احصاء - ماجستير
Permanent URI for this collectionhttps://repository.neelain.edu.sd/handle/123456789/624
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Item SPINORS AND LIE ALGEBRAS WITH APPLICATIONS TO PHYSICAL FIELDS ALNEELAIN UNIVERSITY(جامعة النيلين, 2018) Reem Abdalgadir AbdallaAbstract The purpose of this research is to introduce concept of Lie group and Lie algebra in addition to some theories and examples. Well as some applications on Lie algebra In particular we are concerned with physical applications; we studied elements of particle physics and gravity. We utilized symmetry concepts, in terms of Lie algebra, in order to classify elementary particles. We also used the symmetry properties to study the unifications problem. المستخلص كان القصد من هذا البحث اعطاء مقدمة عن مفهوم الـ (Lie algebra) بالإضافة الى بعض الأمثلة و النظريات ,و تطبيق عمليات الـ (Lie algebra) و بالأخص العمليات الفيزيائية . كذلك درسنا الجزيئات الأولية و الجاذبية , و استخدمنا مفهوم التشابه بواسطة الـ (Lie algebra) و نفنا الجزيئات الأولية , و أستخدمنا خصائص التشابه بدراسة مشكلة التوحيد .Item Mathematical Analysis of a Model for Tuberculosis Transmission Under Treatment and Quarantine(Neelain University, 2018) Samira Abdalaziz Hamid FadulAbstract In this study, historical remarks about Tuberculosis epidemic disease, treatment strategies with quarantine has been briefly outlined. We studied two models for Tuberculosis with different treatment strategies with and without quarantine. We presented conditions for positivity and boundedness of solutions for both models. Furthermore, we proved the existence of disease-free equilibrium and endemic equilibrium, and we gave conditions for which these equilibrium are stable. We presented some numerical simulation to investigate effects of quarantine on system dynamics.Item Mathematical Analysis of Transmission Dynamics of HIV/TB Co-Infection in the Presence of Treatment(Neelain University, 2018) Amani Abdalkreem Nogdalla AbdalkreemAbstract In this study we analyze a mathematical model for the HIV and TB co-infection for different treatment strategies. We analyze the TB and HIV/AIDS sub-models, we presented conditions for positivity and boundedness of solution. The HIV-only model is shown to have asymptotically stable equilibrium and we established conditions of the existence of the endemic equilibrium in terms of the reproduction number associated with the disease-free equilibrium. The TB-only model shows behavior of backward bifurcation, where the stable disease-free equilibrium exists with a stable endemic equilibrium when the associated reproduction number. We further analyze the full HIV/TB model to incorporate the treatment to the both diseases. A numerical simulation of the models is performed to investigate the effect certain parameters on the spread of the diseases.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 Mathematical Analysis of a model for co-infection of HIV/AIDS and TB(2018-01) Salma Salih Abd Alla AliAbstract TB is a disease caused by bacteria called "Mayco Bacterium", when AIDS is caused by HIV virus. In this research a non linear models for TB and HIV co-infection have been studied. The study include presenting conditions for positivity and boundedness of solutions. The study also established conditions for the local and global stability of the sub-models and the full model. Using ode45 of MATLAB numerical simulations has been presented for different parameter values. Sensitivity Analysis has been studied for the model parameters and has shown that the probability of being infected of TB and the contact rate are most sensitive parameters of the spread of disease, and m, B are less sensitive parameter of the spread of disease.Item 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 Mathematical Analysis of a Compartmental Model for Malaria(2018-01) Shahenaz Osman Khalifa MohammedAbstract In this thesis a mathematical model of malaria transmission has been studied, in which we not only considered the recovered humans return to the susceptible class, but also considered the recovered humans return to the infectious class. We explained some historical and biological concepts of the disease. Also we presented conditions for positivity and boundedness of solution. The existence of the disease-free equilibrium and endemic equilibrium points has been proved. The stability of equilibrium points are determined by next generation matrix method. The analytical results are explained numerically. From these results it is found that if we want control and eradicate the malaria, it is very necessary to decrease the relapse rate and increase the recovery rate.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 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 On a linearization method for MHD Newtonian fluid flow over an exponential stretching sheet with radiation effects(2017-09) : HAMDI ABDEL AZEEM MOHAMMED HAMID