Are generalized Lorentz ``spaces' really spaces?

We show that the Lorentz space need not be a linear set for certain ``non-classical" weights . We establish necessary and sufficient conditions on and for this situation to occur.

     

Differential reactivity of alpha- and beta-anomers of glycosyl acceptors in glycosylations. A remote consequence of the endo-anomeric effect?

When phenyl tri-O-benzyl-1-thio-beta-D-galactopyranosiduronic acid esters were coupled with a 1/1 mixture of alpha and beta 2,3 di-O-protected D-galactopyranosiduronic acid esters, the beta-anomer proved to be more reactive. Data from theoretical calculations suggested that the enhanced reactivity of this anomer compared with the alpha one would be due to a stronger hydrogen bond of the C-4 OH with the ring oxygen.     

Complex interpolation spaces on multiply-connected domains

Variants of Calderón's interpolation spaces [A₀, A₁]_θ which are defined using a multiply-connected domain instead of the strip 0 < Re z < 1 are considered. It is shown that they coincide to within equivalence of norms with Calderón's spaces. This result applies also to spaces obtained by generalised forms of Calderón's construction due to Coifman, Cwikel, Rochberg, Sagher, and Weiss (Advan. in Math.43 (1982), 203–229).     

Complex Interpolation of Nonlinear Operators and Lebedev-Milin Inequalities for Taylor Coefficients of Composed Analytic Functions

A generalization of a theorem of Bergh concerning complex interpolation of nonlinear operators is applied to prove Lebedev-Milin type estimates for Taylor coefficients of composed analytic functions.     

Comparative effects of conjugated and deconjugated isomeric enones on the transannular Diels-Alder reaction

Two isomeric cyclic trienones 2 and 3 (with four methyl esters at positions 3 and 10) underwent transannular Diels-Alder (TADA) reaction at very different temperatures. This drastic difference could be traced to the capacity of the enone dienophile to be conjugated or unconjugated at the transition state. Molecular modeling could confirm this explanation. The calculated enone proved to be very distorted in transition state ts2, and the TADA reaction temperature was accordingly much higher than the one corresponding to ts3 in which the enone was flat. [reaction: see text]     

Theoretical and experimental determination of the effects governing the transannular Diels-Alder reaction of trans-trans-cis systems with or without activation of the dienophile

A thorough study of the transannular Diels-Alder (TADA) reaction of trans-trans-cis macrocyclic trienes was carried out. It led to a better understanding of various parameters that govern the TADA reaction in particular and the Diels-Alder reaction in general. Thus, carbonyl activation of the dienophile and substitution of the diene are discussed, as well as the presence of substituents on the macrocycle and their respective effects at the transition-state level.