Positive polynomials on projective limits of real algebraic varieties

We reveal some important geometric aspects related to non-convex optimization of sparse polynomials. The main result, a Positivstellensatz on the fibre product of real algebraic affine varieties, is iterated to a comprehensive class of projective limits of such varieties. This framework includes as necessary ingredients recent works on the multivariate moment problem, disintegration and projective limits of probability measures and basic techniques of the theory of locally convex vector spaces. A variety of applications illustrate the versatility of this novel geometric approach to polynomial optimization.     

A family of $$ 2^{\aleph _1 } $$ logarithmic functions of distinct growth rates

We construct a totally ordered set Γ of positive infinite germs (i.e. germs of positive real-valued functions that tend to +∞), with order type being the lexicographic product ℵ₁ × ℤ². We show that Γ admits $ 2^{\aleph _1 } $ 2^{\aleph _1 } order preserving automorphisms of pairwise distinct growth rates.     

Liquid crystalline G phase of self assembled donor-acceptor molecules by intermolecular hydrogen bonding

The interaction with donor p-n-alkylbenzoic acid and acceptor nonyl-p-hydroxy benzoate molecules was studied. The likely association of these molecules to complexes is studied by intermolecular hydrogen bonding. The textures are observed by polarizing optical microscope with corresponding transitions confirmed by differential scanning calorimetry. The molecular complexes exhibited enantiotropic crystal G phases in both heating and cooling cycles. The relevant functional groups C═O, C-O and OH in formation of molecular complexes are attributed with spectral shifts in infrared spectra and further with absorption studies. The proton NMR studies convinced the structural aspects of hydrogen bonded structure. Crystal parameters were studied with powdered X-ray diffraction. The results show that constituent molecules self organize through intermolecular hydrogen bonding in the formation of crystal G phase.     

Herbicidal activity of flavonoids of mango leaves against Parthenium hysterophorus L

This study was undertaken to investigate the herbicidal activity of mango (Mangifera indica L.) leaves against parthenium weed (Parthenium hysterophorus L.). The aqueous leaf extract at 15% concentration (on fresh weight basis) significantly reduced germination, shoot length and the shoot and root biomasses of parthenium seedlings. In a leaf residue incorporation pot trial, 2% residue incorporation treatment significantly suppressed the root and shoot biomasses of parthenium, while a 5% residue treatment completely stopped the growth of the weed. Five flavonoids, namely (-)-epicatechin-3-O-β-glucopyranoside (1), 5-hydroxy-3-(4-hydroxyphenyl)pyrano[3,2-g]chromene-4(8H)-one (2), 6-(p-hydroxybenzyl)taxifolin-7-O-β-D-glucoside (tricuspid) (3), quercetin-3-O-α-glucopyranosyl-(1 → 2)-β-D-glucopyranoside (4) and (-)-epicatechin(2-(3,4-dihydroxyphenyl)-3,4-dihydro-2H chromene-3,5,7-triol (5) were isolated from mango leaves. In a laboratory bioassay, 50 ppm solution of compounds 3 and 4 caused yellowing of the parthenium seedlings. A 250 ppm solution of compound 4 also significantly reduced germination and the root and shoot lengths of parthenium seedlings. This study concludes that compound 4 exhibits herbicidal activity against parthenium weed.     

Antifungal activity of flavonoids isolated from mango (Mangifera indica L.) leaves

Five flavonoids, namely (-)-epicatechin-3-O-β-glucopyranoside (1), 5-hydroxy-3-(4-hydroxylphenyl)pyrano[3,2-g]chromene-4(8H)-one (2), 6-(p-hydroxybenzyl)taxifolin-7-O-β-D-glucoside (tricuspid) (3), quercetin-3-O-α-glucopyranosyl-(1 → 2)-β-D-glucopyranoside (4) and (-)-epicatechin(2-(3,4-dihydroxyphenyl)-3,4-dihydro-2H-chromene-3,5,7-triol (5), were isolated from the leaves of mango (Mangifera indica L.). Antifungal activity of these compounds was evaluated against five fungal species, namely Alternaria alternata (Fr.) Keissler, Aspergillus fumigatus Fresenius, Aspergillus niger van Tieghem, Macrophomina phaseolina (Tassi) Goid. and Penicillium citrii. Six concentrations, namely 100, 300, 500, 700, 900 and 1000 ppm of each of the five flavonoids were employed by means of the poisoned medium technique. All concentrations of the five test flavonoids significantly suppressed fungal growth. However, the specificity of different test compounds was evident against different fungal species. In general, antifungal activity of the flavonoids was gradually increased by increasing their concentrations. The highest concentration (of 1000 ppm) of compounds 1-5 reduced the growth of different target fungal species by 63-97%, 56-96%, 76-99%, 76-98% and 82-96%, respectively.     

Acousto-optical coherence tomography with a digital holographic detection scheme

Acousto-optical coherence tomography (AOCT) consists in using random phase jumps on ultrasound and light to achieve a millimeter resolution when imaging thick scattering media. We combined this technique with heterodyne off-axis digital holography. Two-dimensional images of absorbing objects embedded in scattering phantoms are obtained with a good signal-to-noise ratio. We study the impact of the phase modulation characteristics on the amplitude of the acousto-optic signal and on the contrast and apparent size of the absorbing inclusion.     

Analysis of phenols in water by high-performance liquid chromatography using coumarin-6-sulfonyl chloride as a fluorogenic precolumn label

A simple, sensitive and rapid reversed-phase high-performance liquid chromatography (RP-HPLC) method is proposed for the analysis of some environmentally important phenols in water. The use of coumarin-6-sulphonyl chloride (C6SCl) as a fluorescence-labeling reagent has been investigated. The compound reacts with phenols within 20 min under mild conditions (ambient temperature, pH 9.0) to give sulphonates that can be separated by RP-HPLC employing fluorescence detection at lambda(ex) = 360 and lambda(em) = 460 nm. The optimum conditions for fluorescence, derivatization and chromatographic separation have been established and detection limits in the range 0.1-0.9 microg l(-1) were obtained for the studied compounds. The calibration curves were linear for the range 6-200 microg l(-1) for phenol, 3-200 microg l(-1) for 2-chlorophenol, 4-chlorophenol and 2,3,5-trichlorophenol and for the range of 3-100 microg l(-1) for 2,3-dichlorophenol and 3,5-dichlorophenol. The practical applicability of the method to environmental samples was demonstrated by analyzing drinking and industrial water samples spiked with the phenolic compounds.     

Lithium diisopropylamide-mediated ortholithiation and anionic fries rearrangement of aryl carbamates: role of aggregates and mixed aggregates

Structural and mechanistic studies of the lithium diisopropylamide (LDA)-mediated anionic Fries rearrangements of aryl carbamates are described. Substituents at the meta position of the arene (H, OMe, F) and the dialkylamino moiety of the carbamate (Me(2)N, Et(2)N, and i-Pr(2)N) markedly influence the relative rates of ortholithiation and subsequent Fries rearrangement. Structural studies using (6)Li and (15)N NMR spectroscopies on samples derived from [(6)Li,(15)N]LDA reveal an LDA dimer, LDA dimer-arene complexes, an aryllithium monomer, LDA-aryllithium mixed dimers, an LDA-lithium phenolate mixed dimer, and homoaggregated lithium phenolates. The highly insoluble phenolate was characterized as a dimer by X-ray crystallography. Rate studies show monomer- and dimer-based ortholithiations as well as monomer- and mixed dimer-based Fries rearrangements. Density functional theory computational studies probe experimentally elusive structural and mechanistic details.     

Medium Initial pH and Carbon Source Stimulate Differential Alkaline Cellulase Time Course Production in Stachybotrys microspora

The production profile of cellulases of the mutant strain A19 from the filamentous fungus Stachybotrys microspora was studied in the presence of various carbon sources (glucose, lactose, cellulose, carboxymethylcellulose (CMC), and wheat bran) and a range of medium initial pH (5, 7, and 8). Two extracellular cellulases from the Stachybotrys strain (endoglucanases and β-glucosidases) were monitored by enzymatic assay, sodium dodecyl sulfate–polyacrylamide gel electrophoresis, and zymogram analysis. Glucose and lactose repressed CMCase time course production while they permitted a strong β-glucosidase one. On Avicel cellulose, CMC, and wheat bran, both activities were highly produced. Wheat bran (WB) is the best carbon source with an optimum of production at days 5 and 6. The production kinetics of both activities were shown to depend on the medium initial pH, with a preference for neutral or alkaline pH in the majority of conditions. The exception concerned the β-glucosidase which was much more produced at acidic pH, on glucose and cellulose. Most interestingly, a constitutive and conditional expression of an alkaline endoglucanase was revealed on the glucose-based medium at an initial pH of 8 units. The zymogram analysis confirmed such conclusions and highlighted that carbon sources and the pH of the culture medium directed a differential induction of various endoglucanases and β-glucosidases.     

CDP-Ethanolamine and CDP-Choline: one-pot synthesis and P NMR study

Herein we report a one-pot multi-step synthesis of the cofactors CDP-Ethanolamine and CDP-Choline starting from cytidine 5′-monophosphate and using commercially available and/or easily prepared reagents. While studying the ³¹P NMR spectrum of CDP-Ethanolamine, an unexpected characteristic for a pyrophosphate diester was observed as it showed a singlet or two doublets depending upon the pH. Therefore, further NMR studies were undertaken to investigate the pH dependence of the peak splitting pattern and measure the acid dissociation constants of the compounds.