phenomenon has gone in the direction of correlation analysis and forecasting. The deep penetration of mathematics into specific sciences and the success achieved through a combination of methods from different branches of knowledge is described by many researchers. The possibilities of applying mathematics are increasingly being explored in areas of knowledge where phenomena are poorly structured and characterized by the high complexity of sociology, political science, management and economics. The article presents a retrospective analysis of the development of scientific and applied research concerning the process of mathematics of science and the possibilities of using mathematical methods in economics in particular. Problems and constraints encountered in applying mathematical methods in economic research have been identified. Measures have been identified to ensure the adequacy of the development of economic and mathematical models from the standpoint of approaches to their construction, the improvement of management processes and the improvement of the training of specialists in economic fields.

Construction of abundant novel analytical solutions of the space–time fractional nonlinear generalized equal width model via Riemann–Liouville derivative with application of mathematical methods

Abstract The space–time fractional generalized equal width (GEW) equation is an imperative model which is utilized to represent the nonlinear dispersive waves, namely, waves flowing in the shallow water strait, one-dimensional wave origination escalating in the nonlinear dispersive medium approximation, gelid plasma, hydro magnetic waves, electro magnetic interaction, etc. In this manuscript, we probe advanced and broad-spectrum wave solutions of the formerly betokened model with the Riemann–Liouville fractional derivative via the prosperously implementation of two mathematical methods: modified elongated auxiliary equation mapping and amended simple equation methods. The nonlinear fractional differential equation (NLFDE) is renovated into ordinary differential equation by the composite function derivative and the chain rule putting together along with the wave transformations. We acquire several types of exact soliton solutions by setting specific values of the personified parameters. The proposed schemes are expedient, influential, and computationally viable to scrutinize notches of NLFDEs.

USING A FUNCTION DERIVATIVE IN ECONOMIC TASKS

The article focuses on the application of mathematical methods in economics, in particular discussing economic problems that are easily solved using derivatives. The purpose of the article is to show students the way and opportunity to use mathematical methods to solve economic problems. To this end, the article discusses and analyzes several economic tasks in detail, which will be interesting and easy for students to master. I considered the derivative of a function as the rate of change and introduced the definition: The instantaneous rate of change of the function f with respect to x at a point is called the derivative if it exists. With the help of this definition I have discussed and explained Task 1: Suppose that the increase in production of a certain product over a period of time is described by a function And population growth is described by the following function: Where is the number of years from the initial period, then the production of these products per capita is given by the function: Find the growth rate of product production. By solving this task I came to the conclusion that after a year the production of products per capita increases. In the following tasks I used the method of finding the extremum values of a function using a derivative, namely I equated the first-order derivative to 0, found the critical points, and with the help of the second-order derivative I determined the extremes of the function. I discussed task 2: For the production of X volume of products, the firm plans a cost that is calculated by the formulan . For what volume of production will the average cost be the smallest? Find the numerical value of this small expense. Solving this problem, I came to the conclusion that the given function of the average cost takes on the least value when the output volume is a unit , and this value is equal to: which is the marginal cost when producing the volume output. I discussed Task 3: How many products should be sold in order for a firm to profit maximally if the derivative cost function is known: And return function: Here I came to the conclusion: if 600 units of the product are sold, then the firm's profit will be maximum and it will be numerically equal At the end of the article I discussed such a task 4 of applied optimization. What is the minimum amount of material needed to make a 2 liter cylindrical jar? Where I came to the conclusion: the smallest amount of material will be spent to get a cylindrical vessel if we take the height 2 times the radius of the base.

Application of Mathematical Methods to the Study of Special-Needs Education in Spanish Journals

This research analyzes the written production on special-needs education in Spanish high-impact journals indexed in the Journal Citation Reports (Web of Science). Its objective is to show the status of this issue in the past 20 years based on updated and relevant information that contributes to the development of the discipline itself and to improving special-needs education. A total of 1201 special-needs education documents published in 15 high-impact journals were analyzed. The results evince the development of this discipline and the principal subjects of study and other relevant aspects associated with this field of knowledge. This research allows for reinforcing the body of knowledge in this field of study, which would be far-reaching for researchers and education administrators alike.

Fractal geometry and design of modern structures

One of the main directions in the application of mathematical methods in construction - is to create the complex objects using simple algorithms of fractal geometry with the use of computer technology. The use of fractal geometry methods to describe real systems, in particular, in the development of the architectural appearance of the city and the design of modern structures of the most amazing shape, will allow solving the problems of research and forecasting the urban environments development.

Совершенствование системы планирования производственной деятельности нефтеперерабатывающих предприятий Группы ЛУКОЙЛ

The paper reviews the issue of the economic and mathematical method application, in particular, the planning systems based on linear programming in improving the efficiency of the enterprise management. The complexity of the task of optimizing the production program of oil refining and petrochemical companies, the solution of which requires taking into account many factors, is noted. A list of LP model improvements at LUKOIL Group refining facilities is provided. The promising trends of corporate linear programming tools implementation are described.

Optimisation of repair and maintenance costs for electrical equipment in agricultural enterprises

Application of mathematical methods of cost optimization for repair and maintenance of electrical equipment of agro-industrial enterprises is one of the important and promising directions for increasing the efficiency of electrical equipment operation management in agriculture. Mathematical programming systems use graphical and related attributive information in solving optimization problems. As graphical information in these systems we used maps, plans, diagrams, schedules of preventive measures from which the list of equipment for certain types of repair and maintenance, their labor intensity for individual objects, types of equipment and in total for the enterprise are established. Databases of electrical equipment are used as attributive information to describe electrical equipment of agro-industrial enterprises. Due to joint processing of graphical and attributive information in optimization systems, all stages of work with spatial data are more operative. Beginning from spatial data search, selection and analysis we can make a specific decision during the operation control of electrical equipment. This article considers maintenance and repair operation (MR) as a task of mathematical programming with cost optimization and deals with three approaches to the organization of this task. The expediency of using each method of solution is analyzed. The structural schemes, equations describing mathematical models, advantages and disadvantages of the presented models are given. We marked prospect of using linear programming programs for the decision of the given optimization problem by means of the inverse matrix method, i.e. the modified simplex method and computing algorithm with a standard sequence of operations.