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11 Ungar, A.A Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession I10899 2002 eBook  
12 Science, Journal of Nonlinear Mechanics: From Theory to Computation I10867 2000 eBook  
13 Zhang, Keqian Electromagnetic Theory for Microwaves and Optoelectronics I08369 2008 eBook  
14 Ratti, Sergio Peppino Introduzione ai frattali in fisica I08303 2011 eBook  
15 Ungar, A.A Hyperbolic Triangle Centers I07921 2010 eBook  
16 Strauch, Dieter Classical Mechanics I07907 2009 eBook  
17 Sharan, Pankaj Spacetime, Geometry and Gravitation I07663 2009 eBook  
18 Gerdjikov, Vladimir Integrable Hamiltonian Hierarchies I06124 2008 eBook  
19 Maia, M. D Geometry of the Fundamental Interactions I05463 2011 eBook  
20 Granas, Andrzej Topological Methods in Differential Equations and Inclusions I05285 1995 eBook  
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11.    
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TitleBeyond the Einstein Addition Law and its Gyroscopic Thomas Precession : The Theory of Gyrogroups and Gyrovector Spaces
Author(s)Ungar, A.A
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2002.
Description464 p : online resource
Abstract NoteEvidence that Einstein's addition is regulated by the Thomas precession has come to light, turning the notorious Thomas precession, previously considered the ugly duckling of special relativity theory, into the beautiful swan of gyrogroup and gyrovector space theory, where it has been extended by abstraction into an automorphism generator, called the Thomas gyration. The Thomas gyration, in turn, allows the introduction of vectors into hyperbolic geometry, where they are called gyrovectors, in such a way that Einstein's velocity additions turns out to be a gyrovector addition. Einstein's addition thus becomes a gyrocommutative, gyroassociative gyrogroup operation in the same way that ordinary vector addition is a commutative, associative group operation. Some gyrogroups of gyrovectors admit scalar multiplication, giving rise to gyrovector spaces in the same way that some groups of vectors that admit scalar multiplication give rise to vector spaces. Furthermore, gyrovector spaces form the setting for hyperbolic geometry in the same way that vector spaces form the setting for Euclidean geometry. In particular, the gyrovector space with gyrovector addition given by Einstein's (M??bius') addition forms the setting for the Beltrami (Poincar??) ball model of hyperbolic geometry. The gyrogroup-theoretic techniques developed in this book for use in relativity physics and in hyperbolic geometry allow one to solve old and new important problems in relativity physics. A case in point is Einstein's 1905 view of the Lorentz length contraction, which was contradicted in 1959 by Penrose, Terrell and others. The application of gyrogroup-theoretic techniques clearly tilt the balance in favor of Einstein
ISBN,Price9780306471346
Keyword(s)1. Astronomy, Observations and Techniques 2. Astronomy???Observations 3. EBOOK 4. EBOOK - SPRINGER 5. GEOMETRY 6. MATHEMATICAL PHYSICS 7. Non-associative Rings and Algebras 8. Nonassociative rings 9. Observations, Astronomical 10. Rings (Algebra) 11. Theoretical, Mathematical and Computational Physics
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12.     
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TitleMechanics: From Theory to Computation : Essays in Honor of Juan-Carlos Simo
Author(s)Science, Journal of Nonlinear
PublicationNew York, NY, 1. Imprint: Springer 2. Springer New York, 2000.
DescriptionX, 532 p : online resource
Abstract NoteStarting in 1996, a sequence of articles appeared in the Journal of Nonlinear Science dedicated to the memory of one of its original editors, Juan-Carlos Simo, Applied Me?? chanics, Stanford University. Sadly, Juan-Carlos passed away at an early age in 1994. We lost a brilliant colleague and a wonderful person. These articles are collected in the present volume. Many of them are updated and corrected especially for this occasion. These essays are in areas of scientific interest of Juan-Carlos, including mechanics (particles, rigid bodies, fluids, elasticity, plastic?? ity, etc.), geometry, applied dynamics, and, of course, computation. His interests were extremely broad-he did not see boundaries between computation, mathematics, me?? chanics, and dynamics, and, in that sense, he ideally reflected the spirit of the journal and many of the most exciting areas of current scientific interest. Juan-Carlos was one of those select and gifted people who could cross interdisci?? plinary boundaries with extremely high quality and productive interactions of lasting value. His contributions, ranging from concrete engineering problems to fundamental mathematical theorems in geometric mechanics, are remarkable. In current conferences as well as in scientific books and articles, and over a wide range of subjects, one frequently hears how his ideas as well as specific results are often used and quoted-this is one indication of just how profound and fundamental his work has impacted the community
ISBN,Price9781461212461
Keyword(s)1. CLASSICAL MECHANICS 2. EBOOK 3. EBOOK - SPRINGER 4. Fluid- and Aerodynamics 5. FLUIDS 6. GEOMETRY 7. MECHANICS
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13.     
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TitleElectromagnetic Theory for Microwaves and Optoelectronics
Author(s)Zhang, Keqian;Li, Dejie
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2008.
DescriptionXX, 711 p : online resource
Abstract NoteThis book is a first year graduate text on electromagnetic fields and waves. At the same time it serves as a useful reference for researchers and engineers in the areas of microwaves and optoelectronics. Following the presentation of the physical and mathematical foundations of electromagnetic theory, the book discusses the field analysis of electromagnetic waves confined in material boundaries, or so-called guided waves, electromagnetic waves in the dispersive media and anisotropic media, Gaussian beams and scalar diffraction theory. The theories and methods presented in the book are foundations of wireless engineering, microwave and millimeter wave techniques, optoelectronics and optical fiber communication
ISBN,Price9783540742968
Keyword(s)1. CLASSICAL ELECTRODYNAMICS 2. Communications Engineering, Networks 3. EBOOK 4. EBOOK - SPRINGER 5. ELECTRICAL ENGINEERING 6. ELECTRODYNAMICS 7. ELECTRONICS 8. Electronics and Microelectronics, Instrumentation 9. GEOMETRY 10. MICROELECTRONICS 11. OPTICS
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14.     
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TitleIntroduzione ai frattali in fisica
Author(s)Ratti, Sergio Peppino
PublicationMilano, 1. Imprint: Springer 2. Springer Milan, 2011.
DescriptionXIII, 309 pagg : online resource
Abstract NoteLa geometria frattale permette di caratterizzare le strutture complesse e irregolari che godono della propriet?? di invarianza di scala. Introdotta da Mandelbrot nel 1975, spiega in modo convincente che la natura ci pone di fronte a molti esempi di strutture complesse che godono di propriet?? peculiari: ?? un fatto che in natura l???irregolarit?? sia molto comune, come dimostrano le strutture di piante, montagne, nuvole e fulmini. Il volume nasce dall???esperienza didattica sviluppata dall???autore in oltre un decennio di insegnamento di Istituzioni di Fisica Superiore presso l???Universit?? di Pavia e intende colmare la lacuna nel panorama italiano di testi didattici su tematiche frattali. Parte dalla definizione di oggetti e di funzioni frattali, introducendo la dimensione ???non intera??? e la ???codimensione??? di un insieme, di una figura geometrica e la sua estensione a una funzione matematica irregolare. Segue l???introduzione dei frattali stocastici che tengono conto della natura parzialmente caotica dei fenomeni fisici. Di particolare rilevanza un capitolo che compendia la trattazione di fenomeni caotici e introduce gli attrattori strani di Edward Lorenz. Infine si affronta l???applicazione dei concetti frattali alla fisica cosmica, all???econofisica e alla descrizione dell???inquinamento prodotto da due disastri ambientali: l???incidente chimico di Seveso e quello nucleare di Chernobyl. Il testo si rivolge in primo luogo agli studenti dei corsi di Laurea Magistrale in Fisica, Chimica, Ingegneria e Scienze Ambientali; pu?? costituire comunque un valido ausilio come testo complementare di natura applicativa. Il carattere propedeutico del volume si presta agevolmente a un apprendimento autonomo individuale
ISBN,Price9788847019621
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. ENGINEERING DESIGN 4. GEOMETRY 5. MATHEMATICS 6. Mathematics, general 7. PHYSICS 8. Physics, general
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15.     
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TitleHyperbolic Triangle Centers : The Special Relativistic Approach
Author(s)Ungar, A.A
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2010.
DescriptionXVI, 319 p : online resource
Abstract NoteAfter A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein???s special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical mechanics where barycentric coordinates are related to the Newtonian mass, barycentric coordinates are related to the Einsteinian relativistic mass in hyperbolic geometry. Contrary to general belief, Einstein???s relativistic mass hence meshes up extraordinarily well with Minkowski???s four-vector formalism of special relativity. In Euclidean geometry, barycentric coordinates can be used to determine various triangle centers. While there are many known Euclidean triangle centers, only few hyperbolic triangle centers are known, and none of the known hyperbolic triangle centers has been determined analytically with respect to its hyperbolic triangle vertices. In his recent research, the author set the ground for investigating hyperbolic triangle centers via hyperbolic barycentric coordinates, and one of the purposes of this book is to initiate a study of hyperbolic triangle centers in full analogy with the rich study of Euclidean triangle centers. Owing to its novelty, the book is aimed at a large audience: it can be enjoyed equally by upper-level undergraduates, graduate students, researchers and academics in geometry, abstract algebra, theoretical physics and astronomy. For a fruitful reading of this book, familiarity with Euclidean geometry is assumed. Mathematical-physicists and theoretical physicists are likely to enjoy the study of Einstein???s special relativity in terms of its underlying hyperbolic geometry. Geometers may enjoy the hunt for new hyperbolic triangle centers and, finally, astronomers may use hyperbolic barycentric coordinates in the velocity space of cosmology
ISBN,Price9789048186372
Keyword(s)1. Applications of Mathematics 2. APPLIED MATHEMATICS 3. ASTRONOMY 4. Astronomy, Astrophysics and Cosmology 5. ASTROPHYSICS 6. Classical and Quantum Gravitation, Relativity Theory 7. EBOOK 8. EBOOK - SPRINGER 9. ENGINEERING MATHEMATICS 10. GEOMETRY 11. GRAVITATION 12. MATHEMATICAL PHYSICS 13. Theoretical, Mathematical and Computational Physics
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16.     
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TitleClassical Mechanics : An Introduction
Author(s)Strauch, Dieter
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2009.
DescriptionXXI, 405 p : online resource
Abstract NoteThis upper-level undergraduate and beginning graduate textbook primarily covers the theory and application of Newtonian and Lagrangian, but also of Hamiltonian mechanics. In addition, included are elements of continuum mechanics and the accompanying classical field theory, wherein four-vector notation is introduced without explicit reference to special relativity. The author's writing style attempts to ease students through the primary and secondary results, thus building a solid foundation for understanding applications. So the text is thus structured around developments of the main ideas, explicit proofs, and numerous clarifications, comments and applications. Numerous examples illustrate the material and often present alternative approaches to the final results. Frequent references are made linking mechanics to other fields of physics. These lecture notes have been used frequently by students to prepare for written and/or oral examinations. Summaries and problems conclude chapters and appendices supply needed background topics
ISBN,Price9783540736165
Keyword(s)1. Applications of Mathematics 2. APPLIED MATHEMATICS 3. CLASSICAL MECHANICS 4. Dynamical Systems and Ergodic Theory 5. DYNAMICS 6. EBOOK 7. EBOOK - SPRINGER 8. ENGINEERING MATHEMATICS 9. ERGODIC THEORY 10. GEOMETRY 11. Mathematical Methods in Physics 12. MECHANICS 13. Mechanics, Applied 14. PHYSICS 15. Theoretical and Applied Mechanics
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17.     
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TitleSpacetime, Geometry and Gravitation
Author(s)Sharan, Pankaj
PublicationBasel, 1. Birkh??user Basel 2. Imprint: Birkh??user, 2009.
DescriptionXIV, 355 p : online resource
Abstract NoteThis is an introductory book on the general theory of relativity based partly on lectures given to students of M.Sc. Physics at my university. The book is divided into three parts. The ?rst part is a preliminary course on general relativity with minimum preparation. The second part builds the ma- ematical background and the third part deals with topics where mathematics developed in the second part is needed. The ?rst chapter gives a general background and introduction. This is f- lowed by an introduction to curvature through Gauss??? Theorema Egregium. This theorem expresses the curvature of a two-dimensional surface in terms of intrinsic quantitiesrelatedtothein?nitesimaldistancefunctiononthesurface.Thestudent isintroducedtothemetrictensor,Christo?elsymbolsandRiemanncurvaturet- sor by elementary methods in the familiar and visualizable case of two dimensions. This early introduction to geometric quantities equips a student to learn simpler topics in general relativity like the Newtonian limit, red shift, the Schwarzschild solution, precession of the perihelion and bending of light in a gravitational ?eld. Part II (chapters 5 to 10) is an introduction to Riemannian geometry as - quired by general relativity. This is done from the beginning, starting with vectors and tensors. I believe that students of physics grasp physical concepts better if they are not shaky about the mathematics involved
ISBN,Price9783764399719
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. EBOOK 3. EBOOK - SPRINGER 4. GEOMETRY 5. GRAVITATION 6. PHYSICS 7. Physics, general
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18.     
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TitleIntegrable Hamiltonian Hierarchies : Spectral and Geometric Methods
Author(s)Gerdjikov, Vladimir;Vilasi, Gaetano;Yanovski, Alexandar Borisov
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2008.
DescriptionXII, 643 p : online resource
Abstract NoteThis book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it is demonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform. The book brings together the spectral and the geometric approaches and as such will be useful to a wide readership: from researchers in the field of nonlinear completely integrable evolution equations to graduate and post-graduate students
ISBN,Price9783540770541
Keyword(s)1. ANALYSIS 2. Analysis (Mathematics) 3. EBOOK 4. EBOOK - SPRINGER 5. GEOMETRY 6. MATHEMATICAL ANALYSIS 7. Mathematical Methods in Physics 8. MATHEMATICAL PHYSICS 9. PHYSICS 10. Physics, general 11. Theoretical, Mathematical and Computational Physics
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19.     
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TitleGeometry of the Fundamental Interactions : On Riemann's Legacy to High Energy Physics and Cosmology
Author(s)Maia, M. D
PublicationNew York, NY, 1. Imprint: Springer 2. Springer New York, 2011.
DescriptionIX, 179 p : online resource
Abstract NoteGravitation, electromagnetics and the two types of nuclear forces constitute the four fundamental forces of nature which regulate our everyday life.?? Amazingly, they are all described by a single idea of the 19th century proposed by Bernhard Riemann, and with the exception of??gravitation, these ideas have been since confirmed by high energy experiments and cosmological observations.?? Geometry of the Fundamental Interactions - On Riemann's Legacy to High Energy Physics and Cosmology is a mathematical narrative of how we have come to agree on such a complex plot of nature, starting with the basic geometrical concepts and ending with hints on the perspective for cosmology. This book originated from lectures given for several years to a mixed audience of mathematicians, physicists, astronomers, engineers, philosophers and sociologists seeking to understand the basics of those interactions and how the concept of Riemann curvature came to occupy such a central position in physics.?? The author takes on the challenge of making the path toward understanding both accessible and interesting to a wide audience
ISBN,Price9781441982735
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. Field theory (Physics) 7. Field Theory and Polynomials 8. GEOMETRY 9. MATHEMATICAL PHYSICS 10. QUANTUM FIELD THEORY 11. Theoretical, Mathematical and Computational Physics
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20.    
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TitleTopological Methods in Differential Equations and Inclusions
Author(s)Granas, Andrzej;Frigon, Marl??ne
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1995.
DescriptionXV, 522 p : online resource
Abstract NoteThe papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations
ISBN,Price9789401103398
Keyword(s)1. DIFFERENTIAL EQUATIONS 2. EBOOK 3. EBOOK - SPRINGER 4. FUNCTIONAL ANALYSIS 5. GEOMETRY 6. ORDINARY DIFFERENTIAL EQUATIONS 7. PARTIAL DIFFERENTIAL EQUATIONS
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