The Geometry of Higher-Order Lagrange Spaces

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Publisher : Springer Science & Business Media
ISBN 13 : 9401733384
Total Pages : 351 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis The Geometry of Higher-Order Lagrange Spaces by : R. Miron

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.

The Geometry of Hamilton and Lagrange Spaces

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Publisher : Springer Science & Business Media
ISBN 13 : 0306471353
Total Pages : 355 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis The Geometry of Hamilton and Lagrange Spaces by : R. Miron

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.

The Geometry of Higher-Order Hamilton Spaces

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Publisher : Springer Science & Business Media
ISBN 13 : 9401000700
Total Pages : 257 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis The Geometry of Higher-Order Hamilton Spaces by : R. Miron

Download or read book The Geometry of Higher-Order Hamilton Spaces written by R. Miron and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to present an overview of higher-order Hamilton geometry with applications to higher-order Hamiltonian mechanics. It is a direct continuation of the book The Geometry of Hamilton and Lagrange Spaces, (Kluwer Academic Publishers, 2001). It contains the general theory of higher order Hamilton spaces H(k)n, k>=1, semisprays, the canonical nonlinear connection, the N-linear metrical connection and their structure equations, and the Riemannian almost contact metrical model of these spaces. In addition, the volume also describes new developments such as variational principles for higher order Hamiltonians; Hamilton-Jacobi equations; higher order energies and law of conservation; Noether symmetries; Hamilton subspaces of order k and their fundamental equations. The duality, via Legendre transformation, between Hamilton spaces of order k and Lagrange spaces of the same order is pointed out. Also, the geometry of Cartan spaces of order k =1 is investigated in detail. This theory is useful in the construction of geometrical models in theoretical physics, mechanics, dynamical systems, optimal control, biology, economy etc.

The Geometry of Lagrange Spaces: Theory and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 9401107882
Total Pages : 302 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis The Geometry of Lagrange Spaces: Theory and Applications by : R. Miron

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.

Jet Single-Time Lagrange Geometry and Its Applications

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Publisher : John Wiley & Sons
ISBN 13 : 1118143779
Total Pages : 212 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Jet Single-Time Lagrange Geometry and Its Applications by : Vladimir Balan

Download or read book Jet Single-Time Lagrange Geometry and Its Applications written by Vladimir Balan and published by John Wiley & Sons. This book was released on 2011-11-22 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the theory of jet single-time Lagrange geometry and presents modern-day applications Jet Single-Time Lagrange Geometry and Its Applications guides readers through the advantages of jet single-time Lagrange geometry for geometrical modeling. With comprehensive chapters that outline topics ranging in complexity from basic to advanced, the book explores current and emerging applications across a broad range of fields, including mathematics, theoretical and atmospheric physics, economics, and theoretical biology. The authors begin by presenting basic theoretical concepts that serve as the foundation for understanding how and why the discussed theory works. Subusequent chapters compare the geometrical and physical aspects of jet relativistic time-dependent Lagrange geometry to the classical time-dependent Lagrange geometry. A collection of jet geometrical objects are also examined such as d-tensors, relativistic time-dependent semisprays, harmonic curves, and nonlinear connections. Numerous applications, including the gravitational theory developed by both the Berwald-Moór metric and the Chernov metric, are also presented. Throughout the book, the authors offer numerous examples that illustrate how the theory is put into practice, and they also present numerous applications in which the solutions of first-order ordinary differential equation systems are regarded as harmonic curves on 1-jet spaces. In addition, numerous opportunities are provided for readers to gain skill in applying jet single-time Lagrange geometry to solve a wide range of problems. Extensively classroom-tested to ensure an accessible presentation, Jet Single-Time Lagrange Geometry and Its Applications is an excellent book for courses on differential geometry, relativity theory, and mathematical models at the graduate level. The book also serves as an excellent reference for researchers, professionals, and academics in physics, biology, mathematics, and economics who would like to learn more about model-providing geometric structures.

Handbook of Differential Geometry

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Publisher : Elsevier
ISBN 13 : 9780080461205
Total Pages : 574 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Handbook of Differential Geometry by : Franki J.E. Dillen

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 574 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

The Geometry of Hamilton and Lagrange Spaces

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Publisher :
ISBN 13 : 9789401741736
Total Pages : 366 pages
Book Rating : 4.7/5 (417 download)

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Book Synopsis The Geometry of Hamilton and Lagrange Spaces by : R. Miron

Download or read book The Geometry of Hamilton and Lagrange Spaces written by R. Miron and published by . This book was released on 2014-03-14 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Geometry of Lagrange Spaces

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Publisher :
ISBN 13 : 9789401107891
Total Pages : 304 pages
Book Rating : 4.1/5 (78 download)

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Book Synopsis The Geometry of Lagrange Spaces by : R. Miron

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:

The Geometry of Ordinary Variational Equations

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Publisher : Springer
ISBN 13 : 3540696571
Total Pages : 261 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis The Geometry of Ordinary Variational Equations by : Olga Krupkova

Download or read book The Geometry of Ordinary Variational Equations written by Olga Krupkova and published by Springer. This book was released on 2006-11-14 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations.

Finslerian Geometries

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Publisher : Springer Science & Business Media
ISBN 13 : 9401142351
Total Pages : 305 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Finslerian Geometries by : P.L. Antonelli

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.

Innovative Security Solutions for Information Technology and Communications

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Publisher : Springer Nature
ISBN 13 : 3030692558
Total Pages : 312 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Innovative Security Solutions for Information Technology and Communications by : Diana Maimut

Download or read book Innovative Security Solutions for Information Technology and Communications written by Diana Maimut and published by Springer Nature. This book was released on 2021-02-03 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 13th International Conference on Security for Information Technology and Communications, SecITC 2020, held in Bucharest, Romania, in November 2020. The 17 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 41 submissions. The conference covers topics from cryptographic algorithms, to digital forensics and cyber security and much more.

Finsler and Lagrange Geometries

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Publisher : Springer Science & Business Media
ISBN 13 : 9401704058
Total Pages : 315 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Finsler and Lagrange Geometries by : Mihai Anastasiei

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.

New Developments in Differential Geometry

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Publisher : Springer Science & Business Media
ISBN 13 : 9400901496
Total Pages : 427 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis New Developments in Differential Geometry by : L. Tamássy

Download or read book New Developments in Differential Geometry written by L. Tamássy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Colloquium on Differential Geometry, Debrecen, Hungary, July 26-30, 1994

New Developments in Differential Geometry, Budapest 1996

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Publisher : Springer Science & Business Media
ISBN 13 : 9401152764
Total Pages : 513 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis New Developments in Differential Geometry, Budapest 1996 by : J. Szenthe

Download or read book New Developments in Differential Geometry, Budapest 1996 written by J. Szenthe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996

Handbook of Finsler geometry. 2 (2003)

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Publisher : Springer Science & Business Media
ISBN 13 : 9781402015564
Total Pages : 746 pages
Book Rating : 4.0/5 (155 download)

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Book Synopsis Handbook of Finsler geometry. 2 (2003) by : Peter L. Antonelli

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.

Lagrange and Finsler Geometry

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Publisher : Springer Science & Business Media
ISBN 13 : 9401586500
Total Pages : 285 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Lagrange and Finsler Geometry by : P.L. Antonelli

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.

Higher Order Contact of Submanifolds of Homogeneous Spaces

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Publisher : Springer
ISBN 13 : 3540371206
Total Pages : 166 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Higher Order Contact of Submanifolds of Homogeneous Spaces by : G. R. Jensen

Download or read book Higher Order Contact of Submanifolds of Homogeneous Spaces written by G. R. Jensen and published by Springer. This book was released on 2006-11-15 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: