Solutions of logarithmic type for elliptic and hypoelliptic equations

LetK be an algebraically closed field withp:=char (K)>0 andX a bielliptic curve over Spec(K) with genus≥6 and such that the canonical model ofX is ordinary. In this paper we determine all the possible gap sequences of Weierstrass points on such curves.     

The law of the solution to a nonlinear hyperbolicSPDE

Let { _s,t ,(s,t ₊ ² } be a white noise on ₊ ² . We consider the hyperbolic stochastic partial differential equation {ie863-3} The purpose of this paper is to study the law of the solution to this equation. We analyze the existence and smoothness of the density using the tools of Malliavin Calculus. Finally we prove a large deviation principle on the space of continuous functions, for the family of probabilities obtained by perturbation of the noise in the equation.This work has been partially supported by the grant of the DGICYT No. PB 930052 and the EU Science project CT 910459.     

An Efficient and Simple Entry to N-Substituted beta-Enamino Acid Derivatives from 2-Alkyl-2-oxazolines and 2-Alkyl-2-thiazolines

Reaction of azaenolates of 2-alkyl-oxa(thia)zolines 6 with imidoyl chlorides 7 as electrophiles to furnish masked N-substituted beta-enamino acid derivatives 1-2 in 70-90% yield is described. Alternative routes are discussed. Compounds 1-2 generally appear in one tautomeric form, imino or enamino, depending on the nature of the imidoyl chloride. The configuration of the enamino moiety (Z) and the conformation (s-cis) of compounds 1-2 obtained were established by an NMR study and unequivocally set by nuclear Overhauser effect difference experiments. An X-ray structure of compound 1e is also reported, showing a strong intramolecular NH.N hydrogen bond. Ab initio calculations (HF/3-21G and HF/3-21+G) have been carried out on several representative examples (1e, 1p, and 1l) in an attempt to support and provide the correct geometry of these derivatives. Structural considerations among the possible isomers of compounds 1 are discussed. From these studies it was concluded that the theoretical calculations agree with the experimental results. In addition, a very simple one-pot procedure for the preparation of masked N-substituted alpha-alkylated beta-enamino acid derivatives 2 from 6, 7, and different alkyl halides (R(3)Y) is described.     

SOOT combustion. co and k catalysts supported on different supports

The catalytic combustion of particulate material was studied on cobalt catalysts promoted with potassium using different supports for its preparation. Silica, aluminium oxides and hydroxides, zirconium oxide and hydroxide were used as supports. The catalytic activity for combustion depends on the type of support used, the higher activity corresponding to the supported catalyst on zirconium oxide. TPR studies indicate that the interaction metal/support allows to explain the higher activity of the CoK/SiO₂ catalyst with respect to the CoK/Al₂O₃ but the high activity found in CoK/ZrO₂is not explained by this interaction. In all cases the Co and K improved the performance of the catalysts.     

Solvent dependent conformational isomerism and ligand oxidation of novel Ru(II) cyclen complexes

The synthesis of cis-[Ru(II)(cyclen)(L)(x)](n+) (cyclen = 1,4,7,10-tetraazacyclododecane and L = 2,2'-bipyridine (bpy), phenanthroline (phen) or 4-cyanopyridinium (4-NCpyH(+))) is reported. The freshly prepared complexes are stable in aprotic solvents and cyclen undergoes oxidative dehydrogenation reaction at high pH. These compounds also present solvent dependent conformational isomerization.     

An effective enantioselective approach to the securinega alkaloids: total synthesis of (-)-norsecurinine

[reaction: see text] A highly versatile approach to the enantioselective synthesis of securinega alkaloids is presented. Crucial steps are a palladium-catalyzed enantioselective imide alkylation, a vinylogous Mannich reaction, and a ring-closing metathesis process. Through this strategy, the synthesis of (-)-norsecurinine has been accomplished in nine steps and 11% overall yield.     

Gas chromatographic quantification of amino acid enantiomers in food matrices by their N(O,S)-ethoxycarbonyl heptafluorobutyl ester derivatives

Several amino acid enantiomer derivatives were prepared with different chloroformates and analysed by gas chromatography (GC) on a Chirasil-L-Val GC column, at a temperature below 200 degrees C. Among them the N(O,S)-ethoxycarbonyl heptafluorobutyl esters presented the best compromise between short retention times, high yield responses and good resolution for almost all the tested amino acids. These derivatives proved to be suited for quantification of amino acids in aqueous media, with L-p-chlorophenylalanine as internal standard. The developed procedure was applied to several food samples for determination of their free amino acid profiles.