Uniqueness Theorems For Variational Problems By The Method Of Transformation Groups

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Uniqueness Theorems For Variational Problems By The Method Of Transformation Groups

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Author : Wolfgang Reichel
language : en
Publisher: Springer
Release Date : 2004-04-30

Uniqueness Theorems For Variational Problems By The Method Of Transformation Groups written by Wolfgang Reichel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-30 with Mathematics categories.

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.

Uniqueness Theorems For Variational Problems By The Method Of Transformation Groups

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Author : Wolfgang Reichel
language : en
Publisher: Springer
Release Date : 2014-03-12

Uniqueness Theorems For Variational Problems By The Method Of Transformation Groups written by Wolfgang Reichel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Mathematics categories.

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.

Statistical Learning Theory And Stochastic Optimization

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Author : Olivier Catoni
language : en
Publisher: Springer Science & Business Media
Release Date : 2004

Statistical Learning Theory And Stochastic Optimization written by Olivier Catoni and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.

Lectures On The Automorphism Groups Of Kobayashi Hyperbolic Manifolds

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Author : Alexander Isaev
language : en
Publisher: Springer
Release Date : 2007-03-11

Lectures On The Automorphism Groups Of Kobayashi Hyperbolic Manifolds written by Alexander Isaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-11 with Mathematics categories.

In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups that were extensively studied in the 1950s-70s.

A Concise Course On Stochastic Partial Differential Equations

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Author : Claudia Prévôt
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-08

A Concise Course On Stochastic Partial Differential Equations written by Claudia Prévôt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-08 with Mathematics categories.

These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material is included in appendices.

The Method Of Approximate Inverse Theory And Applications

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Author : Thomas Schuster
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-07

The Method Of Approximate Inverse Theory And Applications written by Thomas Schuster and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-07 with Mathematics categories.

Inverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one. Besides medical imaging and non-destructive testing, inverse problems also play an increasing role in other disciplines such as industrial and financial mathematics. Hence, there is a need for stable and efficient solvers. The book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings such as L2-spaces, Hilbert spaces or spaces of distributions. The performance and functionality of the method is demonstrated on several examples from medical imaging and non-destructive testing such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography. The book addresses graduate students and researchers interested in the numerical analysis of inverse problems and regularization techniques or in efficient solvers for the applications mentioned above.

Concentration Inequalities And Model Selection

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Author : Pascal Massart
language : en
Publisher: Springer
Release Date : 2007-04-26

Concentration Inequalities And Model Selection written by Pascal Massart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-26 with Mathematics categories.

Concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn to be essential tools to develop a non asymptotic theory in statistics. This volume provides an overview of a non asymptotic theory for model selection. It also discusses some selected applications to variable selection, change points detection and statistical learning.

Quantum Potential Theory

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Author : Philippe Biane
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-23

Quantum Potential Theory written by Philippe Biane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-23 with Mathematics categories.

This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.

Algebraic Groups And Lie Groups With Few Factors

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Author : Alfonso Di Bartolo
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-17

Algebraic Groups And Lie Groups With Few Factors written by Alfonso Di Bartolo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-17 with Mathematics categories.

This volume treats algebraic groups from a group theoretical point of view and compares the results with the analogous issues in the theory of Lie groups. It examines a classification of algebraic groups and Lie groups having only few subgroups.

Biset Functors For Finite Groups

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Author : serge Bouc
language : en
Publisher: Springer
Release Date : 2010-03-10

Biset Functors For Finite Groups written by serge Bouc and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-10 with Mathematics categories.

This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted to biset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors to long-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting of advanced results in the area, with some new ideas and proofs.