Determination of the absolute configuration of the enantiomers of dihydroquinolines, isolated by chiral chromatography, by non empirical analysis of circular dichroism spectra and X-ray analysis

The enantiomers of racemic 3,4-dihydroquinolines with an acetal or thioacetal spiro ring and a quaternary stereogenic carbon have been isolated through semipreparative chiral chromatography using a polysaccharide-derived chiral stationary phase (Chiralpak AD) and n-hexane/ethanol as a mobile phase. The absolute configurations of the enantiomers of four compounds have been determined by a comparison of density functional theory (DFT) calculations of their electronic circular dichroism (ECD) spectra with the experimental ECD data. A detailed conformer population search to achieve a conformational average of these compounds was crucial, due to the flexibility of these molecules. The conformer distribution was evaluated by spartan 02 and the structure of each of the conformers found within 4 kcal/mol energy range was optimized with DFT. The final calculated ECD spectrum obtained after Boltzmann averaging was compared with the ECD spectrum of the less well retained enantiomer and the correlation (R)/(−) was established for all compounds. The monocrystals of both enantiomers of one compound were obtained from the HPLC eluates. Their absolute configurations were determined by X-ray crystallographic analysis and confirmed by ECD analysis. In all cases, the second-eluted enantiomer in chiral HPLC exhibits an (R)-configuration.     

Unprecedented intramolecular [3 + 2] cycloadditions of azido-ketenimines and azido-carbodiimides. Synthesis of indolo[1,2-a]quinazolines and tetrazolo[5,1-b]quinazolines

N-(2-azidomethyl)phenyl ketenimines and N-(2-azidomethyl)phenyl-N'-alkyl(aryl) carbodiimides undergo, under mild thermal conditions, intramolecular [3 + 2] cycloaddition reactions between the azido group and either the C=C or the distal C=N double bonds of the ketenimine and carbodiimide functions respectively. The reaction products are indolo[1,2-a]quinazolines and/or indolo[2,1-b]quinazolines in the case of azido-ketenimines, and tetrazolo[5,1-b]quinazolines in the case of azido-carbodiimides. The formation of the two classes of indoloquinazolines implies the ulterior dinitrogen extrusion from the non-isolated, putative [3 + 2] cycloadducts between the azide and ketenimine functions, whereas in the case of azido-carbodiimides the initial cycloadducts, tetrazoloquinazolines, were cleanly isolated and further converted into 2-aminoquinazolines by thermally induced dinitrogen extrusion.     

Lattice-embedding scales ofL p spaces into orlicz spaces

We study the setP _X of scalarsp such thatL ^p is lattice-isomorphically embedded into a given rearrangement invariant (r.i.) function spaceX[0, 1]. Given 0<α≤β<∞, we construct a family of Orlicz function spacesX=L ^F [0, 1], with Boyd indicesα andβ, whose associated setsP _X are the closed intervals [γ, β], for everyγ withα≤γ≤β. In particular forα>2, this proves the existence of separable 2-convex r.i. function spaces on [0,1] containing isomorphically scales ofL ^p -spaces for different values ofp. We also show that, in general, the associated setP _X is not closed. Similar questions in the setting of Banach spaces with uncountable symmetric basis are also considered. Thus, we construct a family of Orlicz spaces ℓ ^F (I), with symmetric basis and indices fixed in advance, containing ℓ ^p (Γ-subspaces for differentp’s and uncountable Λ⊂I. In contrast with the behavior in the countable case (Lindenstrauss and Tzafriri [L-T₁]), we show that the set of scalarsp for which ℓ ^p (Γ) is isomorphic to a subspace of a given Orlicz space ℓ ^F (I) is not in general closed. Supported in part by DGICYT grant PB 94-0243.     

Onl p-complemented copies in Orlicz spaces II

For anyp > 1, the existence is shown of Orlicz spacesL ^F andl ^F with indicesp containingsingular l ^p-complemented copies, extending a result of N. Kalton ([6]). Also the following is proved:Let 1 <α ≦β < ∞and H be an arbitrary closed subset of the interval [α, β].There exist Orlicz sequence spaces l ^F (resp. Orlicz function spaces L^F)with indices α and β containing only singular l ^p-complemented copies and such that the set of values p > 1for which l ^p is complementably embedded into l^F (resp. L ^F)is exactly the set H (resp. H ∪ {2&#x007D;). An explicitly defined class of minimal Orlicz spaces is given. Supported in part by CAICYT grant 0338-84.     

Onl p-complemented copies in Orlicz spaces

Let 1<α≦β<∞ andF be an arbitrary closed subset of the interval [α,β]. An Orlicz sequence spacel ^φ (resp. an Orlicz function spaceL ^φ(μ)) with associated indices α and β is found in such a way that the set of valuesp for which thel ^p-space is isomorphic to a complemented subspace ofl ^φ (resp.L ^φ(μ)) is precisely the given setF (resp.F ∪ {2}). Also, a recent result of Hernández and Peirats [1] is extended showing that, even for the case in which the indices satisfy α_φ ^∞<2<β_φ ^∞, there exist minimal Orlicz function spacesL ^φ(μ) with no complemented copy ofl ^p for anyp ≠ 2. Supported in part by CAICYT grant 0338-84.     

Strictly localizable measures

It is proved that, under the Continuum Hypotesis (CH), every complete, locally determined, Radon measures of type (H), on a topological space with countable basis, is strictly localizable. This result is useful in the theory of invariant measures on a topological group and, in particular, in the theory of Hausdorff measures.     

Disuguaglianze tra limiti e coefficienti dello sviluppo asintotico di una funzione in un angolo

Sunto Si danno disuguaglianze per i coefficienti e limiti dello sviluppo asintotico di una funzione iu un angolo e disuguaglianze per i limiti delle derivate di una funzione analitica in un angolo. A Giovanni Sansone nel suo 70^mo compleanno