Turkish Journal of Computer and Mathematics Education (TURCOMAT)
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This article has been retracted due to a serious plagiarism issue.
No full textThis article has been retracted due to a serious plagiarism issue
Hybrid Upadhyaya Transform and Power Series Technique for Addressing Nonlinear Volterra Equations of the First Kind
No full textIn Mathematics, biology, physics and engineering, nonlinear Volterra integral equations (NVIEs) of the first kind are frequently encountered when modelling dynamic systems. However, because of their ill-posed nature and nonlinear terms, they present considerable difficulties. This work presents a hybrid methodology that combines a power series expansion with the Upadhyaya transform, a flexible tool from the Laplace family, building on recent developments in integral transforms. This combination resolves nonlinearities through systematic coefficient matching in the series domain and simplifies the handling of convolution kernels via the transform. We describe the fundamentals of the approach, show how it can be applied to four benchmark problems taken from earlier research, and expand it to a new case involving trigonometric nonlinearity. With an emphasis on computational clarity and verification, each example is broken down step-by-step. The results show that the hybrid approach outperforms standalone methods in terms of flexibility and ease, producing exact solutions when feasible and convergent approximations otherwise. There is potential for this method to be applied more widely in solving integral models in the real world
The Geometric Origin of G–c Unification: The Decisive Role of the Space–Mass Coupling Constant μg
No full textThis study reveals the unified geometric origin of the gravitational constant G and the speed of light c. By introducing the rotational scaling length , defining the helical divergence strength and the space–mass coupling relation , we establish a one-to-one correspondence between mass and geometric scale. Under the unique bridging law , we rigorously derive the invariant
This result demonstrates that G and c are not independent constants but are jointly fixed by the space–mass coupling constant and geometric structure. Using observational data from solar redshift, light deflection, planetary perihelion precession, and both Jupiter’s satellites and the white dwarf Sirius B, we verify the universality and cross-modal consistency of this relation. Geometric scaling not only explains the origin of G but also establishes a unified theoretical framework for future high-precision astronomical observations and constant metrology. This offers a more geometric expression than general relativity and proposes testable metrological predictions
Mathematical Modelling and Argumentation: Designing a Task to Strengthen Variational Thinking by Integrating Data Science
No full textThis study explores the significance of task design in fostering variational thinking through the principles of PyLVar and task design in mathematics education, particularly in the incorporation of technological and scientific tools to enhance modelling and argumentation skills among secondary school students. To develop and implement interactive mathematical tasks based on the PyLVar principle and task design, incorporating data science tools and STEAM. A qualitative-descriptive approach was employed to design, implement, and analyse interactive tasks centred on the principles of variational thinking, argumentation, and modelling. The sample consisted of nine participants selected from a group of 11th-grade students at a state school, chosen for convenience. Data were gathered through experimental activities, processed using technological tools, and analysed with variational strategies. Students demonstrated a marked improvement in their abilities in mathematical modelling and argumentation. The tasks designed, structured around the PyLVar principles, enabled the identification of variation patterns and the development of critical and analytical skills. Contextualised interactive mathematical tasks not only bolster variational thinking but also equip students to address real-world problems by connecting abstract concepts to practical applications and encouraging the integration of technological tools and interdisciplinary approaches
Security and Privacy Challenges in IOT: A Global Perspective
No full textThe fast development of the Internet of Things (IoT) has delivered various open doors and advantages across different businesses. Nevertheless, this interconnected biological system of gadgets likewise presents critical security and protection moves that should be tended to on a worldwide scale. This paper looks at the security and protection challenges looked at by IoT frameworks according to a worldwide point of view. Security chances are one more huge worry in the IoT scene. The assortment, stockpiling, and handling of individual information by IoT gadgets bring up issues about individual security privileges. Unapproved admittance to this information can bring about private profiling, reconnaissance, and abuse. Executing securitysaving systems like information anonymization, encryption, and client-driven control is fundamental to protecting security in IoT conditions. Administrative systems and guidelines likewise assume a critical part in tending to IoT security and protection challenges. Guidelines like the Overall Information Assurance Guideline (GDPR) in the European Association assist with implementing information security measures and defending client privileges. Be that as it may, variations in guidelines across locales can introduce difficulties for worldwide IoT arrangements. Fitting guidelines and structures can advance consistency and work with worldwide participation. The paper likewise investigates the capability of arising advances in upgrading IoT security and protection. Advancements, for example, block chain, edge registering, and united learning offer promising arrangements. Block chain’s decentralized and alter safe nature can give secure information stockpiling and exchange the executives. Edge registering decreases dormancy and information openness by handling information nearer to the source. Combined learning empowers cooperative model preparation while protecting information security. Coordinating these innovations into IoT frameworks can add to a safer and protection-mindful worldwide IoT biological system
Adapting to Remote Work: Emerging Cyber Risks and How to Safeguard Your Organization
No full textThe COVID-19 pandemic has rapidly accelerated the shift to remote work, permanently altering organizational dynamics. As businesses and employees adapted to a remote-first environment, they also became exposed to a new set of cybersecurity threats. The traditional cybersecurity measures designed for office environments are no longer sufficient to address the unique risks associated with remote work. These risks include vulnerabilities in home networks, unsecured devices, increased susceptibility to phishing and social engineering attacks, and the rapid adoption of cloud-based collaboration tools. This paper will explore the cybersecurity challenges posed by remote work and suggest proactive steps organizations can take to safeguard their data, assets, and personnel. Key strategies, including enhanced endpoint security, secure communication channels, Multi-Factor Authentication (MFA), security awareness training, and Zero Trust architecture, will be discussed to help organizations minimize their exposure to these emerging risks
Color Image Compression Using Vector Quantization with Fuzzy Logic
No full textImage compression is a critical method for minimizing digital image size for efficient storage and transmission, particularly in bandwidth-constrained applications. A new approach for color image compression by incorporating vector quantization (VQ) and fuzzy logic is introduced in this paper with the aim of further improving performance. Vector quantization is another commonly used lossy compression technique in which an image is divided into small blocks and mapped to a prechosen set of representative vectors called codewords, thereby compressing the image considerably.
In order to solve the problem of maintaining image quality while compressing it, we apply fuzzy logic to increase the accuracy of the codeword selection mechanism. Using the fuzzy logic rules, we define the selection rules adaptively based on the characteristics of the image in order to achieve maximum balance between compression ratio and image quality. Application of fuzzy logic enables smoother movement from one region of images with similar content to another and eliminates quantization errors characteristic for VQ, especially in regions of high variance of pixel intensity.
The new hybrid method was applied to several color images and was proven to surpass the traditional VQ method in terms of compression ratio, PSNR, and SSIM measures. The hybrid method offers an efficient plan for high-compression-quality-image with little computational cost
EYES IN THE SKY: STRENGTHENING PUBLIC AWARENESS AND LAW ENFORCEMENT RESPONSE TO DRONE-DRIVEN INFRINGEMENTS ON PRIVACY RIGHTS IN THE UNITED STATES
No full textThe rapid proliferation of drones in the United States has created urgent challenges concerning individual privacy, institutional readiness, and legal enforcement. While drones serve diverse functions, their use in surveilling private spaces without consent has exposed significant regulatory gaps in both federal and local legal frameworks. This research investigates these gaps by analyzing a real-life case from Silicon Valley, where a civilian encountered a drone hovering above their private residence and was unable to obtain meaningful assistance from law enforcement.Drawing on recent scholarship, including Siddiqui and Muniza’s “Regulatory Gaps in Drone Surveillance” [Annals of Human and Social Sciences, 2025] and “The Drone’s Gaze: Religious Perspectives on Privacy and Human Dignity” [Al-Qamar, 2024], this paper reveals how current laws fail to protect against aerial intrusions, especially in residential zones. The findings are further contextualized within broader institutional weaknesses, as previously identified in “Public Funds, Private Gains” [JARSSH, 2022] and “Hybrid Warfare and the Global Threat of Data Surveillance” [PSSR, 2025].Moreover, the paper critiques recent legislative efforts, such as the U.S. Countering CCP Drones Act (H.R.2864), through the lens of Siddiqui and Muniza’s (2025) analysis published in the Social Sciences & Humanity Research Review, and assesses their ineffectiveness against AIpowered foreign-manufactured surveillance drones. Philosophical and constitutional dimensions are explored through works like “Liberalism in South Asia” [CIBGP, 2008], and “Constitutional Vulnerability in the Age of Digital Surveillance” [CRLSJ, 2025]
The research proposes a three-pronged regulatory framework:
1. Modernization of legal statutes to close regulatory and constitutional loopholes;
2. Institutional upskilling through integrated AI-based geofencing and centralized FAADHS-local reporting platforms;
3. Public empowerment via education, civic engagement, and participatory complaint channels.
The paper concludes that safeguarding privacy and national security in the drone era requires an interdisciplinary approach—bridging law, technology, ethics, and public participation. Only through such coordinated efforts can drone innovation be directed toward public benefit without compromising civil liberties.
An Interdisciplinary Review on Application of Graph Theory
No full textGraph theory is a branch of discrete mathematics that is used to model and analyze interconnected systems. This paper presents a review on application of its concepts and algorithms that support diverse applications in computer science, biology, neuroscience, social sciences, engineering and geosciences. It is also reviewedthat graph theory helped in network optimization, clustering, molecular modelling and brain connectivity, it provides powerful tools for solving complex problems. It is reviewed that spectral methods, probabilistic models and graph neural network let the graph theory to evolve continuously as an essential interdisciplinary framework for understanding and optimizing complex networks in the modern world
Design and Implementation of a Cost-Effective, Network-Based Clinic Management System for Small Healthcare Facilities in Iraq
No full textManaging clinics efficiently requires a cost-effective and user-friendly system that simplifies daily operations while maintaining data security and accessibility. This paper proposes a clinic management system that does not require a dedicated server in order to minimize costs and ease the process of setup. The system is developed using SQLite, a lightweight database management system that enables easy data management on local machines and supports networked terminals. For the best performance, we divide the data into two SQLite files; the first for the basic activities of the clinic and the second for prescriptions and other attachments to enhance the processing and use of the system. The system is developed using C# and has a friendly graphical user interface for doctors and secretaries. It has role-based access control that provides secure user authentication and database is encryption to ensure that patient’s information is well protected. The system is deployed via Windows network sharing, which makes it very easy to connect multiple terminals simultaneously through LAN or Wi-Fi without the need of professional IT personnel. This system has been used in more than 50 clinics and has proven to be reliable, efficient and easy to use and is therefore suitable for small to medium size healthcare institutions. It improves the management of the patient’s records, the flow of work, and provides a cost-effective alternative to traditional clinic management solutions