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The theory of Lie groups has proven to be a most powerful analytical tool in many areas of modern scientific endeavors. It was only a few years ago that economists discovered the usefulness of this approach in their study of the frontiers of modern economic theory. These frontiers include the areas of technical change and productivity, technology and preference, economic conservation laws, comparative statics and integrability conditions, index number problems, and the general theory of ~ observable market behavior (Sato [1980, 1981], Nono [1971], Sato and N~no [1983], Russell [1983]). 1 In Nono [1971] and Sa to [1981, Chapter 4] the concept of "G-neutral" (group neutral) technical change was first introduced as a natural extension of the well-known concepts of Hicks, Harrod, Solow and Sato-Beckmann-Rose neutrality. The present monograph contains a further extension of the G-neutral technical change to the case of non-constant-returns-to-scale technology and to the case of multiple factor inputs. The methodology of total productivity estimation by means of Lie group transformations is also developed in this monograph. We would like to express our sincere thanks to many individuals notably to Professor M. J. Beckmann, Professor F. Mimura, Professor G. Suzawa, T. Mitchell, K. Mino and P. Calem, for their numerous contributions at various stages of this work. We are also grateful to Marion Wathey for her usual superb typing of this difficult manuscript. Providence, R. I. , U. S. A.
In this book Professor Beckmann, with considerable ingenuity, offers a mathematical analysis of productive organizations in the widest sense. Starting with descriptive features he builds up, step by step, production functions, profiting from the rigor of a set of axioms or assumptions and their logical implications. Among the organizations studied hierarchies play a predominant role and are compared with such forms of cooperation as partnerships and "ladders". A number of well-known basic concepts such as span of control, rank, line vs. staff and others serve as starting points. His analysis leads to such refinements as balanced, regular or degenerated organization patterns and interesting comparisons of the efficiency of various structures. Empirical verification of the axioms or assumptions is not the objective chosen by the author--except a few concrete illustra tions--but the book constitutes an excellent basis for such research. Several of the results obtained take simpler forms for very large hierarchies. The renewed interest, shown in political discussions, in the bureaucratization of both large enterprises and government machinery makes Dr. Beckmann's work highly topical. Discussions (by Bahro) of the GDR and by many other authors of Japanese management as compared with American or western European are cases in point. Some additional variables may then have to be added, of a psychological nature: for instance satisfaction from work or irritation evoked by excessive supervision.
Optimal Control theory has been increasingly used in Economi- and Management Science in the last fifteen years or so. It is now commonplace, even at textbook level. It has been applied to a great many areas of Economics and Management Science, such as Optimal Growth, Optimal Population, Pollution control, Natural Resources, Bioeconomics, Education, International Trade, Monopoly, Oligopoly and Duopoly, Urban and Regional Economics, Arms Race control, Business Finance, Inventory Planning, Marketing, Maintenance and Replacement policy and many others. It is a powerful tool of dynamic optimization. There is no doubt social sciences students should be familiar with this tool, if not for their own research, at least for reading the literature. These Lecture Notes attempt to provide a plain exposition of Optimal Control Theory, with a number of economic examples and applications designed mainly to illustrate the various techniques and point out the wide range of possible applications rather than to treat exhaustively any area of economic theory or policy. Chapters 2,3 and 4 are devoted to the Calculus of Variations, Chapter 5 develops Optimal Control theory from the Variational approach, Chapter 6 deals with the problems of constrained state and control variables , Chapter 7, with Linear Control models and Chapter 8, with stabilization models. Discrete systems are discussed in Chapter 9 and Sensitivity analysis in Chapter 10. Chapter 11 presents a wide range of Economics and Management Science applications.
The concept of space has always been a fundamental element in various branches of knowledge. The concept often appears in the evolution of knowledge, either as a basis of theory or as a factor in research. It is associated, more or less directly, with all the history of scientific thought. At the level of simple common sense, the importance of the concept of space is only equaled by its lack of precision. It was part of legend before becoming part of history. To indicate the founding of Rome, Romulus started by drawing the boundaries, locating its landmarks in a discontinuous space after having cut the limits of a continuous space. However, neither geographical explorations nor mathematico-logical speculations have ever completely removed the mystery from the concept of space. For all its simple common sense, its mystique remains intact. The privileged position occupied by the concept of space in the history of science and the vagueness of its meaning in the current use of the term, far from constituting a paradox, are mutually explanatory. Every concept of space is necessarily the result of an abstraction, whether the process by which it is reached is through mathematics, psychology, biology, or any other discipline. At the level of common knowledge, the space-time concept is the base upon which are arranged individual experiences. It is thus easy to understand how the concept of space can be understood only through an orderly arrangement of these experiences and their integration into a logical scheme.
The book contains perspectives on the way new information technology might reorient the spatial organization of activity. The perspectives range from conceptual, high- lighting the role of research and development to case studies from Japan. Considerable debate is focused on the role of distance and the way in which new information technology might re-shape interaction and, eventually, the form and function of urban areas.
The essays in this volume were presented to Professor Isamu Yamada in honor of his seventy-third birthday. In view of his many professional contributions and associations, a single volume of essays is really insufficient to house the works of all those who wish to be part of a venture of this kind. Therefore, the editors would like to apologize to those friends and well-wishers of Professor Yamada who could not be accommodated in this volume. Born in Nagoya in 1909, Professor Yamada began his brilliant career at Nagoya Commercial College where he studied economics, statistics, mathematics and physics. After serving as a Professor of Economics and Statistics at Yokohama College between 1939-1940, Professor Yamada moved to Hitotsubashi University in Tokyo, where he served as a Professor of Econometrics until his retirement in 1973. Currently, he is teaching at Asia University as a Professor of Economics and Statistics. During his long tenure at Hitotsubashi University (where Professor Ichiro Nakayama, a "Japanese Schumpeter", served as President of the University), Professor Yamada was instrumental in introducing several generation of students to the methods of modern econometrics. One of the editors (Ryuzo Sato) of this volume is a direct beneficiary of his lectures on modern econometric techniques. In the 1950's, Professor Yamada was one of several prominent Japanese economists who were selected for study abroad. It was during this time, on a visit to the Cowles Commission at the University of Chicago, that Professor Yamada met the other editor of this volume.
The proceedings collect the latest research trends, methods and experimental results in the field of electrical and information technologies for rail transportation. The topics cover intelligent computing, information processing, communication technology, automatic control, and their applications in rail transportation etc. The proceedings can be a valuable reference work for researchers and graduate students working in rail transportation, electrical engineering and information technologies.