The wave equation on hyperbolic spaces

We study the dispersive properties of the wave equation associated with the shifted Laplace–Beltrami operator on real hyperbolic spaces and deduce new Strichartz estimates for a large family of admissible pairs. As an application, we obtain local well-posedness results for the nonlinear wave equation.     

Generalised power series solutions of sub-analytic differential equations

We show that if a solution $y(x)$ of a sub-analytic differential equation admits an asymptotic expansion ${\sum }_{i=1}^{\infty }{c}_i{x}^{{\mu }_i}$, ${\mu }_i\in {\mathbb{R}}^{+}$, then the exponents ${\mu }_i$ belong to a finitely generated semi-group of ${\mathbb{R}}^{+}$. We deduce a similar result for the components of non-oscillating trajectories of real analytic vector fields in dimension n. To cite this article: M. Matusinski, J.-P. Rolin, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Direct synthesis of 1,1-diarylalkenes from alkenyl phosphates via nickel(0)-catalysed Suzuki-Miyaura coupling

A combination of Ni(COD)(2) and PCy(3) promotes effectively the Suzuki-Miyaura cross coupling of 1-arylalkenyl phosphates with aryl boronic acids with yields attaining 99%.     

Simple pyridylmethylamines: efficient and robust N,N-ligands for Suzuki-Miyaura coupling reactions

A series of pyridylmethylamines have been synthesized in one step from commercially available starting material and identified as effective ligands for Pd-catalyzed carbon-carbon bond formation through Suzuki-Miyaura coupling reaction. The N,N-pyridylmethylamine-Pd catalytic systems appeared as an interesting and robust compromise between catalytic efficiency, substrate compatibility, and practical aspects.     

Non-invasive single bunch monitoring for ps pulse radiolysis

A single-shot electro-optic (EO) diagnostic has been installed on the ELYSE photocathode RF gun accelerator to monitor the electron bunch at the place and under the conditions of the ps pulse radiolysis experiments. The EO signal is due to the coulombic field of the electron bunch and to a contribution of a free-space THz radiation generated by the same electron pulse. This signal is recorded shot-to-shot at the repetition rate of the accelerator. The jitter of the arrival time of the electron bunch is characterized for the first time with a non-invasive method and is confirmed to be around 1 ps.     

A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions

This work investigates the acoustical properties of a multilayer porous material in which periodic inclusions are embedded. The material is assumed to be backed by a rigid wall. Most of the studies performed in this field used the multipole method and are limited to circular shape inclusions. Here, a mode matching approach, more convenient for a layered system, is adopted. The inclusions can be in the form of rigid scatterers of an arbitrary shape, in the form of an air-filled cavity or in the form of a porous medium with contrasting properties. The computational approach is validated on simple geometries against other numerical schemes and with experimental results obtained in an anechoic room on a rigid grating embedded in a porous material made of 2 mm glass beads. The method is used to study the acoustic absorption behavior of this class of materials in the low frequency range and at a range of angles of incidence.     

Lithium-ion Mobility in Li6B18(Li3N) and Li Vacancy Tuning in the Solid Solution Li6B18(Li3N)1−x(Li2O)x

All-solid-state batteries are promising candidates for safe energy-storage systems due to non-flammable solid electrolytes and the possibility to use metallic lithium as an anode. Thus, there is a challenge to design new solid electrolytes and to understand the principles of ion conduction on an atomic scale. We report on a new concept for compounds with high lithium ion mobility based on a rigid open-framework boron structure. The host–guest structure Li₆B₁₈(Li₃N) comprises large hexagonal pores filled with Li₇N] strands that represent a perfect cutout from the structure of α-Li₃N. Variable-temperature ⁷Li NMR spectroscopy reveals a very high Li mobility in the template phase with a remarkably low activation energy below 19 kJ mol⁻¹ and thus much lower than pristine Li₃N. The formation of the solid solution of Li₆B₁₈(Li₃N) and Li₆B₁₈(Li₂O) over the complete compositional range allows the tuning of lithium defects in the template structure that is not possible for pristine Li₃N and Li₂O.