Mathematical System Research Articles

MagnetoShield: A Novel Open-Source Magnetic Levitation Benchmark Device for Mechatronics Education and Research.

This article presents an open-source device illustrating the well-known magnetic levitation experiment. The uniqueness of this particular device lies in its exceptionally small dimensions, affordability and availability, which makes it a perfect design for take-home experiments for education but it can also serve as a referential design for testing various control algorithms in research. In addition, this paper provides a comprehensive hardware design for reproducibility along with the detailed derivation of the mathematical model, system identification and validation. Moreover, the introduced hardware comes with an easy-to-use open-source application programming interface in C/C++ for the Arduino IDE, Simulink and CircuitPython. REXYGEN, another environment similar to Simulink, had also been used to demonstrate the capabilities of the MagnetoShield.

Numerical study of a new time-fractional Mpox model using Caputo fractional derivatives

This study examines the new time-fractional model for Mpox, utilizing Caputo fractional derivatives, specifically focusing on pregnant individuals. The fractional variational iteration method (FVIM) is used to compute a numerical solution for this model. The results of the convergence investigation indicate that the solution obtained exhibits positivity and possesses a well-defined limit. The study yielded significant insights into the intricate dynamics of Mpox viral transmission in pregnant women, affirming the dependability and strength of the Caputo fractional variational approach in forecasting the progression of the illness. The novelty lies in demonstrating how fractional derivatives can capture memory effects in the spread of disease; it provides a more enhanced understanding of the dynamics. Moreover, the suggested model incorporates the notion of optimal control inside different mathematical systems, such as the Fornberg-Whitham equation and the Newell-Whitehead-Segel equation. The convergence of the model described in this study offers empirical support that validates the dependability and suitability of the proposed methodology.

Numerical investigations of the fractional order derivative-based accelerating universe in the modified gravity

In this work, a Liouville–Caputo fractional order (FO) derivative for the mathematical system based on the accelerating universe in the modified gravity (AUMG), i.e. FO-AUMG is proposed to get more accurate solutions. The nonlinear dynamics of the FO-AUMG is classified into five dynamics. The performances of the designed nonlinear FO-AUMG are numerically stimulated with the stochastic procedures of Levenberg–Marquardt backpropagated (LMB) scheme-based neural networks. The statics for FO-AUMS is used for the nonlinear FO-AUMG as 72%, 16% and 12% for training, authorization, and testing. Twenty neurons in hidden layers have been used to approximate the solution of the nonlinear FO-AUMS. The comparison of three different cases of the nonlinear FO-AUMS is performed with dataset generated by Adams method. To validate the uniformity, legitimacy, precision, and competence of LMB-based adaptive neural networks, the outcomes of the state transitions parameters, regression, correlation, error-histogram plots have been exploited.

Research on Teaching Quality Evaluation Model of Higher Mathematics Based on Hierarchical Analysis Approach

Abstract The teaching quality of higher mathematics courses plays a pivotal role in the cultivation of students’ quality and the improvement of their abilities. In this paper, information entropy is added to the hierarchical analysis method to improve it and then combined with the fuzzy synthesis method to construct a model for evaluating the quality of mathematics teaching. The higher mathematics teaching course at a university is selected as the research object, and the constructed model for evaluating the quality of higher mathematics teaching is applied to the teaching of higher mathematics in classrooms. The evaluation index system for higher mathematics teaching quality is established by combining relevant literature, and the improved AHP is used for weighting. Then, the index data is collected through questionnaires to analyze the differences and assess the teaching quality of different genders and majors and then to propose strategies to improve the teaching quality of higher mathematics. The significant effects of teaching methods (0.184), teaching effectiveness (0.176), and teaching content (0.170) on the teaching quality of higher mathematics were revealed. The quality of teaching higher mathematics in the sample universities is located at a good level with scores between 8 and 9 on each evaluation index, with the best performance of 8.934 for teaching content. The evaluation model for higher mathematics teaching quality established by the research has validity and feasibility.

Математические модели поддержки управленческих решений по снижению уровня пожарной опасности в административно-территориальных единицах Вьетнама

Purpose. The article classifies and analyzes significant factors affecting fire situation and fire risks in the administrativeterritorial units (ATUs) of Vietnam from 2019 to 2022. Based on this data, mathematical models have been developed to show the relationship between fire risks and influencing factors. Optimal managerial decisions have been formulated to reduce fire risks and the level of fire hazard in Vietnam's ATUs based on the obtained models. Methods. Methods of mathematical statistics, systems analysis, and mathematical modeling were used. Findings. The study analyzed statistical data and developed three multiple regression mathematical models showing the dependence of fire risks on significant factors. Research application field. The results of the study can be used to support managerial decisions to ensure fire safety in Vietnam. Conclusions. The analysis of various significant and less significant factors affecting fire situation draws attention to specialists in fire prevention. The developed mathematical models have a sufficiently high level of adequacy and significance. The application of the managerial decisions derived from these models had a positive impact on reducing fire risks and the level of fire hazard in ATUs. Specifically, the risk of human fatalities in fires (Rf) decreased by 22.1%, the risk of injuries from fires (Ri) decreased by 14%, and the risk of direct fire damage (Rd) decreased by 16.1%. The obtained research results enable the improvement of managerial decisions in fire safety operations and reduce fire hazard levels across the country's territories.

Applied mathematics in today’s education system in India

Applied mathematics plays a pivotal role in today’s education system in India, offering a dynamic approach to learning that bridges the gap between theoretical knowledge and real-world applications. This paper explores the significance and integration of applied mathematics within India’s contemporary education landscape. It delves into the evolving pedagogical strategies, curriculum enhancements, and the practical implications of applied mathematics in fostering critical thinking, problem-solving, and innovation among students. The first section of this paper provides an overview of the traditional mathematical education system in India and highlights the growing demand for applied mathematics skills in various industries. It emphasizes the need to adapt to the changing educational landscape by incorporating applied mathematics to equip students with practical abilities that align with modern workplace requirements. The second section explores the challenges and opportunities in implementing applied mathematics in Indian schools and higher education institutions. It addresses curriculum design, teaching methodologies, and the role of educators in making mathematics education more application-oriented. It also discusses the potential impact of applied mathematics in nurturing a workforce capable of addressing contemporary societal challenges. Furthermore, this paper examines the role of technology in facilitating applied mathematics education, with a focus on digital tools, simulations, and online resources that can enhance the learning experience. It emphasizes the importance of digital literacy and the integration of technology in mathematics classrooms. The final section assesses the outcomes and potential benefits of integrating applied mathematics in the Indian education system. It considers the impact on students’ problem-solving skills, employability, and their ability to contribute to research and innovation in STEM-related fields.

Design and Assessment of a Personalized Online Mathematics Learning System with Self-Regulated Learning Features: An Educational Design Research

A personalized online learning system incorporating a self-regulated learning approach was developed to deliver the factorization in quadratic polynomials topic on mathematics learning. This system created four learning materials for learning a certain topic in mathematics, corresponding to the students’ characteristics. This study followed the education design research approach to develop a self-regulated-based personalized online learning system and evaluate the system from a technology acceptance perspective. The Pearson correlation was computed and revealed the best fit of the collected data for further stepwise multiple regression analysis through students’ acceptance of learning mathematics before and after using the developed system. Furthermore, the Chi-square test was performed to determine the acceptance change and frequency rated by items to ensure an in-depth understanding of how acceptance changed before and after. Although the findings revealed that students’ perceived ease of use was primarily a predictor of their attitude about the system, they showed an increment in perceived usefulness after participating in the developed system. The students’ perceptions of ease and attitude toward the self-regulated-based personalized online learning system for mathematics learning should be mainly considered in further development, including the different learning approaches for supporting mathematics learning.

ГАРВАРДСКИЙ ЭКОНОМИЧЕСКИЙ БАРОМЕТР (ЗАРУБЕЖНЫЙ ОПЫТ ПРИМЕНЕНИЯ БАРОМЕТРИЧЕСКОГО МЕТОДА В ЭКОНОМИКО-МАТЕМАТИЧЕСКОМ МОДЕЛИРОВАНИИ)

The creation of the Harvard Economic Barometer represents the most interesting experience in building early economic and mathematical systems for analyzing and forecasting economic development. Its successful implementation and functioning for more than two decades was due not only to Prof. Warren Pearson, who harmoniously combined a deep understanding of the laws of economic dynamics with a focus on practical results, but also to the turbulent period of development of American capitalism, which created a market demand for relevant scientific developments. The presented article contains the history of the Harvard Barometer, a review of its functioning principles, as well as an analysis of the reasons for failures in its work, which caused the fading interest of the scientific community in the use of the barometric method in economic modeling.

Analysis of the Agroecological Behavior of Family Farmers in Nova Friburgo (Brazil) and Mendoza (Argentina), Based on the Application of Fuzzy Logic

The analysis of agroecological behaviors, based on indicators using a mathematical system to support decision-making, is something very unusual in academia. Therefore, we propose the use of indicators that take into account the qualitative and quantitative nature. The hypothesis assumes that information expressed through natural language, proposed in fuzzy logic, can lead to a better adaptation of data processing from informants. The comparative perspective addresses the environment and human beings, with their customs and productions in Nova Friburgo (Brazil) and Mendoza (Argentina), and uses fuzzy methodology, in order to facilitate modeling and make the problem solution more viable and realistic for several complex problems, involving many variables. As a result, we have a model that can analyze and identify which factors (peasantry, sustainability, social organization and rural development agency) and respective indicators make the greatest contribution to the adoption of agroecological practices. Encouraging decision makers and policymakers to strategically reflect on scenarios, in the context of the agroecological transition, is fundamental and can be facilitated by implementing an innovative monitoring and evaluation approach.

FEATURES OF THE APPLICATION OF THE SCILAB MATHEMATICAL PACKAGE IN THE PROCESS OF TEACHING THE DISCIPLINE «HIGHER MATHEMATICS»

The article notes that the choice of software is of great importance in teaching the discipline «Higher Mathematics». The complexity and type of tasks to be solved depend on the functionality of the selected program. It is emphasised that the methods of approximate, primarily numerical, solution are used. The methods of numerical solution of mathematical problems have always been an integral part of mathematics and have always been part of the content of natural-mathematical and engineering education. This article uses the Skilab math package as software. It is a multi-functional package designed for performing engineering and scientific calculations, which allows you to perform complex algebraic calculations, solve problems of differentiation and integration. All this contributes to the successful use of the Scilab mathematical package in the process of teaching the discipline «Higher Mathematic». The author draws attention to the fact that Skilab is a computer mathematics system designed to perform engineering and scientific calculations, such as: solving nonlinear equations and systems; solving linear algebra problems; solving optimization tasks; differentiation and integration; processing of experimental data (interpolation and approximation, method of least squares); solution of ordinary differential equations and systems. Skilab provides wide opportunities for creating and editing various types of graphs and surfaces. The Skilab system contains a sufficient number of built-in commands, operators and functions, and its distinctive feature is flexibility. The user can create any new command or function and then use it alongside the built-in ones. The article states that the use of modern mathematical packages significantly increases the intensity of cognitive activity, raises the level of mathematical preparation, improves the knowledge control system, and promotes learning motivation. The perspective of the development of the study of the use of mathematical packages is the development of a database on the issues of their use during the educational process, which should take into account the professional orientation of future activities. This approach provides a more effective application of interdisciplinary connections, which contributes to the in-depth study of the material and the expansion of opportunities for independent learning.

Man-Power-Amplifying Exoskeleton with Pneumatic Actuator

This study describes the activity of developing a force amplifier exoskeleton with one degree of freedom. The system was developed as a research prototype to conduct control system studies. The device consists of an arm with a pneumatic cylinder actuator controlled by a pressure regulator. As for the human–machine interface, the system has a force sensor. The idea is to verify the possibility of developing a simple system from the sensor system’s point of view and the control system’s architecture while simultaneously obtaining an effective, economical, and reliable device. The idea developed in this project is to use the user’s available ability to control movements in unknown environments. The user constitutes the central part of the entire control system: he defines the references for the speeds and forces to be applied to the environment and observes the rates of the controlled robotic system through his own sight and proprioceptive system. On the other hand, the machine produces and controls the forces applied to the environment by the actuator. In this way, the device shows an increased admittance. A mathematical system model was created to verify the idea’s feasibility. Following the results of the simulations, a prototype was built on which experimental tests were carried out. As stated above, it was possible to obtain the described behavior with the use of a force sensor, one-axis type, interposed between the machine and the user, to constitute the human–machine interface; using a pressure regulator, it was possible to avoid the sensors for the force feedback by the environment. The result is a simple architecture for the sensors and the control algorithm. Specific test protocols were proposed to test the performance of the human–machine “system”, and a test bench was developed that allows the tracking of variable signals represented on a monitor, which the user must follow. The system is intuitive to use, with a rapid learning curve, and the user can handle high loads according to the different signals to be followed with good precision, even at high speeds.

Optimal Configuration of Hybrid Energy Storage Capacity in a Grid-Connected Microgrid Considering Laddering Carbon Trading and Demand Response

In order to enhance the carbon emission reduction capability and economy of the microgrid, a capacity optimization configuration method considering laddered carbon trading and demand response is proposed for a grid-connected microgrid consisting of photovoltaic, battery and hydrogen storage devices. Combined with the mathematical model and system structure of each unit in the microgrid, the integrated operation control strategy is determined in this paper. A demand response model containing three load types is developed to reduce the stress on the storage and generation side. A carbon-trading mechanism is introduced into the operating costs to establish a configuration model with annual overall profit and power supply reliability as the optimization objectives. The non-dominated sorting genetic algorithm II is used to optimize the capacity of each unit, and the effectiveness of this model is verified by taking a microgrid in a region in Northwest China as an example to analyze the impacts of ladder carbon trading and demand response on the configuration results and system operation.

Mathematical and 3D Mechanical System Simulation of Arm Robot Modelled as Double Pendulum

<p>Lengan robot telah banyak digunakan dan penelitian ekstensif terkait manipulator telah dilakukan. Permasalahan pada manipulator robot lengan adalah pengendalian dan stabilisasinya. Pemodelan matematis dapat membantu mengendalikan lengan robot dengan parameter yang mudah untuk ditentukan. Penelitian ini bertujuan untuk membandingkan simulasi pemodelan matematis dan simulasi sistem mekanik 3D manipulator yang dimodelkan dengan pendulum ganda. Simulasi dilakukan dengan bantuan MATLAB/Simulink dan MATLAB/Simscape Multibody. Metode penelitian meliputi: (i) Pembentukan persamaan Lagrange untuk manipulator, (ii) Membuat blok MATLAB/Simulink, (iii) Membuat blok MATLAB/Simscape Multibody, (iv) Mendefinisikan parameter matematis dan fisika dan (v) Menjalankan simulasi dan menganalisis hasil. Hasil dari penelitian ini menunjukkan simulasi matematis lengan robot berdasarkan persamaan Lagrange konsisten dalam bentuk gelombang sinus. Sedangkan untuk simulasi 3D hasil grafiknya tidak konsisten. Namun pada hasil simulasi 3D yang parameter lengan robotnya hampir sama, hasilnya menunjukkan tren tertutup.</p>

Unit vector template control strategy‐based harmonic mitigation and charging with three phase–three level–three switch Vienna rectifier for Level 3 electric vehicle charging applications

SummaryFast battery charging units act as non‐linear loads, which induce a more harmonic effect in the utility grid. Hence, maintaining the stable voltage, current ripple, and total harmonic distortions within the permissible IEEE std level during the charging time of grid to electric vehicle (G2V) has become an important task for researchers in the future. In order to mitigate power fluctuations during every charging cycle, it will enhance the battery life cycle in electric vehicles (EVs). Three phase–three level–three switch Vienna rectifier with fuzzy logic controller tuned PID controller is used here for AC/DC conversion with minimum switching loss. A fuzzy intelligent control strategy has been employed with the DC link voltage regulator in order to sustain the DC link voltage as constant and progress the voltage/current profile by injecting active power at the point of common coupling. Unit vector template (UVT)‐based control strategy is employed here to identify the fundamental components from the load side and also estimate the reference phase current. This scheme enhances the performance and reduces the mathematical system complexity to diminish the harmonics in the distribution grid. The adaptability and feasibility of this proposed control method have been verified by the MATLAB simulation tool. To validate the response of the Vienna Rectifier with UVT controller are simulated with different unbalanced load conditions and also verified with 30 kW laboratory prototype experimental results using dsPIC30F4011 controller and the switch is IRFP260 with power diode RHRG30120.

A decision making framework for joint replenishment and delivery scheduling problems under mixed uncertainty

Concerning the essence of risk, a joint replenishment and delivery scheduling problem with fuzzy cost-related parameters and random number of imperfect quality items is developed to make it suitable for the inherent uncertainties of procurement-shipment process. The mathematical modelling-based decision system is formulated as a chance-constrained programming with the idea of embedding decision makers’ risk tolerance. Following this notion, the model is translated into an equivalent non-linear counterpart and a neighbourhood heuristic search is designed based on the properties of the cost function. We introduce an integrated cross-entropy algorithm, incorporating the heuristic in the cross-entropy framework, to solve it. The numerical results demonstrate that ICE is quite effective in comparison to state-of-the-art algorithms. Our framework is helpful for decision makers to determine economically acceptable performance objectives in the presence of uncertain issues, and thus to build resilience in supply chain.

The Method of Mathematical Modeling in Teaching Solving Applied Problems to Secondary School Students

The article describes the relevance of using the method of mathematical modeling in teaching students to solve applied problems, explains the concept of mathematical modeling and considers various ways to use this method in solving problems with practical content. In the course of the research work, psychological, pedagogical, methodological literature was analyzed, as well as a review of domestic and foreign research in the field of information technology and their use in the classroom. The necessity of teaching mathematical modeling in the school course of mathematics is theoretically substantiated. It is shown that the rich resource of mathematics, concentrating the knowledge necessary in everyday life, plays an important role in the intellectual development of the individual, as well as in his professional development, for solving practical problems, orientation and communication in society and life, in the surrounding space as a whole. The article also shows the expediency of preparing students for the study of real situations using mathematical modeling. The authors believe that the use of computer mathematical systems is justified, since it allows stimulating the activity of students in a secondary school, improving the quality of education, raising the professional level of a teacher, and diversifying the forms of communication between participants in the educational process. In addition, the authors believe that the use of computer mathematical systems in the classroom, visualization of information is a great advantage for students to receive it.

Identification of Vivo Material Parameters of Arterial Wall Based on Improved Niching Genetic Algorithm and Neural Networks

Cardiovascular diseases are seriously threatening human health and the incidence rate is high. Many scholars are devoted to studying arterial mechanical properties and material parameters. In this study, the bovine artery was selected as the experimental object and the uniaxial tensile test was carried out by cutting the specimens along its axial, circumferential and [Formula: see text] directions. The finite element software ABAQUS and hyperelastic Holzapfel Gasser Ogden (HGO) constitutive model were used to simulate the experimental process. Niche technology is introduced on the basis of genetic algorithm, and the program of Improved Niche Genetic Algorithm for material parameter identification is compiled based on Python language. In addition, BP Neural Network was constructed based on Tensorflow mathematical system. The material parameters of the constitutive model of bovine artery in different directions were identified by finite element method and experimental data. The results show that Improved Niche Genetic Algorithm and Neural Network, respectively, combined with finite element are both effective and accurate methods for predicting the parameters of arterial vascular hyperelastic materials, which can provide reference and help for the study of arterial vascular mechanical properties.

On the existence and uniqueness of solution to a stochastic Chemotaxis–Navier–Stokes model

In this article, we study a mathematical system modelling the dynamic of the collective behaviour of oxygen-driven swimming bacteria in an aquatic fluid flowing in a two dimensional bounded domain under stochastic perturbation. This model can be seen as a stochastic version of Chemotaxis–Navier–Stokes model. We prove the existence of a unique (probabilistic) strong solution. In addition, we establish some properties of the strong solution. More precisely, we prove that the unique solution is positive and satisfies the mass conservation property and an energy inequality.

Паралельний алгоритм розв’язування систем інтегральних рівнянь Вольтерри II роду

The problem of increasing the effectiveness of the study of integral models of dynamic systems is considered. A parallel algorithm for solving a system of Volterra linear integral equations of the second kind based on the quadrature method of numerical integration is proposed. The algo-rithm was implemented in the MATLAB computer mathematics system in the form of an m-function. The program uses the MATLAB Distributed Computing Toolbox infrastructure to manage workflows and distribute computations between them on multi-core processors. Com-putational experiments were conducted on a model example using the Symbolic Math Toolbox package for symbolic calculations and a comparison of the execution of parallel calculations with the execution time of the implementation of a sequential algorithm. The results showed a significant increase in the speed of research of integral models on multi-core processors when using the proposed algorithm and its computer implementation.

Mathematical Modeling and System Identification of a Piezo-actuated, Cantilever Beam with Interferometric Measurement

Mathematical Modeling and System Identification of a Piezo-actuated, Cantilever Beam with Interferometric Measurement