Browsing by Author "Rahman, Md. Majedur"

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    A Study on Convergence of Newton's Method in Real and Interval Number
    (University of Rajshahi, 2003) Rahman, Md. Majedur; Ali, Md. Zulftkar
    In order to find the approximate numerical solution to a system of nonlinear equations as well as an integral and a differential operator equations, Newton's algorithm is widely used. L. V. Kantorovich [1948] and Moore [1977] studied the existence and uniqueness of solution to the system of nonlinear equations and their error bounds. M. Urabe [ 1965] also studied the existence and uniqueness of the solution to nonlinear operator equations (mainly differential operator equations). Kantorovich and Urabe's methods are two variants of Newton's method in some sense. We study the existence and uniqueness of solutions to the nonlinear systems and their error bounds. Our results will be stated in a theorem that ensures the best possible generalized error bound that is different from that given by Kantorovich and Moore. We also develop a technique that may be applied to find an approximate numerical solution to an algebraic as well as to a system of nonlinear equations both in real and interval number systems. Finally, we have treated the error estimation for the quasiperiodic solution to the Van der pol type differential operator equation based on Urabe's theorem.
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    Decentralized Patient Healthcare record analysis using Blockchain Technology
    (Daffodil International University, 2025-05-14) Rahman, Md. Majedur
    The next-generation distributed healthcare platform is presented in this work on patient identity and record management, focusing on privacy, transparency, security, and operational efficiency. At its root, the platform combines blockchain (Hyperledger Fabric) with decentralized data storage technologies like IPFS (InterPlanetary File System) and Pinata. Together, they achieve just that commercial-grade preservation, immutability, and patient-controlled security of sensitive health data all of which are the weakest links in today’s traditional data silos of healthcare. In a conventional healthcare system, data is owned and controlled by hospitals or third parties, leading to unauthorized access, security breaches, and a lack of data sharing. Centralized systems also constrain patient self-determination such that it becomes difficult for a patient to access, manage, or exchange his or her health record. These problems can be solved by the mentioned platform, which focuses on patient control. Via such a model, users can safely store, retrieve, and share their health data and selectively allow healthcare providers to access them, transforming them into the legitimate owners of their data. The data-sharing policy is enforced automatically using smart contracts. With QR codes and powerful multi-factor authentication (MFA) options, such as Google Sign-In, Apple ID, Face ID, and fingerprint, patients can grant or rescind access to doctors, pathologists, and research labs. Smart contracts guarantee access will be given by verified patient consent, thereby enhancing trust, eliminating manual control, and drastically minimizing the danger of patient data misuse. The platform’s clinical utility is significant. It promotes interoperability among hospitals, clinics, and diagnostic centers, thereby avoiding repetition of tests and medical errors related to information fragmentation. For patients, timely access to complete medical records means faster diagnosis and treatment, better care, and outcomes. Furthermore, the platform facilitates medical research and pharmaceutical discovery, making data sharing in categorized and anonymized form possible and then only with the patient’s explicit consent for privacy-respecting innovation. Cutting-edge AI-driven analytics integrated into the system provide intelligent insights into the early detection of disease, personalized treatment plans, and efficient healthcare delivery. These instruments enable clinicians and researchers to tap into big data for proactive, predictive, and precision medicine. The platform is developed to be scalable with a high-performance and reliable architecture and is implemented as Docker containers managed by a Kubernetes orchestrator and Network File System (NFS). It also features a modern UI, which is sleek and intuitive, including dark/light mode and real-time notifications, along with smooth animations to provide an optimal experience. Environmentally, it promotes e-health by minimizing the use of paper records and attenuating the demand for overcommitted data centers, thus defraying the earth’s carbon manifestations. Conclusively, this decentralized healthcare approach gives patients freedom for control, further secures private data, enables cooperation, aids research, and is in line with the worldwide movement towards digital, secure, and patient-focused healthcare systems.