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Browsing by Author "Hasan, Md. Shahid"

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    Article
    B-Spline Curve Theory: an Overview and Applications in Real Life
    (de Gruyter Poland Sp Z O O, 2024) Hasan, Md. Shahid; Alam, Md. Nur; Fayz-Al-Asad, Md.; Muhammad, Noor; Tunc, Cemil
    This study commences by delving into B-spline curves, their essential properties, and their practical implementations in the real world. It also examines the role of knot vectors, control points, and de Boor's algorithm in creating an elegant and seamless curve. Beginning with an overview of B-spline curve theory, we delve into the necessary properties that make these curves unique. We explore their local control, smoothness, and versatility, making them well-suited for a wide range of applications. Furthermore, we examine some basic applications of B-spline curves, from designing elegant automotive curves to animating lifelike characters in the entertainment industry, making a significant impact. Utilizing the de Boor algorithm, we intricately shape the contours of everyday essentials by applying a series of control points in combination with a B-spline curve. In addition, we offer valuable insights into the diverse applications of B-spline curves in computer graphics, toy design, the electronics industry, architecture, manufacturing, and various engineering sectors. We highlight their practical utility in manipulating the shape and behavior of the curve, serving as a bridge between theory and application.
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    Article
    Bifurcation Analysis and Solitary Wave Analysis of the Nonlinear Fractional Soliton Neuron Model
    (Springer int Publ Ag, 2023) Alam, Md. Nur; Akash, Hemel Sharker; Saha, Uzzal; Hasan, Md. Shahid; Parvin, Mst. Wahida; Tunc, Cemil
    Fractional nonlinear soliton neuron model (FNLSNM) equation is mathematical interpretations employed to describe a wide range of complicated phenomena occurring in neuroscience and obscure mode of action of numerous anesthetics. FNLSNM equation explains how action potential is started and performed along axons depending on a thermodynamic theory of nerve pulse propagation. The signals that pass through the cell membrane were suggested to be in different forms of solitary sound pulses which can be modeled as solitons. So, the scientific community has exposed momentous interest in FNLSNM equation and their Bifurcation analysis (BA) and solitary wave analysis (SWA). This study employs the modified (G '/G)-expansion (M-(G '/G)-E) method to derive BA and SWA for the FNLSNM equation, utilizing the Jumarie's fractional derivative (JFD). 3D and BA figures are presented of FNLSNM equation. Furthermore, 2D plots are produced to examine how the fractional parameter (FP) and time space parameter (TSP) affects the SWA. The Hamiltonian function (HF) is established to advance analyses the dynamics of the phase plane (PP). The simulations were performed through Python and MAPLE software instruments. The effects of different studies showed that the M-(G '/G)-E method is pretty well-organized and is well well-matched for the difficulties arising in neuroscience and mathematical physics.