A generating function for sums of multiple zeta values and its applications

A generating function for specified sums of multiple zeta values is defined and a differential equation that characterizes this function is given. As applications, some relations for multiple zeta values over the field of rational numbers are discussed.

     

Computation of transition to turbulence in the compression stage of a reciprocating engine

The transition to turbulent flow in the compression stage of a reciprocating engine is studied by obtaining the finite-difference numerical solutions to the governing Navier-Stokes equations without using explicit turbulence models. A computational method is developed under the assumption that the flow is in a low-subsonic regime with strong compression. The numerical method is a simple extension of the well known MAC method. Computations were performed for three different chamber geometries at the engine speed of 1400 rpm. The results of the computations clearly demonstrate the transient process in which large tumbling vortices break down into smaller ones near the end of the compression process. The transition process is also caught experimentally by using Mach-Zehnder interferometry.     

Influence of the solvent on nature of gate effect in molecularly imprinted membrane

The solute diffusive permeability in a thin layer of a molecularly imprinted polymer (MIP) is affected by specific binding of the MIP with a template. This phenomenon, termed the "gate effect," would be widely applicable for the development of novel biomimetic sensors. However, the mechanism underlying the gate effect is not totally understood. We present here investigation of the role of specific adsorption of a template and solution content in MIPs on the gate effect. A molecularly imprinted self-supporting membrane was formed by copolymerization of methacrylic acid, 2-vinylpyridine, and triethyleneglycol dimethacrylate in the presence of L- (or D-) phenylalanine as a template. The template adsorbed by membrane with degree of enantio-selectivity in a mixed solvent of methanol and water. The amount of adsorption and binding selectivity showed little sensitivity to the solvent composition. The solution content in the membrane increased with increasing the methanol concentration of the solvent following a sigmoid curve with an inflection point at methanol concentration of 20 wt.%. The content increased in the presence of the template at methanol concentrations higher than the inflection point, and decreased at lower methanol concentrations. The creatinine permeability across the membrane estimated by batchwise dialysis increased in the presence of the template at 50 wt.% methanol in the solvent, and did not change at 20 wt.%. There was no permeability for creatinine in the pure water solvent. Both the solution content and the permeability were not affected by the presence of the enantiomer of the template. The results show that the choice of solvent controls more strongly the nature of the gate effect than the specific binding of the template.     

H Nmr Spectra of Oligosaccharide Substituted Cyclodextrins

ABSTRACT

¹H NMR spectra of some oligosaccharide substituted cyclodextrins composed of only α-D-glucose units are analysed. Chemical shifts of protons of each glucosyl group of the chain were determined by experiments with the HOHAHA pulse technique. In spite of the similar kinds of protons, dispersion of chemical shifts is observed. The most dispersed proton is the anomeric proton, and the largest change in the chemical shifts is 0.5 ppm.     

Structural development of ultra‐high strength polyethylene fibers: Transformation from kebabs to shishs through hot‐drawing process of gel‐spun fibers

Structural development of ultra‐high strength polyethylene fibers via hot‐drawing processes of as‐spun gel fibers was investigated by means of transmission electron microscopy. It is found that the shish‐kebabs developed in both the as‐spun and drawn fibers can be transformed continuously into the micro‐fibril structure composed mostly of the shish structure through the hot‐drawing process. The structure transformation involves a drastic decrease in diameter of the kebab plus the shish but almost no change in the shish diameter. This result suggests that the chains in the kebabs are incorporated into the shishs and consumed to extend the longitudinal dimension of the shishs during the drawing process. The proposed new deformation model well explains the relationship between the fiber morphology and their mechanical properties: the tensile strength and modulus of the fibers can be determined by the number of the shish in the fiber and the macroscopic diameter of the fiber, which are apriori determined at the spinning process. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1861–1872, 2010     

EPMA line analysis of chemical states of chromium

A novel technique for determining the chemical states of elements with a heterogeneous distribution in samples involving EPMA line analysis is proposed. LLS (linear least squares) calculation was applied to a set of reduced spectra measured in the line analysis. The reduced spectra which have several energy points (including two points for backgrounds) were measured in order to save measuring time. The LLS calculation gives the mole fraction of each chemical state. We applied this method to the analysis of corrosion products formed on Cr-containing steel after corrosion tests. EPMA mapping revealed that Cr is enriched only in the inner layer of the corrosion products. From the results of the LLS calculation, it was determined that Cr in the corrosion products exists in the trivalent Cr state whereas in the steel Cr is in the metallic state. This result corresponds to the spectra of characteristic x-rays from the corroded steel. Copyright © 2001 John Wiley & Sons, Ltd.     

Vertically Coupled Microring Resonator Filter : Versatile Building Block for VLSI Filter Circuits

In this review, the recent progress in the development of vertically coupled micro-ring resonator filters is summarized and the potential applications of the filters leading to the development of VLSI photonics are described.