Bifurcations on contact manifolds

Consider a 1-parameter compactly supported family of Legendrian submanifolds of the 1-jet bundle of a compact manifold with its natural contact structure and a path of intersection points of the Legendrian family with the 1-jet of a constant function. Since the contact distribution is a symplectic vector bundle, it is possible to assign a Maslov-type index to the intersection path. We show that the non-vanishing of the Maslov intersection index implies that there exists at least one point of bifurcation from the given path of intersection points. This result can be viewed as a kind of analogue in bifurcation theory of the Arnold-Sandon conjecture on intersections of Legendrian submanifols. The proof is based on the technique of generating functions that relates the properties of Hamiltonian diffeomorphisms to the Morse theory of the associated functions.     

Cooperative work in an e-learning environments: the COMSON case

Coupled Multiscale Simulation and Optimization in Nanoelectronics project isaMarie Curie RTN supported by the European Commission within the 6th Framework Research Programme of the EU. The COMSON project is run by a Consortium whose multiple aims are: to build an experimental software Demonstrator Platform (DP) for coupled simulation of devices, interconnects, circuits, EM fields and thermal effects (one single framework for simulation tool, optimisation in compound design space); to provide an e-learning platform to be used as an inter and extra consortium transfer of knowledge (ToK) infrastructure; to provide a collaborative virtual work environment (CWE) to be used both for industrial activities and training. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fixed-point-free elements in <Emphasis Type="Italic">p</Emphasis>-groups

In this paper we prove that there exists no function F(m, p) (where the first argument is an integer and the second a prime) such that, if G is a finite permutation p-group with m orbits, each of size at least p ^F(m,p), then G contains a fixed-point-free element. In particular, this gives an answer to a conjecture of Peter Cameron; see [4], [6].     

Stability toward alkaline hydrolysis of B. mori silk fibroin grafted with methacrylamide

Bombyx mori silk fibroin fibers were grafted with methacrylamide (MAA) and characterized by Raman and infrared (IR) vibrational spectroscopy before and after hydrolysis in NaOH 5% to elucidate the possible interactions between the two components and the stability of the fibers toward alkaline hydrolysis. Upon grafting, the fibers underwent conformational rearrangements toward a more unordered state and lost orientation at weight gains higher than 60%. Vibrational spectroscopy disclosed the occurrence of intermolecular interactions (mainly hydrogen bonds) between B. mori silk fibroin and polyMAA in the grafted fibers, and the formation of covalent bonds has been explored. These strong interactions made the grafted fibers as a whole more stable toward alkaline hydrolysis because they prevented the solubilization of the polymer upon hydrolysis and made slower the transformation of its CONH₂ groups into COOH and COO⁻ groups. Upon hydrolysis, silk fibroin underwent an enrichment in the β‐sheet crystalline domains, because of the preferential removal of the unordered domains, which were more prone to the OH⁻ attack. IR and Raman spectroscopy proved valid techniques to investigate the degradation mechanism and kinetics of grafted silk fibroin fibers and so for designing high‐performing silk‐based materials. The A₇₃₁/A₁₀₀₄ Raman intensity ratio was proposed to spectroscopically evaluate the composition of the grafted samples; its value was found to linearly increase with weight gain (R² = 0.998), envisaging the possibility of using Raman spectroscopy as a routine analytical technique for qualitative and quantitative characterization of grafted industrial samples. Copyright © 2016 John Wiley & Sons, Ltd.     

Relative binding orientations of adenosine A1 receptor ligands — A test case for Distributed Multipole Analysis in medicinal chemistry

Summary The electrostatic properties of adenosine-based agonists and xanthine-based antagonists for the adenosine A₁ receptor were used to assess various proposals for their relative orientation in the unknown binding site. The electrostatic properties were calculated from distributed multipole representations of SCF wavefunctions. A range of methods of assessing the electrostatic similarity of the ligands were used in the comparison. One of the methods, comparing the sign of the potential around the two molecules, gave inconclusive results. The other approaches, however, provided a mutually complementary and consistent picture of the electrostatic similarity and dissimilarity of the molecules in the three proposed relative orientations. This was significantly different from the results obtained previously with MOPAC AM1 point charges. In the standard model overlay, where the aromatic nitrogen atoms of both agonists and antagonists are in the same position relative to the binding site, the electrostatic potentials are so dissimilar that binding to the same receptor site is highly unlikely. Overlaying the N⁶-region of adenosine with that near C8 of theophylline (the N⁶-C8 model) produces the greatest similarity in electrostatic properties for these ligands. However, N⁶-cyclopentyladenosine (CPA) and 1,3-dipropyl-8-cyclopentylxanthine (DPCPX) show greater electrostatic similarity when the aromatic rings are superimposed according to the flipped model, in which the xanthine ring is rotated around its horizontal axis. This difference is mainly attributed to the change in conformation of N⁶-substituted adenosines and could result in a different orientation for theophylline and DPCPX within the receptor binding site. However, it is more likely that DPCPX also binds according to the N⁶-C8 model, as this model gives the best steric overlay and would be favoured by the lipophilic forces, provided that the binding site residues could accommodate the different electrostatic properties in the N⁶/N7-region. Finally, we have shown that Distributed Multipole Analysis (DMA) offers a new, feasible tool for the medicinal chemist, because it provides the use of reliable electrostatic models to determine plausible relative binding orientations.Abbreviations DMA distributed multipole analysis - SCF self-consistent field - CPA N⁶-cyclopentyladenosine - DPCPX 1,3-dipropyl-8-cyclopentylxanthine - R-PIA R-1-phenyl-2-propyladenosine - S-PIA S-1-phenyl-2-propyladenosine     

EPR study of interaction of vanadium pentoxide with H-ZSM-5 zeolite

The EPR spectroscopy has been used to study the interaction of vanadium pentoxide with H-ZSM-5 zeolite, supplied by ICITPR-Ploiesti, Romania, occurring at the calcination of the mixture at temperatures from 100 to 1000°C, in air, followed by evacuation at 20°C, as well as for those rehydrated at room temperature. The EPR method is also used to follow the thermal stability of the investigated zeolite, the framework alteration and the nature of VO²⁺ complexes formed during solid phase reaction. At least two types VO²⁺ centres were identified in H-ZSM-5 zeolite. One of them being ascribed to dehydrated VO²⁺ complexes in cationic sites, with C_4v ligand field symmetry and the second one corresponding to the hydrated complex with a square bipyramidal symmetry, D_4h. Increasing covalent character, for the in-plane σ-bond and increasing ionic character for the out-of-plane π bond, have been found on rehydrated samples. For a low content of oxide ( 5% wt V₂O₅) in a mixture the thermal stability, T = 1070°C, of the zeolite phase is not affected by the presence of the reaction products.     

Mechanism of aerobic decomposition of Angeli's salt (sodium trioxodinitrate) at physiological pH

The recent determination that Angeli's salt may have clinical application as a nitrogen oxide donor for treatment of cardiovascular diseases such as heart failure has led to renewed interest in the mechanism and products of thermal decomposition of Angeli's salt under physiological conditions. In this report, several mechanisms are evaluated experimentally and by quantum mechanical calculations to determine whether HNO is in fact released from Angeli's salt in neutral, aerobic solution. The mechanism of product autoxidation is also considered.     

Polymeric Ti(IV) glycolate: A heterogeneous catalyst for solvent-free sulfoxidation by t-butyl hydroperoxide

The oxidation of sulfides to sulfoxides has been conveniently performed under heterogeneous and solvent-free conditions employing polymeric Ti(IV) glycolate as reusable catalyst and t-butyl hydroperoxide as oxygen donor. The catalyst can be very efficiently recovered and reused several times without any significant change in reactivity and selectivity.     

New Hints on the Maya Blue Formation Process by PCA-Assisted In Situ XRPD/PDF and Optical Spectroscopy

The exact recipe to prepare the ancient Maya Blue (MB), an incredibly resistant and brilliant pigment prepared from indigo (dye) and Palygorskite (clay), is lost to the ages. To unravel the key features of the MB formation process, several inorganic-dye couples were heated to 200 °C and cooled to RT, to investigate their reactivity and the diffusion and degree of sequestration of the dye into the inorganic host. In situ XRPD/PDF and fiber optic reflectance spectroscopy (FORS) data, along with TGA, provided a comprehensive overview on MB formation mechanism. XRPD/PDF gave information on long/short range behaviors of water desorption/adsorption and indigo sequestration, while TGA and in situ FORS gave information on mass and optical changes within temperature. Ex situ dye removal was used to understand the sample stability after the thermal treatment. A statistical approach based on principal component analysis was exploited to efficiently and jointly analyze the ≈3000 collected patterns. MB formation starts below 110 °C with disordered distribution of indigo within the channels, reaching maximum reaction speed and higher ordering at 150 °C. Above 175 °C, color changes and a stronger sequestration of indigo into framework channels are observed, whereas the affinity for water is dramatically reduced. The origin of different colors, hues, and stability in historical MB samples can then be explained in terms of different thermal histories of the starting mechanical indigo/palygorskite mixtures.