PhD
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/50
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Some Studies of Two-Population Neural Field Model(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Zeeshan Afzal; CIIT/FA13-PMATH-009/LHR; Dr. Muhammad Yousaf Bhatti; LHR TP 5949We investigate the appearance and disappearance of localized activity states, so called bumps in Wilson-Cowan type two population neural field model under the influence of transient spatio-temporal external input with smooth α-type and piecewise-type temporal functions. This two-population model is composed of two coupled nonlinear differential equations derived for the dynamics of spatially localized populations of both excitatory and inhibitory model neurons. The model with no external input corresponds to atmost two bump pair solutions. Such a system can be interpreted as a minimal cortical model for short term working memory, that is the ability of the brain to actively hold stimulus-related information for some seconds in short term memory and discards once it becomes irrele- vant Initially, if there is no activity in the system, persistent activity state can be evoked by switching on a suitable transient excitatory external input. This activity remains stable even though external input is switched off. The effect of external input on appearance and disappearance of bumps for different spatial, smooth α-type and piecewise-type temporal functions of external input is investigated and found that certain parameters play a key role in the generation of persistent activity states in the network e.g. relative inhibition time constant, total duration and the amplitude of external input. It is found that the minimum values of the amplitude and active time to evoke the activity in the network is smaller than those observed in showing that the present choice of temporal functions in the external in- put is more effective and more close to natural behavior.Item Words for Maximal Subgroups in Certain Sporadic Simple Groups(Library Information Services, COMSATS University, Lahore Campus, 2018) Faisal Yasin,; FA13-PMATH-002; Dr. Adeel Farooq,; LHR TP 5946In this thesis we found generators for the Maximal Subgroups (MSs) of the Sporadic Sim ple Groups (SSGs) as words in the generators of the parent group. The idea of standard generators was presented by Wilson. He began a project known as online form of Atlas, ”http://brauer.maths.qmul.ac.uk/Atlas” in which he provides the representation and words for MSs of the SSGs. However there are some cases, which have to be dealed. We pursue the work initiated by R. A. Wilson of finding words for the MSs of SSG. Thus the only cases on the list of World-wide-web Atlas which need to be solved are Co1, HN, Fi23, Fi24, B and M. There are 14 MSs of Harada-Norton group HN. Generators of 11 MSs are already known. In this thesis we have provided generators of remaining 3 MSs. Similarly, we have provided words for four MSs of Fi23, words for sixteen MSs ofCo1, words for 11 MSsofFi24 and words for MSs of some linear groups. In World-Wide-Web Atlas of group representation there is only one copy of S5 of the MSs of L3(5), but we have found words for two non-conjugate copies of S5 in Table 15 of second chapterItem Degree and Distance Based Parameters of Certain Graph Structures(Library Information Services, COMSATS University, Lahore Campus, 2016) Zeshan Saleem Mufti; , FA12-PMATH-006; Dr. M. Fasial Nadeem, Assistant ProfesorDegree and Distance Based Parameters of Certain Graph Structures Topological indices are a rapidly developing area of research in graph theory. There are various topological indices such as degree-based topological indices, spectrum based topological indices and distance related topological indices. These topological indices correlate certain physico-chemical properties such as boiling point, stability of chemical compounds and many more. In this dissertation, we focus on degree based and spectrum based topological indices. Under the degree based topological indices, we study topological indices such Randic index, general Randic index, Zagreb index, general sum connectivity index, first and second multiple Zagreb indices, geometric index, atom bond connectivity index for para-line graphs of some chemical structures such as Phenylene, Anthracene, Benzenoid, Pentacene. Similarly, we study the spectrum based topological indices such as Estrada index for certain chemical graph structures such as Phenylene, Anthracene, Bi-smuth Tri-iodide, benzene ring embedded in P-type-surface in 2D network (BRE). Also we find the energy of above mentioned structures. We also discuss the notion of distance related parameters such as metric dimension and edge metric dimension. We compute the edge metric dimension for the barcycentric Subdivision of Cayley Graphs. Also we have studied the M-polynomial and entropy of generalized Sierpinski graphs.Item H-Magic Behaviors of Some Graphs(Library Information Services, COMSATS University, Lahore Campus, 2015) Imran Zulfiqar Cheema; , FA11-PMATH-001; Dr. Muhammad Hussain,; LHR TP 5297A graph ( , ) G V E has an H-covering if every edge in E belongs to a subgraph of G isomorphic to H . SupposeG admits an H-covering. AnH-magic labeling is a mapping from ( ) ( ) E G VG onto the integers {1,2,...,| ( ) E G VG ( )|} with the property that, for every subgraph Aof G isomorphic toH , there is a positive integer c such that A v ( ) v V A ( ) ( ) . e c e E A ( ) A graph which possess such type of labeling is known as H-magic graph. Further if in a graph vertices are labeled first with smallest positive numbers, then the graph is called H-supermagic. Moreover a graph is said to be H-( , ) ad-anti magic if the magic constant for an arithmetic progression with initial value a and a common difference . d Numerous results on labeling of many families of graphs have been published. In this thesis, research work focuses on to formulate cycle 3 C- ( , ) ad anti-supermagic labeling for the Multi Wheels graph, supermagic labeling for isomorphic copies with its disjoint union of Multi-Wheels graph and cycle ( , ) ad-anti-supermagic labeling for Web graph. Also cycle anti-supermagic labeling for isomorphic copies with its disjoint union of ladder and triangular ladder graphs have been formulated. In addition, investigation of fan, friendship, ladder and wheel line graphs and study of the supermagic and anti-supermagic vertex-edge-face labeling of such graphs and their isomorphic copies have been carried in this thesis. An anti-supermagic labeling of the extension of cycle graphs is also formulated. Lastly the face supermagic labeling of (1,1,1) type of subdivided triangular ladder graph, subdivided mC 4-snake graph and subdivided kmC 4-triangular snake graph with its (1,1,...,1) and (2,2,...,2) string are also the part of this thesis.Item Valuations and Metric Dimensions on Graphs(Library Information Services, COMSATS University, Lahore Campus, 2016) Shahid Imran,; LHR TP 5605; FA12-PmAth-003; Dr. Muhammad Hussain, Assistant ProfesorLabeling of graph is a beautiful and rich technique of Mathematics. It has extensive usage in applications such as data transmission, x-ray, circuit design, astronomy, communication links and coding theory. Labeling of graph is defined as a correspondence from the set } , ,3,2,1{ f e v to the vertices, edges and faces of a plane graph G in such a way that each vertex, edge and face receives exactly one label and each number is used exactly once as a label. The weight of a face under a labeling of type )1,1,1( is the sum of labels carried by that face and all the edges and vertices surrounding it. A labeling of type )1,1,1( of a plane graph G is called d-antimagic if for every positive integer s the set of weights of all s-sided faces is } )1 ( , , 2 , , { d f a d ad aa for some integer a and 0d , where f is the number of s-sided faces. In particular when 0d then the d antimagic labeling of type )1,1,1( is called magic labeling of type )1,1,1( . Moreover, if the vertices are labeled by the smallest possible number. It is known as super magic and anti magic accordingly. Furthermore, let G be a connected graph and ) , ( y x d be the distance between the vertices x and y in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by ). ( dimG This dissertation studies about the construction of super face anti-magic labeling of type )1,1,1( for disjoint union of toroidal fullerenes, magic and anti-magic labeling of type )1,1,1( for union of generalized friendship graphs. Metric dimension of Jahangir related graphs, generalized prism related graphs and graphs obtained by rooted product has been also calculated.Item Dynamical Properties of Specific Black Holes(Library Information Services, COMSATS University, Lahore Campus, 2015) Muhammad Umair Shahzad,; FA13-PMATH-005; Dr. Abdul Jawad, Assistant Profesor; LHR TP 5606Dynamical Properties of Specific Black Holes The present thesis comprises the study of three dynamical phenomenon such as thermal fluctuations, accretion and tidal forces of black holes/regular black holes. We consider the logarithmic corrected entropy in order to analyze the thermal fluctuations. We examine the effects of thermal fluctuations on a regular black hole of the non-minimal Einstein-Yang-Mill theory with gauge field of magnetic Wu-Yang type and a cosmological constant. We investigate the first law of thermodynamics in the presence of logarithmic corrected entropy and non-minimal regular black hole. Furthermore, we discuss the thermal fluctuation problem by utilizing the higher order corrected entropy. We examine the thermodynamical behavior of two well-known black holes such as Reissner-Nordström Anti de Sitter black hole with global monopole and f(R) black hole in the presence of higher order corrected entropy. We also discuss the accretion problem in two phases. In first phase, we analyze the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, non-linear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. In second phase, we develop the Hamiltonian dynamical system to tackle the accretion problem. We investigate the accretion of test fluids onto regular black holes such as Kehagias-Sftesos black hole and regular black holes with Dagum distribution function. We analyze the accretion process when different test fluids are falling onto these regular black holes. The behavior of fluid flow and the existence of sonic points is being checked for these regular black holes. Finally, we investigate the tidal forces occurring in a Kiselev black hole surrounded by radiation and dust fluids. We also solve the geodesic deviation equation for radially free-falling bodies toward Kiselev black hole. We explain the geodesic deviation vector graphically and point out the location of the event and Cauchy horizons for specific values of the radiation and dust parameters.Item Face Anti-magicLabelingsand Deficiency of Graphs(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2018) Ali Tabraiz,; FA14-PMATH-001; Dr. Muhammad Hussain, Assistant Profesor [Supervisor]; LHR TP 5296Face anti-magic labeling is a significant concept in graph theory that extends the idea of anti-magic labeling from edges and vertices to the faces of planar graphs. A face anti-magic labeling assigns distinct integers to the elements of a graph (vertices, edges, or both) such that the sums associated with each face—typically computed from incident vertices and/or edges—are pairwise distinct. This study explores the existence and construction of face anti-magic labelings for various classes of planar graphs, including cycles, grids, and generalized planar structures. Furthermore, the notion of deficiency is introduced as a measure of how far a graph is from admitting a face anti-magic labeling. Specifically, the deficiency of a graph is defined as the minimum number of isolated vertices or additional elements required to extend the graph so that it satisfies the face anti-magic condition. We investigate bounds, exact values, and constructive techniques for determining the deficiency of selected graph families. The results contribute to a deeper understanding of labeling properties in planar graphs and provide new directions for research in combinatorial optimization and graph labeling theory. Potential applications of these findings include network design, frequency assignment, and coding theory, where distinct labeling constraints are essential.Item Automated Detection and Classification of Brain Tumor from MRI Images using Machine Learning Methods(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2018) Ghulam Gilanie; , FA14-PCS-007; Dr. Usama Ijaz Bajwa, Assistant Profesor [Supervisor]; LHR TP 5805Automated Detection and Classification of Brain Tumor from MRI Images using Machine Learning Methods The focus of this thesis is to report an automated, efficient, and robust method of brain tumor detection and classification from Magnetic Resonance Images (MRI) images. Clinically, it is a challenging issue faced by the researchers working in this domain. In routine health care units, Magnetic Resonance (MR) scanners are being used to generate a massive number of brain slices, underlying the anatomical details. Pathological assessment from this medical data is being carried out manually by the radiologists or neuro oncologists. Due to huge volume of brain anatomical data produced by MRI scanners, it is almost impossible to manually analyze every slice. Conclusively, if automated protocols are executed for auto-interpretation; not only the radiologist will be assisted but also a better pathological assessment process would be expected. Several methods have been suggested to address this problem, but still, accuracy, robustness and optimization is still an open issue to address. The development of such automated procedures is difficult due to complex organization of brain cells, several types of tumor, difference in medical traits of a specific ethnicity and many more factors. To achieve the target, research has been started from reviewing the most popular and prominent state-of-the-art methods. Based upon the reviewed literature, automated brain tumor detection and classification techniques have been reported with high computational cost, low classification rates, detection and classification of only one or a few of brain tumor types, lack of robustness, etc. Therefore, step wise research and experiments based upon empirical scientific methodology have been performed in order to achieve the objectives of brain tumor classification.Item Space Spectral Time Fractional Finite Difference Method along with Stability Analysis for Fractional Order Nonlinear Wave Equations(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Muhammad Sarmad Arshad; SP13-PMATH-004; Dr. Ayesha Sohail; LHR TP 5299In this work, nonlinear partial differential equations governing the obscure phenomena of shallow water waves are discussed. Time fractional model is considered to understand the upcoming solutions on the basis of all historical states of the solution. A semi-analytic technique, Homotopy Perturbation Transform Method (HPTM) is used in conjunction with a numerical technique to validate the approximate solutions. With the aid of graphical interpretation, the favorable wave parameters, to avoid wave breaking are estimated. Afterwards, dynamical analysis of fractional order Schr dinger equation governing the optical wave propagation is reported in detail. The validity criteria for the application of the semi-analytic asymptotic methods are exploited. Comparison between the solutions obtained by the two asymptotic techniques, that is, the Fractional Homotopy Analysis Transform Method and the Optimal Homotopy Analysis Method is performed to select the most accurate technique for the stated problem. Space spectral analysis with integrating factor technique and time fraction finite difference method have been implemented to study the pressure waves propagating in bubbly fluids as well as nonlinear phenomena of plasma waves. Dynamical analysis of acoustic/pressure waves propagating in bubbly fluids is of great significance. Such flows arise in many engineering problems including sonochemistry, sonochemical reactors, cavitation around hydrofoils and ultrasonic propagation in medicine and biology. Fractional approach for modeling the propagation of the pressure waves in liquids containing a large number of tiny gas bubbles is proposed. Moreover, numerical solution of the fractional order Modified Korteweg-de Vries equation governing the dynamics is approximated using a novel space spectral time fractional finite difference tool. A spectral technique for space and a multi-step finite difference scheme for time are designed and implemented. The spatial spectral discretization error and the stability bounds are discussed. The nonlinear phenomena of plasma waves are well demonstrated with the aid of graphical analysis. Stability analysis of integer and fractional order KdV equations have been discussed quantitatively with the help of Evans function approximation.Item Topological In Variants Of Graphs(Library Information Services, COMSATS University, Lahore Campus, 2017) Imran Nadeem,; FA13-PMATH-003; Dr. Hani Shaker, Assistant Profesor [Supervisor]Chemical graph theory provides useful tools such as molecular descriptors to develop strong intrinsic relationship between the physicochemical features of chemical com pounds and their molecular graphs. The study of molecular descriptors provides a the oretical basis for the fabrication of chemical materials and is helpful in making up for the lack of chemical experiments. There are two prominent types of molecular descrip tors; the topological indices and counting polynomials. Further, topological indices can be categorized in two major classes: one class is based on degree and the other class is based on distance. In this thesis, we present the study of certain topological indices belonging to degree- and distance-based classes and counting polynomials for some well-known nanostructures. We also present a comparative study between dif ferent topological indices belonging to degree- and distance-based classes for general graphs. In addition, we study the para-line transformation of graphs and obtain the gen eral expressions of certain topological indices for this transformation. We achieve the lower and upper bounds of certain distance-based topological indices for the para-line transformation of graphs