Introduction To The H Principle

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Introduction To The H Principle

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Author : Y. Eliashberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Introduction To The H Principle written by Y. Eliashberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

The latest volume in the AMS's high-profile GSM series. The book presents a very accessible exposition of a powerful, but difficult to explain method of solving Partial Differentiel Equations. Would make an excellent text for courses on modern methods for solvng Partial Differential Equations. Very readable treatise of an important and remarkable technique. Strong bookstore candidate.

Introduction To The H Principle

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Author : Kai Cieliebak
language : en
Publisher:
Release Date : 2024

Introduction To The H Principle written by Kai Cieliebak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Differentiable manifolds categories.

Introduction To The H Principle

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Author : K. Cieliebak
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-30

Introduction To The H Principle written by K. Cieliebak and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-30 with Mathematics categories.

In differential geometry and topology one often deals with systems of partial differential equations as well as partial differential inequalities that have infinitely many solutions whatever boundary conditions are imposed. It was discovered in the 1950s that the solvability of differential relations (i.e., equations and inequalities) of this kind can often be reduced to a problem of a purely homotopy-theoretic nature. One says in this case that the corresponding differential relation satisfies the $h$-principle. Two famous examples of the $h$-principle, the Nash–Kuiper $C^1$-isometric embedding theory in Riemannian geometry and the Smale–Hirsch immersion theory in differential topology, were later transformed by Gromov into powerful general methods for establishing the $h$-principle. The authors cover two main methods for proving the $h$-principle: holonomic approximation and convex integration. The reader will find that, with a few notable exceptions, most instances of the $h$-principle can be treated by the methods considered here. A special emphasis is made on applications to symplectic and contact geometry. The present book is the first broadly accessible exposition of the theory and its applications, making it an excellent text for a graduate course on geometric methods for solving partial differential equations and inequalities. Geometers, topologists, and analysts will also find much value in this very readable exposition of an important and remarkable topic. This second edition of the book is significantly revised and expanded to almost twice of the original size. The most significant addition to the original book is the new part devoted to the method of wrinkling and its applications. Several other chapters (e.g., on multivalued holonomic approximation and foliations) are either added or completely rewritten.

Introduction To The H Principle

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Author : Y. Eliashberg
language : en
Publisher: American Mathematical Soc.
Release Date :

Introduction To The H Principle written by Y. Eliashberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

One of the most powerful modern methods of solving partial differential equations is Gromov's $h$-principle. It has also been, traditionally, one of the most difficult to explain. This book is the first broadly accessible exposition of the principle and its applications. The essence of the $h$-principle is the reduction of problems involving partial differential relations to problems of a purely homotopy-theoretic nature. Two famous examples of the $h$-principle are the Nash-Kuiper$C1$-isometric embedding theory in Riemannian geometry and the Smale-Hirsch immersion theory in differential topology. Gromov transformed these examples into a powerful general method for proving the $h$-principle. Both of these examples and their explanations in terms of the $h$-principle arecovered in detail in the book. The authors cover two main embodiments of the principle: holonomic approximation and convex integration. The first is a version of the method of continuous sheaves. The reader will find that, with a few notable exceptions, most instances of the $h$-principle can be treated by the methods considered here. There are, naturally, many connections to symplectic and contact geometry. The book would be an excellent text for a graduate course on modern methods for solvingpartial differential equations. Geometers and analysts will also find much value in this very readable exposition of an important and remarkable technique.

Smith And Williams Introduction To The Principles Of Drug Design And Action

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Author : H. Jphn Smith
language : en
Publisher: CRC Press
Release Date : 2005-10-10

Smith And Williams Introduction To The Principles Of Drug Design And Action written by H. Jphn Smith and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-10 with Medical categories.

Advances in knowledge and technology have revolutionized the process of drug development, making it possible to design drugs for a given target or disease. Building on the foundation laid by the previous three editions, Smith and Williams Introduction to the Principles of Drug Design and Action, Fourth Edition includes the latest informatio

An Introductory Course On Mathematical Game Theory

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Author : Julio González-Díaz
language : en
Publisher: American Mathematical Society
Release Date : 2021-10-22

An Introductory Course On Mathematical Game Theory written by Julio González-Díaz and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-22 with Mathematics categories.

Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as political science, biology, and, more recently, computer science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises. The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. Cooperative games are explained in detail, with bargaining and TU-games being treated as part of a general framework. The authors stress the relation between game theory and operations research. The book is suitable for a graduate or an advanced undergraduate course on game theory.

An Introduction To Contact Topology

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Author : Hansjörg Geiges
language : en
Publisher: Cambridge University Press
Release Date : 2008-03-13

An Introduction To Contact Topology written by Hansjörg Geiges and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-13 with Mathematics categories.

This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.

An Introduction To Non Life Insurance Mathematics

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Author : Bjørn Sundt
language : en
Publisher: VVW GmbH
Release Date : 1999-10-01

An Introduction To Non Life Insurance Mathematics written by Bjørn Sundt and has been published by VVW GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-01 with Insurance categories.

Introduction To Lie Algebras

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Author : J. I. Hall
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-21

Introduction To Lie Algebras written by J. I. Hall and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-21 with Mathematics categories.

Being both a beautiful theory and a valuable tool, Lie algebras form a very important area of mathematics. This modern introduction targets entry-level graduate students. It might also be of interest to those wanting to refresh their knowledge of the area and be introduced to newer material. Infinite dimensional algebras are treated extensively along with the finite dimensional ones. After some motivation, the text gives a detailed and concise treatment of the Killing–Cartan classification of finite dimensional semisimple algebras over algebraically closed fields of characteristic 0. Important constructions such as Chevalley bases follow. The second half of the book serves as a broad introduction to algebras of arbitrary dimension, including Kac–Moody (KM), loop, and affine KM algebras. Finite dimensional semisimple algebras are viewed as KM algebras of finite dimension, their representation and character theory developed in terms of integrable representations. The text also covers triangular decomposition (after Moody and Pianzola) and the BGG category $mathcal{O}$. A lengthy chapter discusses the Virasoro algebra and its representations. Several applications to physics are touched on via differential equations, Lie groups, superalgebras, and vertex operator algebras. Each chapter concludes with a problem section and a section on context and history. There is an extensive bibliography, and appendices present some algebraic results used in the book.

Embeddings In Manifolds

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Author : Robert J. Daverman
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-10-14

Embeddings In Manifolds written by Robert J. Daverman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-14 with Mathematics categories.

A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embeddings of the same object are equivalent in the sense of differing only by a homeomorphism of the ambient manifold. Knot theory is the special case of spheres smoothly embedded in spheres; in this book, much more general spaces and much more general embeddings are considered. A key aspect of the main problem is taming: when is a topological embedding of a polyhedron equivalent to a piecewise linear embedding? A central theme of the book is the fundamental role played by local homotopy properties of the complement in answering this taming question. The book begins with a fresh description of the various classic examples of wild embeddings (i.e., embeddings inequivalent to piecewise linear embeddings). Engulfing, the fundamental tool of the subject, is developed next. After that, the study of embeddings is organized by codimension (the difference between the ambient dimension and the dimension of the embedded space). In all codimensions greater than two, topological embeddings of compacta are approximated by nicer embeddings, nice embeddings of polyhedra are tamed, topological embeddings of polyhedra are approximated by piecewise linear embeddings, and piecewise linear embeddings are locally unknotted. Complete details of the codimension-three proofs, including the requisite piecewise linear tools, are provided. The treatment of codimension-two embeddings includes a self-contained, elementary exposition of the algebraic invariants needed to construct counterexamples to the approximation and existence of embeddings. The treatment of codimension-one embeddings includes the locally flat approximation theorem for manifolds as well as the characterization of local flatness in terms of local homotopy properties.