The first variation of the total mass of log-concave functions and related inequalities

On the class of log-concave functions on Rⁿ${\mathbb{R}}^n$, endowed with a suitable algebraic structure, we study the first variation of the total mass functional, which corresponds to the volume of convex bodies when restricted to the subclass of characteristic functions. We prove some integral representation formulae for such a first variation, which suggest to define in a natural way the notion of area measure for a log-concave function. In the same framework, we obtain a functional counterpart of Minkowski’s first inequality for convex bodies; as corollaries, we derive a functional form of the isoperimetric inequality, and a family of logarithmic-type Sobolev inequalities with respect to log-concave probability measures. Finally, we propose a suitable functional version of the classical Minkowski’s problem for convex bodies, and prove some partial results towards its solution.     

Designing multifunctional expanded pyridiniums: properties of branched and fused head-to-tail bipyridiniums

The multifaceted potentialities of expanded pyridiniums (EPs), based on one pyridinium core bearing a 4-pyridyl or 4-pyridylium as the N-pyridinio group, are established at both experimental and theoretical levels. Two classes of head-to-tail (htt) EPs were designed, and their first representative elements were synthesized and fully characterized. The branched (B) family is made up of 2,6-diphenyl-4-aryl-1,4'-bipyridin-1-ium (or 1,1'-diium) species, denoted 1B and 2B for monocationic EPs (with aryl = phenyl and biphenyl, respectively) and 1B(Me) and 2B(Me) for related quaternarized dicationic species. The series of fused (F) analogues comprises 9-aryl-benzo[c]benzo[1,2]quinolizino[3,4,5,6-ija][1,6]naphthyridin-15-ium species, denoted 1F and 2F, and their 2,15-diium derivatives referred to as 1F(Me) and 2F(Me). Electrochemistry (in MeCN vs SCE) reveals that branched EPs undergo a single reversible bielectronic reduction at ca. -0.92 V for 1B/2B and -0.59 V for 1B(Me)/2B(Me), whereas pericondensed species show two reversible monoelectronic reductions at ca. -0.83 and -1.59 V for 1F/2F and ca. -0.42 and -1.07 V for 1F(Me)/2F(Me). Regarding electronic absorption features, all htt-EP chromophores show absorptivity in the range of ca. 1-4 × 10(4) M(-1) cm(-1), with red-edge absorptions extending toward 450 and 500 nm (in MeCN) for 2B(Me) and 2F(Me), respectively. These lowest-energy pi-pi* transitions are ascribed to intramolecular charge transfer between the electron-releasing biphenyl group and the htt-bipyridinium electron-withdrawing subsystems. EPs display room-temperature photoemission quantum yields ranging from 10% to 50%, with the exception of 1B, and branched luminophores are characterized by larger Stokes shifts (8000-10?000 cm(-1)) than fused ones. Lastly, a method to predict the efficiency of photobiscyclization of branched EPs into fused ones, based on the analysis of computed difference maps in total electron density for singlet excited states, is proposed.     

Transition from enantioselective high performance to ultra-high performance liquid chromatography: A case study of a brush-type chiral stationary phase based on sub-5-micron to sub-2-micron silica particles

Three brush-type chiral stationary phases (CSPs) differing in the particle size of the starting silica particles have been prepared by covalent grafting of the π-acidic bis-(3,5-dinitrobenzoyl)-derivative of trans-1,2-diaminocyclohexane (DACH-DNB). Starting silica particles of 4.3, 2.6 and 1.9 micron were used to generate the final CSPs using an improved, highly reproducible synthetic methodology, that allowed to assemble and surface-graft the whole chiral selector in only two steps. The different CSPs have been packed in columns of various length and diameters, and fully characterized in terms of flow permeability, kinetic performances and enantioselectivity using a set of test solutes. Very high speed and high resolution applications together with stereodynamic HPLC examples are demonstrated on the columns with reduced particle diameters, on which separations of several enantiomeric pairs are routinely obtained with analysis times in the 15–40 s range.     

Antioxidant and spectroscopic studies of crosslinked polymers synthesized by grafting polymerization of ferulic acid

A novel, simple synthetic strategy for the preparation of crosslinked polymers with significant antioxidant properties is proposed. Ferulic acid (FA), a well‐known antioxidant compound, due to its reactivity toward free radical process, was inserted into a polymeric network with methacrylic acid (MAA) and ethylene glycole dimethacrylate acting as comonomer and crosslinker, respectively. All the reactants were simultaneously mixed in the polymerization feed and one‐pot radical reaction was carried out. Irregular microparticles were prepared by bulk polymerization and microspheres by precipitation polymerization. The materials were characterized by nuclear magnetic resonance–magic angle spinning (NMR‐MAS) studies, to verify effective FA insertion into polymeric networks, and by morphological, dimensional analyses, and water absorption measurement to study their superficial and swelling properties, respectively. Antioxidant properties of materials were evaluated by linoleic acid emulsion system–thiocyanate assay, determination of scavenging activity on DPPH radicals, determination of available phenolic groups in polymeric matrices, and determination of total antioxidant capacity. Copyright © 2009 John Wiley & Sons, Ltd.     

Simple extraction method and gas chromatography-mass spectrometry in the selective ion monitoring mode for the determination of phenols in wine

The concentrations of 22 components of wine, including most of those that have been shown to possess significant biological properties, have been determined by a fast and simple analytical method based on gas chromatography with mass spectrometric detection in the selective ion monitoring mode (GC/MS-SIM). The procedure involves an easy liquid-liquid extraction and derivatization methods of flavanols, phenols and carboxylic acid, using a very small wine volume. The average recovery (Rcv) ranged from 73 to 107% and linear regression coefficients (r(2)) were in a range of 0.981or=0.999. The GC/MS-SIM technique gives good specificity and sensitivity, and can therefore be suitable for routine monitoring of the concentration of individual phenolic antioxidants during winemaking and the aging process.     

Sequential unsymmetrical aryl coupling of o-substituted aryl iodides with o-bromophenols and reaction with olefins: palladium-catalyzed synthesis of 6H-dibenzopyran derivatives

Dibenzopyran derivatives are prepared by palladium- and norbornene-catalyzed reaction of aryl iodides, o-substituted with electron-releasing substituents, o-bromophenols, and activated alkenes.     

A Quantitative Voronovskaya Formula for Mellin Convolution Operators

Here we give a quantitative Voronovskaya formula for a class of Mellin convolution operators of type

The design of efficient and selective routes to a key 1,4-cis-substituted cyclohexylamide intermediate

This Letter describes the synthetic challenges in synthesising key 1,4-cis-substituted cyclohexylamide intermediate 1 for our research programme. Five different routes address the major issues of selectivity to afford the cis product in isomerically pure form and in high yield. Major purification issues were also encountered upon scaling some of the routes. The merits of the diverse routes are assessed and the reasoning given for which one was ultimately used for large-scale synthesis of 1.     

The optimal compliance problem for thin torsion rods: A 3D-1D analysis leading to Cheeger-type solutions

We consider the variational problem which consists in minimizing the compliance of a prescribed amount of isotropic elastic material placed into a given design region when it is subjected to a given load. We perform the asymptotics of this problem when the design region is a straight cylinder with infinitesimal cross section. The results presented in this Note concern the pure torsion regime and state the existence of optimal shapes for the limit problem. When the filling ratio tends in turn to zero, these optimal shapes concentrate on the boundary of the Cheeger set of the section of the design region.