Quasifinite highest weight modules over the superW 1+∞algebra

We study quasifinite highest weight modules over the supersymmetric extension of theW ₁₊ algebra on the basis of the analysis by Kac and Radul. We find that the quasifiniteness of the modules is again characterized by polynomials, and obtain the differential equations for highest weights. The spectral flow, free field realization over the (B, C)-system, and the embedding into (|) are also presented.Address after April 1, 1994: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606, JapanAddress after April 1, 1994: Uji Research Center, Yukawa Institute for Theoretical Physics, Kyoto University, Uji 611, Japan     

An embedding theorem of Sobolev type for an operator with singularity

We discuss spaces of Sobolev type which are defined by the operator with singularity: , where and . This operator appears in a one-dimensional harmonic oscillator governed by Wigner's commutation relations. We study smoothness of and continuity of () where is in each space of Sobolev type, and obtain a generalization of the Sobolev embedding theorem. On the basis of a generalization of the Fourier transform, the proof is carried out. We apply the result to the Cauchy problems for partial differential equations with singular coefficients.

     

High-power sub-100-fs UV pulse generation from a spectrally controlled KrF laser

High-power sub-100-fs UV pulses were generated from a KrF excimer laser by spectral control and chirped-pulse amplification. The spectral width was broadened to 1.6 nm, resulting in 72-fs, nearly transform-limited pulses. The average output powers at 1 kHz were 0.6 and 1.2 W for pulse widths of 72 and 110 fs, respectively.     

Analytical electron microscopy study of diffusion-bonded multiphase system

This study presents diffusion experiments of NiAl coupled with pure Ni (Ni/NiAl). The couple produces the Ni₃Al-based intermetallic phase ( phase) as an intermediate layer at the interface during diffusion annealing. Analytical electron microscopy is used to examine microstructural features, crystallographic orientation and compositional variations across the interface. Interdiffusivities are measured from the compositional variations. It is shown that the growing behavior of the phase changes between higher and lower annealing temperatures. The growth kinetics of the phase is also discussed.     

Mixed-valence states in TCNQ salts of monoalkylbiferrocenes and their mixed crystals with dialkyl derivative

TCNQ salts of 1-monoalkylbiferrocenes showed a temperature-independent trapped-valence state as expected for the unsymmetrical structure of cations. On the other hand, mixed crystals of 1-monobutyl- and 1.1-dibutylbiferrocenium⁺(TCNQ) ₃ ^– showed a temperature dependence of the mixed-valence states, showing that the lattice affects the mixed-valence states.     

Accurate U–Th radioactive disequilibrium analyses of carbonate rock samples using commercially available U and Th reagents and multi-collector ICP-MS

This study aims at developing a new analytical procedure for U–Th radioactive disequilibrium of carbonate rock samples. The procedure utilizes commercially available U and Th reagents as spikes for isotope dilution analysis with a multiple-collector inductively coupled mass spectrometer (MC-ICP-MS). Uranium and thorium in a carbonate sample were purified by Fe-coprecipitation, anion exchange resin, and U/TEVA resin. Isotopic compositions of purified spiked and unspiked U and Th were measured respectively for abundance and isotopic analyses. The correction of mass fractionation and the Daly/Faraday gain factor for Th measurements is carried out with a U standard solution. Accuracy of our method was confirmed by analyses of a coral sample that had been dated with thermal ionization mass spectrometry (TIMS). Our results indicate that U–Th disequilibrium studies are possible using easily available U and Th reagents as spikes.