Mathematical System Research Articles

Research of Stages, Types of Modeling and Methods of Gesture Recognition

It is impossible to leave aside the problem of communication with the outside world and the social integration of people with disabilities in modern society, where there is a rapid development of communication methods between people. Gesture is the only method of communication for people with disabilities (auditory and language). The research provides information on static and dynamic gestures that allow people with communication problems to exchange information. It is noted that the problem of automatic gesture recognition is solved by various mathematical methods, algorithms and computer systems. The advantages and disadvantages of 2D and 3D models for sequential recognition of hand gestures are shown. It is noted that the creation of a national electronic database that recognizes the national dactyl alphabet and gestures in the Republic of Azerbaijan is an urgent problem. The well-known methods of this category are shown. Artificial neural network method, Hidden Markov method, Random Forest method and method of designating a hand gesture using gloves painted with markers of different colors. The creation of a national electronic database that recognizes the national dactyl alphabet and gestures is proposed, which will partially eliminate the existing barrier in education and problems of communication between people.

USING THE GEOGEBRA ENVIRONMENT IN THE MATHEMATICAL TRAININGOF ECONOMIC STUDENTS

The use of information technology in the learning process has of learning in institutions of higher education already become commonplace, but new tools that constantly help teachers and students. In order for education to really meet the demand of modern realities, it is necessary to continuously modernize the forms and methods of education. One such most relevant assistant in teaching mathematics is the Dynamic Mathematics System GeoGebra. The article deals with the issue of modernization of methodological systems for teaching mathematical disciplines studied by students of economic specialties. in IT areas. The possibilities of the GeoGebra tool are revealed, which are important for improving the quality of mathematical training of future economists in the context of the implementation of the didactic principle of visibility and the inclusion of students in research and project activities. Particular attention is paid to the practical aspects of using GeoGebra in solving plot, applied problems associated with the use of active techniques and methods of teaching mathematical disciplines, the growth of students’ creative and intellectual activity when working with topics that require visualization of mathematical concepts and objects. The conditions of methodologically expedient inclusion of Geogebra into the practice of teaching mathematical disciplines for the preparation of economists and the modernization of already existing methodological systems for teaching mathematical disciplines are highlighted. It has been proven that the use of the interactive geometric environment GeoGebra allows visualization of abstract mathematical concepts, which contributes to the fastest possible perception of the material, a deeper understanding of it and increases interest in the discipline being studied. In addition, the use of dynamic mathematics systems both in the classroom and in non-classroom work has a positive effect on the success of students. Completing mathematical tasks using the GeoGebra environment arouses students' cognitive interest in exact sciences and promotes the development of visual and creative thinking. GeoGebra should be considered a special visual environment not only for solving specific problems related to mathematics and mathematical modeling, but also an environment for the implementation of interdisciplinary projects of an integration nature.

Non-similar analysis of MHD hybrid nanofluid flow over an exponentially stretching/shrinking sheet with the influences of thermal radiation and viscous dissipation

This article presents non-similar analysis of Tiwari-Das hybrid nanofluid flow toward the exponentially expanding/shrinking sheet. Aluminum oxide ( A l 2 O 3 ) and copper ( Cu ) nanoparticles have been dispersed in the water. The significance of viscous dissipation, thermal radiation, magnetic fields, and heat sources has been observed in this work. A mathematical system is transmuted into a dimensionless, non-similar form by the utilization of non-similar transformations. The non-similar partial differential system is simulated by employing local non-similarity up to the 3rd order of iteration via bvp4c. The significance of flow constraints versus energy and velocity profiles is demonstrated through figures and tables. The fluid velocity decreases with expanding magnetic field ( M ) and injection parameters ( S ) . Energy profile grows as radiation ( Rd ) and heat generating ( Q ) parameter increases. The thermal profile is thought to be diminished by an expansion in the Prandtl number ( Pr ) . Stretching parameter ( λ ) increases cause a reduction in the temperature profile, whereas the heat profile grows as the Eckert parameter ( Ec ) increases. For particular values of the skin friction ( C f ) and Nusselt number ( Nu ) , numerical values are produced using local similarity and local non-similarity approaches. The findings indicate that skin friction decreases as the magnetic parameter ( M ) rises, but an expansion of the Prandtl number creates a growth in the Nusselt number. Excellent agreement between the current work and the published article is discovered in limiting cases.

An Introduction to Isomorphic Mathematical Analysis System

This paper is to build a primitive framework for a new possible extended system of real mathematical analysis - the Isomorphic Mathematical Analysis System (IMAS). It is based on some new concepts: e.g. isomorphic frame, dualvariable-isomorphic function, and isomorphic coordinate system. More concepts are introduced to constitute the whole IMAS framework. This IMAS attempts to provide current MA with new implements, which include isomorphic frame, thereby effectively putting the MA to work as well in some unevenly distributed coordinate spaces, realized by the isomorphic coordinate system. With these implements, many existing MA concepts are extended and incorporated into the new IMAS.

On the Origins of Randomness

AbstractThis paper is a concept paper, which discusses the definition of randomness, and the sources of randomness in the physical system (the Universe) as well as in the formal mathematical system. I discuss how randomness, through chaos, the second law, the quantum mechanical character of small scales, and stochasticity is an intrinsic property of nature. I then move to our formal mathematical system and show that even in this formal system we cannot do away with randomness and that the randomness in the physical world is consistent with the origins of randomness suggested from the study of mathematical systems. Rules and randomness are blended together and their interaction is shaping all observed forms and structures.

Introduction to the modeling of complex chemical reaction equilibrium using gPROMS® and GAMS®

AbstractIn the present paper several aspects of the simulation of complex chemical equilibrium are discussed, using two research and educational software: gPROMS® and GAMS®. All computations are performed to boost the understanding of chemical engineering students, undergraduate, and graduate, of the complex concepts behind both thermo‐chemical processes and optimization techniques. Four case studies with varying levels of difficulty illustrate the proposed methodology and robustness of the modeling systems: Catalytic steam reforming of bio‐ethanol at high temperatures. Partial oxidation of naphthalene using either air or pure oxygen. Supercritical water gasification of Microalga Spirulina. Dry and mixed reforming of glucose.Our results indicate that the use of optimization tools offered bygPROMS® and GAMS®software are useful and efficient tools to calculate the chemical and phase equilibrium by minimizing the Gibbs energy, provided that adequate initial guesses are used. Furthermore, the computational time spent in the calculations was generally quite short. The obtained equilibrium compositions are benchmarked using the ubiquitous process simulators: ASPEN‐Plus® and/or ASPEN‐Hysys® as well as data available from the open literature. We obtained excellent agreement between our results and their counterpart obtained using ASPEN‐Plus®. In the last part of this manuscript, authors share their experience in supervising senior term projects on the subject. A questionnaire was used to collect qualitative and quantitative feedback from the nine students involved in the projects. Their responses to a questionnaire focused on the chemical engineering thermodynamics theory as well as software usage during their investigations. This questionnaire demonstrates that students can overcome mathematical complexity by either using mathematical software or equivalent modeling systems (e.g., Matlab®, Mathematica©, gPROMS®, and GAMS®).

Fuzzy Logic Speed Regulator for D.C. Motor Tuning

A D.C. motor's rotational speed is regulated in this study using a PID controller and a fuzzy logic controller. In contrast to the fuzzy logic controller, which uses rules based on knowledge and experience, the proportional-integral-derivative (PID) controller requires a mathematical system model. This study investigates the regulation of a DC motor's velocity using PID and fuzzy logic controllers. The PID controller utilizes a mathematical model and parameter tuning by trial and error. Still, the fuzzy logic controller (FLC) operates on rule-based knowledge, enabling it to handle the nonlinear features of the DC motor effectively. The FLC design entails intricate determinations, including the establishment of a rule base and the process of fuzzification. A total of 49 fuzzy rules have been devised to achieve precise control. Based on MATLAB/SIMULINK simulations, the study concludes that the Fuzzy Logic Controller (FLC) beats the Proportional-Integral-Derivative (PID) controller. The FLC exhibits superior transient and steady-state responses, shorter response times, reduced steady-state errors, and higher precision. This study emphasizes the efficacy of the FLC (Fuzzy Logic Controller) in dealing with the difficulties associated with DC motor control. It presents a strong argument for the suitability and efficiency of FLCs in industrial environments compared to conventional PID (Proportional-Integral-Derivative) controllers. There are a wide variety of ways to construct a fuzzy logic controller. The speed error and the rate of change in the speed error are two inputs to the FLC. Defuzzification is done by focusing on the core of the problem. The results show that FLC is superior to PID controllers in efficiency and effectiveness due to its reduced transient and steady-state factors.

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.

Towards the development of an autonomous sailboat: Modelling and simulation of a small autonomous sailboat

This paper presents the mathematical modelling and system identification of a Dragonflite 95 radio-controlled sailboat. The corresponding model will be used in a simulation of the control systems of the sailboat. The mathematical model is based on Fossen’s compact ocean vessel model and adds models for environmental disturbances and actuators. Numerical methods were used to estimate the parameters of the physical sailboat. The simulation model was developed and implemented in MATLAB Simulink. Experiments were performed to verify that the simulated behaviour of the Simulink model agrees with the practical behaviour of the physical sailboat.

Exploring the Design of Entrepreneurship Simulation Experimental Projects Based on Interaction Models

Abstract Entrepreneurship is one of the driving forces of economic development in the new era, but entrepreneurship is also highly risky behavior. The goal of constructing the entrepreneurial interactive decision-making model and entrepreneurial project system model is to provide a theoretical reference value for entrepreneurial teams through simulation experiments. The conceptual model of entrepreneurial team interaction decision-making is constructed based on multi-intelligence under the support of relevant theories, and the main influencing factors affecting the interaction decision-making are analyzed and the specific decision-making model is designed on the basis of this. Then, according to the ideas and principles of system dynamics, the boundary of the system is delineated, the scope of research is clarified, the structure of the system is analyzed, the levels of the system are delineated, and the feedback mechanism of the system is determined. The relationship between the system levels is analyzed, feedback loops and causality diagrams are established, and in this way, a mathematical and canonical system dynamics model is established, and finally, simulation prediction and hypothesis testing are carried out. The regression results show that there is a positive effect of mutual influence among the three variables of the interaction decision model: team initiative, team decision performance. The error between the values of this paper’s model for simulation and the actual values is less than 10%, and the improvement of entrepreneurial R&D investment and the conversion rate of scientific and technological achievements can promote the number of entrepreneurs and entrepreneurial structure to different degrees. Effective predictions of the influencing factors and development trends of entrepreneurship in the future have been made, which provides policy references for entrepreneurship to be carried out more effectively in practice.

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.

Path Planning Algorithm and ID3 Decision Tree Model Application of Scenic Intelligent Navigation System

The assumption space of ID3 algorithm contains all decision trees, and the search space is also a complete assumption space. The current assumptions based on the information gain standard, and uses the information gain to reduce the sensitivity to individual training sample errors. Based on ID3 decision tree algorithm, this paper provides new ideas and methods for the quality optimization of tourist attractions. Firstly, ID3 decision tree algorithm model is constructed based on information entropy theory; Then, based on the literature research and system research methods, the quality evaluation indicator system of tourist attractions is constructed; Finally, based on the mathematical model and evaluation indicator system, the empirical research was carried out, and the data of 17 tourist attractions were collected. The expected research results were obtained according to the data preprocessing, data calculation process, decision tree construction and rule generation process. The research finds that the quality evaluation process of tourist attractions based on ID3 decision tree model, through data preprocessing, data calculation, decision tree construction and decision rules generation, etc. it can be concluded that the "Tourism environment quality" attribute is the most important in this evaluation system, and "Tourism landscape quality" is relatively important. Tourist attractions can improve the work and quality of tourist attractions according to the research results.

Application of Industrial Remote Access Control Laboratory

An industrial-scale remote access control laboratory system was developed to address the potential lack of practical laboratory experience for Control and Automation Engineering (CAE) students at Istanbul Technical University (ITU) in response to the coronavirus pandemic 2019 (COVID-2019). The system consists of six fundamental control theory experiments and aims to test fundamental control engineering topics such as mathematical modeling, system identification, controller design, and design comparison. These experiments are integrated into a remote access system using industry 4.0 methodologies, allowing students to use the experiments remotely over web-based user interfaces. The system has necessary capabilities such as remote control, online experimentation, graphs and charts, live camera view, data storage, accessibility options, and security for robust interaction with students. Two surveys were conducted to collect feedback from students who have not used the system and those who have used it for at least a semester. The results of the first survey showed that students appreciate the opportunity of remote-access laboratory usage on control experiments and would consider using it. The results of the second survey demonstrated that the system fulfills the varied requirements of students and received high overall satisfaction. Overall, the demand for an industrial-scale remote access control laboratory has been met, driven by the COVID-19 pandemic and the dynamic environment of engineering education.

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.