Recursive Fermion System in Cuntz Algebra. I

Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra ?₂ (or ?_{2 d} more generally) are presented by using recursive constructions. As a typical example, an embedding of CAR onto the U(1)-invariant subalgebra of ?₂ is constructed explicitly. Generalizing this construction to the case of ?_{2 p} , an embedding of CAR onto the U(1)-invariant subalgebra of ?_{2 p} is obtained. Restricting a permutation representation of the Cuntz algebra, we obtain the Fock representation of CAR. We apply the results to embed the algebra of parafermions of order p into ?_{2 p} according to Green's ansatz. Received: 3 September 2001 / Accepted: 19 January 2002     

Polarization Sensitive Spectral Interferometric Optical Coherence Tomography for Biological Samples

A spectral interferometric optical coherence tomography (OCT) system which has polarization sensitivity is developed. This system reduces the mechanical scanning dimension by employing the principle of spectral interferometry, and measures a two dimensional cross-sectional image of biological tissue with one dimensional mechanical scanning. Sixteen OCT images with different polarization conditions are measured, and two dimensional distributions of each element of the Müller matrix of a sample to be measured are calculated.     

Spectrophotometric determination of copper(II) with carbon disulfide,a secondary amine and triton X-100

Copper(II) is determined by non-extractive spectrophotometry as a complex of butylene dithiocarbamate formed in situ by reaction between carbon disulfide and pyrrolidine in aqueous Triton X-100 medium. This method is similar to that with butylene dithiocarbamate as starting material in the sense of simplicity, sensitivity, precision and accuracy. Pyrrolidine is the best of seven secondary amines tested in this way for copper determinations.     

Ethylene polymerization by chromium complexes with phosphorous‐bridged bisphenoxy ligand

Chromium catalysts combined with phosphorous‐bridged bisphenoxy ligands were found to be highly active for ethylene polymerization. The most efficient catalyst precursor among them, generated by combining bis[3‐tert‐butyl‐5‐methyl‐2‐hydroxyphenyl](phenyl)phosphine hydrochloride ( 1a ) and CrCl₃(THF)₃, was characterized. X‐ray analysis of (3‐tert‐butyl‐5‐methyl‐2‐phenoxy)(3‐tert‐butyl‐5‐methyl‐ 2‐hydroxyphenyl)(phenyl)phosphine bis(tetrahydrofuran)chromium dichloride ( 6 ), obtained by the reaction of 1a and CrCl₃(THF)₃ in the presence of NaH, revealed a unique structure in which one phenol moiety of the bisphenol did not coordinate to the chromium center. Complex 6 showed higher activities than those observed in the in situ catalyst system. Polyethylene of various molecular weights was obtained with differing activators. The highest activity (113.5 kg mmol (cat)^?1 h^?1) was observed when TIBA/TB was used as a cocatalyst. A medium molecular weight polymer with narrow molecular weight distribution (M_w = 128,700, M_w/M_n = 1.8) was obtained using a 6 ‐TIBA/B(C₆F₅)₃ system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3668–3676, 2007     

Convergent Star Product Algebras on ‘ax+b’

We define nontempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product. The techniques used to achieved the latter come from symmetric spaces geometry and star representation theory.     

Determination of237Np in environmental samples using inductively coupled plasma mass spectrometry

Ammonium uranates (AU) obtained by the addition of aqueous NH₄ OH to a solution of UO₂ (NO₃)₂ or the equilibrium reaction of UO₃ · 2H₂ O with the vapour over concentrated NH₄ OH have been studied by X-ray diffraction (XRD) analysis, diffuse reflectance Fourier transform infrared spectrometry (DR-FTIR) and chemical analysis. Ammonia can be present as either NH₃ or NH ₄ ⁺ . For precipitates obtained at a pH of 3.7, ammonia in the form of NH₃ is predominant. For ammonium uranate obtained by reaction over concentrated NH₄OH, most of the ammonia is bonded as NH ₄ ⁺ . The reaction mechanism and structures of the products are also discussed.     

Efficient [3,3]-sigmatropic rearrangement accelerated by a trifluoroacetyl group: synthesis of benzofurans under mild conditions

The [3,3]-sigmatropic rearrangement took place smoothly during the course of trifluoroacetylation of O-phenyloxime at below room temperature to give the dihydrobenzofuran or benzofuran as a result of concomitant cyclization.     

Adsorption Isotherm of Water Vapor and Its Large Hysteresis on Highly Ordered Mesoporous Silica

The first and second adsorption–desorption isotherms of water vapor on a new mesoporous material derived from kanemite have been measured. The isotherms show unusual type V isotherms and large hysteresis. The type V isotherms, which have never been observed for the other adsorbates, suggest that the mesoporous material has a hydrophobic surface, although the hydrophobicity decreased after treatment with water vapor because of rehydration of the surface. The significantly large hysteresis could be explained by the difference in contact angle between adsorption and desorption.