The application of triphenylmethane dyes to visualization of selected aliphatic compounds in thin-layer chromatography

Selected triphenylmethane dyes were used as new visualizing agents in thin-layer chromatography of higher fatty acids, higher fatty alcohols, and higher aliphatic amines.     

Nonlinear diffusion and Nelson-Brown movement

The nonlinear diffusion process, which can be described as the Nelson-Brown motion, is considered. The obtained equation becomes the classical linear diffusion equation for small relaxation times, and for long relaxation times it is transferred into the Schrödinger-like equation. The possible nonequilibrium stationary states are discussed.     

Imaging electron trajectories in a laser-wakefield cavity using betatron X-ray radiation

We demonstrate that betatron x-ray radiation accurately provides direct imaging of electrons trajectories accelerated in laser wakefields. Experimental far field x-ray beam profiles reveal that electrons can follow similar transverse trajectories with typical excursions of 1.5 microm+/-0.5 microm in the plane of laser polarization and 0.7 microm+/-0.2 microm in the plane perpendicular.     

Formation of Amphiphilic Molecules from the Most Common Marine Polysaccharides,toward a Sustainable Alternative?

Marine polysaccharides are part of the huge seaweeds resources and present many applications for several industries. In order to widen their potential as additives or bioactive compounds, some structural modifications have been studied. Among them, simple hydrophobization reactions have been developed in order to yield to grafted polysaccharides bearing acyl-, aryl-, alkyl-, and alkenyl-groups or fatty acid chains. The resulting polymers are able to present modified physicochemical and/or biological properties of interest in the current pharmaceutical, cosmetics, or food fields. This review covers the chemical structures of the main marine polysaccharides, and then focuses on their structural modifications, and especially on hydrophobization reactions mainly esterification, acylation, alkylation, amidation, or even cross-linking reaction on native hydroxyl-, amine, or carboxylic acid functions. Finally, the question of the necessary requirement for more sustainable processes around these structural modulations of marine polysaccharides is addressed, considering the development of greener technologies applied to traditional polysaccharides.     

Probabilistic representation and approximation for coupled systems of variational inequalities

Our study is dedicated to the probabilistic representation and numerical approximation of solutions of coupled systems of variational inequalities. We interpret the unique viscosity solution of a coupled system of variational inequalities as the solution of a one-dimensional constrained BSDE with jumps. This new representation allows for the introduction of a natural probabilistic numerical scheme for the resolution of these systems.     

A simple constructive approach to quadratic BSDEs with or without delay

This paper provides a simple approach for the consideration of quadratic BSDEs with bounded terminal conditions. Using solely probabilistic arguments, we retrieve the existence and uniqueness result derived via PDE-based methods by Kobylanski (2000) [14]. This approach is related to the study of quadratic BSDEs presented by Tevzadze (2008) [19]. Our argumentation, as in Tevzadze (2008) [19], highly relies on the theory of BMO martingales which was used for the first time for BSDEs by Hu et al. (2005) [12]. However, we avoid in our method any fixed point argument and use Malliavin calculus to overcome the difficulty. Our new scheme of proof allows also to extend the class of quadratic BSDEs, for which there exists a unique solution: we incorporate delayed quadratic BSDEs, whose driver depends on the recent past of the Y$Y$ component of the solution. When the delay vanishes, we verify that the solution of a delayed quadratic BSDE converges to the solution of the corresponding classical non-delayed quadratic BSDE.     

Decompositions of the free additive convolution

We introduce and study a new type of convolution of probability measures, denoted μν and called the s-free additive convolution, which is defined by the subordination functions associated with the free additive convolution. We derive an alternating decomposition of μν for compactly supported μ and ν, using another convolution called orthogonal additive convolution. This decomposition leads to two types of ‘complete’ alternating decompositions of the free additive convolution μ?ν. More importantly, we develop an operatorial approach to the subordination property and introduce the associated notion of s-free independence. Moreover, we establish relations between convolutions associated with the main notions of noncommutative independence (free, monotone and boolean). Finally, our result leads to natural decompositions of the free product of rooted graphs.     

Multicentered effective group potentials: ligand-field effects in organometallic clusters and dynamical study of chemical reactivity

A new multicentered effective group potential (EGP) is obtained for η⁶-benzene. Applications on $[\hbox{Ru}_{4}(\hbox{H})_{4}(\hbox{C}_{6}\hbox{H}_{6})_{4}]^{n+}$ clusters (n = 0 or 2) are in excellent agreement with reference DFT studies in terms of geometries, energies and electronic structures. In particular, the small singlet–triplet energy difference (3.8 kcal mol^?1) in [Ru₄(H)₄(C₆H₆)₄]²⁺ is very well reproduced. This new EGP is nevertheless not free from the limitations associated to this first generation of molecular pseudopotentials. A cautious analysis of the nature and exact role of this EGP is made, which provides new directions for the elaboration of the next generation of EGPs. In addition, the η⁵-cyclopentadienyl EGP has been used to perform a constrained dynamical simulation for the reaction of Cp₂LaH with H₂. The energy conservation during the simulation as well as the activation barrier extracted from the simulation clearly demonstrate the good behavior of this EGP in the context of molecular dynamics. Anharmonic effects on this reaction are underlined, further demonstrating the high accuracy of the potential energy surface obtained with EGPs. From a more general point of view, such EGPs are expected to provide accurate albeit low-cost ligand-field effects in organometallic clusters or nanoparticles and to allow dynamical studies at the surface of such compounds.     

Hydrogen Isotope Exchange Catalyzed by Ru Nanocatalysts: Labelling of Complex Molecules Containing N-Heterocycles and Reaction Mechanism Insights

Ruthenium nanocatalysis can provide effective deuteration and tritiation of oxazole, imidazole, triazole and carbazole substructures in complex molecules using D₂ or T₂ gas as isotopic sources. Depending on the substructure considered, this approach does not only represent a significant step forward in practice, with notably higher isotope uptakes, a broader substrate scope and a higher solvent applicability compared to existing procedures, but also the unique way to label important heterocycles using hydrogen isotope exchange. In terms of applications, the high incorporation of deuterium atoms, allows the synthesis of internal standards for LC-MS quantification. Moreover, the efficacy of the catalyst permits, even under subatmospheric pressure of T₂ gas, the preparation of complex radiolabeled drugs owning high molar activities. From a fundamental point of view, a detailed DFT-based mechanistic study identifying undisclosed key intermediates, allowed a deeper understanding of C−H (and N−H) activation processes occurring at the surface of metallic nanoclusters.