An Existence Theorem for Generalized von Kármán Equations

Using techniques from formal asymptotic analysis, the first two authors have recently identified generalized von Kármán equations, which constitute a two-dimensional model for a nonlinearly elastic plate where only a portion of the lateral face is subjected to boundary conditions of von Kármán's type, the remaining portion being free. In this paper, we establish an existence theorem for these equations. To this end, we first reduce them to a single equation, which generalizes a cubic operator equation introduced by M.S. Berger and P. Fife. We then directly solve this equation, notably by adapting a crucial compactness method due to J.-L. Lions. Résumé. En utilisant les techniques de l'analyse asymptotique formelle, les deux premiers auteurs ont récemment identifié des équations de von Kármán généralisées, qui constituent un modèle bi-dimensionnel de plaque non linéairement élastique dont une partie seulement de la face latérale est soumise à des conditions aux limites de von Kármán, la partie restante étant libre. Dans cet article, on établit un théorème d'existence pour ces équations. À cette fin, elles sont d'abord réduites à une seule équation, qui généralise une équation faisant intervenir un opérateur cubique, introduite par M.S. Berger et P. Fife. On résout ensuite directement cette équation, en adaptant notamment une méthode cruciale de compacité due à J.-L. Lions.     

Diastereoselective radical mediated alkylation of a chiral glycolic acid derivative

Radical alkylation of 2-(tert-butyl)-2-methyldioxolan-4-one, a chiral equivalent of glycolic acid, occurs with good to high diastereoselectivity that compares favorably with the corresponding enolate alkylation. The importance of the position of the transition state position, early or late, is highlighted.     

Stabilization of Natural Pigments in Ethanolic Solutions for Food Applications: The Case Study of Chlorella vulgaris

Chlorella vulgaris is a green microalga with a high chlorophyll content, representing a valuable source of green pigments for food applications. As the application of whole biomass can promote an unpleasant fish-like flavor, the use of chlorophyll extract can overcome this drawback. However, chlorophylls tend to easily degrade when out of the chloroplasts, decreasing their potential as a food ingredient. Thus, to study the suitable conditions for isolated chlorophylls preservation, in this work, the influence of temperature (4 to 60 °C), light (dark or 24 h photoperiod), alkaline conditions (with or without aqueous NaOH addition), and modified atmosphere (air or argon atmosphere) on the stability of the color in ethanolic solutions obtained from C. vulgaris were studied. The loss of green color with temperature followed the first-order kinetics, with an activation energy of 74 kJ/mol. Below 28 °C and dark conditions were suitable to preserve isolated chlorophylls. The addition of NaOH and an inert argon-rich atmosphere did not exhibit a statistically positive effect on color preservation. In the case study, cooked cold rice was colored to be used in sushi. The color remained stable for up to 3 days at 4 °C. Therefore, this work showed that C. vulgaris chlorophylls could be preserved in ethanolic solutions at room or lower temperatures when protected from light, allowing them to obtain a suitable natural food ingredient to color foodstuffs.     

Semisynthetic Abietic and Dehydroabietic Acid Derivatives and Triptoquinone Epimers Interfere with LPS-Triggered Activation of Dendritic Cells

Abietic acid (AA), dehydroabietic acid (DHA) and triptoquinones (TQs) are bioactive abietane-type diterpenoids, which are present in many edible vegetables and medicinal herbs with health-promoting properties. Evidence suggests that beneficial effects of diterpenes operate, at least in part, through effects on cells in the immune system. Dendritic cells (DCs) are a key type of leukocyte involved in the initiation and regulation of the immune/inflammatory response and natural or synthetic compounds that modulate DC functions could be potential anti-inflammatory/immunomodulatory agents. Herein, we report the screening of 23 known semisynthetic AA and DHA derivatives, and TQs, synthesized previously by us, in a multi-analyte DC-based assay that detects inhibition of pro-inflammatory cytokine production. Based on the magnitude of the inhibitory effect observed and the number of cytokines inhibited, a variety of activities among compounds were observed, ranging from inactive/weak to very potent inhibitors. Structurally, either alcohol or methyl ester substituents on ring A along with the introduction of aromaticity and oxidation in ring C in the abietane skeleton were found in compounds with higher inhibitory properties. Two DHA derivatives and two TQs exhibited a significant inhibition in all pro-inflammatory cytokines tested and were further investigated. The results confirmed their ability to inhibit, dose dependently, LPS-stimulated expression of the co-stimulatory molecules CD40 and/or CD86 and the production of the pro-inflammatory cytokines IL-1β, IL-6, IL-12 and TNFα. Our results demonstrate that DC maturation process can be targeted by semisynthetic DHA derivatives and TQ epimers and indicate the potential of these compounds as optimizable anti-inflammatory/immunomodulatory agents.     

Total Aseptization of Boar Semen,to Increase the Biosecurity of Reproduction in Swine

The aim of the study was to establish the complete microbiological profile of boar semen (Sus scrofa domesticus) and to choose the most effective antiseptic measures in order to control and optimize AI reproduction in pig farms. One hundred and one semen samples were collected and analyzed from several pig farms. The microbiological profile of ejaculates was determined by evaluating the degree of contamination of fresh semen and after dilution with specific extenders. The bacterial and fungal load of fresh boar semen recorded an average value of 82.41/0.149 × 10³ CFU/mL, while after diluting the ejaculates the contamination value was 0.354/0.140 × 10³ CFU/mL. Twenty-four germs (15 bacterial and 9 fungal species) were isolated, the most common being Candida parapsilosis/sake (92%) and Escherichia coli (81.2%). Modification of the sperm collection protocol (HPBC) reduced contamination in raw sperm by 49.85% in bacteria (significant (p < 0.00001) and by 9.67% in fungi (non-significant (p < 0.111491). The load in bacteria and filamentous fungi can be controllable, but not in levuras fungi. Some fluconazole-added extenders (12.5 mg%), ensure fungal aseptization, and even an increase in sperm progressivity (8.39%) for at least a 12 h shelf life after dilution. Validation of sperm aseptization was done by maintaining sow fecundity unchanged after AI (insignificant p > 0.05).     

Application of metabolic engineering to the production of scopolamine

Scopolamine is an alkaloid widely used in medicine for its anticholinergic activity. The aim of this review is to show that metabolic engineering techniques constitute a suitable tool to improve the production of tropane alkaloids, focusing in particular on scopolamine. We present an overview of results obtained by various research groups, including our own, who have studied the overexpression of genes involved in the biosynthesis of scopolamine in different plant species that produce tropane alkaloids. Experiments carried out to improve production in hairy root cultures will also be described, as well as those attempting to biotransform hyoscyamine into scopolamine in roots and transgenic tobacco cells.     

Distribution of amines in water/AOT/n-hexane reverse micelles: influence of the amine chemical structure

The distribution of different aliphatic and aromatic amines: n-butylamine (n-BA), isobutylamine (i-BA), tert-butylamine (t-BA), piperidine (PIP), N,N-dimethylaniline (DMA) and N-methylaniline (MA) in water/sodium 1,4-bis(2-ethylhexyl)sulfosuccinate(AOT)/n-hexane reverse micelles was investigated by steady-state fluorescence measurements. The partition constants were measured by an indirect method based on the effect that amine partitioning exert on the bimolecular rate of the reaction between a microphase incorporated fluorophore (Ru(bpy)2+(3)) and the quencher, (Fe(CN)3-(6)). For MA, that can act as a quencher of the fluorophore a direct method was used. The results show that primary amines have larger partition constants than the secondary ones. For tertiary amines the distribution constants were practically negligible. Laser flash photolysis experiments confirmed that tertiary amines, both aliphatic and aromatic, are not incorporated to the micellar pseudophase. The effect of the amine structure on the partition constant was analyzed through linear solvation free energy relationships (LSER) using solute parameters and compared with those obtained for alcohols. Hydrogen bond interactions with the AOT polar heads appear to be the main driving force for the distribution of amines between the organic and micellar pseudophases, whereas the size of the alkyl or aromatic group tends to hinder it.     

Generalized and potential symmetries of the Rudenko-Robsman equation

The paper presents a concrete study of the existence of generalized and potential symmetries for the 1+1 dimensional version of the Rudenko-Robsman equation, an interesting fourth-order partial differential equation that describes the evolution of nonlinear waves in a dispersive medium. As the main results, the existence of a two-parameter algebra of generalized symmetries and of an infinite-dimensional algebra when potential symmetries are taken into account is proven.     

New formulations of linearized elasticity problems,based on extensions of Donati's theorem

The classical Donati theorem is used for characterizing smooth matrix fields as linearized strain tensor fields. In this Note, we give several generalizations of this theorem, notably to matrix fields whose components are only in $H^{\mathrm{?1}}$. We then show that our extensions of Donati's theorem allow to reformulate in a novel fashion linearized three-dimensional elasticity problems as quadratic minimization problems with the strains as the primary unknowns. To cite this article: C. Amrouche et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).