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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.

News Archive

Breeding of unique game requires a balance between conservation and sustainable use
2014-05-20

 

Game bred for qualities such as unconventional hair colour or horn quality, may on the long term have unexpected consequences for biodiversity and game farming.

This is according to the inaugural lecture of Prof Paul Grobler from the Department of Genetics at the University of the Free State (UFS).

Prof Grobler feels that the consequences of selective breeding should be examined carefully, as there is currently much speculation on the subject without sound scientific information to back it.

“At the moment, colour variation invokes much interest among game farmers and breeders. Unusual colour variants are already available in different game species. These unusual animals usually fetch much higher prices at auctions compared to prices for the ‘normal’ individuals of the species.”

Examples of these unusual variants are springbuck being bred in white, black or copper colours, the black-backed or ‘saddleback’ impala, and the gold-coloured and royal wildebeest.

A black-backed impala was recently sold for R5,7 million.

“Based on genetic theory, good reason exists why these practices need to be monitored, but one should also take care not to make the assumption that selective breeding will inevitably lead to problems,” warns Prof Grobler.

Grobler says that negative characteristics in a species can sometimes unwittingly be expressed during the selection process for a unique colour. “It is seen, for example, in purebred dogs where the breeding of a new race sometimes brings underlying genetic deviations in the species to the front.” He also believes that some of these animals may not be able to adapt to changing environmental conditions.

“However, one should also look at the positive side: because of the good demand for game, including unusual variants, there is much more game in South Africa today than in many decades. Balance should be found between the aims of conservation and the sustainable utilisation of game.”

Research at the UFS’s Department of Genetics is now trying to establish the genetic effects of intensive game breeding and predict the impact on biodiversity.

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