احصاء - ماجستير
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Item Uniqueness Traveling Waves for Evolution Systems and Non-monotone Integral Equations(Al-Neelain University, 2010) Haijr Abdelmola Eldoma MohammedAbstract We investigate a class of integral equations without monotonicity and nonlocal reaction- diffusion population models. We develop a theory of spreading speeds and traveling waves for abstract monostable evolution systems with spatial structure. Under appropriate assumptions we show that the spreading speeds coincide with the minimal wave speeds for monotone traveling waves in the positive and negative direction. We concerned with the spreading speeds and traveling wavefront for second order integrodifference equation. It is show that the spreading speed coincides with the minimal wave speed for monotonic traveling wavefront. We concerned with the traveling waves in a class of non monotone integral 4 equations. We establish the existence of traveling waves. The approach is based on the construction of two associated auxili monotone integral equations and a profile set .inaBanachspace الخلاصة تمت مناقشة عائله من المعادلات التكامليه دون الرتيبية ونمازج سكان أو الانتشارالتفاعل غبر الموضيعية. تم إنماءنظرية سرعات التوزيع و موجات الإنتقال لاجل الأنظمه الحركيه آحاديه الأستقرار المجرده طبقا ً للبناء الحيزي تحت الفروضات الموافقه تم توضيح أن سرعات التوزيع تنطبق مع سرع ات الموجة الاصغرية لأجل موجات الانتقال الرتيبية فى الاتجاهات السالبة و الموجبة . تم الاهتمام بسرعت توزيع جبهات الموجه الإنتقالية لأجل معادلات الفرق المكمل . بواسطه إدخال نظام الفرق المكمل المساعد تم تأسيس سرعة توزيع لأجل معادلات الفرق المكمل . تم إيضاح أن سرعة التوزيع تتطبق مع سرعة الموجه الاصغريه لأجل جبهات موجه الإنتقال الرتيبيه . تم الإهتمام بوجات الإنتقال فى عائله من معادلات التكامل غير الرتيبية تم تأسيس وجود معادلات الإنتقال الإقتراب مؤسس على تشييد معادلين تكامليتين رتيبين مساعدتين مشاركتين وفئه جانبية فى فضاء باناخ مناسبItem the three fundamental theorems in functional analysis(Al-Neelain University, 2015) safia mahgoub alsadaigA BSTRACT This thesis treats functional analysis and its application. We study function spaces with analytical structures, such as normed spaces, banach spaces and Hilbert spaces. Our prime interest is in the most fundamental theorems of functional analysis. There is Hanh-banach theorem, uniform boundedness theorem, and closed graph theorem. We give applications to Fourier analysis and applications on existence of solution of differential and integration equations.Item A THESIS SUBMITTED IN FULFILMENT OF THE ACADEMIC REQUIREMENTS FOR THE DEGREE OF(Al-Neelain University, 2016) Hadeel Salah El-Deen Mahgoub AL-BaroudyAbstract In this thesis, we used a new computational technique to solve a system of nonlinear boundary value problems that governed heat and mass transfer in a fluid flow in porous medium. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation then solved numerically using the spectral Adomian decomposition method. The convergence of the obtained results are checked. The effects of selected physical parameters are determined and discussed graphically. iii Abstract (Arabic) في هذا البحث إستخدمنا إحدى الطرق العددية الحديثة لحل نظام من المعادلات التفاضلية الغير خطية وهي طريقة أدوميان الطيفية. تم تطبيق الطريقة على نموذج لإنتقال الحرارة والكتلة في وسط مسامي بعد تحويلة الى نموذج من المعادلات التفاضلية العادية وقد تم التأكد من تقارب الحل وتم دراسة أثر بعض البارميترات الفيزيائية في الإنسيابItem The Theory of Lie Algebra with Some Applications(Al-Neelain University, 2016) Amir Bashir Mohammed AliAbstract: Lie algebras and their representations are very important to study several problems in mathematics, physics and Sciences. Lie algebra is an associated algebra of a Lie group, that is usually a symmetry group of a problem, such as a differential equation. In this study we gave alternative descriptions of Lie algebra. The descriptions are analytical, algebraic and geometrical. For instance a Lie algebra is a tangent space to the identity to a Lie group. For the sake of applications of Lie algebra we concentrated on the theory of representations of Lie algebras. IV مستخلص الدراسة إن جبر لي وتمثيالته هام جدا لدراسة المسائل المختلفة في الرياضيات و الفيزياء والعلوم. لقد تم ربط جبر لي بمجموعة لي، حيث طبق هذا الجبر في مسائل عديدة كالمعادالت التفاضلية. في هذه الدراسة قدمنا وصفا تحليليا وجبريا وهندسيا لجبر لي، فمثال الوصف الهندسي لجبر لي يمثل فضاء المماس عند العنصر المحايد. من أجل التطبيق ركزنا على نظرية التمثيل لجبر لي.Item Theory of Lie algebra with applications to symmetry and conservation laws(Al-Neelain University, 2016) Ismail Mustafa Mohammed OthmanAbstract In this research we studied Lie groups and Lie algebras . We considered the classification theory of complex and semi-simple Lie algebras , provided with sufficient knowledge of the properties of Lie algebras . We then concentrated on the application of Lie algebra to the conservation laws , in particular Noether theorem . We also studied the application of Lie algebra to particle physics including the utility of the representation theory of the five dimensional special unitary group. We concluded our research program with the study of symmetry groups of differential equations . IV المستخلص في هذا البحث درسنا زمر لي و جبر لي. درسنا نظرية تصنيف جبر لي المركبة وشبه البسيطة، مع توفير قدر كاف من المعرفة عن خصائص جبر لي. ثم ركزنا على تطبيق جبر لي لقوانين الحفظ ، وال سيما نظرية نوثر . درسنا أيضا تطبيق جبر لي لفيزياء الجسيمات يضم استخدام نظرية تمثيل الزمر ذات البعد الخامس في دراسة زمرة الوحدة الخاصة. ختمنا بحثنا بدراسة زمر التماثل للمعادالت التفاضلية.Item Stability analysis of vertical curved channel flow with radial Temperature Gradient(Al-Neelain University, 2010) sharaf mohmoud ahamedAbstract: The linear stability analysis of a Newtonian incompressible fluid in a vertical curved channel formed by two coaxial cylindrical surfaces with a radial temperature gradient and an azimuthal pressure gradient shows that critical modes are oscillatory and non-axisymmetric. We have derived a generalized Ray Leigh discriminate which includes both the curvature and buoyancy effects. Centrifugal buoyancy induces weak asymmetry of the dependence of the control parameter critical value on the sign of the temperature gradient. The critical parameters depend on the temperature gradient the radius ratio and the nature of the fluid for a wide curvature channel flow. There are two critical modes. Oscillatory Dean Modes for small temperature gradient and oscillatory centrifugal. Thermal modes for relatively large temperature gradients.Item Some applications of Gauss – Bonnet Theorem(Al-Neelain University, 2016) Hibatalla Mahjoub Mohamed Al khierAbstract: Our objective in this study is to prove Gauss – Bonnet theorem on surfaces in Euclidean space . We first consider the geometry of curves and surfaces using frame fields and Cartan method . The curvature is studied , in particular Gauss curvature , which has been related to the topology of the surface via Euler characteristics . IV (عربي) Abstract . هدفنا في هذه الدراسه هو برهان نظرية ) قاوس – بونيت ( على السطوح في الفضاء االقليدي اوال درسنا هندسة المنحنيات والسطوح مستخدمين حقول االطارات وطريقة كارتان . االنحناء الذي درسناه , تحديدا انحناء قاوس حيث تم ربطه بتوبولوجيا السطوح من خالل مميز اويلر .Item Some Applications Of Functional Analysis(Al-Neelain University, 2015) Osama Mustafa BabikerAbstract In this thesis we study the concept of completespaces , We process this concept on some spaces (Normed spaces –Banach spaces – Hilbert spaces),discuss some fundamental theorem's by using the concept of completeness to support the concept of extension for linear functions (Hahn – Banach theorem's ) together with linear operators (uniform boundedness principle ) .we study open and closed linearsoperators as an Introduction to The closed graph theorem .We apply thesetheorems to solve and prove some problems and theorems, andfinally we consider calculus on Normed spaces.Item Solving Some Chaotic Systems Using the Multistage Spectral Relaxation Method (MSRM)(Al-Neelain University, 2016) Gisma Ahmed Eisa AdamAbstract In this thesis we studied some chaotic systems using the multistage spectral relaxation method (MSRM). This method have been presented to solve initialvalue problems by discretized the time domain into sub-interval where the solutions can be obtained. The chaotic systems we studied were the Lorenz system, the Rössler system, the Chen system and the Genesio-Tesi system. These systems were known for having strange attractors for some parameter values. We used the MSRM method to solve these systems and we compared our results to the results that obtained from the MATLAB built-in function ode45. We presented some numerical results that compared the solutions of the two methods.Item Solving Meta-Population Models Using the Multistage Spectral Relaxation Method (MSRM)(Al-Neelain University, 2016) Rogia Ahmed Mahmmoud AbdallahAbstract In this thesis we presented two mathematical models for herbivore/vegetation interactions. The first model is a metaphysiological model in a single patch environment. The second model is a metaphysiological model for herbivore and vegetation interactions in two patches environment. We applied the multistage spectral relaxation method (MSRM) to solve these models. The MSRM method was presented to solve initial-value problems when the time domain is decomposed to sub-domains. We compared our results to the results that obtained from the MATLAB built-in function ode45.