On Saint Venant's compatibility conditions and Poincaré's lemma

Saint Venant's theorem constitutes a classical characterization of smooth matrix fields as linearized strain tensor fields. This theorem has been extended to matrix fields with components in $L^2$ by the second author and P. Ciarlet, Jr. in 2005. One objective of this Note is to further extend this characterization to matrix fields whose components are only in $H^{\mathrm{?1}}$. Another objective is to demonstrate that Saint Venant's theorem is in fact nothing but the matrix analog of Poincaré's lemma. To cite this article: C. Amrouche et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Quality control system design through the goal programming model and the satisfaction functions

The goal programming (GP) model has been utilized for designing a quality control system (QCS) where several features are simultaneously considered. In the context of the quality control, the parameters can be imprecise and expressed through intervals. The aim of this paper is to propose two formulations for designing a QCS based on the imprecise GP model. The concept of satisfaction functions will be utilized to integrate explicitly the decision-maker’s preference. The developed formulations are illustrated through an example of a paper factory.     

Quality of treated wastewater: method validation of AOX

The reuse of treated wastewater and its release into the environment calls for a validated method for the determination of toxic compounds. We validate the method recommended by EN 1485 standard for AOX that are water soluble organic halides and describe it in two parts. The first part shows the validation by parameters such as applicability, accuracy, and reproducibility. After testing the normality of the statistical distribution of “the measured AOX concentration”, linearity, repeatability, limits of detection and limits of quantitation are calculated. The second part describes the routine use of the validated method.     

Design,Microwave-Assisted Synthesis and In Silico Prediction Study of Novel Isoxazole Linked Pyranopyrimidinone Conjugates as New Targets for Searching Potential Anti-SARS-CoV-2 Agents

A series of novel naphthopyrano[2,3-d]pyrimidin-11(12H)-one containing isoxazole nucleus 4 was synthesized under microwave irradiation and classical conditions in moderate to excellent yields upon 1,3-dipolar cycloaddition reaction using various arylnitrile oxides under copper(I) catalyst. A one-pot, three-component reaction, N-propargylation and Dimroth rearrangement were used as the key steps for the preparation of the dipolarophiles3. The structures of the synthesized compounds were established by ¹H NMR, ¹³C NMR and HRMS-ES means. The present study aims to also predict the theoretical assembly of the COVID-19 protease (SARS-CoV-2 M^pro) and to discover in advance whether this protein can be targeted by the compounds 4a–1 and thus be synthesized. The docking scores of these compounds were compared to those of the co-crystallized native ligand inhibitor (N3) which was used as a reference standard. The results showed that all the synthesized compounds (4a–l) gave interesting binding scores compared to those of N3 inhibitor. It was found that compounds 4a, 4e and 4i achieved greatly similar binding scores and modes of interaction than N3, indicating promising affinity towards SARS-CoV-2 M^pro. On the other hand, the derivatives 4k, 4h and 4j showed binding energy scores (−8.9, −8.5 and −8.4 kcal/mol, respectively) higher than the M^pro N3 inhibitor (−7.0 kcal/mol), revealing, in their turn, a strong interaction with the target protease, although their interactions were not entirely comparable to that of the reference N3.     

Non-PGM Electrocatalysts for PEM Fuel Cells: A DFT Study on the Effects of Fluorination of FeNx-Doped and N-Doped Carbon Catalysts

Fluorination is considered as a means of reducing the degradation of Fe/N/C, a highly active FeN_x-doped disorganized carbon catalyst for the oxygen reduction reaction (ORR) in PEM fuel cells. Our recent experiments have, however, revealed that fluorination poisons the FeN_x moiety of the Fe/N/C catalytic site, considerably reducing the activity of the resulting catalyst to that of carbon only doped with nitrogen. Using the density functional theory (DFT), we clarify in this work the mechanisms by which fluorine interacts with the catalyst. We studied 10 possible FeN_x site configurations as well as 2 metal-free sites in the absence or presence of fluorine molecules and atoms. When the FeN_x moiety is located on a single graphene layer accessible on both sides, we found that fluorine binds strongly to Fe but that two F atoms, one on each side of the FeN_x plane, are necessary to completely inhibit the catalytic activity of the FeN_x sites. When considering the more realistic model of a stack of graphene layers, only one F atom is needed to poison the FeN_x moiety on the top layer since ORR hardly takes place between carbon layers. We also found that metal-free catalytic N-sites are immune to poisoning by fluorination, in accordance with our experiments. Finally, we explain how most of the catalytic activity can be recovered by heating to 900 °C after fluorination. This research helps to clarify the role of metallic sites compared to non-metallic ones upon the fluorination of FeN_x-doped disorganized carbon catalysts.     

Controlled ring‐opening polymerization of lactide by bis‐sulfonamide/amine associations: Cooperative hydrogen‐bonding catalysis

The bis‐sulfonamide m‐C₆H₄(SO₂NHPh)₂ efficiently promotes the ring‐opening polymerization of lactide when combined with tertiary amines, such as N,N‐dimethylaminopyridine. Polylactides of controlled molecular weights (M_n up to 17,700 g mol^?1) and very narrow molecular weight distributions (M_w/M_n < 1.11) are obtained under mild conditions and in a living fashion. The reaction takes place through a bifunctional mechanism involving activation of both the alcohol and the monomer. Modulation of the sulfonamide component supports cooperative dual hydrogen‐bonding of lactide involving the two (SO₂NHAr) moieties. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 959–965, 2010