Masters theses : Statistics

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Start date: 2003End date: 2009

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    Lubrication Theory
    (Al-Neelain University, 2004) Jawahir Zakaria Adam
    This 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 .
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    APPLICATION OF LIE GRoUPs IN THE SOLUTION OF SoME ORDINARY DIFFERENTIAL EQUATIONS
    (ALNEELAIN UNIVERSITY, 2003) MOHAMMED ABD AL—BAcI MOHAMMED
    ABSTRACT 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). IV
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    SOME APPLICATIONS OF GREEN'S FUNCTIONS METHOD
    (Alneelain University, 2005) TARIQA. AZIME A. HALEEM
    This 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. .
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    STUDY OF SOME Problems In Bubble Dynamics
    (Al Neelain University, 2003-08) Mohamed Saad El-Din Abdel Gafoor
    Some 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.
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    Functional Analysis Based Methods on Existence and Uniqueness Problems for Partial Differential Equations
    (Al Neelain University, 2007-11) Um Kalthoum Suliman Kanona
    In 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.
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    Approximation by the Method of Least Square
    (Al Neelain University, 2003-05) Sara Ahmed Ebrahim
    Numerical 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.
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    Indefinite Quadratic Programming
    (Neelain University, 2008) Hager Elhadi Gibrcel
    ABSTRACT - By ageneral quadratic programming QP problem we mean aQP problem with ageneral indefinite Hessian matrix . In this research an algorithm to 'solve general QP problems is designed .It is based on the extended Dantzig-Wolfe method. The main idea of the method is to use stable factorizations of the Lagrangian matrix ,where QR-factorization of the active set matrix is used. The algorithm is tested using different problems.
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    symmetry condition of algebraic differential equations
    (Neelain University, 2005) mnahil mohammed bashier
    This study deals with the application of symmetry concept of the solution of the differential equations. The study covers the meaning of symmetry for the differential equation and it gives some examples of it, for centain group especially the rotation group in theplane. »=~ - ~ ~-’ " " We examine if a centain group represents symmetry group of a differential equation, by considering the differential equation as algebraic equation. This is done by studding the partial derivatives of the dependent variables with respect to the independent variables. This leads to consider space called Jet space. The differential equation is a kernel of a map, whose kernel is in fact subspace of the Jet space, which is invariant under group prolongation G, the symmetry group for differential equation. The study introduced some basic concepts which we need to calculate the symmetry group for the differential equations. One of these is the infinitesimal generator for the one parameter group. For this we consider the vector fields with some examples and we give the important features of it. We also provide the criterion of the group G to be a symmetry group for the differential equation. We calculate the symmetry group for the heat equation and we define all the one parameter groups which represent the symmetry of heat equation and we conclude-with the general form of the solution of the heat equation. i To prove this utility we studied the integration theory of ordinaiy differential equation through the symmetry concept. The theory shows that this concept unified several ways for solving the differential equation of first order especially the ideas of separation of variables and exactness which represent the basis of solving the first ODE.
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    ON THE LINEAR INTEGRAL I: EQUATIONS
    (Neelain University, 2006) KHALID ABD ASSALAM ATEIA
    The reader may be surprised about what the linear integral equations. And that for the little importance that had paid for this topic. The integral equations is a mathematics method which had used to solve many problems in physics arid chemistry, and also at mathematic. Our considerable mathematic method can be also used to solve the differential equations which can be also reduces to a one of the integral equation. Our research will consider the following points:- l\ the definition of the linear integral equations, and explain some of its usefulness. 2\ some method of solution for the linear integral equations. So in our first section we had to define the linear integral equations and we obtained some of its uses in mathematics, physics and chemistry , also we take the numerical solution for the linear integral equations. But we had just explained the method of solution for some reason we had written. _ In the second section we explained a method to solve the integral equations of the first kind , and also it uses to solve the integral equations of the second kind . At the third section we had the approximation solution, and we clear the co-theory for this method of solution. More over our fourth section is specialized on the algebraically solution to the linear integral equations with the assistance theorems for it. And at special case for the kernel of the linear integral equations we take our fifth section and we joined our algebraically solution with Fourier series. _ The sixth section had taken as applications to some problems which had reduced to an integral equations. . At last we had a conclusion to our research, and we take some problems in the last section as applications for the methods of solutions which we had explained in the previous sections.
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    the geometric formulation of electromagnetic field
    (Neelain University, 2008) Tagreed Ahmed F adeel
    Abstract In this research we studied Maxwell's field equations. The treatment is different from the classical approach. It is both global and free of coordinates. So we used the language of difl’erential forms and fiber bundle whose base space is a general manifold. The geometrical description is neat and short. Moreover the gravitational force is incorporated in the electromagnetic field, being written in curved space —time.