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.     

A highly diastereoselective synthesis of 4-octulose and 2-deoxy-4-octulose from a -fructose derivative

Bishydroxylation of methyl

Full-size image

1 with osmium tetraoxide proceeded with extremed high diastereoselectivity to give only methyl

Full-size image

2. Configurations of the new stereogenic centers (C-2,3) in 2 were determined by degradation of the C-5,6,7,8 fragment to the well-known methyl

Full-size image

7. Transformation of 2 into the required

Full-size image

10, was achieved by a methodology that implied, protection to 8, reduction of the ester group in 8 to a hydroxymethyl group in 9, and finally deprotection to the free

Full-size image

10. On the other hand, epoxidation reaction on

Full-size image

11 afforded only the corresponding 2,3-anhydro derivative 12 with configuration, as could be demonstrated by degradation to (S)-1,2,4-trimetoxybutane 16, which synthesis is reported herein.     

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.     

Cold tests of open coaxial resonators in the range 9–17 GHz

A study of selective properties of coaxial open cylindrical resonators have been conducted experimentally and compared with theory. The resonator consists of an inner circular cylinder symmetrically located inside an outer weakly irregular open waveguide. Several fundamental TE modes were identified over the range 9 to 17 GHz through measurements of the resonant frequencies and the associated loaded quality factors. It has been verified that the structure and the number of resonant modes are both strongly dependent on the diameter of the coaxial insert. Such an electrodynamical system proves to be useful in guided wave applications requiring, for example, filters, frequency-tunable resonators and devices for analyzing the modal composition of a signal.     

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.     

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.     

Enantioselective synthesis of 1-deoxy-d-gulonojirimycin from a phenylglycinol-derived lactam

Cyclocondensation of (R)-phenylglycinol with appropriately γ-substituted δ-oxo acid derivatives provides bicyclic lactams from which the enantioselective synthesis of 1-deoxy-d-gulonojirimycin has been reported.     

Synthesis and structure of [(Sn(mu-PCy))3(Na x PMDETA)2], containing an electron-deficient [(Sn(mu-PCy))3]2- dianion

The reaction of CyPHNa with Sn(NMe2)2 in the presence of PMDETA (= (Me2NCH2CH2)2NMe) gives the title compound [(Sn(mu-PCy))3(Na x PMDETA)2] (1), containing an electron-deficient [(Sn(mu-PCy))]3(2-) dianion with a novel two-electron, three centre (2e-3c) bonding arrangement.     

Enantiopure Chiral Macrocyclic Lanthanide Complexes Derived from (R)-2,2′-Diamino-1,1′-binaphthyl and 2,6-Diformylpyridine

The template condensation of (R)-2,2′-diamino-1,1′-binaphthyl and 2,6-diformylpyridine leads to lanthanide(III) complexes of the new chiral hexaaza macrocycle L that adopts highly twisted conformation in [LnL](NO₃)₃ complexes. The complexes have been characterised by ESI MS spectrometry and NMR spectroscopy. The analogous N₂O₄ chiral crown ether L2 that has the same carbon skeleton as L does not exhibit tendency to bind lanthanide(III) ions. The X-ray crystal structure of L2 exhibit squeezed conformation of the macrocycle and spatial disposition of donor atoms that does not predispose it for coordination of lanthanide(III) ions.