Download or read book The Geometry of Lagrange Spaces Theory and Applications written by R. Miron and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential-geometric methods are gaining increasing importance in the understanding of a wide range of fundamental natural phenomena. Very often, the starting point for such studies is a variational problem formulated for a convenient Lagrangian. From a formal point of view, a Lagrangian is a smooth real function defined on the total space of the tangent bundle to a manifold satisfying some regularity conditions. The main purpose of this book is to present: (a) an extensive discussion of the geometry of the total space of a vector bundle; (b) a detailed exposition of Lagrange geometry; and (c) a description of the most important applications. New methods are described for construction geometrical models for applications. The various chapters consider topics such as fibre and vector bundles, the Einstein equations, generalized Einstein--Yang--Mills equations, the geometry of the total space of a tangent bundle, Finsler and Lagrange spaces, relativistic geometrical optics, and the geometry of time-dependent Lagrangians. Prerequisites for using the book are a good foundation in general manifold theory and a general background in geometrical models in physics. For mathematical physicists and applied mathematicians interested in the theory and applications of differential-geometric methods.
Download or read book The Geometry of Lagrange Spaces written by R. Miron and published by . This book was released on 2014-01-15 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Geometry of Hamilton and Lagrange Spaces written by R. Miron and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: The title of this book is no surprise for people working in the field of Analytical Mechanics. However, the geometric concepts of Lagrange space and Hamilton space are completely new. The geometry of Lagrange spaces, introduced and studied in [76],[96], was ext- sively examined in the last two decades by geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and U.S.A. Many international conferences were devoted to debate this subject, proceedings and monographs were published [10], [18], [112], [113],... A large area of applicability of this geometry is suggested by the connections to Biology, Mechanics, and Physics and also by its general setting as a generalization of Finsler and Riemannian geometries. The concept of Hamilton space, introduced in [105], [101] was intensively studied in [63], [66], [97],... and it has been successful, as a geometric theory of the Ham- tonian function the fundamental entity in Mechanics and Physics. The classical Legendre’s duality makes possible a natural connection between Lagrange and - miltonspaces. It reveals new concepts and geometrical objects of Hamilton spaces that are dual to those which are similar in Lagrange spaces. Following this duality Cartan spaces introduced and studied in [98], [99],..., are, roughly speaking, the Legendre duals of certain Finsler spaces [98], [66], [67]. The above arguments make this monograph a continuation of [106], [113], emphasizing the Hamilton geometry.
Download or read book Handbook of Differential Geometry written by Franki J.E. Dillen and published by Elsevier. This book was released on 2005-11-29 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent).All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas.. Written by experts and covering recent research. Extensive bibliography. Dealing with a diverse range of areas. Starting from the basics
Download or read book The Geometry of Higher Order Lagrange Spaces written by R. Miron and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations. It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved. Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with. Applications to higher-order analytical mechanics and theoretical physics are included as well. Audience: This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology.
Download or read book Finslerian Geometries written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Finsler and Lagrange Geometry and its Applications: A Meeting of Minds, took place August 13-20, 1998 at the University of Alberta in Edmonton, Canada. The main objective of this meeting was to help acquaint North American geometers with the extensive modern literature on Finsler geometry and Lagrange geometry of the Japanese and European schools, each with its own venerable history, on the one hand, and to communicate recent advances in stochastic theory and Hodge theory for Finsler manifolds by the younger North American school, on the other. The intent was to bring together practitioners of these schools of thought in a Canadian venue where there would be ample opportunity to exchange information and have cordial personal interactions. The present set of refereed papers begins ·with the Pedagogical Sec tion I, where introductory and brief survey articles are presented, one from the Japanese School and two from the European School (Romania and Hungary). These have been prepared for non-experts with the intent of explaining basic points of view. The Section III is the main body of work. It is arranged in alphabetical order, by author. Section II gives a brief account of each of these contribu tions with a short reference list at the end. More extensive references are given in the individual articles.
Download or read book Finsler and Lagrange Geometries written by Mihai Anastasiei and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade several international conferences on Finsler, Lagrange and Hamilton geometries were organized in Bra§ov, Romania (1994), Seattle, USA (1995), Edmonton, Canada (1998), besides the Seminars that periodically are held in Japan and Romania. All these meetings produced important progress in the field and brought forth the appearance of some reference volumes. Along this line, a new International Conference on Finsler and Lagrange Geometry took place August 26-31,2001 at the "Al.I.Cuza" University in Ia§i, Romania. This Conference was organized in the framework of a Memorandum of Un derstanding (1994-2004) between the "Al.I.Cuza" University in Ia§i, Romania and the University of Alberta in Edmonton, Canada. It was especially dedicated to Prof. Dr. Peter Louis Antonelli, the liaison officer in the Memorandum, an untired promoter of Finsler, Lagrange and Hamilton geometries, very close to the Romanian School of Geometry led by Prof. Dr. Radu Miron. The dedica tion wished to mark also the 60th birthday of Prof. Dr. Peter Louis Antonelli. With this occasion a Diploma was given to Professor Dr. Peter Louis Antonelli conferring the title of Honorary Professor granted to him by the Senate of the oldest Romanian University (140 years), the "Al.I.Cuza" University, Ia§i, Roma nia. There were almost fifty participants from Egypt, Greece, Hungary, Japan, Romania, USA. There were scheduled 45 minutes lectures as well as short communications.
Download or read book The Theory of Finslerian Laplacians and Applications written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finslerian Laplacians have arisen from the demands of modelling the modern world. However, the roots of the Laplacian concept can be traced back to the sixteenth century. Its phylogeny and history are presented in the Prologue of this volume. The text proper begins with a brief introduction to stochastically derived Finslerian Laplacians, facilitated by applications in ecology, epidemiology and evolutionary biology. The mathematical ideas are then fully presented in section II, with generalizations to Lagrange geometry following in section III. With section IV, the focus abruptly shifts to the local mean-value approach to Finslerian Laplacians and a Hodge-de Rham theory is developed for the representation on real cohomology classes by harmonic forms on the base manifold. Similar results are proved in sections II and IV, each from different perspectives. Modern topics treated include nonlinear Laplacians, Bochner and Lichnerowicz vanishing theorems, Weitzenböck formulas, and Finslerian spinors and Dirac operators. The tools developed in this book will find uses in several areas of physics and engineering, but especially in the mechanics of inhomogeneous media, e.g. Cofferat continua. Audience: This text will be of use to workers in stochastic processes, differential geometry, nonlinear analysis, epidemiology, ecology and evolution, as well as physics of the solid state and continua.
Download or read book Lagrange and Finsler Geometry written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The differential geometry of a regular Lagrangian is more involved than that of classical kinetic energy and consequently is far from being Riemannian. Nevertheless, such geometries are playing an increasingly important role in a wide variety of problems in fields ranging from relativistic optics to ecology. The present collection of papers will serve to bring the reader up-to-date on the most recent advances. Subjects treated include higher order Lagrange geometry, the recent theory of -Lagrange manifolds, electromagnetic theory and neurophysiology. Audience: This book is recommended as a (supplementary) text in graduate courses in differential geometry and its applications, and will also be of interest to physicists and mathematical biologists.
Download or read book Handbook of Finsler geometry 2 2003 written by Peter L. Antonelli and published by Springer Science & Business Media. This book was released on 2003 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are several mathematical approaches to Finsler Geometry, all of which are contained and expounded in this comprehensive Handbook. The principal bundles pathway to state-of-the-art Finsler Theory is here provided by M. Matsumoto. His is a cornerstone for this set of essays, as are the articles of R. Miron (Lagrange Geometry) and J. Szilasi (Spray and Finsler Geometry). After studying either one of these, the reader will be able to understand the included survey articles on complex manifolds, holonomy, sprays and KCC-theory, symplectic structures, Legendre duality, Hodge theory and Gauss-Bonnet formulas. Finslerian diffusion theory is presented by its founders, P. Antonelli and T. Zastawniak. To help with calculations and conceptualizations, a CD-ROM containing the software package FINSLER, based on MAPLE, is included with the book.
Download or read book Theory of the Electron written by J. Keller and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first century after its discovery, the electron has come to be a fundamental element in the analysis of physical aspects of nature. This book is devoted to the construction of a deductive theory of the electron, starting from first principles and using a simple mathematical tool, geometric analysis. Its purpose is to present a comprehensive theory of the electron to the point where a connection can be made with the main approaches to the study of the electron in physics. The introduction describes the methodology. Chapter 2 presents the concept of space-time-action relativity theory and in chapter 3 the mathematical structures describing action are analyzed. Chapters 4, 5, and 6 deal with the theory of the electron in a series of aspects where the geometrical analysis is more relevant. Finally in chapter 7 the form of geometrical analysis used in the book is presented to elucidate the broad range of topics which are covered and the range of mathematical structures which are implicitly or explicitly included. The book is directed to two different audiences of graduate students and research scientists: primarily to theoretical physicists in the field of electron physics as well as those in the more general field of quantum mechanics, elementary particle physics, and general relativity; secondly, to mathematicians in the field of geometric analysis.
Download or read book Nonperturbative Quantum Field Theory and the Structure of Matter written by T. Borne and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book, which presents a new view of quantum field theory, may serve as a research monograph and an alternative textbook examining topics which are not usually treated in conventional works." "Audience: This volume will appeal to researchers concerned with the foundation of the theory of matter and forces including gravitation. It will also be interesting to those working with quantum field theoretic methods in various disciplines, such as particle physics, nuclear physics, condensed mater physics, and relativity."--Jacket.
Download or read book Classical Electromagnetic Theory written by Jack Vanderlinde and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, physicist and astronomer (1564-1642) This book is a second edition of “Classical Electromagnetic Theory” which derived from a set of lecture notes compiled over a number of years of teaching elect- magnetic theory to fourth year physics and electrical engineering students. These students had a previous exposure to electricity and magnetism, and the material from the ?rst four and a half chapters was presented as a review. I believe that the book makes a reasonable transition between the many excellent elementary books such as Gri?th’s Introduction to Electrodynamics and the obviously graduate level books such as Jackson’s Classical Electrodynamics or Landau and Lifshitz’ Elect- dynamics of Continuous Media. If the students have had a previous exposure to Electromagnetictheory, allthematerialcanbereasonablycoveredintwosemesters. Neophytes should probable spend a semester on the ?rst four or ?ve chapters as well as, depending on their mathematical background, the Appendices B to F. For a shorter or more elementary course, the material on spherical waves, waveguides, and waves in anisotropic media may be omitted without loss of continuity.
Download or read book Kinematical Theory of Spinning Particles written by M. Rivas and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical spin is described in terms of velocities and acceleration so that knowledge of advanced mathematics is not required. Written in the three-dimensional notation of vector calculus, it can be followed by undergraduate physics students, although some notions of Lagrangian dynamics and group theory are required. It is intended as a general course at a postgraduate level for all-purpose physicists. This book presents a unified approach to classical and quantum mechanics of spinning particles, with symmetry principles as the starting point. A classical concept of an elementary particle is presented. The variational statements to deal with spinning particles are revisited. It is shown that, by explicitly constructing different models, symmetry principles are sufficient for the description of either classical or quantum-mechanical elementary particles. Several spin effects are analyzed.
Download or read book Theory of High Temperature Superconductivity written by S. Fujita and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Flux quantization experiments indicate that the carriers, Cooper pairs (pairons), in the supercurrent have charge magnitude 2e, and that they move independently. Josephson interference in a Superconducting Quantum Int- ference Device (SQUID) shows that the centers of masses (CM) of pairons move as bosons with a linear dispersion relation. Based on this evidence we develop a theory of superconductivity in conventional and mate- als from a unified point of view. Following Bardeen, Cooper and Schrieffer (BCS) we regard the phonon exchange attraction as the cause of superc- ductivity. For cuprate superconductors, however, we take account of both optical- and acoustic-phonon exchange. BCS started with a Hamiltonian containing “electron” and “hole” kinetic energies and a pairing interaction with the phonon variables eliminated. These “electrons” and “holes” were introduced formally in terms of a free-electron model, which we consider unsatisfactory. We define “electrons” and “holes” in terms of the cur- tures of the Fermi surface. “Electrons” (1) and “holes” (2) are different and so they are assigned with different effective masses: Blatt, Schafroth and Butler proposed to explain superconductivity in terms of a Bose-Einstein Condensation (BEC) of electron pairs, each having mass M and a size. The system of free massive bosons, having a quadratic dispersion relation: and moving in three dimensions (3D) undergoes a BEC transition at where is the pair density.
Download or read book Mathematical Combinatorics vol II 2014 written by Linfan Mao and published by Infinite Study. This book was released on with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on Ruled Surfaces in Minkowski 3-Space, Enumeration of k-Fibonacci Paths Using Infinite Weighted Automata, The Natural Lift Curves and Geodesic Curvatures of the Spherical Indicatrices of The Spacelike-Timelike Bertrand Curve Pair, Magic Properties of Special Class of Trees, and other topics. Contributors: V. Ramachandran, C. Sekar, Rodrigo De Castro, Jose L. Ramirez, Nagesh.H.M, R. Chandrasekhar, A. Vijayalekshmi, S. Suganthi, V. Swaminathan, Arunesh Pandey, V.K. Chaubey, T.N. Pandey, and others.
Download or read book Nuclear Matter in Different Phases and Transitions written by Jean-Paul Blaizot and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This understandable and inspiring book brings together both theorists and experimentalists working on the properties of nuclear and hadronic matter produced in heavy-ion collisions in various energy ranges. The main focus is on experimental signals revealing the possible phase changes of the matter.
