Antisymmetry of solutions for some weighted elliptic problems

This article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-dimensional case, we introduce the continuous odd rearrangement of an increasing function and we show that it decreases the energy functional when the weights satisfy a certain convexity-type hypothesis. This leads to the antisymmetry or oddness of increasing solutions (and not only of minimizers). We also prove a uniqueness result (which leads to antisymmetry) where a convexity-type condition by Berestycki and Nirenberg on the weights is improved to a monotonicity condition. In addition, we provide with a large class of problems where antisymmetry does not hold. Finally, some rather partial extensions in higher dimensions are also given.     

Stable pairs on elliptic K3 surfaces

We study semistable pairs on elliptic K3 surfaces with a section: we construct a family of moduli spaces of pairs, related by wall crossing phenomena, which can be studied to describe the birational correspondence between moduli spaces of sheaves of rank 2 and Hilbert schemes on the surface. In the 4-dimensional case, this can be used to get the isomorphism between the moduli space and the Hilbert scheme described by Friedman.     

Characterization of the Phytochemical Profiles and Biological Activities of Ajuga chamaepitys subsp. chia var. chia and Ajuga bombycina by High-Performance Liquid Chromatography–Electrospray Ionization–Tandem Mass Spectrometry (HPLC–ESI–MSn)

This study investigates into the pharmacological potential of three solvent extracts (ethyl acetate, methanol, and water) of two Ajuga species (Ajuga chamaepitys subsp. chia var. chia and Ajuga bombycina) based on their antioxidant activity and enzyme inhibitory effects along with establishing the phytochemical profile. Spectrophotometric and high-performance liquid chromatography–electrospray ionization–tandem mass spectrometry (HPLC–ESI–MSⁿ) were used to determine the total and individual phytocompounds, respectively. Antioxidant potential was assessed using different assays such as DPPH, ABTS, CUPRAC, FRAP, phosphomolybdenum, and metal chelation. Enzyme inhibitory effects were studied against acetylcholinesterase, butyrylcholinesterase, tyrosinase, α-amylase, and α-glucosidase. The aqueous extract of both plants showed better ABTS scavenging, FRAP, and metal chelating activities. The methanol extracts displayed the highest tyrosinase inhibitory and antioxidant activity in the phosphomolybdenum assay while the ethyl acetate extracts of both plants showed better butyrylcholinesterase (BChE), α-amylase, and α-glucosidase inhibition. The total phenolic content was highest in the aqueous extract of A. chamaepitys while the methanolic extract of A. bombycina showed the highest flavonoid content. Identification by HPLC–ESI–MSⁿ revealed the presence of some individual compounds including phenolic acids, flavonoids, iridoid glycosides, phenylethanoid glycosides, and other compounds. To conclude, both A. chamaepitys and A. bombycina can be considered as rich sources of phytocompounds to manage chronic diseases.     

Antioxidant activity and chemical composition of three Tunisian Cistus: Cistus monspeliensisCistus villosus and Cistus libanotis☆

The chemical composition of three rockrose Cistus species, Cistus monspeliensis, Cistus libanotis and Cistus villosus, collected in Tunisia, was studied by HPTLC, focusing on the terpenes and phenols constituents. Diterpenes of Cistus are important as the main constituents of the leaf sticky aromatic resin, known as labdanum, which are highly appreciated in perfumery. Polyphenols in the methanolic extracts of each species were identified, quantified as total and as flavonoids and tannins, and tested for antioxidant activity. Diterpenes were evident in C. libanotis and C. monspeliensis, whereas they were practically absent in C. villosus; C. libanotis had higher phenolic amount, whereas antioxidant activities were important, but different according to the following tests: DPPH radical scavenging, conversion of the Fe^3+/ferricyanide complex and inhibition of β-carotene bleaching. The reported data confirm the validity of utilisation of Cistus sp. in marketed herbal products, as well as the relevant presence of diterpenes in species actually not used for labdanum production.     

ESR and calculations on electronic structure of phenalenyl and phenalenyl derivative radicals

Calculations on electronic structure of the perinaphthenyl radical and phenalenyl derivative radicals responsible for the composition of the ESR spectrum of marine diesel under heating were performed to obtain support for the experimental ESR results. The parameters calculated were the hyperfine coupling constants (A), which were then used for comparison with the experimental data. The energy‐minimized structures were obtained using the density functional theory method. In all cases, the symmetry system was taken into account in theoretical calculations. The differences between experimental and theoretical values were below 7% for nearest hydrogens in molecules, named hyperfine coupling constant A (first neighbors) and 18% for farthest hydrogens atoms named hyperfine coupling constants A′ (second neighbors), for all structures analyzed. Copyright © 2014 John Wiley & Sons, Ltd.     

Chemical composition and insecticidal activity of the essential oil from Helichrysum faradifani endemic to Madagascar

Helichrysum faradifani (Asteraceae) is a perennial shrub growing in rocky and sandy places of Madagascar. The plant is used in the Malagasy traditional medicine as a wound-healing agent, disinfectant and for the treatment of syphilis, diarrhea, cough and headache. In the present work, we analysed the chemical composition of the essential oil distilled from the aerial parts of H. faradifani by GC-MS and evaluated its insecticidal activity against 2nd, 3rd and 4th instar larvae of the lymphatic filariasis vector Culex quinquefasciatus by acute toxicity assays. The most sensitive were 2nd instar (LC₅₀ = 85.7 μL L^?1) larvae. For the 3rd and 4th instar larvae, the estimated LC₅₀ were 156.8 and 134.1 μL L^?1, respectively. Monoterpene hydrocarbons (51.6%) were the major fraction of the essential oil, with the bicyclic α-fenchene (35.6%) as the predominant component. Sesquiterpene hydrocarbons (34.0%) were the second major group characterising the oil, with γ-curcumene (17.7%) as the most abundant component.