On the internal stepsize of an extrapolation algorithm for IVP in ODE

We propose an extrapolation algorithm for initial value problems in ordinary differential equations. In the algorithm, an appropriately chosen stepsizeH is divided into smaller stepsizes by a sequence and a new stopping rule is proposed. The sequences applied to the algorithm are Romberg {2,4,8,16,32,...}, Bulirsch {2,4,6,8,16...} and Harmonic {2,4,6,8,10,12,...} types. The proposed algorithm is compared numerically with the algorithm introduced by Stoer. In view of the accuracy of numerical solutions, the relatively small number of calculations, the stability and reliability of the algorithm, we found that the algorithm with the Romberg sequence is the best.     

Palladium-catalyzed novel addition-elimination reaction of alkenyltin reagents to norbornene

Palladium-catalyzed reaction between 1-alkenyltin trichlorides and norbornene resulted in stereoselective formation of 3-alkylidenepentacyclo[9.2.1.^5,81.^1,110.^2,100^4,9]pentadecane instead of an expected simple alkenylstannylation product. Generation of trichlorostannane and its decomposition product, tin(II) chloride, was confirmed by trapping it with methyl propiolate and norbornene and analysis of the reaction by ¹¹⁹Sn NMR, respectively.     

Preparation and lithium doping of gallium oxynitride by ammonia nitridation via a citrate precursor route

Gallium oxynitride, isostructural to hexagonal gallium nitride (h-GaN), was obtained by ammonia nitridation of a precursor prepared from the addition of citric acid to an aqueous solution of gallium nitrate. Gallium oxynitride produced at 750 °C had a small amount of gallium vacancies, and was formulated as (Ga_0.89□_0.11) (N_0.66O_0.34) where the symbol □ stands for gallium vacancy. Both the gallium vacancies and oxygen substituted for nitrogen were randomly distributed within the structure. The amount of vacancies decreased with nitridation temperatures in the range of 750-850 °C. Approximately, 10 at% Li⁺ was doped into the gallium oxynitride, using a similar preparation with the additional presence of lithium nitrate, resulted in the random substitution of Ga³⁺ in an atomic ratio of Li/Ga<1 at 750 °C. Oxygen was codoped with lithium and substituted nitrogen in the wurtzite-type crystal lattice. These substitutions reduced the electrical conductivity in the gallium oxynitride semiconductor. A new oxynitride, Li₂Ga₃NO₄, was also obtained with Li₂CN₂ impurity using similar preparations from a mixture of Li/Ga?1. The crystal structure was isostructural with h-GaN, and was refined as P6₃mc with a=0.31674(1) nm, and c=0.50854(2) nm. The Ga and Li occupancies at the 2b site were refined to be 0.6085 and 0.3915, respectively, assuming that the other 2b site was randomly occupied with 1/5O and 4/5N. When the new compound was washed for over 1 min for the removal of Li₂CN₂ impurities, it was decomposed to a mixture of α-GaOOH and α-LiGaO₂. The as-prepared product with Li/Ga=1 showed the highest intensity in yellow luminescence among the products under excitation at 254 nm.     

Radiation-induced emission from golden hamster embryo cells

Emission from high-energy-electron-irradiated golden hamster embryo (GHE) cells has been studied over the temperature range 12–300 K both by a one-shot-single-photon-counting method and by photocurrent measurements with an oscilloscope. Emission from the irradiated phosphate buffered saline (PBS) also has been studied. The emission spectra from PBS at 12 and 77 K show a maximum around 330 and 380 nm, respectively, which are the same spectra as those from irradiated pure H₂O. The emission from irradiated GHE consists of the new band at 480 nm in addition to the emission from H₂O. The 480 nm emission is observed at the temperature range of 12–300 K, though the emission at 300 K is much lower than that at low temperature. The 480 nm emission is ascribed to the transition from excited organic substances in GHE cells. The intensity of 480 nm emission at 300 K increases linearly with increasing irradiation-dose in the range of 11–600 Gy.     

Total synthesis of (+)-tubelactomicin A. 2. Synthesis of the upper-half segment and completion of the total synthesis

[reaction: see text]. We have completed the total synthesis of natural (+)-tubelactomicin A (1), a 16-membered macrolide antibiotic. This Letter presents a highly efficient synthesis of the upper-half segment (C14-C24) and the completion of the total synthesis featuring a high-yielding Stille coupling for the connection of the upper-half and lower-half segments and Mukaiyama macrolactonization for the construction of the entire structure of 1.     

Stereoselective ring-opening polymerization of racemic lactide using aluminum-achiral ligand complexes: exploration of a chain-end control mechanism

Stereoselective polymerization of racemic lactide (rac-LA) was examined using Al-achiral ligand complexes. By introduction of substituents in aromatic rings of Schiff base ligands, a higher selectivity was obtained without any chiral auxiliaries in the catalyst via a chain-end control mechanism. The T(m) values (T(m) 170-192 degrees C) were comparable to or higher than that of homochiral polymer, poly(L-LA) (T(m) 162 degrees C), and a thermally more stable polylactide than poly(L-LA) was prepared from rac-LA.     

Synthesis and properties of new polyesters having tetrahydrofuran rings in their main chains

New polyesters 6a–6c consisting of 2,4-linked tetrahydrofuran rings were synthesized by bulk polycondensation of methyl trans- and cis-4-hydroxytetrahydrofuran-2-carboxylates ( 5a and 5b ) and a stereoisomeric mixture of methyl 4-hydroxy-5-methyltetrahydrofuran-2-carboxylate ( 5c ) at high temperature. These monomers were prepared from methyl glycolate or methyl lactate and diethyl maleate through a four-step reaction sequence. The polycondensation was carried out without solvent at different temperatures ranging from 150 to 220°C. Titanium isopropoxide was most effective among the catalysts examined, giving polyesters with number-average molecular weights up to 2 × 10⁴. Polyester 6a consisting of trans-2,4-linked tetrahydrofuran rings was soluble in trifluoroacetic acid and a mixed solvent of chloroform and methanol (10/1, v/v). Polyester 6b composed of cis-2,4-linked tetrahydrofuran rings was soluble in dimethyl sulfoxide and dimethylformamide in addition to the two solvents for 6a . Polyester 6c with 5-methyl-substituted tetrahydrofuran rings was composed of a mixture of stereoisomeric units and thus was soluble in a variety of solvents including chloroform, tetrahydrofuran, acetonitrile, dimethyl sulfoxide, and dimethylformamide. The glass transition temperatures of 6a, 6b , and 6c determined by DSC were 109, 88, and 66°C. These polyesters were found to be very slowly hydrolyzed in a neutral phosphate buffer solution at ambient temperature. © 1993 John Wiley & Sons, Inc.     

Mechanism of the CO oxidation reaction on O-precovered Pt(111) surfaces studied with near-edge x-ray absorption fine structure spectroscopy

The mechanism of CO oxidation reaction on oxygen-precovered Pt(111) surfaces has been studied by using time-resolved near-edge x-ray absorption fine structure spectroscopy. The whole reaction process is composed of two distinct paths: (1) a reaction of isolated oxygen atoms with adsorbed CO, and (2) a reaction of island-periphery oxygen atoms after the CO saturation. CO coadsorption plays a role to induce the dynamic change in spatial distribution of O atoms, which switches over the two reaction paths. These mechanisms were confirmed by kinetic Monte Carlo simulations. The effect of coadsorbed water in the reaction mechanism was also examined.     

A twin optically-pumped far-infrared CH3OH laser for plasma diagnostics

A twin optically-pumped far-infrared CH₃OH laser has been constructed for use in plasma diagnostics. The antisymmetric doublet due to the Raman-type resonant two-photon transition is reproducibly observed at 118.8 m. With the 118.8-m line, it is obtained from the frequency separation of the anti-symmetric doublet that CH₃OH absorption line center is 16±1 MHz higher than the pump 9.7-m P(36) CO₂ laser line center. It is shown that the Raman-type resonant two-photon transition is useful in order to get several-MHz phase modulation for the far-infrared laser interferometer. Some preliminary performances of this twin laser for the modulated interferometer are described.This work was carried out under the collaborating research program at the Institute of Plasma Physics, Nagoya University, Nagoya 464, Japan.     

Profiling and comprehensive expression analysis of ABC transporter solute-binding proteins of Bacillus subtilis membrane based on a proteomic approach

We analyzed ABC transporter solute-binding proteins (SBPs) of the Bacillus subtilis membrane using a proteomic approach. We prepared a washed cell membrane fraction that was insoluble in 134 mM nondetergent sulfobetaine and then extracted proteins using mixtures of detergents in a stepwise manner. The membrane proteins were resolved by three two-dimensional polyacrylamide gel electrophoresis (2-D PAGE) or two one-dimensional (1-D) PAGE procedures, electroblotted, and digested in the presence of 5% or 80% acetonitrile. Thereafter, matrix-assisted laser desorption/ionization-time of flight-mass spectrometry (MALDI-TOF MS) identified 637 proteins corresponding to 15.9% of the total cellular proteins. We predicted that among these, 256 were membrane proteins, 101 were lipoproteins or secretory proteins and 280 were soluble proteins containing peripheral proteins that function in both the cytoplasm and the cell membrane such as SecA and FtsY. Among the 637 proteins, we identified 30 SBPs among 38 importers predicted by a bioinformatic search of the genome. We confirmed expression of the genes for the 30 SBPs using DNA microarray analysis. We compared the 2-D gel separation profiles of submembrane fractions solubilized by 1% n-dodecyl-beta-D-maltoside from cells cultured on Luria Bertani (LB), S7, and S7 medium without glutamate as well as DNA microarray data on LB and S7. The results suggested that YcdH, YtmK and YurO are binding proteins for Mn(++), glutamate and glucose, respectively, and that YqiX and YxeM are binding proteins for amino acids (tryptophan in S7 medium).