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     

On-line preconcentration method for the determination of trace metals in water samples using a fully automated pretreatment system coupled with ICP-AES.

An automated on-line sample-preparation method using a computer-controlled pretreatment system (Auto-Pret AES system) coupled with ICP-AES was developed. In this work, an iminodiacetate chelating resin, packed in a mini-column and installed in the system was employed for the collection/concentration of 13 trace metals, including such toxic metals as Be, Cd, Cr, Cu and Pb. The limits of detection of the proposed method for trace metals were in the range of 0.001 (Be) -0.18 (Pb) ng mL-1. The enrichment factors for metal ions were about 19 times, when 5 mL of samples were used. The sample throughput was 11 h-1. The accuracy and the precision of the method were evaluated using river-water reference materials, SLRS-4 from NRCC, JSAC 0301-1 and JSAC 0302 from the Japan Society for Analytical Chemistry. The proposed method can be favorably applied to the collection/concentration of trace metals in natural water samples.     

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.     

Synthesis of aromatic poly(thioether ketone)

Aromatic poly(thioether ketone)s were prepared by the direct polycondensation of aromatic dicarboxylic acids with aryl compounds containing ether or sulfide structures using phosphorus pentoxide/methanesulfonic acid (PPMA) as a condensing agent and solvent. Polycondensation proceeded smoothly and produced aromatic poly(thioether ketone)s with inherent viscosities up to 0.73 dL/g. The synthesis of substituted aryl ketones by the reaction of substituted benzoic acids with aryl compounds in PMMA was studied in detail to demonstrate the feasibility of the reaction for polymer formation. The thermogravimetry of the aromatic poly(thioether ketone)s showed a 10% weight loss in air and nitrogen at around 450 and 460°C, respectively. © 1992 John Wiley & Sons, Inc.     

Synthesis of 5-heteroarylazulenes: first selective electrophilic substitution at the 5-position of azulene

1,3-Di-tert-butylazulene reacted with highly electrophilic trifluoromethanesulfonate of N-containing heterocycles to give 5-(dihydroheteroaryl)azulene derivatives in good yield and treatment of the 5-(dihydroheteroaryl)azulene derivatives with KOH afforded 5-(heteroaryl)azulenes in excellent yield.     

Lightness Change as Perceived in Relation to the Size of Recognized Visual Space of Illumination

According to the concept of the recognized visual space of illumination (RVSI) the lightness of an object surface is perceived in relation to its conceptualized size. To prove this proposition the lightness of gray test patches was judged when they were located at various positions inside an illuminated space composed of two rooms in the depth direction from a subject. No retinal image arrangement was changed in the test patch and its immediate surroundings, but the front room had walls, floors and furniture lower in lightness by the amount of N1.5 than the back room to make the RVSI of the former smaller despite the illuminance in the entire space being the same. The results showed that the apparent lightness of the patches was perceived higher by amount of about 13 in L units for the N4 test patch and about 20 for N6 when the patches were located in the front room, in accordance with the prediction. It was stressed that the experiment of lightness judgment should be conducted in a three dimensional space rather than two dimensional plane as done by several investigators.     

Novel flow injection-fluorometric method for the determination of trace silicate and its application to ultrapurified water analysis

A highly sensitive fluorescence quenching method for the determination of silicate based on the formation of an ion associate between molybdosilicate and Rhodamine B (RB) in nitric acid medium was developed. A flow injection system coupled with a fluorescence detector was used for the measurement of fluorescence intensity at 560 and 580 nm as excitation and emission wavelengths, respectively. The calibration graph for Si showed a linear range of 0.1–5 ng cm⁻³ with correlation coefficient of 0.9999, and the detection limit of 0.06 ng cm⁻³. The proposed method was successfully applied to the determination of silicate in ultrapurified water with satisfactory results.