Scalar curvature of spheres

Financial support from the FRD is gratefully acknowledged     

Analysis of Spectral Reflectance Using Normalization Method from Endoscopic Spectroscopy System

Objective assessment of gastrointestinal mucosal color is extremely important in the endoscopic diagnosis of digestive tract disease. In this paper, we propose a method to clarify the spectral characteristics of gastric and colon cancer. A large number of spectral reflectance data of mucous membrane are measured by the endoscopic spectroscopy system (ESS) in the National Cancer Center Hospital East, Kashiwa, Japan and the Department of Internal Medicine, Self-Defense Force Center Hospital, Tokyo, Japan. We assume that early cancer appears primarily in the spectral data of short wavelength, because it is usually present in a superficial cell where short wavelength light is scattered more strongly than long wavelength light. To identify the features in the short wavelength components, the spectral reflectance was divided by the reflectance of a long wavelength. We investigated the possibility of distinguishing early cancer from normal spectral data through statistical analysis, employing the projection axis as the mean difference between them. Early cancer and normal spectral data were projected on the projection axis, and the Student’s T-test was applied to evaluate the mean of the distribution between these data.     

Proper action on a homogeneous space of reductive type

Partially supported by Grant-in-Aid for Scientific Research (No. 63740074)     

A compact optical heterodyne interferometer by optical integration and its application

A compact high-resolution optical heterodyne interferometer combining a two-frequency light module and a minute optical system is described. The light module, which generates two independent frequencies of light, is fabricated by proton exchange method on LiNbO₃ substrate. We report an experiment evaluating measurement accuracy using a micro-displacement measurement system which incorporates this interferometer. Results of the experiment with a standard thickness sample show high thermal stability with maximum measurement error of 1.8 nm at a temperature from 19°C to 33°C. The system was used to measure the hysteresis of a piezoelectric element for displacements of several nm, thereby making it possible to analyze the system quantitatively in practice.     

Mesomorphic properties of orthopalladated complexes of laterally substituted azobenzene derivatives, 2-alkoxycarbonyl-4-(4-ethoxyphenylazo)phenyl 4-methoxybenzoates

Homologous series of 2-alkoxycarbonyl-4-(4-ethoxyphenylazo)phenyl 4-methoxybenzoates (L) and their orthopalladated μ-chloro dimers (Pd₂Cl₂L₂) have been synthesized and their thermotropic phase transition behaviour has been characterized. The ligands, L, are three-ring nematogens with their central rings substituted in the 2-position by n-alkyl chains of varied length. The thermal stability of the nematic phases decreases rapidly with increasing side chain length and then levels off as the series is ascended. In every case the mesomorphic phase appears only over a small temperature range (less than 20° C). The orthopalladated species also proved to be nematogenic. Melting and clearing points rise on the average by 87° C and 126° C, respectively, and thus the temperature ranges of the nematic phases are enlarged considerably upon metallation. In relation to the observed stabilization of the nematic phases, particularly of higher homologues, a lath-like molecular structure, in which the side chains of the ligands fill up the clefts of the core part, has been deduced for a Pd2Cl2L2 homologue from its solution ¹H-NMR spectrum.     

On the possibility of a radical decrease in the strength of many-body interactions in the organic metal α-(BETS)<Subscript>2</Subscript> KHg(SCN)<Subscript>4</Subscript>

Behavior of the de Haas-van Alphen (dHvA) oscillations depending on the angle between the magnetic field direction and the perpendicular to conducting layers in the quasi-two-dimensional organic metal α-(BETS)₂ KHg(SCN)₄ was studied in detail. The angular dependence of the dHvA oscillation amplitude exhibits a series of minima (at ±43.2°, ±64.6°, and ±72.0°) related to the “zero spin” effect, through which it is possible to estimate the splitting factor. An analysis of this value suggests that many-body interactions in the compound studied are either absent or at least radically weakened.