Controlling the α/γ-Reactivity of Vinylogous Ketone Enolates in Organocatalytic Enantioselective Michael Reactions

The first regio-, diastereo-, and enantioselective direct Michael reaction of β,γ-unsaturated ketones with nitroolefins is enabled by Brønsted base/hydrogen-bonding bifunctional catalysis. A squaramide-substituted tertiary amine catalyzes the reaction of a broad range of β,γ-unsaturated ketones to proceed at the α-site exclusively, giving rise to adducts with two consecutive tertiary carbon stereocenters in diastereomeric ratios of up to >20:1 and enantioselectivities generally in the 90–98 % ee range.     

Synergism in mixtures of cationic surfactant and anionic copolymers

Surface tension measurements have been made in aqueous solutions of anionic hemiesters of an alternating copolymer of maleic acid and styrene, MAS-n with n=0-12, in the presence of dodecyltrimethylammonium bromide, DTAB. A synergistic aspect of surface tension reduction efficiency was observed for all systems studied. The pseudo-phase separation approach and regular solution approximation have been applied, and the interaction parameter, beta, and the mole fraction of DTAB in the adsorbed layer (on a surfactant/repetitive unit basis), X, were obtained. Negative values of beta, ranging from -3 to -11, were calculated. On the other hand, the molar fraction of DTAB varies from 0.52 to 0.26. These results are discussed in terms of hydrophobic effects on the distribution of the aggregates between the interface and the bulk of the solution. The conditions predicted by the model to obtain synergism in the tension reduction efficiency are completely satisfied in all cases.     

Path-integral formulation of chiral invariant fermion models in two dimensions

We study the Thirring and chiral-invariant Gross-Neveu (CGN) models using the functional integral method. By introducing an auxiliary vector field we disclose a relation with two-dimensional gauge theories coupled to fermions and then extend a technique based on a chiral change in the functional variables to study purely fermionic models.We obtain the exact Klaiber solution for the massless Thirring model (for spin $\text{1}\text{2}$) in a very simple way and we then extend our technique to investigate the CGN model. We show the factorization of a free fermionic part at the level of Green functions on very general grounds. We then impose certain restrictions on the behavior of the fields — which render our treatment exact only in the zero winding number sector, but allow the computation of the U(1) part of the CGN Green functions exactly, showing, in particular, its complete decoupling from the color part and the almost long-range order behaviour in the infrared region.In our approach, the non-triviality of the jacobian arising from the chiral transformation — directly related to the topological density and the axial anomaly — appears to be crucial for the functional integral treatment of these models.     

Path-integral formulation of two-dimensional gauge theories with massless fermions

We study (1 + 1) dimensional gauge theories [with SU(N) and diagonal SU(N) color symmetry] using the functional integral method. We construct an effective lagrangian by performing a change in the fermionic variables, and then investigate relevant phenomena such as the intrinsic Higgs mechanism and color screening.     

An algorithm to compute orders and ramification indices of cyclic actions on compact surfaces,II

In this paper we obtain an effective algorithm to compute all even orders and ramification indices of homeomorphisms of finite order acting on compact surfaces, orientable or not. This completes the case of odd orders, previously studied by the authors. E. Bujalance and A. F. Costa were partially supported by DGICYT PB 92-0716 and CEE-CHRX-CT93-0408. J. M. Gamboa was partially supported by DGICYT PB 92-0498-C02-02 and CEE-CHRX-CT93-0408. J. Lafuente was partially supported by DGICYT PB 92-0220.     

Combined use of tandem mass spectrometry and computational chemistry to study 2H‐chromenes from Piper aduncum

Natural 2H‐chromenes were isolated from the crude extract of Piper aduncum (Piperaceae) and analyzed by electrospray ionization tandem mass spectrometry (ESI‐MS/MS) applying collision‐induced dissociation. Density functional theory (DFT) calculations were used to explain the preferred protonation sites of the 2H‐chromenes based on thermochemical parameters, including atomic charges, proton affinity, and gas‐phase basicity. After identifying the nucleophilic sites, the pathways were proposed to justify the formation of the diagnostic ions under ESI‐MS/MS conditions. The calculated relative energy for each pathway was in good agreement with the energy‐resolved plot obtained from ESI‐MS/MS data. Moreover, the 2H‐chromene underwent proton attachment on the prenyl moiety via a six‐membered transition state. This behavior resulted in the formation of a diagnostic ion due to 2‐methylpropene loss. These studies provide novel insights into gas‐phase dissociation for natural benzopyran compounds, indicating how reactivity is correlated to the intrinsic acid‐base equilibrium and structural aspects, including the substitution pattern on the aromatic moiety. Therefore, these results can be applied in the identification of benzopyran derivatives in a variety of biological samples.     

Automorphism groups of the real projective plane with holes and their conjugacy classes within its mapping class group

For each integer g2 we give the complete list of groups acting as a group of dianalytic automorphisms of a real projective plane with g holes, which, in algebraic terms, correspond to birational automorphisms of real algebraic (M–1)-curves. We also determine those acting as the full group of automorphisms of such a surface. Furthermore, the conjugacy classes of the finite subgroups of its mapping class group are calculated.Mathematics 2000 Subject Classification (2000): 30F, 32G, 14H.Partially supported by BFM2002-04801.Partially supported by BFM2002-04801 and RAAG HPRN-CT-2001-00271.Partially supported by GAAR BFM2002-04797 and RAAG HPRN-CT-2001-00271