Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schr?dinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in . Received: 13 July 2000 / Published online: 1 February 2002     

Classification for dimethylarsenate-decomposing bacteria using a restrict fragment length polymorphism analysis of 16S rRNA genes.

A new monitoring system for bacterial communities involving dimethylarsinic acid (DMAA) decomposition was provided by combining the MPN (Most Probable Number) method and RFLP (restriction-fragment-length polymorphism analysis). The abundance of DMAA decomposing bacteria was estimated by the MPN method using a bacterial culture medium, which included DMAA as the sole carbon source, indicating bacterial cell densities of 1700 cells/ml in Lake Kahokugata and 330 cells/ml in Lake Kibagata. After isolating the dominant bacteria using agar plates, the isolates were classified into some genotype groups by RFLP analysis using 16S rDNA sequences. Classification of the RFLP analysis indicated that 14 isolates of Lake Kahokugata were classified into 6 types, which included 2 dominant types related to genus Pseudomonas, while 8 isolates of Lake Kibagata displayed 6 types including one or two isolates. Moreover, the RFLP types were unique for each lake, suggesting that DMAA decomposing bacteria were specific for the aquatic environment related to the arsenic cycle. The activities of DMAA decomposition mostly matched with the RFLP type category of the isolates. Accordingly, combining the MPN method with the RFLP analysis will play an important role in elucidating the distributions and dynamics of the DMAA-decomposing bacterial community.     

Development of a “Built-in” Scanning Near Field Microscope Head for an Atomic Force Microscope System and Stress Mapping of an Al2O3/ZrO2 Eutectic Composite

We constructed a scanning near-field optical microscope (SNOM) on a commercially available atomic force microscopy (AFM) apparatus (SPM-9500J2; Shimadzu Corp.) to measure the stress distribution in ceramic composite materials. Features of our SNOM system are: (1) a compact SNOM head substituted for the original AFM head; (2) a wide scanning range (125 × 125 μm²) inherited from the original scanner; (3) use of conventional shear-force regulation; (4) an optical system for the illumination-collection (I-C) mode; (5) excitation by a 488 nm line of an Ar-ion laser, and (6) light detection by photon counting or a polychromator equipped with an electronically cooled charge coupled device (CCD). This SNOM system was used to measure the surface structure and stress distribution of an Al₂O₃/ZrO₂ eutectic composite. We simultaneously measured topographic images and fluorescence spectra of an Al₂O₃/ZrO₂ eutectic composite. We estimated its peak intensity, peak position, and peak width from the fluorescence spectrum during scanning, which respectively correspond to the abundance of Al₂O₃, stress in the grain, and the anisotropy of that stress. Mapping images showed that the stress and its anisotropy were weaker in the center of the Al₂O₃ grain than its boundary between Al₂O₃ and ZrO₂. That observation suggests that Al₂O₃ underwent intense anisotropic stress induced by volume expansion in the phase transition of ZrO₂ from the cubic phase to the monoclinic phase during preparation.     

Temperature and velocity measurement of a 3-D thermal flow field using thermo-sensitive liquid crystals

It is an important challenge to analyze a three-dimensional thermal flow field in engineering, science, and agriculture. For such an analysis, it is essential to measure physical quantities such as temperature and velocity over the entire thermal flow field. This paper presents a measurement system based on color image processing for temperature and velocity vector distributions in a three-dimensional thermal flow field. Flow visualization is accomplished by the use of thermo-sensitive liquid crystal tracers. An algorithm for the color-to-temperature transformation using a multi-layer feed-forward neural network is applied to three-dimensional natural convection in a rotating cylindrical cell. Two-dimensional temperature distributions in a slit plane are obtained by using the algorithm. A three-dimensional temperature distribution is consequently constructed by interpolating the two-dimensional distributions using the B-spline function. In addition, the Spatio-Temporal correlation method is applied to the natural convection to obtain a three-dimensional velocity vector distribution.     

Selective and simultaneous determination of phosphate and silicate ions in leaching process waters for ceramics glaze raw materials of narutal origin by ion-exclusion chromatography coupled with UV-detection after postcolumn derivatization.

The selective and simultaneous ion-exclusion chromatography (IEC) with UV-detection on a weakly acidic cation-exchange resin column in the H+ -form (TSKgel Super IC-A/C) was developed and applied for the simultaneous determination of phosphate and silicate ions as the water quality parameters required for optimizing the water-leaching process for ceramics glaze raw materials of natural origin including feldspar, woods-ash, and straw-ash. Phosphate and silicate ions in these water-leaching process water samples were separated selectively from the coexisting anions such as sulfate, chloride, nitrate and carbonate ions, based on the ion-exclusion separation mechanism. They were detected selectively and simultaneously by a postcolumn derivatization with molybdenum-yellow using the UV-detector. Under the optimized separation and detection conditions (eluent, 0-1 mM sulfuric acid; reactant, 10 mM sodium molybdate-25 mM sulfuric acid; detector, UV at 370 nm; temperature, 45 degrees C), the linearity of calibration was in the range 0.1 - 10 ppm for both phosphate and silicate ions, and the detection limits at S/N = 3 were 2.58 ppb for silicate ions and 4.75 ppb for phosphate ions. The effectiveness of this method was demonstrated in practical applications to the water-leaching process for some ceramics glaze raw materials.     

A generalization of the weighted Strichartz estimates for wave equations and an application to self‐similar solutions

Weighted Strichartz estimates with homogeneous weights with critical exponents are proved for the wave equation without a support restriction on the forcing term. The method of proof is based on expansion by spherical harmonics and on the Sobolev space over the unit sphere, by which the required estimates are reduced to the radial case. As an application of the weighted Strichartz estimates, the existence and uniqueness of self‐similar solutions to nonlinear wave equations are proved on up to five space dimensions. © 2006 Wiley Periodicals, Inc.     

High-performance liquid chromatographic assay for glucuronidation activity of 7-ethyl-10-hydroxycamptothecin (SN-38), the active metabolite of irinotecan (CPT-11), in human liver microsomes

A simple and sensitive assay for glucuronidation activity of 7-ethyl-10-hydroxycamptothecin (SN-38), the active metabolite of irinotecan (CPT-11), in human liver microsomes by high-performance liquid chromatography (HPLC) with fluorescence detection is reported. The method was validated for the determination of SN-38 glucuronide (SN-38G) with respect to specificity, linearity, recovery, stability, precision, accuracy, and limits of detection and quantitation. There was no interference from matrix and non-enzymatic reactions. The calibration curve for SN-38G was linear from 5 to 500 nM. Average recoveries ranged from 98 to 100% in spiked human liver microsome samples, and the SN-38G was stable at 4 degrees C for at least 72 h. The newly developed method was found to be more sensitive and selective than previous methods using thin layer chromatography and HPLC. The limit of quantitation for SN-38G was 5 nM (2.5 pmol/assay). The intra- and inter-day precision and accuracy were less than 7 and 4%, respectively. The intra- and inter-day precision of enzyme assay for UDP-glucuronosyltransferase (UGT) activity toward SN-38 in human liver microsomes was less than 4%. With this improved sensitivity, the kinetics of SN-38 glucuronidation in human liver microsomes could be determined more precisely. Therefore, this method is applicable to in vitro study on the side effects and drug interactions of CPT-11 using small amounts of biological sample.