ABSTRACT Given a Lie algebra g and its complexication gC, the representations of gC are isomorphic to those of g. Moreover, if g is the corresponding Lie algebra of a connected and simply connected Lie group G then the representations of the Lie group in question are isomorphic to those of gC. This thesis explains the basic concepts of Lie groups and Lie algebras. Further, the basic representation theory of Lie groups and Lie algebras, particularly those of semisimple Lie algebras is discuss...
ABSTRACT The study of Green’s Functions and applications of BVPs solving different integration has been put in place in order to provide a broad understanding to the existence of Green’s Functions on solving Ordinary Differential Equations with nth order. The Green’s Functions plays an important role in solving boundary value problems of Ordinary Differential Equations. The solutions of some BVPs for linear ODEs can be denoted by its Green’s Function. Some BVPs for nonlinear Differen...
ABSTRACT The main objective of this study is on a global solution of the Navier-Stokes equations with internal body forces. The internal body forces play very important in both theory and application with Navier-Stokes equations. We discussed about the general solution for ordinary differential equations (ODES) and partial differential equations (PDES). Also they used the MAC model for incompressible flow. The study has been conducted in order to provide abroad understanding the existence of...
ABSTRACT This study aimed at finding a minimum cost of investment in Renewable Energy (RE) sources, specifically in Hydro, Wind, Solar and Biomass that will meet projected demand levels in specific time periods in the future and ensure a modest (10%), (20%) or an ambitious (30%) incorporation of these renewable energy sources. To do this, a relevant optimization model was formulated and discussed. The Levelized Cost of Energy (LCOE) model adopted for the purpose was also discussed in detail....
ABSTRACT This study was undertaken to examine the nature and quantify the magnitude of Genotype by Environment interaction effects on rice (Oryia Sativa L.) grain yield and to determine the most stable and winning genotype (s) in terms of yield stability and performance in two rice producing hubs. The study was conducted at four locations within two rice producing hubs in Northern Ghana on fifteen (15) rice genotypes including a checking genotype GR18 red. A randomized complete block design ...
ABSTRACT The role of weight-for-age babies in the early childhood and its effects on later lives of children cannot be over emphasized. Birth weight according to Murthy (1991) is a key indicator of the incidence of infant mortality and thus, a reflection of the socio-economic development of a country. The main objective is to use statistical models to assess the change in weight of children over time and to investigate whether maternal characteristics such as marital status, educational leve...
ABSTRACT It is known that certain polynomials of degree one, with integer coefficients, admit infinitely many primes. In this thesis, we provide an alternative proof of Dirichlets theorem concerning primes in arithmetic progressions, without applying methods involving Dirichlet characters or the Riemann Zeta function. A more general result concerning multiples of primes in short-intervals is also provided. This thesis also considers problems concerning the existence of odd perfect numbers. T...
ABSTRACT Residue Number System (RNS) has found a wide spread usage in a number of digital signal processing applications such as digital filtering, Discrete Fourier transform , Convolution, Correlation, communication, and cryptography. This is due to the following RNS inherent features: modularity, parallelism, carry free addition, borrow free subtraction, and fault tolerance. The major challenges ofRNS architecture lie in moduli set selection and in the reverse conversion (conversion from r...
ABSTRACT In this study, the average recovery time of Tuberculosis patients and the associated risk of treatment failure/death were examined based on a retrospective moving cohort of sixty-one patients. Mainly, four models: Cox regression, Kaplan-Meier estimator, Log-Pearson III, and the generalized gamma distributions were employed in the analysis to explore all useful information that may be of help to policy makers and stakeholders in their quest to improve service delivery to patients.
ABSTRACT Let H be a real Hilbert space. Let K, F : H → H be bounded, continuous and monotone mappings. Let {un}∞ n=1 and {vn}∞ n=1 be sequences in E defined iteratively from arbitrary u1, v1 ∈ H by
The properties of graphs can be studied via the algebraic characteristics of its adjacency or Laplacian matrix. The second eigenvector of the graph Laplacian is one very useful tool which provides information as to how to partition a graph. In this thesis, we study spectral clustering and how to apply it in solving the image segmentation problem in computer vision.
Abstract In this thesis, an iterative algorithm for approximating the solutions of a variational inequality problem for a strongly accretive, L-Lipschitz map and solutions of a multiple sets split feasibility problem is studied in a uniformly convex and 2-uniformly smooth real Banach space under the assumption that the duality map is weakly sequentially continuous. A strong convergence theorem is proved.
Abstract This paper looks at the study of a derivation of a known inequality for spectral functions of products of exponentials using the Baker - Campbell - Hausdor for- mula. This known inequality is called the Golden-Thompson inequality. The Kalman and the Gramian matrices, Lyapunov equation and matrix exponen- tial, Hadamard's lemma and Duhamel formula as well as the trace inequality due to Araki-Lieb-Thirring are all considered in this work.
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 farreaching result for the exi...
Abstract Chaos poses technical challenges to constrained Hamiltonian systems. This is an important topic for discussion, because general relativity in its Hamiltonian formulation is a constrained system, and there is strong evidence that it exhibits chaotic features. We review concepts in gauge systems and their association with Hamiltonian constraints, relational Dirac observables as gauge-invariant encodings of physical information, and chaos in unconstrained Hamiltonian systems. We then ...