The dimension of a variety

We invent the notion of a {\it dimension of a variety} $V$ as the cardinality of all its proper {\it derived} subvarieties (of the same type). The dimensions of varieties of lattices, varieties of regular bands and other general algebraic structures are determined.Comment: The results of the paper were presented at the workshop AAA71 and CYA21 at B\c{e}dlewo, Poland on February 11, 2006. the paper is submitted to Discussiones Mathematicae Algebra and Stochastc Methods, special issu

Sensitivity of xylem vessel size and frequency to rainfall and temperature: implications for palaeontology

Based on the xylem vessel size and frequency in fossil wood, a number of studies have developed theories on climate change through time. The basic premise of these studies is that xylem vessel size decreases while vessel frequency increases with intensifying aridity. In this paper the relationship between rainfall and xylem vessel size and frequency is examined in two extant tree species. The results indicate that rainfall is related positively to vessel diameter and negatively to vessel frequency in Combretum apiculatum and Protea caffra. Xylem vessel size of both species is between 50 and 100 µm. However, the two species exhibit different responses to rainfall in that P. caffra has much smaller diameter vessels than C. apiculatum in high rainfall areas. These differences indicate that the potential for using xylem anatomy as a palaeoclimatic indicator has not been fully utilised. A more precise picture of climate change through time is possible with a more refined statistical analysis of reliably identified fossil wood.Water Research Commissio

Do shifts in self-descriptions occur when the concept of self-image is mediated to teenage learners through creative movement?

This thesis sought to explore whether an intervention using Creative Movement could improves the ways in which teenagers described themselves. The theoretical framework of L.S. Vygotsky (1978) was employed as a lens through which to understand the concepts of self-image, mediation, identity and adolescence. An eight week programme was devised by the researcher in which eight volunteer participants at two local South African secondary schools used improvised Creative Movement in various activities facilitated by the researcher. These activities explored various aspects of the self in an attempt to mediate participants towards positive and stable self-description. Data were collected by way of a pre- and post-test in which participants were required to self-describe in a series of written and verbal responses to open and closed questions. The pre- and post-tests were compared in order to track any shifts in self description. These tests included a self-esteem inventory, open-ended written questions and a personal interview. Further data were collected during the intervention in the form of journals kept by participants and observation schedules. Qualitative and quantitative analysis was performed. Quantitative analysis included t-tests in order to ascertain statistical significance of any shifts observed. The research conducted found that significant positive shifts in self-description did occur in all eight participants. Further findings involved the relationship between these shifts and the Zone of Proximal Development and the social structures in which participants found themselves. It was also noted that Creative Movement served as an excellent mediational tool for the concept of self-image

Factors that contribute towards students' successful participation and completion of the intercontinental Masters Programme (Adult Learning and Global Change) at one of the partner universities

Magister Educationis - MEdThis Research sets out to understand the participation experiences of a selected group of adult learners at one of the partner institutionsof the online Intercontinental Masters in Adult Learning and Global Change. The study offers an understanding of adult learners' experiences of success and persistence in relation to online study within a higher education context, and also offers insights into what may costitute successful learning communities. In relation to literature, , the student perceptions obtained via the study largely affirm what 'successiful' can mean to a group of postgraduate adult learners in an online learning environment. This stidy also contributes to the ongoing conversation in terms of the unique experiences of students in one particular cohort of the programme.South Afric

Rendering dark energy void

Includes abstract.Includes bibliographical references (leaves 114-120).The current model of cosmology, the Friedman-Lemaitre-Robertson-Valker model, assumes that the universe is approximately homogeneous and isotropic on very large scales. Further assuming flatness and dark energy in the form of Einstein's cosmological constant A then implies that the latter contributes roughly 73% of the total energy of the universe, cold dark matter (CD'I) 23SiC, and baryons, the matter we are made, only 4%

Climatic reconstruction using wood charcoal from archaeological sites

Bibliography: pages 87-98.This thesis assesses the feasibility of using wood charcoal from archaeological sites as a palaeoclimatic indicator. Three techniques are described: (i) charcoal identification from Xylem Anatomy. (ii) Ecologically Diagnostic Xylem Analysis and (iii) stable carbon isotope analysis on wood charcoal. The first is a well established method of environmental reconstruction. This is the first systematic application of Ecologically Diagnostic Analysis and the first application of stable carbon isotope analysis on wood charcoal. Charcoal identification shows that the most common woody species at Elands Bay today are also evident in the archaeological record over the last 4000 years, indicating a relatively stable plant community composition. Previous studies of wood anatomy have shown that there are links between vessel size, vessel number and climate. This study demonstrates that the wood anatomy of Rhus is not simply related to climatic factors, necessitating the employment of a wide range of statistical analytical techniques to identify climatic signals. In contrast, the anatomy of Diospyros shows strong correlations with temperature. Factor analysis of anatomical parameters of charcoal from Elands Bay archaeological sites indicates that there have been temperature changes over the last 4000 years. Stable carbon isotope ratios (¹³C/¹²C) of plants have been found to be a useful indicator of water use efficiency; plants in drier habitats exhibit more positive values than their more mesic relatives. The results of an isotopic analysis on modern wood charcoal show that ¹³C/¹²C ratios can be related to temperature and rainfall. The climatic component of the range in variation of ¹³C/¹²C in the archaeological record is not as easy to identify due to increased use of fossil fuels since the beginning of the Industrial Revolution. Indications are that wood charcoal does carry a climatic signal. A larger sample from more areas may give more dependable results

Plant xylem anatomy, dendrochronology and stable carbon isotopes as tools in rainfall reconstruction in Southern Africa

Within South Africa there is a growing need for a high resolution proxy rainfall data set that goes back beyond the historic record. As a contribution to meeting this need four techniques for rainfall reconstruction are evaluated. It is only from a new technique utilising measurements of vessel size and frequency in the cross-sectional xylem anatomy of archaeological charcoal that statements may be made on rainfall trends over the last 2000 years. These results indicate a general decrease in rainfall from 2300 BP to the present with a slightly wetter period during the Little Ice Age (1300 to 1800 A.D.). The results also suggest that present conditions are much drier than at any other time within the last 2000 years. The only limitations on this method are the resolution of the radiocarbon dates, a suitable distribution of sites and a calibration curve for the species analysed