Quasi-Hopf twistors for elliptic quantum groups

The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al. [FIJKMY1], Felder [Fe]). Frønsdal [Fr1, Fr2] made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebraU _q(g). In this paper we present an explicit formula for the twistors in the form of an infinite product of the universalR matrix ofU _q(g). We also prove the shifted cocycle condition for the twistors, thereby completing Frønsdal's findings.This construction entails that, for generic values of the deformation parameters, the representation theory forU _q(g) carries over to the elliptic algebras, including such objects as evaluation modules, highest weight modules and vertex operators. In particular, we confirm the conjectures of Foda et al. concerning the elliptic algebraA _q,p ( ).Dedicated to Professor Mikio Sato on the occasion of his seventieth birthday     

Inhibition of urease activity by dipeptidyl hydroxamic acids.

A series of dipeptidyl hydroxamic acids (H-X-Gly-NHOH: X = amino acid residues) was synthesized, and the inhibitory activity against Jack bean and Proteus mirabilis ureases [EC 3.5.1.5] was examined. A number of H-X-Gly-NHOH inhibited Jack bean urease with an I50 of the order of 10(-6) M and inhibited Proteus mirabilis urease with an I50 of the order of 10(-5) M. The inhibition against Jack bean urease was more potent than that with the corresponding aminoacyl hydroxamic acids (H-X-NHOH).     

Formation of the high pressure graphite and BC8 phases in a cold compression experiment by Raman scattering

We use Raman scattering to study phase transition in the graphitic g‐BC₈ phase and graphite at high pressure up to 84 GPa. The E_2g Raman active mode of graphite (G peak) can be detected up to 84 GPa. We demonstrate that there is (1) a phase transition in g‐BC₈ and in graphite at 35 GPa and (2) that above 35 GPa, the g‐BC₈ and graphite transform under high pressure to possibly fully sp³‐bonded, disordered hp‐BC₈, and hp‐C phases. Below the phase transition, a polynomial fit to the G peak position versus pressure data yielded a quadratic relation; above the phase transition, it demonstrates linear behavior. The phase transition at high pressure in BC₈ system and graphite is reversible. Quenched hp‐BC₈ and hp‐C phases have the Raman spectrum typical to that of the graphitic phases. Copyright © 2013 John Wiley & Sons, Ltd.     

Imaging of internal stress around a mineral inclusion in a sapphire crystal: application of micro‐Raman and photoluminescence spectroscopy

We developed a micro‐Raman and photoluminescence imaging technique for visualizing the internal stress fields in a sapphire crystal. The technique was applied to an Australian sapphire gemstone with a zircon inclusion. Considering piezospectroscopic effects on Raman and photoluminescence spectra, the Raman shifts of sapphire around the zircon inclusion were converted to hydrostatic pressure and deviatoric components of stress tensor. The internal stress was highly concentrated at the tips of the zircon crystal, where the deviatoric stress and the hydrostatic pressure component reached 700 and 470 MPa, respectively. Generation of compressive stress on the crystal surface of zircon can be explained by the difference in thermal expansion coefficients and elastic constants between sapphire and zircon. In general, internal stress fields induced by mineral inclusions reflect the pressure and temperature conditions at which the host sapphire gemstones were crystallized. Thus, the present technique can be utilized to identify the origin of gemstones. Copyright © 2012 John Wiley & Sons, Ltd.     

Flow injection spectrophotometric determination of sub-mg dm(-3) silver(I) in a strongly acidic solution containing concentrated copper(II) using a pyridylazo reagent

A novel spectrophotometric flow injection method for determination of silver(I) in a strongly acidic solution containing concentrated copper(II) was developed using a coloring ligand, 4-(3,5-dibromo-2-pyridylazo)-N-ethyl-N-(3-sulfopropyl)aniline (3,5-diBr-PAESA). The method was first investigated by batch method. The interference from copper(II) chelate could be eliminated by the masking effect of EDTA. By utilizing the large formation constant (K = 12.3) of AgBr, one could determine silver(I) as a decrease of absorption by silver(I) chelate due to formation of AgBr by addition of KBr. Based on the results of batch experiments, two types of flow injection analysis (FIA) systems were constructed. Sub-mg dm(-3) determination of silver(I) was attained without interference from excess copper(II). The proposed method was successfully applied to determination of silver in a copper plating solution used in a plant to manufacture copper printed circuit boards, where the concentration of silver was critically important in the process control.     

Integral representations of the Macdonald symmetric polynomials

Multiple-integral representations of the (skew-)Macdonald symmetric polynomials are obtained. Some bosonization schemes for the integral representations are also constructed.JSPS fellow.     

Free oscillator realization of Laguerre polynomials

Theoretical and Mathematical Physics - We revisit the radial oscillator from the standpoint of a free oscillator realization. By using a free oscillator, namely, the creation/annihilation operators...     

Vertebrate collagenase inhibitor. I. Tripeptidyl hydroxamic acids

A series of tripeptidyl analogues carrying hydroxamic acid residue at the C-terminus of the molecule were synthesized, and their inhibitory activities against vertebrate collagenase and other metalloenzymes including bacterial collagenase were examined. Both Z-Pro-Leu-Ala-NHOH and Z-Pro-D-Leu-D-Ala-NHOH showed highly specific and potent inhibitory activity against tadpole and human skin collagenases with an IC50 of 10(-6) M order.     

Character and determinant formulae of quasifinite representation of theW 1+∞ algebra

We diagonalize the Hilbert space of some subclass of the quasifinite module of theW ₁₊ algebra. States are classified according to their eigenvalues for infinitely many commuting charges and the Young diagrams. The parameter dependence of their norms is explicitly derived. The full character formulae of the degenerate representations are given as summation of the bilinear combinations of the Schur polynomials.     

Heisenberg realization for U q (sl n ) on the flag manifold

We give the Heisenberg realization for the quantum algebra U _q (sl _n ), which is written by theq-difference operator on the flag manifold. We construct it from the action of U _q (sl _n ) on theq-symmetric algebraA _q (Mat _n ) by the Borel-Weil-like approach. Our realization is applicable to the construction of the free field realization for U _q [2].