Download or read book The Differential Geometry of Finsler Spaces written by Hanno Rund and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry. Secondly, it is hoped that this monograph may serve also as an introduction to a branch of differential geometry which is closely related to various topics in theoretical physics, notably analytical dynamics and geometrical optics. With this second object in mind, an attempt has been made to describe the basic aspects of the theory in some detail - even at the expense of conciseness - while in the more specialised sections of the later chapters, which might be of interest chiefly to the specialist, a more succinct style has been adopted. The fact that there exist several fundamentally different points of view with regard to Finsler geometry has rendered the task of writing a coherent account a rather difficult one. This remark is relevant not only to the development of the subject on the basis of the tensor calculus, but is applicable in an even wider sense. The extensive work of H. BUSEMANN has opened up new avenues of approach to Finsler geometry which are independent of the methods of classical tensor analysis. In the latter sense, therefore, a full description of this approach does not fall within the scope of this treatise, although its fundamental l significance cannot be doubted.
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 Complex Spaces in Finsler Lagrange and Hamilton Geometries written by Gheorghe Munteanu and published by Springer Science & Business Media. This book was released on 2012-11-03 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a historical point of view, the theory we submit to the present study has its origins in the famous dissertation of P. Finsler from 1918 ([Fi]). In a the classical notion also conventional classification, Finsler geometry has besides a number of generalizations, which use the same work technique and which can be considered self-geometries: Lagrange and Hamilton spaces. Finsler geometry had a period of incubation long enough, so that few math ematicians (E. Cartan, L. Berwald, S.S. Chem, H. Rund) had the patience to penetrate into a universe of tensors, which made them compare it to a jungle. To aU of us, who study nowadays Finsler geometry, it is obvious that the qualitative leap was made in the 1970's by the crystallization of the nonlinear connection notion (a notion which is almost as old as Finsler space, [SZ4]) and by work-skills into its adapted frame fields. The results obtained by M. Matsumoto (coUected later, in 1986, in a monograph, [Ma3]) aroused interest not only in Japan, but also in other countries such as Romania, Hungary, Canada and the USA, where schools of Finsler geometry are founded and are presently widely recognized.
Download or read book Metric Methods of Finsler Spaces and in the Foundations of Geometry AM 8 written by Herbert Busemann and published by Princeton University Press. This book was released on 2016-03-02 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8), will be forthcoming.
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 Theory of Sprays and Finsler Spaces with Applications in Physics and Biology written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book has been written by two mathematicians and one physicist: a pure mathematician specializing in Finsler geometry (Makoto Matsumoto), one working in mathematical biology (Peter Antonelli), and a mathematical physicist specializing in information thermodynamics (Roman Ingarden). The main purpose of this book is to present the principles and methods of sprays (path spaces) and Finsler spaces together with examples of applications to physical and life sciences. It is our aim to write an introductory book on Finsler geometry and its applications at a fairly advanced level. It is intended especially for graduate students in pure mathemat ics, science and applied mathematics, but should be also of interest to those pure "Finslerists" who would like to see their subject applied. After more than 70 years of relatively slow development Finsler geometry is now a modern subject with a large body of theorems and techniques and has math ematical content comparable to any field of modern differential geometry. The time has come to say this in full voice, against those who have thought Finsler geometry, because of its computational complexity, is only of marginal interest and with prac tically no interesting applications. Contrary to these outdated fossilized opinions, we believe "the world is Finslerian" in a true sense and we will try to show this in our application in thermodynamics, optics, ecology, evolution and developmental biology. On the other hand, while the complexity of the subject has not disappeared, the modern bundle theoretic approach has increased greatly its understandability.
Download or read book Stochastic Geometry written by W. Weil and published by Springer. This book was released on 2006-10-26 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September 2004. The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets. These are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents a comprehensive and up-to-date description of important aspects of Stochastic Geometry.
Download or read book Finsler Geometry Relativity and Gauge Theories written by G.S. Asanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods of differential geometry have been so completely merged nowadays with physical concepts that general relativity may well be considered to be a physical theory of the geometrical properties of space-time. The general relativity principles together with the recent development of Finsler geometry as a metric generalization of Riemannian geometry justify the attempt to systematize the basic techniques for extending general relativity on the basis of Finsler geometry. It is this endeavour that forms the subject matter of the present book. Our exposition reveals the remarkable fact that the Finslerian approach is automatically permeated with the idea of the unification of the geometrical space-time picture with gauge field theory - a circumstance that we try our best to elucidate in this book. The book has been written in such a way that the reader acquainted with the methods of tensor calculus and linear algebra at the graduate level can use it as a manual of Finslerian techniques orientable to applications in several fields. The problems attached to the chapters are also intended to serve this purpose. This notwithstanding, whenever we touch upon the Finslerian refinement or generalization of physical concepts, we assume that the reader is acquainted with these concepts at least at the level of the standard textbooks, to which we refer him or her.
Download or read book Micromechanics of Fracture in Generalized Spaces written by Ihar Alaksandravich Miklashevich and published by Elsevier. This book was released on 2008-01-08 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: By the detailed analysis of the modern development of the mechanics of deformable media can be found the deep internal contradiction. From the one hand it is declared that the deformation and fracture are the hierarchical processes which are linked and unite several structural and scale levels. From the other hand the sequential investigation of the hierarchy of the deformation and destruction is not carried out. The book's aim is filling this mentioned gap and investigates the hot topic of the fracture of non-ideal media. From the microscopic point of view in the book we study the hierarchy of the processes in fractured solid in the whole diapason of practically used scales. According the multilevel hierarchical system ideology under "microscopic we understand taking into account the processes on the level lower than relative present strata. From hierarchical point of view the conception of "microscopic fracture can be soundly applied to the traditionally macroscopic area, namely geomechanics or main crack propagation. At the same time microscopic fracture of the nanomaterials can be well-grounded too. This ground demands the investigation on the level of inter-atomic interaction and quantum mechanical description. The important feature of the book is the application of fibred manifolds and non-Euclidean spaces to the description of the processes of deformation and fracture in inhomogeneous and defected continua. The non-Euclidean spaces for the dislocations' description were introduced by J.F. Nye, B.A. Bilby, E. Kröner, K. Kondo in fiftieth. In last decades this necessity was shown in geomechanics and theory of seismic signal propagation. The applications of non-Euclidean spaces to the plasticity allow us to construct the mathematically satisfying description of the processes. Taking into account this space expansion the media with microstructure are understood as Finsler space media. The bundle space technique is used for the description of the influence of microstructure on the continuum metrics. The crack propagation is studied as a process of movement in Finsler space. Reduction of the general description to the variational principle in engineering case is investigated and a new result for the crack trajectory in inhomogeneous media is obtained. Stability and stochastization of crack trajectory in layered composites is investigated. The gauge field is introduced on the basis of the structure representation of Lie group generated by defects without any additional assumption. Effective elastic and non-elastic media for nanomaterials and their geometrical description are discussed. The monograph provides the basis for more detailed and exact description of real processes in the material. The monograph will be interesting for the researchers in the field of fracture mechanics, solid state physics and geomechanics. It can be used as well by the last year students wishing to become more familiar with some modern approaches to the physics of fracture and continual theory of dislocations. In Supplement, written by V.V.Barkaline, quantum mechanical concept of physical body wholeness according to H. Primas is discussed with relation to fracture. Role of electronic subsystem in fracture dynamics in adiabatic and non-adiabatic approximations is clarified. Potential energy surface of ion subsystem accounting electron contribution is interpreted as master parameter of fracture dynamics. Its features and relation to non-euclidean metrics of defected solid body is discussed. Quantum mechanical criteria of fracture arising are proposed.
Download or read book Advances in Differential Geometry and General Relativity written by John K. Beem and published by American Mathematical Soc.. This book was released on 2004 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of expanded versions of invited lectures given at The Beemfest: Advances in Differential Geometry and General Relativity (University of Missouri-Columbia) on the occasion of Professor John K. Beem's retirement. The articles address problems in differential geometry in general and in particular, global Lorentzian geometry, Finsler geometry, causal boundaries, Penrose's cosmic censorship hypothesis, the geometry of differential operators with variable coefficients on manifolds, and asymptotically de Sitter spacetimes satisfying Einstein's equations with positive cosmological constant. The book is suitable for graduate students and research mathematicians interested in differential geometry.
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 Geometry and Applications written by Aurel Bejancu and published by . This book was released on 1990 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integral Geometry And Convexity Proceedings Of The International Conference written by Eric L Grinberg and published by World Scientific. This book was released on 2006-04-20 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral geometry, known as geometric probability in the past, originated from Buffon's needle experiment. Remarkable advances have been made in several areas that involve the theory of convex bodies. This volume brings together contributions by leading international researchers in integral geometry, convex geometry, complex geometry, probability, statistics, and other convexity related branches. The articles cover both recent results and exciting directions for future research.
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2013 with total page 1480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book P Z written by Library of Congress. Office for Subject Cataloging Policy and published by . This book was released on 1990 with total page 1644 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopaedia of Mathematics set written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1994-02-28 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
