An ordinal analysis for theories of self-referential truth

The first attempt at a systematic approach to axiomatic theories of truth was undertaken by Friedman and Sheard (Ann Pure Appl Log 33:1–21, 1987). There twelve principles consisting of axioms, axiom schemata and rules of inference, each embodying a reasonable property of truth were isolated for study. Working with a base theory of truth conservative over PA, Friedman and Sheard raised the following questions. Which subsets of the Optional Axioms are consistent over the base theory? What are the proof-theoretic strengths of the consistent theories? The first question was answered completely by Friedman and Sheard; all subsets of the Optional Axioms were classified as either consistent or inconsistent giving rise to nine maximal consistent theories of truth.They also determined the proof-theoretic strength of two subsets of the Optional Axioms. The aim of this paper is to continue the work begun by Friedman and Sheard. We will establish the proof-theoretic strength of all the remaining seven theories and relate their arithmetic part to well-known theories ranging from PA to the theory of ${\Sigma^1_1}The first attempt at a systematic approach to axiomatic theories of truth was undertaken by Friedman and Sheard (Ann Pure Appl Log 33:1–21, 1987). There twelve principles consisting of axioms, axiom schemata and rules of inference, each embodying a reasonable property of truth were isolated for study. Working with a base theory of truth conservative over PA, Friedman and Sheard raised the following questions. Which subsets of the Optional Axioms are consistent over the base theory? What are the proof-theoretic strengths of the consistent theories? The first question was answered completely by Friedman and Sheard; all subsets of the Optional Axioms were classified as either consistent or inconsistent giving rise to nine maximal consistent theories of truth.They also determined the proof-theoretic strength of two subsets of the Optional Axioms. The aim of this paper is to continue the work begun by Friedman and Sheard. We will establish the proof-theoretic strength of all the remaining seven theories and relate their arithmetic part to well-known theories ranging from PA to the theory of S¹₁{\Sigma^1_1} dependent choice.     

Switchable dual binding mode molecular shuttle

[Structure: see text] Protonation controls the location of a dual binding mode macrocycle in a [2]rotaxane. In the neutral form, amide-amide hydrogen bonds hold the macrocycle over a dipeptide residue; when the thread is protonated, polyether-ammonium cation interactions dominate and the macrocycle changes position.     

Surface-Enhanced Hyper-Raman Spectroscopy

Abstract

Hyper-Raman scattering (HRS), first theoretically predicted by Decius and Rauch in 1959 [l] and experimentally demonstrated by Terhune et al. in 1965 [2], is a nonlinear optical process involving two incident photons (ω₀) and one emitted photon (ω). The emitted hyper- Raman photon frequencies are Raman-shifted relative to the second harmonic frequency (2ω₀) of the incident laser radiation [3–6]. The energy difference (2ω₀ – w) corresponds to one of the characteristicvibrational frequencies of the scattering medium or molecule. In Fig. 1 is given a schematic illustration of resonant and nonresonant HRS. The primary advantage of this nonlinear optical technique lies in its more relaxed selection rules compared with IR and Raman [7,8]. AlllR-active vibrational modes are hyper-Raman allowed, and those modes inactive in both IR and Raman (i.e., the “silent” modes) may be active in hyper-Raman scattering.     

Graduate attributes: teaching as learning

Recent graduates of degrees in the mathematical sciences were interviewed in depth about their work and the skills required to perform those tasks. One common undertaking could be described as teaching: demonstrating to colleagues, training their assistants or explaining mathematics to their managers. The paper describes how this understanding of teaching in the workplace can inform curriculum design at university level to better prepare graduates for work. Examples of assessment activities that lecturers can adapt for use in their classes in the mathematical sciences are presented.     

Threshold concepts in finance: conceptualizing the curriculum

Graduates with well-developed capabilities in finance are invaluable to our society and in increasing demand. Universities face the challenge of designing finance programmes to develop these capabilities and the essential knowledge that underpins them. Our research responds to this challenge by identifying threshold concepts that are central to the mastery of finance and by exploring their potential for informing curriculum design and pedagogical practices to improve student outcomes. In this paper, we report the results of an online survey of finance academics at multiple institutions in Australia, Canada, New Zealand, South Africa and the United Kingdom. The outcomes of our research are recommendations for threshold concepts in finance endorsed by quantitative evidence, as well as a model of the finance curriculum incorporating finance, modelling and statistics threshold concepts. In addition, we draw conclusions about the application of threshold concept theory supported by both quantitative and qualitative evidence. Our methodology and findings have general relevance to the application of threshold concept theory as a means to investigate and inform curriculum design and delivery in higher education.     

The role of universities in preparing graduates to use software in the financial services workplace

The role of universities in preparing students to use spreadsheet and other technical software in the financial services workplace has been investigated through surveys of university graduates, university academics, and employers. It is found that graduates are less skilled users of software than employers would like, due at least in part to a lack of structured formal training opportunities in the workplace, and a lack of targeted, coherent learning opportunities at university. The widespread and heavy use of software in the workplace means that there is significant potential for productivity gains if universities and employers address these issues.     

Nearest neighbour diagnostic statistics on the accuracy of APT solute cluster characterisation

Diagnostic statistics and information theory techniques have been developed to investigate the accuracy to which solute clusters characterised in atom probe tomography (APT) data can reflect the true nature of the physical clusters in the original specimen. Simulated atom-probe datasets representing a range of atomic solute clustering within a pseudo-binary alloy upon an fcc aluminium lattice were generated for the study. The effectiveness of partitioning the APT-like simulated data based upon a binary classification defined by a distance threshold d _max upon the kth nearest neighbour distance distribution was investigated. Information theory was also used to optimise the selection of the threshold d _max. Analysis of variation was performed upon a factorial design of data simulations with low and high levels of: solute concentration; short-range order; and background to the mass-to-charge-state-ratio spectrum. This meta-analysis showed that the background levels have a significant compromising effect upon the binary classification in low solute systems with relatively low or random levels of clustering. Although the random clustering of higher solute concentrations is better analysed, significantly non-random clustering in both low and high solute concentrations is analysed well despite the presence of high levels of background. A meta-analysis of the binary classification upon a simulated dispersion of coherent precipitates within a similar matrix was also undertaken. Optimal k and d _max parameters are likely a dependent upon the physical dimensions of precipitate size as well as the precipitate/matrix solute concentrations.     

Synthesis and crystal structure of tetraiminediphenolate diiron(II) macrocyclic complex

The crystal structure of the binuclear tetraiminediphenolate diiron(II) macrocyclic complex [Fe₂(tidf)(CH₃OH)₄](ClO₄)₂ (tidf = tetraiminediphenolate ligand) is presented. The molecular structure (monoclinic, space group C2/c, Z = 4, a = 20.6903(14)Å, b = 11.0827(11) Å, c = 16.0494(15) Å, = 99.911(6) shows two iron(II) cores occupying distorted octahedral geometries with four methanol molecules bound axially. Main equatorial bond distances are 2.050(3) Å for Fe—O1 and 2.067(4) Å for Fe—N1 with a Fe Fe distance of 3.108(1) Å. Contrasting to the monoiron complex the macrocycle does not adopt a bent conformation being nearly coplanar with the maximum deviation from the least-squares plane of 0.18 Å.