Generalized rational identities of subnormal subgroups of skew fields

Let be a skew field with infinite center such that , and let be a non-central subnormal subgroup of the multiplicative group of . Then there are no non-trivial generalized rational identities of . This generalizes a theorem proved by Makar-Limanov.

     

Positron lifetime and 2D-ACAR studies of divacancies in Si

We have measured positron lifetime and Two Dimensional Angular Correlation of Annihilation Radiation (2D-ACAR) distributions of Floating-Zone grown (FZ) Si specimens containing divacancies (V₂) with the definite charge states, V ₂ ⁰ , V ₂ ^–1 or V ₂ ^–2 from room temperature to about 10 K. These charge states are accomplished by an appropriate combination of dopant species, their concentration and irradiation doses of 15 MeV electrons. with reference to the currently accepted ionization level of divacancies. The positron lifetime of the negatively charged divacancy increases with temperature, while that of the neutral divacancy shows little change with temperature. The positron trapping rate, obtained from lifetime and 2D-ACAR measurements, increases markedly with decreasing temperature. This is found not only for the negative divacancies but also for the neutral divacancy. We need a model which explains this temperature dependence. The 2D-ACAR distribution from positrons trapped at divacancies shows nearly the same distribution for the different charge states, which differs considerably from the case of As vacancies in GaAs studied by Ambigapathy et al. We have observed a small but definite anisotropy in the distribution of trapped positrons in V ₂ ^– using a specimen containing oriented divacancies.Paper presented at the 132nd WE-Heraeus-Seminar on Positron Studies of Semiconductor Defects, Halle, Germany, 29 August to 2 September 1994     

Scanning near-field optical images of ordered polystyrene particle layers in transmission and luminescence excitation modes

Scanning near-field optical images of hexagonally close-packed layers of polystyrene spherical particles with a diameter of 1.0 microm have been investigated. The layers were composed of particles that were doped either totally or partially with an organic fluorescent dye. Observations were made in the transmission and luminescence excitation modes with a scanning near-field optical microscope (SNOM) with a spatial resolution shorter than the wavelength of light. The patterns observed in the SNOM images are significantly dependent on the microstructures of layers, that is, the layers are either single or double layered, and the particles are either totally or partially doped. These results are discussed in terms of specific modes of electromagnetic waves transmitting across and along the layers after the local excitation at the tip end of the scanning microprobe.     

Optical recognition of surface chirality at Au(hkl) single crystalline surfaces by second harmonic generation rotational anisotropy

Two-dimensional chirality at naturally chiral gold single crystalline surfaces was detected and characterized using optical second harmonic generation (SHG) measurements. SHG rotational anisotropy (SH-RA) patterns at Au(643)S and Au(643)R surfaces were mirror symmetric to each other. Systematic SH-RA measurements at chiral Au(hkl) surfaces with the same step and kink structures but different (111) terrace widths showed a linear correlation between surface step density and SH-RA fitting parameters arising from defects. These results indicate that SH-RA measurements provide information not only on surface chirality but also on density of surface defects.     

Michael addition of stannyl ketone enolate to alpha,beta-unsaturated esters catalyzed by tetrabutylammonium bromide and an ab initio theoretical study of the reaction course

Michael addition of stannyl ketone enolates to alpha,beta-unsaturated esters was accomplished in the presence of a catalytic amount of tetrabutylammonium bromide (Bu(4)NBr). Other typical systems using lithium enolate or silyl enolate with catalysts (TiCl(4) or Bu(4)NF) failed to give the desired products. The bromide anion from Bu(4)NBr coordinates to the tin center in enolate to accelerate the conjugate addition where a five-coordinated tin species was generated. The coordination of the bromide anion significantly raises the HOMO level of tin enolate and enhances its nucleophilicity. The conjugate addition provides the intermediate Michael adduct, which has an ester enolate moiety, and the adduct immediately transforms to alpha-stannyl gamma-ketoester by keto-enol tautomerization. This step contributes to the stabilization of the product system and leads to a thermodynamically favorable reaction course. An ab initio calculation reveals that the activation energy in the reaction using the bromide anion is lower than that of the reaction without using it. The transition state in either reaction course has a linear structure, not a cyclic one. This system can be applied to a variety of tin enolates and alpha,beta-unsaturated carbonyls involving enoates, enones, and unsaturated amides.