Modelling Hyperbolic Space: Designing a Computational Context for Learning Non-Euclidean Geometry

This paper describes and analyses the iterative design and development of a computational context for non-euclidean geometry. Drawing on three episodes from the design process, the paper discusses the epistemological implications associated with interplay between learning hyperbolic geometry and context in which that learning takes place. In particular, it explores the ways in which learners can become designers of the computational context, and the designer can become a learner. The paper concludes with a discussion of the microworld paradigm in relation to what might be called ‘advanced’ mathematics. This revised version was published online in July 2006 with corrections to the Cover Date.     

High-Spatial-Resolution Low-Energy Electron Beam X-Ray Microanalysis

 Performing X-ray microanalysis at beam energies lower than those conventionally used (< 10 keV) is known to significantly improve the spatial resolution for compositional analysis. However, the reduction in the beam energy which reduces the X-ray interaction diameter also introduces analytical difficulties and constraints which can diminish the overall analytical performance. This paper critically assesses the capabilities and limitations of performing low beam energy, high spatial resolution X-ray microanalysis. The actual improvement in the spatial resolution and the reduction in the X-ray yield are explored as the beam energy is reduced. The consequences for spectral interpretation, quantitative analysis and imaging due to the lower X-ray yield and the increased occurrence of X-ray line overlaps are discussed in the context of currently available instrumentation.     

On Objectivity and Material Symmetry for Simple Elastic Solids

Restrictions imposed on stress response functions by objectivity and material symmetry are usually obtained by appeal to both a reference configuration and a response function common to all observers. Here these restrictions are obtained by regarding the reference configuration to be observer-dependent in a natural manner, and without the need to assume the existence of a common response function. Remarks are made on the distinction which should be drawn between the notions of observer transformation and rigid deformation, the consequences of this distinction for the correct interpretation of ‘invariance under superposed rigid motions’, and on the domains of response functions. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Facile Synthesis of Substituted Phenylglycines

A convenient scaleable process for the preparation of substituted phenylglycines 2 by a modified Strecker reaction is described. Bisulfite-mediated addition of benzylamine and cyanide anion to substituted benzaldehydes 3 gave the aminonitriles 4 which were hydrolysed in two steps to the N-protected amino acid 1. Debenzylation using catalytic transfer hydrogenation gave the title compounds in good yield.     

2‐Chloro‐3‐(pyrrolidin‐1‐yl)‐1,4‐naphtho­quinone

The structure of the title compound, C₁₄H₁₂ClNO₂, (I), comprises essentially planar mol­ecules which crystallize in a monoclinic lattice. C—H?O interactions exist to both naphtho­quinone O atoms and the Cl atom.