Linear theory of wave generation by a moving bottom

The computation of long wave propagation through the ocean obviously depends on the initial condition. When the waves are generated by a moving bottom, a traditional approach consists in translating the ‘frozen’ sea bed deformation to the free surface and propagating it. The present study shows the differences between the classical approach (passive generation) and the active generation where the bottom motion is included. The analytical solutions presented here exhibit some of the drawbacks of passive generation. The linearized solutions seem to be sufficient to consider the generation of water waves by a moving bottom. To cite this article: D. Dutykh et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Mehrfachbindungen zwischen Hauptgruppenelementen und Übergangsmetallen : XLIV. Synthesen von Hydrogensulfido- und Hydrogenselenido-Komplexen der Metalle Chrom, Molybdän und Wolfram

Hydrogenchalcogenido complexes of general composition (η⁵-C₅R₅)(CO)₃M(EH) (R = H, CH₃; M = Cr, Mo, W; E = S, Se) can be obtained by three different routes, sometimes in quite good yields. Thus, the sulfur and selenium derivatives can be synthesized by insertion of the respective elements into the metal-hydrogen bonds of the precursor compounds (η⁵-C₅R₅)(CO)₃MH. This species also reacts with potassium selenocyanate to yield the hydrogenselenido derivatives (η⁵-C₅R₅)(CO)₃M(SeH) which can also be obtained by treatment of the methyl complexes (η⁵-C₅R₅)(CO)₃M(CH₃ (M = Mo, W) with HBF₄ and Li[SeH]. The corresponding hydrogentellurido compounds are probably formed by these preparative methods but appear to be quickly converted into either the dinuclear tellurium bridge products (μ-Te)[(η⁵-C₅R₅)(CO)₃M]₂ (M = Mo) or into the hydrido complexes (η⁵-C₅R₅)(CO)₃MH (M= Mo, W) by release of elemental tellurium.     

Multiscale kernels

This paper reconstructs multivariate functions from scattered data by a new multiscale technique. The reconstruction uses standard methods of interpolation by positive definite reproducing kernels in Hilbert spaces. But it adopts techniques from wavelet theory and shift-invariant spaces to construct a new class of kernels as multiscale superpositions of shifts and scales of a single compactly supported function φ. This means that the advantages of scaled regular grids are used to construct the kernels, while the advantages of unrestricted scattered data interpolation are maintained after the kernels are constructed. Using such a multiscale kernel, the reconstruction method interpolates at given scattered data. No manipulations of the data (e.g., thinning or separation into subsets of certain scales) are needed. Then, the multiscale structure of the kernel allows to represent the interpolant on regular grids on all scales involved, with cheap evaluation due to the compact support of the function φ, and with a recursive evaluation technique if φ is chosen to be refinable. There also is a wavelet-like data reduction effect, if a suitable thresholding strategy is applied to the coefficients of the interpolant when represented over a scaled grid. Various numerical examples are presented, illustrating the multiresolution and data compression effects.     

On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear M?ller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a soliton in a slowly varying background potential W(ɛx). We prove that the soliton decomposes into a soliton plus a scattering wave (radiation) up to times of order ɛ⁻¹. To leading order, the center of the soliton follows the trajectory of a classical particle in the potential W(ɛx). Received: 30 June 2000 / Accepted: 25 June 2001     

Intersegmental interaction and critical concentrations in PET–HFIP solutions

Spectroscopic determinations of the concentrations associated with the onset of intermolecular interaction in solutions of poly(ethylene terephthalate) (PET) are described. The intersegment forces perturb the electronic spectra and induce ground-state aggregation. These phenomena become observable at different chain densities, reflecting the influence of concentration on the coil dimensions, as well as the dynamical nature of the interactions. An estimate of the equilibrium constant for PET dimer formation in hexafluoroisopropanol is reported.