Elliptic systems with nonlinearity q greater or equal than two with controlled growth. Global Hölder continuity of solutions to the Dirichlet problem

Hölder regularity up to the boundary of the solutions to the Dirichlet problem for second order elliptic systems with nonlinearity q>2 and with controlled growth is proved when n?q+2.     

Positive solutions for a quasilinear degenerate elliptic equation inR n

In questa nota proviamo un teorema di esistenza di soluzioni positive su tuttoR ⁿ della equazionediv(|Du| ^p?2Du)+f(u)=0.     

A Formal Total Synthesis of (+)-Methyl Trachyloban-18-oate and (+)-Methyl 16-Oxo-17-norkauran-18-oate: Regio- and Diastereoselective Preparation of Methyl (13S)-13-Hydroxyisoatisiren-18-oate from (−)-Abietic Acid

A novel preparation of methyl (13S)-13-hydroxyisoatisiren-18-oate ( 4 ), a key-intermediate in a synthesis of (+)-methyl trachyloban-18-oate ((+)- 1 ), from (?)-abietic acid, is described. Since (?)- 1 has been previously converted into (?)-methyl 16-oxo-17-norkauran-18-oate ((?)- 16 ), our preparation of 4 constitutes also a formal total synthesis, from (?)-abietic acid, of (+)- 16 . Key steps in this approach were the allene photoaddition to podocarp-8(14)-en-13-one ( 5 ) and the conversion of the endo-toluene-4-sulfonate 11 into the exo-benzoate 12b .     

Comparison of solid-phase microextraction and purge-and-trap methods for the analysis of the volatile fraction of butter

The volatile fraction of butter stored at three different temperatures was investigated to monitor quality during commercial shelf-life (90 days). Two different extraction techniques were compared: dynamic headspace (purge-and-trap), and static headspace (solid-phase microextraction, SPME). As expected, the dynamic extraction provided a generally higher amount of volatile compounds than that obtained by SPME, but, with reference to individual compounds, SPME seemed to provide better extraction for volatiles having a higher molecular mass. Despite the different performances, both methods were able to detect volatiles useful for evaluating changes during storage.     

Recognition of guests bearing donor and acceptor hydrogen bonding groups by heteroditopic calix[4]arene receptors

The synthesis of new hosts specifically designed for the recognition of neutral guests bearing donor-acceptor hydrogen bonding groups is described. These hosts are characterized by the presence of two distinct binding region in close proximity: the rigid π-donor cavity and the H-bond donor N-methylene-N′-phenylureido group inserted onto the upper rim of the calix[4]arene skeleton. The binding abilities of these receptors were investigated toward a series of neutral ditopic organic molecules in CDCl₃ solution by ¹H NMR spectroscopy. The results obtained show that rigidity of the calix[4]arene apolar cavity is the control element in determining efficiency. In fact, compared with the more rigid 2, host 10, where the rigidity of the cone structure is maintained by hydrogen bonding of the OH of the lower rim, a decrease of efficiency of almost one order of magnitude was observed. The cooperative effect of the two binding region of host 2 was verified with different classes of ditopic guests. Good efficiency in the recognition of urea derivatives and dimethylsulfoxide was achieved.     

Solid-state supramolecular organization, established directly from powder diffraction data, and photoluminescence efficiency of rigid-core oligothiophene-S,S-dioxides

The "rigid-core" material 3,5-dimethyl-2,3'-bis(3-methylthiophene)-dithieno[3,2-b:',3'-d]thiophene-4,4-dioxide (DTTOMe4) has the highest photoluminescence ever reported for thiophene-based molecules in the solid state. We report the structure of this material, determined directly from powder X-ray diffraction data using the Genetic Algorithm method for structure solution, followed by Rietveld refinement, and the structural properties are discussed in relation to the structures of the corresponding subsystems DTTO and DTTOMe. While the crystal structures of the latter compounds contain cofacial dimers, the crystal structure of DTTOMe4 comprises layers of molecules aligned in an antiparallel fashion. Intermediate neglect of differential overlap with single configuration interaction (INDO/SCI) calculations on the intermolecular interactions in the three crystal structures show that the different solid-state photoluminescence efficiencies of DTTOMe4, DTTOMe, and DTTO cannot be correlated with the different types of dipole-dipole alignment in the solid state. Instead, photoluminescence efficiencies correlate well with the rate of formation of nonradiatively decaying charge-transfer pairs upon photoexcitation. Because of larger intermolecular distances in DTTOMe4, the photoluminescence is less effectively quenched by charge-transfer processes than in DTTOMe and DTTO.     

On the stereochemistry of photoaddition between α,β-unsaturated ketones and olefins—II

Some years ago an empirical rule, which allows the prediction of product stereochemistry in cis-photocycloaddition reactions of α,β-unsaturated ketones and olefins was tentatively proposed. Several additional examples, both selected from the literature and synthesized in our laboratory, seem to strengthen the validity of the rule.     

Trinuclear heterobimetallic complexes with binucleating dithioxamides: stereoselective synthesis and solution behavior involving Pd-N bond rupture

Bischelate platinum(II) complexes of the type [Pt(H-R(2)-N(2)C(2)S(2))(2)] (H-R(2)-N(2)C(2)S(2)(-) = dialkyl-dithioxamidate) are ditopic receptors which, after coordination of the first Pd(eta(3)-allyl)(+) moiety, induce the orientation of the second palladium-allyl fragment. Thus, a series of trimetallic complexes of formula bis-[(eta(3)-allyl)-palladium(II)](mu-bis-dialkyl-dithioxamidate-platinum(II) kappa-S,S-kappa-S',S'-Pt-kappa-N,N-Pd-kappa-N',N'-Pd') has been prepared in which the allyl fragments are oriented toward the same side of the molecular plane. We have also prepared the trimetallic complex using a dithioxamide obtained from the racemic phenylethylamine. Only two isomers were produced in equimolar ratio: the racemate that has four homochiral alkyl substituents and the mesoform containing the meso-dithioxamide that has homochiral substituents on the same side of molecular plane. Under the effect of the temperature, the trimetallic Pd-Pt-Pd complexes undergo rapid allyl isomerization; the mechanism of the isomerization, which is similar to that found by us in an analogue Pt-Pd bimetallic complex, is discussed. The crystal and molecular structure of bis-[(eta(3)-allyl)-palladium(II)](mu-bis-[S]-phenylethyl-dithioxamidate-platinum(II) kappa-S,S-kappa-S',S'-Pt-kappa-N,N-Pd-kappa-N',N'-Pd') has been reported.     

Regiocontrolled synthesis of enantiopure 3,3'-thiosubstituted biphenyls

Sulfenylation of 6,6'-dimethoxy-2,2'-dihydroxybiphenyl, used as a racemic mixture and single enantiomers, by phthalimidesulfenyl chloride afforded the corresponding 3,3'-N,N'-dithiophthalimide with complete regioselectivity. Simple manipulations of the latter compound allowed access to the corresponding bis-thiol or o-thioquinone as useful intermediates for the synthesis of new sulfur-containing open-chain and macrocyclic C(2) enantiopure ligands. The application of this methodology to the preparation of a biphenyl bearing two cysteine units as potential HIV-1 protease inhibitor is also described.