Semiclassical approximation in Batalin-Vilkovisky formalism

The geometry of supermanifolds provided with $Q$-structure (i.e. with odd vector field $Q$ satisfying $\{ Q,Q\} =0$), $P$-structure (odd symplectic structure ) and $S$-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion.Comment: 27 page

Threatened plants of the Albany Centre of Floristic Endemism, South Africa

We present Red List assessments of threatened plants of the Albany Centre of Floristic Endemism in the Eastern Cape province of South Africa. We evaluated the status of taxa using categories and criteria adopted by the World Conservation Union (IUCN) in 1994 and updated in 2001. In total, 126 taxa are threatened with extinction in the Albany Centre, and six are now extinct. A further 22 are listed as Data Deficient. In the past, agriculture has been a severe threat to the survival of rare species in this part of the Eastern Cape; the main threats to the continuing existence of threatened plants in this area are illegal collecting, residential development and urban growth

Traditional veterinary medicine in the Alice district of the Eastern Cape Province, South Africa

Resource-poor farmers in rural and peri-urban areas have limited access to veterinary care in terms of support services (from state and private veterinarian and animal health technicians), information about the prevention and treatment of livestock diseases, and preventative and therapeutic veterinary medicines. This results in reduced productivity and in livestock disease and deaths, which is a great burden on these farmers, who can least afford the loss of their animals. There is a need to encourage disadvantaged farmers to use available resources and methods, at minimal cost, and to improve their productivity. One of these resources is ethnoveterinary medicine. A list of 53 plants used as veterinary medicines by stock farmers in the Alice district in the Eastern Cape is presented together with their preparation and methods of administration

The role of 'African Chemists' in the health care system of the Eastern Cape province of South Africa

Self-medication is documented as an integral part of health care therapy in developing countries such as Ethiopia, Cameroon, Uganda and Mexico. In South Africa the types of illnesses and health problems that are referred to both traditional healers and biomedical practices have been well documented. However, very little literature exists on self-diagnosis, self-medication or sources of the medicines used for self-medication. This bias in the literature has come about largely because anthropological studies have focused on the later stages of the illness referral system when treatment is sought from a specialist for symptoms which have not responded to forms of self-medication. As a result of this, health care studies have documented the more exceptional exotic healing rituals and culturally bound syndromes of a particular society or community, and not discussed the more ordinary practices of self-medication of everyday illness. Self-medication is however an important initial response to illness and many illnesses are successfully managed at this stage. Amayeza stores (singular-iyeza store) — or ‘African chemists’ — are an important source of medicines for self-diagnosed illnesses. The current discussion focuses on the types of medicines and treatments that are obtained from amayeza stores without professional consultation in the Eastern Cape province of South Africa

Mine waste characterization, management and remediation

Mining is a vital part of the Global economy, but the extraction of metals, metalloids, and other mineral products generates vast quantities of liquid and solid waste. Currently the volume is estimated at several thousand million tons per annum, but is increasing exponentially as demand and exploitation of lower-grade deposits increases. The high concentrations of potentially toxic elements in these wastes can pose risks to ecosystems and humans, but these risks can be mitigated by implementing appropriate management or remediation schemes. Although there are a large number of such schemes available, there is still a need to research the processes, products, and effectiveness of implementation, as well as the nature of the mine wastes themselves. This Special Issue is aimed at bringing together studies in the areas of mine waste characterization, management, and remediation, to review the current state of knowledge and to develop improvements in current schemes. Fourteen manuscripts are published for this Special Issue, and these are summarized below.[...

Drimia chalumnensis (Hyacinthaceae - Urgineoideae), a new species from Eastern Cape, South Africa

Drimia chalumnensis, a new inconspicuous dwarf species from the Albany Centre of Floristic Endemism in Eastern Cape, South Africa, is restricted to the coastal plains of the Chalumna river in small scattered aggregated colonies on exposed sandstone sheets in pockets of loose sandy soil. It is distinguished by its capitate inflorescence, separate, petiolate bulb scales, and prostrate, coriaceous, linear-lanceolate leaves with cartilaginous margins

The trade in medicinal plants in the Eastern Cape Province, South Africa

A study of the trade in medicinal plants in the Eastern Cape Province of South Africa undertook to document the species traded, to determine the quantities harvested annually, and to assess the economic value of the trade. All the participants involved at the different levels of the trade were included in the survey, that is, informal street hawkers, owners of amayeza esiXhosa stores, traditional healers, and consumers of traditional medicines. In total, 282 questionnaires were administered in six urban centres. It was found that poorly educated black middle-aged women of low economic standing dominate the trade. A minimum of 166 medicinal plant species were traded at the study sites alone, providing 525 tonnes of plant material valued at approximately R27 million annually. Plants were harvested from a diverse range of vegetation types including Valley Thicket, Afromontane Forest, Coastal Forest and Moist Upland Grassland, the most frequently sold species differing significantly from those documented in similar studies in other regions. The Forest Biome was the vegetation type found to be most threatened by over-harvesting. Of the species documented, 93% were being harvested unsustainably and 34 species have been prioritised for conservation management

A Tverberg type theorem for matroids

Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d+1, then for any continuous map f from the matroidal complex M into the d-dimensional Euclidean space there exist t \geq \sqrt{b(M)}/4 disjoint independent sets \sigma_1,\ldots,\sigma_t \in M such that \bigcap_{i=1}^t f(\sigma_i) \neq \emptyset.Comment: This article is due to be published in the collection of papers "A Journey through Discrete Mathematics. A Tribute to Jiri Matousek" edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by Springe

Shadows and traces in bicategories

Traces in symmetric monoidal categories are well-known and have many applications; for instance, their functoriality directly implies the Lefschetz fixed point theorem. However, for some applications, such as generalizations of the Lefschetz theorem, one needs "noncommutative" traces, such as the Hattori-Stallings trace for modules over noncommutative rings. In this paper we study a generalization of the symmetric monoidal trace which applies to noncommutative situations; its context is a bicategory equipped with an extra structure called a "shadow." In particular, we prove its functoriality and 2-functoriality, which are essential to its applications in fixed-point theory. Throughout we make use of an appropriate "cylindrical" type of string diagram, which we justify formally in an appendix.Comment: 46 pages; v2: reorganized and shortened, added proof for cylindrical string diagrams; v3: final version, to appear in JHR

Making precise predictions of the Casimir force between metallic plates via a weighted Kramers-Kronig transform

The possibility of making precise predictions for the Casimir force is essential for the theoretical interpretation of current precision experiments on the thermal Casimir effect with metallic plates, especially for sub-micron separations. For this purpose it is necessary to estimate very accurately the dielectric function of a conductor along the imaginary frequency axis. This task is complicated in the case of ohmic conductors, because optical data do not usually extend to sufficiently low frequencies to permit an accurate evaluation of the standard Kramers-Kronig integral used to compute $\epsilon(i \xi)$. By making important improvements in the results of a previous paper by the author, it is shown that this difficulty can be resolved by considering suitable weighted dispersions relations, which strongly suppress the contribution of low frequencies. The weighted dispersion formulae presented in this paper permit to estimate accurately the dielectric function of ohmic conductors for imaginary frequencies, on the basis of optical data extending from the IR to the UV, with no need of uncontrolled data extrapolations towards zero frequency that are instead necessary with standard Kramers-Kronig relations. Applications to several sets of data for gold films are presented to demonstrate viability of the new dispersion formulae.Comment: 18 pages, 15 encapsulated figures. In the revised version important improvements have been made, which affect the main conclusions of the pape