On some Graphs with a Unique Perfect Matching

We show that deciding whether a given graph $G$ of size $m$ has a unique perfect matching as well as finding that matching, if it exists, can be done in time $O(m)$ if $G$ is either a cograph, or a split graph, or an interval graph, or claw-free. Furthermore, we provide a constructive characterization of the claw-free graphs with a unique perfect matching

Culture (and religion) in constitutional adjudication

The faculty of law of the Potchefstroom University for Christian Higher Education in corroboration with the Konrad-Adenauer-Stifttung embarked on a study on Politics, Socio-Economic Issues and Culture in Constitutional Adjudication. The aim of the project is twofold. The first aim is to analyse the influence of political, socio-economic and cultural considerations on the constitutional court’s interpretation and application of the Bill of Rights. The second aim is to develop practical guidelines (based on the findings during the analysing process) for South African courts confronted with issues of a political, socio-economic and cultural nature. This article is concerned with initiating discussions of the decisions of the constitutional court with regard to cultural and religious rights. Before we can explore the role of political, socio-economic and cultural (and religious) rights in the decisions of the constitutional court it is important to discuss a few preliminary issues. In this article the meaning of culture and religion within the South African context receives some attention. Secondly, some preliminary comments regarding constitutional protection of culturally and religiously based rights will be made. We are well aware that this is a daunting task, not only in view of the seemingly abysmal gap between the applicable constitutional rights and values enshrined in the 1996 Constitution that, in some instances over centuries, brought about customs and practices within “traditional” communities which, seemingly, infringe on certain constitutional values and rights

Books

Ask the Doctor. Hypertension By Vincent Friedewald. Pp. xiv + 120. R59.95. Kansas City:Andrews and McMeel. ISBN 0-8362-7022-3.How to Survive in Anaesthesia*By P Neville Robinson and George M Hall. Pp. xi + 172. £22.00.1997. London: BMJ. ISBN 0-7279-1066-3.Epidemiology. A Manual for South Africa* Edited by J M Katzenellenbogen, G Joubert and S S Abdool Karim. Pp. 295. R120. 1997. Cape Town: Oxford University Press. ISBN 0-19-571308-7

Geometry viewer for PGADMIN4 : a process guided by the Google Summer of Code

The latest version of pgAdmin4 was released in mid-2016 and moved to a web-based application that was written in Python and jQuery with Bootstrap, using the Flask framework. This new architecture of pgAdmin4 provided an excellent opportunity to integrate a geometry viewer into the application. This progress started as the geometry viewer was selected as a project for the 2018 Google Summer of Code (GSoC). The requirements for the geometry viewer was elicited through conversations with the mentors and emails to the discussion list of PostGIS and pgAdmin. Once the formal design was finalized the development started. The spatial technology stack implemented to expand pgAdmin4 with a geometry viewer was the JavaScript mapping library Leaflet JS and WKX - parser/serializer library that supports several spatial vector formats. Both these fulfilled the requirements of the coding standard of pgAdmin that all client-side code must be developed in JavaScript using jQuery and other plugins. Leaflet JS is well known for its ease of use and compatibility. WKX is lesser known but well supported and concise to the need to parse the spatial data before rendering on the Leaflet map. The decision on both of these libraries was motivated by their minimal size and possibilities for expansion for future extensions of the viewer. The first version of the geometry viewer was well-received and is currently integrated into the latest versions of pgAdmin4.https://www.isprs.orgpm2020Geography, Geoinformatics and Meteorolog

Предварительный расчет толщины обечайки шестигранного контейнера для утилизации среднеактивных ядерных отходов

AbstractLet α∈(0,1) and let G=(VG,EG) be a graph. According to Dunbar et al. [α-Domination, Discrete Math. 211 (2000) 11–26], a set D⊆VG is an α-dominating set of G if |NG(u)∩D|⩾αdG(u) for all u∈VG⧹D. Similarly, we define a set D⊆VG to be an α-independent set of G if |NG(u)∩D|⩽αdG(u) for all u∈D. The α-domination number γα(G) of G is the minimum cardinality of an α-dominating set of G and the α-independent α-domination number iα(G) of G is the minimum cardinality of an α-dominating set of G that is also α-independent. A graph G is α-domination perfect if γα(H)=iα(H) for all induced subgraphs H of G.We characterize the α-domination perfect trees in terms of their minimally forbidden induced subtrees. For α∈(0,12] there is exactly one such tree whereas for α∈(12,1) there are infinitely many

A review of South African research in atmospheric science and physical oceanography during 2000-2005

The purpose of this article is to review progress in the fields of atmospheric science and physical oceanography made by workers based at South African institutions over approximately the last 5 years. Research published by South African scientists working abroad is not included. Most published research in these fields falls within the broad areas of climate variability, climate change, aerosols and atmospheric pollution, seasonal forecasting, numerical modelling (both atmospheric and oceanic), and the physical oceanography of the Agulhas and Benguela current systems. Most but not all of the atmospheric science papers relate to South Africa or southern Africa; however, some work pertaining to the southern hemisphere as a whole or to other regions has been done. We note that funding and institutional support for atmospheric science and physical oceanography research in South Africa remains poor and this situation significantly hampers local efforts

Packing and covering immersion models of planar subcubic graphs

A graph $H$ is an immersion of a graph $G$ if $H$ can be obtained by some sugraph $G$ after lifting incident edges. We prove that there is a polynomial function $f:\Bbb{N}\times\Bbb{N}\rightarrow\Bbb{N}$, such that if $H$ is a connected planar subcubic graph on $h>0$ edges, $G$ is a graph, and $k$ is a non-negative integer, then either $G$ contains $k$ vertex/edge-disjoint subgraphs, each containing $H$ as an immersion, or $G$ contains a set $F$ of $f(k,h)$ vertices/edges such that $G\setminus F$ does not contain $H$ as an immersion

The Lingering Environmental Impact of Repressive Governance: The Environmental Legacy of the Apartheid Era for the New South Africa

This article aims to explore the historical link between contemporary environmental problems and the environmental, economic and political policies of the apartheid government. The analysis draws on an examination of the detrimental environmental impacts of the apartheid era and how international isolation impacted on governmental environmental management in the country, before turning attention to the way in which the ANC government has managed the South African natural and human environments in the period after 1994. The article shows that despite many important new developments since 1994, that there are high levels of continuity between the environmental management practices of the old and the new regimes. This state of affairs negatively impacts on the ability of the ANC government to provide every South African citizen with the clean and safe environment guaranteed to all within the 1996 Bill of Rights.This article also appeared unchanged as a chapter in the following edited collection: Jan Oosthoek and Barry K. Gills (eds), _The Globalization of Environmental Crisis_ (Abingdon: Routledge, 2008), pp. 109-120