Approximations simultanées de nombres algébriques de Q p par des rationnels

 In this paper, we prove that if β₁,…, β _n are p-adic numbers belonging to an algebraic number field K of degree n + 1 over Q such that 1, β₁,…,β _n are linearly independent over Z, there exist infinitely many sets of integers (q ₀,…, q _n ), with q ₀ ≠ 0 and

Irreducibility, Brill-Noether loci, and Vojta's inequality

This paper deals with generalizations of Hilbert's irreducibility theorem. The classical Hilbert irreducibility theorem states that for any cover of the projective line defined over a number field , there exist infinitely many -rational points on the projective line such that the fiber of over is irreducible over . In this paper, we consider similar statements about algebraic points of higher degree on curves of any genus. We prove that Hilbert's irreducibility theorem admits a natural generalization to rational points on an elliptic curve and thus, via a theorem of Abramovich and Harris, to points of degree 3 or less on any curve. We also present examples that show that this generalization does not hold for points of degree 4 or more. These examples come from an earlier geometric construction of Debarre and Fahlaoui; some additional necessary facts about this construction can be found in the appendix provided by Debarre. We exhibit a connection between these irreducibility questions and the sharpness of Vojta's inequality for algebraic points on curves. In particular, we show that Vojta's inequality is not sharp for the algebraic points arising in our examples.

     

Synthesis of a potent antagonist of E-selectin

A synthesis of an antagonist of E-selectin previously reported by a group at Novartis Pharma in Basel is described. An important feature involves the formation of an ether linkage based on a Rh(II)-catalyzed reaction. Stereocontrolled glycosylations rely on the anomeric activation of 2-pyridylthio carbonate as leaving group for the attachment of beta-D-galactopyranosyl and alpha-L-fucopyranosyl units on a common 1,5-anhydro D-glucitol scaffold.     

Quasi-solitonic behavior of self-written waveguides created by photopolymerization

We investigated the condition of unique self-written channel and multichannel propagation inside bulk photopolymerizable materials. Light was introduced in the medium by a single-mode optical fiber. At a very low beam power of 5 muW , a unique uniform-channel waveguide without any broadening was obtained by polymerization. When the input power is increased to 100 muW , the guide becomes chaotic and multichannel. We connected two fibers separated by a 1-cm distance. The results open the door to studies of the optical and electro-optical properties of photopolymerized guides doped by nonlinear optical chromophores and to possible applications in integrated optical devices.     

Corrosion Products Formed on Mild Steel Samples Submerged in Various Aqueous Solutions

Corroded samples, from the steel shell of an industrial evaporator system were investigated. A protective magnetite layer had formed, which subsequently dissolved in localised areas, resulting in failure of the shell. To clarify the mechanisms involved, mild steel samples of similar composition to the steel shell were submerged in the condensate and experiments were performed at room temperature and at 90°C under both static and dynamic conditions for exposure times up to 30 days. Control samples were submerged in deionised water under similar conditions. The dynamic corrosion rates in the industrial condensate were a factor of 2 higher than the rates for the deionised water, whilst static corrosion rates, measured in both media, were lower by a factor of 3 to 4 found for the dynamic experiments. The corrosion products were identified by means of CEMS analyses. The main components were magnetite and oxyhydroxides of iron. Additional to the species mentioned, -Fe₂O₃, goethite and hematite formed.     

High resolution 2D 1H-13C correlation of cholesterol in model membrane

High resolution 2D NMR MAS spectra of liposomes, in particular 1H-13C chemical shifts correlations have been obtained on fluid lipid bilayers made of pure phospholipids for several years. We have investigated herein the possibility to obtain high resolution 2D MAS spectra of cholesterol embedded in membranes, i.e. on a rigid molecule whose dynamics is characterized mainly by axial diffusion without internal segmental mobility. The efficiency of various pulse sequences for heteronuclear HETCOR has been compared in terms of resolution, sensitivity and selectivity, using either cross polarization or INEPT for coherence transfer, and with or without MREV-8 homonuclear decoupling during t1. At moderately high spinning speed (9 kHz), a similar resolution is obtained in all cases (0.2 ppm for 1H(3,4), 0.15 ppm for 13C(3,4) cholesterol resonances), while sensitivity increases in the order: INEPT < CP(x4) < CP + MREV. At reduced spinning speed (5 kHz), the homonuclear dipolar coupling between the two geminal protons attached to C(4) gives rise to spinning sidebands from which one can estimate a H-H dipolar coupling of 10 kHz which is in good agreement with the known dynamics of cholesterol in membranes.     

Sur un théorème de connexité de Mumford pour les espaces homogènes

We prove some consequences of an old unpublished connectivity result of Mumford. These mostly deal with the fundamental group of some (ramified) coverings of homogeneous spaces; for example, it is shown that the fundamental group of a complex projective irreducible normal variety which is a covering of a simple (in the sense of 2.2) homogeneous space V, of degree ≤dim (V), is isomorphic to π₁ (V).