Browsing by Author "LHR TP 9888"

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    Discussions on Solutions of Fredholm Integral Equations
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Muhammad Adeel Khan; CIIT/SP21-BSM-022/LHR; Dr. Kashif Nazar; LHR TP 9888
    This thesis investigates the analytical and numerical solutions of Fredholm integral equa- tions of the second kind, focusing on both homogeneous and non-homogeneous cases. In the analytical framework, we explore solutions with degenerate kernels and methods to ap- proximate complex kernels by degenerate forms, providing efficient pathways for problem simplification. The study covers both theoretical and applied aspects, emphasizing cases where the kernel exhibits specific structures that facilitate closed-form solutions. Numer- ical methods are also developed and analyzed for solving these integral equations in both homogeneous and non-homogeneous settings. The numerical approaches are evaluated for their accuracy and computational efficiency, providing insights into practical implemen- tations and approximations for real-world applications. Through comprehensive analysis and comparison of methods, this research contributes to the effective solution of Fredholm integral equations, offering new perspectives for both theoretical exploration and applied problem-solving.
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    On Some Degree Based Topological Indices of Tetracyano Benzene Metal Organic Framework
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Aqib Javaid; CIIT/SP21-BSM-028/LHR; Dr. M. Faisal Nadeem; LHR TP 9888
    Metal–organic frameworks (MOFs) play a pivotal role in modern materials science due to their highly porous and customizable structures, which are ideal for applications such as gas storage, catalysis, and drug delivery. To model these complex structures, chem- ical graph theory offers a powerful mathematical framework that captures the molecular architecture of MOFs. Within this framework, topological indices—also known as molec- ular descriptors—serve as mathematical formulations derived from the molecular models. These descriptors allow researchers to analyze the physicochemical properties of MOFs without resorting to expensive laboratory experiments, thus streamlining the study of struc- ture–property and structure–activity relationships in mathematical chemistry. In this project, we focus on the tetracyanobenzene-based metal–organic framework, systematically computing and examining its various molecular descriptors. A numerical comparison of these descriptors is provided, offering insights into the framework’s charac- teristics and potential applications.