Star-polarization: A natural link between phase space representation and operator representation of quantum mechanics

The method of *-polarization connects phase space mechanics to the usual operator formulation of quantum theory. A *-polarization is a linear submanifold of the space of C functions on phase space. Elements of a *-polarization are in direct correspondence with the Schroedinger wave functions and this correspondence induces the Weyl correspondence between classical observables and operators. All generalized Moyal algebras admit *-polarizations and a general method is thus available for translating *-quantization into operator language.     

Liquid Nickel Salts: Synthesis,Crystal Structure Determination,and Electrochemical Synthesis of Nickel Nanoparticles

New nickel‐containing ionic liquids were synthesized, characterized and their electrochemistry was investigated. In addition, a mechanism for the electrochemical synthesis of nanoparticles from these compounds is proposed. In these so‐called liquid metal salts, the nickel(II) cation is octahedrally coordinated by six N‐alkylimidazole ligands. The different counter anions that were used are bis(trifluoromethanesulfonyl)imide (Tf₂N^?), trifluoromethanesulfonate (OTf^?) and methanesulfonate (OMs^?). Several different N‐alkylimidazoles were considered, with the alkyl sidechain ranging in length from methyl to dodecyl. The newly synthesized liquid metal salts were characterized by CHN analysis, FTIR, DSC, TGA and viscosity measurements. An odd‐even effect was observed for the melting temperatures and viscosities of the ionic liquids, with the complexes with an even number of carbon atoms in the alkyl chain of the imidazole having a higher melting temperature and a lower viscosity than the complexes with an odd number of carbons. The crystal structures of several of the nickel(II) complexes that are not liquid at room temperature were determined. The electrochemistry of the compounds with the lowest viscosities was investigated. The nickel(II) cation could be reduced but surprisingly no nickel deposits were obtained on the electrode. Instead, nickel nanoparticles were formed at 100 % selectivity, as confirmed by TEM. The magnetic properties of these nanoparticles were investigated by SQUID measurements.     

Estimating searching cost of regular path queries on large graphs by exploiting unit-subqueries

Journal of Heuristics - Regular path queries (RPQs) are widely used on a graph whose answer is a set of tuples of nodes connected by paths corresponding to a given regular expression. Traditional...     

On the colored Jones polynomial and the Kashaev invariant

We express the colored Jones polynomial as the inverse of the quantum determinant of a matrix with entries in the q-Weyl algebra of q-operators, evaluated at the trivial function (plus simple substitutions). The Kashaev invariant is proved to be equal to another special evaluation of the determinant. We also discuss the similarity between our determinant formula of the Kashaev invariant and the determinant formula of the hyperbolic volume of knot complements, hoping it will lead to a proof of the volume conjecture. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 57–78, 2005.     

Bacteriostatic Behavior of PLA-BaTiO3 Composite Fibers Synthesized by Centrifugal Spinning and Subjected to Aging Test

The present work investigated the effect of Polylactic acid (PLA) fibers produced by centrifugal spinning with incorporated BaTiO₃ particles to improve their bacteriostatic behavior. The PLA matrix and three composites, presenting three different amounts of fillers, were subjected to UV/O₃ treatment monitoring the possible modifications that occurred over time. The morphological and physical properties of the surfaces were characterized by different microscopic techniques, contact angle, and surface potential measurements. Subsequently, the samples were tested in vitro with human dermal fibroblasts (HDF) to verify the cytotoxicity of the substrates. No significant differences between the PLA matrix and composites emerged; the high hydrophobicity of the fibers, derived by the polymer structure, represented an obstacle limiting the fibroblast attachment. Samples underwent bacterial exposure (Staphylococcus epidermidis) for 12 and 24 h. Increasing the concentration of BT, the number of living bacteria and their distribution decreased in comparison with the PLA matrix suggesting an effect of the inorganic filler, which generates a neutralization effect leading to reactive oxygen species (ROS) generation and subsequently to bacterial damages. These results suggest that the barium titanate (BT) fillers clearly improve the antibacterial properties of PLA fibers after aging tests made before bacterial exposure, representing a potential candidate in the creation of composites for medical applications.     

Magic-angle-spinning-induced local ordering in polymer electrolytes and its effects on solid-state diffusion and relaxation NMR measurements

Magic-angle-spinning (MAS) enhances sensitivity and resolution in solid-state nuclear magnetic resonance (NMR) measurements. MAS is obtained by aerodynamic levitation and drive of a rotor, which results in large centrifugal forces that may affect the physical state of soft materials, such as polymers, and subsequent solid-state NMR measurements. Here, we investigate the effects of MAS on the solid-state NMR measurements of a polymer electrolyte for lithium-ion battery applications, poly(ethylene oxide) (PEO) doped with the lithium salt LiTFSI. We show that MAS induces local chain ordering, which manifests itself as characteristic lineshapes with doublet-like splittings in subsequent solid-state ¹ H, ⁷ Li, and ¹⁹ F static NMR spectra characterizing the PEO chains and solvated ions. MAS results in distributions of stresses and hence local chain orientations within the rotor, yielding distributions in the local magnetic susceptibility tensor that give rise to the observed NMR anisotropy and lineshapes. The effects of MAS were investigated on solid-state ⁷ Li and ¹⁹ F pulsed-field-gradient (PFG) diffusion and ⁷Li longitudinal relaxation NMR measurements. Activation energies for ion diffusion were affected modestly by MAS. ⁷Li longitudinal relaxation rates, which are sensitive to lithium-ion dynamics in the nanosecond regime, were essentially unchanged by MAS. We recommend that NMR researchers studying soft polymeric materials use only the spin rates necessary to achieve the desired enhancements in sensitivity and resolution, as well as acquire static NMR spectra after MAS experiments to reveal any signs of stress-induced local ordering.     

Spotlight on Photoinduced Aryl Migration Reactions

Rearrangement reactions are certainly one of the most useful approaches towards complex structures in organic chemistry. With efficient conditions, it is indeed possible to convert simple substrates into highly functionalized products. Moreover, combining this approach with an attractive initiation process, such as visible-light catalysis, makes these reactions particularly powerful. Recently, tremendous improvements have been made, owing to a better understanding of photoredox mechanisms. In this review, recent progress on visible-light aryl migration reactions is discussed, focusing especially on Smiles rearrangement and related reactions.