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 Slip Effects Of Creeping Flow Of Couple Stress …(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Muhammad Saqib Iqbal; SP19-RMT-012; LHR TP 7411; Dr. Muhammad Younasmetal industry it is used in metal cutting process, in polymer industry it is used in plas- tic processing and also used in chemical processing. Our discussion is scattered around the speci c type of non-Newtonian uid called couple stress uid. Couple stress uid is a polar form of uid as it has polar e ects. Couple stress uid [1] rst studied by Stokes and Vijay Kumar, they considered e ects of couple stresses on a uid. A series of di erent boundary value problems was solved by them to express the result of couple stresses. The study of couple stress uid [2] is exceptionally valuable in understanding di erent physical problems, it has system to depict the logically complex uids for ex- ample, \liquid crystals, colloidal uids, liquid crystals containing long chain molecules as polymeric suspensions, animal and human blood and lubrication" M.Farooq and A. M. Siddiqui [3] investigated an incompressible torque-strained uid to study the non- isothermal Poiseuille ow between two parallel inclined plates, also they discuss Reynold number which are depend on temperature. K. S. Mekheimer [4] studied the creeping ow of couple stress uid in regular and irregular 2D channels under zero Reynolds num-Item Some Notions of Picture Fuzzy Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Rashid; SP19-RMT-034; LHR TP 7349; Dr. Atiq ur RehmanIn this thesis, we first present the concept of Picture Fuzzy Graphs (PFGs), which is the generalization of the intuitionistic fuzzy graphs (IFGs). Then we discuss some operations on of Picture Fuzzy Graphs (PFGs), including cartesian product of Picture Fuzzy Graphs (PFGs), composition of Picture Fuzzy Graphs (PFGs), union and join of Picture Fuzzy Graphs (PFGs), direct product of Picture Fuzzy Graphs (PFGs), and lexicographic product of Picture Fuzzy Graphs (PFGs). Finally, we discussed application of Picture Fuzzy social network (PFSN).Item Irregularities, Energies and Pattern of Bridge Chain Graph Network(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Faisal Javed; SP19-RMT-036; LHR TP 7348; Dr. Muhammad HussainThe graph ? consists of some vertex ?(?) are connected by ?(?) where the position of vertices does not matter. The degree of a graph vertex is basically a number of incident edges ?(?) and vertex ? can be denoted by du. The upper and lower bound of graph energy with minimal and maximal energy is abroad field of Spectral Graph theory. The energy of Graph ?(?) in term of vertices and number of edges in graph ? is involved in absolute value of eigenvalue adjacency matrix of G where λ is the spectral radius. The Graph has energy equal to ?(?) = ∑ |? ? ?=1 |. An irregular graph G is totally defined as ??𝑡(?) = |𝑢 − 𝑣|. Finally, we determine the energy, pattern and irregularities of chain like cyclic graph. Our exploring outputs will rely upon Size and Order of Graph, Degree of Graph, Irregular Graph, Multi Graph, Cyclic Graph, Wheel Graph, Bridge Graph, Prism Graph, Connected and Planarity Graph, and Concept of Distance and Degree in Graph.Item Cohen-Macaulayness in Codimension for Line Simplicial Complexes(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Nasim Aftab; SP19-RMT-014; LHR TP 7350; Dr. Imran AhmedCohen-Macaulay complexes were first proposed in the mid-1970s. As the primary devel- oper of these inventions, Stanley has made major contributions over a long period of time. The idea of CMt simplicial complexes was itroduced by Nahandi, Yassemi, and Haghighi in 2012. We show that cycle graph having j vertices is unmixed for odd j 3 and it is not unmixed for even j 6 and prism graph having Jj vertices with J 3, j 2 is unmixed for odd J 3 and it is not unmixed for even J 6. Furthermore, we prove that the line simplicial complexes associated to cycle graph having j vertices are unmixed for odd j 3 and it is not unmixed for even j 6 and line simplicial complexes associated to prism graph YJ,2 with J 3 is unmixed. Also, we show that the line simplicial complexes associated to ladder graph having 2n vertices is Cohen-Macaulay and consequently it is CMt, for t 0. We provide example that DL(C5) is not CM0 but it is CMt, for t 1 .Item Formation and Analysis of Ahlfors Map Integral Equations for the Regions with Multiple(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Usman Ashraf; Sp19-RMT-005; LHR TP 7410; Dr. Kashif NazarThis research work elaborates the detailed numerical analysis of the integr equation related to Szegö kernel and Ahlfors map with the assistance Mathematica 12.0. The Ahlfors map and Szegö kernel are both associated to ea other. This is a Fredholm integral equation of second kind via Kerzman-Stein kern where Szegö kernel is the solution of this integral equation. The solution of integr equation is obtained by transforming the integral equations into matrix form aft discretizing. This work presents the computation techniques of Ahlfors map, zeros, boundary values and the interior points of a region under Ahlfors map. Th research construct one new Ahlfors map integral equation with Neumann-ty kernel for the regions with multiple connectivity onto a unit disk. The kernel an non-homogeneous term of this equation contain zeros of Ahlfors map. This integr equations is constructed by a non-homogeneous boundary relationship for t regions with multiple connectivity. The new Ahlfors map integral equation analyzed by parameterizing and discretizing. Discretized integral equations leadItem Degree Based Topological Co-Indices of Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Muhammad Nasir; SP19-RMT-032; LHR TP 6481; Dr. Muhammad Kamran SiddiquiGraph theory is playing a key role in applied and pure mathematics. The scope of graph theory is expanding day by day. In this thesis we computed some topological coindices like as First and Second zagreb co-index, First and Second multiplicative zagreb coindex, Forgotton topological coindex, Atom bond connectivity coindex, Geometric arithmetic coindex and general Randic coindex for ∝= 1,−1, ଵ ଶ ,−ଵ ଶ for some chemical and networking graphs like as David derived network; ??(2), Dominating david derived network; ???(2), Regular Triangular Silicate network of dimension n; ????(?), Triangular chain cactus; ??, Oraganosilicon dendrimer ?[?]; ? ≥ 1; 2, Para chain square cactus; ?? ,Ortho chain square cactus; ??, Tetrathiafulvalene dendrimers; ??2[?]. My thesis comprising of four chapters. In the first chapter we will define some fundamental definitions. In the 2nd chapter, we will find Co-indices for David derived network, dominating David derived network, Regular triangular silicate network of dimension ? and Oraganosilicon dendrimer ?[?] graphs. In the 3rd chapter, we will find Triangular chain cactus, Para chain square cactus, Ortho chain square cactus, Tetrathiafulvalene dendrimers. In the 4th chapter, we will present the conclusion of our thesis. In the last, we will present the refrences of our thesis.Item Generalized Chaplygin Gas Traversable Wormhole Solutions by Using GUP Corrected Casimir Energy(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Ubaid Ur Rehman; SP19-RMT-019; LHR TP 6477; Dr. Abdul JawadIn this thesis, we explore the wormhole solutions (which are initially pro- sed by Garattoni (Eur. Phys. J. C 79(2019)951) who take generalized certainty principle (GUP) with Casimir energy) in the framework of two ll-known dark energy models, generalized Chaplygin gas and polytropic s. We consider the GUP corrected pressure (force per unit surface area) the equation of state of these dark energy models to construct the gener- zed Chaplygin gas corrected energy density and polytropic gas corrected ergy density. Three models of redshift function are taken into account construct shape function as well as wormhole geometry for both cases corrected energy densities. We find the behavior of some parameters ough equation of state, energy conditions (null, weak and strong) at the oat of the wormhole with radius r0.Item Cosmic Thermodynamics of Matter Creation Models in Alternative Theories of Gravity(LHR TP 6477, 2020) Farzan Mushtaq; SP19-RMT-021; LHR TP 6477; Dr. Shamaila RaniThis thesis is devoted to study some cosmological models in the scenar- ios of two gravitational theories like fractal universe model and dynamical Chern-Simons modi¯ed theory in particle creation mechanism. In the case of fractal universe model, we consider particle creation rate as constant and variable with two models. We use Gibbs equation to ¯nd out pressure of particle creation rate adiabatic matter phenomenon. For these cases, cosmological parameters like e®ective equation of state and deceleration parameter are studied. Also, we investigate the behavior of generalized sec- ond law of thermodynamics for Barrow entropy by taking constant particle creation rate. For dynamical Chern-Simons theory, two variable particle creation rate models are used for which we explore e®ective equation of state parameter and deceleration parameter.Item Numerical Solution of Coupled Delay Differential Equations in the Field of Oncology(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Robia Arif; SP19-RMT-037; LHR TP 6484; Dr. Ayesha SohailIn the dissertation, the models of delay differential equations from the math- ematical biology are considered, focusing on the oncology. For the study of these kinds of models, one should be capable to establish linear stability of the steady states. In Chapter 2, I have apply the method on models. Adoptive im- munotherapy against cancer has received remarkable consideration. The cyto- toxic CD8+ T cells have been studied for a long time and experimented with re- ceptor engineering techniques through the creation of chimeric receptors called CAR (Chimeric Antigen Receptor). This fact puts a cell line in the background which, on the other hand, is fundamental for the organization of the antitumor response: “CD4+” T cells. In this article, a model is constructed in which the ability of “CD4+” T cells to induce control of the tumor cell population is ana- lyzed, using a mediator such as the cytokine IFN- , and to quantify the action of the same which, although indirect, also carry out a control of the persistence of the antitumor action itself. The model focuses on the modalities of cellular interaction where it is possible to imagine a future development on the basis of recent data and idealize a therapeutic scheme where “CD4+” T cells play a leading role. The linear stability analysis is analyzed and analysis of Hopf bifur- cation is established. Finally, the numerical simulations are executed to validate analytical results.Item On lcm Lattice of Edge Ideals associated to Cycle and Complete Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Alia; SP19-RMT-008; LHR TP 6468; Dr. Sarfraz Ahmad