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.     

Reducibility of rational functions in several variables

We prove an analogous of Stein theorem for rational functions in several variables: we bound the number of reducible fibers by a formula depending on the degree of the fraction.     

Generalisations of disjunctive sequences

The present paper proposes a generalisation of the notion of disjunctive (or rich) sequence, that is, of an infinite sequence of letters having each finite sequence as a subword. Our aim is to give a reasonable notion of disjunctiveness relative to a given set of sequences F. We show that a definition like “every subword which occurs at infinitely many different positions in sequences in F has to occur infinitely often in the sequence” fulfils properties similar to the original unrelativised notion of disjunctiveness. Finally, we investigate our concept of generalised disjunctiveness in spaces of Cantor expansions of reals. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solution-phase synthesis of ICG-001, a β-turn peptidomimetic molecule inhibitor of β-catenin–Tcf-mediated transcription

The solution-phase synthesis of the β-turn peptidomimetic ICG-001, a selective inhibitor of Wnt/β-catenin signalling, which has been found to be important for both initiation and progression of cancers of different tissues and has been exploited as an extremely useful chemogenomic tool, was developed. This route is particularly suitable for the multigram scale preparation of ICG-001.