General Jacobi Identity Revisited

In a previous paper (Nishimura, 1997) we probedthe deeper structure of the Jacobi identity of vectorfields with respect to Lie brackets within the realm ofsynthetic differential geometry to find what might be called the general Jacobi identity ofmicrocubes. The main objective of this paper is topresent a less esoteric and more lucid proof ofit.     

Combinatorial synthesis and optical characterization of alloy and superlattice films based on SrTiO3 and LaAlO3

We have grown alloy and superlattice films consisting of SrTiO₃ (STO) and LaAlO₃ (LAO) by pulsed laser deposition using composition-spread technique. All the (STO)_x(LAO)_1−x (0 ≤ x ≤ 1) alloy and superlattice films exhibited a single-phase perovskite structure. The optical properties of these films were characterized by absorption spectroscopy at room temperature. The spectra show a broad absorption due to O 2p-Ti 3d(t_2g) transition in an ultraviolet region. We found that absorption edges of both alloy and superlattice films systematically shifted to higher energy with increasing LAO composition. Clear difference was observed in the composition dependence of the indirect and a direct band edges.     

Optical nonlinearities in semiconductor optical amplifier and electro-absorption modulator: their applications to all-optical regeneration

Semiconductors have large optical nonlinearity with response speed in the several tens of picosecond range, making them ideal use as all-optical regenerators and wavelength converters. We theoretically and experimentally investigated optical nonlinearities induced by carrier dynamics both in forward biased semiconductor waveguide (SOA) and in reverse biased semiconductor waveguide (EAM). We made a detailed theoretical study of carrier dynamics in semiconductor waveguides by using the newly developed time-dependent transfer matrix method. To confirm the simulation results, we propose utilizing a polarization discriminating delayed interferometer (PD-DI) configuration as a simple technique for measuring optical nonlinearities such as cross gain modulation (XGM), cross absorption modulation (XAM), and cross phase modulation (XPM). In the first part of the paper, we reviewed SOA-based regenerators. As expected from the simulation results, we confirmed that injection of the transparent assist light was very effective in reducing of the SOA gain recovery time of down to a few tens of picoseconds. We further demonstrated 40 Gbit/s regeneration using an SOA-one-arm MZI (so-called UNI) configuration. The superior regeneration capability of two-stage UNI was successfully confirmed by a recirculating loop experiment up to 30,000 km with 150 regenerations. In the latter part of the paper, we reviewed all-optical regenerators using EAM. A bit-synchronized rf-driven XAM 3R regenerator consisting of only one EAM for both gating and timing correction was demonstrated at 20 Gbit/s. An EAM in conjunction with delayed interferometer configuration, which utilizes XPM as well as XAM in the EAM, has structurral simplicity and fast regeneration operability up to 100 Gbit/s. The fast response of EAM allows the optical regeneration with a small pattern word effect.     

Logical quantization of topos theory

Traditionally set theory lies at the hub of all mathematics in the sense that every branch of mathematics, ranging from algebraic geometry to functional analysis, is to be considered as developed within some formal system of set theory. Recently topos theory, which is a natural generalization of set theory, has provided an alternative foundation of mathematics, not to say the foundation of mathematics. With these considerations in mind, we quantize topos theory logically along the lines of our previous papers. The paper culminates in the quantum treatment of classifying toposes.     

Relationship between 237Np Mössbauer parameters and bond distances in nitrogen coordinated [NpO2(acac)2py]

We now report the ²³⁷Np Mössbauer spectra for [NpO₂(acac)₂py] I. The neptunium(VI) ion in I is coordinated by six oxygen atoms and the one nitrogen atom of pyridine. The isomer shift value obtained for I is ?40 mm/s, which falls in the range for the Np(VI) oxidation state. The relationship between the isomer shift and Np–O bond distance of the neptunyl group for oxygen coordination compounds is in good agreement with the reported structure of I. It is well known that the mean Np–O bond distance of the neptunium compounds is shorter by 0.01 Å than that of analogous uranium compounds. The good agreement in the ²³⁷Np–Mössbauer parameters and the Np–O distance has indicated that the reported analogous [UO₂(acac)₂py] structure may have some inaccuracies. Therefore, we have re-determined the crystal structure of [UO₂(acac)₂py]. The U–O bond distance we have obtained is reasonable.