Nonexistence Results of Minimal Immersions

Let M be a Riemannian m-dimensional manifold with m ≥ 3, endowed with non zero parallel p-form. We prove that there is no minimal isometric immersions of M in a Riemannian manifold N with constant strictly negative sectional curvature. Next we show that, under the conform flatness of the manifold N and some assumptions on the Ricci curvature of N, there is no α-pluriharmonic isometric immersion.     

Detection of potentially skin sensitizing hydroperoxides of linalool in fragranced products

On prolonged exposure to air, linalool can form sensitizing hydroperoxides. Positive hydroperoxide patch tests in dermatitis patients have frequently been reported, but their relevance has not been established. Owing to a lack of analytical methods and data, it is unclear from which sources the public might be exposed to sufficient quantities of hydroperoxides for induction of sensitization to occur. To address this knowledge gap, we developed analytical methods and performed stability studies for fine fragrances and deodorants/antiperspirants. In parallel, products recalled from consumers were analysed to investigate exposure to products used in everyday life. Liquid chromatography–mass spectrometry with high mass resolution was found to be optimal for the selective and sensitive detection of the organic hydroperoxide in the complex product matrix. Linalool hydroperoxide was detected in natural linalool, but the amount was not elevated by storage in a perfume formulation exposed to air. No indication of hydroperoxide formation in fine fragrances was found in stability studies. Aged fine fragrances recalled from consumers contained a geometric mean linalool concentration of 1,888 μg/g and, corrected for matrix effects, linalool hydroperoxide at a concentration of around 14 μg/g. In antiperspirants, we detected no oxidation products. In conclusion, very low levels of linalool hydroperoxide in fragranced products may originate from raw materials, but we found no evidence for oxidation during storage of products. The levels detected are orders of magnitude below the levels inducing sensitization in experimental animals, and these results therefore do not substantiate a causal link between potential hydroperoxide formation in cosmetics and positive results of patch tests. Graphical Abstract

Formation of hydroperoxides from linalool and detection by LC-MS with high resolution     

Survey of Phenolic Acids,Flavonoids and In Vitro Antioxidant Potency Between Fig Peels and Pulps: Chemical and Chemometric Approach

In the present study, chromatic coordinates, phenolic acids, flavonoids and antioxidant capacity assessed by 1,1-diphenyl-2-picrylhydrazyl (DPPH), 2,2′-azino-bis (3-ethylbenzothiazoline-6-sulfonate (ABTS) and lipid peroxidation inhibition capacity (LPIC) essays and their relative IC50 were investigated in 25 fig cultivars growing in Morocco. The aims of this study were to determine (i) the variation in these compounds among light and dark-colored cultivars, (ii) their partitioning between fruit peel and pulp and (iii) to display network connections among these variables. Twelve phenolic compounds (PCs) were isolated in peel extract versus eight in pulp samples. Anthocyanins, mainly cyanidin-3,5-diglucoside and cyanidin-3-O-rutinoside, were the predominant compounds in peels, where the mean concentrations were 75.90 ± 18.76 and 77.97 ± 18.95 µg/g dw, respectively. On the other hand, (−)-epicatechin and cyanidin-3-O-rutinoside were the major compounds in the pulp extracts, where the mean values were 5.23 ± 4.03 and 9.01 ± 5.67 µg/g dw, respectively. A two-dimensional hierarchically clustered heatmap was applied to the dataset to explore correlations in the dataset and similarities between cultivars, without dimensionality reduction. Results showed that anthocyanins, particularly pelargonidin-3-O-rutinoside, cyanidin-3,5-diglucoside and cyanidin-3-O-rutinoside, were the main contributors to the peels’ free radical scavenging capacity. This capacity was particularly higher in the peel of dark-colored figs compared to the fruit pulp. The local cultivar “INRA 1301” showed the most promising phenolic profile due to its very high levels of almost all detected PCs, especially (−)-epicatechin, quercetin-3-O-rutinoside, quercetin-3-O-glucoside, cyanidine-3,5-diglucoside, cyanidine-3-O-rutinoside and pelargonidin-3-O-rutinoside (54.66, 141.08, 35.48, 494.08, 478.66, 12.56 µg/g dw, respectively). Having the darkest figs in the collection (L* = 25.72, c* = 22.09 and h° = 20.99), this cultivar has also combined promising IC50 values, which were of 19.85, 40.58 and 124.78 µg/mL for DPPH, ABTS and LPIC essays, respectively.     

Regularity properties for evolution families governed by non-autonomous forms

Evolution families are the non-autonomous counterpart of operator semigroups in the well-posedness theory of non-autonomous evolution equations. This note is devoted to fundamental operator theoretical properties, beginning with norm continuity—which we regard as a fingerprint of analyticity. While no known analogue of analytic semigroups is known in the non-autonomous case, we give a sufficient condition for norm-continuity of evolution families. Furthermore, we develop a theory of compact and trace class evolution families. The abstract results are applied to the Laplace operator with time dependent Robin boundary conditions.     

Ultracontractivity and Gaussian bounds for evolution families associated with nonautonomous forms

We develop a variational approach in order to study qualitative properties of nonautonomous parabolic equations. Based on the method of product integrals, we discuss invariance properties and ultracontractivity of evolution families in Hilbert space. Our main results give sufficient conditions for the heat kernel of the evolution family to satisfy Gaussian-type bounds. Along the way, we study examples of nonautonomous equations on graphs, metric graphs, and domains.     

Thermodynamics of hydrophobic interaction chromatography of acetyl amino acid methyl esters

Thermodynamic analysis of hydrophobic interaction chromatography of amino acid methyl esters showed entropy-driven adsorption, consistent with solvophobic theory, except for phenyl ester on the Toyopearl resins. All esters adsorbed more strongly to the Toyopearl resins, including the polymethacrylate base matrix, than to Butyl Sepharose. Enthalpy changes were more favorable with the former, explaining the retention difference between Toyopearl Butyl and Butyl Sepharose. An enthalpy change versus heat capacity change plot showed Van der Waals interactions predominantly with the resin matrix. Literature data revealed the same effect for dansylamino acids, shown by isothermodynamic temperature analysis to adsorb more entropically than the esters.     

Dynamic transcritical bifurcations in a class of slow-fast predator-prey models

We study the stability loss delay phenomenon in a dynamic transcritical bifurcation in a class of three-dimensional prey and predator systems. The dynamics of the predator is assumed to be slow comparatively to the dynamics of the prey. As an application, a well-known model considered by Clark will be discussed.     

Optoelectronic properties of SnO_2 thin films sprayed at different deposition times

This article presents the elaboration of tin oxide(SnO_2) thin films on glass substrates by using a home-made spray pyrolysis system. Effects of film thickness on the structural, optical, and electrical film properties are investigated. The films are characterized by several techniques such as x-ray diffraction(XRD), atomic force microscopy(AFM), ultravioletvisible(UV–Vis) transmission, and four-probe point measurements, and the results suggest that the prepared films are uniform and well adherent to the substrates. X-ray diffraction(XRD) patterns show that SnO_2 film is of polycrystal with cassiterite tetragonal crystal structure and a preferential orientation along the(110) plane. The calculated grain sizes are in a range from 32.93 nm to 56.88 nm. Optical transmittance spectra of the films show that their high transparency average transmittances are greater than 65% in the visible region. The optical gaps of SnO_2 thin films are found to be in a range of 3.64 e V–3.94 e V. Figures of merit for SnO_2 thin films reveal that their maximum value is about 1.15 × 10-4-1?atλ = 550 nm. Moreover, the measured electrical resistivity at room temperature is on the order of 10-2?·cm.     

Algorithme RLS en deux étapes pour l'estimation d'un modèle ARCH

The aim of this Note is, on the one hand, the development of a recursive method, in two stages, for estimating ARCH models, and, on the other hand, the analysis of the statistical properties of the estimators provided by this method. We show that these estimators are asymptotically Gaussian and that the estimator of the second stage is asymptotically efficient. To cite this article: A. Aknouche, H. Guerbyenne, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

F-harmonic maps as global maxima

In this note, we show that some $F$ -harmonic maps into spheres are global maxima of the variations of their energy functional on the conformal group of the sphere. Our result extends partially those obtained in El Soufi and Lejune [C.R.A.S. 315(Serie I):1189–1192, 1992] and El Soufi [Compositio Math 95:343–362,1995] for harmonic and $p$ -harmonic maps.