Multiplicity results for fractional Schrödinger-Kirchhoff systems involving critical nonlinearities

In this article, we study certain critical Schrödinger-Kirchhoff-type systems involving the fractional $p$-Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari manifold sets and exploiting the analysis of the fibering map, we establish the multiplicity of solutions for such systems

Multiplicity results for fractional Schrödinger-Kirchhoff systems involving critical nonlinearities

In this article, we study certain critical Schrödinger-Kirchhoff-type systems involving the fractional pp-Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari manifold sets and exploiting the analysis of the fibering map, we establish the multiplicity of solutions for such systems

La transition terre-mer dans la transgression du crétace inférieur d’Afrique du nord : exemple du wealdien des chotts, Tunisie méridionale

International audienc

Do evaporites record tides ? Observations in the Lower Cretaceous of Southern Tunisia

International audienc

High Performance InP-Based Quantum Dash Semiconductor Mode-Locked Lasers for Optical Communications

Several applications are pushing the development of high performance mode-locked lasers: generation of short pulses for extremely high bit rate transmission at 100 Gb/s and beyond, all-optical clock recovery at 40 Gb/s and beyond, generation of millimeter wave signals through mode-beating on a high speed photodiode, optical sampling for analog-to-digital conversion, and generation of wavelength-division-multiplexing channels. This paper will report on new advances in InP-based quantum dash mode-locked lasers, which largely surpass the performance of their bulk or quantum well counterparts in terms of the mode-beating spectral purity and the bandwidth of optical spectrum. In particular, we will describe the quantum dash nanostructures used for the mode-locked lasers and the dependence of the mode-locking properties on detailed quantum dash structures. We will demonstrate that these quantum dash lasers can be actively mode-locked, generating sub-picosecond or picosecond pulses at different repetition frequencies with extremely low timing jitter. They can also be used to achieve all-optical clock recovery, with timing jitter compliant with International Telecommunication Union (ITU) standards even for highly degraded input optical signal-to-noise ratio. Finally, we demonstrate that, owing to the very wide and flat optical spectrum and the low relative-intensity noise level of the mode-locked laser, error-free transmission over 50 km single mode fiber has been achieved for eight wavelength division multiplexing ITU channels at 10 Gb/s with a channel spacing of 100 GHz. (C) 2009 Alcatel-Lucent