Department of Mathematics

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    Application of Ranking Heptagonal Neutrosophic Fuzzy Numbers to a Tansportation Problem
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Mudasir Nazar, Umer Farooq; CIIT/FA22-BSM-031/LHR, CIIT/FA22-BSM-59/LHR; Dr. Madiha Khalid; LHR TP 9924
    This thesis introduces the concept of neutrosophic heptagonal numbers and presents a novel approach for their ranking. Neutrosophic heptagonal numbers extend the realm of neutrosophic numbers to a seven-dimensional space, offering a more comprehensive representation of uncertainty in various real-world appli- cations. The developed ranking method provides a structured framework to assess and order these complex numbers, facilitating decision-making processes in uncertain environments. To demonstrate the practical utility of this approach, we apply it to solve a transportation problem framed within the context of a cost matrix. By lever- aging the ranking methodology on the cost matrix, we effectively address the uncertainties inherent in transportation planning, optimizing routes, and mini- mizing costs. Through computational experiments, we validate the effectiveness and efficiency of the proposed method in handling real-world scenarios charac- terized by intricate uncertainties. This research contributes to advancing the understanding and application of neutrosophic heptagonal numbers in decision sciences, offering a valuable tool for analyzing complex systems where uncertainty plays a significant role
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    Computational aspects of SSC of Wheel Graphs
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Rimsha Amber; CIIT/FA20-BSM-058/LHR; Dr. Imran Ahmed; LHR TP 9923
    Simplicial complexes represent crucial mathematical structures with broad applications. Stanley-Reisner ideals encode combinatorial information about these complexes, bridg- ing combinatorial geometry and commutative algebra. Simplicial complexes, comprised of simplices, capture complex topological and combinatorial relationships, serving as founda- tional tools in numerous mathematical disciplines. Shellable complexes, a significant sub- class, allow systematic decomposition into ”shells,” revealing insights into their topological and homological properties. Studying the spanning simplicial complexes of wheel graphs elucidates the connection between graph theory and algebraic topology. Investigation into the shellability of line simplicial complexes sheds light on their combinatorial intricacies, contributing to a deeper understanding of their geometric and algebraic nature. Through these explorations, we uncover the rich interplay between combinatorial geometry, alge- braic structures, and topological properties inherent in simplicial complexes, facilitating broader comprehension and application across mathematical domains.
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    Deviation of Rotating Black Hole in Loop Quantum Gravity from Kerr Black Hole
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) MADIHA KANWAL; CIIT/FA20-BSM-041/LHR; Dr. Muhammad Zubair; LHR TP 9916
    First and foremost, I would like to thank ALLAH Almighty (the most beneficent and most merciful) for giving me the strength, knowledge, ability and opportunity to undertake this research study and to preserve and complete it satisfactorily. My heartiest gratitude to Hazrat Muhammad (S.A.W) for His guidance to humanity and for material and spiritual uplift. I would like to express my deepest gratitude to my supervisor Dr. Muhammad Zubair, for his excellent guidance, interest, patience, and for providing me a decent atmo- sphere for the research. It was not an easy task but his extraordinary support made it so. I am also thankful to my senior research fellow Muhammad Ali Raza (PhD student) who always taught me with his humble attitude and with whom I collaborated and learned many things. Lastly, I would like to thank my parents and siblings, who always supported me and prayed for my success. Without their support, love and efforts, I would have not achieved all this. They gave me wings to fly.
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    Characterizing Localized Wave Structures in High-Dimensional Nonlinear PDEs
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Bismah Nazir; Fa23-rmt-008; Dr. Hafiz Muhammad Afzal Siddiqui; LHR TP 9756
    This thesis investigates the extraction of solitons that arise in nonlinear dynamics, focus ing on two important models: the Stochastic Davey–Stewartson equation and the Ben jamin–Bona–Mahony (BBM) equation well known Nonlinear Evolution equation. Numer ous physical events are described by these models, which are well known for their intricacy in nonlinear wave propagation. These models are solved using the Extended Modified Aux iliary Equation Method (EMAEMM), a potent yet effective technique for resolving nonlin ear partial differential equations (NLPDEs). By simplifying the equations, the EMAEMM approach facilitates the search for precise solutions, making it a valuable tool in nonlinear analysis. Optical fibers, fluid dynamics, and plasma physics are just a few of the many applications that benefit from the soliton’s ability to maintain its shape while propagating. A variety of graphical representations, all created using Mathematica, are displayed, in cluding 2D, 3D, density linear, 1D, slice contour plotting, and stream density plots, and the stability and sensitivity of the resulting solitons are investigated. Bright, dark, kink, periodic, and optical solitons are among the many different behaviors of the reported soli tons. This thorough analysis of soliton dynamics in nonlinear systems offers insights on the stability and representation of solitons in mathematical physics