Department of Mathematicshttp://hdl.handle.net/11394/812023-12-09T18:56:16Z2023-12-09T18:56:16ZConjugacy classes of some projective linear groupsDietrich, Ernest Athurhttp://hdl.handle.net/11394/105082023-11-03T00:04:01Z1992-01-01T00:00:00ZConjugacy classes of some projective linear groups
Dietrich, Ernest Athur
Given a finite set X of distinct symbols the symmetric group S* and the alternating group A* are obtained without further constructions. More interesting groups are contrived, however, by imposing a certain structure on the set X and observing the subgroups formed by those elements of S* that preserve this structure. In this thesis, we concern ourselves with one such imposition viz. that defining the notion of
a finite projective plane. We look at the different subgroups of S* arising in this manner, with particular emphasis on the projective linear groups and their action on the projective plane. We conclude this work with a detailed study of the structure of the projective linear groups
of orders 168 and 5616, respectively. Of particular interest to us are the distinct conjugacy classes of these groups, and the manner in which they relate to one another, within each particular group.
>Magister Scientiae - MSc
1992-01-01T00:00:00ZComputation of the character tables of certain group extensionsJames, Chttp://hdl.handle.net/11394/103482023-06-27T00:02:19Z1997-01-01T00:00:00ZComputation of the character tables of certain group extensions
James, C
In this chapter some basic theory on group extensions is first given in section 1.1 and then a method for finding the conjugacy classes of group extensions is described in section i.2. In section 1.3 we look at an example due to Whitley[ 19 ] to illustrate how the theory developed in section 1.2 is used to calculate the conjugacy classes of the group 23 : GLs(2). For section 1.1 , the books by Rotman[l7] and Gorenstein[8] were used as references while for section 1.2 we used the works of Whitley[l9], Moori[15], Moori and Nlpono[16] and Salleh[18].
>Magister Scientiae - MSc
1997-01-01T00:00:00ZMathematical epidemiology of malaria disease transmission and its optimal control analysesOare, Okosun Kazeemhttp://hdl.handle.net/11394/103342023-06-23T00:02:12Z2010-01-01T00:00:00ZMathematical epidemiology of malaria disease transmission and its optimal control analyses
Oare, Okosun Kazeem
In this thesis, we present and analyse an SEIR (susceptible-exposed infectious-recovered) model for malaria disease transmission. The model consists treatment and control strategies such as the use of bed nets and spray of insecticides with the costs associated with each control measure. Firstly, we analyse the model without treatment and investigate its stability and bifurcation behaviour. Then, we incorporate treatment and investigated the effects of different control strategies on the spread of malaria. Further, we use optimal control methods to determine the necessary conditions for the optimality of the disease eradication or control. We determined the most cost-effective strategies in fighting malaria disease by carrying out a cost-effectiveness study. We found that mass action model exhibited transcritical bifurcation. The disease-free equilibrium (DFE) is globally stable whenever, basic reproductive number is less than unity, while the models with standard incidence form exhibited backward bifurcation. In examining the cost-effectiveness analysis, we found that the most cost-effective strategy is the combination of insecticides spray and treatment of infective individuals. Furthermore, we modified the SEIR model to incorporate treatment and vaccination with waning immunity and an appropriate cost function. We analyse the model and investigated its stability and bifurcation property. Also, we use optimal control theory to determine the necessary optimal conditions for the disease eradication, and when eradication of the disease is unachievable, we derived the necessary conditions for its control. Further, we carried out a cost-effectiveness analysis of the control strategies. In our findings, the mass action model exhibits a backward bifurcation phenomenon, while the standard incidence model exhibited a phenomenon of multiple endemic equilibria. We also found that the most cost-effective strategy to eliminate malaria is the combination of treatment of infective individuals and vaccination. From the analysis, we found that eradication will be possible and optimal when the community marginal cost is less than the community marginal benefits.
Doctor Scientiae
2010-01-01T00:00:00ZSingular integral equations and realization: A survey of the state space methodGantsho, Yolanda Vuyokazihttp://hdl.handle.net/11394/103222023-06-22T00:02:24Z1996-01-01T00:00:00ZSingular integral equations and realization: A survey of the state space method
Gantsho, Yolanda Vuyokazi
Different methods for solving singular integral equations exist. One of the most recent methods is the so-called state space method. This method is based on the fact that a rational matrix function VV(^) which is analytic and invertible at infinity can be represented by
vv(^): D * C(AI - A)-'B, (0.1) where A is a square matrix whose order may be larger than that of I,7()), and .8. C and D are matrices of appropriate sizes. The representation (0.1) allows one to reduce analytic problems about rational matrix functions to linear algebra ones involving constant matrices, and often it provides explicit and readily computable formulas for the solutions. In the last fifteen years the state space
approach has proved to be effective in solving various problems of mathematical analysis (see the survey paper [BGK3]). In this mini-thesis we employ the state space method to solve singular integral equations. These equations serve as a tool to solve problems in numerous fields of application. For the general theory and examples of applications (see, for instance, [GKr], [M] and [V]).
Doctor Educationis
1996-01-01T00:00:00Z