Regio- and stereoselective ring opening of enantiomerically enriched 2-aryl oxetanes and 2-aryl azetidines with aryl borates

The regioselective ring opening of 2-aryl-substituted four-membered heterocyclic rings with phenols, including catechol, was achieved by the use of aryl borates in mild and neutral reaction conditions without the aid of any transition metal catalysts. While N-alkyl azetidines were found not to be reactive, optically active N-tosyl azetidines gave the corresponding beta-aryloxy amines in a racemic form, thus indicating the considerable carbocationic character of the transition state. The introduction of a hydroxyl group in the azetidine ring (i.e., an azetidinol), able to anchor the aryl borate and to direct the subsequent nucleophilic delivery, was shown to determine the ring-opening process with predominant inversion of configuration. When enantiomerically enriched 2-aryl oxetanes were used, the reduced extent of racemization observed (up to 93:7 er) was rationalized by an intramolecular delivery through a six-membered transition state, giving beta-aryloxy alcohols with a predominant retention of configuration (i.e., a syn-stereoselective ring opening). The aryloxy alcohols obtained, endowed with suitable functionalities, can be cyclized to give access to enantiomerically enriched 2-aryl-1,5-benzodioxepins.     

Competition among parties and power: an empirical analysis

This study develops a bi-objective method for burn-in decision makings with a view to achieving an optimal trade-off between the cost and the performance measures. Under the proposed method, a manufacturer specifies the relative importance between the cost and the performance measures. Then a single-objective optimal solution can be obtained through optimizing the weighted combination of these two measures. Based on this method, we build a specific model when the performance objective is the survival probability given a mission time. We prove that the optimal burn-in duration is decreasing in the weight assigned to the normalized cost. Then, we develop an algorithm to populate the Pareto frontier in case the manufacturer has no idea about the relative weight.     

Development of singularities for nonlinear hyperbolic systems with periodic data

We prove two blow-up results for classical (C ¹) solutions of the Cauchy problem for nonlinear hyperbolic systems in one space variable. The initial conditions are periodic and the systems are supposed to be in diagonal form. The first result concernsN×N genuinely nonlinear systems, and the second one is devoted to 2×2 systems with weak nonlinearities. In both cases we give an estimate of the lifespan of the classical solutions.     

Reactions of [Mo(N2)2(dppe)2] with organic isocyanates

The reactions of [Mo(N₂₂(dppe)₂], (dppe  Ph₂PCH₂CH₂PPh₂) with RC₆H₄NCO (R  H, p-CH₃, p-Cl) in benzene under irradiation produces [Mo(RC₆H₄NCO)₂(dppe)₂] in good yields. Comparison of the infrared data for these complexes, with those previously reported for metal complexes of CO₂-like molecules suggest a η²-C,O coordination to the metal.     

A Survey on Retrieval of Mathematical Knowledge

We present a survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 77 papers and tentative taxonomies of both retrieval problems and recurring techniques.     

Portable X-ray fluorescence device reveals the artistic palette of Carlo Bononi,Baroque artist from Ferrara

The principal aim of the in situ X-ray fluorescence (XRF) analysis on the canvas “The Coronation of the Virgin” was to characterise the colour palette of Carlo Bononi (Ferrara, 1580–1632), a lesser-known artist of the early Baroque period in Ferrara. More than 100 points were collected by means of an XRF spectrometer, but the presence of many overlapping painted layers left some doubts about the preparation and the background layers. The scanning electron microscopy with energy dispersive spectrometer analysis on two samples resolved some of these doubts. The results obtained indicate the use of typical 17th century pigments, such as lead white, vermilion, azurite and a copper-based green. For yellow pigments, the artist used the yellow ochre in some cases, while in others he used lead-tin yellow. We also individuated at least three different shades of umber. Almost all the pigments have been identified and they are the first step in establishing the technical apparatus necessary to understand the modus operandi of the Ferrarese artist.     

One-dimensional local rings with reduced associated graded ring and their Hilbert functions

Let A be a one-dimensional reduced local ring with finite normalization. Let G(A) be the associated graded ring of A. In this paper we analyse the two conditions: Proj (G(A)) reduced and G(A) reduced together with their relations with the equality H(n)=H_R (n), where H(n) and H_R (n) are respectively the Hilbert function of the ring A and of the local ring R of G(A)_red=G(A)/nil (G(A)) at its homogenous maximal ideal. As a consequence of our results we get a class of ordinary singularities with H(n) locally decreasing for any embedding dimension H(1) greater then 4.