MS or Mphil

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A generalization of nadler fixed point result in hausdorff double controlled metric type space
(UMT Lahore, 1-8-2022) Muhammad Tariq
In 2020, Nayab Alamgir [9] showed that every controlled metric type space (; q) induces a Hausdorff controlled metric type space on the class of closed subsets of which is also complete if (; q) is complete. He also defined multivalued almost F-contractions on Hausdorff controlled metric type spaces and proved some fixed point results. In this thesis, we will show that every double controlled metric type space makes a Hausdorff double controlled metric type space (H; CD()) where CD() is the collection of all non-empty closed subsets of and if (; q) is complete then (H; CD()) is also complete. We will also demonstrate multivalued almost F-contractions on Hausdorff double controlled metric type space and we will derive a few fixed point results.
An extension of normalizer, centralizer, centre and automorphism of groups in soft groups
(UMT Lahore, 2014) Muhammad Nadeem Ahmed
The theory of soft sets, introduced by Molodtsov [13], is an extension of set theory for the study of intelligent systems characterized by insufficient and incomplete information. H. Aktas and N. C˘agman [1] studied algebraic structure on this particular set called soft groups and define the soft homomorphism. The main purpose of this thesis is to explore the knowledge about soft groups, center of soft groups, centralizer of soft groups, normalizer of soft groups, soft automorphism, soft inner automorphism and soft outer automorphism.
A study of some common fixed point theorems for four maps in cone metric spaces
(UMT Lahore, 2014) Zaheer Munawar Hussain
Our present work is about coincidence and common fixed points results for four mappings in a cone metric space which satisfy a new and advanced contractive condition. The functions we consider in this work are weakly compatible. It is worth mentioning that we did not assume any kind of commuting or continuity condition on the functions to review the above results. The results we studied here unified, generalized, and extended the comparable results in the existing literature.
General solutions for free convection flow of Casson fluid over an infinite vertical plate
(UMT Lahore, 2015) Allia Naseem
In this thesis, we consider the flow behaviour of Casson fluid under different circumstances. Firstly, some basic definitions and concepts regarding the fundamentals of fluid motion and methods to solve the flow problems have been discussed. In chapter 2, the free convection flow of Casson fluid past an upright plate subject to the time dependent velocity f(t) with constant wall temperature has been investigated. The vertical plate is set in motion with a time dependent velocity f(t) at time t = 0+. And so the motion will be produced in the fluid. Exact solutions are obtained through the Laplace transform method. The solutions corresponding to Newtonian fluid for γ → ∞ is obtained as a limiting case. Also, we have discussed some consequences of various parameters like Casson parameter, Grashöf and Prandtl numbers on velocity and temperature and presented them graphically. Chapter 3, particularly deals with the jerky and unformed free convection flow of Casson fluid subject to an upright plate with mass transfer and Newtonian heating. With the help of Laplace transform, the expressions for velocity and temperature will be established. For particular cases when (a) Pr=1, Sc=1, (b) Pr ≠ 1, Sc=1 and (c) Pr = 1, Sc ≠ 1, solutions are investigated. For different physical parameters, graphical representation is displayed and discussed.
A study of generalized variational-like inequalities in normed spaces for pseudo-monotone type III operators
(UMT Lahore, 2015) Muhammad Talha Nazir
In this thesis, we shall review some existence results for solutions of generalized variational-like inequalities for Pseudo monotone type III operators. These results will be extensively and thoroughly studied in normed spaces on non-compact sets.
Design optimization of vehicle suspension with quarter car model
(UMT Lahore, 2015) Nagina Fatima
Optimization includes the determination of optimum point of an objective function, supply system and test functions. Here we do the comparative study of three optimization methods, hooke-jeeves method, nelder-mead method and multidirectional search method and these methods have been applied to the solution of the fully constrained optimization problem. There are many derivative free methods which could be used for solving different constrained optimization models. These methods will also be implemented to different models, test functions and then compare the results. The focus of this research project is to execute and evaluate these optimization methods and those methods which do not need gradient information. In order to discuss the solution of the completely constrained optimization problems, numerous constraint handling methods are evaluated, including the penalty function level. Here we also discuss a model which is called quarter vehicle model with different types of constrains which involve the comparative study of three optimization method, named as hooke-jeeves, nelder-mead and multidirectional search method for design optimizing vehicle suspensions constructed on quarter vehicle model with different types of constrains. It was resulted from the comparative study that hooke-jeeves search method is more reliable than multidirectional and nelder-mead search methods. The optimum results of quarter car model were obtained by using matlab programming which demonstrated the effectiveness and applicability of the methods.
Fifth order numerical methods for heat equation with variable coefficient subject to non homogeneous boundary conditions
(UMT Lahore, 2015) Naveed Ahmad
In this thesis, two numerical methods, based upon Pade’s approximation to the matrix exponential function, for solving one dimensional heat diffusion equations with variable coefficients, are developed. These methods are L-stable and fifth order accurate in space and time. These methods are tested on heat conduction problems through a thermally insulated thin wire. The solution of these problems gives the temperature at any distance from one end of the wire after any time of the heat conduction. The methods are found to be highly accurate and stable.
Existence of n symmetric positive solutions for singular second order two-point and four-point boundary value problems
(UMT Lahore, 2015) Marfua Alam
In this dissertation, we find positive symmetric solution of singular second order two-point boundary value problem using fixed point theory, monotone iterative technique and then extend this method to find solution for singular second order four point boundary value problem. By symmetric solution we mean a solution w is positive w(t) > 0 and w(t) = w(1 − t), 0 ≤ t ≤ 1. Here we consider the coefficient h(t) is singular at end points t = 0 and t = 1 and w(t) is symmetric and concave whereas w′(t) is skew-symmetric on interval [0, 1]. We consider ordered Banach space having an appropriate norm and cone k of continuous differentiable functions. Then we construct an integral operator t (w) using Green’s function and take its mapping on cone (on k into itself) and use Arzela-Ascoli theorem to show that this operator is completely continuous. This operator is symmetric and concave whereas its derivative is skew-symmetric in [0, 1]. Then by selecting some suitable constants and imposing conditions on norm we construct the monotone iterative technique to obtain the fixed point of the operator and this fixed point is positive symmetric solution of our considered boundary value problem. First we do it for one symmetric positive solution and then extend this technique to find n symmetric positive solutions of second order two-point and four-point boundary value problems.
General solutions for unsteady free convective flow for Brinkman type fluid
(UMT Lahore, 2015-10) Maryam Aleem
The main aspire of this desertion is to represent generalized solutions for Brinkman type non-Newtonian fluids in which we will reckon time dependent velocity along the boundary. In chapter 1, a few cardinal concepts concerning the rates of flows, dissimilar types of fluids, a couple of constitutive equations and equations of apparent movement, Navier Stokes equations and integral transform i.e., The Laplace transform are discoursed. In chapter 2, an analysis is followed by the un-firm or jerky free convection stream of a Brinkman type fluid flowing across an upright plate subject to time dependent velocity f(t) which fulfills the condition of f(0)=0. By inserting the suitable variables, the basic governing equations are abbreviated to dimensionless equations sound to all levied initial and boundary conditions. The exact solutions of initial value problem has been attained by using Laplace transform technique. When β∗ = 0, the results will be true for Newtonian fluid for the analogous motion. The impression of assorted values of the tangible parameters specified for temperature, skin friction, velocity and Nusselt number is underscored diagrammatically. In chapter 3, the velocity domain of jerky convection stream of Brinkman type flowing materials passing through an upright plate imbedded in permeable medium with mass diffusion and Newtonian heating condition is dissected. The exact solution is received by means of Laplace transform and deduced to the results for Newtonian fluids. The effects of several parameters upon the velocity dispersion, temperature, mass diffusion and skin friction is tested graphically.
General solutions for free convection flow of Casson fluid over an infinite vertical plate
(UMT Lahore, 2015-11) Allia Naseem
In this thesis, we consider the flow behaviour of Casson fluid under different circumstances. Firstly, some basic definitions and concepts regarding the fundamentals of fluid motion and methods to solve the flow problems have been discussed. In chapter 2, the free convection flow of Casson fluid past an upright plate subject to the time dependent velocity f(t) with constant wall temperature has been investigated. The vertical plate is set in motion with a time dependent velocity f(t) at time t = 0+. And so the motion will be produced in the fluid. Exact solutions are obtained through the Laplace transform method. The solutions corresponding to Newtonian fluid for γ → ∞ is obtained as a limiting case. Also we have discussed some consequences of various parameters like Casson parameter, Grashöf and Prandtl numbers on velocity and temperature and presented them graphically. Chapter 3, particularly deals with the jerky and unformed free convection flow of Casson fluid subject to an upright plate with mass transfer and Newtonian heating. With the help of Laplace transform, the expressions for velocity and temperature will be established. For particular cases when (a) Pr=1, Sc=1, (b) Pr ≠ 1, Sc=1 and (c) Pr = 1, Sc ≠ 1, solutions are investigated. For different physical parameters, graphical representation is displayed and discussed.
COMPARATIVE study of teaching learning based optimization algorithm, shuffled frog leaping algorithm and imperialist competitive algorithm on some engineering design problems
(UMT Lahore, 2016) Syeda Bint e Zahra
Optimization involves the determination of best results or to maximize or minimize an objective function such as hydrostatic thrust bearing, robot gripper, rolling element bearing. Different methods have been used for solving a variety of constrained optimization models. These methods have been applied to different test functions, models and also compare the results. The aim of this research project is to implement and assess these optimization methods, with emphasis on procedures that do not require gradient information. In practice, these problems additionally require the satisfaction of equal, unequal and bounded constraints. Due to different types of constraints the non-linear optimization problems are great challenges for most of the methods. In this work comparative study of three popular optimization methods, teaching-learning based optimization method, shuffled frog leaping method and imperialist competitive method have been applied to the solution of the fully constrained optimization problem. In order to address the solution of the fully constrained optimization problem, different constraint handling techniques are investigated, including the penalty function approach. The results of the application of these methods indicate that these methods with penalty function treatment is an efficient solution of mathematical models.
Fourth order parallel splitting techniques for two dimensional heat equation with nonlocal boundary condition
(UMT Lahore, 2016) Mahar Muhammad Ehsan
This thesis develops a fourth-order parallel splitting algorithm for solving two-dimensional linear partial differential equations with nonlocal boundary condition. We have used fourth-order approximations to calculate spatial derivative, and a matrix exponential function existed during the process, and this matrix is replaced by a rational approximation. The nonlocal boundary conditions have been approximated by using Simpson’s 1/3 rule. Different numerical experiments are approximated and compared with the exact solution by using this parallel algorithm.
N-framed soft set with basic operations
(UMT Lahore, 2016) Azhar Hussain
The main purpose of this thesis is to introduce the basic operations of union, intersection, difference and relative complement of double framed soft sets, discussed in Chapter 3. Extension of double framed soft sets into triple framed soft sets and to propose the basic operations of union, intersection, difference and relative complement of triple framed soft sets, discussed in Chapter 4. Finally, the introduction of n-framed soft sets, as a generalization of double framed soft sets, and the basic operations of union, intersection, difference and relative complement of n-framed soft sets, discussed in Chapter 5.
Applications of fuzzy soft set theory in multi-criteria decision making problems by multi-decision makers
(UMT Lahore, 2016) Fazal Dayan
In our real life, many problems in economics, engineering, medical, social, and management sciences etc. involve imprecise data. The solution of these problems involves the use of mathematical principles based on imprecision and uncertainty. A number of theories have been developed to deal with such type of problems. In today's fast moving world, decision-making problems with imprecise data have a special significance. Decision making involves the selection of one alternative from two or more. The decision maker has to choose the best one from the present alternatives. A method of multi-criteria decision making with performance evaluation of multi-observer and performance weightage of the multi-decision maker using the concept of fuzzy soft matrix theory is presented here.
Fifth order parallel splitting techniques for two dimensional heat equation with nonlocal boundary condition
(UMT Lahore, 2016) Naveed Zaman
The NLBC is calculated by using Simpson’s 1/3 formula, while the derivatives involved are solved by adopting higher-order formulas of finite difference (FD). By the method of lines (MOL) and semi-discretization approximation, we transform the PDEs into a linear system of first-order differential equations whose result fulfills a recurrence relation including the exponential function of a matrix. The techniques used are L0-stable, factual (reliable), and do not compel the application of complicated computation. The refined parallel algorithm is also applied to a problem and is seen to be highly factual, with less error than the methods already existing.
3-Total edge product cordial labeling of some new classes of graphs
(UMT Lahore, 2016-03-14) Madiha Saqlain
Our aim in this thesis is to study 3-total edge product cordial (3-TEPC) labeling of some new classes of graphs. We study ladder graph, wheel graph, m isomorphic copies of n cycle graph and Dutch windmill graph in the context of 3-TEPC labeling. We also studied 3-TEPC labeling of some particular examples of graph operations like corona graphs and subdivision graphs.
MHD free convection flow with exponential heating and mass diffusion over an infinite plate that applies shear stress to a viscous fluid
(UMT Lahore, 2016-05-09) Kashif Sadiq
The idea of this work is to find analytical solutions of MHD free convection flow with exponential heating and mass dispersion over an infinite vertical plate that applies shear stress to a viscous fluid. Precise solutions for non-dimensional temperature, concentration, and velocity fields are attained by using the Laplace transform method. Some results are attained as limiting cases. The results satisfy all the initial and boundary conditions. Influences of some flow factors for the special case of the velocity field are graphically illustrated.
Some new cases of free convection of second grade fluid with ramped wall temperature and slip condition at the boundary
(UMT Lahore, 2016-06-21) Mubarik Saleem
The purpose of this work is to find the exact solutions of unsteady free convection of non-Newtonian fluid by assuming the slip at the heated wall. The relative velocity of the fluid is assumed to be proportional to the shear stress at the wall. By means of Laplace transform technique, the exact expressions for the temperature and velocity fields are obtained in dimensionless form. The velocity fields corresponding to both slip and non-slip conditions for the second-grade and Newtonian fluids are obtained in the general case when the vertical plate is moved with velocity A0h(t). Solutions for particular and limiting cases are also obtained. Some physical aspects of flow parameters and the slip coefficient are presented graphically.
Comparative study of fuzzy soft matrix (FSM) and interval valued fuzzy soft matrix (IVFSM) in decision making
(UMT Lahore, 2016-10) MUHAMMAD ZULQARNAIN
In this work, we study soft matrices (SMs), FSM and IVFSM. First of all, we use FSM and the IVFSM in decision-making problems with examples. Secondly, we compare results which are found by FSM and IVFSM and see that the values by FSM method do not lie in the intervals which are found by IVFSM. Finally, for perfect comparison of FSM and IVFSM in decision-making, we redefined the product of IVFSM. Now we see that FSM is more appropriate for decision-making.
Third order parallel splitting techniques for the solution of two dimensional heat equation with nonlocal boundary condition
(UMT Lahore, 2017) Muhammad Aziz
In this thesis our goal is to develop a third-order parallel splitting algorithm for solving linear partial differential equations in two dimensions with non-local boundary conditions. In this method, third-order approximations are used to approximate spatial derivatives, and Simpson’s 1/3 rule is used to approximate the non-local boundary condition. Using this parallel algorithm, the results of numerical experiments are examined, presented, and compared with the exact solution, as well as with the results already existing in the literature, and found to be highly accurate.

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