ABSTRACT In this dissertation, it is considered, the investigation of the Fourier Transform and the fundamental solutions of mechanical models with internal body forces. Although, there are many models, only two models are considered on the review, namely heat conduction and linear isotropic elasticity. For the investigation, the statement of the problem bases only on the linear isotropic elasticity problem. In working with calculations, the Fourier Transform, Inverse Fourier Transform, Resi...

ABSTRACT Different physical phenomena can be represented in terms of nonlinear problems for partial differential equations, however such problems are often subjected to singularities. Thus it gives rise to a permanent research interest to such problems. In the present study we provide reviews of essential approach applied to Cauchy problems and initial-boundary problems for hyperbolic equations based on latest results in this field. Also in this research we investigate the following problem ...

ABSTRACT This research presents the existence and uniqueness of a solution to nonlocal problem for a loaded parabolic equation. The nonlocal condition of first kind is expressed to its equivalent nonlocal condition of second kind, which is necessary for qualitative study about the solvability of the problem. The theoretical analysis of study on existence and uniqueness of a generalized solution to a nonlocal problem is studied using Galerkin method, apriori method to obtain the approximate s...

Abstract We present in this thesis the numerical solution to the partial differential equations of parabolic type using the finite-difference methods, namely explicit and Crank-Nicolson methods. We account the local truncation error of the two schemes by using Taylor series and discuss the consistency or compatibility, convergence and stability of these schemes for the parabolic equations. We present vector and matrix norms, also a necessary and sufficient condition for stability. Finally s...

Abstract We show that if a pair of weights (u, ) satisfies a sharp Ap - bump condition in the scale of all log bumps certain loglog bumps , then Haar shifts map ( ) into (u) with a constant quadratic in the complexity of the shift . This in turn implies the two weight boundedness for all Calderón – Zygmund operators. We obtain a generalized version of the former theorem valid for a larger family of Calderón – Zygmund operators in any ambient space . We present a bilinear Tb theorem for...

Abstract Dynamical Systems is the study of the long-term behavior of evolving systems. In this research we studied Lagrangian and Hamiltonian Dynamical systems using Clifford manifolds. The Clifford analogue of Lagrangian and Hamilton Dynamical systems is introduced. In fact a new dynamics on Clifford manifold has been constructed via some local canonical basis. This construction provides wide applications to Physical equations and their geometrical interpretation.

Abstract We find the approximate solution for hyperbolic equation in one space dimension using two finite different schemes: Lax- Wendroff and upwind schemes Then, we study Fourier analysis of these two schemes. we also approximate the numerical solution of system of hyperbolic equations by using finite volume scheme and leap-frog schemes. As well, we study the Fourier analysis of these two schemes. Finally, we study the consistency, convergence and stability for hyperbolic equation in one s...

ABSTRACT The study of magnetohydrodynamics (MHD) flow has received much attention in the past years owing to its applications in MHD generators, plasma studies, nuclear reactor, geothermal energy extractions, purifications of metal from non-metal enclosures, polymer technology and metallurgy. In view of the above, theoretical analysis of the effects of buoyancy force, velocity slip, temperature jump and thermal radiation on entropy generation rate were investigated on electrically conducting...

ABSTRACT There are several real life data sets that do not follow the Normal distribution; these category of data sets are either negatively or positively skewed. However, some could be slightly skewed while others could be heavily skewed. Meanwhile, most of the existing standard theoretical distributions are deficient in terms of performance when applied to data sets that are heavily skewed. To this end, the aim of this study is to extend the Inverse Exponential distribution by inducing it ...

Abstract The role of generalized ordinary differential equation (Kurzweil equation) in applying the technique of topological dynamics to the study of classical ordinary differential equation as outlined in [3, 4, 47, 51-58, 88-90] is a major motivation for studying this class of equations associated with the weak forms of the Lipschitzian quantum stochastic differential equations. In this work, existence and uniqueness of solution of quantum stochastic differential equations associated with ...

Abstract The numerical solutions of initial value problems of general second order ordinary differential equations have been studied in this work. A new class of continuous implicit hybrid one step methods capable of solving initial value problems of general second order ordinary differential equations has been developed using the collocation and interpolation technique on the power series approximate solution. The one step method was augmented by the introduction of offstep points in order ...

ABSTRACT In this work, Susceptible-Vaccination-Exposed-Infection-Treatment-Recovery mathematical model is proposed to study dog rabies disease transmission dynamics with vaccination and treatment in dog population group. Disease free and endemic equilibria were determined and subsequently their local and global stabilities were carried out. Tracedeterminant technique was used to determine local stability of disease free equilibrium point while Lyapunov function technique was used to determin...

Abstract Currently, the demand of Pleurotus HK-37 (oyster mushroom) in Tanzania is growing rapidly due to the increasing of awareness on its nutrition, health, and economic benefits. Despite the increasing demand, the availability of strains of Pleurotus HK-37 species is still a challenge due to high cost of tissue culture technology. ,e high cost of importing agar seems to be among the factors for this failure. ,is study aimed at investigating the performance of low-cost agar from local Grac...

Abstract In this work, we try to set up a geometric setting for Lagrangian systems that allows to appreciate both theorems of Emmy Noether. We consistently use differential form and a geometric approach, in this research, we also discuss electrodynamics with gauge potentials as an instance of differential co-homology. Also we emphasize the role of observables with some examples and applications.

Abstract This project work examines the use of Lagrange multipliers to calculus of variation (isoperimetric problem). Basic definition of terms were given, necessary and sufficient condition for a function to be maxima or minima, how to identify Lagrange multipliers .in any given problem and general useage of largange multipliers, Lagrange multiplier in unconstraint and constraint problems, theorems and proof related to Lagrange multipliers. Literature review, Euler's Multiplier rule anisoper...