The Theory of Singularities and Its Applications

The Theory of Singularities and Its Applications

Author: Vladimir Igorevich Arnolʹd

Publisher: Cambridge University Press

Published: 1991-05-31

Total Pages: 88

ISBN-13: 9780521422802

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In this book, which is based on lectures given in Pisa under the auspices of the Accademia Nazionale dei Lincei, the distinguished mathematician Vladimir Arnold describes those singularities encountered in different branches of mathematics. He avoids giving difficult proofs of all the results in order to provide the reader with a concise and accessible overview of the many guises and areas in which singularities appear, such as geometry and optics; optimal control theory and algebraic geometry; reflection groups and dynamical systems and many more. This will be an excellent companion for final year undergraduates and graduates whose area of study brings them into contact with singularities.


Dynamical Systems VI

Dynamical Systems VI

Author: Vladimir Igorevich Arnold

Publisher: Springer Science & Business Media

Published: 1993

Total Pages: 264

ISBN-13: 9783540505839

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'EMS 6' is the latest volume in the sub series 'Dynamical Systems of the Encyclopaedia'. It is the first of two volumes covering Singularity Theory, which, besides its fundamental use in Dynamical Systems and Bifurcation Theory, is an important part of other fields such as algebraic geometry, differential geometry and geometric optics.


Singularities of Caustics and Wave Fronts

Singularities of Caustics and Wave Fronts

Author: Vladimir Arnold

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 271

ISBN-13: 9401133301

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One service mathematics has rendered the 'Et moi ...) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.


Valuation Theory and Its Applications

Valuation Theory and Its Applications

Author: Franz-Viktor Kuhlmann

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 472

ISBN-13:

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This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). The special feature of this book is its focus on current applications of valuation theory to a broad range of topics. This first volume contains research and survey papers on a variety of valuation-theoretic topics, including rigid analytic geometry, real algebraic geometry, resolution of singularities, noncommutative valuation theory, valuations on fields, and Galois theory. Also included is a paper on the history of valuation theory. The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.


Introduction to Singularities and Deformations

Introduction to Singularities and Deformations

Author: Gert-Martin Greuel

Publisher: Springer Science & Business Media

Published: 2007-02-23

Total Pages: 482

ISBN-13: 3540284192

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Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.


Tight Closure and Its Applications

Tight Closure and Its Applications

Author: Craig Huneke

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 152

ISBN-13: 082180412X

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This monograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995.


Singularities Physics Engineering Secohb

Singularities Physics Engineering Secohb

Author: SENTHILKUMARAN

Publisher: IOP Publishing Limited

Published: 2024-01-25

Total Pages: 0

ISBN-13: 9780750349802

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The book gives a thorough introduction to singularities and their development. It explains in detail important topics such as the types of singularities, their properties, detection and application, and emerging research trends.


Functions of Several Complex Variables and Their Singularities

Functions of Several Complex Variables and Their Singularities

Author: Wolfgang Ebeling

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 334

ISBN-13: 0821833197

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The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.


Geometric Measure Theory and the Calculus of Variations

Geometric Measure Theory and the Calculus of Variations

Author: William K. Allard

Publisher: American Mathematical Soc.

Published: 1986

Total Pages: 482

ISBN-13: 0821814702

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Includes twenty-six papers that survey a cross section of work in modern geometric measure theory and its applications in the calculus of variations. This title provides an access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field.


Singularity Theory and its Applications

Singularity Theory and its Applications

Author: David Mond

Publisher: Springer

Published: 2006-11-14

Total Pages: 416

ISBN-13: 3540470603

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A workshop on Singularities, Bifurcation and Dynamics was held at Warwick in July 1989 as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory, and applications in the sciences. The papers are orginal research, stimulated by the symposium and workshops: All have been refereed, and none will appear elsewhere. The main topic, deformation theory, is represented by several papers on descriptions of the bases of versal deformations, and several more on descriptions of the generic fibres. Other topics include stratifications, and applications to differential geometry.