The catwalk task: Reflections and synthesis: Part 2

In this article we recount our experiences with a series of encounters with the catwalk task and reflect on the professional growth that these opportunities afforded. First, we individually reflect on our own mathematical work on the catwalk task. Second, we reflect on our experiences working with a group of community college students on the catwalk task and our interpretations of their mathematical thinking. In so doing we also detail a number of innovative and novel student-generated representations of the catwalk photos. Finally, we each individually reflect on the entire experience with the catwalk problem, as mathematics learners, as teachers, and as professionals.     

Oscillator strengths and photoionisation cross sections for Rydberg transitions in acetaldehyde

Oscillator strengths for electronic transitions involving Rydberg states of acetaldehyde, as well as cross sections for all the dipole allowed photoionisation channels, all ending in the ground state of the molecular cation, are reported. The molecular quantum defect orbital method, which has proved to be reliable in previous applications to molecular Rydberg states, has been used. Despite its relevance for atmospheric chemistry and astrophysics, only a few data seem to be available in the literature. The continuity of the calculated differential oscillator strength across the ionisation threshold has been adopted as a quality criterion. To our knowledge, predictions of oscillator strengths for transitions to high-lying Rydberg states, as well as of photoionisation profiles on acetaldehyde are made here for the first time and we are not aware of any reported experimental data. We, thus, hope the present results may be useful in the interpretation of the spectrum of acetaldehyde and might be of help in future experimental measurements.     

Fast multidimensional localized parallel NMR spectroscopy for the analysis of samples

A parallel localized spectroscopy (PALSY) method is presented to speed up the acquisition of multidimensional NMR (nD) spectra. The sample is virtually divided into a discrete number of nonoverlapping slices that relax independently during consecutive scans of the experiment, affording a substantial reduction in the interscan relaxation delay and the total experiment time. PALSY was tested for the acquisition of three experiments 2D COSY, 2D DQF‐COSY and 2D TQF‐COSY in parallel, affording a time‐saving factor of 3–4. Some unique advantages are that the achievable resolution in any dimension is not compromised in any way: it uses conventional NMR data processing, it is not prone to generate spectral artifacts, and once calibrated, it can be used routinely with these and other combinations of NMR spectra. Copyright © 2010 John Wiley & Sons, Ltd.     

Gas permeability and selectivity of hexafluoroisopropylidene aromatic isophthalic copolyamides

The synthesis, thermal, and gas transport properties of poly(hexafluoroisopropylidene isophthalamide), HFA/ISO homopolymer, and HFA/TERT‐co‐HFA/ISO copolyamides with different poly(hexafluoroisopropilydene‐5‐t‐butylisophthalamide), HFA/TERT, ratios are reported. The results indicate that the glass transition temperatures of the copolyamides increase as the concentration of HFA/TERT in the polyamide increases. The gas permeability coefficients in the polyamides and copolyamides are independent of pressure or decrease slightly particularly with CO₂, N₂, and CH₄. It was seen that HFA/TERT is 2–6 times more permeable than HFA/ISO, depending on the gas being considered. This was assigned to the presence of the bulky lateral substituent, t‐butyl group in HFA/TERT and HFA/TERT‐co‐HFA/ISO copolyamides. This substituent increases fractional free‐volume, as expected. Therefore, the gas permeability and diffusion coefficients generally increase with increasing fractional free‐volume. The experimental results for the gas permeability and permselectivity for the copolyamides was well represented by a logarithmic mixing rule of the homopolyamides permeability coefficients and their volume fraction. The selectivity of gas pairs, such as O₂/N₂, CO₂/CH₄, and N₂/CH₄ decreased slightly with the addition of HFA/TERT. The temperature dependence of permeability for homopolyamides and copolyamides can be described by an Arrhenius type equation. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2625–2638, 2005