Euler Systems

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Euler Systems. (AM-147), Volume 147

Author : Karl Rubin
Publisher : Princeton University Press
ISBN 13 : 1400865204
Total Pages : 241 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Euler Systems. (AM-147), Volume 147 by : Karl Rubin

Download or read book Euler Systems. (AM-147), Volume 147 written by Karl Rubin and published by Princeton University Press. This book was released on 2014-09-08 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.

Euler Systems

Author : Karl Rubin
Publisher : Princeton University Press
ISBN 13 : 0691050767
Total Pages : 240 pages
Book Rating : 4.6/5 (91 download)

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Book Synopsis Euler Systems by : Karl Rubin

Download or read book Euler Systems written by Karl Rubin and published by Princeton University Press. This book was released on 2000-05-21 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.

Passivity-based Control of Euler-Lagrange Systems

Author : Romeo Ortega
Publisher : Springer Science & Business Media
ISBN 13 : 1447136039
Total Pages : 560 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Passivity-based Control of Euler-Lagrange Systems by : Romeo Ortega

Download or read book Passivity-based Control of Euler-Lagrange Systems written by Romeo Ortega and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essence of this work is the control of electromechanical systems, such as manipulators, electric machines, and power converters. The common thread that links together the results presented here is the passivity property, which is at present in numerous electrical and mechanical systems, and which has great relevance in control engineering at this time. Amongst other topics, the authors cover: Euler-Lagrange Systems, Mechanical Systems, Generalised AC Motors, Induction Motor Control, Robots with AC Drives, and Perspectives and Open Problems. The authors have extensive experience of research and application in the field of control of electromechanical systems, which they have summarised here in this self-contained volume. While written in a strictly mathematical way, it is also elementary, and will be accessible to a wide-ranging audience, including graduate students as well as practitioners and researchers in this field.

Circular Distributions and Euler Systems

Author : Soogil Seo
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.:/5 (34 download)

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Book Synopsis Circular Distributions and Euler Systems by : Soogil Seo

Download or read book Circular Distributions and Euler Systems written by Soogil Seo and published by . This book was released on 1999 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Galois Representations in Arithmetic Algebraic Geometry

Author : A. J. Scholl
Publisher : Cambridge University Press
ISBN 13 : 0521644194
Total Pages : 506 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Galois Representations in Arithmetic Algebraic Geometry by : A. J. Scholl

Download or read book Galois Representations in Arithmetic Algebraic Geometry written by A. J. Scholl and published by Cambridge University Press. This book was released on 1998-11-26 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.

The Grothendieck Festschrift, Volume I

Author : Pierre Cartier
Publisher : Springer Science & Business Media
ISBN 13 : 0817645748
Total Pages : 514 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis The Grothendieck Festschrift, Volume I by : Pierre Cartier

Download or read book The Grothendieck Festschrift, Volume I written by Pierre Cartier and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-volume work contains articles collected on the occasion of Alexander Grothendieck’s sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world’s greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck’s own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.

Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

Author : Robert Bryant
Publisher : University of Chicago Press
ISBN 13 : 9780226077932
Total Pages : 230 pages
Book Rating : 4.0/5 (779 download)

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Book Synopsis Exterior Differential Systems and Euler-Lagrange Partial Differential Equations by : Robert Bryant

Download or read book Exterior Differential Systems and Euler-Lagrange Partial Differential Equations written by Robert Bryant and published by University of Chicago Press. This book was released on 2003-07 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Exterior Differential Systems, the authors present the results of their ongoing development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincaré-Cartan forms. They also cover certain aspects of the theory of exterior differential systems, which provides the language and techniques for the entire study. Because it plays a central role in uncovering geometric properties of differential equations, the method of equivalence is particularly emphasized. In addition, the authors discuss conformally invariant systems at length, including results on the classification and application of symmetries and conservation laws. The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws. This timely synthesis of partial differential equations and differential geometry will be of fundamental importance to both students and experienced researchers working in geometric analysis.

Integrable Hamiltonian Systems

Author : A.V. Bolsinov
Publisher : CRC Press
ISBN 13 : 0203643429
Total Pages : 752 pages
Book Rating : 4.2/5 (36 download)

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Book Synopsis Integrable Hamiltonian Systems by : A.V. Bolsinov

Download or read book Integrable Hamiltonian Systems written by A.V. Bolsinov and published by CRC Press. This book was released on 2004-02-25 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,

Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations

Author : Simon Markfelder
Publisher : Springer Nature
ISBN 13 : 3030837858
Total Pages : 244 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations by : Simon Markfelder

Download or read book Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations written by Simon Markfelder and published by Springer Nature. This book was released on 2021-10-20 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies the convex integration method to multi-dimensional compressible Euler equations in the barotropic case as well as the full system with temperature. The convex integration technique, originally developed in the context of differential inclusions, was applied in the groundbreaking work of De Lellis and Székelyhidi to the incompressible Euler equations, leading to infinitely many solutions. This theory was later refined to prove non-uniqueness of solutions of the compressible Euler system, too. These non-uniqueness results all use an ansatz which reduces the equations to a kind of incompressible system to which a slight modification of the incompressible theory can be applied. This book presents, for the first time, a generalization of the De Lellis–Székelyhidi approach to the setting of compressible Euler equations. The structure of this book is as follows: after providing an accessible introduction to the subject, including the essentials of hyperbolic conservation laws, the idea of convex integration in the compressible framework is developed. The main result proves that under a certain assumption there exist infinitely many solutions to an abstract initial boundary value problem for the Euler system. Next some applications of this theorem are discussed, in particular concerning the Riemann problem. Finally there is a survey of some related results. This self-contained book is suitable for both beginners in the field of hyperbolic conservation laws as well as for advanced readers who already know about convex integration in the incompressible framework.

Kolyvagin Systems

Author : Barry Mazur
Publisher : American Mathematical Soc.
ISBN 13 : 0821835122
Total Pages : 112 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Kolyvagin Systems by : Barry Mazur

Download or read book Kolyvagin Systems written by Barry Mazur and published by American Mathematical Soc.. This book was released on 2004 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their introduction by Kolyvagin, Euler systems have been used in several important applications in arithmetic algebraic geometry. For a $p$-adic Galois module $T$, Kolyvagin's machinery is designed to provide an upper bound for the size of the Selmer group associated to the Cartier dual $T^*$. Given an Euler system, Kolyvagin produces a collection of cohomology classes which he calls ``derivative'' classes. It is these derivative classes which are used to bound the dual Selmer group. The starting point of the present memoir is the observation that Kolyvagin's systems of derivative classes satisfy stronger interrelations than have previously been recognized. We call a system of cohomology classes satisfying these stronger interrelations a Kolyvagin system. We show that the extra interrelations give Kolyvagin systems an interesting rigid structure which in many ways resembles (an enriched version of) the ``leading term'' of an $L$-function. By making use of the extra rigidity we also prove that Kolyvagin systems exist for many interesting representations for which no Euler system is known, and further that there are Kolyvagin systems for these representations which give rise to exact formulas for the size of the dual Selmer group, rather than just upper bounds.

Physics of Long-range Interacting Systems

Author : Alessandro Campa
Publisher : Oxford University Press, USA
ISBN 13 : 0199581932
Total Pages : 429 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis Physics of Long-range Interacting Systems by : Alessandro Campa

Download or read book Physics of Long-range Interacting Systems written by Alessandro Campa and published by Oxford University Press, USA. This book was released on 2014 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with an important class of many-body systems: those where the interaction potential decays slowly for large inter-particle distances; in particular, systems where the decay is slower than the inverse inter-particle distance raised to the dimension of the embedding space. Gravitational and Coulomb interactions are the most prominent examples, however it has become clear that long-range interactions are more common than previously thought. A satisfactory understanding of properties, generally considered as oddities only a couple of decades ago, has now been reached: ensemble inequivalence, negative specific heat, negative susceptibility, ergodicity breaking, out-of-equilibrium quasi-stationary-states, anomalous diffusion. The book, intended for Master and PhD students, tries to gradually acquaint the reader with the subject. The first two parts describe the theoretical and computational instruments needed to address the study of both equilibrium and dynamical properties of systems subject to long-range forces. The third part of the book is devoted to applications of such techniques to the most relevant examples of long-range systems.

Introduction to Avionics Systems

Author : R.P.G. Collinson
Publisher : Springer Science & Business Media
ISBN 13 : 9781402072789
Total Pages : 804 pages
Book Rating : 4.0/5 (727 download)

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Book Synopsis Introduction to Avionics Systems by : R.P.G. Collinson

Download or read book Introduction to Avionics Systems written by R.P.G. Collinson and published by Springer Science & Business Media. This book was released on 2002-12-31 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evaluation copies are available. Please contact [email protected]. Provide the course number, number of students and present textbook used.Introduction to Avionics Systems, Second Edition explains the basic principles and underlying theory of modern avionic systems and how they are implemented with current technology for both civil and military aircraft in a clear and easy to read manner.All systems are explained so that their design and performance can be understood and analysed. Worked examples are included to illustrate the application of the theory and principles covered. The latest developments and directions of research for future systems are included.This new second edition has approximately 25% new material and takes into account the technology developments which have taken place since the first edition was published in January 1996. The book is well illustrated with line drawings and photos, with some in colour where appropriate.Readership: Graduates (or equivalent) from a range of disciplines entering the avionics and aerospace industries.Engineers at all levels engaged in the design and development of avionic systems and equipment in the avionic and aerospace industries.Students and post graduate students taking avionics and aeronautical engineering courses.Staff in the armed services and civil airlines engaged in the support or operation of aircraft who wish to acquire a deeper understanding of the design and implementation of avionic systems and equipment.

Microscopic Simulations of Complex Hydrodynamic Phenomena

Author : Michel Mareschal
Publisher : Springer Science & Business Media
ISBN 13 : 1489923144
Total Pages : 437 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Microscopic Simulations of Complex Hydrodynamic Phenomena by : Michel Mareschal

Download or read book Microscopic Simulations of Complex Hydrodynamic Phenomena written by Michel Mareschal and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a NATO Advanced Study Institute which was held in Alghero, Sardinia, in July 1991. The development of computers in the recent years has lead to the emergence of unconventional ideas aiming at solving old problems. Among these, the possibility of computing directly fluid flows from the trajectories of constituent particles has been much exploited in the last few years: lattice gases cellular automata and more generally Molecular Dynamics have been used to reproduce and study complex flows. Whether or not these methods may someday compete with more traditional approaches is a question which cannot be answered at the present time: it will depend on the new computer architectures as well as on the possibility to develop very simple models to reproduce the most complex phenomena taking place in the approach of fully developed turbulence or plastic flows. In any event, these molecular methods are already used, and sometimes in an applied engineering context, to study strong shock waves, chemistry induced shocks or motion of dislocations in plastic flows, that is in domains where a fully continuum description appears insufficient. The main topic of our Institute was the molecular simulations of fluid flows. The project to hold this Institute was made three years ago, in the summer of 1989 during a NATO workshop in Brussels on the same subject.

Nonlinear Systems and Their Remarkable Mathematical Structures

Author : Taylor & Francis Group
Publisher : CRC Press
ISBN 13 : 9780367732431
Total Pages : 582 pages
Book Rating : 4.7/5 (324 download)

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Book Synopsis Nonlinear Systems and Their Remarkable Mathematical Structures by : Taylor & Francis Group

Download or read book Nonlinear Systems and Their Remarkable Mathematical Structures written by Taylor & Francis Group and published by CRC Press. This book was released on 2020-12-18 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Systems and Their Remarkable Mathematical Structures aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Written by experts, each chapter is self-contained and aims to clearly illustrate some of the mathematical theories of nonlinear systems. The book should be suitable for some graduate and postgraduate students in mathematics, the natural sciences, and engineering sciences, as well as for researchers (both pure and applied) interested in nonlinear systems. The common theme throughout the book is on solvable and integrable nonlinear systems of equations and methods/theories that can be applied to analyze those systems. Some applications are also discussed. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-expert in this field Written to be accessible to some graduate and postgraduate students in mathematics and applied mathematics Serves as a literature source in nonlinear systems

Applications of Symmetry Methods to Partial Differential Equations

Author : George W. Bluman
Publisher : Springer Science & Business Media
ISBN 13 : 0387680284
Total Pages : 415 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis Applications of Symmetry Methods to Partial Differential Equations by : George W. Bluman

Download or read book Applications of Symmetry Methods to Partial Differential Equations written by George W. Bluman and published by Springer Science & Business Media. This book was released on 2009-10-30 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.

Recent Progress in the Theory of the Euler and Navier–Stokes Equations

Author : James C. Robinson
Publisher : Cambridge University Press
ISBN 13 : 131658934X
Total Pages : 247 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Recent Progress in the Theory of the Euler and Navier–Stokes Equations by : James C. Robinson

Download or read book Recent Progress in the Theory of the Euler and Navier–Stokes Equations written by James C. Robinson and published by Cambridge University Press. This book was released on 2016-01-21 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rigorous mathematical theory of the Navier–Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier–Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier–Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

Hyperbolic Problems: Theory, Numerics, Applications

Author : Heinrich Freistühler
Publisher : Springer Science & Business Media
ISBN 13 : 9783764367091
Total Pages : 494 pages
Book Rating : 4.3/5 (67 download)

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Book Synopsis Hyperbolic Problems: Theory, Numerics, Applications by : Heinrich Freistühler

Download or read book Hyperbolic Problems: Theory, Numerics, Applications written by Heinrich Freistühler and published by Springer Science & Business Media. This book was released on 2002-01-01 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Eighth International Conference on Hyperbolic Problems - Theory, Nu merics, Applications, was held in Magdeburg, Germany, from February 27 to March 3, 2000. It was attended by over 220 participants from many European countries as well as Brazil, Canada, China, Georgia, India, Israel, Japan, Taiwan, und the USA. There were 12 plenary lectures, 22 further invited talks, and around 150 con tributed talks in parallel sessions as well as posters. The speakers in the parallel sessions were invited to provide a poster in order to enhance the dissemination of information. Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. Despite considerable progress, the mathematical theory is still strug gling with fundamental open problems concerning systems of such equations in multiple space dimensions. For various applications the development of accurate and efficient numerical schemes for computation is of fundamental importance. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended ther modynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability ofshock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite ele ment schemes, adaptive, multiresolution, and artificial dissipation methods.