Lattice Knots in a Slab

In this paper the number and lengths of minimal length lattice knots confined to slabs of width $L$, is determined. Our data on minimal length verify the results by Sharein et.al. (2011) for the similar problem, expect in a single case, where an improvement is found. From our data we construct two models of grafted knotted ring polymers squeezed between hard walls, or by an external force. In each model, we determine the entropic forces arising when the lattice polygon is squeezed by externally applied forces. The profile of forces and compressibility of several knot types are presented and compared, and in addition, the total work done on the lattice knots when it is squeezed to a minimal state is determined

Minimal knotted polygons in cubic lattices

An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe

The Compressibility of Minimal Lattice Knots

The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our results show that the compressibility is generally not monotonic, but in some cases increases with pressure. Differences of the compressibility for different knot types show that topology is a factor determining the compressibility of a lattice knot, and differences between the three lattices show that compressibility is also a function of geometry.Comment: Submitted to J. Stat. Mec

The inadequacy of the Social Grant System available to children in South Africa

The purpose of this article is to examine the current social assistance grant system available to children in South Africa and to indicate its major shortcomings. The new Children’s Bill and Social Assistance Bill, soon to be enacted, will also be examined to establish whether there are any positive changes with regard to the socio-economic situation of children. Proposals made by the South African Law Commission, South African Human Rights Commission, Committee of Inquiry into a Comprehensive System of Social Security for South Africa, the United Nations Committee on the Rights of the Child and several other interested parties will also be considered to establish whether in fact government is in compliance with its constitutional and international duty towards realising the social security and social assistance rights of children. It is submitted that the exclusion of children of the ages of (currently) 11 to 18 from the child support grant infringes on their  constitutional rights to social assistance, human dignity, life and equality. Another problem with the current grants is the unavailability thereof to households where an adult caregiver is absent as well as the complicated means test. The unavailability of these grants to children of refugees is also a cause for concern. Due to the categorical nature of children’s social assistance grants, it is submitted that the state is not currently conforming to the standards set by the Bill of Rights and international law

Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

Blended teaching and learning: Exploring the concept, barriers to implementation and designing of learning resources

With the advent of the coronavirus disease 2019 (COVID-19), several institutions worldwide have adopted the blended mode of teaching and learning. However, literature on this concept in South Africa and on the African continent is scarce. This scoping review explores the concept of blended approach to training and how to design resources for the blended teaching and learning approach. In addition, the review investigates barriers to the implementation of blended learning. The findings of this study demonstrate that the understanding of the concept of blended teaching and learning is not homogenous and is often left to individual academics to decide on the approach. The review identified several hurdles that need to be addressed for successful implementation of blended teaching and learning, however these are not specific to South African institutions. Available literature on studies done elsewhere and in South African, suggest that some of the identified barriers to adoption of blended teaching and learning are real, while others are perceived or imagined. Lastly, the authors observed that there are several approaches to designing learning resources for the blended mode of teaching and learning. The choice of approach is dependent on the intended purpose for which the specific design is adopted. There is a need for studies that specifically investigate blended learning in Universities in South Africa and on the continent to help identify barriers to adopting blended teaching and learning among institutions that are specific to the South African and African context. Institutions adopting the blended teaching and learning mode of delivery, need to be unambiguous in their philosophy of blending teaching and learning and not leave it to the implementing academics. Policymakers can use the information generated in this review to recommend minimum requirements for a blended delivery mode in public institutions of higher learning

Iliopsoas haematoma in a rugby player

Traumatic iliopsoas haematoma is a serious complication of haemorrhage disorders rarely seen in young healthy athletes. It is mostly describedin patients on anticoagulant therapy and commonly associated with various degrees of femoral nerve palsy. A 22-year-old male rugby playerpresented with severe onset of pain in the lower back, right hip flexor/pelvic area following a tackle during a rugby match. Magnetic resonanceimaging identified a distinct, hyperechoic heterogeneous mass within the right iliopsoas muscle, confirming a diagnosis of iliopsoas haematoma.The case resolved completely after conservative medical treatment in addition to a period of rest and intense active physical therapy. This casestudy reports the rare diagnosis of an uncomplicated iliopsoas haematoma following a sports injury in a young athlete

Corticosteroids in sports-related injuries: Friend or Foe

Corticosteroids act as potent anti-inflammatory drugs and have been used in various sport settings for the treatment of both acute and chronic injuries. Basic physiology and mechanisms of action for gluco- and mineralocorticoids are discussed. Methods of administration, the action on the inflammatory response, and potential short and long-term side effects of corticosteroid use are also deliberated. More specifically, corticosteroid use in the treatment and management of sport-related injuries are discussed, elucidating on the ethical boundaries and anti-doping regulations pertaining to corticosteroid use in sports, as well as putting forth suggestions for the use of local steroid injections and their contraindications. In conclusion, it was found that, despite some controversy in the use of corticosteroid treatment in the sports environment, little empirical evidence exists that could conclusively rule for or against its use. It is however clear that, if clinically justified, there is a significant role for corticosteroid treatment in the realm of sports injury and notably with a relatively low risk profile, if administered correctly.Keywords: Steroid hormones, athlete, sports, injury, inflammation

Resources and infrastructure for the delivery of antiretroviral therapy at primary health

There are concerns as to whether South Africa\'s public health system has sufficient resources, human and otherwise, to ensure universal access to antiretroviral treatment (ART). We report on public sector implementation of the Comprehensive Care Management and Treatment (CCMT) programme in the Free State Province, South Africa, in particular whether the primary health care (PHC) infrastructure was able to mobilise the necessary inputs to effectively provide ART, without undermining other services within facilities. A longitudinal study was conducted of the first 16 PHC facilities accredited to provide ART in the province. The facilities were visited on three occasions over 2 years, involving both structured and open-ended interviews with professional and lay staff, and observations of available resources. The resources assessed were staffing, space, essential equipment, drug supplies and laboratory systems. Approximately one-fifth (20%) of professional nurses were allocated to the CCMT programme in the facilities, although the overall number of professional nurses increased by only 14%. This process resulted in some displacement of professional nurses towards the CCMT Programme away from other services in the facilities. However, this could have been partially compensated for by task shifting towards community health workers and the appointment of additional support staff. Staff were largely positive about the programme. Drug supplies, availability of equipment and laboratory systems, although good at the baseline, improved further over the period of observation. The lack of adequate space to accommodate the new programme was a frequently reported problem. Overall, our assessment is that the PHC infrastructure in the Free State\'s public health system is capable of implementing and benefiting from the CCMT programme. Nevertheless, constraints in the availability of professional staff threaten future implementation of both the CCMT and other PHC programmes. Keywords: Resources, infrastructure, antiretroviral therapy, primary health care facilities.SAHARA-J Vol. 5 (3) 2008: pp.106-11

Incidence of heat-labile enterotoxin-producing Escherichia coli detected by means of polymerase chain reaction amplification

CITATION: Winterbach, R. et al. 1994. Incidence of heat-labile enterotoxin-producing Escherichia coli detected by means of polymerase chain reaction amplification. South African Medical Journal, 84:85-87.The original publication is available at http://www.samj.org.zaDiarrhoea can be caused by many different organisms, some of which are notoriously difficult to identify. One of these is enterotoxin-producing Escherichia coli. Recently a new diagnostic technique that uses polymerase chain reaction DNA amplification was developed for detection of the 'A' subunit of the labile enterotoxin-producing E. coli gene. This technique was used to evaluate the incidence of heat-labile (LT+) enterotoxin-producing E. coli in the causation of diarrhoea. The results from this study showed that LT+ E. coli is a cause of diarrhoea in the western Cape and that 5,3% of non-diagnosed diarrhoea patients in Tygerberg Hospital were infected with this pathogen. This represented less than 1% of the total number of cases of diarrhoea investigated in this hospital. The peak coincides with the wetter months in this locality and the infection rate is lower than that reported in most other countries. Given the low incidence of occurrence of this organism we do not recommend routine implementation of the diagnostic procedure. However, this test may be useful at times, e.g. to ascertain the source of a diarrhoea epidemic.Publisher’s versio