Lecture Notes On O Minimal Structures And Real Analytic Geometry
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Lecture Notes On O Minimal Structures And Real Analytic Geometry
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Author : Chris Miller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-14
Lecture Notes On O Minimal Structures And Real Analytic Geometry written by Chris Miller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.
This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations.
Lecture Notes In Real Algebraic And Analytic Geometry
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Author :
language : de
Publisher: Cuvillier Verlag
Release Date : 2005-08-21
Lecture Notes In Real Algebraic And Analytic Geometry written by and has been published by Cuvillier Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-21 with Mathematics categories.
We presume throughout some familiarity with basic model theory, in particular with the notion of a definable set. An excellent reference is [24]. A dense linearly ordered structure M= (M,
Lecture Notes On O Minimal Structures And Real Analytic Geometry
DOWNLOAD
Author : Chris Miller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-14
Lecture Notes On O Minimal Structures And Real Analytic Geometry written by Chris Miller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.
This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations.
Handbook Of Geometry And Topology Of Singularities V Foliations
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Author : Felipe Cano
language : en
Publisher: Springer Nature
Release Date :
Handbook Of Geometry And Topology Of Singularities V Foliations written by Felipe Cano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Tame Topology And O Minimal Structures
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Author : Lou Van den Dries
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-07
Tame Topology And O Minimal Structures written by Lou Van den Dries 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 1998-05-07 with Mathematics categories.
These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.
O Minimal Structures
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Author : Mário J. Edmundo
language : en
Publisher: Cuvillier Verlag
Release Date : 2005
O Minimal Structures written by Mário J. Edmundo and has been published by Cuvillier Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Tame Topology And O Minimal Structures
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Author : Lou Van den Dries
language : en
Publisher:
Release Date : 2014-05-14
Tame Topology And O Minimal Structures written by Lou Van den Dries and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
These notes give a self-contained treatment of the theory of o-minimal structures.
Analyzable Functions And Applications
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Author : Ovidiu Costin
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Analyzable Functions And Applications written by Ovidiu Costin 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 2005 with Asymptotic expansions categories.
The theory of analyzable functions is a technique used to study a wide class of asymptotic expansion methods and their applications in analysis, difference and differential equations, partial differential equations and other areas of mathematics. Key ideas in the theory of analyzable functions were laid out by Euler, Cauchy, Stokes, Hardy, E. Borel, and others. Then in the early 1980s, this theory took a great leap forward with the work of J. Ecalle. Similar techniques and conceptsin analysis, logic, applied mathematics and surreal number theory emerged at essentially the same time and developed rapidly through the 1990s. The links among various approaches soon became apparent and this body of ideas is now recognized as a field of its own with numerous applications. Thisvolume stemmed from the International Workshop on Analyzable Functions and Applications held in Edinburgh (Scotland). The contributed articles, written by many leading experts, are suitable for graduate students and researchers interested in asymptotic methods.
Introduction To Lipschitz Geometry Of Singularities
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Author : Walter Neumann
language : en
Publisher: Springer Nature
Release Date : 2021-01-11
Introduction To Lipschitz Geometry Of Singularities written by Walter Neumann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-11 with Mathematics categories.
This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves. While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category. The book is aimed at graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.
Asymptotic Differential Algebra And Model Theory Of Transseries
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Author : Matthias Aschenbrenner
language : en
Publisher: Princeton University Press
Release Date : 2017-06-06
Asymptotic Differential Algebra And Model Theory Of Transseries written by Matthias Aschenbrenner and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-06 with Mathematics categories.
Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.