PHD theses : Statistics
Permanent URI for this collectionhttps://repository.neelain.edu.sd/handle/123456789/12106
Browse
32 results
Search Results
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 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 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 Generalization on LP - Contractivity of Semigroups Commutators and C 0-Semigroups of Resolvent Estimates(Neelain University, 2008) Ria Hassan MohamrnedWe derive a pointwise estimate on the absolute difference between two corresponding diffusion kernels of two diffusion semigroups , as well as an L” —operator norm bound. We show that linear partial differential operators of order higher than two can not generate contraction semigroups on the Lebesgue space except for some fourth order operators in a restricted compact interval . We consider a comparison between two semigroups , a semigroup acting on scalar valued functions and a semigroup acting on vector valued functions . We give a sufficient condition for the criterion in the setting of square field operator. We also consider the essential self a djointness of a perturbed semigroup . We discuss the existence and the continuity of the boundary values problem on the Lebesgue space of the resolvent of a self — adjoint operator of the conjugate operator method . we allow the conjugate operator to be the generator of a Co —semigroup and that first commutator is not comparable to the self —adjoint operator . Strong application include the spectral theory of zero mass quantum field models are considered .Item Symmetric Spaces and Their Applications(Neelain University, 2007) Mohamed Alamin Abdalla HamidAbstract Syrnrnet:n'c spaces is a special topic in Riemannian geometry . These spaces werefirst studied and classified by Elie Cartan . _ In this research we study in a logical ordering their snucture through manifolds , Lie groups , Lie algebras and basics of Riemannian geometry. _ The study covers locally and globally symmetric spaces , endowed with some examples for them such as Euclidean spaces , spheres hyperbolic spaces and some applications on locally syrrunetric spaces in the field of arithmetic and algebraic groups , including quadratic and modular fonns , lattices , the realization of discrete series representations of groups , Poincare and linear symmetric spaces . Their classification is also discussed by introducing compact and noncompact symmetric spaces besides the types ( l , ll , Ill , IV ) . This classification is carried through Lie algebras , root systems and their Dynkin diagrams . The aim of the research is to display in a simplified manner the connection between symmetric spaces and the differential geometric temis such as manifolds , Lie groups , Lie algebras and basics of Riemannian geometry with some of the applications of symmetric spaces.Item An Appraisal of the Educational Statistical System of the Sudan(Neelain University, 2006) Abbas Ali AAMIRAbstract The Thesis is about improvement of the current educational statistical system. It concentrates on the deficiencies and shortcomings inherent in the present system and on ways and means of their alleviation and improving their contents. A good statistical database will help education authorities to assess the well-being of the system and to pinpoint areas of weaknesses. Thus, it would help to layout policies for possible remedies and improvements. This can better be done through calculation of comparative educational indicators and by building of models that single out variables or factors that have significant effects on the progress of the educational system as a whole. Impoltant indicators are defined and ways of calculating them are shown with illustrative examples that are based on the currently existing data. Limitations of the currently available educational data rendered it unattainable to calculate other important indicators. However, the purpose of an indicator is to characterize the components of a system: how they are related and how they change overtime. Indicators are descriptive tools that do not have the ability to measure the significance of the changes that they reflect. Indicator systems, however, unlike a single indicator measure distinct components of the system and provide information about how the individual components work together to produce the overall effect. Models are more efficient means of testing real variations. While expectations from social indicators are generally modest and, hence, can not substitute for a well designed, in-depth evaluations of social programs, models do the job. They give scientifically verifiable information about the different variables that are contained in them. Data collected should cover the complex variables that compose and interfere with the educational process and that are essential elements to be included in the planned models. There are different methods of data collection that can be used to suit the planned goals. Besides full coverage which, like all censuses, is limited in scope of coverage, other means of data collection like sample surveys, experimentation and case study evaluations can be applied wherever suitable. The World Conference on Education For All of 1990 and its assessment of Sub-Saharan Africa has urged the necessity of the establishment of National Educational Statistical Information Systems NESIS in all countries of Sub-Saharan Africa. Details of the findings of that conference with-respect-to NESIS program are included in the thesis with an illustration of the experience of Zambia in applying that program. Our educational system has gone through a multiplicity of changes in size, curriculum, policies and in economic, political and social conditions. The educational statistical system should be able to supply a wide variety of data that enables researchers to study the effect of those changes on the educational process. Examination results tell a lot about the quality of education students get and about the attainment of students from that education. Examinations usually comprise a number of components which may vary in the importance of their contribution to the final assessment of the students’ academic achievement. A weighting system is thus sometimes introduced on the examination results to give more weight to some components that are considered more effective in infonning about the educational attaimnent of a student. It is also sometimes introduced for reasons the examiners think are justified by the findings of those particular examination results. Certain weighting methods are provided and discussed in the thesis and the formulae for a scientifically verifiable weighting system is discussed in detail. But the practice in the final assessment of the Secondary School Certificate’s examination results of Sudan seems to differ from what has been originally meant by the introduction of the aforementioned weighting procedures. Those results were analyzed in detail throughout the years 1993-2001 for two components, Mathematics and English, being normally hypothesized to be the weakest areas of the students’ educational attaimnent. This comparative statistical analysis reflected that, rather than an introduction of a verifiable weighting system, the actual marks attained by the candidates were in fact seemingly adjusted to cover up the apparently weak student attainment. The true examinations results are one mean for the education system to hold itself accountable for whatever weaknesses that occur and remedy them in the best way it can afford putting in mind the known limitations of the economic conditions of the country.Item Thethory of vanianalsymmetry Qroup and Conservationlawsa(Neelain University, 2007)Abstract In this research we talk about symmetry of D.E"‘ via symmetry of variation and we write the variation by modern methods 0lD.E"‘. So we utilize methods of global analysis such as differential geometry . ln this research we introduce the theory of fiber bundles .We give application ol" fiber bundles : Gauge theory and variational principles .Als0 we formulate Euler — Lagrange equations by three methods ( without coordinate ) our treatment is global since we employed fiber bundle formulation .Item A CONTRIBUTION TO RISK AND DECISION ANALYSIS OF PETROLEUM EXPLORATION(Neelain University, 2006) Hala Abbas BedawiAbstract In this study the problem specifications are as follows: 1) Assessment of the factors of risk in petroleum exploration. 2) Evaluation of the geological risk. 3) Estimating prospect reserves. 4) Utilization of the probability of geological risk and the results of estimating prospect reserves in the decision making for drilling. ln petroleum exploration the basic concept in assigning risk for the geologic factors is contraverse; therefore, the subjective probability is used to assess the factors which are independent thus; the multiplication rule of probability is used to evaluate the geological risk. The prospect reserves distribution being a lognormal distribution, is estimated by finding out first the mean and variance of all the reserve parameters in the prospect reserves. In our study two methods were explained for finding the mean and variance of the reserve parameters: 1) Swanson's 30-40-30 rule. 2) Three-point method Since the prospect drilling is too expensive, and to avoid the loss if a dry hole is resulted, one can use the decision tree initially to decide whether to drill or not. The calculation of prospect reserve will be illustrated by the use of worksheet from one of the Sudanese Petroleum Companies.