Minimum Action Curves In Degenerate Finsler Metrics

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Minimum Action Curves in Degenerate Finsler Metrics

Author : Matthias Heymann
Publisher : Springer
ISBN 13 : 3319177532
Total Pages : 195 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Minimum Action Curves in Degenerate Finsler Metrics by : Matthias Heymann

Download or read book Minimum Action Curves in Degenerate Finsler Metrics written by Matthias Heymann and published by Springer. This book was released on 2015-07-08 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a study of geometric action functionals (i.e., non-negative functionals on the space of unparameterized oriented rectifiable curves), this monograph focuses on the subclass of those functionals whose local action is a degenerate type of Finsler metric that may vanish in certain directions, allowing for curves with positive Euclidean length but with zero action. For such functionals, criteria are developed under which there exists a minimum action curve leading from one given set to another. Then the properties of this curve are studied, and the non-existence of minimizers is established in some settings. Applied to a geometric reformulation of the quasipotential of Wentzell-Freidlin theory (a subfield of large deviation theory), these results can yield the existence and properties of maximum likelihood transition curves between two metastable states in a stochastic process with small noise. The book assumes only standard knowledge in graduate-level analysis; all higher-level mathematical concepts are introduced along the way.

Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications

Author : Luis L. Bonilla
Publisher : Springer
ISBN 13 : 331976599X
Total Pages : 312 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications by : Luis L. Bonilla

Download or read book Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications written by Luis L. Bonilla and published by Springer. This book was released on 2018-06-20 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers selected contributions from the participants of the Banff International Research Station (BIRS) workshop Coupled Mathematical Models for Physical and Biological Nanoscale Systems and their Applications, who explore various aspects of the analysis, modeling and applications of nanoscale systems, with a particular focus on low dimensional nanostructures and coupled mathematical models for their description. Due to the vastness, novelty and complexity of the interfaces between mathematical modeling and nanoscience and nanotechnology, many important areas in these disciplines remain largely unexplored. In their efforts to move forward, multidisciplinary research communities have come to a clear understanding that, along with experimental techniques, mathematical modeling and analysis have become crucial to the study, development and application of systems at the nanoscale. The conference, held at BIRS in autumn 2016, brought together experts from three different communities working in fields where coupled mathematical models for nanoscale and biosystems are especially relevant: mathematicians, physicists (both theorists and experimentalists), and computational scientists, including those dealing with biological nanostructures. Its objectives: summarize the state-of-the-art; identify and prioritize critical problems of major importance that require solutions; analyze existing methodologies; and explore promising approaches to addressing the challenges identified. The contributions offer up-to-date introductions to a range of topics in nano and biosystems, identify important challenges, assess current methodologies and explore promising approaches. As such, this book will benefit researchers in applied mathematics, as well as physicists and biologists interested in coupled mathematical models and their analysis for physical and biological nanoscale systems that concern applications in biotechnology and medicine, quantum information processing and optoelectronics.

Handbook of Global Analysis

Author : Demeter Krupka
Publisher : Elsevier
ISBN 13 : 0080556736
Total Pages : 1243 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Global Analysis by : Demeter Krupka

Download or read book Handbook of Global Analysis written by Demeter Krupka and published by Elsevier. This book was released on 2011-08-11 with total page 1243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents

The Adaptive Curve Evolution Model for Interest Rates

Author : Matthias Heymann
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781986844611
Total Pages : 278 pages
Book Rating : 4.8/5 (446 download)

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Book Synopsis The Adaptive Curve Evolution Model for Interest Rates by : Matthias Heymann

Download or read book The Adaptive Curve Evolution Model for Interest Rates written by Matthias Heymann and published by Createspace Independent Publishing Platform. This book was released on 2018-06-18 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ACE model - in its original form developed by Gregory Pelts and now carefully rephrased, refined, and made more accessible by Matthias Heymann in the present book - is the first to combine all of the most desirable analytical properties in one interest rate model. It is low-dimensional (with the dimension n=1,3,4,5... of its state space coinciding with the one of the driving Brownian motion), complete (i.e., it models all tenors), consistent (i.e., arbitrage-free), highly flexible (it provides 2n+1 discrete parameters in addition to the functional noise parameter sigma(x, t)), and time homogeneous if desired, and it imposes a lower bound on rates. Moreover, it has the rare feat of being unspanned (i.e., its bond price function does not depend on sigma), which can increase calibration leverage, and which allows the yield curve calibration to be separated from the calibration to caps, swaptions, and other interest rate derivatives. Chapter 1 explains all of our desired model features and provides a detailed comparison with other models. Chapter 2 ("A Fast Track To ACE"), which is tailored to the reader who merely wishes to understand the ACE model well enough to use it in practice, lays out all of the results in an easily understandable R^n-based formulation, along with some straightforward proofs that require only standard knowledge in analysis, stochastic processes, and mathematical finance. Finally, Chapters 3-6 contain the actual derivation of the model equations, utilizing a variety of compelling non-standard mathematical techniques - carefully introduced along the way - that may well hold the key also to other financial modeling problems.

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9400903650
Total Pages : 743 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

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 743 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.

Proceedings of the National Academy of Sciences of the United States of America

Author : National Academy of Sciences (U.S.)
Publisher :
ISBN 13 :
Total Pages : 912 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Proceedings of the National Academy of Sciences of the United States of America by : National Academy of Sciences (U.S.)

Download or read book Proceedings of the National Academy of Sciences of the United States of America written by National Academy of Sciences (U.S.) and published by . This book was released on 1990 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the National Academy of Sciences (PNAS) publishes research reports, commentaries, reviews, colloquium papers, and actions of the Academy. PNAS is a multidisciplinary journal that covers the biological, physical, and social sciences.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 916 pages
Book Rating : 4.3/5 (91 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 2008 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Russian Mathematical Surveys

Author :
Publisher :
ISBN 13 :
Total Pages : 734 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Russian Mathematical Surveys by :

Download or read book Russian Mathematical Surveys written by and published by . This book was released on 1982 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Moduli Spaces of Riemann Surfaces

Author : Benson Farb
Publisher : American Mathematical Soc.
ISBN 13 : 0821898876
Total Pages : 371 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Moduli Spaces of Riemann Surfaces by : Benson Farb

Download or read book Moduli Spaces of Riemann Surfaces written by Benson Farb and published by American Mathematical Soc.. This book was released on 2013-08-16 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Geodesic Flows

Author : Gabriel P. Paternain
Publisher : Springer Science & Business Media
ISBN 13 : 1461216001
Total Pages : 160 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Geodesic Flows by : Gabriel P. Paternain

Download or read book Geodesic Flows written by Gabriel P. Paternain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold. The topics covered are close to my research interests. An important goal here is to describe properties of the geodesic flow which do not require curvature assumptions. A typical example of such a property and a central result in this work is Mane's formula that relates the topological entropy of the geodesic flow with the exponential growth rate of the average numbers of geodesic arcs between two points in the manifold. The material here can be reasonably covered in a one-semester course. I have in mind an audience with prior exposure to the fundamentals of Riemannian geometry and dynamical systems. I am very grateful for the assistance and criticism of several people in preparing the text. In particular, I wish to thank Leonardo Macarini and Nelson Moller who helped me with the writing of the first two chapters and the figures. Gonzalo Tomaria caught several errors and contributed with helpful suggestions. Pablo Spallanzani wrote solutions to several of the exercises. I have used his solutions to write many of the hints and answers. I also wish to thank the referee for a very careful reading of the manuscript and for a large number of comments with corrections and suggestions for improvement.

Gradient Flows

Author : Luigi Ambrosio
Publisher : Springer Science & Business Media
ISBN 13 : 376438722X
Total Pages : 333 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Gradient Flows by : Luigi Ambrosio

Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-10-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.

Metric Spaces of Non-Positive Curvature

Author : Martin R. Bridson
Publisher : Springer Science & Business Media
ISBN 13 : 3662124947
Total Pages : 665 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Metric Spaces of Non-Positive Curvature by : Martin R. Bridson

Download or read book Metric Spaces of Non-Positive Curvature written by Martin R. Bridson and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.

Optimal Transport

Author : Cédric Villani
Publisher : Springer Science & Business Media
ISBN 13 : 3540710507
Total Pages : 970 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Optimal Transport by : Cédric Villani

Download or read book Optimal Transport written by Cédric Villani and published by Springer Science & Business Media. This book was released on 2008-10-26 with total page 970 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.

Chemical Abstracts

Author :
Publisher :
ISBN 13 :
Total Pages : 2762 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Chemical Abstracts by :

Download or read book Chemical Abstracts written by and published by . This book was released on with total page 2762 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Calculus of Variations in the Large

Author : Marston Morse
Publisher : American Mathematical Soc.
ISBN 13 : 0821810189
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Calculus of Variations in the Large by : Marston Morse

Download or read book The Calculus of Variations in the Large written by Marston Morse and published by American Mathematical Soc.. This book was released on 1934-12-31 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.

Problems on Mapping Class Groups and Related Topics

Author : Benson Farb
Publisher : American Mathematical Soc.
ISBN 13 : 0821838385
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Problems on Mapping Class Groups and Related Topics by : Benson Farb

Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.

A Course in Metric Geometry

Author : Dmitri Burago
Publisher : American Mathematical Society
ISBN 13 : 1470468530
Total Pages : 415 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Course in Metric Geometry by : Dmitri Burago

Download or read book A Course in Metric Geometry written by Dmitri Burago and published by American Mathematical Society. This book was released on 2022-01-27 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Metric geometry” is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Carathéodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with “easy-to-touch” mathematical objects using “easy-to-visualize” methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.