On some properties of the number of permutations being products of pairwise disjoint d-cycles

Monatshefte für Mathematik - Let $$d\ge 2$$ be an integer. In this paper we study arithmetic properties of the sequence $$(H_d(n))_{n\in \mathbb {N}}$$, where $$H_{d}(n)$$ is the number of...     

Raman and FTIR spectroscopy applied to the conservation report of paleontological collections: identification of Raman and FTIR signatures of several iron sulfate species such as ferrinatrite and sideronatrite

Fossil materials that contain iron sulfide are well known for their instability when exposed to oxygen and humidity. This term however combines a great variety of materials showing different types of damages. Most of them consist of crystal efflorescence appearing on the surface and inside the matrix. In this work, a methodology was determined for the analysis of these damages by the use of Raman and infrared spectroscopy. The infrared and Raman signatures of a large set of iron sulfates were characterized. Specific attention was paid to sideronatrite and ferrinatrite, which are two associated sodium/iron(III) sulfates, and their infrared and Raman bands were partially assigned. Analysis performed on a selection of 11 damaged fossils showed a great variety of degradation products: besides one case that appeared to be a synthetic resin close to polyvinylchloride acetate, which was applied with a brush on the fossil surface, all degradation products belong to the sulfate group. However, many iron‐free sulfates, such as gypsum, halotrichite, epsomite, or pentahydrite were found, often in association with iron sulfates. In one case, despite the presence of iron in the matrix, no iron sulfate could be detected. This shows that the term ‘pyritic fossil’, commonly used by collection managers, is not appropriate as it oversimplifies the reality. A name such as ‘sulfide‐containing fossil’ would be more suitable. Copyright © 2012 John Wiley & Sons, Ltd.     

Influence of the SiO thickness on the photoluminescence properties of Er-doped SiO/SiO2 multilayers

Er-doped SiO single layer and Er-doped SiO/SiO₂ multilayers with different SiO thicknesses were prepared by evaporation. In the as-deposited samples, the erbium ions exhibit a very weak photoluminescence emission at 1.54 μm. This luminescence is strongly enhanced after annealing treatments between 500 and 1050 °C, with an optimal annealing temperature which is dependent from the SiO thickness. For the SiO single layer, this optimal temperature is around 700 °C while it is shifted at highest temperature for the multilayers. The origin of the higher luminescence intensity in the SiO layer is also discussed.     

Simulation of MCAO on (extremely) large telescopes

In this article, we describe the different methods to simulate Multi-Conjugate Adaptive Optics (MCAO) systems. First, analytical (error-budget type) and semi-analytical (Fourier) methods are described. We then describe the different modules required to make end-to-end (Monte Carlo) simulations of these systems. Finally, we present some of the computational challenges associated with the simulation of MCAO on Extremely Large Telescopes (ELTs). To cite this article: M. Le Louarn et al., C. R. Physique 6 (2005).     

MAD: practical implementation of MCAO concepts

The European Southern Observatory (ESO) together with external research institutes have built a Multi-Conjugate Adaptive Optics (MCAO) Demonstrator (MAD) to perform wide field-of-view adaptive optics correction (2′ in K band). The aim of MAD is to demonstrate the on-sky feasibility of the MCAO technique and to evaluate its critical aspects in the framework of both the 2nd generation instrumentation for the Very Large Telescope (VLT) and the Overwhelmingly Large Telescope (OWL). The MAD module will be installed on the VLT to perform on-sky observations. MAD comprises two deformable mirrors and two different multi-reference wavefront sensors with natural guide stars. In this article we present the MAD design, some aspects of the MAD calibration and the first closed-loop results in the laboratory in Single Conjugated Adaptive Optics (SCAO) and Ground Layer Adaptive Optics (GLAO) configurations. To cite this article: E. Marchetti et al., C. R. Physique 6 (2005).     

Ground Layer Adaptive Optics

We will introduce the present knowledge of the turbulence profile and in particular we will emphasise the existence of a turbulence layer close to the ground. Then we will present the concept of Ground Layer Adaptive Optics and will provide estimates of performance expected from such systems and their potential for astronomical applications. Finally we will provide practical implementation concepts for two instruments at the VLT, MUSE and HAWK-I using multi-Laser Guide Stars and a large Deformable Secondary Mirror. The latter will also be described as its use is optimum for GLAO systems. To cite this article: N. Hubin et al., C. R. Physique 6 (2005).     

Synthesis of an Iron(IV) Aqua–Oxido Complex Using Ozone as an Oxidant

The iron(IV) oxido complex [(tmc)Fe=O(OTf)]OTf with the macrocyclic ligand 1,4,8,11‐tetramethyl‐1,4,8,11‐tetraazacyclo‐tetradecane (tmc) has been synthesized using ozone as an oxidant. By adding water to this compound the complex [(H₂O)(tmc)Fe=O)](OTf)₂ could be prepared. This complex is important in regard to a better understanding of the reactivity of Fe^IV oxido complexes. Mössbauer measurements using the solid compound showed an isomer shift of δ=0.19 mm s^?1 and a quadrupole splitting ΔE_Q=1.38 mm s^?1, confirming the high‐valent Fe^IV state. DFT calculations were performed and led to an assignment of triplet spin multiplicity. Crystallographic characterization of [(H₂O)(tmc)Fe=O)](OTf)₂ as well as of starting materials [(tmc)Fe(CH₃CN)](OTf)₂ and [(tmc)Fe(OTf)]OTf together with previous results strongly suggest that [(H₂O)(tmc)Fe=O)](OTf)₂ was formed similar to the oxido–hydroxido tautomerism analogous to heme systems.