NdHO, a novel oxyhydride

A new metal oxyhydride; neodymium oxyhydride, NdHO, has been synthesized from a reactant mixture of metal hydride (CaH₂ or NdH₃) and neodymium oxide (Nd₂O₃). The unit cell dimensions decrease smoothly in the series from LaHO, CeHO, PrHO to NdHO, in line with the lanthanide contraction. The crystal structure of NdHO is described on the basis of Rietveld refinement on neutron powder diffraction data:

Space group: P4/nmm (no. 129, D_4h⁷).

Axis lengths: a=7.8480(5) Å, c=5.5601(8) Å.

Volume: V=342.46(6) Å³.

The tetragonal structure is derived from the fluorite structure, showing complete ordering of hydride and oxide ions over the anion sublatttice. The formation of NdHO was further substantiated by Raman spectroscopy.     

An axially chiral, electron-deficient borane: synthesis, coordination chemistry, Lewis acidity, and reactivity

An axially chiral dihydroborepine with a binaphthyl backbone and a C(6)F(5) substituent at the boron atom was prepared by transmetalation from the corresponding tin precursor. This novel motif was structurally characterized by X-ray diffraction analysis as its THF and its PhCN Lewis acid/base complex. (1)H NMR measurements at variable temperatures of the former adduct revealed a remarkable dynamic behavior in solution. Several more Lewis pairs with oxygen, nitrogen, carbon, and phosphorus σ-donors were synthesized and analyzed by multinuclear NMR spectroscopy. The determination of the borane's Lewis acidity with the Gutmann-Beckett method attests its substantial Lewis acidity [85% with Et(3) PO as well as 74% with Ph(3) PO relative to the parent B(C(6)F(5))(3)]. Representative examples of Si-H bond activation (carbonyl reduction and dehydrogenative Si-O coupling) are included, demonstrating the chemical stability and the synthetic potential of the new chiral boron-based Lewis acid.     

Ruled quartic surfaces,models and classification

New historical aspects of the classification, by Cayley and Cremona, of ruled quartic surfaces and the relation to string models and plaster models are presented. In a ‘modern’ treatment of the classification of ruled quartic surfaces the classical one is corrected and completed. The string models of Series XIII of some ruled quartic surfaces (manufactured by L. Brill and by M. Schilling) are based on a result of Rohn concerning curves in \mathbbP¹×\mathbbP¹{\mathbb{P}^1\times \mathbb{P}^1} of bi-degree (2, 2). This is given here a conceptional proof.     

Weak Solutions for the Motion of a Self-propelled Deformable Structure in a Viscous Incompressible Fluid

We consider the three-dimensional motion of a self-propelled deformable structure into a viscous incompressible fluid. The deformation of the solid is given whereas its position is unknown. Such a system could model the propulsion of fish-like swimmers. The equations of motion of the fluid are the Navier-Stokes equations and the equations for the structure are deduced from Newton’s laws. The corresponding system is a free boundary problem and the main result of the paper is the existence of weak solutions for this problem.     

Analyticity and Gevrey-Class Regularity for the Second-Grade Fluid Equations

We address the global persistence of analyticity and Gevrey-class regularity of solutions to the two and three-dimensional visco-elastic second-grade fluid equations. We obtain an explicit novel lower bound on the radius of analyticity of the solutions that does not vanish as t → ∞, and which is independent of the Rivlin–Ericksen material parameter α. Applications to the damped incompressible Euler equations are also given.     

Chloride‐Free Method to Synthesise New Ionic Liquids with Mixed Borate Anions

Chloride avoided! A new chloride‐free method to synthesise ionic liquids (ILs) with mixed borate anions, starting from tetrafluoroborate compounds, has been developed and a number of examples including some new ILs are presented (see scheme; [CAT]⁺=cation). It is widely applicable and allows access to mixed borates with various types of ligands in a straightforward manner.

     

Vector Potential Theory on Nonsmooth Domains in R3 and Applications to Electromagnetic Scattering

We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for L^p-integrable bounday data for optimal values of p’s. We also discuss a number of relevant applications in electromagnetic scattering.     

Sharp Hodge decompositions in two and three dimensional Lipschitz domainsDécompositions de Hodge optimales pour les domaines lipschitziens en dimensions deux et trois

We identify the optimal range of coefficients s, p for which differential forms with coefficients in the Sobolev space $\text{L}{}^{\mathrm{p}}{}_{\mathrm{s}}\text{(Ω)}$ admit natural Hodge decompositions in arbitrary two and three dimensional Lipschitz domains $\text{Ω}$. To cite this article: D. Mitrea, M. Mitrea, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 109–112