Scope of the formal [3+2] cycloaddition for the synthesis of five-membered ring of functionalized indanes

We report our research about the synthesis of functionalized indanes in the pentagonal ring by a formal [3+2] cycloaddition using benzhydrols and styrene derivatives with electron-withdrawing groups joined to C-β, such as carboxyl, carboxymethyl, carbonyl of ketones, and nitro groups. We also report the configurational assignment of the indanic structures synthesized using several experiments of NMR.     

Singular random matrix decompositions: Jacobians

For a singular random matrix X, we find the Jacobians associated to the following decompositions: QR, Polar, Singular Value (SVD), L′U, L′DM and modified QR (QDR). Similarly, for the cross-product matrix S=X′X we find the Jacobians of the Spectral, Cholesky's, L′DL and symmetric nonnegative definite square root decompositions.     

General equilibrium and social choice in economies with increasing returns

For any intransitive community preference, we construct a non-convex economy where all the marginal cost pricing general equilibria are Pareto inefficient (theorem 3.2). The result is valid without requiring a fixed income distribution rule (corollary 3.3). Intransitive community preferences are a frequent occurrence (theorem 3.1): necessary and sufficient conditions for transitivity of the community preference fail in a set which is open and dense in the space of individual preferences with a standard topology.     

Solvatochromic dipolarity micro‐sensor behaviour in binary solvent systems of the (water + ionic liquid) type: application of preferential solvation model and linear solvation energy relationships

The type of specific intermolecular and interionic interactions that are established when an ionic liquid is dissolved in water was here analysed. The study of the solvatochromic response of dipolarity micro‐sensors based on Reichardt E_T(30) and Kamlet–Abboud–Taft solvent scales and the application of the solvent exchange model confirmed the formation of different intersolvent complexes in binary mixtures of (water + [C₄mim] [BF₄]/[Br]) type. These complexes provide H‐bond or electron pairs to the polar network, respectively. Moreover, for 4‐methoxybenzenesulfonyl chloride hydrolysis reaction in the (water + [C₄mim] [BF₄]) system, a higher inhibition (13 times) on the k_obs values was observed. Multiple linear regression analysis that allows confirming the solvent effect upon the reactive system is due to the hydrogen‐bond donor properties of intersolvent complex formed. Then, the correlation between two different solvent‐dependent processes proved to be successful. Copyright © 2014 John Wiley & Sons, Ltd.     

Inorganic pigment study of the San Pedro Gonzalez Telmo Sibyls using total reflection X-ray fluorescence

This article describes the study carried out on a series of oil paintings on canvas from the eighteenth century that were restored at Centro de Producción e Investigación en Restauración y Conservación Artística y Bibliográfica - Tarea (CEIRCAB-Tarea), Buenos Aires, Argentina: the San Pedro González Telmo Sibyls. Experimental study was undertaken to identify inorganic pigments and the technique used in their confection; and, in this way, try to add information about their local origin. Therefore special emphasis was put to infer technologies used in the manufacturing of these paintings. Elemental analysis was performed by total reflection X-ray fluorescence spectrometry (TXRF) and complemented by optical and polarized light microscopy. Microsampling was carefully done over areas of the paintings which were damaged and where a small additional loss will not be noticed. This investigation has shown that a variety of pigments were used, namely earth pigments (red and yellow ochres), white lead, vermilion, etc., and they were used either pure or in mixtures. This characterization helped conservators in their decisions regarding a better understanding of the deterioration processes. In addition, this research about the material composition allowed the art historians and restorers the possibility to obtain information about where, when or by whom The San Pedro González Telmo Sibyls may have been painted.     

Only acridine derivative from Hantzsch-type one-pot three-component reactions

Abstract  

A three-component Hantzsch-type condensation of different anilines with dimedone and benzaldehyde leads to the formation of a unique acridine derivative with an unusual breaking of a C–N bond. The reaction was also carried out employing rapid microwave or conventional heating and sonication as alternative energy sources, and only this 1,8-dioxodecahydroacridine was obtained.     

A full conformational space analysis of bilirubin

Ab initio methods were utilized in a gas-phase systematic conformational search of bilirubin conformers. The whole molecule was divided into four fragments. Most stable conformers of them were employed to build 196 conformers of the complete bilirubin molecule. Initial geometries were optimized using HF/3-21G level of theory and the minimum energy conformers were then reoptimized at B3LYP/6-31G(d) level. Ridge-tile conformer was the most stable one, in perfect agreement with X-ray data. We found that while tetrapyrrole backbone shows some flexibility, propionic acid side chains have a greater influence in bilirubin conformation because they can interact through different hydrogen bond patterns with the backbone and between them.     

Microwave-assisted tandem reactions for the synthesis of 2-hydrazolyl-4-thiazolidinones

A tandem method for the synthesis of 2-hydrazolyl-4-thiazolidinones (5) from commercially available materials in a 3-component reaction has been developed. The reaction connects aldehydes, thiosemicarbazides, and maleic anhydride, effectively assisted by microwave irradiation. The synthesis of a new type of compound, 2-hydrazolyl-5,5-diphenyl-4-thiazolidinone (7), obtained by treatment of thiosemicarbazone with benzil in basic media is also reported. HOMO/LUMO energies, orbital coefficients, and charge distribution were used to explain the proposed reaction mechanism.     

Inference under functional proportional and common principal component models

In many situations, when dealing with several populations with different covariance operators, equality of the operators is assumed. Usually, if this assumption does not hold, one estimates the covariance operator of each group separately, which leads to a large number of parameters. As in the multivariate setting, this is not satisfactory since the covariance operators may exhibit some common structure. In this paper, we discuss the extension to the functional setting of the common principal component model that has been widely studied when dealing with multivariate observations. Moreover, we also consider a proportional model in which the covariance operators are assumed to be equal up to a multiplicative constant. For both models, we present estimators of the unknown parameters and we obtain their asymptotic distribution. A test for equality against proportionality is also considered.