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Distance measures in graphs
No full textThis thesis details the results of an investigation of bounds on four distances measures,
namely, radius, diameter, the Gutman index and the edge-Wiener index, in
terms of other graph parameters, namely, order, irregularity index and the three
classical connectivity measures, minimum degree, vertex-connectivity and edgeconnectivity.
The thesis has six chapters. In Chapter 1, we de ne the most important terms used
throughout the thesis and we also give a motivation for our research and provide
background for relevant results. In this chapter we include the importance of the
distance measures to be studied.Chapter 2 focuses on the radius, diameter and the degree sequence of a graph. We
give asymptotically sharp upper bounds on the radius and diameter of
(i) a connected graph,
(ii) a connected triangle-free graph,
(iii) a connected C4-free graph of given order, minimum degree, and given number
of distinct terms in the degree sequence of the graph.
We also give better bounds for graphs with a given order, minimum degree and
maximum degree. Our results improve on old classical theorems by Erd os, Pach,
Pollack and Tuza [24] on radius, diameter and minimum degree.In Chapter 3, we deal with the Gutman index and minimum degree. We show that for nite connected graphs of order n and minimum degree , where is a
constant, Gut(G) 24 3
55( +1)n5 +O(n4). Our bound is asymptotically sharp for every
2 and it extends results of Dankelmann, Gutman, Mukwembi and Swart [18]
and Mukwembi [43], whose bound is sharp only for graphs of minimum degree 2:
In Chapter 4, we develop the concept of the Gutman index and edge-Wiener index in
graphs given order and vertex-connectivity. We show that Gut(G) 24
55 n5 +O(n4)
for graphs of order n and vertex-connectivity , where is a constant. Our bound
is asymptotically sharp for every 1 and it substantially generalizes the bound
of Mukwembi [43]. As a corollary, we obtain a similar result for the edge-Wiener
index of graphs of given order and vertex-connectivity.Chapter 5 completes our study of the Gutman index, the edge-Wiener index and
edge-connectivity. We study the Gutman index Gut(G) and the Edge-Wiener index
We(G) of graphs G of given order n and edge-connectivity . We show that the
bound Gut(G) 24 3
55( +1)n5 + O(n4) is asymptotically sharp for 8. We improve
this result considerably for 7 by presenting asymptotically sharp upper bounds
on Gut(G) and We(G) for 2 7.
We complete our study in Chapter 6 in which we use techniques introduced in
Chapter 5 to solve new problems on size. We give asymptotically sharp upper
bounds on the size, m of (i) a connected triangle-free graph in terms of order, diameter and minimum
degree,(ii) a connected graph in terms of order, diameter and edge-connectivity,
(iii) a connected triangle-free graph in terms of edge-connectivity, order and diameter.
The result is a strengthening of an old classical theorem of Ore [49] if edge-connectivity
is prescribed and constant
On the Fundamental Origins of the Dirac Equation
No full textDespite its great success in explaining the physical world as we know it, the fundamental origins of the Dirac equation remains for the most part, enshrouded in deep mystery. What are the fundamental origins of this beautiful equation? To begin with, why does this equation exist and what does it tell us about the nature of spacetime or the World? Professor Dirac’s derivation of requiring that there exists a first order differential equation which upon ‘squaring’ reproduces the Klein-Gordon equation by no means offers any real and tangible clue as to its reason for existence. At best, Professor Dirac’s derivation is an agile, prudent, very wise and esoteric guess that led to an equation with a direct correspondence with experience. This reading makes the modest endeavour to unlock the fundamental origins of the Dirac equation from the vantage-point of a proposed Unified Field Theory whose succinct exposition we give herein
Dirac equation for the proton (I) -- Why three quarks for muster mark?
No full textPublished Article,The present reading is the first in a series where
we suggest a Dirac equation for the Proton. Despite its great
success in explaining the physical world as we know it, in its
bare form, not only is the Dirac equation at loss but fails to
account e.g. for the following: (1)Why inside hadrons (Proton
in this case) there are three, not four or five quarks; (2)
Why quarks have fractional electronic charges; (3) Why the
gyromagnetic ratio of the Proton is not equal to two as the
Dirac equation requires. In the present reading, we make an
attempt to answer the first question of why inside the proton,
there are three, not four or five quarks
Exploring the causes of low conviction rates in teenage and adult rape cases
No full textThis dissertation explores the response of the criminal justice system in particular the
courts to teenage and adult rape cases. Trial practices are as a result investigated through court observations, perusal of court records as well as discussions and interviews with key players at the courts. These provided an insight into what actually takes place at courts as well as addressing the gaps identified. The potential effect of negative perceptions by magistrates and prosecutors towards teenage and adult victims of rape is considered as well as how these negatively impact on the outcome of such cases. The laws in regard to rape cases in Zimbabwe are also looked at as well as the extent to which these are effectively implemented in our courts. The author of this dissertation who is also a player within the criminal justice system goes on to provide potential measures to address the gaps within the system based on the findings of this study.,NORA
An empirical investigation of foreign aid effectiveness in reducing poverty in some selected SADC countries: 2005-2013
No full textHistorically, aid flows from the developed to developing countries have been economically
justified for reducing poverty either through directly targeting the poor or indirectly via
economic growth. This present study investigates whether or not aid has produced the
anticipated results in 12selected SADC countries using panel data analysis covering a period
of nine years (2005-2013). The variable of choice for measuring aid effectiveness in reducing
poverty in this present study is the human development index (HDI), a non-monetary poverty
measure. Overally, the study finds thataid has a negative and no significant impact on poverty
reduction, supporting the works of the public choice hypothesis. The negative and
insignificant results could beexplained by aid misallocation, misuse and lack of absorptive
capacity by recipient countries. Secondly for the analysis of how aid can be made more
effective in reducing poverty, empirical evidence suggests that institutional quality, control of
corruption and trade openness are vital for aid effectiveness. Economic growth and trade
openness have been found to be necessary conditions for poverty reductio
Quality delivery service as a strategy: Profile and perspectives for excellence achievement within OPRAG
No full textConference Paper,The use of human experiments in operations management is still fairly novel despite a small stream of publications (Bendoly, Donohue and Schultz, 2005). Hence, this study was conducted with the ultimate interest of advancing research and knowledge in OM with an empirical contribution and, therefore, to foster the quick attainment of the goals set to OPRAG as a Port Authority in Gabon with a major challenge of modernisation of port facilities.
The author attempts to share findings of this experience, particularly on how to elaborate,formulate and implement a winning strategy which will serve the pivot for and lead the OPRAG‟s management of operations to the excellence
Arguments for an appraisal linguistic discourse approach to the analysis of `objectivity' in 'hard' news reports
No full textStudies focusing on the ideal of 'objectivity' in *hard' news reports are numerous, with most of them within journalistic studies and theorised from diverse theoretical insights. This article departs from journalistic to a linguistic discourse approach-presenting evidence that the linguistic discourse analytical framework of Appraisal Theory provides alternative ways of analysing 'objectivity' and ideological bias in 'hard' news reports. Couched in Systemic Functional Linguistics (SFL) Appraisal is a model that explains the way(s) in which language construes attitude and enables writers and speakers to position themselves evaluatively with
respect the viewpoints of potential respondents and other speakers/writers (White, 2007: Thomson. White and Kitley, 2008). The paper argues that the analysis of the construction of journalistic reality can also be adequately done from a linguistic perspective, specifically from analysing how lexical choices journalists make betray their ideological positioning both in terms of the content as well as context of the news report. In discussing this, the paper comparatively analyses two news reports in two Zimbabwean newspapers on the death of Retired General Solomon Mujuru
Effectiveness of podcasting in water, sanitation and hygiene (WASH) education: a case of Bindura town
No full textThe world particularly developing countries such as Zimbabwe have continued to experience recurrent water and sanitation related diseases outbreaks despite efforts by various governments and Non-Governmental Organisations (NGOs) to educate community. In Bindura, in 2015 Practical Action Southern Africa has used podcasting technology to raise WASH awareness and improve the relationship between residence and municipality with the aim of reducing the burden of diarrhoeal diseases. This study seeks to assess the effectiveness of podcasting in raising WASH related awareness in Bindura with the aim of reducing the burden of diarrhoeal diseases. The project assesses WASH behaviour practise and knowledge at project inception and at project end. Focus Group Discussions and key informant interviews were used to collect
information on WASH behaviour change as a result of hygiene session through podcasting. It was observed that after six months of WASH education on various topics through the use of podcasting, health clubs members could now articulate how to prevent ailments and how to deal with them in the event they occur. Most of the club members were also now practicing improved waste management. Messages received through podcasting helped to improve hygiene practices at individual and home level. Signs of hygiene practice were seen around the home surroundings, bathrooms, kitchens and gardens. Health club members together with family members now wash their hands before engaging in any activity for example before eating and after visiting the toilet. Washing of hands using soap has now become a habit to many. Participants are no longer using the traditional method of washing hands in one dish. Use of jugs, soap and running water is now in use. In conclusion therefore, it is evident that podcasting improves WASH behaviour practise. Municipality and stakeholder need to support community effort to obtain WASH knowledge
