The experiences of first-year students in mathematics in using an e-learning platform at a university of technology

AbstractUniversities of technology in South Africa have been trying to provide effective and flexible learning experiences to cater for the influx of students enrolling in the institutions who come from diverse educational backgrounds. One of the challenges arising from their diverse educational backgrounds is their poor background in the use of technologies for teaching and learning. The teaching of mathematics, particularly, is made more difficult because of the large number of students who have many misconceptions as a result of problems from the basic education that they were part of, for a period of 12 years. Consequently, a number of them do not make it to the mainstream education system due to poor performance in first-year mathematics. The purpose of the study on which this article reports was to determine the impact that an e-learning platform could have on mathematics first-year students when used as a supplement to the traditional methods of teaching. The study utilised quantitative and qualitative methods, with the qualitative data being used to interpret and make sense of the quantitative data. Participants were 35 first-year students in the Department of Civil Engineering at a university of technology. Data were generated from questionnaires and focus group interviews. It was found that the actual use of the system is dependent not only on student behavioural intention to use the system, but external factors also contribute negatively to the actual system use. Some external factors that were identified include poor Internet connectivity, insufficient computers and an inflexible timetable. The study recommends that universities of technology should take greater care in designing their academic calendars, so that it alleviates instead of tighten the constraints under which students work. 

Lie symmetries for equations in conformal geometries

We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been found in practice. We use the method of Lie analysis of differential equations to obtain new group invariant solutions to conformally related Petrov type D spacetimes. Four cases arise depending on the nature of the Lie symmetry generator. In three cases we are in a position to solve the master field equation in terms of elementary functions. In the fourth case special solutions in terms of Bessel functions are obtained. These solutions contain known models as special cases.Comment: 19 pages, To appear in J. Phys.

Gravitating fluids with Lie symmetries

We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means of Lie point symmetries. The method utilised reduces the partial differential equation to an ordinary differential equation according to the Lie symmetry admitted. We show that a class of solutions found previously can be characterised by a particular Lie generator. Several new families of solutions are found explicitly. In particular we find the relevant ordinary differential equation for all one-dimensional optimal subgroups; in several cases the ordinary differential equation can be solved in general. We are in a position to characterise particular solutions with a linear barotropic equation of state.Comment: 13 pages, To appear in J. Phys. A: Math. Theo

Collapsing shear-free perfect fluid spheres with heat flow

A global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow. We apply a compact formalism, which simplifies the isotropy condition and the condition for conformal flatness. This formalism also presents the simplest possible version of the main junction condition, demonstrated explicitly for conformally flat and geodesic solutions. It gives the right functions to disentangle this condition into well known differential equations like those of Abel, Riccati, Bernoulli and the linear one. It yields an alternative derivation of the general solution with functionally dependent metric components. We bring together the results for static and time- dependent models to describe six generating functions of the general solution to the isotropy equation. Their common features and relations between them are elucidated. A general formula for separable solutions is given, incorporating collapse to a black hole or to a naked singularity.Comment: 26 page

Global patient outcomes after elective surgery: prospective cohort study in 27 low-, middle- and high-income countries.

BACKGROUND: As global initiatives increase patient access to surgical treatments, there remains a need to understand the adverse effects of surgery and define appropriate levels of perioperative care. METHODS: We designed a prospective international 7-day cohort study of outcomes following elective adult inpatient surgery in 27 countries. The primary outcome was in-hospital complications. Secondary outcomes were death following a complication (failure to rescue) and death in hospital. Process measures were admission to critical care immediately after surgery or to treat a complication and duration of hospital stay. A single definition of critical care was used for all countries. RESULTS: A total of 474 hospitals in 19 high-, 7 middle- and 1 low-income country were included in the primary analysis. Data included 44 814 patients with a median hospital stay of 4 (range 2-7) days. A total of 7508 patients (16.8%) developed one or more postoperative complication and 207 died (0.5%). The overall mortality among patients who developed complications was 2.8%. Mortality following complications ranged from 2.4% for pulmonary embolism to 43.9% for cardiac arrest. A total of 4360 (9.7%) patients were admitted to a critical care unit as routine immediately after surgery, of whom 2198 (50.4%) developed a complication, with 105 (2.4%) deaths. A total of 1233 patients (16.4%) were admitted to a critical care unit to treat complications, with 119 (9.7%) deaths. Despite lower baseline risk, outcomes were similar in low- and middle-income compared with high-income countries. CONCLUSIONS: Poor patient outcomes are common after inpatient surgery. Global initiatives to increase access to surgical treatments should also address the need for safe perioperative care. STUDY REGISTRATION: ISRCTN5181700

Rapid epidemic expansion of the SARS-CoV-2 Omicron variant in southern Africa

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemic in southern Africa has been characterised by three distinct waves. The first was associated with a mix of SARS-CoV-2 lineages, whilst the second and third waves were driven by the Beta and Delta variants, respectively1-3. In November 2021, genomic surveillance teams in South Africa and Botswana detected a new SARS-CoV-2 variant associated with a rapid resurgence of infections in Gauteng Province, South Africa. Within three days of the first genome being uploaded, it was designated a variant of concern (Omicron) by the World Health Organization and, within three weeks, had been identified in 87 countries. The Omicron variant is exceptional for carrying over 30 mutations in the spike glycoprotein, predicted to influence antibody neutralization and spike function4. Here, we describe the genomic profile and early transmission dynamics of Omicron, highlighting the rapid spread in regions with high levels of population immunity