Sur la densité d'état de l'opérateur de Schrödinger quasi-périodique unidimensionnel

We prove two results on the density of states of the discrete one dimensional quasi-periodic Schrödinger equation with an analytic potential and Diophantine frequencies in the perturbed regime. On the one hand, we prove that this function has the behavior of a Hölder-$\frac{1}{2}$ function. On the other, we show that the length of the gaps has a sub-exponential estimate which depends on its label given by the gap-labeling theorem. To cite this article: S. Hadj Amor, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

A note on nil power serieswise Armendariz rings

A ring R is called nil power serieswise Armendariz if $ \forall f = \sum\limits_{i = 0}^\infty {a_i X^i } $ \forall f = \sum\limits_{i = 0}^\infty {a_i X^i } and $ g = \sum\limits_{i = 0}^\infty {b_i X^i } $ g = \sum\limits_{i = 0}^\infty {b_i X^i } in R[[X]] such that f g ∈ Nil(R)[[X]], then a _i b _j ∈ Nil(R) for all i and j. In this note we characterize completely nil power serieswise Armendariz rings with their nilradical Nil(R) (where the nilradical is the set of nilpotent elements). We prove that a ring is nil power serieswise Armendariz if and only if Nil(R) is an ideal of R. We prove that each power serieswise Armendariz ring is nil power serieswise Armendariz and we give examples of nil power serieswise Armendariz rings.     

Magnetic Field-Assisted Direct Immersion SPME of Endogenous Aldehydes in Human Urine

Direct immersion solid-phase microextraction (DI-SPME) is an effective microsampling strategy for polar and ionic species in aqueous media. Nevertheless, the fiber coating is in direct contact with sample solution and affected by its conditions. To compensate this limitation and to improve the extraction efficiency, a magnetic fiber coating was prepared and employed for DI-SPME sampling under the enhancing effect of a magnetic field. Magnetic iron oxide core–shell silica nanoparticles were synthesized and embedded in polypyrrole using an in situ electropolymerization method along with simultaneous coating on the surface of a platinized stainless-steel fiber. It was then applied for magnetic-assisted DI-SPME (MA-DI-SPME) sampling of endogenous aldehydes in human urine. Sample solution pH, the magnetic field intensity, ionic strength and extraction time were evaluated as the important affecting variables. Limits of detection were obtained 0.01–0.1 ng mL^?1; the calibration graphs were linear over the range of 0.1–10000 ng mL^?1. The inter-fiber (fiber-to-fiber) reproducibility was found to be 10.7–12.5%. Matrix effect from urine samples was not observed at concentration levels of 0.2, 2, and 8 µg mL^?1. The results showed that magnetic field increased the efficiency of DI-SPME method about two to four times. The developed strategy was successfully applied for the extraction and quantification of hexanal and heptanal (as the most important aldehyde biomarkers) in urine samples.

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Evaluation of polypyrrole/silver/polyethylene glycol nanocomposite sorbent for electroenhanced direct-immersion solid-phase microextraction of carvacrol and thymol from medicinal plants

The unique features of nanostructured polypyrrole, conductivity enhancement effect of silver nanoparticles and high polar adsorptivity of polyethylene glycol were merged into polypyrrole/silver/polyethylene glycol (PPy/Ag/PEG) nanocomposite. It was synthesized and simultaneously coated on the surface of a stainless-steel fiber using an amended electropolymerization procedure. Before coating, the fiber substrate was made porous and sticky by allocating platinum dots on the surface of the stainless-steel fiber using the electrophoretic method. The prepared fiber was applied for the extraction of carvacrol and thymol (the most important antioxidants in medicinal plants) through an electroenhanced direct-immersion solid-phase microextraction (EE-DI-SPME) sampling strategy, followed by GC-FID quantification. To achieve the best efficiency, the effectual experimental variables including pH of sample solution, applied voltage, extraction temperature and time, stirring rate, and ionic strength were investigated. Under the optimal experimental conditions, the calibration curves were linear over the range of 0.5–30 µg mL^?1 for thymol and 0.01–30 µg mL^?1 for carvacrol. The detection limits (3S_b) and relative standard deviation (RSD%, n?=?6) were obtained to be 0.15, 0.003 µg mL^?1 and 10.2, 8.7% for thymol and carvacrol, respectively. The results demonstrated the priority of the proposed fiber compared with polypyrrole and polyacrylate fibers, in terms of extraction efficiency, durability and stability. The developed method was successfully employed for the analysis of thymol and carvacrol in medicinal plants.     

Size dependence of transition temperature in polymer nanowires

We studied the effect of changing temperature on the mechanical properties of nanosized poly(methyl methacrylate) wires fabricated by two-photon fabrication. At around room temperature, the nanowires showed a transition temperature where the shear modulus suddenly changed. This transition temperature was observed to decrease more than 40 K by decreasing the radius of the nanowires from 450 to 150 nm. This size is several times larger in nanowires than reported values of polymer thin film thickness showing a depression of the glass transition temperature.     

Inhibitory Effects of Tunisian Marine Algal Extracts on Digestive Lipases

The lipase inhibitory activity of ethanol extracts obtained from some marine algae collected on the Tunisian coast was evaluated. Caulerpa prolifera extract markedly reduced both dog gastric (DGL) and human pancreatic lipase (HPL) activities. Generally, the inhibition reached 100% after 40 to 60 min of incubation depending on lipase types and on substrates used. Moreover, the inhibitory effect of C. prolifera extract on lipases appeared to be accelerated by adding bile salts, which likely modified the interface and allowed the inhibitory compound to inactivate the lipase. The separation of C. prolifera extract by thin-layer chromatography (TLC) resulted in eight fractions showing efficient inhibition rate against DGL, compared to the crude extract. In the case of HPL, TLC fractionation reduced the inhibitory rates, suggesting that the effect of algal extract on lipases may be caused by a synergetic action of several compounds within the extract. High-performance liquid chromatograph separation resulted in isolation of a major compound displaying high inhibition capacity of HPL activity. Caulerpa prolifera extract may therefore be useful in developing antiobesity drugs.     

Functional Convergence of Linear Processes with Heavy-Tailed Innovations

We study convergence in law of partial sums of linear processes with heavy-tailed innovations. In the case of summable coefficients, necessary and sufficient conditions for the finite dimensional convergence to an \(\alpha \)-stable Lévy Motion are given. The conditions lead to new, tractable sufficient conditions in the case \(\alpha \le 1\). In the functional setting, we complement the existing results on \(M_1\)-convergence, obtained for linear processes with nonnegative coefficients by Avram and Taqqu (Ann Probab 20:483–503, 1992) and improved by Louhichi and Rio (Electr J Probab 16(89), 2011), by proving that in the general setting partial sums of linear processes are convergent on the Skorokhod space equipped with the \(S\) topology, introduced by Jakubowski (Electr J Probab 2(4), 1997).     

Amino acid and peptide synthesis and functionalization by the reaction of thioacids with 2,4-dinitrobenzenesulfonamides

Readily prepared amino thioacids react at room temperature in DMF in the presence of cesium carbonate with 2,4-dinitrobenzenesulfonamides to give amides. When the sulfonamide is derived from an amino acid the method results in peptide bond formation, whereas the use of carbohydrate derived sulfonamides gives neoglycoconjugates.     

Improved solubilization of surface proteins from Listeria monocytogenes for 2-DE

Solubilization of bacterial surface (cell wall and membrane-associated) proteins for 2-DE is challenging, particularly in the case of Gram-positive bacteria. This is primarily due to strong protein association with the cell wall peptidoglycan and protein hydrophobicity. We solubilized surface proteins for 2-DE from the Gram-positive pathogen Listeria monocytogenes using mutanolysin, which digests cell wall peptidoglycan, and one of three different mixtures of zwitterionic detergent and chaotropes: (i) CHAPS/urea, (ii) amidosulfobetaine-14 (ASB-14)/urea/thiourea (iii) N-decyl-N,N'-dimethyl-3-ammonio-1-propanesulfonate/urea/thiourea. Cell lysis with mutanolysin followed by solubilization with ASB-14/urea/thiourea gave the highest overall protein yield with the best 2-DE resolution. Protein spot identification by MALDI-TOF/TOF-MS analysis revealed 29 characterized surface proteins of L. monocytogenes, 17 of which have not previously been reported on the surface proteome map. This is the first report describing the successful solubilization and 2-DE of L. monocytogenes proteins bound to the cell surface via an LPXTG motif or by a hydrophobic tail. The increase in surface proteome coverage obtained by mutanolysin and ASB-14/urea/thiourea solubilization suggests the utility of this method for future analytical and comparative studies of surface proteins from Listeria, and possibly other Gram-positive bacteria, using 2-DE proteomic analysis. An updated 2-DE reference map of L. monocytogenes surface proteins is presented.