Mathematical System Research Articles

Carbon option pricing and carbon management under uncertain finance theory

Against the backdrop of increasingly severe global climate change issues, more and more countries and regions are adopting carbon emission trading, which is an effective market mechanism. As an important component of the carbon market, American carbon options provide more flexible trading tools to help companies avoid price risks. Therefore, the pricing research of American carbon options is of great significance for promoting the healthy development of the carbon market. Nonetheless, existing pricing methods are all based on probability theory, which need to satisfy the premise that the distribution function is close to the true frequency sufficiently. However, usually such premise is ill-suited in carbon market. To alleviate the predicament of the need for satisfying probability theory’s premise, this work investigates American carbon option pricing under the framework of uncertainty theory, which is another axiomatic mathematical system. For this purpose, uncertain differential equation is adopted to model the price of carbon future, and pricing formulae for American call and put carbon options are derived based on this model. Real data analyses illustrate the proposed method in details. Furthermore, it provides a detailed schema of applying the American carbon option for carbon asset management, which can optimize risk control for carbon consuming enterprises.

Global Exponential Synchronization of Delayed Quaternion-Valued Neural Networks via Decomposition and Non-Decomposition Methods and Its Application to Image Encryption

With the rapid advancement of information technology, digital images such as medical images, grayscale images, and color images are widely used, stored, and transmitted. Therefore, protecting this type of information is a critical challenge. Meanwhile, quaternions enable image encryption algorithm (IEA) to be more secure by providing a higher-dimensional mathematical system. Therefore, considering the importance of IEA and quaternions, this paper explores the global exponential synchronization (GES) problem for a class of quaternion-valued neural networks (QVNNs) with discrete time-varying delays. By using Hamilton’s multiplication rules, we first decompose the original QVNNs into equivalent four real-valued neural networks (RVNNs), which avoids non-commutativity difficulties of quaternions. This decomposition method allows the original QVNNs to be studied using their equivalent RVNNs. Then, by utilizing Lyapunov functions and the matrix measure method (MMM), some new sufficient conditions for GES of QVNNs under designed control are derived. In addition, the original QVNNs are examined using the non-decomposition method, and corresponding GES criteria are derived. Furthermore, this paper presents novel results and new insights into GES of QVNNs. Finally, two numerical verifications with simulation results are given to verify the feasibility of the obtained criteria. Based on the considered master–slave QVNNs, a new IEA for color images Mandrill (256 × 256), Lion (512 × 512), Peppers (1024 × 1024) is proposed. In addition, the effectiveness of the proposed IEA is verified by various experimental analysis. The experiment results show that the algorithm has good correlation coefficients (CCs), information entropy (IE) with an average of 7.9988, number of pixels change rate (NPCR) with average of 99.6080%, and unified averaged changed intensity (UACI) with average of 33.4589%; this indicates the efficacy of the proposed IEAs.

A besyian regularisation neural network approach for hepatitis B virus spread prediction and immune system therapy model

The primary aim of the article is to analyze the response of the human immune system when it encounters the hepatitis B virus. This is done using a mathematical system of differential equations. The differential equation system has six components, likely representing various aspects of the immune response or virus dynamics. A Bayesian regularization neural network has been presented in the process of training. These networks are employed to find solutions for different categories or scenarios related to hepatitis B infection. The Adams method is used to generate reference data sets. The back-propagated artificial neural network, based on Bayesian regularization, is trained and validated using the generated data. The data is divided into three sets: 90% for training and 5% each for testing and validation. The correctness and effectiveness of the proposed neural network model have been assessed using various evaluation metrics. The metrics have been used in this study are Mean Square Error (MSE), histogram errors, and regression plots. These measures provide support to the neural network to approximate the immune response to the hepatitis B virus.

Исследование многоуровневых моделей управления вагонопотоками в адрес припортовых станций с применением теории дифференциальных уравнений

Purpose: To consider the issue of sustainability of multi-level control systems for car flows to port railway stations in the conditions of intellectualization of transportation management processes. To assess the influence of three-level and two-level control systems for the operational work of port roads on the quality of planning the supply of trains to port stations under various modes of operational operation of railways. Determine the conditions for the stability of the car flow control system by constructing and studying the corresponding hard and soft mathematical models described by autonomous systems of ordinary linear differential equations. Methods: In this study, the methods of the theory of stability of solutions of differential equations, as well as the theory of control and dynamical systems are used. A phase space is used in a visual representation, a qualitative and quantitative analysis of the behavior of phase trajectories in it is performed, corresponding to undisturbed and perturbed solutions of systems of differential equations describing the constructed models of control systems. Results: A comparison of the characteristics of multistage car traffic control systems is given. A study of the stability of multilevel models of car traffic management in the context of the intellectualization of management functions is proposed. In the environment of the analytical computing system, the conditions of asymptotic stability in time of a two-level wagon traffic control system are found and studied. Practical importance: The results obtained by computational experiment make it possible to assess the stability of the functioning of port-side transport and technological systems in the context of changes in the organization of production and the intellectualization of transportation management processes. Computer mathematics systems make it possible to implement the heuristic component of research and obtain theoretically sound and visual solutions to problems of optimizing cargo and wagon traffic control modes.

Finite-time output-feedback fault tolerant adaptive fuzzy control framework for a class of MIMO saturated nonlinear systems

This paper presents a finite-time fault-tolerant fuzzy adaptive controller for uncertain interconnected nonlinear systems in strict-feedback form. The controller addresses input saturation, state-dependent actuator faults, external disturbances, and unavailable states for measurement. To avoid any unexpected alteration due to failures, the proposed control scheme design addresses all types of actuator faults that are bias, drift, and loss of accuracy as additive faults, as well as a multiplicative fault that results in loss of effectiveness with nonaffine state-dependency. Restrictions on control gains and unmatched interconnections are eliminated, and the explosion complexity caused by recursive back-stepping designs is avoided. Fuzzy Systems approximate the unknown ideal control laws along side the acutator faults and disturbances. The stability analysis guarantees that tracking errors converge to a small compact set around the origin in finite time. Simulation results on a quad-rotor UAV and a mathematical system confirm the effectiveness of the proposed approach.

Some Aspects of Neutrosophic Set Theory

This article aims to introduce my work on constructing neutrosophic set theory. Neutrosophy is a new branch of mathematical systems proposed by Smarandache in 1995 as an extension of an intuitionistic fuzzy set according to three-degree membership functions. The new perspective of neutrosophic sets consists of two paths, the first path depends on the three degrees including the degree of truth-membership, degree of indeterminacy-membership, and degree of false-non-membership respectively, while the second path depends on the generated classical set by three types of neutrosophic sets and study the concepts of neutrosophic theory. In previous work, I Presented the concepts of neutrosophic sets including universal, empty, compliment, and subsets. I also explored neutrosophic operations and their properties, such as neutrosophic unions and neutrosophic intersections. In this article, I shall delve into additional materials and theorems related to these concepts and discuss neutrosophic and symmetric differences, including their properties. Furthermore, I shall present a generalization of De Morgan's theorem.

MATHEMATICAL MODEL AND STRUCTURE OF A NEURAL NETWORK FOR DETECTION OF CYBER ATTACKS ON INFORMATION AND COMMUNICATION SYSTEMS

The paper discusses the principles of creating a mathematical model and system architecture by applying the method of artificial intelligence to detect cyberattacks on information and communication systems, where a neural network capable of learning and detecting cyberattacks is used. The proposed approach, based on the application of the developed mathematical model and architecture of artificial neural networks, as a detector of network attacks on information and communication systems, allows to increase the level of detection of network intrusions into computer systems, Web and Internet resources. An algorithm for processing network traffic parameters in real-time systems by structuring a neural network is proposed, which allows to optimize the redundancy of its multi-level structure at the level of inter-element connections.

Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations

Multiplicative calculus is a mathematical system that offers an alternative to traditional calculus. Instead of using addition and subtraction to measure change, as in traditional calculus, it uses multiplication and division. The framework of nonlinear equations is an incredibly powerful tool that has proven invaluable in advancing our understanding of various phenomena across a wide range of applied sciences. This framework has enabled researchers to gain deeper insights into a vast array of scientific problems. The physical interpretation of iterative methods for nonlinear equations using multiplicative calculus offers a unique perspective on solving such equations and opens up potential applications across various scientific disciplines. Multiplicative calculus naturally aligns with processes characterized by exponential growth or decay. In many physical, biological, and economic systems, quantities change in a manner proportional to their current state. Multiplicative calculus models these processes more accurately than traditional additive approaches. For example, population growth, radioactive decay, and compound interest are all better described multiplicatively. The primary objective of this work is to modify and implement the Adomian decomposition method within the multiplicative calculus framework and to develop an effective class of multiplicative numerical algorithms for obtaining the best approximation of the solution of nonlinear equations. We build up the convergence criteria of the multiplicative iterative methods. To demonstrate the application and effectiveness of these new recurrence relations, we consider some numerical examples. Comparison of the multiplicative iterative methods with the similar ordinary existing methods is presented. Graphical comparison is also provided by plotting log of residuals. The purpose in constructing new algorithms is to show the implementation and effectiveness of multiplicative calculus.

A reliable Bayesian regularization neural network approach to solve the global stability of infectious disease model

The purpose of this study is to perform the numerical results of the global stability of infectious disease mathematical model by using the stochastic computing scheme. The design of proposed solver is presented by one of the efficient and reliable schemes named as Bayesian regularization neural network (BRNN). The global stability of infectious disease mathematical nonlinear model is categorized into susceptible, infected, recovered and vaccinated. The construction of dataset is performed through the Runge-Kutta scheme in order to lessen the mean square error (MSE) by dividing the statics as training 74 %, while 13 % for both testing and endorsement. The proposed stochastic process contains log-sigmoid merit function, twenty neurons and optimization through RBNN for the numerical solutions of the global stability of infectious disease mathematical system. The best training values for each model's case are performed around 10–11. The scheme's correctness is performed by the matching of the results and the minor calculated absolute error performances. Moreover, the regression, state transmission, error histogram and MSE indicate the trustworthiness of the designed solver.

Penerapan Media Pembelajaran Audio Visual Berbasis Canva untuk Meningkatkan Motivasi dan Hasil Belajar Siswa dalam Mata Pelajaran TIK

Mathematics learning activities at SMP Negeri 4 Ciawigebang in general still use textbooks or package books as one of the references used. The school where the research was conducted still uses package books as a learning medium and the method used uses the lecture method, so that in this case Mathematics learning becomes monotonous and less interesting and less motivating to students. This research aims to improve mathematical skills by using Scratch media. The research method used is quantitative with a quasi-experimental type using a research design, namely pretest posttest control design which was carried out at SMP Negeri 4 Ciawigebang. The population used in this study is students in grades 8b and 8e with a total of 54 students. Data collection techniques through observation, tests and questionnaires. The analysis of research data uses a t-test. The results of the analysis showed that there was a change in the improvement of student learning outcomes after the application of scratch learning media to the material of the two-variable linear equation system in mathematics in grade VII of SMP Negeri 4 Ciawigebang

Mathematical model for predicting the yield of apple trees on rootstock 62-396

Traditionally, forecasting apple tree yields was carried out on the basis of statistics of already obtained long-term yield dynamics or based on generative formations formed on the tree. The purpose of the work is to identify the most significant soil parameters for the formation of the apple tree varieties yield on the dwarf rootstock 62-396 and to build a mathematical model for predicting fruit yield in the conditions of the Central Chernozem region of the Russian Federation. Field research was carried out in 2004-2022 in industrial apple tree plantations at the age of full fruiting in the Lipetsk (two farms) and Tambov (eight farms) regions. Seven horticultural soil types have been studied. Based on statistical analysis, a mathematical model of apple tree productivity was obtained in the form of an analytical dependence on three factors. A geometric interpretation of the regression model is given using the Mathcad symbolic mathematics system in the form of response surfaces and the corresponding level lines. Practical recommendations are given for choosing rational parameters within selected intervals of factor variation.

DNA N-gram analysis framework (DNAnamer): A generalized N-gram frequency analysis framework for the supervised classification of DNA sequences

In 1948, Claude Shannon published a mathematical system describing the probabilistic relationships between the letters of a natural language and their subsequent order or syntax structure. By counting unique, reoccurring sequences of letters called N-grams, this language model was used to generate recognizable English sentences from N-gram frequency probability tables. More recently, N-gram analysis methodologies have been successfully applied to address many complex problems in a variety of domains, from language processing to genomics. One such example is the common use of N-gram frequency patterns and supervised classification models to determine authorship and plagiarism. In this paradigm, DNA is a language model where nucleotides are analogous to the letters of a word and nucleotide N-grams are analogous to the words of a sentence. Because DNA contains highly conserved and identifiable nucleotide sequence frequency patterns, this approach can be applied to a variety of classification and data reduction problems, such as identifying species based on unknown DNA segments. Other useful applications of this methodology include the identification of functional gene elements, microorganisms, sequence contamination, and sequencing artifacts. To this end, I present DNAnamer, a generalized and extensible methodological framework and analysis toolkit for the supervised classification of DNA sequences based on their N-gram frequency patterns.

Applying satellite sea surface temperature as Dirichlet-type surface thermal boundary condition in an ocean model

Following the Dirichlet-type boundary condition that specifies value at boundary of a system in mathematics and physics, this study suggests applying satellite sea surface temperature (SST) as Dirichlet-type surface thermal boundary condition (STBC) in ocean models. Numerical experiments with Dirichlet-type and Combined-type STBC with different configurations of satellite SST, for the period of January to April 2019 in the Northwest Pacific Ocean, were carried out based on the Princeton Ocean Model. The experiments were assessed using satellite and in situ observations of temperature, GOFS3.1 analysis and GLORYS12v1 reanalysis. Results show that applying satellite SST as Dirichlet-type STBC could constrain the modeled SST and near-surface temperature in upper 50 m depth well, which is better than the scheme that uses satellite SST as the relaxation terms of Combined-type STBC. The temperature section along the 137°E resulted from the Dirichlet-type STBC is comparable with GOFS3.1 analysis and better than GLORYS12v1 reanalysis in upper 50 m depth. These results suggest that applying high-accuracy satellite SST as Dirichlet-type STBC in ocean models has a promising prospect in numerical simulation.

Analysis of some dynamical systems by combination of two different methods

In this study, we introduce a novel iterative method combined with the Elzaki transformation to address a system of partial differential equations involving the Caputo derivative. The Elzaki transformation, known for its effectiveness in solving differential equations, is incorporated into the proposed iterative approach to enhance its efficiency. The system of partial differential equations under consideration is characterized by the presence of Caputo derivatives, which capture fractional order dynamics. The developed method aims to provide accurate and efficient solutions to this complex mathematical system, contributing to the broader understanding of fractional calculus applications in the context of partial differential equations. Through numerical experiments and comparisons, we demonstrate the efficacy of the proposed Elzaki-transform-based iterative method in handling the intricate dynamics inherent in the given system. The study not only showcases the versatility of the Elzaki transformation but also highlights the potential of the developed iterative technique for addressing similar problems in various scientific and engineering domains.

A neural network computational procedure for the novel designed singular fifth order nonlinear system of multi-pantograph differential equations

The current investigations present the numerical solutions of the novel singular nonlinear fifth-order (SNFO) system of multi-pantograph differential model (SMPDM), i.e., SNFO–SMPDM. The novel SNFO–SMPDM is obtained using the sense of the second kind of typical Emden–Fowler and prediction differential models. The features of shape factor, pantograph along with singular points are provided for all four obtained classes of the SNFO–SMPDM. The extensive use of the singular models is observed in the engineering and mathematical systems, e.g., inverse systems and viscoelasticity or creep systems. For the correctness of the proposed novel SNFO–SMPDM, one case of each class is numerically handled by applying supervised neural networks (SNNs) along with the optimization of Levenberg–Marquardt backpropagation scheme (LMBS), i.e., SNNs–LMBS. A dataset using the traditional variational iteration scheme is designed to compare the proposed results of each case of SNFO–SMPDM. The obtained approximate solutions of each class using the novel SNFO-SMPDM are presented based on the training (80 %), authentication (10 %) and testing (10 %) measures to evaluate the mean square error. Fifteen numbers of neurons, and sigmoid activation function are used in this SNN process. To authenticate the competence, and precision of SNFO–SMPDM, the numerical simulations are accessible by applying the relative measures of regression, error histogram plots, and correlation.

Multiobjective optimal control problems. Stationary Navier–Stokes equations

This paper deals with the solution of some multi-objective optimal control problems for stationary Navier–Stokes equations. More precisely, we look for Pareto and Nash equilibria associated to standard cost functionals. First, we prove the existence of equilibria and we deduce appropriate optimality systems. Then, we analyse the existence and characterization of Pareto and Nash equilibria for the Navier–Stokes equations. Here, we use the formalism of Dubovitskii and Milyoutin., see [Girsanov FV. Lectures on mathematical theory of extremum problems. Berlin: Springer-Verlag; 1972. (Notes in economics and mathematical systems; vol. 67)]. Finally, we also present a finite element approximation of the bi-objective problem, we illustrate the techniques with several numerical experiments and we compare the Pareto and Nash equilibria.

3D Chaotic Nonlinear Dynamic Population-Growing Mathematical System Modeling with Multiple Controllers

Modeling, stabilization, and identification processes are significant stages in the process of developing knowledge about chaotic dynamical systems which entail the effective prediction depending on the degree of uncertainty toleration in the forecast, accuracy of the current state to be measured as well as a time scale resting on the dynamics of the system. Control of under-activated dynamical systems has been considered substantially, and it is for periods and is currently developing in various domains such as biology, data analysis, computing systems, and so forth. Dynamic systems of growing population signifies a model describing the way a population evolves over time during which population goes through major life events, split into discrete time periods. The size of the population at a given time period is determined by the rate of growth as well as other related factors. Most progress has been made in model-based control theory, which has drawbacks when the system under consideration is exceedingly complicated, and no model can be constructed. Accordingly, a 3D-discrete and dynamic human population growth system with many controllers is proposed by examining the stability and symmetry of controller system clarifications. The symmetric stability control results are presented by considering a special parametric dynamic system in its coefficients besides suggesting periodic functional coefficients in terms of sin and cos functions. The controllers have the ability to reduce population growth rate unpredictability or enhance system stability under various external conditions. The unique and very effective strategies in relevant domains could provide a deeper understanding of their impact as well as the theoretical or technological innovations thereof. These controllers are capable of reducing population growth rate unpredictability or improving system stability under various external conditions, and applicable strategies in the relevant domains can provide profound comprehension over the impact along with the theoretical as well as technological advancements.

A capturing math language use during block play: Creation of the spatial and quantitative mathematical language coding system

The goals of the current study were: 1) to modify and expand an existing spatial mathematical language coding system to include quantitative mathematical language terms and 2) to examine the extent to which preschool-aged children used spatial and quantitative mathematical language during a block play intervention. Participants included 24 preschool-aged children (Age M = 57.35 months) who were assigned to a block play intervention. Children participated in up to 14 sessions of 15-to-20-minute block play across seven weeks. Results demonstrated that spatial mathematical language terms were used with a higher raw frequency than quantitative mathematical language terms during the intervention sessions. However, once weighted frequencies were calculated to account for the number of codes in each category, spatial language was only used slightly more than quantitative language during block play. Similar patterns emerged between domains within the spatial and quantitative language categories. These findings suggest that both quantitative and spatial mathematical language usage should be evaluated when considering whether child activities can improve mathematical learning and spatial performance. Further, accounting for the number of codes within categories provided a more representative presentation of how mathematical language was used versus solely utilizing raw word counts. Implications for future research are discussed.

ОСОБЛИВОСТІ ВИКОРИСТАННЯ СУЧАСНИХ ІНФОРМАЦІЙНОКОМУНІКАЦІЙНИХ ТЕХНОЛОГІЙ У ВИЩІЙ МАТЕМАТИЧНІЙ ОСВІТІ

The article discusses the relevance of using information and communication technologies (ICT) in higher mathematical education within the context of the contemporary educational environment characterized by rapid technological changes. It is noted that effective utilization of ICT, such as electronic journals, multimedia technologies, testing systems, and computer mathematics systems, contributes to the improvement of the teaching and learning process. Emphasis is placed on the necessity of reviewing and modifying teaching methodologies for mathematical disciplines to integrate innovative solutions. Furthermore, the use of information and communication technologies in higher mathematical education is deemed highly relevant due to the rapid development of the modern technological environment and the needs of the contemporary job market. The implementation of electronic journals, multimedia technologies, testing systems, and computer mathematics not only enhances the efficiency of teaching mathematical disciplines but also helps create a solid foundation for the future professional success of students. Electronic journals serve not only as convenient tools for administrative processes but also as platforms for active interaction among students, teachers, and administration, fostering the development of academic community and stimulating discussions and collaboration. Multimedia technologies, such as video lessons, interactive exercises, and simulations, provide students with opportunities to better grasp material and understand complex concepts, opening up new possibilities for personalized learning and adaptation to various learning styles. Testing systems, particularly those based on interactive platforms, enable instructors to effectively monitor students' knowledge and track their progress, as well as provide opportunities for personalized learning through automatic adaptation of task complexity Computer mathematics systems, including software packages for numerical and symbolic computations, become an integral part of modern mathematical education, empowering students to efficiently solve complex mathematical problems and explore new concepts, thus stimulating their creative potential and innovative approach to problem-solving. Together with educational platforms and distance learning systems, these tools contribute to the modernization and optimization of the educational process, leading to the improvement of the quality of higher mathematical education and the preparation of qualified professionals for the contemporary world.

Assessment of the quality of the labour safety management system in accordance with the requirements of the international standard ISO 45001:2018 at the stage of operation

The subject matter of the article is the assessment of the quality of the occupational safety management system. The goal of the article is to develop a methodology for assessment of the occupational safety management system at the stage of operation. The article solves the following task: to investigate the possibility of applying methods for analysing the dynamic characteristics of the occupational safety management system and to develop algorithms and methods for using the criteria of non-parametric statistics. Methods are used: qualimetry and mathematical statistics. The following results were obtained: an analysis of the requirements of the international standard ISO 45001:2018 was carried out to determine the need to monitor, measure and analyse the functioning of the occupational safety management system, which revealed that the effectiveness of the development and implementation of the occupational safety management system depends on the assessment methodology. An analysis of existing research and publications on the evaluation of processes, including those related to occupational safety, is carried out. The methods for evaluating mathematical systems for processing and controlling gross errors and stationarity, which are key to the analysis of occupational safety management processes, are considered. Non-parametric criteria for checking the stationarity of random processes are considered in detail. Sequences of means and means squares are compared with expected values to determine whether rejections of the stationary hypothesis are justified. The expediency of using these methods for analysing occupational safety management systems is determined. The dynamic nature of the processes and the importance of monitoring and data analysis to ensure effective safety management practices are analysed. Conclusions: The application of methods for analysing the dynamic characteristics of the occupational safety management system is substantiated and algorithms and methods for using the criteria of non-parametric statistics are developed, which allow to obtain an assessment of the system, taking into account the limited information about its indicators and the lack of knowledge of the law of their distribution as a random variable.