Estimation du nombre des μ-valeurs propres

La notion de -valeur propre de –+V sera définie pour un ouvert borné de R ^d ; étant une mesure dans la classe de Kato généralisée. On établira une estimation du nombre des -valeurs propres inférieures à un réel positif E.The notion of -eigenvalue of –+V will be defined for a bounded open subset of R ^d ; is in the generalized Kato class. An estimate for the number of -eigenvalues which are smaller then a positive real E is given.     

Influence of attenuation on the behavior of refracted elastic waves at the interface between anisotropic media

During the ultrasonic non-destructive evaluation of complex materials, like multilayer or composite materials, the behavior of the ultrasonic waves at the interface of samples is strongly dependent upon the anisotropy as well as the attenuation characteristics of the propagation media. In the generally arbitrary case, the incident wave is assumed to be inhomogeneous. Therefore the application of the Snell-Descartes laws requires to consider the real as well as the imaginary parts of all the quantities encountered during the study. In that aim, we use a representation of the complex slowness curves so-called slowness interface curves which point out the evolution of the interaction of the waves at the interface with the inhomogeneity factors, i.e. the imaginary part of the slowness vectors. The continuous distortion of the curves with the inhomogeneity factor increasing is an interesting approach of these complicated phenomena.     

New chromogenic probes into nanoscopic pockets in enhanced sensing protocols for amines in aqueous environments

[structure: see text] A new sensory MCM-41-based material for the colorimetric sensing and discrimination of amines has been developed.     

Solution processable high band gap hosts based on carbazole functionalized cyclic phosphazene cores for application in organic light‐emitting diodes

A new class of solution processable dendrimers based on cyclic phosphazene (CP) cores have been prepared and used as host materials for blue and green organic light emitting diodes (OLEDs). The dendrimers are prepared in high yield from minimal step reactions, are soluble in common solvents for solution processing, are amorphous, and have excellent thermal properties necessary for application in OLEDs. OLED efficiencies of 10.3 cd/A (4.2 lm/W) and 35.3 cd/A (33.5 lm/W) were achieved using commercially available FIrpic and Ir(mppy)₃ as blue and green phosphorescent emitters, respectively. These efficiencies were 2× higher than control devices prepared using poly(N‐vinylcarbazole), the most commonly used host material in solution processed phosphorescent OLEDs. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Direct and Inverse Spectral Theory of One-dimensional Schrödinger Operators with Measures

We present a direct and rather elementary method for defining and analyzing one-dimensional Schrödinger operators H = −d²/dx² + μ with measures as potentials. The basic idea is to let the (suitably interpreted) equation −f′′ + μ f = zf take center stage.We show that the basic results from direct and inverse spectral theory then carry over to Schrödinger operators with measures.