Mayberry-Murasugi's formula for links in homology 3-spheres

We prove the Mayberry-Murasugi formula for links in homology 3-spheres, which was proved before only for links in the 3-sphere. Our proof uses Franz-Reidemeister torsions.

     

Synthesis and thermal crosslinking of oxazolidine‐functionalized polyurethanes

A new oxazolidine derivative was obtained from phenol, 2‐amino‐2‐methylpropane‐1,3‐diol and paraformaldehyde. The reaction of this novel oxazolidine diol with phenylisocyanate lead to a urethane model compound which can be polymerized thermally by oxazolidine ring opening to give a Mannich bridge structure. Linear segmented polyurethanes were prepared by reaction of different ratios of oxazolidine diol and commercial polyethylenglycol (M_w ～ 400) with 4,4′‐methylenbis (cyclohexylisocyanate) (HMDI, 90% isomers mixture). The polyurethanes were thermally characterized and crosslinked by oxazolidine ring opening to obtain materials which showed improved thermal stability. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4965–4973, 2007     

On the permanence of the null character of Maxwell fields

A critical review of known results about the permanence conditions for the null character of the solutions to the (vacuum) Maxwell equations, is presented. Concomitants of the electromagnetic field and the metric tensor are constructed, which give the principal directions of the field in covariant form. The known permanence conditions are generalized in order to includeall the (local) null fields; the above concomitants allow these conditions to be explicitly formulated in terms of the electromagnetic field.Supported in part by Conselleria de Cultura, Educació i Ciència de la Generalitat Valenciana.     

Efficient combination of task-specific ionic liquid and microwave dielectric heating applied to one-pot three component synthesis of a small library of 4-thiazolidinones

The first report of the use of task-specific ionic liquid as synthetic equivalent of ionic liquid-phase matrice for the preparation of a small library of 4-thiazolidinones is reported in this paper. The starting (ethyleneglycol)ionic liquid-phase is functionalized in good yields with 4-(formylphenoxy)butyric acid by using usual esterification reaction conditions (DCC/DMAP as catalyst). The synthesis of the ionic liquid-phase bound 4-thiazolidinones was performed by a one-pot three-component condensation under microwave dielectric heating. The final cleavage under microwave/catalysis strategy provides the expected 4-thiazolidinones in high purity after flash-chromatography purification. According to the ionic liquid-phase organic synthesis (IoLiPOS) methodology, it was found that optimized reaction conditions were performed by standard analytical methods (NMR, TLC). The ¹H, ¹³C NMR spectrum of some representative 4-thiazolidinones and ionic liquid-phase bound benzaldehyde are also reported.     

Fast solid-phase extraction-gas chromatography-mass spectrometry procedure for oil fingerprinting. Application to the Prestige oil spill

A rapid and simple fractionation procedure using solid-phase extraction (SPE) cartridges was developed for an accurate determination of aliphatic and polycyclic aromatic hydrocarbons in petroleum residues and further application in chemical fingerprinting of oil spills by gas chromatography-mass spectrometry (GC-MS). Among the adsorbents evaluated, SiO2/C3-CN exhibited the best selectivity, providing, by elution with n-hexane (4 ml) and n-hexane-CH2Cl2 (1:1) (5 ml), two well-resolved aliphatic and aromatic hydrocarbon fractions, with recoveries of 97 +/- 7.2 and 99.7 +/- 13.9%, respectively. The SPE fractionation procedure was compared with the conventional silica-alumina adsorption chromatography showing similar results but practical advantages in terms of reproducibility, analysis time, solvent reduction and cost. Moreover, is particularly suitable for routine analysis with a high sample throughput. The developed methodology was tested in the characterization of fuel-oil samples collected along the Spanish north-west coast, after the Prestige oil spill accident.     

Synthesis of Enantiomeric Pure E-Nor-15-azayohimbines

A stereodivergent synthesis of enantiomerically pure E-nor-15-azayohimbines via condensation of tryptamine with derivatives of pyroglutamate 4 is reported. When the Pictet-Spengler reaction was induced in refluxing aqueous AcOH a nearly equimolar ratio of lactams 7 and 8 was obtained, whereas under kinetic control (TFA, room temperature) the trans-derivative 8 was the major product. In contrast, cyclization of amido acetal 12 with TsOH gave the cis-derivative 7 as preponderant component.     

Limit Cycles Bifurcating from a k-dimensional Isochronous Center Contained in ?n with k ? n

The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum periodic orbits of a k-dimensional isochronous center contained in ℝ ⁿ with n ⩾ k, when we perturb it in a class of differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree. As far as we know this is one of the first examples that this study can be made for a polynomial differential system having a center and a non-rational first integral. The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550. The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the joint project CAPES–MECD grant HBP2003-0017.     

Hyperbolic polygons of minimal perimeter with given angles

We prove that, among all convex hyperbolic polygons with given angles, the perimeter is minimized by the unique polygon with an inscribed circle. The proof relies on work of Schlenker (Trans Am Math Soc 359(5): 2155–2189, 2007).