The Earth's future is hanging by a thread and we stand together holding the spool. Two contrasting stories of man-made environmental disasters that are lessons of how our political and social choices affect our future.
Gait analysis is the systematic study of human walking, using the eye and brain of experienced observers, augmented by instrumentation for measuring body movements, body mechanics, and the activity of the muscles. Since Aristotle’s work on gait analysis more than 2000 years ago, it has become an established clinical science used extensively in the healthcare and rehabilitation fields for diagnosis and treatment. Forensic Gait Analysis details the more recent, and rapidly developing, use of gait analysis in the forensic sciences. The book considers the use of observational gait analysis, based on video recordings, to assist in the process of identification or exclusion. With the increase in use of CCTV and surveillance systems over the last 20 to 30 years, there has been a steady and rapid increase in the use of gait as evidence. Currently, gait analysis is widely used in the UK in criminal investigations, with increasing awareness of its potential use in the US, Europe, and globally. The book details the history of the science, current practices, and of the emergent application to establish best-practice standards that conform to those of other forensic science disciplines. Engagement with the Forensic Science Regulator, and the Chartered Society of Forensic Sciences in the UK, and the International Association for Identification has helped to ensure and enhance the quality assurance of forensic gait analysis. However, there remains a fundamental lack of standardized training and methodology for use in evidentiary and investigative casework. This book fills that void, serving as one of the first to describe the current state of practice, capabilities and limitations, and to outline methods, standards of practice and expectations of the gait analyst as a forensic practitioner. Forensic Gait Analysis reflects current research and forensic practice and will serve as a state-of-the-art guide to the use of gait analysis in the forensic context—for both education and training purposes. It will be a welcome addition to the libraries of professionals in the areas of podiatry, gait analysis, forensic video analysis, law enforcement, and legal practice.
Liberties Journal of Culture and Politics is devoted to educating the general public about the history, current trends, and possibilities of culture and politics.
This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
Hilberts talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateaus problem by Douglas and Rad. This third edition gives a concise introduction to variational methods and presents an overview of areas of current research in the field, plus a survey on new developments.
Landmark Experiments in Molecular Biology critically considers breakthrough experiments that have constituted major turning points in the birth and evolution of molecular biology. These experiments laid the foundations to molecular biology by uncovering the major players in the machinery of inheritance and biological information handling such as DNA, RNA, ribosomes, and proteins. Landmark Experiments in Molecular Biology combines an historical survey of the development of ideas, theories, and profiles of leading scientists with detailed scientific and technical analysis. Includes detailed analysis of classically designed and executed experiments Incorporates technical and scientific analysis along with historical background for a robust understanding of molecular biology discoveries Provides critical analysis of the history of molecular biology to inform the future of scientific discovery Examines the machinery of inheritance and biological information handling
Explores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations.
This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.
Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.
How does our understanding of the reality (or lack thereof ) of race as a category of being affect our understanding of racism as a social phenomenon, and vice versa? This book focuses on the underlying assumptions that inform this view of race and racism, arguing that it is ultimately bound up in a politics of purity-an understanding of human agency, and reality itself, as requiring all-or-nothing categories with clear and unambiguous boundaries. Monahan calls for the emergence of a creolizing subjectivity that would place such ambiguity at the center of our understanding of race.
The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. In includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (Peter Lax, SIAM review, June 1998)
The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis. ^
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
This volume contains the proceedings of the QMATH13: Mathematical Results in Quantum Physics conference, held from October 8–11, 2016, at the Georgia Institute of Technology, Atlanta, Georgia. In recent years, a number of new frontiers have opened in mathematical physics, such as many-body localization and Schrödinger operators on graphs. There has been progress in developing mathematical techniques as well, notably in renormalization group methods and the use of Lieb–Robinson bounds in various quantum models. The aim of this volume is to provide an overview of some of these developments. Topics include random Schrödinger operators, many-body fermionic systems, atomic systems, effective equations, and applications to quantum field theory. A number of articles are devoted to the very active area of Schrödinger operators on graphs and general spectral theory of Schrödinger operators. Some of the articles are expository and can be read by an advanced graduate student.
This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.
Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.
This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Companion texts, which take the theory of partial differential equations further, are AMS volume 116, treating more advanced topics in linear PDE, and AMS volume 117, treating problems in nonlinear PDE. This book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis
Authors Dave Nelson and Mike Cox combine the best of the laboratory and best of the classroom, introducing exciting new developments while communicating basic principles of biochemistry.
Landmark Experiments in Molecular Biology critically considers breakthrough experiments that have constituted major turning points in the birth and evolution of molecular biology. These experiments laid the foundations to molecular biology by uncovering the major players in the machinery of inheritance and biological information handling such as DNA, RNA, ribosomes, and proteins. Landmark Experiments in Molecular Biology combines an historical survey of the development of ideas, theories, and profiles of leading scientists with detailed scientific and technical analysis. Includes detailed analysis of classically designed and executed experiments Incorporates technical and scientific analysis along with historical background for a robust understanding of molecular biology discoveries Provides critical analysis of the history of molecular biology to inform the future of scientific discovery Examines the machinery of inheritance and biological information handling
Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.
Conservative Reductionism sets out a new theory of the relationship between physics and the special sciences within the framework of functionalism. It argues that it is wrong-headed to conceive an opposition between functional and physical properties (or functional and physical descriptions, respectively) and to build an anti-reductionist argument on multiple realization. By contrast, (a) all properties that there are in the world, including the physical ones, are functional properties in the sense of being causal properties, and (b) all true descriptions (laws, theories) that the special sciences propose can in principle be reduced to physical descriptions (laws, theories) by means of functional reduction, despite multiple realization. The book develops arguments for (a) from the metaphysics of properties and the philosophy of physics. These arguments lead to a conservative ontological reductionism. It then develops functional reduction into a fully-fledged, conservative theory reduction by means of introducing functional sub-types that are coextensive with physical types, illustrating that conservative reductionism by means of case studies from biology (notably the relationship between classical and molecular genetics).
This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III. For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter.
The Jewish intellectual tradition has a long and complex history that has resulted in significant and influential works of scholarship. In this book, the authors suggest that there is a series of common principles that can be extracted from the Jewish intellectual tradition that have broad, even life-changing, implications for individual and societal achievement. These principles include respect for tradition while encouraging independent, often disruptive thinking; a precise system of logical reasoning in pursuit of the truth; universal education continuing through adulthood; and living a purposeful life. The main objective of this book is to understand the historical development of these principles and to demonstrate how applying them judiciously can lead to greater intellectual productivity, a more fulfilling existence, and a more advanced society.
Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field — that of mathematics — and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes.A list of Fields Medallists and their contributions provides a bird's-eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from Fields Medallists and so provides a highly interesting and varied picture.The second edition of Fields Medallists' Lectures features additional contributions from the following Medallists: Kunihiko Kodaira (1954), Richard E Borcherds (1998), William T Gowers (1998), Maxim Kontsevich (1998), Curtis T McMullen (1998) and Vladimir Voevodsky (2002).
In December 1235, Pope Gregory IX altered the mission of a crusade he had begun to preach the year before. Instead of calling for Christian magnates to go on to fight the infidel in Jerusalem, he now urged them to combat the spread of Christian heresy in Latin Greece and to defend the Latin empire of Constantinople. The Barons' Crusade, as it was named by a fourteenth-century chronicler impressed by the great number of barons who participated, would last until 1241 and would represent in many ways the high point of papal efforts to make crusading a universal Christian undertaking. This book, the first full-length treatment of the Barons' Crusade, examines the call for holy war and its consequences in Hungary, France, England, Constantinople, and the Holy Land. In the end, Michael Lower reveals, the pope's call for unified action resulted in a range of locally determined initiatives and accommodations. In some places in Europe, the crusade unleashed violence against Jews that the pope had not sought; in others, it unleashed no violence at all. In the Levant, it even ended in peaceful negotiation between Christian and Muslim forces. Virtually everywhere, but in different ways, it altered the relations between Christians and non-Christians. By emphasizing comparative local history, The Barons' Crusade: A Call to Arms and Its Consequences brings into question the idea that crusading embodies the religious unity of medieval society and demonstrates how thoroughly crusading had been affected by the new strategic and political demands of the papacy.
A classic treatment of the Atiyah-Singer index theorem from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Marks’ Basic Medical Biochemistry: A Clinical Approach, 6th Edition links biochemistry to physiology and pathophysiology, empowering students to confidently apply fundamental concepts to the practice of medicine — from diagnosing patients to recommending effective treatments. This proven, application-centered approach builds biochemical coverage around related clinical concepts to anchor students’ understanding to a clinical context from day one. Intuitively organized chapters center on hypothetical patient vignettes to emphasize clinical applications, and helpful icons, images, and review questions make complex concepts easier to grasp.
Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field - that of mathematics - and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes. The restriction to 40 years is of marginal significance, since most mathematicians have made their mark long before this age.A list of Fields Medallists and their contributions provides a bird's eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from 22 Fields Medallists and so provides a highly interesting and varied picture.The contributions themselves represent the choice of the individual Medallists. In some cases the articles relate directly to the work for which the Fields Medals were awarded. In other cases new articles have been produced which relate to more current interests of the Medallists. This indicates that while Fields Medallists must be under 40 at the time of the award, their mathematical development goes well past this age. In fact the age limit of 40 was chosen so that young mathematicians would be encouraged in their future work.The Fields Medallists' Lectures is now available on CD-ROM. Sections can be accessed at the touch of a button, and similar topics grouped together using advanced keyword searches.
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