Foundations of Computational Mathematics, Budapest 2011

Foundations of Computational Mathematics, Budapest 2011

Author: Society for the Foundation of Computational Mathematics

Publisher: Cambridge University Press

Published: 2013

Total Pages: 249

ISBN-13: 1107604079

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A diverse collection of articles by leading experts in computational mathematics, written to appeal to established researchers and non-experts.


Analytic Semigroups and Semilinear Initial Boundary Value Problems

Analytic Semigroups and Semilinear Initial Boundary Value Problems

Author: Kazuaki Taira

Publisher: Cambridge University Press

Published: 2016-04-28

Total Pages: 348

ISBN-13: 1316757358

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A careful and accessible exposition of a functional analytic approach to initial boundary value problems for semilinear parabolic differential equations, with a focus on the relationship between analytic semigroups and initial boundary value problems. This semigroup approach is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of pseudo-differential operators, one of the most influential works in the modern history of analysis. Complete with ample illustrations and additional references, this new edition offers both streamlined analysis and better coverage of important examples and applications. A powerful method for the study of elliptic boundary value problems, capable of further extensive development, is provided for advanced undergraduates or beginning graduate students, as well as mathematicians with an interest in functional analysis and partial differential equations.


Graded Rings and Graded Grothendieck Groups

Graded Rings and Graded Grothendieck Groups

Author: Roozbeh Hazrat

Publisher: Cambridge University Press

Published: 2016-05-26

Total Pages: 244

ISBN-13: 1316727947

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This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.


Dynamics and Analytic Number Theory

Dynamics and Analytic Number Theory

Author: Dzmitry Badziahin

Publisher: Cambridge University Press

Published: 2016-11-10

Total Pages: 341

ISBN-13: 1107552370

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Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.


Regular and Irregular Holonomic D-Modules

Regular and Irregular Holonomic D-Modules

Author: Masaki Kashiwara

Publisher: Cambridge University Press

Published: 2016-05-26

Total Pages: 119

ISBN-13: 1316613453

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A unified treatment of the Riemann-Hilbert correspondence for (not necessarily regular) holonomic D-modules using indsheaves.


Polynomials and the mod 2 Steenrod Algebra

Polynomials and the mod 2 Steenrod Algebra

Author: Grant Walker

Publisher: Cambridge University Press

Published: 2018

Total Pages: 371

ISBN-13: 1108414486

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The first of two volumes covering the Steenrod algebra and its various applications. Suitable as a graduate text.


Geometry in a Fréchet Context

Geometry in a Fréchet Context

Author: C. T. J. Dodson

Publisher: Cambridge University Press

Published: 2016

Total Pages: 315

ISBN-13: 1316601951

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A new approach to studying Fréchet geometry using projective limits of geometrical objects modelled on Banach spaces.


Random Walks and Heat Kernels on Graphs

Random Walks and Heat Kernels on Graphs

Author: Martin T. Barlow

Publisher: Cambridge University Press

Published: 2017-02-23

Total Pages: 239

ISBN-13: 1108124593

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This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincaré inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.