Inégalités de Harnack pour les solutions d'équations du type courbure scalaire prescrite

We prove some a priori estimates in dimension $n?2$ for equations of type prescribed scalar curvature. In the particular case of the unit sphere ${\mathbb{S}}_2$ we give an estimation of the constant c in the inequality ${\sup }_{{\mathbb{S}}_2}u+{\inf }_{{\mathbb{S}}_2}u?c$. To cite this article: S. Skander Bahoura, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Hexafluoroacetone as Protecting and Activating Reagent. A New Approach to N-Glycosides

N-Glycosides of Asn and homologues have been synthesized starting from hexafluoroacetone-protected -activated Asp, Glu, and Aad derivatives and glycosylamines. The synthetic value of the new building blocks was demonstrated by the concise incorporation of N-glycosylated Asn, Gln, and Aad -amides into glycopeptides.     

Comparison of Two Stability-Indicating Chromatographic Methods for the Determination of Mirabegron in Presence of Its Degradation Product

Mirabegron is a novel β₃-adrenoceptor agonist containing an amide group. It was subjected to stress conditions of acidic and alkaline hydrolyses. The hydrolytic degradation product was isolated and its structure was confirmed using mass and IR spectrometry. Two stability-indicating chromatographic methods have been proposed for the determination of mirabegron. TLC method was applied using silica gel as stationary phase and chloroform–methanol–ammonia (9.0:1.0:0.1 by volume) as the mobile phase, and chromatograms were scanned at 250 nm. Accurate determination of the drug was achieved over the concentration range of 2–12 μg per band. In addition, an isocratic HPLC method was developed on Agilent C18 column (150 mm × 4.5 mm I.D., particle size 5 µm) using ethanol-phosphate buffer pH 2.5 (30:70, by volume) as a mobile phase with flow rate of 1 mL min^?1.The intact drug was detected at 250 nm with running time less than 5 min. Mirabegron was determined accurately in a concentration range of 1–25 µg mL^?1. The proposed chromatographic methods were applied successfully for the assay of mirabegron in pharmaceutical dosage form and both methods were validated as per the International Conference on Harmonization guidelines and statistically compared with a reported gradient HPLC method.     

Synthesis and crystal structure of some 3,5-pyrazolidinediones

Syntheses of various derivatives of 3,5-pyrazolidenedione are reported. This includes 4-arylidene (alkylidene or aralkylidene)-3,5-pyrazolidinediones, which on epoxidation gave unreported oxiranes. The syntheses of these derivatives were based on either the Knoevenagel reaction of carbonyl derivatives with 3,4-pyrazolidinedione or cyclization of arylidene (alkylidene) malonic acid hydrazide with glacial acetic acid. 4-Arylazo-3,5-pyrazolidinedione derivatives were also prepared by coupling of aryldiazonium salts with 3,5-pyrazolidinedione or cyclization of arylazomalonic acid hydrazide. Reduction of 4-benzylidene derivatives gave the corresponding benzyl derivatives. The structure of the new products was confirmed by elemental and spectral analyses and X-ray crystallography.     

Mean field theory for nonequilibrium network reconstruction

There has been recent progress on inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for nonequilibrium systems. Here we introduce an approach to this problem, considering, as an example, the question of recovering the interactions in an asymmetrically coupled, synchronously updated Sherrington-Kirkpatrick model. We derive an exact iterative inversion algorithm and develop efficient approximations based on dynamical mean-field and Thouless-Anderson-Palmer equations that express the interactions in terms of equal-time and one-time-step-delayed correlation functions.     

Development and validation of a stability-indicating RP-HPLC method for the determination of paracetamol with dantrolene or/and cetirizine and pseudoephedrine in two pharmaceutical dosage forms

A stability-indicating reversed-phase high-performance liquid chromatography (RP-HPLC) method has been developed which can separate and accurately quantitate paracetamol, dantrolene, cetirizine and pseudoephedrine. The method was successfully validated for the purpose of conducting stability studies of the four analytes in quality control (QC) laboratories. The stability-indicating capability of the method was demonstrated by adequate separation of these four analytes from all the degradant peaks. A gradient mobile phase system consisting of (A) 50 mmol L⁻¹ sodium dihydrogen phosphate, 5 mmol L⁻¹ heptane sulfonic acid sodium salt, pH 4.2 and (B) acetonitrile was used with Discovery reversed-phase HS C₁₈ analytical column (250 mm × 4.6 mm i.d., 5 μm particle size). Quantitation was achieved with UV detection at 214 nm, based on peak area.The proposed method was validated and successfully applied for the analysis of pharmaceutical formulations and laboratory-prepared mixtures containing the two multicomponent combinations.     

Simple-direct-modules

A right R-module M is called simple-direct-injective if, whenever, A and B are simple submodules of M with A?B, and B?^⊕M, then A?^⊕M. Dually, M is called simple-direct-projective if, whenever, A and B are submodules of M with M∕A?B?^⊕M and B simple, then A?^⊕M. In this paper, we continue our investigation of these classes of modules strengthening many of the established results on the subject. For example, we show that a ring R is uniserial (artinian serial) with J²(R) = 0 iff every simple-direct-projective right R-module is an SSP-module (SIP-module) iff every simple-direct-injective right R-module is an SIP-module (SSP-module).     

Selectivity among two lectins: probing the effect of topology, multivalency and flexibility of "clicked" multivalent glycoclusters

The design of multivalent glycoconjugates has been developed over the past decades to obtain high-affinity ligands for lectin receptors. While multivalency frequently increases the affinity of a ligand for its lectin through the so-called "glycoside cluster effect", the binding profiles towards different lectins have been much less investigated. We have designed a series of multivalent galactosylated glycoconjugates and studied their binding properties towards two lectins, from plant and bacterial origins, to determine their potential selectivity. The synthesis was achieved through copper(I)-catalysed azide-alkyne cycloaddition (CuAAC) under microwave activation between propargylated multivalent scaffolds and an azido-functionalised carbohydrate derivative. The interactions of two galactose-binding lectins from Pseudomonas aeruginosa (PA-IL) and Erythrina cristagalli (ECA) with the synthesized glycoclusters were studied by hemagglutination inhibition assays (HIA), surface plasmon resonance (SPR) and isothermal titration microcalorimetry (ITC). The results obtained illustrate the influence of the scaffold's geometry on the affinity towards the lectin and also on the relative potency in comparison with a monovalent galactoside reference probe.