University of Johannesburg

Given a graph G and an integer k, the objective of the \(\varPi \) -Contraction problem is to check whether there exists at most k edges in G such that contracting them in G results in a graph satisfying the property \(\varPi \). We investigate the problem where \(\varPi \) is ‘H-free’ (without any induced copies of H). It is trivial that \(H\) -free Contraction is polynomial-time solvable if H is a complete graph of at most two vertices. We prove that, in all other cases, the problem is NP-complete. We then investigate the fixed-parameter tractability of these problems. We prove that whenever H is a tree, except for seven trees, \(H\) -free Contraction is W[2]-hard. This result along with the known results leaves behind only three unknown cases among trees.

In this chapter, we analyze and discuss teaching, learning and well-being in Finnish education during the COVID-19 pandemic between Spring 2020 and Fall 2022. First, we analyze the preconditions, such as teachers’ and students’ digital competences and the digital infrastructure necessary to switch to distance teaching and learning. Second, we present the results of a survey concerning the organization and experience of teaching and learning during the COVID-19 pandemic. Third, we discuss the engagement and well-being of teachers, principals and students during the pandemic based on survey data. During the pandemic, teachers developed digital pedagogy and students enhanced their digital competence, and several digital pedagogy and co-teaching innovations were created. However, we identified decreased engagement among students, teachers, and principals during the pandemic and an increase in stress and burnout among teachers and principals. Principals felt the impact of the stress their teachers faced, and teachers struggled to make up for the differing efforts among families to cope with distance learning. Overall, the switch to distance teaching and learning was organized effectively, but the distance-learning period weakened the equality of teaching and the conditions that encourage learning and well-being.

Eva Schmidt argues that facts about incoherent beliefs can be non-evidential epistemic reasons to suspend judgment. In this commentary, I argue that incoherence-based reasons to suspend are epistemically superfluous: if the subjects in Schmidt’s cases ought to suspend judgment, then they should do so merely on the basis of their evidential reasons. This suggests a more general strategy to reduce the apparent normativity of coherence to the normativity of evidence. I conclude with some remarks on the independent interest that reasons-first epistemology might have within an evidentialist framework.

Editorial for: A new science of suffering, the wisdom of the soul, and the new behavioral economics of happiness: towards a general theory of well-being This Research Topic is designed to extend the theme of existential positive psychology (EPP) to new research areas. Theoretically, it is oriented toward a general theory of global well-being, which incorporates three pillars of EPP (Wong et al., 2022).

The viscosity properties of GNP-alumina hybrid nanofluids are of significant importance in various engineering applications. This study compares the predictive performance of response surface methodology (RSM), artificial neural network (ANN), and adaptive neuro-fuzzy inference system (ANFIS) for the viscosity (µrel) and relative viscosity (µrel) of GNP-alumina hybrid nanofluid at varying mixing ratio (0–3) and temperature (15–55 °C). The ANN and ANFIS models were optimised by varying the number and type of neurons and membership functions (MFs), respectively. In contrast, the RSM model was optimised by varying the source model. The efficacy of the models was assessed using various measures of performance metrics, including residual sum of squares, root mean square error, mean absolute error, and mean absolute percentage error (MAPE). The ANN architecture with 4 neurons exhibited exceptional proficiency in forecasting the µnf, achieving an R² value of 0.9997 and a MAPE of 0.3100. Meanwhile, the best ANN architecture for the µrel was achieved with 5 neurons, resulting in an R² of 0.9817 and MAPE of 0.2588. Furthermore, the ANFIS model with the difference of two sigmoidal MFs and the product of two sigmoidal MFs for µnf and Generalized Bell MFs for µrel exhibited the best performance with (3 5) and (4 5) input membership functions, respectively. An R² value of 0.9999 and 0.9872, with a corresponding MAPE value of 0.0945 and 0.1214, were reported for the optimal ANFIS architecture of µnf and µrel, respectively. The RSM model also produced its most accurate prediction with the quadratic model for both µnf and µrel, with an R² value of 0.9986 and 0.8835, respectively. Thus, comparative analysis across various models indicated that the ANFIS model outperformed others regarding performance metrics for both µnf and µrel. This study underscores the potential of ANN and ANFIS models in accurately forecasting the viscosity properties of GNP-alumina hybrid nanofluids, thus offering reliable tools for future applications.

Energy is playing a more fundamental function in human growth and advancement. Many rural households in developing nations, like South Africa, are still lacking access to basic electricity due to being located far away from the national grid and grid expansion to these areas is quite expensive. Fewer rural communities are electrified through the use of diesel and grid systems of which are having a high operating and maintenance cost and are the biggest carbon emissions producers. The deployment of renewable energy sources (RES) based microgrid systems are considered as a more viable approach to supply power to rural communities in the world. RE-based microgrid systems have the greatest potential to meet load demand, improve quality of life and create job opportunities, and provide electricity access for rural communities of SA. In this study, a case study is utilized to design and simulate a suitable grid-tied hybrid microgrid system architecture for rural communities’ conditions. The study selected three isolated rural communities (Tjiane, Phosiri, and Malekapane villages) of Ga-Mphahlele in Limpopo province (SA) as case studies, and these communities have similar weather conditions because they are located in close proximity. The unreliable national grid system is the main source of power in these communities while diesel generators (DG) are used as backup system during load shedding. In this study, HOMER software was used to design a grid-tied hybrid microgrid power system of which will help with eradicating system power failure and load shedding from the national grid. Based on the simulation, optimization, and sensitivity analyses results show that the optimal grid-tied microgrid system architecture was proposed based on lower net present cost (NPC), lower cost of energy (COE), a maximum renewable fraction (RF), loss of power supply probability (LPSP), and the optimal system should produce fewer carbon emissions. The achieved results for all examined rural communities show that the optimum microgrid system architecture consists of a grid, solar PV, wind turbine (WT), DG, battery, and power converter is more capable of satisfying customer electricity demand in a dependable approach and provide good power quality. The results showed that Grid/PV/WT/DG/Battery/Converter is a winning hybrid microgrid system architecture that is more cost-effective and environmentally friendly with NPC of R2.973793; COE of R0.02842 and an RF of 97.8% with total emissions of 58.626 kg/yr for Tjiane, NPC of R1.836202; COE of R0.03092 and an RF of 97.9% with a total emission of 32,888 kg/yr for Phosiri, and NPC of R1.209773; COE of R0.02370 and an RF of 97.9% with total emissions of 28.002 kg/yr for Malekapane. The proposed Grid/PV/WT/DG/Battery/Converter microgrid is considered the most favorable grid-connected hybrid microgrid system architecture which is a more suitable and relaible electricity supply solution for rural communities. The results showed that sensitivity variables, financial parameters, wind speed, solar irradiations, and diesel price differences have a substantial influence on the optimal design of grid-connected hybrid power systems for rural electrification.

The chapters presented in this book originate from several years of intensive research work conducted by mostly experienced teams of international authors from various affiliations worldwide. The main criteria, which were relied upon in order to constitute the different parts of this book, were based on the thematic convergence of the topics proposed.

The huge attention currently afforded to renewable energy-based decentralised energy systems, as means for accelerating rural electrification and hence development, has triggered massive consideration and interest given the cost involved in extending existing grids to rural communities of Sub-Saharan Africa (SSA). In most of these communities, access to electricity is essentially restricted to basic domestic utilisation or needs such as: lighting, cooking and storage purposes. Although, small-scale farming consists of the main occupation in rural communities of SSA, it remains less developed and does not take advantage of available renewable energy resources succeptible to promote its expansion and development. However, the potential in renewable energy resources (solar PV, wind, etc.) in SSA countries could be counted as important attribute for the enablement of access to electricity. As a direct consequence of this, sustainable agricultural development may be achieved in order to ensure food security and to prevent urban migration by promoting employment opportunities and poverty alleviation in rural communities of SSA countries as dictated by the United Nations (UN) sustainable development goals (SDGs). Despite the promotion of access to clean electricity being advocated in the literature as the stepping-stone for sustainable development and growth, the gap remains the choice of suitable policy option susceptible to balance access to electricity with sustainable development in rural communities of SSA. In this work, the six-step policy analysis is applied to probe the effectiveness of market-based policies in enhancing access to electricity and agricultural development in rural communities of selected SSA countries. Results show that despite the shortcomings in the implementation of this policy in many SSA countries, this policy approach proves to be favorable to increased share of renewable energies, which translates into increased electrification of the agriculture sector.

The energy utility industry's evolution instigated a technological shift where the global community is moving into digital technology and where modification and changes of systems are automated and computerized. While some philosophers are convinced that we are at the exodus of the 4IR into the 5th Industrial revolution, a big question is whether the 4IR was a success or not. It is unclear to determine the successes and failures since the energy industry is divided according to the first to the third world countries and their technologies. Due to technological limitations, many studies have proven that even the 3IR has not kicked in their power grid infrastructures. Developing countries like South Africa, India, Brasil, Argentina, and more have the 4IR concept in place but are not fully functional in most areas where their power grid extends. Since the power infrastructure already exists, the main limitation is ICT infrastructure. Most parts of the power grid do not have any real-time communication infrastructure and protocols, making it difficult for utilities to procure smart devices and grid monitors if there’s no means to transmit and receive real-time information. These predicaments point to the 4IR enabler, that is, big data. There is no big data significance to harvest fundamental data. This book chapter addresses methods and ways to farm data, meaning putting entire systems in place to collect data. When data is available, it can be harvested to perform real-time tasks. Real data yields accurate information is vital for planning, simulation purposes, maintenance, and power outages computerized troubleshooting.

In this chapter, a thorough discussion regarding technology as it advanced in the past few years of Moulded Case Circuit Breakers, Solid-State Circuit Breakers, Hybrid Circuit Breakers and modern Power Monitoring Systems for application in Battery Tripping Units is presented. Additionally, a design of a low-cost circuit breaker testing system, as well as a mobile battery tripping unit, is provided. A large part of the discussion centres around how the available technology would assist emerging markets with the inclusion of availability of testing equipment, as well as the technical expertise required to use this equipment. Technicians will be able to use this as a background in developing new testing techniques especially for emerging markets to ensure that circuit breakers are relatively reliable. This discussion can be used by newly trained technicians to gain valuable knowledge in the protection and testing of power distribution centres. Technicians will be able to develop techniques and systems to test circuit breakers where funding is low. Additionally, techniques are discussed to try and alleviate substation tripping issues, which result in power distribution centres overloading and then burning. Once this happens, power outages occur, which take time to repair. With the implementation of remote monitoring functionality, efficiency levels for maintenance, aspects will increase tremendously, keeping the areas functional and costs relatively low. By keeping these costs low, funding that was typically used for maintenance can be used elsewhere and downtime is reduced significantly. Thus, the advantages of these implementations are staggering. In order to ensure that power distribution systems long-viability in emerging markets, it is essential to ensure that functionality is correct. Two essential aspects that are of great importance is the functionality of the circuit breakers and the ability to properly disconnect a power distribution system when too much energy is drawn. Unfortunately, limited work has been done in the development of testing techniques for circuit breakers, post-manufacturing. Additionally, power stations need to trip effectively when an overload condition is experienced; however, this is not possible if substandard circuit breakers are used. Providentially, recent battery-tripping unit technology has advanced to the point where a mobile system can be designed that also allows for enough power injection to trip a substation effectively. In emerging markets, several problems exist such as the technical ability of staff, funding, the time it takes to determine a fault as well as the availability of components and devices. Additionally, the availability of testing equipment can also be severely limited. For instance, in remote areas, technicians travel long distances to arrive at a site where there is potential problem is at a power distribution centre.

The increasing social and political instability in South Africa and an emergent view that links it to the negotiated political settlement invite for a critical review of the ‘South African political miracle’. A central question such a review should attempt to address is whether the political settlement dealt fundamentally with the legacy of colonialism and apartheid, which came to define so much of social, economic and political life in South Africa. This article attempts such a review. Unlike critics of the negotiated settlement who tend to dismiss it totally, I contend, following on Mamdani's Neither Settler nor Native ( 2021 ), that its major achievement was establishing an inclusive political order in which civil and political rights were extended to all South Africans. The article begins by providing a broad outline of the colonial and apartheid orders in South Africa. While Mamdani (2021) details the political dimensions of these two exclusionary political orders, especially the divisive political identities they fostered and enforced, this article summarises the social and economic dimensions, focusing in particular on land and cattle dispossession. By highlighting these two dimensions, the article seeks to demonstrate the limitations of the negotiated settlement and the risk these limitations pose to the sustainability of inclusive democracy in South Africa. The article then examines what Mamdani calls the ‘South African moment’, which was marked by a challenge to the logic of apartheid and colonialism and the transformation of the political identities those orders had imposed. The third section of the article discusses the promise and limitations of the negotiated settlement. Overall, the article questions the desirability of the ‘South African model’ where social justice is compromised to achieve political inclusion.

Curriculum reform worldwide has often reflected changing perspectives on the teaching and learning of science. Such perspectives underline the notion that not only the teaching of science content knowledge is relevant but also the aims and methods scientists use to further their knowledge and the social context in which science is applied. We call this the ‘cognitive-epistemic’ and ‘social institutional aspects’ of science. They form the hard core of the nature of science (NOS) concept for curriculum reform. In South Africa, after years of Apartheid, a key focus of school science curriculum reform is for importance to be given to NOS due to the potential benefits of learning and understanding of NOS for students. This study analyses cognitive-epistemic and social-institutional categories of NOS in the South African Life Sciences and Physical Sciences school curricula. A critical finding for both Life Sciences and Physical Sciences curricula was the imbalance in the NOS categories. In the curricula, there is less presence of the social-institutional categories compared to the cognitive-epistemic categories. In general, there was poor interconnectedness amongst NOS categories, with the strongest interconnectedness revealed for the cognitive-epistemic categories ‘scientific practices’ and ‘methods and methodological rules’. Implications for the design of future curricula and recommendations for future research are discussed.

This work is considered as the first comprehensive review, that covers all types of meshfree method including the traditional or developed meshless techniques that have been implemented for the purpose of investigating static analysis (bending, stability) besides dynamic analysis (free vibration, force vibration and other types of dynamic behaviors) of linear and nonlinear mechanical system. The secondary methods utilized together with the meshless methods are also highlighted such as; Hamilton’s principle, first-order shear deformation theory, high-order shear deformation theory, Monte Carlo, local/nonlocal theories and others. Also, some computational mechanics approaches are briefly addressed. The basic fundamental equations of meshfree methods and the error analysis are presented. Various types of schematics and structure size are discussed. Else, the implementation of composite material in solid mechanics are concisely highlighted. As a key finding, in each unique schematic in specific scale, various implemented parameters like boundary conditions, thickness to length ratio (t/l), as well as the aspect ratio have different impacts on the mechanical performance in both static and dynamic analysis. Additionally, as each meshfree method is considered unique by itself and has its own developed mathematical model, each method has different application and numerical problems to solve. Galerkin, reproducing kernel particle method, moving least square are the most common meshfree. Based on the literature, many studies mainly show interest in investigating the piezoelectric and diverse distribution of carbon nanotubes, and some in fictional graded material in different structures. This review is recommended for researchers interested in solid mechanics analysis at various scales using meshfree techniques.

Myosorex varius is a South African generalist shrew, which has been found to consist of several genetic clades across its range. A northern clade inhabits the more mesic, summer-rainfall areas of grassland and savannah in the east of South Africa. A southern clade occupies areas of fynbos in the south, and can be further divided into a western subclade occupying winter-rainfall areas and an eastern subclade occupying areas with aseasonal rainfall. Non-South-African members of the African genus Myosorex primarily are limited to isolated montane habitats along the East African Rift System. Here, we used palaeoclimatic niche modelling to examine the effects of Pliocene and Pleistocene climate change on the distributions of M. varius , its clades and the genus as a whole. Results indicate that repeated cycles of range expansion during glacial periods and fragmentation during interglacials are responsible for current phylogeographic patterns within M. varius . Based on their close alignment with rainfall zones and lack of genetic mixing despite areas of contact, it is likely that these (sub)clades are locally adapted to their respective areas. Earlier climatic fluctuations allowed the genus to ‘island hop’ south from East Africa along the East African Rift System, expanding in range during cooler periods and retreating to montane refugia during warmer periods. Areas currently occupied by Myosorex species largely correspond with predicted montane refugia that have allowed them to survive previous warm periods.

Octahedral chiral‐at‐metal complexes MX2(a‐chel)2 (a‑chel = asymmetric chelate) can rearrange their ligands by four mechanisms known as the Bailar (B), Ray‐Dutt (RD), Conte‐Hippler (CH), and Dhimba‐Muller‐Lammertsma (DML) twists. Racemization involves their interconnections, which were computed for MoO2(acnac)2 (acnac = β‐ketoiminate) using density functional theory at ωB97x‐D with the 6‐31G(d,p) and 6‐311G(2d,p) basis sets and LANL2DZ for molybdenum. Racemizing the cis(NN) isomer, being the global energy minimum with trans oriented imine groups, is a three step process (DML‐CH‐DML) that requires 17.4 kcal/mol, while all three cis isomers (cis(NN), cis(NO), and cis(OO)) interconvert at ≤ 17.9 kcal/mol. The B and RD twists are energetically not competitive and neither are the trans isomers. The interconnection of all enantiomeric minima and transition structures is summarized in a graph that also visualizes valley ridge inflection points for two of the three CH twists. Geometrical features of the minima and twists are given. Lastly, the influence of N‐substitution on the favored racemization pathway is evaluated. The present comprehensive study serves as a template for designing chiral‐at‐metal MX2(a‐chel)2 catalysts that may retain their chiral integrity.

An equimolar reaction of 5-chlorosalicylaldehyde and 2-bromo-4-chloroaniline yielded the Schiff base ( Z )-2-((2-bromo-4-chlorophenyl)imino)methyl)-4-chlorophenol) (HL), which was used for complexation to Co ²⁺ , Ni ²⁺ , Cu ²⁺ , and Zn ²⁺ metal salts.

The effect of mechanical alloying on the development of Ni–Al–Ti–Mn–Co–Fe–Cr high entropy alloys (HEAs) utilizing the spark plasma sintering (SPS) method is the main goal of this study. A bulk sample was fabricated using SPS after the alloys were mixed for 12 h. Thermodynamic simulation, X-ray diffraction, scanning electron microscopy, nanoindentation, and microhardness were used to investigate the microstructure and mechanical properties of the as-mixed powders. The master alloy was made of NiAl and was subsequently alloyed with Ti, Mn, Co, Fe, and Cr at different compositions to develop HEAs at a sintering temperature of 850 °C, a heating rate of 100 °C/min, a pressure of 50 MPa, and a dwelling time of 5 min. A uniform dispersion of the alloying material can be seen in the microstructure of the sintered HEAs with different weight elements. The grain size analysis shows that the Ni 25 Al 25 Ti 8 Mn 8 Co 15 Fe 14 Cr 5 alloy exhibited a refined structure with a grain size of 2.36 ± 0.27 µm compared to a coarser grain size of 8.26 ± 0.43 μm attained by the NiAl master alloy. Similarly, the HEAs with the highest alloying content had a greater microstrain value of 0.0449 ± 0.0036, whereas the unalloyed NiAl had 0.00187 ± 0.0005. Maximum microhardness of 139 ± 0.8 HV, nanohardness of 18.8 ± 0.36 GPa, elastic modulus of 207.5 ± 1.65 GPa, elastic recovery ( W e / W t ) of 0.556 ± 0.035, elastic strain to failure ( H / E r ) of 0.09.06 ± 0.0027, yield pressure ( H ³ / $$E_{{\text{r}}}^{2}$$ E r 2 ) of 0.154 ± 0.0055 GPa, and the least plasticity index ( W p / W t ) of 0.444 ± 0.039 were attained by Ni 25 Al 25 Ti 8 Mn 8 Co 15 Fe 14 Cr 5 . A steady movement to the left may be seen in the load–displacement curve. Increased resistance to indentation by the developed HEAs was made possible by the increase in alloying metals, which ultimately led to higher nanohardness and elastic modulus.