A Graphic Apology for Symmetry and Implicitness

Succinct representation and fast access to large amounts of data are challenges of our time. This unique book suggests general approaches of 'complexity of descriptions'.

Author: Alessandra Carbone

Publisher: Oxford Mathematical Monographs

ISBN: 0198507291

Category: Computers

Page: 501

View: 250

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Succinct representation and fast access to large amounts of data are challenges of our time. This unique book suggests general approaches of 'complexity of descriptions'. It deals with a variety of concrete topics and bridges between them, while opening new perspectives and providing promising avenues for the 'complexity puzzle'.

Some Novel Types of Fractal Geometry

G. Macdonald : Symmetric functions and Hall polynomials 2nd edition B. L. R. Shawyer and B. B. Watson : Borel's ... manifolds with special holonomy A. Carbone and S. Semmes : A graphic apology for symmetry and implicitness Johann Boos ...

Author: Stephen Semmes

Publisher: Oxford University Press

ISBN: 0198508069

Category: Mathematics

Page: 164

View: 175

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The present book deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being quite different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of Sobolev or Poincare inequalities,concerning the relationship between the average behaviour of a function and the average behaviour of its small-scale oscillations. Remarkable results in the last few years of Bourdon-Pajot and Laakso have shown that there is much more in the way of geometries like this than has been realized.Examples related to nilpotent Lie groups and Carnot metrics were known previously. On the other hand, 'typical' fractals that might be seen in pictures do not have these same kinds of features. 'Some Novel Types of Fractal Geometry' will be of interest to graduate students and researchers inmathematics, working in various aspects of geometry and analysis.

The Universality of the Radon Transform

... of the symmetric groups I. Györi and G. Ladas: The oscillation theory of delay differential equations J. Heinonen, ... Compact Manifolds with Special Holonomy A. Carbone and S. Semmes: A graphic apology for symmetry and implicitness ...

Author: Leon Ehrenpreis

Publisher: OUP Oxford

ISBN: 9780191523267

Category: Mathematics

Page: 740

View: 242

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Written by a leading scholar in mathematics, this monograph discusses the Radon transform, a field that has wide ranging applications to X-ray technology, partial differential equations, nuclear magnetic resonance scanning, and tomography. In this book, Ehrenpreis focuses on recent research and highlights the strong relationship between high-level pure mathematics and applications of the Radon transform to areas such as medical imaging. The first part of the book discusses parametric and nonparametric Radon transforms, Harmonic Functions and Radon transform on Algebraic Varieties, nonlinear Radon and Fourier transforms, Radon transform on groups, and Radon transform as the interrelation of geometry and analysis. The later parts discuss the extension of solutions of differential equations, Periods of Eisenstein and Poincaré, and some problems of integral geometry arising in tomography. Examples and proofs are provided throughout the book to aid the reader's understanding. This is the latest title in the Oxford Mathematical Monographs, which includes texts and monographs covering many topics of current research interest in pure and applied mathematics. Other titles include: Carbone and Semmes: A graphic apology for symmetry and implicitness; Higson and Roe: Analytic K-Homology; Iwaniec and Martin: Geometric Function Theory and Nonlinear Analysis; Lyons and Qian: System Control and Rough Paths. Also new in paperback Johnson and Lapidus: The Feynman Integral and Feynman's Operational Calculus; Donaldson and Kronheimer: The geometry of four-manifolds.

Threading Homology Through Algebra

... paperback Evens: Cohomology of groups Hoffman and Humphreys: Projective representations of the symmetric groups: ... Compact manifolds with special holonomy Carbone and Semmes: A graphic apology for symmetry and implicitness Boos: ...

Author: G. Boffi

Publisher: Oxford University Press

ISBN: 9780198524991

Category: Mathematics

Page: 255

View: 179

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Aimed at graduate students and researchers in mathematics, this book takes homological themes, such as Koszul complexes and their generalizations, and shows how these can be used to clarify certain problems in selected parts of algebra, as well as their success in solving a number of them.

Fourier Mukai Transforms in Algebraic Geometry

... J.F. Humphreys: Projective representations of the symmetric groups: Q-Functions and Shifted Tableaux B. Amberg, ... Compact Manifolds with Special Holonomy A. Carbone and S. Semmes: A graphic apology for symmetry and implicitness ...

Author: Daniel Huybrechts

Publisher: Oxford University Press on Demand

ISBN: 9780199296866

Category: Mathematics

Page: 307

View: 723

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This work is based on a course given at the Institut de Mathematiques de Jussieu, on the derived category of coherent sheaves on a smooth projective variety. It is aimed at students with a basic knowledge of algebraic geometry and contains full proofs and exercises that aid the reader.

Hilbert Modular Forms and Iwasawa Theory

... paperback Evens: Cohomology of groups Hoffman and Humphreys: Projective representations of the symmetric groups: ... Compact manifolds with special holonomy Carbone and Semmes: A graphic apology for symmetry and implicitness Boos: ...

Author: Haruzo Hida

Publisher: Clarendon Press

ISBN: 9780191513879

Category: Mathematics

Page: 420

View: 621

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The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, authored by a leading researcher, describes the striking applications that have been found for this technique. In the book, the deformation theoretic techniques of Wiles-Taylor are first generalized to Hilbert modular forms (following Fujiwara's treatment), and some applications found by the author are then discussed. With many exercises and open questions given, this text is ideal for researchers and graduate students entering this research area.

The Porous Medium Equation

... paperback Evens: Cohomology of groups Hoffman and Humphreys: Projective representations of the symmetric groups: ... Compact manifolds with special holonomy Carbone and Semmes: A graphic apology for symmetry and implicitness Boos: ...

Author: Juan Luis Vazquez

Publisher: Oxford University Press on Demand

ISBN: 9780198569039

Category: Mathematics

Page: 624

View: 172

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Aimed at research students and academics in mathematics and engineering, as well as engineering specialists, this book provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation.

Classical and Modern Methods in Summability

... Galois geometries P. N. Hoffman and J. F. Humphreys : Projective representations of the symmetric groups I. Györi ... manifolds with special holonomy A. Carbone and S. Semmes : A graphic apology for symmetry and implicitness Johann ...

Author: Johann Boos

Publisher: Clarendon Press

ISBN: 019850165X

Category: Mathematics

Page: 586

View: 945

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Summability is a mathematical topic with a long tradition and many applications in, for example, function theory, number theory, and stochastics. It was originally based on classical analytical methods, but was strongly influenced by modern functional analytical methods during the last seven decades. The present book aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used. Part I contains a short general introduction to summability, the basic classical theory concerning mainly inclusion theorems and theorems of the Silverman-Toeplitz type, a presentation of the most important classes of summability methods, Tauberian theorems, and applications of matrix methods. The proofs in Part I are exclusively done by applying classical analytical methods. Part II is concerned with modern functional analytical methods in summability, and contains the essential functional analytical basis required in later parts of the book, topologization of sequence spaces as K- and KF-spaces, domains of matrix methods as FK-spaces and their topological structure. In this part the proofs are of functional analytical nature only. Part III of the present book deals with topics in summability and topological sequence spaces which require the combination of classical and modern methods. It covers investigations of the constistency of matrix methods and of the bounded domain of matrix methods via Saks space theory, and the presentation of some aspects in topological sequence spaces. Lecturers, graduate students, and researchers working in summability and related topics will find this book a useful introduction and reference work.

The Feynman Integral and Feynman s Operational Calculus

... General Galois geometrics P.N. Hoffman and J.F. Humpherys : Projective representations of the symmetric groups I. ... manifolds with special holonomy A. Carbone and S. Semmes : A graphic apology for symmetry and implicitness Johann ...

Author: Gerald W. Johnson

Publisher: Clarendon Press

ISBN: 9780191546266

Category: Mathematics

Page: 790

View: 954

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This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results.