Synthesis of substituted quinolines by electrophilic cyclization of N-(2-alkynyl)anilines

Quinolines substituted in the 3-position by an iodo or phenylseleno group are readily prepared in good to excellent yields by the reaction of propargylic anilines with appropriate electrophiles under mild reaction conditions. [reaction: see text]     

Nonlinear Schrödinger equations: concentration on weighted geodesics in the semi-classical limit

We consider the problem

${?}^2\mathrm{\Delta }u?V(x)u+u^p=0,u>0,u\in H^1({\mathbb{R}}^2),$

where $p>1$, $?>0$ is a small parameter and V is a uniformly positive, smooth potential. Let Γ be a closed curve, nondegenerate geodesic relative to the weighted arclength ${\int }_{\Gamma }{V}^{\sigma }$, where $\sigma =\frac{p+1}{p?1}?\frac{1}{2}$. We prove the existence of a solution $u_{\mathrm{\epsilon }}$ concentrating along the whole of Γ, exponentially small in ? at any positive distance from it, provided that ? is small and away from certain critical numbers. This proves a conjecture raised in [A. Ambrosetti, A. Malchiodi, W.-M. Ni, Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I, Commun. Math. Phys. 235 (2003) 427–466] in the two-dimensional case. To cite this article: M. del Pino et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

An accelerated closed universe

We study a model in which a closed universe with dust and quintessence matter components may look like an accelerated flat Friedmann–Robertson–Walker (FRW) universe at low redshifts. Several quantities relevant to the model are expressed in terms of observed density parameters, _M and , and of the associated density parameter _Q related to the quintessence scalar field Q.     

Synthesis of fused polycycles by 1,4-palladium migration chemistry

Novel palladium migration/arylation methodology for the synthesis of complex fused polycycles has been developed, in which one or more sequential Pd-catalyzed intramolecular migration processes involving C-H activation are employed. The chemistry works best with electron-rich aromatics, which is in agreement with the idea that these palladium-catalyzed C-H activation reactions parallel electrophilic aromatic substitution.     

Liquid-liquid extraction followed by solid-phase extraction for the determination of lipophilic pesticides in beeswax by gas chromatography-electron-capture detection and matrix-matched calibration

Analytical methods for the simultaneous analysis of lindane, chlorpyriphos, z-chlorfenvinphos, endosulfan A and B, 4,4'-DDE, 4,4'-TDE, acrinathrine, bromopropylate, tetradifon, coumaphos and fluvalinate in pure beeswax samples are studied. For the analysis of bleached beeswaxes, a liquid-liquid extraction with acetonitrile followed by a clean-up on polymeric cartridges is the best option in terms of recovery and precision. However, some interferences that hinder the identification and quantification of important varroacides are found when non-bleached beeswaxes are analyzed. The analysis of all compounds in the latter samples require a clean-up by coupling an ODS cartridge before the polymeric cartridge. Considerations about the influence of the matrix in the quantitative analysis by a classical external standard calibration are also made and the use of a matrix-matched calibration is advised. Recoveries resulted to be about 100% with coefficients of variation between 10% and 20% (n = 5) for concentrations of 0.5 and 5 mg/kg.     

Ferromagnetic exchange in the ground and (4)A(1) excited states of (Et(4)N)(3)Fe(2)F(9). A magnetic and optical spectroscopic study

The synthesis, crystal growth, magnetic susceptibility, and polarized optical absorption spectra in the visible and near UV of (Et(4)N)(3)Fe(2)F(9) are reported. From single-crystal magnetic susceptibility data and high-resolution absorption spectra in the region of the (6)A(1) --> (4)A(1) spin-flip transition, exchange splittings in the ground and excited states are derived. Ferromagnetic ground and excited state exchange parameters J(GS) = -1.55 cm(-1) and J(ES) = -0.53 cm(-1) are determined, respectively, and the relevant orbital contributions to the net exchange are derived from the spectra. The results are compared with those reported earlier for the structurally and electronically analogous [Mn(2)X(9)](5-) pairs in CsMgX(3):Mn(2+) (X = Cl(-), Br(-)), in which the splittings are antiferromagnetic. This major difference is found to be due to the increased metal charge of Fe(3+) compared to Mn(2+), leading to orbital contraction and thus to a strong decrease of the orbital overlaps and hence the antiferromagnetic interactions.     

The Yamabe problem for almost Hermitian manifolds

The conformal class of a Hermitian metric g on a compact almost complex manifold (M^2m, J) consists entirely of metrics that are Hermitian with respect to J. For each one of these metrics, we may define a J-twisted version of the Ricci curvature, the J-Ricci curvature, and its corresponding trace, the J-scalar curvature s^J. We ask if the conformal class of g carries a metric with constant s^J, an almost Hermitian version of the usual Yamabe problem posed for the scalar curvature s. We answer our question in the affirmative. In fact, we show that (2m−1)s^J−s=2(2m−1)W(ω, ω), where W is the Weyl tensor and ω is the fundamental form of g. Using techniques developed for the solution of the problem for s, we construct an almost Hermitian Yamabe functional and its corresponding conformal invariant. This invariant is bounded from above by a constant that only depends on the dimension of M, and when it is strictly less than the universal bound, the problem has a solution that minimizes the almost complex Yamabe functional. By the relation above, we see that when W (ω, ω) is negative at least one point, or identically zero, our problem has a solution that minimizes the almost Hermitian Yamabe functional, and the universal bound is reached only in the case of the standard 6-sphere equipped with a suitable almost complex structure. When W(ω, ω) is non-negative and not identically zero, we prove that the conformal invariant is strictly less than the universal bound, thus solving the problem for this type of manifolds as well. We discuss some applications.     

Bicyclic units of

We prove that the group generated by the bicyclic units of has torsion for . This answers a question of Sehgal (1993).

     

Supershell structure in alkali metal nanowires

Nanowires are formed by indenting and subsequently retracting two pieces of sodium metal. Their cross section gradually reduces upon retraction and the diameters can be obtained from the conductance. In previous work we have demonstrated that when one constructs a histogram of diameters from large numbers of indentation-retraction cycles such histograms show a periodic pattern of stable nanowire diameters due to shell structure in the conductance modes. Here, we report the observation of a modulation of this periodic pattern, in agreement with predictions of a supershell structure.