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).     

Refraction holodiagrams and Snell's law

The refraction holodiagram RHD is analyzed here with respect to the law of refraction. Particularly, we study the surface that exactly conjugates by refraction a virtual point source with a real image or conversely. By using the total optical path as a parameter we build a diagram that consists in a family of Descartes ovals of the apple type that contains the Pascal's limaçon as a particular extreme case and the spherical surface with the Weierstrass points as another. These representations permit the straightforward application of Fermat's principle in the case of arbitrary refracting surfaces and show the shape of generalized Fresnel's zones in the intersections with any surface. Snell's law is applied to rays incident on the apple type surfaces to find out the conditions for exact conjugation. Sensitivity to optical path variations is also discussed. The RHD curves family can be represented in a Cartesian way where the ovals appear as equally spaced straight lines.     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

Rigorous Generalization of Young's Law for Heterogeneous and Rough Substrates

We consider a SOS type model of interfaces on a substrate which is both heterogeneous and rough. We first show that, for appropriate values of the parameters, the differential wall tension that governs wetting on such a substrate satisfies a generalized law which combines both Cassie and Wenzel laws. Then in the case of an homogeneous substrate, we show that this differential wall tension satisfies either the Wenzel's law or the Cassie's law, according to the values of the parameters.     

High order linear initial-value problems and Schauder bases

In this paper we approximate the solution of a linear initial-value problem, making use of a Schauder basis for certain Banach space associated with such a differential problem. In addition, we apply that results in order to calculate numerically the response from a structure modelled by a three degree-of-freedom mass–damper–spring system.     

A SAXS study of the nanostructural characteristics of TEOS-derived sonogels upon heat treatment up to 1100 °C

Xerogels obtained from the acid-catalyzed and ultrasound stimulated hydrolysis of TEOS were submitted to heat treatment at temperatures ranging from 60 to 1100 °C and studied by small-angle X-ray scattering (SAXS). The SAXS intensity as a function of the modulus of the scattering vector q was obtained in the range from q₀=0.19 to q_m=4.4 nm⁻¹. At 60 °C the xerogels exhibit an apparent surface fractal structure with a fractal dimension D_S∼2.5 in a length scale ranging from 1/q₁∼1 to 1/q_m∼0.22 nm. This structure becomes extremely rough at 120 °C (D_S∼3) and at 150 °C, it apparently converts to a mass fractal with a fractal dimension D∼2.4. This may mean an emptying of the pores with preservation of a share of the original mass fractal structure of the wet aged gel, for it had presented a mass fractal dimension D∼2.2. A well characterized porous structure formed by 2.0 nm mean size pores with smooth surface of about 380 m²/g is formed at 300 °C and remains stable until approximately 800 °C. At 900 °C the SAXS intensity vanishes indicating the disappearance of the pores in the probed length scale. The elimination of the nanopores occurs by a mechanism in which the number of pores diminishes keeping constant their mean size. The xerogels exhibit a foaming phenomenon above 900 °C and scatter following Porod's law as does a surface formed by a coarse structure.     

Generating well-behaved utility functions for compromise programming

The purpose of this paper is to seek utility functions satisfying a weak condition which guarantees that the utility optimum always belongs to the compromise set. This set is a special subset of the attainable or feasible set, which is generated through the application of the well-known operational research approach called compromise programming. It is shown that there are large families of utility functions satisfying this condition, thus reinforcing the value of compromise programming as a good surrogate of the traditional utility optimum.Thanks are due to the reviewers for their helpful suggestions. The English editing by Ms. Christine Méndez is appreciated. The authors have been supported by the Comisión Interministerial de Ciencia y Tecnología (CICYT), Madrid, Spain.     

Asymmetry and magnetism in bis(oximato)-bridged heterobimetallic compounds: a computational approach

A density functional study of exchange coupling was carried out for a series of heterobinuclear oximato-bridged transition metal complexes. Model calculations were used to examine the influence of the electronic configuration of the metal atoms on the coupling constants. This analysis was complemented by a study of the variation of the coupling constant with the most usual structural distortions within this family of compounds. The influence of the nature of the terminal ligands as well as that of the symmetry on the bridge were also investigated.     

A Method for Clustering and Screening of Long-dimensional Chemical Data Based on Fingerprints and Similarity Measurements

A method for the treatment of long-dimensional chemical data arrays is presented in this work with the aim of maximising classification models. The method is based on the construction of fingerprints and the subsequent generation of a similarity matrix. The similarity calculation has been modified through a scaling process to take into account different significance shown by the variables. The method was applied to spectral measurements of wines and several aspects were studied, namely: threshold considered in the construction of fingerprints and patterns, weighting factor used for scaling, normalisation method, etc. The application of both Principal Components Analysis and Soft-Independent Modelling of Class Analogies to the similarity matrices gave better classifications of the information than those obtained using original data.     

High yield synthesis and reactivity of a phosphinidene bridged dimolybdenum complex

Protonation of [Mo2Cp2(mu-H)(mu-PHR*)(CO)4] (Cp = eta5-C5H5, R* = 2,4,6-C6H2tBu3) with HBF4.OEt2 gives the hydridophosphinidene complex [Mo2Cp2(mu-H)(mu-PR*)(CO)4]BF4, which is easily deprotonated with H2O to give the known phosphinidene complex [Mo2Cp2(mu-PR*)(CO)4] in 95% yield. Reaction of the latter with I2 gives the unsaturated phosphinidene complex [Mo2Cp2I2(mu-PR*)(CO)2], which exhibits an intermetallic distance of 2.960(2) A. Irradiation of solutions of [Mo2Cp2(mu-PR*)(CO)4] with UV light gives a mixture of the triply bonded [Mo2Cp2(mu-PR*)(mu-CO)2] and the hydridophosphido derivative [Mo2Cp2(mu-H){mu-P(CH2CMe2)C6H2tBu2}(CO)4] as major species. The latter complex results from an intramolecular C-H bond cleavage from a tBu group and has been characterized by spectroscopy and an X-ray study. Irradiation in the presence of HCC(p-tol) results in the insertion of the alkyne into the Mo-P bond to give [Mo2Cp2{mu-eta1:eta2,kappa-C(p-tol)CHPR*}(CO)4] structurally characterized through an X-ray study.