PURE AND APPLIED MATHEMATICS PROJECT TOPICS
LaSalle Invariance Principle for Ordinary Differential Equations and Applications
ABSTRACT The most popular method for studying stability of nonlinear systems is introduced by a Russian Mathematician named Alexander Mikhailovich Lyapunov. His work ”The General Problem of Motion Stability ” published in 1892 includes two methods: Linearization Method, and Direct Method. His work was then introduced by other scientists like Poincare and LaSalle . In […]
A Modified Subgradient Extragradeint Method for Variational Inequality Problems and Fixed Point Problems in Real Banach Spaces
ABSTRACT Let E be a 2-uniformly convex and uniformly smooth real Banach space with dual space E ∗. Let A: C → E ∗ be a monotone and Lipschitz continuous mapping and U: C → C be relatively nonexpansive. An algorithm for approximating the common elements of the set of fixed points of a relatively nonexpansive map U and the set of […]
Foundation of Stochastic Modeling and Applications
ABSTRACT This thesis presents an overview on the theory of stopping times, martingales and Brownian motion which are the foundations of stochastic modeling. We started with a detailed study of dis- crete stopping times and their properties. Next, we reviewed the theory of martingales and saw an application to solving the problem of “extinction of […]
Variational Inequality in Hilbert Spaces and their Applications
– Variational Inequality in Hilbert Spaces and their Applications – Download Variational Inequality in Hilbert Spaces and their Applications project materials: This project material is ready for students who are in need of it to aid their research. ABSTRACT The study of variational inequalities frequently deals with a mapping F from a vector space X or […]
Monotone Operators and Applications
– Monotone Operators and Applications – Download Monotone Operators and Applications project materials: This project material is ready for students who are in need of it to aid their research. PREFACE This project is mainly focused on the theory of Monotone (increasing) Operators and its applications. Monotone operators play an important role in many branches of […]
Integration in Lattice Spaces
– Integration in Lattice Spaces – Download Integration in Lattice Spaces project materials: This project material is ready for students who are in need of it to aid their research. ABSTRACT The goal of this thesis is to extend the notion of integration with respect to a measure to Lattice spaces. To do so the paper […]
Sobolev Spaces and Variational Method Applied to Elliptic Partial Differential Equations
Sobolev Spaces and Variational Method Applied to Elliptic Partial Differential Equations. INTRODUCTION Variational methods have proved to be very important in the study of optimal shape, time, velocity, volume or energy. Laws existing in mechanics, physics, astronomy, economics and other fields of natural sciences and engineering obey variational principles. The main objective of variational method […]
A Hybrid Algorithm for Approximating a Common Element of Solutions of a Variational Inequality Problem and a Convex Feasibility Problem
A Hybrid Algorithm for Approximating a Common Element of Solutions of a Variational Inequality Problem and a Convex Feasibility Problem. ABSTRACT In this thesis, a hybrid extragradient-like iteration algorithm for approximating a common element of the set of solutions of a variational inequality problem for a monotone. k–Lipschitz map and common fixed points of a […]
Maximal Monotone Operators on Hilbert Spaces
Maximal Monotone Operators on Hilbert Spaces. ABSTRACT Let H be a real Hilbert space and A: D(A) ⊂ H → H be an unbounded, linear, self-adjoint, and maximal monotone operator. The aim of this thesis is to solve u 0 (t) + Au(t) = 0, when A is linear but not bounded. The classical theory of differential […]
A Naive Finite Difference Approximations for Singularly Perturbed Parabolic Reaction-Diffusion Problems
A Naive Finite Difference Approximations for Singularly Perturbed Parabolic Reaction-Diffusion Problems. ABSTRACT A naive finite difference approximations for singularly perturbed parabolic reaction-diffusion problems In this thesis, we treated a Standard Finite Difference Scheme for a singularly perturbed parabolic reaction-diffusion equation. We proved that the Standard Finite Difference Scheme is not a robust technique for solving […]
