Hamiltonian And Lagrangian Flows On Center Manifolds
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Hamiltonian And Lagrangian Flows On Center Manifolds
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Author : Alexander Mielke
language : en
Publisher: Springer
Release Date : 2006-11-14
Hamiltonian And Lagrangian Flows On Center Manifolds written by Alexander Mielke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists, from graduate student level.
Hamiltonian And Lagrangian Flows On Center Manifolds
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Author : Alexander Mielke
language : en
Publisher:
Release Date : 1991
Hamiltonian And Lagrangian Flows On Center Manifolds written by Alexander Mielke and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
Topics In Finite Elasticity
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Author : Michael Hayes
language : en
Publisher: Springer
Release Date : 2014-05-04
Topics In Finite Elasticity written by Michael Hayes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Science categories.
More than fifty years ago, Professor R. S. Rivlin pioneered developments in both the theory and experiments of rubber elasticity. These together with his other fundamental studies contributed to a revitalization of the theory of finite elasticity, which had been dormant, since the basic understanding was completed in the nineteenth century. This book with chapters on foundation, models, universal results, wave propagation, qualitative theory and phase transitions, indicates that the subject he reinvigorated has remainded remarkably vibran and has continued to present significant deep mathematical and experimental challenges.
Nonlinear Wave Equations
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Author : Satyanad Kichenassamy
language : en
Publisher: CRC Press
Release Date : 2021-05-30
Nonlinear Wave Equations written by Satyanad Kichenassamy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-30 with Mathematics categories.
This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.
The Blocking Technique Weighted Mean Operators And Hardy S Inequality
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Author : Karl-Goswin Grosse-Erdmann
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-01-19
The Blocking Technique Weighted Mean Operators And Hardy S Inequality written by Karl-Goswin Grosse-Erdmann 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 1998-01-19 with Mathematics categories.
This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa. Such norms appear throughout analysis. The blocking technique is a powerful, yet elementary, tool whose usefulnes is demonstrated in the book. In particular, it is shown to lead to the solution of three recent problems of Bennett concerning the inequalities of Hardy and Copson. The book is addressed to researchers and graduate students. An interesting feature is that it contains a dictionary of transformations between section and block norms and will thus be useful to researchers as a reference text. The book requires no knowledge beyond an introductory course in functional analysis.
Projective Modules And Complete Intersections
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Author : Satya Mandal
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-10-10
Projective Modules And Complete Intersections written by Satya Mandal 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 1997-10-10 with Mathematics categories.
In these notes on "Projective Modules and Complete Intersections" an account on the recent developments in research on this subject is presented. The author's preference for the technique of Patching isotopic isomorphisms due to Quillen, formalized by Plumsted, over the techniques of elementary matrices is evident here. The treatment of Basic Element theory here incorporates Plumstead's idea of the "generalized dimension functions". These notes are highly selfcontained and should be accessible to any graduate student in commutative algebra or algebraic geometry. They include fully self-contained presentations of the theorems of Ferrand-Szpiro, Cowsik-Nori and the techniques of Lindel.
Lie Algebras And Lie Groups
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Author : Jean-Pierre Serre
language : en
Publisher: Springer
Release Date : 2009-02-07
Lie Algebras And Lie Groups written by Jean-Pierre Serre and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-07 with Mathematics categories.
This book reproduces J-P. Serre's 1964 Harvard lectures. The aim is to introduce the reader to the "Lie dictionary": Lie algebras and Lie groups. Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on p-adic fields. Some knowledge of algebra and calculus is required of the reader, but the text is easily accessible to graduate students, and to mathematicians at large.
Small Amplitude Steady Water Waves With Vorticity
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Author : Evgeniy Lokharu
language : en
Publisher: Linköping University Electronic Press
Release Date : 2017-01-30
Small Amplitude Steady Water Waves With Vorticity written by Evgeniy Lokharu and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-30 with categories.
The problem of describing two-dimensional traveling water waves is considered. The water region is of finite depth and the interface between the region and the air is given by the graph of a function. We assume the flow to be incompressible and neglect the effects of surface tension. However we assume the flow to be rotational so that the vorticity distribution is a given function depending on the values of the stream function of the flow. The presence of vorticity increases the complexity of the problem and also leads to a wider class of solutions. First we study unidirectional waves with vorticity and verify the Benjamin-Lighthill conjecture for flows whose Bernoulli constant is close to the critical one. For this purpose it is shown that every wave, whose slope is bounded by a fixed constant, is either a Stokes or a solitary wave. It is proved that the whole set of these waves is uniquely parametrised (up to translation) by the flow force which varies between its values for the supercritical and subcritical shear flows of constant depth. We also study large-amplitude unidirectional waves for which we prove bounds for the free-surface profile and for Bernoulli’s constant. Second, we consider small-amplitude waves over flows with counter currents. Such flows admit layers, where the fluid flows in different directions. In this case we prove that the initial nonlinear free-boundary problem can be reduced to a finite-dimensional Hamiltonian system with a stable equilibrium point corresponding to a uniform stream. As an application of this result, we prove the existence of non-symmetric wave profiles. Furthermore, using a different method, we prove the existence of periodic waves with an arbitrary number of crests per period.
Mathematical Research Today And Tomorrow
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Author : Carlos Casacuberta
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-12-14
Mathematical Research Today And Tomorrow written by Carlos Casacuberta 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 1992-12-14 with Mathematics categories.
The Symposium on the Current State and Prospects of Mathematics was held in Barcelona from June 13 to June 18, 1991. Seven invited Fields medalists gavetalks on the development of their respective research fields. The contents of all lectures were collected in the volume, together witha transcription of a round table discussion held during the Symposium. All papers are expository. Some parts include precise technical statements of recent results, but the greater part consists of narrative text addressed to a very broad mathematical public. CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S. Novikov: Role of Integrable Models in the Development of Mathematics.- S.-T. Yau: The Current State and Prospects of Geometry and Nonlinear Differential Equations.- A. Connes: Noncommutative Geometry.- S. Smale: Theory of Computation.- V. Jones: Knots in Mathematics and Physics.- G. Faltings: Recent Progress in Diophantine Geometry.
Equadiff 2003 Proceedings Of The International Conference On Differential Equations
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Author : Freddy Dumortier
language : en
Publisher: World Scientific
Release Date : 2005-02-23
Equadiff 2003 Proceedings Of The International Conference On Differential Equations written by Freddy Dumortier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-23 with Mathematics categories.
This comprehensive volume contains the state of the art on ODE's and PDE's of different nature, functional differential equations, delay equations, and others, mostly from the dynamical systems point of view.A broad range of topics are treated through contributions by leading experts of their fields, presenting the most recent developments. A large variety of techniques are being used, stressing geometric, topological, ergodic and numerical aspects.The scope of the book is wide, ranging from pure mathematics to various applied fields. Examples of the latter are provided by subjects from earth and life sciences, classical mechanics and quantum-mechanics, among others.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences