A solvent-free synthesis of coumarins using a Wells-Dawson heteropolyacid as catalyst

Substituted coumarins are synthesized from phenols and β-ketoesters by the Pechmann reaction, using a Wells-Dawson heteropolyacid (H₆P₂W₁₈O₆₂·24H₂O) as catalyst by a solvent-free procedure. This one requires low reaction times, 130 °C temperature and as little as 1 mol % of Wells-Dawson acid, obtaining good to excellent yields of coumarins. The catalyst showed to be reusable with no differences in the yields. The results are compared with those of the reactions performed in toluene solution. The presented synthetic procedure is a convenient, clean and fast alternative for synthesizing 4-substituted coumarins (17 examples).     

Design of an experimental procedure for energy evaluation from biomass

The rational and sustainable exploitation of nature resources is one of the priority objectives of our society. In this article a method is proposed to evaluate and exploit the energetic resources contained in different forest formations. This method is based on the use of a combustion bomb calorimeter to determine the calorific values of the different samples studied. These results were complemented with chemical analysis of the samples and with environmental and geomorphological studies of the zones were samples were taken. The results obtained during the last 3 years for the residual biomass originated from the forest formations existing in Galicia ensure the reliability and usefulness of the method that can be extended to any forest formation all over the world.     

Unavoidable Traces Of Set Systems

Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set system consisting of sufficiently many sets contains at least one of these structures with many sets.     

Higher Order Peak Algebras

Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))_N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N=1 and N=2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities related to the multisection of formal power series with noncommutative coefficients. Received November 19, 2004     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Derivation of fluorine-containing pyridine dicarboxylates. II. Elaboration at the 4-position

In response to the bio-activity found in fluorine-containing 4-alkyl-3, 5-pyridinedicarboxylates, a series of novel 4-substituted derivatives, not directly available by Hantzsch sequences, were prepared. Starting 4-alkylpyridines, 1 , were converted via enamine 2 to materials 3–8 . Derivatives 9–16 in turn were derived from aldehyde 3 , while acid derivatives 28–36 were prepared from 14 . Addition of oxygen, sulfur, and carbenoids effected conversion of 4-allylpyridine 16 to epoxy and cyclopropyl derivative 16–22 . A number of neighboring group effects were noted, including those forming the fused-ring systems 23-27 .