Multipliers of L which vanish at infinity

The main results of this paper are as follows.

1.

(i) If p ≠ 2, there exists a continuous multiplier (function) of L^p(Rⁿ) which vanishes at infinity, but which is not in the closure, in the multiplier norm, of the space of Fourier transforms of integrable functions.     

Which pi-clamped conjugated monocycles exhibit ring currents?

Quenching/survival of ring currents in pi-clamped conjugated monocycles is controlled by the match or mismatch in parity between the frontier orbitals of the central pi-conjugated 4n+2/4n monocycle and those of the clamps. Changes in ring current are not primarily caused by bond alternation or 'Mills-Nixon' effects; current and geometry changes on clamping are both consequences of electronic structure.     

Engineering of layer-by-layer coated capsules with the prospect of materials for efficient and directed electron transfer

Intermolecular electron transfer is investigated in a dye-doped polyelectrolyte (PE) multilayer film. Hollow PE capsules, with a mean diameter of 2 microm, were prepared by stepwise adsorption of a pyrene (PY)-labeled polyanion and various polycations onto charged colloids and subsequent dissolution of the colloidal core. The high concentration of dye molecules within the capsule wall and the control of the medium polarity on a nanometer length scale are proposed to facilitate light-induced charge separation over distances of a few nanometers. In particular, a PY-labeled poly(styrene sulfonate) (PSS-PY) has been synthesized and used as polyanion for the polyelectrolyte capsule preparation. A polarity gradient across the wall of the PE shells is assumed to be achieved by adsorbing diverse polycations at different film positions. The high effective film area followed by high optical density of the PE capsule solution enables time-resolved optical spectroscopy. Using pulsed excited state absorption (ESA) the transient absorption peaks of the radical anion and cation state of pyrene were measured, respectively. In the presence of additional electron donor (or acceptor) molecules in the capsule solution the pyrene anion (cation) is observed in the ESA spectra, while both transient states are seen if no additional molecules are present. These results are interpreted as an electron transfer from pyrene to the donor (acceptor) molecule or between two pyrene molecules. An asymmetry of the electron donor and electron acceptor efficiency was observed when multilayer shells were used that are supposed to carry an internal polarity gradient.     

Coarsening process in one-dimensional surface growth models

Surface growth models may give rise to instabilities with mound formation whose typical linear size L increases with time (coarsening process). In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (corresponding to model B of dynamics): coarsening is known to be logarithmic in the absence of noise ( L(t) ∼ ln t) and to follow a power law ( L(t) ∼t ^1/3) when noise is present. If the surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stages of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster : if α is the exponent describing the steepening of the maximal slope M of mounds ( M ^α∼L) we find that L(t) ∼t ⁿ: n is equal to for 1≤α≤2 and it decreases from to for α≥2, according to n = α/(5α - 2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t) ∼t ^1/4, irrespectively of α. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model α = 1, both in the absence and in the presence of noise. Received 28 September 2001 and Received in final form 21 November 2001     

New synthesis of pyrrolidine homoazasugars via aminohomologation of furanoses and their use for the stereoselective synthesis of aza-C-disaccharides

The introduction of a formyl group at the anomeric center of 2,3,5-tri-O-benzyl furanoses and substitution of the ring oxygen with a basic nitrogen atom (aminohomologation) was carried out via stereoselective addition of 2-lithiothiazole to N-benzyl, N-furanosylhydroxylamines (masked N-benzyl sugar nitrones), followed by reductive dehydroxylation of the resulting open-chain adducts, and then ring closure via intramolecular displacement of the free hydroxy group by the amino group and unmasking of the formyl group from the thiazole ring. The resulting formyl aza-C-glycosides were transformed into 2,5-dideoxy-2,5-imino-hexitols (pyrrolidine homoazasugars) by reduction of the formyl to the hydroxymethyl group and removal of the O- and N-benzyl groups by hydrogenolysis. This reaction sequence was applied to four furanoses (D-arabino, D-ribo, D-lyxo, L-xylo) to give the hydroxy- and amino-free homoazasugars, including the natural product 2,5-dideoxy-2,5-imino-D-mannitol, in 17% overall yields (six steps). The formyl aza-C-glycosides proved to be valuable intermediates for the synthesis of more complex derivatives. In fact, these sugar aldehydes were employed in Wittig-type coupling reactions with galactose and ribose phosphoranes to give bis-glycosylated alkenes, which upon reduction of the double bond were transformed into methylene isosteres of (1-->6)- and (1-->5)-linked disaccharides in which one of the two sugar moieties was an azasugar (aza-(1-->x)-C-disaccharides).     

A CASPT2 and CASSCF approach to the cycloaddition of ketene and imine: a new mechanistic scheme of the Staudinger reaction

We report a new theoretical study of the mechanism of the parent Staudinger reaction between ketene and formaldimine. This mechanism, in contrast with previously reported computational studies, involves the formation of two different intermediates, gauche and trans, which can be interconnected on the potential energy surface depending upon reaction conditions. This novel CASPT2/CASSCF mechanistic scheme may be considered a new starting point to rationalize stereochemical outcome and solvent effects in these reactions.