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Theory of hierarchical multilevel systems
Book Reviews
RAMAN SPECTROSCOPY,VOL. ~-THEORY AND PRACTICE. 221 pages, diagrams, 6 x 9 in. New York, Plenum, 1970. Price, $17.50. This second volume of the contributed work published in 1967 suffers from the disadvantages of the genre to an even greater extent than its predecessor. No individual is likely to be interested in such of articles, a disparate collection particularly considering the very different levels at which they are written. The result is more in the tradition of serial publications, than a textbook. However, (despite the blurb), the title “Advances in Raman Spectroscopy” would have been inappropriate. This is partly because of the delay in publication (up to three years). In particular, undue attention is given to obsolescent experimental procedures relating to mercury arcs. L. A. Woodward is always worth reading, in this case his article is a “cautionary tale”, suitable for a newcomer to inorganic vibrational spectroscopy. J. Tang and A. C. Albrecht have a highly mathematical article, “Developments in the Theories of Vibrational Raman Intensities”, which may be of interest to physicists; the parameters in the equations are, however, mostly inaccessible. H. W. Schrotter’s article on laser excitation is informative, but does not add much to previously published texts. “Low-frequency Reman Spectra of Liquids” (L. A. Blatz) offers no interpretation of the results described, most of which were obtained by methods which would not now be used. R. E. Hester describes many of the published high and low temperature cell and furnace designs; his article will be particularly useful as a source of ideas for designers of such equipment. He also outlines the usefulness of Raman spectroscopy at temperatures other than ambient. Finally, E. Steger’s article on poor scatterers is of largely historical interest and written in clumsy English. It could be useful as a source of information on purification techniques.
In summary, one may say that except for the articles by Woodward, Albrecht and Tang, this book published in 1970 is out of date. T. R. GILSON Department of Chemistry University of Southampton Southampton, England
THEORY OF ISIERARCHICAL, MULTILEVEL SYSTEMS, by M. D. Messarovich, D. Macko and Y. Takahara. 293 pa,ges, diagrams, 6 x 9 in. New York, Academic Press, 1970. Price, $15.00. A vertical arrangement of systems where the higher level systems act upon the lower level systems and depend upon the performance of the lower level systems and where priority of action is oriented downwards in a command fashion is a hierarchical multilevel system. The monograph under consideration, the result of recent research of the authors and others, deals with such systems on essentially three levels. In the first two chapters, the authors attempt to justify such a study by discussing a number of practical examples and explain their objective. Such systems are described in formal mathematical language and the central problem of coordination, i.e. of influencing the subsystems in such a manner that the whole system acts harmoniously towards an overall goal, is explained. In the following three chapters, the authors propose a mathematical theory of coordination for two-level systems under the assumption that the system is completely stratified, i.e. that there are no external disturbances. The individual decision problems, defined as optimizations, are considered on unconstrained decision sets and, in Chap. 7, constraints on the decision sets are taken into account. External disturbances are discussed in the last chapter. Because of the organization of the material, there is a fair amount of
85
Book Reviews repetition. The various concepts that are associated with such a theory are introduced and explained on various levels of abstraction but evolve only with any clarity in the last four chapters. In a number of examples, where linear dynamical systems are considered, it would be natural to assume the nonhomogeneous term to be bounded and measurable rather than square integrable. The solution is absolutely continuous and need not a priori be assumed to be square integrable. Those who are interested in the general area of operations research will find this volume stimulating.
HANS SAGAN North Carolina State University Raleigh, Nort.h Carolina
THE THEORY OF LINEAR SYSTEMS, by Julio Rubio. 329 pages, diagrems, 6 x 9 in. New York, Academic Press, 1971. Price, $14.00. In the Preface of The Theory of Linear System, Dr. Rubio declares that it was his “intention to have the basic material serve as preparation and motivation for more advanced subjects, so that the reader is led naturally and smoothly from the more elementary concepts into deeper matters” . In addition, it was his “objective to put the advanced topics at the reach of graduate students with a good knowledge of advanced calculus”. The reviewer believes that this g-chapter text portrays the author’s success in fulfillment of purpose. A complete and comprehensible transition from classical control theory to state variable descriptions of linear systems is first discussed. Then the author gives a careful and concise treatment of vector spaces, inner products, norms, matrices, transformations, etc. Chapters 3, 4 and 7 deal quite adequately with characterization and analysis differential and difference systems. Controllability, observability and an introduction to system synthesis form the basis for Chaps. 5 and 6, which also illustrate engineering applications of the overall theory. Lyapunov methods for determining system stability are then
86
discussed. Finally in Chap. 9 the author challenges his readers with a brief introduction to infinite-dimensional systems characterized by partial differential equations. The intent, apparently, is to motivate his readers to transcend the conventional boundaries at which most of us have stopped in the past. The book makes an excellent self-study text for the practicing engineer who wishes to up-date his knowledge of current topics; and it has enough numerically illustrated examples to enable the reader to verify constantly his own grasp of the material. Considering the complexity of the subjectmittter, the reviewer finds the book couched in language which is remarkably understandable, and difficult concepts are conveyed with ease. As there is also a sufficient number of exercises attending all appropriate sections (there is no solutions manual available), the use of this text can serve well as the foundation for an introductory graduate course in linear control theory. It is a pleasure to note the arrival of one of those seldom-written books that has strong potential value accessible to a variety of readers. R. DAVID PITTLE Electrical Engineering Carnegie-Mellon, University Pittsburgh, Pennsylvania
AQUATIC CHEBIISTRY, by W. Stumm and J. J. Morgan. 583 pages, diagrams, 6 x 9 in. New York, John Wiley, 1970. Price, $24.95. We live in an era of concern for the environment. Ecology is a popular study and a working knowledge of the factors which influence the composition of natural waters is essential to an understanding of ecology. There are many books that describe pollution and the technical means for controlling it, but there is a need for a text devoted to the scientific principles that explain the composition of natural waters. This is such a text. It is written by two recognized Stumm, experts : Werner Professor of Applied Chemistry at Harvard University and a member of Harvard’s
Journal
of The Franklin
Institute
RAMAN SPECTROSCOPY,VOL. ~-THEORY AND PRACTICE. 221 pages, diagrams, 6 x 9 in. New York, Plenum, 1970. Price, $17.50. This second volume of the contributed work published in 1967 suffers from the disadvantages of the genre to an even greater extent than its predecessor. No individual is likely to be interested in such of articles, a disparate collection particularly considering the very different levels at which they are written. The result is more in the tradition of serial publications, than a textbook. However, (despite the blurb), the title “Advances in Raman Spectroscopy” would have been inappropriate. This is partly because of the delay in publication (up to three years). In particular, undue attention is given to obsolescent experimental procedures relating to mercury arcs. L. A. Woodward is always worth reading, in this case his article is a “cautionary tale”, suitable for a newcomer to inorganic vibrational spectroscopy. J. Tang and A. C. Albrecht have a highly mathematical article, “Developments in the Theories of Vibrational Raman Intensities”, which may be of interest to physicists; the parameters in the equations are, however, mostly inaccessible. H. W. Schrotter’s article on laser excitation is informative, but does not add much to previously published texts. “Low-frequency Reman Spectra of Liquids” (L. A. Blatz) offers no interpretation of the results described, most of which were obtained by methods which would not now be used. R. E. Hester describes many of the published high and low temperature cell and furnace designs; his article will be particularly useful as a source of ideas for designers of such equipment. He also outlines the usefulness of Raman spectroscopy at temperatures other than ambient. Finally, E. Steger’s article on poor scatterers is of largely historical interest and written in clumsy English. It could be useful as a source of information on purification techniques.
In summary, one may say that except for the articles by Woodward, Albrecht and Tang, this book published in 1970 is out of date. T. R. GILSON Department of Chemistry University of Southampton Southampton, England
THEORY OF ISIERARCHICAL, MULTILEVEL SYSTEMS, by M. D. Messarovich, D. Macko and Y. Takahara. 293 pa,ges, diagrams, 6 x 9 in. New York, Academic Press, 1970. Price, $15.00. A vertical arrangement of systems where the higher level systems act upon the lower level systems and depend upon the performance of the lower level systems and where priority of action is oriented downwards in a command fashion is a hierarchical multilevel system. The monograph under consideration, the result of recent research of the authors and others, deals with such systems on essentially three levels. In the first two chapters, the authors attempt to justify such a study by discussing a number of practical examples and explain their objective. Such systems are described in formal mathematical language and the central problem of coordination, i.e. of influencing the subsystems in such a manner that the whole system acts harmoniously towards an overall goal, is explained. In the following three chapters, the authors propose a mathematical theory of coordination for two-level systems under the assumption that the system is completely stratified, i.e. that there are no external disturbances. The individual decision problems, defined as optimizations, are considered on unconstrained decision sets and, in Chap. 7, constraints on the decision sets are taken into account. External disturbances are discussed in the last chapter. Because of the organization of the material, there is a fair amount of
85
Book Reviews repetition. The various concepts that are associated with such a theory are introduced and explained on various levels of abstraction but evolve only with any clarity in the last four chapters. In a number of examples, where linear dynamical systems are considered, it would be natural to assume the nonhomogeneous term to be bounded and measurable rather than square integrable. The solution is absolutely continuous and need not a priori be assumed to be square integrable. Those who are interested in the general area of operations research will find this volume stimulating.
HANS SAGAN North Carolina State University Raleigh, Nort.h Carolina
THE THEORY OF LINEAR SYSTEMS, by Julio Rubio. 329 pages, diagrems, 6 x 9 in. New York, Academic Press, 1971. Price, $14.00. In the Preface of The Theory of Linear System, Dr. Rubio declares that it was his “intention to have the basic material serve as preparation and motivation for more advanced subjects, so that the reader is led naturally and smoothly from the more elementary concepts into deeper matters” . In addition, it was his “objective to put the advanced topics at the reach of graduate students with a good knowledge of advanced calculus”. The reviewer believes that this g-chapter text portrays the author’s success in fulfillment of purpose. A complete and comprehensible transition from classical control theory to state variable descriptions of linear systems is first discussed. Then the author gives a careful and concise treatment of vector spaces, inner products, norms, matrices, transformations, etc. Chapters 3, 4 and 7 deal quite adequately with characterization and analysis differential and difference systems. Controllability, observability and an introduction to system synthesis form the basis for Chaps. 5 and 6, which also illustrate engineering applications of the overall theory. Lyapunov methods for determining system stability are then
86
discussed. Finally in Chap. 9 the author challenges his readers with a brief introduction to infinite-dimensional systems characterized by partial differential equations. The intent, apparently, is to motivate his readers to transcend the conventional boundaries at which most of us have stopped in the past. The book makes an excellent self-study text for the practicing engineer who wishes to up-date his knowledge of current topics; and it has enough numerically illustrated examples to enable the reader to verify constantly his own grasp of the material. Considering the complexity of the subjectmittter, the reviewer finds the book couched in language which is remarkably understandable, and difficult concepts are conveyed with ease. As there is also a sufficient number of exercises attending all appropriate sections (there is no solutions manual available), the use of this text can serve well as the foundation for an introductory graduate course in linear control theory. It is a pleasure to note the arrival of one of those seldom-written books that has strong potential value accessible to a variety of readers. R. DAVID PITTLE Electrical Engineering Carnegie-Mellon, University Pittsburgh, Pennsylvania
AQUATIC CHEBIISTRY, by W. Stumm and J. J. Morgan. 583 pages, diagrams, 6 x 9 in. New York, John Wiley, 1970. Price, $24.95. We live in an era of concern for the environment. Ecology is a popular study and a working knowledge of the factors which influence the composition of natural waters is essential to an understanding of ecology. There are many books that describe pollution and the technical means for controlling it, but there is a need for a text devoted to the scientific principles that explain the composition of natural waters. This is such a text. It is written by two recognized Stumm, experts : Werner Professor of Applied Chemistry at Harvard University and a member of Harvard’s
Journal
of The Franklin
Institute