Department of Mathematics
http://ugspace.ug.edu.gh/handle/123456789/4860
20200530T09:18:11Z

Mathematical Models for a 3D Container Packing Problem
http://ugspace.ug.edu.gh/handle/123456789/34838
Mathematical Models for a 3D Container Packing Problem
Ocloo, V.E.
We address the single container packing problem of a company that has to serve its
customers by first placing the products in boxes and then loading the boxes into a
container. We approach the problem by developing and solving mixedinteger linear
models. Our models consider geometric constraints which feature nonoverlappping
constraints, box orientation constraints, dimensionality constraints, relative packing
position constraints and linearity constraints. We also consider extension of the models
by integrating load balance as well as deviation of the center of gravity. The
models have been tested on a large set of real instances involving up to 41 boxes and
obtaining optimal solutions in most cases and very small gaps when optimality could
not be proven.
MPhil. Mathematics
20190601T00:00:00Z

Lie Groups, Lie Algebras and some applications in Physics
http://ugspace.ug.edu.gh/handle/123456789/34762
Lie Groups, Lie Algebras and some applications in Physics
Dzikpor, D.N.
Given a Lie algebra g and its complexi_cation gC; the representations of gC are isomorphic
to those of g. Moreover, if g is the corresponding Lie algebra of a connected
and simply connected Lie group G then the representations of the Lie group in question
are isomorphic to those of gC. This thesis explains the basic concepts of Lie
groups and Lie algebras. Further, the basic representation theory of Lie groups and
Lie algebras, particularly those of semisimple Lie algebras is discussed. In addition,
an exposition of a method of constructing induced representations, with the particular
case of the PoincarĂ© group and an application in Physics is given. Finally, some
physical applications of Lie groups and Lie algebras are outlined and discussed.
MPhil. Mathematics
20190701T00:00:00Z

Tracking pollutants using Lagrangian Coherent Structures.
http://ugspace.ug.edu.gh/handle/123456789/27481
Tracking pollutants using Lagrangian Coherent Structures.
Amengor, C.M.
In steady flows, the notion of boundaries separating dynamically distinct regions is
not ambiguous. This is because the invariant manifolds of timeindependent flows and
the critical points of timeperiodic flows provide adequate information to determine
the behaviour of the solutions of these systems. However, for time dependent systems,
it is strenuous to determine the nature of their solutions due to their dependence on
time. Nevertheless, it was observed that just like steady flows, most timedependent
systems have boundaries that prevent crossmixing of dynamically distinct regions.
They are known as Lagrangian Coherent Structures(LCSs) and they are embedded
in timedependent flows as robust structures that determine the flow pattern of fluid
particles.
This project investigates LCSs and also employs a numerical method to compute the
Finite Time Lyapunov Exponent to detect these structures. Initially, the coherent
structures are defined as hyperbolic material lines that separate dynamically distinct
regions in an unsteady flow. Then, the LCSs are classified into attracting and repelling
structures based on their in_uence on the timedependent flow. Subsequently,
the LCSs are also defined as a second derivative ridges of the FTLE fields. This defi
nition is perceptible from the numerical computations of the doublegyre model where
the coherent structures are extracted as ridges of the computed FTLE fields. Furthermore,
we employ the Finite time Lyapunov Exponent model to carry out numerical
simulations on satellite observed surface velocities along the coast of Ghana. The aim
of this realistic application is to determine the Lagrangian Coherent Structures that
are formed in geophysical flows. Finally, based on these results, we hypothesize the
implications of a crude oil spill along the coast of Ghana. It was realized that in the
event of a spill, the oil is likely to be confined to the coast temporarily due to the concentration of repelling LCSs. Also, for a longer time interval the oil spill is likely
to be advected from the coastline.
MPhil.
20180601T00:00:00Z

On The Geometric View Of Pentagram Integrals Of Polygons Inscribed In NonDegenerate Conics.
http://ugspace.ug.edu.gh/handle/123456789/26569
On The Geometric View Of Pentagram Integrals Of Polygons Inscribed In NonDegenerate Conics.
Opoku, G.E.
The Pentagram map is a well notable integrable system that is de_ned on the moduli
space of polygons. In 2005, Richard Evan Schwartz introduced certain polynomials
called pentagram integrals (Monodromy invariants) of the pentagram map and
de_ned certain associated integrals, the analogous _rst integrals. Schwartz further
studied in 2011 with S. Tabachnikov on how these integrals behave on inscribed
polygons.
They discovered that the integrals are equal for every given weight of polygons inscribed
in nondegenerate conics. However, the proof of their outcome was combinatorial
which appeared to be more involving hence there was a need for quite a simple
proof.
Anton Izosimov in 2016 gave quite a simple conceptual geometric proof of these
invariants of polygons inscribed in nondegenerate conics.
In this thesis, we seek to analyse the geometry of these invariants by reviewing Anton's
work. Our core analyses is that for any polygon inscribed in a nondegenerate conic,
the analogous monodromy should satisfy a certain selfduality relation.
MSc.
20180701T00:00:00Z