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21 Schroeck Jr., Franklin E Quantum Mechanics on Phase Space I04439 1996 eBook  
22 Tanner, Elizabeth A Noncompact Lie Groups and Some of Their Applications I04271 1994 eBook  
23 Sim??, Carles Hamiltonian Systems with Three or More Degrees of Freedom I03898 1999 eBook  
24 Antonelli, P.L Fundamentals of Finslerian Diffusion with Applications I03156 1999 eBook  
25 Rodino, Luigi Microlocal Analysis and Spectral Theory I02671 1997 eBook  
26 Clarkson, P.A Applications of Analytic and Geometric Methods to Nonlinear Differential Equations I02446 1993 eBook  
27 Schlomiuk, Dana Bifurcations and Periodic Orbits of Vector Fields I01719 1993 eBook  
28 Hurtubise, Jacques Gauge Theory and Symplectic Geometry I01274 1997 eBook  
29 Chossat, Pascal Dynamics, Bifurcation and Symmetry I01266 1994 eBook  
30 Prugovecki, Margaret Quantum Geometry I01015 1992 eBook  
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21.    
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TitleQuantum Mechanics on Phase Space
Author(s)Schroeck Jr., Franklin E
PublicationDordrecht, Springer Netherlands, 1996.
DescriptionXVI, 672 p : online resource
Abstract NoteIn this monograph, we shall present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics. Here, we motivate this new formulation and sketch how it developed. Since the publication of Dirac's famous book on quantum mechanics [Dirac, 1930] and von Neumann's classic text on the mathematical foundations of quantum mechanics two years later [von Neumann, 1932], there have appeared a number of lines of development, the intent of each being to enrich quantum theory by extra?? polating or even modifying the original basic structure. These lines of development have seemed to go in different directions, the major directions of which are identified here: First is the introduction of group theoretical methods [Weyl, 1928; Wigner, 1931] with the natural extension to coherent state theory [Klauder and Sudarshan, 1968; Peremolov, 1971]. The call for an axiomatic approach to physics [Hilbert, 1900; Sixth Problem] led to the development of quantum logic [Mackey, 1963; Jauch, 1968; Varadarajan, 1968, 1970; Piron, 1976; Beltrametti & Cassinelli, 1981], to the creation of the operational approach [Ludwig, 1983-85, 1985; Davies, 1976] with its application to quantum communication theory [Helstrom, 1976; Holevo, 1982), and to the development of the C* approach [Emch, 1972]. An approach through stochastic differential equations ("stochastic mechanics") was developed [Nelson, 1964, 1966, 1967]
ISBN,Price9789401728300
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GLOBAL ANALYSIS (MATHEMATICS) 4. Global Analysis and Analysis on Manifolds 5. Imaging / Radiology 6. LIE GROUPS 7. Manifolds (Mathematics) 8. Neurosciences 9. QUANTUM PHYSICS 10. Radiology 11. Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences 12. Statistics?? 13. TOPOLOGICAL GROUPS 14. Topological Groups, Lie Groups
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22.     
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TitleNoncompact Lie Groups and Some of Their Applications
Author(s)Tanner, Elizabeth A;Wilson, R
PublicationDordrecht, Springer Netherlands, 1994.
Description512 p : online resource
Abstract NoteDuring the past two decades representations of noncompact Lie groups and Lie algebras have been studied extensively, and their application to other branches of mathematics and to physical sciences has increased enormously. Several theorems which were proved in the abstract now carry definite mathematical and physical sig?? nificance. Several physical observations which were not understood before are now explained in terms of models based on new group-theoretical structures such as dy?? namical groups and Lie supergroups. The workshop was designed to bring together those mathematicians and mathematical physicists who are actively working in this broad spectrum of research and to provide them with the opportunity to present their recent results and to discuss the challenges facing them in the many problems that remain. The objective of the workshop was indeed well achieved. This book contains 31 lectures presented by invited participants attending the NATO Advanced Research Workshop held in San Antonio, Texas, during the week of January 3-8, 1993. The introductory article by the editors provides a brief review of the concepts underlying these lectures (cited by author [*]) and mentions some of their applications. The articles in the book are grouped under the following general headings: Lie groups and Lie algebras, Lie superalgebras and Lie supergroups, and Quantum groups, and are arranged in the order in which they are cited in the introductory article. We are very thankful to Dr
ISBN,Price9789401110785
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GLOBAL ANALYSIS (MATHEMATICS) 4. Global Analysis and Analysis on Manifolds 5. GROUP THEORY 6. Group Theory and Generalizations 7. LIE GROUPS 8. Manifolds (Mathematics) 9. MATHEMATICAL PHYSICS 10. Non-associative Rings and Algebras 11. Nonassociative rings 12. Rings (Algebra) 13. Theoretical, Mathematical and Computational Physics 14. TOPOLOGICAL GROUPS 15. Topological Groups, Lie Groups
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23.     
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TitleHamiltonian Systems with Three or More Degrees of Freedom
Author(s)Sim??, Carles
PublicationDordrecht, Springer Netherlands, 1999.
DescriptionXXIV, 658 p : online resource
Abstract NoteA survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schr??dinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions
ISBN,Price9789401146739
Keyword(s)1. Applications of Mathematics 2. APPLIED MATHEMATICS 3. CLASSICAL MECHANICS 4. DIFFERENTIAL EQUATIONS 5. EBOOK 6. EBOOK - SPRINGER 7. ENGINEERING MATHEMATICS 8. GLOBAL ANALYSIS (MATHEMATICS) 9. Global Analysis and Analysis on Manifolds 10. Manifolds (Mathematics) 11. MECHANICS 12. ORDINARY DIFFERENTIAL EQUATIONS 13. PARTIAL DIFFERENTIAL EQUATIONS
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24.     
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TitleFundamentals of Finslerian Diffusion with Applications
Author(s)Antonelli, P.L;Zastawniak, T.J
PublicationDordrecht, Springer Netherlands, 1999.
DescriptionVII, 205 p : online resource
Abstract NoteThe erratic motion of pollen grains and other tiny particles suspended in liquid is known as Brownian motion, after its discoverer, Robert Brown, a botanist who worked in 1828, in London. He turned over the problem of why this motion occurred to physicists who were investigating kinetic theory and thermodynamics; at a time when the existence of molecules had yet to be established. In 1900, Henri Poincare lectured on this topic to the 1900 International Congress of Physicists, in Paris [Wic95]. At this time, Louis Bachelier, a thesis student of Poincare, made a monumental breakthrough with his Theory of Stock Market Fluctuations, which is still studied today, [Co064]. Norbert Wiener (1923), who was first to formulate a rigorous concept of the Brownian path, is most often cited by mathematicians as the father of the subject, while physicists will cite A. Einstein (1905) and M. Smoluchowski. Both considered Markov diffusions and realized that Brownian behaviour nd could be formulated in terms of parabolic 2 order linear p. d. e. 'so Further?? more, from this perspective, the covariance of changes in position could be allowed to depend on the position itself, according to the invariant form of the diffusion introduced by Kolmogorov in 1937, [KoI37]. Thus, any time?? homogeneous Markov diffusion could be written in terms of the Laplacian, intrinsically given by the symbol (covariance) of the p. d. e. , plus a drift vec?? tor. The theory was further advanced in 1949, when K
ISBN,Price9789401148245
Keyword(s)1. DIFFERENTIAL GEOMETRY 2. EBOOK 3. EBOOK - SPRINGER 4. Evolutionary Biology 5. GLOBAL ANALYSIS (MATHEMATICS) 6. Global Analysis and Analysis on Manifolds 7. Manifolds (Mathematics) 8. PROBABILITIES 9. Probability Theory and Stochastic Processes
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25.     
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TitleMicrolocal Analysis and Spectral Theory
Author(s)Rodino, Luigi
PublicationDordrecht, Springer Netherlands, 1997.
DescriptionVIII, 444 p : online resource
Abstract NoteThe NATO Advanced Study Institute "Microlocal Analysis and Spectral The?? ory" was held in Tuscany (Italy) at Castelvecchio Pascoli, in the district of Lucca, hosted by the international vacation center "11 Ciocco" , from September 23 to October 3, 1996. The Institute recorded the considerable progress realized recently in the field of Microlocal Analysis. In a broad sense, Microlocal Analysis is the modern version of the classical Fourier technique in solving partial differential equa?? tions, where now the localization proceeding takes place with respect to the dual variables too. Precisely, through the tools of pseudo-differential operators, wave-front sets and Fourier integral operators, the general theory of the lin?? ear partial differential equations is now reaching a mature form, in the frame of Schwartz distributions or other generalized functions. At the same time, Microlocal Analysis has grown up into a definite and independent part of Math?? ematical Analysis, with other applications all around Mathematics and Physics, one major theme being Spectral Theory for Schrodinger equation in Quantum Mechanics
ISBN,Price9789401156264
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GLOBAL ANALYSIS (MATHEMATICS) 4. Global Analysis and Analysis on Manifolds 5. INTEGRAL TRANSFORMS 6. Integral Transforms, Operational Calculus 7. Manifolds (Mathematics) 8. Operational calculus 9. OPERATOR THEORY 10. PARTIAL DIFFERENTIAL EQUATIONS 11. QUANTUM PHYSICS
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26.     
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TitleApplications of Analytic and Geometric Methods to Nonlinear Differential Equations
Author(s)Clarkson, P.A
PublicationDordrecht, Springer Netherlands, 1993.
DescriptionX, 477 p : online resource
Abstract NoteIn the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlev?? analysis of partial differential equations, studies of the Painlev?? equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlev?? analysis of partial differential equations, studies of the Painlev?? equations and symmetry reductions of nonlinear partial differential equations
ISBN,Price9789401120821
Keyword(s)1. Applications of Mathematics 2. APPLIED MATHEMATICS 3. DIFFERENTIAL EQUATIONS 4. EBOOK 5. EBOOK - SPRINGER 6. ENGINEERING MATHEMATICS 7. GLOBAL ANALYSIS (MATHEMATICS) 8. Global Analysis and Analysis on Manifolds 9. Manifolds (Mathematics) 10. Mathematical and Computational Engineering 11. MATHEMATICAL PHYSICS 12. ORDINARY DIFFERENTIAL EQUATIONS 13. PARTIAL DIFFERENTIAL EQUATIONS 14. Theoretical, Mathematical and Computational Physics
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27.     
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TitleBifurcations and Periodic Orbits of Vector Fields
Author(s)Schlomiuk, Dana
PublicationDordrecht, Springer Netherlands, 1993.
DescriptionXVIII, 474 p : online resource
Abstract NoteThe last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "Bifurcations and periodic orbits of vector fields". This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy?? namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work
ISBN,Price9789401582384
Keyword(s)1. DIFFERENTIAL EQUATIONS 2. EBOOK 3. EBOOK - SPRINGER 4. Functions of a Complex Variable 5. FUNCTIONS OF COMPLEX VARIABLES 6. GEOMETRY 7. GLOBAL ANALYSIS (MATHEMATICS) 8. Global Analysis and Analysis on Manifolds 9. Manifolds (Mathematics) 10. Numeric Computing 11. NUMERICAL ANALYSIS 12. ORDINARY DIFFERENTIAL EQUATIONS 13. Sequences (Mathematics) 14. Sequences, Series, Summability
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28.     
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TitleGauge Theory and Symplectic Geometry
Author(s)Hurtubise, Jacques;Lalonde, Fran??ois
PublicationDordrecht, Springer Netherlands, 1997.
DescriptionXVII, 212 p : online resource
Abstract NoteGauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of Seiberg-Witten theory, which has revolutionised the subjects since its introduction in late 1994. Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of pseudo-holomorphic curves and to quantum cohomology; algebraically integrable Hamiltonian systems and moduli spaces; the stable topology of gauge theory, Morse-Floer theory; pseudo-convexity and its relations to symplectic geometry; generating functions; Frobenius manifolds and topological quantum field theory
ISBN,Price9789401716673
Keyword(s)1. ALGEBRAIC TOPOLOGY 2. Applications of Mathematics 3. APPLIED MATHEMATICS 4. DIFFERENTIAL GEOMETRY 5. EBOOK 6. EBOOK - SPRINGER 7. ENGINEERING MATHEMATICS 8. GLOBAL ANALYSIS (MATHEMATICS) 9. Global Analysis and Analysis on Manifolds 10. Manifolds (Mathematics) 11. PARTIAL DIFFERENTIAL EQUATIONS
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29.     
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TitleDynamics, Bifurcation and Symmetry : New Trends and New Tools
Author(s)Chossat, Pascal
PublicationDordrecht, Springer Netherlands, 1994.
DescriptionXV, 354 p : online resource
Abstract NoteThis book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci?? entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic?? ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam?? ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc?? cess of this conference
ISBN,Price9789401109567
Keyword(s)1. Applications of Mathematics 2. APPLIED MATHEMATICS 3. DIFFERENTIAL EQUATIONS 4. EBOOK 5. EBOOK - SPRINGER 6. ENGINEERING MATHEMATICS 7. GLOBAL ANALYSIS (MATHEMATICS) 8. Global Analysis and Analysis on Manifolds 9. Manifolds (Mathematics) 10. ORDINARY DIFFERENTIAL EQUATIONS
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30.    
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TitleQuantum Geometry : A Framework for Quantum General Relativity
Author(s)Prugovecki, Margaret
PublicationDordrecht, Springer Netherlands, 1992.
DescriptionXIV, 530 p : online resource
ISBN,Price9789401579711
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GLOBAL ANALYSIS (MATHEMATICS) 4. Global Analysis and Analysis on Manifolds 5. Manifolds (Mathematics) 6. MATHEMATICAL PHYSICS 7. Theoretical, Mathematical and Computational Physics
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