This research monograph presents results in a rapidly developing area of great contemporary interest. Guillemin, Ginzburg, and Karshon show that the underlying topological thread in the computation of invariants of G-manifolds is a consequence of a linearization theorem involving equivariant cobordisms. The book incorporates a novel approach and showcases progressive research. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an abstract moment map'.
This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather.
Proceedings of the 20th annual conference for the Australasian Association for Engineering Education, held at the University of Adelaide in December 2009. Papers were presented by Australian and international delegates. The conference was focused on the engineering curriculum in higher education.
This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather.
Developing Cross-Cultural Measurement in Social Work Research and Evaluation, Second Edition is a practical, hands-on guide for social work researchers to learn how to develop, assess, and validate meaningful measurements across cultures and populations. The book takes the reader from conceptualization to analysis, using specific techniques with SEM and IRT for cross-cultural research.
This book explores the references to Egypt in the Pentateuch--twice as dense as in the rest of the Hebrew Bible--in the context of the production of the text's final form during the Persian period. Here, as Greifenhagen shows, Egypt functions ideologically as the primary "other" over against which Israel's identity is constructed, while its role in Israel's formation appears as subsidiary and as a superseded stage in a master narrative which locates Israel's ethnic roots in Mesopotamia. But the presentation of this powerful neighbour is equivocal: a dominant anti-Egyptian stance coexists with alternative, though subordinate, pro-Egyptian views, suggesting that the Pentateuchal narrative was produced within a context of ideological conflict over attitudes towards a land that provided a home for Jewish fugitives and emigrants.
How many people could read and write in the ancient world of the Greeks and Romans? No one has previously tried to give a systematic answer to this question. Most historians who have considered the problem at all have given optimistic assessments, since they have been impressed by large bodies of ancient written material such as the graffiti at Pompeii. They have also been influenced by a tendency to idealize the Greek and Roman world and its educational system. In Ancient Literacy W. V. Harris provides the first thorough exploration of the levels, types, and functions of literacy in the classical world, from the invention of the Greek alphabet about 800 B.C. down to the fifth century A.D. Investigations of other societies show that literacy ceases to be the accomplishment of a small elite only in specific circumstances. Harris argues that the social and technological conditions of the ancient world were such as to make mass literacy unthinkable. Noting that a society on the verge of mass literacy always possesses an elaborate school system, Harris stresses the limitations of Greek and Roman schooling, pointing out the meagerness of funding for elementary education. Neither the Greeks nor the Romans came anywhere near to completing the transition to a modern kind of written culture. They relied more heavily on oral communication than has generally been imagined. Harris examines the partial transition to written culture, taking into consideration the economic sphere and everyday life, as well as law, politics, administration, and religion. He has much to say also about the circulation of literary texts throughout classical antiquity. The limited spread of literacy in the classical world had diverse effects. It gave some stimulus to critical thought and assisted the accumulation of knowledge, and the minority that did learn to read and write was to some extent able to assert itself politically. The written word was also an instrument of power, and its use was indispensable for the construction and maintenance of empires. Most intriguing is the role of writing in the new religious culture of the late Roman Empire, in which it was more and more revered but less and less practiced. Harris explores these and related themes in this highly original work of social and cultural history. Ancient Literacy is important reading for anyone interested in the classical world, the problem of literacy, or the history of the written word.
Lactogenic hormone activity was first observed in bovine pituitary extracts by Stricker and Griiter in 1928, working in Bouin's laboratory in Strasbourg. Since that time prolactin has been shown to exist in anterior pituitary extracts of almost all vertebrate species investigated. Although its biology was extensively studied in many mammalian species, the existence of prolactin in the human was generally doubted, despite the positive evidence produced by such researchers as Pasteels. This can partly be explained by the fact that human growth hormone isolated in 1961, is itself a potent lactogen, in contrast to nonprimate growth hormones, and is present in the normal human pituitary in much greater amounts than prolactin. As a result there was a lag of nearly 10 years until prolactin was unanimously accepted as a hormone of the human pituitary, separate from human growth hormone. In 1970 new bioassay techniques permitted the demonstration of prolactin bioactivity in the serum of postpartum women and galactorrhea patients, and chromatographic methods led to the isolation and purification of human prolactin allowing the establishment of a specific radioimmunoassay for this hormone. This opened the road to the understanding of prolactin physiology and pathophysiology in the human, which has revolutionized clinical neuroendocrinology and reproductive endocrinology. Particularly hyperprolactinemia has turned out to be one of the most common endocrine syndromes.
Mammalian Neuroendocrinology presents a concise examination of how the nervous and endocrine systems interact to regulate physiological processes. Selected experimental results are presented to illustrate the current understanding of neuroendocrine processes. Neural influences and endocrine feedback mechanisms related to the secretion of adenohypophysial hormones are summarized for each hormone. The book's concise nature and readable style are highly suited for use as a graduate textbook. There are also chapters devoted to each of the following topics: neurohypophysis, pineal gland, adrenal medulla, hormones and behavior, and neuroendocrine immunology. Comparisons are made among species of mammals, including laboratory rodents, domesticated ungulates, and primates. Agricultural and/or clinical aspects relevant to these topics are covered when appropriate. Mammalian Neuroendocrinology is excellent for students and professionals in neuroendocrinology, neuroscience, endocrinology, reproduction studies, and animal sciences.
This volume is intended to be used as a textbook for a special topic course in computer science. It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision. The work incorporates many new research ideas, and focuses on the role of continuous mathematics. Audience: This book will be valuable to graduate students interested in theoretical computer topics, algorithms, expert systems, neural networks, and software engineering.
“Gamkrelidze and Ivanov’s wide-ranging and interdisciplinary work, superbly translated from Russian, is a must for every student of Indo-European prehistory. Its erudition is unsurpassed, and its unorthodox conclusions are a continuing challenge.” Prof. Dr. Martin Haspelmath, Max-Planck-Institut für Evolutionäre Anthropologie
Widely praised as a seminal contribution to the study of the Old Testament when it first appeared, Michael V. Fox's Character and Ideology in the Book of Esther is now available in a second edition, complete with an up-to-date critical review of recent Esther scholarship. Fox's commentary, based on his own translation of the Hebrew text, captures the meaning and artistry of Esther's inspiring story. After laying out the background information essential for properly reading Esther, Fox offers commentary on the text that clearly unpacks its message and relevance. Fox also looks in depth at each character in the story of Esther, showing how they were carefully shaped by the book's author to teach readers a new view of how to live as Jews in foreign lands.
Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Many features oflight propagation can be analyzed in terms ofrays,ofcourse, subtle effects near foci, caustics or turning points would need an analysis based on the wave natureoflight. Allofgeometric optics can be derived from Fermat's principle which is an extremum principle. The counterpart in classical mechanics is of course Hamilton's principle. There is a very close analogy between mechanics ofparticles and optics oflight rays. Much insight (and useful results) can be obtained by analyzing these analogies. Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, 1956), classical mechanics is only a geometrical optics approximation to a wave theory! In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of ray propagation through various media. Given the current interest and activity in optical fibers and optical communication, analysis of light propagation in inhomogeneous media is dealt with in great detail. The past decade has witnessed great advances in adaptive optics and compensation for optical aberrations. The formalism described herein can be used to calculate aberrations ofoptical systems. Toward the end of the book, we present application of the formalism to current research problems. Of particular interest is the use of dynamic programming techniques which can be used to handle variational/extremum problems. This method has only recently been applied to opticalproblems.
This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.
Physics and mathematics have always been closely intertwined, with developments in one field frequently inspiring the other. Currently, there are many unsolved problems in physics which will likely require new innovations in mathematical physics. Mathematical physics is concerned with problems in statistical mechanics, atomic and molecular physics, quantum field theory, and, in general, with the mathematical foundations of theoretical physics. This includes such subjects as scattering theory for n bodies, quantum mechanics (both non-relativistic and relativistic), atomic and molecular physics, the existence and properties of the phases of model ferromagnets, the stability of matter, the theory of symmetry and symmetry breaking in quantum field theory (both in general and in concrete models), and mathematical developments in functional analysis and algebra to which such subjects lead. This book presents leading-edge research in this fast-moving field.
Remarks by JVS. Volumes 1 and 2 of Feldspar Minerals were published in 1974, but Volume 3 was not completed because I was forced to devote 3 years to the resolution of unforeseen problems in the construction of an ion probe. By 1977, the incomplete draft for Volume 3 had become obsolete because of the enormous advances in knowledge of feldspars, particularly those in lunar rocks and meteorites, and in both deep-seated and ancient terrestrial rocks. Furthermore, it soon became obvious that a completely new version of Feldspar Minerals was needed because of the important new results on the physical and chemical properties. I had kept up with the interesting but tedious chore of weekly reading of the incoming literature and maintenance of the files. By 1980, the intense day-to day pressure had gone from my research programs on lunar rocks and on the development of the ion microprobe as a quantitative geochemical instrument, and I began preparation of a second edition of Feldspar Minerals.
The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are “minimal” in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory.
Quantitative Neurophysiology is supplementary text for a junior or senior level course in neuroengineering. It may also serve as an quick-start for graduate students in engineering, physics or neuroscience as well as for faculty interested in becoming familiar with the basics of quantitative neuroscience. The first chapter is a review of the structure of the neuron and anatomy of the brain. Chapters 2-6 derive the theory of active and passive membranes, electrical propagation in axons and dendrites and the dynamics of the synapse. Chapter 7 is an introduction to modeling networks of neurons and artificial neural networks. Chapter 8 and 9 address the recording and decoding of extracellular potentials. The final chapter has descriptions of a number of more advanced or new topics in neuroengineering. Throughout the text, vocabulary is introduced which will enable students to read more advanced literature and communicate with other scientists and engineers working in the neurosciences. Numerical methods are outlined so students with programming knowledge can implement the models presented in the text. Analogies are used to clarify topics and reinforce key concepts. Finally, homework and simulation problems are available at the end of each chapter.
For me, the word "infant" has always had a strange and compelling fascination. This book, in essence, represents the first step of what I hope will be a long and fruitful journey into the mysteries of the infant psyche, with special emphasis on the phenomenon of early-life depressive symptomatology. From the outset of my medical training, I was particularly attracted to the field of psychiatry. As a resident exposed to adult patients in a psychiatric ward, I can vividly recall, even these many years later, the deep sense of poignancy and distress while in the presence of minds gone awry. It is my belief that psy chiatry, more than any other branch of medicine, presents the physician with the ultimate paradox-the elusive diagnosis. By this I mean that while the symp tomatology of psychiatry may be classified and analyzed, while diagnoses, prog noses, and treatment schedules can be devised, within psychiatry the unique configuration of each individual patient emerges with a clarity and distinction unparalleled in any other medical field. Before any psychiatric diagnosis can be formulated, the therapist must first delve deeply into the ultimate singularity of the patient. As a consequence, psychiatry is, in the final analysis, concerned with the dignity of each patient, and the psychiatrist is continually challenged to explore the most formidable and elaborate aspect of each person-the human mind. That said, I need to express the reasons for my dedication to child psychiatry.
Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.
Details the principles and mechanisms of, and the equipment and optimal working conditions for, the liquid-chromatographic separation of well-defined oligomeric species and fraction with narrow molecular weight distribution. The work provides a complete description of the applications and possible performance of liquid chromatography in the field of oligomer separation.
This book provides an up-to-date information on a number of important topics in Linear Systems.Salient Features:" Introduces discrete systems including Z-transformations in the analysis of Linear Systems including synthesis." Emphasis on Fourier series analysis and applications." Fourier transforms and its applications." Network functions and synthesis with Laplace transforms and applications." Introduction to discrete-time control system." Z-Transformations and its applications." State space analysis of continuous and discrete-time analysis." Discrete transform analysis." A large number of solved and unsolved problems, review questions, MCQs." Index
This book reveals the rich collection of mathematical works located at the nation's first military school, the U.S. Military Academy at West Point. It outlines the relevant history of the Academy, discusses the mathematics department and curriculum, and describes the development of the library during the nineteenth century. A major part of this book is an annotated catalog of the more than 1300 works published between 1496 and 1915 found in the West Point library. Mathematics and its instruction greatly influenced the development of the Academy, the technological growth of America's army, and the standards of the military profession. These events, in turn, were crucial to the overall development of mathematics, mechanics, and engineering during the nineteenth century in the United States. Three individuals played a prominent role in this chronicle: Sylvanus Thayer, Charles Davies, and Albert Church. Listed are rare and historically valuable works in a broad range of mathematical subjects. The collection clearly shows the strong European influence on the early Academy. Also listed are numerous textbooks by West Point faculty and graduates; significant contributions were made by these writers to algebra, geometry, calculus, descriptive geometry, mechanics, surveying, and mathematics education. This book provides an important resource for the general audience as well as for those in pursuit of more scholarly information. It contains many interesting photographs and valuable details about the West Point collection. It is a must-have for anyone interested in mathematical books and collections.
Social workers engage in cross-cultural research in order to understand how diverse populations cope with life situations, to identify risk and protective factors across cultures, and to evaluate the effectiveness of policies and programs on the well-being of individuals from different cultures. In order to do so, it is necessary to begin with meaningful, appropriate, and practical research instruments, yet such instruments are not always readily available, or they may be misleading or biased. In this clearly written pocket guide, social work researchers will find a concise, easy-to-follow explanation of how to develop and assess cross-cultural measures that sidestep such complications and provide reliable, valid data. Using a step-by-step approach, expert cross-cultural researcher Thanh V. Tran carefully explores the issues and methodology in cross-cultural measurement development in social work research and evaluation. The book draws on existing cross-cultural research in social sciences and related areas to illustrate how to formulate research questions, select observable statistics, understand cross-cultural translation, evaluate and implement measurement equivalence, and discern quality within practices of measurement development. Tran also discusses how to use statistics software programs such as SPSS to generate data for LISREL analyses, providing enough detail to help readers grasp the programs' applications in this area but not so much as to overwhelm. This concise text offers a wealth of knowledge about using and interpreting the use of culturally relevant research instruments. Doctoral students and social researchers in the field seeking guidance in selecting and adapting such instruments in their studies, or developing and assessing their own, will find it a terrific source of essential information for their work. For additional resources, visit http://www.oup.com/us/pocketguides.
All over the world, people are experiencing increasing levels of stress due to a variety of reasons which include pressures at the workplace, marital or family stress and changing social mores, among others. This has contributed to deteriorating health and an alarming growth in lifestyle-related diseases, such as diabetes and chronic heart problems. The author presents an absorbing and comprehensive look at the concept of stress and explores its physiological effects, our body's stress responses and its results. He presents a guide to choosing the most appropriate techniques to manage stress a.
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