Department of MathematicsNo Descriptionhttps://hdl.handle.net/10566/1582024-11-08T20:19:18Z2024-11-08T20:19:18Z691One-sided maximal inequalities for a randomly stopped bessel processCloud, Makasuhttps://hdl.handle.net/10566/92602024-01-26T00:00:36Z2023-01-01T00:00:00Zdc.title: One-sided maximal inequalities for a randomly stopped bessel process
dc.contributor.author: Cloud, Makasu
dc.description.abstract: We prove a one-sided maximal inequality for a randomly stopped Bessel process of dimension (Formula presented.) For the special case when α = 1, we obtain a sharp Burkholder-Gundy inequality for Brownian motion as a consequence. An application of the present results is also given.
2023-01-01T00:00:00ZModeling the impact of combined use of Covid Alert SA app and vaccination to curb Covid-19 infections in South AfricaKinyili, MusyokaMunyakazi, Justin B.Mukhtar, Abdulaziz Y. A.https://hdl.handle.net/10566/90842024-09-16T09:21:45Z2023-01-01T00:00:00Zdc.title: Modeling the impact of combined use of Covid Alert SA app and vaccination to curb Covid-19 infections in South Africa
dc.contributor.author: Kinyili, Musyoka; Munyakazi, Justin B.; Mukhtar, Abdulaziz Y. A.
dc.description.abstract: The unanticipated continued deep-rooted trend of the Severe Acute Respiratory Syndrome
Corona-virus-2 the originator pathogen of the COVID-19 persists posing concurrent anxiety
globally. More effort is affixed in the scientific arena via continuous investigations in a prolific
effort to understand the transmission dynamics and control measures in eradication of the
epidemic. Both pharmaceutical and non-pharmaceutical containment measure protocols
have been assimilated in this effort. In this study, we develop a modified SEIR deterministic
model that factors in alternative-amalgamation of use of COVID Alert SA app and vaccination
against the COVID-19 to the Republic of South Africa’s general public in an endeavor to
discontinue the chain of spread for the pandemic. We analyze the key properties of the
model not limited to positivity, boundedness, and stability.
2023-01-01T00:00:00ZA NSFD method for the singularly perturbed Burgers-Huxley equationDerzie, Eshetu B.Munyakazi, Justin B.Dinka, Tekle G.https://hdl.handle.net/10566/90712024-09-16T09:18:59Z2023-01-01T00:00:00Zdc.title: A NSFD method for the singularly perturbed Burgers-Huxley equation
dc.contributor.author: Derzie, Eshetu B.; Munyakazi, Justin B.; Dinka, Tekle G.
dc.description.abstract: This article focuses on a numerical solution of the singularly perturbed
Burgers-Huxley equation. The simultaneous presence of a singular perturbation
parameter and the nonlinearity raise the challenge of finding a reliable and e cient
numerical solution for this equation via the classical numericalmethods. To overcome
this challenge, a nonstandard finite dierence (NSFD) scheme is developed in the
following manner. The time variable is discretized using the backward Euler method.
This gives rise to a system of nonlinear ordinary dierential equations which are then
dealt with using the concept of nonlocal approximation. Through a rigorous error
analysis, the proposed scheme has been shown to be parameter-uniformconvergent.
Simulations conducted on two numerical examples confirm the theoretical result. A
comparison with other methods in terms of accuracy and computational cost reveals
the superiority of the proposed scheme.
2023-01-01T00:00:00ZBinary codes from m-ary n-cubes Q(n) (m)Key, Jennifer D.Rodrigues, Bernardo G.https://hdl.handle.net/10566/89742024-09-16T09:20:40Z2021-01-01T00:00:00Zdc.title: Binary codes from m-ary n-cubes Q(n) (m)
dc.contributor.author: Key, Jennifer D.; Rodrigues, Bernardo G.
dc.description.abstract: We examine the binary codes from adjacency matrices of the graph with vertices the nodes
of the m-ary n-cube Qmn
and with adjacency de ned by the Lee metric. For n = 2 and m odd,
we obtain the parameters of the code and its dual, and show the codes to be LCD. We also
nd s-PD-sets of size s + 1 for s < m1
2 for the dual codes, i.e. [m2; 2m 1;m]2 codes, when
n = 2 and m 5 is odd.
2021-01-01T00:00:00ZOn the exact constants in one-sided maximal inequalitiesfor Bessel processesMakasu, Cloudhttps://hdl.handle.net/10566/86202024-09-16T09:19:38Z2023-01-01T00:00:00Zdc.title: On the exact constants in one-sided maximal inequalitiesfor Bessel processes
dc.contributor.author: Makasu, Cloud
dc.description.abstract: In this paper, we establish a one-sided maximal moment inequalitywith exact constants for Bessel processes. As a consequence, weobtain an exact constant in the Burkholder-Gundy inequality. Theproof of our main result is based on a pure optimal stopping prob-lem of the running maximum process for a Bessel process. The pre-sent results extend and complement a number of related resultspreviously known in the literature.
2023-01-01T00:00:00ZA NSFD method for the singularly perturbed Burgers-Huxley equationDerzie, Eshetu B.Munyakazi, Justin B.Dinka, Tekle G.https://hdl.handle.net/10566/85842024-09-16T09:24:11Z2023-01-01T00:00:00Zdc.title: A NSFD method for the singularly perturbed Burgers-Huxley equation
dc.contributor.author: Derzie, Eshetu B.; Munyakazi, Justin B.; Dinka, Tekle G.
dc.description.abstract: This article focuses on a numerical solution of the singularly perturbed Burgers-Huxley equation. The simultaneous presence of a singular perturbation parameter and the nonlinearity raise the challenge of finding a reliable and efficient numerical solution for this equation via the classical numerical methods. To overcome this challenge, a nonstandard finite difference (NSFD) scheme is developed in the following manner. The time variable is discretized using the backward Euler method. This gives rise to a system of nonlinear ordinary differential equations which are then dealt with using the concept of nonlocal approximation. Through a rigorous error analysis, the proposed scheme has been shown to be parameter-uniform convergent. Simulations conducted on two numerical examples confirm the theoretical result. A comparison with other methods in terms of accuracy and computational cost reveals the superiority of the proposed scheme.
2023-01-01T00:00:00ZA fitted numerical method for parabolic turning point singularly perturbed problems with an interior layerMunyakazi, Justin B.Patidar, Kailash C.Sayi, Mbani T.https://hdl.handle.net/10566/85672024-09-16T09:17:39Z2019-01-01T00:00:00Zdc.title: A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer
dc.contributor.author: Munyakazi, Justin B.; Patidar, Kailash C.; Sayi, Mbani T.
dc.description.abstract: The objective of this paper is to construct and analyzea fitted operator finite difference method (FOFDM) forthe family of time-dependent singularly perturbed parabolicconvection–diffusion problems. The solution to the problemswe consider exhibits an interior layer due to the presence ofa turning point. We first establish sharp bounds on the solu-tion and its derivatives. Then, we discretize the time variableusing the classical Euler method. This results in a system ofsingularly perturbed interior layer two-point boundary valueproblems. We propose a FOFDM to solve the system above.
2019-01-01T00:00:00ZSome meta-cayley graphs on dihedral groupsAllie, ImranMwambene, Erichttps://hdl.handle.net/10566/85652024-09-16T09:28:43Z2019-01-01T00:00:00Zdc.title: Some meta-cayley graphs on dihedral groups
dc.contributor.author: Allie, Imran; Mwambene, Eric
dc.description.abstract: In this paper, we define meta-Cayley graphs on dihedral groups. We fully determine the automorphism groups of the constructed graphs in question. Further, we prove that some of the graphs that we have constructed do not admit subgroups which act regularly on their vertex set; thus proving that they cannot be represented as Cayley graphs on groups.
2019-01-01T00:00:00ZModeling the dynamics of an epidemic under vaccination in two interacting populationsAhmed, Ibrahim H. I.Witbooi, Peter J.Patidar, Kailashhttps://hdl.handle.net/10566/85562024-09-16T09:27:43Z2012-01-01T00:00:00Zdc.title: Modeling the dynamics of an epidemic under vaccination in two interacting populations
dc.contributor.author: Ahmed, Ibrahim H. I.; Witbooi, Peter J.; Patidar, Kailash
dc.description.abstract: Mathematical modeling of the numerical evolution of infectious diseases has become an
important tool for disease control and eradication when possible. Much work has been done
on the problem of how a given population is affected by another population when there
is mutual interaction. The mere presence of migrant people poses a challenge to whatever
health systems are in place in a particular region. Such epidemiological phenomena have been
studied extensively, described by mathematical models with suggestions for intervention
strategies. The epidemiological effect of migration within the population itself was modeled
for sleeping sickness in a paper 1 by Chalvet-Monfray et al. In the case of malaria, there
is for instance a study 2 by Tumwiine et al. on the effect of migrating people on a fixed
population. The latter two diseases are vector borne. Diseases that propagate without a vector
spread perhaps more easily when introduced into a new region. Various studies of models
with immigration of infectives have been undertaken for tuberculosis, see for instance 3 by
Zhou et al., or the work 4 of Jia et al., and for HIV, see the paper 5 of Naresh et al.
2012-01-01T00:00:00ZGeneralizing the Hilton–Mislin genus groupWitbooi, Peter J.https://hdl.handle.net/10566/85372024-09-16T09:18:48Z2001-01-01T00:00:00Zdc.title: Generalizing the Hilton–Mislin genus group
dc.contributor.author: Witbooi, Peter J.
dc.description.abstract: For any group H, let H be the set of all isomorphism classes of groups K
such that K H . For a finitely generated group H having finite commu-
Ž .tator subgroup H, H , we define a group structure on H in terms of embed-
dings of K into H, for groups K of which the isomorphism classes belong to
Ž . H . If H is nilpotent, then the group we obtain coincides with the genus group
Ž .GG H defined by Hilton and Mislin. We obtain some new results on Hilton Mislin
genus groups as well as generalizations of known results.
2001-01-01T00:00:00Z