Explicit limits for nonperiodic homogenization and reduction of dimensionLimites explicites pour l'homogénéisation non-périodique et la réduction de dimension

The aim of this Note is to give explicit limit expressions, for diffusion equations involving a small parameter ε, describing both nonperiodic homogenization and reduction of dimension. We consider two kinds of reduction of dimension: the case of plates and the case of thin cylinders. In particular, we give the limit diffusion equation for stratified plates. This is completely explicit and requires no special assumption, except stratification. In the case of thin cylinders, the formulae are less explicit, but we also indicate some simple applications to fibered materials. To cite this article: B. Gustafsson, J. Mossino, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 977–982.     

The Angle Defect for Odd-Dimensional Simplicial Manifolds

In a 1967 paper, Banchoff stated that a certain type of polyhedral curvature, that applies to all finite polyhedra, was zero at all vertices of an odd-dimensional polyhedral manifold; one then obtains an elementary proof that odd-dimensional manifolds have zero Euler characteristic. In a previous paper, the author defined a different approach to curvature for arbitrary simplicial complexes, based upon a direct generalization of the angle defect. The generalized angle defect is not zero at the simplices of every odd-dimensional manifold. In this paper we use a sequence based upon the Bernoulli numbers to define a variant of the angle defect for finite simplicial complexes that still satisfies a Gauss-Bonnet-type theorem, but is also zero at any simplex of an odd-dimensional simplicial complex K (of dimension at least 3), such that χ(link(ηⁱ, K)) = 2 for all i-simplices ηⁱ of K, where i is an even integer such that 0 ≤ i ≤ n – 1. As a corollary, an elementary proof is given that any such simplicial complex has Euler characteristic zero.     

Planar Chromatographic Study of Flavonoids and Soyasaponins for Validation of Fingerprints of Desmodium adscendens of Different Origin

JPC – Journal of Planar Chromatography – Modern TLC - The flavonoid and triterpenoid soyasaponin content of the aerial parts of Desmodium adscendens from four geographical origins of...     

The crystal and molecular structure of 12,13-dibromopseurotin.

The crystal structure of 12,13-dibromopseurotin has been determined by single crystal X-ray analysis. The crystals belong to space group P2₁ with a = 16.75, b = 9.63, c = 7.42 Å, β 95.9°, Z = 2. The structure was solved by the heavy atom technique and refined to R = 0.062 with 819 significant reflexions for 299 parameters.     

DNA electrochemistry through the base pairs not the sugar-phosphate backbone

Using intercalated, covalently bound daunomycin as a redox probe, ground state charge transport in DNA films with a perturbation in base pair stacking was examined in comparison with breaks in the sugar-phosphate backbone. While the introduction of one or even two nicks in the sugar-phosphate backbone yields no detectable effect on electron transfer, a CA mismatch significantly attenuates the electron transfer yield. These results confirm that the base pair stack is the pathway for DNA-mediated charge transfer, not the sugar-phosphate backbone.     

Synthesis of the C(43)-C(67) fragment of amphidinol 3

[reaction: see text] A synthesis of the C(43)-C(67) fragment of amphidinol 3 (AM3) has been accomplished by a route that features the use of a double allylboration reaction for synthesis of 1,5-diol 4b, which serves as a precursor to dihydropyran 11.     

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.