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, 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...
Abstract We Show the uniqueness of the norm on the Lebesgue space of the compact group. We give some applications of the property of Kazhdan to the method of automatic continuity. We determine the similarity of quasinilpotent operators. The symmetric Meixner- Pollaczek polynomials and a system of orthogonal polynomials with Hardy spaces for the strip are considered. We investigate the behaviour of the Lebesgue space of the integral means of the analytic functions and the vector- valued BMOA ...
Abstract We give characterizations of isometric shift operators and Backward shifts on Banach spaces with linear isometries between subspaces of continuous functions. We show the inverse spectral theory for the Ward equation and for the 2+1. Chiral model, we also consider the isometric shifts and metric spaces. We also study the Cauchy problem of the Ward equation. We discuss the relative Position of four subspaces in of Hilbert space, with an indecomposable representations ofQuivers on infi...
In this research, we deal with three forms of Stokes’ theorem. The version known to Stokes’ appears in the last chapter, along with its inseparable companions, Green’s theorem and the Divergence theorem. We discuss how these three theorems can be derived from the modern Stokes theorem, which appears in chapter (4), with some applications on oriented manifolds with boundary. In addition to applications of Maxwell’s field equations.
Abstract This work takes a look at different computational algorithms used in solving initial value problems and how these algorithms arc derived from Taylor's series. It also made use of the Euler and Runge-Kutta method to solve initial value problems in order to compare the performance of the two methods.
Abstract This project report deals with the class of asymptotically demicontractive mappings in Hilbert spaces. We noted some historical aspects concerning the concept of asymptotically demicontractivity and studied a regularized variant of the Krasnoselskii-Mann iteration scheme, which ensured the strong convergence of the generated sequence towards the least norm element of the set of _xed points of asymptotically demicontractive mapping.