Catalytic enantioselective oxaziridination

The first catalytic enantioselective synthesis of oxaziridines is presented. The oxidation of aryl and alkyl aldimines with m-CPBA under organocatalytic conditions using cinchona alkaloid-derived catalysts furnished optically active oxaziridines in good yields and high enantioselectivities (up to 94% ee). Mechanistic investigations indicate a stepwise enantioselective oxidation process.     

On the Binding of Congo Red to Amyloid Fibrils

Amyloids are characterized by their capacity to bind Congo red (CR), one of the most used amyloid‐specific dyes. The structural features of CR binding were unknown for years, mainly because of the lack of amyloid structures solved at high resolution. In the last few years, solid‐state NMR spectroscopy enabled the determination of the structural features of amyloids, such as the HET‐s prion forming domain (HET‐s PFD), which also has recently been used to determine the amyloid–CR interface at atomic resolution. Herein, we combine spectroscopic data with molecular docking, molecular dynamics, and excitonic quantum/molecular mechanics calculations to examine and rationalize CR binding to amyloids. In contrast to a previous assumption on the binding mode, our results suggest that CR binding to the HET‐s PFD involves a cooperative process entailing the formation of a complex with 1:1 stoichiometry. This provides a molecular basis to explain the bathochromic shift in the maximal absorbance wavelength when CR is bound to amyloids.     

Phosphinothiolates as Ligands for Polyhydrido Copper Nanoclusters

The reaction of [CuI(HSC₆H₄PPh₂)]₂ with NaBH₄ in CH₂Cl₂/EtOH led to air‐ and moisture‐stable copper hydride nanoparticles (CuNPs) containing phosphinothiolates as new ligands, one of which was isolated by crystallization. The X‐ray crystal structure of [Cu₁₈H₇L₁₀I] (L=^?S(C₆H₄)PPh₂) shows unprecedented features in its 28‐atom framework (18 Cu and 10 S atoms). Seven hydrogen atoms, in hydride form, are needed for charge balance and were located by density functional theory methods. H₂ was released from the copper hydride nanoparticles by thermolysis and visible light irradiation.     

Perfect and bipartite IMTL-algebras and disconnected rotations of prelinear semihoops

IMTL logic was introduced in [12] as a generalization of the infinitely-valued logic of Lukasiewicz, and in [11] it was proved to be the logic of left-continuous t-norms with an involutive negation and their residua. The structure of such t-norms is still not known. Nevertheless, Jenei introduced in [20] a new way to obtain rotation-invariant semigroups and, in particular, IMTL-algebras and left-continuous t-norm with an involutive negation, by means of the disconnected rotation method. In order to give an algebraic interpretation to this construction, we generalize the concepts of perfect, bipartite and local algebra used in the classification of MV-algebras to the wider variety of IMTL-algebras and we prove that perfect algebras are exactly those algebras obtained from a prelinear semihoop by Jenei's disconnected rotation. We also prove that the variety generated by all perfect IMTL-algebras is the variety of the IMTL-algebras that are bipartite by every maximal filter and we give equational axiomatizations for it.     

Classifying spaces of Kač-Moody groups

We study the structure of classifying spaces of Kač-Moody groups from a homotopy theoretic point of view. They behave in many respects as in the compact Lie group case. The mod p cohomology algebra is noetherian and Lannes'T functor computes the mod p cohomology of classifying spaces of centralizers of elementary abelian p-subgroups. Also, spaces of maps from classifying spaces of finite p-groups to classifying spaces of Kač-Moody groups are described in terms of classifying spaces of centralizers while the classifying space of a Kač-Moody group itself can be described as a homotopy colimit of classifying spaces of centralizers of elementary abelian p-subgroups, up to p-completion. We show that these properties are common to a larger class of groups, also including parabolic subgroups of Kač-Moody groups, and centralizers of finite p-subgroups. Received: 15 June 2000 / in final form: 20 September 2001 / Published online: 29 April 2002     

On the Cores of cooperative games and the stability of the Weber set

In this paper conditions are given guaranteeing that the Core equals the D-core (the set of unDominated imputations). Under these conditions, we prove the non-emptiness of the intersection of the Weber set with the imputation set. This intersection has a special stability property: it is externally stable. As a consequence we can give a new characterization (th. 3.2) for the convexity of a cooperative game in terms of its stability (von Neumann-Morgenstern solutions) using the Weber set.     

Remarks on Nonlinear Schrödinger Equations with Harmonic Potential

Bose-Einstein condensation is usually modeled by nonlinear Schrödinger equations with harmonic potential. We study the Cauchy problem for these equations. We show that the local problem can be treated as in the case with no potential. For the global problem, we establish an evolution law, which is the analogue of the pseudo-conformal conservation law for the nonlinear Schrödinger equation. With this evolution law, we give wave collapse criteria, as well as an upper bound for the blow up time. Taking the physical scales into account, we finally give a lower bound for the breaking time. This study relies on two explicit operators, suited to nonlinear Schrödinger equations with harmonic potential, already known in the linear setting.     

On the Brownian-directed polymer in a Gaussian random environment

In this paper, we introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are able to separate a weak and strong disorder regime under some reasonable assumptions on the spatial covariance of the environment. Some further developments, concerning some concentration inequalities for the partition function, are given for the weak disorder regime.