كلية العلوم الرياضية والاحصاء
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Item 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 APPLICATIONS OF GREEN'S FUNCTIONS METHOD(Alneelain University, 2005) TARIQA. AZIME A. HALEEMThis thesis deals with solving the Boundary Value Problems by applying the Green's Function Method, on the Ordinary Differential Equations of the second order, and Partial Differential Equations of the first and second order including higher orders. Using Green's Function Method to solve such equations by using simple ways such as: Laplace and Fourier transformations and their inverse transformations, including Bessel's functions, and F0urier's series. It also include the basic concepts, i.e. inner product, differential operators, adjoint operator, self—adjoint operator, unit-step function, the delta function, convolution and known integrals. .Item The Qeometry Of Space - time(Al-Neelain University, 2007) Mohammed Hassen ElzubairIn this research we utilized twister theory to describe the geometry of space-time. The twistors are derived from Spinors which are also used to write zero rest- mass fields equations. We mainly used the properties of twistor function to generate zero rest- mass fields, where this function is formulated from both the geometry and topology of Minkowski spaceItem STOCHASTIC CONTROL PROBLEM WITH PARTIAL OBSERVATIONS(Al-Neelain University, 2006-09) HOYAM TAG ELDINThe problem of stochastic control with observations had been discussed. First we start with the problem of linear filtering to get the best estimate for the system according to the given observations. To obtained the solution we solve Kalman filter equation. In the case of nonlinear filtering the problem reduces to complete study of Zakai equation. The optimal stochastic control dynamic system had been discussed in the case of partial infonnation which yields Kalman filter. But in the case of complete observation we solve the problem using Hamilton-Jacobi equation. Finally we introduce and discuss some applications of the problem of stochastic control.Item STUDY OF SOME Problems In Bubble Dynamics(Al Neelain University, 2003-08) Mohamed Saad El-Din Abdel GafoorSome problems of the bubble dynamics are discussed and the solutions are found. The fluid in which the bubble is moving is asstuned to be incompressible, irrotational and inviscid. The stability of the fluid flows with spherical symmetry is studied and the conditions for its occurrence are deduced. The motion of the bubble produced during Taylor instability of superposed fluids in cylindrical tubes is studied and the effect of the surface tension force and the curvature of the interface are taken into account. Both the steady and the unsteady state of motion are considered. i Spherical — cap models are presented, and the comparison between the theoretical studies and the experimental results is found. V The potential solution for the boundary value problem of the toroidal bubble in an infinite fluid is found by using the toroidal coordinate system. Botl1 the three dimensional and the axisymmetric case are considered.Item Functional Analysis Based Methods on Existence and Uniqueness Problems for Partial Differential Equations(Al Neelain University, 2007-11) Um Kalthoum Suliman KanonaIn this study, we considered existence and uniqueness problems for partial differential . equations. . We used functional analysis techniques, where a partial differential equation is regarded as an operator on an appropriate Hilbert space. This Hilbert space is in fact a Sobolev space. In particular, we have dealt with two me/thods, variation methods and energy integral method. We have illustrated the techniques with some examples.Item The Algebraic Treatment of Symmetric Spaces A thesis submitted(Neelain University, 2008) Nemaat Hamed TalebABSTRACT We study manifolds spaces which lead to Lie group, then by definition of transitive action of a Lie group in a manifold we get homogeneous spaces. Also we study symmetric spaces, which are particular homogeneous spaces. We classify simple Lie algebra over C according to Dykin diagram. Also by means of real form we classify simple Lie algebra over DR. We show that every symmetric space gives rise to an orthogonal symmetric Lie algebra. Finally we classify Riemannian symmetric spaces of types I, II, III and IV according to the classification of the irreducible orthogonal symmetric Lie algebra of types I, II, III, and IV.Item STOCHASTIC CONTROL PROBLEM WITH PARTIAL OBSERVATIONS(Neelain University, 2006) HOYAM TAG ELDIN AHMEDAbstract The problem of stdchastic control with observations had been discussed. First we start with the problem of linear filtering to get the best estimate for the system according to the given observations. To obtained the solution we solve Kalman filter equation. In the case of nonlinear filtering the problem reduces to complete study of Zakai equation. The optimal stochastic control dynamic system had been discussed in the case of partial infonnation which yields Kalman filter. But in the case of complete observation we solve the problem using Hamilton-Jacobi equation. Finally we introduce and discuss some applications of the problem of stochastic control.Item Approximation by the Method of Least Square(Al Neelain University, 2003-05) Sara Ahmed EbrahimNumerical analysis is concerned with developing methods to find approximate solutions for scientific problems, these methods are used extensively to treat commercial and industrial problems. The problem is first put in a mathematical model, in a form that describes the behavior of the variables, after applying particular relations between them. In this thesis we study some methods in approximation theory. There are several reasons for studying approximation theory and methods, ranging from a need to represent functions in computer calculations to an interest in the mathematics of the subject. Although approximation algorithms are used through out the science and in many industrial and commercial fields, some of the theory has became highly specialized and abstract. Work in numerical analysis and in mathematical s oflware is the o ne of the main links between these two extremes, for it’s purpose is to provide computer users with the efficient programs for general approximation calculations, in order that useful advances in the subject can be applied. This work presents methods using polynomials to approximate a given function or a given discrete data. The work shows many approximation methods, begining with graphical methods, and the methods of average briefly, then the method of least square is given in more details and it is the main topic of this thesis. Some programs are designed to solve general problems in discrete least square problems, and special problems in continuous one.