Tau Functions of q-Painlevé III and IV Equations

We present a geometric approach to τ-functions of the q-Painlevé III and IV equations via rational surfaces with affine Weyl group symmetry of type (A ₂+A ₁)⁽¹⁾. We also study a similarity reduction of the q-KP hierarchy to the equations. Mathematics Subject Classification (2000). 34M55, 37K10, 39A13     

A Class of Integrable and Nonintegrable Mappings and their Dynamics

We analyse a class of mappings which by construction do not belong to the QRT family. We show that some of the members of this class have invariants of high degree. A new linearisable mapping is also identified. A mapping which possesses confined singularities while having nonzero algebraic entropy is presented. Its dynamics are studied in detail and shown to be related intimately to the Fibonacci recurrence.      

Catalytic epoxidation of cyclohexene by covalently linked manganese porphyrin–viologen complex

When a viologen-linked Mn(III)porphyrin complex with a short methylene-chain, in which a viologen is covalently linked by the methylene-chain into one phenyl group of 5,10,15,20-tetraphenylporphyrinatomanganese(III)chloride (Mn(III)(tpp)Cl), was used as a catalyst for a monooxygenation of cyclohexene in an air-equilibrated acetonitrile solution containing insoluble zinc powder as a reductant, more cyclohexene oxide was obtained as a single product than when Mn(tpp)Cl was used as a catalyst. Benzoic acid as a cleaving reagent of the dioxygen double-bond and 1-methylimidazole as a ligand to Mn porphyrin were further contained in the reaction mixture. This result implies that the viologen moiety in the viologen-linked Mn(III)porphyrin acted effectively as a mediator for electron transfer from zinc powder to the Mn(III)porphyrin moiety in the epoxidation cycle activating molecular dioxygen reductively. Though Mn(tpp)Cl was remarkably demetallated by H⁺ ion from benzoic acid during the epoxidation reaction in the mixed system of Mn(III)(tpp)Cl and viologen, the demetallation of the viologen-linked Mn porphyrin with the short methylene-chain was partly prevented because the reduction of a Mn(II)porphyrin-dioxygen adduct was easily caused by fast intramolecular electron-transfer between the two moieties of the viologen and the Mn porphyrin, proceeding the epoxidation cycle smoothly.     

Leakage of immobilized IgG from therapeutic immunoadsorbents

In developing therapeutic immunoadsorbents (IAs), antibodies (IgG molecules) covalently immobilized on porous carriers, a leak of IgG was determined both in the storage test with buffers at 25 and 4 degrees C and in contact with plasma at room temperature (RT). The amount of antibody released from therapeutic IAs must be minimized to avoid side effects during treatment. The amount of IgG released was a. Dependent on the amount of IgG immobilized b. Much greater with CNBr-activated Sepharose 4B, or Formyl-Cellulofine as a support material than with aminopropyl CPG (controlled pore glass) c. Found to yield again during another storage in buffers after the IAs were washed and their buffers replaced with fresh ones and d. Decreased after the IAs were treated with glutaraldehyde (GA) solutions. Whereas treating the IAs with GA solutions significantly reduced the amount of IgG released, it caused some deterioration of the adsorption characteristics of the IAs. An irradiation dose of 2.5 Mrad as a crosslinking procedure also reduced the amount of IgG released; its effect was comparable to that of 0.025% GA, the lowest concentration used.     

Stereochemistry in Lewis acid-catalyzed silylation of alcohols, silanols, and methoxysilanes with optically active methyl(1-naphthyl)phenylsilane

Stereochemistry in silylation reactions of alcohols, silanols, and methoxysilanes with optically pure (R)-methyl(1-naphthyl)phenylsilane were studied in the presence of Lewis acid catalysts. Tris(pentafluorophenyl)borane [B(C₆F₅)₃] was found to be highly reactive and stereoselective in the reactions. Optically active (R)-(alkoxy)methyl(1-naphthyl)phenylsilanes with 91–97% ee were produced from alcohols through the inversion stereochemistry of the silane. Stereoselectivity in the reaction with triphenylsilanol was moderate (64% ee). (R)-1,3-Dimethyl-1-(1-naphthyl)-1,3,3-triphenyldisiloxane with 94% ee was obtained from the silane with (methoxy)methyldiphenylsilane. The reaction with (R)-(methoxy)methyl(1-naphthyl)phenylsilane (88% ee) gave (R, R)-1,3-dimethyl-1,3-di(1-naphthyl)-1,3-diphenyldisiloxane [(R, R):(R, S):(S, S) = 87:12:0.5]. The stereochemistry was proved to almost completely inversion and retention for the chiral silicon centers of the silane and methoxysilane, respectively.     

Exposed crystal surface-controlled TiO2 nanorods having rutile phase from TiCl3 under hydrothermal conditions

Size-, shape-, and phase structure-controlled synthesis of TiO₂ nanocrystallites has long been one of the main themes in TiO₂ research. Many synthetic techniques have been utilized in the preparation of TiO₂ nanocrystals, among which hydrothermal treatment has been drawing much attention because it directly produces well-crystallized nanocrystallities of a wide range of compositions of crystal phases within a short reaction time. In this study, we carried out hydrothermal growth of rutile TiO₂ rods by using aqueous titanium trichloride (TiCl₃) solutions containing NaCl. Uniform ultrafine rutile TiO₂ particles were obtained, and developed crystal faces were observed by TEM, SEM, XRD, and specific surface area measurements. The obtained rutile fine particles showed high levels of activity for degradation of 2-propanol and acetaldehyde under UV irradiation compared to the activity levels of anatase fine particles (ST-01) developed for environmental clean-up. The surface chemistry of the rutile TiO₂ particles was also investigated. From photodeposition of Pt and PbO₂, we suggest that the (1 1 0) face provides reductive sites and that the (1 1 1) face provides oxidative sites. These results indicate that the crystal faces facilitate the separation of electrons and holes, resulting in improvement of photocatalytic activity.     

Determination of 3,6-dinitrobenzo[e]pyrene in surface soil and airborne particles by high-performance liquid chromatography with fluorescence detection

We developed a sensitive analytical method and an efficient clean-up method to quantify 3,6-dinitrobenzo[e]pyrene (3,6-DNBeP) in surface soil and airborne particles. After purification using a silica gel column and two reversed-phase columns, 3,6-DNBeP was reduced to 3,6-diaminobenzo[e]pyrene by a catalyst column and analyzed by high-performance liquid chromatography (HPLC) with a fluorescence detector. 3,6-DNBeP was detected in all of the soil samples and airborne particles examined. The concentration of 3,6-DNBeP in surface soil and airborne particles was determined in the ranges of 347-5007 pg/g of soil and 137-1238 fg/m3, respectively.     

A recyclable dendritic osmium catalyst for homogeneous dihydroxylation of olefins

A series of osmate (OsO₄²⁻) core dendrimers was prepared by an ion-exchange technique through the mixing of K₂OsO₄ and a bis(quaternary ammonium bromide) core dendrimer, which consisted of poly(benzyl ether) dendron. By employing an osmate core dendrimer as a homogeneous catalyst, dihydroxylation reactions of olefins proceeded rapidly, and the dendritic osmium catalyst was recovered by reprecipitation and then reused. Furthermore, a dendritic effect on the recyclability of a catalyst was observed. In the case of asymmetric dihydroxylation reactions, the corresponding diol was obtained in a high chemical yield with a fair enantiomeric excess (ee). In this case, not only the dendritic osmium catalyst but also the chiral ligand could be recovered by reprecipitation and reused efficiently up to five times.     

q-Painlevé VI Equation Arising from q-UC Hierarchy

We study the q-difference analogue of the sixth Painlevé equation (q-P_VI) by means of tau functions associated with the affine Weyl group of type D₅. We prove that a solution of q-P_VI coincides with a self-similar solution of the q-UC hierarchy. As a consequence, we obtain in particular algebraic solutions of q-P_VI in terms of the universal character which is a generalization of the Schur polynomial attached to a pair of partitions.