M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Studies On Inner Product Spaces And Hilbert Spaces(Library Information Services COMSATS University Lahore Campus, 2024-03-18) Laraib Akram; SP23-RMT-013; Dr. Kashif Nazar; LHR TP 9578Studies On Inner Product Spaces And Hilbert SpacesItem Analysis of the Formulations and Continuities of Kernels of Integral Equations for Ahlfors Map(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Muhammad Amin Khan; FA22-RMT-017; Dr. Kashif Nazar; LHR TP 9380This study aims to examine and analyze the boundary integral equations of the Ahlfors map specifically for multiply connected regions. The Ahlfors map, known for mapping the boundary of a domain to the unit circle, helps in understanding the domain’s structure. Our goal is to rederive boundary integral equations that are more effective in determining the Ahlfors map and its unknown zeros. Identifying these zeros is crucial as they provide important information about the map’s behavior and the domain’s geometry. By develop ing these new equations, we hope to address existing challenges and solve long-standing problems in the field, ultimately advancing mathematical understanding and applications of the Ahlfors map in complex analysis and related disciplines.Item Integral Equations Method for Ahlfors Map and its Zeros(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Muhammad Ilyas; SP19-RMT-023; LHR TP 7409; Dr. Kashif NazarThe purposeofthisstudyistoexamineandanalyzetheboundaryintegral equations ofanAhlforsmapformultiplyconnectedregions.Alsotoderive some newboundaryintegralequationsrelatedtoanAhlforsmapwhich maymorebesuitableforfindingtheAhlforsmapanditsunknownzeros. The Nystr¨om methodwiththetrapezoidalrulewillbeusedtoparametrize and discretizetheseintegralequationsintosystemsofequations.Item Analyzing the Nystrom Method for Second Kind Fredholm Integral Equations(Library Information Services COMSATS University Islamabad Lahore Campus, 2023-03-12) Kainat Tahir; SP22-RMT-017; LHR TP 8724; Dr. Kashif NazarThis research proposal aims to study if second-kind Fredholm Integral Equations can possibly be solved using the Nystrom Method, which are common in many different fields and which require for the development of effective numerical solutions. The Nystrom Method will be thoroughly examined, along with an explanation of how it applies to second-kind Fredholm Integral Equations. Additionally, it will look at how different parameters influence the convergence of the Nystrom Method, such as the number of discretization points and the choice of numerical quadrature. The expected outcomes are meant to deepen our understanding and facilitate the advancement of numerical algorithms, leading to a more reliable and efficient solutions for integral equations. This discovery holds importance for numerous scientific and engineering domains, and it can lead in advancements in computer methodologies