A new semiclassical elementary particle model

A semiclassical model in which elementary particles are represented as systems of charged shells with associated quark-like quantum numbers is presented. Specifically the baryons are considered. Formulas are obtained which express baryon masses and magnetic moments in terms of model parameters which relate baryon and quark properties. Basically, the mass and moment formulas are expressions for mass ratios and magnetic moment ratios. Simple identifications for the model parameters lead to a prediction for the proton-electron mass ratio and to fairly accurate predictions for the baryon magnetic moments in units of the proton moment. The mass and moment formulas, which relate corresponding properties of different particles, are generalised such as to express relationships between the members of a sequence of particles, where such a sequence is conceived of as containing only one (normal) baryon. A specific sequence, containing the proton and electron, is proposed; various physical properties of the particles in the sequence are determined. In particular, a second prediction for the proton-electron mass ratio is obtained; the two predictions differ numerically but both agree with the measured value of the mass ratio within experimental error.     

A validation study of the use of mathematical knowledge for teaching measures in Ireland

Researchers who study mathematical knowledge for teaching (MKT) are interested in how teachers deploy their mathematical knowledge in the classroom to enhance instruction and student learning. However, little data exists on how teachers’ scores on the US-developed measures relate to classroom instruction in other countries. This article documents a validation study of Irish teachers’ scores on measures of MKT that were adapted for use in Ireland. A validity argument is made identifying elemental, structural and ecological assumptions. The argument is evaluated using qualitative and quantitative data to analyse inferences related to the three assumptions. The data confirmed the elemental assumption but confirming the structural and ecological assumptions was more difficult. Only a weak association was found between teachers’ MKT scores and the mathematical quality of instruction. Possible reasons for this are outlined and challenges in validating the use of measures are identified.     

Local Observation of Field Polarity Dependent Flux Pinning by Magnetic Dipoles

A scanning Hall probe microscope is used to study flux pinning in a thin superconducting Pb film covering a square array of single-domain Co dots with in-plane magnetization. We show that single flux quanta of opposite sign thread the superconducting film below T(c) at the opposite poles of these dipoles. Depending on the polarity of the applied field, flux lines are attracted to a specific pole of the dipoles, due to the direct interaction with the vortexlike structures induced by the local stray field.     

On invariants of modular categories beyond modular data

We study novel invariants of modular categories that are beyond the modular data, with an eye towards a simple set of complete invariants for modular categories. Our focus is on the W-matrix—the quantum invariant of a colored framed Whitehead link from the associated TQFT of a modular category. We prove that the W-matrix and the set of punctured S-matrices are strictly beyond the modular data $(S,T)$. Whether or not the triple $(S,T,W)$ constitutes a complete invariant of modular categories remains an open question.     

Determining a 'safe' high-mass limit in matrix-assisted laser desorption/ionisation time-of-flight mass spectra of coal derived materials with reference to instrument noise

Three methods for determining a 'safe' estimate for high-mass limits of MALDI spectra of coal derived liquids were explored, using a sample of coal-tar pitch and its pyridine-insoluble fraction. Co-addition of increasing numbers of single-shot spectra (10, 30, 50 and 100 pulses) showed visually observable reductions in noise levels, consistent with robust and statistically meaningful signals. Three separate types of post-acquisition calculation were used to identify high-mass limits of the spectra. (i) A literature method indicated high-mass limits similar to those observed visually-as a shift from baseline at the highest masses, nearly 350 000 u for the coal tar pitch and about 390 000 u for its pyridine insoluble fraction. (ii) Comparing instrument signal with pre-selected multiples of the standard deviation, upper mass estimates of between 40-60 000 u for the coal-tar pitch and about 95 000 u for its pyridine-insoluble fraction were found. (iii) Calculation of the slope was used to identify 'lift-off' of the spectrum from baseline. The angle between the smoothed spectrum and the baseline was matched to a pre-selected value (e.g. 0.5 degrees and 1 degrees ). However, the arbitrary specification of the key parameter did not establish this last method on a firm basis. The choice of a criterion for estimating high-mass limits of MALDI spectra remains a semi-quantitative procedure; a reasonably conservative high-mass limit may be estimated by comparison of signal with five times the standard deviation. However, evaluation of size exclusion chromatograms of the present samples using polystyrene standards suggests that molecular mass distributions of pitch samples arrived at by MALDI mass spectrometry are, at least partly, determined by the limitations of available instruments. Copyright 1999 John Wiley & Sons, Ltd.     

Synthesis of Z-5-carboxymethylene-1,3-dioxolan-4-ones: a better way

The title compounds were prepared by a straightforward two-step procedure. Tartaric acid was first protected as either a bis(ketal) or a bis(acetal). This intermediate was then treated with potassium tert-butoxide at reduced temperature to effect a stereoselective elimination leading to the Z diastereomer of the alpha,beta-unsaturated acid. This protocol is useful for the laboratory-scale synthesis of these compounds but can also be scaled up to produce kilogram quantities of the material.