Masters theses : Statistics
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Item TENSORS ANALYSIS WITH SOME APPLICATIONS(AlNEElAN UNVERSLTY, 2018) Rimaz Awad AikheederItem Lubrication Theory(Al-Neelain University, 2004) Jawahir Zakaria AdamThis thesis is a study of Lubrication theory .Thc consept of Lubrication its to types and practice and some definitions are introduced in chapter one . In chapter Two the Reyn0ld's equation is derived. Chapter three deals with Further theory of Lubrication. In chapter four the variational ,approach to Lubrication problems is studied boundary conditions uses are also discussed .Item APPLICATION OF LIE GRoUPs IN THE SOLUTION OF SoME ORDINARY DIFFERENTIAL EQUATIONS(ALNEELAIN UNIVERSITY, 2003) MOHAMMED ABD AL—BAcI MOHAMMEDABSTRACT Lie's group theory of diflerential equations was initiated by the Norwegian mathematician Marius Sophus Lie (1842-1899). Today, this area of research is actively engaged. In chapter one of this thesis, we give the fundamental concepts of the one-parameter Lie group of transformations, and it also contains the main theorems and definitions. In chapter two, we apply the Lie's theory to the following second order ODE's x:_v3+xy1-1=0, (1) xiv; —y,: —l = 0. (2) _v: —y1 —£=O. (3) y -t:(1”:+,t:_v]: — Zxyl + 2 = 0 . (4) k d y h . = i . k = 1.2. w ere y_ LN In this chapter. we obtain the following results (i) The symmetry groups of(1), (2). (3). and (4). (ii) Reduce the order of (1). (2), (3), and (4) to the first order ordinary differential equations. (111) The general solution of (1). (2), (3), and (4). In chapter three, we considered the non-linear third order ODE y;+Zyy:-_v|2=O. (5)where _vk which is k In this cha (i) (ii) Red equ (m) The (iv) Ne The symmetry groups of (0) w __-Q _ ,___ _ k — d f k -1 v 3 dx nown as Goldstein equation [7]. pter, we obtain the following results uce the order of (5) to the first order ordinary diflerential ation. invariant solutions of (5). solutions from known solutions for (5). IVItem Some problems in the conducation of heat in solids(Al-Neelain University, 2014) Asmaa ElgassimAbstract In this dissertation we studied the equation of conduction of heat in solids in the Cartesian coordinates. Comparison is also made between an example in conduction of heat and diffusion. Finally a study is made for the flow of heat in composite mediaItem Oscilation of second order differetial equations(Al-Neelain University, 2014) mawadah hassan babekerABSTRACT Qualitative properties of solutions of differential equation assume importance in the absence ofclosed form solutions. In case the solution is not expressible in term ol' the usual “known functions. An analysis of the equation is necessary to find the facets of the solution . One such qualitative property, which has wide applications, is the oscillation of solution, which unfortunately is not always possible. A rewarding alternative is to resort to qualitative study. This point is asserted once again to justify the inclusion of qualitative theory to students who think that it’s otherwise out ofplace.Item Application of la place transform on orddinary and fractional ordianry differential equations(Al-Neelain University, 2014) Samah Abd Elazim Ali\ i Abstract In this thesis we focused on the concept of Ordinary Differential Equations which appears to be important in physical systems, electri- cal mechanical, Fractional Ordinary Differential Equations and other fields, in particular the basic theory of Fractional Ordinary Differential Equations involving Riernman-Liouville operators and some examples explain their applications. The Laplace transform method has been successfully applied to solve the Ordinary and Fractional Ordinary Differential Equati0ns.The method is very powerful and eflicient in finding solution.Item Mathematical Analysis for Malaria Model in Constant Environment(ALNEELAIN UNIVERSITY, 2019-07) Mojahed Abdalwahab Eisa AbdelgadirAbstract In this thesis a mathematical model for malaria disease has been studied. The model neglected the incubation period for human and any possible variations over the time. We proved positivity and boundedness of solutions, furthermore , we proved the existence of disease free-equilibrium, and we explain the number of disease freeequilibriurn. We present condition for which these equilibria are sta— ble. Also, we compute the basic reproduction number using the next generation matrix approach. The analytical results are verified and justified numerically.Item Homotopy and Homology Theory with Some Applications(AL-Neelain University, 2014) ELHAM DAUOED HAMDOUN ADAMThe purpose of this project is to study topological spaces in terms of certain groups as~ sociated with them, these groups are topological invariants in the sense that isomorphic groups are associated with hornomeomorphic spaces. We discuss two types of groups. The homotopy group for the lower~dimension spaces and homology groups for higher-dimension spaces. As an application of this study we present some computation of homotopy and homology group and prove several theorems in algebra and analysis.Item Optimal control problem by using Ito calculus(AL-Neelain University, 2014) Abdelrahman HammadIn this research were discussed stochastic differential equation and how to solve it. Where we studied the theory of measurement and integration, and explain concept of a random variable and its relation to the function of measurable how to change measure the integration. And then studied the Brownian motion and the most important properties and not to the possibility of integration by Lebesgue integrating. To solve the stochastic differential equation we used ITO integral after studying this integration and its properties. It also contains research on applications of stochastic differential equation and the most important issue of control random.Item An SEIR Model for Tuberculosis(AL-Neelain University, 2015) Yousra adil saleh khalfallaIn this research, we present mathematical models for the study of tuber— culosis disease. We briefly indicated to some important information about tuberculosis and how the disease can be transmitted to human bodies. We conducted some statistical data about the disease in Sudan to highlight the risk of getting infected. We also present some concepts from the mathematical modelling of infectious diseases such as IRQ. We study an SEIR model for tuberculosis to study the stability under different hypotheses. We present a number of numerical simulations for different parameter values.