Generic initial ideals of Artinian ideals having Lefschetz properties or the strong Stanley property

For a standard Artinian k-algebra A=R/I, we give equivalent conditions for A to have the weak (or strong) Lefschetz property or the strong Stanley property in terms of the minimal system of generators of gin(I). Using the equivalent condition for the weak Lefschetz property, we show that some graded Betti numbers of gin(I) are determined just by the Hilbert function of I if A has the weak Lefschetz property. Furthermore, for the case that A is a standard Artinian k-algebra of codimension 3, we show that every graded Betti number of gin(I) is determined by the graded Betti numbers of I if A has the weak Lefschetz property. And if A has the strong Lefschetz (respectively Stanley) property, then we show that the minimal system of generators of gin(I) is determined by the graded Betti numbers (respectively by the Hilbert function) of I.     

Indium- and zinc-mediated allylation of difluoroacetyltrialkylsilanes in aqueous media

Metal-mediated allylations of difluoroacetyltriakylsilanes with various allyl bromides in aqueous media form homoallylic alcohols exclusively. The common Brook rearrangement, carbon to oxygen-silyl migration, is totally suppressed with no detectable formation of silyl enol ether. Influence of solvents on reaction is studied. Reactivity differences between indium and zinc are also described.     

Synthesis and characterization of Ni magnetic nanoparticles in AlMCM41 host

Superparamagnetic nickel nanoparticles were prepared by incorporating nickel ion into AlMCM41 as a nanoreactor and then reduced with sodium borohydride or H₂ gas. Products were characterized by elemental analysis, transmission electron microscopy, X-ray powder diffraction, and magnetic susceptibility. The nickel particle size and blocking temperature depend on the reduction method.     

White electroluminescence from a single polyfluorene containing bis‐DCM units

A series of fluorene‐based copolymers composed of blue‐ and orange‐light‐emitting comonomers were synthesized through palladium‐catalyzed Suzuki coupling reactions. 9,9‐Dihexylfluorene and 2‐(2,6‐bis‐{2‐[1‐(9,9‐dihexyl‐9H‐fluoren‐2‐yl)‐1,2,3,4‐tetrahydroquinolin‐6‐yl]‐vinyl}‐pyran‐4‐ylidene)‐malononitrile (DCMF) were used as the blue‐ and orange‐light‐emitting chromophores, respectively. The resulting single polymers exhibited simultaneous blue (423/450 nm) and orange (580–600 nm) emissions from these two chromophores. By adjusting the fluorene and DCMF contents, white light emission could be obtained from a single polymer; a device with an ITO/PEDOT:PSS/polymer/Ca/Al configuration was found to exhibit pure white electroluminescence with Commission Internationale de L'Eclairage (CIE) coordinates of (0.33, 0.31), a maximum brightness of 1180 cd/m², and a current efficiency of 0.60 cd/A. Furthermore, the white light emission of this device was found to be very stable with respect to variation of the driving voltage. The CIE coordinates of the device were (0.32, 0.29), (0.32, 0.29), and (0.33, 0.31) for driving voltages of 7, 8, and 10 V, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3380–3390, 2007     

Simple, Rapid, and Sensitive Determination of Odorous Compounds in Water by GC–MS

A gas chromatographic–mass spectrometric method has been developed for rapid and sensitive determination of odorous compounds in water. The water sample (200 mL), at pH 6.5, was extracted with 1 mL pentane in a 250-mL separatory funnel. Fluorobenzene was added to the water sample as internal standard and the solution was mechanically shaken for 5 min and analyzed by GC–MS, with selected ion monitoring, without further concentration or purification steps. The peaks had good chromatographic properties and extraction of the compounds from water resulted in relatively high recoveries with small variations. The detection limits of the assay were 0.1 ng L^–1 for 2-isopropyl-3-methoxypyrazine, 2-isobutyl-3-methoxypyrazine, 2-methylisoborneol, and geosmin, 0.5 ng L^–1 for anisole, and 1.0 ng L^–1 for 2,4,6-trichloroanisole and trans, trans-2,4-heptadienal. Turn-around time was one day for up to approximately 40 samples. The method is simple, convenient, and can be learned easily by relatively inexperienced personnel. It was used to analyze seven odorous compounds in water from Decheung-Lake in Korea, and raw and treated water originating from the same lake. In the summer of 2001 significant levels of anisole (up to 225 ng L^–1) were observed, and geosmin and 2-methylisoborneol were detected at concentrations of up to 23.8 and 26.7 ng L^–1, respectively. 2-Isopropyl-3-methoxypyrazine, 2-isobutyl-3-methoxypyrazine, and trans, trans-2,4-heptadienal levels during that period were not significant. The method can used for simultaneous detection of several odorous compounds in water.     

Essay: A New Era in High-Energy Physics

In TeV-scale gravity, scattering of particles with center-of-mass energy of the order of a few TeV can lead to the creation of nonperturbative, extended, higher-dimensional gravitational objects: Branes. Neutral or charged, spinning or spinless, Einsteinian or supersymmetric, low-energy branes could dramatically change our picture of high-energy physics. Will we create branes in future particle colliders, observe them from ultra high energy cosmic rays, and discover them to be dark matter?     

Cone-shaped structures of GeO2 fabricated by a thermal evaporation process

We have synthesized cone-like GeO₂ structures via thermal heating of Ge powders. We have investigated the effects of substrate temperature on the sample morphology, revealing that cone-shaped structures are preferentially obtained at higher temperature. The cone-shaped structures, which gradually become thinner to form a sharp tip, appear to be a single-crystalline, hexagonal structure of GeO₂. Room-temperature photoluminescence measurement revealed two emission peaks, at about 2.78 and 3.04 eV.     

Optically detected electrophonon resonance effects in quantum wells

Optical detected electrophonon resonance (ODEPR) effects in quantum wells of n-GaAs materials are investigated for square potential and parabolic potential, respectively. We also obtain the ODEPR conditions as functions of confinement frequency in parabolic potential and well-width in square potential for the various photon frequencies, respectively. In particular, anomalous behaviors of the ODEPR lineshape such as the splitting of ODEPR peaks for incident photon frequency are discussed. Furthermore, we obtain the selection rules for transition in quantum wells of two different potentials, respectively.