Noncommutative algebras related with Schubert calculus on Coxeter groups

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 B_n-, D_n- and G₂-bracket algebras, and as an application, discover a Pieri-type formula in the B_n-bracket algebra. As a corollary, we obtain a Pieri-type formula for multiplication of an arbitrary B_n-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.     

Constructive and Destructive Two-Pulse Excitation Investigated with a White-Light Michelson Interferometer

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.     

Investigation of the drying conditions for amidosulfuric acid.

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.     

HCN laser scattering on the JIPP T-IIU tokamak

A 4-channel HCN laser scattering system has been developed and applied to the JIPP T-IIU tokamak. Main aim of this system is to study microturbulence excited in the plasma, especially in the high power ICRF heating experiment. The observed density fluctuations are in a frequency range of the electron diamagnetic drift wave and have broad frequency spectra. The main part of the wavenumber is found to satisfy the condition of . In the heating experiments, deterioration of the energy confinement time is observed, and the density fluctuation level increases with the increase of the heating power.     

In Situ Immobilization of Ultrafine Particles Synthesized in a Water/Oil Microemulsion

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.     

Effects of Shosaikoto (kampo medicine) on lipid metabolism in macrophages.

We investigated effects of Shosaikoto treatment on cholesterol metabolism in macrophages. Although macrophages, harvested from mice treated with Shosaikoto, took up a small amount of control low density lipoprotein (LDL) (thiobarbituric acid-reactive substance (TBA-RS) value was 0.27 pmol/mg of protein) as control macrophages, they took up more LDL modified with CuSO4 (TBA-RS value was 6.12 pmol/mg of protein) than control macrophages. Degradation of both control LDL and oxidized LDL was enhanced in Shosaikoto treated macrophages. In the presence of control LDL or in the absence of LDL, incorporation of [3H]oleic acid into chlesteryl oleate was significantly reduced in Shosaikoto treated macrophages. This suggests that acyl-coenzyme A:cholesterol acyltransferase (ACAT) activity in macrophages was partly inhibited by Shosaikoto treatment. On the other hand, in the present of oxidized LDL, cholesteryl ester accumulated in Shosaikoto treated macrophages as much as in controls. However, cholesteryl oleate efflux from macrophages in the presence of high density lipoprotein (HDL) was enhanced in Shosaikoto treated macrophages. These result indicate that Shosaikoto facilitates oxidized LDL catabolism in macrophages, resulting in the augmentation of oxidized LDL uptake and the elimination of cholesterol from macrophages by HDL. These Shosaikoto effects may prevent foam cell formation and the progression of atherosclerotic lesions.     

Magnetic interactions in a series of paramagnetic Ln(III) complexes with a chelated imino nitroxide radical

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.