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 Extension of Isotropic Solutions into Anisotropic Domain Via Gravitational Decoupling Approach(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) MOBEEN AMIN; CIIT/FA19-RMT-048/LHR; Dr. Muhammad Zubair; LHR TP 7437In this thesis, we study known charged and uncharged isotropic Heintzmann solution and Durgapal IV solution and extend it to its well anisotropic domain by manipulating gravitational decoupling through extended geometric defor- mation (EGD) approach. We employ linear transformation on both metric po- tentials and convert the single set of EFEs into two less-complicated subsys- tems. The first one is related to the standard Einstein-Maxwell field equations (EFEs), while the other one is related to additional source. The matching con- ditions at the stellar surface are discussed in detail, where outer geometry is represented by Reissner-Nordstrom solution in the presence and schwarzschild solution in the absence of charge and also evaluate the expressions for ther- modynamical quantities ρtot, ptot r and ptot t using mimic constraint and equation of state (EoS).We discuss the physical properties of the stellar model. Physical analysis is carried out using different physical indicators i.e, energy conditions, equilibrium equation, casualty condition, Herrera’s cracking concept, adiabatic index, compactness and surface redshift. In order to check the viability of the anisotropic version of the solution, we consider three different realistic stars, namely SAXJ1808.4 − 3652, SMCX − 4 and PSRJ1614 − 2230, and analyze the behavior of the model against different values of intensity parameter, i.e., γ = 0, 0.2 and 0.3 and also evaluate the graphical behavior of compact star PSRJ1614 − 2230 against different values of γ = 0.25, 0.55 and 0.75 for different model.Item Metric Dimension Of Different Chemical Structures(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Muhammad Umer Farooq; SP17-RMT-001; Dr. Muhammad Hussain; LHR TP 5431Item Explicit Formulas and Bounds on General Randic Index for Complex Graph Models(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Muhammad Sajjad Asghar; SP23-RMT-021; Dr. Maqsood Ahmad; LHR TP 9586In chemical graph theory, a topological index is a numeric value extracted from the graph ical model of the molecule that provides insight into the structural, physical, bio-active, and chemical properties of the corresponding chemical compound. Randi´c index is very influential, well investigated, and considered to be the prototype of degree-based indices. General Randi´c index Rγ(Γ) is defined as the sum over all edges of the molecular graph Γ with weights dΓ(x)×dΓ(y) γ when γ is a positive integer. Graph operations play a phenomenal role in obtaining new and complex graphs, either of general or of chemical in terest. It is pertinent to explore various graph operations to establish a relationship with the topological indices of the base graphs. In this article, we intend to derive some explicit ex pressions and bounds on the general Randi´c index when γ ∈ Z+ for various complex graph operations like the cartesian product, tensor product, lexicographic product, strong prod uct, co-normal product, corona product, splices, links, and Haj´ os construction of graphs. Besides, we compute the general Randi´c index by applying the formulas obtained for few small cases to check the validity and reliability of our results.Item Stationary Solutions And Optical Solitons For Nonl(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Insibat Afzal; FA17-RMT -012; Dr. Syed Tahir Raza Rizvi; LHR TP 5649Solitons are vastly growing field of research not only in the field of nonlinear optics but they also appear in applied mathematics, telecommunication industry and in various branches of physics and biology. Specially, optical solitons arises in many different f ields including nonlinear optics. They are the light pulses that do not diffract in the mediumthrough which they passes. These days, optical solitons play a significant role in many branches of modern telecommunication mediums including internet industry, twitter, Facebook and many more. Due to the property of not changing shape and path after collision, optical solitons are used to transfer data without using repeaters. A lot of work have been done in retrieving optical and exact solutions of the solitary waves in nonlinear optics. In this dissertation, we will obtain the stationary solutions of Gerdjikov-Ivanov (GI) equation, cubic-quintic NLSE and paraxial equation by using the help of Lie group analysis. And also, we will get chirped sub-pico bright, dark and dark singular combo optical soliton solutions for Triki-Biswas equation by using some constraints. To solve Triki-Biswas equation we will use two different integrating methods namely, sine Gordon method and modified extended direct algebraic method.Item Different Cases of Singular Domains in Two Population Synaptic Drive Model(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Wasim Shahid; SP16-RMT-008; Dr. Muhammad Yousaf; LHR TP 5198In this work we have investigated the dynamics of synaptic drive two-population neural firing rate model for the case of steep firing rate function by applying the theory of switching dynamical systems. The switching dynamic theory simplifies the dynamical system and receive the approximation of the solution for the system with certain modes of parameters. In such type of outlook, the phase space is divided into regular as well as singular domains. These singular domains are characterized into black, white and transparent on the basis of the behavior of trajectories on the sides of singular domain. Moreover, there has been investigation of the existence and uniqueness solutions with corresponding singular and regular stationary points. It has been observed that regular stationary point, which are located within regular domain, are always constant and this characteristic is secured for smooth and sufficiently steep firing rate function. Yousaf.et al investigated the dynamics for the same model. They investigated the dynamics only for some particular cases. We have explored some more cases of singular domains and investigated the dynamics in regular and singular domains. Moreover, general formulae for the stationary points of the system have been calculated and the existence of singular stationary points which belong to the singular domains have been investigated. Furthermore, these singular domains in new dynamical system have also been transformed. Besides, the stability of singular stationary points has been investigated. In the wake of outcomes, the stationary points are attended by implementing the singular perturbation analysis and Thikhonov theorem.Item Imex Methods For Ordinary Differential Equations(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Nida Khalid; FA17-RMT-053; Dr. Yousaf Habib; LHR TP 5674The aim of this thesis is to construct partitioned Runge-Kutta methods (PRK) for the numerical solution of non-separable system of ordinary differential equations y0 = f(y; z), z0 = g(y; z) as IMEX scheme (implicit explicit). The partitioned Runge-Kutta methods consist of two RK methods such that one method solve y0 = f(y; z), the non stiff differential equation, the other method solve z0 = g(y; z), the stiff differential equation. Explicit RK method is used for the solution of non stiff part and implicit RK method is used for the solution of stiff part. In order to construct PRK method, we have used the idea of effective order methods. The development of these methods require the solution of large number of order conditions, however, there exist simplifying assumptions which reduce the number of order conditions. In this thesis, simplifying assumptions for PRK method for non-separable differential equations are derived for the first time and applied successfully to reduce the effective order conditions, thus allowing us to construct effective order 3 PRK method with just two stages. This result in huge savings in terms of computational cost.Item Study of Cosmological Aspects in Chern - Simons Modified Gravity(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2022) Waheed Ahmad; FA20-RMT-006; LHR TP 7914We offer a cosmological model where the cosmos recovers in an non-unique recovery. Following the bounce, it slows down in some cases, the main evolu tion is similar to matter The era of deceleration, and finally the current era, is evolving through a phase of acceleration. Our goal is to investigate this behav ior using the modified F(R) gravity, Chern-Simons theory, and to compare the concept to other empirical evidence. We calculate the shape of the entire F(R) conceivable cosmic time horizon using enabled the development and the rele vant process parameters. The quasi jump appears to be associated with periods of DE, particularly from quasi bounces to slowdowns as well as from the re tardation era to the late acceleration era, according to the structure of F(R). It is vital to recognize that the script’s rebound in this situation is an uneven bounce, particularly because the Hubble radius is monotonic. It gradually increases and gradually differentiates in the latter part of ca, while it seems to decrease grad ually over time now. Decreasing behavior of Hubble beam ensures delayed acceleration cosmic age. Furthermore, due to the aforementioned the Hubble radius’s development, prototype disturbance patterns occur during deep con tractions awayfromrebounds,whenalltheperturbationfunctioniscoming. We calculate gradient and tensile strength separately spectral, so we evaluate raw observations such as spectral metrics gradient curvature misalignment, stretch ing the gradient ratio, therefore, in I agree with the most recent Planck 2018 limitations. The term CS¢aappears to, in this meaning, it has a significant effect on the development of tensor barriers, but keeps the gradient part constant, the perturbation in the case of the vacuum modelF(R), therefore, CS the term seems to play an vital role in reconciling observable with Planck result.Item Randic, Seidel And Laplacian Energy Of NEPS Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Yasir Ali; FA17-RMT-007; Dr. Sarfarz Ahmad; LHR TP 5645Let be the simple graph, then we can obtained the energy of a graph by taking the absolute sum of the eigenvalues of the adjacency matrix of . In this research we have computed different energy invariants of the Non-completed Extended P-Sum (NEPS) of graph . In particular we investigate the Randic, Seidel and Laplacian energies of the NEPS of path graph with any base . Here denotes number of vertices and denotes the number of copies of path graph . Our some of the results depend on the number of zeroes in base elements, for which we use the notation .Item Metric Dimension Of Different Chemical Structures(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Hafiz Muhammad Bilal; FA16-RMT-027; Dr. Muhammad Hussain; LHR TP 5191The Metric Dimension of a graph G is the minimum number of basis element in a resolving set. Let G = (V,E) be a connected graph and length of a shortest path between u and v is known as distance, denoted by d(u,v) in G. Let B = {b1,b2,...,bk} be an ordered set of vertices of G. The representation r(u|B) of u with respect to B is the k − tuple {d(u,b1),d(u,b2),d(u,b3),...,d(u,bk)}, where B is called a resolving set or locating set if every vertex of G is uniquely identified by its distances from the vertices of B or equivalently if distinct vertices of G have distinct representations with respect to B. A resolving set of minimum cardinality is called a basis for G and cardinality is the metric dimension of G is denoted by dim(G). In this thesis we investigated metric dimension of subdivided honeycomb network and Aztec diamond networkItem Consensus Based Group Decision Making With Incomplete Reciprocal Fuzzy Preference Relations Using Product T-norm.(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Mustanser Hussain; FA17-RMT-035; Dr. Adeel Farooq; LHR TP 5661In this dissertation, a consensus-based method for group decision making (GDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in GDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the GDM process. ix