On Higher Riesz Transforms for Gaussian Measures

Given an n × n matrix B, positive definite and symmetric, let L_B be the differential operator in Rⁿ given by A class of higher Riesz transforms associated with L_B is defined by means of higher gradients of order k. It is shown that these transformations are bounded in the space with respect to the measure that makes L_B selfadjoint. The constants obtained are independent of the dimension n and depend only on k,p, and the number of different eigenvalues of the matrix B. The proof of the results uses an extension of the Littlewood-Paley-Stein theory of square functions to the vector-valued case and inequalities previously proved by one of the authors in the context of the Riesz transforms of order one.     

On the conjecture of Birch and Swinnerton-Dyer

In this paper we complete Rubin's partial verification of the conjecture for a large class of elliptic curves with complex multiplication by .

     

Reaction of cinnamaldehyde and derivatives with Raney Ni–Al alloy and Al powder in water. Reduction or oxido-reduction?

A series of experiments dealing with the reduction of cinnamaldehyde and parent compounds was carried out in completely aqueous media in order to assess the character of this process. We wish to show that the treatment of these substrates in water with Raney catalysts is an oxido-reductive process.     

2D‐ and 3D‐microstructured biodegradable polyester resins

Biodegradable polyester resins were prepared via photo crosslinking of functional polyesters obtained by copolymerization of ε‐caprolactone and the functional cyclic esters γ‐acryloyloxy‐ε‐caprolactone (ACL) and γ‐methacryloyloxy‐ε‐caprolactone (MCL). The cyclic esters were prepared via Baeyer‐Villiger oxidation of the corresponding 4‐acyloyloxy‐cyclohexanone derivatives. Copolymers with different content of either acryloyloxy or methacryloyloxy functional groups were prepared via catalyzed ring‐opening polymerization (ROP) of γ‐acyloyloxy‐ε‐caprolactones and ε‐caprolactone using Al(OiPr)₃ as catalyst and initiator. 2D‐ and 3D‐micropatterning of the copolymers was performed via UV‐crosslinking of polymer films on a suitable substrate and by UV replica molding on both rigid and elastic masters, showing the processability of these novel functional polyesters and their potential as substrates for biomedical devices. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6789–6800, 2008     

Existence results for inequality problems on various subsets of Banach spaces and applications

Several existence results for a class of perturbed inequality problems on various subsets of Banach spaces are proved. A concrete application to a problem from Nonsmooth Mechanics illustrates is given. This paper is dedicated to the memory of Professor P.D. Panagiotopoulos     

Variational Bounds for the Generalized Random Energy Model

We compute the pressure of the random energy model (REM) and generalized random energy model (GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra’s “broken replica symmetry bounds,” and identify the random probability cascade as the appropriate random overlap structure for the model. For the REM the lower bound is obtained, in the high temperature regime using Talagrand’s concentration of measure inequality, and in the low temperature regime using convexity and the high temperature formula. The lower bound for the GREM follows from the lower bound for the REM by induction. While the argument for the lower bound is fairly standard, our proof of the upper bound is new.     

New active-iron based reducing system for carbonyl compounds and imines. Stereoselective reduction of cyclic ketones

The reaction of different carbonyl compounds and imines with a mixture of iron(II) chloride tetrahydrate, an excess of lithium powder, and a catalytic amount of 4,4′-di-tert-butylbiphenyl (DTBB, 5 mol%) in THF at room temperature, led to the formation of the corresponding alcohols and amines, respectively. The process was also applied to the transformation of α,β-unsaturated carbonyl compounds into the corresponding saturated alcohols. The new reducing system exhibited good to excellent diastereoselectivity toward the reduction of different monocyclic and polycyclic ketones.     

Interaction of [Mo6Cl14]2− with H2Se: Selective Preparation of [Mo6SeCl13]3−

Reaction of [Mo₆(μ₃-Cl)₈Cl₆]²⁻ with H₂Se, generated in situ from ZnSe and 4 M HCl under hydrothermal conditions lead to the substitution of one or two bridging chlorides, depending on the reagents ratio. With the Mo₆/ZnSe 1:3 molar ratio [Mo₆(μ₃-SeCl₇)Cl₆]³⁻ forms selectively in high yield. Further substitution is more hindered, and even at 1:20 cluster-to-selenide molar ratio a mixture of [Mo₆(μ₃-SeCl₇)Cl₆]³⁻ and [Mo₆(μ₃-Se₂Cl₆)Cl₆]⁴⁻ is formed. The products were characterized by X-ray, Raman spectra and electrospray ionization mass spectrometry.