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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On the Construction of Higher Order Conservative Methods
(Library Information Services COMSATS University Islamabad Lahore Campus, 2012) Zareen Akhtar; FA19-RMT-026; LHR TP 7417; Dr. Yousaf Habib
For the numerical solution of conservative differential equations such as Hamiltonian system or differential equations that arise in different physical phenomena with some structure, we use structure preserving numerical methods. In particular, symplectic Runge-Kutta methods, G-symplectic General Linear methods and Variational Integrators have been explored. In this thesis Variational Integrators for degenerate Lagrangian and non- degenerate Lagrangian have been discussed. For degenerate Lagrangian, we obtain multi-step numerical methods which suffer from parasitic corruption. In order to control the parasitism we write Variational Integrators as General Linear methods and then employ the projection technique to project the numerical solution onto the desired manifold
Dispersion Free Finite Difference Scheme for Time Harmonic Wave Equation
(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2012) CIIT/FA10-MSMATH-011/LHR; Muhammad Sarmad Arshad 05/LHR; Dr. Hafiz Abdul Wajid; FA10
Dispersion Free Finite Difference Scheme for Time Harmonic Wave Equation In this work, we construct novel central finite difference schemes for solving the Helmholtz equation by following the idea of Nehrbass and Yau Shu in one and two dimensions. We present an alternative construction by which not only central f inite difference schemes but all types of schemes (forward, backward) can be made exact for Helmholtz equation. We give explicit expressions for the coefficient of the central node in the standard central finite difference scheme of any order which makes the novel scheme dispersion free in one dimension and optimal in two dimensions. Such schemes add no cost for the implementation and one needs not to write brand new code instead just need to change the central node coefficient with the new one presented in this work to have highly accurate results. Comparison of numerical solutions obtained using novel schemes with standard schemes for Helmholtz equation in single and higher dimensions are given.
Optimal Finite Difference Schemes for Wave Equation
(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2012) Hifza Iqbal; CIIT/FA10-MSMATH-011/LHR; Master of Science in Mathematics; Dr. Hafiz Abdul Wajid
In this research work the novel optimal central finite difference schemes for solving the transient wave equation, are developed and analyzed. The novel schemes (a) give exact value at the nodes of the grid, meaning that an exact solution is possible for the transient wave equation; (b) the key advantage is that they have the simple structure as that of the standard central finite difference schemes, so we just need to make few amendments in the standard codes, instead of writing the new codes altogether; (c) above all, the beauty lies in the fact that they do not require fine mesh size and works for any wave number, specially for high wave number. Finally, in order to display the actual power of the novel schemes, numerical computations and graphical representations for two model problems are added, by using both novel and standard central finite difference schemes, which support our theoretical results, by showing the superiority of the novel schemes compared to the standard schemes
Group H-magic labelings of graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2015) Syed Tahir Raza Rizvi; FA11-PMT-002; Dr. Kashif Ali; LHR TP 5283
A simple graph G admits an H-covering if each edge in E G is a member of a sub- graph of G isomorphic to H. An H-magic labeling of a graph G possessing an H-covering is a bijective function from the vertex-set and the edge-set of the graph G onto the set 1 2 V G E G if there occurs a positive integer , called the magic sum, such that for every subgraph H of G isomorphic to H, the sum wt H v V H v e E H e is equal to . The sum wt H is termed as, the H-weight. A graph is called H-magic (H-supermagic) if it possesses an H-magic (H-supermagic) labeling. If H is isomorphic to K2, then resulting labeling is known as edge-magic total labeling. This dissertation studies about the formulation of cycle-supermagic labelings for the disjoint union of isomorphic and non isomorphic copies of different families of graphs. We also evaluate the K2-supermagic labelings of some families of alpha trees. More- over, we ﬁnd the cycle-(super)magic labelings of uniform subdivided graph and cycle- supermagic labelings for non uniform subdivisions of fans and triangular ladders graphs. We also articulate about the introduction of H-groupmagic total labeling of a graph G over a ﬁnite abelian group A . In this study, we determine the H-groupmagic total labelings of fan graphs and disjoint union of isomorphic as well as non-isomorphic copies of fan graphs over ﬁnite abelian group A 3 n, where n 3
Chromatic Equivalence and Uniqueness of Subdivided K4 Graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Areeb; FA14-MSMATH-009; LHR TP 6935; Dr. Sana Javed
In this thesis, various chromatically unique and correspondent pairs of several families of graphs with same girths have been attained. Subdivided complete graphs are related to these families, indeed. Our major goal in this paper is to carry on the study of chromaticity of the subdivided complete graphs. We are dealing particularly with four vertices which is called 𝑘4-homeomorph. Distinctiveness of two particular classes of 𝑘4-homeomorph graphs with girth 11 has been explained in detail. The cycles of different lengths from graph has been removed during the discussion. In order to make them chromatically unique, vital and satisfactory conditions have been established. All well known definitions, results and terms are given in Chapter 1. Chapter 2 is covering a brief literature review about chromatic uniqueness and correspondence. While the chapter 3 is focused on the chromatic uniqueness along with chromatic equivalence of two 𝐾4-homeomorph graphs with same girth. At the end of the thesis, few open problems have been recommended as well.
Fractional Order Model of Tumor-Induced Angiogenesis
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Sufian Asgher; SP15-RMT-001; LHR TP 6936; Dr. Ayesha Sohail
Methods of blood vessel formation is termed angiogenesis. Two distinguishing features of cancer, uncontrollable cell growth and metastasis, cannot be sustained in the absence of neovascularisation. Angiogenesis enhances the arrangement of solid tumors and their metastasis. During this research, present progress in understanding the procedure of angiogenesis in dynamic tumor development is talked about. The development of strong tumors, including neck and head squamous cell carcinomas, relies on upon the foundation of a blood supply inside the tumor (neovascularization or angiogenesis). For this procedure to occur, tumors create development components which stimulate the expansion, movement, and separation of endothelial cells. Nonlinear pde model of tumour induced angiogenesis is discussed during this research. The semi-analytic solution of this model is presented.
DEGREE BASE TOPOLOGICAL INDICES OF SOME FAMILIES OF GRAPHS
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Mahrukh; SP15-RMT-009; LHR TP 6828; Dr. Kashif Ali
Atopological index is a numerical value associated with chemical constitution for cor relation of chemical structure with various physical properties, chemical reactivity or biological activity. In this thesis, we will discuss the different degree based topological indices i.e. Randic index, Zagreb index, Atom-bond connectivity index, Geometric arithmetic index, Augmented Zagreb index, Harmonic index, Sum-connectivity index for benzene BCZ, Benzene BTA diamond like graph, line graph of ladder and line graph of nanostar dendrimers. We will also compute ABC4 and GA5 for benzene BCZ, Benzene BTA diamond like graph
Anti-Magic Labeling on Harary Graph and Subdivided Caterpiller
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Muhammad Mubashar; FA14-RMT-029; LHR TP 6839; Dr. Muhammad Hussain
Graphs play an important and vital role in Mathematics. Graph labeling creates new ideas graph theory. Can labeling be helped us to solve problems in Mathematics and other fields? The answer of this question increases the deep value of Graph Labeling. A magic labeling of a graph is described by Kotzig and Rosa [22] in 1970 as an important iniative. A graph labeling (or valuation) is a unique way that gives the labels to graph elements (commonly, these are non negative or positive integers). if we consider the domain set of all vertices and edges; such labelings are called total labelings. Sometime we use labelings for vertex set or the edge set alone and these labelings would be called as vertex-labeling and edge-labeling respectively. Many other domains are also possible. There are some famous labelings like as harmonious, cordial, graceful and antimagic. In 2000, Baˇca et al. [2] discussed a (a,d)-vertex-antimagic total labeling. A (a,d) vertex-antimagic total labeling is called super (a,d)-vertex-antimagic total labeling, when we give smallest labels to the vertices. An (a,d)-edge-antimagic total labeling was defined by Simanjuntak et al. [41]. An (a,d)-edge-antimagic total labeling is called a super (a,d)-edge-antimagic total labeling, when we give the least labels to the vertices. A graph G, which is made up of cycles with chords is known as Harary Graph. A brief discussion exposed important results on super (a,d)-edge-antimagic total labeling Harary graph by M. Baˇca and M. Murugan [1, 6]. This work is designed for the construction of (a,d)-vertex-antimagic total labeling of Harary graph as well as for super (a,d)-vertex antimagic total labeling of Harary graph for the different value of d.
Effect of Slip Velocity on Membrane Surface in Channel Flow System Using Power Series Method
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Saba Qummer; SP15-RMT-013; LHR TP 6990
This thesis presents the general solution for two dimensional, laminar and fully developed flow in the parallel flat membrane system. The fourth order, non linear differential equation contain a free parameter Rw. This parametric Equation is solved by using a very general method i.e power series method. From this general solution expression are developed for velocity components, Normalized velocity and pressure distribution .We also discussed the effect of slip velocity at a porous surface. The effect of slip coefficient on velocity profiles is also examined graphically.
Analysis of Plasma Modified KdV Waves using Discrete Periodic Inverse Scattering Transformation
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Muhammad Noaman Akbar; SP15-RMT-005; LHR TP 6989; Dr. Ayesha Sohail
Discrete Periodic Inverse Scattering Transformation (DPIST) are presented in this paper for solution of the well-known Korteweg-de Vries equations that has been hypothesized hypothetically such that non-linear dispersive waves spreading on interface of length only a joined of products fluid profundity fulfill a development condition with more extreme non-linearity than ordinary Korteweg-de Vries (KdV) equations for shallow water hypothesis. In this paper non-linear Fourier investigation is processed on time and space arrangement of surface relocation create at two areas downstream of a wavering film. Comes about because of a DPIST in view of the KdV equation, that decays a flag into soliton, sinusoidal and cnoidal parts, demonstrate while the amplitude of direct modes are preserved as unsettling influence spreads among two sensors, amplitudes of nonlinear modes increment. This recommends non-linearity of such surface waves is without a doubt more grounded than that anticipated by the KdV equations.
Effect of Slip Velocity at a Porous Surface in Tube Flow System using Series Solution Method
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Zil-e-Huma; SP15-RMT-002; LHR TP 6987; Dr. Muhammad Younas
In this thesis, an attempt has been made on the effect of slip velocity at a mem brane surface in a tube flow system. The Navier-Stokes equations in cylindrical coordinates reduced to fourth order non-linear ordinary differential equation, con taining a parameter Rew, the wall Reynolds number. The semi-analytical solution of the set of governing equations with suitable slip flow boundary conditions is presented by using power series method to obtain velocity profile, pressure gradi ent and friction coefficient. Also the effect of slip coefficient on velocity profiles and pressure gradient is studied and their graphical solutions are also provided
On Some Topological Indices and Algebraic Properties of the Polyomino Chains of 4K-Cycles
(LHR TP 6988, 2016) Farah Iqbal; SP15-RMT-007; LHR TP 6988
In the present age of science and technology, topological indices have sig nificant role in the study of Quantitative Structure-activity (QSPR) and Structure-property (QSPR) relationships, to understand the chemical prop erties of the chemical compounds. In mathematical chemistry distance-based molecular descriptors are used to depict the structure of various molecules. For a simple connected graph G=(V,E), the Harary index is described as the sum of reciprocals of dis tances between all pairs of the vertices of the graph G. In this work, we derived some conjectures about the Harary index of the linear polyomino chain of 4k-cycles provided that k = 2 for both the cases i.e. linear and zig-zag chains, also there are expressions to get the sum of distances of the vertices while keeping one vertex as fix by dividing the chain into four dif ferent levels. This technique provide a basis to extend the idea for some other values of k
Face Labeling of Graph Embedded on the Surface of Klein Bottle
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Sharafat Ali; SP15-RMT-004; LHR TP 7004; Dr. Saad Ihsan Butt
We deal with the problem of labeling the Klein Grid’s Km n vertices, edges and faces with mn squares by the consecutive positive integers from 1 up to jV(Km n )j + jE(Km n )j + jF(Km n )j in such a way that if we add up all the labels of a 4-sided face that becomes the weight of that face. With common difference d these weight of the faces form an arithmetic progression. We will ﬁnd out the existence of such type of labelings for several differences of d.
Computing Degree Based Topological Indices Of HAC5
(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2016) Ahsan Raza,; FA14-MSMAT-010; Dr. M. Faisal Nadeem, Assistant Profesor [Supervisor]; LHR TP 4624
Computing Degree Based Topological Indices of HAC5C7 and VC5C7 Nanotubes There are certain types of topological indices such as degree based topological indices, distance based topological indices and spectrum based topological indices, which are used by researchers in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) to predict physico-chemical properties of chemical compounds. A large number of topological indices are based on vertex-degree of molecular graphs. The purpose of current study is the discussion of the line graphs of HAC5C7[p,q] and VC5C7[p,q] nanotubes constructed by joinig left right side and as well as constructed by joining upside down, and computing some vertex-degree based topological indices of the line graphs of these nanotubes. Graph theory is a very powerful tool of applied mathematics. It concerns with different fields of science and has wide applications. In the first chapter we give some basic introduction and some definitions of graph theory. In the second chapter we give brief description about vertex-degree based topological indices. In the third chapter of this dissertation, we discussed the line graphs of HAC5C7[p,q] nanotube constructed by joinig left right side and as well as constructed by joining upside down. We also computed some well known degree based topological indices of the line graphs of HAC5C7[p,q] nanotube. This dissertation also includes discussion of the line graph of VC5C7[p,q] nanotube constructed by joinig left right side and as well as constructed by joining upside down. We also computed some well known degree based topological indices of the line graphs of VC5C7[p,q] nanotube given in last chapter.
On Fuzzy Generalizations Of Some Results In Finite
(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2016) Ghous Ali,; FA14-MSMAT-025; Dr. Adeel Farooq, Assistant Profesor [Supervisor]; LHR TP 4631
In this thesis, we have investigated some basic results of fuzzy group theory by constructing various examples. In particular, we have studied the notions of fuzzy subgroup, normal fuzzy subgroup, fuzzy coset and fuzzy quotient group and have elaborated these concepts through examples. We have proved that if ξ1 and ξ2 are fuzzy subgroups of a group G, then intersection of ξ1 and ξ2 is again a fuzzy subgroup of G. Also, we have shown that for two fuzzy subgroups ξ1 and ξ2 of a group G, if ξ1 is a normal fuzzy subgroup of ξ1, then ξ1 ∩ ξ2 is a normal fuzzy subgroup of ξ1 ∩ ν. Furthermore, we have defined the concept of a fuzzy subgroup of a fuzzy group. We have formulated the notion of an m-polar fuzzy group as a generalization of a fuzzy group. Moreover, we have introduced m-polar fuzzy analogs of some results in fuzzy group theory
Dynamics Of Two Population Synaptic Drive Model
(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2016) Iqra Khan,; FA14-MSMAT-018; Dr. Muhammad Yousaf Bhatti, Assistant Profesor [Supervisor]; LHR TP 4627
In this work we have investigated the two population synaptic drive model with a relatively complex temporal kernal for steep firing rate function. We have done this justification by deriving four dimensional autonomous dynamical system from Volterra equations using linear chain trick. Both of the local and global wellposedness of the model has been in vestigated. The existence of stationary point has also been investigated and the general formula for stationary point is derived. We get two different models for delay and non delay case. Theorem on the existence and stability has also been formulated. The stability issue has also been addressed for both cases for the steepness parameter q = 0, and q > 0, which leads us to the conclusion that delays in the system with weak kernel does not effect the stability properties of the model
Super Edge Magic Deficiencies Of Forests Of Alpha
(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2016) Abdul Rau; f, FA14-MSMAT-008; Assistant Profesor [Supervisor]; LHR TP 4633
Let G be a graph which is admitting an edge-magic total valuation. The edge magic deficiency [38] of this graph G is the positive numbers α required to make it a edge magic total graph. The general notation for edge-magic deficiency is μ(G). If there does not exist such α then edge magic deficiency will be ∞. The super edge magic deficiency of graph G [17], follows the same definition and it is denoted by μs(G). This dissertation studies about the super edge-magic deficiencies of forests of alpha families of trees. Firstly, We show that alpha trees with caterpillars as its components have super edge-magic deficiency is μs =0. We also prove that if the alpha tree has w-trees and alpha trees as its components then its super edge-magic deficiency is μs =0. At the end, we prove that forest of alpha trees with components as banana tree and stars preserve super edge-magic deficiency μs =1
On Some Polynomials Of The Chemical Nanotubes
(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2016) Nighat Farah,; FA14-MSMAT-003; Dr. Sarfraz Ahmad, Assistant Profesor [Supervisor]; LHR TP 4635
In the thesis we have calculated toplogical indices of some Carbon and Boron nan otubes. We have formulated for Omega and Counting polynomials of these nanotubes very firstly in literature. The counting polynomials are valuable in forecasting of dif ferent structures. It also helps to describe its topological indices by virtue of quasi orthogonal cuts of the edge strips in the polycyclic graphs. In this thesis we have given a complete description of the Omega and the Sadhana polynomial of the nan otube TUC4[p,q] and provide its mathematical proof. We also give explicit formulae for the PI and the theta polynomial of TUC4[p,q] nanotubes. We have also given a brief note on different types of the Zagreb indices of the nanotubes TUC4[p,q] and TUC5C6C8[p,q]. In QSAR/QSPR study, the topological indices are being utilized for envisioning the biological and physical properties of compunds. These indices are very important in mathematical chemistry as well. These topological indices have many applications of statistical tools in chemical reactivity, physical properties and biological activities. In this thesis we have exactly computed the Zagreb indices, GA index, the randic index and the ABC index of the TUC5C8 nanotubes. In mathe matical chemistry, a topological index is computed using structure of the molecular graph and is a numerical parameter which describe its topology. Using combinato rial techniques we also provide explicit formulae of the different types of the Zagreb indices, GA index, the Randic index and ABC index of the zigzag boron triangular nanotubes BNT[p,q] and armchair boron triangular nanotubes
Thermal Fluctuations Of A Regular And Einstein
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Hafiza Zarish Arshad; , FA14-BSM-001; Dr. Abdul Jawad, Assistant Profesor; LHR TP 5252
In this thesis, we study the effects of thermal fluctuations on regular black hole solutions with cosmological constant and Einstein-aether black hole with coupling constant respectively. We consider the logarithmic corrected entropy in order to analyzing the thermal fluctuations on regular black hole solutions and Einstein-aether black hole. We also obtain various thermo dynamical quantities such as entropy, pressure, specific heats, Gibb’s free energy and Helmholtz free energy. We also investigate the stability of reg ular black hole solution and Einstein-aether black hole in terms of γ, phase transition, grand canonical ensemble and canonical ensemble. We analyze that regular black hole are stable when we increase the value of cosmologi cal constant and Einstein-aether black hole are stable when we increase the value of coupling constant respectively.
On Characterization Of Spanning Forest Complexes
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Muhammad Asif,; FA14-MSMAT-004; Dr. Hani Shaker, Assistant Profesor [Supervisor]; LHR TP 4636
In this thesis, we discuss the algebraic and combinatorial aspects of spanning forest complex ∆s(G) associated to simple disconnected graph G. We mainly emphasis on disjoint union of isomorphic copies graph G and provide special importance to tCn where tCn is the disjoint union of t cycles of length n and call this graph t-cycle graph. We give the characterization of s(tCn), all spanning forests, of tCn. We intend to provide the algebraic and combinatorial characterization of spanning forest complex ∆s(tCn) associated to tCn. In particular, we compute the formula for the f-vector of spanning forest complex of t-cycle graph. We also compute the h-vector and Hilbert series of Stanley Riesner ring k[∆s(tCn)]