An algebra of meromorphic corner symbols

Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.     

Resonant Raman scattering by strained and relaxed germanium quantum dots

This paper reports on the results of resonant Raman scattering investigations of the fundamental vibrations in Ge/Si structures with strained and relaxed germanium quantum dots. Self-assembled strained Ge/Si quantum dots are grown by molecular-beam epitaxy on Si(001) substrates. An ultrathin SiO₂ layer is grown prior to the deposition of a germanium layer with the aim of forming relaxed germanium quantum dots. The use of resonant Raman scattering (selective with respect to quantum dot size) made it possible to assign unambiguously the line observed in the vicinity of 300 cm^?1 to optical phonons confined in relaxed germanium quantum dots. The influence of confinement effects and mechanical stresses on the vibrational spectra of the structures with germanium quantum dots is analyzed.     

Justification of the Shallow-Water Limit for a Rigid-Lid Flow with Bottom Topography

The so-called lake equations arise as the shallow-water limit of the rigid-lid equations—three-dimensional Euler equations with a rigid-lid upper boundary condition—in a horizontally periodic basin with bottom topography. We prove an a priori estimate in the Sobolev space H ^m for m≥ 3 which shows that a solution to the rigid-lid equations can be approximated by a solution of the lake equations for an interval of time which can be estimated in terms of the initial deviation from a columnar configuration and the magnitude of the initial data in H ^m , the gradient of the bottom topography in H ^m+1 , and the aspect ratio of the basin. In particular, any solution to the lake equations remains close to some solution of the rigid-lid equations for an interval of time that can be made arbitrarily large by choosing the aspect ratio of the basin small. Received 10 October 1996 and accepted 15 May 1997     

Une axiomatisation de la substitution

We investigate the notion of substitution in an abstract way, without defining it explicitly. We single out the essential features of the operation of performing a substitution in order to define a concept of substitutive structure, called logos. We then prove a completeness theorem making precise and justifying the intuition that formulas true for the usual substitution can be proved from the logos axioms only. To cite this article: M. Crabbé, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Stability of translating solutions to mean curvature flow

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates. The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions of Non-linear Evolution Equations”.     

The Dedekind-MacNeille completion as a reflector

We introduce a special type of order-preserving maps between quasiordered sets, the so-called cut-stable maps. These form the largest morphism class such that the corresponding category of quasiordered sets contains the category of complete lattices and complete homomorphisms as a full reflective subcategory, the reflector being given by the Dedekind-MacNeille completion (alias normal completion or completion by cuts). Suitable restriction of the object class leads to the category of separated quasiordered sets and its full reflective subcategory of completely distributive lattices. Similar reflections are obtained for continuous lattices, algebraic lattices, etc.     

Untersuchung von Textilien und Textilrohstoffen

Ohne Zusammenfassung     

Rigid nitronyl-nitroxide-labelled anchoring molecules: syntheses, structural and magnetic investigations

The syntheses of two rigid organic molecular rods bearing a nitronyl-nitroxide radical and a terminal nitrogen-based functionality like a pyridine or a cyano group are reported. Both new paramagnetic molecules are fully characterized, including crystal structure analysis. Furthermore their magnetic behaviours in the crystalline state are investigated and their spin concentration corroborate their excellent purity. While the pyridine functionalized rod is synthesized by converting the corresponding benzaldehyde to the phenyl-nitronyl-nitroxide radical, the synthesis of the cyano functionalized rod demonstrates the accessibility of highly sophisticated spin-labelled molecules via cross-coupling reaction with a meta-iodo-phenyl-nitronyl-nitroxide moiety.