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.     

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.     

Controlling the variation of axial water exchange rates in macrocyclic lanthanide(III) complexes

The rate of axial water exchange in well-defined series of lanthanide complexes depends on the extent of second sphere hydration which is determined by complex hydrophobicity and the nature of the lanthanide ion and its counter-ion.     

Temperature and composition dependence of the refractive indices of the 2-chloroethanol + 2-methoxyethanol binary mixtures

Measurements of the refractive index n for the binary mixtures 2-chloroethanol + 2-methoxyethanol in the 0 < or = t/degree C < or = 70 temperature range have been carried out with the purpose of checking the capability of empirical models to express physical quantity as a function of temperature and volume fraction, both separately and together, i.e., in a two independent variables expression. Furthermore, the experimental data have been used to calculate excess properties such as the excess refractive index, the excess molar refraction, and the excess Kirkwood parameter delta g over the whole composition range. The quantities obtained have been discussed and interpreted in terms of the type and nature of the specific intermolecular interactions between the components.     

Experimental and theoretical studies on three spiromuscar-3-one M1 agonist derivatives

Muscarone analogues are compounds that have been proposed for the prevention or treatment of senile dementias. ARL-16607 (I), ARL-15467 (II), ARL-14995 (III) and YM-796 (IV) are spiromuscar-3-one derivatives and behave as muscarinic M₁ agonists, with different binding selectivity and efficacy at the M₁ receptors. In this work, we have elucidated the solid-state structures of I-III and compared the results obtained with the data available in the literature for IV.The solid-state arrangements of I-IV have then been used to input a series of theoretical calculations. For each molecule, eight conformations have been modeled and the obtained structures (1-32) have been submitted to a series of molecular dynamics/simulated annealing and molecular mechanics calculations aimed to explore the conformational freedom of the spiromuscar-3-one moiety. Some hints about the reactivity of I-IV have been obtained by performing Hartree-Fock, density functional theory and semiempirical quantum mechanics calculations. These studies analyzed the properties of the frontier orbitals and of the molecular electrostatic potential of I-IV.The information gained has been used to explain the better efficacy and poorer selectivity shown by III. Our results suggest that the behavior of III is due to its smaller size, the features of its molecular surface, the shape of its electrostatic potential and the orientation of its reactive domains.