Left-symmetric algebra structures on the W-algebra W(2, 2)

We study the compatible left-symmetric algebra structures on the W-algebra W(2, 2) with some natural grading conditions. The results of earlier work on left-symmetric algebra structures on the Virasoro algebra play an essential role in determining these compatible structures. As a corollary, any such left-symmetric algebra contains an infinite-dimensional trivial subalgebra that is also a submodule of the regular module.     

Atom Transfer Radical Polymerization of Styrene Using a Bifunctional Initiator

A bifunctional alkyl halide, namely l, 2-bis(2′-bromobutyryl) ethane (BBrBE), was synthesized and used to initiate the bulk atom transfer radical polymerization (ATRP) of styrene (St) at 110°C in the presence of CuBr/2,2′-bipyridyl. The narrow polydispersity of polystyrene (PSt) with precisely two arms could be synthesized. The initiate ability of the two active bromide functional groups at both sides of BBrBE for St and the propagation ability of the two arms were confirmed to be similar by the characterization of the individual arms obtained upon hydrolysis of the ester link between the core and the branches.     

A study on the detection of weak photoacoustic signals by stochastic resonance

On the basis of stochastic resonance (SR) theory a study of the detection of photoacoustic (PA) signals without a lock-in amplifier is presented. The applicability of the SR method is investigated both with simulated signals calculated by use of a Gaussian model and with experimental PA signals. Signal-to-noise ratio (SNR) is improved substantially by adjusting the properties of a non-linear system to realize SR. By use of this method the lock-in amplifier can be removed from a PA spectrometer.     

A low temperature route to nanocrystalline Co9S8

Nanocrystalline Co₉S₈ has been successfully prepared by a hydrothermal-reduction method at 120°C. The reducing agents were produced from disproportionation of white phosphorus in alkaline medium. X-ray diffraction pattern reveals that the product is single phase of Co₉S₈. Transmission electron microscopy shows that the average particle size of Co₉S₈ is about 20 nm. The possible mechanism for the formation of Co₉S₈ and the influence of experimental conditions are discussed.     

Synthesis of polyurethane/clay intercalated nanocomposites

 A kind of polyurethane/organophilic montmorillonite (PU/OMT) nanocomposite based on polyether, OMT, phenylmethane diisocyante and diglycol was synthesized and characterized by X-ray diffraction (XRD) and high-resolution electron microscopy (HREM). A polyether/OMT hybrid was first prepared in a nanocomposite form as confirmed by XRD. It was shown that there is a multilayered structure consisting of alternating PU chains stacked with the layers of the silicate layers in the microstructure of the PU/OMT nanocomposite as confirmed by study of the XRD patterns and the HREM images. The contents of the hard segment of PU and OMT had an effect on the basal spacing of the PU/OMT nanocomposite. Received: 29 August 2000 Accepted: 16 February 2001     

A condition on the chiral symmetry breaking solution of the Dyson–Schwinger equation in three-dimensional QED

In three-dimensional QED, which is analyzed in the 1/N expansion, we obtain a sufficient and necessary condition for a nontrivial solution of the Dyson–Schwinger equation to be chiral symmetry breaking solution. In the derivation, a normalization condition of the Goldstone bound state is used. It is showed that the existent analytical solutions satisfy this condition.     

Syntheses and micellar properties of well‐defined amphiphilic AB2 and A2B Y‐shaped miktoarm star copolymers of ε‐caprolactone and 2‐(dimethylamino)ethyl methacrylate

Well‐defined amphiphilic PCL‐b‐(PDMA)₂ and (PCL)₂‐b‐PDMA Y‐shaped miktoarm star copolymers and PCL‐b‐PDMA linear diblock copolymer were synthesized via a combination of ring‐opening polymerization (ROP) and atom transfer radical polymerization (ATRP), where PCL is poly (ε‐caprolactone) and PDMA is poly(2‐(dimethylamino)ethyl methacrylate). All of these three types of copolymers have comparable PCL contents and overall molecular weights. The PCL block is hydrophobic while the PDMA block is hydrophilic, and they behave like polymeric surfactants and self‐assemble into PCL‐core micelles in aqueous media. The chain architectural effects on the micellization properties, including the aggregation number, size, polydispersity, and micelle densities of (PCL₂₉)₂‐b‐PDMA₄₅, PCL₆₁‐b‐(PDMA₂₄)₂, and PCL₅₆‐b‐PDMA₄₉ in dilute aqueous solution, were then explored by dynamic and static laser light scattering (LLS). The intensity–average hydrodynamic radius, 〈R_h〉, the aggregation number per micelle, N_agg, and the core radius, R_core, of the PCL‐core micelles all increased in the order PCL₆₁‐b‐(PDMA₂₄)₂ < (PCL₂₉)₂‐b‐PDMA₄₅ < PCL₅₆‐b‐PDMA₄₉. The surface area occupied per soluble PDMA block at the core/corona interface increased in the order PCL₆₁‐b‐(PDMA₂₄)₂ < PCL₅₆‐b‐PDMA₄₉ < (PCL₂₉)₂‐b‐PDMA₄₅. PCL₆₁‐b‐(PDMA₂₄)₂ micelles had the largest overall micelle density, possibly because of that the presence of two soluble PDMA arms at the junction point favors the bending of the core–corona interface and thus the formation of densely‐packed core‐shell nanostructures. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1446–1462, 2007     

Synthesis of carbon nanotubes via Fe-catalyzed pyrolysis of phenolic resin

Carbon nanotubes (CNTs) with 40–100 nm in diameter and tens of micrometers in length were prepared via catalytic pyrolysis of phenol resin in Ar at 673–1273 K using ferric nitrate as a catalyst precursor. Structure and morphology of pyrolyzed resin were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and Raman spectroscopy. Ferric nitrate was transformed to Fe₃O₄ at 673 K, and to metallic Fe and Fe_xC carbide at 873–1273 K. The optimal weight ratio of Fe catalyst to phenol resin for growing CNTs was 1.00 wt%, and the optimal temperature was 1073 K. In addition, use of a high pressure increased the yield of CNTs. Density functional theory (DFT) calculations suggest that Fe catalysts facilitate the CNTs growth by increasing the bond length and weakening the bond strength in C₂H₄ via donating electrons to the C atoms in it.     

Riemann-Hilbert method and N-soliton for two-component Gerdjikov-Ivanov equation

We consider the Riemann–Hilbert method for initial problem of the vector Gerdjikov–Ivanov equation, and obtain the formula for its N-soliton solution, which is expressed as a ratio of (N + 1) × (N + 1) determinant and N × N determinant. Furthermore, by applying asymptotic analysis, the simple elastic interactions of N-soliton are confirmed, and the shifts of phase and position are also explicitly displayed.