Thesis | Page 57 | جامعة النهرين

On Optimality of Stochastic Non-Linear Tracking Control Systems

The tracking problem for differential stochastic equations in the present of stochastic uncertainty of white noise, and control input have been considered. In this work, our consideration have been focused on the case where both original dynamic state stochastic system and the desired stochastic dynamic system, are driven by white noise stochastic process. The main aim of this work is to make the behavior of the original dynamic system following the behavior of the desired one for arbitrary controller, using tracking control system approach.

اللغة إنجليزية

Existence Theorems of the Solutions for the Boundary Value Problems of the Impulsive Ordinary Differential Equations

The main theme of this work can be divided into three categories, which can be summarized as follows:
First, we give some definitions of impulsive differential equations with or without delays with some illustrative examples and some real life applications.

اللغة إنجليزية

Taylor Expansion Method for Solving the Non-Linear Integral and Integro-Differential Equations

The main purpose of this work is to study Volterra-Fredholm integral and integro-differential equations. This study include the classification of Volterra-Fredholm integral and integro-differential equations.Also, some theorems for the existence and uniqueness of the solution for linear Volterra-Freadholm integral and integro-differential equations are presented. Moreover, Taylor expansion method for solving special types of nonlinear Volterra-Freadholm integral and integro-differential equations with some illustrate examples are discussed.

اللغة إنجليزية

Estimation of Reliability Function for Inverse Gaussian Distribution Model with Application by Using Monte Carlo Simulation

In this work we consider the Inverse Gaussian distribution model of two parameters, because it have many applications in the fields of statistics and reliability. Mathematical and statistical properties of the distribution are given together with illustration. Moments and higher moments of the distribution properties and of the reliability and hazard functions are discussed theoretically. Two methods of estimation namely moments method and maximum likelihood method are used to estimate the distribution parameters.

اللغة إنجليزية

About the Completeness of Fuzzy Metric Spaces

The objective of this work may be oriented toward two objectives.The first objective is to study fuzzy set theory, as well as some of its basic algebraic properties and theoretical results.The second objective is to study D-metric spaces and M-fuzzy metric spaces, and some of their properties. Also, this objective includes the study of complete fuzzy metric spaces using M-fuzzy distance function. In addition, some additional results are presented and proved in this work.

اللغة إنجليزية

Solutions of Fractional Boundary Value Problems

In this thesis, we introduce a modified approach for solving fractional order boundary value problems. This approach is given by applying the Riesz-Feller operator to obtain a modified finite difference equation, which is symmetric to the equation of fractional boundary value problems. Also, the main objective of this work is to study the existence and uniqueness theorem of solutions of the fractional boundary value problems, and to present their proof depending on Schauder fixed point theorem for fractional order integral operator.

اللغة إنجليزية

Monte carlo integrations and variance reduction techniques for N-Dimensional Integrals

In this work, we consider two Monte Carlo methods for evaluating the n-dimensional integrals for bounded integrand. Statistical properties of these methods are illustrated and unified. The supported number of trials to estimate the integrals, confidence interval and the efficiency for each method were derived theoretically and assessed practically.

اللغة إنجليزية

Estimation of Parameters for Weibull Distribution with Application by Using Monte Carlo Simulation

In this work, we consider the Weibull distribution of two parameters for its importance in statistics and its applications. Mathematical and statistical properties of Weibull distribution are considered, moments and higher moments are illustrated and unified.

اللغة إنجليزية

Solutions of Ordinary Homogenous Fractional Order Differential Equations with Variable Coefficients

In this work the solutions of ordinary homogenous fractional order (with values between zero and one) differential equations with variable coefficients are investigated. Also the existence of the solution is by presenting theorems, using the method of Power Series for ordinary and singular type of fractional order differential equations with variable coefficients. Example has been presented for each case.

اللغة إنجليزية

Linear Programming Techniques for Network Project Management

In this work, Linear Programming Problems have been implemented to build four linear models for projects management. An Interior – Point Method has been implemented to solve such linear models, instead of using the usual techniques "Simplex Method", by implementing the "what's Best 9.0 " software, and obtaining the critical path in minimum completion time, minimum crashing cost and optimal total ( direct & indirect ) costs for a simple real project.

اللغة إنجليزية