On Critical Stability of Three Quantum Charges Interacting Through Delta Potentials

We consider three one-dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.     

Une méthode de calcul des coefficients de réflexion et de transmission d'une houle bidimensionnelle en milieu confinéA new method for the calculation of transmission and reflection coefficients for water waves in a small basin

This paper presents a method to estimate reflected and transmitted wave amplitude spectra in a bounded domain such as a wave tank, when available data signals must be shortened due to interferences and wall effects. This paper extends the well known Goda and Suzuki two-probe method to three probes. The paper also suggests solutions to compute reliable transmission and reflection coefficients in spite of problems linked to higher harmonics and to the interference between different wave trains propagating in the tank. To cite this article: G. Duclos, A.H. Clément, C. R. Mecanique 331 (2003).     

Polyhydroxylated nortropanes starting from D-glucose: Synthesis of homochiral (+) and (−)-calystegines B2

The cycloheptano-isoxazoline 1, prepared from D-glucose, is converted to 6,7-dideoxy cycloheptitols which are suitable precursors for the synthesis of enantiomerically pure (+) and (−)-Calystegines B₂.     

Curvature vs. Thickness in quantum waveguides

It is known that there is at least one bound state in a curved quantum waveguide provided it is sufficiently thin. In this paper we investigate the critical thickness of two-dimensional waveguides above which the discrete spectrum becomes void. We have found an expression for it in the case of a small bending angle. In the general case, its asymptotic behaviour with respect to the bending angle is shown to be governed by local smoothness properties of the boundary. Uniqueness of the critical thickness is also discussed.Dedicated to the memory of M. Gmitro.One of the authors (P.E.) is grateful for the hospitality extended to him at the University of Toulon and C.N.R.S. Marseille where the most part of this work was done. A partial support by Czechoslovak Grant Agency under Contract No. 14814 is acknowledged.     

Diastereoselectivity in the Carroll rearrangement of β-keto esters of tertiary allylic alcohols

Carroll rearrangement of β-keto esters derived from tertiary allylic alcohols, for example, 7, under basic conditions followed by decarboxylation of the resulting β-keto acids yielded the expected γ,δ-unsaturated methyl ketones 8 with a range of olefin geometries from 100:0 to 1:1.8 E/Z, depending on the relative steric requirements of the two groups at the allylic center.     

Absolute Continuity in Periodic Thin Tubes and Strongly Coupled Leaky Wires

Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube is sufficiently thin. In a similar way we demonstrate absolute continuity at the bottom of the spectrum for generalized Schrödinger operators with a sufficiently strongly attractive interaction supported by a periodic curve in R^d = 2, 3.