Generalized Longo–Rehren Subfactors and α-Induction

We study the recent construction of subfactors by Rehren which generalizes the Longo–Rehren subfactors. We prove that if we apply this construction to a non-degenerately braided subfactor N⊂M and α^±-induction, then the resulting subfactor is dual to the Longo–Rehren subfactor M⊗M ^opp⊂R arising from the entire system of irreducible endomorphisms of M resulting from α^plusmn;-induction. As a corollary, we solve a problem on existence of braiding raised by Rehren negatively. Furthermore, we generalize our previous study with Longo and Müger on multi-interval subfactors arising from a completely rational conformal net of factors on S ¹ to a net of subfactors and show that the (generalized) Longo–Rehren subfactors and α-induction naturally appear in this context. Received: 11 September 2001 / Accepted: 7 October 2001     

Synthesis of oligomeric poly[(1, 2-propanediamine)-alt-(oxalic acid)] and anomalous proton conductivities of the thin films

New proton-conductive polyamide oligomers, oligomeric poly[(1, 2-propanediamine)-alt-(oxalic acid)], were synthesized to investigate the proton transport properties of bulk and thin films. The obtained oligomers were characterized by the X-ray diffraction, FT-IR spectra, ¹H NMR, Matrix Assisted Laser Desorption/Ionization Time of Flight (MALDI-TOF) mass spectrum, and electrical conductivity measurements. The bulk proton conductivity is 3.0 × 10^? 4 S cm^? 1 at the relative humidity (RH) of 80%. The proton conductivity of thin film is relatively higher than that of bulk sample. Thickness dependence of the proton conductivity was observed in these thin films. The maximum proton conductivity of the thin film is 4.0 × 10^? 3 S cm^? 1 at the relative humidity (RH) of 80%, which is higher one order magnitude than that of the bulk sample. The activation energies of bulk and 200 nm thick film are 1.0 and 0.69 eV at the RH of 60%, respectively.     

A miniaturization of the multi-degree-of-freedom ultrasonic actuator using a small cylinder fixed on a substrate

Multi-degree-of-freedom ultrasonic actuator has been studied for robot arms and multidimensional precision table and so on because of its simple structure, silent operation, and holding force. In this study, we aim to miniaturize multi-degree-of-freedom ultrasonic actuator for fabrication on a substrate. This actuator consists of a stainless steel cylinder and a PZT ring. The cylinder is fixed on a substrate and the PZT ring is glued to the substrate near the cylinder. The 1st longitudinal vibration and the 2nd bending vibration are simultaneously excited in the cylinder to make elliptical motion at the top of the cylinder and a ball rotor placed on the cylinder rotates because of the friction force. Length of the cylinder was decided so as to tune the resonance frequency of the 1st longitudinal vibration to the 2nd bending one. Actuator performances are evaluated experimentally using a 14 mm height and 7 mm diameter stainless steel cylinder with a 0.5 mm thickness PZT ring. The rotation about the cylinder axis is tested using the two orthogonal bending vibrations with 90 degrees phase difference. Also, the rotation about horizontal axes were investigated using the combination of the longitudinal vibration and one of two bending vibrations. We measured the rotation speed of a steel ball and obtained 15.8 rps using a 6 mm diameter ball rotor.     

Modulational instability and parametric amplification induced by loss dispersion in optical fibers

We show that modulational instability may arise even in the normal group-velocity dispersion regime of an optical fiber when the fiber loss (gain) varies depending on the wavelength. A simple analytical expression for the instability gain is obtained, which reveals that the odd-order terms of the loss dispersion are responsible for this phenomenon. The instability gain is measured experimentally in an optical-parametric-amplification configuration. Large parametric gain is induced in a non-phase-matched regime as we apply narrow band loss at the idler wavelength.     

Measurement of Cu K-shell and Ag L-shell ionization cross sections by low-energy positron impact

Inner shell ionization cross sections by low-energy positron impact have been measured. Development of an x-ray detector with thin Si(Li) crystals has enabled the first measurements of the absolute cross sections for the positron impacts in the energy range below 30 keV. Threshold behavior of the measured cross sections for the Cu K shell and Ag L shell are compared with the theoretical results of Gryzinski and Kowalski [Phys. Lett. A 183, 196 (1993)]] and Khare and Wadehra [Can. J. Phys. 74, 376 (1996)]]. Good agreement has been found for the Cu K shell, while the experimental values for the Ag L shell were found to be smaller than the corresponding theoretical results.     

Ultrahigh-resolution laser spectroscopy of the S1B2u ← S0Ag transition of perylene

A rotationally resolved ultrahigh-resolution fluorescence excitation spectrum of the S₁ ← S₀ transition of perylene has been observed using a collimated supersonic jet technique in conjunction with a single-mode UV laser. We assigned 1568 rotational lines of the band, and accurately determined the rotational constants. The obtained value of inertial defect was positive, accordingly, the perylene molecule is considered to be planar with D_2h symmetry. We determined the geometrical structure in the S₀ state by ab initio theoretical calculation at the RHF/6-311+G(d,p) level, which yielded rotational constant values approximately identical to those obtained experimentally. Zeeman broadening of each rotational line with the external magnetic field was negligibly small, and the mixing with the triplet state was shown to be very small. This evidence indicates that intersystem crossing (ISC) in the S₁¹B_2u state is very slow. The rate of internal conversion (IC) is also inferred to be small because the fluorescence quantum yield is high. The rotational constants of the S₁¹B_2u state were very similar to those of the S₀¹A_g state. The slow internal conversion (IC) at the S₁ zero-vibrational level is attributed to a small structural change upon electronic transition.     

Polymerization of 5-Substituted Cyclooctenes with Tungsten and Molybdenum Catalysts

Polymerizations of cyclooctene, 5-methyl, 5-chloro-, and 5-methoxycyclooctenes were studied. Cyclooctene (CO) and 5-methylcyclooctene (MCO) provided high polymers in 80% yield with the use of WCl₆/AlEti._B Cl_u5 or WCl₆/AlEtCl₂ catalyst. 5-Chlorocyclooctene gave oligomer in 50% yield with WCl₆/AlEt₂Cl catalyst. Neither polymer nor oligomer was produced from 5-methoxycyclooctene. These polymers were found to be produced through a ring-opening mechanism. The ratio of cis to trans structure in poly(CO) and poly(MCO) was determined by measurements of the decoupled ′H-NMR spectrum. Poly(CO) containing more than 50% trans structure was a crystalline solid at room temperature, while the polymer containing 30% of trans structure did not crystallize at room temperature. Poly(MCO) was amorphous, regardless of the content of trans structure. Poly(CO) and poly(MCO) obtained with MoCU/AlEtaCl or MoCU/AlEtCb catalyst contained no carbon-carbon double bond, and a vinyl polymerization mechanism was expected for this system.     

Reactions of 2-Pyridyl Substituted Phosphine Oxides and Phosphonium Salts with Organometallic Reagents and in Aqueous Media

Phosphine oxides bearing two or three 2-pyridyl groups react with organometallic reagents affording 2,2′-bipyridyl, 2-substituted pyridines and pyridine in good yields. Phosphonium salts and phosphine oxides, bearing at least two 2-pyridyl or substituted 2-pyridyl groups also give the corresponding 2,2′-bipyridyls and pyridines upon treatment with acid or neutral solvents such as water and alcohols in substantial yields. The 2,2′-bipyridyls are considered to be formed by ligand coupling within the pentacoordinated phosphorus intermediate formed incipiently during the reaction.     

Studies on the syntheses of polymetalloxanes and their properties as a precursor for amorphous oxide. IV. Properties of SiO2–TiO2 oxide fibers from polytitanosiloxane

From polytitanosiloxanes (PTS), SiO₂–TiO₂ oxide fibers with fairly good tensile strength were prepared, and their mechanical and thermal properties were investigated. The precursor fibers PTS-0.5 and PTS-1.0 were obtained by dry spinning of a highly viscous PTS solution which were formed as the reaction mixture of silicic acid (SA) with bis(2,4-pentanedionato)titanium diisopropoxide (PTP) in the molar ratios (SA/PTP) of 0.5 and 1.0. The precursor fibers PTS-0.5 were too brittle to measure their tensile strength, whereas PTS-1.0 and the heat-treated fibers were found to have tensile strength of 130 (precursor), 540 (500°C), and 450 (900°C) MPa, respectively. Heat-treatment of the fibers PTS-1.0 at above 1000°C forms anatase and rutile of titanium dioxide. The crystallization is resulted from the unreacted PTP which is not incorporated into the polymer network.