Beyond Pseudo Rotations in Pseudo Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein’s special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas. Introduces the study of generalized gyrogroups and gyrovector spaces Develops new algebraic structures, bi-gyrogroups and bi-gyrovector spaces Helps readers to surmount boundaries between algebra, geometry and physics Assists readers to parametrize and describe the full set of generalized Lorentz transformations in a geometric way Generalizes approaches from gyrogroups and gyrovector spaces to bi-gyrogroups and bi-gyrovector spaces with geometric entanglement

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  • Author : Abraham Ungar
  • Publisher : Academic Press
  • Pages : 418 pages
  • ISBN : 0128117745
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKBeyond Pseudo Rotations in Pseudo Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces
  • Author : Abraham Ungar
  • Publisher : Academic Press
  • Release : 10 January 2018
GET THIS BOOKBeyond Pseudo-Rotations in Pseudo-Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein’s special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing

Geometric Science of Information

Geometric Science of Information
  • Author : Frank Nielsen,Frédéric Barbaresco
  • Publisher : Springer
  • Release : 23 September 2019
GET THIS BOOKGeometric Science of Information

This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications.

Analytic Hyperbolic Geometry

Analytic Hyperbolic Geometry
  • Author : Abraham A. Ungar
  • Publisher : World Scientific
  • Release : 01 August 2021
GET THIS BOOKAnalytic Hyperbolic Geometry

This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean geometry regulates classical mechanics. The book presents a novel gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. A gyrovector is a hyperbolic vector. Gyrovectors are equivalence classes of directed gyrosegments that add according to the gyroparallelogram law just as vectors are equivalence classes of directed

Hyperbolic Triangle Centers

Hyperbolic Triangle Centers
  • Author : A.A. Ungar
  • Publisher : Springer Science & Business Media
  • Release : 18 June 2010
GET THIS BOOKHyperbolic Triangle Centers

After 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

Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession

Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession
  • Author : Abraham A. Ungar
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKBeyond the Einstein Addition Law and its Gyroscopic Thomas Precession

"I cannot define coincidence [in mathematics]. But 1 shall argue that coincidence can always be elevated or organized into a superstructure which perfonns a unification along the coincidental elements. The existence of a coincidence is strong evidence for the existence of a covering theory. " -Philip 1. Davis [Dav81] Alluding to the Thomas gyration, this book presents the Theory of gy rogroups and gyrovector spaces, taking the reader to the immensity of hyper bolic geometry that lies beyond the Einstein special theory of

A History of Non-Euclidean Geometry

A History of Non-Euclidean Geometry
  • Author : Boris A. Rosenfeld
  • Publisher : Springer Science & Business Media
  • Release : 08 September 2012
GET THIS BOOKA History of Non-Euclidean Geometry

The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics

Geometry and Its Applications

Geometry and Its Applications
  • Author : Walter A. Meyer
  • Publisher : Elsevier
  • Release : 21 February 2006
GET THIS BOOKGeometry and Its Applications

Meyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other

Convex Optimization & Euclidean Distance Geometry

Convex Optimization & Euclidean Distance Geometry
  • Author : Jon Dattorro
  • Publisher : Meboo Publishing USA
  • Release : 01 January 2005
GET THIS BOOKConvex Optimization & Euclidean Distance Geometry

The study of Euclidean distance matrices (EDMs) fundamentally asks what can be known geometrically given onlydistance information between points in Euclidean space. Each point may represent simply locationor, abstractly, any entity expressible as a vector in finite-dimensional Euclidean space.The answer to the question posed is that very much can be known about the points;the mathematics of this combined study of geometry and optimization is rich and deep.Throughout we cite beacons of historical accomplishment.The application of EDMs

The Landscape of Theoretical Physics: A Global View

The Landscape of Theoretical Physics: A Global View
  • Author : M. Pavsic
  • Publisher : Springer Science & Business Media
  • Release : 11 April 2006
GET THIS BOOKThe Landscape of Theoretical Physics: A Global View

Today many important directions of research are being pursued more or less independently of each other. These are, for instance, strings and mem branes, induced gravity, embedding of spacetime into a higher dimensional space, the brane world scenario, the quantum theory in curved spaces, Fock Schwinger proper time formalism, parametrized relativistic quantum the ory, quantum gravity, wormholes and the problem of “time machines”, spin and supersymmetry, geometric calculus based on Clifford algebra, various interpretations of quantum mechanics including the Everett

Elements for Physics

Elements for Physics
  • Author : Albert Tarantola
  • Publisher : Springer Science & Business Media
  • Release : 30 December 2006
GET THIS BOOKElements for Physics

Reviews and extends the theory of Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. Uses a unifying illustration: two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media. Shows that the resulting equations derived in this manner differ quantitatively and qualitatively from those usually presented.

Foliations and the Geometry of 3-Manifolds

Foliations and the Geometry of 3-Manifolds
  • Author : Danny Calegari
  • Publisher : Oxford University Press
  • Release : 17 May 2007
GET THIS BOOKFoliations and the Geometry of 3-Manifolds

This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies

Analytic Hyperbolic Geometry in N Dimensions

Analytic Hyperbolic Geometry in N Dimensions
  • Author : Abraham Albert Ungar
  • Publisher : CRC Press
  • Release : 17 December 2014
GET THIS BOOKAnalytic Hyperbolic Geometry in N Dimensions

The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author’s gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her

The Geometry of Special Relativity

The Geometry of Special Relativity
  • Author : Tevian Dray
  • Publisher : CRC Press
  • Release : 02 July 2012
GET THIS BOOKThe Geometry of Special Relativity

The Geometry of Special Relativity provides an introduction to special relativity that encourages readers to see beyond the formulas to the deeper geometric structure. The text treats the geometry of hyperbolas as the key to understanding special relativity. This approach replaces the ubiquitous γ symbol of most standard treatments with the appropriate hyperbolic trigonometric functions. In most cases, this not only simplifies the appearance of the formulas, but also emphasizes their geometric content in such a way as to make them