Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

Non-perturbative approach to high-index-contrast variations in electromagnetic systems

We present a method that formally calculates exact frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary shifts. Degenerate eigenmode frequencies pose no problems in the presented method. The approach relies on operator algebra to derive an equation for the frequency shifts, which eventually turn out in a simple and physically sound form. Numerically the equations are well-behaved, easy implementable, and can be solved very fast. Like in perturbation theory a reference system is first considered, which then subsequently is used to solve another related, but different system. For our method precision is only limited by the reference system basis functions and the error induced in frequency is of second order for first-order basis set error. As an example we apply our method to the problem of variations in the air-hole diameter in a photonic crystal fiber.     

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals is theoretically studied. Using a scattering-matrix approach and the Wigner–Smith delay time concept, we show that optical absorbance benefits both from slow-light phenomena as well as a high filling factor of the energy residing in the liquid. Utilizing strongly dispersive photonic crystal structures, we numerically demonstrate how liquid-infiltrated photonic crystals facilitate enhanced light–matter interactions, by potentially up to an order of magnitude. The proposed concept provides strong opportunities for improving existing miniaturized absorbance cells for optical detection in lab-on-a-chip systems.     

The response of microstructure to processing in a series of poly(siloxaneimide) copolymers

Poly(siloxaneimide) (PSI) segmented copolymers exhibit organized microdomains if the blocks are sufficiently incompatible. As with neat diblock and triblock copolymers, the processing route employed to prepare films of PSI materials is expected to influence the dimensions and/or morphology of the resultant microstructure. In this work, small-angle neutron scattering (SANS) is utilized to characterize the disordered microstructure found in films of a series of PSI copolymers which are subjected to solvent casting and various thermal treatments. Microstructural dimensions such as the periodicity and correlation length are deduced from the Teubner-Strey (TS) model for disordered microemulsions. The scattering intensity of each copolymer up to q = 5.0 nm^?1, where q is the scattering vector, is found to scale as q^?2.8+?0.1. Results indicate that processing the materials as cast films or as melt-pressed films allowed to cool slowly has a small, but discernible, effect on microstructural characteristics. SANS profiles of films quenched from elevated temperatures reveal a clear transition in microdomain periodicity, which correlates well with the glass transition temperature of the imide microphase in these and other materials of similar chemical structure. © 1993 John Wiley & Sons, Inc.     

Recent advances of group 14 dimetallenes and dimetallynes in bond activation and catalysis

Since the first heavy alkene analogues of germanium and tin were isolated in 1976, followed by West''s disilene in 1981, the chemistry of stable group 14 dimetallenes and dimetallynes has advanced immensely. Recent developments in this field veered the focus from the isolation of novel bonding motifs to mimicking transition metals in their ability to activate small molecules and perform catalysis. The potential of these homonuclear multiply bonded compounds has been demonstrated numerous times in the activation of H₂, NH₃, CO₂ and other small molecules. Hereby, the strong relationship between structure and reactivity warrants close attention towards rational ligand design. This minireview provides an overview on recent developments in regard to bond activation with group 14 dimetallenes and dimetallynes with the perspective of potential catalytic applications of these compounds.

This minireview highlights the recent advances in small molecule activation and catalytic applications of homonuclear dimetallenes, dimetallynes and interconnected bismetallylenes of heavier group 14 elements.     

Scavenging of acetylperoxyl radicals and quenching of triplet diacetyl by beta-carotene: mechanisms and kinetics

Beta-carotene scavenges triplet diacetyl generated by laser flash photolysis with a second-order rate constant of 9.1+/-0.9 x 10(9) M(-1) s(-1) in deaerated benzene at 20 degrees C. In the presence of oxygen diacetyl dissociates to generate acetylperoxyl radicals. It is demonstrated that diacetyl does not dissociate to any appreciable extent in the absence of oxygen. The acetylperoxyl radical is scavenged by beta-carotene with second-order rate constant 9.2+/-0.6 x 10(8) M(-1) s(-1) in aerated benzene at 20 degrees C to give an adduct between the acetylperoxyl radical and beta-carotene, whereas no evidence of oxidation of beta-carotene by the strongly oxidizing acetylperoxyl radical to give the beta-carotene radical cation is found. This adduct decays with first-order rate constant 1.35+/-0.16 x 10(3) s(-1) to give (presumably) a beta-carotene epoxide and the acetyloxyl radical.     

Negatively charged hyperbranched polyether-based polyelectrolytes

The preparation of carboxylated hyperbranched polyglycerols of narrow polydispersity was achieved by modification (78–90%) of the hydroxyl end groups via Michael addition of acrylonitrile, followed by hydrolysis. High conversion could only be achieved for low molecular weight starting materials (520 and 1,030 g mol⁻¹). The solution properties of the resulting materials were investigated by dynamic light scattering (DLS), showing the formation of large aggregates with size depending on the pH value. After deposition on a negatively charged mica surface, the structures observed by atomic force microscope (AFM) show the coexistence of aggregates and single macromolecules. Most interesting, in the case of the lower molecular weight sample (PG 520 g mol⁻¹), extended and ordered terrace structures were formed, which are unprecedented for hyperbranched polymers and are of interest for surface modification in general.     

Specific determination of 20 primary aromatic amines in aqueous food simulants by liquid chromatography-electrospray ionization-tandem mass spectrometry

A multi-analyte method without any pre-treatment steps using reversed-phase liquid chromatography-electrospray ionization-tandem mass spectrometry (LC-ESI-MS/MS) was developed and applied for the determination of 20 primary aromatic amines (PAA) associated with polyurethane (PUR) products or azo-colours. The method was validated in-house for water and 3% acetic acid food simulants using spiked migrates from plastic laminates. Detection limits ranged from 0.27 to 3 microg amine/L food simulants, and RSD values of within-laboratory reproducibility at the 2 microg PAA/L level ranged from 3.9 to 19%. PAA migration from plastic laminates and black nylon cooking utensils were determined with the method, and high levels of 4,4'-methylenedianiline and aniline were found in migrates from about half of the tested cooking utensils. The method fulfils present legislative demands in the EU for screening and verification of PAA migration from food contact materials.     

Kinetic Analysis of the Reactions between GG-Containing Oligonucleotides and Platinum Complexes. 1. Reactions of Single-Stranded Oligonucleotides with cis-[Pt(NH(3))(2)(H(2)O)(2)](2+) and [Pt(NH(3))(3)(H(2)O)](2+)

Using concentration measurements based on high performance liquid chromatography, we have investigated the kinetics of reaction between single-stranded oligonucleotides containing a d(GpG) sequence, i.e., d(GG), d(TGG), d(TTGG), and d(CTGGCTCA), and the platinum complexes cis-[Pt(NH(3))(2)(H(2)O)(2)](2+) (1) and [Pt(NH(3))(3)(H(2)O)](2+) (2). The rate constants for the substitution of one aqua ligand of platinum in 1 or 2 by each guanine of the oligonucleotides were individually measured, as well as, for 1, those for the subsequent conversion of the monoadducts to the diadduct. For the platination of d(GG) and d(TGG), the rate constants are similar for the 5'- and 3'-guanines. The longer oligonucleotides d(TTGG) and d(CTGGCTCA) are platinated slightly faster on the 5'-G than on the 3'-G. 2 shows a similar slight preference for the 5'-guanine, but it reacts by a factor of 4-10 more slowly than 1. For both complexes, the platination rate constants increase with increasing oligonucleotide length. Platination of the 5'-G by 1 is 1 order of magnitude faster on d(CTGGCTCA) than on d(GG). Concerning the chelation step giving the GG diadduct of 1, the longer the oligonucleotide, the larger is the ratio between the rates of the cyclization of the 3'- and 5'-monoadducts k(3)(')(c) and k(5)(')(c): k(3)(')(c)/k(5)(')(c) equals 1.4 for d(GG) and 3.3 for d(CTGGCTCA).     

Analysing fluorobenzoate tracers in groundwater samples using liquid chromatography-tandem mass spectrometry. A tool for leaching studies and hydrology

A sensitive LC-MS-MS method for the direct determination and quantification of 15 fluorobenzoic acids (FBAs) was developed. FBAs are used as conservative tracers for hydrological modelling of water flow and in studies of pesticides and other xenobiotic compounds. The use of FBAs is discussed in relation to other tracers (bromide, chloride, uranine). The method covers mono-substituted fluorobenzoic acid, difluorobenzoic acid, trifluorobenzoic acid, and tetrafluorobenzoic acid. The general detection limit in ground water was 1 microg/l using electrospray ionisation and 20 microg/l using atmospheric pressure chemical ionisation. Analysis time was less than 10 min, small sample volumes were needed and no clean-up was required.