Transversal infinitesimal automorphisms of harmonic foliations on complete manifolds

Summary In this paper we study infinitesimal automorphisms of finiteL ²-norm for harmonic Riemannian and Kähler foliations admitting a complete bundle-like metric. The results generalize facts established recently in the compact case.1980 Mathematics Subject Classification: Primary 57 R 30, Secondary 58 E 20.Work supported in part by a grant from the National Science Foundation.     

Three-dimensional simulation of quasi-particle structures in nano-scaled superconductors

We have developed numerical simulation method for quasi-particle structures in the three-dimensional nano-sized superconductors, using the three-dimensional finite element method and the Bogoliubov-de Gennes equation. Using this method, we analyzed the superconducting state in the nano-sized cubic superconductors. We found the spatial oscillations of order parameter because of the confinement of superconducting electrons, and also we found the quasi-particle bound states at the corners of the cubic superconductors because of suppression of superconductivity at the corners.     

Hall effect of FeTe and Fe(Se1–xTex) thin films

The Hall effect is investigated in thin-film samples of iron–chalcogenide superconductors in detail. The Hall coefficient (R_H) of FeTe and Fe(Se_1–xTe_x) exhibits a similar positive value around 300 K, indicating that the high-temperature normal state is dominated by hole-channel transport. FeTe exhibits a sign reversal from positive to negative across the transition to the low-temperature antiferromagnetic state, indicating the occurrence of drastic reconstruction in the band structure. The mobility analysis using the carrier density theoretically calculated reveals that the mobility of holes is strongly suppressed to zero, and hence the electric transport looks to be dominated by electrons. The Se substitution to Te suppresses the antiferromagnetic long-range order and induces superconductivity instead. The similar mobility analysis for Fe(Se_0.4Te_0.6) and Fe(Se_0.5Te_0.5) thin films shows that the mobility of electrons increases with decreasing temperature even in the paramagnetic state, and keeps sufficiently high values down to the superconducting transition temperature. From the comparison between FeTe and Fe(Se_1–xTe_x), it is suggested that the coexistence of ‘itinerant’ carriers both in electron and hole channels is indispensable for the occurrence of superconductivity.     

The first total synthesis and structural determination of antibiotics K1115 B1s (alnumycins)

K1115 B₁, isolated from the broth of Streptomyces species, was found to be a mixture of stereoisomers. Authors synthesized all stereoisomers of K1115 B₁ by convergent synthesis coupling a rhamnose derivative, an isobenzofuranone, and a chiral tetraol. Comparison of ¹H NMR spectra and optical rotations made it clear that the absolute structures of K1115 B_1α (the major isomer) and K1115 B_1β (the minor isomer) were (1R, 17S)- and (1R, 17R)-configurations, respectively. The optical rotations of the stereoisomers revealed that alnumycin, reported as the identical structure with K1115 B₁, might be another mixture of stereoisomers.     

Generalized Cheeger-Gromoll metrics and the Hopf map

We show that there exists a family of Riemannian metrics on the tangent bundle of a two-sphere, which induces metrics of constant curvature on its unit tangent bundle. In other words, given such a metric on the tangent bundle of a two-sphere, the Hopf map is identified with a Riemannian submersion from the universal covering space of the unit tangent bundle, equipped with the induced metric, onto the two-sphere. A hyperbolic counterpart dealing with the tangent bundle of a hyperbolic plane is also presented.     

Temperature Characteristics of Vibrating Type Sensor Using Micromachined Optical Fiber-Tip

An optical sensor using a quartz core microcantilever was fabricated by etching clad layer from optical fiber. The temperature dependence of the resonance frequency of this sensor was measured in atmosphere and water. The temperature coefficient of the resonance frequency in water was 1.3×10⁻³/°C, which was about one order larger than that (2.3×10⁻⁴/°C) in atmosphere. This was caused by increase of additional mass due to temperature dependence of the viscosity of water, while, the increase of the resonance frequency in atmosphere was caused by temperature dependence of Young’s modulus of the quartz core. These results were evaluated theoretically using a “string-of-beads” model.