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Ricci Flow and the Poincare Conjecture

Ricci Flow and the Poincare Conjecture PDF Author: John W. Morgan
Publisher: American Mathematical Soc.
ISBN: 9780821843284
Category : Poincaré conjecture
Languages : en
Pages : 586

Book Description
For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Ricci Flow and the Poincare Conjecture

Ricci Flow and the Poincare Conjecture PDF Author: John W. Morgan
Publisher: American Mathematical Soc.
ISBN: 9780821843284
Category : Poincaré conjecture
Languages : en
Pages : 586

Book Description
For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Molecular Modelling and Synthesis of Nanomaterials

Molecular Modelling and Synthesis of Nanomaterials PDF Author: Ihsan Boustani
Publisher: Springer Nature
ISBN: 3030327264
Category : Technology & Engineering
Languages : en
Pages : 594

Book Description
This book presents nanomaterials as predicted by computational modelling and numerical simulation tools, and confirmed by modern experimental techniques. It begins by summarizing basic theoretical methods, then giving both a theoretical and experimental treatment of how alkali metal clusters develop into nanostructures, as influenced by the cluster's "magic number" of atoms. The book continues with a discussion of atomic clusters and nanostructures, focusing primarily on boron and carbon, exploring, in detail, the one-, two-, and three-dimensional structures of boron and carbon, and describing their myriad potential applications in nanotechnology, from nanocoating and nanosensing to nanobatteries with high borophene capacity. The broad discussion of computational modelling as well as the specific applications to boron and carbon, make this book an essential reference resource for materials scientists in this field of research.

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Basic Inorganic Chemistry PDF Author: F. Albert Cotton
Publisher: John Wiley & Sons
ISBN: 0471505323
Category : Science
Languages : en
Pages : 858

Book Description
Explains the basics of inorganic chemistry with a primary emphasis on facts; then uses the student's growing factual knowledge as a foundation for discussing the important principles of periodicity in structure, bonding and reactivity. New to this updated edition: improved treatment of atomic orbitals and properties such as electronegativity, novel approaches to the depiction of ionic structures, nomenclature for transition metal compounds, quantitative approaches to acid-base chemistry, Wade's rules for boranes and carboranes, the chemistry of major new classes of substances including fullerenes and silenes plus a chapter on the inorganic solid state.

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Physics of Ferromagnetism 2e PDF Author: Soshin Chikazumi
Publisher: Oxford University Press, USA
ISBN: 0199564817
Category : Science
Languages : en
Pages : 669

Book Description
This book is a textbook for graduate students and researchers who are interested in ferromagnetism. The emphasis is primarily on explanation of physical concepts rather than on a rigorous theoretical treatment.

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Patient-centered Medicine PDF Author: Moira Stewart
Publisher: Radcliffe Publishing
ISBN: 9781857759815
Category : Medical
Languages : en
Pages : 380

Book Description
Divided into four parts, this volume comprehensively covers the evolution of patient-centered care, the six interactive components of the patient-centered clinical method, teaching and learning, and research including findings and reviews. It explains the basis and development of the clinical method.

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Motivational Interviewing, 2E PDF Author: Thomas M. Kelly
Publisher: Oxford University Press
ISBN: 0197583873
Category : Education
Languages : en
Pages : 457

Book Description
This may be the single most important book you ever buy during your medical training. Rotations come and go, exams come and go, but regardless of specialty, patient-care will be at the heart of your practice. It is no exaggeration to say that motivational interviewing (MI) has transformed the way doctors engage with patients, families, and colleagues alike. MI is among the most powerful tools available to promote behavior change in patients. In an age of chronic diseases (diabetes, hypertension, heart disease, obesity), behavior change is no longer limited to substance use or the field of psychiatry - maladaptive choices and behaviors that negatively impact health outcomes are rampant. There is an explosion of research projects using MI or adaptations of MI in the behavioral health medicine field in the past decade. Hospitalizations can't make people change. How marvelous is it that an evidence-based health behavior change approach (MI) can help people change the outcomes of their illnesses and the course of their lives. This therapeutic approach is not a form of psychotherapy and is not the stuff of cobwebs and old leather couches. MI is readily integrated into regular ward rounds and office visits and provides an effective and efficient approach to patients clinical encounters. Written by experts in the field and medical trainees across medicine, the second edition of the MI guide explores how MI enhances contact with patients from every level of training, following an accessible, succinct approach. This book covers the application of MI method and skills into practice and also includes numerous clinical scenarios, personal reflections and online animated clinical vignettes (video clips) that share the challenges and successes the authors have focused. Furthermore this book is endorsed by the pioneers of MI: William R. Miller & Stephen Rollnick.

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The Physics of Fullerene-Based and Fullerene-Related Materials PDF Author: W. Andreoni
Publisher: Springer Science & Business Media
ISBN: 9780792362340
Category : Science
Languages : en
Pages : 474

Book Description
Krätschmer and Huffman's revolutionary discovery of a new solid phase of carbon, solid C60, in 1990 opened the way to an entire new class of materials with physical properties so diverse that their richness has not yet been fully exploited. Moreover, as a by-product of fullerene research, carbon nanotubes were later identified, from which novel nanostructures originated that are currently fascinating materials scientists worldwide. Rivers of words have been written on both fullerenes and nanotubes, in the form of journal articles, conference proceedings and books. The present book offers, in a concise and self-contained manner, the basics of the science of these materials as well as detailed information on those aspects that have so far been better explored. Structural, electronic and dynamical properties are described as obtained from various measurements and state-of-the-art calculations. Their interrelation emerges as well as their possible dependence on, for example, preparation conditions or methods of investigation. By presenting and comparing data from different sources, experiment and theory, this book helps the reader to rapidly master the basic knowledge, to grasp important issues and critically discuss them. Ultimately, it aims to inspire him or her to find novel ways to approach still open questions. As such, this book is addressed to new researchers in the field as well as experts.

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Biochemistry PDF Author: Donald Voet
Publisher: John Wiley & Sons
ISBN: 1119770645
Category : Biochemistry
Languages : en
Pages : 1490

Book Description
The "Gold Standard" in Biochemistry text books. Biochemistry 4e, is a modern classic that has been thoroughly revised. Don and Judy Voet explain biochemical concepts while offering a unified presentation of life and its variation through evolution. It incorporates both classical and current research to illustrate the historical source of much of our biochemical knowledge.

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Matter and Interactions PDF Author: Ruth W. Chabay
Publisher: John Wiley & Sons
ISBN: 0470503475
Category : Science
Languages : en
Pages : 1128

Book Description
Matter and Interactions offers a modern curriculum for introductory physics (calculus-based). It presents physics the way practicing physicists view their discipline and integrates 20th Century physics and computational physics. The text emphasizes the small number of fundamental principles that underlie the behavior of matter, and models that can explain and predict a wide variety of physical phenomena. Matter and Interactions will be available as a single volume hardcover text and also two paperback volumes.

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Banach Algebras and Applications PDF Author: Mahmoud Filali
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110600439
Category : Mathematics
Languages : en
Pages : 307

Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.