Fundamental Group for Some Cuspidal Curves

In [1], Hirano gives a method for constructing families of curveswith a large number of singularities. The idea is to consideran abelian covering of P² ramified along three lines in generalposition, and to take the pull-back of a curve C intersectingthe lines non-generically. Similar constructions are used byShimada in [10] and Oka in [8]. We apply this method for thecase where C is a conic, constructing a family of curves withthe following asymptotic behaviour (see [9]): The goal of this paper is to calculate the fundamentalgroup for the curves in this family as well as their Alexanderpolynomial. 1991 Mathematics Subject Classification 14H20, 14H30,14E20.     

A Hahn-Banach theorem for integral polynomials

We study the problem of extendibility of polynomials over Banach spaces: when can a polynomial defined over a Banach space be extended to a polynomial over any larger Banach space? To this end, we identify all spaces of polynomials as the topological duals of a space spanned by evaluations, with Hausdorff locally convex topologies. We prove that all integral polynomials over a Banach space are extendible. Finally, we study the Aron-Berner extension of integral polynomials, and give an equivalence for non-containment of .

     

Fuzzy nilpotent algebras

We define the concept of fuzzy nilpotent algebra, prove that the homomorphic inverse image of a fuzzy nilpotent algebra is also nilpotent and study the intersection and union of fuzzy nilpotent algebras.     

Improved formal total synthesis of tetrahydrometinoxocrinine

An improved, isomer-free synthesis of Tetrahydrometinoxocrinine ($\text{1}$) is described.     

The Helmholtz equation with impedance in a half-space

In this Note we obtain existence and uniqueness results for the Helmholtz equation in the half-space ${\mathbb{R}}_{+}^3$ with an impedance or Robin boundary condition. Basically, we follow the procedure we have already used in the bi-dimensional case (the half-plane). Thus, we compute the associated Green's function with the help of a double Fourier transform and we analyze its far field in order to obtain radiation conditions that allow us to prove the uniqueness of an outgoing solution. Again, these radiation conditions are somewhat unusual due to the appearance of a surface wave guided by the boundary. An integral representation of the solution is presented by means of the Green's function and the boundary data. To cite this article: M. Durán et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Global regular and singular solutions for a model of gravitating particles

The existence of solutions of a nonlinear parabolic equation describing the gravitational interaction of particles is studied for the initial data in spaces of (generalized) pseudomeasures. This approach permits us to relax regularity assumptions on the initial conditions and to prove asymptotic stability results for the above problem.Mathematics Subject Classification (2000):35B40, 35K15, 82C21     

Deuterium-labeling and NMR study of the dearomatization of N-alkyl-N-benzyldiphenylphosphinamides through anionic cyclization: ortho and benzylic lithiation directed by complex-induced proximity effects

The mechanism of the anionic cyclization dearomatizing reaction of N-benzyl-N-methyldiphenylphosphinamide (1) upon treatment with s-BuLi in tetrahydrofuran (THF) at -90 degrees C has been analyzed by deuterium-labeling and natural abundance multinuclear magnetic resonance ((1)H, (2)H, (7)Li, (13)C, (31)P) studies. In the absence of coordinating cosolvents such as hexamethylphosphoramide (HMPA), eight major anionic species were identified, which allowed us to unravel the pathway of the metalation reaction. In agreement with the complex-induced proximity effect (CIPE) mechanism, the sequence of transformations emerging from this study involves the coordination of the lithium base to the P=O group of 1 to give four dimeric precomplexes whose NMR data are consistent with structures Va/Vb and VIIIa/VIIIb. The diastereomers Va/Vb are the precursors of the monomeric benzylic anion II, whereas the VIIIa/VIIIb diastereomers are assumed to undergo ortho deprotonation leading to anions I. Translocation from the ortho anion to the benzylic one is not observed. Intramolecular conjugate addition of anion II to the P-phenyl rings happens in a reversible way, affording the monomeric dearomatized anions III, IV, VI, and VII. The reaction progresses to yield a mixture containing only the species I, III, and IV. HMPA acts as a catalyst for the ortho-to-benzylic translocation and anionic cyclization reactions. Two-dimensional (2D) (7)Li,(31)P[(1)H] shift correlations and (7)Li[(31)P] NMR spectra proved to be crucial for the structural assignment of the anionic species. These techniques also demonstrated the diastereotopicity of the two achiral ligands involved in a dimer with s-BuLi (Vb) owing to the slow configuration inversion of the carbanion center.     

Electrically forced coaxial nanojets for one-step hollow nanofiber design

The outer liquid of a two-liquid coaxial electrified jet is gelled before the onset of natural instabilities to yield hollow nanofibers. By using sol-gel chemistry, innocuous solvents such as glycerol and olive oil, and electrohydrodynamics, it is possible to make such structures in a rather straightforward manner.     

Density estimation using game theory

In this note we show that the mathematical tools of cooperative game theory allow a successful approach to the statistical problem of estimating a density function. Specifically, any random sample of an absolutely continuous random variable determines a transferable utility game, the Shapley value of which proves to be an estimator of the density function of binned kernel and WARPing types, with good computational and statistical properties.Authors acknowledge the financial support of Spanish Ministry for Science and Technology and FEDER through projects BFM2002-03213 and BEC2002-04102-C02-02 and of Xunta de Galicia through projects PGIDT00PXI20104PR and PGIDT03PXIC20701PN. They also thank the comments of two anonymous referees.