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.
Browse
20 results
Search Results
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 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 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. ixItem General Linear Methods With Projection(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Lubna Mustafa; FA16-RMT-031; Dr. Yousaf Habib; LHR TP 5194The present work deals with the structure-preserving numerical methods for the solution of ordinary differential equations representing dynamic systems from the Hamiltonian perspective of classical mechanics. These differential systems involve quantities that should remain constant over the course of enquiry. Whereas the usual numerical methods do not account for the preservation of these invariants, structure-preserving methods such as the symplectic Runge-Kutta methods and the G-symplectic general linear methods faithfully maintain these characteristic properties of a Hamiltonian system during the numerical discretization of the problem. Physically significant invariant properties of a Hamiltonian system include the conservation of total energy and the symplecticity of flow. In Chapter 1, basic theory of ordinary differential equations is introduced. The exposition combines definitions with the construction and implementation of numerical methods for ordinary differential equations and is central to all the subsequent investigations carried out in this work. In Chapter 2, long - term integrators for a Hamiltonian system are treated in detail. The general linear methods subsume the Runge-Kutta methods as well as the linear multi-step methods introduced previously. In Chapter 3, the important notion of projection is also introduced here. The basic idea of the standard projection technique is generalized to develop the heterogeneous class of numerical methods collectively known as the general linear methods. Projection technique is applied to the general linear methods and the similarity of the symplectic Runge-Kutta methods to the G-symplectic general linear methods is discussed.Item Topological Indices On Chemical Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Tayyaba Razzaq; SP16-RMT-002; Dr. Muhammad Hussain; LHR TP 5345Topological index is a numeric parameter which describe some silent features (con nectivity, boiling point, stability and melting point) of a Molecular graph representing some chemical compounds. These indices characterize topology and are usually hold mathematical properties of Graph invariant.The process of transforming chemical information of chemical molecules into useful numerical results is known as molec ular descriptor. These molecular descriptors are extensively used in the study of Quantitative structure-activity relationships (QSARs) which give insight to the bio logical properties based upon chemical structures. We will investigate R˜andic indices Rλ(G), where λ ∈ R. First, second and third Z˜agreb indices, First and second Z˜agreb Polynomials, Multi Z˜agreb indices, Atom bond connectivity ABC index, Geometric arithmetic GA index, fourth version of ABC index, Harmonic index and fifth version of GA index to estimate biological properties of chemical graphsItem Analytical Study of Bio-Heat Transfer in Blood and Tissue by LTNE Model(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Dillawar Ali; FA17-RMT-013; Dr. Mohsan Hassan; LHR TP 5650Consider the fully developed heat flow in biological porous channel consisting of blood and tissue phase. Fluid flow through a partially filled porous channel, in which porous layer is considered at center of the channel. The problem is formulated by taking two energies equations for blood and tissue phases under two types of boundary conditions. In first case, heat flux is imposed on top wall and second wall is taken as isolated core region. In second case, heat flux is imposed on one wall and taken the uniform core temperature for the second wall. Results of both cases are calculated in form of temperature profile for blood and tissue phases for discussion.