Painlevé III: A Case Study in the Geometry of Meromorphic Connections

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Author: Martin A. Guest,Claus Hertling

Publisher: Springer

ISBN: 331966526X

Category: Mathematics

Page: 204

View: 4988

The purpose of this monograph is two-fold: it introduces a conceptual language for the geometrical objects underlying Painlevé equations, and it offers new results on a particular Painlevé III equation of type PIII (D6), called PIII (0, 0, 4, −4), describing its relation to isomonodromic families of vector bundles on P1 with meromorphic connections. This equation is equivalent to the radial sine (or sinh) Gordon equation and, as such, it appears widely in geometry and physics. It is used here as a very concrete and classical illustration of the modern theory of vector bundles with meromorphic connections. Complex multi-valued solutions on C* are the natural context for most of the monograph, but in the last four chapters real solutions on R>0 (with or without singularities) are addressed. These provide examples of variations of TERP structures, which are related to tt∗ geometry and harmonic bundles. As an application, a new global picture o0 is given.

The Geometry of Ecological Interactions

Simplifying Spatial Complexity

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Author: Ulf Dieckmann,Richard Law

Publisher: Cambridge University Press

ISBN: 9780521642941

Category: Mathematics

Page: 564

View: 4886

Spatial ecology, space.

The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds

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Author: Peter B. Gilkey

Publisher: Imperial College Press

ISBN: 1860948588

Category: Curvature

Page: 388

View: 1898

Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and StanilovOCoTsankovOCoVidev theory."

The Geometry of the Word Problem for Finitely Generated Groups

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Author: Noel Brady,Tim Riley,Hamish Short

Publisher: Springer Science & Business Media

ISBN: 9783764379506

Category: Mathematics

Page: 206

View: 3359

The origins of the word problem are in group theory, decidability and complexity. But through the vision of M. Gromov and the language of filling functions, the topic now impacts the world of large-scale geometry. This book contains accounts of many recent developments in Geometric Group Theory and shows the interaction between the word problem and geometry continues to be a central theme. It contains many figures, numerous exercises and open questions.

The Geometry of Biological Time

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Author: Arthur T. Winfree

Publisher: Springer Science & Business Media

ISBN: 9780387989921

Category: Mathematics

Page: 779

View: 8274

Dealing with dynamics of processes that repeat themselves regularly, this revised and updated edition extends the thread from 1980 to the present day, concentrating on areas of interest where there will be much activity in the future. This involves going through spatial biochemical, electrophysiological, and organismic dynamical systems and patterns that were discovered by pursuing the theme of phase singularities introduced in the original book. In particular the work on excitability in cell membranes will be thoroughly updated as will the references throughout the book.

Handbook of the Geometry of Banach Spaces

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Author: William B. Johnson,Joram Lindenstrauss

Publisher: Elsevier

ISBN: 9780444513052

Category: Mathematics

Page: 1866

View: 4714

Encouraged by new perspectives in Banach space theory, the editors present this second volume that opens with an introductory essay that explains the basics of the theory. The rest of the chapters focus on specific directions of Banach space theory or its applications.

The Geometry of Supermanifolds

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Author: C. Bartocci,U. Bruzzo,Daniel Hernández-Ruipérez

Publisher: Springer Science & Business Media

ISBN: 9780792314400

Category: Mathematics

Page: 242

View: 9358

'Et moi, ...• si favait III mmment en revenir, One service mathematics has rendered the je n'y serais point aile:' human race. It has put CXlUImon sense back Iules Verne where it belongs. on the topmost shelf next to the dUlty canister lahelled 'discarded non- The series i. divergent; therefore we may be able to do something with it. Eric T. Bell O. Hesvi.ide 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't!tre of this series.

Notions of Positivity and the Geometry of Polynomials

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Author: Petter Brändén,Mikael Passare,Mihai Putinar

Publisher: Springer Science & Business Media

ISBN: 3034801424

Category: Mathematics

Page: 404

View: 7281

The book consists of solicited articles from a select group of mathematicians and physicists working at the interface between positivity and the geometry, combinatorics or analysis of polynomials of one or several variables. It is dedicated to the memory of Julius Borcea (1968-2009), a distinguished mathematician, Professor at the University of Stockholm. With his extremely original contributions and broad vision, his impact on the topics of the planned volume cannot be underestimated. All contributors knew or have exchanged ideas with Dr. Borcea, and their articles reflect, at least partially, his heritage.