Poisson Geometrical Symmetries Associated to Non-Commutative Formal Diffeomorphisms

Let be the group of all formal power series starting with x with coefficients in a field of zero characteristic (with the composition product), and let F [ ] be its function algebra. In [BF] a non-commutative, non-cocommutative graded Hopf algebra was introduced via a direct process of disabelianisation of F [ ], taking the like presentation of the latter as an algebra but dropping the commutativity constraint. In this paper we apply a general method to provide four one-parameter deformations of , which are quantum groups whose semiclassical limits are Poisson geometrical symmetries such as Poisson groups or Lie bialgebras, namely two quantum function algebras and two quantum universal enveloping algebras. In particular the two Poisson groups are extensions of , isomorphic as proalgebraic Poisson varieties but not as proalgebraic groups.Acknowledgements. The author thanks Alessandra Frabetti and Loic Foissy for many helpful discussions.     

de Sitter vacua via consistent terms

We introduce a new mechanism for producing locally stable de Sitter or Minkowski vacua, with spontaneously broken N = 1 supersymmetry and no massless scalars, applicable to superstring and M-theory compactifications with fluxes. We illustrate the mechanism with a simple N = 1 supergravity model that provides parametric control on the sign and the size of the vacuum energy. The crucial ingredient is a gauged U(1) that involves both an axionic shift and an R symmetry, and severely constrains the F- and D-term contributions to the potential.     

Stability of rocksalt (111) polar surfaces: beyond the octopole

Stable polar oxide surfaces must be simultaneously electrostatically compensated and in thermodynamic equilibrium with the environment. As a paradigm, the MgO(111)-p(2x2) reconstructed surface is shown to involve combinations of Mg-covered terminations with peculiar insulating electronic structure, favored in O-poor conditions, and the O-terminated octopole, stabler in more O-rich environments. Such a picture, which could not have been foreseen by either experiments or simulations separately, goes beyond the Wolf model and reconciles the theory with the experimental data taken in variable thermodynamic conditions.     

Assembly of sugars on polystyrene plates: a new facile microarray fabrication technique

The work presented herein is a new noncovalent glycoarray assembly method for microplates created by simply mixing together an isocyanate-containing C₁₄-hydrocarbon and an amine-containing carbohydrate. 2-Aminoethyl-β-d-galactopyranoside (1) was utilized in model studies and product formation was detected by both ESI-MS and lectin binding. The method has been further extended to array complex carbohydrates.     

Regioselective cis-trans isomerization of arachidonic double bonds by thiyl radicals: the influence of phospholipid supramolecular organization

Trans unsaturated fatty acids in humans may be originated by two different contributions. The exogenous track is due to dietary supplementation of trans fats and the endogenous path deals with free-radical-catalyzed cis-trans isomerization of fatty acids. Arachidonic acid residue (5c,8c,11c,14c-20:4), which has only two out of the four double bonds deriving from the diet, was used to differentiate the two paths and to assess the importance of a radical reaction. A detailed study on the formation of trans phospholipids catalyzed by the HOCH2CH2S* radical was carried out on L-alpha-phosphatidylcholine from egg lecithin and 1-stearoyl-2-arachidonoyl-L-alpha-phosphatidylcholine (SAPC) in homogeneous solution or in large unilamellar vesicles (LUVET). Thiyl radicals were generated from the corresponding thiol by either gamma-irradiation or UV photolysis, and the reaction course was followed by GC, Ag/TLC, and 13C NMR analyses. The isomerization was found to be independent of cis double bond location (random process) in i-PrOH solution. In the case of vesicles, the supramolecular organization of lipids produced a dramatic change of the isomerization outcome: (i) in egg lecithin, the reactivity of arachidonate moieties is higher than that of oleate and linoleate residues, (ii) in the linoleate residues of egg lecithin, the 9t,12c-18:2 isomer prevailed on the 9c,12t-18:2 isomer (3:1 ratio), and (iii) a regioselective isomerization of SAPC arachidonate residues occurred in the 5 and 8 positions. This effect of "positional preference" indicates that thiyl radicals entering the hydrophobic region of the membrane bilayer start to isomerize polyunsaturated fatty acid residues having the double bonds nearest to the membrane surfaces. We propose that arachidonic acid and its trans isomers can function as biomarkers in membranes for distinguishing the two trans fatty acid-forming pathways.     

Kac limit for finite-range spin glasses

We consider a finite-range spin glass model in arbitrary dimension, where the strength of the two-body coupling decays to zero over some distance gamma(-1). We show that, under mild assumptions on the interaction potential, the infinite-volume free energy of the system converges to that of the Sherrington-Kirkpatrick one, in the Kac limit gamma-->0. This could be a first step toward an expansion around mean-field theory, for spin glass systems.     

Molecular dynamics study of temperature dehydration of a C12E6 spherical micelle

Hydration of a spherical micelles of C12E6 in solution is studied by molecular dynamics simulation. The interface is found to be separated in an inner part composed of water and hydrophobic and hydrophilic moieties and an outer part with hydrophilic moiety and water only. Hydration numbers in the inner and in the outer parts are in excellent agreement with experimental data from various different methods. Temperature dehydration occurs in the inner region only and is related to the presence of water molecules directly in contact with the hydrophobic core at low temperature.