Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.
Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.
A comprehensive history of one of the major players in the world of international finance. Over the course of its 150-year history, Deutsche Bank has established itself as a major player in the world of international finance, but has also been confronted by numerous challenges that have changed the face of Europe – from two world wars, to the rise and subsequent fall of communism. In this major work on the bank's history, Werner Plumpe, Alexander Nützenadel and Catherine R. Schenk deliver a vibrant account of the measures the bank undertook in order to address the profound upheavals of the period, as well as the diverse and unusual demands it had to face. These included the First World War, which brought the world's first period of globalization to a sudden and dramatic end, but also the development of the predominantly national framework within which the bank had to operate from 1914 until the fall of the Berlin Wall in 1989. More recently, the focus has shifted back to European and global activities, with Deutsche Bank forging new paths into the Anglo-American capital markets business – so opening another extraordinary chapter for the bank.
The 3rd edition has been extensively re-written and many topics of particular interest to food technologists have been added or completely revised. The book now comprises more than 620 tables and 472 figures, including the structural formulae of around 1,100 food components. This standard text and reference is logically organized according to food constituents and commodities. It provides students and researchers in food science, food technology, agricultural chemistry and nutrition with the up-to-date information they require. The extensive tables for easy reference, the wealth of information, and the comprehensive subject index aid advanced students to acquire in-depth insight into food chemistry and technology and make this book also a valuable on-the-job reference for chemists, food chemists, food technologists, and more. Praise for the first edition: "Few books on food chemistry treat the subject as exhaustively researchers will find it to be a useful source of information. It is easy to read and the material is systematically presented." (JACS)
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