Inégalités de Poincaré cinétiques

In this Note we prove Poincaré type inequalities for a family of kinetic equations. We apply this inequality to the variational solution of a linear kinetic model by generalizing the STILS method (Azerad, 1996 [1]; Azerad and Pousin, 1996 [2]) to a kinetic setting.     

Nevanlinna counting function and Carleson function of analytic maps

We show that the maximal Nevanlinna counting function and the Carleson function of analytic self-maps of the unit disk are equivalent, up to constants.     

Dual-Color Photoconvertible Fluorescent Probes Based on Directed Photooxidation Induced Conversion for Bioimaging

We herein present a new concept to produce dual-color photoconvertible probes based on a mechanism called Directed Photooxidation Induced Conversion (DPIC). As a support of this mechanism, styryl-coumarins ( SCs ) bearing Aromatic Singlet Oxygen Reactive Moieties (ASORMs) like furan and pyrrole have been synthesized. SCs are bright fluorophores, which undergo a hypsochromic conversion upon visible light irradiation due to directed photooxidation of the ASORM that leads to the disruption of conjugation. SC-P , a yellow emitting probe bearing a pyrrole moiety, converts to a stable blue emitting coumarin with a 68 nm shift allowing the photoconversion and tracking of lipid droplet in live cells. This new approach might pave the way to a new generation of photoconvertible dyes for advanced bioimaging applications.     

Super-Oxidizing Covalent Triazine Framework Electrocatalyst for Two-Electron Water Oxidation to H2O2

Electrochemical two-electron water oxidation (2e WOR) is gaining surging research traction for sustainable hydrogen peroxide production. However, the strong oxidizing environment and thermodynamically competitive side-reaction (4e WOR) posit as thresholds for the 2e WOR. We herein report a custom-crafted covalent triazine network possessing strong oxidizing properties as a proof-of-concept metal-free functional organic network electrocatalyst for catalyzing 2e WOR. As the first-of-its-kind, the material shows a maximum of 89.9 % Faradaic Efficiency and 1428 μmol/h/cm² H₂O₂ production rate at 3.0 V bias potential (vs reversible hydrogen electrode, RHE), which are either better or comparable to the state-of-the-art electrocatalysts. We have experimentally confirmed a stepwise 2e WOR mechanism which was further computationally endorsed by density functional theory studies.     

Vertex partitions of (C3,C4,C6)-free planar graphs

A graph is $(k_1,k_2)$-colorable if it admits a vertex partition into a graph with maximum degree at most $k_1$ and a graph with maximum degree at most $k_2$. We show that every $(C_3,C_4,C_6)$-free planar graph is $(0,6)$-colorable. We also show that deciding whether a $(C_3,C_4,C_6)$-free planar graph is $(0,3)$-colorable is NP-complete.     

Incorporation of a minimal nucleotide into DNA

Abasic sites are amongst the most frequent DNA lesions and result from spontaneous hydrolysis of the glycosidic bond or from the removal of damaged nucleobases. These depurination events can also occur on free deoxyribonucleoside triphosphates present in cells and lead to the formation of an abasic site triphosphate of which very little is known. Herein, we report the synthesis and biochemical characterization of the minimal triphosphate dФTP. Unexpectedly, dФTP is tolerated by various DNA polymerases and the incorporation efficiency obeys the A-rule. Single incorporation of dФMP units were also observed opposite abasic sites and the addition of prosthetic molecules mimicking base-pairs do not seem to favor the process.     

Cyclic and ruled Lagrangian surfaces in Euclidean four space

We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a Legendrian curve in the 3-sphere or a Legendrian curve in the anti-de Sitter 3-space. We describe ruled Lagrangian surfaces and characterize the cyclic and ruled Lagrangian surfaces which are solutions to the self-similar equation of the Mean Curvature Flow. Finally, we give a partial result in the case of Hamiltonian stationary cyclic surfaces.     

Ionic Liquid Crystals Formed by Self‐Assembly around an Anionic Anthracene Core

We have designed and synthesised a series of modular, mesogenic complexes based on anthracene‐2,6‐disulfonate and trialkoxybenzyl‐functionalised imidazolium cations. Each complex contains a central, rigid, dianionic anthracene core and two flexible monocations bearing paraffin chains anchored on imidazolium rings. Anthracene‐2,6‐disulfonate can be crystallised with various simple alkylammonium ions and, in the case of ⁺N(CH₃)₂(C₁₆H₃₃)₂, a crystal structure determination has shown that the long paraffinic chains are intercalated between the anthracene moieties. The dianion forms columnar mesophases with trialkoxybenzylimidazolium cations, as identified by polarising optical microscopy and X‐ray scattering measurements. Differential scanning calorimetry studies confirmed mesomorphic behaviour from room temperature to about 200 °C for alkyl chains containing 8, 12 and 16 carbon atoms. The strong luminescence of anthracene is maintained in the mesophase and fluorescence measurements confirmed the presence of J aggregates in all cases. The new functional materials described herein provide an easy access to stable and luminescent mesomorphic materials engineered by an ionic self‐assembly process.