Mitsuo Gen / Runwei Cheng (Both of Ashikaga Institute of Technology, Japan) 0-471-31531-1 Hardcover: US$99.00 (Reviewer: Hae Chang Gea, Rutgers University) This well-written book provides in-depth discussions of many engineering applications using GA and a comprehensive reference. Because of the broad range of subjects covered in the book, it is more a reference book than a textbook. This book is divided into nine chapters. Chapter 1 covers fundamental concepts of GA such as encoding, genetic operators, adaptation and optimization. It is a very compact introduction. Therefore, for readers who are new to GA, further reading is recommended. The focus of this book is on its in-depth discussion of engineering applications. Starting from Chapter 2, a variety of engineering optimization problems are presented. Chapter 2 discusses combinatorial optimization problems including set-covering problem, bin-packing problem, knapsack problem and minimum spanning tree problem. For each kind of problems, detailed description of formulation, application of GA and their numerical experiences are provided. Chapter 3 devotes to multi-objective optimization problems. Multi-objective optimization arises in many engineering design applications. It is pleasant to read this chapter because it covers basic concepts and many different approaches to solving multi-objective optimization including Pareto ranking and tournament methods, weighted-sum, distance method, comprise approach and goal programming. Furthermore, it provides GA implementation on each of them. Chapter 4 discusses fuzzy optimization problems on account of uncertainty and imprecision problem in engineering applications. Similar to Chapter 3, many methods and their GA implementation are presented such as fuzzy linear programming, fuzzy nonlinear programming, and fuzzy multi-objective programming. Chapters 2 to 4 present not only GA practice in engineering optimization but also many important issues in engineering design applications. Equipped with these concepts, the next five chapters are moving to specific topics of the adaptation and application of GA. Chapter 5 presents reliability design problems. It covers network reliability design, tree-based network reliability and LAN design, and multi-objective reliability design. Unfortunately, discussion is very limited to network design problems. Concepts for probabilistic design optimization such as Limit State, reliability index and safety index are not included. Chapter 6 covers scheduling problems. Unlike chapter 5, it gives a comprehensive review and discussion in this subject. This chapter begins with basic approaches to scheduling problems and then moves to specific job scheduling problems including grouped job scheduling, resource-constrained project scheduling, parallel machine scheduling and multi-processor scheduling. GA implementations and numerical examples are also presented. The last three chapters discuss advanced transportation problems, network design and routing, and manufacturing cell design. They are extensions of chapters 5 and 6 with some advanced applications and discussions. Therefore, they may not be interesting to general readers. However, researchers in these areas may find many useful discussions and references. The bibliography, with 737 entries, is very useful. The authors obviously have spent enormous time and energy to prepare this book. However, in some cases, one could have wished for more recent journal publications and less Ph.D. dissertations. In brief, this book is a very fine reference book for GA in engineering application. This reviewer would recommend this book for graduate students and researchers in this area as an excellent resource for the topics covered. -o-
When I first started to read this book, I wasn't sure what could be said about a man who was only interested in numbers. But quickly I began to learn much about not only Paul Erdös (pronounced "air-dish"), but about a large part of the mathematical world that revolved about him, and about which he orbited. We learn some interesting facts. For example, Erdös was a prolific researcher who published 485 papers with co-authors. His total papers published numbers 1475. This is an astounding number, especially considering that many are considered monumental. This quantity was only surpassed by the great Leonhard Euler. Beyond the statistics of the man, we find out that he is a kind person. He is generous with ideas, passing them on to his colleagues without a worry regarding attribution. We meet many of Erdös' colleagues, upon whose friendship and generosity he depended for room and board. This is because Erdös did not maintain a home, but rather traveled from one location to another, continuing his mathematics wherever and whenever he went. Ronald Graham, a mathematician at AT&T Bell Labs, who Erdös visited regularly, even added a room and bathroom to his house to make the visit more comfortable for everyone. Erdös believed that there is no more important activity than doing mathematics. He was a "mathematical monk. He renounced physical pleasure and material possessions for an ascetic, contemplative life, a life devoted to a single narrow mission: uncovering mathematical truth." Of course, he had a significant cadre of friends and colleagues who did everything else for him, thus permitting him to live such a cloistered life. He put out contracts on problems he was unable to solve, ranging from $10-$3,000, depending on the difficulty of the problem. Erdös lived to the age of eighty-three, passing into the company of the SF (Supreme Fascist) on 20 September 1996. SF was Erdös' shorthand for God. He has other shorthand terms, for example, epsilon, the mathematical symbol used to signify small, was the term for children. Erdös was born in Budapest on March 26, 1913, the son of two high school mathematics teachers. He lived through the trials and tribulations of Europe during the first half of this century, moving about many times in response to the political chasms that opened and closed. Erdös circumvented anti-Jewish laws regarding admissions to universities by winning a national competition to enter in 1930 the University Pázmány Péter in Budapest at the age of 17 and graduating four years later with a Ph.D. This book is more than about Erdös, although his is the binding thread throughout. By virtue of his travels and his abilities, his life was intertwined with the scientific and intellectual life of the twentieth century. We read about Germaine, Hardy, Russell, Ramanujan, Gödel, Einstein, Fermat, Bellman and Weils, among many others. There is also the news story from the 15 August 1945 Daily News with the headline 3 Aliens Nabbed at Short-Wave Station. Well, you guessed it, Erdös was one of the three, all of whom were mathematicians, who happened to ignore a no trespassing sign and decided to walk around on a Long Island beach. A policeman reported that they were speaking some foreign language. That language turned out to be mathematics. Of course, there are numbers all over the place that even non-mathematicians can appreciate. Here is an example: 2,682,4404 + 15,365,6394 + 18,796,7604 = 20,615,6734 To find out what the meaning of this equation is, you will have to look in the book on page 217. The math is interesting and followable. I tend to enjoy books about mathematicians and scientists. Even so, I must say that
this is one of the best written such books. I found myself looking forward to every spare
minute I could spend with Paul Hoffman's book. I enjoyed the photographs. I recommend it
wholeheartedly. It is more than just a story about a mathematician. It is a story that
touches all of us in many ways.
Mechanical Engineers’ Handbook, Second Edition (Reviewed by Haym Benaroya, Rutgers)
The second edition of the Mechanical Engineers’ Handbook edited by Myer Kutz, offers contributions from more than 80 leading experts in industry, government and academia. Myer Kutz, MSME, is founder and President of Myer Kutz Associates, Inc., publishing and information service consultants. This single, easy-to-use volume covers a broad spectrum of critical engineering topics, updating both engineers and engineering managers with developments in materials, methods, and equipment - from concurrent engineering and computer aided technology, to new composite materials and design and packaging techniques. In addition to material that remains unchanged, a third of the book consists of entirely new chapters, and some of the revisions, made by new authors, are so different from their predecessors that they could count as new chapters. This edition opens with a thorough revision of the structure of solid materials, and includes important updates on nickel, aluminum, plastics and elastomers, and composites. Many of the chapters covering mechanical design fundamentals have been updated, and new requirements in manufacturing engineering called for essential revisions as well. New chapters focus on the roles of virtual reality, ergonomic design, electronic packaging, and pollution control technology, and the teamwork-based methods of product development that have evolved have also earned a prominent place in the second edition. The final section of the Handbook focuses on topics that address career growth, including developments in project management, detailed cost estimating, certifications and awards, and legal issues for engineers. I immediately went to a chapter I have some knowledge about, Chapter 23 on Vibration and Shock, to investigate the thoroughness of the discussion. Although a different individual writes each chapter, this may be considered a measure of the quality of the remaining chapters. I read useful discussions of basic and more advanced topics. The figures are of good quality. However, the photos of equipment seemed to be from a previous generation. This appears to be borne out by the list of references that date from 1961-1981 (books) and a list of references from the Shock and Vibration Information Center that only reach 1979. With the major advances in materials and electronics, one would have hoped for a more up to date exposition. The Mechanical Engineers’ Handbook has the following features:
The two editions of the Mechanical Engineers’ Handbook are
separated by a dozen years. This is a massive book, weighing in at 2352 pages. The
production is first-rate, with all chapters prepared in a visually professional style,
including the figures. The cost, while breathtaking, is still minor for an office or a
library that depends on such a reference. Even with the above specific comments about one
chapter, this is still a worthwhile resource. (Reviewed by Haym Benaroya). 
Here is a problem that is at once a simple extension of the central limit question and a prototype of approximation issues in analysis of stochastic models. Take a random walk with independent steps, each having a zero mean and a variance s2. For a positive integer n, simultaneously rescale time so n steps are taken in each time unit and rescale step size by the central limit factor 1/sÖn. Define the value of the process between step times by linear interpolation, so that sample paths are continuous, and denote the resulting process by Xn = {Xn(t);t ł 0}. At any fixed time t, Xn(t) is a normalized sum of independent random variables plus a negligible error, and hence, by the central limit theorem, Xn(t) converges in distribution as n® Ą to a normal random variable, regardless of the distribution of the original, unscaled steps. Likewise, the multi-dimensional central limit theorem identifies a normal limit of the sequence of random vectors {(Xn(t1),... ,Xn(tM))}, for any finite set of times. Is it possible to go further and find a limit in distribution of the sequence of processes {Xn}? This would be a process X that captures the limiting statistical behavior not just of Xn at fixed times, but of the paths of Xn; for example, the distributional limit of {sup[0,1]|Xn(t)|} would be given by {sup[0,1]|X(t)|}. How does one properly define distributional limits of processes, and what are general techniques for identifying them? The answer in the case of {Xn} -the limit is Brownian motion-can be interpreted as a functional central limit theorem. Think of each process Xn, not as a collection of random variables, but as a random element whose value is the continuous sample path t® Xn(t). From this point of view, a limit theorem for {Xn} is a generalization to random functions of the central limit theorem for finite-dimensional random vectors. The central limit question for {Xn} is the motivating problem of Billingsley's text. The book presents the general theory of convergence in distribution for stochastic processes and uses it for an in-depth study of scaled random walks. This may not be apparent from the abstruse-sounding title,Weak Convergence of Probability Measures, but it is weak convergence theory for probability measures on a metric space that underpins the subject. The generality of the metric space setting covers both random variables and stochastic processes at once. A random variable takes values in the metric space consisting of the real line with the distance metric; for a stochastic process, we find a metric space of paths including all sample paths and interpret the process as a random element taking values in this space. For instance, the process {Xn(t); t Î [0,1]} of our example takes values in the space of continuous functions on [0,1], for which it is natural to use the supremum norm metric. The theory of weak convergence then provides both the right general definition of distributional convergence and the theoretical framework for finding limits. Billingsley's book covers both the abstract theory and the methods for applying it to stochastic processes. The book under review is billed as a second edition of a text originally published in 1968. In the thirty plus years since, applications and theory of weak convergence have developed extensively, but the core material of the text is still basic and still makes a good introduction. In preparing a second edition, Billingsley has made major revisions, almost to the point of producing a different book. True, the basic sections reappear in recognizable form and the same pedagogical motivations remain intact, but some old material has been dropped, all the exposition has been reworked, and entirely new topics appear. In short, it has been thoroughly updated. Billingsley's book is more textbook than monograph; it pays careful attention to exposition and conceptual understanding and includes problems. At the same time, it goes deeply and brings the reader to a sophisticated level. The treatment starts with basic theory for an abstract, separable metric space. After thoroughly exploring the weak convergence concept, it presents the important theorem of Prohorov, which gives a necessary and sufficient condition that a sequence of probability measures admit a weakly converging subsequence. These abstract results are then generalized to the two metric spaces that really matter for stochastic processes, the space C of continuous functions and the space D of right continuous functions with left limits. Each merits a separate chapter. The space C is endowed with the supremum norm metric and is the easier case to handle. Here Prohorov's theorem takes the form of uniform estimates on the modulus of continuity of a sample path. This result is used to give straightforward proofs of the existence of Brownian motion and of Donsker's invariance principle, which states that the processes Xn defined above indeed converge in distribution to Brownian motion, regardless of the precise probability distribution of the original steps. The supremum norm metric, which will not allow two paths with different jump times to be close, is no longer appropriate for the space D. Instead, a special topology called the Skorohod topology is used, which Billingsley describes in careful and explicit detail. He then derives the basic convergence criterion on D. For applications beyond Donsker's theorem, Billingsley focuses on central limit theorems for scaled random walks with dependent steps. He derives limit theorems for asymptotic behavior of lacunary trigonometric series and of the number of prime divisors in a sequence of integers, and theorems for scaled martingales and ergodic processes. Finally, a new chapter touches on useful complements: how the basic functional central limit theorem can be used to discuss convergence and approximation in a fixed probability space, and Strassen's functional version of the law of the iterated logarithm. The first edition is known for its excellent and accessible exposition. The second edition carries on the tradition. The subject of weak convergence ought to be standard knowledge for all researchers in stochastic processes. Unfortunately, the entrance cost is high; it requires a good grounding in graduate measure and integration theory and basic point-set topology. However, Billingsley has a gift for clear, motivated exposition, and guides the novice well. An appendix provides a helpful review of the required facts about metric spaces. New tools are introduced carefully with plenty of discussion and examples. Important applications are introduced as soon as possible, illustrating utility of the abstract theory as it is being developed and before it overwhelms. Many proofs, already elegant in the first edition, have been burnished even further, and some of the tougher results, such as maximal inequalities or limit theorems for mixing process, have simpler, more insightful proofs. These improvements make it a pleasure to read, even for those familiar with the old book. The applications in Billingsley's book have been updated in the second edition, but they still focus heavily on scaled random walks. Since the first edition was published, applications of weak convergence have extended dramatically in many areas of applied and theoretical stochastic processes: the martingale theory approach to Markov processes [SV, EK], large deviation theory [DE], approximate models in control and electrical engineering applications [K], high traffic limits of queuing networks, etc. Billingsley's book does not try to touch on these; he has even dropped a section on diffusion processes in the first edition. However, the fundamental theory in the spaces C and D behind all applications is the same. Because of its pedagogical virtues, I would recommend his book as a starting place to any student of the topic, whatever his or her applied interests ultimately are. For its elegance of presentation and its nice examples, it should appeal to the expert as well. [DE] P. Dupuis and R.S. Ellis, A Weak Convergence Approach to the Theory of Large Deviations, John Wiley & Sons, New York, 1997. [EK] S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence, John Wiley & Sons, New York, 1986. [K] H.J. Kushner, Approximation and Weak Convergence Methods for Random Processes, MIT Press, Cambridge, 1984. [SV] D.W. Stroock and S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, New York, 1979. File translated from TEX by TTH,
version 2.60. The Fabric of Reality by David Deutsch Penguin Books 1997 (Reviewed
by Haym Benaroya, Rutgers) As part of his worldview, Deutsch makes the emphatic point that predicting what will happen is not the same as understanding why things happen. He also takes the holistic approach to explaining our environment, that is, taking the larger view rather than the usual reductionist views that is more common in science. The reductionist view explains things by developing theories about smaller and smaller building blocks. In this book, the view is put forward that evolution, computation, epistemology and quantum physics, together, provide an understanding of our reality. “Considered jointly, these four strands of explanation reveal a unified fabric of reality that is objective and comprehensible.” The Fabric of Reality explains and connects many topics at the
leading edge of current research and thinking, from quantum computers to time travel and
from the physical limits of virtual reality to the ultimate fate of the universe. This
book is suitable for scientist and lay person alike, for philosopher and science fiction
reader, biologist and computer expert. Be prepared to see the views of establishment
scientists taken to task. The book is optimistic about the prospects that we are close to
a theory that provides an explanation of why things exist as they do. This book must be
read carefully, because each paragraph is chock full of thought. In fact, after I finish
writing this review, I am going back to re-read the whole book. I am sure there are
dimensions of this multiverse view that I have missed. To be greatly enjoyed.
Biographies of Four Mathematicians:
(Reviewed by Haym Benaroya, Rutgers) Jacques Hadamard, A
Universal Mathematician, by Vladimir Maz'ya and Tatyana Shaposhnikova, Linköping
University - AMS | LMS, 1998, 574 pp., Softcover, ISBN 0-8218-1923-2. John von Neumann: The
Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and
Much More, by Norman Macrae - AMS, 1992, 406 pp., Hardcover, ISBN 0-8218-2064-8. Ramanujan: Letters and
Commentary, by Bruce C. Berndt, University of Illinois, Urbana, and Robert A.
Rankin, University of Glasgow - AMS | LMS, 1995, 347 pp., Hardcover, ISBN
0-8218-0287-9. Stephen Smale: The
Mathematician Who Broke the Dimension Barrier, by Steve Batterson, Emory
University - AMS, 2000, 306 pp., Hardcover, ISBN 0-8218-2045-1. All these mathematicians are considered to be among the most creative of this (and
the last) centuries. Nevertheless, they could not have had different lives. Hadamard lived
to the age of 98, but Ramanujan lived to only 33, and was in poor health during the last
few years of his life. Hadamard was born at the end of the US Civil War (1865) and died in
the year of President Kennedy’s assassination (1963): A truly remarkable span of time
especially when considering the changes in society and science, and the two world wars
that he witnessed. Hadamard Von Neumann Ramanujan Smale In 1957, Stephen Smale startled the mathematical world by showing
that, in a theoretical sense, it is possible to turn a sphere inside out. A few years
later, from the beaches of Rio, he introduced the horseshoe map, demonstrating that simple
functions could have chaotic dynamics. His next stunning mathematical accomplishment was
to solve the higher-dimensional Poincaré conjecture, thus demonstrating that higher
dimensions are simpler than the more familiar three. In 1966 in Moscow, he was awarded the
Fields Medal, the most prestigious prize in mathematics. Concluding Thoughts I wholeheartedly recommend all these books. While all can be read by
interested lay people, there are differences. Von
Neumann has no equations and would be easily read by anyone with an interest. Hadamard is written in two parts. The first part
also contains no equations. Part II is a detailed mathematical exposition of the branches
of mathematics where Hadamard made his contributions. Smale follows a similar approach with technical
content placed in appendices. Ramanujan, except
for historical portions, would be difficult for the non-mathematician to follow.
Mathematics in interspersed throughout the biography. However, I still found enjoyable
what I could understand. < All these books contained extensive references. Only Hadamard is, regrettably, in softcover. Otherwise, the productions
are attractive and pleasant to work with. In this day of exorbitant prices, these are
priced moderately at between $35 and $59.
-o-
Analytical Mechanics, by J.S.
Török, (Reviewed by H. Baruh, Rutgers University) This book compiles concepts from analytical dynamics into a concise text. The author begins with a discussion of Newtonian concepts. Then, the basic concepts of Lagrangian mechanics are introduced. Lagrange's equations are derived and issues such as impulsive motion and motion integrals are discussed. The next chapter deals with variational calculus. Hamilton's principle is derived and Lagrange's equations are shown to be derivable from that principle, as well. The author continues with the dynamics of rotating bodies, together with some qualitative analysis of gyroscopic motion. The last two chapters are devoted to Hamiltonian systems and to basic stability theory. The author derives Hamilton's canonical equations, the Hamilton-Jacobi equation, and discusses the phase space. Then, stability of linear and nonlinear systems are discussed and methods are introduced to test for stability. The book ends with three appendices that explain the various mathematical concepts used throughout the book. While the author indicates that this book is suitable for an engineering course, the book seems more like a theoretical physics text, where the emphasis is more on particle mechanics and the subject material is seen as a springboard to more advanced concepts from physics, such as quantum theory. The book puts little emphasis on rigid body motion; there is little discussion of angular velocity in three dimensions, quantification of angular velocity, Lagrangian mechanics and three dimensional motion, nonholonomic systems, and impulse-momentum relations. Constrained systems are considered only lightly. The material on the calculus of variations should have appeared before the sections on Lagrangian mechanics, this way the reader would get a better understanding of the concept of a variation. One advantage of the book is that it contains a very large set of problems at the end of each chapter.The problems are interesting and well-posed, and solving a good number of them certainly enriches one's knowledge of dynamics. However, this advantage is countered by the disadvantage that there are very few illustrative examples throughout the text. While the writing is clear and easy to follow, the lack of examples make it difficult for the reader to grasp applications of the basic concepts. Any faculty member teaching out of this book should solve as many examples as possible in the classroom. The last two chapters of the book are usually found in more advanced texts and the subjects are usually covered in graduate level courses. These chapters are well-written, they make interesting reading, and they can be used as a good source of references. In conclusion, Analytical Mechanics appears
more like a physics textbook (which, of course, is not a disadvantage for someone in a
physics curriculum). I would recommend marketing this text to physics curricula. The
book is written clearly and is easy to read. It suffers from a lack of examples in
the text, as well as a lack of emphasis on three-dimensional rigid body dynamics. On
the other hand, the book makes a good reference text; a lot of information is presented
very concisely. At Home in the Universe: (Reviewed by Haym Benaroya, Rutgers) This is a very exciting and understandable book. The subtitle of
the book: The Search for the Laws of
Self-Organization and Complexity actually gives the reader the underlying thrust. The
thesis is that life evolved due to a combination of two underlying realities: Darwinian
evolution coupled with the tendency of complex systems to self-organize. This
self-organization has as its components, the organization of autocatalytic (nonequilibrium
chemical) systems into closed catalytic living molecular groups. These groups are
dynamically stable but can evolve and mutate. The laws of natural selection govern such
evolution. In addition, these living systems exist either near or at the border between
chaotic and complex but ordered state spaces. The book is written in a casual style, giving the reader the feel of
actually engaging in conversation with the author. This book is not, however, only about
evolution. Rather, at its heart is the discovery of the order that lies deep within the
most complex of systems, from the origin of life, to the workings of giant corporations,
to the rise and fall of great civilizations. Kauffman contends that complexity itself
triggers self-organization, what he calls “order for free,” and that if enough
different molecules pass a certain threshold of complexity, they begin to self-organize
into a new entity: a living cell. In turn, Kauffman extends this new paradigm to economic
and cultural systems, showing that all may evolve according to similar general laws. Besides the excitement of learning this revolutionary view about how
“all this evolution took place in such a short time,” the reader is introduced
to relatively simple example systems that demonstrate the concept and its workings.
This reader is not versed in chemistry or biology and found it possible to follow
the arguments (while being impressed by the long biochemical words). Those who wish to be
exposed to a more rigorous monograph on this subject need only look to Kauffman’s
earlier work, The Origins of Order:
Self-Organization and Selection in Evolution. It would be a wonderful follow-on to At Home in the Universe. As one who has some background in dynamics, seeing how complexity and
chaos theories have an impact on the evolution of life on Earth is truly a profound
experience. In this time of doubt and argument amongst many that life could have evolved
to its amazing current complexity in the time available since Earth became hospitable to
life, this book presents an important argument on how it could have happened. As Kauffman
puts it, rather than We the Improbable,
referring to life on Earth, the reality is: We the
Expected. The evolution of life on Earth was a likely, highly probable, event.
Darwin’s Evolution worked hand-in-hand with Complexity and Self-Organization to build
a rich, diverse and robust ecosystem. At Home in the Universe is
concluded on a very philosophical and, I think, optimistic note. The author observes the
emergence of a global civilization, the ultimate complex system of human experience, and
expresses the hope (belief?) that the result of the mixing of humanity will result in
completely new cultures. The last section, “Reinventing the Sacred,” states that
“awe and respect have become powerfully unfashionable in our confused postmodern
society.” Kauffman humbly concludes that his is a proposed thesis; he is gratified
that it seems to fit with the reality around us. “We are all part of the process,
created by it, creating it.” Be awed. Read this book!
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