The Lévy Laplacian and Stochastic Processes

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 #enIn this paper, we give infinite dimensional stochastic processes generated by functions of the Lévy Laplacian. Moreover we introduce an operator to connect the Lévy Laplacian with the Number operator and also give a relationship between a (Co)-semigroup generated by the Lévy Laplacian and an infinite dimensional Ornstein-Uhlenbeck process

Depth profiles of radioactive cesium in soil using a scraper plate over a wide area surrounding the Fukushima Dai-ichi Nuclear Power Plant, Japan

AbstractDuring the Fukushima Dai-ichi Nuclear Power Plant (NPP) accident, radioactive cesium was released in the environment and deposited on the soils. Depth profiles of radioactive cesium in contaminated soils provide useful information not only for radiation protection and decontamination operations but also for geoscience and radioecology studies. Soil samples were collected using a scraper plate three times between December 2011 and December 2012 at 84 or 85 locations within a 100-km radius of the Fukushima Dai-ichi NPP. In most of the obtained radioactive cesium depth profiles, it was possible to fit the concentration to a function of mass depth as either an exponential or hyperbolic secant function. By using those functions, following three parameters were estimated: (i) relaxation mass depth β (g cm−2), (ii) effective relaxation mass depth βeff (g cm−2), which is defined for a hyperbolic secant function as the relaxation mass depth of an equivalent exponential function giving the same air kerma rate at 1 m above the ground as the inventory, and (iii) 1/10 depth L1/10 (cm), at which the soil contains 90% of the inventory. The average β value (wet weight) including ones by hyperbolic secant function in December 2012, was 1.29 times higher than that in December 2011. In fact, it was observed that depth profiles at some study sites deviated from the typical exponential distributions over time. These results indicate the gradual downward migration of radioactive cesium in the soils. The L1/10 values in December 2012 were summarized and presented on a map surrounding the Fukushima Dai-ichi NPP, and the average value of L1/10 was 3.01 cm (n = 82) at this time. It was found that radioactive cesium remained within 5 cm of the ground surface at most study sites (71 sites). The sech function can also be used to estimate the downward migration rate V (kg m−2 y−1). The V values in December 2012 (n = 25) were in good agreement with those found by a realistic approach using a diffusion and migration model. Almost all values ranged between 1.7 and 9.6 kg m−2 y−1 in this study

ARTICLE Development of radionuclide distribution database and map system on the Fukushima nuclear accident

The Radionuclide distribution database and map system, which provide basic information for evaluations and countermeasures of the accident at Fukushima Daiichi nuclear power plant, are explained. Due to massive earthquake and tsunami, Fukushima Daiichi nuclear power plant had been damaged and spread out radioactive materials around the Fukushima region. In order to meet the various requirements from government, local government, residents, and/or researchers, we developed two systems to provide those data to the public. One of the systems is a database system which is designed to provide quantitative data for detailed analysis. Another is a map system which provides intuitive images for the qualitative estimation. In the two systems, it is possible to provide the information requested by a wide range of people

Dem investigation of horizontal high shear mixer flow behaviour and implications for scale-up

In high shear granulation, various dimensionless or dimensioned parameter groups such as constant Froude number, tip speed, relative swept volume and specific energy input are commonly used as scale-up criteria, in order to maintain the powder bed internal flow or stress field across scales. One major challenge is obtaining the internal flow and stress field through experimentation given the lack of precise measurement techniques. Hence, this work employs DEM (discrete element method) simulations to study the internal flow patterns and behaviour of different scale batch, horizontal high shear mixers. The simulations provide a deeper understanding of the interaction of scale, impeller speed and fill level on the flow field, and show that the particle velocity is correlated with the relative swept volume in these mixers. It shows that the relative particle velocity is correlated, independent of scale, to the relative swept volume per rotation and highlights its values as a parameter for understanding and comparing mixer behaviour. The work also demonstrates the importance of the particle size chosen for the simulation as well as the tool-wall gap in the mixer, and highlights its importance as we interpret DEM results

Post-intervention Status in Patients With Refractory Myasthenia Gravis Treated With Eculizumab During REGAIN and Its Open-Label Extension

OBJECTIVE: To evaluate whether eculizumab helps patients with anti-acetylcholine receptor-positive (AChR+) refractory generalized myasthenia gravis (gMG) achieve the Myasthenia Gravis Foundation of America (MGFA) post-intervention status of minimal manifestations (MM), we assessed patients' status throughout REGAIN (Safety and Efficacy of Eculizumab in AChR+ Refractory Generalized Myasthenia Gravis) and its open-label extension. METHODS: Patients who completed the REGAIN randomized controlled trial and continued into the open-label extension were included in this tertiary endpoint analysis. Patients were assessed for the MGFA post-intervention status of improved, unchanged, worse, MM, and pharmacologic remission at defined time points during REGAIN and through week 130 of the open-label study. RESULTS: A total of 117 patients completed REGAIN and continued into the open-label study (eculizumab/eculizumab: 56; placebo/eculizumab: 61). At week 26 of REGAIN, more eculizumab-treated patients than placebo-treated patients achieved a status of improved (60.7% vs 41.7%) or MM (25.0% vs 13.3%; common OR: 2.3; 95% CI: 1.1-4.5). After 130 weeks of eculizumab treatment, 88.0% of patients achieved improved status and 57.3% of patients achieved MM status. The safety profile of eculizumab was consistent with its known profile and no new safety signals were detected. CONCLUSION: Eculizumab led to rapid and sustained achievement of MM in patients with AChR+ refractory gMG. These findings support the use of eculizumab in this previously difficult-to-treat patient population. CLINICALTRIALSGOV IDENTIFIER: REGAIN, NCT01997229; REGAIN open-label extension, NCT02301624. CLASSIFICATION OF EVIDENCE: This study provides Class II evidence that, after 26 weeks of eculizumab treatment, 25.0% of adults with AChR+ refractory gMG achieved MM, compared with 13.3% who received placebo