Connected monomial invariants

We define the monomial invariants of a projective variety Z; they are invariants coming from the generic initial ideal of Z.We prove that, under suitable hypotheses, a variety of codimension at least two has connected monomial invariants; as a corollary, we generalize a result of Cook [C]: if Z is an integral variety of codimension two, satisfying the hypothesis s_Z=s, then its monomial invariants are connected.The authors are members of CNR–GNSAGA (Italy).During the preparation of this paper the authors were partially supported by National Research Project Geometria sulle varietà algebriche COFIN 2002 of MIUR–Italy.Mathematics Subject Classification (2001): 14M07Acknowledgement The authors had fruitful discussions–either in person or via e-mail–on the topics of this paper with many people, among them Matsumi Amasaki, Iustin Coanda, Wolfram Decker, Mark Green, Francesco Russo, Enrico Sbarra, Enrico Schlesinger, Frank Schreyer; their help is gratefully acknowleged. Last, but by no means least, one of the referees pointed out that our original result, Corollary 2.7, could be significantly enlarged in its scope, thus giving Theorem 2.4.     

Observation of amplitude and phase in ridge and photonic crystal waveguides operating at 1.55 microm by use of heterodyne scanning near-field optical microscopy

We apply heterodyne scanning near-field optical microscopy (SNOM) to observe with subwavelength resolution the amplitude and phase of optical fields propagating in several microfabricated waveguide devices operating around the 1.55 microm wavelength. Good agreement between the SNOM measurements and predicted optical mode propagation characteristics in standard ridge waveguides demonstrates the validity of the method. In situ observation of the subwavelength-scale distribution and propagation of optical fields in straight and 90 degrees bend photonic crystal waveguides facilitates a more detailed understanding of the optical performance characteristics of these devices and illustrates the usefulness of the technique for investigating nanostructured photonic devices.     

Solomonamides A and B, new anti-inflammatory peptides from Theonella swinhoei

Two unprecedented cyclic peptides, solomonamides A and B, were isolated from the marine sponge Theonella swinhoei. The structures were elucidated on the basis of comprehensive 1D and 2D NMR analysis and high-resolution mass spectrometry. A combined approach, involving Marfey's method, QM J based analysis, and DFT J/(13)C calculations, was used for establishing the absolute configuration of the entire molecule. Solomonamide A showed in vivo anti-inflammatory activity.     

Functionalization of the corrole ring: the role of isocorrole intermediates

Bromination of 3-nitro-5,10,15-triarylcorrole selectively provides two regioisomers, depending on the reaction pathway. An isocorrole species is the key intermediate to drive the reaction towards the 2-Br-17-nitro regioisomer.     

Condensation of self-assembled lyotropic chromonic liquid crystal sunset yellow in aqueous solutions crowded with polyethylene glycol and doped with salt

We use optical and fluorescence microscopy, densitometry, cryo-transmission electron microscopy (cryo-TEM), spectroscopy, and synchrotron X-ray scattering to study the phase behavior of the reversible self-assembled chromonic aggregates of an anionic dye Sunset Yellow (SSY) in aqueous solutions crowded with an electrically neutral polymer polyethylene glycol (PEG) and doped with the salt NaCl. PEG causes the isotropic SSY solutions to condense into a liquid-crystalline region with a high concentration of SSY aggregates, coexisting with a PEG-rich isotropic (I) region. PEG added to the homogeneous nematic (N) phase causes separation into the coexisting N and I domains; the SSY concentration in the N domains is higher than the original concentration of PEG-free N phase. Finally, addition of PEG to the highly concentrated homogeneous N phase causes separation into the coexisting columnar hexagonal (C) phase and I phase. This behavior can be qualitatively explained by the depletion (excluded volume) effects that act at two different levels: at the level of aggregate assembly from monomers and short aggregates and at the level of interaggregate packing. We also show a strong effect of a monovalent salt NaCl on phase diagrams that is different for high and low concentrations of SSY. Upon the addition of salt, dilute I solutions of SSY show appearance of the condensed N domains, but the highly concentrated C phase transforms into a coexisting I and N domains. We suggest that the salt-induced screening of electric charges at the surface of chromonic aggregates leads to two different effects: (a) increase of the scission energy and the contour length of aggregates and (b) decrease of the persistence length of SSY aggregates.     

Probing the dark matter issue in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>)-gravity via gravitational lensing

For a general class of analytic f(R)-gravity theories, we discuss the weak field limit in view of gravitational lensing. Though an additional Yukawa term in the gravitational potential modifies dynamics with respect to the standard Newtonian limit of General Relativity, the motion of massless particles results unaffected thanks to suitable cancellations in the post-Newtonian limit. Thus, all the lensing observables are equal to the ones known from General Relativity. Since f(R)-gravity is claimed, among other things, to be a possible solution to overcome for the need of dark matter in virialized systems, we discuss the impact of our results on the dynamical and gravitational lensing analyses. In this framework, dynamics could, in principle, be able to reproduce the astrophysical observations without recurring to dark matter, but in the case of gravitational lensing we find that dark matter is an unavoidable ingredient. Another important implication is that gravitational lensing, in the post-Newtonian limit, is not able to constrain these extended theories, since their predictions do not differ from General Relativity.     

Reuse of Food Waste: The Chemical Composition and Health Properties of Pomelo (Citrus maxima) Cultivar Essential Oils

The aim of the present study is to investigate the chemical profile, antioxidant activity, carbohydrate-hydrolysing enzyme inhibition, and hypolipidemic effect of essential oils (EOs) extracted from Sicilian Citrus maxima (pomelo) flavedo. Using gas-chromatography-mass spectrometry analysis (GC-MS) we analysed the Eos of five cultivars of C. maxima, namely, ‘Chadock’, ‘Maxima’, ‘Pyriformis’, ‘Terracciani’, and ‘Todarii’, and their blends. The antioxidant activity was performed by using a multi-target approach using 2,2′-Azino-Bis-3-Ethylbenzothiazoline-6-Sulfonic acid (ABTS), 2,2-Diphenyl-1-picrylhydrazyl (DPPH), ferric reducing ability power (FRAP), and β-carotene bleaching tests. The α-amylase, α-glucosidase, and lipase-inhibitory activities were also assessed. GC-MS analyses revealed D-limonene as the main monoterpene hydrocarbon in all cultivars, albeit with different percentages in the range of 21.72–71.13%. A good content of oxygenated monoterpenes was detected for all cultivars, especially for ‘Todarii’. The analysis of the principal components (PCA), and related clusters (HCA), was performed to find chemo-diversity among the analysed samples. EOs from ‘Chadock’ and ‘Maxima’ were statistically similar to each other, and they differed from P3 in the smaller amount of sesquiterpene hydrocarbons, while the oils from ‘Terracciani’ and ‘Todarii’ were found to be chemically and statistically different. ‘Chadock’ EO was the most active to scavenge radicals (IC₅₀ values of 22.24 and 27.23 µg/mL in ABTS and DPPH tests, respectively). ‘Terracciani’ EO was the most active against both lipase and α-amylase, whereas the blends obtained by the combination (1:1 v/v) of C. maxima ‘Maxima’ + ‘Todarii’ were the most active against α-glucosidase. Generally, the blends did not exert a unique behaviour in potentiating or reducing the bioactivity of the pomelo EOs.