احصاء - ماجستير
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Item D'Alembert Solution For Wave Equation(Al-Neelain University, 2010) Abd Alfatah Mohammed Osman AbasherAbstract In this research , introduction to wave equation , two new proofs and extensions are proposed . at the same time ,two equivalent equation systems for the wave equation and the corresponding initial value problems are advanced and proved by using the characteristics concepts and methods . and some interesting discussions of the initial –boundary value problems (IBVP) and the different cases for at the boundary point . 5 خلاصة البحث: تطرقنا فى ھذا البحث لمقدمة عن الموجة ، والتوصل للمعادلة التفاضلیة التى تصف حركة الموجة والشروط الابتدائیة لھا من ثم حل ھذه المعادلة التفاضلیة باستخدام اسلوب دالمبرت والذى اعتمدنا فیھ على طریقة تحویل ھذه المعادلة الى نظامین من أنظمة المعادلات التفاضلیة تكافئ ھذه المعادلة . وتطرقنا أیضا لحل دالمبرت لمسائل القیم الابتدائیة والحدیة ، سلوك الموجة عند النقاط الحدیة ، من حیث انھا ثابتة فى الطرفین ، او ثابتة فى طرف ومتحركة فى الاخر أو متحركة فى الطرفین ، تصف ھذه الحركة فى كل حالة . mapleوأخیرا برامج بلغةItem Analysis of a Mathematical Model of Malaria Disease(2018-01) Mohamed Kamalaldin Mohamed BabekirAbstract Malaria is one of the deadliest diseases around the world causing the death of around 429,000 person in the year 2015 only. This led the scientists around the world to work hard to fight against the disease. In this study, we analyzed the mathematical model of malaria transmission. We calculated R0 which could determine the future of the disease. We examined two sets of parameters, low prevalence and high prevalence and we calculated the effect rate of all parameters using sensitive analysis. Numerical simulations are carried out to confirm the analytical results and explore the possible behavior of the formulated model.Item And classification of Lie algebras On the characterization(Al-Neelain University, 2016) Anwar Adam Ahmed MohammedAbstract In this work we studied Lie groups and Lie algebras. We Considered several examples of Lie groups and their associated Lie algebras .We treated the representation theory of Lie groups And used this theory in the problem of classification of some Lie algebras such as semi simple and solvable Lie .algebras .Other Lie algebras have also been characterized 5 المستخلص في هذا البحث درسنا زمر لي وجبر لي. تناولنا عدة امثلة لزمر لي وجبر لي المتعلقة بتلك الزمر. عالجنا نظرية التمثيل لزمر لي وإستخدمنا هذه النظرية في مسألة تصنيف بعض جبر لي كجبر شبه بسيط وكذلك جبر قابلية الحل. كما تم تصنيف جبر لي اخرItem application of homotopy perturbation method to predator-prey models(2016) gehan abdalgafar ahmed mohammedItem Application of Spectral Adomian Decomposition Method on Heat and Mass Transfer of Boundary Layer(Al-Neelain University, 2015) Salma Hassan Mohammed HassanAbstract In this study, we proposed numerical method for solving non-linear differential equations. The method is hybired of spectral and Adomian decomposition method. The method will applied on the problem of convection heat and mass transfer, the convergence of the method tested and displayed on tables. The velocity, temperature and concentration have been obtained and discussed for various physical parameter.Item APPLICATION OF SPECTRAL HOMOTOPY PERTURBATION METHOD ON BOUNDARY LAYER FLOW WITH RADIATION EFFECT(Al-Neelain University, 2015) Abdalaziz Elhaj Bakhit ElkhwadAbstract In this thesis we study the effect of radiation on the boundary layer flow and heat transfer of viscous fluid. The Spectral Homtopy Perturbation Method (S-HPM) used to solve the system of the governing equations. We also determine the convergent series of the solution. The accuracy and rate of convergence of the solution has been tested and compared for different orders and the results are presented in tables . The physical interpretation to these expressions is assigned through graphs.Item Application of Spectral Quasilinearization Method on Fluid Flow(Al-Neelain University, 2015) Hisham Ali Ahmed GhanimAbstract In this thesis, we solve the problem of Soret and Dufour effects on mixed convection from an exponentially stretching surface of the flow of viscous incompressible fluid. The method of Quasilinearization is used to solve the problem described the flow. The method is very simple and effective and can be used instead of traditional numerical methods.Item Application of the Spectral Local Linearization Method on a System of Nonlinear Ordinary Di erential Equations(Alneelain University, 2016-12) Abubakr Eltayeb Mohammed EltayebIn this study the problem of unsteady nano uid ow over a stretching sheet subject to couple stress e ects is presented. Instead of assuming that the nano-particle volume fraction at the boundary surface may be actively controlled, a realistic boundary condition for the nanoparticle volume fraction model is that the nano-particle ux at the boundary be set to zero. We assume there is no active control of the nano-particle volume fraction at boundary. The spectral local linearisation method has been used to solve the governing equations, moreover the results were further con rmed by using the quasi-linearization method. The qualitative and quantitative e ects of the dimensionless parameters in the problem such as the couple stress parameter, the Prandtl number, the Brownian motion parameter, the thermophoresis parameter and the Lewis number on the uid behavior are determined. iItem Application of the Spectral Local Linearization Method on a System of Nonlinear Ordinary Differential Equations(Al-Neelain University, 2016) Abubakr Eltayeb Mohammed EltayebAbstract In this study the problem of unsteady nanofluid flow over a stretching sheet subject to couple stress effects is presented. Instead of assuming that the nano-particle volume fraction at the boundary surface may be actively controlled, a realistic boundary condition for the nanoparticle volume fraction model is that the nano-particle flux at the boundary be set to zero. We assume there is no active control of the nano-particle volume fraction at boundary. The spectral local linearisation method has been used to solve the governing equations, moreover the results were further confirmed by using the quasi-linearization method. The qualitative and quantitative effects of the dimensionless parameters in the problem such as the couple stress parameter, the Prandtl number, the Brownian motion parameter, the thermophoresis parameter and the Lewis number on the fluid behavior are determined. ivItem Application of the successive linearization method to micropolar flow in a porous channel(2016) Mohammed Ahmed Ali Mohammed Ahmed MohammedAbstract In this study the successive linearization method is applied to the problem of mi- cropolar flow in a porous channel. The governing partial differential equations are transformed into a system of ordinary differential equations and then solved via SLM. The effects of various parameters are discussed and analysed.Item Application of the successive linearization method to unsteady MHD ow over stretching sheet(Al-Neelain University, 2016) Mona Jaafar Elamin AhmedAbstract The aim of this study is to present the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a fluid over a stretching sheet in the presence of viscous dissipation and heat source. The governing nonlinear partial differential equations are first transformed into a system of non-linear ordinary differential equations and then solved numerically by the successive linearization method (SLM). Effects of various physical parameters on the velocity and temperature profiles are presented graphically and in tabular form. Numerical comparison is also presented with the existing results in literature which shows that the present results are in an excellent agreement.Item APPLICATIONS OF BANACH FIXED POINT THEOREM AND APPROXIMATION THEORY(Al-Neelain University, 2004) Moram Adam MohammedAbstract This dissertation consists of four chapters : In chapter one we present concept of fixed point and some examples of it and discusses the Banach fixed point theorem and some definitions in a metric space . The second chapter is devoted to applications of Banach fixed point theorem . In chapter three we present approximation in normed spaces and deals with problem of existence and uniqueness of best approximation . In last chapter we define the uniform approximation and present a brief introduction about approximation in Hilbert spaces and Chebyshev polynomials.الخلـصــــــــة هذه الرسالة تتكون من اربعة فصول : الفصل اللول: يقدم تعريـف للنقطـة الثابتــة لوبعـض المثلة عليها لويناقش مبرهنة باناخ للنقطة الثابتة لوبعـض التعريفات في الفضاء المتري . الفصل الثاني : مخصص لتطبيقات نظريــة النقطــة الثابتة لباناخ . الفصــل الثــالث : يقــدم نظريــة التقريــب علــي الفضاءات المنتظمة لويعالج مشكلة الوجــود لوالوحدانيــة للتقريب الحسن . الفصل الرابـع : يعــرف التقريــب المنتظــم لويقــدم مقدمــة مــوجزة عــن التقريــب فــي فضــاءات هلــبرت لوكثيرات حدلود تشيبشف .Item Applications of Conformal map to Potential Theory and Fluid Mechanics(2017-11) Abdalbagy Hatim AlshikhAbstract In this work we study the theory of complex variables . Being motivated by the vast applications of this theory , we considered the analytical properties provided by the theory of complex functions in the field of electrostatics , Fluid mechanics and Harmonic analysis .We introduced the important theorems relating derivatives and integrals such as Cauchy integral formulas . We have also utilized conformal transformations in several applications such as solving Poisson equationItem Applications of Finite Element Method on Beams(Al-Neelain University, 2015) Eman Jamal-Aldeen Alkhair Altahirمستلخص طریقة العناصر المنتھیة ھي عرض بطریقة متغایره لحل المعادلھ التفاضلیھ . نضع فیھا المسألھ المستمره في cjj ،الدالھ التقریبیھ شكل معادلھ تفاضلیھ مكافئة لصیغھ التغایر، ویفترض الحل في صورة تركیب خطي، ھي j . البارمتیرات cj تحدد باستخدام صیغة التغایر . طریقة العناصر المنتھیھ تحسن تقنیھ النظام للدالھ التقریبیھ لمجال بسیط مركب ھندسیا . في طریقة العناصر المنتھیة، الدالھ التقریبیھ ھي كثیرة حدود (كثیره الحدود تعرف لكل مجال وتسمي بالعنصر) Abstract The finite element method is introduced as a variationaly based technique of solving differential equations. A continuous problem described by a differential equations is put into an equivalent variational from, and the approximate solution is assumed to be a linear combination , Pcjφj , of approximation function φj . The parameters cj a determined using the associated varitional form. The finite element method provides a systematic technique for deriving the approximation function for simple subregions by which a geometrically complex region can be represented. In the finite element method, the approximation function are piecewise polynomials (i.e, polynomials that are defined only on a subregion, called an element)Item Applications of Homotopy Perturbation and Variational Iteration Methods in Fractional Calculsus(Al-Neelain University, 2016) Altayb Ahmed Mohammed AliAbstract This research aims to solve some problems of differential equations which contain fractional derivatives by using homotopy perturbation method (HPM) and variational iteration method (V IM). Chapter one contains Homotopy perturbation (HPM) and its use in solving differential equations. Chapter two contains some examples in fractional derivatives. Chapter three contains applications of the (HPM) to solve the equations that contain fractional derivatives. Chapter four contains applications of variational iteration method (V IM) to differential equations. Comparison with (HPM) is made through examples.Item Applications of Spectral Homotopy Perturbation Method on a Steady Tow-dimensional Hydro Magnetic Flow(2016) Sahwa Ahmed Elabaid AhmedAbstract The purpose of this research is to discuss the flow of forced convection model over a flat plate. The governing partial differential equations are transformed into ordinary differential equations using suitable transformations. The resulting equations will solv using a recent semi-numerical scheme known as the Spectral Homotopy Perturbation Method (S-HPM). A comparison between the obtained results with different orders has been included. The accuracy and convergence of the solution will be tested .Item Applications of the Homotopy Perturbation Method and Sumudu Transform of the Linear and Nonlinear Differential Equations(2018) Sana Hassan Magboul AhmedAbstract This study is mainly focusing on the application of the homotopy perturbation method and Sumudu transform of the linear and nonlinear differential equations. It has established some defnitions and properties of homotopy perturbation method and Sumudu transform. The study combines the homotopy perturbation method and Sumudu transform. Consequently, it gives the solution in series form and approximates components, and _nds the exact solution. Then, it is applied to solve linear and nonlinear differential equations . Finally, the solutions of linear and nonlinear differential equations by this method, and the other methods will be compared. الخلاصة تتمركز هذه الدراسة مجملا في تطبيق طريقة ارتجاج الهموتوبيا وتحويل سمودو في حل المعادلات التفاضلية الخطية وغير الخطية . ستقوم الدراسة بتاسيس بعض التعريفات والخصائص بالنسبة لطريقة الارتجاج الهموتوبيا وتحويل سمودو.قامت الدراسة بدمج طريقة الارتجاج الهموتوبيا وتحويل سمودو. مما ادى الي ايجاد الحل فى شكل متسلسلة وتقريب المكونات لايجاد الحل التام. من ثم طبقت الدراسة لحل المعادلات التفاضلية الخطية وغير الخطية. واخيرا تمت مقارنة حلول المعادلات التفاضلية الخطية وغير الخطية بطرق اخرى.Item APPLICATIONS OF THE QUASILINEARIZATION FOR METHOD ON A FLUID FLOW MODEL(جامعة النيلين, 2016) Zainab widdat alla mohamed AhmedIn this thesis, we apply the quasi-linearization method (QLM)to a system of nonlinear ordinary di erential equations with boundary conditions derived from the model in uid mechanics. The method approximates the solution by treating the nonlinear terms. The solution has be checked to validate the accuracy of the obtained results in tables.Item Applications of the Successive linearization method to Casson fluid flow over an unsteady stretching surface(2017-10) Sufana Salahaldin Mohammed AwadalkaremAbstract The unsteady two-dimensional flow of a non-Newtonian fluid over a stretching surface having a prescribed surface temperature is investigated. The Casson fluid model is used to characterise the non-Newtonian fluid behaviour. Similarity transformations are employed to transform the governing partial differential equations into ordinary differential equations. The transformed equations are then solved numerically by the successive linearization method(SLM). The flow features and heat transfer character- istics for different values of unsteadiness parameter, Casson parameter and Prandtl number are analysed and discussed in detail. Abstract Arabic تمت دراسة الأنسياب لمائع غير نيوتن فوق سطح متحدد له حرارة محددة . لقد استخدم نمو مائع كاسون لوصف سلوك المائع الغير نيوتوني . بأستخدام تحويلة متماثلة لقد حولت المعادلات التفاضلية الجزئية التي تصف الإنسياب إلى معادلات تفاضلية عادية و من ثم حلت بأستخدام طريقة الطيف المتعاقبة . و تأثير بعض الوسائط لكل خصائص الأنسياب و سبل انتقال الحرارة قد نُقشت .Item ARIMAالتحليل الإحصائى في السودان (1970 - 2001) بالتطبيق علي السلاسل الزمنية ونماذج(2003) بلقيس محجوب حسن باديAbstract. This Study deals with the analysis of Inflation in Sudan during period (1970-2001) applying Time Series and Autoregressive Integrated Moving Average (ARIMA) models ~ The Study is based upon the hypotheses that relationship between Inflation in the time t , Y, and before it t-I , Y,_| Y: Z 7~1Yi-1 + $1 under the assumption E [Q] = 0 E [e,es]=52e , if t=s = 0 , if tvé s E IQY:-ll = 0 The study tackled the analysis of Inflation by using the regression and ARIMA models analysis for estimating and forecasting the Inflation in Sudan - The Study concludes that : 1) The ARlMA(l,1,0) model , mh = —0.287AY,_1 , Is best model for forecasting the Inflation in Sudan - 2) The Inflation in the year 2002 had high rate - The Study recommends the following points : I) The work for constant Exchange price - 2) Opening new markets for Sudan foreign trade