PURE AND APPLIED MATHEMATICS PROJECT TOPICS Archives - Current School News : Current School News

PURE AND APPLIED MATHEMATICS PROJECT TOPICS

LaSalle Invariance Principle for Ordinary Differential Equations and Applications

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 […]

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A Modified Subgradient Extragradeint Method for Variational Inequality Problems and Fixed Point Problems in Real Banach Spaces

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 […]

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Foundation of Stochastic Modeling and Applications

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 […]

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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 […]

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Integration in Lattice Spaces

Integration in Lattice Spaces. 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 is first summarizing the notion of integration with respect to a measure on R. Then, a construction of an integral on Banach spaces called the […]

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Monotone Operators and Applications

Monotone Operators and Applications. 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 Mathematics such as Convex Analysis, Optimization Theory, Evolution Equations Theory, Variational Methods and Variational Inequalities. Basic examples of monotone operators are positive semi-definite matrices A […]

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Variational Inequality in Hilbert Spaces and their Applications

Variational Inequality in Hilbert Spaces and their Applications. ABSTRACT The study of variational inequalities frequently deals with a mapping F from a vector space  X  or  a  convex  subset  of  X  into  its  dual  Xj . Let  H  be  a  real  Hilbert  space and  a(u, v)  be  a  real  bilinear  form  on  H.   Assume  that  the […]

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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 […]

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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 […]

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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 […]

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