كلية العلوم الرياضية والاحصاء
Permanent URI for this communityhttps://repository.neelain.edu.sd/handle/123456789/623
Browse
Item Representation Theory of Finite Group with Some Applications(AL-Neelain University, 16) Hiba NasrEldin MohamedThis research aims to study the representation theory as a tool that transform abstract groups to groups of linear transformations easy to deal with. This research depends on groups and fields theory and vector spaces to construct the structure of these spaces. We studied vector spaces because of structures. In particular we dealt with finite groups and we gave some applications.Item القوى العاملة بجمهورية السودان الديمقراطية وتقديراتها حتى عام 2000(1976) بيرتا فهمى سعيدItem سكان جمهورية السودان الديمقراطية واختياجاتهم الغذائية حتي سنة الفين وطرق تدبيرها(1976) منى عبدالفتاح خليفةItem تطبيقات السلاسل الزمنية علي الايرادات النقدية لشركة الخطوط البحرية السودانية المحدودة في الفترة من 1974م الي 2001م(جامعة النيلين, 2002) هنادي عبداللهABSTRACT The research deals with "The Applications of Time series in the Financial Revenues of Sudan Shipping Line C0. in The Period 1974 to 2001 ". The research contains five chapters: the first one includes the problem of the research, its objectives, study hypotheses, frame of the study and prior studies. The Second Chapter devotes to the establishment and development of the company, its capital, fleet progress, operational and commercial development and the fleet building fund, also the Company strategic dimensions such as the Economical, Political, national Security and the Cultural dimensions. Beside that the local and international obstacles have been facing the Company up to now. In addition to the agreements, projects, financial performance and the situation of the Company loans had been achieved. The future plan include the integrated and specialized services projects. The current problems and the proposed solutions had been added. V ' The Third Chapter contains the definition of time series, its components such as the secular trend, seasonal, random and cyclical variations. Also, the importance of the time series analysis, its models, the secular trend estimation methods such as the graphic, semi — average, moving averages and the least squares methods. Also, this chapter devote to the correlation and determination coefficients and F, t tests. In addition to, the properties of estimator and finally the econometric problems. The fourth Chapter represents the results of the data analysis which is multi regression analysis. The fifth chapter, the last, deals with the conclusion and the recommendations. The references and appendixes are in the end of the research.Item تحليل السلاسل الزمنية لعلاقة الإصابة بالملاريا مع بعض العوامل المناخية والديمغرافية في السودان(2003) عواطف محمد النورABSTRACT This dissertation studies the relation between the lllt‘l(l€l‘lt‘t‘ of Malaria and weather indicators (temperature. relative humidity, rainfall and wind-speed) in addition to lllt number of population The study covers three different geographical areas which are the state of Khartoum, Gazira and the Northern tlLll'lllI‘ the time period of (1998-2002). The analyzed data of malaria eases were collected from hospitals (inpatients) monthly record and the influence ol the weather data was registered in meteorological publie corporation. The population data was collected from the Central Bureau of Statistics by using the transfer lunction models The research is constituted of an introduction about malaria sickness, the behavior of vector mosquitoes and the way ol data collection was exposed, as the numbers of incidence oi malaria, weather indicators and numbers of population. A statistical description of the variables of the study and the analysis of the data was conducted and the study ~. ame lt some important points which are as follows: Khartoum state is an endemic area of malaria lll which there is a progressive tendency in the numbei of malaria cases. The research through statistical analysis showed strong correlations bet\reen tht rainfall, population and the incidence of lllt malaria. Gezira state is depicted as a region in which malaria is an endemic disease. However, the analysis showed a decrease in number of the malaria cast->. in past years. The analysis shows that there is strong correlation between the climatic lactor.~- (rainfall, minimum of temperature and relati\-<- humidity) and the incidence of malaria. The analysis of data of the Northern state \'ll()\\'t'tl that it is not a malaria endemic region. l|'l\\'L‘\'t‘I through the analysis we get strong Co1'1't"latio1i,\ between climatic factors (minimum and maxinium of temperture) and the incidence of malaria.Item ARIMAالتحليل الإحصائى في السودان (1970 - 2001) بالتطبيق علي السلاسل الزمنية ونماذج(2003) بلقيس محجوب حسن باديAbstract. This Study deals with the analysis of Inflation in Sudan during period (1970-2001) applying Time Series and Autoregressive Integrated Moving Average (ARIMA) models ~ The Study is based upon the hypotheses that relationship between Inflation in the time t , Y, and before it t-I , Y,_| Y: Z 7~1Yi-1 + $1 under the assumption E [Q] = 0 E [e,es]=52e , if t=s = 0 , if tvé s E IQY:-ll = 0 The study tackled the analysis of Inflation by using the regression and ARIMA models analysis for estimating and forecasting the Inflation in Sudan - The Study concludes that : 1) The ARlMA(l,1,0) model , mh = —0.287AY,_1 , Is best model for forecasting the Inflation in Sudan - 2) The Inflation in the year 2002 had high rate - The Study recommends the following points : I) The work for constant Exchange price - 2) Opening new markets for Sudan foreign tradeItem 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 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.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 APPLICATIONS OF BANACH FIXED POINT THEOREM AND APPROXIMATION THEORY(Al-Neelain University, 2004) Moram Adam MohammedAbstract This dissertation consists of four chapters : In chapter one we present concept of fixed point and some examples of it and discusses the Banach fixed point theorem and some definitions in a metric space . The second chapter is devoted to applications of Banach fixed point theorem . In chapter three we present approximation in normed spaces and deals with problem of existence and uniqueness of best approximation . In last chapter we define the uniform approximation and present a brief introduction about approximation in Hilbert spaces and Chebyshev polynomials.الخلـصــــــــة هذه الرسالة تتكون من اربعة فصول : الفصل اللول: يقدم تعريـف للنقطـة الثابتــة لوبعـض المثلة عليها لويناقش مبرهنة باناخ للنقطة الثابتة لوبعـض التعريفات في الفضاء المتري . الفصل الثاني : مخصص لتطبيقات نظريــة النقطــة الثابتة لباناخ . الفصــل الثــالث : يقــدم نظريــة التقريــب علــي الفضاءات المنتظمة لويعالج مشكلة الوجــود لوالوحدانيــة للتقريب الحسن . الفصل الرابـع : يعــرف التقريــب المنتظــم لويقــدم مقدمــة مــوجزة عــن التقريــب فــي فضــاءات هلــبرت لوكثيرات حدلود تشيبشف .Item Applications Of Symmetry Methods to Differential equation(Al Neelain University, 2004) Sami H i gazi MustafaIn this research we utilize the symmetry condition of differential equations to solve some of these equations . Also we show how Lie algebra methods are much advanced for understanding and unifying all classical methods of solving differential equations . At the end of our research we discuss the variational methods and Euler — Lagrange equations on the light of symmetryItem Differntial Equations on Manifolds(جامعة النيلين, 2004) Nidal Hassan Elbadawi EljaneidA manifold is a topological space where any neighborhood of a point looks like an open set in a Euclidean space . Thus a diffeomorphism yields an equivalence relation such that two manifolds are not only topologically equivalent but also have equivalent differentiable structures . In this research we utilized Lie-group in solving differential equation The Lie-algebra will be determined by the tangent space T(G,e) at e and the action of G determines the values of the vector fields at any other point in G. One of the most appealing applications of Lie-group theory is to the problem of integrating ordinary differential equations, Lie's fundamental observation was that knowledge of a sufficiently . Large group of symmetry of the system of ordinary differential equation allows one to integrate the system by quadratures and thereby deduce the general solution. This approach unifies and significatly extends the various special methods introduced for integration of certain types of first order equation such as homogeneous , separable ,exact and so similar results hold for system of ordinary differential equation . Symmetry group can also be used to aid in the solution of higher order ordinary differential equation . تبحث هذه الدراسة في متعددة الجوانب والتي تعرف بأنها الفضاءات التبولولجيية التي تشبه فيها جوار أي نقطة مجاورة مجموعة مفتوحة في الفضاء الإقليدي . لذا فإن الأشكال الثنائية تعطي علاقة متساوية بحيث تكون ثنائية الجوانب متساوية تبولوجياً ولها تراكيب يمكن تفاضلها .تبحث هذه الدراسة في إستخدام زمـر (لي ) . تستخدم زمـر (لي) في حل المعادلات التفاضلية حيث تحدد (لي) جبرياً بالفضاء المماس والذي يعطي بالعلاقة T(G,e) حيث يحدد عمل G قيم مجال المتجهات عند أي نقطة بالنسبة لـ G . واحدة من التطبيقات المهمة لنظرية زمـر (لي) هي حل مسائل معادلات التكامل التفاضلي الاعتيادية حيث نجد أن واحدة من الملاحظات الأساسية لنظرية زمـر (لي) أن معرفة مجموعة كبيرة بما فيه الكفاية لمتناظرات نظام المعادلات التفاضلية الاعتيادية تسمح بحساب تكامل النظام بواسطة التربيع وبالتالي يمكن إيجاد الحل العام . هذه الطريقة تمتاز بأنها توحد وتوسع بصورة هامة المجالات الخاصة المتعددة التي تستخدم لتكامل بعض أنواع معادلات الدرجة الأولي مثل المتجانسة ، المنفصلة ، المحددة … الخ . ويمكن التوصل لنفس النتائج بالنسبة لمعادلات التفاضل الاعتيادية أيضاً حيث يمكن استخدام الزّمر المتناظرة للمساعدة في حل معادلات التفاضل الاعتيادية من الدرجة العليا.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 The Geometric Structure 0f Group Invariant Solutions Of Difierential Operators(Neelain University, 2005) Abdelgadir Ahmed Hammdan OmerAbstract Group invariant solutions have been used to a great effect in the description of the asymptotic behaviour of many general solution to systems of partial differential equations. The rigorous foundation of the general method for constructing group — invariant solution requires advanced formalism of differential geometry. From our point of view the Fibre bundle over a quotient manifold approach seems very promising in analyzing the mechanism of group-invariant solutions and classifying different types of behaviour of a system. In this research we shall explore the bundle over a quotient space approach. Our applications will are on some partial differential equationsItem 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 symmetry condition of algebraic and differential equations(Neelain University, 2005) mnahil mohammed bashierThis 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 ODEItem The Geometric Structure 0f Group Invariant Solutions Of Difierential Operators(Neelain University, 2005) Abdelgadir Ahmed Hammdan OmerAbstract Group invariant solutions have been used to a great effect in the description of the asymptotic behaviour of many general solution to systems of partial differential equations. The rigorous foundation of the general method for constructing group — invariant solution requires advanced formalism of differential geometry. From our point of view the Fibre bundle over a quotient manifold approach seems very promising in analyzing the mechanism of group-invariant solutions and classifying different types of behaviour of a system. In this research we shall explore the bundle over a quotient space approach. Our applications will are on some partial differential equations.Item symmetry condition of algebraic differential equations(Neelain University, 2005) mnahil mohammed bashierThis 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.Item Boundary Element Method For Porous Media Flow(Al Neelain University, 2005-07) Azhari Ahmed AbdallaThe focus point of this study is to develop BEM formulation to overcome the difflculties caused by nonlinearity and heterogeneity in the solution of partial differential equations governing the porous media flow .This dissertation consist of two major parts ,theory of BEM , and applications of BEM to two important fields of porous media ,water flow in aquifers and oil flow in reservoirs. The contribution done in the theory sections is mainly a mathematical derivation of the standard boundary element method for Lapiace's equation and the step by step formulation to the BEM , starting from its correspondence differential equation ,beside the developed form of BEM based on GEM and DRBEM that has presented. to handle both heterogeneous and nonlinearity. In the applications section a novel boundary integral solution was applied for determining : (1) Water table elevation in an unconfined homogeneous aquifer subjected to recharge and dewatering from a stream as well as fluctuations induced by constant and continuous recharge in a two stream unconfined-aquifer system. (2) Changes in water table exposed to a transient boundary condition and space- dependent recharge. This technique was compared with the closed form solution obtained in [111] and excellent results were obtained. (3) Characteristics of the flow through heterogeneous unsaturated porous aquifer . (4) Solution of reservoir engineering problems. This work adapted the most recent developments in boundary element methods to reservoir engineering problems. The transient pressure (diffusion) and convection- diffusion equations were solved in heterogeneous media using the Dual Reciprocity Boundary Element Method (DRBEM) and the Green Element Method (GEM). Numerical experiments showed that DRBEM is more accurate than a standard finite difference method. However like finite difference methods, DRBEM is subject to spurious oscillation at high Peclet numbers. DRBEM also requires the solution of a dense system of equations. GEM, which is a hybrid boundary elementlfinite element method, overcomes these disadvantages. The method was found to produce very accurate solutions to convection-diffusion problems and only shows small oscillations in the solution at very high Peclet numbers. A further important advantage is the sparse nature of the matrix system. GEM is also amenable to solving transient nonlinear problems, which makes it the basis for a new technique for multiphase flow simulation. This work explores the advantages of a hybrid boundary element method known as the Green element method for modeling pressure transient tests. Boundary element methods are a natural choice for the problem because they are based on Green's functions, which are an established part of well test analysis. The classical boundary element method is limited to single phase flow in homogeneous media. This works presents formulations which give computationally efflcient means to handle heterogeneity. Comparisons of the proposed Green element approach to standard finite difference simulation show that both methods are able to model the pressure change in the well over time. When pressure derivative is considered however the finite difference method produces very poor results which would give misleading interpretations. The Green element method in conjunction with singularity programming reproduces the derivative curve very accurately. Boundary element method was applied for solving Stokes flow equations on multi particle system. Also, the method is modified for estimating flow parameters for a specified porous media. A new method for the so/ut/‘an of the unsteady incompressible Navier-Sta/res equations was presentedItem SOLVING SOME PROBLEMS OF LINEAR ALGEBRA WITH COMPUTATIONS(Al Neelain University, 2005-07) ALI MOHAMED ABU OAMThis thesis provides a computational solution for some problems in Linear Algebra, giving many examples and applications. I considered the computational solution that depends on maple sofiware, version 9 which is distributed in June 2003. To deal with any math soltware, you have to use packages and commands to display results. A package is a collection of routines (and perhaps other data) that are collected together in some way. Typically a package provided a range of functionality for solving problems in some well-defined problem domain. The scope of a package may be quite wide or very small. The package must be writ- ten afier the " with " command, which is an interactive package management utilities. and is effective only at the top level. The packages which were used in this text are : O plots I is a graphics package. 0 linalg 1 is a linear algebra package based on array data structures. 0 Linear Algebra : is a linear algebra package based on rtable data structures. 6 The "rrab/e( )" function is the low level routine which is used by maple to build an array. a matrix and a vector. I student[LinearAlgebra]: is a subpackage from LinearAlgebra package which has three princ- ipals components : interactive, visualization and matrix computation Each package provided many commands to activate the functions that the package is based on. A command is a direct order for a certain problem to be solved. a command can be short or a long stat- ment. The command is in red ( input ), and the result is in blue ( output). To display the result, end the command's statement with a semicolon. otherwise end the statement with a colon. l explained each co- mmand in its location when it has been used.