The Theory Of Finslerian Laplacians And Applications

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The Theory of Finslerian Laplacians and Applications

Author : P.L. Antonelli
Publisher : Springer Science & Business Media
ISBN 13 : 9401152829
Total Pages : 305 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis The Theory of Finslerian Laplacians and Applications by : P.L. Antonelli

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.

Handbook of Finsler geometry. 1 (2003)

Author : Peter L. Antonelli
Publisher : Springer Science & Business Media
ISBN 13 : 9781402015557
Total Pages : 760 pages
Book Rating : 4.0/5 (155 download)

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Book Synopsis Handbook of Finsler geometry. 1 (2003) by : Peter L. Antonelli

Download or read book Handbook of Finsler geometry. 1 (2003) written by Peter L. Antonelli and published by Springer Science & Business Media. This book was released on 2003 with total page 760 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.

Fundamentals of Finslerian Diffusion with Applications

Author : P.L. Antonelli
Publisher : Springer Science & Business Media
ISBN 13 : 9401148244
Total Pages : 208 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Fundamentals of Finslerian Diffusion with Applications by : P.L. Antonelli

Download or read book Fundamentals of Finslerian Diffusion with Applications written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The erratic motion of pollen grains and other tiny particles suspended in liquid is known as Brownian motion, after its discoverer, Robert Brown, a botanist who worked in 1828, in London. He turned over the problem of why this motion occurred to physicists who were investigating kinetic theory and thermodynamics; at a time when the existence of molecules had yet to be established. In 1900, Henri Poincare lectured on this topic to the 1900 International Congress of Physicists, in Paris [Wic95]. At this time, Louis Bachelier, a thesis student of Poincare, made a monumental breakthrough with his Theory of Stock Market Fluctuations, which is still studied today, [Co064]. Norbert Wiener (1923), who was first to formulate a rigorous concept of the Brownian path, is most often cited by mathematicians as the father of the subject, while physicists will cite A. Einstein (1905) and M. Smoluchowski. Both considered Markov diffusions and realized that Brownian behaviour nd could be formulated in terms of parabolic 2 order linear p. d. e. 'so Further more, from this perspective, the covariance of changes in position could be allowed to depend on the position itself, according to the invariant form of the diffusion introduced by Kolmogorov in 1937, [KoI37]. Thus, any time homogeneous Markov diffusion could be written in terms of the Laplacian, intrinsically given by the symbol (covariance) of the p. d. e. , plus a drift vec tor. The theory was further advanced in 1949, when K.

Comparison Finsler Geometry

Author : Shin-ichi Ohta
Publisher : Springer Nature
ISBN 13 : 3030806502
Total Pages : 324 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Comparison Finsler Geometry by : Shin-ichi Ohta

Download or read book Comparison Finsler Geometry written by Shin-ichi Ohta and published by Springer Nature. This book was released on 2021-10-09 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area. Divided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner–Weitzenböck formula and the corresponding Bochner inequality, gradient estimates, Bakry–Ledoux’s Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger–Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement. Comparison Finsler Geometry offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.

Finslerian Geometries

Author : P.L. Antonelli
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.

The Geometry of Higher-Order Hamilton Spaces

Author : R. Miron
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 Hamilton and Lagrange Spaces

Author : R. Miron
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.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author : Sirakov Boyan
Publisher : World Scientific
ISBN 13 : 9813272899
Total Pages : 5396 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Sirakov Boyan

Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Visualization and Processing of Higher Order Descriptors for Multi-Valued Data

Author : Ingrid Hotz
Publisher : Springer
ISBN 13 : 3319150901
Total Pages : 378 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Visualization and Processing of Higher Order Descriptors for Multi-Valued Data by : Ingrid Hotz

Download or read book Visualization and Processing of Higher Order Descriptors for Multi-Valued Data written by Ingrid Hotz and published by Springer. This book was released on 2015-07-03 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern imaging techniques and computational simulations yield complex multi-valued data that require higher-order mathematical descriptors. This book addresses topics of importance when dealing with such data, including frameworks for image processing, visualization and statistical analysis of higher-order descriptors. It also provides examples of the successful use of higher-order descriptors in specific applications and a glimpse of the next generation of diffusion MRI. To do so, it combines contributions on new developments, current challenges in this area and state-of-the-art surveys. Compared to the increasing importance of higher-order descriptors in a range of applications, tools for analysis and processing are still relatively hard to come by. Even though application areas such as medical imaging, fluid dynamics and structural mechanics are very different in nature they face many shared challenges. This book provides an interdisciplinary perspective on this topic with contributions from key researchers in disciplines ranging from visualization and image processing to applications. It is based on the 5th Dagstuhl seminar on Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. This book will appeal to scientists who are working to develop new analysis methods in the areas of image processing and visualization, as well as those who work with applications that generate higher-order data or could benefit from higher-order models and are searching for novel analytical tools.

Advances in Analysis and Geometry

Author : Tao Qian
Publisher : Birkhäuser
ISBN 13 : 3034878389
Total Pages : 380 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Advances in Analysis and Geometry by : Tao Qian

Download or read book Advances in Analysis and Geometry written by Tao Qian and published by Birkhäuser. This book was released on 2012-12-06 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the heart of Clifford analysis is the study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool. This book focuses on the study of Dirac operators and related ones, together with applications in mathematics, physics and engineering. This book collects refereed papers from a satellite conference to the ICM 2002, plus invited contributions. All articles contain unpublished new results.

Hokkaido Mathematical Journal

Author :
Publisher :
ISBN 13 :
Total Pages : 750 pages
Book Rating : 4.:/5 (7 download)

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Book Synopsis Hokkaido Mathematical Journal by :

Download or read book Hokkaido Mathematical Journal written by and published by . This book was released on 2005 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Riemann-Finsler Geometry

Author : D. Bao
Publisher : Springer Science & Business Media
ISBN 13 : 1461212685
Total Pages : 453 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis An Introduction to Riemann-Finsler Geometry by : D. Bao

Download or read book An Introduction to Riemann-Finsler Geometry written by D. Bao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. "This book offers the most modern treatment of the topic ..." EMS Newsletter.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 764 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2000 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Current Trends in Analysis, its Applications and Computation

Author : Paula Cerejeiras
Publisher : Springer Nature
ISBN 13 : 3030875024
Total Pages : 663 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Current Trends in Analysis, its Applications and Computation by : Paula Cerejeiras

Download or read book Current Trends in Analysis, its Applications and Computation written by Paula Cerejeiras and published by Springer Nature. This book was released on 2022-10-03 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.

Geometric Function Theory In Several Complex Variables, Proceedings Of A Satellite Conference To The Int'l Congress Of Mathematicians In Beijing 2002

Download Geometric Function Theory In Several Complex Variables, Proceedings Of A Satellite Conference To The Int'l Congress Of Mathematicians In Beijing 2002 PDF Online Free

Author : Sheng Gong
Publisher : World Scientific
ISBN 13 : 9814481912
Total Pages : 353 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Geometric Function Theory In Several Complex Variables, Proceedings Of A Satellite Conference To The Int'l Congress Of Mathematicians In Beijing 2002 by : Sheng Gong

Download or read book Geometric Function Theory In Several Complex Variables, Proceedings Of A Satellite Conference To The Int'l Congress Of Mathematicians In Beijing 2002 written by Sheng Gong and published by World Scientific. This book was released on 2004-09-23 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.

Geometric Function Theory in Several Complex Variables

Author : Carl Hanson FitzGerald
Publisher : World Scientific
ISBN 13 : 9812560238
Total Pages : 353 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Geometric Function Theory in Several Complex Variables by : Carl Hanson FitzGerald

Download or read book Geometric Function Theory in Several Complex Variables written by Carl Hanson FitzGerald and published by World Scientific. This book was released on 2004 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.

Introduction To Modern Finsler Geometry

Author : Yi-bing Shen
Publisher : World Scientific Publishing Company
ISBN 13 : 981470492X
Total Pages : 406 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Introduction To Modern Finsler Geometry by : Yi-bing Shen

Download or read book Introduction To Modern Finsler Geometry written by Yi-bing Shen and published by World Scientific Publishing Company. This book was released on 2016-02-25 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.