Magister Scientiae - MSc (Mathematics and Applied Mathematics)
http://hdl.handle.net/11394/82
Thu, 22 Apr 2021 10:07:55 GMT2021-04-22T10:07:55ZBoundedness and pseudocompactness in pointfree topology
http://hdl.handle.net/11394/7848
Boundedness and pseudocompactness in pointfree topology
Alderaz, Fatma Hussien Shbani
This dissertation is a presentation to generalize boundedness and pseudocompactness
in pointfree topology. We rst obtain and introduce a boundedness
notion for elements of a frame. This is then further inspiration to introduce a
de nition of bounded frame homomorphism whose domain may be any frame
E, not just the frame of open sets of the reals.
>Magister Scientiae - MSc
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11394/78482019-01-01T00:00:00ZEstimating the cost of deposit insurance for a commercial bank following an optimal investment strategy
http://hdl.handle.net/11394/7845
Estimating the cost of deposit insurance for a commercial bank following an optimal investment strategy
Matamba, Itani
Commercial banks play a dominant role in facilitating the economic growth of a country by acting
as an intermediary between the de cit spending unit (borrowers) and the surplus spending
unit (lenders). In particular, they transform short-term deposits into medium and long-term
loans. Due to their important role in the economy and the nancial system as a whole, commercial
banks are subject to high regulation standards in most countries. According to an
international set of capital standards known as the Basel Accords, banks are required to hold
a minimum level of capital as a bu er to protect their depositors and the nancial market in
an event of severe unexpected losses caused by nancial risk. Moreover, government regulators
aim to maintain public con dence and trust in the banking system through the use of a deposit
insurance scheme (DIS). Deposit insurance (DI) has the e ect of eliminating mass withdrawals
of deposits in an event of a bank failure. However, DI comes at a cost. The insuring agent is
tasked with estimating a fairly priced premium that the bank should be charged for DI.
>Magister Scientiae - MSc
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11394/78452020-01-01T00:00:00ZThe paradox of enrichment in predator-prey systems
http://hdl.handle.net/11394/7737
The paradox of enrichment in predator-prey systems
Sogoni, Msimelelo
In principle, an enrichment of resources in predator-prey systems show prompts
destabilisation of a framework, accordingly, falling trophic communication, a phenomenon
known to as the \Paradox of Enrichment" [54]. After it was rst genius postured by
Rosenzweig [48], various resulting examines, including recently those of Mougi-Nishimura
[43] as well as that of Bohannan-Lenski [8], were completed on this problem over
numerous decades. Nonetheless, there has been a universal none acceptance of the
\paradox" word within an ecological eld due to diverse interpretations [51].
In this dissertation, some theoretical exploratory works are being surveyed in line with
giving a concise outline proposed responses to the paradox. Consequently, a quantity of
di usion-driven models in mathematical ecology are evaluated and analysed.
Accordingly, piloting the way for the spatial structured pattern (we denote it by SSP)
formation in nonlinear systems of partial di erential equations [36, 40].
The central point of attention is on enrichment consequences which results toward
a paradoxical state. For this purpose, evaluating a number of compartmental models in
ecology similar to those of [48] will be of great assistance. Such displays have greater
in
uence in pattern formations due to diversity in meta-population.
Studying the outcomes of initiating an enrichment into [9] of Braverman's model,
with a nutrient density (denoted by n) and bacteria compactness (denoted by b)
respectively, suits the purpose. The main objective behind being able to transform [9]'s
system (2.16) into a new model as a result of enrichment. Accordingly, n has a logistic-
type growth with linear di usion, while b poses a Holling Type II and nonlinear
di usion r2 nb2 [9, 40].
Five fundamental questions are imposed in order to address and guide the study in
accordance with the following sequence:
(a) What will be the outcomes of introducing enrichment into [9]'s model?
(b) How will such a process in (i) be done in order to change the system (2.16)'s stability
state [50]?
(c) Whether the paradox does exist in a particular situation or not [51]? Lastly,
(d) If an absurdity in (d) does exist, is it reversible [8, 16, 54]?
Based on the problem statement above, the investigation will include various matlab
simulations. Therefore, being able to give analysis on a local asymptotic stability state
when a small perturbation has been introduced [40]. It is for this reason that a bifurcation
relevance comes into e ect [58]. There are principal de nitions that are undertaken as
the research evolves around them.
A study of quantitative response is presented in predator-prey systems in order to
establish its stability properties. Due to tradeo s, there is a great likelihood that the
growth rate, attack abilities and defense capacities of species have to be examined in line
with reviewing parameters which favor stability conditions. Accordingly, an investigation
must also re
ect chances that leads to extinction or coexistence [7].
Nature is much more complex than scienti c models and laboratories [39]. Therefore,
di erent mechanisms have to be integrated in order to establish stability even when a
system has been under enrichment [51]. As a result, SSP system is modeled by way of
reaction-di usion di erential equations simulated both spatially and temporally.
The outcomes of such a system will be best suitable for real-world life situations which
control similar behaviors in the future. Comparable models are used in the main
compilation phase of dissertation and truly re
ected in the literature. The SSP model
can be regarded as between (2018-2011), with a stability control study which is of an
original.
>Magister Scientiae - MSc
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11394/77372020-01-01T00:00:00ZUltrafilters and Compactification
http://hdl.handle.net/11394/7374
Ultrafilters and Compactification
Nxumalo, Mbekezeli Sibahle
In this thesis, we construct the ultrafilter space of a topological space using ultrafilters as points, study some of its properties and describe a method of generating compactifications through the ultrafilter space. As part of investigating some properties of the ultrafilter space, we show that the ultrafilter space forms a monad in the category of topological spaces. Furthermore, we show that rendering the ultrafilter space suitably separated results in a generation of separated compactifications which coincide with some well-known compactifications. When the ultrafilter space is rendered T0 or sober, the resulting compactifications is a stable Compactifications. Rendering the ultrafilter space T2 or Tychono results in the Stone_ Cechcompactification
>Magister Scientiae - MSc
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11394/73742020-01-01T00:00:00Z