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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
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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
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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
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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