A priori estimates for rough PDEs with application to rough conservation laws

We introduce a general weak formulation for PDEs driven by rough paths, as well as a new strategy to prove well-posedness. Our procedure is based on a combination of fundamental a priori estimates with (rough) Gronwall-type arguments. In particular this approach does not rely on any sort of transformation formula (flow transformation, Feynman–Kac representation formula etc.) and is therefore rather flexible. As an application, we study conservation laws driven by rough paths establishing well–posedness for the corresponding kinetic formulation.     

A Copper(I)-Catalyzed Sulfonylative Hiyama Cross-Coupling

An air-tolerant Cu-catalyzed sulfonylative Hiyama cross-coupling reaction enabling the formation of diaryl sulfones is described. Starting from aryl silanes, DABSO and aryliodides, the reaction tolerates a large variety of polar functional groups (amines, ketones, esters, aldehydes). Control experiments coupled with DFT calculations shed light on the mechanism, characterized by the formation of a Cu(I)-sulfinate intermediate via fast insertion of a SO₂ molecule.     

Dissolved Cu(II) Speciation in Unpolluted Soil Solutions of a Planosolic Horizon

Dissolved Cu(II) speciation in unpolluted soil solutions from different horizons was studied using differential pulse anodic stripping voltammetry (DPASV). Three sites were selected according to topography and monitored for three years. Experiments evidence Cu(II) can be bound by DOM (Dissolved Organic Matter) through complexation and/or adsorption reactions. The complexation capacity and the corresponding conditional stability constant were determined for complexation reactions. The adsorbing sites were titrated. A potential binding coefficient was calculated to compare both types of reactions. Results show adsorption is less frequent than complexation but exhibits higher binding coefficient.     

Surface characterizations of fluorescent-functionalized silica nanoparticles: from the macroscale to the nanoscale

Journal of Nanoparticle Research - Fluorescent silica nanoparticles are widely used for various applications from mechanical reinforcement to biology. In many cases, their surface has to be...     

Improved method for the iodine(III)-mediated preparation of aryl sulfonimidates

[reaction: see text] One-pot hypervalent iodine-mediated oxidations of arylsulfinamides to arylsulfonimidates is reported. Contrary to the case of alkylsulfinamides, use of iodosobenzene was not satisfactory. The reaction worked best with diacetoxyiodosobenzene (DIB) and a mild base (MgO). The influence of substituents on the iodine(III) reagent arene has been examined.     

Capillary electrophoresis–electrospray mass spectrometry and HR–ICP–MS for the detection and quantification of 10B-boronophenylalanine (10B–BPA) used in boron neutron capture therapy

Boron neutron capture therapy (BNCT) is a bimodal radiotherapeutic treatment based on the irradiation of neoplastic tissues with neutrons after the tissues have selectively accumulated molecules loaded with nuclides with large neutron capture cross-sections (such boron-10). Boron-10 carriers have been tested to a limited extent, and clinical trials have been conducted on sulfhydryl borane (¹⁰B-BSH) and boronophenylalanine (¹⁰B-BPA). However, precise and accurate measurements of boron-10 concentrations (0.1–100 μg/g) in specimens and samples of limited size (μg scale) are needed in order to be able to biologically characterise new compounds in predictive tissue dosimetry, toxicology and pharmacology studies as well as in clinical investigations. A new approach based on fast separation and detection of ¹⁰B-BPA performed by coupling capillary electrophoresis to electrospray mass spectrometry is reported. This method allows the quantitative analysis and characterisation of ¹⁰B-BPA in a short time with a high separation efficiency. Detection limits of 3 μM for ¹⁰B-BPA and 30 ng/mL for ¹⁰B were obtained with CE–ESI–MS. A quantification limit of 10 μM for ¹⁰B-BPA (100 ng/mL for ¹⁰B) was attained. The total boron-10 concentration was determined by high-resolution inductively coupled mass spectrometry in order to validate the method. Boron-10 isotope measurements were carried out by HR–ICP–MS at medium resolution (R=4000) due to the presence of an isobaric interference at mass 10. Good agreement was obtained between the values from CE–ESI–MS and those from HR–ICP–MS. The method has been successfully used to determine the ¹⁰B-BPA in two lines of cultured cells.     

Real-space observation of spectral degeneracy breaking in a waveguide-coupled disk microresonator

We report on the real-space observation of resonant frequency splitting in a high-Q waveguide-coupled silicon-on-insulator microdisk resonator. Phase sensitive near-field analysis reveals the stationary nature of the two resonant states, and spectral investigations clearly show their orthogonality. These measurements emphasize the role of the coupling waveguide in this splitting phenomenon. The symmetry of the two stationary whispering gallery modes is clearly observed and is found to follow the axial symmetry of the waveguide-coupled microdisk as it has been reported by earlier theoretical predictions.     

On stochastic calculus with respect to q-Brownian motion

Following the approach and the terminology introduced in Deya and Schott (2013) [6], we construct a product Lévy area above the q-Brownian motion (for $q\in [0,1)$) and use this object to study differential equations driven by the process.We also provide a detailed comparison between the resulting “rough” integral and the stochastic “Itô” integral exhibited by Donati-Martin (2003) [7].