Abstract We show that the normal Appell subgroup of the Riordan group is a pseudo ring under a multiplication given by the componentwise composition. We develop formulae for calculating the degree of the root in generating trees and we establish isomorphisms between the four groups : the hitting time, Bell, associated and the derivative which are all subgroups of the Riordan group. We have found the average number of trees with left branch length in the class of ordered trees and the Motzkin ...
Abstract Linear Quadratic Control Problems are control problems with a quadratic cost function and linear dynamic sytem and a linear terminal constraint. This work looks at linear quadratic control problems without terminal conditions. We will first look at the controllability and observability of linear dynamical systems and then establish the necessary conditons for the variation in the cost criterion to be nonnegative for strong perturbations in the control. These conditions are the first ...
Abstract ln this work, the researchers consider the concept of Information Security by the application of firewall and encryption techniques. Also, the problem of explicitly exposing infonnation in transit is discussed. We developed several algorithms. Among the algorithms are those of random sequence and non-arithmetic sequence using modified ' generators for the problem to secure information that may pass through intermediate computers l inked in the Internet. Some of these algorithms emplo...
ABSTRACT A Krasnoselskii-type algorithm for approximating a common element of the set of solutions of a variational inequality problem for a monotone, k-Lipschitz map and solutions of a convex feasibility problem involving a countable family of relatively nonexpansive maps is studied in a uniformly smooth and 2-uniformly convex real Banach space. A strong convergence theorem is proved. Some applications of the theorem are presented.
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 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...