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Item 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 ZahraOptimization 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.Item Comparative study of fuzzy soft matrix (FSM) and interval valued fuzzy soft matrix (IVFSM) in decision making(UMT Lahore, 2016-10) MUHAMMAD ZULQARNAINIn 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.Item 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 SadiqThe 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.Item Applications of fuzzy soft set theory in multi-criteria decision making problems by multi-decision makers(UMT Lahore, 2016) Fazal DayanIn 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.Item 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 SaleemThe 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.Item Fourth order parallel splitting techniques for two dimensional heat equation with nonlocal boundary condition(UMT Lahore, 2016) Mahar Muhammad EhsanThis 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.Item Fifth order parallel splitting techniques for two dimensional heat equation with nonlocal boundary condition(UMT Lahore, 2016) Naveed ZamanThe 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.Item 3-Total edge product cordial labeling of some new classes of graphs(UMT Lahore, 2016-03-14) Madiha SaqlainOur 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.Item N-framed soft set with basic operations(UMT Lahore, 2016) Azhar HussainThe 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.