10 research outputs found
Some topological aspects of modular quasi-metric spaces
No full textA thesis submitted to the Faculty of Science in fulfilment of the requirement for the degree Doctor of Philosophy (PhD) in Science, University of the Witwatersrand, Johannesburg, 2019In this PhD thesis, we present the modular quasi-pseudometric on a nonempty
set, a concept that generalises modular pseudometrics to the framework of
quasi-metric spaces. We investigate the topological aspects of a set equipped
with a modular quasi-pseudometric. It turns out that a set equipped with
a modular quasi-pseudometric is a bitopological space in the sense of Kelly.
Moreover, we introduce the theory of Isbell-convexity in the setting of modular
quasi-pseudometrics which we shall call w-Isbell-convexity. Furthermore,
we prove that given a modular set, w-Isbell-convexity is equivalent to Isbellconvexity
whenever the modular quasi-pseudometric is continuous from the
right on the set of positive numbers. We also study the boundedness of
a set endowed with a modular quasi-pseudometric and we shall call it w-
boundedness. Consequently, we show that a self w-nonexpansive map in a
w-Isbell-convex modular set has a xed point and the set of xed points
is w-Isbell-convex whenever the modular quasi-pseudometric is continuous
from the right on the set of positive numbers.PH202
On w-Isbell-convexity
No full text[EN] Chistyakov introduced and developed a concept of modular metric for an arbitrary set in order to generalise the classical notion of modular on a linear space. In this article, we introduce the theory of hyperconvexity in the setting of modular pseudometric that is herein called w-Isbell-convexity. We show that on a modular set, w-Isbell-convexity is equivalent to hyperconvexity whenever the modular pseudometric is continuous from the right on the set of positive numbers.Olela Otafudu, O.; Sebogodi, K. (2022). On w-Isbell-convexity. Applied General Topology. 23(1):91-105. https://doi.org/10.4995/agt.2022.15739OJS91105231A. A. N. Abdou, Fixed points of Kannan maps in modular metric spaces, AIMS Maths 5 (2020), 6395-6403.https://doi.org/10.3934/math.2020411A. A. N. Abdou and M. A. Khamsi, Fixed point results of pointwise contractions in modular metric spaces, Fixed Point Theory Appl. 2013 (2013):163.https://doi.org/10.1186/1687-1812-2013-163C. Alaca, M. E. Ege and C. Park, Fixed point results for modular ultrametric spaces, J. Comput. Anal. Appl. 20 (2016), 1259-1267.A. H. Ansari, M. Demma, L. Guran, J. R. Lee and C. Park, Fixed point results for C-class functions in modular metric spaces. J. Fixed Point Theory Appl. 20, no. 3 (2018), Paper No. 103.https://doi.org/10.1007/s11784-018-0580-zV. V. Chistyakov, A fixed point theorem for contractions in modular metric spaces, arXiv:1112.5561.V. V. Chistyakov, Metric modular spaces: Theory and applications, SpringerBriefs in Mathematics, Springer, Switzerland, 2015.https://doi.org/10.1007/978-3-319-25283-4V. V. Chistyakov, Modular metric spaces generated by F-modulars, Folia Math. 15 (2008), 3-24.V. V. Chistyakov, Modular metric spaces, I: Basic concepts, Nonlinear Anal. 72 (2010), 1-14.https://doi.org/10.1016/j.na.2009.04.057S. Cobzas, Functional Analysis in Asymmetric Normed Spaces, Frontiers in Mathematics, Springer, Basel, 2012.https://doi.org/10.1007/978-3-0348-0478-3M. E. Ege and C. Alaca, Fixed point results and an application to homotopy in modular metric spaces, J. Nonlinear Sci. Appl. 8 (2015), 900-908.https://doi.org/10.22436/jnsa.008.06.01M. E. Ege and C. Alaca, Some properties of modular S-metric spaces and its fixed point results, J. Comput. Anal. Appl. 20 (2016), 24-33.M. E. Ege and C. Alaca, Some results for modular b-metric spaces and an application to system of linear equations, Azerb. J. Math. 8 (2018), 3-14.R. Espínola and M. A. Khamsi, Introduction to hyperconvex spaces, in: Handbook of Metric Fixed Point Theory, Kluwer Academic, Dordrecht, The Netherlands (2001), pp. 39135.https://doi.org/10.1007/978-94-017-1748-9_13A. Gholidahneh, S. Sedghi, O. Ege, Z. D. Mitrovic and M. de la Sen, The Meir-Keeler type contractions in extended modular b-metric spaces with an application, AIMS Math. 6 (2021), 1781-1799.https://doi.org/10.3934/math.2021107H. Hosseinzadeh and V. Parvaneh, Meir-Keeler type contractive mappings in modular and partial modular metric spaces, Asian-Eur. J. Math. 13 (2020): 2050087.https://doi.org/10.1142/S1793557120500874E. Kemajou, H.-P. Künzi and O. Olela Otafudu, The Isbell-hull of di-space, Topology Appl. 159 (2012), 2463-2475.https://doi.org/10.1016/j.topol.2011.02.016M. A. Khamsi and W. A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, Pure and Applied Mathematics, Wiley-Interscience, New York, NY, USA, 2001.https://doi.org/10.1002/9781118033074H.-P. Künzi, An introduction to quasi-uniform spaces, Contemp. Math. 486 (2009), 239-304.https://doi.org/10.1090/conm/486/09511H.-P. Künzi and O. Olela Otafudu, q-hyperconvexity in quasipseudometric spaces and fixed point theorems, J. Funct. Spaces Appl. 2012 (2012): Art. ID 765903.https://doi.org/10.1155/2012/765903N. Kumar and R. Chugh, Convergence and stability results for new three step iteration process in modular spaces, Aust. J. Math. Anal. Appl. 14 (2017): 14.Y. Mutemwa, O. Olela Otafudu and H. Sabao, On gluing of quasi-pseudometric spaces, Khayyam J. Math. 6 (2020), 129-140.O. Olela Otafudu, On one-local retract in quasi-metric spaces, Topology Proc. 45 (2015), 271-281.O. Olela Otafudu and H. Sabao, Set-valued contractions and -hyperconvex spaces, J. Nonlinear Convex Anal. 18 (2017), 1609-1617.https://doi.org/10.4995/agt.2017.5818R. C. Sine, On nonlinear contraction semigroups in sup norm spaces, Nonlinear Anal. 3 (1979), 885-890.https://doi.org/10.1016/0362-546X(79)90055-5H. Sabao and O. Olela Otafudu, On soft quasi-pseudometric spaces, Appl. Gen. Topol. 22 (2021), 17-30.https://doi.org/10.4995/agt.2021.13084S. Salbany, Injective objects and morphisms, in: Categorical Topology and Its Relation to Analysis, Algebra and Combinatorics, Prague, 1988, World Sci. Publ., Teaneck, NJ, 1989, pp. 394-409.S. Yamamuro, On conjugate space of Nakano space, Trans. Amer. Math. Soc. 90 (1959), 291-311.https://doi.org/10.1090/S0002-9947-1959-0132378-1C. I. Zhu, J. Chen, X. J. Huang and J. H. Chen, Fixed point theorems in modular spaces with simulation functions and altering distance functions with applications, J. Nonlinear Convex Anal. 21 (2020), 1403-1424
Mean-Variance Optimisation of A South African Index Based Portfolio Using Machine Learning
No full textA research report submitted in partial fulfillment of the requirements for the degree of Master of Business Administration to the Faculty of Commerce, Law and Management, Wits Business School, University of the Witwatersrand, Johannesburg, 2021This study embarked on a comparison of the effectiveness of the Markowitz Mean- Variance Portfolio Optimisation against utilising a Machine Learning Technique to construct an optimal portfolio. The study aimed to: Construct an optimal portfolio using the Mean-Variance Analysis Framework, Construct an optimal portfolio using a Machine Learning Technique (Support Vector Regression), Contrast the results of the Minimum-Variance Portfolio and the Machine Learning Portfolio. The stocks of the FTSE JSE FIN15 index were chosen to construct the portfolio. The historical returns of the stocks in the index were used to trained (December 2014 to June 2019) and test the models(June 2019 to December 2020). The Mean-Variance Analysis and Minimum-Variance Portfolio were constructed using Python code that the author compiled. Similarly, the Support Vector Regression model was built in Python. The weights for the Machine Learning portfolio were calculated using the pseudo-inverse matrix and the predicted value of the Regression Model. It was found that the Minimum-Variance and Machine Learning portfolio produced
different portfolios, but both containing fewer holdings than the original index. The performance of the Minimum-Variance Portfolio exceeded that of the index and the Machine Learning Portfolio with regards to relative(excess) returns and total returns in the out of sample period. It was found that the Machine Learning portfolio performs well at replicating the index returns but fails to exceed them and typically has a higher risk associated with it. It was concluded that the Minimum-Variance portfolio would be the most attractive to a risk-averse investor and the Machine Learning portfolio underperforms the Minimum variance and the index. Therefore confirming the effectiveness of Mean-variance Optimisation in a South African context against a Machine Learning TechniqueMM202
Impact of parametric seasonal variations on water quality in the Crocodile River and Inyaka Dam in the Mpumalanga Province, South Africa
No full textDATA AVAILABILITY :
The datasets generated during and/or analysed during the current study are available from the corresponding author upon reasonable request.Please read abstract in the article.http://www.cell.com/heliyonhj2024School of Health Systems and Public Health (SHSPH)SDG-06:Clean water and sanitationSDG-13:Climate actio
Estimating mountainous plant species richness and diversity for monitoring global change in a protected grassland park
No full textDATA AVAILABILITY STATEMENT : The data supporting this study's findings are available from the corresponding author upon request at [email protected] of species diversity and richness are essential to understand present ecological and biodiversity conditions for effective conservation management strategies. Biodiversity indicators determine rangeland health and response to grazing, fire regimes and climate change. This research examined species richness, diversity and composition in a protected mountainous grassland. Two data sets, both collected from a 30 × 30 m plot, with similar species composition and cover were combined. One data set was collected using a 100-step point survey and the other from a series of 16 plots. A single-factor analysis of variance was used to test if the mean species richness and diversity of the sites differed across the study area. Species accumulation curves were used to determine the relationship between species richness and the number of sampling units per site. The results from fitting a species–area equation showed that the estimated maximum species richness was slightly greater than the observed species pool in all sites, meaning that the sampling units were not adequate (albeit by small margins) to capture all vascular plant species in the sites. Diversity metrics could, thus, be used to monitor species change within grassland plant communities.http://www.wileyonlinelibrary.com/journal/ajeGeography, Geoinformatics and Meteorolog
A simple model of the Draupner Wave Experiment
No full textRogue Waves are large waves that appear “out of nowhere” in the open ocean and in near-shore waters. The Mathematics in Industry Study Group organized by Professor David Mason at the University of Witwatersrand in January, 2024, considered these waves due to their frequency at locations off the South African coast. There are a number of quite sophisticated models of these waves, but in this work we try to reproduce something like a rogue wave with a very simple free surface model, and in particular consider a wave generated in a circular tank by wave activity at the outer edge. Linear and nonlinear equations are derived and integrated to obtain the wave activity due to different generation mechanisms. The results indicate that a relatively simple model can produce something that approaches the form of a rogue wave
DNA barcoding of southern African mammal species and construction of a reference library for forensic application
No full textCombating wildlife crimes in South Africa requires accurate identification of traded species and their products. Diagnostic morphological characteristics needed to identify species are often lost when specimens are processed and customs officials lack the expertise to identify species. As a potential solution, DNA barcoding can be used to identify morphologically indistinguishable specimens in forensic cases. However, barcoding is hindered by the reliance on comprehensive, validated DNA barcode reference databases, which are currently limited. To overcome this limitation, we constructed a barcode library of Cytochrome c oxidase subunit 1 (COI) and Cytochrome b (Cyt b) sequences for threatened and protected mammals exploited in southern Africa. Additionally, we included closely related or morphologically similar species and assessed the database’s ability to identify species accurately. Published southern African sequences were incorporated to estimate intraspecific and interspecific variation. Neighbor-joining trees successfully discriminated 94-95% of the taxa. However, some widespread species exhibited high intraspecific distances (>2%), suggesting geographic sub-structuring or cryptic speciation. Lack of reliable published data prevented the unambiguous discrimination of certain species. This study highlights the efficacy of DNA barcoding in species identification, particularly for forensic applications. It also highlights the need for a taxonomic re-evaluation of certain widespread species and challenging genera.The presentation of the authors' names and (or) special characters in the title of the pdf file of the accepted manuscript may differ slightly from what is displayed on the item page. The information in the pdf file of the accepted manuscript reflects the original submission by the author
Analysis of the Hadley cell, subtropical anticyclones and their effect on South African rainfall
No full textDATA AVAILABILITY : The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.This study investigates the behaviour of subtropical high-pressure systems and the Hadley cell, which affect the weather of South Africa, using the ERA-Interim database and ensemble of 14 global circulation models from Phase 6 of the Coupled Model Intercomparison Project (CMIP6). Mass stream function was used to represent the Hadley cell. To analyse the behaviour of the subtropical anticyclones, monthly sea level pressure, the 1018 hPa isobar and the maximum isobar in the study area were used. The seasonal variation of the anticyclones and Hadley circulation is consistent with rainfall over South Africa. During austral summer, a less intense, narrow mass stream function, South Atlantic Subtropical Anticyclone and Mascarene High are located more southwards, causing rainfall over the eastern parts of South Africa. During the austral winter, Hadley circulation, as well as the anticyclones, is stronger and located more northwards, causing rainfall over the southern and southwestern parts of South Africa.https://link.springer.com/journal/704hj2024Geography, Geoinformatics and MeteorologySDG-13:Climate actio
A comprehensive review of water quality indices for lotic and lentic ecosystems
No full textDATA AVAILABILITY : The datasets generated during and/or analysed
during the current study are available from the corresponding
author upon reasonable request.Freshwater resources play a pivotal role in sustaining life and meeting various domestic, agricultural, economic, and industrial demands. As such, there is a significant need to monitor the water quality of these resources. Water quality index (WQI) models have gradually gained popularity since their maiden introduction in the 1960s for evaluating and classifying the water quality of aquatic ecosystems. WQIs transform complex water quality data into a single dimensionless number to enable accessible communication of the water quality status of water resource ecosystems. To screen relevant articles, the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) method was employed to include or exclude articles. A total of 17 peer-reviewed articles were used in the final paper synthesis. Among the reviewed WQIs, only the Canadian Council for Ministers of the Environment (CCME) index, Irish water quality index (IEWQI) and Hahn index were used to assess both lotic and lentic ecosystems. Furthermore, the CCME index is the only exception from rigidity because it does not specify parameters to select. Except for the West-Java WQI and the IEWQI, none of the reviewed WQI performed sensitivity and uncertainty analysis to improve the acceptability and reliability of the WQI. It has been proven that all stages of WQI development have a level of uncertainty which can be determined using statistical and machine learning tools. Extreme gradient boosting (XGB) has been reported as an effective machine learning tool to deal with uncertainties during parameter selection, the establishment of parameter weights, and determining accurate classification schemes. Considering the IEWQI model architecture and its effectiveness in coastal and transitional waters, this review recommends that future research in lotic or lentic ecosystems focus on addressing the underlying uncertainty issues associated with the WQI model in addition to the use of machine learning techniques to improve the predictive accuracy and robustness and increase the domain of application.Open access funding provided by University of South Africa.http://link.springer.com/journal/10661am2024School of Health Systems and Public Health (SHSPH)SDG-06:Clean water and sanitatio
A review on progress and prospects of diatomaceous earth as a bio-template material for electrochemical energy storage : synthesis, characterization, and applications
No full textPublisher Copyright: © The Author(s) 2024.This comprehensive review explores the remarkable progress and prospects of diatomaceous earth (DE) as a bio-template material for synthesizing electrode materials tailored explicitly for supercapacitor and battery applications. The unique structures within DE, including its mesoporous nature and high surface area, have positioned it as a pivotal material in energy storage. The mesoporous framework of DE, often defined by pores with diameters between 2 and 50 nm, provides a substantial surface area, a fundamental element for charge storage, and transfer in electrochemical energy conversion and storage. Its bio-templating capabilities have ushered in the creation of highly efficient electrode materials. Moreover, the role of DE in enhancing ion accessibility has made it an excellent choice for high-power applications. As we gaze toward the future, the prospects of DE as a bio-template material for supercapacitor and battery electrode material appear exceptionally promising. Customized material synthesis, scalability challenges, multidisciplinary collaborations, and sustainable initiatives are emerging as key areas of interest. The natural abundance and eco-friendly attributes of DE align with the growing emphasis on sustainability in energy solutions, and its contribution to electrode material synthesis for supercapacitors and batteries presents an exciting avenue to evolve energy storage technologies. Its intricate structures and bio-templating capabilities offer a compelling path for advancing sustainable, high-performance energy storage solutions, marking a significant step toward a greener and more efficient future.Peer reviewe
