Samples of algebraic central limit theorems based on Z/2Z

This is the proceedings of the 2nd Japanese-German Symposium on Infinite Dimensional Harmonic Analysis held from September 20th to September 24th 1999 at the Department of Mathematics of Kyoto University.この論文集は, 1999年9月20日から9月24日の日程で京都大学理学研究科数学教室において開催された第2回日独セミナー「無限次元調和解祈」の成果をもとに編集されたものである.編集 : ハーバート・ハイヤー, 平井 武, 尾畑 信明Editors: Herbert Heyer, Takeshi Hirai, Nobuaki Obata #e

Investigation of the feasibility of a simple method for verifying the motion of a binary multileaf collimator synchronized with the rotation of the gantry for helical tomotherapy

In this paper, we suggest a new method for verifying the motion of a binary multileaf collimator (MLC) in helical tomotherapy. For this we used a combination of a cylindrical scintillator and a general-purpose camcorder. The camcorder records the light from the scintillator following photon irradiation, which we use to track the motion of the binary MLC. The purpose of this study is to demonstrate the feasibility of this method as a binary MLC quality assurance (QA) tool. First, the verification was performed using a simple binary MLC pattern with a constant leaf open time; secondly, verification using the binary MLC pattern used in a clinical setting was also performed. Sinograms of simple binary MLC patterns, in which leaves that were open were detected as "open" from the measured light, define the sensitivity which, in this case, was 1.000. On the other hand, the specificity, which gives the fraction of closed leaves detected as "closed", was 0.919. The leaf open error identified by our method was -1.3 +/- 7.5%. The 68.6% of observed leaves were performed within +/- 3% relative error. The leaf open error was expressed by the relative errors calculated on the sinogram. In the clinical binary MLC pattern, the sensitivity and specificity were 0.994 and 0.997, respectively. The measurement could be performed with -3.4 +/- 8.0% leaf open error. The 77.5% of observed leaves were performed within +/- 3% relative error. With this method, we can easily verify the motion of the binary MLC, and the measurement unit developed was found to be an effective QA tool.ArticleJOURNAL OF APPLIED CLINICAL MEDICAL PHYSICS. 13(1):27-43 (2012)journal articl

Electron transfer channel in the sugar recognition system assembled on nano gold particle

Existence of 1D spin diffusion in the electrochemical sugar recognition system consisting of a nano-sized gold particle (GNP), a ruthenium complex and a phenylboronic acid was investigated by NMR and muSR. When sugar molecules are recognized by the phenylboronic site, the response of electrochemical voltammetry of the Ru site changes, enabling the system to work as a sensitive sugar-sensor. In this recognition process, the change in the electronic state at the boron site caused by sugar must be transferred to the Ru site via alkyl chains. We have utilized the muon-labelled electrons method and the proton NMR to find out a channel of the electron transfer from the phenylboronic acid site to the gold nano particle via the one dimensional alkyl chain. If this transfer is driven by diffusive spin channel, characteristic field dependence is expected in the longitudinal spin relaxation rate of muSR and 1H-NMR. We have observed significant decrease in the spin relaxation rates with increasing applied field. The result is discussed in terms of low dimensional spin diffusion