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Call number: | 9783319008318:ONLINE Show nearby items on shelf |
Title: | Analytic Inequalities and Their Applications in PDEs |
Author(s): |
Yuming Qin |
Date: | 2017 |
Size: | 1 online resource (XIII, 564 p p.) |
Contents: | Preface -- 1 Integral Inequalities -- 2 Differential and Difference Inequalities -- 3 Global Attractors for Evolutionary Differential Equations -- 4 Global Existence and Uniqueness for Evolutionary PDEs -- 5 Asymptotic Behavior for |
Evolutionary PDEs.-6 Blow-up of Solutions to Evolutionary PDEs -- 7 Appendix: Basic Inequalities. | |
ISBN: | 9783319008318 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Operator theory , Partial differential equations , Mathematical physics , Mathematics , Partial Differential Equations , Classical Mechanics , Operator Theory , Mathematical Physics |
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Call number: | 9780805301021:ONLINE Show nearby items on shelf |
Title: | Foundations of mechanics: a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the three-body problem |
Author(s): |
Ralph Abraham |
Date: | 1978 |
Edition: | 2d ed., rev., enl., and reset. |
Publisher: | Reading, Mass.: Benjamin/Cummings |
Size: | 1 online open access resource (789 p) |
Note: | Caltech open access |
ISBN: | 9780805301021 |
Keywords: | Mechanics, Analytic. , Geometry, Differential. , Celestial mechanics. |
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Call number: | SPRINGER-2014-9783319018065:ONLINE Show nearby items on shelf |
Title: | Harmonic and Complex Analysis and its Applications [electronic resource] |
Author(s): |
Alexander Vasil'ev |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This volume highlights the main results of the research performed within the network Harmonic and Complex Analysis and its Applications (HCAA), which was a five-year (20072012) European Science Foundation Programmeintended to explore and to strengthe n the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. Itcoordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings,potential theory, Banach spaces of analytic functions and their applications to the problem s of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveyswritten as a result of activities of the Programme and will be interesting and useful for professionals and novi ces in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader willundoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme |
Contents: | L.D. Abreu, H.G. Feichtinger: Function spaces of polyanalytic functions |
F. Bracci, M.D. Contreras, S. Daz | |
Madrigal,A. Vasil'ev: Classical and stochastic Lwner | |
Kufarev equations | |
M. Elin, F. Jacobzon, M. Levenshtein, D. Shoikhet: The Schwarz Lemma. Rigidity and Dynamics | |
H.G. Feichtinger, M. Pap: Coorbit theory and Bergman spaces | |
S.J. Gardiner, T. Sjdin: Quadrature domains and their two | |
phase counterparts | |
B. Gustafsson: Exponential transforms, resultants and moments | |
M. Schlichenmaier: From the Virasoro Algebra to KricheverNovikov Type Algebras and Beyond | |
ISBN: | 9783319018065 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Functional analysis , Functions of complex variables , Potential theory (Mathematics) |
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Call number: | SPRINGER-2013-9781461459811:ONLINE Show nearby items on shelf |
Title: | The Implicit Function Theorem [electronic resource] History, Theory, and Applications |
Author(s): |
Steven G Krantz Harold R Parks |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The implicit function theorem is part ofthe bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theoremshave now blossomed into p owerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classicalformulation forCkfunctions, (ii) formulations in ot her function spaces, (iii) formulations for non-smooth functions, and (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems,such as the NashMoser theorem, have been developed for specific applications ( e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present uncorrected reprint of thisclassicmonograph. Originally published in 2002,The Implicit Function Theoremis an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians,graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in mo dern mathematics. It serves to document and placein context a substantial body ofmathematical ideas |
Note: | Springer eBooks |
Contents: | Preface |
Introduction to the Implicit Function Theorem | |
History | |
Basic Ideas | |
Applications | |
Variations and Generalizations | |
Advanced Implicit Function Theorems | |
Glossary | |
Bibliography | |
Index | |
ISBN: | 9781461459811 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Differential Equations , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2013-9781461459408:ONLINE Show nearby items on shelf |
Title: | Plasticity [electronic resource] : Mathematical Theory and Numerical Analysis |
Author(s): |
Weimin Han B. Daya Reddy |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book focuses on the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis. It isdivided into three parts, wi th the first part providing a detailed introduction to plasticity, the second part covering the mathematical analysis of the elasticity problem, and the third part devoted to error analysis of varioussemi-discrete and fully discrete approximations for var iational formulations of the elastoplasticity. This revised and expanded edition includes material on single-crystal and strain-gradient plasticity. In addition, the entire bookhas been revised to make it more accessible to readers who are actively involv ed in computations but less so in numerical analysis. Reviews of earlier edition: The authors have written an excellent book which can berecommended for specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics ofplasticity theory. (ZAMM, 2002) In summary, the book represents an impressive comprehensive overview of the mathematical approach to the theor y and numerics of plasticity. Scientists as well as lecturers and graduate studentswill find the book very useful as a reference for research or for preparing courses in this field. (Technische Mechanik) The book is professionally written and will be a us eful reference to researchers and students interested inmathematical and numerical problems of plasticity. It represents a major contribution in the area of continuum mechanics and numerical analysis. (Math Reviews) |
Note: | Springer eBooks |
Contents: | Preface to the Second Edition |
Preface to the First Edition | |
Preliminaries | |
Continuum Mechanics and Linearized Elasticity | |
Elastoplastic Media | |
The Plastic Flow Law in a Convex | |
Analytic Setting | |
Basics of Functional Analysis and Function Spaces | |
Variational Equations and Inequalities | |
The Primal Variational Problem of Elastoplasticity | |
The Dual Variational Problem of Classical Elastoplasticity | |
Introduction to Finite Element Analysis | |
Approximation of Variational Problems | |
Approximations of the Abstract Problem | |
Numerical Analysis of the Primal Problem | |
References | |
ISBN: | 9781461459408 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Interdisciplinary Applied Mathematics, 0939-6047 : v9 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Numerical analysis , Mechanics, applied , Materials |
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Call number: | SPRINGER-2013-9781461458685:ONLINE Show nearby items on shelf |
Title: | Functional Analysis in Mechanics [electronic resource] |
Author(s): |
Leonid P Lebedev Iosif I Vorovich Michael J Cloud |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract butpowerful mathematical not ions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value problems for mechanical objects. This second edition includes more extended coverage of the classical andabstract portions of functional analysis. Taken togethe r, the first three chapters now constitute a regular text on applied functional analysis. This potential use of the book is supported by a significantly extended set of exerciseswith hints and solutions. A new appendix, providing a convenient listing of e ssential inequalities and imbedding results, has been added. The book should appeal to graduate students and researchers in physics, engineering, andapplied mathematics. Reviews of first edition: This book covers functional analysis and its application s to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics whowish to understand the mathematical underpinnings of the discipline. . . . Detailed solutions of the exercises are provided in an app endix. (LEnseignment Mathematique, Vol. 49 (1-2), 2003) The reader comes away with aprofound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood.Numerous exercises. . .test the readers comprehension at every stage. Summing Up: Recommended. (F. E. J. Linton, Choice, September, 2003) |
Note: | Springer eBooks |
Contents: | Introduction |
Metric, Banach, and Hilbert Spaces | |
Mechanics Problems from the Functional Analysis Viewpoint | |
Some Spectral Problems of Mechanics | |
Elements of Nonlinear Functional Analysis | |
Summary of Inequalities and Imbeddings | |
Hints for Selected Problems | |
References | |
In Memoriam: Iosif I. Vorovich | |
Index | |
ISBN: | 9781461458685 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Differential equations, partial , Mechanics , Materials |
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Call number: | SPRINGER-2012-9783642295119:ONLINE Show nearby items on shelf |
Title: | Quantum Many Body Systems [electronic resource] : Cetraro, Italy 2010, Editors: Alessandro Giuliani, Vieri Mastropietro, Jakob Yngvason |
Author(s): |
Vincent Rivasseau Robert Seiringer Jan Philip Solovej Thomas Spencer |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book is based on the lectures given at the CIME school Quantum many body systems held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written byfour leading experts in the f ield: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity R. Seiringer describes a proof of Bose-Einsteincondensation in the Gross-Pitaevski limit and explains th e effects of rotating traps and the emergence of lattices of quantized vortices J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to thefunctional analytic methods used to prove their thermodynamic stability finally, T. Spen cer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures arecharacterized by their mathematical rigor combined with physical insights |
Note: | Springer eBooks |
Contents: | 1.Introduction to the Renormalization Group with Applications to Non |
Relativistic Quantum Electron Gases. Vincent Rivasseau | |
2.Cold Quantum Gases and Bose | |
Einstein Condensation. Robert Seiringer | |
3. Quantum Coulomb gases. Jan Philip Solovey | |
4. SUSY Statistical Mechanics and Random Band Matrices. Thomas Spencer | |
ISBN: | 9783642295119 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2051 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2012-9783642251320:ONLINE Show nearby items on shelf |
Title: | Homotopy Analysis Method in Nonlinear Differential Equations [electronic resource] |
Author(s): |
Shijun Liao |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Homotopy Analysis Method in Nonlinear Differential Equations presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM).Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all,it provides a convenient way to guarantee the converg ence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0for nonlinear boundary-value problems and its applications. Part III shows the v alidity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a numberof nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are free ly available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers andpostgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professo r of Shanghai Jiaotong University, is a pioneer of the HAM. |
Note: | Springer eBooks |
Contents: | Basic Ideas |
Systematic Descriptions | |
Advanced Approaches | |
Convergent Series For Divergent Taylor Series | |
Nonlinear Initial Value Problems | |
Nonlinear Eigenvalue Problems | |
Nonlinear Problems In Heat Transfer | |
Nonlinear Problems With Free Or Moving Boundary | |
Steady | |
State Similarity Boundary | |
Layer Flows | |
Unsteady Similarity Boundary | |
Layer Flows | |
Non | |
Similarity Boundary | |
Layer Flows | |
Applications In Numerical Methods | |
ISBN: | 9783642251320 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential Equations , Differential equations, partial , Engineering mathematics |
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Call number: | SPRINGER-2012-9783034804172:ONLINE Show nearby items on shelf |
Title: | Advances in Applied Analysis [electronic resource] |
Author(s): |
Sergei V Rogosin Anna A Koroleva |
Date: | 2012 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book contains survey papers based on the lectures presented at the 3rd International Winter School Modern Problems of Mathematics and Mechanics held in January 2010 at the Belarusian State University, Minsk. Theselectures are devoted to differen t problems of modern analysis and its applications. An extended presentation of modern problems of applied analysis will enable the reader to get familiar with new approaches of mostly interdisciplinarycharacter. The results discussed are application orie nted and present new insight into applied problems of growing importance such as applications to composite materials, anomalous diffusion, and fluid dynamics |
Note: | Springer eBooks |
Contents: | Introduction |
Kisil, Vladimir V.: Erlangen Program at Large: Brief Outline | |
Laurincikas, A.: The Riemann zeta | |
function: approximation of analytic functions | |
Luchko, Yury: Anomalous diffusion: models, their analysis, and interpretation | |
Mityushev, Vladimir, V.: R | |
linear and Riemann | |
Hilbert problems for multiply connected domains | |
Plaksa, S. A.: Commutative algebras associated with classic equations of mathematical physics | |
Rogosin, Sergei V.: 2D Free Boundary Value Problems | |
ISBN: | 9783034804172 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables , Differential equations, partial , Number theory |
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Call number: | SPRINGER-2012-9780817649449:ONLINE Show nearby items on shelf |
Title: | Stochastic Models, Information Theory, and Lie Groups, Volume 2 [electronic resource] : Analytic Methods and Modern Applications |
Author(s): |
Gregory S Chirikjian |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other. This unique two-volume set presents these topics in a unified setting, thereby building bridges betweenfields that are rarely stu died by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, andgroup-theoretic concepts in the modeling of physical p henomena. Volume 1 establishes the geometric and statistical foundations required to understand the fundamentals of continuous-time stochastic processes, differential geometry, andthe probabilistic foundations of information theory. Volume 2 delves deeper into relationships between these topics, including stochastic geometry, geometric aspects of the theory of communications and coding, multivariate statisticalanalysis, and error propagation on Lie groups. Key features and topics of Volume 2: * The author reviews the concept ofandfunctions and integration onLie groups with many concrete examples. * Extensive exercises andmotivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes on Lie groups or geometric aspects of probability and statistics. *Specific application areas are explored,including biomolecular statistical mechanics and information-driven motion in robotics. * The concrete presentation style makes it easy for readers to obtain numeri cal solutions for their own problems the emphasis is on how tocalculate quantities rather than how to prove theorems. * Modern problems at the interface of mechanics, control theory, and communications are handled in a unified framework and multiple direc tions for future research are explored.Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practition |
Note: | Springer eBooks |
Contents: | Lie Groups I: Introduction and Examples |
Lie Groups II: Differential Geometric Properties | |
Lie Groups III: Integration, Convolution, and Fourier Analysis | |
Variational Calculus on Lie Groups | |
Statistical Mechanics and Ergodic Theory | |
Parts Entropy and the Principal Kinematic Formula | |
Estimation and Multivariate Analysis in R^n | |
Information, Communication, and Group Therapy | |
Algebraic and Geometric Coding Theory | |
Information Theory on Lie Groups | |
Stochastic Processes on Lie Groups | |
Locomotion and Perception as Communication over Principal Fiber Bundles and A Survey of Addi | |
ISBN: | 9780817649449 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global differential geometry , Distribution (Probability theory) , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2011-9780857291097:ONLINE Show nearby items on shelf |
Title: | Many-Body Boson Systems [electronic resource] : Half a Century Later |
Author(s): |
Andr F Verbeure |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Many-body Boson Systems: Half a Century Later offers a modern way of dealing with the problems of equilibrium states of Bose systems. Starting with the variation principle of statistical mechanics and the energy-entropy balanceprinciple as equilibriu m criteria, results for general boson systems and models are explicitly derived using simple functional analytic calculus. Bridging the gap between ideas of general theoretical physics and the phenomenologicalresearch in the field of Bose systems, this bo ok provides an insight into the fascinating quantum world of bosons. Key topics include the occurrence of BEC and its intimate structural relation with the phenomena of spontaneous symmetrybreaking and off-diagonal long range order the condensate equation the issue concerning the choice of boundary conditions solvable versus non-solvable boson models the set of quasi-free boson states the role of dissipativeperturbations and the surprising but general relation between general quantum fluctuations and boso n systems. Only some knowledge of quantum mechanics and undergraduate algebra and analysis is assumed. This textbook brings studentsand researchers smoothly from general concepts to vivid applications |
Note: | Springer eBooks |
Contents: | Introduction |
Bose systems | |
Equilibrium States | |
Bose Einstein Condensation (BEC) | |
Bose System Dynamics | |
Quantum Fluctuations and Bosonization | |
Appendix | |
ISBN: | 9780857291097 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Functional analysis , Operator theory , Quantum theory , Mathematical physics |
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Call number: | SPRINGER-2011-9780817682477:ONLINE Show nearby items on shelf |
Title: | The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator [electronic resource] |
Author(s): |
J. J Duistermaat |
Date: | 2011 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Interest in the spin-c Dirac operator originally came about from the study of complex analytic manifolds, where in the non-Khler casethe Dolbeault operator is no longer suitable for getting local formulas for theRiemannRoch number or the holomorphic Lefschetz number. However, every symplectic manifold (phase space in classical mechanics) also carries an almost complex structure and hence a corresponding spin-c Dirac operator. Using the heatkernels theory of Berline, Getzler, and Vergne,this workrevis its some fundamental concepts of the theory, and presents the application to symplectic geometry. J.J. Duistermaat was well known for his beautiful and conciseexpositions of seemingly familiar concepts, and this classic studyis certainly no exception. Rep rinted as it was originally published,this workis as an affordable textthat will be of interest to a range of researchers ingeometric analysis and mathematical physics. Overall this is a carefully written, highly readable book on a very beautiful subject. Mathematical Reviews The book of J.J. Duistermaat is a nice introduction to analysis related[tothe]spin-c Dirac operator. ... The book is almost self contained, [is] readable, and will be useful for anybody who is interested in the topic. EMS Newsletter The author's book is a marvelous introduction to [these] objects andtheories. Zentralblatt MATH |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 The Dolbeault | |
Dirac Operator | |
3 Clifford Modules | |
4 The Spin Group and the Spin | |
c Group | |
5 The Spin | |
c Dirac Operator | |
6 Its Square | |
7 The Heat Kernel Method | |
8 The Heat Kernel Expansion | |
9 The Heat Kernel on a Principal Bundle | |
10 The Automorphism | |
11 The Hirzebruch | |
Riemann | |
Roch Integrand | |
12 The Local Lefschetz Fixed Point Formula | |
13 Characteristic Case | |
14 The Orbifold Version | |
15 Application to Symplectic Geometry | |
16 Appendix: Equivariant Forms | |
ISBN: | 9780817682477 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Global analysis , Operator theory , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2010-9783642046292:ONLINE Show nearby items on shelf |
Title: | Nonlinear Dynamics and Chaos: Advances and Perspectives [electronic resource] |
Author(s): |
Marco Thiel Jrgen Kurths M. Carmen Romano Gyrgy Krolyi Alessandro Moura |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is a collection of contributions on various aspects of active frontier research in the field of dynamical systems and chaos. Each chapter examines a specific research topic and, in addition to reviewing recent results,also discusses future perspectives. The result is an invaluable snapshot of the state of the field by some of its most important researchers. The first contribution in this book, How did you get into Chaos?, is actually acollection of personal accounts by a number of distingui shed scientists on how they entered the field of chaos and dynamical systems, featuring comments and recollections by James Yorke, Harry Swinney, Floris Takens, Peter Grassberger,Edward Ott, Lou Pecora, Itamar Procaccia, Michael Berry, Giulio Casati, Vale ntin Afraimovich, Robert MacKay, and last but not least, Celso Grebogi, to whom this volume is dedicated |
Note: | Springer eBooks |
Contents: | How Did you Get Into Chaos? |
Singular Perturbations of Complex Analytic Dynamical Systems | |
Heteroclinic Switching in Coupled Oscillator Networks: Dynamics on Odd Graphs | |
Dynamics of Finite | |
Size Particles in Chaotic Fluid Flows | |
Langevin Equation for Slow Degrees of Freedom of Hamiltonian Systems | |
Stable Chaos | |
Superpersistent Chaotic Transients | |
Synchronization and Climate Dynamics | |
Stochastic Synchronization | |
Experimental Huygens Synchronization of Oscillators | |
Controlling Chaos: The OGY Method, its Use in Mechanics, and an Alternative Unified Framework for Control of No | |
ISBN: | 9783642046292 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Understanding Complex Systems, 1860-0832 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Differentiable dynamical systems , Systems theory , Vibration |
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Call number: | SPRINGER-2010-9783034604253:ONLINE Show nearby items on shelf |
Title: | Visions in Mathematics [electronic resource] : GAFA 2000 Special volume, Part II |
Author(s): |
N Alon J Bourgain A Connes M Gromov V Milman |
Date: | 2010 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Visions in Mathematics - Towards 2000 was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematiciansworldwide. The goals of the conf erence were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas. The aims ofthe conference are reflected in the present set of sur vey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the second part of a two-volume set that will serve anyresearch mathematician or advanced student as an overview and guideline thr ough the multifaceted body of mathematical research in the present and near future |
Note: | Springer eBooks |
Contents: | Foreword |
Algebraic and probabilistic methods in discrete mathematics | |
Challenges in analysis | |
Noncommutative geometry | |
Year 2000 | |
Indtroduction to symplectic field theory | |
Holomorphic curves and real three | |
dimensional dynamics | |
Perspectives on the analytic theory of L | |
functions | |
Combinatorics with a geometric flavor | |
Topics in asymptotic geometric analysis | |
Quantum information theory: results and open problems | |
Universality, phase transitions and statistical mechanics | |
How classical physics helps mathematics | |
Addendum: Discussions at the Dead Sea | |
Introduction | |
Di | |
ISBN: | 9783034604253 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2010-9781441960535:ONLINE Show nearby items on shelf |
Title: | Mathematics and Its History [electronic resource] |
Author(s): |
John Stillwell |
Date: | 2010 |
Edition: | 3 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | From the reviews of the second edition: This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and thesolution of polynomial equation s. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topicscentral to a history course, then they would closely resem ble those chosen here. (David Parrott, Australian Mathematical Society) The book...is presented in a lively style without unnecessary detail. It is very stimulating and willbe appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interestingresults. It can be recommended for seminars and will be enjoyed by the broad mathematical community. ( European Mathematical Society) Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well asthey will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branchesof mathematics interact. (Denis Bonheure, Bulletin of the Belgian Society) This third edition includes new chapters on simple groups and combinatori cs, and new sections on several topics, including the Poincare conjecture. The bookhas also been enriched by added exercises |
Note: | Springer eBooks |
Contents: | The Theorem of Pythagoras |
Greek Geometry | |
Greek Number Theory | |
Infinity in Greek Mathematics | |
Number Theory in Asia | |
Polynomial Equations | |
Analytic Geometry | |
Projective Geometry | |
Calculus | |
Infinite Series | |
The Number Theory Revival | |
Elliptic Functions | |
Mechanics | |
Complex Numbers in Algebra | |
Complex Numbers and Curves | |
Complex Numbers and Functions | |
Differential Geometry | |
Non | |
Euclidean Geometry | |
Group Theory | |
Hypercomplex Numbers | |
Algebraic Number Theory | |
Topology | |
Simple Groups | |
Sets, Logic, and Computation | |
Combinatorics | |
ISBN: | 9781441960535 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Geometry , Mathematics_$xHistory , Number theory |
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Call number: | SPRINGER-2009-9783642001390:ONLINE Show nearby items on shelf |
Title: | Spectral Methods in Quantum Field Theory [electronic resource] |
Author(s): |
Herbert Weigel Markus Quandt Noah Graham |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This concise text introduces techniques from quantum mechanics, especially scattering theory, to compute the effects of an external background on a quantum field in general, and on the properties of the quantum vacuum inparticular. This approach can be succesfully used in an increasingly large number of situations, ranging from the study of solitons in field theory and cosmology to the determination of Casimir forces in nano-technology. The methodintroduced and applied in this book is shown to give a n unambiguous connection to perturbation theory, implementing standard renormalization conditions even for non-perturbative backgrounds. It both gives new theoretical insights, forexample illuminating longstanding questions regarding Casimir stresses, and also provides an efficient analytic and numerical tool well suited to practical calculations. Last but not least, it elucidates in a concrete context many ofthe subtleties of quantum field theory, such as divergences, regularization and renormalization, by connecting them to more familiar results in quantum mechanics. While addressed primarily at young researchers entering the field andnonspecialist researchers with backgrounds in theoretical and mathematical physics, introductory chapters on the theoret ical aspects of the method make the book self-contained and thus suitable for advanced graduate students |
Note: | Springer eBooks |
Contents: | Introduction |
Review of Scattering Theory | |
Quantum Field Theory and the Spectral Method | |
Applications in One Space Dimension | |
Spectral Analysis of Charges | |
Hedgehog Configurations in d=3+1 | |
Boundary Conditions and Casimir Forces | |
String Type Configurations | |
Quantum Corrections to Q | |
Balls | |
References | |
Index | |
ISBN: | 9783642001390 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v777 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory |
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Call number: | SPRINGER-2008-9780817647032:ONLINE Show nearby items on shelf |
Title: | Shape-Preserving Approximation by Real and Complex Polynomials [electronic resource] |
Author(s): |
Sorin G Gal |
Date: | 2008 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph presents the first comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables. Such approximation methods are useful in many problems thatarise in science and engin eering and require an optimal mathematical representation of physical reality. The main topics are structured in four chapters, followed by an appendix: shape-preserving approximation and interpolation of realfunctions of one real variable by real polynom ials shape-preserving approximation of real functions of several real variables by multivariate real polynomials shape-preserving approximation of analytic functions of one complexvariable by complex polynomials in the unit disk and shape-preserving appro ximation of analytic functions of several complex variables on the unit ball or the unit polydisk by polynomials of several complex variables. The appendixtreats related results of non-polynomial and non-spline approximations preserving shape including th ose by complexified operators with applications to complex partial differential equations. Shape-Preserving Approximation by Real andComplex Polynomials contains many open problems at the end of each chapter to stimulate future research along with a rich and updated bibliography surveying the vast literature. The text will be useful to graduate students andresearchers interested in approximation theory, mathematical analysis, numerical analysis, computer aided geometric design, robotics, data fitting, che mistry, fluid mechanics, and engineering |
Note: | Springer eBooks |
Contents: | Preface |
Shape Preserving Approximation by Real Univariate Polynomials | |
Shape Preserving Approximation by Real Multivariate Polynomials | |
Shape Preserving Approximation by Complex Univariate Polynomials | |
Shape Preserving Approximation by Complex Multivariate Polynomials | |
Appendix: Some Related Topics | |
References | |
Index | |
ISBN: | 9780817647032 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Functions of complex variables , Computer science Mathematics , Engineering mathematics |
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Call number: | SPRINGER-2008-9780817645953:ONLINE Show nearby items on shelf |
Title: | Integrable Systems in Celestial Mechanics [electronic resource] |
Author(s): |
Diarmuid Mathna |
Date: | 2008 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This work presents a unified treatment of three important integrable problems relevant to both Celestial and Quantum Mechanics. Under discussion are the Kepler (two-body) problem and the Euler (two-fixed center) problem, thelatter being the more comp lex and more instructive, as it exhibits a richer and more varied solution structure. Further, because of the interesting investigations by the 20th century mathematical physicist J.P. Vinti, the Euler problemis now recognized as being intimately linked t o the Vinti (Earth-satellite) problem. Here the analysis of these problems is shown to follow a definite shared pattern yielding exact forms for the solutions. A central feature is thedetailed treatment of the planar Euler problem where the solutions are expressed in terms of Jacobian elliptic functions, yielding analytic representations for the orbits over the entire parameter range. This exhibits the rich andvaried solution patterns that emerge in the Euler problem, which are illustrated in the appendix . A comparably detailed analysis is performed for the Earth-satellite (Vinti) problem. Key features: * Highlights shared features in theunified treatment of the Kepler, Euler, and Vinti problems * Raises challenges in analysis and astronomy, placing this trio of problems in the modern context * Includes a full analysis of the planar Euler problem * Highlights thecomplex and surprising orbit patterns that arise from the Euler problem * Provides a detailed analysis and solution for the Earth-satellite probl em The analysis and results in this work will be of interest to graduate students inmathematics and physics (including physical chemistry) and researchers concerned with the general areas of dynamical systems, statistical mechanics, and mathematical physi cs and has direct application to celestial mechanics, astronomy,orbital mechanics, and aerospace engineering |
Note: | Springer eBooks |
Contents: | General Introduction |
The Kepler Problem (Two | |
Body Problem): the central Newtonian potential | |
Bernoulli solution | |
Features of the central Newtonian potential | |
The Non | |
Central Newtonian Potential | |
The Euler problem: two fixed centers of attraction | |
The Vinti problem: earth | |
satellite theory | |
Implications for perturbation theories | |
Relativistic context | |
Index | |
ISBN: | 9780817645953 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematical Physics : v51 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Mathematical physics , Statistical physics , Mechanics , Astronomy |
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Call number: | SPRINGER-2007-9783540365822:ONLINE Show nearby items on shelf |
Title: | Lost Causes in and beyond Physics [electronic resource] |
Author(s): |
R.F Streater |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Lost Causes in and Beyond Physics deals with a selection of research topics mostly from theoretical physics that have been shown to be a dead-end or continue at least to be highly controversial. Nevertheless, whether it is aboutBohmian mechanics, phy sics from Fisher information or the quantum theory of the brain, small but dedicated research communities continue to work on these issues. R.F. Streater, renowned mathematical physicist and co-author of thefamous book PCT, Spin and Statistics, and all th at, in a series of essays describes the work and struggle of these research commnities, as well as the chances of any breakthrough in these areas. This book is written as both anentertainment and serious study and should be accessible to anyone with a bac kground in theoretical physics and mathematics |
Note: | Springer eBooks |
Contents: | Munchausens Syndrome by Proxy |
Elementary Probability | |
Quantum Probability | |
Bayesians | |
EPR and the Dangers of Cannabis | |
Stapps Theory of the Brain | |
Hidden Variables | |
Bohmian Mechanics | |
The Analytic S | |
matrix Bootstrap | |
Nelson and Wiener | |
Other Lost Causes | |
Some Good Ideas | |
ISBN: | 9783540365822 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory , Mathematical physics , Particles (Nuclear physics) , Plasma (Ionized gases) , Condensed matter |
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Call number: | SPRINGER-2004-9783662063903:ONLINE Show nearby items on shelf |
Title: | Condensed Matter Physics and Exactly Soluble Models Selecta of Elliott H. Lieb |
Author(s): | |
Date: | 2004 |
Size: | 1 online resource (675 p.) |
Note: | 10.1007/978-3-662-06390-3 |
Contents: | A Survey by the Editors -- I.1 Violation of the Noncrossing Rule: The Hubbard Hamiltonian for Benzene -- I.2 Two Theorems on the Hubbard Model -- I.3 The Hubbard Model: Some Rigorous Results and Open Problems -- I.4 Flux Phase of the |
Half-Filled Band -- II.1 Proof of the Peierls Instability in One Dimension -- II.2 Stability of the Peierls Instability for Ring Shaped Molecules -- III.1 A Model for Crystallization: A Variation on the Hubbard Model -- III.2 Phase | |
Separation due to Quantum Mechanical Correlations -- IV.1 Theory of Ferromagnetism and the Ordering of Electronic Energy Levels -- IV.2 Ordering Energy Levels of Interacting Spin Systems -- IV.3 Magnetic Properties of Some | |
Itinerant-Electron Systems at T > 0 -- V.1 Phase Transitions in Reservoir-Driven Open Systems with Applications to Lasers and Superconductors -- V.2 Equilibrium Statistical Mechanics of Matter Interacting with the Quantized Radiation | |
Field -- V.3 Constructive Macroscopic Quantum Electrodynamics -- V.4 The Laser: A Reversible Quantum Dynamical System with Irreversible Classical Macroscopic Motion -- VI.1 A Proof of Part of Haldane’s Conjecture on Spin Chains -- VI.2 | |
Rigorous Results on Valence-Bond Ground States in Antiferromagnets -- VI.3 Valence Bond Ground States in Isotropic Quantum Antiferromagnets -- VI.4 Ground State Properties of a Fully Frustrated Quantum Spin System -- VII.1 Exact Ground | |
State Energy of the Strong-Coupling Polaron -- VIII.1 Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas -- VIII.2 Bose—Einstein Quantum Phase Transition in an Optical Lattice Model -- VIII.3 The Quantum-Mechanical | |
Many-Body Problem: The Bose Gas -- Some of the Early History of Exactly Soluble Models -- IX.1 Exact Solution of the Problem of the Entropy of Two-Dimensional Ice -- IX.2 Exact Solution of the F Model of an Antiferroelectric -- IX.3 | |
Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric -- IX.4 Residual Entropy of Square Ice -- IX.5 Two-Dimensional Ferroelectric Models -- IX.6 Relations Between the ‘Percolation’ and ‘Colouring’ Problem and Other | |
Graph-Theoretical Problems Associated with Regular Planar Lattices: Some Exact Results for the ‘Percolation’ Problem -- IX.7 Analytic Properties of the Free Energy for the “Ice” Models -- X.1 Two-Dimensional Ising Model as a Soluble | |
Problem of Many Fermions -- X.2 Solution of the Dimer Problem by the Transfer Matrix Method -- XI.1 Two Soluble Models of an Antiferromagnetic Chain -- XII.1 Exact Analysis of an Interacting Bose Gas. I. The General Solution and the | |
Ground State -- XII.2 Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum -- XIII.1 Delta-Function Fermi Gas with Two-Spin Deviates -- XIII.2 Absence of Mott Transition in an Exact Solution of the Short-Range, | |
One-Band Model on One Dimension -- XIV.1 Exact Solution of a Many-Fermion System and Its Associated Boson Field -- Selecta of Elliott H. Lieb -- Publications of Elliott H. Lieb | |
ISBN: | 9783662063903 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Functional analysis , Atoms , Phase transformations (Statistical physics) , Condensed materials , Condensed matter , Physics , Mathematical Methods in Physics , Condensed Matter Physics , Functional Analysis , Atomic, Molecular, Optical and Plasma Physics , Quantum Gases and Condensates |
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Call number: | SPRINGER-2004-9781475738094:ONLINE Show nearby items on shelf |
Title: | Lines and Curves A Practical Geometry Handbook |
Author(s): |
Victor Gutenmacher |
Date: | 2004 |
Size: | 1 online resource (156 p.) |
Note: | 10.1007/978-1-4757-3809-4 |
Contents: | 1 Sets of Points -- 2 The Alphabet -- 3 Logical Combinations -- 4 Maximum and Minimum -- 5 Level Curves -- 6 Quadratic Curves -- 7 Rotations and Trajectories -- 8 Drawings, Animation, and the Magic Triangle -- Answers, Hints, |
Solutions -- A Summary of Results from Analytic Geometry -- B Some Facts from School Geometry -- B.1 Proportional segments -- B.2 Distances, perpendiculars -- B.3 The circle -- B.4 Triangles -- C A Dozen Assignments -- C.1 Name the | |
“letters” -- C.2 Transformations and constructions -- C.3 Rotating straight lines -- C.4 Straight lines and linear relations -- C.5 The tangency principle (conditional extremum) -- C.6 Partitions -- C.7 Ellipses, hyperbolas, and | |
parabolas -- C.8 Envelopes, infinite unions -- C.9 Tangents to cycloids -- C.1O Equations of curves -- C.11 Geometrical practical work -- C.12 Small investigations -- About Victor Gutenmacher -- About N. B. Vasilyev | |
ISBN: | 9781475738094 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Computer graphics , Computer-aided engineering , Geometry , Mechanics , Mechanics, Applied , Mathematics , Geometry , Theoretical and Applied Mechanics , Computer-Aided Engineering (CAD, CAE) and Design , Computer Graphics |
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Call number: | SPRINGER-2004-9780817681845:ONLINE Show nearby items on shelf |
Title: | Integral Methods in Science and Engineering Analytic and Numerical Techniques |
Author(s): | |
Date: | 2004 |
Size: | 1 online resource (280 p.) |
Note: | 10.1007/978-0-8176-8184-5 |
Contents: | 1 A Finite Volume Scheme for a Nonlinear Reaction- Diffusion PDE Arising in Combustion -- 2 High Perfomance Algorithms for Computing Nonsingular Jacobian-Free Piecewise Linearization of Differential Algebraic Equations -- 3 Multiple |
Scattering of Water Waves by N Floating Bodies Using Boundary Integral Equation Methods Lahcene Bencheikh -- 4 An Application of Semigroup Theory to a Fragmentation Equation -- 5 Solution of a Sommerfeld Diffraction Problem with a Real | |
Wave Number -- 6 A Mixed BEM Applied to Scattering of Thermal Waves in Composite Materials -- 7 Stellar Atmosphere Modeling -- 8 Time-Dependent Bending of a Plate with Mixed Boundary Conditions -- 9 Finite-Difference Schemes for a | |
Nonlinear Parabolic Problem with Nonlocal Boundary Conditions -- 10 Absolute Stability for Neutral Systems with Infinite Delay -- 11 Large Scale Acoustic Simulations on Clusters of SMPs -- 12 Models for the Simulation of Electrostatic | |
Precipitators -- 13 A Method for Modeling Nonharmonic Periodic Acoustic Radiation from a Loudspeaker -- 14 Implicit Function Theorems and Discontinuous Implicit Differential Equations -- 15 Numerical Method for Solving Differential | |
Algebraic Equations by Power Series -- 16 On Hemivariational Inequalities in Coupled Thermoelasticity -- 17 Asymptotic Stability in Functional Differential Equations with Delay -- 18 On Optimal Stabilization of Nonautonomous Systems -- | |
19 A New Superconvergent Projection Method -- 20 Spectral Approximation for Compact Integral Operators -- 21 Fundamental Solutions and Functionally Graded Materials -- 22 Applications of Fixed Point Theorems to a Chemical Reactor | |
Problem -- 23 About Localized Boundary-Domain Integro-Differential Formulations for a Quasilinear Problem with Variable Coefficients -- 24 Uniqueness for Inverse Inhomogeneous Transmission Problems in Lipschitz Domains -- 25 Analytic | |
Solution for an Enhanced Theory of Bending of Plates -- 26 On Stabilization of Solutions of Elliptic Equations Containing Bessel Operators -- 27 New Zonal, Spectral Solutions for Compressible Navier-Stokes Partial Differential | |
Equations -- 28 Crack Problems and Boundary Variational Inequalities -- 29 Spline Approximations for Weakly Singular Volterra Integro-Differential Equations -- 30 Hybrid Laplace and Poisson Solvers. II: Robin BCs -- 31 Vibrating | |
Systems with Many Concentrated Masses: on the Low Frequencies and the Local Problem -- 32 Terminal-Edge Algorithms: an Integrated Approach for Mesh Generation -- 33 On the Identifiability of a Geometric Inverse Problem of Parabolic | |
Type -- 34 Multiple Scattering Theory and Integral Equations -- 35 A Resonance Problem for a Second-Order Vector Differential Equation -- 36 Numerical Calculations for a Mullins-Sekerka Problem in 2D -- 37 On Anisotropic Elliptic | |
Equations in Bounded Domains -- 38 Uniqueness and Symmetry for Some Singular Ground State Problems in Rn, n?3 -- 39 Reduction of Computation in the Numerical Resolution of a Second-Kind Weakly Singular Fredholm Equation -- 40 A | |
Parallel Code for Integral Equations on a Cluster of Computers -- 41 Analytic Solution of the SN Equations by Integral Transform Technique -- 42 Integral Equation Methods for Scattering by Periodic Lipschitz Surfaces | |
ISBN: | 9780817681845 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Integral equations , Differential equations , Partial differential equations , Computer mathematics , Physics , Mechanics , Mechanics, Applied , Mathematics , Integral Equations , Ordinary Differential Equations , Partial Differential Equations , Computational Mathematics and Numerical Analysis , Numerical and Computational Physics , Theoretical and Applied Mechanics |
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Call number: | SPRINGER-2002-9781468492811:ONLINE Show nearby items on shelf |
Title: | Mathematics and Its History |
Author(s): |
John Stillwell |
Date: | 2002 |
Edition: | Second Edition |
Size: | 1 online resource (544 p.) |
Note: | 10.1007/978-1-4684-9281-1 |
Contents: | 1 The Theorem of Pythagoras -- 2 Greek Geometry -- 3 Greek Number Theory -- 4 Infinity in Greek Mathematics -- 5 Number Theory in Asia -- 6 Polynomial Equations -- 7 Analytic Geometry -- 8 Projective Geometry -- 9 Calculus -- 10 |
Infinite Series -- 11 The Number Theory Revival -- 12 Elliptic Functions -- 13 Mechanics -- 14 Complex Numbers in Algebra -- 15 Complex Numbers and Curves -- 16 Complex Numbers and Functions -- 17 Differential Geometry -- 18 | |
Noneuclidean Geometry -- 19 Group Theory -- 20 Hypercomplex Numbers -- 21 Algebraic Number Theory -- 22 Topology -- 23 Sets, Logic, and Computation | |
ISBN: | 9781468492811 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Geometry , History , Number theory , Mathematics , History of Mathematical Sciences , Geometry , Number Theory , Analysis |
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Call number: | SPRINGER-2002-9781461513155:ONLINE Show nearby items on shelf |
Title: | Applied Mathematics |
Author(s): |
Gerald Dennis Mahan |
Date: | 2002 |
Size: | 1 online resource (368 p.) |
Note: | 10.1007/978-1-4615-1315-5 |
Contents: | 1. Determinants -- 1.1. Cramer’s Rule -- 1.2. Gaussian Elimination -- 1.3. Special Determinants -- 2. Matrices -- 2.1. Several Theorems -- 2.2. Linear Equations -- 2.3. Inverse of a Matrix -- 2.4. Eigenvalues and Eigenvectors -- 2.5. |
Unitary Transformations -- 2.6. Hon-Hermitian Matrices -- 2.7. A Special Matrix -- 2.8. Gram-Schmidt -- 2.9. Chains -- 3. Group Theory -- 3.1. Basic Properties of Groups -- 3.2. Group Representations -- 3.3. Characters -- 3.4. Direct | |
Product Groups -- 3.5. Basis Functions -- 3.6. Angular Momentum -- 3.7. Products of Representations -- 3.8. Quantum Mechanics -- 3.9. Double Groups -- 4. Complex Variables -- 4.1. Introduction -- 4.2. Analytic Functions -- 4.3. | |
Multivalued Functions -- 4.4. Contour Integrals -- 4.5. Meromorphic Functions -- 4.6. Higher Poles -- 4.7. Integrals Involving Branch Cuts -- 4.8. Approximate Evaluation of Integrals -- 5. Series -- 5.1. Taylor Series -- 5.2. | |
Convergence -- 5.3. Laurent Series -- 5.4. Meromorphic Functions -- 5.5. Asymptotic Series -- 5.6. Summing Series -- 5.7. Padé Approximants -- 6. Conformal Mapping -- 6.1. Laplace’s Equation -- 6.2. Mapping -- 6.3. Examples -- 6.4. | |
Schwartz-Christoffel Transformations -- 6.5. van der Pauw -- 7. Markov Averaging -- 7.1. Random Walk -- 7.2. Speckle -- 7.3. Inhomogeneous Broadening -- 8. Fourier Transforms -- 8.1. Fourier Transforms -- 8.2. Laplace Transforms -- | |
8.3. Wavelets -- 9. Equations of Physics -- 9.1. Boundary and Initial Conditions -- 9.2. Boltzmann Equation -- 9.3. Solving Differential Equations -- 9.4. Elliptic Integrals -- 10. One Dimension -- 10.1. Introduction -- 10.2. Diffusion | |
Equation -- 10.3. Wave Equation -- 11. Two Dimensions -- 11.1. Rectangular Coordinates -- 11.2. Polar Coordinates -- 12. Three Dimensions -- 12.1. Cartesian Coordinates -- 12.2. Cylindrical Coordinates -- 12.3. Spherical Coordinates -- | |
12.4. Problems Inside a Sphere -- 12.5. Vector Wave Equation -- 13. Odds and Ends -- 13.1. Hypergeometric Functions -- 13.2. Orthogonal Polynomials -- 13.3. Sturm-Liouville -- 13.4. Green’s Functions -- 13.5. Singular Integral | |
Equations | |
ISBN: | 9781461513155 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Applied mathematics , Engineering mathematics , Physics , Engineering , Materials science , Mathematics , Applications of Mathematics , Theoretical, Mathematical and Computational Physics , Engineering, general , Characterization and Evaluation of Materials |
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Call number: | SPRINGER-2002-9781461505396:ONLINE Show nearby items on shelf |
Title: | Flexible Robot Dynamics and Controls |
Author(s): |
Rush D Robinett |
Date: | 2002 |
Size: | 1 online resource (339 p.) |
Note: | 10.1007/978-1-4615-0539-6 |
Contents: | 1 Introduction -- 1.1. Sandia National Laboratories -- 1.2. Flexible Robotics Research Historical Background -- 1.3. Outline of the Book -- 1.4. Chapter 1 Summary -- 1.5. Chapter 1 References -- 1.6. Chapter 1 Problems -- 2 |
Mathematical Preliminaries -- 2.1. Introduction -- 2.2. Linear Algebra -- 2.3. Linear Control Systems -- 2.4. Digital Systems -- 2.5. Calculus of Variations -- 2.6. Hamilton’s Principle & Lagrange’s Equations -- 2.7. Analytical | |
Optimization -- 2.8. Numerical Optimization -- 2.9. Chapter 2 Summary -- 2.10. Chapter 2 References -- 2.11. Chapter 2 Problems -- 3 Flexible Robot Dynamic Modeling -- 3.1. Introduction -- 3.2. Flexible Link Modeling Preliminaries -- | |
3.3. The Method of Quadratic Modes -- 3.4. Planar Flexible Robot Dynamics -- 3.5. Actuator Dynamics -- 3.6. Chapter 3 Summary -- 3.7. Chapter 3 References -- 3.8. Chapter 3 Problems -- 4 System Identification -- 4.1. Introduction -- | |
4.2. Linear Least Squares (LSS) -- 4.3. Nonlinear Least Squares -- 4.4. Homotopy Methods -- 4.5. Robot and Actuator System ID -- 4.6. Chapter 4 Summary -- 4.7. Chapter 4 References -- 4.8. Chapter 4 Problems -- 5 Input Shaping for Path | |
Planning -- 5.1. Introduction -- 5.2. Analytic Solutions for Input Shaping -- 5.3. Input Shaping Filters -- 5.4. Constrained Optimization with RQP -- 5.5. Dynamic Programming -- 5.6. Chapter 5 Summary -- 5.7. Chapter 5 References -- | |
5.8. Chapter 5 Problems -- 6 Linear Feedback Control -- 6.1. Introduction -- 6.2. PD Control of a Gantry Robot -- 6.3. Lag-Stabilized Feedback Control -- 6.4. Non-collocated Controls -- 6.5. Feedforward Control -- 6.6. Linear Quadratic | |
Regulator -- 6.7. Linear Optimal Estimation -- 6.8. Linear Quadratic Gaussian (LQG) Control -- 6.9. Chapter 6 Summary -- 6.10. Chapter 6 References -- 6.11. Chapter 6 Problems -- 7 Nonlinear Systems and Sliding Mode Control -- 7.1. | |
Introduction -- 7.2. State-Space Representation of a Dynamic System -- 7.3. Stability -- 7.4. Sliding Mode Control -- 7.5. Chapter 7 Summary -- 7.6. Chapter 7 References -- 7.7. Chapter 7 Problems -- 8 Adaptive Sliding Mode Control -- | |
8.1. Introduction -- 8.2. Adaptive Sliding Mode Control -- 8.3. Examples -- 8.4. Chapter 8 Summary -- 8.5. Chapter 8 References -- 8.6. Chapter 8 Problems -- Appendix A: VFO2AD Optimization -- Appendix C: Hardware &: Software Support | |
ISBN: | 9781461505396 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | International Federation for Systems Research International Series on Systems Science and Engineering: 19 |
Keywords: | Engineering , Calculus of variations , Mechanics , Mechanical engineering , Control engineering , Robotics , Mechatronics , Engineering , Mechanical Engineering , Control, Robotics, Mechatronics , Calculus of Variations and Optimal Control Optimization , Mechanics |
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Call number: | SPRINGER-2002-9780817681302:ONLINE Show nearby items on shelf |
Title: | A Distributional Approach to Asymptotics Theory and Applications |
Author(s): |
Ricardo Estrada |
Date: | 2002 |
Edition: | Second Edition |
Size: | 1 online resource (454 p.) |
Note: | 10.1007/978-0-8176-8130-2 |
Contents: | 1 Basic Results in Asymptotics -- 1.1 Introduction -- 1.2 Order Symbols -- 1.3 Asymptotic Series -- 1.4 Algebraic and Analytic Operations -- 1.5 Existence of Functions with a Given Asymptotic Expansion -- 1.6 Asymptotic Power Series |
in a Complex Variable -- 1.7 Asymptotic Approximation of Partial Sums -- 1.8 The Euler-Maclaurin Summation Formula -- 1.9 Exercises -- 2 Introduction to the Theory of Distributions -- 2.1 Introduction -- 2.2 The Space of Distributions | |
D? -- 2.3 Algebraic and Analytic Operations -- 2.4 Regularization, Pseudofunction and Hadamard Finite Part -- 2.5 Support and Order -- 2.6 Homogeneous Distributions -- 2.7 Distributional Derivatives of Discontinuous Functions -- 2.8 | |
Tempered Distributions and the Fourier Transform -- 2.9 Distributions of Rapid Decay -- 2.10 Spaces of Distributions Associated with an Asymptotic Sequence -- 2.11 Exercises -- 3 A Distributional Theory for Asymptotic Expansions -- 3.1 | |
Introduction -- 3.2 The Taylor Expansion of Distributions -- 3.3 The Moment Asymptotic Expansion -- 3.4 Expansions in the Space P? -- 3.5 Laplace’s Asymptotic Formula -- 3.6 The Method of Steepest Descent -- 3.7 Expansion of | |
Oscillatory Kernels -- 3.8 Time-Domain Asymptotics -- 3.9 The Expansion of f (?x) as ? ? ? in Other Cases -- 3.10 Asymptotic Separation of Variables -- 3.11 Exercises -- 4 Asymptotic Expansion of Multidimensional Generalized Functions | |
-- 4.1 Introduction -- 4.2 Taylor Expansion in Several Variables -- 4.3 The Multidimensional Moment Asymptotic Expansion -- 4.4 Laplace’s Asymptotic Formula -- 4.5 Fourier Type Integrals -- 4.6 Time-Domain Asymptotics -- 4.7 Further | |
Examples -- 4.8 Tensor Products and Partial Asymptotic Expansions -- 4.9 An Application in Quantum Mechanics -- 4.10 Expansion of Kernels of the Type f (?x, x) -- 4.11 Exercises -- 5 Asymptotic Expansion of Certain Series Considered by | |
Ramanujan -- 5.1 Introduction -- 5.2 Basic Formulas -- 5.3 Lambert Type Series -- 5.4 Distributionally Small Sequences -- 5.5 Multiple Series -- 5.6 Unrestricted Partitions -- 5.7 Exercises -- 6 Cesàro Behavior of Distributions -- 6.1 | |
Introduction -- 6.2 Summability of Series and Integrals -- 6.3 The Behavior of Distributions in the (C) Sense -- 6.4 The Cesàro Summability of Evaluations -- 6.5 Parametric Behavior -- 6.6 Characterization of Tempered Distributions -- | |
6.7 The Space K? -- 6.8 Spherical Means -- 6.9 Existence of Regularizations -- 6.10 The Integral Test -- 6.11 Moment Functions -- 6.12 The Analytic Continuation of Zeta Functions -- 6.13 Fourier Series -- 6.14 Summability of | |
Trigonometric Series -- 6.15 Distributional Point Values of Fourier Series -- 6.16 Spectral Asymptotics -- 6.17 Pointwise and Average Expansions -- 6.18 Global Expansions -- 6.19 Asymptotics of the Coincidence Limit -- 6.20 Exercises | |
-- 7 Series of Dirac Delta Functions -- 7.1 Introduction -- 7.2 Basic Notions -- 7.3 Several Problems that Lead to Series of Deltas -- 7.4 Dual Taylor Series as Asymptotics of Solutions of Equations -- 7.5 Boundary Layers -- 7.6 | |
Spectral Content Asymptotics -- 7.7 Exercises -- References | |
ISBN: | 9780817681302 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Applied mathematics , Engineering mathematics , Statistics , Mathematics , Analysis , Applications of Mathematics , Statistical Theory and Methods |
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Call number: | SPRINGER-2001-9789401724142:ONLINE Show nearby items on shelf |
Title: | New Developments in the Dynamics of Planetary Systems Proceedings of the Fifth Alexander von Humboldt Colloquium on Celestial Mechanics held in Badhofgastein (Austria), 19–25 March 2000 |
Author(s): | |
Date: | 2001 |
Size: | 1 online resource (380 p.) |
Note: | 10.1007/978-94-017-2414-2 |
Contents: | Statistics for Twenty-First Century Astrometry -- Synthetic Proper Elements for Outer Main Belt Asteroids -- Invariant Tori in the Secular Motions of the Three-Body Planetary Systems -- Improvements of Planetary Theories Over 6000 |
Years -- The Distribution of Energy Perturbations at Planetary Close Encounters -- Dynamics of Small Earth-Approachers on Low-Eccentricity Orbits and Implications for their Origins -- The Phase Space Structure Around L4 in the | |
Restricted Three-Body Problem -- Why Do Trojan ASCS (not) Escape? -- The 2/1 and 3/2 Resonant Asteroid Motion: A Symplectic Mapping Approach -- Twist and Non-Twist Bifurcations in a System of Coupled Oscillators -- The Mel’nikov | |
Subharmonic Function and the Non-Existence of Analytic Integrals in Non-Autonomous Systems -- On the Structure of Symplectic Mappings. The Fast Lyapunov Indicator: A Very Sensitive Tool -- Crossing of Various Cantori -- Fractal | |
Dimensions as Chaos Indicators -- Normal Form Invariants Around Spin-Orbit Periodic Orbits -- The Third Integral in a Self-Consistent Galactic Model -- Counterrotating Galaxies and Memory of Cosmological Initial Conditions -- The | |
Family P12 of the Three-Body Problem — The Simplest Family of Periodic Orbits, with Twelve Symmetries Per Period -- The Caledonian Symmetrical Double Binary Four-Body Problem I: Surfaces of Zero-Velocity using the Energy Integral -- | |
Application of the Nonrestricted Three-bodies Problem to the Stellar System ? UMA -- Periodic Solutions of the Planetary 5:2 Resonance Three-body Problem -- Limits of Stability for Planets in Double Star Systems Using the Fast Lyapunov | |
Indicators -- On a Fokker-Planck Approach to Asteroidal Transport -- Fractality in a Galactic Model -- Transformation Methods fo Trigonometric Parallaxes -- The Search for Exosolar systems -- The Two Fixed Centers Problem Revisited -- | |
The Phase Space Structure of the General Sitnikov Problem | |
ISBN: | 9789401724142 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Mechanics , Observations, Astronomical , Astronomy , Astrophysics , Physics , Astronomy, Observations and Techniques , Astrophysics and Astroparticles , Theoretical, Mathematical and Computational Physics , Mechanics |
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Call number: | SPRINGER-2001-9789401008426:ONLINE Show nearby items on shelf |
Title: | Recent Developments in Infinite-Dimensional Analysis and Quantum Probability Papers in Honour of Takeyuki Hida’s 70th Birthday |
Author(s): | |
Date: | 2001 |
Size: | 1 online resource (464 p.) |
Note: | 10.1007/978-94-010-0842-6 |
Contents: | A White-Noise Approach to Stochastic Calculus -- Stochastic Dynamics of Compact Spins: Ergodicity and Irreducibility -- Infinite-Dimensional Analysis and Analytic Number Theory -- Bell Numbers, Log-Concavity, and Log-Convexity -- |
Poisson Equations Associated with Differential Second Quantization Operators in White Noise Analysis -- Exponential Moments of Solutions for Nonlinear Equations with Catalytic Noise and Large Deviation -- Ornstein-Uhlenbeck Path | |
Integral and Its Application -- Remarks on a Noncanonical Representation for a Stationary Gaussian Process -- A White Noise Approach to Stochastic Neumann Boundary-Value Problems -- Quantum Cable Equations in Terms of Generalized | |
Operators -- Large Deviation Theorems for Gaussian Processes and Their Applications in Information Theory -- Generalized Functions in Signal Theory -- Ergodic Properties of Random Positive Semigroups -- Wiener-Itô Theorem in Terms of | |
Wick Tensors -- Donsker’s Delta Function of Lévy Process -- Approximation of Hunt Processes by Multivariate Poisson Processes -- Bayes Formula for Optimal Filter with n-ple Markov Gaussian Errors -- One Loop Approximation of the | |
Chern-Simons Integral -- Quantum Mechanics and Brownian Motions -- Complex White Noise and Coherent State Representations -- Complexity in Dynamics and Computation -- On the Theory of KM20-Langevin Equations for Stationary Flows (2): | |
Construction Theorem -- Vector Bundle-Valued Poisson and Cauchy Kernel Functions on Classical Domains -- On Differential Operators in White Noise Analysis -- Stochastic Differentiation — A Generalized Approach -- A Stochastic Process | |
Generated by the Lévy Laplacian -- Recurrence-Transience for Self-similar Additive Processes Associated with Stable Distributions -- Semigroup Domination on a Riemannian Manifold with Boundary -- The Product of Independent Random | |
Variables with Regularly Varying Tails -- Entropy in Subordination and Filtering -- Asymptotic Windings of Brownian Motion Paths on Riemann Surfaces | |
ISBN: | 9789401008426 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Number theory , Probabilities , Quantum physics , Statistics , Mathematics , Probability Theory and Stochastic Processes , Number Theory , Quantum Physics , Statistics, general |
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Call number: | SPRINGER-2000-9781461212584:ONLINE Show nearby items on shelf |
Title: | Coherent States, Wavelets and Their Generalizations |
Author(s): |
Syed Twareque Ali |
Date: | 2000 |
Size: | 1 online resource (418 p.) |
Note: | 10.1007/978-1-4612-1258-4 |
Contents: | 1 Introduction -- 2 Canonical Coherent States -- 2.1 Minimal uncertainty states -- 2.2 The group-theoretical backdrop -- 2.3 Some functional analytic properties -- 2.4 A complex analytic viewpoint (?) -- 2.5 Some geometrical |
considerations -- 2.6 Outlook -- 2.7 Two illustrative examples -- 3 Positive Operator-Valued Measures and Frames -- 3.1 Definitions and main properties -- 3.2 The case of a tight frame -- 3.3 Example: A commutative POV measure -- 3.4 | |
Discrete frames -- 4 Some Group Theory -- 4.1 Homogeneous spaces, quasi-invariant, and invariant measures -- 4.2 Induced representations and systems of covariance -- 4.3 An extended Schur’s lemma -- 4.4 Harmonic analysis on locally | |
compact abelian groups -- 4.5 Lie groups and Lie algebras: A reminder -- 5 Hilbert Spaces with Reproducing Kernels and Coherent States -- 5.1 A motivating example -- 5.2 Measurable fields and direct integrals -- 5.3 Reproducing kernel | |
Hilbert spaces -- 5.4 Some properties of reproducing kernel Hilbert spaces -- 6 Square Integrable and Holomorphic Kernels -- 6.1 Square integrable kernels -- 6.2 Holomorphic kernels -- 6.3 Coherent states: The holomorphic case -- 7 | |
Covariant Coherent States -- 7.1 Covariant coherent states -- 7.2 Example: The classical theory of coherent states -- 7.3 Square integrable covariant CS: The general case -- 8 Coherent States from Square Integrable Representations -- | |
8.1 Square integrable group representations -- 8.2 Orthogonality relations -- 8.3 The Wigner map -- 8.4 Modular structures and statistical mechanics -- 9 Some Examples and Generalizations -- 9.1 A class of semidirect product groups -- | |
9.2 A generalization: ?- and V-admissibility -- 10 CS of General Semidirect Product Groups -- 10.1 Squeezed states (?) -- 10.2 Geometry of semidirect product groups -- 10.3 CS of semidirect products -- 11 CS of the Relativity Groups -- | |
11.1 The Poincaré groups (1, 3) and (1,1) -- 11.2 The Galilei groups (11) and (1, 3) (?) -- 11.3 The anti-de Sitter group SOo(1,2) and its contraction(s) (?) -- 12 Wavelets -- 12.1 A word of motivation -- 12.2 Derivation and properties | |
of the 1-D continuous wavelet transform (?) -- 12.3 A mathematical aside: Extension to distributions -- 12.4 Interpretation of the continuous wavelet transform -- 12.5 Discretization of the continuous WT: Discrete frames -- 12.6 Ridges | |
and skeletons -- 12.7 Applications -- 13 Discrete Wavelet Transforms -- 13.1 The discrete time or dyadic WT -- 13.2 Towards a fast CWT: Continuous wavelet packets -- 13.3 Wavelets on the finite field ?p (?) -- 13.4 Algebraic wavelets | |
-- 14 Multidimensional Wavelets -- 14.1 Going to higher dimensions -- 14.2 Mathematical analysis (?) -- 14.3 The 2-D case -- 15 Wavelets Related to Other Groups -- 15.1 Wavelets on the sphere and similar manifolds -- 15.2 The affine | |
Weyl-Heisenberg group (?) -- 15.3 The affine or similitude groups of space-time -- 16 The Discretization Problem: Frames, Sampling, and All That -- 16.1 The Weyl—Heisenberg group or canonical CS -- 16.2 Wavelet frames -- 16.3 Frames | |
for affine semidirect products -- 16.4 Groups without dilations: The Poincaré groups (?) -- 16.5 A group-theoretical approach to discrete wavelet transforms -- 16.6 Conclusion -- Conclusion and Outlook -- References | |
ISBN: | 9781461212584 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Topological groups , Lie groups , Quantum physics , Quantum computers , Spintronics , Physics , Quantum Physics , Topological Groups, Lie Groups , Quantum Information Technology, Spintronics |
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Call number: | SPRINGER-2000-9781461205074:ONLINE Show nearby items on shelf |
Title: | The Physics of Quantum Fields |
Author(s): |
Michael Stone |
Date: | 2000 |
Size: | 1 online resource (271 p.) |
Note: | 10.1007/978-1-4612-0507-4 |
Contents: | 1 Discrete Systems -- 1.1 One-Dimensional Harmonic Crystal -- 1.2 Continuum Limit -- 2 Relativistic Scalar Fields -- 2.1 Conventions -- 2.2 The Klein-Gordon Equation -- 2.3 Symmetries and Noether’s Theorem -- 3 Perturbation Theory -- |
3.1 Interactions -- 3.2 Perturbation Theory -- 3.3 Wick’s Theorem -- 4 Feynman Rules -- 4.1 Diagrams -- 4.2 Scattering Theory -- 5 Loops, Unitarity, and Analyticity -- 5.1 Unitarity of the S Matrix -- 5.2 The Analytic S Matrix -- 5.3 | |
Some Loop Diagrams -- 6 Formal Developments -- 6.1 Gell-Mann Low Theorem -- 6.2 Lehmann-Källén Spectral Representation -- 6.3 LSZ Reduction Formulae -- 7 Fermions -- 7.1 Dirac Equation -- 7.2 Spinors, Tensors, and Currents -- 7.3 Holes | |
and the Dirac Sea -- 7.4 Quantization -- 8 QED -- 8.1 Quantizing Maxwell’s Equations -- 8.2 Feynman Rules for QED -- 8.3 Ward Identity and Gauge Invariance -- 9 Electrons in Solids -- 9.1 Second Quantization -- 9.2 Fermi Gas and Fermi | |
Liquid -- 9.3 Electrons and Phonons -- 10 Nonrelativistic Bosons -- 10.1 The Boson Field -- 10.2 Spontaneous Symmetry Breaking -- 10.3 Dilute Bose Gas -- 10.4 Charged Bosons -- 11 Finite Temperature -- 11.1 Partition Functions -- 11.2 | |
Worldlines -- 11.3 Matsubara Sums -- 12 Path Integrals -- 12.1 Quantum Mechanics of a Particle -- 12.2 Gauge Invariance and Operator Ordering -- 12.3 Correlation Functions -- 12.4 Fields -- 12.5 Gaussian Integrals and Free Fields -- | |
12.6 Perturbation Theory -- 13 Functional Methods -- 13.1 Generating Functionals -- 13.2 Ward Identities -- 14 Path Integrals for Fermions -- 14.1 Berezin Integrals -- 14.2 Fermionic Coherent States -- 14.3 Superconductors -- 15 | |
Lattice Field Theory -- 15.1 Boson Fields -- 15.2 Random Walks -- 15.3 Interactions and Bose Condensation -- 15.4 Lattice Fermions -- 16 The Renormalization Group -- 16.1 Transfer Matrices -- 16.2 Block Spins and Renormalization Group | |
-- 17 Fields and Renormalization -- 17.1 The Free-Field Fixed Point -- 17.2 The Gaussian Model -- 17.3 General Method -- 17.4 Nonlinear ? Model -- 17.5 Renormalizing ??4 -- 18 Large N Expansions -- 18.1 O(N) Linear ?-Model -- 18.2 | |
Large N Expansions -- A Relativistic State Normalization -- B The General Commutator -- C Dimensional Regularization -- C.1 Analytic Continuation and Integrals -- C.2 Propagators -- D Spinors and the Principle of the Sextant -- D.1 | |
Constructing the ?-Matrices -- D.2 Basic Theorem -- D.3 Chirality -- E Indefinite Metric -- F Phonons and Momentum -- G Determinants in Quantum Mechanics | |
ISBN: | 9781461205074 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Quantum physics , Elementary particles (Physics) , Quantum field theory , Quantum computers , Spintronics , Physics , Elementary Particles, Quantum Field Theory , Quantum Physics , Quantum Information Technology, Spintronics |
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Call number: | SPRINGER-1999-9789401147163:ONLINE Show nearby items on shelf |
Title: | Feynman Integral and Random Dynamics in Quantum Physics A Probabilistic Approach to Quantum Dynamics |
Author(s): |
Zbigniew Haba |
Date: | 1999 |
Size: | 1 online resource (367 p.) |
Note: | 10.1007/978-94-011-4716-3 |
Contents: | 1 Preliminaries -- 2 Markov chains -- 3 Stochastic differential equations -- 4 Semi-groups and the Trotter product formula -- 5 The Feynman integral -- 6 Feynman integral and stochastic differential equations -- 7 Random perturbations |
of the classical mechanics -- 8 Complex dynamics and coherent states -- 9 Quantum non-linear oscillations -- 10 Feynman integral on analytic submanifolds -- 11 Interaction with the environment -- 12 Lindblad equation and stochastic | |
Schrödinger equation -- 13 Hamiltonian time evolution of the density matrix -- 14 Stochastic representation of the Lindblad time evolution -- 15 Decoherence and estimates on dissipative dynamics -- 16 Diffusive behaviour of the Wigner | |
function and decoherence -- 17 Scattering and tunnelling in an environment -- 18 The Feynman integral in quantum field theory -- 19 The phase space methods in QFT -- 20 Computer simulations of quantum random dynamics -- The | |
Bibliography | |
ISBN: | 9789401147163 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 480 |
Keywords: | Physics , Probabilities , Quantum physics , Elementary particles (Physics) , Quantum field theory , Physics , Quantum Physics , Theoretical, Mathematical and Computational Physics , Probability Theory and Stochastic Processes , Elementary Particles, Quantum Field Theory |
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Call number: | SPRINGER-1999-9789401146098:ONLINE Show nearby items on shelf |
Title: | Superanalysis |
Author(s): |
Andrei Khrennikov |
Date: | 1999 |
Size: | 1 online resource (357 p.) |
Note: | 10.1007/978-94-011-4609-8 |
Contents: | I Analysis on a Superspace over Banach Superalge-bras -- 1. Differential Calculus -- 2. Cauchy-Riemann Conditions and the Condition of A-Linearity of Derivatives -- 3. Integral Calculus -- 4. Integration of Differential Forms of |
Commuting Variables -- 5. Review of the Development of Superanalysis -- 6. Unsolved Problems and Possible Generalizations -- II Generalized Functions on a Superspace -- 1. Locally Convex Superalgebras and Supermodules -- 2. Analytic | |
Generalized Functions on the Vladimirov-Volovich Superspace -- 3. Fourier Transformation of Superanalytic Generalized Functions -- 4. Superanalog of the Theory of Schwartz Distributions -- 5. Theorem of Existence of a Fundamental | |
Solution -- 6. Unsolved Problems and Possible Generalizations -- III Distribution Theory on an Infinite-Dimensional Superspace -- 1. Polylinear Algebra over Commutative Supermodules -- 2. Banach Supermodules -- 3. Hilbert Supermodules | |
-- 4. Duality of Topological Supermodules -- 5. Differential Calculus on a Superspace over Topological Supermodules -- 6. Analytic Distributions on a Superspace over Topological Supermodules -- 7. Gaussian and Feynman Distributions -- | |
8. Unsolved Problems and Possible Generalizations -- IV Pseudodifferential Operators in Superanalysis -- 1. Pseudodifferential Operators Calculus -- 2. The Correspondence Principle -- 3. The Feynman-Kac Formula for the Symbol of the | |
Evolution Operator -- 4. Unsolved Problems and Possible Generalizations -- V Fundamentals of the Probability Theory on a Superspace -- 1. Limit Theorems on a Superspace -- 2. Random Processes on a Superspace -- 3. Axiomatics of the | |
Probability Theory over Superalgebras -- 4. Unsolved Problems and Possible Generalizations -- VI Non-Archimedean Superanalysis -- 1. Differentiale and Analytic Functions -- 2. Generalized Functions -- 3. Laplace Transformation -- 4. | |
Gaussian Distributions -- 5. Duhamel non-Archimedean Integral. Chronological Exponent -- 6. Cauchy Problem for Partial Differential Equations with Variable Coefficients -- 7. Non-Archimedean Supersymmetrical Quantum Mechanics -- 8. | |
Trotter Formula for non-Archimedean Banach Algebras -- 9. Volkenborn Distribution on a non-Archimedean Super-space -- 10. Infinite-Dimensional non-Archimedean Superanalysis -- 11. Unsolved Problems and Possible Generalizations -- VII | |
Noncommutative Analysis -- 1. Differential Calculus on a Superspace over a Noncommutative Banach Algebra -- 2. Differential Calculus on Noncommutative Banach Algebras and Modules -- 3. Generalized Functions of Noncommuting Variables -- | |
VIII Applications in Physics -- 1. Quantization in Hilbert Supermodules -- 2. Transition Amplitudes and Distributions on the Space of Schwinger Sources -- References | |
ISBN: | 9789401146098 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 470 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Physics , Mathematics , Analysis , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-1999-9783540484103:ONLINE Show nearby items on shelf |
Title: | Advances in Cold-Region Thermal Engineering and Sciences Technological, Environmental, and Climatological Impact Proceedings of the 6th International Symposium Held in Darmstadt, Germany, 22–25 August 1999 |
Author(s): | |
Date: | 1999 |
Size: | 1 online resource (610 p.) |
Note: | 10.1007/BFb0104166 |
Contents: | Some observations on the historical development of conduction heat transfer -- Numerical and experimental investigation on frosting of energy-recovery ventilator -- Melting of unfixed material inside an elliptical capsule -- |
Experimental study on the critical heat flux of ice accretion along a fine wire immersed in a cold air flow with water spray -- The characteristics of frost growth on parallel plates -- Effect of ultrasonic waves on freezing of | |
supercooled water -- Numerical modeling of dendritic ice crystals -- Measurement of temperature and velocity fields of freezing water using liquid crystal tracers -- Heat transfer enhancement of a direct contact melting process by | |
oscillating motion -- Permeability of an aqueous solution in a state of partial solidification -- Lateral freezing of a porous medium saturated with an aqueous salt solution -- Spontaneous melting of ice in a CaCl2 solution -- An | |
analytic solution prescribing the time-dependent formation of a solid crust inside a convectively cooled plane channel -- Melting heat-transfer characteristics of an inclined ice plate immersed in a hydrophobic liquid -- Plane flow of | |
an ice sheet exhibiting strain-induced anisotropy -- A meso-macro model for the description of induced anisotropy of natural ice, including grain interaction -- Classical mixture models for polythermal ice -- Modelling the ice | |
single-crystal viscoplastic behaviour -- Remarks on self-consistent modelling of polycrystalline ice -- Anisotropic isothermal ice-cap flow with the shallow ice approximation -- Orthotropic viscous model for ice -- Tertiary flow | |
relations for compression and shear components in combined stress tests on ice -- An iterative solution procedure for shallow stokes flows. The shallow ice approximation revisited -- Nested high-resolution modelling of the greenland | |
summit region -- Numerical age computation of the antarctic ice sheet for dating deep ice cores -- Three-dimensional isothermal boundary layer solutions of slow creeping ice flows based on the shallow ice approximation -- A comparison | |
study between two visco-plastic sea-ice models -- Influence of ice accumulation distribution on ice sheet stability -- A computational procedure for instationary temperature-dependent snow creep -- Transformation of the snow crystal to | |
a particle of ice -- Temperature and temperature gradient dependence of snow recrystallization in depth hoar snow -- On creep flow of snow and firn -- Relation of temperature gradient to heat transfer in snow -- Methods of similitude | |
in granular avalanche flows -- Experimental study of gas hydrate formation in porous media -- Electroacoustic technique to study changes in the liquid phase state of frozen soils -- Permeability effects on winter-time natural | |
convection in gravel embankments -- Barothermic effect and temperature regime of frozen soil -- Detecting alpine permafrost using electro-magnetic methods -- Climatic warming and permafrost -- The monitoring and prediction of | |
permafrost temperature, distribution and geocryological processes within russia under global climate changes -- Thermally induced temporal strain variations in rock walls observed at subzero temperatures -- Soil microstructure and the | |
thermodynamic behaviour of permafrost affected soils -- Heat transfer in heat storage arrangements under melting -- Microscale analysis of ice crystals made from aqueous solutions by scanning tunneling microscope -- Development study | |
of a novel tower-style tank for simultaneous storing warm water and ice -- Latent heat storage in a fixed-bed packed with cross-linked polymer particles -- Development of an efficient static-type ice thermal energy storage vessel using | |
a low concentration aqueous solution -- Heat storage for a bus petrol internal-combustion engine -- Heat pumps and heat pipes for applications in cold regions | |
ISBN: | 9783540484103 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Physics: 533 |
Keywords: | Physics , Geophysics , Thermodynamics , Statistical physics , Dynamical systems , Engineering , Mechanics , Mechanics, Applied , Engines , Machinery , Physics , Thermodynamics , Statistical Physics, Dynamical Systems and Complexity , Engine Technology , Engineering, general , Theoretical and Applied Mechanics , Geophysics/Geodesy |
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Call number: | SPRINGER-1999-9781475758672:ONLINE Show nearby items on shelf |
Title: | Modern Analytic Mechanics |
Author(s): |
Richard K Cooper |
Date: | 1999 |
Size: | 1 online resource (341 p.) |
Note: | 10.1007/978-1-4757-5867-2 |
Contents: | 1 Newtonian Mechanics -- 2 Hamilton’s Principle -- 3 Gravitational Law and Planetary Motion -- 4 Hamiltonian Description -- 5 Oscillations I -- 6 Oscillations II -- 7 Rigid Bodies -- 8 Waves in Mechanical Systems -- 9 Special |
Relativity -- 10 Problems -- Appendix A Linear Algebra -- A.1. Properties of Determinants -- A.2. Matrix Notation -- A.3. Matrix Operations -- A.4. Types of Matrices -- A.5. Eigenvalue Analysis -- Appendix B Linear Differential | |
Equations -- Appendix C Numerical Methods -- C.1. Numerical Evaluation of Integrals -- C.2. Numerical Integration of Ordinary Differential Equations -- Appendix D Fourier Series -- D.1. Series Representation of Periodic Functions -- | |
D.2. Evaluation of Series -- D.3. Numerical Evaluation of Series Coefficients -- D.4. Complex Series -- Appendix E Computer Exercises in Classical Mechanics -- E.1. Using the Computer -- E.2. Starting Out -- Appendix F FORTRAN -- F.1. | |
Basic Elements of a FORTRAN Program -- F.2. Other Data Types -- F.3. FORTRAN Functions -- F.4. Looping -- F.5. Variables with Many Values -- F.6. Subroutines -- Appendix G Mathcad | |
ISBN: | 9781475758672 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Applied mathematics , Engineering mathematics , Physics , Mechanics , Mathematics , Applications of Mathematics , Mechanics , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-1999-9781461221661:ONLINE Show nearby items on shelf |
Title: | Analysis and Geometry in Several Complex Variables Proceedings of the 40th Taniguchi Symposium |
Author(s): | |
Date: | 1999 |
Size: | 1 online resource (314 p.) |
Note: | 10.1007/978-1-4612-2166-1 |
Contents: | The Bergman Kernel and a Theorem of Tian -- Some Involutive Structures in Analysis and Geometry -- The Bergman Kernel in Quantum Mechanics -- WKB and the Periodic Table -- Local Sobolev-Bergman Kernels of Strictly Pseudoconvex Domains |
-- Quantitative Estimates for Global Regularity -- Pdes Associated to the CR Embedding Theorem -- $$ \bar{\partial } $$ and $$ {\bar{\partial }_b} $$ Problems on Nonsmooth Domains -- A Note on the Closed Rangeness of Vector Bundle | |
Valued Tangential Cauchy-Riemann Operator -- Discrete Groups of Complex Hyperbolic Isometries and Pseudo-Hermitian Structures -- Pseudoconvex Domains in ?n: A Question on the 1-Convex Boundary Points -- Existence and Applications of | |
Analytic Zariski Decompositions -- Segre Polar Correspondence and Double Valued Reflection for General Ellipsoids -- G2-Geometry of Overdetermined Systems of Second Order289 | |
ISBN: | 9781461221661 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Algebra , Algebraic geometry , Functions of complex variables , Geometry , Mathematics , Several Complex Variables and Analytic Spaces , Algebraic Geometry , Algebra , Geometry , Functions of a Complex Variable |
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Call number: | SPRINGER-1998-9789401150361:ONLINE Show nearby items on shelf |
Title: | Clifford Algebras and Their Application in Mathematical Physics Aachen 1996 |
Author(s): | |
Date: | 1998 |
Size: | 1 online resource (447 p.) |
Note: | 10.1007/978-94-011-5036-1 |
Contents: | Dirac Operators and Clifford Geometry — New Unifying Principles in Particle Physics ? -- On the Hayman uniqueness problem for polyharmonic functions -- Left-linear and Nonlinear Riemann problems in Clifford analysis -- Spin structures |
and harmonic spinors on nonhyperelliptic Riemann surfaces of small genera -- Decomposition of analytic hyperbolically harmonic functions -- Spin Gauge Theories: A Summary -- Manifolds with and without embeddings -- Dirac equation in | |
the Clifford algebra of Space -- Dirac theory from a field theoretic point of view -- On some applications of the biharmonic equation -- Spinor Particle Mechanics -- Clifford analysis and elliptic boundary value problems in unbounded | |
domains -- Twistors and Clifford Algebras -- How Many Essentialy Different Function Theories Exist? -- Variational Property of the Peano Kernel for Harmonicity Differences of Order p -- Clifford Analysis on the Sphere -- Type-changing | |
transformations of pseudo-Euclidean Hurwitz pairs, Clifford Analysis, and particle lifetimes -- Modified quaternionic analysis in ?4 -- Geometric Algebra and Lobachevski Geometry -- Generalizing the (F,G)- derivative in the sense of | |
Bers -- Formes quadratiques de Hardy-Weinberg et algèbres de Clifford -- On Dirac equations in curved space-times -- Some Partial Differential Equations in Clifford Analysis -- Teaching Clifford Algebra as Physical Mathematics -- | |
Polydimensional Relativity, a Classical Generalization of the Automorphism Invariance Principle -- Subluminal and Superluminal Electromagnetic Waves and the Lepton Mass Spectrum -- Higher Spin and the Spacetime Algebra -- Curved Radon | |
Transforms in Clifford Analysis -- On a class of non-linear boundary value problems -- Pin structures and the Dirac operator on real projective spaces and quadrics -- Construction of monopoles and instantons by using spinors and the | |
inversion theorem -- Determinants, Manifolds with Boundary and Dirac Operators -- New dynamical equations for many particle system on the basis of multicomplex algebra | |
ISBN: | 9789401150361 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Fundamental Theories of Physics, An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application : 94 |
Keywords: | Mathematics , Associative rings , Rings (Algebra) , Functions of complex variables , Integral transforms , Operational calculus , Partial differential equations , Mathematical logic , Mathematics , Functions of a Complex Variable , Mathematical Logic and Foundations , Associative Rings and Algebras , Integral Transforms, Operational Calculus , Partial Differential Equations |
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Call number: | SPRINGER-1998-9781461220282:ONLINE Show nearby items on shelf |
Title: | Introductory Statistics and Random Phenomena Uncertainty, Complexity and Chaotic Behavior in Engineering and Science |
Author(s): |
Manfred Denker |
Date: | 1998 |
Size: | 1 online resource (509 p.) |
Note: | 10.1007/978-1-4612-2028-2 |
Contents: | I Descriptive Statistics-Compressing Data -- 1 Why One Needs to Analyze Data -- 2 Data Representation and Compression -- 3 Analytic Representation of Random Experimental Data -- II Modeling Uncertainty -- 4 Algorithmic Complexity and |
Random Strings -- 5 Statistical Independence and Kolmogorov’s Probability Theory -- 6 Chaos in Dynamical Systems: How Uncertainty Arises in Scientific and Engineering Phenomena -- III Model Specification-Design of Experiments -- 7 | |
General Principles of Statistical Analysis -- 8 Statistical Inference for Normal Populations -- 9 Analysis of Variance -- A Uncertainty Principle in Signal Processing and Quantum Mechanics -- B Fuzzy Systems and Logic -- C A Critique | |
of Pure Reason -- D The Remarkable Bernoulli Family -- F Tables | |
ISBN: | 9781461220282 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Engineering , Applied mathematics , Engineering mathematics , Computer mathematics , Probabilities , Statistics , Engineering , Appl.Mathematics/Computational Methods of Engineering , Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Scien , Applications of Mathematics , Probability Theory and Stochastic Processes , Computational Science and Engineering |
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Call number: | SPRINGER-1997-9789401589390:ONLINE Show nearby items on shelf |
Title: | The Riemann Legacy Riemannian Ideas in Mathematics and Physics |
Author(s): |
Krzysztof Maurin |
Date: | 1997 |
Size: | 1 online resource (719 p.) |
Note: | 10.1007/978-94-015-8939-0 |
Contents: | I Riemannian Ideas in Mathematics and Physics -- 1 Gauss Inner Curvature of Surfaces -- 2 Sectional Curvature. Spaces of Constant Curvature. Weyl Hypothesis -- 3 Cohomology of Riemann spaces. Theorems of de Rham, Hodge, Kodaira -- 4 |
Chern—Gauss—Bonnet theorem -- 5 Curvature and Topology or Characteristic Forms of Chern, Pontriagin, and Euler -- 6 Kähler Spaces. Bergman Metrics. Harish-Chandra-Cartan Theorem. Siegel Space (once again!) -- II General Structures of | |
Mathematics -- 1 Differentiable Structures. Tangent Spaces. Vector Fields -- 2 Projective (Inverse) Limits of Topological Spaces -- 3 Inductive Limits. Presheaves. Covering Defined by Presheaf -- 4 Algebras. Groups, Tensors, Clifford, | |
Grassmann, and Lie Algebras. Theorems of Bott—Milnor, Wedderburn, and Hurwitz -- 5 Fields and their Extensions -- 6 Galois Theory. Solvable Groups -- 7 Ruler and Compass Constructions. Cyclotomic Fields. Kronecker—Weber Theorem -- 8 | |
Algebraic and Transcendental Elements -- 9 Weyl principle -- 10 Topology of Compact Lie Groups -- 11 Representations of Compact Lie Groups -- 12 Nilpotent, Semimple, and Solvable Lie Algebras -- 13 Reflections, Roots, and Weights. | |
Coxeter and Weyl groups -- 14 Covariant Differentiation. Parallel Transport. Connections -- 15 Remarks on Rich Mathematical Structures of Simple Notions of Physics Based on Example of Analytical Mechanics -- 16 Tangent Bundle TM. | |
Vector, Fiber, Tensor and Tensor Densities, and Associate Bundles -- 17 G-spaces. Group Representations -- 18 Principal and Associated Bundles -- 19 Induced Representations and Associated Bundles -- 20 Vector Bundles and Locally Free | |
Sheaves -- 21 Axiom of Covering Homotopy -- 22 Serre Fibering. General Theory of Connection. Corollaries -- 23 Homology. Cohomology. de Rham Cohomology -- 24 Cohomology of Sheaves. Abstract de Rham Theorem -- 25 Homotopy Group ?k(X, | |
x0). Hopf Fibering. Serre Theorem on Exact Sequence of Homotopy Groups of a Fibering -- 26 Various Benefits of Characteristic Classes (Orientability, Spin Structures). Clifford Groups, Spin Group -- 27 Divisors and Line Bundles. | |
Algebraic and Abelian Varieties -- 28 General Abelian Varieties and Theta Function -- 29 Theorems on Algebraic Dependence -- III The Idea of the Riemann Surface -- IV Riemann and Calculus of Variations -- 1 Introduction -- 2 The | |
Plateau Problem -- 3 Teichmüller Theory. Riemann Moduli Problem -- 4 Riemannian Approach to Teichmiiller Theory. Harmonic Maps and Teichmüller Space -- 5 Teichmüller theory and Plateau—Douglas problem -- 6 Rescuing Riemann’s Dirichlet | |
Principle. Potential Theory -- 7 The Royal Road to Calculus of Variations (Constantin Carathéodory) -- 8 Symplectic and Contact Geometries. Conservation Laws -- 9 Direct Methods in Calculus of Variations for Manifolds with Isometries. | |
Equivariant Sobolev Theorems. Yamabe Problem and its Relation to General Relativity -- V Riemann and Complex Geometry -- 1 Introduction -- 2 On Complex Analysis in Several Variables -- 3 Ellipticity, Runge Property, and Runge Type | |
Theorems -- 4 Hörmander Method in Complex Analysis -- 5 Wirtinger Theorems. Metric Theory of Analytic Sets -- 6 The Problem of Poincaré and the Cousin Problems -- 7 Ringed Spaces and General Complex Spaces -- 8 Construction of Complex | |
Spaces by Gluing and by Taking Quotient -- 9 Differential Geometry of Holomorphic Vector Bundles over Compact Riemann Surfaces and Kähler manifolds. Stable Vector Bundles, Hermite-Einstein Connections, and their Moduli Spaces -- VI | |
Riemann and Number Theory -- 1 Introduction -- 2 The Riemann ? function -- 3 Hecke Theory -- 4 Dedekind ?K function for number field K and Selberg ? function -- Concluding Remarks -- Suggestions for Further Reading | |
ISBN: | 9789401589390 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 417 |
Keywords: | Mathematics , Algebra , Mathematical analysis , Analysis (Mathematics) , Applied mathematics , Engineering mathematics , Geometry , Mathematics , Applications of Mathematics , Algebra , Geometry , Analysis |
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Call number: | SPRINGER-1997-9789400914834:ONLINE Show nearby items on shelf |
Title: | Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models |
Author(s): |
Andrei Khrennikov |
Date: | 1997 |
Size: | 1 online resource (376 p.) |
Note: | 10.1007/978-94-009-1483-4 |
Contents: | I. Measurements and Numbers -- 1. Mathematics and Reality -- 2. Measurements and Natural Numbers -- 3. Measurements and Rational Numbers -- 4. Real Numbers: Infinite Exactness of Measurements -- 5. On the Boundary of the Real |
Continuum -- 6. Finite Exactness and m-adic Numbers -- 7. Rings of m-adic Numbers -- 8. Ultrametric Spaces -- 9. Ultrametric Social Space -- 10. Non-Real Models of Space -- II. Fundamentals -- 1. Einstein-Podolsky-Rosen Paradox -- 2. | |
Foundations of Quantum Mechanics -- 3. Foundations of Probability Theory -- 4. Statistical Interpretation of Quantum mechanics -- 5. Quantum Probabilities Two Slit Experiment -- 6. Bell’s Inequality and the Death of Reality -- 7. | |
Individual Realists Interpretation and Hidden Variables -- 8. Orthodox Copenhagen Interpretation -- 9. Einstein-Podolsky-Rosen Paradox and Interpretations of Quantum Mechanics -- III. Non-Archimedean Analysis -- 1. Exponential Function | |
-- 2. Normed and Locally Convex Spaces -- 3. Locally Constant Functions -- 4. Kaplansky’s Theorem -- 5. Differentiate Functions -- 6. Analytic Functions -- 7. Complex Non-Archimedean Numbers -- 8. Mahler Basis -- 9. Measures on the | |
Ring of p-adic Integers -- 10. Volkenborn Integral (Uniform Distribution) -- 11. The Monna-Springer Integration Theory -- IV. The Ultrametric Hilbert Space Description of Quantum Measurements with a Finite Exactness -- 1. Critique of | |
Interpretations of Quantum Mechanics -- 2. Preparation Procedures and State Spaces -- 3. Ultrametric (m-adic) Hilbert Space -- 4. m-adic (Ultrametric) Axiomatic of Quantum Measurements -- 5. Heisenberg Uncertainty and Inexactness | |
Relations -- 6. Energy Representation for the Harmonic Oscillator -- 7. Einstein-Podolsky-Rosen Paradox and Infinite Exactness of Measurements -- 8. Fuzzy Reality -- 9. Quantum-Classical Heisenberg Inexactness Relation for the Harmonic | |
Oscillator and Free Particle -- V. Non-Kolmogorov Probability Theory -- 1. Frequency Probability Theory -- 2. Measure and Probability -- 3. Densities -- 4. Integration Technique -- 5. Non-Kolmogorov Axiomatics -- 6. Products of | |
Probabilities -- 7. Proportional and Classical Definitions of Probability -- 8. p-adic Asymptotic of Bernoulli Probabilities -- 9. More Complicated p-adic Asymptotics -- 10. p-adic Bernoulli Theorem -- 11. Non-symmetrical Bernoulli | |
Distributions -- 12. The Central Limit Theorem -- VI. Non-Kolmogorov Probability and Quantum Physics -- 1. Dirac, Feynman, Wigner and Negative Probabilities -- 2. p-adic Stochastic Point of View of Bell’s Inequality -- 3. An Example of | |
p-adic Negative Probability Behaviour -- 4. p-adic Stochastic Hidden Variable Model with Violations of Bell’s Inequality -- 5. Quadri Variate Joint Probability Distribution -- 6. Non-Kolmogorov Statistical Theory -- 7. Physical | |
Interpretation of Negative Probabilities in Prugovecki’s Empirical Theory of Measurement -- 8. Experiments to Find p-adic Stochastics in the Two Slit Experiment -- VII. Position and Momentum Representations -- 1. Groups of Unitary | |
Isometric Operators in a p-adic Hilbert Space -- 2. p-adic Valued Gaussian Integration and Spaces of Square Integrable Functions -- 3. A Representation of the Translation Group -- 4. Gaussian Representations for the Position and | |
Momentum Operators -- 5. Unitary Isometric One Parameter Groups Corresponding to the Position and Momentum Operators -- 6. Operator Calculus -- 7. Exactness of a Measurement of Positions and Momenta -- 8. Spectrum of p-adic Position | |
Operator -- 9. L2-space with respect to p-adic Lebesgue distributions -- 10. Fourier Transform of L2-maps and Momentum Representation -- 11. Schrödinger Equation -- VIII. p-adic Dynamical Systems with Applications to Biology and Social | |
Sciences -- 1. Roots of Unity -- 2. Dynamical Systems in Non-Archimedean Fields -- 3. Dynamical Systems in the Field of Complex p-adic Numbers -- 4. Dynamical Systems in the Fields of p-adic Numbers -- 5. Computer Calculations for | |
Fuzzy Cycles -- 6. The Human Subconscious as a p-adic Dynamical System -- 7. Ultrametric on the Genealogical Tree -- 8. Social Dynamics -- 9. Human History as a p-adic Dynamical System -- 10. God as p-adic Dynamical System -- 11. | |
Struggle of Civilizations -- 12. Economical and Social Effectiveness -- Open Problems -- 1. Newton’s Method (Hensel Lemma) -- 2. Non-Real Reality -- 5. Quantum Mechanics of Vladimirov and Volovich | |
ISBN: | 9789400914834 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Mathematics and Its Applications : 427 |
Keywords: | Physics , Functional analysis , Number theory , Quantum physics , Statistics , Physics , Quantum Physics , Functional Analysis , Number Theory , Statistics, general , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-1997-9783540695219:ONLINE Show nearby items on shelf |
Title: | Integrability of Nonlinear Systems Proceedings of the CIMPA School Pondicherry University, India, 8–26 January 1996 |
Author(s): | |
Date: | 1997 |
Size: | 1 online resource (380 p.) |
Note: | 10.1007/BFb0113690 |
Contents: | Nonlinear waves, solitons and IST -- Integrability — and how to detect it -- to the Hirota bilinear method -- Lie bialgebras, poisson Lie groups and dressing transformations -- Analytic and asymptotic methods for nonlinear singularity |
analysis: a review and extensions of tests for the Painlevé property -- Bifurcations, chaos, controlling and synchronization of certain nonlinear oscillators -- Eight lectures on integrable systems -- Bilinear formalism in solition | |
theory -- Quantum and classical integrable systems | |
ISBN: | 9783540695219 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Physics: 495 |
Keywords: | Physics , Mechanics , Fluids , Physics , Theoretical, Mathematical and Computational Physics , Fluid- and Aerodynamics , Mechanics |
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Call number: | SPRINGER-1997-9781468400328:ONLINE Show nearby items on shelf |
Title: | Nonlinear Physics with Maple for Scientists and Engineers |
Author(s): |
Richard H Enns |
Date: | 1997 |
Note: | 10.1007/978-1-4684-0032-8 |
Contents: | 1 Introduction -- 1.1 It’s a Nonlinear World -- 1.2 Symbolic Computation -- 1.3 Nonlinear Activities -- 1.4 Structure of the Text -- 2 Some Nonlinear Systems -- 2.1 Nonlinear Mechanics -- 2.2 Competition Phenomena -- 2.3 Nonlinear |
Electrical Phenomena -- 2.4 Chemical and Other Oscillators -- 2.5 Pattern Formation -- 2.6 Solitons -- 2.7 Chaos and Maps -- 3 Topological Analysis -- 3.1 Introductory Remarks -- 3.2 Types of Simple Singular Points -- 3.3 Classifying | |
Simple Singular Points -- 3.4 Examples of Phase Plane Analysis -- 3.5 Isoclines -- 4 Analytic Methods -- 4.1 Introductory Remarks -- 4.2 Some Exact Methods -- 4.3 Some Approximate Methods -- 4.4 The Krylov-Bogoliubov (KB) Method -- 4.5 | |
Ritz and Galerkin Methods -- 5 The Numerical Approach -- 5.1 Finite-Difference Approximations -- 5.2 Euler and Modified Euler Methods -- 5.3 Rungé-Kutta (RK) Methods -- 5.4 Adaptive Step Size -- 5.5 Stiff Equations -- 5.6 Implicit and | |
Semi-Implicit Schemes -- 6 Limit Cycles -- 6.1 Stability Aspects -- 6.2 Relaxation Oscillations -- 6.3 Bendixson’s First Theorem: The Negative Criterion -- 6.4 The Poincaré-Bendixson Theorem -- 6.5 The Brusselator Model -- 7 Forced | |
Oscillators -- 7.1 Duffing’s Equation -- 7.2 The Jump Phenomenon and Hysteresis -- 7.3 Subharmonic and Other Periodic Oscillations -- 7.4 Power Spectrum -- 7.5 Chaotic Oscillations -- 7.6 Entrainment and Quasiperiodicity -- 7.7 The | |
Rössler and Lorenz Systems -- 8 Nonlinear Maps -- 8.1 Introductory Remarks -- 8.2 The Logistic Map -- 8.3 Fixed Points and Stability -- 8.4 The Period-Doubling Cascade to Chaos -- 8.5 Period Doubling in the Real World -- 8.6 The | |
Lyapunov Exponent -- 8.7 Stretching and Folding -- 8.8 The Circle Map -- 8.9 Chaos versus Noise -- 8.10 2-Dimensional Maps -- 9 Nonlinear PDE Phenomena -- 9.1 Introductory Remarks -- 9.2 Burger’s Equation -- 9.3 Bäcklund | |
Transformations -- 9.4 Solitary Waves -- 10 Numerical Simulation -- 10.1 Finite Difference Approximations -- 10.2 Explicit Methods -- 10.3 Von Neumann Stability Analysis -- 10.4 Implicit Methods -- 10.5 Method of Characteristics -- | |
10.6 Higher Dimensions -- 11 Inverse Scattering Method -- 11.1 Lax’s Formulation -- 11.2 Application to KdV Equation -- 11.3 Multi-Soliton Solutions -- 11.4 General Input Shapes -- 11.5 The Zakharov-Shabat/AKNS Approach | |
ISBN: | 9781468400328 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Physics , Theoretical, Mathematical and Computational Physics , Numerical and Computational Physics , Mathematical Methods in Physics |
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Call number: | SPRINGER-1996-9789401154307:ONLINE Show nearby items on shelf |
Title: | Maximum Entropy and Bayesian Methods Santa Fe, New Mexico, U.S.A., 1995 Proceedings of the Fifteenth International Workshop on Maximum Entropy and Bayesian Methods |
Author(s): | |
Date: | 1996 |
Size: | 1 online resource (458 p.) |
Note: | 10.1007/978-94-011-5430-7 |
Contents: | Reconstruction of the Probability Density Function Implicit in Option Prices from Incomplete and Noisy Data -- Model Selection and Parameter Estimation for Exponential Signals -- Hierarchical Bayesian Time-Series Models -- Bayesian |
time Series: Models and Computations for the Analysis of time Series in the Physical Sciences -- Maxent, Mathematics, and Information Theory -- Bayesian Estimation of the von Mises Concentration Parameter -- A Characterization of the | |
Dirichlet Distribution with Application to Learning Bayesian Networks -- The Bootstrap is Inconsistent with Probability Theory -- Data-Driven Priors for Hyperparameters in Regularization -- Mixture Modeling to Incorporate Meaningful | |
Constraints Into Learning -- Maximum Entropy (Maxent) Method in Expert Systems and Intelligent Control: new Possibilities and Limitations -- The De Finetti Transform -- Continuum Models for Bayesian Image Matching -- Mechanical Models | |
as Priors in Bayesian Tomographic Recontruction -- The Bayes Inference Engine -- A Full Bayesian Approach for Inverse Problem -- Pixon-Based Multiresolution Image Reconstruction and Quantification of Image Information Content -- | |
Bayesian Multimodal Evidence Computation by Adaptive Tempering Mcmc -- Bayesian Inference and the Analytic Continuation of Imaginary-Time Quantum Monte Carlo Data -- Spectral Properties from Quantum Monte Carlo Data: a Consistent | |
Approach -- An Application of Maximum Entropy Method to Dynamical Correlation Functions at Zero Temperature -- Chebyshev Moment Problems: Maximum Entropy and Kernel Polynomial Methods -- Cluster Expansions and Iterative Scaling for | |
Maximum- Entropy Language Models -- A Maxent Tomography Method for Estimating fish Densities in a Commercial Fishery -- Toward Optimal Observer Performance of Detection and Discrimination Tasks on Reconstructions from Sparse Data -- | |
Entropies for Dissipative Fluids and Magnetofluids Without Discretization -- On the Importance of a Marginalization in Maximum Entropy -- Quantum Mechanics as an Exotic Probability Theory -- Bayesian Parameter Estimation of | |
Nuclear-Fusion Confinement time Scaling Laws -- Hierarchical Segmentation of Range and Color Images Based on Bayesian Decision Theory -- Priors on Measures -- Determining Whether two Data Sets are from the Same Distribution -- Occam’s | |
Razor for Parametric Families and Priors on the Space of Distributions -- Skin and Maximum Entropy: a Hidden Complicity? -- Predicting the Accuracy of Bayes Classifiers -- Maximum Entropy Analysis of Genetic Algorithms -- Data Fusion | |
in the field of non Destructive Testing -- Dual Statistical Mechanical Theory for Unsupervised and Supervised Learning -- Complex Sinusoid Analysis by Bayesian Deconvolution of the Discrete Fourier Transform -- Statistical Mechanics of | |
Choice -- Rational Neural Models Based on Information Theory -- A new Entropy Measure with the Explicit Notion of Complexity -- Maximum Entropy States and Coherent Structures in Magnetohydrodynamics -- A Lognormal State of Knowledge -- | |
Pixon-Based Multiresolution Image Reconstruction for Yohkoh’S Hard X-Ray Telescope -- Bayesian Methods for Interpreting Plutonium Urinalysis Data -- The Information Content of Sonar Echoes -- Objective Prior for Cosmological Parameters | |
-- Meal Estimation: Acceptable-Likelihood Extensions of Maxent -- On Curve Fitting with Two-Dimensional Uncertainties -- Bayesian Inference in Search for the in Vivo T2 Decay-Rate Distribution in Human Brain -- Bayesian Comparison of | |
fit Parameters: Application to Time-Resolved X-Ray Spectroscopy -- Edge Entropy and Visual Complexity -- Maximum Entropy Tomography -- Bayesian Regularization of Some Seismic Operators -- Multimodality Bayesian Algorithm for Image | |
Reconstruction in Positron Emission Tomography -- Evidence Integrals | |
ISBN: | 9789401154307 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Fundamental Theories of Physics, An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application : 79 |
Keywords: | Mathematics , Probabilities , Physics , Statistical physics , Dynamical systems , Statistics , Electrical engineering , Mathematics , Probability Theory and Stochastic Processes , Physics, general , Statistics, general , Statistical Physics, Dynamical Systems and Complexity , Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Scien , Electrical Engineering |
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Call number: | SPRINGER-1996-9781461240846:ONLINE Show nearby items on shelf |
Title: | Geometry of Harmonic Maps |
Author(s): |
Yuanlong Xin |
Date: | 1996 |
Size: | 1 online resource (246 p.) |
Note: | 10.1007/978-1-4612-4084-6 |
Contents: | I. Introduction -- 1.1 Vector Bundles -- 1.2 Harmonic Maps -- 1.3 A Bochner Type Formula -- 1.4 Basic Properties of Harmonic Maps -- II. Conservation Law -- 2.1 Stress-Energy Tensor and Conservation Law -- 2.2 Monotonicity Formula -- |
2.3 Applications of Conservation Law to Liouville type Theorems -- 2.4 Further Generalizations -- III. Harmonic Maps and Gauss Maps -- 3.1 Generalized Gauss Maps -- 3.2 Cone-like Harmonic Maps -- 3.3 Generalized Maximum Principle -- | |
3.4 Estimates of Image Diameter and its Applications -- 3.5 Gauss Image of a Space-Like Hypersurface in Minkowski Space -- 3.6 Gauss Image of a Space-Like Submanifold in Pseudo-Euclidean Space -- IV. Harmonic Maps and Holomorphic Maps | |
-- 4.1 Partial Energies -- 4.2 Harmonicity of Holomorphic Maps -- 4.3 Holomorphicity of Harmonic Maps -- V. Existence, Nonexistence and Regularity -- 5.1 Direct Method of the Calculus of Variations -- 5.2 Regularity Theorems -- 5.3 | |
Nonexistence and Existence -- 5.4 Regularity Results of Harmonic Maps into Positively Curved Manifolds -- VI. Equivariant Harmonic Maps -- 6.1 Riemannian Submersions and Equivariant Harmonic Maps -- 6.2 Reduction Theorems -- 6.3 | |
Equivariant Variational Formulas -- 6.4 On Harmonic Representatives of ?m(Sm) -- 6.5 Harmonic Maps via Isoparametric Maps -- 6.6 Harmonic Maps of Projective Spaces -- 6.7 Equivariant Boundary Value Problems -- References | |
ISBN: | 9781461240846 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Nonlinear Differential Equations and Their Applications : 23 |
Keywords: | Mathematics , Partial differential equations , Functions of complex variables , Differential geometry , Probabilities , Physics , Continuum mechanics , Mathematics , Differential Geometry , Probability Theory and Stochastic Processes , Partial Differential Equations , Several Complex Variables and Analytic Spaces , Mathematical Methods in Physics , Continuum Mechanics and Mechanics of Materials |
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Call number: | SPRINGER-1996-9781461207757:ONLINE Show nearby items on shelf |
Title: | Partial Differential Equations and Mathematical Physics The Danish-Swedish Analysis Seminar, 1995 |
Author(s): | |
Date: | 1996 |
Size: | 1 online resource (376 p.) |
Note: | 10.1007/978-1-4612-0775-7 |
Contents: | On perturbation of embedded eigenvalues -- Blowup of classical solutions of nonlinear hyperbolic equations: a survey of recent results -- Global time decay of the amplitude of a reflected wave -- Weyl quantization and Fourier integral |
operators -- The local index theorem without smoothness -- How ideas from microlocal analysis can be applied in 2-D fluid mechanics -- Lp spectral independence for certain uniformly elliptic operators -- Trace asymptotics via almost | |
analytic extensions -- A microlocal version of concentration-compactness -- Complete heat trace, resolvent and zeta expansions for general Atiyah-Patodi-Singer problems -- Semi-classical analysis for the transfer operator: WKB | |
constructions in dimension 1 -- Several recent results in nonlinear geometric optics -- Stabilization of the wave equation by the boundary -- About small-power semilinear wave equations -- The Faddeev approach to inverse scattering | |
from a micro-local perspective -- Fibrations, compactifications and algebras of pseudodifferential operators -- Degree theory beyond continuous maps -- On the Weyl formula for obstacles -- On the asymptotic completeness for particles | |
in constant electromagnetic fields -- The size of atoms in Hartree-Fock theory -- Holomorphic extension of CR functions: a survey -- Local solvability in a class of overdetermined systems of linear PDE -- Neumann resonances in linear | |
elasticity | |
ISBN: | 9781461207757 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Nonlinear Differential Equations and Their Applications : 21 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Partial differential equations , Applied mathematics , Engineering mathematics , Physics , Mathematics , Analysis , Partial Differential Equations , Mathematical Methods in Physics , Applications of Mathematics |
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Call number: | SPRINGER-1995-9783642794407:ONLINE Show nearby items on shelf |
Title: | Computational Fluid Dynamics Selected Topics |
Author(s): | |
Date: | 1995 |
Size: | 1 online resource (287 p.) |
Note: | 10.1007/978-3-642-79440-7 |
Contents: | Continuum Hypothesis in the Computation of Gas-Solid Flows -- 1. Introduction -- 2. Governing Equations -- 3. Numerical Procedure -- 4. Numerical Results -- 5. Conclusions -- Numerical Modelling of Two- and Three-Dimensional External |
and Internal Unsteady Incompressible Flow Problems -- 1. Introduction -- 2. The Mathematical Model — The Governing Equations -- 3. The Numerical Solution Method -- 4. The Solution of the Equation Systems (3.9) and (3.10) — Solvability | |
Conditions -- 5. The Application of the Solution Methods to Crystal Melt Flow -- 6. The External Flow Around a Cylinder -- Numerical Experiments in Double-Diffusive Convection -- 1. Introduction -- 2. The Motion Equations and Their | |
Numerical Solution -- 3. Lateral Heating of a Stratified Fluid -- 4. Conclusion -- New Potentialities of Computational Experiment in Tsunami Problem -- 1. Introduction -- 2. Basic Mathematical Models -- 3. Methodological Principles of | |
Some Applied Problems of Tsunami by Computational Experiment -- 4. Computational Experiment Facilities Employed for the Training of the Tsunami Warning Service Personnel and of the Population in the Threatened Zones -- General Balance | |
Equations for a Fluid—Fluid Interface in Magnetofluiddynamics Soubbaramayer -- 1. Introduction -- 2. MFD Model: Integral Conservative Form -- 3. Balance Equations for the Interface -- 4. Application to the Calculation of the Surface | |
Depression in a High-Current Arc Weld Pool -- 5. Conclusion -- Group-Invariant Solutions of Hydrodynamics -- 1. Introduction -- 2. Lie Groups Applied to Differential Equations -- 3. Hydrodynamics Model -- 4. One-Dimensional Solutions | |
-- 5. Two-Dimensional Solutions -- 6. 3-D Solutions -- 7. Analytic Solutions -- Survey on Exact Solutions for Discrete Models of the Boltzmann Equation -- 1. Introduction -- 2. Broad well Equations -- 3. Models with 14 Velocities -- 4. | |
Models with Triple Collisions -- 5. Two-Dimensional Semi-Continuous Model Ill -- 6. Conclusion -- Boundary Conditions for Discrete Models of Gases and Applications to Couette Flows Amah D’Almeida and Renée Gatignol -- 1. Introduction | |
-- 2. Discrete Kinetic Theory -- 3. Boundary Conditions -- 4. Couette Flows -- 5. Results -- 6. Conclusion -- Computation of Viscous Transonic Flow Around the F5 Wing -- 1. Introduction -- 2. Governing Equations and Boundary Conditions | |
-- 3. Numerical Method -- 4. Results -- 5. Conclusions -- A Time-Dependent Space Marching Algorithm for Three-Dimensional PNS Equations -- 1. Introduction -- 2. Governing Equations -- 3. The Flux-Difference Splitting -- 4. | |
Explicit-Implicit Difference Scheme -- 5. Numerical Tests -- 6. Conclusions -- New Potential-Field Properties of General Laminar and Turbulent Motions of Newtonian Fluids -- I. Introduction -- 2. Physical and Mathematical Preliminaries | |
-- 3. Derivation of Some Field Properties of NSE -- 4. Thermo dynamical Stability Criterion for Instationary Flows -- 5. The Instationary Turbulent Flow in Temporal Mean -- 6. Conclusion -- Boundary Layer Turbulence and the Control by | |
Suction -- 1. Introduction -- 2. Flow Change with the Development of Boundary Layer -- 3. Discussion on Energy -- 4. Self-Organization of Turbulent Boundary Layer -- 5. Experiment on Control of Turbulent Boundary Layer -- 6. | |
Conclusions -- On the Quasi-Geostrophic Drag on a Rising Sphere in a Rotating Fluid -- 1. Introduction -- 2. Solution -- 3. Results -- Two-Dimensional Nonlinear Saturation Behaviour of Instability Waves in a Boundary Layer at Mach 5 -- | |
1. Introduction -- 2. Governing Equations -- 3. Numerical Method -- 4. Simulation Results -- 5. Perturbation Evolution -- 6. Evolution of the Flow Field -- 7. Shock Identification -- 8. Conclusions -- Inertia! Convection in Turbulent | |
Rayleigh-Bénard Convection at Small Prandtl Numbers -- 1. Introduction -- 2. Simulation Method -- 3. Case Specifications and Initial Data -- 4. Results -- 5. Conclusions -- The GRP Treatment of Flow Singularities -- 1. Tracking of | |
Singularities -- 2. Geometrical Singularities -- 3. Narrow Reaction Zones in Combustion Calculations -- Application of the Multidomain Local Fourier Method for CFD in Complex Geometries -- 1. Introduction -- 2. Multidomain Local | |
Fourier Method (MDLF) -- 3. Problems in Complex Geometries -- 4. Preconditioned Iteration Method with Spectral Preconditioner -- 5. Demonstration for the Navier-Stokes System -- Confined Swirling Flows - A Continuing Challenge -- 1. | |
Introduction -- 2. Statement of the Problem -- 3. Numerical Formulation -- 4. Results and Discussion -- 5. Conclusions -- Eshelbian Continuum Mechanics and Nonlinear -- 1. Introduction -- 2. Momentum and Pseudo-Momentum Force and | |
Pseudo-Force -- 3. Field Formulation -- 4. Non-Equivalence Between Global Formulations -- 5. The Role of Pseudomomentum and Energy in Nonlinear-Wave Propagation -- 6. A Newtonian Mechanics for Global Material Forces? | |
ISBN: | 9783642794407 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Geology , Geophysics , Oceanography , Fluids , Atoms , Mechanical engineering , Physics , Fluid- and Aerodynamics , Atomic, Molecular, Optical and Plasma Physics , Mechanical Engineering , Oceanography , Geophysics/Geodesy , Geology |
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Call number: | SPRINGER-1995-9781461384489:ONLINE Show nearby items on shelf |
Title: | Hamiltonian Dynamical Systems History, Theory, and Applications |
Author(s): | |
Date: | 1995 |
Size: | 1 online resource (385 p.) |
Note: | 10.1007/978-1-4613-8448-9 |
Contents: | History -- The Concept of Elastic Stress in Eighteenth-Century Mechanics: Some Examples from Euler -- Book Two of Radical Principia -- Factoring the Lunar Problem: Geometry, Dynamics, and Algebra in the Lunar Theory from Kepler to |
Clairaut -- Theory and Applications -- A Limiting Absorption Principle for Separated Dirac Operators with Wigner von Neumann Type Potentials -- Lax Pairs in the Henon-Heiles and Related Families -- Poincaré Compactification of | |
Hamiltonian Polynomial Vector Fields -- Transverse Homoclinic Connections for Geodesic Flows -- A New Proof of Anosov’s Averaging Theorem -- Bifuracation in the Generalized van der Waals Interaction: The Polar Case (M = 0) -- Energy | |
Equipartition and Nekhoroshev-Type Estimates for Large Systems -- Suspension of Symplectic Twist Maps by Hamiltonians -- Global Structural Stability of Planar Hamiltonian Vector Fields -- Analytic Torsion, Flows and Foliations -- | |
Linearized Dynamics of Symmetric Lagrangian Systems -- A 1:—1 Semisimple Hamiltonian Hopf Bifurcation in Vortex Dynamics -- Stability of Hamiltonian Systems over Exponentially Long Times: The Near-Linear Case -- Constrained Variational | |
Principles and Stability in Hamiltonian Systems -- The Global Phase Structure of the Three Dimensional Isosceles Three Body Problem with Zero Energy -- Non-canonical Transformations of Nonlinear Hamiltonians -- Linear Stability | |
Analysis of Some Symmetrical Classes of Relative Equilibria -- Identical Maslov Indices from Different Symplectic Structures -- Discretization of Autonomous Systems and Rapid Forcing -- Computing the Motion of the Moon Accurately -- On | |
the Rapidly Forced Pendulum -- Existence of Invariant Tori for Certain Non-Symplectic Diffeomorphisms | |
ISBN: | 9781461384489 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | The IMA Volumes in Mathematics and its Applications: 63 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis |
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Call number: | SPRINGER-1995-9781461208150:ONLINE Show nearby items on shelf |
Title: | Applied Functional Analysis Applications to Mathematical Physics |
Author(s): |
Eberhard Zeidler |
Date: | 1995 |
Size: | 1 online resource (481 p.) |
Note: | 10.1007/978-1-4612-0815-0 |
Contents: | 1 Banach Spaces and Fixed-Point Theorems -- 1.1 Linear Spaces and Dimension -- 1.2 Normed Spaces and Convergence -- 1.3 Banach Spaces and the Cauchy Convergence Criterion -- 1.4 Open and Closed Sets -- 1.5 Operators -- 1.6 The Banach |
Fixed-Point Theorem and the Iteration Method -- 1.7 Applications to Integral Equations -- 1.8 Applications to Ordinary Differential Equations -- 1.9 Continuity -- 1.10 Convexity -- 1.11 Compactness -- 1.12 Finite-Dimensional Banach | |
Spaces and Equivalent Norms -- 1.13 The Minkowski Functional and Homeomorphisms -- 1.14 The Brouwer Fixed-Point Theorem -- 1.15 The Schauder Fixed-Point Theorem -- 1.16 Applications to Integral Equations -- 1.17 Applications to | |
Ordinary Differential Equations -- 1.18 The Leray-Schauder Principle and a priori Estimates -- 1.19 Sub- and Supersolutions, and the Iteration Method in Ordered Banach Spaces -- 1.20 Linear Operators -- 1.21 The Dual Space -- 1.22 | |
Infinite Series in Normed Spaces -- 1.23 Banach Algebras and Operator Functions -- 1.24 Applications to Linear Differential Equations in Banach Spaces -- 1.25 Applications to the Spectrum -- 1.26 Density and Approximation -- 1.27 | |
Summary of Important Notions -- 2 Hilbert Spaces, Orthogonality, and the Dirichlet Principle -- 2.1 Hilbert Spaces -- 2.2 Standard Examples -- 2.3 Bilinear Forms -- 2.4 The Main Theorem on Quadratic Variational Problems -- 2.5 The | |
Functional Analytic Justification of the Dirichlet Principle -- 2.6 The Convergence of the Ritz Method for Quadratic Variational Problems -- 2.7 Applications to Boundary-Value Problems, the Method of Finite Elements, and Elasticity -- | |
2.8 Generalized Functions and Linear Functionals -- 2.9 Orthogonal Projection -- 2.10 Linear Functionals and the Riesz Theorem -- 2.11 The Duality Map -- 2.12 Duality for Quadratic Variational Problems -- 2.13 The Linear Orthogonality | |
Principle -- 2.14 Nonlinear Monotone Operators -- 2.15 Applications to the Nonlinear Lax-Milgram Theorem and the Nonlinear Orthogonality Principle -- 3 Hilbert Spaces and Generalized Fourier Series -- 3.1 Orthonormal Series -- 3.2 | |
Applications to Classical Fourier Series -- 3.3 The Schmidt Orthogonalization Method -- 3.4 Applications to Polynomials -- 3.5 Unitary Operators -- 3.6 The Extension Principle -- 3.7 Applications to the Fourier Transformation -- 3.8 | |
The Fourier Transform of Tempered Generalized Functions -- 4 Eigenvalue Problems for Linear Compact Symmetric Operators -- 4.1 Symmetric Operators -- 4.2 The Hilbert-Schmidt Theory -- 4.3 The Fredholm Alternative -- 4.4 Applications to | |
Integral Equations -- 4.5 Applications to Boundary-Eigenvalue Value Problems -- 5 Self-Adjoint Operators, the Friedrichs Extension and the Partial Differential Equations of Mathematical Physics -- 5.1 Extensions and Embeddings -- 5.2 | |
Self-Adjoint Operators -- 5.3 The Energetic Space -- 5.4 The Energetic Extension -- 5.5 The Friedrichs Extension of Symmetric Operators -- 5.6 Applications to Boundary-Eigenvalue Problems for the Laplace Equation -- 5.7 The Poincaré | |
Inequality and Rellich’s Compactness Theorem -- 5.8 Functions of Self-Adjoint Operators -- 5.9 Semigroups, One-Parameter Groups, and Their Physical Relevance -- 5.10 Applications to the Heat Equation -- 5.11 Applications to the Wave | |
Equation -- 5.12 Applications to the Vibrating String and the Fourier Method -- 5.13 Applications to the Schrödinger Equation -- 5.14 Applications to Quantum Mechanics -- 5.15 Generalized Eigenfunctions -- 5.16 Trace Class Operators -- | |
5.17 Applications to Quantum Statistics -- 5.18 C*-Algebras and the Algebraic Approach to Quantum Statistics -- 5.19 The Fock Space in Quantum Field Theory and the Pauli Principle -- 5.20 A Look at Scattering Theory -- 5.21 The | |
Language of Physicists in Quantum Physics and the Justification of the Dirac Calculus -- 5.22 The Euclidean Strategy in Quantum Physics -- 5.23 Applications to Feynman’s Path Integral -- 5.24 The Importance of the Propagator in Quantum | |
Physics -- 5.25 A Look at Solitons and Inverse Scattering Theory -- Epilogue -- References -- Hints for Further Reading -- List of Symbols -- List of Theorems -- List of the Most Important Definitions | |
ISBN: | 9781461208150 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Applied Mathematical Sciences: 108 |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , System theory , Calculus of variations , Mathematics , Analysis , Systems Theory, Control , Calculus of Variations and Optimal Control Optimization |
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Call number: | SPRINGER-1994-9789401118965:ONLINE Show nearby items on shelf |
Title: | Deformations of Mathematical Structures II Hurwitz-Type Structures and Applications to Surface Physics. Selected Papers from the Seminar on Deformations, Łódź-Malinka, 1988/92 |
Author(s): | |
Date: | 1994 |
Size: | 1 online resource (464 p.) |
Note: | 10.1007/978-94-011-1896-5 |
Contents: | I. Hurwitz-Type Structures -- General Theory -- Editors’ note -- Composition of sums of squares with integer coefficients -- Hurwitz-Type Structures Equipped With Additional Geometric and Analytic Structures -- Helmholtz operator with |
a quaternionic wave number and the associated function theory -- Clifford algebra derivation of the characteristic hypersurfaces of Maxwell’s equations -- Hermitian Hurwitz pairs -- Operator realizations of quantum Heisenberg-Weyl and | |
SU(2)q algebras -- Some generalizations of the Jacobi identity with application to the curvature- and torsion-dependent hamiltonians of physical systems -- Special Hurwitz-Type Structures and the Many-Particle Problem -- On dualities | |
generated by the generalised Hurwitz problem -- The duality theorem for the Hurwitz pairs of bidimension (8,5) and the Penrose theory -- Stochastical mechanics of particle systems in Clifford-analytical formulation related to Hurwitz | |
pairs of bidimension (8,5) -- II. Surface Physics Structures -- Boundary Conditions: Broken Symmetry and Surafce Decorations -- Statistical mechanics of a crystal surface -- A Hurwitz-pair approach to the pre-melting problem -- On the | |
existence conditions for surface states in tight-binding thin films -- Spin wave resonance profiles -- Deformation of physical and chemical properties of solids caused by the existence of a solid surface -- Spin polarization transport | |
in thin magnetic film -- Nonlinear Solutions and Dynamical Properties: A Near-Surface Region -- Quasilinear quantum field theory (a program of quantization) -- A study on torsion vibrations in linear chains -- Etude monodimensionnelle | |
d’sune barre vibrante avec contants unilateraux -- A generalization of the Landau-Lifschitz equation including non-magnetic phenomena -- Chaotic domain wall dynamics and coherent spatial structures in a magnetic system with surfaces | |
ISBN: | 9789401118965 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Algebraic geometry , Functions of complex variables , Quantum physics , Condensed matter , Materials , Thin films , Mathematics , Algebraic Geometry , Several Complex Variables and Analytic Spaces , Surfaces and Interfaces, Thin Films , Condensed Matter Physics , Quantum Physics |
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Call number: | SPRINGER-1994-9783034885362:ONLINE Show nearby items on shelf |
Title: | The Complex WKB Method for Nonlinear Equations I Linear Theory |
Author(s): |
Victor P Maslov |
Date: | 1994 |
Size: | 1 online resource (304 p.) |
Note: | 10.1007/978-3-0348-8536-2 |
Contents: | I. Equations and problems of narrow beam mechanics -- II. Hamiltonian formalism of narrow beams -- III. Approximate solutions of the nonstationary transport equation -- IV. Stationary Hamilton-Jacobi and transport equations -- V. |
Complex Hamiltonian formalism of compact (cyclic) beams -- VI. Canonical operators on Lagrangian manifolds with complex germ and their applications to spectral problems of quantum mechanics -- References -- Appendix A Complex germ | |
generated by a linear connection -- Appendix B Asymptotic solutions with pure imaginary phase and the tunnel equation -- Appendix C Analytic asymptotics of oscillatory decreasing type (heuristic considerations) | |
ISBN: | 9783034885362 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Physics : 16 |
Keywords: | Physics , Mathematical analysis , Analysis (Mathematics) , Physics , Theoretical, Mathematical and Computational Physics , Analysis |
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Call number: | SPRINGER-1994-9783034875158:ONLINE Show nearby items on shelf |
Title: | Seminar on Dynamical Systems Euler International Mathematical Institute, St. Petersburg, 1991 |
Author(s): | |
Date: | 1994 |
Size: | 1 online resource (292 p.) |
Note: | 10.1007/978-3-0348-7515-8 |
Contents: | I. KAM theory and related topics -- 1. The dynamical foundation of classical statistical mechanics and the Boltzmann-Jeans conjecture -- 2. Stability of nearly integrable convex hamiltonian system over exponentially long times -- 3. |
On the stability problem for nearly-integrable hamiltonian systems -- 4. Separatrices splitting for the rapidly forced pendulum -- 5. Exponentially small expressions for separatrix splitting -- 6. An unusual variational problem | |
connected with Mather’s theory for monotone twist mappings -- 7. Periodic Metrics -- 8. On the inclusion of analytic symplectic maps in analytic hamiltonian flows and its applications -- 9.Poincaré Compacti-fication of the Kepler and | |
the collinear three body problems -- 10. A note on the existence of heteroclinic orbits in the planar three-body problem -- 11. KAM tori for modulated symplectic maps -- 12. Analyticity of normalizing transformations for area | |
preserving maps -- 13. On the frequencies of quasi-periodic solutions of analytic nearly integrable hamiltonian systems -- 14. New results in the reversible KAM theory -- II. Infinite dimensional dynamical systems -- 15. Maximal almost | |
periodic solutions for Lagrangian equations on infinite dimensional tori -- 16. Nonpersistence of breather solutions under perturbation of the Sine-Gordon equation -- III. Miscellanea -- 17. Attractors, integrable hamiltonian systems | |
and the Reidemeister torsion -- 18. Linear connections for hamiltonian dynamics over isotropic submanifold -- 19. Four-dimensional integrable hamiltonian systems with simple singular points -- 20. Periodic points and Symbolic Dynamics | |
-- 21. On the perturbation of locally non-unique invariant manifolds -- 22. Complex geometry of the billiard on the ellipsoid and quasicristallic curves | |
ISBN: | 9783034875158 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Nonlinear Differential Equations and Their Applications : 12 |
Keywords: | Science , Science , Science, general |
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