Evaluating the role of environmental quality in the sustainable rural economic development of England

The issue of the sustainable development of rural economies in England has recently received considerable attention. This is because many of the poorest areas in the country are rural, often of high environmental quality, but suffering from high unemployment and a lack of services and facilities. The rapid decline in agricultural incomes and in-migration of affluent urban workers since 1990 has exacerbated economic inequality in such areas. A number of factors have the potential to drive rural development and this paper applies, and considers, the feasibility of a method from the USA for combining economic and environmental variables in a regional growth model to examine the hypothesis that environmental quality is an important determinant of sustainable rural development in England. The model output suggests that, although environmental quality does play a role in sustainable rural development in England there are other, more important, factors driving development. These include business and communications infra-structure, the degree and opportunities for commuting and underlying employment prospects. The robustness and limitations of the method for combining economic and environmental variables is discussed in relation to the spatial interrelatedness of Local Authority Districts in England, and conclusions are drawn about areas for refinement and improvement of the method.

Inspecting the teaching of singing in the teacher training colleges of England, Wales and Scotland 1883-1899

This paper investigates the links between the teaching of singing, training and inspection during the late Victorian era. It utilises as a primary source the annual inspection reports of the music inspector, Sir John Stainer. More specifically it focuses upon the musical background of the students in the training colleges of England, Wales and Scotland, the methods employed to teach sight singing and voice production, the vocal repertoire and preparation for the teaching of singing in schools. Finally, some comparison is made with the present day and the relationship between the teaching of singing, training and inspection.

Perspex machine VIII: axioms of transreal arithmetic

Transreal arithmetic is a total arithmetic that contains real arithmetic, but which has no arithmetical exceptions. It allows the specification of the Universal Perspex Machine which unifies geometry with the Turing Machine. Here we axiomatise the algebraic structure of transreal arithmetic so that it provides a total arithmetic on any appropriate set of numbers. This opens up the possibility of specifying a version of floating-point arithmetic that does not have any arithmetical exceptions and in which every number is a first-class citizen. We find that literal numbers in the axioms are distinct. In other words, the axiomatisation does not require special axioms to force non-triviality. It follows that transreal arithmetic must be defined on a set of numbers that contains{-8,-1,0,1,8,&pphi;} as a proper subset. We note that the axioms have been shown to be consistent by machine proof.