Evaluation formulas for Tornheim's type of alternating double series

In this paper, we give some evaluation formulas for Tornheim's type of alternating series by an elementary and combinatorial calculation of the uniformly convergent series. Indeed, we list several formulas for them by means of Riemann's zeta values at positive integers.

     

Development of a new file search system for nuclear magnetic resonance spectra: Production of an Enlarged Data Base and Search Test

A practical search system for proton n.m.r. spectra is reported. The coding rules and search algorithms are described in detail. Data for 8000 spectra have been converted into a computer-readable file from printed charts. Several search tests are used to evaluate the usefulness of the search system, and various effects of experimental conditions such as different instruments, frequencies and solvents on recall efficiency are described. The results presented indicate that the system should be applicable to routine analytical work.     

Simultaneous determination of residues of emamectin and its metabolites, and milbemectin, ivermectin, and abamectin in crops by liquid chromatography with fluorescence detection.

A liquid chromatographic (LC) method was developed for the determination of emamectin and its metabolites (8,9-Z-isomer, N-demethylated, N-formylated, and N-methylformylated emamectin) in various crops. The analytes were extracted with acetone, cleaned up on cartridge columns (C18 and NH2), derivatized with trifluoroacetic anhydride and 1-methylimidazole, and determined by LC with fluorescence detection. Because radish inhibited the formation of the fluorescent derivatives, an additional Bond Elut PRS cartridge was used in the cleanup of Japanese radish samples. During sample preparation, N-formylated emamectin partially degraded to emamectin B1b and emamectin B1a, and the 8,9-Z-isomer partially degraded to N-demethylated emamectin. Therefore, emamectin and its metabolites were determined as total emamectin, i.e., their sum was estimated as emamectin benzoate. Their recoveries from most crops were approximately 80-110% with the developed method. The detection limits for the analytes in vegetables were 0.1-0.3 parts per trillion (ppt). The results for these compounds were confirmed by LC/mass spectrometry (LC/MS; electrospray ionization mode). Because the fluorescent derivative of emamectin was undetectable by LC/MS, the results for the analyte were confirmed by using a sample solution without derivatization. Limits of detection by LC/MS were similar to the fluorescence detection limits, 0.1-0.3 ppt in vegetables. In addition to the emamectins, milbemectin, ivermectin, and abamectin were also determined by the developed method.     

Stable first-order particle-frame relativistic hydrodynamics for dissipative systems

We propose a stable first-order relativistic dissipative hydrodynamic equation in the particle frame (Eckart frame) for the first time. The equation to be proposed was in fact previously derived by the authors and a collaborator from the relativistic Boltzmann equation. We demonstrate that the equilibrium state is stable with respect to the time evolution described by our hydrodynamic equation in the particle frame. Our equation may be a proper starting point for constructing second-order causal relativistic hydrodynamics, to replace Eckart's particle-flow theory.     

Measuring Light Field of Light Source with High Directional Resolution Using Mirrored Ball and Pinhole Camera

This paper presents a method of measuring a light field of a light source with high directional resolution using a mirrored ball and a pinhole camera. The light field describes a spatial and directional distribution of radiances from the light source. The directional distribution is expanded by a reflection on the mirrored ball, and the radiances are measured by a charge-coupled device (CCD) camera with a pinhole lens. The light source is laterally moved by a robot arm to measure the directionally expanded light field, and each pixel on a CCD can obtain the radiances from the light source through the pinhole lens with high directional resolution. The light field is estimated from the pixel value and the position of each pixel using a ray tracing technique. The light field of a krypton lamp was experimentally measured by the proposed method, and the accuracy of the measurement was evaluated against the irradiances measured by a spectro-radiometer at sample points.     

Determination of clethodim and its oxidation metabolites in crops by liquid chromatography with confirmation by LC/MS

A method was developed for determination of the herbicide clethodim (C0) and its oxidation metabolites clethodim sulfoxide (C1) and clethodim sulfone (C2) in agricultural products. Upon extraction, both C0 and C1 were oxidized to C2 by m-chloroperoxybenzoic acid, and C2 was determined by liquid chromatography (LC). The C2 peak was confirmed by liquid chromatography/mass spectrometry (LC/MS) with electrospray ionization (ESI). Recoveries of C0 from radish, tomato, onion, sweet potato, kidney bean, carrot, cabbage, and lettuce ranged from 91 to 118% following fortification at 0.05-1.0 ppm. The detection limit of C2 in crops was 0.01 ppm (S/N > 3). The fortified samples of onion, sweet potato, kidney bean, and carrot were confirmed by LC/MS (ESI), and the peak of C2 was detected.     

Regression-based model of skin diffuse reflectance for skin color analysis

A simple regression-based model of skin diffuse reflectance is developed based on reflectance samples calculated by Monte Carlo simulation of light transport in a two-layered skin model. This reflectance model includes the values of spectral reflectance in the visible spectra for Japanese women. The modified Lambert Beer law holds in the proposed model with a modified mean free path length in non-linear density space. The averaged RMS and maximum errors of the proposed model were 1.1 and 3.1%, respectively, in the above range.