A Convenient Preparation of Carboxylic Acid Anhydrides Using a “Supported” Phosphorus Pentoxide Reagent

Treatment of carboxylic acids with a “supported” phosphorus pentoxide reagent provides a convenient route to the corresponding anhydrides.     

Examining the didactic contract when handheld technology is permitted in the mathematics classroom

The use of mathematics analysis software (MAS) including handheld scientific and graphics calculators offers a range of pedagogical opportunities. Its use can support change in the didactic contract. MAS may become an alternative source of authority in the classroom empowering students to explore variation and regularity, manipulate simulations and link representations. Strategic use may support students to direct their own learning and explore mathematics, equipping them to share their findings with the teacher and the class with more confidence. This paper offers a framework for examining the impact of the use of MAS on the didactic contract. Lessons were observed in 12 grade 10 classes, with 12 different teachers new to MAS. MAS technology was used with a variety of didactic contracts, mostly traditional. The framework drew attention to many ways in which the teaching differed. Analysis of the didactic contract must consider both the teaching of mathematics and of technology skills, because these have different characteristics. In all classes, both teachers and students saw the teacher as having a responsibility to teach technology skills. Students saw technology skills as the main point of the lesson, but the teachers saw the lesson as primarily teaching mathematics—one of the mismatches which may need negotiation to adapt didactic contracts to teaching with MAS.     

Normal subgroups of nonstandard symmetric and alternating groups

Let be a nonstandard model of Peano Arithmetic with domain M and let be nonstandard. We study the symmetric and alternating groups S _n and A _n of permutations of the set internal to , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide evidence that A _n and S _n are not split extensions by these normal subgroups, by showing that any such complement if it exists, cannot be a limit of definable sets. We conclude by identifying an -valued metric on and (where B _S , B _A are the maximal normal subgroups of S _n and A _n identified earlier) making these groups into topological groups, and by showing that if is -saturated then and are complete with respect to this metric.      

A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems

This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date.     

Review of atom probe FIB-based specimen preparation methods.

Several FIB-based methods that have been developed to fabricate needle-shaped atom probe specimens from a variety of specimen geometries, and site-specific regions are reviewed. These methods have enabled electronic device structures to be characterized. The atom probe may be used to quantify the level and range of gallium implantation and has demonstrated that the use of low accelerating voltages during the final stages of milling can dramatically reduce the extent of gallium implantation.     

Quantitative x-ray phase-contrast imaging using a single grating of comparable pitch to sample feature size

The ability to quantitatively retrieve transverse phase maps during imaging by using coherent x rays often requires a precise grating or analyzer-crystal-based setup. Imaging of live animals presents further challenges when these methods require multiple exposures for image reconstruction. We present a simple method of single-exposure, single-grating quantitative phase contrast for a regime in which the grating period is much greater than the effective pixel size. A grating is used to create a high-visibility reference pattern incident on the sample, which is distorted according to the complex refractive index and thickness of the sample. The resolution, along a line parallel to the grating, is not restricted by the grating spacing, and the detector resolution becomes the primary determinant of the spatial resolution. We present a method of analysis that maps the displacement of interrogation windows in order to retrieve a quantitative phase map. Application of this analysis to the imaging of known phantoms shows excellent correspondence.     

Effect of molecular architecture on DBS-induced block copolymer gels: A rheological study

Dibenzylidene sorbitol (DBS) is capable of gelling a variety of organic solvents and polymeric materials by forming a rigid, 3-D hydrogen-bonded network. In this work, two poly(siloxane)/poly(propylene oxide) segmented copolymers of equal composition and molecular weight, but different architectures (endblocked vs. pendant), as well as a pure poly(propylene oxide), have been gelled with DBS. We have investigated the dynamic rheological properties of these gels to ascertain the effect of copolymer architecture, PDMS comonomer and DBS concentration on network formation.     

1H NMR‐based kinetic and mechanistic study of unusual skeletal rearrangements of a spirobornyl tosylate derivative

¹H NMR analysis of the kinetics of skeletal rearrangement of optically pure 3,3‐xylyl‐2‐exo‐bornyl tosylate in CDCl₃ indicates the operation of tandem autocatalytic and pseudo‐first‐order transformations, leading sequentially to a pair of isomeric camphene derivatives and involving partial racemization. Changing the solvent system has been shown to permit the chemoselective isolation of either of the isomeric camphenes. Copyright © 2010 John Wiley & Sons, Ltd.