Student interpretations of the terms in first-order ordinary differential equations in modelling contexts

A study of first-year undergraduate students′ interpretational difficulties with first-order ordinary differential equations (ODEs) in modelling contexts was conducted using a diagnostic quiz, exam questions and follow-up interviews. These investigations indicate that when thinking about such ODEs, many students muddle thinking about the function that gives the quantity to be determined and the equation for the quantity's rate of change, and at least some seem unaware of the need for unit consistency in the terms of an ODE. It appears that shifting from amount-type thinking to rates-of-change-type thinking is difficult for many students. Suggestions for pedagogical change based on our results are made.     

Solvophobically Driven Complexation of Adamantyl Mannoside with β-Cyclodextrin in Water and Structured Organic Solvents

The effects of solvent and temperature on the complexation of adamantyl mannoside with β-cyclodextrin and 6-O-monotosyl-6-deoxy-β-cyclodextrin were explored experimentally and by means of molecular dynamics simulations. Efficient binding was observed only in hydrogen-bonded solvents, which indicated solvophobically driven complexation. The stability of the inclusion complex was considerably higher in aqueous media. A pronounced temperature dependence of Δ_rH^○ and Δ_rS^○, resulting in perfect enthalpy–entropy compensation, was observed in water. The complexation thermodynamics was in line with classical rationale for the hydrophobic effect at lower temperatures and the nonclassical explanation at higher temperatures. This finding linked cyclodextrin complexation thermodynamics with insights regarding the effect of temperature on the hydration water structure. The complexation enthalpies and entropies were weakly dependent on temperature in organic media. The signs of Δ_rH^○ and Δ_rS^○ were in accordance with the nonclassical hydrophobic (solvophobic) effect. The structures of the optimized product corresponded to those deduced spectroscopically, and the calculated and experimentally obtained values of Δ_rG^○ were in very good agreement. This investigation clearly demonstrated that solvophobically driven formation of cyclodextrin complexes could be anticipated in structured solvents in general. However, unlike in water, adamantane and the host cavity behaved solely as structure breakers in the organic media explored so far.     

Killing Magnetic Curves in Sol Space

We determine magnetic curves corresponding to the Killing magnetic fields in the 3-dimensional homogenous Riemannian space Sol₃.     

Metal-support interactions in systems palladium deposited on oxidized tungsten surfaces

The morphology of the palladium (Pd) overlayers on oxidized tungsten (W) tips has been studied by Field Emission Microscopy (FEM). The effect of thermal treatment on the interaction of Pd with the support and chemisorption of CO on variously treated Pd-containing samples has been investigated. The results are discussed in relation to complementary macroscopic experiments by synchrotron radiation excited photoelectron spectroscopy (SRPES) and thermally programmed desorption (TPD) of carbon monoxide (CO) on a polycrystalline W foil. A distinct influence of support pre-oxidation on the Pd layer growth has been demonstrated. Two types of oxidized supports have been used: tungsten with oxygen pre-adsorbed at room temperature (RT) and then heated to 700 K (WO_x/W (RT) system) and tungsten oxidized at 1300 K (WO_x/W (1300 K) system) in situ. The surface of WO_x/W (1300 K) sample is fully oxidized in contrast to WO_x/W (RT), where the presence of un-oxidized patches has been demonstrated by SRPES measurements. A Pd layer grows on the WO_x/W (RT) surface mostly on the densely populated planes (1 1 0) and (2 1 1) of the W tip. Heating of this system up to 700 K results in disaggregation of the original Pd layer. Pd clusters on the tungsten tip oxidized at 1300 K are localized on the atomically rough (1 1 1) plane. The observed differences in CO adsorption on the aforementioned types of investigated samples can be attributed to differences in the chemical nature of their surfaces.     

Measurement of isotope ratios on transient signals by MC-ICP–MS

Precise and accurate isotope ratio measurements are an important task in many applications such as isotope-dilution mass spectrometry, bioavailability studies, or the determination of isotope variations in geological or nuclear samples. The technique of MC-ICP–MS has attracted much attention because it permits the precise measurement of isotope compositions for a wide range of elements combined with excellent detection limits due to high ionisation efficiencies. However, the results are based mainly on measurements using continuous sample introduction. In the present study the determination of isotope ratios on various transient signals with a time duration of 30 to 60 s has been achieved by coupling high-performance liquid chromatography to a multicollector inductively coupled plasma mass spectrometer. In order to investigate the origin of ratio drifts across the transient signals for this hyphenated technique, measurements with the same standard solutions were also carried out using a flow-injection device for sample introduction. As a result of this application it could be concluded that the main source of the bias in the measured isotope ratios is within the ICP–MS instead of fractionation effects on the chromatographic column material. Preliminary studies on short transient signals of gaseous samples (dry plasma) showed a reverse fractionation effect compared with wet plasma conditions (flow injection and HPLC).Presented at the 2003 European Winter Conference on Plasma Spectrochemistry, Garmisch-Partenkirchen, Germany, January 2003     

On quadratic convergence bounds for theJ-symmetric Jacobi method

Summary This paper deals with quadratic convergence estimates for the serialJ-symmetric Jacobi method recently proposed by Veseli. The method is characterized by the use of orthogonal and hyperbolic plane rotations. Using a new technique recently introduced by Hari we prove sharp quadratic convergence bounds in the general case of multiple eigenvalues.     

Vibrational spectra and force constants of Ch3HgI and CD3HgI

The infrared and Raman spectra of CH₃HgI and CD₃HgI were studied in the solid state. All the fundamental wavenumbers are assigned. A general harmonic force field was used as the basis, and the force constants were modified by means of the Jacobian matrix. The force constants fit the observed wavenumbers better than 1 %. The normal coordinates are also given.     

Spectrophotometric behaviour of quinolinium oxime-palladium(II) complexes

Summary It has been established that 1-(2-phenyl-2-hydroxyiminoethyl)-1-quinolinium chloride, 1-(2-phenyl-2-hydroxyiminoethyl)-1-isoqui-nolinium chloride, 1-(2-phenyl-2-hydroxyiminoethyl)-1-(4-methyl)-quinolinium chloride and 1-(2-phenyl-2-hydroxyiminoethyl)-1-(6-methyl)quinolinium chloride react with palladium(II) chloride in the pH range 3.3–7.1 and form yellow water-soluble 11 complexes with maximum absorbance at 413 nm. The conditional stability constants of the complexes at the optimum pH of 6.5 are all about 10^4.7, and the molar absorptivities are in the range 2.2–2.6×10³ l·l mole^–1·cm^–1 at pH 6.5 and 413 nm. Beer's law is obeyed up to 3–4×10^–4 M oxime concentration, depending on the oxime determined.