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.     

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.     

THEORETICAL PREDICTIONS OF STRUCTURES AND VIBRATIONAL INFRARED FREQUENCIES. I. MERCAPTANS AND SULFIDES

Abstract

We report the computed equilibrium geometries and vibrational infrared frequencies of a group of thirteen mercaptans and sulfides. The computations were based on the Gaussian 86 Program Package utilizing 3-21G basis sets. The theoretical bond distances and bond angles are in agreement with the available experimental data. The agreement between computed frequencies and available experimental values seems reasonable. We also used the computations as guidelines for the assignment of available experimental infrared frequencies. We believe that it is possible to make reliable frequency predictions by combining computations with available experimental data for groups of similar molecules. However, it is necessary to introduce different correction factors for different types of vibrational modes if we use 3-21G basis sets.     

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.     

Annelated Pyridines as Highly Nucleophilic and Lewis Basic Catalysts for Acylation Reactions

New heterocyclic derivatives of 9‐azajulolidine have been synthesized and characterized with respect to their nucleophilicity and Lewis basicity. The Lewis basicity of these bases as quantified through their theoretically calculated methyl‐cation affinities correlate well with the experimentally measured reaction rates for addition to benzhydryl cations. All newly synthesized pyridines show exceptional catalytic activities in benchmark acylation reactions, which correlate only poorly with Lewis basicity or nucleophilicity parameters. A combination of Lewis basicity with charge and geometric parameters in the framework of a three‐component quantitative structure–activity relationship (QSAR) model is, however, highly predictive.