On an alternative functional equation related to the Cauchy equation

We consider the following problem: Let (G, +) be an abelian group,B a complex Banach space,a, bB,b0,M a positive integer; find all functionsf:G B such that for every (x, y) G ×G the Cauchy differencef(x+y)–f(x)–f(y) belongs to the set {a, a+b, a+2b, ...,a+Mb}. We prove that all solutions of the above problem can be obtained by means of the injective homomorphisms fromG/H intoR/Z, whereH is a suitable proper subgroup ofG.     

Crystal,molecular and electronic structure of 1,1-diaryl-2-halogenoethylenes

On the basis of semiempirical calculations, the conformation of the isolated molecule of 2-bromo-1,1-diphenylprop-1-ene corresponding to the minimum of total energy was determined. Assuming some information on the localization of the molecules in the crystal, also the conformation in a theoretical crystal was studied. The results have been compared with the crystal structure of 2-bromo-1,1-diphenylprop-1-ene, as obtained by X-ray diffraction. From the comparison a slight displacement of the C2 atom was suggested.

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Zusammenfassung Die dem Minimum der Gesamtenergie entsprechende Konformation des isolierten Moleküls von 2-Brom-1,1-diphenylprop-1-en wurde durch halb-empirische Methoden bestimmt. Gewisse Ergebnisse über die Anordnung der Moleküle im Kristall machten es möglich, die Konformation in einem theoretischen Kristall zu untersuchen. Nach Vergleich der Resultate mit der durch Röntgen-Analyse bestimmten Kristallstruktur des 2-Brom-1,1-diphenylprop-1-en wurde eine kleine Verschiebung des C2-Atoms vorgeschlagen.

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Résumé Par le moyen de calculs semiempiriques on a déterminé la conformation de la molécule isolée de 2-bromo-1, 1-diphénilprop-1-ène, correspondant au minimum d'énergie totale. On a aussi étudié la conformation dans le cristal théorique en se basant sur des informations concernant la localisation des molécules dans le cristal. On a comparé ces résultats avec ceux que nous avons obtenus par la détermination de la structure cristalline du 2-bromo-1, 1-diphénilprop-1-ène avec la diffraction des rayons X: cette comparaison nous a porté à déplacer un petit peu l'atome C 2.

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This work was supported by a grant from the Italian Consiglio Nazionale delle Ricerche.     

Synthesis of 4,5-dihydro-2,4-benzoxazepin-3( 1H)ones and 1,3,4,5-tetrahydro-2,4-benzoxazepines

o- Aminomethylbeiizyl alcohols (X) easily cyclize with phosgene in an aqueous alkaline medium to form 4,5-dihydro-2,4-benzoxazepin-3(1H)ones (IV) and with aldehydes in acidic conditions to yield 1,3,4,5-tetrahydro-2,4-benzoxazepines (V). The characteristics and chemical behaviour of these new heterocyclic ring systems are reported.     

Determination of aliphatic aldehydes by liquid chromatography with pulsed amperometric detection

An electrochemical detection method for short-chain saturated and unsaturated aliphatic aldehydes separated by liquid chromatography in moderately acidic medium is described. A triple-step waveform of the potentials applied to the polycrystalline platinum electrode, is proposed for sensitive detection of aliphatic aldehydes in flowing streams avoiding tedious pre- or post-column derivatization and/or cleanup procedures. The influences of the perchloric acid concentration and dissolved oxygen in the mobile phase, on the amperometric and chromatographic performance were evaluated and considered in terms of sensitivity and selectivity. Under the optimised experimental conditions (i.e., deoxygenated 50mM HClO4) the proposed analytical method allowed detection limits between 0.2 microM for acrolein and 2.5 microM for valeraldehyde. Regression analysis of calibration data indicates that responses for all investigated compounds are linear over about 2 orders of magnitude above the LOD, with correlation coefficients >0.990. The method was successfully applied to the determination of formaldehyde, acetaldehyde, propionaldehyde and acrolein in real matrices such as spiked water and red wines with good mean recoveries (81-97%).     

The ring-opening reaction of chromenes: a photochemical mode-dependent transformation

The efficiency of the photochemical ring-opening of chromenes (or benzopyrans) depends on the vibronic transition selected by the chosen excitation wavelength. In the present work, ab initio CASPT2//CASSCF calculations are used to determine the excited-state ring-opening reaction coordinate for 2H-chromene (C) and 2,2-diethyl-2H-chromene (DEC) and provide an explanation for such an unusual mode-dependent behavior. It is shown that excited-state relaxation and decay occur via a multimodal and barrierless (or nearly barrierless) reaction coordinate. In particular, the relaxation out of the Franck-Condon involves a combination of in-plane skeletal stretching and out-of-plane modes, while the second part of the reaction coordinate is dominated exclusively by a different out-of-plane mode. Population of this last mode is shown to be preparatory with respect to both C-O bond breaking and decay via an S(1)/S(0) conical intersection. The observed mode-dependent ring-opening efficiency is explained by showing that the vibrational mode corresponding to the most efficient vibronic transition has the largest projection onto the out-of-plane mode of the reaction coordinate. To support the computationally derived mechanism, we provide experimental evidence that the photochemical ring-opening reaction of 2,2-dimethyl-7,8-benzo(2H)chromene, that similarly to DEC exhibits a mode-dependent photoreaction, has a low ( approximately 1 kcal mol(-1)) activation energy barrier.     

RuO4-promoted oxidative polycyclization of isoprenoid polyenes. A further insight into the stereochemistry of the process

Further studies on the RuO₄-catalyzed oxidative polycyclization of isoprenoid polyenes have been carried out. The configuration of the tris-THF product from the oxidation of geranylgeranyl acetate has been determined by a combination of spectral and chemical correlation methods. The oxidation of (E,Z)-farnesyl acetate, synthesized from nerol, has been carried out. This process stops at the first cyclization indicating that an E configuration of the Δ⁶ double bond is needed for the second cyclization to occur. The results are discussed in comparison with previous knowledge on the related Re(VII) polycyclization of polyenic bis-homoallylic alcohols.     

A method for solving a conditional cauchy equation on abelian groups

Sunto In questa Nota è descritto wn metodo per la determinazione delle soluzioni della seguente equazione condizionale f(x+y) f(x) + f(y) + a implica f(x + y)=f(x) + f(y) dove f:GH, a H e G ed H sono gruppi abeliani qualsiasi. Sono poi determinate esplicitamente le soluzioni nei casi G=(r), G= e G=(p).

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Lavoro svolto nell'ambito del G.N.A.F.A.-C.N.R.     

Modelling the soundscape quality of urban waterfronts by artificial neural networks

The renewal of the urban waterfronts has become a major focus of attention for politicians and decision makers in the city’s management programs. The recognition of the patterns that define the waterfronts’ identity is essential to select new strategies of intervention for the environmental recovery. In order to create adequate environments for everyday life within a sustainable development, new links between human senses, human perception and design need to be created. Within this wide approach, the landscape and the soundscape play a significant role and can become a key driving force in the implementation of the changes. New techniques have to be tested to identify the sonic and visual parameters capable to explain the specificity of a waterfront. With this purpose, an artificial neural network (ANN) was developed, and the relative importance of the input variables was evaluated. The collected database was also analysed by multiple linear regression (MLR) to compare the outcomes of both models. The urban waterfront of Naples (Italy) was chosen as case study. The results obtained show that the performance of the neural network is better than the one of the linear regression (rANN = 0.949, rMLR = 0.639). The interpretation of the relative importance method is also quite satisfactory in the ANN.     

Redox switchable ligands suitable for transition metal ions: Protonation,complexation and electrochemical properties of a ferrocene-modified tetraamine diketone and its saturated analogue

Abstract

The new ferrocene-containing water-soluble ligands 1 and 2 were synthesized and their protonation and complexation properties toward Ni^II and Cu^II studied as a function of pH, by means of potentiometric titration experiments. Electrochemical measurements were performed in aqueous solution on pure 1 and 2 and in the presence of Ni^II and Cu^II cations, in the pH range 2–12, allowing us to determine the redox potential values relative to the ferrocene oxidation in the free ligands and in their Ni^II and Cu^II complexes. 1 and 2 behave as redox switchable ligands, the former enhancing, the latter decreasing its binding ability upon oxidation of the appended ferrocene function. Besides, the Cu^II complex of ligand 1 and the Ni^II complex of ligand 2 behave as two-centre two-electron redox systems, the complexed metal cation being subject to further oxidation to M^III.     

Realizing the Promise—The Development of Research on Carbon Nanotubes

The present reflection on the development of research on carbon nanotubes (CNTs) stems from the publication of the report “Realizing the Promise of Carbon Nanotubes” by the US National Nanotechnology Initiative in 2015. The report is a critical assessment of the state‐of‐art of CNT research and highlights some unresolved issues related with this field. Starting from the results of this assessment, we carried out an analysis of the publications’ pool in CNTs and related domains, by exploiting bibliometric tools. We focused on the item of competition/collaboration between disciplines and nations, with the purpose of evaluating the position of chemistry (as a discipline) as well as the position of the main European countries and the European Union (EU) as a whole in the context of CNT research. The results of such analysis outline very clearly the interdisciplinary landscape wherein CNT research is situated and show the highly competitive place occupied by EU in the field.