Supramolecular Wiring of Benzo‐1,3‐chalcogenazoles through Programmed Chalcogen Bonding Interactions

The high‐yielding synthesis of 2‐substituted benzo‐1,3‐tellurazoles and benzo‐1,3‐selenazoles through a dehydrative cyclization reaction has been reported, giving access to a large variety of benzo‐1,3‐chalcogenazoles. Exceptionally, these aromatic heterocycles proved to be very stable and thus very handy to form controlled solid‐state organizations in which wire‐like polymeric structures are formed through secondary N???Y bonding interactions (SBIs) engaging the chalcogen (Y=Se or Te) and nitrogen atoms. In particular, it has been shown that the recognition properties of the chalcogen centre at the solid state could be programmed by selectively barring one of its σ‐holes through a combination of electronic and steric effects exerted by the substituent at the 2‐position. As predicted by the electrostatic potential surfaces calculated by quantum chemical modelling, the pyridyl groups revealed to be the stronger chalcogen bonding acceptors, and thus the best ligand candidate for programming the molecular organization at the solid state. In contrast, the thiophenyl group is an unsuitable substituent for establishing SBIs in this molecular system as it gives rise to chalcogen–chalcogen repulsion. The weaker chalcogen donor properties of the Se analogues trigger the formation of feeble N???Se contacts, which are manifested in similar solid‐state polymers featuring longer nitrogen–chalcogen distances.     

Definitions and examples in elementary calculus: the case of monotonicity of functions

This paper is devoted to the investigation of students’ understanding and handling of examples in the framework of an example-based introductory mathematics undergraduate course. The plan of the course included a wide use of graphs in standard lectures, tutoring sessions as well as in examinations. This study deals with the notion of increasing function, which has been introduced by means of both the standard definition and a range of examples and non-examples, most often conveyed through graphs. We have analysed students’ interpretations of the notion of increasing function as they applied them in a set of written examination tests. The data gathered have been completed by a number of interviews of students whose answers were difficult to interpret. The outcomes underline the importance of linguistic and semiotic competence and suggest that the design of innovative teaching paths should take care of the linguistic and semiotic skills needed to handle the representations involved.     

Amino acid functionalisation of water soluble carbon nanotubes

High solubility of SWNTs and MWNTs in water is obtained by organic functionalisation; derivatisation with N-protected glycine is also easily achieved.     

Poly(ethylene glycol)-supported tetrahydroxyphenyl porphyrin: a convenient,recyclable catalyst for photooxidation reactions

[reaction: see text] A new poly(ethylene glycol)-supported porphyrin has been prepared and its ability as a promoter in photooxidation reactions has been studied. The PEG-supported catalyst exhibits high activity, comparable to that of a nonanchored sensitizer, and it is easily removable by filtration from the reaction mixture. The polymer-bound porphyrin has been recycled up to six times with no loss of chemical and stereochemical efficiency.     

X-ray double-crystal rocking curves in GaAlAs/GaAs heterostructures

Summary X-ray double-crystal rocking curves of Ga_1−x Al _x As/GaAs heterostructures have been calculated using a dynamical diffraction model for the general case of Bragg reflection geometry. Different experimental configurations have been considered and the possibility of studying both slightly mismatched and relatively thin layers has been investigated. Experimental rocking curves have been measured using the CuKα ₁ radiation, the 004 symmetric reflection and a perfect crystal as the monochromator. An excellent agreement between calculated and experimental rocking curves has been found and this demonstrates the reliability of both the experimental procedure and the theoretical approach.     

Vanishings for the cohomology of certain families of stable rank two vector bundles onP 3

Sunto Si analizzano delle condizioni per l'annullamento della coomologia di fibrati stabili di rango 2su P ³.Dopo i primi risultati di annullamento dovuti principalmente ad Hartshorne, Chang congetturò che alcune disuguaglianze sulle, classi di Chern fossero sufficienti per l'annullamento del primo gruppo di coomologia. La congettura finora è provata solo in alcuni casi particolari. Nel lavoro si dimostra la congettura in molti altri casi. In particolare si completano alcuni risultati recenti dovuti ad Ellia affrontando il caso in cui la prima classe di Chern è dispari.     

The Singularity of Kontsevich’s Solution for QH<Superscript>*</Superscript>(CP<Superscript>2</Superscript>)

In this paper we study the nature of the singularity of the Kontsevichs solution of the WDVV equations of associativity. We prove that it corresponds to a singularity in the change of two coordinates systems of the Frobenius manifold given by the quantum cohomology of CP². Mathematics Subject Classifications (2000) 53C99, 32D99, 14N35, 88A99.