On general solution of a first-order non-linear differential equation of the formx(dy/dx)=y (λ+f (x,y)) with negative rational λ

Summary This paper studies an equation of the form x dy/dx=y(+f(x, y)),f(0,0)=0, where is a negative rational number andf(x, y) is a holomorphic function of (x, y) near (0, 0). It is known that by a formal transformation this equation is formally reduced to an equation of the form (R). The simplest case such that ==0 was studied by H. Dulac. The general case was studied by M. Hukuhara and he obtained an analytic expression (but not convergent) for a general solution. We will discuss how to construct a convergent one.Dedicated to Professor Taro Yoshizawa on his sixtieth birthday     

On orthogonal groups over the integers of a non-dyadic local field

Let L be a lattice in a quadratic space over a non-dyadic local field. We shall answer the question: What are the lattices whose unit groups coincide with that of L? If the residue class field has more than three elements the question is easy. In this case such a lattice must be $\text{a}$L or $\text{a}$L^# with a fractional ideal $\text{a}$ and the dual lattice L^# by Satz 2 of A. Kallmann, M. Kneser, and U. Stuhler (J. Reine Angew. Math.258 (1978), 51–54) or Theorem 5.2 of C. R. Riehm (Amer. J. Math.89 (1967), 549–577). But it is not easy in the case of the residue class field of three elements.     

Simultaneous liquid chromatographic determination of 39 polycyclic aromatic hydrocarbons in indoor and outdoor air and application to a survey on indoor air pollution in Fuji, Japan

An analytical method was established for the simultaneous determination of 39 polycyclic aromatic hydrocarbons (PAHs) in air. The method was applied to a survey of gaseous and particulate PAHs in household indoor air. The survey was performed in 21 houses in the summer of 1999 and in 20 houses in the winter of 1999-2000 in Fuji, Japan. Thirty-eight PAHs were determined in indoor and outdoor air in the summer, and 39 PAHs were determined in indoor and outdoor air in the winter. The concentrations of gaseous PAHs in indoor air tended to be higher than those in outdoor air in the summer and winter. The concentrations of particulate PAHs in indoor air were the same as or lower than those in outdoor air in the summer and winter. PAH profiles, correlations between PAH concentrations, and multiple regression analysis were used to determine the factors affecting the indoor PAH concentrations. These results showed that gaseous PAHs in indoor air were primarily from indoor emission sources, especially during the summer, and that indoor particulate PAH concentrations were significantly influenced by outdoor air pollution.     

Synthesis of (±)‐Kempa‐6,8‐dien‐3‐ol (=(2aRS,3SR,4aSR,7RS,7aSR,10bSR,10cSR)‐2,2a,3,4,4a,5,6,7,7a,8,10b,10c‐Dodecahydro‐2a,7,10,10c‐tetramethylnaphth[2,18‐cde]azulen‐3‐ol)

The synthesis of kempa‐6,8‐dien‐3β‐ol ( 4a ), as a synthetic leading model of the natural product 4b , was carried out starting from intermediate 12 , the synthetic route of which has been developed previously (Scheme 1). The conversion of 12 to the model compound 4a involved the elaboration of three structure modifications by three processes, Tasks A, B, and C (see Scheme 2). Task A was achieved by epoxy‐ring opening of 41 with Me₃SiCl (Scheme 9), and Task B being performed by oxidation at the 13‐position, followed by hydrogenation, and then epimerization (Schemes 4 and 5). The removal of the 2‐OH group from 12 (Task C) was achieved via 30b according to Scheme 6, whereby 30b was formed exclusively from 30a / 31a 1 : 1 (Scheme 7). In addition, some useful reactions from the synthetic viewpoint were developed during the course of the present experiments.     

Extraction Behavior of Amino Acids by Calix[6]arene Carboxylic Acid Derivatives

A series of calixarene carboxylic acid derivatives were synthesized for the extraction of amino acids. A calix[6]arene carboxylic acid derivative showed the highest extractability to the target tryptophan ester. The main driving forcefor the complexation was the interaction between the ammonium cation of the aminoacid and the oxygen atoms of the host molecule. Stripping of amino acids was alsoaccomplished by contacting the organic solution with a fresh acidic solution. Basedon slope and Job method analyses, it was confirmed that the calix[6]arene formsa 1 : 1 complex with the amino acid ester. The structure of the complex between the calix[6]arene and the amino acid was investigated by ¹H-NMR and CD spectra. The calix[6]arene includes a guest molecule in the cavity, and the inclusion induces the asymmetrization of the host molecule. This host compound functions as a novel recognition tool for amino acids.     

Multicolor photochromism of two- and three-component diarylethene crystals

Novel photochromic single crystals composed of three different kinds of diarylethenes, 1,2-bis(3,5-dimethyl-2-thienyl)perfluorocyclopentene (1a), 1,2-bis(2,5-dimethyl-3-thienyl)perfluorocyclopentene (2a), and 1,2-bis(2-methyl-5-p-methoxyphenyl-3-thienyl)perfluorocyclopentene (3a), have been prepared. The three-component crystals turned yellow, orange, red, purple, blue, green, or black upon irradiation with light of appropriate wavelengths. The colors of the crystals were thermally stable in the dark and completely bleached by irradiation with visible light. Such multicolored photochromic crystals have potential for the application to optoelectronic devices, such as multifrequency three-dimensional optical memory media or full-color displays.     

Carbamate mediated 1,3-asymmetric induction. A stereoselective synthesis of acyclic 1,3-diol systems

A highly regio- and stereo-selective functionalization of homoallylic carbamates with iodine is reported. The reaction has been applied to the preparation of key 1,3,5-triol intermediate $\text{2}$ employed in the synthesis of compactin ($\text{1}$).     

Presence of peroxyradicals in cigarette smoke and the scavenging effect of shikonin, a naphthoquinone pigment

Using a new method having been developed for the purpose of quantitative determination for peroxyradicals, the presence of peroxyradicals was proved in cigarette smoke. In brief, peroxyradicals in cigarette smoke were measured by ESR spectrometry coupled to non-reductive scavenging of 1,1-diphenyl-2-picrylhydrazyl (DPPH). As a result, peroxyradicals were found to be major reactive oxygen species (ROS) since the concentration of peroxyradicals recovered from cigarette smoke was much higher than that of any of other ROS (superoxide and hydroxyl radical) and nitric oxide. Furthermore, several antioxidants (ascorbic acid, reduced glutathione, epigallocatechin gallate, shikonin) were examined for scavenging activity against peroxyradicals in the cigarette smoke. Among them shikonin alone exerted the scavenging activity, suggesting that shikonin is promising antioxidant for cigarette filters because of its effectiveness against broad range of ROS including peroxyradicals, heat resistance, nonvolatility and high affinity to the filter.     

One-step furan ring formation: Synthesis of furo[3,2-h]quinolones

The one-pot reaction of ethyl 1-cyclopropyl-6,7,8-trifluoro-1,4-dihydro-4-oxoquinoline-3-carboxylate ( 6 ) with tert-butyl acetoacetate gave 3-tert-butyl 7-ethyl 9-cyclopropyl-4-fluoro-6,9-dihydro-2-methyl-6-oxofuro[3,2-h]quinoline-3,7-dicarboxylate ( 5 ). This regioselective cyclization was rationalized by the Hard and Soft Acids and Bases principle. By use of a similar furan-forming reaction, we prepared 2-(amino-methyl)furo[3,2-h]quinoline-7-carboxylic acid 4 . Compound 4 showed weak antibacterial activity.     

New photoswitching unit for magnetic interaction: diarylethene with 2,5-bis(arylethynyl)-3-thienyl group

Photoswitching of the intramolecular magnetic interaction was demonstrated using diarylethenes with 2,5-bis(arylethynyl)-4-methyl-3-thienyl side group. Two nitroxide radicals were placed at each end of the 2,5-bis(arylethynyl)-4-methyl-3-thienyl group. Three kinds of aryl groups, 2,5-thienylene, p-phenylene, and m-phenylene groups, were used in the arylethynyl moiety. The diarylethene photoswitching units have an extended pi-conjugated chain on one side of the diarylethene. The photochromic reactivity was dependent on the arylethynyl group. Diarylethenes with m-phenylene group showed an efficient photochromic reactivity. Along with the photochromic reaction the diarylethenes showed photoswitching of an ESR spectrum originating from the change in the magnetic interaction between two unpaired electrons. The open-ring isomer showed stronger exchange interaction than the photogenerated closed-ring isomer. The magnetic interaction between two radicals via the pi-conjugated chain was altered by photocyclization due to the change of the hybrid orbital at the 2-position of the thiophene ring from sp(2) to sp(3).