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 Edge Irregularity Strength of Some Path Related Graphs(Library Information Services, COMSATS University, Lahore Campus, 2018) Muhammad Imran,; FA17-RMT-008; r. M. Faisal Nadeem, Assistant Profesor; LHR TP 5646Edge Irregularity Strength of Some Path RelatedGraphs Graph theory is playing a key role in applied and pure mathematics. The scope of graph theory is expanding day by day. In graph theory, there are many categories of graph labeling, such as, graceful label ing, cordial labeling, magic labeling and irregular labeling. Graph labeling is being used in different fields, such as, computer networking, coding theory, circuit design and data management. In this thesis, we will try to find irregular labeling of some path related graphs. Mythesis comprising of six chapters. In the first chapter we will define some funda mental definitions. In the 2nd chapter, we will discuss various types of graph labelings, such as, edge and vertex labeling, total labeling, irregular labeling, edge irregular labeling, vertex irregular labeling and irregularity strength. In the 3rd chapter, we will find vertex irregular labeling and evaluate edge irregularity strength of triangular snake graph, alternate triangular snake graph. In and 4th chapter, we will find vertex irregular labeling and evaluate edge irregularity strength of different variations of comb graph. Results regarding edge irregularity strength and some relevant references are given in the 5th and 6th chapters respectivelyItem Two Population Neural Field Model With Constant External Input(Library Information Services, COMSATS University, Lahore Campus, 2018) Ammara Basharat,; FA16-RMT-032; Dr. Muhammad Yousaf, Assistant Profesor; LHR TP 5195In this work, We have study the two-population neural field Model under the effect of constant external inputs. Earlier, Blomquist et al.[1] investigated the stationary symmetric solution of two population model with no external input.They found that Amari stability analysis and linearized stability analysis produces same results. Later on Yousaf et al. [2] investigated the same model under the influence of spatial dependent external input and proved that the Amari technique and linearized stability technique does not produce same results. They also investigate the number of bumps as a function of amplitude parameter of external input and found at most four bump pairs. In our research work, We have to explore the two population neural field model under the effect of constant external input on bump solutions. We further, have to investigate the stability properties of stationary symmetric solutions by using two approaches (i) Amari approach (ii) standard linearized approach. Numerically, We will investigate the number of bumps as a function of width and amplitude parameter of external inputItem Total Labellings of Some Connected Graphs(Library Information Services, COMSATS University, Lahore Campus, 2019) SP17-RMT-014; Mujahid Shehzad,; Dr. Kashif Ali, Assistant Profesor; LHR TP 5428Ashraf et al. in [3] introduced the concept of vertex H irregular labelling and edge H irregular labelling. Let H be sub graph of given graph G. If each edge of graph G is contained in any subgraph Hi where i ={ 1,2,3,…, k } of G and if each Hi is isomorphic to given subgraph H. then the collection Hi of subgraphs of G is said to be H-covering of G. They also introduced the concept of edge H irregular strength ehs(G) that is the minimum k for which the graph has total H irregular k labelling and vertex H irregular strength vhs(G) that is the minimum k for which the graph has total H irregular k labelling The thesis is devoted to study the total vertex C3 irregular strength wheel graph and triangular ladder graph taking subgraph C3. We also found the total vertex C4 irregular strength ladder graph and grid graph. Furthermore, we find the total vertex C8 irregular strength of a connected graph Qn.Item Analysis of Integral Equations of Ahlfors Map for Multiply Connected Regions(Library Information Services, COMSATS University, Lahore Campus, 2018) Razi Ahmad,; FA16-RMT-025; Dr. Kashif Nazar, Assistant Profesor [; LHR TP 5433This research is to analyze the boundary integral equation of Ahlfors map of multiply connected region also the derivation of a new boundary integral equation related to Ahlfors map. These integral equations are then parameterized and discretized into the system of equations by using the Nystrom method with trapezoidal rule.Item Stokes Flow Through a Permeable Slit With Periodic Reabsorption and Porous Medium(Library Information Services, COMSATS University, Lahore Campus, 2019) Zernab Shafiq,; FA17-RMT-005; Dr. Quart-Ul-Ain Azim, Assistant ProfesorOne of the main and most important organs of the body of an organism is Kidney. Nephron is the functional unit of Kidney which has a tubular part called renal tubule. The walls of renal tubules are porous and fluid reabsorption takes place in these tubules. Due to various diseases, the medium inside the tubules becomes porous and the flow permeability is reduced. There are numerous studies in literature that address uniform reabsorption in renal tubules through porous slits. We have done the study of two di mensional reabsorption flow through porous slits in renal tubules that are diseased and are under the effect of biofouling. We model this physical problem into a mathematical form, which result in a high order differential equation as well as associated bound ary conditions. The problem then solve exactly, and expressions for various physical quantities are computed. At last, the obtained results are analyzed graphicallyItem Cosmological Analysis of Reconstructed Einstein-Aether Models(Library Information Services, COMSATS University, Lahore Campus, 2018) Irfan Ullah Malik; SP 17-RMT-007; Dr. Shamaila RaniIn this thesis, we reconstruct various solutions for the accelerated universe in the Einstein-Aether theory of gravity. For this purpose, we obtain the effective density and pressure for Einstein-Aether theory. We reconstruct the Einstein-Aether model parameter by comparing its energy density with various holographic dark energy models such as Tsallis, R´enyi and Sharma Mittal holographic dark energy models. For this reconstruction, we use two forms of scale factor, power-law and exponential forms. The cosmological analysis of underlying scenario has been done by exploring different cos mological parameters. This includes equation of state parameter, squared speed of sound and evolutionary equation of state parameter via graphical representation. We obtain some favorable results for some model parametric valuesItem Hybrid Projection Algorithm for Generalized Split Equilibrium Problem in Hibert Spaces(Library Information Services, COMSATS University, Lahore Campus, 2019) Hammad Sarwar,; SP17-RMT-008; Dr. Muhammad Aqeel Ahmad Khan, Assistant Profesor [Supervisor]; LHR TP 5430In this thesis we suggest and examine Extra Gradient-Proximal Point algorithm to find the solution of Split Equilibrium Problem and Fixed Point Problem for nonexpansive semigroup in real Hilbert spaces. Our purpose is to address fixed point problems(FPP), variational inequality problems (VIP) and generalized Split Equilibrium Problems(GSEP) in the setting of Hilbert spaces. We propose a hybrid shrinking projection algorithm, which exhibits strong convergence, for the construction of a common element in the set of common fixed points of an infinite family of k-strict pseudo contractions and the set of common solutions of a finite family of Generalized Split Equilibrium Problems(GSEP) in Hilbert spaces. Our results generalize and improve various existing results in the current literature.Item Classifications of Determinantal Varieties(Library Information Services, COMSATS University, Lahore Campus, 2019) Sana Zahoor; , FA17-RMT-054; Dr. Imran Ahmed; LHR TP 5675Let Mns be a space of matrices of order n×s with complex enteries. The determinantal singularities are defined by vanishing of all the minors of a certain size of an n ×s matrix α : Ck → Mns. The class of determinantal singularities is a more general class than the class of complete intersection singularities. The G-finite deteminacy gives a special class of determinantal varieties known as essentially isolated determinantal singularities (EIDS), firstly introduced by Ebeling and Gusein-Zade in 2009. We give a computational method to find linear forms of EIDS by programming in CItem Computing Metric Dimension of M-Level Wheel Related Graphs(Library Information Services, COMSATS University, Lahore Campus, 2018) Ayesha Razzaq,; SP16-RMT-010; Dr. Hafiz Muhammad Afzal Siddiqui, Assistant Profesor; LHR TP 5332An ordered subset set for of nodes of is called a resolving set or locating if each node is individually determined by its code of distances to the nodes in . A resolving set of minimum number of nodes is called a basis for and this cardinality is the metric dimension or location number of , represented as In this thesis, we compute the metric dimension of some wheel related graphs, such as m-level gear graph, m-level antiweb-wheel graph, m-level antiweb-gear graph and an infinite class of convex polytopes denoted by respectively. We prove that the metric dimension of aforementioned wheel related graphs and a family of convex polytope is not bounded. The unbounded metric dimension of convex polytope also furnish a negative answer to the problem given in [19]: Open Problem: “Is it the case that the graph of every convex polytope has constant metric dimension?” It is natural to ask for characterization of graphs with unbounded metric dimension.Item Two Population Neural Field Model With Gaussian External Input(Library Information Services, COMSATS University, Lahore Campus, 2019) Sana Javed,; FA17-RMT-006; Dr. Muhammad Yousaf,; LHR TP 5644In this, we have explored Gaussian spatio-temporal external input on per sistent activity states. The aim of work was to build up a numerical scheme of action for two population model with Gaussian external input. We breakup the external input into 3 parts i.e., amplitude, the spatial part and the tem poral part . In temporal part, we use Gaussian type external input. We have explored the boundedness, uniqueness for the present choice of work. We check the emergence then we examine the stationary solution called ”bumps”. This model is the continuation of Patrick et al [37] by extending the spatio-temporal Gaussian type external input. We have check thoroughly the broad bump so lution. We also check the activity will converge, when the broad bump is less than cr. The present choice of H(x,t) produce better result as compare to Yousaf et al