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Item Charged cylindrical gravitating systems in f(R, T) gravity(UMT Lahore, 2019-11) Muhammad Asad SaeedBy the end of the evaluation of this research artifact, readers will be able to describe the effect of charged anisotropic viscous fluid on the evolution of stellar objects. In this script, the stability of charged cylindrically symmetric stellar objects has been analyzed in the context of f (R, T ) theory of gravity. The modified field equations and their conforming dynamical equations have been constructed and then the perturbation scheme has been used to describe the dynamics of the gravitating sources. Adiabatic index Γ has been used to sort the corrections to weak field limit i.e., in the Newtonian and the post Newtonian regimes. It is observed that electromagnetism has significant effect on the collapse as well as the stability of stellar objects.Item Evolution of charged viscous fluids in f(R, T) gravity(UMT Lahore, 2019-11) Usman Ul HaqIn this thesis, dynamical analysis for spherically symmetric gravitating sources is presented in f (r, t ) gravity, where r and t are scalar curva- ture and trace of energy momentum tensor respectively. The inner fluid distribution is considered to be charged, viscous, anisotropic and modified field equations are constructed. Dynamical equations are developed by tak- ing divergence of energy momentum tensor. The perturbation scheme is applied to dynamical equations for stability analysis. Perturbed form of dynamical equations leads to the development and study of gravitational evolution. The stability analysis is carried out in newtonian limit (nl) and post newtonian limit (pnl) to workout corrections in weak field regime. It is observed that fluid distribution such as heat flux, viscosity, anisotropy and mass of the celestial objects have significant implications on collapsing process as well as stability.Item Effect of coupled heat and mass transfer on MHD viscous fluid over an infinite inclined plane(UMT Lahore, 2019-04) Ammara AkramIn this work, we investigated the influence of coupled heat and mass transfer on MHD viscous fluid over an infinite inclined plane, generate because of heat and mass transfer effects. The non-dimensional temperature, concentration and velocity fields are calculated by Laplace and Laplace inverse transform. The fluid is considered over an infinite plate under the action of varying temperature and varying mass diffusion. The effects of heat generation and chemical reaction is also studied. Finally, the influence of different parameters on the fluid motion is graphically illustrated.Item Metric dimension of the combination of antiprism and some convex polytopes.(UMT Lahore, 2019-07-16) Hafsa MaqsoodThis thesis is devoted to the study of metric dimension by combining antiprism graph to outer cycle of convex polytopes found in [21, 22, 23, 24, 25]. The metric dimension is constant for the combination of antiprism with some convex polytope and only three vertices are enough to resolve all the vertices of these graphs.Item Heronian mean aggregation operator for hesitant probabilistic fuzzy elements(UMT Lahore, 2019-07-20) Muhammad WaqasIn this thesis, we have proposed hesitant probabilistic fuzzy linguistic set and some new operators by combining the power average operator and the generalized Heronian mean operator under hesitant probabilistic fuzzy linguistic environment, such as the hesitant probabilistic fuzzy linguistic power generalized Heronian mean (HPFLPGHM) operator, the hesitant probabilistic fuzzy linguistic power generalized geometric Heronian mean (HPFLPGGHM) operator, the hesitant probabilistic fuzzy linguistic weighted power generalized Heronian mean (HPFLWPGHM) operator and the hesitant probabilistic fuzzy linguistic weighted power generalized geometric Heronian mean (HPFLWPGGHM) operator. Then, some special cases of the proposed HPFLPGHM and HPFLPGGHM operators are discussed in detail. Finally, a numerical example is given to illustrate the application of the developed operators.Item 4-total edge product cordial labeling of the subdivision of some classes of graphs(UMT Lahore, 2019-08-02) Hina NawazOur task in this thesis focuses on 4-total edge product cordial (4-TEPC) labeling of the subdivision of some standard classes of graphs, and the main aim of the study is to discuss prism graph, wheel graph, book graph, banana tree graph, recracker graph, and star graph in the context of 4-TEPC labeling.Item Antimagic total labeling on a class of acyclic graphs(UMT Lahore, 2019) Sidra MahmoodLet (G = (V(G), E(G))) be a simple graph with finite vertex set (V(G)) and edge set (E(G)) as a two-element subset of (V(G)). Precisely, a mapping ( \phi : V(G) \cup E(G) \to {1,2,3,\dots,v+e} ) is called an ((a,d))-edge antimagic total labeling if the set ( {\phi(u)+\phi(v)+\phi(uv) : uv \in E(G)} ) forms an arithmetic progression with first term (a) and common difference (d). Moreover, this labeling becomes super ((a,d))-edge antimagic total labeling if the vertices attain the smallest labels, i.e., (\phi(V(G)) = {1,2,3,\dots,v}). In this thesis, we prove the results related to the super ((a,d))-edge antimagic total labeling of a class of acyclic graphs under certain conditions.Item Topological indices of complete t-partite graphs with applications in neural networks(UMT Lahore, 2019-09) Aneeqa AslamLet be a collection of graphs and R be a set of real numbers. A mapping: R is called topological index if it associates each graph of to a unique real no of R. Let G1, G2, G3 and Gt be the null graphs with cardinalities of their vertex-sets S1, S2, S3 …, and St respectively, where Si ≥ 1 for 1 ≤ i ≤ t. A graph G = KS1 S2 S3 … St is called a t-partite graph if it is obtained from G1, G2, G3 … Gt such that V(G) = V(G1) ∪ V(G2) ∪ V(G3) … ∪ V(Gt) and for uv ∈ V(G), uv ∈ E(G) if one end u of the edge uv is in some V(Gi) and the other end v of the edge uv is in some V(Gj), where 1 ≤ i, j ≤ t and i ≠ j. In this thesis, we compute various degree-based topological indices (TIs) of t-partite graphs (KS1 S2 S3 … St) in their general form. We also apply the obtained results on the neural networks to discuss their various properties.Item Hesitant fuzzy rankings for hesitant preference relations(UMT Lahore, 2019-04-12) Muhammad KhanIn this thesis the transformation of fuzzy rankings and hesitant fuzzy rankings into fuzzy preference relations and hesitant fuzzy preference relations is presented to evaluate the problems of group decision making. Furthermore, the similarity measures for a binary vectors is discussed and also similarity measures applied between fuzzy rankings to evaluate the level of understanding among the experts.Item A study of optimal coincidence point solutions for nonlinear operator equations with applications.(UMT Lahore, 2019-07) Wali Ullah BalochIn this thesis, we defined a multivalued Suzuki type contraction and Suzuki type modified proximal and modified proximal contraction and proved some best proximity point results in metric and b metric spaces. Some examples are also illustrated to support the main results proved herein. We also studied the best proximity point results in partially ordered metric and b metric spaces. As an application, for self mappings, we discussed some fixed point results in the setup of metric and b metric space.Item Development of multipolar intuitionistic fuzzy soft set and similarity measures with application in medical diagnosis(UMT Lahore, 2019) Asad ZiaSimilarity measures for intuitionistic fuzzy soft sets play a pivotal role for handling the problem that holds uncertain information, but unable to tackle the blurriness and fuzziness of the issue having multipolar information. In this thesis, the introduction of m-polar intuitionistic fuzzy soft set (mIFS set) and some operations have been presented. In addition, some certain distances between two mIFS sets has been initiated to analyze the best approximation. The distance based similarity measure (SM) has also been utilized for mIFS sets. The application of this new developed technique depicted in the example for medical diagnosis of kidney disease.Item Solution of nonlinear multivalued operator equations in generalized metric space(UMT Lahore, 2019) Muhammad Bilal IqbalIn the present thesis, the aim is to study and discuss the fixed point theorems, coincidence point theorems and common fixed point theorems in the context of generalized metric spaces (in the sense of Jheli and Samet). The main goal is to prove some new fixed point theorems for multivalued F-contractions involving a reflexive and transitive binary relation that is not necessarily a partial order, in the context of generalized metric spaces (in the sense of Jheli and Samet) by adding and relaxing some conditions and generalizing the existing results.Item Different convex polytopes labeled by 3-total edge mean cordial labeling(UMT Lahore, 2019-11-07) Ayesha ShahidIn this thesis, we worked on k-total edge mean cordial (k-TEMC) labeling of graphs introduced by Fakhir Aslam et al. (see [3]), which is a generalization of edge mean cordial labeling (see [14]). We discussed prism graph, double prism graph, antiprism graph, double antiprism graph and combination of different convex polytopes in the context of k-TEMC labeling for k = 3.Item Correlation coefficients of interval-valued intuitionistic hesitant fuzzy sets and their application to clustering analysis(UMT Lahore, 2019-07-15) ADINA ASIMIn this study, we inspect the group decision making uncertainties present in interval-valued intuitionistic hesitant fuzzy sets. Firstly, we extended the correlation coefficient formulas of intuitionistic hesitant fuzzy sets to interval-valued intuitionistic hesitant sets, to pile up the interval-valued intuitionistic hesitant fuzzy set values. Then, these values are represented in the form of a decision matrix. After which, we have performed the composition of a matrix to establish the given data within the several clusters. Then grade the choices in line according to the correlation coefficients between interval-valued intuitionistic hesitant fuzzy values and choose the most desirable one. Finally, two real world examples are utilized to elaborate the necessity of the presented approach.Item 4-Total edge mean cordial labeling of some classes of convex polytopes(UMT Lahore, 2019-11-07) Fakhra Malik AwanIn this thesis, we study the type of graph labeling known as k-total edge mean cordial (k-TEMC) labeling of graphs introduced by F. Aslam at al. (see [2]), which is a generalization of edge mean cordial labeling (see [17]). We discussed some classes of convex polytopes graphs and their different combinations in the context of k-TEPC labeling for k = 4Item Semi analytical solutions of convective flows of second grade fluid with the effect of generalized Fourier's and Fick's laws(UMT Lahore, 2019-08-02) Syeda Mahwish BukhariThe main purpose of this dissertation is to find the semi analytical solution of fractional incompressible differential type fluid of mixed convection flow subject to Newtonian heating near a vertical plate. Fractional derivative Caputo-Fabrizio (CF) and Atangna Baleanu (ABC) with non singular kernel is investigated in the constitutive equations of mass flux and thermal process to describe the diffusion and thermal flux respectively. In starting some preliminaries and basic concepts related to heat transfer, Newtonian heating, constitutive equations and fractional calculus have been presented. Then in the next chapters we succesfully applied the fractional derivative to find the semi analytical solutions of second grade fluid with non-integer derivatives by using Fourier's and Fick's laws. In Chapter 2, we study the unsteady natural convection flow of an incompressible differential type fluid with fractional thermal transport near an infinite vertical plate. Modern definitions of fractional derivatives Atangana-Baleanu (ABC) and Caputo Fabrizio (CF) are depleted in the constitutive equations of thermal flux to describe the thermal process. Semi analytical solutions of the dimensionless temperature and velocity fields with (ABC) and (CF) fractional derivatives are investigated by means of the Laplace transform. Some solutions are established for ordinary case and obvious results from articles are retrieved as limiting cases. Expressions of coefficients of Nusselt number and skin friction are examined too. Further, impact of opportune parameters on the temperature and velocity fields are discussed graphically. Finally, a comparison for ordinary case, (ABC) and (CF) models are also depicted. It is found that memory of the physical aspects of the problem is well explained by fractional order models (ABC) and compared to ordinary one. Moreover, it is noticed that, (ABC) model is the best fit to explain the memory effect of temperature and velocity fields. In Chapter 3, we study an unsteady mixed convection flows of an incompressible differential type fluid occurrence of first order chemical reaction, heat source, radiative heat source and Newtonian heating near an infinite vertical plate. The fractional derivative Caputo-Fabrizio (CF) which is defined recently with non-singular kernel is used in constitutive equations of the mass flux and thermal flux respectively. Semi analytical solutions of the dimensionless concentration, temperature and velocity fields in addition the rates of heat and mass relocation to the fluid by the plate are established by means of the inversion of Laplace numerical algorithm Tzou's and Stehfest's. Some solutions for ordinary case and obvious results from articles are retrieved as limiting cases. Further, an impact of fewer flow and fractionalize parameters and β on concentration, temperature and velocity profiles are tabularly and graphically underlined and discussed. Finally, we present a valuation between (fractional and ordinary) which are second grade and viscous fluids is also interpreted. It is identified that the ordinary fluid has high velocity as comparable to fractional fluids.Item Higher order numerical method for the solution of heat equation with non-homogeneous boundary condition(UMT Lahore, 2019-09) M.Umer FarooqIn this thesis, a family of numerical methods, based on rational approximation to matrix exponential function, is developed for solving parabolic partial differential equation. These methods are sixth order accurate in space and time, due to combination of sixth order finite approximation and fifth order PDEs approximation. These methods don’t require complex arithmetic. In these methods second order spatial derivatives are approximated by sixth order finite difference approximation. Parallel algorithm is developed and tested on one dimensional heat equation, with variable coefficients, subject to non-homogeneous boundary conditions and time dependent boundary conditions. It is checked that the results obtained are highly accurate and can be coded on parallel computers.Item Hybrid order numerical method for homogeneous boundary conditions with variable coefficients for the solution of heat equation(UMT Lahore, 2019-09) Aqsa NawazFourth order numerical method is used in this thesis with variable coefficient subject to homogeneous boundary conditions for heat equation. The proposed method does not require composite, complex arithmetic. The method is L-stable and fourth-order accurate. Finally, numerical algorithm is also given and results are compared with existing ones which shows that our results are more accurate.Item Stability of galaxy filaments in F(R) gravity(UMT Lahore, 2019-01) Muhammad AdeelThis thesis is devoted to study the dynamics of collapsing stellar ¯lament in the presences of exotic matter. We use f(R) theory to involve exotic terms in the collapsing scenario. We apply Darmois junction conditions on collapsing surface boundary and obtain the collapse equation. It is found that radial pressure associated with baryonic matter remains non zero at. We then apply two different approaches of f(R) gravity: metric f(R) gravity and Palatini f(R) approach as candidates of exotic material to explore stability criteria of the collapsing process. Firstly, we use Starobinsky model, f(R) = R + R², then, we apply three parameter model of Palatini f(R) gravity. It is found that the stability of flamentary structure relates radial pressure of baryonic matter directly with the gravitational effects of exotic terms. Stability criteria of family of polytropic flamentary structures are discussed by applying polytropic equation of state to baryonic contribution. For all stable polytropic ¯laments, it turns out that the visible matter density is exponentially related to gravitational effects of exotic terms. Finally, we explore theoretical relation between gravitational waves and dark terms. It is theoretically predicted that the presences of exotic material can affect the propagation of gravitational waves.Item Decision making by using intuitionistic fuzzy sets under intuitionistic fuzzy measure based granular uncertainty.(UMT Lahore, 2019-06-26) Syed Husnain AbbasA large space where the uncertainty variable value takes place, we use granulation in large space to analyze the knowledge asset process that can come into related decision process. In this thesis, in order to provide an approach by using intuitionistic fuzzy sets to decision maker, presence of uncertainty where the uncertainty is expressed as a granular object. Moreover, the payoff matrix is an important class which can be the best described of uncertain problems in response of challenges. To make a precise decision, decision attitude is also considered to compute the result. An example is given to show how this method handles uncertain decision problems.
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