Multiple elliptic hypergeometric series. An approach from the Cauchy determinant

A multiple generalization of elliptic hypergeometric series is studied through the Cauchy determinant for the Weierstrass sigma function. In particular, a duality transformation for multiple hypergeometric series is proposed. As an application, two types of Bailey transformations for very well-poised multiple elliptic hypergeometric series are derived.     

Stochastic Simulation of Controlled Radical Polymerization Forming Dendritic Hyperbranched Polymers

Stochastic simulation of the formation process of hyperbranched polymers (HBPs) based on the reversible deactivation radical polymerization (RDRP) using a branch-inducing monomer, evolmer, has been carried out. The simulation program successfully reproduced the change of dispersities (Đs) during the polymerization process. Furthermore, the simulation suggested that the observed Đs (=1.5–2) are due to the distribution of the number of branches instead of undesired side reactions, and that the branch structures are well controlled. In addition, the analysis of the polymer structure reveals that the majority of HBPs have structures close to the ideal one. The simulation also suggested the slight dependence of branch density on molecular weight, which was experimentally confirmed by synthesizing HBPs with an evolmer having phenyl group.     

Baryogenesis in false vacuum

The null result in the LHC may indicate that the standard model is not drastically modified up to very high scales, such as the GUT/string scale. Having this in the mind, we suggest a novel leptogenesis scenario realized in the false vacuum of the Higgs field. If the Higgs field develops a large vacuum expectation value in the early universe, a lepton number violating process is enhanced, which we use for baryogenesis. To demonstrate the scenario, several models are discussed. For example, we show that the observed baryon asymmetry is successfully generated in the standard model with higher-dimensional operators.     

First observation of a smectic A-cholesteric phase transition in a thermotropic liquid crystal consisting of a rigid-rod helical polysilane

A smectic A-cholesteric phase transition for a rigid-rod helical polymer, poly[n-decyl-(S)-2-methylbutylsilane] (PD2MBS), with a narrow molecular weight distribution, has been observed for the first time. Polarizing optical microscopy showed that the fan-shaped texture of the smectic A phase turned into the characteristic planar texture of the cholesteric phase upon heating. The positive CD band, which corresponds to the reflection band of the cholesteric phase, gradually decreased in intensity within a range 30°C below the transition temperature on cooling, while the peak maximum shifted towards shorter wavelengths. It was concluded that the system has a very wide temperature region over which the cholesteric-smectic A phase transition occurs and in which the cholesteric pitch varies with temperature.     

Instrumental Requirements for Non-Invasive Blood Glucose Measurement Using NIR Spectroscopy

The magnitude of spectral change in blood glucose measurements with diffuse reflectance spectroscopy is investigated. Spectral change is estimated by simulation of light propagation in skin tissue and measurements of absorbance spectra of aqueous glucose solution. Required sensitivity of spectrophotometers for monitoring change in the blood glucose concentration as small as 10 mg/dL has been obtained using the estimated change in the absorbance spectrum and mean pathlength of light in tissue.     

Relative position of four subspaces in a Hilbert space

We study the relative position of several subspaces in a separable infinite-dimensional Hilbert space. In finite-dimensional case, Gelfand and Ponomarev gave a complete classification of indecomposable systems of four subspaces. We construct exotic examples of indecomposable systems of four subspaces in infinite-dimensional Hilbert spaces. We extend their Coxeter functors and defect using Fredholm index. The relative position of subspaces has close connections with strongly irreducible operators and transitive lattices. There exists a relation between the defect and the Jones index in a type II₁ factor setting.     

Bistable Optical Devices Using Laser Diodes Coupled to Interference Filters

A bistable optical device was demonstrated by using the longitudinal mode hopping of the laser diode and the narrow transmission spectrum of an interference filter. The device is capable of converting changes in the wavelength of the laser diode into changes in intensity by transmitting it through the filter. Exclusive OR operation was observed with the use of triple signal outputs. In addition, an optical switch-off phenomenon was confirmed by directly injecting a pulse 500 ps wide into an external dye laser.