DSpace Collection:http://hdl.handle.net/123456789/121062020-12-03T14:34:39Z2020-12-03T14:34:39ZThe Qeometry Of Space - timeMohammed Hassen Elzubairhttp://hdl.handle.net/123456789/153842020-01-08T13:11:54Z2007-01-01T00:00:00ZTitle: The Qeometry Of Space - time
Authors: 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 function to generate zero rest-
mass ﬁelds, where this function is formulated from both the
geometry and topology of Minkowski space2007-01-01T00:00:00ZSTOCHASTIC CONTROL PROBLEM WITH PARTIAL OBSERVATIONSHOYAM TAG ELDINhttp://hdl.handle.net/123456789/153812020-01-08T10:17:08Z2006-09-01T00:00:00ZTitle: STOCHASTIC CONTROL PROBLEM WITH PARTIAL OBSERVATIONS
Authors: HOYAM TAG ELDIN
Abstract: The 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.2006-09-01T00:00:00ZRidge Regression and the Multicollinearity ProblemTahani Ali Esmail Adamhttp://hdl.handle.net/123456789/138572018-12-05T12:56:33Z2016-02-01T00:00:00ZTitle: Ridge Regression and the Multicollinearity Problem
Authors: Tahani Ali Esmail Adam
Abstract: 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.2016-02-01T00:00:00ZGeometrical Reformulation of some Equations of Fluid MechanicsMansour Hassan Mansourhttp://hdl.handle.net/123456789/135962018-11-19T06:12:50Z2015-01-01T00:00:00ZTitle: Geometrical Reformulation of some Equations of Fluid Mechanics
Authors: Mansour Hassan Mansour
Abstract: 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.
Description: A thesis Submitted for the Degree of PhD
In Mathematics2015-01-01T00:00:00Z