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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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Fumie Takei Daisuke Kodama Sugiko Nakamura Kiyotaka Onitsuka Shigetoshi Takahashi 《Journal of polymer science. Part A, Polymer chemistry》2006,44(1):585-595
Aryl isocyanides bearing free‐base and metallo‐porphyrins were prepared and polymerized with a Pd–Pt μ‐ethynediyl complex as the initiator to give polymers with narrow polydispersity indices. The molecular weights of the resulting polymers were precisely controlled by the initial feed ratio of the porphyrin monomer to the initiator. The UV–VIS spectra suggested that the porphyrin pendants are regularly arranged to form stacked columns. Metallo‐porphyrin polymers were also prepared by reacting free‐base porphyrin polymers with metal salts. The successive reactions of free‐base and zinc‐porphyrin monomers resulted in the formation of diblock polymers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 585–595, 2006 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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Zusammenfassung Es wird eine Korrekturformel zur 8. Potenzformel von Philippoff-Heß vorgeschlagen, die auch die Fälle gut wiedergibt, wo die einfache 8. Potenzformel ebenso wie andere Viskositätsgleichungen bisher versagten. Im einzelnen wird die Gleichung geprüft an folgenden bisherigen Ausnahmen: Cellit in Eisessig (Philippoff-Heß), polymere-Hydroxydekansäuren in sym-Tetrachloräthan(Kraemer-von Natta), polymere Polystyrole in Benzol (Dane). In jedem Falle stellen diek-Werte gute Konstanten dar.Die charakteristische Viskositätskonstantek zeigt eine lineare Zunahme mit dem Molekulargewicht der Polymerhomologen.Die Temperaturabhängigkeit vonk unda wird geprüft. 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
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Brown coals have a considerable number of acidic functional groups of which the main component is carboxyl groups, and the acidity has a wide distribution. In this paper, changes of the acidity distribution were examined by aqueous titration when brown coal was heat-treated to control its acidity distribution. For Loy Yang brown coal from Australia dried at 50 degrees C under vacuum (LY50), the acid dissociation constant, Ka, was distributed over a wide pKa range between 2 and 9. Then, using Gaussian functions, the acidity distribution was divided into four groups, which were characterized by average pKa values: average pKa value of 3.8 (hereafter referred to as Group A), 5.2 (Group B), 6.8 (Group C), and 8.3 (Group D). Among them, Groups A, B, and C were assigned to carboxyl groups. From the changes of the number of carboxyl groups when brown coal was heat-treated up to 400 degrees C, it was found that the way of decrease was different among these acidic groups. The decrease of the amount of carboxyl groups in Group C was significant, and at 325 degrees C most of them disappeared. On the other hand, the carboxyl groups in Group A remained even at a high temperature of 400 degrees C. We estimated approximately the structures around carboxyl groups for LY50 and their structural changes by heat treatment using the known pKa values for simple carboxylic acids and the pKa values calculated by the MOPAC program for complicated carboxylic acids. 相似文献