ABSTRACT Game theory has been used to study a wide variety of human and animal behaviours. It looks for states of equilibrium, sometimes called solutions. Nash equilibrium is the central solution concept with diverse applications for most games in game theory. However some games have no Nash equilibrium, others have only one Nash equilibrium and the rest have multiple Nash equilibria. For games with multiple equilibria, dierent equilibria can have dierent rewards for the players thus causing ...
BSTRACT In this thesis the Gaussian plume model is proposed as a method for solving problems related to the transportation of pollutants due to advection by wind and turbulent dif- fusion. The idea of advection and diusion is fundamental to this thesis as well as its mathematical derivations from the initial principles to the explanation of the governing partial dierential equation. Dimensional analysis technique has been employed as well as Fick's rst and second law of diusion. The concentra...
ABSTRACT The determination of the components of stress on a pipe made of either linearly elastic or non-linearly elastic material and subjected to internal fluid pressure is of immense benefit to engineers. Chung et al [2] worked on a class of non-linearly elastic type with some degree of success. This work seeks an improvement on [2]. It will do this by obtaining such components of stress in a form that engineers will find easy to use. Towards obtaining the required components, the r...
ABSTRACT The study of existence results on two point boundary value problems by fixed point methods, monotone iterative techniques, matching solution techniques and integral boundary conditions has been put in place in order to provide a broad understanding to the existence of two point boundary value problems by fixed point methods, monotone iterative techniques and solution matching techniques. The two point boundary value problem for ordinary differential equation has an important role i...
ABSTRACT The new exact solutions for the charged anisotropic stellar object were found by using Einstein-Maxwell field equations. In this study, the metric function, linear equation of state, and a new choice of the measure of anisotropy were used to formulate new quark star models. The field equations were transformed by adopting Bannerji and Durgapal transformation variables. The general differential equation governing the model was generated with the help of Einstein field equations, and ...
Abstract . New models for a charged anisotropic star in general relativity are found. We consider a linear equation of state consistent with a strange quark star. In our models a new form of measure of anisotropy is formulated; our choice is a generalization of other pressure anisotropies found in the past by other researchers. Our results generalize quark star models obtained from the Einstein-Maxwell equations. Well-known particular charged models are also regained. We indicate that relativ...
Abstract In this mini thesis, we study the application of Lyapunov functions in epidemiological modeling. The aim is to give an extensive discussion of Lyapunov functions, and use some specific classes of epidemiological models to demonstrate the construction of Lyapunov functions. The study begins with a review of Lyapunov functions in general, and their usage in global stability analysis. Lyapunov’s “direct method” is used to analyse the stability of the disease-free equilibrium. More...
ABSTRACT We studied two models describing transmission dynamics of tuberculosis (TB) and discussed their implications to human health. The first model is analyzed in the presence of treatment of active TB persons and the screened asymptomatic TB infectives. The second model is analyzed by looking at treatment of drug sensitive TB as well as drug resistant TB individuals. The models are built with a motive to study the dynamical behaviors of the trajectories which has the potential to guide T...
Abstract Using the concept of parallel transport of vectors in curved manifolds, the Riemann curvature tensor in terms of Christoffel symbols is obtained. Making use of the Riemann curvature tensor’s symmetry properties, the Ricci curvature tensor and Einstein’s tensor are derived. Through Einstein’s tensor and the Poisson equation for Newtonian gravity, the Einstein field equations are introduced. Upon using Kerr metric (Kerr, 1963) as a solution for Einstein’s field equations, extra...
Abstract The Cape horse mackerel (Trachurus trachurus capensis ) has traditionally made an important contribution to the South African fishing industry and is a key component of the Benguela ecosystem. This thesis concerns the assessment and management of the South African horse mackerel resource. It starts with a brief review of the biology of the Cape horse mackerel and the history of the fishery, as well as of the Management Strategy Evaluation approach, which was applied in this work. Ass...
Abstract It is common to think of our universe according to the “block universe” idea, which says that spacetime consists of many “stacked” 3-surfaces varied as a function of some kind of proper time τ . Standard ideas do not distinguish past and future, but Ellis’ “evolving block universe” tries to make a fundamental distinction. One proposal for this proper time is the proper time measured along the timelike Ricci eigenlines, starting from the big bang. The main idea of this ...
Abstract In this thesis, we develop the 1 + 1 + 2 formalism, a technique originally devised for General Relativity, to treat spherically symmetric spacetimes in for fourth order theories of gravity. Using this formalism, we derive equations for a static and spherically symmetric spacetime for general f(R) gravity. We apply these master eqautions to derive some exact solutions, which are used to gain insight on Birkhoff's theorem in this framework. Additionally, we derive a covariant form of t...
Abstract The non-life insurance pricing consists of establishing a premium or a tariff paid by the insured to the insurance company in exchange for the risk transfer. A key factor in doing that is properly estimating the distribution that the claim and frequency of claim follows. This thesis aim at having a deep knowledge of loss function and their estimation, several concept from Measure Theory, Probability Theory and Statistics were combined in the study of loss function and estimating the...
Let us first introduce some keywords that will enable us to specify our principal objective. Given a nonempty set X and a function f : X → R which is bounded below, computing the number
Abstract Let X be a uniformly convex and uniformly smooth real Banach space with dual space X∗ . Let F : X → X∗ and K : X∗ → X be bounded monotone mappings such that the Hammerstein equation u + KF u = 0 has a solution in X. An explicit iteration sequence is constructed and proved to converge strongly to a solution of the equation. This is achieved by combining geometric properties of uniformly convex and uniformly smooth real Banach spaces recently introduced by Alber with our met...