Nonlinear Cauchy problems with small analytic data

We study the lifespan of solutions to fully nonlinear Cauchy problems with small real- or complex-analytic data. Our proofs are based on the method of majorants and the fixed point theorem for a contraction mapping.

     

Spherical dye-doped silica particles

Organic dyes such as water soluble porphyrins were incorporated into monodispersed SiO₂ particles using the sol-gel technique (the Stober synthesis) and their monomeric and dimeric properties were investigated by aiming at the microcavity effect. Doping efficiencies of dyes into SiO₂ particles depended on dye's hydrophilic properties. The doping efficiency of a porphyrin, TTMAPP, decreased with increasing the nominal content in the starting solution and the doping content showed the maximum value of 1.6×10^–5 mol/g SiO₂. With increasing the TTMAPP content, spectra of doped particles were changed from dimeric to monomeric nature; the absorption peak due to dimers disappeared and halfwidth of absorption at Soret band decreased. This unusual change was caused by the decrease of particle sizes by dye doping. The TTMAPP-doped sample having monomeric spectrum showed the fluorescence life time of 8.5 nsec and photochemical hole burning at about 5 K.     

Synthesis and properties of furo[4,3,2-de][1]benzopyran

A new heterocycle, furo[4,3,2-de][1]benzopyran ( 2 ), was synthesized. A key step in the sequence was the allylic bromination of 3,4-dihydrofuro[4,3,2-de][1]benzopyran ( 8 ) to give 3-bromo-3,4-dihydrofuro[4,3,2-de][1]-benzopyran ( 10 ) using N-bromosuccinimide under irradiation and high dilution conditions. Bromide 10 was dealt with 1,8-diazabicyclo[5.4.0]undec-7-ene to afford compound 2 . Several reactions of 2 were examined. Protonation of 2 in trifluoroacetic acid occurred at the 2-position to form a pyrylium ion 12 . Catalytic hydrogenation of 2 with palladium on charcoal proceeded smoothly to give 8 . Reduction of 2 by sodium and ethanol afforded 3-ethyl-4-hydroxybenzofuran ( 14 ). Electrophilic substitutions of 2 such as formylation, acetylation, and bromination, occurred easily at the 2-position. The above results show that compound 2 has both properties of benzofuran and 4-methylenepyran.     

Regioselective allylation reactions using crotyl Grignard reagent-CeCl3 systems

Regioselective allylation reactions using crotyl Grignard reagent-CeCl₃ systems are described. Regioselectivity depends on the lanthanide salts: α-product was predominantly produced with light rare earth elements such as La, Ce, Pr, Nd, whereas γ-product was formed when heavy rare earth elements were used.     

Crystal structure of the clathrate of 5,12-dihydro-5,12-o-benzenonaphthacene-1,4-dione with benzene (2:1).

In the crystal of the title compound, the quinone fragment of the host (1) participates in weak D-A interactions with a neighboring naphthalene moiety of 1 and with the guest molecule via fairly short intermolecular face-to-face contacts. An intermolecular electrostatic interaction between a quinone-oxygen atom and a neighboring quinone ring is suggested by short O...C contacts. There exist several C-H...O hydrogen bonds, one of which seems to contribute to the formation of a centrosymmetric dimer of 1.     

Dihydroboronium derivatives of (S,S)-1,2-bis(t-butylmethylphosphino)ethane as convenient chiral ligand precursors

Dihydroboronium derivatives of (S,S)-1,2-bis(t-butylmethylphosphino)ethane (t-Bu-BisP*) were prepared and used as chiral diphosphine ligand precursors in Rh-catalyzed asymmetric hydrogenation of methyl (Z)-acetamidocinnamate to afford the hydrogenation product in up to 94% enantioselectivity.     

Enhancement of electronic excitation energy transfer in the colloidal crystals of colloidal silica suspensions doped with fluorescent dyes

The efficiency of electronic excitation energy transfer from photo-excited rhodamine 110 (Rh110, energy donor) to rhodamine B (RhB, energy acceptor) in an exhaustively deionized colloidal silica suspension has been studied. This colloidal suspension shows Bragg reflection due to the formation of colloidal crystals and the Bragg-peak wavelength is controllable by the volume fraction of the silica spheres. When the Bragg-peak wavelength matches with the fluorescence band of Rh110, a depletion was observed in the Rh110 fluorescence spectrum. This means the fluorescence of Rh110 is partially trapped due to the Bragg reflection inside the crystal lattice. In the coexistence of RhB, the enhancement of RhB fluorescence intensity was observed. These facts clearly indicate the trapped photon energy of Rh110 is efficiently transferred to RhB within the colloidal crystals. The quantitative measurements showed that the enhancement of the transfer efficiency is 20% (or slightly more) in the present experimental conditions.     

Preparation and thermal analysis of synthetic malachite CuCO3·Cu(OH)2

The synthesis of malachite CuCO₃·Cu(OH)₂ or Cu₂CO₃(OH)₂ was studied through titrations of copper(II) salt solutions with a solution of sodium carbonate at different temperatures. The precipitates were characterized by TG, IR and chemical analysis. The composition varies depending on thepH of the solution and the temperature. Purer malachite was synthesized by simple mixing of a solution of copper(II) nitrate or sulfate with a solution of sodium carbonate at 50°C.The kinetics of the thermal decomposition of synthetic malachite was described by eitherR ₃ orA _m(m=1.2–1.4) law, according to TG analysis, both isothermal and nonisothermal. The Arrhenius parameters determined using three different integral methods showed the kinetic compensation effect, which is correlated to the working temperature interval analyzed.The authors thank Mr. H. Takemoto for analyzing kinetics of the thermal decomposition of synthetic malachite.     

Effect of extracts of Zingiberaceae herbs on gastric secretion in rabbits

Some of the Zingiberaceae herbs are known to be useful as stomachics. Water extracts and methanol extracts of eight such herbs were examined in intact unanesthetized rabbits for their effect on gastric secretion. Oral administration of either water extracts or methanol extracts caused a significant decrease in gastric secretion. A significant effect of these extracts appeared at 3 h after administration. The effect of water extracts on gastric secretion was very similar to that of cimetidine, with a significant decrease in acid output. The effect of the methanol extracts was primarily observed as decreased pepsin output.     

Overproduction of riboflavin by anArthrobacter sp. mutant resistant to 5-fluorouracil

Effects of pH and dissolved oxygen concentration on batchwise riboflavin production by a 5-fluorouracil (5-FU)-resistant mutant ofArthrobacter sp. were investigated. The reaction was carried out in a jar fermentor. The optimal pH of culture medium was around 7.3. Dissolved oxygen concentration was almost constant during fermentation at 600 rpm of agitation rate. Production of riboflavin reached a maximum of 160 mg/L after 70 h fermentation under the agitation rate of 600 rpm, aeration rate of 1.0 L/min, and pH 7.0.