Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Digital volume gratings

An optical element constructed by stacking a set of binary-phase grating sheets can simulate the functions of optically recorded volume gratings. Our electromagnetic numerical study also shows that if one of the grating sheets is replaced by another one with different grating period, power spectrum of the diffracted wave changes completely with extra diffraction orders. This property will claim strong advantage in security document applications. Analysis of alignment error reveals interesting phenomena concerning to how misalignment affects diffraction efficiency.     

Analytical approach to the discoloration of edible laver "nori" in the Ariake Sea.

To understand the cause of discoloration of the sea laver "nori," which is found in the Ariake Sea, the concentrations of pigments and elements in the normal and discolored laver samples were determined. In the discolored samples, a decrease in all of the pigments, chlorophyll a and carotenoids, and proteinous pigments, phycobiliproteins, was clearly observed. This was accompanied by a decrease in the content of Fe, Zn, Mn, Cu, and P. Good correlations between these elements and chlorophyll a, as well as between these elements and phycobiliproteins, were confirmed, indicating that, in addition to the deficiency of nitrogen and phosphorus, the deficiency of trace elements (Fe, Zn, Mn, and Cu), which are specifically required for photosynthesis, could be a reason for the discoloration of nori. The cause of elemental deficiency is also discussed.     

Alternative copolymerization of aziridines and carbon monoxide by γ-ray irradiation

The copolymerization of carbon monoxide and aziridines such as ethylenimine and propylenimine was carried out by γ-ray irradiation. Aziridines and carbon monoxide were allowed to copolymerize under γ-ray irradiation from a Co⁶⁰ source and gave a crystalline solid copolymer. The yield of the copolymer increased with reaction temperature. The composition of copolymers obtained did not depend on the feed ratio of monomers and was found to be almost equimolar. The copolymer of ethylenimine and carbon monoxide melted at about 322–335°C. with decomposition and has an infrared spectrum identical with that of poly-β-alanine obtained by the hydrogen-migration polymerization of acrylamide. The hydrolyzed product of the ethylenimine–carbon monoxide copolymer was confirmed to be β-alanine by paper chromatography. These results lead to the conclusion that the copolymerization of aziridines and carbon monoxide took place alternatively by γ-ray irradiation, and produced crystalline poly-β-alanines.     

Determination of daidzein and genistein in soybean foods by automated on-line in-tube solid-phase microextraction coupled to high-performance liquid chromatography

An automated on-line method for the determination of the isoflavones, daidzein and genistein, was developed using in-tube solid-phase microextraction coupled to high-performance liquid chromatography (in-tube SPME-HPLC). In-tube SPME is a new extraction technique for organic compounds in aqueous samples, in which analytes are extracted from the sample directly into an open tubular capillary by repeated draw/eject cycles of sample solution. Daidzein, genistein and their glucosides tested in this study were clearly separated within 8 min by HPLC using an XDB-C8 column with diode array detection. In order to optimize the extraction of these compounds, several in-tube SPME parameters were examined. The glucosides daidzin and genistin were analyzed as aglycones after hydrolysis because the glucosides were not concentrated by in-tube SPME. The optimum extraction conditions for daidzein and genistein were obtained with 20 draw/eject cycles of 40 microl of sample using a Supel-Q porous layer open tubular capillary column. The extracted compounds were easily desorbed from the capillary by mobile phase flow, and carryover was not observed. Using the in-tube SPME-HPLC method, the calibration curves of these compounds were linear in the range 5-200 ng/ml, with a correlation coefficient above 0.9999 (n = 18), and the detection limits (S/N = 3) were 0.4-0.5 ng/ml. This method was successfully applied to the analysis of soybean foods without interference peaks. The recoveries of aglycones and glucosides spiked into food samples were above 97%.     

Preparation of crystalline polyamides by the alternating copolymerization of aziridines and cyclic imides

The copolymerization of aziridines and cyclic imides was studied. Aziridines copolymerized alternately with cyclic imides to give crystalline polyamides. Ethylenimine and succinimide copolymerized to nylon 2,4, melting near 300°C., without any catalyst. Similarly, the corresponding crystalline polyamides were obtained from the systems of 1,2-propylenimine–succinimide, ethylenimine–glutarimide, and ethylenimine–phthalimide. The copolymerization of aziridines and cyclic imides in the presence of BF₃OEt₂ gave a copolymer which was rich in aziridine units, whereas, the addition of triethylamine had no influence on the copolymer composition. A mechanism of copolymerization was proposed based on the facts that N-tetramethylenesuccinamide was obtained by the reaction of pyrrolidine and succinimide, N-acetylethylenimine reacted with acetamide to yield N,N′-diacetylethylenediamine and that the rate of this copolymerization was dependent on the electrophilicity of imide.     

Immunochemical determination of dioxins in sediment and serum samples

Polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) are considered highly toxic contaminants and the environmental and biological monitoring of these compounds is of great concern. Immunoassays may be used as screening methods to satisfy the growing demand for rapid and low cost analysis. In this work, we describe the application of an immunoassay that uses 2,3,7-trichloro-8-methyldibenzo-p-dioxin (TMDD) as a surrogate standard for 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) to sediment and human serum samples. Sample extraction and preparation methods were developed with the aim to establish the simplest, cost-effective and efficient removal of the matrix interferences in the enzyme-linked immunosorbent assay (ELISA). The overall method for sediments is based on a hexane extraction; clean up by a multilayered silica gel column and an activated carbon column; an organic solvent exchange with DMSO–Triton X-100 and ELISA measurement. The gas chromatography–high resolution mass spectrometry (GC–HRMS) validation studies (n = 13) revealed that the method is suitable for the toxic equivalents (TEQ) screening of dioxin in sediments with a method detection limit of about 100 pg g⁻¹ dry sediment with a precision of 13–33% R.S.D. The analysis of a large number of samples originating from different sources would be required to establish more precisely the screening level, as well as the number of false positives and negatives of dioxin TEQ by the immunoassay for sediments. The immunoassay method for sediment analysis offers improvement in speed, sample throughput, and cost in comparison to GC–HRMS. Dioxins were determined in serum samples after a simple liquid–liquid extraction and solvent exchange into DMSO–Triton X-100 without further dilution. The current method (approximate method LOQ of 200 pg ml⁻¹ serum) is not sufficiently sensitive for the determination of dioxins in serum to measure acceptable exposure limit.     

Identification of α-type subunits of the Xenopus 20S proteasome and analysis of their changes during the meiotic cell cycle

Background  

The 26S proteasome is the proteolytic machinery of the ubiquitin-dependent proteolytic system responsible for most of the regulated intracellular protein degradation in eukaryotic cells. Previously, we demonstrated meiotic cell cycle dependent phosphorylation of α4 subunit of the 26S proteasome. In this study, we analyzed the changes in the spotting pattern separated by 2-D gel electrophoresis of α subunits during Xenopus oocyte maturation.     

Monomer-isomerization polymerization. XX. Monomer-isomerization polymerization of 2-, 3-, and 4-octenes with Ziegler–Natta catalyst

A study of the monomer isomerization polymerization of 2-, 3-, and 4-octenes has been made with TiCl₃–(C₂H₅)₃Al catalyst at 80°C in comparison with the ordinary polymerization of 1-octene. It was found that all these octenes underwent monomer-isomerization polymerization to give high-molecular-weight homopolymer consisting exclusively of the 1-octene unit. The addition of an isomerization catalyst such as nickel acetylacetonate accelerated this polymerization. The rates of polymerization were found to decrease in the following order: 1-octene > 2-octene > 3-octene > 4-octene. These results indicate that the isomerization proceeded by a stepwise double-bond migration. It was also found that the monomer-isomerization copolymerization of 2-octene and 2-butene occurred under similar conditions and produced copolymers of both 1-olefin units.