Positivity of Lyapunov Exponents for a Continuous Matrix-Valued Anderson Model

We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all energies in (2, +∞) except those in a discrete set, which leads to absence of absolutely continuous spectrum in (2, +∞). This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions.      

Direct 2-Arylation of Thiophene Using Low Loading of a Phosphine-Free Palladium Catalyst

The direct coupling of aryl halides with thiophene would be a considerable advantage for sustainable development because of only HBr associated with a base as by-product is formed and the number of steps to prepare these compounds is less than in more classical coupling reactions. We observed that through the use of only 0.2 mol% Pd(OAc)₂ as the catalyst, a range of aryl bromides undergoes coupling via a C-H bond activation/functionalization reaction with thiophene to give 2-arylated thiophenes in good yields. In most cases, only traces of polyarylated thiophenes were detected when a large excess of thiophene was employed. This air-stable catalyst can be used with a wide variety of aryl bromides.      

Palladium-catalysed direct arylations of heteroaromatics using more eco-compatible solvents pentan-1-ol or 3-methylbutan-1-ol

The palladium-catalysed direct coupling of aryl halides with heteroaromatics in greener solvents than DMF or DMAc, which are often employed for such couplings, would be a considerable advantage for both industrial application and sustainable development. We observed that a range of aryl bromides undergoe coupling via C-H bond activation/functionalisation reaction of thiazoles or imidazoles in moderate to good yields using pentan-1-ol or 3-methylbutan-1-ol as the solvents. Pentan-1-ol and 3-methylbutan-1-ol are less toxic than DMF or DMAc, moreover they are bioresources as they can be obtained by fermentation. Therefore, these reaction conditions are certainly more eco-compatible than those generally employed for such couplings.     

Photoelectrochemical study of La2NiO4 synthesized using citrate sol gel method—application for hydrogen photo-production

Journal of Solid State Electrochemistry - The semi conducting properties of La2NiO4 synthesized through sol gel method are studied for the first time using photoelectrochemistry. The X-ray...     

Mechanistic study on the enzymatic oxidation of flavonols

Several flavonols have been transformed upon treatment by Trametes versicolor laccase. Most of the major oxidation products have been isolated by HPLC as pure compounds and their structures have been, when possible, investigated through spectral methods (HPLC-MS and NMR). The results are coherent with the predominance of a dismutation process, leading to cation formation, over direct radical-radical coupling.     

Flavonoids: hemisynthesis, reactivity, characterization and free radical scavenging activity

Phenolic compounds form one of the main classes of secondary metabolites. They display a large range of structures and they are responsible for the major organoleptic characteristics of plant-derived-foods and beverages, particularly color and taste properties and they also contribute to the nutritional qualities of fruits and vegetables. Phenolic compounds are also highly unstable compounds which undergo numerous enzymatic and chemical reactions during postharvest food storage and processing thus adding to the complexity of plant polyphenol composition. Among these compounds flavonoids constitute one of the most ubiquitous groups of all plant phenolics. Owing to their importance in food organoleptic properties and in human health, a better understanding of their structures, their reactivity and chemical properties in addition to the mechanisms generating them appears essential to predict and control food quality. The purpose of this work is an overview of our findings concerning the hemisynthesis, the reactivity and the enzymatic oxidation of some flavonoids and shed light on the mechanisms involved in some of these processes and the structures of the resulting products. The free radical scavenging activity of some of the synthesized compounds is also presented and a structure-activity relationship is discussed. The first part of this review concerns the synthesis and structural characterization of modified monomeric flavanols. The use of these compounds as precursor for the preparation of natural and modified dimeric procyanidin derivatives was then explored through different coupling reactions. The full characterization of the synthesized compounds was achieved by concerted use of NMR and ESI-MS techniques. The free radical scavenging activity of some of the synthesized compounds was investigated. The second part of this review concerns the enzymatic oxidation of several flavonols by Trametes versicolor laccase. Most of the major oxidation products have been isolated as pure compounds and their structures unambiguously established through spectroscopic methods. Correlation between the structure of the oxidation product and the substitution pattern of the starting materials allows mechanistic features of this transformation to be elucidated.     

A Matrix-Valued Point Interactions Model

We study a matrix-valued Schrödinger operator with random point interactions. We prove the absence of absolutely continuous spectrum for this operator by proving that, away from a discrete set, its Lyapunov exponents do not vanish. For this we use a criterion by Gol’dsheid and Margulis and we prove the Zariski denseness, in the symplectic group, of the group generated by the transfer matrices. Then we prove estimates on the transfer matrices which lead to the Hölder continuity of the Lyapunov exponents. After proving the existence of the integrated density of states of the operator, we also prove its Hölder continuity by proving a Thouless formula which links the integrated density of states to the sum of the positive Lyapunov exponents.     

Localization for a Matrix-valued Anderson Model

We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schrödinger operators, acting on $L^2(\mathbb R)\otimes \mathbb C^NWe study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr?dinger operators, acting on , for arbitrary N ≥ 1. We prove that, under suitable assumptions on the Fürstenberg group of these operators, valid on an interval , they exhibit localization properties on I, both in the spectral and dynamical sense. After looking at the regularity properties of the Lyapunov exponents and of the integrated density of states, we prove a Wegner estimate and apply a multiscale analysis scheme to prove localization for these operators. We also study an example in this class of operators, for which we can prove the required assumptions on the Fürstenberg group. This group being the one generated by the transfer matrices, we can use, to prove these assumptions, an algebraic result on generating dense Lie subgroups in semisimple real connected Lie groups, due to Breuillard and Gelander. The algebraic methods used here allow us to handle with singular distributions of the random parameters.