PHD theses : Statistics

Permanent URI for this collectionhttps://repository.neelain.edu.sd/handle/123456789/12106

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2011 - 201612

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Start date: 2011End date: 2016

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Now showing 1 - 10 of 12
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    Ridge Regression and the Multicollinearity Problem
    (Al Neelain University, 2016-02) Tahani Ali Esmail Adam
    This research primarily aims at evaluating the performance of the ridge regression estimators as remedial techniques to the multicollinearity problem. The study is based on Monte Carlo experiments in which the performance of ridge estimators is investigated under different levels of multicollinearity, population variance & sample size. A new method suggested by the author and based on using a variable biasing constant with values proportional to the variances of the estimates of the regression coefficients led to great improvement in the performance of the ridge estimate. This weighted estimator resulted not only in increased precision of the regression estimate compared to the unweighted estimate, but also worked as a controlling factor to the mean squares of the regression estimates when these explode at large values of biasing constants. The thesis also reviews in detail the performance of the weighted & unweighted ridge regression estimators under varying levels of sample size, population variance & degree of linear correlation. It also examined the effect of linear correlation under different levels of variance & sample size on the ordinary regression estimates. A value of the biasing constant of 0.1 appeared to be a dividing line for the mean square of the ridge regression estimates as it explodes greatly after it if weighing is not used. Hence the author recommended that weighted estimates should be used for biasing factor greater than 0.1 as well as when the independent variables differ greatly in their variances.
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    Geometrical Reformulation of some Equations of Fluid Mechanics
    (Neelain University, 2015) Mansour Hassan Mansour
    Abstract The aim of this thesis is to explain some of the connections between fluid mechanics and differential geometry and to shed light on formulation of classical fluid mechanics in a differential geometric language. The thesis presents a reformulation of some of the most basic entities and equations of fluid mechanics, the continuity equation and the momentum equation of motion, in a modern differential geometric language using calculus of exterior differential forms on manifold (exterior calculus). Also, the study investigates the integrability of some fluid problems from geometrical perspective, with particular attention to the Eulefequations of motion.
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    The Formulation Of Equivalence Problems And Its Application
    (Neelain University, 2014) Runda Abdalhafiz Abdelrhim . Bashir
    Abstract In this research we considered Cartans equivalence problem . We defined the concept of equivalence and illustrated that by several cases . We introduced the equivalence problem for Coframs and then used Cartans equivalence method to determine whether two differential operators are equivalent , we also handle the classification problem of Lie algebras, ln particular we treated the case of semi-simple Lie algebras.
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    Geometrical Analysis of Differential Operator Theory on Complex Manifolds
    (Neelain University, 2011) Riyad Mohammed Ibrahim
    Abstract In this research we have used the theory of classification of Fiber bundles and Atiyah-Singer index theorem to study the geometrical and topological properties of differential operator on complex manifolds. Of particular interest is Dirac equation and the generalized global form of Laplace equation. We have also treated the index of De Rham complex that generalizes the Gauss-Bonnet theorem. Our point of view in this treatment is that the De Rham complex represents only one possibility of other complexes that describe differential operators. These geometrical complexes include spin complex which give the moduli space of Dirac equation. All these concepts are related by the topological index of the operator. .
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    ciphring with elliptic curves
    (Neelain University, 2011) Maha Toufig Fadle Elseid
    ABSTRACT This research deals with different operations of encryption These are illustrated using elliptic curves where a program for this operation is used to embed a message in an elliptic curve and convert it to a point, so as to encrypt/decrypt the message. This is illustrated by finite field of order p(where p is a prime number).The message is embed in an elliptic curve and transformed as a point and then, encrypt/decrypt it. A program is designed to do this operation using Java Programming and in particular Java Biglnteger to make it more difficult
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    Numerical solution of poisson equation using pascal language
    (Alneelain University, 2013) Nada Osman Hassan
    An Introduction :- Numerical solution isto be considered as one of the modem methods in solving the partial differential equations. This method of numerical solution has provided only With the spreed of computers which contributed to reflect its importance, and helps in accuracy and speed in solving this type of equations which can not be solved manually. The researcher has classified the topic into three categories where as the firest has the following title : the numerical solution for the partial deferential equation which consists of the concepet and difinition of the partial defferential equations and also some models of the method to solve any mathemetical problem with the definition of any linear equations.The second categories is titled as : the classification of partial differential equations of the second degree ,which involves the transforming the partial differential equations to ordinary ones by using Taylor formular and also using some of the numerical methods in solving the equations such as difference quotients. This section also consists of aphysical example for apartial differential equation .The third category titled as algorithms which involves poissons algorithms, laplac algorithem,each of the aforementioned algorithms has aproblem and the applicable problem for the solution using pascal problem language in writing the prblem.
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    Mathematics '
    (Alneelain University, 2014) Mohammed Hassen Elzubair
    Abstract In 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 filnction to generate zero rest- mass fields, where this function is formulated from both the geometry and topology of Minkowski space
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    Some Harvesting Problems
    (Alneelain University, 2015-07) Ranya Hamid El Nour
    ABSTRACT. The aim of this thesis is to study and solve optimal control problems for systems driven by both: Brownian motion and Levy processes. The methods of solution used are: Dynamic programming, and Maximum principle where the known Clark-Ocone theorem is applied. The application of Clark-Ocone theorem needs the existence of Malliavin derivative and its extesion in L2 spaces. As an application , the thesis considered an example of harvesting problem in a crowded media as well as searching for optimal portfolio strategies in hedging options in markets driven by both: Brovmian motion and Levy processes.
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    The Technical Efficiency of Wheat Growers in the Gezira Scheme: An Econometric Model
    (Neelain University, 2012) Fuad Saeed Yousif Saad
    ABSTRACRT The objectives of this study briefly were to examine the technical efficiency of the tenant farmers of wheat in the Gezira Scheme, and to investigate the causal factors explaining this efficiency in the scheme, and hence draw conclusions and recommendations to be considered by the management and policy-makers. The technical efficiency of the ith tenant farmer is defined in terms of the ratio of his mean production to the corresponding mean production if the farmer effect is zero. The scope of this thesis was limited to an analysis of data collected from selected sample of tenant farmers in an attempt to investigate the technical efficiency of the wheat producers in relation to the economic and socio-cultural complex in which tenant live and make decisions. A stochastic frontier production function is used to estimate the technical efficiency of the wheat tenant farmers in the Gezira Scheme. A frontier production function of Cobb-Douglas type is specified for panel 1 data. The number of observations on the different farmers needs not to be the same. Estimates of the productive efficiency of individual tenant farmers are found to be very low, ranging between 0.274 and 0.713, and the bulk of them- about 52 percent- scored a rate of technical efficiency less than or equal to 0.400. Many factors contributed to this low rate of productive efficiency, among which it seems that management and polices are of significant role.
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    Optimality Problem of Portfolio in an Incomplete Markets
    (Al Neelain University, 2015-07) Budoor Mohammed Abd Elati
    The main objective of this thesis is to study the optimal portfolio problem in incomplete markets. The problem of finding such optimal ponfolio is of connection to solve partial differential equations corresponding to the infinitesimal generator of the process describing the risky assets in the given markets.Is the method used to find the solution of the a rising partial differential equation is a viscosity concept .As an application for finding optimal portfolio a consumption problem is considered. Due to the incompleteness of the markets they the problem is challenging because the best strategy We aim will not be perfect.