Recurrence relations for four-electron integrals over Gaussian basis functions

In the spirit of the Head-Gordon-Pople algorithm, we report vertical, transfer and horizontal recurrence relations for the efficient and accurate computation of four-electron integrals over Gaussian basis functions. Our recursive approach is a generalization of our algorithm for three-electron integrals [J.~Chem.~Theory Comput.~12, 1735 (2016)]. The RRs derived in the present study can be applied to a general class of multiplicative four-electron operators. In particular, we consider various types of four-electron integrals that may arise in explicitly-correlated F12 methods.Comment: 11 pages, 3 figures and 2 table

You need only one bull to cover fifty cows: Zulu women and 'traditional' dress

African Studies Seminar series. Paper presented June 1987This paper tries to place the contemporary dress of married Zulu women into a broad historical framework. It therefore addresses the the problem of why, despite radical economic and political transformations, some of the present conventions of female dress have remained virtually unchanged since Shakan times.(1) By looking particularly at the history of the institution of marriage, it attempts to demonstrate how the meanings ascribed to, but also the roles of these conventions have been affected by the codification of so-called customary law and the growth of migrant labour. Given the paucity of information on past perceptions and interpretations of female dress it must be pointed out, though, that many of the observations which follow are necessarily speculative

Effect of weak disorder on the ground state of uniaxial dipolar spin systems in the upper critical dimension

Extensive Monte Carlo simulations are used to investigate the stability of the ferromagnetic ground state in three-dimensional systems of Ising dipoles with added quenched disorder. These systems model the collective ferromagnetic order observed in various systems with dipolar long-range interactions. The uniaxial dipolar spins are arranged on a face-centred cubic lattice with periodic boundary conditions. Finite-size scaling relations for the pure dipolar ferromagnetic system are derived by a renormalisation group calculation. These functions include logarithmic corrections to the expected mean field behaviour since the system is in its upper critical dimension. Scaled data confirm the validity of the finite-size scaling description and results are compared with subsequent analysis of weakly disordered systems. A disorder-temperature phase diagram displays the preservation of the ferromagnetic ground state with the addition of small amounts of disorder, suggesting the irrelevance of weak disorder in these systems.Comment: 6 pages, 4 figures; proceedings of the 3rd NEXT-Sigma-Phi Conference, Kolymbari, Greece, August 200

Editorial: South African Research in Management, Informatics and Governance in a 21st Century Hyper Connected World

Alternation Special Edition 22,1 of 2015 forms a continuation of on-going research in the fields of Management, Business Leadership, Informatics, and Governance at a number of South African universities. This issue contains nineteen contributions from authors in South Africa, Britain and New Zealand. Contributions vary from the nature of transformational leadership, integrity in research and organisational management, and the ubiquitous role of informatics in the present-day digitally hyper-connected world in which we all now live. In one way or another, these nineteen contributions all focus on, relate to, or depend on Informatics as organisational management and communication backbone.The image of the front page of this is a blend of a painting in my possession, painted by my former colleague and friend Jan Zaal who is now deceased, which I photographed and which I overlaid with a simulated threedimensional image of digital information code. Jan Zaal’s painting is of a display window of the former Stuttafords in West Street Durban. Having witnessed the various phases that the painting went through, and having had privilege of discussing them with Jan Zaal, it is worth mentioning that he took over 700 photographs of the display window at various times of the day in different seasons over a nine month period and that his painting is a composite image, capturing the essential spirit of that display window

Editorial: Management, Informatics and Governance

As we live through the digital revolution and, for that matter, have entered the much acclaimed fourth industrial revolution, we need to also take a glance back, to look at where this has all began. There are many academic scenarios – and some not so academic – but in principle, it appears that, like many other scientific endeavours, it was started by and for the military. With regard to Alternation’s own trajectory, Smit and Chetty (2018a; and 2018b) provide a few brief insights.But be that as it may. Tim Berners-Lee was the first to connect the dots, and provide a vision for the future, in 1989, with the sketch on the cover of this issue of Alternation. And, after the 30 years, since, we want to dedicate this issue to him

Local versus landscape effects of bush encroachment on plant available light, soil moisture, frost occurrence and herbaceous productivity and composition

Bush encroachment is a global phenomenon and a pressing concern for South Africa rangelands. The expansion and increase in density of Vachellia karroo (hereafter referred to aAcacia karroo) has been documented in the Eastern Cape and KwaZulu Natal in South Africa. This increase in woody species in savannas is often at the expense of grass cover and thus is causing concern about how this will impact agriculture due to possible loss of grazing capacity. To understand the impacts of bush encroachment the effect of trees on their micro-climate and abiotic factors and in turn on the herbaceous layer needs to be examined. The objective of this study was to quantify the effect of Acacia karroo encroachment on the light environment, soil moisture and frost occurrence in the sub-canopy and inter-canopy micro-habitats, and how these changes affected herbaceous player productivity and composition. Another question that is being addressed here is whether, and how, the local tree effects scale up in the landscape and whether prediction can be made based on the effects of individual trees. The study was undertaken on a farm, Endwell, in the Smaldeel, Eastern Cape. At the study site, a semi-arid savanna, Acacia karroo has been encroaching since the 1980’s. The study was conducted at three scales: landscape, stand-wide and local scale. The landscape scale was represented by four areas with 0, 21, 45 and 72% tree canopy cover, the stand-wide scale consisted of transects with varying percentages of tree canopy cover within each of the four levels of encroachment. The local scale was represented by the sub-canopy and inter-canopy environment to test the effect of trees. At the local scale plant available light and soil moisture were lower in the sub-canopy than intercanopy regions, with leaf area index being higher in the sub-canopy. This local negative effect of the tree canopy on light and soil moisture in the sub-canopy did not scale up predictably in the landscape. At the stand-wide scale light in the inter-canopy was reduced as shading increased. Frost was excluded from under the canopies and frost incidence decreased at higher tree cover. Grass productivity was reduced in the sub-canopy, possibly due to lower light and soil moisture. Overall biomass increased from the low to medium level of encroachment but lowest at the high level of encroachment. Grass composition and cover was only slightly affected by tree canopies cover and C4 grass species were still present in the sub-canopy and at lower light environments. At the levels of Acacia karroo encroachment encountered at this study site, it seems unlikely that palatable or desirable C4 would be excluded from the system and that a shift from C4 to shade-tolerant species would occur. This is due to tree canopies at the site not reducing light to such anextent that they would outcompete grasses, and likely the very low grazing pressure at thesesites. Herbaceous biomass at these sites were still sufficient to carry a fire in the inter-canopyregion and sufficient grazing for herbivores. In the sub-canopy region fires will be excluded thus with higher the portion of sub-canopy areas increasing at the high levels of encroachment they may interrupt fire spread. Thus it was concluded that Acacia karroo encroachment up to 45% tree cover is currently not creating negative feedback on herbivory, but low stocking rates appear to be key to maintain this

Management, Informatics and Governance

The article by Matete Lerutla and Renier Steyn is titled ‘Definition of Leadership in Africa within the Twenty-first Century Context: Empirical Research on Leadership in Africa’. Granted that leadership is a widely used construct and there are numerous articles across multiple disciplines that researche the ‘leadership’ phenomenon, this research investigates the construct of leadership in Africa. Much of what is written is conceptual, and empirical articles on African leadership remain sparse. The article reports on the findings of a systematic literature review that was conducted on leadership in Africa. It presents a qualitative review of empirical research, highlighting key findings and implications for future research. The research investigation followed the traditional body of knowledge framework of concepts, statements, definitions, and conceptual frameworks to systemize reports on leadership in Africa. Articles were identified, selected and analysed using the systematic literature review methodology. Articles, statements, definitions, models, typologies, theories, and paradigms were explored and interrogated in each article, so as to understand how they are linked to leadership in Africa

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Report on the 2016 KwaZulu-Natal Pearson eLearning Pilot Project

Governments and institutions in Africa are increasingly turning to ICT-based solutions in order to improve the education performance of their students. Specifically, the promise of eLearning to improve and to better facilitate learning has spurred innovation towards provision of eLearning resources on mobile devices such as tablets. Tablets hold enormous potential in delivery of eLearning due to their portability and provision for multiple uses. This study aimed at understanding the efficacy of tablet-based digital content on teachers and learners and consequently, to offer recommendations for sustainable, scalable eLearning models. This report presents key findings from an eLearning research pilot conducted in 12 schools at KwaZulu-Natal province in South Africa. The results indicate that an eLearning intervention could have an impact on the learners’ subject-specific skills, that teachers and learners gained digital literacy in their use of the eLearning intervention, that learners gained confidence in using the eLearning intervention and integrated various digital resources in their learning over time, that learners were sharing content more over time, that the majority of the teachers felt comfortable integrating the digital content in their teaching over time. The findings in this report would help educational leaders, content developers, technological providers and the Department of Education to make sound decisions in relation to developing and implementing eLearning interventions, especially in South African schools. Based on the findings of the eLearning research pilot, this report also presents recommendations based on pedagogy, eLearning, training, support and facilitation, implementation, hardware, partnerships and provides possible considerations for tablets in educational rollouts

Factors that influence public primary school teachers’ work engagement

Abstract:M.Ed. (Education Leadership and Management