Metric Affine Geometry

Author: Ernst Snapper,Robert J. Troyer

Publisher: Elsevier

ISBN: 1483269337

Category: Mathematics

Page: 456

View: 445

DOWNLOAD NOW »

Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated. The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group. This monograph is suitable for students and aspiring geometry high school teachers.
Release

The Twelfth Marcel Grossmann Meeting

On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories(In 3 Volumes)

Author: Thibault Damour,Robert Jantzen,Remo Ruffini

Publisher: World Scientific

ISBN: 9814458031

Category: Science

Page: 2660

View: 1323

DOWNLOAD NOW »

Marcel Grossmann Meetings are formed to further the development of General Relativity by promoting theoretical understanding in the fields of physics, mathematics, astronomy and astrophysics and to direct future technological, observational, and experimental efforts. In these meetings are discussed recent developments in classical and quantum gravity, general relativity and relativistic astrophysics, with major emphasis on mathematical foundations and physical predictions, with the main objective of gathering scientists from diverse backgrounds for deepening the understanding of spacetime structure and reviewing the status of test-experiments for Einstein's theory of gravitation. The range of topics is broad, going from the more abstract classical theory, quantum gravity and strings, to the more concrete relativistic astrophysics observations and modeling. The three volumes of the proceedings of MG12 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting includes 29 plenary talks stretched over 6 mornings, and 74 parallel sessions over 5 afternoons. Volume A contains plenary and review talks ranging from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theories, to precision tests of general relativity including progress towards the detection of gravitational waves, to relativistic astrophysics including such topics as gamma ray bursts, black hole physics both in our galaxy, in active galactic nuclei and in other galaxies, neutron stars, pulsar astrophysics, gravitational lensing effects, neutrino physics and ultra high energy cosmic rays. The rest of the volumes include parallel sessions on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, binary systems, radiative transfer, accretion disks, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, cosmic background radiation & observational cosmology, numerical relativity & algebraic computing, gravitational lensing, variable “constants” of nature, large scale structure, topology of the universe, brane-world cosmology, early universe models & cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, gamma ray burst modeling, supernovas, global structure, singularities, cosmic censorship, chaos, Einstein–Maxwell systems, inertial forces, gravitomagnetism, wormholes & time machines, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors & data analysis, precision gravitational measurements, history of relativity, quantum gravity & loop quantum gravity, Casimir effect, quantum cosmology, strings & branes, self-gravitating systems, gamma ray astronomy, cosmic rays, gamma ray bursts and quasars. Sample Chapter(s) Space-Time from the Spectral Point of View (467k) Contents: Space-Time from the Spectral Point of View (Ali H Chamseddine and Alain Connes)The Formation of Black Holes in General Relativity (Demetrios Christodoulou)Matching Conditions in Relativistic Astrophysics (Hernando Quevedo)Black Holes as a Source of Information (Juan Maldacena)Black Hole Microstate Counting and Its Macroscopic Counterpart (Ipsita Mandal and Ashoke Sen)Transplanckian String Collisions: An Update (Gabriele Veneziano)Ultraviolet Divergences and Scale-Dependent Gravitational Couplings (Herbert W Hamber)The Black Hole Stability Problem for Linear Scalar Perturbations (Mihalis Dafermos and Igor Rodnianski)The Global Network of Laser Interferometer Gravitational Wave Detectors (David H Reitze)Analytical Relativity of Black Holes (Thibault Damour)Detection of Gravitational Waves Using Pulsar Timing (Richard N Manchester)Relativistic Spin-Precession in Binary Pulsars (Michael Kramer)Supernovae and Gamma-Ray Bursts: 10 Years of Observations (Massimo Della Valle)Gamma-Ray Bursts as Relativistic Objects (Tsvi Piran)Fundamental Physics from Black Holes, Neutron Stars and Gamma-Ray Bursts (Remo Ruffini)The Fascinating TeV Sky (Felix Aharonian)Galaxy Clusters and Their Central Supermassive Black Holes: Case of M87 (Eugene Churazov, Sergey Sazonov, Rashid Sunyaev, William Forman, Christine Jones and Hans Böhringer)Intergalactic Shock Fronts (Maxim Markevitch)Studies of Dark Energy with X-Ray Observations of Galaxy Clusters (Alexey Vikhlinin)and other papers Keywords:General Relativity;Gravitation;Astrophysics;Quantum Gravity;Particle Physics;Cosmology;Theoretical Physics
Release

Matter Particled

Patterns, Structure and Dynamics : Selected Research Papers of Yuval Ne'eman

Author: Yuval Ne'eman,Remo Ruffini,Yosef Verbin

Publisher: World Scientific

ISBN: 9812774033

Category: Science

Page: 875

View: 6156

DOWNLOAD NOW »

This unique volume contains a selection of more than 80 of Yuval Ne''eman''s papers, which represent his huge contribution to a large number of aspects of theoretical physics. The works span more than four decades, from unitary symmetry and quarks to questions of complexity in biological systems and evolution of scientific theories. In keeping with the major role Ne''eman has played in theoretical physics over the last 40 years, a collaboration of very distinguished scientists enthusiastically took part in this volume. Their commentary supplies a clear framework and background for appreciating Yuval Ne''eman''s significant discoveries and pioneering contributions. Contents: (Authors of Commentaries in Parentheses): SU(3), Quarks and Symmetry Breaking (Y Verbin); Algebraic Theory of Particle Physics and Spectrum Generating Algebras (N Cabibbo); Supersymmetry and Supergravity (R Kerner); Geometrization of Physics (T Regge); SU(2/1) Super-Unification of the Standard Model and Non Commutative Geometry (J Thierry-Mieg); Spinor Representations of GL ( N, P ) and Chromogravity (I Kirsch); Metric-Affine Gravity (F W Hehl); Strings, Branes and Other Extendons (Dj aijaiki); Various Topics in Astrophysics (J Bahcall); Foundations of Physics (A Botero); Philosophy and Sociology of Science: Evolution and History (J Rosen). Readership: Researchers in physics and mathematical physics, and scientists interested in history of physics and philosophy of science."
Release

Projective Geometry and Projective Metrics

Author: Herbert Busemann,Paul J. Kelly

Publisher: Courier Corporation

ISBN: 0486154696

Category: Mathematics

Page: 352

View: 5638

DOWNLOAD NOW »

This text examines the 3 classical geometries and their relationship to general geometric structures, with particular focus on affine geometry, projective metrics, non-Euclidean geometry, and spatial geometry. 1953 edition.
Release

Lie Groups

A Problem Oriented Introduction Via Matrix Groups

Author: Harriet Pollatsek

Publisher: MAA

ISBN: 9780883857595

Category: Mathematics

Page: 177

View: 4484

DOWNLOAD NOW »

The work of the Norwegian mathematician Sophus Lie extends ideas of symmetry and leads to many applications in mathematics and physics. Ordinarily, the study of the "objects" in Lie's theory (Lie groups and Lie algebras) requires extensive mathematical prerequisites beyond the reach of the typical undergraduate. By restricting to the special case of matrix Lie groups and relying on ideas from multivariable calculus and linear algebra, this lovely and important material becomes accessible even to college sophomores. Working with Lie's ideas fosters an appreciation of the unity of mathematics and the sometimes surprising ways in which mathematics provides a language to describe and understand the physical world.Lie Groups is an active learning text that can be used by students with a range of backgrounds and interests. The material is developed through 200 carefully chosen problems. This is the only book in the undergraduate curriculum to bring this material to students so early in their mathematical careers.
Release

Encyclopedia of Distances

Author: Michel Marie Deza,Elena Deza

Publisher: Springer Science & Business Media

ISBN: 364200234X

Category: Mathematics

Page: 590

View: 7931

DOWNLOAD NOW »

Distance metrics and distances have become an essential tool in many areas of pure and applied Mathematics, and this encyclopedia is the first one to treat the subject in full. The book appears just as research intensifies into metric spaces and especially, distance design for applications. These distances are particularly crucial, for example, in computational biology, image analysis, speech recognition, and information retrieval. Here, an assessment of the practical questions arising during selection of a "good'' distance function has been left aside in favor of a comprehensive listing of the main available distances, a useful tool for the distance design community. This reader-friendly reference offers both independent introductions and definitions, while at the same time making cross-referencing easy through hyperlink-like boldfaced references to original definitions. This high-quality publication is a mix of reference resource and coffee-table book.
Release

Affine Differential Geometry

Geometry of Affine Immersions

Author: Katsumi Nomizu,Nomizu Katsumi,Takeshi Sasaki

Publisher: Cambridge University Press

ISBN: 9780521441773

Category: Mathematics

Page: 263

View: 5606

DOWNLOAD NOW »

A self-contained account of the theory of differential geometry, suitable for graduate students.
Release