Department of Mathematics

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Author: search.filters.author.Dr. Muhammad Faisal NadeemSubject: search.filters.subject.FA19

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    Mittag-Leffler Theorem and Series Representation of Meromorphic Functions
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Waseem Akram; CIIT/FA19-RMT-002/LHR; Dr. Muhammad Faisal Nadeem; LHR TP 7404
    The goal of this thesis is to present a complete proof of Mittag-Leffler theorem, and to present some applications. We first give a simpler proof, valid for open disks and the whole complex plane. This proof uses in a crucial way the approximation of holomorphic function by means of polynomials on such domains, by means of their Taylor series. The proof of Mittag-Leffler theorem for an arbitrary domain G ⊂ ℂ is much more involved and requires the development of a more general theory of approximation of holomorphic function on complex domains. We present this theory and prove Runge’s theorem, a fundamental result in complex analysis providing conditions to have the required approximations. This allows us to complete the proof of the general version of Mittag-Leffler theorem. We complete this thesis by presenting some applications of the above results.
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    Fault Tolerance Metric Dimension of Biswapped Graph
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Navid Alam; CIIT/FA19-RMT-090/LHR; Dr. Muhammad Faisal Nadeem; LHR TP 7401
    The biswapped networks is a new interconnection networks in multiprocessor systems. These are networks of devices or processors and connection of these devices or processors. Here network can be expressed in the form of graph. Devices or processors represent vertices (nodes) and connection of devices or processors represent edges (links). The subset of the nodes set is called the resolving set if all the representations are different. The minimum cardinality of resolving set is called the locating number or metric dimension. If after the removal of any vertex from the resolving set the set remain the resolving set then the set is called fault tolerant resolving set and the minimum cardinality of this set is called fault tolerant metric dimension. In this article we found the fault tolerant metric dimension of biswapped graph.
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    On Metric Dimension of Biswapped Networks
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Waqar Ali; CIIT/FA19-RMT-099/LHR; Dr. Muhammad Faisal Nadeem; LHR TP 7384
    The biswapped networks is a new interconnection networks in multiprocessor systems. These are networks of devices or processor and connection of these devices or processors. Here network can be expressed in the form of graph. Devices or processors represent vertices (nodes) and connection of devices or processors represent edges (links). The subset of the nodes set is called the resolving set if all the representations are different. The minimum cardinality of resolving set is called the locating number or metric dimension. In this article we found the locating number of different types of interconnection networks. We found the exact value of locating number for biswapped networks developed by different basic graphs like, path, cycle, and power graph of path graph.