Browsing AUS Theses & Dissertations by College/Dept "Department of Mathematics and Statistics"
Now showing items 116 of 16

Additive Cyclic Codes Over Rings
(201502)This Master's thesis introduces a reader with an average knowledge of mathematics to coding theory. A background in algebra is included with the required details needed in coding theory. The thesis guides the reader from ... 
Alternating Direction Implicit Method for the ElectroCardiology Models
(201705)Electrophysiology is an area of science that led to innovative experimentations between clinicians and scientists. Studying and understanding cardiac dynamics plays a key role in designing therapies, preoperative planning, ... 
Graph of Linear Transformations over a Field
(201906)This research is an attempt to introduce a connection between graph theory and linear transformations of finite dimensional vector spaces over a field F (in our case we will be considering R). Let Rᵐ, Rⁿ be finite vector ... 
High Order Methods for Solving Cardiac Models
(202005)Modeling of the heart became of great interest for both mathematicians and bioengineers over the past 25 years for the increasing impact of cardiovascular system problems in our every day lives. The bidomain model and its ... 
Iterative Methods for the Numerical Solutions of Boundary Value Problems
(201406)The aim of this thesis is twofold. First of all, in Chapters 1 and 2, we review the wellknown Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM) for obtaining exact and numerical solutions for ... 
Neural Networks as a Convex Problem
(201609)We reformulated the problem of training the neural networks model into a convex optimization problem by performing a local quadratic expansion of the cost function and adding the necessary constraints. We designed a new ... 
On Some Applications of the Maximum Principles to a Variety of Elliptic and Parabolic Problems
(201907)One of the most important and useful tools used in the study of partial differential equations is the maximum principle. This principle is a natural extension to higher dimensions of an elementary fact of calculus: any ... 
On some bounds for frequencies of membranes and plates.
(202005)The problem of optimizing a domain dependent functional, while keeping a domain’s measure (its volume, perimeter, etc.) fixed, is called an isoperimetric problem. The isoperimetric inequalities have a long history in ... 
On The Unit Dot Product Graph Of A Commutative Ring.
(201601)In 2015, Ayman Badawi (Badawi, 2015) introduced the dot product graph associated to a commutative ring A. Let A be a commutative ring with nonzero identity, 1 n < 1 be an integer, and R =A x A x ... x A (n times). We ... 
Solution of Fractional Differential Equations: Transform and Iterative Methods Approach
(201912)Fractional calculus is a novel and highly active area of research in the literature as it has a wide spectrum of applications in the physical sciences and engineering. In this thesis, we study the numerical solution of ... 
Solution of Fractional Differential Equations: Variational Iteration Approach
(201912)This thesis discusses a newly introduced numerical scheme for fractional differential equations. The strategy is an extension of the Variational Iteration Method (VIM) and is suitable for boundary value problems (BVPs). ... 
Solving Fourth Order Differential NonLinear Equations, Existence and Uniqueness
(201705)The aim of this thesis is to present a novel numerical approach for the solution of a class of nonlinear fourthorder boundary value problems. The method is based on embedding Green's function into some fixed point iteration ... 
Solving The 2D Biharmonic Equation: A Numerical Approach Based On Spline Collocation
(201607)In this thesis, several numerical methods, that are based on spline basis functions, are suggested for the solution of a general class of fourth order boundary value problems. In particular, The twodimensional biharmonic ... 
Some applications of the Hyperbolic Metric
(201506)This thesis is an expository of the hyperbolic geometry in general and the hyperbolic metric for several domains in particular. The thesis also focuses on the differences between the Euclidean geometry and hyperbolic ... 
Study of the Electromechanical Models for Cardiac Activity
(201705)The mathematical modeling of the complex physical phenomena occurring in the heart is an area of increasing interest, as it facilitates the better understanding of relevant mechanisms driving the behavior of the system in ... 
Subsonic Flow over a Thin Airfoil in Ground Effect: a Functional Analytic Approach
(201705)In this work, the problem of subsonic compressible flow over a thin airfoil located near the ground is studied. A singular integral equation, also known as the Possio integral equation [29], that relates the pressure jump ...