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07 September 2018 Photo Stephen Collett
Mathematician makes popular contribution to science Prof Atangana
Prof Atangana is the first African under 40 years of age to be selected as African Academic of Science affiliated in Mathematics. He recently delivered his inaugural lecture and is pictured with Eelco Lukas, Director of the Institute for GroundwaterStudies at the UFS (middle) and Prof Hendri Kroukamp, Acting Vice-Rector: Academic

Prof Abdon Atangana, researcher in the Institute for Groundwater Studies at the University of the Free State (UFS), recently delivered his inaugural lecture on the topic: Understanding God’s Nature with Non-Local Operators.

His research interests are methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modelling. Prof Atangana is the founder of the fractional calculus with non-local and non-singular kernels popular in applied mathematics today. He has introduced more than 12 mathematical operators, most of which bear his name (such as the Atangana-Baleanu fractional integral).

He stated: “We will not stop until we change the classical view of doing mathematics. Mathematics is not a subject but a tool given to mankind by God to understand nature. One single mathematical operator cannot portray God’s nature accurately. Therefore the Atangana Baleanu was suggested.”

New weapons

Most physical problems can be expressed in terms of mathematical formulations called differential equations. According to him the differential equation’s aim is to analyse, understand, and predict the future of a physical problem. Prof Atangana introduced the Atangana-Baleanu fractional integral. This brought new weapons into applied mathematics to model complex real-world problems more accurately.

Prof Atangana explained: “The Atangana-Baleanu fractional derivative is able to describe real-world problems with different scales, or problems that change their properties during time and space for instance, the spread of cancer, the flow of water within heterogeneous aquifers, movement of pollution within fractured aquifers, and many others. This crossover behaviour is observed in many empirical systems.”

Sudden change

The Atangana-Baleanu fractional derivative is also able to describe physical or biological phenomena, such as a heart attack, the physiological progression from life to death, structural failure in an aeroplane, and many other physical occurrences with sudden change with no steady state.

The new differential and integral operators are nowadays in fashion and are being applied with great success in many fields to model complex natural phenomena. It is believed that the future of modelling complex real-world problems relies on these non-local operators.

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Dr Charlotte Boucher and Lindi Heyns examine possible anti-microbial activity in the skin of Western olive toad species
2014-12-22

 

Researchers Lindi Heyns and Dr Charlotte Boucher are working together on an interdisciplinary project between the Departments of Zoology and Entomology and Veterinary Biotechnology at the University of the Free State (UFS). The focus of their research is on the preliminary biochemical description of skin secretions in some South African toads.

The project forms part of an Honours study executed by Dwayne Pike under Heyns’ supervision. He is co-supervised by Dr Boucher who is assisting with the biochemical and microbiological assays.

Dr Boucher said, “Amphibians are characterised by the presence of cutaneous glands spread over the skin. There are two types of glands, namely mucous and granular (poison), located on the inner surface of the epidermis. Mucous glands are widely dispersed over the skin, while granular glands can be grouped and enlarged in specific regions. Mucous glands are generally associated with maintenance of humidity and cutaneous respiration, whereas granular glands function in chemical defence against predators and/or microbial infection. Studies indicate that the compounds produced by the granular glands belong to numerous chemical classes with diverse pharmacological activities.”

The products secreted by granular glands are rich in low molecular weight constituents of varied molecular types, including proteins, peptides and toxins. These secretions make the toad foul-tasting to predators and even toxic to other frog species. In addition, amphibians offer an attractive source of novel antimicrobials. Studies indicate that as a response to inhabiting microorganism-rich environments they synthesise and secrete a diverse array of antimicrobial peptides (AMPs) as an innate form of defence. Extensive research by various other research groups has been carried out on antimicrobial peptides of the genus Rana; however, hardly any studies have investigated the antimicrobial activity of African frog species.

The focus of this preliminary project is to determine the protein composition of the glandular secretions of the Western olive toad (Amietophrynus poweri), using biochemical tests, such as SDS-PAGE also known as protein gel electrophoresis combined with mass-spectrometry used to identify unknown peptides and proteins. This will give us an overview of the composition of the glandular secretions. Furthermore, we are also looking at microbiological tests, which include assays that test for possible anti-microbial activity against various bacterial and fungal species.

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