Liouville Type Equations with Singular Data¶and Their Applications to Periodic Multivortices¶for the Electroweak Theory

Motivated by the study of multivortices in the Electroweak Theory of Glashow–Salam–Weinberg [33], we obtain a concentration-compactness principle for the following class of mean field equations: on M, where (M,g) is a compact 2-manifold without boundary, 0 < a≤K(x)≤b, x∈M and λ > 0. We take with α _i > 0, δ _{p i} the Dirac measure with pole at point p _i ∈M, i= 1,…,m and ψ∈L ^∞(M) satisfying the necessary integrability condition for the solvability of (1)_λ. We provide an accurate analysis for solution sequences of (1)_λ, which admit a “blow up” point at a pole p _i of the Dirac measure, in the same spirit of the work of Brezis–Merle [11] and Li–Shafrir [35]. As a consequence, we are able to extend the work of Struwe–Tarantello [49] and Ding–Jost–Li–Wang [21] and derive necessary and sufficient conditions for the existence of periodic N-vortices in the Electroweak Theory. Our result is sharp for N= 1, 2, 3, 4 and was motivated by the work of Spruck–Yang [46], who established an analogous sharp result for N= 1, 2. Received: 24 September 2001 / Accepted: 7 December 2001     

Amygdaloidins A-L, twelve new 13 α-OH jatrophane diterpenes from Euphorbia amygdaloides L.

Twelve new diterpenes, named amygdaloidins A-L (1-12), possessing a unique substitution pattern of the jatrophane skeleton, have been isolated from the wood spurge, Euphorbia amygdaloides L. (Euphorbiaceae). The chemical structures of amygdaloidins A-L have been established through a combination of extensive nuclear magnetic resonance and mass spectrometry methods. To deeper investigate the conformations adopted by such compounds in solution, we have carried out a molecular mechanic and dynamics calculation on amygdaloidin A and on the previously isolated euphodendroidin I. The data obtained gave further information on the endo- and exo-type conformations, the two main orientations of the jatrophane diterpenes.     

An Effective Simulation of Aqueous Micellar Aggregates by Computational Models

Summary We have computationally studied the interaction modes, localization and orientation of a benzene (Bz) molecule on the surface of micelles formed by cetyltrimethylammonium salts CTAX. Experimental ¹H-NMR data on complexation shifts induced by Bz on the polar head hydrogens and on the adjacent methylene hydrogens of CTAX have been interpreted using a computational approach that combines an automatic molecular docking procedure with a calculation module that accounts for NMR complexation shifts due to ring current diamagnetic anisotropy. Three different models were used to reduce the complexity of the micellar system. Computational results, in good agreement with available experimental data, point to a preferential localization of the Bz molecule along the CTAX alkyl tail, about 3.9 Å away from the charged nitrogen. The Bz molecular plane is predicted perpendicular to the C-H bonds of the alkyl tail. The good results obtained with the simplest model suggest that it could be used to study more complex systems involving surfactants endowed with molecular recognition or catalytic abilities.     

A quantization property for blow up solutions of singular Liouville-type equations

Motivated by the study of self-dual vortices in gauge field theory (cf. (Vortices and Monopoles, Birkhauser, Boston, 1980; Solitons in Field Theory and Nonlinear Analysis, Monographs in Mathematics, Springer, New York, 2001)), we consider a “concentrating”solution-sequence u_k satisfying

     

Organocatalyzed solvent-free aza-Henry reaction: a breakthrough in the one-pot synthesis of 1,2-diamines

A nitrogen-containing superbase such as TMG was found to be an effective catalyst for the reaction between N-diphenylphosphinoyl imines and nitroalkanes. Exploiting a protocol that avoids the use of any solvent also during workup procedure, we synthesized a series of beta-nitroamines in excellent yields and high diastereomeric ratios. These results, combined with the capability of the indium in conjunction with Zn as the stoichiometric reducing agent to perform in aqueous medium reduction of the nitro group under mild reaction conditions, led us to devise a three-step, one-pot synthesis of a range of 1,2-diamines, making use of environmentally friendly procedures in the various steps.     

Selfdual Maxwell-Chern-Simons Vortices

No Abstract. .Supported in part by MIUR project: Variational Methods and Nonlinear Differential Equations.Lecture held in the Seminario Matematico e Fisico on April 14, 2003Received: May, 2004     

Kinetic considerations on the electrogenerated luminescence of luminol at platinum electrode in the presence of hydrogen peroxide and oxygen

The ECL behavior of the luminol/H2O2 and luminol/O2 systems was evaluated at Pt electrode by using different electroanalytical techniques such as chronoamperometry, cyclic and rotating disk electrode (RDE) voltammetry. Diffusive and kinetic parameters such as the diffusion coefficient of luminol, D, the number of exchanged electrons, n, and the apparent heterogeneous rate constant, kap, were determined in the maximum light emission conditions achieved at pH 11, at an electrode potential of 750 mV vs. SCE. The experimental order of reaction were determined from the relation between the reactant concentrations and the emitted light intensity.     

Comparison of the Redox Properties of Iron Incorporated in Different Amounts into MCM-41

Kinetics of dehalogenation of the bromobenzenes 4-RC₆H₄Br (R=F, Cl, H, CH₃, CH₃O and N(CH₃)₂) with the title hydride (SDMA) and with SDMA in the presence of Co(acac)₂ have been examined. The rate constants of the debromination were correlated with Hammett substituent constants _p and E_1/2 reduction potentials of the bromobenzenes. values (+4.3 for SDMA reduction and +1.9 for the Co-catalyzed debromination) imply a negative charge concentration effect in transition states of both debrominations. Differences in the course of these reactions are discussed.     

Synthesis of dihydrolysergol analogues

As a part of a search for novel biological active ergoline derivatives, the indole ring present in the ergoline skeleton (indole[4,3‐f,g]quinoline) was converted into different heterocyclic ring systems such as quinazoline 2 , benzofurane 3 and benzoxazole 4 . Due to the paramount importance of chirality to attain biological activity, natural dihydrolysergic acid 1 was chosen as starting material and a synthetic pathway conservative in term of chirality was followed.     

Uniformities of Fréchet-Nikodym Type on Vitali Spaces

Vitali spaces are a simultaneous generalization of Riesz spaces, Boolean rings, MV-algebras. We study uniformities on Vitali spaces which make lattice operations, partial sum and subtraction uniformly continuous, proving that every such uniformity is generated by its 0-neighbourhood system. This result is not true in general for lattice uniformities on lattices. As consequence we obtain general decomposition theorems for exhaustive and locally exhaustive group-valued measures and decompositions of Lebesgue and Hewitt-Yosida type.