Cubic Curves, Finite Geometry and Cryptography

Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a `shared secret' related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.Comment: This is a version of our article to appear in Acta Applicandae Mathematicae. In this version, we have corrected a sentence in the third paragraph. The final publication is available at springerlink.com at http://www.springerlink.com/content/xh85647871215644

Intersections of Hyperconics in Projective Planes of Even Order

AbstractWe show how to lift the even intersection equivalence relation from the hyperovals of PG(2, 4) to an equivalence relation amongst sets of hyperconics in π=PG(2, F). Here, F is any finite or infinite field of characteristic two that contains a subfield of order 4, but does not contain a subfield of order 8. Moreover, we are able to determine the number of points that two hyperconics in π will have in common provided some projective subplane of order 4 intersects both of them in hexads

What passengers really want : assessing the value of rail innovation to improve experiences

Technology has the potential to provide more up-to-date information and customised services to train passengers and therefore improve the rail journey experience. However, there is a lack knowledge about which innovations and services are preferred by the travelling public. The purpose of this study was to understand the value which passengers placed on technological innovations to improve the overall passenger journey experience. A conjoint analysis survey based on the best-worst scale of preference was developed to evaluate how passengers (N = 398) value different system features proposed to improve passenger experience in the UK. Results show that the automatic compensation for delayed or cancelled trains was valued the highest, and the ability to pre-order special services ranked as least value from a set of ten features. Additional results include the segmentation of responses according to passenger type (commuters, business and leisure) and the similarities and differences in responses from the public versus those working directly in the rail industry. The insights gained from this study suggest which features should be prioritised to improve rail passenger journey experiences

New Codes from Old; A New Geometric Construction

AbstractWe describe a new technique for obtaining new codes from old ones using geometric methods. Several applications are described

Assessing the applicability of the Revised Universal Soil Loss Equation (RUSLE) to Irish Catchments

Elevated suspended sediment concentrations in fluvial environments have important implications for system ecology and even small concentrations may have serious consequences for sensitive ecosystems or organisms, such as freshwater pearl mussels (<i>Margaritifera margaritifera</i>). Informed decision making is therefore required for land managers to understand and control soil erosion and sediment delivery to the river network. However, given that monitoring of sediment fluxes requires financial and human resources which are often limited at a national scale, sediment mobilisation and delivery models are commonly used for sediment yield estimation and management. The Revised Universal Soil Loss Equation (RUSLE) is the most widely used model for overland flow erosion and can, when combined with a sediment delivery ratio (SDR), provide reasonable sediment load estimations for a catchment. This paper presents RUSLE factors established from extant GIS and rainfall datasets that are incorporated into a flexible catchment modelling approach. We believe that this is the first time that results from a RUSLE application at a national scale are tested against measured sediment yield values available from Ireland. An initial assessment of RUSLE applied to Irish conditions indicates an overestimation of modelled sediment yield values for most of the selected catchments. Improved methods for model and SDR factors estimation are needed to account for Irish conditions and catchment characteristics. Nonetheless, validation and testing of the model in this study using observed values is an important step towards more effective sediment yield modelling tools for nationwide applications

Migration and linguistic diversity in higher education: Implications for language teaching practice and policy

An increase in migration has led in recent years to growing diversity in society, particularly linguistic diversity, which in turn is influencing higher education. A significant percentage of students now present with a mother tongue different to the medium of instruction. Many also possess additional competencies in a range of other languages. This chapter considers the challenges and opportunities which this situation poses for language teaching practice and policy in a university context. It also discusses possible implications for the design and delivery of foreign language degree programmes, if they are to better reflect the linguistic and cultural diversity in an increasingly multilingual student body, and to enhance the experience of all students studying foreign languages at university