Three types of mathematical representational translations: Comparing empirical and theoretical results

Previous research has investigated the representational translation practices of high school students, high school teachers, and college preservice teachers in various mathematical contexts including linear functions. Findings from qualitative research has frequently led to new notions about participant work and understanding. Many quantitative research has investigated the degree to which some in these populations correctly perform these translations. However, it seems that only infrequently have empirical research investigated findings from qualitative studies and vice versa, and findings regarding one population are rarely compared with findings of another population. This study (a) empirically explores the frequency of success of preservice teachers (N = 80) regarding representational translations in the context of linear functions, (b) quantifies results from previous qualitative, literature‐based research regarding high school students and teachers, and (c) quantitatively compares the results. This study demonstrates that some mathematical representational translations are more difficult than others.     

On quasi-contraction mappings of Ćirić and Fisher type via ω-distance

Kada, Suzuki, and Takahashi introduced and studies the concept of ω- distance in fixed point theory. In this paper, we generalize and unify ?iri?’ and Fisher fixed points results for quasi-contractions on metric space to ω-distance on complete metric spaces. We also extend some results of Kada, Suzuki and Takahashi, and Suzuki. Our methods of proofs are new and even simpler than the corresponding methods in metric spaces.     

Existence of frequency modes coupling seismic waves and vibrating tall buildings

We prove in this paper an existence result for frequency modes coupling seismic waves and vibrating tall buildings. The derivation from physical principles of a set of equations modeling this phenomenon was done in previous studies. In this model all vibrations are assumed to be anti-plane and time harmonic so the two dimensional Helmholtz equation can be used. A coupling frequency mode is obtained once we can determine a wavenumber such that the solution of the corresponding Helmholtz equation in the lower half plane with relevant Neumann and Dirichlet conditions at the interface satisfies a specific integral equation at the base of an idealized tall building. Although numerical simulations suggest that such wavenumbers should exist, as far as we know, to date, there is no theoretical proof of their existence. This is what this present study offers to provide.     

A NUMERICAL BOUNDARY EIGENVALUE PROBLEM FOR ELASTIC CRACKS IN FREE AND HALF SPACE

We present in this paper a numerical method for hypersingular boundary integral equations.This method was developed for planar crack problems:additional edge si...     

Effects of gas adsorption and collisions on electrical transport in single-walled carbon nanotubes

Degassing of bundles of single-walled carbon nanotubes in vacuum at 500 K is found to drive the thermoelectricpower (TEP) strongly negative, indicating that the degassed metallic tubes in a bundle are n type. The magnitude of the negative TEP indicates that important asymmetry in the electronic carbon pi bands exists near the Fermi energy. Easily measurable increases in the TEP ( approximately 5-10 &mgr;V/K) and resistivity ( 2%-10%) are observed at 500 K upon exposure to N2 and He, suggesting that even gas collisions with the nanotube wall can contribute significantly to the transport properties.     

Elemental analysis of particulate matter in a metal workshop and of biological samples from exposed workers

During metal welding and cutting, large amounts of particulate matter (PM) are produced that might represent a significant health risk for the exposed workers. In the present pilot study, we performed an elemental analysis of fine PM collected in a metal workshop. Also, elemental analysis of the hair and nail samples collected from workers exposed to the workshop dust and control group was done. Concentrations of 15 elements in PM were measured with X‐Ray Fluorescence (XRF) and Particle Induced X‐ray Emission (PIXE), whereas inductively coupled plasma mass spectrometry (ICP‐MS) was used to determine 12 elements in hair and nail samples. Mean 8‐hr concentrations of PM_2.5, Fe, and Mn in the vicinity of welders were up to 1803, 860, and 30 μg/m³, respectively, whereas in the nearby city, daily PM_2.5 concentrations are on average 11 μg/m³. We found that several elements, especially Fe and Mn, had substantially higher concentrations in hair and nail samples of exposed workers than in the control group, which indicates the accumulation of metals in workers' tissues, although limit values were not exceeded.     

Preliminary studies on 226Ra, 228Ra, 228Th and 40K concentrations in foodstuffs consumed by inhabitants of Accra metropolitan area, Ghana

Knowledge of radioactivity levels in human diet is of particular concern for the estimation of possible radiological hazards to human health. However, very few surveys of radioactivity in food have been conducted in Ghana. The natural radionuclides ²²⁶Ra, ²²⁸Ra, ²²⁸Th and ⁴⁰K were measured in the foodstuffs using gamma ray spectrometry. All samples were found to contain high ⁴⁰K content in the range 87.77?C368.50?Bq?kg^?1. The maximum concentration of ²²⁸Th and ⁴⁰K were found in cassava to be 14.93?±?3.86 and 368.50?±?19.20?Bq?kg^?1, respectively. The total annual committed effective dose was estimated to be 4.64?mSv. The daily intake of radionuclides from food consumption reveals that cassava and plantain are the highest contributors, while millet is the lowest. The daily radionuclide intake from the foodstuffs consumed by the general public was 411.32?Bq and the daily internal dose resulting from ingestion of the radionuclides in the foodstuffs was 0.01?mSv. The radionuclide concentrations were comparable with those reported from other countries.     

Validation of an oil-in-water microemulsion liquid chromatography method for analysis of perindopril tert-butylamine and its impurities

This paper describes the development and validation of a microemulsion liquid chromatography (MELC) method for simultaneous determination of perindopril tert-butylamine and its impurities in bulk active substances and the pharmaceutical dosage form of tablets. An appropriate resolution with reasonable retention times was obtained for a microemulsion containing 0.24% (w/v) butyl acetate, 0.30% (w/v) ethyl acetate, 2% (w/v) sodium dodecyl sulfate, 7.75% (w/v) n-butanol, and 20.0 mM potassium dihydrogen phosphate, the pH of which was adjusted to 3.70 with 85% orthophosphoric acid. Separations were performed on a Nucleosil 120-5 butyl modified (C4), 250 x 4 mm, 5 microm particle size silica column at 40 degrees C, with a mobile phase flow rate of 1.25 mL/min. UV detection was performed at 254 nm. The established method was subjected to method validation, and required validation parameters were defined. Robustness testing, an important part of method validation, was performed as well. Since robustness validation can be conducted using different experimental designs, the Plackett-Burman design was applied due to its possibility of testing many factors at the same time. The validated MELC method was found to be suitable for the simultaneous determination of perindopril tert-butylamine and its impurities in pharmaceuticals.     

Desirability-based optimization and its sensitivity analysis for the perindopril and its impurities analysis in a microemulsion LC system

In the current paper the application of multiobjective optimization (MOOP) technique, via Derringer's desirability function, to a microemulsion liquid chromatographic (MELC) method is described. Chromatographic separation of perindopril tert-butylamine and its four impurities was selected as the case study. Central composite design (CCD) with fractional factorial design, ± 0.5 α star design and four replications in central point was applied for a response surface study, in order to examine in depth the effects of the most important factors. As factors that influence the system mostly (i) content of ethyl acetate and (ii) butyl acetate in composite internal phase, (iii) content of sodium dodecyl sulfate (surfactant) and (iv) n-butanol (co-surfactant), as well as (v) pH of the mobile phase were selected. Retention factor of (a) perindoprilat and (b) impurity Y 31 and (c) resolution factor for impurities Y 32 and 33 were chosen for simultaneous optimization. By adjustment of the importance coefficients and weights, according to defined objectives, the optimal mobile phase composition was predicted to be: 0.24% w/v butyl acetate, 0.3% w/v ethyl acetate, 2% w/v SDS, 7.75% w/v n-butanol and pH of the mobile phase 3.7. The sensitivity analysis of desirability function for these optimal conditions was conducted for the first time in LC separations, by applying a sensitivity procedure. The performed sensitivity analysis confirmed that the higher overall desirability does not necessarily mean a better solution. The accuracy of prediction might be affected if the optimal levels of input variables, achieved from several design points, end up with equal settings and different corresponding overall desirability. In our study this was not the issue, which confirmed the adequacy of predicted optimum.