During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open-
Proceedings in Memory of Robert Brooks, December 29, 2003-January 2, 2004 [and] January 5-9, 2004, Technion-Israel Institute of Technology, Haifa, Israel
Proceedings in Memory of Robert Brooks, December 29, 2003-January 2, 2004 [and] January 5-9, 2004, Technion-Israel Institute of Technology, Haifa, Israel
This volume contains articles based on talks given at the Robert Brooks Memorial Conference on Geometry and Spectral Theory and the Workshop on Groups, Geometry and Dynamics held at Technion - the Israel Institute of Technology (Haifa). Robert Brooks' (1952 - 2002) broad range of mathematical interests is represented in the volume, which is devoted to various aspects of global analysis, spectral theory, the theory of Riemann surfaces, Riemannian and discrete geometry, and numbertheory. A survey of Brooks' work has been written by his close colleague, Peter Buser. Also included in the volume are articles on analytic topics, such as Szego's theorem, and on geometric topics, such as isoperimetric inequalities and symmetries of manifolds. The book is suitable for graduate studentsand researchers interested in various aspects of geometry and global analysis.
George III was one of the longest reigning British monarchs, ruling over most of the English speaking world from 1760 to 1820. Despite his longevity, George’s reign was one of turmoil. Britain lost its colonies in the War of American Independence and the European political system changed dramatically in the wake of the French Revolution. Closer to home, problems with the King’s health led to a constitutional crisis. Charlotte Papendiek’s memoirs cover the first thirty years of George III’s reign, while Mary Delany’s letters provide a vivid portrait of her years at Windsor. Lucy Kennedy was another long-serving member of court whose previously unpublished diary provides a great deal of new detail about the King’s illness. Finally, the Queen herself provides further insights in the only two extant volumes of her diaries, published here for the first time. The edition will be invaluable to scholars of Georgian England as well as those researching the French and American Revolutions and the history and politics of the Regency period more widely.
A detailed mathematical derivation of space curves is presented that links the diverse fields of superfluids, quantum mechanics, and hydrodynamics by a common foundation. The basic mathematical building block is called the theory of quantum torus knots (QTK).
This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.
The design and implementation of the Maple system is an on-going project of the Symbolic Com putation Group at the University of Waterloo in Ontario, Canada. This manual corresponds with version V (roman numeral five) of the Maple system. The on-line help subsystem can be invoked from within a Maple session to view documentation on specific topics. In particular, the command ?updates points the user to documentation updates for each new version of Maple. The Maple project was first conceived in the autumn of 1980, growing out of discussions on the state of symbolic computation at the University of Waterloo. The authors wish to acknowledge many fruitful discussions with colleagues at the University of Waterloo, particularly Morven Gen tleman, Michael Malcolm, and Frank Tompa. It was recognized in these discussions that none ofthe locaIly-available systems for symbolic computation provided the facilities that should be expected for symbolic computation in modern computing environments. We concluded that since the basic design decisions for the then-current symbolic systems such as ALTRAN, CAMAL, REDUCE, and MACSYMA were based on 1960's computing technology, it would be wise to design a new system "from scratch". Thus we could take advantage of the software engineering technology which had become available in recent years, as well as drawing from the lessons of experience. Maple's basic features (elementary data structures, Input/output, arithmetic with numbers, and elementary simplification) are coded in a systems programming language for efficiency.
This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results. In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.
The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).
Considering the support behind Brexit and Donald Trump's 'America first' policies, this book challenges the idea that they are motivated solely by fear and instead looks at the hope and promises that drive these renewed forms of nationalism. Addressing these neglected motivations within contemporary populism, Michael Mack explores how our current sense of disappointment with our ecological, economic and political state of affairs partakes of a history of failed promises that goes back to the inception of modernity; namely, to Spinoza's radical enlightenment of diversity and equality. Through this innovative approach, Spinoza emerges less as a single isolated figure and more as a sign for an intellectual constellation of thinkers and writers who – from the romantics to contemporary theory and literature – have introduced various shifts in the way we see humanity as being limited and prone to disappointment. Combining intellectual history with literary and scientific theory, the book traces the collapse of traditional values and orders from Spinoza to Nietzsche and then to the literary modernism of Joseph Conrad and postmodernism of Philip Roth and Thomas Pynchon.
Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.
The geometric approach to quantization was introduced by Konstant and Souriau more than 20 years ago. It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic. The ideas have proved useful in pure mathematics, notably in representation theory, as well as in theoretical physics. The most recent applications have been in conformal field theory and in the Jones-Witten theory of knots. The successful original edition of this book was published in 1980. Now it has been completely revised and extensively rewritten. The presentation has been simplified and many new examples have been added. The material on field theory has been expanded.
In a detailed analysis of the field of eating problems and disorders, this book highlights the connections between the prevention of eating problems and disorders, and theory and research in the areas of prevention and health promotion. It also looks at models of risk development and prevention, specific issues and challenges, the status of current prevention research, and lessons for prevention program development. In this unique text Levine and Smolak draw on a range of interdisciplinary perspectives, including prevention science, developmental psychology, public health, and neuroscience, to provide a thorough review, history, and critique of the topic in light of a range of empirical studies. The only authored volume with a broad, detailed and integrated view of theories, research, and practice, this expanded, fully revised, and updated new edition features new chapters on dissonance-based approaches, public health, biopsychiatry and neuroscience, gender, culture(s), technology, obesity, protective factors, and ecological approaches. The Prevention of Eating Problems and Eating Disorders: Theories, Research, and Applications is essential reading for clinicians, academics, researchers, graduate students, upper-level undergraduates, and activists and advocates involved in work pertaining to eating disorders, disordered eating, prevention, health promotion, body image, obesity and biopsychosocial perspectives.
The framework of algorithms presented in this book is called Cost Approximation. It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the updating of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of the book is to offer this framework as an intuitively appealing tool for describing an algorithm. Another purpose is to provide a convergence analysis of the algorithms in the framework. Audience: The book will be of interest to all researchers in the field (it includes over 800 references) and can also be used for advanced courses in non-linear optimization with the possibility of being oriented either to algorithm theory or to the numerical aspects of large-scale nonlinear optimization.
This book describes a promising approach to problems in the foundations of quantum mechanics, including the measurement problem. The dynamics of ensembles on configuration space is shown here to be a valuable tool for unifying the formalisms of classical and quantum mechanics, for deriving and extending the latter in various ways, and for addressing the quantum measurement problem. A description of physical systems by means of ensembles on configuration space can be introduced at a very fundamental level: the basic building blocks are a configuration space, probabilities, and Hamiltonian equations of motion for the probabilities. The formalism can describe both classical and quantum systems, and their thermodynamics, with the main difference being the choice of ensemble Hamiltonian. Furthermore, there is a natural way of introducing ensemble Hamiltonians that describe the evolution of hybrid systems; i.e., interacting systems that have distinct classical and quantum sectors, allowing for consistent descriptions of quantum systems interacting with classical measurement devices and quantum matter fields interacting gravitationally with a classical spacetime.
A Timely Exploration of Multiuser Detection in Wireless Networks During the past decade, the design and development of current and emerging wireless systems have motivated many important advances in multiuser detection. This book fills an important need by providing a comprehensive overview of crucial recent developments that have occurred in this active research area. Each chapter is contributed by noted experts and is meant to serve as a self-contained treatment of the topic. Coverage includes: Linear and decision feedback methods Iterative multiuser detection and decoding Multiuser detection in the presence of channel impairments Performance analysis with random signatures and channels Joint detection methods for MIMO channels Interference avoidance methods at the transmitter Transmitter precoding methods for the MIMO downlink This book is an ideal entry point for exploring ongoing research in multiuser detection and for learning about the field's existing unsolved problems and issues. It is a valuable resource for researchers, engineers, and graduate students who are involved in the area of digital communications.
For most of the eighteenth century the best minds in Europe took up the task of providing a foundation for human life and human society in which individual fulfillment was to be achieved within a rational public order. When it became apparent that this task was based on an illusion—the separation of self and world—and was thus doomed to failure, however, that insight and the consequent crisis were forgotten and repressed. After 1815 all parties, reactionary and liberal, chose to proceed as if we had achieved what we knew, somewhere, we could not carry off. To secure that false confidence the challenges of the late Enlightenment had to be silenced and its doubts swept under the carpet. This book concerns a founding act of bad faith and of willed blindness, the self-forgetting of the rootlessness and the falsity of the basic presuppositions of the modern world, that have haunted that world from its birth. Enlightenment Interrupted takes the metaphysical arguments of the idealists seriously. Its methodological foundation is the belief that in every era there are deep structures of thought and experience that define the range of theoretical and political possibilities available. The great achievement of the post-Kantian generation was to critique and ultimately to move beyond the self-world dichotomy at the heart of Western thought. This can be seen as a continuation of the Enlightenment project of subjecting everything to the test of reason, but it was also part of a larger cultural movement that found expression in Romanticism, in an openness to Indian and other non-Western thought, and in the political and social experimentation of the French Revolution. What followed in the post-Revolutionary years was not a development of those tendencies to openness and egalitarian, common process but a retreat to the opposition of self and world and a drastic reduction in intellectual and social possibilities. This is one source of the collective impotence that sees the twenty-first century in a lockstep march to disaster.
Studies of the writing of Herman Melville are often divided among those that address his political, historical, or biographical dimensions and those that offer creative theoretical readings of his texts. In Herman Melville and the Politics of the Inhuman, Michael Jonik offers a series of nuanced and ambitious philosophical readings of Melville that unite these varied approaches. Through a careful reconstruction of Melville's interaction with philosophy, Jonik argues that Melville develops a notion of the 'inhuman' after Spinoza's radically non-anthropocentric and relational thought. Melville's own political philosophy, in turn, actively disassembles differences between humans and nonhumans, and the animate and inanimate. Jonik has us rethink not only how we read Melville, but also how we understand our deeply inhuman condition.
Johann Gottfried Herder (1744-1803) is a towering figure in modern thought, but one who has hitherto been severely underappreciated. Michael Forster seeks to rectify that situation He considers Herder's philosophy in the round and argues that it is both far more impressive in quality and far more influential in modern thought than has previously been realized. After an introduction on Herder's intellectual biography, philosophical style, and general program in philosophy, there are chapters on his philosophy of language, his hermeneutics, his theory of translation, his contribution of the philosophical foundations for both linguistics and cultural anthropology, his philosophy of mind, his aesthetics, his moral philosophy, his philosophy of history, his political philosophy, his philosophy of religion, and his intellectual influence. Forster argues that Herder contributed vitally important ideas in all of these areas; that in many of them his ideas were seminal for major subsequent philosophers, including Friedrich Schlegel, Schleiermacher, Wilhelm von Humboldt, Hegel, and Nietzsche; that they indeed founded whole new disciplines, such as linguistics, anthropology, and comparative literature; and that moreover they were in many cases even better than what these subsequent thinkers and disciplines went on to make of them.
Advanced Engineering Analysis: The Calculus of Variations and Functional Analysis with Applications in Mechanics Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, and control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study. Book jacket.
A new, comprehensive biography of the life and work of Karl Marx For over a century, Karl Marx’s critique of capitalism has been a crucial resource for social movements. Now, recent economic crises have made it imperative for us to comprehend and actualize Marx’s ideas. But without a knowledge of Karl Marx’s life as he lived it, neither Marx nor his works can be fully understood. There are more than twenty-five comprehensive biographies of Marx, but none of them consider his life and work in equal, corresponding measure. This biography, planned for three volumes, aims to include what most biographies have reduced to mere background: the contemporary conflicts, struggles, and disputes that engaged Marx at the time of his writings, alongside his complex relationships with a varied assortment of friends and opponents. This first volume will deal extensively with Marx’s youth in Trier and his studies in Bonn and Berlin. It will also examine the function of poetry in his intellectual development and his first occupation with Hegelian philosophy and with the so-called “young Hegelians” in his 1841 Dissertation. Already during this period, there were crises as well as breaks in Marx’s intellectual development that prompted Marx to give up projects and re-conceptualize his critical enterprise. This volume is the beginning of an astoundingly dimensional look at Karl Marx – a study of a complex life and body of work through the neglected issues, events, and people that helped comprise both. It is destined to become a classic.
Tracing the origins of modern political thought through three sets of arguments over history, morality, and freedom In this wide-ranging work, Michael Sonenscher traces the origins of modern political thought and ideologies to a question, raised by Immanuel Kant, about what is involved in comparing individual human lives to the whole of human history. How can we compare them, or understand the results of the comparison? Kant’s question injected a new, future-oriented dimension into existing discussions of prevailing norms, challenging their orientation toward the past. This reversal made Kant’s question a bridge between three successive sets of arguments: between the supporters of the ancients and moderns, the classics and romantics, and the Romans and the Germans. Sonenscher argues that the genealogy of modern political ideologies—from liberalism to nationalism to communism—can be connected to the resulting discussions of time, history, and values, mainly in France but also in Germany, Switzerland, and Britain, in the period straddling the French and Industrial revolutions. What is the genuinely human content of human history? Everything begins somewhere—democracy with the Greeks, or the idea of a res publica with the Romans—but these local arrangements have become vectors of values that are, apparently, universal. The intellectual upheaval that Sonenscher describes involved a struggle to close the gap, highlighted by Kant, between individual lives and human history. After Kant is an examination of that struggle’s enduring impact on the history and the historiography of political thought.
This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, and although the focus is on approximating higher- dimensional integrals the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.
This book covers systematically and in a simple language the mathematical and physical foundations of controlling deterministic and stochastic evolutionary processes in systems with a high degree of complexity. Strong emphasis is placed on concepts, methods and techniques for modelling, assessment and the solution or estimation of control problems in an attempt to understand the large variability of these problems in several branches of physics, chemistry and biology as well as in technology and economics. The main focus of the book is on a clear physical and mathematical understanding of the dynamics and kinetics behind several kinds of control problems and their relation to self-organizing principles in complex systems. The book is a modern introduction and a helpful tool for researchers, engineers as well as post-docs and graduate students interested in an application oriented control theory and related topics.
The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical techniques required to study nonlinear dynamics, helping the reader with little mathematical background to understand the text. The Duffing Equation provides a reference text for postgraduate and students and researchers of mechanical engineering and vibration / nonlinear dynamics as well as a useful tool for practising mechanical engineers. Includes a chapter devoted to historical background on Georg Duffing and the equation that was named after him. Includes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation. Contains a comprehensive treatment of the various forms of the Duffing equation. Uses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.
This book covers everything you need to know to write professional-level cryptographic code. This expanded, improved second edition includes about 100 pages of additional material as well as numerous improvements to the original text. The chapter about random number generation has been completely rewritten, and the latest cryptographic techniques are covered in detail. Furthermore, this book covers the recent improvements in primality testing.
In 1962 a strike force of elite special agents for a clandestine group is sent to unearth and recover four powerful artifacts from a temple buried in the Middle Eastern desert. The artifacts are recovered, but only the three mission leaders survive, making off with two of the artifacts. In 1976, the surviving junior member of the desert mission is now an agent on a special assignment: he is to abduct, artificially inseminate, and release Angela Trelaine, the wife of billionaire industrialist Reginald Trelaine. His mission is a success. The next year, Angela dies in childbirth as she delivers twins, Jack and Sarah Trelaine. Her husband, Reginald, blames his wife's death on the infant Jack but vows to wait until the boy is older to take revenge. It is now 2004 and when a convenience store clerk is attacked and sexually assaulted by a group of gangbangers, the rape is cut short by a man wearing black leather and Kevlar that covers everything but the red goggles over his eyes. He tears the gangbangers apart with his bare hands before hurling a titanium hammer through the skull of the last attacker. This starts a chain of events that bathes the Indianapolis streets in blood.Now a grown Jack must strive to save those closest to him while struggling to uncover the Nature of the Beast. About the Author: First-time novelist Michael L. Romansky resides with his family in Indianapolis. He has three books in the works including the sequel. Publisher's website: http: //SBPRA.com/MichaelLRomansk
Renowned for his metaphysics, Spinoza made significant contributions to understanding the human mind, the emotions, moral philosophy, and political philosophy. Beginning with an overview of Spinoza's life, Michael Della Rocca carefully unpacks and explains Spinoza's philosophy: his metaphysics of substance and argument at the center of his whole system that God is the sole independent substance; his account of the human mind and its relation to the body; his theory that human beings tend towards self-preservation and his most famous work, the Ethics, including the problem of free will; and his writings on the state, religion and scripture. Della Rocca concludes with a chapter on Spinoza's legacy and how modern philosophers, Hume, Hegel, and Nietzsche, responded to Spinoza's challenge. Ideal for those coming to Spinoza for the first time as well as those already acquainted with his thought, Spinoza is essential reading for anyone studying philosophy.
The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a state-of-the-art reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes.
In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire. Templates offer three distinct advantages: they are general and reusable; they are not language specific; and they exploit the expertise of both the numerical analyst, who creates a template reflecting in-depth knowledge of a specific numerical technique, and the computational scientist, who then provides "value-added" capability to the general template description, customizing it for specific needs. For each template that is presented, the authors provide: a mathematical description of the flow of algorithm; discussion of convergence and stopping criteria to use in the iteration; suggestions for applying a method to special matrix types; advice for tuning the template; tips on parallel implementations; and hints as to when and why a method is useful.
A comprehensive introduction to various numerical methods used in computational finance today Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem.
This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic reference frames, the celestial mechanics of N-body systems, and high-precision astrometry, navigation, and geodesy, which are then treated in the following five chapters. The final chapter provides an overview of the new field of applied relativity, based on recent recommendations from the International Astronomical Union. The book is suitable for teaching advanced undergraduate honors programs and graduate courses, while equally serving as a reference for professional research scientists working in relativity and dynamical astronomy. The authors bring their extensive theoretical and practical experience to the subject. Sergei Kopeikin is a professor at the University of Missouri, while Michael Efroimsky and George Kaplan work at the United States Naval Observatory, one of the world?s premier institutions for expertise in astrometry, celestial mechanics, and timekeeping.
In this clear, critical examination of the ideas of one of the greatest and most influential of modern philosophers, M.J. Inwood makes Hegel's arguments fully accessible. He considers Hegel's system as a whole and examines the wide range of problems that it was designed to solve - metaphysical, epistemological theological and political. He concentrates especially on the logical and metaphysical ideas which underpin the system and which supply the key to understanding much of what is obscure in Hegel's thought. Throughout the book, M.J Inwood reconstructs Hegel's thought by arguing with him. He examines Hegel's arguments and restates his views precisely and clearly. He also conveys the impressive unity of Hegel's system and its links with the thought of such philosophers as Aristotle, Spinoza and Kant.
This book deals with the determinants of linear operators in Euclidean, Hilbert and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators, enable us to describe the spectra, to evaluate the multiplicities of eigenvalues, etc. We derive upper and lower bounds, and perturbation results for determinants, and discuss applications of our theoretical results to spectrum perturbations, matrix equations, two parameter eigenvalue problems, as well as to differential, difference and functional-differential equations.
This history of the discipline of public law in Germany covers three dramatic decades of the Twentieth century. It opens with the First World War, analyses the highly creative years of the Weimar Republic, and recounts the decline of German public law that began in 1933 and extended to the downfall of the Third Reich.
In the twentieth century, we often think of Nietzsche, nihilism, and the death of God as inextricably connected. But, in this pathbreaking work, Michael Gillespie argues that Nietzsche, in fact, misunderstood nihilism, and that his misunderstanding has misled nearly all succeeding thought about the subject. Reconstructing nihilism's intellectual and spiritual origins before it was given its determinitive definition by Nietzsche, Gillespie focuses on the crucial turning points in the development of nihilism, from Ockham and the nominalist revolution to Descartes, Fichte, the German Romantics, the Russian nihilists and Nietzsche himself. His analysis shows that nihilism is not the result of the death of God, as Nietzsche believed; but the consequence of a new idea of God as a God of will who overturns all eternal standards of truth and justice. To understand nihilism, one has to understand how this notion of God came to inform a new notion of man and nature, one that puts will in place of reason, and freedom in place of necessity and order.
This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained. The resulting formulation of perturbative quantum field theory is a version of the Epstein-Glaser renormalization that is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum field theory is also elaborated on, and the formalism is illustrated in a wealth of examples and exercises.
Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.
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