We study the mathematical models with the help of the age of children by authors[2, 3, 4, 5] and according: this paper addresses a five-year longitudinal study’s first year, which introduces mathematical modeling to young children and provides professional development for their teachers. Four classes of third graders (8 years of age) and their teacher participated in the first year of the program, which involved several preliminary modeling experiences followed by two comprehensive modeling problems over a span of 6 months. Regular teacher meetings, including preparatory workshops and reflective analyses, occurred. Analyses of children’s responses to one of the modeling problems show the spontaneous ways in which children engaged in sense making, problem posing, hypothesizing, and mathematizing (including representing). Modeling tasks of this type powerfully develop important ideas and problem-solving processes in the early school years.
In this study, we introduce an enhanced electronic SQEIJS model (e-SQEIJS), designed to analyze and mitigate the behavior of malicious codes within computer networks. The model incorporates key compartments: Susceptible (S), Quarantined (Q), Exposed (E), Infectious (I), and Isolated (J), to represent the progression of malicious code attacks and the impact of defense strategies like quarantine and isolation. By employing stability analysis, we evaluate the system’s behavior under varying conditions. A crucial metric, the basic reproduction number (R0), is derived to determine the model’s stability. When R0< 1, the system achieves a stable, virus-free equilibrium, indicating successful control of the malicious code. Conversely, R0>1 denotes instability, suggesting the potential spread of the malware within the network. The system of equations is solved using numerical techniques, allowing for comprehensive analysis and validation of the model. This approach reveals critical insights into the dynamics of malware propagation and the efficacy of the proposed containment strategies. The findings emphasize the importance of quarantine and isolation in securing networks, providing a robust framework for understanding and controlling malicious code outbreaks in digital environments.
In this paper, we find the necessary and sufficient condition for a Finsler space with special L= ?1a+?2ß2/a to be a Berwald space and also to be a Berwald space, where (a) could be a Riemannian metric and (ß) may be a differential one form. In this paper, we give the conformal condition for the special metric as (3.7). In the Finsler space, we see special (a,ß)-metrices such as Randers metric, Kropina metric, and Matsumoto metric, etc. MSC: 53B40, 53C60.
We have studied many research papers and found that today our planet is facing a serious problem of climate change due to the rise in its average temperature, which is caused by the discharge of global warming gases from various industrial and other sources, leading to undesirable consequences such as the melting of glaciers, sea level rise, etc. Many more critical situations are arising in other fields during the study. Mathematical modeling is one of the bases of mathematical education. Therefore, mathematical modeling might be offered to all age groups in higher learning, high school, and primary school. In this study, the importance of modeling is a theoretical study in other words.
Photonic crystals (PhCs) also known as Photonic band-gap materials have been found very suitable and attractive optical materials for controlling and manipulating the flow of light. This paper gives a comprehensive overview and technical Methodology of Computation of Photonic Band Structure. Soliton compression has been briefly discussed. Fabrication and Characterization of Photonic Crystals in Photopolymer SZ2080 by Two-Photon Polymerization have been described. The case of dispersion engineered slow-light silicon photonic crystal waveguide has been theoretically discussed. Technology of controlling the emission of single excitons in Photonic Crystal Cavities has been briefly explained. A qualitative review of some important studies on the subject, especially in the research area has also been provided. Most importantly, some important recent breakthroughs in this field have been presented and technically discussed. It is expected that the paper should be really useful for the researchers and designers working in this evolving field.
This work examines how different machine learning models perform using the digits dataset, concentrating on Multi-Layer Perceptrons (MLPs) and Decision Trees. We contrast models with various hidden units and optimization methods, such as the Mann iteration theorem in conjunction with stochastic gradient descent (SGD). According to our findings, the accuracy of MLPs increases with the number of hidden units; the MLP model with 128 hidden units achieved an accuracy of 96.11%. This model’s accuracy was further enhanced to 96.94% using SGD and the Mann iteration theorem, proving the efficacy of sophisticated optimization methods. By contrast, the Decision Tree model’s accuracy of 84.16% was much lower. To get good performance in multi-class classification problems, the study emphasizes the significance of model complexity and optimization techniques. Comprehensive confusion matrices offer more information about the classification performance and possible areas for development. These results highlight the potential of MLPs optimized using cutting-edge approaches for precise digit classification and point to directions for further study, such as feature engineering, hyperparameter tweaking, and ensemble method investigation.
This research paper explores how cognitive flexibility and adaptive thinking influence the high-stress environment and its navigation. Cognitive flexibility and adaptive thinking are essential for maintaining performance in high-stress environments. Research indicates cognitive flexibility enhances learning processes[1]. Environmental stressors such as heat, cold, and altitude can impair cognitive performance, varying depending on exposure duration and task complexity[2]. In resuscitation scenarios, stress factors like illness severity and noise influence decision-making but can be mitigated through cognitive aids and stress management training[3]. Executive functions, particularly working memory and flexibility, are linked to stress resilience[4]. Understanding these factors and their interrelationships can guide the development of strategies to enhance cognitive performance and resilience in high-stress environments, potentially through targeted training programs and decision-support tools.
The quest for sustainable and clean energy solutions has recently increasingly turned towards photonics innovations. This technology, centered around the science and engineering of light, can enhance certain renewable system technologies or enable other infrastructure like as data centers to get closer to renewable energy sources. This paper presents novel concepts and applications of Photonic crystals in Renewable Energy and Energy Storage. Solar power has recently become very popular as a clean energy source, promising energy independence and environmental benefits while becoming increasingly cost-effective. This has led to an extensive range of applications, including photovoltaics. Photonic crystals can be used as antireflective (AR) and light-trapping surfaces, back reflectors, spectrum splitters, absorption enhancers, radiation coolers and electron transport layers. This paper presents an overview of the developments and trends in designing photonic structures for different renewable energy and energy storage applications.
In this paper, we have introduced the definition of q–binomial and some properties. The theme of this paper is to give an introductory study of the Gaussian q–binomial formula and q–Taylor’s formula. They are useful for finding properties of binomial coefficients.
Artificial Intelligence (AI) is revolutionizing the food industry by enhancing efficiency, ensuring quality, and optimizing workflows. AI-powered technologies, including computer vision, machine learning, and Internet of Things (IoT)-enabled sensors, are transforming food production, packaging, and safety monitoring. Automated quality control systems detect contaminants, assess freshness, and maintain product consistency, ensuring higher standards in food processing. AI-driven predictive analytics optimize supply chain operations, reducing food waste and improving inventory management. Additionally, robotic automation accelerates grading and sorting processes while minimizing human error. AI applications in food safety compliance and traceability further enhance consumer trust. However, challenges such as the demand for skilled labor, high implementation costs, and data privacy concerns remain significant barriers. Despite these challenges, the integration of AI continues to drive innovation, advancing food sustainability, safety, and overall quality.
The application of machine learning (ML) techniques has led to notable breakthroughs in oncology, the study and treatment of cancer, especially in the field of early cancer diagnosis. By detecting cancer at its most curable stages, early detection is essential for increasing survival rates and treatment results. This study examines how machine learning models can be used to analyse patient data, such as symptoms, genetic information, and medical histories, to predict and diagnose cancer in its early stages. When processing huge, complicated datasets to find patterns and forecast cancer risk, machine learning methods including logistic regression, random forests, support vector machines, and gradient boosting have demonstrated encouraging results. Compared to conventional techniques, machine learning (ML) in cancer offers the advantages of speedy analysis of large volumes of data, the capacity to spot hidden trends, and more precise predictions. There are still issues to be resolved, though, such as managing data imbalance, making sure models are interpretable, and the requirement for strong, varied datasets to improve generalizability. Obstacles to integrating machine learning algorithms into clinical practice also include ethical considerations, regulatory issues, and the requirement for physician collaboration. Notwithstanding these obstacles, machine learning in oncology has a bright future ahead of it in terms of enhancing early cancer detection, cutting medical expenses, and facilitating individualized treatment plans. With an emphasis on how machine learning could transform cancer diagnosis and treatment, this study explores the field’s present uses as well as anticipated future developments.
We study the teaching learning process which using technology, individual learning lecturer best teaching learning, teaching mathematical model simple models for epidemics by various author[7, 8, 10, 11, 15]. By containing the mathematical modeling studies for above mention areas we have discussed of current research paper how to develop teaching and learning through technology, in addition we discuss the need to an optimal uses of technology to balance between achieving the objective of the class and attaining the goals of mathematical models.
The evolution of Finsler geometry has taken place over multiple phases, each contributing to its theoretical and applied aspects. This study aims to explore the fundamental principles and definitions that form the basis of Finsler geometry. Additionally, we will examine contemporary research that builds upon these concepts, highlighting recent advancements and their connections to this field.
Cadmium sulfide nanomaterial is synthesized by the chemical precipitation method. Its structural properties are studied using scanning electron microscopy (SEM), transmission electron microscopy (TEM) micro-structure, and the particle sizes of the nanomaterial. FTIR spectra represent the band position. The average particle size is found to be in the range of 50-200 nm, and they are spherical in shape. Fourier transform infrared spectroscopic studies have been performed to investigate the bond information between different elements present in the nanoparticles. The spectral properties of the nanoparticles are suitable for LED, sensor, and photo-detector applications.
In the computational fluid dynamics field, the study of fluid flow coupled with chemical reactions has garnered significant attention due to its practical implications across various industrial domains. This research is particularly critical in applications like nuclear reactors; understanding the flow behavior and its interaction with chemical processes is essential for system design and optimization. Motivated by this study, we investigate the influence of chemical reactions on MHD extracting flow of Casson fluid amongst a penetrable medium below the slip state, incorporating the effects of emission, viscous dissipation, and radiation. The flow is produced by the compression of two plates moving toward each other, causing the formation of a thin liquid layer between them. By changing the ruling PDEs into ODEs, the similarity transformation technique is used to make them amenable to numerical solution. The FDM method is applied to solve the resulting ODEs, with a particular focus on the dominant parameters that influence the flow dynamics, temperature, concentration, and mass transfer rates in this system. Numerical results show that as the gap between the plates increases, both the velocity and wall tangential shear increase. The influence of the Hartmann and Casson parameters is also significant; these parameters lead to a reduction in the velocity, temperature, along with the concentration of the gas. Furthermore, the effect of viscous dissipation is found to enhance both the temperature and heat transfer rate. Regarding chemical reactions, the study reveals that the rate of mass transfer increases under ruin synthetic reactions but decreases during constructive reactions, highlighting the crucial role of reaction type in controlling the overall performance of the system.
We have study, the research paper in the past several decades, there have been sufficient consultations among mathematicians and mathematics professors on elevating mathematical modelling (a method of utilizing mathematics to handle real world problems) as a pedagogical practice. For some time, mathematics mentors and syllabus developers have been advocating for the teaching of mathematical modelling in schools. Even though there is concurrence on its significance and consequence, mathematical modelling endures a tough activity for both trainer and trainees to fully take part in. For students, we inspect some of these challenges in this paper and deliberate how technology can play an integral role in providing the vital support to make mathematical modelling a more reachable mathematical activity. Using a set of examples drawn from different fields and topics, we portray how a spectrum of technological devices may be successfully and efficiently exploited in modelling tasks. In continuous study of teaching and learning model with technology here we discuss the need for an optimal use of technology to balance between achieving the objectives of the chores and accomplishing the aims of learning mathematics.
During the study of this paper, we have to study R. Miron’s concept of L-duality in Lagrange and Finsler spaces in [1987]. We have continued this study, and here we give some special conditions for the same theory. The factual L-duals of the Randers metric, Kropina metric, Matsumoto metric, exponential metric, as well as some more unique metrics, are really just some of the extraordinary results obtained. The importance of L-duality, however, is basically limited to finding the dual of a few key Finsler functions. In this paper, we find the L-dual of a Finsler space with a special (a, ß)-metric F = (a + ß2 /a), where a is a Riemannian metric and ß is a differential one-form. 2010MSC: 53B40 & 53C60
In this study, we have derived the connection between complex octonions and the SU(3)C color group, providing a comprehensive knowledge of quark color theory within the framework of complex octonionic space. We investigated the octonionic interaction of color quark-antiquark and the connection between complex octonions with quark fluxtube. We have discussed the interaction of quark and anti-quark flavors in triplet complex octonion spaces. This study can explain the quark fluxtube in generalized complex octonion spaces. We have addressed the quark fluxtube for each complex-octonion space. We have also discussed the color fluxtube, meson fluxtube, or color string in complex-octonion space.
