Takashi Kumagai - Böcker

This book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups. Both the limit Lévy process and the limit Lie group carrying this process are determined by and depend on the law of the original random walk.

In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits.

The hydrogen bond represents an important interaction between molecules, and the dynamics of hydrogen bonds in water create an ever-present question associated with the process of chemical and biological reactions.

The hydrogen bond represents an important interaction between molecules, and the dynamics of hydrogen bonds in water create an ever-present question associated with the process of chemical and biological reactions. In spite of numerous studies, the process remains poorly understood at the microscopic level because hydrogen-bond dynamics, such as bond rearrangements and hydrogen/proton transfer reactions, are extremely difficult to probe. Those studies have been carried out by means of spectroscopic methods where the signal stems from the ensemble of a system and the hydrogen-bond dynamics were inferred indirectly. This book addresses the direct imaging of hydrogen-bond dynamics within water-based model systems assembled on a metal surface, using a scanning tunneling microscope (STM). The dynamics of individual hydrogen bonds in water clusters, hydroxyl clusters, and water-hydroxyl complexes are investigated in conjunction with density functional theory. In these model systems, quantum dynamics of hydrogen bonds, such as tunneling and zero-point nuclear motion, are observed in real space. Most notably, hydrogen atom relay reactions, which are frequently invoked across many fields of chemistry, are visualized and controlled by STM. This work presents a means of studying hydrogen-bond dynamics at the single-molecule level, providing an important contribution to wide fields beyond surface chemistry.

This volume collects, in written form, eight plenary lectures and twenty-five selected contributions from invited and contributed lectures delivered at the International Workshop on Potential Theory 2004. The workshop was held at Shimane University, Matsue, Japan, from 23 to 28 August, 2004. The topic of the workshop was Potential Theory and its related fields. There were stimulus talks from classical potential theory to pluri-potential theory and probabilistic potential theory.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America