Post-primary students’ images of mathematics: findings from a survey of Irish ordinary level mathematics students

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination – the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for ‘image of mathematics’ was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students’ images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.     

Standard reference materials for foods and dietary supplements

Well-characterized certified reference materials are needed by laboratories in the food testing, dietary supplement, and nutrition communities to facilitate compliance with labeling laws and improve the accuracy of information provided on product labels, so that consumers can make good choices. As a result of the enactment of the Nutrition Labeling and Education Act of 1990 and the Infant Formula Act of 1980, the National Institute of Standards and Technology (NIST) worked to develop a series of food-matrix standard reference materials (SRMs) characterized for nutrient concentrations. These include SRM 1544 Fatty Acids and Cholesterol in a Frozen Diet Composite, SRM 1546 Meat Homogenate, SRM 1548a Typical Diet, SRM 1566b Oyster Tissue, SRM 1846 Infant Formula, SRM 1946 Lake Superior Fish Tissue, SRM 1947 Lake Michigan Fish Tissue, SRM 2383 Baby Food Composite, SRM 2384 Baking Chocolate, SRM 2385 Slurried Spinach, and SRM 2387 Peanut Butter. With the enactment of the Dietary Supplement Health and Education Act of 1994, NIST has been working to develop suites of dietary supplement SRMs characterized for active and marker compounds and for toxic elements and pesticides, where appropriate. An updated SRM 1588b Organics in Cod Liver Oil, a suite of ephedra-containing materials (SRMs 3240–3245), a carrot extract in oil (SRM 3276), and a suite of ginkgo-containing materials (SRMs 3246–3248) are available. Several other materials are currently in preparation. Dietary supplements are sometimes provided in forms that are food-like; for these, values may also be assigned for nutrients, for example SRM 3244 Ephedra-Containing Protein Powder. Both the food-matrix and dietary supplement reference materials are intended primarily for validation of analytical methods. They may also be used as “primary control materials” in assignment of values to in-house (secondary) control materials to confirm accuracy and to establish measurement traceability to NIST.     

Synthesis, structural characterization, and multifrequency electron paramagnetic resonance studies of mononuclear thiomolybdenyl complexes

Reaction of Tp*MoVSCl2 with a variety of phenols and thiols in the presence of triethylamine produces mononuclear, thiomolybdenyl complexes Tp*MoVSX2 [Tp* = hydrotris(3,5-dimethylpyrazol-1-yl)borate; X = 2-(ethylthio)phenolate (etp), 2-(n-propyl)phenolate (pp), phenolate; X2 = benzene-1,2-dithiolate (bdt), 4-methylbenzene-1,2-dithiolate (tdt), benzene-1,2-diolate (cat)]. The complexes have been characterized by microanalysis, mass spectrometry, IR, EPR, and UV-visible spectroscopic data, and X-ray crystallography (for the etp, pp, bdt, and cat derivatives). The mononuclear, six-coordinate, distorted-octahedral Mo centers are coordinated by terminal sulfido (MoS = 2.123(1)-2.1368(8) A), tridentate facial Tp*, and monodentate or bidentate O/S-donor ligands. Multifrequency (S-, X-, Q-band) EPR spectra of the complexes and selected molybdenyl analogues were acquired at 130 K and 295 K and yielded a spin Hamiltonian of Cs symmetry or lower, with gzz < gyy < gxx < ge and Az'z' > Ax'x' approximately Ay'y', and a noncoincidence angle in the range of beta = 24-39 degrees . Multifrequency EPR, especially at S-band, was found to be particularly valuable in the unambiguous assignment of the spin Hamiltonian parameters in these low-symmetry complexes. The weaker pi-donor terminal sulfido ligand yields a smaller SOMO-LUMO gap and reduced g-values for the thiomolybdenyl complexes compared with molybdenyl analogues, supporting existing crystallographic and EPR data for an apically coordinated oxo group in the active site of xanthine oxidase.     

Effects of masking noise on vowel and sibilant contrasts in normal-hearing speakers and postlingually deafened cochlear implant users

The role of auditory feedback in speech production was investigated by examining speakers' phonemic contrasts produced under increases in the noise to signal ratio (N/S). Seven cochlear implant users and seven normal-hearing controls pronounced utterances containing the vowels /i/, /u/, /e/ and /ae/ and the sibilants /s/ and /I/ while hearing their speech mixed with noise at seven equally spaced levels between their thresholds of detection and discomfort. Speakers' average vowel duration and SPL generally rose with increasing N/S. Average vowel contrast was initially flat or rising; at higher N/S levels, it fell. A contrast increase is interpreted as reflecting speakers' attempts to maintain clarity under degraded acoustic transmission conditions. As N/S increased, speakers could detect the extent of their phonemic contrasts less effectively, and the competing influence of economy of effort led to contrast decrements. The sibilant contrast was more vulnerable to noise; it decreased over the entire range of increasing N/S for controls and was variable for implant users. The results are interpreted as reflecting the combined influences of a clarity constraint, economy of effort and the effect of masking on achieving auditory phonemic goals-with implant users less able to increase contrasts in noise than controls.     

A chirp-compensated, injection-seeded alexandrite laser

A Q-switched alexandrite laser suitable for high-resolution spectroscopy is described which produces pulses of 35 mJ energy in a 10 MHz bandwidth, with a high-purity TEM₀₀ mode. The laser can be synchronised to external event to within 100 ns. The output pulse length is 120 ns and the repetition rate 25 Hz. The laser is injection-seeded by a Ti:sapphire laser operating around 730 nm. To preserve single-mode seeding under external triggering conditions, and to obtain small time-jitter, active cavity length control was used. In order to achieve the 10 MHz output bandwidth, intra-cavity electro-optic modulators were used to compensate for the frequency chirp. The refractive index of alexandrite was found to vary linearly with inversion density with a constant of proportionality equal to 1.6᎒^-24 cm³. In pulsed operation at 730 nm, the index change due to this effect is only partially compensated by changes due to ground state phonon relaxation.     

Identification of \mathrm{\ensuremath J^{\pi} = 19/2^+} and \mathrm{\ensuremath 23/2^+} isomeric states in 127Sb

The nucleus $\ensuremath {\rm ^{127}Sb}$ , which is on the neutron-rich periphery of the $\ensuremath \beta$ -stability region, has been populated in complex nuclear reactions involving deep-inelastic and fusion-fission processes with $\ensuremath {\rm {}^{136}Xe}$ beams incident on thick targets. The previously known isomer at 2325 keV in $\ensuremath {\rm {}^{127}Sb}$ has been assigned spin and parity $\ensuremath 23/2^+$ , based on the measured $\ensuremath \gamma$ - $\ensuremath \gamma$ angular correlations and total internal conversion coefficients. The half-life has been determined to be 234(12) ns, somewhat longer than the value reported previously. The 2194 keV state has been assigned $\ensuremath J^{\pi} = 19/2^+$ and identified as an isomer with $\ensuremath T_{1/2} = 14(1) {\rm ns}$ , decaying by two $\ensuremath E2$ branches. The observed level energies and transition strengths are compared with the predictions of a shell model calculation. Two $\ensuremath 15/2^+$ states have been identified close in energy, and their properties are discussed in terms of mixing between vibrational and three-quasiparticle configurations.     

Computational determination of effects of electric fields upon “trigger linkages” of prototypical energetic molecules

For five prototypical energetic molecules (nitrobenzene, methyl azide, methyl nitrate, nitromethane, and dimethylnitramine), we examine computationally the effects of external electric fields upon their “trigger linkage” bonds, the breaking of which is believed to play a key role in detonation initiation. The bonds are, respectively, C? NO₂, N? N₂, O? NO₂, C? NO₂, and N? NO₂. The calculations are at the B3PW91/6–31G** level. We find that fields along these bonds that reinforce the molecules' intrinsic polarities also lower their energies and increase the bonds' stretching vibration frequencies. This suggests a strengthening of the bonds. Fields in the opposite direction do the reverse. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Analysis of hexabromocyclododecane diastereomers and enantiomers by liquid chromatography/tandem mass spectrometry: chromatographic selectivity and ionization matrix effects

Hexabromocyclododecane (HBCD) is a flame retardant that is undergoing environmental risk assessment. The liquid chromatographic retention and electrospray ionization matrix effects were investigated for HBCD methods of analysis for environmental matrices. Column selectivity towards HBCD diastereomers was evaluated for C30 and C18 stationary phases under different mobile phase conditions and column temperatures. The HBCD elution order was dependent on the shape selectivity of the stationary phase and the mobile phase composition. Greater resolution, on columns with reduced shape selectivity, of beta-HBCD and gamma-HBCD was achieved with the use of an acetonitrile/water (compared with a methanol/water) mobile phase composition. A liquid chromatography/electrospray ionization tandem mass spectrometry (LC/ESI-MS/MS) method for the analysis of HBCD in biological tissues was evaluated for potential matrix effects. The influence of extracted matrix components on HBCD diastereomer and enantiomer analysis was investigated using a postextraction addition approach. Although the analysis of HBCD diastereomers was relatively unaffected by the sample matrix, the responses of the HBCD enantiomers in tissue samples were significantly influenced by matrix effects and other changes to the ionization conditions. The use of racemic 13C-labeled HBCD diastereomers as internal standards for enantiomer fraction measurements corrected for the changes in the mass spectrometer response.     

Arraying of intact liposomes into chemically functionalized microwells

Here, we describe a protocol to bind individual, intact phospholipid bilayer liposomes, which are on the order of 1 microm in diameter, in microwells etched in a regular array on a silicon oxide substrate. The diameter of the wells is on the order of the liposome diameter, so only one liposome is located in each well. The background of the silicon oxide surface is functionalized with a PEG oligomer using the contact printing of a PEG silane to present a surface that resists the adsorption of proteins, lipid material, and liposomes. The interiors of the wells are functionalized with an aminosilane to facilitate the conjugation of biotin, which is then bound to Neutravidin. The avidin-coated well interiors bind the liposomes whose surfaces contain biotinylated lipids. The specific binding of the liposomes to the surface using the biotin-avidin linkage, together with the resistant nature of the background and the physical confinement of the wells, allows the liposomes to remain intact and to not unravel, rupture, and fuse onto the surface. We demonstrate this intact arraying using confocal laser scanning microscopy of fluorophores specifically tagging the microwells, the lipid bilayer, and the aqueous interior of the liposome.     

The lowest 2A' excited state of the water-hydroxyl complex

Vertical and adiabatic excitation energies of the lowest (2)A(') excited state in the water-hydroxyl complex have been determined using coupled cluster, multireference configuration interaction, multireference perturbation theory, and density-functional methods. A significant redshift of about 0.4 eV in the vertical excitation energy of the complex compared to that of the hydroxyl radical monomer is found with the coupled cluster calculations validating previous results. Electronic excitation leads to a structure with near-equal sharing of the hydroxyl hydrogen by both oxygen atoms and a concomitantly large redshift of the adiabatic excitation energy of approximately 1 eV relative to the vertical excitation energy. The combination of redshifts ensures that the electronic transition in the complex lies well outside the equivalent excitation in the hydroxyl radical monomer. The complex is approximately five times more strongly bound in the excited state than in the ground state.