Topological Superconductivity in Cu(x)Bi(2)Se(3)

A topological superconductor (TSC) is characterized by the topologically protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator Cu(x)Bi(2)Se(3), which superconducts below ～3 K, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting Cu(x)Bi(2)Se(3) present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topological superconductivity in Cu(x)Bi(2)Se(3). In addition, we found an unusual pseudogap that develops below ～20 K and coexists with the topological superconducting state.     

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.     

Solution‐processable colorless polyimides derived from hydrogenated pyromellitic dianhydride with controlled steric structure

This work presents novel colorless polyimides (PIs) derived from 1R,2S,4S,5R‐cyclohexanetetracarboxylic dianhydride (H″‐PMDA). Isomer effects were also discussed by comparing with PI systems derived from conventional hydrogenated pyromellitic dianhydride, that is, 1S,2R,4S,5R‐cyclohexanetetracarboxylic dianhydride (H‐PMDA). H″‐PMDA was much more reactive with various diamines than H‐PMDA, and the former led to PI precursors with much higher molecular weights. The results can be explained from the quite different steric structures of these isomers. The thermally imidized H″‐PMDA‐based films were colorless regardless of diamines because of inhibited charge‐transfer interaction. In particular, the H″‐PMDA/4,4′‐oxydianiline system simultaneously achieved a very high T_g exceeding 300 °C, high toughness (elongation at break > 70%), and good solution processability. In contrast, the H‐PMDA‐based counterparts were essentially insoluble. The outstanding solubility of the former probably results from disturbed chain stacking by its nonplanar steric structure. An advantage of chemical imidization process is also proposed. In some cases, a copolymerization approach with an aromatic tetracarboxylic dianhydride was effective to improve the thermal expansion property. The results suggest that the H″‐PMDA‐based PI systems can be promising candidates for novel high‐temperature plastic substrate materials in electronic paper displays. A potential application as optical compensation film materials in liquid crystal displays (LCD) is also proposed in this work. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Unitary representations of the quantum group SU q (1,1): Structure of the dual space ofU q (sl(2))

Real forms of the quantum universal enveloping algebraU _q (sl(2)) and a topological quantum group associated with this algebra are discussed.     

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.