Presents the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. This book offers introduction of a canonically invariant scheme for the computation of the splitting matrix.
Presents the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. This book offers introduction of a canonically invariant scheme for the computation of the splitting matrix.
Presents the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. This book offers introduction of a canonically invariant scheme for the computation of the splitting matrix.
Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.
A wandering domain for a diffeomorphism of is an open connected set such that for all . The authors endow with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map of a Hamiltonian which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of , in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the “quantitative Hamiltonian perturbation theory” initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.
In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.
The updated 2nd edition of this book presents a variety of image analysis applications, reviews their precise mathematics and shows how to discretize them. For the mathematical community, the book shows the contribution of mathematics to this domain, and highlights unsolved theoretical questions. For the computer vision community, it presents a clear, self-contained and global overview of the mathematics involved in image procesing problems. The second edition offers a review of progress in image processing applications covered by the PDE framework, and updates the existing material. The book also provides programming tools for creating simulations with minimal effort.
Since the 1980s, society’s wealthiest members have claimed an ever-expanding share of income and property. It has been a true counterrevolution, says Pierre Rosanvallon—the end of the age of growing equality launched by the American and French revolutions. And just as significant as the social and economic factors driving this contemporary inequality has been a loss of faith in the ideal of equality itself. An ambitious transatlantic history of the struggles that, for two centuries, put political and economic equality at their heart, The Society of Equals calls for a new philosophy of social relations to reenergize egalitarian politics. For eighteenth-century revolutionaries, equality meant understanding human beings as fundamentally alike and then creating universal political and economic rights. Rosanvallon sees the roots of today’s crisis in the period 1830–1900, when industrialized capitalism threatened to quash these aspirations. By the early twentieth century, progressive forces had begun to rectify some imbalances of the Gilded Age, and the modern welfare state gradually emerged from Depression-era reforms. But new economic shocks in the 1970s began a slide toward inequality that has only gained momentum in the decades since. There is no returning to the days of the redistributive welfare state, Rosanvallon says. Rather than resort to outdated notions of social solidarity, we must instead revitalize the idea of equality according to principles of singularity, reciprocity, and communality that more accurately reflect today’s realities.
The new digital media offers us an unprecedented memory capacity, an ubiquitous communication channel and a growing computing power. How can we exploit this medium to augment our personal and social cognitive processes at the service of human development? Combining a deep knowledge of humanities and social sciences as well as a real familiarity with computer science issues, this book explains the collaborative construction of a global hypercortex coordinated by a computable metalanguage. By recognizing fully the symbolic and social nature of human cognition, we could transform our current opaque global brain into a reflexive collective intelligence.
This work is devoted to the theory and approximation of nonlinear hyper bolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors, and we shall make frequent references to Godlewski and Raviart (1991) (hereafter noted G. R. ), though the present volume can be read independently. This earlier publication, apart from a first chap ter, especially covered the scalar case. Thus, we shall detail here neither the mathematical theory of multidimensional scalar conservation laws nor their approximation in the one-dimensional case by finite-difference con servative schemes, both of which were treated in G. R. , but we shall mostly consider systems. The theory for systems is in fact much more difficult and not at all completed. This explains why we shall mainly concentrate on some theoretical aspects that are needed in the applications, such as the solution of the Riemann problem, with occasional insights into more sophisticated problems. The present book is divided into six chapters, including an introductory chapter. For the reader's convenience, we shall resume in this Introduction the notions that are necessary for a self-sufficient understanding of this book -the main definitions of hyperbolicity, weak solutions, and entropy present the practical examples that will be thoroughly developed in the following chapters, and recall the main results concerning the scalar case.
We could be on the threshold of a scientific revolution. Quantum mechanics is based on unique, finite, and discrete events. General relativity assumes a continuous, curved space-time. Reconciling the two remains the most fundamental unsolved scientific problem left over from the last century. The papers of H Pierre Noyes collected in this volume reflect one attempt to achieve that unification by replacing the continuum with the bit-string events of computer science. Three principles are used: physics can determine whether two quantities are the same or different; measurement can tell something from nothing; this structure (modeled by binary addition and multiplication) can leave a historical record consisting of a growing universe of bit-strings. This book is specifically addressed to those interested in the foundations of particle physics, relativity, quantum mechanics, physical cosmology and the philosophy of science. Contents: Non-Locality in Particle Physics; On the Physical Interpretation and the Mathematical Structure of the Combinatorial Hierarchy (with T Bastin, J Amson & C W Kilmister); On the Construction of Relativistic Quantum Theory: A Progress Report; Foundations of a Discrete Physics (with D McGoveran); Comment on OC Statistical Mechanical Origin of the Entropy of a Rotating Charged Black HoleOCO Anti-Gravity: The Key to 21st Century Physics; Crossing Symmetry is Incompatible with General Relativity; Operationalism Revisited: Measurement Accuracy, Scale Invariance and the Combinatorial Hierarchy; Discrete Physics and the Derivation of Electromagnetism from the Formalism of Quantum Mechanics (with L H Kauffman); Are Partons Confined Tachyons?; A Short Introduction to Bit-String Physics; Process, System, Causality and Quantum Mechanics: A Psychoanalysis of Animal Faith (with T Etter); and other papers. Readership: Researchers interested in the foundations of particle physics, relativity, quantum mechanics, physical cosmology and the philosophy of science.
This book is the eighth in the successful line of Intelligent Agents books published in LNAI. It is based on the Eighth International Workshop on Agent Theories, Architectures, and Languages, ATAL 2001, held in Seattle, WA, USA, in August 2001. The 31 revised full papers presented together with an overall introduction and two special session overviews were carefully reviewed and selected during two rounds of improvement from 68 submissions. The papers are organized in topical sections on agent modeling; formal specification and verification of agents; agent architectures and languages; agent communication; collaborative planning and resource allocation; trust and safety, formal theories of negotiation; and agents for hand-held, mobile, or embedded devices.
The impact and influence of J.-P. Serre ́s work have been notable ever since his doctoral thesis on homotopy groups. The abundance of findings and deep insights found in his research and survey papers ranging from topology, several complex variables, and algebraic geometry to number theory, group theory, commutative algebra and modular forms, continues to provide inspiring reading for mathematicians working in these areas, in their research and their teaching. Characteristic of Serre ́s publications are the many open questions he formulates pointing to further directions for research. In four volumes of Collected Papers he has provided comments on and corrections to most articles, and described the current status of the open questions with reference to later findings. In this softcover edition of volume IV, two recently published articles have been added, one on the life and works of André Weil, the other one on Finite Subgroups of Lie Groups. From the reviews: "This is the fourth volume of J-P. Serre's Collected Papers covering the period 1985-1998. Items, numbered 133-173, contain "the essence'' of his work from that period and are devoted to number theory, algebraic geometry, and group theory. Half of them are articles and another half are summaries of his courses in those years and letters. Most courses have never been previously published, nor proofs of the announced results. The letters reproduced, however (in particular to K. Ribet and M.-F. Vignéras), provide indications of some of those proofs. Also included is an interview with J-P. Serre from 1986, revealing his views on mathematics (with the stress upon its integrity) and his own mathematical activity. The volume ends with Notes which complete the text by reporting recent progress and occasionally correct it. Zentralblatt MATH
From the reviews of Vols. I-III: "Since their publication in 1986 J-P. Serre's Collected Papers have already become one of the classical references in mathematical research. This is on the one hand due to the completeness of the collection (132 items) and on the other, of course, due to the beautiful and clear expositions of Serre's papers and their influence on mathematics. As listed in the preface, the three volumes cover almost all articles published in mathematical journals between 1949 and 1984, the summaries of the author's courses at the Collège de France since 1956, some of his Séminaire notes, and some items not previously published. [...] The author's notes at the end of each volume giving corrections and important recent progress as well as improvements of the main results represent a highlight of this collection. The mathematical community definitely looks forward to further volume(s) of Serre's outstanding work." Zentralblatt MATH
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