The Classification of Real Singularities Using SINGULAR. Part I: Splitting Lemma and Simple Singularities

We present algorithms to classify isolated hypersurface singularities over the real numbers according to the classification by V.I. Arnold (Arnold et al., 1985). This first part covers the splitting lemma and the simple singularities; a second and a third part will be devoted to the unimodal singularities up to corank 2. All algorithms are implemented in the SINGULAR library realclassify.lib (Marais and Steenpass, 2012).Comment: 12 pages, 1 tabl

An analysis of factors linked to the decline in maternal mortality in Nepal

Peer reviewedPublisher PD

Suid-afrika en sy ekonomies selfstandige toekoms

Waarom streef nasies onafhanklikheid so naarstiglik na? Is onafhanklikheid terselfdertyd ’n woord sonder werklik praktiese betekenis in die wêreld van vandag? Dit wil voorkom asof die ideale van sommige vir „één wêreldstaat” tans verder en verder op die agtergrond skuif. Inteendeel is ’n opwelling van nasionalisme duidelik waarneembaar in die meeste dele van die wêreld. Selfs die ideaal van ,,’n Verenigde Europa” skyn, afgesien van groter ekonomiese samewerking, vandag minder van ’n werklikheid te wees as ooit tevore. Dit skyn onmoontlik te wees om die eie nasionale trots van ’n erkende volk sonder meer uit te wis. Onafhanklikheid bly dus ’n begrip wat in die ware sin van die woord groot betekenis vir elke volk van naam inhou

A novel semi-passive process for sulphate removal and elemental sulphur recovery centred on a hybrid linear flow channel reactor

South Africa (SA) currently faces a major pollution problem from mining impacted water, including acid rock drainage (ARD), as a consequence of the mining activities upon which the economy has been largely built. The environmental impact of ARD has been further exacerbated by the country's water scarce status. Increasingly scarce freshwater reserves require the preservation and strategic management of the country's existing water resources to ensure sustainable water security. In SA, the primary focus on remediation of ARDcontaminated water has been based on established active technologies. However, these approaches are costly, lead to secondary challenges and are not always appropriate for the remediation of lower volume discharges. Mostly overlooked, ARD discharges from diffuse sources, associated with the SA coal mining industry, have a marked impact on the environment, similar to those originating from underground mine basins. This is due to the large number of deposits and their broad geographic distribution across largely rural areas of SA. Semi-passive ARD treatment systems present an attractive alternative treatment approach for diffuse sources, with lower capital and operational costs than active systems as well as better process control and predictability than traditional passive systems. These semi-passive systems typically target sulphate salinity through biological sulphate reduction catalysed by sulphate reducing bacteria (SRB). These anaerobic bacteria reduce sulphate, in the presence of a suitable electron donor, to sulphide and bicarbonate. However, the hydrogen sulphide product generated is highly toxic, unstable, easily re-oxidised and poses a significant threat to the environment and human health, so requires appropriate management. An attractive strategy is the reduction of sulphate to sulphide, followed by its partial oxidation to elemental sulphur, which is stable and has potential as a value-added product. A promising approach to achieve partial oxidation is the use of sulphide oxidising bacteria (SOB) in a floating sulphur biofilm (FSB). These biofilms develop naturally on the surfaces of sulphide rich wastewater streams. Its application in wastewater treatment and the feasibility of obtaining high partial oxidation rates in a linear flow channel reactor (LFCR) has been described. The use of a floating sulphur biofilm overcomes many of the drawbacks associated with conventional sulphide oxidation technologies that are costly and require precise operational control to maintain oxygen limiting conditions for partial oxidation. In the current study a hybrid LFCR, incorporating a FSB with biological sulphate reduction in a single reactor unit, was developed. The integration of the two biological processes in a single LFCR unit was successfully demonstrated as a ‘proof of concept'. The success of this system relies greatly on the development of discrete anaerobic and microaerobic zones, in the bulk liquid and at the airliquid interface, that facilitate sulphate reduction and partial sulphide oxidation, respectively. In the LFCR these environments are established as a result of the hydrodynamic properties associated with its design. Key elements of the hybrid LFCR system include the presence of a sulphate-reducing microbial community immobilised onto carbon fibres and the rapid development of a floating sulphur biofilm at the air-liquid interface. The floating sulphur biofilm consists of a complex network of bacterial cells and deposits of elemental sulphur held together by an extracellular polysaccharide matrix. During the Initial stages of FSB development, a thin transparent biofilm layer is formed by heterotrophic microorganisms. This serves as ‘scaffolding' for the subsequent attachment and colonisation of SOB. As the biofilm forms at the air-liquid interface it impedes oxygen mass transfer into the bulk volume and creates a suitable pH-redox microenvironment for partial sulphide oxidation. Under these conditions the sulphide generated in the bulk volume is oxidised at the surface. The biofilm gradually thickens as sulphur is deposited. The produced sulphur, localised within the biofilm, serves as an effective mechanism for recovering elemental sulphur while the resulting water stream is safe for discharge into the environment. The results from the initial demonstration achieved near complete reduction of the sulphate (96%) at a sulphate feed concentration of 1 g/L with effective management of the generated sulphide (95-100% removal) and recovery of a portion of the sulphur through harvesting the elemental sulphur-rich biofilm. The colonisation of the carbon microfibres by SRB ensured high biomass retention within the LFCR. This facilitated high volumetric sulphate reduction rates under the experimental conditions. Despite the lack of active mixing, at a 4-day hydraulic residence time, the system achieved volumetric sulphate reduction rates similar to that previously shown in a continuous stirred-tank reactor. The outcome of the demonstration at laboratory scale generated interest to evaluate the technology at pilot scale. This interest necessitated further development of the process with a particular focus on evaluating key challenges that would be experienced at a larger scale. A comprehensive kinetic analysis on the performance of the hybrid LFCR was conducted as a function of operational parameters, including the effect of hydraulic residence time, temperature and sulphate loading on system performance. Concurrently, the study compared the utilisation of lactate and acetate as carbon source and electron donor as well as the effect of reactor configuration on system performance. Comparative assessment of the performance between the original 2 L LFCR and an 8 L LFCR variant that reflected the pilot scale design with respect to aspect ratio was conducted. Pseudo-steady state kinetics was assessed based on carbon source utilisation, volumetric sulphate reduction, sulphide removal efficiency and elemental sulphur recovery. Additionally, the hybrid LFCR provided a unique synergistic environment for studying the co-existence of the sulphate reducing (SRB) and sulphide oxidising (SOB) microbial communities. The investigation into the microbial ecology was performed using 16S rRNA amplicon sequencing. This enabled the community structure and the relative abundance of key microbial genera to be resolved. These results were used to examine the link between process kinetics and the community dynamics as a function of hydraulic residence time. Results from this study showed that both temperature and volumetric sulphate loading rate, the latter mediated through both sulphate concentration in the feed and dilution rate, significantly influenced the kinetics of biological sulphate reduction. Partial sulphide oxidation was highly dependent on the availability and rate of sulphide production. Volumetric sulphate reduction rates (VSRR) increased linearly as hydraulic residence time (HRT) decreased. The optimal residence time was determined to be 2 days, as this supported the highest volumetric sulphate reduction rate (0.21 mmol/L.h) and conversion (98%) with effective sulphide removal (82%) in the 2 L lactate-fed LFCR. Lactate as a sole carbon source proved effective for achieving high sulphate reduction rates. Its utilisation within the process was highly dependent on the dominant metabolic pathway. The operation at high dilution rates resulted in a decrease in sulphate conversion and subsequent increase in lactate metabolism toward fermentation. This was attributed to the competitive interaction between SRB and fermentative bacteria under varying availability of lactate and concentrations of sulphate and sulphide. Acetate as a sole carbon source supported a different microbial community to lactate. The lower growth rate associated with acetate utilising SRB required longer start-up period and was highly sensitive to operational perturbations, especially the introduction of oxygen. However, biomass accumulation over long continuous operation led to an increase in performance and system stability. Microbial ecology analysis revealed that a similar community structure developed between the 2 L and 8 L lactate-fed LFCR configurations. This, in conjunction with the kinetic data analysis, confirmed that the difference in aspect ratio and scale had minimal impact on process stability and that system performance can be reproduced. The choice of carbon source selected for distinctly different, highly diverse microbial communities. This was determined using principle co-ordinate analysis (PCoA) which highlighted the variation in microbial communities as a function of diversity and relative abundance. The SRB genera Desulfarculus, Desulfovibrio and Desulfomicrobium were detected across both carbon sources. However, Desulfocurvus was found in the lactate-fed system and Desulfobacter in acetate-fed system. Other genera that predominated within the system belonged to the classes Bacteroidetes, Firmicutes and Synergistetes. The presence of Veillonella, a lactate fermenter known for competing with SRB, was detected in the lactate-fed systems. Its relative abundance corresponded well with the lactate fermentation and oxidation performance, where an apparent shift in the dominant metabolic pathway was observed at high dilution rates. Furthermore, the data also revealed preferential attachment of selective SRB onto carbon microfibers, particularly among the Desulfarculus and Desulfocurvus genera. The microbial ecology of the floating sulphur biofilm was consistent across both carbon sources. Key sulphur oxidising genera detected were Paracoccus, Halothiobacillus and Arcobacter. The most dominant genera present in the FSB were Rhizobium, well-known nitrogen fixing bacteria, and Pannonibacter. Both genera are members of the class Alphaproteobacteria, a well-known phylogenetic grouping in which the complete sulphur-oxidising, sox, enzyme system is highly conserved. An aspect often not considered in the operation of these industrial bioprocess systems is the microbial community dynamics within the system. This is particularly evident within biomass accumulating systems where the proliferation of non-SRB over time can compromise the performance and efficiency of the process. Therefore, the selection and development of robust microbial inoculums is critical for overcoming the challenges associated with scaling up, particularly with regards to start-up period, and long-term viability of sulphate reducing bioreactor systems. In the current study, long-term operation demonstrated the robustness of the hybrid LFCR process to maintain relatively stable system performance. Additionally, this study showed that process performance can be recovered through re-establishing suitable operational conditions that favor biological sulphate reduction. The ability of the system to recover after being exposed to multiple perturbations, as explored in this study, confirms the resilience and long-term viability of the hybrid process. A key feature of the hybrid process was the ability to recover the FSB intermittently without compromising biological sulphate reduction. The current research successfully demonstrated the concept of the hybrid LFCR and characterised sulphate reduction and sulphide oxidation performance across a range of operating conditions. This, in conjunction with a clearer understanding of the complex microbial ecology, illustrated that the hybrid LFCR has potential as part of a semi-passive approach for the remediation of low volume sulphate-rich waste streams, critical for treatment of diffuse ARD sources

Career role modelling: a challenge to career education

The aim of this article is to determine to what extent a career role modelling programme as method of career information dissemination for all communities, but especially of service to the disadvantaged, can be instrumental in addressing the existing void in the career information dissemination system in South Africa. It was determined that a career role modelling programme can make a significant contribution to establishing an inexpensive and effective career information system in a diverse South African society

An Approach to Dealing with the Difficulties Undergraduate Chemistry Students Experience with Stoichiometry

Chemistry for first year students has been identified by Tshwane University of Technology as one of the subjects with a low pass rate. It is apparent that students often memorize formulae and definitions, without understanding the underlying concepts required to work with abstract units of measure. We have found that the majority of students at this university are unable to balance reaction equations satisfactorily. They are also unable to predict the reaction yield, or identify limiting reagents. It is imperative that these and other related problems are overcome before any meaningful change to the high failure rate at first year level will be realized. All conventional forms of lecture presentation failed to make any significant impact on the success rate. Structured worksheets were developed and used, together with tactile models, to address the problems and the initial findings showed a marked improvement. It was discovered that the students’ problems originated from their inability to understand the meaning of subscripts and coefficients in chemical equations. The worksheets and the impact they have made on the students’ understanding of stoichiometry are shared in this paper.Keywords: Stoichiometry, limiting reagent, worksheets, tactile model