Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the doub le zeta functions; and poly-Bernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new.
Japan’s Backroom Politics is the translation of a classic study of the rough and tumble of Japanese politics and conservative party factions in the first two decades of postwar Japan. The original book, published in 1967, was written by the preeminent political writer at the time, Watanabe Tsuneo, who later became the controversial owner of the Yomiuri Shimbun. The book was written when a generational change was occurring in Japanese politics after several of the early party leaders had passed away, including his political mentor, Ono Bamboku. Comprising ten chapters, including a comprehensive preface on the author, Japan’s Backroom Politics discusses in great detail the history of and personalities within the near-dozen factions and sub-factions that existed at the time. He introduces the resiliency of factions within the ruling Liberal Democratic Party, noting the role of money, influence, party presidency, and the chance at the premiership, among other factors, which subsequent commentators and scholars have elaborated on. Moreover, using extensive data and a penetrating analysis, Watanabe provides a historical as well as an international comparison of Japanese factions, making predictions about the future of Japanese politics.
Colloidal Organization presents a chemical and physical study on colloidal organization phenomena including equilibrium systems such as colloidal crystallization, drying patterns as an example of a dissipative system and similar sized aggregation. This book outlines the fundamental science behind colloid and surface chemistry and the findings from the author's own laboratory. The text goes on to discuss in-depth colloidal crystallization, gel crystallization, drying dissipative structures of solutions, suspensions and gels, and similar-sized aggregates from nanosized particles. Special emphasis is given to the important role of electrical double layers in colloidal suspension. Written for students, scientists and researchers both in academia and industry and chemical engineers working in the fields of colloid and surface chemistry, biological chemistry, physical chemistry, physics, chemical technology, and polymer technology this book will help them to exploit recent developments recognizing the potential applications of colloid science in enhancing the efficiency of their processes or the quality and range of their products. - Written by world leading expert in the field of colloids and surface chemistry - Outlines the underlying fundamental science behind colloidal organization phenomena - Written in an easy and accessible style, utilizing full color and minimal usage of mathematical equations
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