The Gibbs' phenomenon

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of given improper integrals, but also intuitive questions and some paradoxical results too (for example, a figure with an infinite longitude which closes the same area as the unit circumference, or an infinite figure with a finite volume). In particular, the students were asked to interpret most of the results they had obtained. Answers given by the students to each of the questions were categorized, which allowed some initial conclusions to be reached regarding this research. From analyses carried out, one can conclude that there are students who have difficulties in articulating the different systems of representation, and have problems in connecting and relating this knowledge as a generalization of previous concepts, such as definite integrals, series and sequences.     

Convexity preserving C 0 splines

Linear conditions for a C ⁰ spline to be convex are developed and used to create some convexity preserving interpolation and approximation methods.     

MOVIPAC: Vibrational spectroscopy with a robust meta‐program for massively parallel standard and inverse calculations

We present the software package MO VI PAC for calculations of vibrational spectra, namely infrared, Raman, and Raman Optical Activity (ROA) spectra, in a massively parallelized fashion. MO VI PAC unites the latest versions of the programs SNF and AKIRA alongside with a range of helpful add‐ons to analyze and interpret the data obtained in the calculations. With its efficient parallelization and meta‐program design, MO VI PAC focuses in particular on the calculation of vibrational spectra of very large molecules containing on the order of a hundred atoms. For this purpose, it also offers different subsystem approaches such as Mode‐ and Intensity‐Tracking to selectively calculate specific features of the full spectrum. Furthermore, an approximation to the entire spectrum can be obtained using the Cartesian Tensor Transfer Method. We illustrate these capabilities using the example of a large π‐helix consisting of 20 (S)‐alanine residues. In particular, we investigate the ROA spectrum of this structure and compare it to the spectra of α‐ and 3₁₀‐helical analogs. © 2012 Wiley Periodicals, Inc.     

Isolation,anticholinesterase properties and acute toxicity of the four stereoisomers of the nerve agent soman

Abstract

The four stereoisomers of pinacolyl methylphospho-nofluoridate (soman) were isolated with more than 99% optical purity. The bimolecular rate constants for inhibition of electric eel acetylcholinesterase and the LD₅₀-values (sc, mice) of the stereoisomers were determined.     

Metalloid Cluster Compounds of Group 14: Bonding Properties and Subsequent Reactions

Abstract

Metalloid cluster compounds of group 14 of the general formulae E_nR_m with n > m (E = Si, Ge, Sn, Pb; R = ligand), where naked as well as ligand bound tetrel atoms are present, represent a novel class of cluster compounds in group 14 chemistry and can be seen as intermediates on the way to the elemental state. Therefore, interesting properties are expected for these compounds, which might complement results from nanotechnology. In this article, first results for germanium are discussed, together with novel build-up reactions on the way to novel materials based on metalloid cluster compounds.

GRAPHICAL ABSTRACT     

Ozone‐Induced Band Bending on Metal‐Oxide Surfaces Studied under Environmental Conditions

Ozone adsorption and decomposition on metal oxides is of wide interest in technology and in atmospheric chemistry. Here, ozone‐adsorption‐induced band bending is observed on Ti‐ and Fe‐oxide model surfaces under dry and humid conditions. Photoelectron spectroscopic studies indicate the effect of charge transfer to O₃, which limits the surface coverage of the precursor to decomposition reactions. This is also consistent with the negative pressure dependence observed in previous studies. These results contribute to our fundamental understanding of ozone adsorption and decomposition mechanisms on metal oxides of environmental and technological relevance.