The contribution of this project falls within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: Inequalities in Banach spaces and applications. As is well known, among all infinite dimensional Banach spaces, Hilbert spaces generally have simple geometric structures. This makes problems posed in them easier to handle, this is as a result of the existence of inner product, the proximity map, and the two characteristic identitie...
ABSTRACT The Pentagram map is a well notable integrable system that is dened on the moduli space of polygons. In 2005, Richard Evan Schwartz introduced certain polynomials called pentagram integrals (Monodromy invariants) of the pentagram map and dened certain associated integrals, the analogous rst integrals. Schwartz further studied in 2011 with S. Tabachnikov on how these integrals behave on inscribed polygons. They discovered that the integrals are equal for every given weight of polygon...
ABSTRACT Optimization techniques are called into play everyday in decision making processes involving resource allocation in almost every discipline. However, the development and implementation of algorithm for solving optimization problems are fraught with many difficulties and frustrations. The aim of this thesis has been to examine and identify some of the problems associated with the development and implementation of a class of optimization algorithms and to develop a means of improving u...
ABSTRACT The study addressed the curriculum problem of the placement of the teaching and learning of quadratic equation in the Senior High School. Its purpose was to assess the ability of S.H.S 1 students to solve quadratic equation by investigating their performance, using four methods. Stratified sampling method was used to select four schools in four districts in the Central Region. Eight classes were randomly selected for the study. The sample size was 286 of which 160 were girls. A pret...
ABSTRACT It is of great interest and concern to human beings to know why we do what we do in every sphere of life. Of particular interest is education because, it is a key factor in the developmental process or, in the affairs of every developing nation of which Ghana is one and that is what motivated the researcher into finding out the issues Cape Coast Polytechnic students consider in choosing to study at the Cape Coast Polytechnic. Purposive sampling technique was used to select the stude...
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...
Most experimental situations call for standard designs that can be constructed with many statistical software packages. In some situations, however, standard designs are not appropriate or practicable. Computer-aided designs are experimental designs that are generated based on a particular optimality criterion and are generally optimal only for a specified model. In this work designs are generated for non-standard multifactor experiment using D-optimality criterion. The experiment invo...
This dissertation presents a systematic and critical study of the fundamenta.lli of soft set theory which includes soft set operations, soft set relations and functions, soft matrices and their properties. In course of studying operations on soft sets, the complementation operation is strengthened, some new results on distributive and absorption properties with respect to various soft set operations are obtained,and soft set operations and their corresponding soft matrix operations are s...
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 This study deals with the reliability and availability characteristics of two different systems, the second system differs from the first system due to the additional feature of preventive maintenance. Reliability and Availability analysis of system having one active unit and one warm standby unit with self-reset function and one maintenance facility. The failure unit is repaired through self-reset or maintenance according to different failure model.( Mean Time to System Failure...
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 A problem of the ratio-type estimators in Stratified Sampling is the use of non-attribute auxiliary information. In this study, some ratio-type estimators in stratified random sampling using attribute as auxiliary information are proposed. The sample mean of study variable and proportion of auxiliary attribute were transformed linearly and using auxiliary parameters respectively. Biases and mean square errors (MSE) for these estimators were derived. The MSE of these estimators were c...
ABSTRACT This study investigated whether the use of the balance model in the teaching and learning of linear equations can improve students‟ conceptual understanding in the principles of solving linear equations in one variable. The data was gathered using tests. A pre-test conducted on thirty (30) Form two pupils of Buasi Roman Catholic Junior High School and an analysis of the interviews enabled the development and the use of the balance model in the teaching of linear equations ...
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 ...