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Blow up method for studying bifurcation of solution in singular perturbation ordinary differential equation and differential algebraic equation

Author name: حوراء كريم مناهي
Supervisor name: كمال حامد ياسر الياسري
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Thi-Qar - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Dhi Qar
Key words:
  • Blow up Method
  • Bifurcation Theory
  • Singular perturbation system Di erential - Algebraic Equations
First pages:
Abstract: This thesis deals with studying a new subject of a singularity perturbed ordinary di erential equations system. It is considered the foundation base to get a di erential algebraic equations, where the concept of singularity perturbed ODEs is explained. Thenit studies the ways to deal with the perturbation parameter ϵ through two case studies : The rst case : Is the study of behavior of solution for singularity perturbed ODEs when perturbation parameter 0

الحلول العددية للمعادلات التفاضلية باستخدام طريقة التفاضلات التربيعية المعتمدة على دوال السبلاي G == Numerical Solutions of Differential Equations Via G - Spline Based Differential Quadrature Method

Author name: مصطفى اكرم سعيد
Supervisor name: اسامة حميد محمد | فاضل صبحي فاضل
General topic: Mathematics
Specific topic: Numerical Analysis
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: This thesis have two main objectives, namely : 1 - The first objective is to study the mathematical background of the differential quadrature method and its application to solve boundary value problems of the fourth order ordinary differential equations.2 - The second objective is first about function approximation by G - spline interpolation method. Secondly the numerical solution of two applications relating the vibration of a uniform beam problem which are represented by a boundary value problem of the fourth order ordinary differential equation and the vibration of a square thin plate given by a boundary value problem of the forth order partial differential equation, by using G - spline based differential quadrature method have been obtained

حول الحلول العددية لبعض المعادلات التفاضلية الاعتيادية الصدفية == On Numerical Solutions of Some Stochastic Ordinary Differential Equations

Author name: عادل سفيان حسين
Supervisor name: راضي علي زبون الساعدي
General topic: Mathematics
Specific topic: Numerical Analysis
Degree: Master
University: Al-Nahrain University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
First pages:
Abstract: الهدف الرئيس لهذه الرسالة هو دراسة بعض الطرق العددية لحل المعادلات التفاضلية الصدفية (Stochastic Differential Equations) حلا عدديا. لقد تم عرض المفاهيم الاساسية لفهم ودراسة الطرق العددية المقترحة.بسبب صعوبة ايجاد الحلول التحليلية لكثير من المعادلات التفاضلية الصدفية، تم استخدام طريقتي اويلر ميرما وميلستين العدديتين. ولقد تم تنفيذ بعض المحاكات العددية لعدد من الامثلة الاختيارية. وقدمت الملاحظات الاستنتاجية الضرورية لذلك.لقد تم كذلك دراسة وتقديم الخطا المطلق، خطا التقارب القوي، خطا التقارب الضعيف بالاضافة الى الاستقرارية الخطية لطريقتي اويلر ميرما وميلستين مدعمة باختبارات عددية.عرضت مع المناقشة المقارنة لانواع مختلفة من التقاربات والخطا العددية للطريقتين (اويلر - ميرما وميلستين) ولبعض الامثلة الاختيارية واخيرا لقد قدمت ونوقشت بعض الاستنتاجات والمقارنات لانواع معينة من الدراسة. مع عرض البرامج الحاسوبية مبرمجة ضمن لغة Matlab Software مع الشروحات الكافية لفهما. | The aim of this thesis is studying some numerical methods for solving Stochastic Differential Equation. The mathematical preliminary required to understand these numerical methods is proposed. Since many stochastic differential equations do not have explicit solution, Euler - Maruyama and Milstein numerical methods are used. The numerical simulation for different selected examples are implemented. The necessary concluding remarks are provided. The absolute error, the strong convergence error, the weak convergence error and the linear stability for Euler - Maruyama and Milstein's schemes are discussed and supported by numerical test problems. The comparison different type of convergence and error between Euler - Maruyama and Milstein's for some test problems are presented. Some conclusions and comparison in some sense have been presented with discussions. The programs coded in Matlab software are also given with useful discussion

توليد المتغيرات العشوائية لتخمين معلات توزيع لوجستك باستخدام محاكاة منت كارلو == Generating Random Variates for Estimating the Parameters of Logistic Distribution by Monte Carlo Simulation

Author name: زهراء امروي علي حيدر الحجار
Supervisor name: اكرم محمد العبود
General topic: Mathematics
Specific topic: Statistics
Degree: Master
University: Al-Nahrain University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
First pages:
Abstract: In this work, we consider the Logistic distribution of two parameters for its importance in statistics. Mathematical and statistical properties of Logistic distribution are considered, moments and higher moments are illustrated to the distribution parameters, namely, moments methods, maximum likelihood method, modified moments method, least squares method are discussed theoretically and assessed practically by utilizing two procedures of Monte Carlo simulation for generating random variates from the Logistic distribution. Properties of the estimators, such as Bias, variance, skewness, kurtosis and mean square error measurement are tabulated.

طريقة التربيعات الصغرى لايجاد المساحات الماصة لدوال المستوي التربيعية == Least Square Method for Finding Absorbing Areas of Planar Quadratic Maps

Author name: مهند نافع جعفر
Supervisor name: زينب عبد النبي سلمان
General topic: Mathematics
Specific topic: Dynamic Systems
Degree: Master
University: Al-Nahrain University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
Key words:
  • المساحات الماصة
  • منحنيات الحرجة
  • معادلات التربيعية.
First pages:
Abstract: First objective : introduce the mathematical background of the main notions and proposition on the theory of the dynamical system. Specifically we shall foucus our study on planar nonivertiable continuously differentiable maps T : 22. Definitionof critical curves and some different types of noninvertible maps related to their critical curves and some properties of critical curves are presented.Second objective : we have studied some properties of such kind of maps in particular absorbing areas, invariant areas of such maps. Also, we give proposed algorithm to approximate the equations of the critical curves LCi which cause find an approximated absorbing and invariant areas such as least square method. Third objective : give some illustrative examples that use the proposed algorithm to find an approximated absorbing.

مسالة تصميم نظام سيطرة دينامي غير خطي وتطبيقات للمسائل الفوضـــوية == NONLINEAR DYNAMIC CONTROL SYSTEMS DESIGN PROBLEM AND APPLICATIONS TO CHAOS

Author name: زينب رياض شاكر عبد العظيم الياسري
Supervisor name: راضي علي زبون الساعدي
General topic: Mathematics
Specific topic: Applied Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
Key words:
  • Non - linear control system
  • Chaotic dynamic system
  • Numerical solution of dynamic system
First pages:
Abstract: لقد برزت المعادلات التفاضلية غير الخطية في دراسة انظمة السيطرة غير الخطية وانظمة الفوضى الديناميه وغيرها بشكل فعال ومهم.تعتبر دراسة السلوك الفوضوي من المواضيع المهمة والاساسية في نظرية الانظمة الديناميه وتصميمها. لقد تم في هذه الرسالة تطوير وعرض مشروع عمل جديد لبعض انظمة السيطرة غير الخطية وتصميمها, مستندين على قاعده رياضيه مدعومة بالبراهين الضرورية اللازمة ومرفق معها الخوارزميات العددية الضرورية.لقد تم كذلك عرض بامانه قدر الاستطاعة بعض الاستنتاجات والملاحظات المهمه والضرورية.وكذلك تم عرض بعض التطبيقات المهمه والمرتبطة بالسلوك الفوضوي لبعض الانظمة غير الخطية مثل نظام لورنز Lorenz system) ( غير الخطي الفوضوي , نظام جويس) Chua's system (غير الخطي الفوضوي ودراستهما ومحاولة السيطرة على سلوكهما من خلال تصميم مسيطر خطي او غير خطي ومحاولة عرض نتائج المحاكات العددية المعتمدة على الخوارزميات المسنده على القاعدة الرياضية وعرضها بشكل جداول ومخططات ورسوم. | Non - linear differential equations appear prominently in the study of dynamical control systems, chaotic dynamical systems etc. Chaotic behavior study is very important in the nonlinear dynamical system theory and design.In this thesis, a new scheme and procedure for nonlinear dynamical control system design are proposed and developed. The proposed scheme is based on some suggested theorems. The proofs of the presented Theorems as well as their computational algorithm have been developed and presented. The concluding and necessary remarks have also been discussed. Some real life applications of chaotic dynamic system like nonlinear chaotic Lorenz system and nonlinear chaotic Chua's system have been considered and their non - linear controller have also been designed and developed to overcome the problem of undesirable chaos in these systems.The numerical solutions of chaotic Lorenz and Chua’s system before and after controlling their behaviors are simulated and shown in graphs and tables

القيود الصريحة للمتراجحات التكاملية التفاضلية اللاخطية == Integro - Differential Inequalities

Author name: اسماء خلدون عبد اللطيف
Supervisor name: احلام جميل خليل
General topic: Mathematics
Specific topic: Integral Equations
Degree: Master
University: Al-Nahrain University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
Key words:
  • المتراجحات التكاملية
  • المتراجحات التفاضلية
  • الماراجحات التكاملية التفاضلية
First pages:
Abstract: The main purpose of this work can be classified into four objectives. These are summarized as follows : The first objective, is to classify the one - dimensional integral inequalities.The second objective, is to find explicit bounds for the unknown function that appeared in special types of the one - dimensional Volterra linear and non - linear integral inequalities.The third objective, is to classify the ordinary integro - differential inequalities.The fourth objective, is to give explicit bounds for the unknown function that appeared in special types of the ordinary Volterra first order and second order linear and non - linear integro - differential inequalities.

حول قابلية السيطرة الاحتمالية لانظمة سيطرة غير خطية ماغيرة العشوائية == On Controllability Probabilities of Stochastic non - linear Control Systems

Author name: محمد عاشور شنيور داود
Supervisor name: راضي علي زبون الساعدي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
First pages:
Abstract: The main aim of this thesis is focused on studying some non - linear uncertain stochastic dynamical system.The necessary background for stochastic process, stochastic integral for Brownian motion and fractional Brownian motion, stochastic dynamical system driven by Brownian motion and fractional Brownian motion are studied and discussed supported by useful comments and examples.Some class of non - linear stochastic ordinary control system driven by Brownian motion as well as fractional Brownian motion have been considered and discussed. ItoˆA necessary theorem of solvability and controllability of some class of non - linear dynamical control system driven by Brownian motion are discussed and proved using Banach fixed point theorem and supported by useful concluding remark and illustration.ItoˆA theorem of solvability and controllability of some class of non - linear dynamical system driven by fractional Brownian motion are also stated and proved supported by illustration.

حلول المعادلات التفاضلية متغيرة العشوائية الخطية التباطؤية الاعتيادية == Solution of Stochastic Linear Ordinary Delay Differential Equations

Author name: حسنى احمد جاسم
Supervisor name: فاضل صبحي فاضل
General topic: Mathematics
Specific topic: Differential Equations
Degree: Master
University: Al-Nahrain University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
Key words:
  • معادلات تفاضلية متغيرة العشوائية
  • السيرورة العشوائية
  • معادلات تفاضلية تباطؤية
  • طريقة اويلر
First pages:
Abstract: لهذه الاطروحة ثلاثة اهداف رئيسية. الهدف الاول هو اعطاء دراسة شاملة لموضوع التفاضل والتكامل متغير العشوائية، حيث تتضمن الدراسة التعاريف الاساسية والمفاهيم الاساسية المتعلقة بهذا الموضوع متضمنة برهان بعض النتائج، ومن بين هذه النتائج برهان متباينة هولدر للتوقع، نظرية ومبرهنة وجود ووحدانية حلول المعدلات التفاضلية متغيرة العشوائية وطريقة اويلر العددية لحل المعادلات التفاضلية متغيرة العشوائية. الهدف الثاني هو لدراسة الطرق التحليلية والعددية لحل المعادلات التفاضلية متغيرة العشوائية. بينما كان الهدف الثالث هو تطوير طرق الحل المتبعة للمعادلات التفاضلية متغيرة العشوائية وذلك لحل المعادلات التفاضلية متغيرة العشوائية التباطؤية. | This thesis have three main objectives. The first objective is to give a study of stochastic calculus, including the basic definitions and fundamental concepts related to this topic including the proof of some results, and among such results is the proof of Hölder's inequality of expectation, the existence and uniqueness theorem of stochastic differential equations and the Euler's method for solving stochastic differential equations. The second objective is to study the analytical and numerical methods for solving stochastic differential equations. The third objective is to modify the methods of solution to solve delay stochastic differential equations

الصياغة التغايرية لبعض الانظمة التفاضلية ذات التباطؤ المتغير == Variational Formulations of Some Variable Delay Differential Systems

Author name: سارة علاء الدين عبد القادر
Supervisor name: فاضل صبحي فاضل
General topic: Mathematics
Specific topic: Applied Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
Key words:
  • الصياغة التغايرية
  • المعادلات التفاضلية التباطؤية الاعتيادية
  • المعادلات التفاضلية التباطؤية الجزئية
  • طريقة رتز المباشرة
First pages:
Abstract: The main theme of this work is to introduce the general form and fundamental concepts in ordinary and partial delay - differential equations with variable delays and then to find the variational formulation of delay - differential equations with variable delays in both cases, ordinary and partial and to provide the rules of minimizing the obtained functional in the subject of calculus of variation. Finally, to minimize the variational formulation using the direct - Ritz method and finding the approximate solution of delay - differential quations with variable delays.

قابلية الاستقرارية لنظام سيطرة غير خطي متغير العشوائية مع الزمن بوساطة مسيطر استرجاعي لمخرجات النظام == Stabilization of Nonlinear Stochastic Control System via Output - Feedback Control

Author name: ايناس عاجل جاسم محمد الركابي
Supervisor name: راضي علي زبون الساعدي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: Stochastic differential equations are one of the most useful areas of the theory of stochastic processes and its applications in mathematics.Some nonlinear (Itô) 1 dynamic stochastic control system driven by Brownian motion 2 based on dynamic observer have been considered.Output feedback (observer - based) robust and optimal control law which guarantees global (local) asymptotic stable in probability for the nonlinear stochastic dynamic system are discuss and developed. The necessary theorems regarding the globalty asymptotic stable in the probability of the equilibrium point at the origin of the closed loop stochastic system have been developed and proved. The Lyapunov function approach of stochastic dynamic system has been adapted to justify our proofs.The inverse optimal stabilization in probability with suitable performance index has also discussed and developed. The necessary mathematical requirements have also been provided. Concluding remarks, future work, computational algorithm based on the theoretical results and illustrations have been presented.

طرق متسلسلة تشيبتشيف لحل بعض المسائل الخطية == Chebyshev Series Methods for Solving Some Linear Problems

Author name: نور نبيل محمود القيسي
Supervisor name: احلام جميل خليل
General topic: Mathematics
Specific topic: Applied Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: The main purpose of this work may be divided into the following aspects : 1.Study the Chebyshev polynomials of the first and second kinds defined on the intervals [0,1] and [ - 1,1] and modify some of their properties.2.Use two methods to solve the linear ordinary differential equations with nonconstant coefficients, namely, Chebyshev - matrix method and Chebyshev series method.3.Devote Chebyshev series method to solve system of linear Fredholm integral equations and integro - differential equations

قابلية الاستقرارية في نظام سيطرة غير خطي متغير العشوائية باستعمال الامثلية المعكوسة == Stochastic Nonlinear Control Stablizability Based on Invers Optimality

Author name: نورا علي عزيز
Supervisor name: راضي علي زبون الساعدي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: The main aim of this work is focused on studying the global asymptotic stability in the probability for some class of closed - loop control system of Itotype in the presence of system uncertainty.Some nonlinear continuous - time Ito - dynamic stochastic system deriven by unbounded stochastic noise input have been considered, where the equilibrium point of the stochastic system is preserved even in the presence of noise .The global asymptotic stability in probability has been developed by using stabilization controller and Lyapunov stochastic approach.The stochastic Lyapunov function is computed to guarantee the global asymptotic stability in probability. Some resulte of estimation of exponential stability is also discussed.The necessary theorem for finding the controller design and stability Lyapunov stochastic function have been stated and proved which are supported by some concluding remarks and illustrations.

حول امثلية انظمة السيطرة المتابعة التصادفية اللاخطية == On Optimality of Stochastic Non - Linear Tracking Control System

Author name: مریم یاقو یوسف رمو
Supervisor name: راضي علي زبون الساعدي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: The tracking problem for differential stochastic equations in the presentof stochastic uncertainty of white noise, and control input have beenconsidered.In this work, our consideration have been focused on the case whereboth original dynamic state stochastic system and the desired stochasticdynamic system, are driven by white noise stochastic process.The main aim of this work is to make the behavior of the originaldynamic system following the behavior of the desired one for arbitrarycontroller, using tracking control system approach.The tracking and stabilizing controller that guarantee the optimumtracking error system between the original system and the desired one havebeen derived and developed.The necessary theorems for optimum tracking have been stated andproved supported with some concluding remarks. The controller can also beendivided into robust one and optimal one.The optimum controller can be obtained as a solution of some lineardeterministic differential Riccati equation, while the robust one can be obtained so that some controllability properties are ensured.The Riccati equation associated with linear stochastic optimal controller and tracking one, have also been desired and discussed.Finally some illustration ranking for time varying system and for law order differential system to larger one, have been illustrated, with details and corresponding Riccati equation for justification of the present work.

دوال السبلاين G - لتقريب حلول المعادلات التفاضلية الاعتيادية باستخدام طرائق متعددة الخطوات == G - Spline Interpolation for Approximating the Solution of the Ordinary Differential Equations Using Linear Multistep Methods

Author name: زهراء جواد كاظم السوداني
Supervisor name: فاضل صبحي فاضل
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: The main objectives of this thesis, is oriented toward function approximation using special type of spline functions, which is called the “G - spline “including the details of the subject.The second objective consider the 1st order ordinary differential equations of the form : . ]b,a[x),y,x(F)x(y∈=′y(a)=. 0yWhere the study concern the approximate solution of the above differential equation using linear multistep methods based on G - spline interpolation and then a generalization to this approach have been extended to solve Boundary value problems of the second order ordinary differential equations.

خوارزميات محورة لحل مسائل البرمجة الخطية

Author name: ياسمين معين محمد الاسدي
Supervisor name: علاء الدين نوري احمد
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: In this work, we studied the Path - FollowingAlgorithm, which is one of the family algorithms, calledInterior - Point Algorithms.We are discussed two modifications, the firstone concerned with the path solution, while the secondone is concerned with the feasibility solution. Thesetwo modifications are combined in a new manner, toconstruct a hybrid method. The same test problem hadbeen run for all the algorithms, as well as, number oftested problems had been implemented for comparison.From this comparision we have shown that ourmodifications give better results in the number of iterationsand the accuracy of the results.

نظريات وجود الحلول لمسائل القيم الحدودية للمعادلات التفاضلية الاعتيادية الدفعية == Existence Theorems of the Solutions for the Boundary Value Problems of the Impulsive Ordinary Differential Equations

Author name: نور شوقي كامل محمد
Supervisor name: احلام جميل خليل
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: 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.Second, we give the explicit forms of the solutions of the boundary value problems (periodic and nonperiodic) which consist of the first order linear ordinary differential equations with non - constant coefficients together with finite impulsive conditions and boundary condition (periodic and nonperiodic).Third, we transform the boundary value problems (periodic and nonperiodic) which consists of the first order nonlinear ordinary differential equations together with finite impulsive conditions and boundary condition (periodic and nonperiodic) into equivalent integral equations. Also the existence of the solutions for the above periodic boundary value problemsare discussed.

طريقة توسيع تيلر لحل المعادلات التكاملية والتكاملية التفاضلية اللاخطية == Taylor Expansion Method for Solving the Non - Linear Integral and Integro - Differential Equations

Author name: هدى عبـد الرزاق محمـد الجنابي
Supervisor name: احلام جميل خليل
General topic: Mathematics
Specific topic: Integral Equations
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: 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.

حول كمال الفضاءات المترية الضبابية == About the Completeness of Fuzzy Metric Spaces

Author name: اماني التفات كاظم
Supervisor name: فاضل صبحي فاضل
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: لهذه الاطروحة هدفين رئيسيين، وهما : الهدف الاول هو لدراسة المجموعات الضبابية (Fuzzy Sets) بالاضافة الى بعض الخواص الجبرية لهذه المجموعات وبعض النتائج النظرية المهمة.الهدف الثاني هو لدراسة الفضاءات المترية - D (D - Metric Spaces) والفضاءات المترية الضبابية - M (M - Fuzzy Metric Spaces) واعطاء بعضا من النتائج المهمة في هذين الفضائين. كما ويتضمن هدف الاطروحة دراسة كمال الفضاءات المترية الضبابية (Completeness of Fuzzy Metric Spaces) باستخدام الدوال المترية الضبابية - M. | 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.

حلول المعادلات التفاضلية الكسرية الحدودية == Solutions of Fractional Boundary Value Problems

Author name: سيماء عبد الستار محمد الفياض
Supervisor name: فاضل صبحي فاضل
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: في هذه الرسالة، قمنا بتقديم اسلوب مطور لحل المعادلات التفاضلية الحدودية ذات الرتب الكسرية (Fractional order boundary value problems). حيث اعتمدنا في هذا الاسلوب على تطبيق مؤثر رايسز - فيلر(Riesz - Feller operator) والحصول على الصيغة المطورة لمعادلة الفروقات المنتهية المناظرة للمعادلة التفاضلية الحدودية الكسرية.كما وان من اهداف هذا العمل هو دراسة مبرهنة وجود ووحدانية حلول المعادلات التفاضلية الحدودية الكسرية، وتقديم برهان لهتين المبرهنتين بالاعتماد على مبرهنة شاودر للنقطة الصامدة (Schauder fixed point theorem) للمؤثر التكاملي الكسري (Fractional integral operator). | 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

حول تحويلات لابلاس المتعددة الابعاد == On the Multi - Dimensional Laplace Transforms

Author name: وسن عجيل حمود
Supervisor name: احلام جميل خليل
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: الهدف من هذا العمل هو دراسة تحويلات لابلاس المتعددة الابعاد مع تطبيقاتها. هذه الدراسة شملت المحاور التالية : - 1 - تبني تحويلات لابلاس ذات البعد الواحد للدوال التي تعتمد على متغير مستقل واحد فقط مع بعض الخواص المهمة. اضافة الى ذلك بعض التطبيقات الرياضياتية لتحويلات لابلاس ذات البعد الواحد قدمت .2 - توسيع دراسة تحويلات لابلاس ذات البعد الواحد الى تحويلات لابلاس المتعددة الابعاد. اضافة الى ذلك قمنا باعطاء بعض الخواص المهمة الموسعة لتحويلات لابلاس المتعددة الابعاد.3 - استعمال تحويلات لابلاس المتعددة الابعاد لحل انواع خاصة من المعادلات التفاضلية الجزئية, المعادلات التكاملية المتعددة الابعاد والمعادلات التكاملية - التفاضلية المتعددة الابعاد. | The aim of this work is to study the multi - dimensional Laplace transforms and their applications. This study includes the following aspects : - 1 - Devote the one - dimensional Laplace transforms for functions of only one independent variable with some of their important properties. Also some mathematical applications for the one - dimensional Laplace transforms are presented.2 - Extend the study of the one - dimensional Laplace transforms to the multi - dimensional Laplace transforms. Also some generalized important properties of the multi - dimensional Laplace transforms are obtaind.3 - Use the multi - dimensional Laplace transforms to solve special types of the partial differential equations, the multi - dimensional integral equations and the multi - dimensional integro - differential equations

تكاملات مونت كارلو وتقنيات تخفيض التباين للتكاملات المتعدد الابعاد

Author name: اكرم عباس جاسم الصباغ
Supervisor name: اكرم محمد العبود
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: In this work, we consider two Monte Carlo methods for evaluating the ndimensional 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. Variance Reduction for Monte Carlo methods is discussed theoretically and explained by algorithms where four techniques are considers, namely, the Importance Sampling, the Correlated Sampling, the Partition of the region, and the Biased Estimator.The computer programs are illustrated in appendices by the run is made by using MathCAD 2001i.

تخمين معلمات توزيع ويبل مع تطبيق باستخدام محاكاة مونت كارلو == Estimation of Parameters for Weibull Distribution with Application by Using Monte Carlo Simulation

Author name: سلام عادل احمد
Supervisor name: اكرم محمد العبود
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: تطرقنا في هذه الرسالة الى توزيع ويبل ذو المعلمتين لاهميته في مجالات الاحصاء وتطبيقاته من حيث استعراض لخواص التوزيع الرياضية والاحصائية والعزوم والعزوم العليا. ثم تطرقنا الى التخمين وخواصه ومناقشة اربعة طرق لتخمين معالم التوزيع وهي : طريقة الترجيح الاعظم, طريقة العزوم, طريقة العزوم المعدلة وطريقة المربعات الصغرى. نوقشت هذه الطرق نظريا وطبقت عمليا باستخدام ستة اساليب من محاكاة مونت كارلو لتوليد المتغيرات العشوائية من توزيع ويبل. اوجدت كفاءة بعض هذه الاساليب نظريا وقورنت عمليا. تمت المقارنة بين الطرائق الاربعة التخمينية باستخدام مقياس معدل مربعات الخطا. | 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. Four methods of estimation to the distribution parameters namely (Maximum likelihood Method, Moments Method, Modified Moments Method, Least Square Method) are discussed theoretically and assessed practically by utilizing six procedures of Monte - Carlo simulation for generating random variates from the distribution. Efficiency of some procedures are found theoretically and compared practically. Comparisons are made among four methods of estimation by considering the mean square error measurement.

حلول المعادلات التفاضلية الاعتيادية المتجانسة من الرتب الكسرية ذات المعاملات المتغيرة == Solutions of Ordinary Homogenous Fractional Order Differential Equations with Variable Coefficients

Author name: ضمياء سالم
Supervisor name: علاء الدين نوري احمد
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: في هذا العمل تم دراسة حلول المعادلات التفاضلية الاعتيادية المتجانسة من الرتب الكسرية (والتي قيمها مابين الصفر والواحد) ذات المعاملات المتغيرة.لقد تم استنباط وجود هذه الحلول من خلال عرض نظرية استخدم فيها طريقة Power Series للحالات الاعتيادية(ordinary point) والمفردة(singular point) من المعادلات التفاضلية الاعتيادية من الرتب الكسرية ذات المعاملات المتغيرة وقد تم عرض مثال لكل نوع | 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

اساليب النمذجة الخطية في ادارة شبكة المشاريع == Linear Programming Techniques for Network Project Management

Author name: ايلاف محمد عبد
Supervisor name: علاء الدين نوري احمد
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Al-Nahrain University - College Of Science
Language: English
University location: Baghdad
First pages:
Abstract: 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. Then we are verified the results obtained by implementing " Project 2000 " software to construct the project network and obtain the same critical path.Finally, the Programming Evaluation Review Technique (PERT) has been used, to find the probabilities of completing the project.
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