Singularities of integrals

Singularities of integrals
Title Singularities of integrals PDF eBook
Author Frédéric Pham
Publisher Springer Science & Business Media
Pages 218
Release 2011-04-22
Genre Mathematics
ISBN 0857296035

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Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.

Singularities of Differentiable Maps, Volume 2

Singularities of Differentiable Maps, Volume 2
Title Singularities of Differentiable Maps, Volume 2 PDF eBook
Author Elionora Arnold
Publisher Springer Science & Business Media
Pages 500
Release 2012-05-16
Genre Mathematics
ISBN 0817683437

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​​The present volume is the second in a two-volume set entitled Singularities of Differentiable Maps. While the first volume, subtitled Classification of Critical Points and originally published as Volume 82 in the Monographs in Mathematics series, contained the zoology of differentiable maps, that is, it was devoted to a description of what, where, and how singularities could be encountered, this second volume concentrates on elements of the anatomy and physiology of singularities of differentiable functions. The questions considered are about the structure of singularities and how they function.

Boundary Integral and Singularity Methods for Linearized Viscous Flow

Boundary Integral and Singularity Methods for Linearized Viscous Flow
Title Boundary Integral and Singularity Methods for Linearized Viscous Flow PDF eBook
Author C. Pozrikidis
Publisher Cambridge University Press
Pages 276
Release 1992-02-28
Genre Mathematics
ISBN 9780521406932

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In addition to theory, this study focuses on practical application and computer implementation in a coherent introduction to boundary integrals, boundary element and singularity methods for steady and unsteady flow at zero Reynolds numbers.

Bifurcations of Planar Vector Fields

Bifurcations of Planar Vector Fields
Title Bifurcations of Planar Vector Fields PDF eBook
Author Freddy Dumortier
Publisher
Pages 240
Release 2014-01-15
Genre
ISBN 9783662191552

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Methods of Analysis and Solutions of Crack Problems

Methods of Analysis and Solutions of Crack Problems
Title Methods of Analysis and Solutions of Crack Problems PDF eBook
Author George C. Sih
Publisher Springer Science & Business Media
Pages 578
Release 1973-01-31
Genre Science
ISBN 9789001798604

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It is weH known that the traditional failure criteria cannot adequately explain failures which occur at a nominal stress level considerably lower than the ultimate strength of the material. The current procedure for predicting the safe loads or safe useful life of a structural member has been evolved around the discipline oflinear fracture mechanics. This approach introduces the concept of a crack extension force which can be used to rank materials in some order of fracture resistance. The idea is to determine the largest crack that a material will tolerate without failure. Laboratory methods for characterizing the fracture toughness of many engineering materials are now available. While these test data are useful for providing some rough guidance in the choice of materials, it is not clear how they could be used in the design of a structure. The understanding of the relationship between laboratory tests and fracture design of structures is, to say the least, deficient. Fracture mechanics is presently at astandstill until the basic problems of scaling from laboratory models to fuH size structures and mixed mode crack propagation are resolved. The answers to these questions require some basic understanding ofthe theory and will not be found by testing more specimens. The current theory of fracture is inadequate for many reasons. First of aH it can only treat idealized problems where the applied load must be directed normal to the crack plane.

Numerical Integration 1

Numerical Integration 1
Title Numerical Integration 1 PDF eBook
Author W. F. Eberlein
Publisher
Pages 18
Release 1954
Genre Numerical integration
ISBN

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Singular Integrals and Related Topics

Singular Integrals and Related Topics
Title Singular Integrals and Related Topics PDF eBook
Author Shanzhen Lu
Publisher World Scientific
Pages 281
Release 2007
Genre Mathematics
ISBN 9812770569

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This book introduces some important progress in the theory of CalderonOCoZygmund singular integrals, oscillatory singular integrals, and LittlewoodOCoPaley theory over the last decade. It includes some important research results by the authors and their cooperators, such as singular integrals with rough kernels on Block spaces and Hardy spaces, the criterion on boundedness of oscillatory singular integrals, and boundedness of the rough Marcinkiewicz integrals. These results have frequently been cited in many published papers."