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1.
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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. 相似文献
3.
The pentafluorobenzenethiyl radical is an efficient hydrogen abstractor from an activated methylene or methine group and bis(pentafluorophenyl) disulfide is an efficient electron acceptor from the resulting radical intermediate. Thus benzyl-OTBS ether was easily converted into the corresponding pinacol, and 2-phenyl-1,3-dioxanes are converted into the monobenzoates of diols. 相似文献
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For any finite Coxeter system (W,S) we construct a certain noncommutative algebra, the so-called bracket algebra, together with a family of commuting elements, the so-called Dunkl elements. The Dunkl elements conjecturally generate an algebra which is canonically isomorphic to the coinvariant algebra of the Coxeter group W. We prove this conjecture for classical Coxeter groups and I2(m). We define a “quantization” and a multiparameter deformation of our construction and show that for Lie groups of classical type and G2, the algebra generated by Dunkl’s elements in the quantized bracket algebra is canonically isomorphic to the small quantum cohomology ring of the corresponding flag variety, as described by B. Kim. For crystallographic Coxeter systems we define the so-called quantum Bruhat representation of the corresponding bracket algebra. We study in more detail the structure of the relations in Bn-, Dn- and G2-bracket algebras, and as an application, discover a Pieri-type formula in the Bn-bracket algebra. As a corollary, we obtain a Pieri-type formula for multiplication of an arbitrary Bn-Schubert class by some special ones. Our Pieri-type formula is a generalization of Pieri’s formulas obtained by A. Lascoux and M.-P. Schützenberger for flag varieties of type A. We also introduce a super-version of the bracket algebra together with a family of pairwise anticommutative elements, the so-called flat connections with constant coefficients, which describes “a noncommutative differential geometry on a finite Coxeter group” in the sense of S. Majid. 相似文献
6.
Linear propagation of two pulses through methanol solution of aluminum phthalocyanine chloride is investigated using a modified white-light Michelson interferometer. The observed coherence time of the white light is 6 fs, and the separation between the two-excitation pulses is set to about 10 fs. The excitation is dependent on the phase-relation between the two pulses. We have observed an enhancement of the excitation when the two pulses are in-phase and strong suppression of the excitation when the two pulses are out of phase by π. 相似文献
7.
Toshiaki Asakai Ryota Minegishi Norie Inaba Yutaka Ishimura Mariko Murayama Tatsuhiko Tanaka 《Analytical sciences》2006,22(3):461-463
The drying conditions for primary standards of volumetric analysis have a significant effect on the titration results due to changes in the purity, stability and homogeneity. Amidosulfuric acid, a strong acid used as a reference material for volumetric analysis in Japan, was dried in a vacuum desiccator or heated at different temperatures, and then measured by Karl-Fischer titration, thermogravimetry/mass spectroscopy (TG-MS), ion chromatography and coulometric titration. The optimum drying conditions were at 50 degrees C for 24 h with crushing. 相似文献
8.
Hanaoka T Hayashi H Tago T Kishida M Wakabayashi K 《Journal of colloid and interface science》2001,235(2):235-240
We investigated the in situ immobilization of ultrafine particles synthesized in a water/oil (w/o) microemulsion to silica for its possible application to supported metal catalysts. ZnS particles immobilized to silica by the ME method were consistent with those synthesized in a w/o microemulsion. Therefore, ZnS particles in a w/o microemulsion could be immobilized to silica without aggregation by this method. The relationship between the method of synthesizing Rh ultrafine particles in a w/o microemulsion and the diameter and diameter distribution of Rh particles immobilized to silica was studied. Rh-SiO(2) catalysts with a sharp diameter distribution could be prepared by immobilizing Rh-hydrazine complex particles because these complex particles would be very stable in a w/o microemulsion. The Rh particle diameters of Rh-SiO(2) catalysts prepared by changing the amount of silica produced were almost identical. Accordingly, the Rh particle diameter of Rh-SiO(2) catalysts could be controlled independently of Rh content by the ME method. Copyright 2001 Academic Press. 相似文献
9.
The magnetic interactions in a new series of isostructural imino nitroxide radical lanthanide(III) complexes, [Ln(hfac)3(IM2py)] (Ln = Gd–Yb: IM2py = 2-(2′-pyridyl)-4,5-dihydro-4,4,5,5-tetramethyl-1H-imidazoline-1-oxy; hfac = 1,1,1,5,5,5-hexafluoro-2,4-pentanedione), are examined by considering the intrinsic paramagnetic contribution of the Ln(III) ion from the corresponding [Ln(hfac)3(pybzim)] with a diamagnetic pybzim(2-(2-pyridyl)benzimidazole) ligand; the Ln(III)–IM2py interaction being antiferromagnetic for the 4f7 to 4f13 Ln(III) complexes and negligibly small for the other complexes. This series is the first example reverse to the previous cases for the series of Ln–Cu or Ln–aminoxyl(NIT) radical (4,5-dihydro-4,4,5,5-tetramethyl-1H-imidazoline-3-oxide-1-oxy) complexes, other than only a few examples of semiquinone Ln complexes. This reverse nature of the magnetic interaction, as compared with the NIT complexes, validates the empirical approach by O. Kahn et al. [Inorg. Chem. 38 (1999) 3692; J. Am. Chem. Soc. 122 (2000) 3413] in the spin-coupled systems for a series of Ln(III) complexes. 相似文献
10.
Noriyuki Asakura Toshiaki Kamachi Ichiro Okura 《Research on Chemical Intermediates》2006,32(3-4):341-355
The behavior of redox molecules in solution that was not detected by electrochemical techniques was measured by a highly-sensitive electrochemical quartz crystal microbalance (EQCM) technique that has been improved in this study to obtain a high sensitivity of EQCM measurement in solution. The improved EQCM technique allowed to monitor the motion of a redox molecule, that is an access of the molecule to an electrode surface and repulsion from the surface during redox. An EQCM technique currently in use has measured adsorption of redox molecules on an electrode surface or polymerization on the surface caused by a chemical reaction following redox, which exhibits an enough large mass change response to detect with an EQCM measurement. However, access and repulsion of redox molecule, which is a slight motion of the molecule near on electrode surface, has not been detected and investigated by an EQCM technique, because the mass change response seems to be very small. In this study, the redox behavior of methyl viologen on a bare gold surface, pyridinethiol surface and methylpyridinethiol surface was investigated. Although the three electrodes give the same cyclic voltammogram of methyl viologen, the three are different in QCM response recorded at the same time as the voltammetry. Access/repulsion of methyl viologen within an electrical double layer was monitored by the highly-sensitive EQCM technique. 相似文献