Théorèmes de trace de type Szegö dans le cas singulier

Let f be a function eiθ→f(eiθ)=|1−eiθ|^2αf₁(eiθ) with f₁ a regular strictly positive function and a real number α in ]−1/2,1/2[?{0}. In a previous paper for such a number α we have obtained the asymptotic behaviour of the entries of the inverse of the Toeplitz matrix TN,f when N goes to infinity. These results allow us to give trace formulas, which extend a classical expression of Szegö's limits theorems.     

Estimateur hiérarchique robuste pour un problème de perturbation singulière

In this Note, we show that a modified and simplified version of the estimator of Bank–Weiser can be used to define a robust a posteriori error estimator for singularly perturbed problem. We prove without comparison with a residual estimator or saturation assumption, the equivalence of the estimator with the error in the energy norm and the robusteness with respect to the diffusion coefficient. To cite this article: B. Achchab et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Additive Maps Preserving Local Spectrum

Let X be a complex Banach space, and let be the space of bounded operators on X. Given and x ∈ X, denote by σ_T (x) the local spectrum of T at x. We prove that if is an additive map such that

Bioactive Compounds from Ephedra fragilis: Extraction Optimization,Chemical Characterization,Antioxidant and AntiGlycation Activities

Response surface methodology (RSM) with a Box–Behnken design (BBD) was used to optimize the extraction of bioactive compounds from Ephedra fragilis. The results suggested that extraction with 61.93% ethanol at 44.43 °C for 15.84 h was the best solution for this combination of variables. The crude ethanol extract (CEE) obtained under optimum extraction conditions was sequentially fractionated with solvents of increasing polarity. The content of total phenolic (TP) and total flavonoid (TF) as well as the antioxidant and antiglycation activities were measured. The phytochemical fingerprint profile of the fraction with the highest activity was characterized by using RP-HPLC. The ethyl acetate fraction (EAF) had the highest TP and TF contents and exhibited the most potent antioxidant and antiglycation activities. The Pearson correlation analysis results showed that TP and TF contents were highly significantly correlated with the antioxidant and antiglycation activities. Totally, six compounds were identified in the EAF of E. fragilis, including four phenolic acids and two flavonoids. Additionally, molecular docking analysis also showed the possible connection between identified bioactive compounds and their mechanisms of action. Our results suggest new evidence on the antioxidant and antiglycation activities of E. fragilis bioactive compounds that may be applied in the treatment and prevention of aging and glycation-associated complications.     

Studies with enaminonitriles: Synthesis and chemical reactivity of 2‐phenyl‐3‐piperidin‐1‐yl acrylonitrile under microwave heating

Benzyl cyanide reacts with triethylorthoformate and piperidine in DMF solution to yield the title compound 2 . This reacted with aromatic amines to yield either aminoacrylonitriles or quinoline depending on reaction conditions and substitution pattern on the aromatic amine. The reaction of compound 2 with hydrazine hydrate could only be effected in the microwave oven and resulted in the formation of aminopyrazole 7 . Diazotization of 7 and coupling with an active methylene reagent afforded pyrazolo[5,1‐c]‐[1,2,4]triazine derivatives.     

Projection stabilized nonconforming finite element methods for the stokes problem

In this article we study a projection‐stabilized nonconforming finite element discretization of the Stokes problem. We present a priori error analysis and give a recovery‐based a posteriori error estimator for the considered problem. Numerical results illustrate the theoretical performance of the error estimator. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 218–240, 2017     

Selective Monoesterification of Unprotected Mono and Disaccharides

Abstract

Under mild conditions, treatment of unprotected methyl-α-D-glucopyranoside, N-acetylglucosamine and maltose with triphenylphosphine, diethylazodicarboxylate and equimolar amount of various carboxylic acids allowed regioselective 6-O-esterifications (6′-O for maltose) of the carbohydrate without esterification of other hydroxyl groups. This reaction found an application in the synthesis of liposoluble, labelled sugars and hydrosoluble polymers.     

Heterocyclic Synthesis with Nitriles: Synthesis of Pyrazolopyrimidine and Pyrazolopyridine Derivatives

The reaction of N ₁-substituted-5-amino-4-cyanopyrazoles with malononitrile and diethylmalonate occurs with formation of 6-substituted pyrazolo[3,4-d]pyrimidines, and pyrazolo[3,4-b]pyridines respectively. The structures of the products and conceivable mechanisms are discussed.