The trace of totally positive algebraic integers

For all totally positive algebraic numbers except a finite number of explicit exceptions, the following inequality holds:

\max(1.780022,1.66+\alpha_1), \end{displaymath}">

where is the degree of and its conjugates. This improves previous results of Smyth, Flammang and Rhin.

     

Polymer-nanoparticle complexes: from dilute solution to solid state

We report on the formation and the structural properties of "supermicellar" aggregates made from mineral nanoparticles and polyelectrolyte-neutral block copolymers in aqueous solutions. The mineral particles put under scrutiny are ultrafine and positively charged yttrium hydroxyacetate nanoparticles. Combining light, neutron, and X-ray scattering experiments, we have characterized the sizes and the aggregation numbers of the organic-inorganic complexes. We have found that the hybrid aggregates have typical sizes in the range of 100 nm and exhibit a remarkable colloidal stability with respect to ionic strength and concentration variations. Solid films with thicknesses up to several hundreds of micrometers were cast from solutions, resulting in a bulk polymer matrix in which nanoparticle clusters are dispersed and immobilized. It was found in addition that the structure of the complexes remains practically unchanged during film casting.     

Observation of three behaviors in confined liquid water within a nanopool hosting proton-transfer reactions

In this contribution, we report on studies of rotational and diffusional dynamics of 7-hydroxyquinoline (7HQ) within a reverse micelle (RM) containing different amounts of water. Analyzed in terms of the wobbling-in-a-cone model, the data reveal structural and dynamical properties of the nanopool. We clearly observed three regions in the behavior of confined water molecules within the RM hosting a double proton-transfer reaction between the probe and water. This observation remarkably reproduces the change of calculated water density within this life-mimicking medium. The number of water molecules per AOT head in the transition regions changes from 2 to 5, the latter being very near to the full solvation number (6) of the RM heads. Moreover, the H-bonds breaking and making within the RM to give new structures of the probe strongly affect the environment fluidization in different extents, reflected in different relaxation times of these structures; however, they are of similar sizes. We discuss the role of RM confinement and the proton-transfer dynamics on the behavior of water and their relationships to the packing of water molecules in the studied range of concentrations.     

Current progress in the asymmetric aldol addition reaction

Control of stereochemistry during aldol addition reactions has attracted considerable interest over the years as the aldol reaction is one of the most fundamental tools for the construction of new carbon-carbon bonds. Several strategies have been implemented whereby eventually any single possible stereoisomeric aldol product can be accessed by choosing the appropriate procedure. With earlier methods, stoichiometric quantities of chiral reagents were required for efficient asymmetric induction, with the auxiliary most often attached covalently to the substrate carbonyl. Lewis acid catalyzed addition reactions of silyl enolates to aldehydes (Mukaiyama reaction) later opened the way for catalytic asymmetric induction. In the last few years, both chiral metal complexes and small chiral organic molecules have been found to catalyse the direct aldol addition of unmodified ketones to aldehydes with relatively high chemical and stereochemical efficiency. These techniques along with the more recent developments in the area are discussed in this tutorial review.     

Intramolecular sulfur transfer in N-enoyl oxazolidine-2-thiones promoted by Brønsted acids. Practical asymmetric synthesis of beta-mercapto carboxylic acids and mechanistic insights

The ability of Br?nsted acids alone to efficiently promote the sulfur transfer process in N-enoyl oxazolidine-2-thiones to give beta-mercapto carbonyl derivatives is demonstrated. The reactions proceed with essentially perfect diastereocontrol for a range of alkyl-substituted N-enoyl oxazolidine-2-thiones (d.r. regularly above 98:2) and high selectivity for most aryl-substituted counterparts (d.r. typically above 92:8). Importantly, the reaction works remarkably well in beta,beta-disubstituted N-enoyl oxazolidine-2-thiones as well, giving rise to quaternary C-S stereocenters in selectivities usually above 95:5. The relative efficiency of a range of acids (trifluoroacetic, difluoroacetic, acetic, triflic) is assessed showing TFA and TfOH as the most efficient and acetic acid as a totally inefficient reaction promoter. The new procedure complements the Lewis acid promoted reaction previously described by our group in two aspects: First, stereodivergent results are obtained for the Lewis acid or Br?nsted acid promoted reactions of beta,beta-disubstituted enoyl compounds. Second, while the Br?nsted acid promoted reactions are stereospecific, providing a good correlation between the substrate E/Z configuration and products stereochemistry, the reactions mediated by Lewis acids (BF3/OEt2) provide invariant d.r. values regardless of the E/Z composition of the starting olefin. The synthetic value of the method is illustrated by (a) removal of the oxazolidinone moiety from the rearranged products under reducing conditions (NaBH4, H2O-THF) which yields beta-mercapto alcohols and (b) treatment with Sm(OTf)3 in MeOH which affords the corresponding beta-mercapto carboxylic esters, both categories of compounds being isolated in up to 97% ee. Remarkably, the method constitutes the first general approach to highly enantioenriched building blocks bearing a quaternary C-S stereocenter. On the other hand, spectroscopic and inhibition experiments are carried out that demonstrate the participation of protons also in the Lewis acid promoted reactions. Finally, the computational studies carried out at the B3LYP/6-31G* level give support for an activation of the substrate enoyl by complexation with two molecules of either the Br?nsted or Lewis acid and serve to explain the stereochemical outcome of the reactions.     

The aldol addition reaction: an old transformation at constant rebirth

The main recent conceptual advances in asymmetric aldol reactions are presented. Methods ranging from stoichiometric chiral auxiliary-mediated to direct, catalytic reactions are covered, including the Mukaiyama aldol reactions which use stoichiometric base and silylating reagents, but catalytic (substoichiometric) amounts of the chiral inductor. The salient features of each new development are noted, paying special attention to practical concerns and to the potential implementation for large scale production. After examination of pros and cons of each strategy, gaps and limitations that deserve further investigation are highlighted.     

Classification of extended chaotic inflation potentials

Brans-Dicke gravity is remarkable not only in that General Relativity and Mach's Principle find a common enlarged scenario where they are mutually consistent, but also in that it provides a very interesting quantum cosmological model within the inflationary paradigm. The interplay between the Brans-Dicke scalar Φ and the inflaton field σ plays an important rôle during the course of inflation, and although the dynamics as such is governed by the potential, the onset and the end of inflation are determined by the values of both fields jointly. The relative position of the beginning – and end-of-inflation curves (BoI and EoI respectively) is the most relevant factor in determining the resulting quantum cosmological scenario. The classification of potentials that is given in this paper is based on the criterion of whether the BoI and EoI boundaries enclose a finite or infinite area in the (σ,Φ) plane where inflation takes place. It is shown that this qualitative classification distinguishes two classes of potentials that yield very different cosmologies and it is argued that only those theories in which BoI and EoI enclose a finite area in the (σ,Φ) plane are compatible with our observable universe.