Asymptotic Behaviors for Eigenvalues and Eigenfunctions Associated to Stokes Operator in the Presence of Small Boundary Perturbations

We consider the Stokes eigenvalue problem in a bounded domain of \(\mathbb {R}^{n}\), n = 2,3 with Dirichlet boundary conditions. The aim of this paper is to advance the development of high-order terms in the asymptotic expansions of the perturbations in the eigenvalues for the Stokes system caused by small perturbations of the boundary or due to interface changes of an inclusion. Our derivation is rigorous and proved by layer potential techniques.     

Cytotoxic and Antioxidant Activities of Imine Analogs of Trans-Resveratrol towards Murine Neuronal N2a Cells

Trans-resveratrol is a natural polyphenol showing numerous biological properties, especially anti-tumoral and antioxidant activity. Among numerous resveratrol derivatives, aza-stilbenes, which bear an imine bound, show interesting biological activities. In the present study, we synthesized a series of imine analogs of trans-resveratrol (seven aza-stilbenes) following an easy and low-cost procedure of green chemistry. The toxicity of synthesized aza-stilbenes, which is currently unknown, was evaluated on murine neuronal N2a cells, comparatively to trans-resveratrol, by considering: cell density evaluated by staining with sulforhodamine 101; esterase activity, which is a criteria of cell viability, by staining with fluorescein diacetate; and transmembrane mitochondrial potential, which is known to decrease during cell death, by staining with DiOC₆(3) using flow cytometry. In addition, the antioxidant activity was quantified with the KRL (Kit Radicaux Libres) assay, the DPPH (2,2′-diphenyl-1-picrylhydrazyl radical) assay and the FRAP (ferric reducing antioxidant power) assay. The PAOT (Pouvoir Antioxidant Total) score was also used. The aza-stilbenes provide different cytotoxic and antioxidant activities, which are either higher or lower than those of trans-resveratrol. Based on their cytotoxic and antioxidant characteristics, all synthesized aza-stilbenes are distinguished from trans-resveratrol.     

Spectra energy levels and symmetry assignments of Sm3+ doped in YAl3(BO3)4 single crystal

Single crystals of YAl₃(BO₃)₄ doped with 5% Sm³⁺ were grown by spontaneous nucleation from K₂Mo₃O₁₀ and B₂O₃ flux. Photoluminescence spectra at room and low temperatures were measured. Four emission transitions have been observed from the ⁴G_5/2 excited state to the lower lying states ⁶H_5/2, ⁶H_7/2, ⁶H_9/2 and ⁶H_11/2 upon exciting the sample with 400 nm wavelength. Polarized absorption spectra in UV, visible and NIR regions were recorded for two light polarizations (π and σ) relative to the C₃ crystal axis.Energy levels scheme of the doping ion has been compiled after a careful analysis of the spectra by reproducing the observed transitions by means of theoretical calculations based on a Hamiltonian including the free-ion and the crystal-field (CF) terms. Free-ion and crystal-field analyses are performed based on a D₃ point-group symmetry Hamiltonian. A best fit between theoretical and experimental energy levels is obtained with a root-mean-square (rms) deviation of 16 cm^?1. The general trend of the crystal-field parameters of rare earth ions in YAB host is confirmed. The calculated N_V crystal-field strength parameter presents a linear variation with the rare earth ionic radii and with the 4fⁿ electron number.     

Entropy generation in gas absorption into a falling liquid film

The study of mass transfer into falling films constitutes a significant aspect for numerous applications in the chemical technology and is considered the subject of many theoretical and experimental researches. Evaluating the second law of thermodynamics is one of the contemporarily used methods to determine the performances of an industrial process and to study various sources of irreversibility. Expressions of the liquid velocity, the gas concentration, the entropy generation rate as well as the main sources of irreversibility in the case of gas absorption (carbon dioxide) into a laminar falling viscous incompressible liquid film (water) without chemical reaction, are analytically derived and graphically presented and discussed.     

Practical Uniform Stability of Nonlinear Differential Delay Equations

In this paper, we investigate the problem of global uniform practical exponential stability of a general nonlinear non autonomous differential delay equations. Using the global uniform practical exponential stability of the corresponding differential equation without delay, we show that the differential delay equation will remain globally uniformly practically exponentially stable provided that the time-lag is small enough. Finally, some illustrative examples are given to demonstrate the validity of the results.     

Photochemical isomerization of norbornadiene‐containing polytriazoles obtained by click chemistry polyaddition

Polyesters and polyethers containing norbornadiene (NBD) and 1,2,3‐triazole units in the main chain are prepared by step growth polymerization of diester or diether NBD‐based dialkynes with different aromatic diazides using copper‐catalyzed azide–alkyne cycloaddition. The solubility and the physical properties of the resulting polytriazoles are investigated by differential scanning calorimetry, thermogravimetric analysis, size exclusion chromatography, and ¹H NMR spectroscopy, and are discussed taking into account of the chemical structures of the monomers. All of them are amorphous with glass transition temperatures ranging from 51 to 117 °C, number average molecular weight (M_n) values from 16 to 43 kDa and thermal degradation (T_d10) values from 175 to 292 °C. The photochemical valence isomerization (PVI) of the NBD units into quadricyclanes (QC) is investigated using UV–vis spectroscopy of polymer films spin‐coated onto quartz substrates. For the first time the PVI of NBD into QC is demonstrated by ¹H NMR spectroscopy. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 223–231     

A new look at probability-weighted moments estimators

In this article, we propose to study, in more generality, the probability-weighted moments method used by Hosking and Wallis (1987) in the case of generalized Pareto distributions which depend on two parameters γ and σ. The objective is to extend the domain of validity: γ<1/2 required in order to obtain the asymptotic properties of their estimators. By simulations, we show the efficiency of our technique. To cite this article: J. Diebolt et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Explicit characterization of the super-replication strategy in financial markets with partial transaction costs

We consider a continuous time multivariate financial market with proportional transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in Bouchard and Touzi [B. Bouchard, N. Touzi, Explicit solution of the multivariate super-replication problem under transaction costs, The Annals of Applied Probability 10 (3) (2000) 685–708] except that some of the assets can be exchanged freely, i.e. without paying transaction costs. In this context, we generalize the result of the above paper and prove that the super-replication price is given by the cost of the cheapest hedging strategy in which the number of non-freely exchangeable assets is kept constant over time. Our proof relies on the introduction of a new auxiliary control problem whose value function can be interpreted as the super-hedging price in a model with unbounded stochastic volatility (in the directions where transaction costs are non-zero). In particular, it confirms the usual intuition that transaction costs play a similar role to stochastic volatility.     

Production of Anti-Methicillin-Resistant <Emphasis Type="Italic">Staphylococcus</Emphasis> Activity from <Emphasis Type="Italic">Bacillus subtilis</Emphasis> sp. Strain B38 Newly Isolated from Soil

B38 bacterial strain, isolated from Tunisian soil showed a strong antimicrobial activity. Based on biochemical characterization and 16S rDNA sequence analysis, B38 strain was identified as Bacillus subtilis. Cell culture supernatant showed antibacterial activity against clinical isolates of methicillin-resistant Staphylococcus species and several Gram-positive and Gram-negative bacteria. Antifungal activity against phytopathogenic fungi was also observed. Antibacterial activity production started at early exponential growth phase, and maximum activity was reached at the stationary phase. This antibacterial activity was neither affected by proteases, lipase, and organic solvents, nor by surfactants. It was stable over a wide pH range and still active after autoclaving at 121 °C during 20 min. Thin layer chromatography followed by bioautography assay allowed the detection of four active spots with R _f values of 0.30, 0.47, 0.70, and 0.82. The single spot with R _f 0.30 showed antifungal activity, whereas the spots with R _f values of 0.47, 0.70, and 0.82 exhibited antibacterial activity.     

Global chemical composition and antioxidant and anti-tuberculosis activities of various extracts of Globularia alypum L. (Globulariaceae) leaves

In this work, an evaluation of the biological activities of Globularia alypum L. extracts and their global chemical composition was realized. Extracts from G. alypum were obtained by two extraction methods. The composition of polyphenols (8.5-139.95 g gallic acid equivalent/Kg of dry mass), tannins (1.39-18.65 g catechin equivalent/Kg of dry mass), anthocyanins (8.17-70.69 mg cyanidin equivalent/Kg of dry mass) and flavonoids (0.31-19.28 g quercetin equivalent/Kg of dry mass) was evaluated. The samples were subjected to a screening for their antioxidant activities using the DPPH* and ABTS*+ assays. For the first time, the anti-tuberculosis activity (H(37)Rv) for G. alypum was tested against Mycobacterium tuberculosis. The strongest antioxidant activity was obtained for the methanol extract (IC(50 ) = 15.58 ± 0.168 mg/L) and the best anti-tuberculosis activity was obtained for the petroleum ether extract (IC(50 )= 77 mg/L). We have found a positive correlation between the total phenolics content and the antioxidant activity R2 = 0.88 (DPPH*) and R2 = 0.97 (ABTS*+). We have found also a positive correlation between the flavonoid content and the antioxidant activity R2 = 0.91 (DPPH*) and R2 = 0.91 (ABTS*+).