Analytic and Geometric Study of Stratified Spaces

Analytic and Geometric Study of Stratified Spaces PDF

Author: Markus J. Pflaum

Publisher: Springer

Published: 2003-07-01

Total Pages: 233

ISBN-13: 3540454365

DOWNLOAD EBOOK →

The book provides an introduction to stratification theory leading the reader up to modern research topics in the field. The first part presents the basics of stratification theory, in particular the Whitney conditions and Mather's control theory, and introduces the notion of a smooth structure. Moreover, it explains how one can use smooth structures to transfer differential geometric and analytic methods from the arena of manifolds to stratified spaces. In the second part the methods established in the first part are applied to particular classes of stratified spaces like for example orbit spaces. Then a new de Rham theory for stratified spaces is established and finally the Hochschild (co)homology theory of smooth functions on certain classes of stratified spaces is studied. The book should be accessible to readers acquainted with the basics of topology, analysis and differential geometry.

Topology of Stratified Spaces

Topology of Stratified Spaces PDF

Author: Greg Friedman

Publisher: Cambridge University Press

Published: 2011-03-28

Total Pages: 491

ISBN-13: 052119167X

DOWNLOAD EBOOK →

This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups PDF

Author: Wolfgang Reichel

Publisher: Springer Science & Business Media

Published: 2004-05-13

Total Pages: 172

ISBN-13: 9783540218395

DOWNLOAD EBOOK →

A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying space V does {\cal L} have at most one critical point? A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.

Pseudo-Differential Operators

Pseudo-Differential Operators PDF

Author: Hans G. Feichtinger

Publisher: Springer

Published: 2008-08-15

Total Pages: 235

ISBN-13: 3540682686

DOWNLOAD EBOOK →

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.

Point Estimation of Root Finding Methods

Point Estimation of Root Finding Methods PDF

Author: Miodrag Petkovic

Publisher: Springer

Published: 2008-05-29

Total Pages: 222

ISBN-13: 3540778519

DOWNLOAD EBOOK →

The problem of solving nonlinear equations and systems of equations ranks among the most signi?cant in the theory and practice, not only of applied mathematicsbutalsoofmanybranchesofengineeringsciences,physics,c- puter science, astronomy, ?nance, and so on. A glance at the bibliography and the list of great mathematicians who have worked on this topic points to a high level of contemporary interest. Although the rapid development of digital computers led to the e?ective implementation of many numerical methods, in practical realization, it is necessary to solve various problems such as computational e?ciency based on the total central processor unit time, the construction of iterative methods which possess a fast convergence in the presence of multiplicity (or clusters) of a desired solution, the control of rounding errors, information about error bounds of obtained approximate solution, stating computationally veri?able initial conditions that ensure a safe convergence, etc. It is the solution of these challenging problems that was the principal motivation for the present study. In this book, we are mainly concerned with the statement and study of initial conditions that provide the guaranteed convergence of an iterative method for solving equations of the form f(z) = 0. The traditional approach to this problem is mainly based on asymptotic convergence analysis using some strong hypotheses on di?erentiability and derivative bounds in a rather wide domain.

Stable Approximate Evaluation of Unbounded Operators

Stable Approximate Evaluation of Unbounded Operators PDF

Author: C. W. Groetsch

Publisher: Springer Science & Business Media

Published: 2007

Total Pages: 134

ISBN-13: 3540399429

DOWNLOAD EBOOK →

Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.

Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems PDF

Author: Heinz Hanßmann

Publisher: Springer

Published: 2006-10-18

Total Pages: 248

ISBN-13: 3540388966

DOWNLOAD EBOOK →

This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.

Lanterna Rally - Theme by Grace Themes