Palladium-catalysed Heck reaction on 1,2-dien-1-ols: a stereoselective synthesis of α-arylated α,β-unsaturated aldehydes

A new methodology for preparing α-arylated α,β-unsaturated aldehydes is reported. The starting materials are all commercially available alkyn-1-ols (1a-c) that have been easily isomerised to the corresponding allenes (2a-c). The key step is the Heck coupling of the 1,2-dien-1-ols with a series of iodo- and bromoarene. The products have been synthesised in good yields, and the reactions were carried out under very mild conditions.     

Solid-Phase Synthesis of Fluorescent Probes for Plasma Membrane Labelling

The cellular plasma membrane plays a fundamental role in biological processes, including cell growth, signaling and transport. The labelling of the plasma membrane with targeted fluorescent probes offers a convenient and non-invasive way to image the morphological changes and dynamics of a membrane in real-time and, despite many examples of fluorescent plasma membrane probes, a “universal targeting/anchoring moiety” is still required. In this study, a small number of stearic acid-based probes labelled with 6-carboxyfluorescein was designed and fabricated via solid-phase synthesis in which variations in both charge and hydrophobicity were explored. To ease the synthesis process, a gram-scale synthesis of the Fmoc-Lys(6-carboxyfluoresein diacetate)-OH building block was developed, allowing the discovery of optimal probes that carried a positively charged amino group and a stearic acid tail that exhibited intense plasma membrane brightness and robust retention.     

Synthesis and esterolytic activity of catalytic peptide dendrimers

Peptide dendrimers were prepared by solid-phase peptide synthesis. Monomeric dendrimers were first obtained by assembly of a hexapeptide sequence containing alternate standard alpha-amino acids with diamino acids as branching units. The monomeric dendrimers were then dimerized by disulfide-bridge formation at the core cysteine. The synthetic strategy is compatible with functional amino acids and different diamino acid branching units. Peptide dendrimers composed of the catalytic triad amino acids histidine, aspartate, and serine catalyzed the hydrolysis of N-methylquinolinium salts when the histidine residues were placed at the outermost position. The dendrimer-catalyzed hydrolysis of 7-isobutyryl-N-methylquinolinium followed saturation kinetics with a rate constant of catalysis/rate constant without catalysis (k(cat)/k(uncat)) value of 3350 and a rate constant of catalysis/Michaelis constant (k(cat)/K(M)) value 350-fold larger than the second-order rate constant of the 4-methylimidazole-catalyzed reaction; this corresponds to a 40-fold rate enhancement per histidine side chain. Catalysis can be attributed to the presence of histidine residues at the surface of the dendrimers.     

Biomonitoring of traffic originated PAHs in the air

This article sets out the results of air quality biomonitoring along a transect bordering on the A32 Turin–Bardonecchia motorway (Italy). The results were obtained using aeroponic sampling units, an innovation insofar as the plants acting as monitor live and grow in these units above ground, assuring that atmospheric pollutants are absorbed only through the leaves. The accumulation of 15 polynuclear aromatic hydrocarbons (PAHs) on the leaves of Brassica oleracea var. Acephala, used as biosampler, was determined on samples taken in the months of February, July and October 2002, in each case after two months' exposure. The results highlight: (i) the influence of the seasons on the accumulation of pollutants, (ii) that phenanthrene, fluoranthene, pyrene and chrysene generally account for more than 80% of total PAHs, (iii) that the data may be considered representative of both volatile and non-volatile compounds. Comparison with other sampling methods are supplied and discussed.     

The Levi Monge-Ampère equation: Smooth regularity of strictly Levi convex solutions

We prove smoothness of strictly Levi convex solutions to the Levi equation in several complex variables. This equation is fully non linear and naturally arises in the study of real hypersurfaces in ℂⁿ⁺¹, for n ≥ 2. For a particular choice of the right-hand side, our equation has the meaning of total Levi curvature of a real hypersurface ℂⁿ⁺¹ and it is the analogous of the equation with prescribed Gauss curvature for the complex structure. However, it is degenerate elliptic also if restricted to strictly Levi convex functions. This basic failure does not allow us to use elliptic techniques such in the classical real and complex Monge-Ampère equations. By taking into account the natural geometry of the problem we prove that first order intrinsic derivatives of strictly Levi convex solutions satisfy a good equation. The smoothness of solutions is then achieved by mean of a bootstrap argument in tangent directions to the hypersurface.     

On Lagrange duality theory for dynamics vaccination games

The authors study an infinite dimensional duality theory finalized to obtain the existence of a strong duality between a convex optimization problem connected with the management of vaccinations and its Lagrange dual. Specifically, the authors show the solvability of a dual problem using as basic tool an hypothesis known as Assumption S. Roughly speaking, it requires to show that a particular limit is nonnegative. This technique improves the previous strong duality results that need the nonemptyness of the interior of the convex ordering cone. The authors use the duality theory to analyze the dynamic vaccination game in order to obtain the existence of the Lagrange multipliers related to the problem and to better comprehend the meaning of the problem.

     

Continuity of solutions for parametric variational inequalities in Banach space

We consider here a type of pseudo-monotone parametric variational inequalities on a class of Banach spaces and show that such problems admit continuous (with respect to the parameter) solutions, as long as generic existence and uniqueness conditions for these solutions are satisfied. In particular, we show that such results are valid on a class of Banach spaces whenever we deal with strong pseudo-monotonicity, while others are valid in Hilbert spaces, whenever strict monotonicity is present. We also provide examples to illustrate the new results.     

Preface to Variational Analysis for Beginners

Set-Valued and Variational Analysis -