Lie superalgebraic approach to super Toda lattice and generalized super KdV equations

We propose a super Lax type equation based on a certain class of Lie superalgebra as a supersymmetric extension of generalized (modified) KdV hierarchy. We are able to construct an infinite set of conservation laws and the consistent time evolution generators for generalized modified super KdV equations. Thefirst few of the conserved currents, the (modified) super KdV equation and the super Miura transformation are worked out explicitly in the case of twisted affine Lie superalgebraOSp(2/2)⁽²⁾.Partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (#01540246 and #01790203).RIFP will be known as Yukawa Institute for Theoretical Physics from June 8, 1990     

Improved detectability with a polymer-based trapping device in rapid HPLC analysis for ultra-low levels of bisphenol A (BPA) in environmental samples.

A new high-performance liquid chromatography (HPLC) method has been developed to detect ultra-low concentrations of bisphenol-A (BPA) (below 1 ng/L (ppt)) using column switching electrochemical detection (ECD). The results were superior to those obtained from manual pretreatment procedure with membrane stationary phase. BPA is inherently ubiquitous in the environment, including tools and solvents used for its analysis; to obtain meaningful results, therefore, the concentration of the overall BPA contamination must be below the detection limit for BPA using the analytical system. Therefore, purified water for preparing the standard BPA solution must be filtered with a hydrophobic membrane to suppress BPA background levels of contamination. In addition, we investigated methods for effectively preserving environmental water containing BPA. The addition of a small amount of ethylenediaminetetraacetic acid (EDTA) provided good recovery even after overnight storage. By employing these precautionary measures and procedures to reduce BPA contamination from the analytical procedure, we could accurately determine l(-10) ppt of BPA in environmental water samples using a column switching HPLC system.     

On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm

In this paper we focus on the problem of identifying the index sets P(x):=i|x_i>0, N(x):={i|F_i(x)>0 and C(x):=i|x_i=F_i(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan.Mathematics Subject Classification (2000): 90C33, 65K10     

Development and features of hydro-membrane gas chromatography.

Hydro-membrane gas chromatography (HMGC) is achieved by the annular condensation of water in a capillary column at less than 70 degrees C. The annular membrane of water is formed as a result of the wettability of the stationary phase, which is induced at a water contact angle ranging from 75 degrees to 79 degrees, as derived from a solubility parameter (delta) range of 15.7 +/- 0.3 MPa(1/2) of the coated resin. The range of the liquid to gas volume ratio (beta) required to support the annular membrane should be kept between 0.00005 and 0.0003. In the case of a 0.25-mm i.d. column, the ratio can be set by the combination of a 0.1 to 0.2 microl min(-1) water supply rate and helium gas flow rate. Separation by HMGC develops not only a gas-solid partition but also a focusing effect on the water membrane. One feature of HMGC is that it gives a non-adsorption chromatogram based on the blocking effect of pre-adsorbed water; furthermore, despite the presence of a relatively large quantity of water, the electron impact ionization efficiency is kept the same as in the usual GC/MS condition. The detection limit with the injection of 1 microl of aquatic solution was estimated to be less than 0.1 ppb of low-molecular-weight fatty acids with s/n = 5 on a mass chromatogram at m/z 45. The HMGC/EI-MS system can be applied to the trace analysis of C1 to C3 volatile acids, volatile inorganic acids, and halogenated organic acids in water.     

Basic study of the gelation of dimethacrylate‐type crosslinking agents

An investigation was made of the gelation of dimethacrylate‐type crosslinking agents in view of an application for separation media. The study mainly centered on a crosslinking agent, glycerol dimethacrylate (GDMA), which is relatively hydrophilic because of a hydroxyl group in the middle of its structure. The gelation of GDMA was compared with that of other hydrophobic crosslinking agents such as ethylene glycol dimethacrylate and 1,6‐hexanediol dimethacrylate. The diluents used in the study were toluene, toluene with methanol, and cyclohexanol. The gelation was observed in real time with a charge coupled device camera and dynamic light scattering (DLS). Also, the separated dry gels were extensively characterized with scanning electron microscopy, BET (N₂ absorption and desorption isotherm), and Fourier transform infrared. DLS analysis showed a stronger molecular interaction of GDMA gelation in toluene, whereas this interaction was much weaker in an alcoholic solvent such as toluene with methanol or cyclohexanol. This indicated that GDMA gelation might proceed through hydrogen bonding as well as a crosslinking reaction of vinyl groups. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 949–958, 2006     

Bis(5‐hydroxy‐2‐hydroxy­methyl‐4‐pyrone‐κ2O4,O5)bis(2‐hydroxy­methyl‐5‐oxido‐4‐pyrone‐κ2O4,O5)­calcium(II) tetrahydrate

In the title compound, [Ca(C₆H₅O₄)₂(C₆H₆O₄)₂]·4H₂O, which is a kojic acid–Ca²⁺ complex, the Ca atom is on a twofold axis and is octacoordinated by O atoms from four pyrone ligand mol­ecules. The hydroxyl and ketone O atoms of each ligand form a five‐membered chelate ring with the Ca atom. The crystal structure is stabilized by partial stacking and O—H?O hydrogen bonds.     

Frequency measuring system using mirror gap stabilized Fabry-Perot interferometer

The mirror gap of a Fabry-Perot interferometer was stabilized with two laser diodes; one locked to the line frequency 385,243,555.14445 MHz of the F=3<--1 in 5D(3/2)<--5S(1/2) (87Rb) and the other to the 385,284,566.3663 MHz of the F=4<--2 in 5D(5/2)<--5S(1/2) (87Rb) [Opt. Commun. 102 (1993) 432]. The length of the mirror gap was adjusted to generate the zero-cross points simultaneously at both of the two line positions. The fringe signals obtained from an interferometer thus stabilized can be used as frequency markers having accuracies of the order of 10(10) depending on the finesse of the interferometer used. Based on measurement using Cs D1 hyperfine lines reported by Udem et al. [Phys. Rev. Lett. 82 (1999) 3568], the uncertainty of markers in the region 50 THz apart from the reference lines is +/- 5 MHz.