Topological mappings between graphs, trees and generalized trees

We present novel topological mappings between graphs, trees and generalized trees that means between structured objects with different properties. The two major contributions of this paper are, first, to clarify the relation between graphs, trees and generalized trees, a graph class recently introduced. Second, these transformations provide a unique opportunity to transform structured objects into a representation that might be beneficial for a processing, e.g., by machine learning techniques for graph classification. (c) 2006 Elsevier Inc. All rights reserved.

Phase transformations in maraging steels

Research on the kinetics of precipitate formation and austenite reversion in maraging steels has received great attention due to their importance to steel properties. Judging from the literature in recent years, research into maraging steels has been very active, mainly extending to new types of steels, for new applications beyond the traditional strength requirements. This chapter provides an in-depth overview of the literature in this area. In addition, the kinetics of precipitate formation are analysed using the Johnson–Mehl–Avrami (JMA) theory.

On the Mechanism of Lewis Acid Catalyzed Glucose Transformations in Ionic Liquids

A complementary computational and experimental study of the reactivity of Lewis acidic CrCl2, CuCl2 and FeCl2 catalysts towards glucose activation in dialkylimidazolium chloride ionic liquids is performed. The selective dehydration of glucose to 5-hydroxymethylfurfural (HMF) proceeds through the intermediate formation of fructose. Although chromium(II) and copper(II) chlorides are able to dehydrate fructose with high HMF selectivity, reasonable HMF yields from glucose are only obtained with CrCl2 as the catalyst. Glucose conversion by CuCl2 is not selective, while FeCl2 catalyst does not activate sugar molecules. These differences in reactivity are rationalized on the basis of in situ X-ray absorption spectroscopy measurements and the results of density functional theory calculations. The reactivity in glucose dehydration and HMF selectivity are determined by the behavior of the ionic liquid-mediated Lewis acid catalysts towards the initial activation of the sugar molecules. The formation of a coordination complex between the Lewis acidic Cr2+ center and glucose directs glucose transformation into fructose. For Cu2+ the direct coordination of sugar to the copper(II) chloride complex is unfavorable. Glucose deprotonation by a mobile Cl- ligand in the CuCl42- complex initiates the nonselective conversion. In the course of the reaction the Cu2+ ions are reduced to Cu+. Both paths are prohibited for the FeCl2 catalyst.

Are systemizing and autistic traits related to talent and interest in mathematics and engineering? Testing some of the central claims of the empathizing-systemizing theory.

In two experiments, we tested some of the central claims of the empathizing-systemizing (E-S) theory. Experiment 1 showed that the systemizing quotient (SQ) was unrelated to performance on a mathematics test, although it was correlated with statistics-related attitudes, self-efficacy, and anxiety. In Experiment 2, systemizing skills, and gender differences in these skills, were more strongly related to spatial thinking styles than to SQ. In fact, when we partialled the effect of spatial thinking styles, SQ was no longer related to systemizing skills. Additionally, there was no relationship between the Autism Spectrum Quotient (AQ) and the SQ, or skills and interest in mathematics and mechanical reasoning. We discuss the implications of our findings for the E-S theory, and for understanding the autistic cognitive profile.

The link between logic, mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children

This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain-general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief-laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief-neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real-life referents) develops later than the ability to reason about belief-inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8.

Does flexibility in secondary level mathematics curriculum affect degree performance?

The authors have much experience in developing mathematics skills of first-year engineering students and attempting to ensure a smooth transition from secondary school to university. Concerns exist due to there being flexibility in the choice of modules needed to obtain a secondary level (A-level) mathematics qualification. This qualification is based on some core (pure maths) modules and a selection from mechanics and statistics modules. A survey of aerospace and mechanical engineering students in Queen’s University Belfast revealed that a combination of both mechanics and statistics (the basic module in both) was by far the most popular choice and therefore only about one quarter of this cohort had studied mechanics beyond the basic module within school maths. Those students who studied the extra mechanics and who achieved top grades at school subsequently did better in two core, first-year engineering courses. However, students with a lower grade from school did not seem to gain any significant advantage in the first-year engineering courses despite having the extra mechanics background. This investigation ties in with ongoing and wider concerns with secondary level mathematics provision in the UK.