Electron spectroscopy using excited atoms and photons IV. Penning ionization of ethylene

Using helium metastable atoms (2¹S, 2³S), the Penning ionization of C₂H₄ has been studied using a high resolution electrostatic electron analyzer. The Franck—Condon envelope for the ground state of C₂H₄⁺ (X²B_3u) is found to be the same for He* (2³S) Penning ionization and 584 Å photoionization. The ΔE shift values and the relative electronic transition probabilities are reported for four ionic states. Unusually large differences have been found for the relative electronic transition probabilities for Penning ionization and photoionization.     

Teachers' funds of knowledge and the teaching and learning of mathematics in multi-ethnic primary schools: Two teachers' views of linking home and school

In this paper we explore two teachers' views on the role(s) of parents, the local community and children's home lives in the learning of mathematics in primary school. We use Moll and Greenberg's concept of ‘funds of knowledge’ and apply it to the case studies of two teachers working in the UK context. Issues of teachers' professional experience, ethnicity, class and gender emerge as significant in examining similarities and differences in the teachers' beliefs, understandings and practices in the area of linking home and school. We end with a discussion of some implications for teacher education and professional development.     

Nanovoid relaxation in a series of copolyester glasses under cyclic loading using synchronous PALS

This study examines if correlation between a specific molecular motion and the growth and relaxation of nanovoids, which are precursors to crazes, can be established. A novel technique, positronium annihilation lifetime spectroscopy (PALS) synchronized with cyclic stress, is reported. In this technique the positronium annihilation signal was accumulated in sixteen channels corresponding to sixteen phases of the sinusoidal load, which allowed statistically significant data for nanovoid generation and relaxation due to the fluctuating stress to be accumulated. This technique was applied to a series of copolymers of poly(ethylene terephthalate) (PET) and poly(1,4-cyclohexylenedimethylene terephthalate) (PCT). Previous studies have shown that the cyclohexylene rings in the main chain of PCT actively undergo chair-boat-chair conformational transitions in the glassy PCT at around room temperature. The PET-co-PCT series was also chosen for this study because the crazing stress increases systematically with the cyclohexylene content. The synchronized PALS data are consistent with the hypothesis that transient nanovoids generated by the cyclic stress in polymers containing more cyclohexylene rings relax more readily than those with fewer rings. The results also correlate well with the crazing stress in this series of copolymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1410–1417, 2007     

Measuring the triple-gluon vertex

The triple-gluon vertex can be measured from the gluon jet spread using the energy-cone distribution functions.     

Synthesis and properties of a new polydiacetylene: Poly[1,6-di(N-carbazolyl)-2,4-hexadiyne]

The solid-state synthesis and properties are reported for a new polydiacetylene: poly[1,6-di(N-carbazolyl)-2,4-hexadiyne]. The monomer crystals polymerize quantitatively with γ irradiation or thermal annealing. An Autocatalytic effect is observed in both γ-ray polymerization and thermal polymerization and is attributed to an increase in chain propagation length at about 5% conversion. The activation energy for thermal polymerization is about 25 kcal/mole, independent of the degree of conversion to polymer. The exceptional thermal stability of the polymer crystals allowed a thermomechanical analysis over a large temperature range, ?50 to 300°C. With increasing temperature, the polymer contracts in the chain direction linearly with temperature over the entire range, yielding a thermal expansion coefficient of (?2.32 ± 0.02) × 10^?5°C^?1. Photoconductivity action spectra are reported for the polymer crystals. The energies for the photoconductivity onset (ca. 2.3 eV) and for the lowest energy optical transition (1.89 eV) are the lowest reported for the polydiacetylenes. The photoconduction onset is blue-shifted with respect to optical absorption—a result which is consistent with the excitonic assignment for the lowest energy optical transition in the polydiacetylenes.     

Rotational analysis of the 1Π-X1Σ+ system of phosphorous antimonide

Seven bands of the ¹Π-X¹Σ⁺ band system of P¹²¹Sb have been analyzed in detail. A large number of strong rotational perturbations in the v = 0 and 1 levels and a vibrational perturbation in the v = 0 level of the Π state have been observed. The term values of the rotational levels and rotational constants for the two isotopic species, P¹²¹Sb and P¹²³Sb, are presented.     

Solid-state synthesis of a ladder polymer

Solid-state synthesis of a cyclically bound ladder polymer from a cyclic tetradiyne (cyclodotriaconta-1,3,9,11,17,19,25,27-octayne) is described. Irradiation of the colorless, needlelike monomer crystals with interstitially incorporated chloroform with 50 Mrad of ⁶⁰Co γ-ray radiation results in red-brown polymer fibers in nearly quantitative yield. Infrared, Raman, and x-ray diffraction analyses of the polymer are consistent with polymerization by a 1,4-addition reaction at each diacetylene linkage to produce four fully conjugated chains joined together in pairs by a total of four ? (CH₂)₄? interchain linkages per 4.8-Å polymer repeat unit. Conformationally, it appears that the cyclic tetradiyne monomer polymerizes via a chair form. The results of the mechanical and thermal analyses indicate the presence of unreacted diacetylene functionality in the ladder polymer crystals.     

Ramanujan’s partial theta series and parity in partitions

A partial theta series identity from Ramanujan’s lost notebook has a connection with some parity problems in partitions studied by Andrews in Ramanujan J., to appear  where 15 open problems are listed. In this paper, the partial theta series identity of Ramanujan is revisited and answers to Questions 9 and 10 of Andrews are provided.