Abstract This thesis presents a detailed description and analysis of Bregman’s iterative method for convex programming with linear constraints. Row and block action methods for large scale problems are adopted for convex feasibility problems. This motivates Bregman type methods for optimization. A new simultaneous version of the Bregman’s method for the optimization of Bregman function subject to linear constraints is presented and an extension of the method and its application to solving...

Abstract We show that the right derived functors of the limits of the Khovanov presheaf describes the Khovanov homology. We also look at the cellular cohomology of a poset P with coecients in a presheaf F and show by example that the Khovanov homology can be computed cellularly.

ABSTRACT In steady ows, the notion of boundaries separating dynamically distinct regions is not ambiguous. This is because the invariant manifolds of time-independent ows and the critical points of time-periodic ows provide adequate information to determine the behaviour of the solutions of these systems. However, for time dependent systems, it is strenuous to determine the nature of their solutions due to their dependence on time. Nevertheless, it was observed that just like steady ows, most...

Abstract Nonlinear parabolic interface problems are frequently encountered in the modelling of physical processes which involved two or more materials with different properties. Research had focused largely on solving linear parabolic interface problems with the use of Finite Element Method (FEM). However, Spectral Element Method (SEM) for approximating nonlinear parabolic interface problems is scarce in literature. This work was therefore designed to give a theoretical framework for the con...

ABSTRACT This thesis is concerned with the qualitative properties of solutions of neutral functional differential equations, neutral functional difference equations and dynamic equations on time scale. Some of the equations are of the first and second order whereas some are systems of equations. All these equations are delay equations with constant or variable delays. Fixed point theory is used extensively in this thesis to investigate the qualitative properties of solutions of neutral delay ...

ABSTRACT Developing therapeutics for infectious diseases requires understanding the main processes driving host and pathogen through which molecular interactions influence cellular functions. The outcome of those infectious diseases, including influenza A (IAV) depends greatly on how the host responds to the virus and how the virus manipulates the host, which is facilitated by protein-protein functional inter-actions and analyzing infection associated genes at the systems level, which may ena...

ABSTRACT The numerical solution of the linear system Ax = b, arises in many branches of applied mathematics, sciences, engineering and statistics. The most common source of these problems is in the numerical solutions of ordinary and partial differential equations, as well as integral equations. The process of discretization by means of finite differences often leads to the solution of linear systems, whose solution is an approximation to the solution of the original differential equation. If...

Abstract American Power Put Option (APPO) is a financial contract with a nonlinear payoff that can be applied at any time on or before its expiration date and offers flexibility to investors. Analytical approximations and numerical techniques have been proposed for the valuation of Plain American Put Option (PAPO) but there is no known closed-form solution for the price of APPO. Mellin transform is a useful method for dealing with unstable mathematical systems. This study was designed to der...

ABSTRACT T-cell diversity has a great influence on the ability of the immune system to recognise and fight the wide variety of potential pathogens in our environment. The current state of art approach to profiling T-cell diversity involves high-throughput sequencing and analysis of T-cell receptors (TCR). Although this approach produces huge amounts of data, the data has noise which might obscure the underlying biological picture. To correct these errors, two computational methods have been d...

ABSTRACT Loan default is one of the major problems facing most financial institutions. The solution to this problem has been the use of a mathematical model to determine the probability of default of clients of these financial institutions. This study proposes a mathematical model for predicting the probability of default of clients from a microfinance institution. The logistic and survival analysis methods were used in building the model. The results from the logistic regression model showed...

ABSTRACT Many infectious diseases including malaria are preventable, yet they remain endemic in many communities due to lack of proper, adequate and timely control policies. Strategies for controlling the spread of any infectious disease include a rapid reduction in both the infected and susceptible populations. (if a cure is available) as well as a rapid reduction in the susceptible class if a vaccine is available. For diseases like malaria where there is no vaccine, it is still possible to ...

ABSTRACT This study was undertaken to assist DBE ONE „A‟ students of St. Francis College of Education, Hohoe to improve on their conceptual knowledge of linear inequalities in one variable using the beam balance model. The entire DBE ONE „A‟ students represented the population of the study. Data was gathered through instruments such as test in the form of pre-test and post-test. Due to the large size of the population a total of 40 students which represented 20% of the 200 DBE ONE �...

ABSTRACT The non-differentiable L1-norm penalty in the L1-norm regularized least squares problem poses a major challenge to obtaining an analytic solution. The study thus explores smoothing and non-smoothing approximations that yields differentiable loss functional that ensures a close-form solution in over-determined systems. Three smoothing approximations to the L1-norm penalty have been examined. These include the Quadratic, Sigmoid and Cubic Hermite. Tikhonov regularization is then a...

ABSTRACT This research work was set out to see, if Geometer’s Sketchpad could be used to enhance the ability level of SHS 4 students of Osei Tutu II College in the location of the coordinate of the image of a point or geometrical object under Rigid Motion in a Cartesian plane. A non-probability sampling technique known as purposive sampling was employed to select the sample for the study. In all, 45 SHS 4 students comprising 34 girls and 11 boys were involved in the study. The main resear...

ABSTRACT In this work, necessary and sufficient conditions are investigated and proved for the controllability of nonlinear functional neutral differential equations. The existence, form, and uniqueness of the optimal control of the linear systems are also derived. Global uniform asymptotic stability for nonlinear infinite neutral differential systems are investigated and proved and ultimately, the Shaefers’ fixed point theorem is used to forge a new and far- reaching result for the...