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دراسة بعض الاصناف الجزئية في نظرية الدوال الاحادية والمتعددة التكافؤ للمتغير العقدي == A Study of Some Subclasses in Univalent and Multivalent Function Theory of a Complex Variable

Author name: اسراء عباس عبد السادة
Supervisor name: وقاص غالب عطشان
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:

الخواص الفوضوية لدالة كابلان يورك == chaotic properties of Kaplan York map and modified Kaplan York map

Author name: سعاد محمد حسن الصافي
Supervisor name: افتخار مضر طالب الشرع
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:

قابلية الحل في الفضاءات التوبولوجية الامنة == Resolvability In Soft Topological Spaces

Author name: ذو الفقار فاخر نصيف العامري
Supervisor name: لؤي عبد الهاني السويدي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:

بعض التوزيعات الموزونة المضاعفة وتوزيع موزون مضاعف معمم بمتغيرين == Some Double Weighted Distributions and Bivariate Generalized Double Weighted Distribution

Author name: مهند محمد فاضل
Supervisor name: كريمة عبد الكاظم الخفاجي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:

انظمة - S القابلة للانضغاط == s Compressible S - System

Author name: امنة صلاح حسن
Supervisor name: اسعد محمد علي الحسيني
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:

التقريب باستخدام الشبكات العصبية شبه اسيه == Nearly Exponential Approximation For

Author name: زهراء محمود فاضل
Supervisor name: ايمان سمير بهية
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:

دراسة خصائص بعض التوزيعات متعددة المتغيرات

Author name: افراح ساهم سالم
Supervisor name: كريمة عبد الكاظم مخرب
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:

بعض النتائج حول التوزيعات المحولة == Some Results on Transmuted Distributions

Author name: ميساء حميد محمد الدهيمي
Supervisor name: كريمه عبد الكاظم مخرب
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:

التقريب للشبكات العصبية الامامية == APPROXIMATION FOR FEED FORWARD NEURAL NETWORK

Author name: سارة عبد الرضا رحمن
Supervisor name: ايمان سمير بهيه
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:

تقريب الدوال المعرفة على كرات الوحدة بدلالة الدالي - K

Author name: هند اياد شاكر
Supervisor name: ايمان سمير بهية
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:

تفرع الحل في المعادلة التفاضلية الاعتيادية ذات الاضطراب المنفرد والمعادلة التفاضلية الجبرية باستخدام طريقة ليابانوف شمدت - للاختزال == Bifurcation of Solution in Singularly Perturbed Ordinary Differential Equation and Differential - Algebraic Equation by Liapunov Schmidt Reduction.

Author name: احمد حميد كامل الكناني
Supervisor name: كمال حامد ياسر الموسوي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Thi-Qar - College Of Science
Language: English
University location: Dhi Qar
First pages:

حول الحلقة HX الواهنة الضبابية والحلقة HX الواهنة الحدسية الضبابية == On Fuzzy Soft HX Ring and Intuitionistic Fuzzy Soft HX Ring

Author name: ولاء حسن عاشور
Supervisor name: محمد جاسم محمد ال مسافر | ربيع هادي جاري
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Thi-Qar - College Of Science
Language: English
University location: Dhi Qar
First pages:

حول نظرية النقطة الصامدة في الفضاء المتري الواهن والفضاء المتري الضبابي الواهن == On Fixed Point Theory in Soft Metric Space and Fuzzy soft Metric Space

Author name: دعاء ارحيم جلاب
Supervisor name: محمد جاسم محمد
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Thi-Qar - College Of Science
Language: English
University location: Dhi Qar
First pages:

ترتيب النتاجات لتصغير مسالة جدولة الماكنة

Author name: سارة كامل حنون
Supervisor name: محمد كاظم زغير
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Thi-Qar - College Of Computer Science And Mathematics
Language: English
University location: Dhi Qar
First pages:

مقاييس النعومة وتقريب الدوال في الفضاءات L - p المعرفة على كرة الوحدة == Moduli of Smoothness and Approximation of Functions in L_pSpaces Defined on Unit Sphere

Author name: اخلاص عنون موسى
Supervisor name: ايمان سمير عبد علي بهية
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:
Abstract: هذه الرسالة هي دراسة لافضل تقريب للدوال في الفضاءات L_p والمعرفة على كرة الوحدة .ان مشكلتنا الاساسية هنا هي وصف عملية التقريب للدوال في الفضاءات L_p عندما 0<p<1 باستخدام متعددات الحدود بدلالة مقياس النعومة للدالة .سنحدد في عملنا الاداة الصحيحة لوصف او دراسة معامل النعومة للدالة في الفضاءات L_p من ناحية معامل النعومة للدالة او الدالي K . سنبرهن فيما بعد ان الاداتين متكافئتين ركزنا في نتائجنا الاساسية على وصف افضل تقريب من خلال المبرهنات المباشرة واخرى معكوسة لها بدلالة ثلاث انواع مختلفة من مقاييسالنعومة وثلاث انواع من الدالي K . | This thesis is a study on best polynomial L_P , approximation on unit sphere . Our central problem is to describe the approximation behavior of functions in L_P - spaces for 0<p<1 by polynomials via higher order modulus of smoothness of function. In this work we identity the correct gadget to characterize smoothness of functions in L_P - spaces in terms of, either modulus of smoothness or K - functional, that are then we prove they are equivalent.In our main results we concentrate on characterization of best approximation , given in terms of direct and inverse theorem in terms of three types of moduli of smoothness and K - functional

استخدام النموذج الرياضي والشبكات العـصبية لتحديد نسبة تلوث البيئة == Employ Mathematical Model and Neural Networks for Determining Rate of the Environmental Contamination

Author name: فرح فيصل غازي
Supervisor name: لمى ناجي محمد توفيق
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Baghdad
Language: English
University location: Baghdad
First pages:
Abstract: هناك العديد من الاهداف في هذه الرسالة : الهدف الاول هو تطوير نموذج المعادلة التي تصف انتشار التلوث خلال التربة والتي يمكن استخدامها لتحديد نسبة التلوث البيئي وذلك بتقدير تركيز المعادن الثقيلة في التربة. نموذج المعادلة التي تم تطويرها يمكن اعتبارها تمثيل جيد لمشكلة التلوث البيئي.الهدف الثاني في هذه الرسالة هو تصميم شبكتين عصبيتين ذات تغذية تقدمية باعتبارها تقنية دقيقة بديلة لتحديد نسبة التلوث البيئي والتي يمكن استخدامها في حل معادلة النموذج. الشبكة الاولى تحاكي معلمات التربة التي يمكن استخدامها في ادخال البيانات في الشبكة الثانية المقترحة، في حين تحاكي الشبكة الثانية لتقدير تركيز المعادن الثقيلة.الهدف الثالث هو تطوير المفهوم النظري لمرحلة تدريب الشبكات العصبية من وجهة نظر التحليل الدالي والطرق الامثلية. ضمن هذه الصيغة، التعلم يعني حل مشكلة متغايرة بواسطة تصغير دالة الاداء المتعلقة بالشبكة العصبية. ان اختيار دالة الهدف يعتمد على تطبيق معين. من جهة اخرى، فاننا نقترح تعديل على دالة الاداء لتحسين تعميم الشبكات المقترحة وعلى الجانب الاخر، لعلاج التوقف المبكر ومشاكل النهاية الصغرى المحلية.الهدف الرابع هو مقارنة اداء الخوارزميات المذكورة اعلاه فيما يتعلق بقدرة التنبؤ. ثم تطبيق التقنية المقترحة لتقدير تركيز المعادن الثقيلة مثل : النحاس والرصاص والكادميوم والكوبالت والزنك والنيكل في تربة بغداد. اولا، تم اختيار اربعة وستين عينة من التربة من المواقع الملوثة تقع في بعض المناطق في مدينة بغداد (السكنية والصناعية والتجارية والزراعية والطرق الرئيسية). ثانيا، تم اجراء سلسلة من القياسات على عينات التربة وتحليلها لقياس تراكيز المعادن الثقيلة بواسطة اجهزة الامتصاص الطيف الذري (AAS)، فلورية الاشعة السينية (XRF) المطياف الكتلي البلازمي بالتقارون الحثي (ICP - MS) ومن خلالها نحصل على تراكيز اولية لهذه المعادن الثقيلة. ثالثا، محاكاة وتدريب الشبكات المقترحة للحصول على تركيز المعادن الثقيلة بالطريقة المقترحة ومن ثم مقارنة اداء الشبكات المقترحة مع فحص المختبر التقليدي باستخدام مجموعة بيانات التدريب والاختبار. نتائج هذا العمل تبين ان الشبكات المقترحة والمتدربة على القياسات التجريبية يمكن تطبيقها بنجاح لتقدير تركيز المعادن الثقيلة بسرعة ودقة.اخيرا، نقترح بعض الطرق لمعالجة التربة الملوثة باستخدام بعض النباتات العشبية. | There are many aims of this thesis : The first aim is to develop a model equation that describes the spread of contamination through soils which can be used to determine the rate of environmental contamination by estimate the concentration of heavy metals (HMs) in soil. The developed model equation can be considered as a good representation for a problem of environmental contamination. The second aim of this thesis is to design two feed forward neural networks (FFNN) as an alternative accurate technique to determine the rate of environmental contamination which can be used to solve the model equation. The first network is to simulate the soil parameters which can be used as input data in the second suggested network, while the second network simulates to estimate the concentration of heavy metals. The third aim is to develop a conceptual theory of training stage of neural networks from the perspective of functional analysis and optimization methods. Within this formulation, learning means to solve a variational problem by minimizing a performance function associated to the neural network. The choice of the objective functional depends on the particular application. On the other side, we suggest modification of the performance function to improve the generalization of the suggested networks and to treat the early stopping and local minima problems. The fourth aim is to compare the performance of aforementioned algorithms with regard to predicting ability. Then applied the suggested technique to estimate the concentration of heavy metals such as : Copper(Cu), Lead(Pb), Cadmium(Cd), Cobalt(Co), Zinc(Zn) and Nickel(Ni) in Baghdad soils. First, sixty four soil samples were selected from a phytoremediated contaminated site located in some zones in Baghdad city (residential, industrial, commercial, agricultural and main roads). Second, a series of measurements were performed on the soil samples and analyzed measuring of concentrations for heavy metals using devices such as : Atomic Absorption Spectrophotometer (AAS), X - Ray Fluorescence (XRF) and Inductively Coupled Plasma - Mass Spectrometry (ICP - MS) to get initial concentrations for those heavy metals. Third, simulate and train the suggested networks to get the concentration of heavy metals. The performance of the suggested networks was compared with the traditional laboratory inspecting using the training and test data sets. The results of this work show that the suggested networks trained on experimental measurements can be successfully applied to the rapid and accuracy estimation of concentration of heavy metals. Finally, we suggest some methods contaminated soil by using some herbal plants.

مسالة السيطرة الامثلية التقليدية المستمرة لمعادلات تفاضلية جزئية == The Continuous Classical Optimal Control Problem of Partial Differential Equations

Author name: غفران مناتي كاظم
Supervisor name: جميل اميرعلي الهواسي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Mustansiriyah University - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Baghdad
First pages:
Abstract: الهدف الرئيسي لهذه الرسالة هو دراسة مسالة السيطرة الامثلية التقليدية المستمرة لزوج من المعادلات التفاضلية الجزئية الخطية واللاخطية من النوع المكافئ )stateفي برهان مبرهنة وجود ووحدانية الحل للحالة ( Galerkin حيث استخدمنا طريقة لزوج من المعادلات المذكورة اعلاه ولكن من النوع اللا خطي عندما يكون متجه السيطرة التقليدية المستمرة ثابت . قمنا ايضا ببرهان مبرهنات خاصة بوجود سيطرة (متجه السيطرة) التقليدية المستمرة لزوج من المعادلات التفاضلية الجزئية الخطية واللاخطية من النوع المكافئ. برهنا ايضا مبرهنة وجود ووحدانية الحل لزوج المعادلات التفاضلية الجزئية الخطية واللاخطية للحالة. طورت بشكل يتناسب مع المسالة Kuhn - Tucker - Lagrange’s Multipliers مبرهنات السيطرة التقليدية المستمرة المقترحة في هذه الرسالة وصيغت وبرهنت مبرهنتا الشرط الضروري لوجود السيطرة الامثلية | The main aim of this thesis is to study the continuous classical optimal control problem of a couple of linear and nonlinear parabolic partial differential equations. With a suitable assumptions, the existence and the uniqueness of solution of the state vector of couple of linear parabolic PDEs for a given continuous classical control vector are proved by using Galerkin method. The existence theorems of a continuous classical optimal control vector associated with a couple of nonlinear parabolic equations are developed and proved. The existence and the uniqueness theorem of a solution of the couple of adjoint equations associated with the considered state equations of nonlinear parabolic equations with equality and inequality constraints is also proved once again. The Kuhn - Tucker - Lagrange multipliers theorems are developed and used to prove the necessary conditions theorem and the sufficient conditions theorem of optimality of a couple of nonlinear parabolic equations with equality and inequality constraints

طرق تكرارية موثوقة لحساب تراكيز ثنائي اوكسيد الكاربون الممتص بواسطة فينيل غلايسيدل الايثر == Reliable Iterative Methods for Calculating the Concentrations of Carbon Dioxide Absorbed into Phenyl Glycidyl Ether

Author name: غسان حسن محمود راضي
Supervisor name: مجيد احمد ولي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Baghdad
Language: English
University location: Baghdad
First pages:
Abstract: In this thesis, two reliable iterative methods are used to calculate the concentrations of carbon dioxide CO2 and phenyl glycidyl ether PGE. The first one is the variational iteration method. It is used to get an approximate solution for a system of two coupled nonlinear ordinary differential equations which represent the concentrations of CO2 and PGE. The other method is the standard homotopy analysis method which is implemented on this system. Formerly, this system has been solved by the Adomiandecomposition method. In solving this system by Adomian’s method, the nonlinearity needs calculating the Adomian’s polynomials. On the other hand, the two methods do not require any assumptions like the calculating of the Adomian’s polynomials. In this system there are boundary conditions of Dirichlet type and the other is a mix of Neumann and Dirichlet type. Our calculations are evidenced by tables and figures for the analysis of the maximal error remainder values. The variational iteration method givesapproximate solutions with fast convergence. Comparison with the results obtained by the Adomian decomposition method shows that the numerical solutions obtained by the variational iteration method converge faster than those of Adomian's method. Also, the homotopy analysis method which is implemented on this system has a very fast convergence in giving approximate solutions. Moreover, the numerical solutions resulted from the homotopy analysis method converge faster than those of Adomian's methodwhich has been implemented previously for the same problem. The numerical results also show high rates of convergence which are obtained at the increasing of the iterations. The used software of the contained calculations in our study is Mathematica 9.

New Distributions on Proposed Classes == New Distributions on Proposed Classes

Author name: Bnadheer Dhea'a Mohammad Al_sultani
Supervisor name: Kareema Abed Al - Kadim Makrib Al - Khafaji
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Babylon
First pages:
Abstract: There are many important problems where the real data does not fit any of the classical or standard probability models, and the lifetime distributions have been used to model analyses the lifetime data in many applied sciences such as medicine, engineering, finance, biostatistics , reliability and survival analyses because a statistical analysis depends heavily on the assumed probability model or distributions.The distributions, generalization distributions there were derived in this thesis that can be used in life applications. It is hoped that findings of this work will be useful for the practitioners in various fields of theoretical and applied sciences. This thesis is our contribution in this field throughout finding these distributions .Three distributions are introduced, Rayleigh - Pareto distribution, Rayleigh - Lomax distribution and Uniform - Lomax Distribution, as well as discussion of some their important properties , and estimate their parameters. These distributions depend on the original distribution, Rayleigh distribution, Pareto distribution, Lomax(Pareto II) distribution, and Uniform distribution. The idea of the subject that is companied two distributions by one of the methods that are used to generalize distribution.Therefore there is an application using certain real data set to illustrate the usefulness of the proposed distribution to real data using MATLAB (R2011b) software.In the application of Rayleigh - Pareto distribution, we used real data set ,and make a compare between Rayleigh - Pareto distribution used in thesis with others distributions. Its appear that Rayleigh - Pareto distribution is the best in comparison with other distributions.Introduction The statistical distributions used to describe and interpret the phenomena, there are continuous motivations for developing these distributions to become more flexible or more fitting for specific real data sets. Because there are many important problems where the real data does not fit any of the classical or standard probability models.&#34;The lifetime distributions have been used to model analysis the lifetime data in many applied sciences such as medicine, engineering, finance, biostatistics , reliability and survival analysis because a statistical analysis depends heavily on the assumed probability model or distributions.&#34;So the aim of the thesis is to derive some distributions, generalization of distributions ,with of their properties, and estimating the parameters. One generalized distribution F(x) was defined as follows F(x)=I_G(x) (a,b)=(∫_0^G(x)▒〖w^(a - 1) (1 - w)^(b - 1) 〗 dw)/B(a,b) , 00 ,b

بعض طرائق التقدير لمعلمة القياس لتوزيع لابلاس : دراسة مقارنة == Some Baye,s Estimators for the Scale Parameter of the Laplace Distribution / A Comparison Study

Author name: عماد فرهود محي الشريفي
Supervisor name: هدى عبد الله رشيد
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Mustansiriyah University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
First pages:
Abstract: The Laplace distribution is important to the development of mathematics ,statistics, physics, and astronomy, and usually used as its characteristics apply to a large ratio of natural, social and economic phenomenon. Hence, the importance of this thesis is to Find the best estimator for the scale parameter θ, when location parameter (a) is known and unknown through obtaining and comparing the classical estimators (Maximum Likelihood Estimator, Uniformly Minimum variance unbiased Estimator, and Minimum Mean Squared Error), as well as Bayesian estimators under different loss functions (Quadratic loss function, squared - Log error loss function, Generalized squared error loss function, Entropy loss function, Suggested loss function).In order to get a better understanding of our Bayesian analysis, we consider the non - informative prior for the scale parameter () using Jeffreys prior information, as well as informative prior density represented by Gumbel Type II Prior.All these estimators are compared empirically using Mont - Carlo simulation by employing the mean squared errors (MSE's).Also we derived the Minimax estimators of the scale parameter θ for the Laplace distribution for all loss functions referred to above and reach to the estimators under Quadratic loss function, Squared - log error loss function, special case of Suggested loss function and Entropy loss function are Minimax estimators.Among conclusions that have been reached, the Suggested loss function with Gumble prior has recorded the best performance of the used for other loss functions. On the other hand, Gumble prior under different loss functions with Gumble Type II prior is better comparing to the corresponding Jeffrey's prior (under the same loss function) for all cases.

الجدوله لمقاييس متعددة الاداء == Scheduling with Multiple Performance Measures

Author name: علي عباس نعمان المالكي
Supervisor name: طارق صالح عبد الرزاق
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Mustansiriyah University - College Of Education For Pure Sciences - Department Of Mathematics
Language: English
University location: Baghdad
First pages:
Abstract: في هذه الرسالة تصغير دالة لمعياريين او ثلاثة والحاصلة من جدولة n من الاعمال على ماكنة واحدة . تم التركيزفي هذه الدراسة والاخذ بنظر الاعتبار على حالة التاخير اللاسالب والعمل المتاخر ووقت الاتمام الكلي . ونوقشت المسائل التالية : 1 . تصغير الدالة (Tmax+Vmax) . 2 .تصغيرالدالة ذات ثلاث معايير والتي تاخذ الصيغة Lex(Tmax+Vmax ,Σ■(n@i)Ci) وLex(Σ■(n@i)Ci , Tmax+Vmax ) . . (■(n@i)Ti + ■(n@i)Vi) تصغير الدالة .3 للمسالة الاولى اقترحنا خوارزمية التفرع والتقييد لايجاد الحل الامثل كذلك برهنا بعض الحالات الخاصة التي تؤدي الى الحل الامثل .كذلك اقترحنا خوارزمية (A) المطورة من خوارزمية لولر لحل المسالة وهذا قادنا الى ملاحظة مشجعه وهي ان اغلب النتائج الحسابية تؤدي الى الحل الامثل. كما واجرينا تجارب حسابية لطريقة التفرع والتقييد على مجموعة كبيرة لمسائل اختبارية. .للمسالة الثانية والتي هي تعميم للمسالة الاولى قمنا باستخدمنا قاعدة (SPT) وكذلك الخوارزمية (A) المطورة لايجاد افضل الحلول . للمسالة الثالثة اقترحنا خوارزمية التفرع والتقييد مع قيدين سفلي وقيد علوي الذي هو اصغر ثلاث قيود تقريبيه مقترحة لايجاد الحل كذلك برهنا بعض الحالات الخاصة واستخدمنا قواعد الهيمنة مع خوارزمية التفرع والتقييد لتحسين النتائج الحسابية لهذه المسالة. | This thesis intends, to minimize a function of two and three cost criteria for scheduling n jobs on a single machine. The study focuses on the case where Tardiness, late work and total Completion times are considered. The following problems are discussed 1. Minimizing a function of two criteria (Tmax+Vmax). 2.Minimizing a function of three criteria of the forms Lex(Tmax+Vmax,Σ■(n@i=1)Ci) and Lex(Σ■(n@i=1)Ci , Tmax+Vmax ). 3. Minimizing a function of two criteria (■(n@i=1)Ti + ■(n@i=1)Vi). For the first problem 1// Tmax+Vmax , a branch and bound algorithm are proposed to find optimal solution . Also, we proved some special cases for this problem which lead to optimal solution. An improved algorithm (A) for Lawler algorithm has been constructed for solving this problem, which leads to an interesting observation that the algorithm (A) will yield optimal solutions in all instances of the test problems. Also computational experience for the (BAB) algorithm is presented. For the second problem which is a generalization of the first problem we use either the SPT rule or modified algorithm (A) to find the best solutions. For the third problem we proposed a (BAB) algorithm with two lower bounds and upper bound which is the minimum of three heuristic methods .We proved some special cases which lead to the optimal solution . We used dominance rules with BAB algorithm to enhance the computational results for this problem

طرق تكرارية كفوءة لحل مسائل القيم الحدودية ذات النقطتين == Efficient Iterative Methods for Solving Two - Point Boundary Value Problems

Author name: علي حسين عباس
Supervisor name: مجيد احمد ولي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Baghdad
Language: English
University location: Baghdad
First pages:
Abstract: قدمت في هذه الرساله ثلاثه طرق تكراريه موثوقه لحل مسائل القيم الحدوديه ذات النقطتين الخطيه وغير الخطيه. الطريقه الاولى تتناول تطبيق الاسلوب الشبه تحليلي لحل هذه المشكله. وفي هذه الطريقه تم الحصول على الحل بشكل متسلسله وبحسابات سهله. ان النتائج التي تم الحصول عليها لقيم الخطا المتبقي تبين ان هذه الطريقه فعاله جدا وموثوقهالطريقه الثانيه هي الطريقه التكراريه المطوره وتسمى DJM لحل هذه المشكله. هذه الطريقه تعطي حلا تقريبيا مع تقارب سريع. النتائج العدديه تثبت ان الطريقه المستخدمه هي طريقه موثوقه وفعاله. اما الطريقه الثالثه والاخيره تسمى طريقه متسلسله القوى لحل هذه المشكله. وهناك بعض الامثله العدديه قدمت لاثبات كفاءه هذه الطريقه وكما استخدمت بعض التطبيقات على هذه المشكله وحلها بواسطه هذه الطرق المذكوره. ان البرنامج المستخدم لايجاد هذه النتائج العدديه هو الماثيماتيك | In this thesis, three reliable iterative methods have been introduced to solve linear and nonlinear two - point boundary value problems (TPBVPs). The first method deals with the implementation of the semi - analytic method namely (TAM) to solve two - point boundary value problems. In TAM, the solution is obtained in the series form with easily computed components. The results of the maximal error remainder values show that the present method is very effective and reliable. The second method namely a new iterative method (NIM or DJM) to solve the TPBVPs. DJM gives an approximate solution with fast convergence. The numerical results prove that the suggested method is reliable and effective. The third and final method is called Power series method (PSM). It is presented to solve TPBVPs. Numerical examples are given to demonstrate the efficiency of the proposed method and some application of TPBVPs will be solved by this methods. The software used for the numerical calculation was MATHEMATICA® 10.0.

درجة افضل تقريب للدوال غير المقيدة في الفضاءات المحلية العامة الموزونة == The Degree of Best Approximation of Unbounded Functions in Locally - Global Weighted Spaces

Author name: علي حسين زبون
Supervisor name: صاحب كحيط جاسم الساعدي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Mustansiriyah University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
First pages:
Abstract: The aim of this thesis is to obtain the degree of best approximation of unbounded functions in locally - global weighted - space L_(P,δ,w) (X),1≤P<∞ using many kinds of polynomials such as I - Bernstein polynomials in terms of weighted Ditzain - Totik modulus of smoothness.II - Trigonometric polynomials S_n^* (f,x) and in addition to that we defined a new operator, which depends on Dirchlet Kernel G_(2n - 3n) - operator in terms of weighted Ditzain - Totik modulus of smoothness.III - q - Bernstein - Kantorovich B ̃_(n,q)^* (f,x) operator by using the locally second usual weighted modulus of smoothness.IV - The linear positive operators L_n^*⁡〖(f,x)〗 and K_n^*⁡〖(f,x)〗 for f∈L_(P,δ,w) (X),X=[0,∞) which is used to obtain the degree of the best approximation of this function in weighted space in terms of weighted modulus of function f.V - Szasz - Mirakjan - Beta U_n^* (f,x) and R ̃_n^* (f,x) operators in terms of weighted locally averaged modulus of smoothness.VI - Also supported by some important results to improve the approximation of unbounded functions classes.

المقاسات الجزيئة المقاسات المستحوذة على 2 وبعض اعماماتها == 2 - Absorbing Submdules (Modules) and Some of Their Generalizations

Author name: عبد الرحمن عبد الله حرفش
Supervisor name: انعام محمد علي هادي
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: University of Baghdad
Language: English
University location: Baghdad
First pages:
Abstract: Let R be a commutative ring with identity, and let M be a unitary left Rmodule. Prime ideals one of the main concepts in ring theory and many generalizations of this concept are introduced such as strongly prime ideals, almost prime ideals, weakly prime ideals, semi - prime ideals, weakly semiprime ideals and 2 - absorbing ideals. Moreover each of the above concepts generalized to submodules. Main goals in this work :  Presenting a comprehensive study of 2 - absorbing submodules and giving many new characterizations and properties related with this concept. Also we use this concept to define and study a new class of modules which is called 2 - absorbing modules.  Introducing and studying many generalizations of 2 - absorbing submodules, 2 - absorbing modules. In fact we introduce and study semi - 2 - absorbing submodules, semi - 2 - absorbing modules, Endo 2 - absorbing submodules, Endo semi - 2 - absorbing submodules, Endo 2 - absorbing modules and Endo semi - 2 - absorbing modules.  Presenting other kinds of 2 - absorbing submodules(resp.2 - absorbing modules) namely small 2 - absorbing submodules (resp. small 2 - absorbing modules ). Then Endo small 2 - absorbing submodules (resp. Endo small 2absorbing modules) are introduced and studied.

القابلية على السيطرة لبعض انظمة السيطرة بواسطة نظرية شبه الزمرة == The Controllability of Some Control Systems Via Semigroup Theory

Author name: عبد الرحمن حميد نجم حسين
Supervisor name: نصيف جاسم الجواري
General topic: Mathematics
Specific topic: Mathematics
Degree: Master
University: Mustansiriyah University - College Of Science - Department Of Mathematics
Language: English
University location: Baghdad
First pages:
Abstract: في هذا العمل، تم ادخال الشروط الكافية لمفهوم القابلية على السيطرة لانظمة غير خطية ذات الشرط الابتدائي والحدودي في فضاءات بناخ المحدبة بشكل منتظم, واثباتها باستخدام نظرية شبه الزمرة (شبه الزمرة المستمرة بقوة) وبعض الطرائق التقنية ضمن التحليل الدالي غير الخطي مثل نظرية النقطة الصامدة لكيرك. علاوة على ذلك, تم اعطاء بعض الامثلة التي توضح قيمة النتائج اعلاه. كذلك تم تقديم النتائج التي تتعامل مع قابلية السيطرة لانظمة غير خطية ذات الشرط الابتدائي والحدودي في فضاءات بناخ وذلك باستخدام نظرية النقطة الصامدة لكل من بناخ وشويدر. | In this thesis, the sufficient conditions for controllability concept of certain nonlinear initial and boundary - value systems in uniformly convex Banach spaces are introduced, and proved by using semigroup theory "strongly continuous semigroup" and some techniques of nonlinear functional analysis, such as, Kirk fixed point theorem. Moreover, examples which illustrate mathematical justification of these theorems are given. Also, the above results for controllability of nonlinear initial and boundary - value systems in any Banach spaces have been presented by using Banach's and Schauder's fixed point theorem.
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