Large Parameter Cases of the Gauss Hypergeometric Function

We consider the asymptotic behaviour of the Gauss hypergeometric function when several of the parameters a, b, c are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Krawtchouk, Meixner, etc.), which results are already available and which cases need more attention. We also consider a few examples of 3F2-functions of unit argument, to explain which difficulties arise in these cases, when standard integrals or differential equations are not available.Comment: 21 pages, 4 figure

Beyond Turf and Lawn: Poaceae in This Age of Climate Change

Grassland ecosystems dominated by Poaceae are estimated to cover 40.5% of Earth’s land base, and domestication of a few edible grass species into highly productive cereal grains aided the shift from nomadic food gathering to field cultivation and higher density habitation. In the Northern Hemisphere, grasses are used ornamentally and for pasture, fodder and forage with little thought that the grasses livestock grazed upon, or those we gaze upon have multi-functional uses elsewhere. In this age of climate change, the use of Poaceae solely for aesthetics and amenity depletes finite potable water supplies that are needed for human survival. Agricultural land is consumed for turf seed production, and land is removed from food production. Cereals and their growing regions, which we have depended upon as food for millennia, are unlikely to adapt to climate change, and this will result in food insecurity and famines. Despite traditional uses of Poaceae in various cultures, many unrealized needs for food, medicine and other material goods could be met elsewhere with knowledge transfer. Our modern relationship with grass as an ornamental or amenity must end. As designers, gardeners and urban dwellers, we must use Poaceae for its multi-functions, which will lead to resilience and survival

Exploring Multiliteracies and Other Approaches to Second Language Teaching

This teaching portfolio offers a selection from the author’s graduate coursework, teaching experience, and research undertaken while enrolled in the Utah State University Master of Second Language Teaching (MSLT) program. The documents included are a reflection of her pedagogical approach and teaching practice, developed through varying contexts of professional experiences, including teaching English and French as a second language. This portfolio includes: reflections on the author’s teaching environment, a teaching philosophy statement, a professional development peer observation, a reflection paper that demonstrates the author’s experiences teaching with stories within the context of the multiliteracies framework, specifically multimodal fairy tales with The Fable Cottage platform, and finally, a consideration of future career goals related to language learning and teaching

Conical: an extended module for computing a numerically satisfactory pair of solutions of the differential equation for conical functions

Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module CONICAL for the computation of conical functions. Specifically, the module includes now a routine for computing the function ${{\rm R}}^{m}_{-\frac{1}{2}+i\tau}(x)$, a real-valued numerically satisfactory companion of the function ${\rm P}^m_{-\tfrac12+i\tau}(x)$ for $x>1$. In this way, a natural basis for solving Dirichlet problems bounded by conical domains is provided.Comment: To appear in Computer Physics Communication

Developing a methodology for the non-destructive analysis of British soft-paste porcelain

Soft-paste porcelain was produced in Britain in great quantities between the mid-18th and early 19th centuries. Due to industrial secrecy and the complexities of creating a product that would survive high-temperature firing, a range of paste recipes was employed by dozens of factories. This has resulted in an array of porcelains which vary in their elemental composition and mineralogy. This research carries out a meta-analysis of the published data for porcelain bodies and glazes and concludes that some discrimination can be achieved using the major and minor elemental composition of the bodies, and that for the glazes intra-factory variation is often greater than inter-factory variation in composition. A pilot investigation of the trace elemental composition of British porcelain is carried out using Laser Ablation Inductively Coupled Plasma Mass Spectroscopy, which finds compositional groups corresponding to different sources of clay and silica raw materials. In the interests of preserving intact objects, there is recognised a need for a non-destructive method for analysing British porcelain, in order to provenance and date objects. Such a method would rely on data from the surface of the object, which is typically covered by glaze and over-glaze coloured enamels, and this research demonstrates that the formulae used for the glaze and enamels are in some cases characteristic of the factory, or workshop, and period at which they were created. Hand-Held XRF analysis is used to analyse the glaze, underglaze blue and polychrome enamels on a selection of porcelain objects from different factories, and compositional traits are identified that allow some factories and periods to be distinguished. Glass standards are developed, which are representative of the glaze and enamel composition, and which could allow X-ray fluorescence (XRF) data to be calibrated for fully quantitative results