Morse Theory Of Gradient Flows Concavity And Complexity On Manifolds With Boundary
DOWNLOAD
Download Morse Theory Of Gradient Flows Concavity And Complexity On Manifolds With Boundary PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Morse Theory Of Gradient Flows Concavity And Complexity On Manifolds With Boundary book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Morse Theory Of Gradient Flows Concavity And Complexity On Manifolds With Boundary
DOWNLOAD
Author : Gabriel Katz
language : en
Publisher: World Scientific
Release Date : 2019-08-21
Morse Theory Of Gradient Flows Concavity And Complexity On Manifolds With Boundary written by Gabriel Katz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-21 with Mathematics categories.
This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps.The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it.The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters.
Foundations Of Computational Mathematics
DOWNLOAD
Author : Ronald A. DeVore
language : en
Publisher: Cambridge University Press
Release Date : 2001-05-17
Foundations Of Computational Mathematics written by Ronald A. DeVore and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-17 with Mathematics categories.
Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.
Optimal Transportation Networks
DOWNLOAD
Author : Marc Bernot
language : en
Publisher: Springer Science & Business Media
Release Date : 2009
Optimal Transportation Networks written by Marc Bernot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Business & Economics categories.
The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.
Metric Structures For Riemannian And Non Riemannian Spaces
DOWNLOAD
Author : Mikhail Gromov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-25
Metric Structures For Riemannian And Non Riemannian Spaces written by Mikhail Gromov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-25 with Mathematics categories.
Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metric theory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the Gromov–Hausdorff distance between Riemannian manifolds. This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosis, stimulated by the Levy–Milman concentration phenomenon, encompassing the law of large numbers for metric spaces with measures and dimensions going to infinity. The first stages of the new developments were presented in Gromov's course in Paris, which turned into the famous "Green Book" by Lafontaine and Pansu (1979). The present English translation of that work has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices – by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures – as well as an extensive bibliographyand index round out this unique and beautiful book.
Random Fields And Geometry
DOWNLOAD
Author : R. J. Adler
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-01-29
Random Fields And Geometry written by R. J. Adler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-29 with Mathematics categories.
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.
Mathematical Analysis
DOWNLOAD
Author : Mariano Giaquinta
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-31
Mathematical Analysis written by Mariano Giaquinta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-31 with Mathematics categories.
This volume! aims at introducing some basic ideas for studying approxima tion processes and, more generally, discrete processes. The study of discrete processes, which has grown together with the study of infinitesimal calcu lus, has become more and more relevant with the use of computers. The volume is suitably divided in two parts. In the first part we illustrate the numerical systems of reals, of integers as a subset of the reals, and of complex numbers. In this context we intro duce, in Chapter 2, the notion of sequence which invites also a rethinking of the notions of limit and continuity2 in terms of discrete processes; then, in Chapter 3, we discuss some elements of combinatorial calculus and the mathematical notion of infinity. In Chapter 4 we introduce complex num bers and illustrate some of their applications to elementary geometry; in Chapter 5 we prove the fundamental theorem of algebra and present some of the elementary properties of polynomials and rational functions, and of finite sums of harmonic motions. In the second part we deal with discrete processes, first with the process of infinite summation, in the numerical case, i.e., in the case of numerical series in Chapter 6, and in the case of power series in Chapter 7. The last chapter provides an introduction to discrete dynamical systems; it should be regarded as an invitation to further study.
Generalized Curvatures
DOWNLOAD
Author : Jean-Marie Morvan
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-13
Generalized Curvatures written by Jean-Marie Morvan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-13 with Mathematics categories.
The central object of this book is the measure of geometric quantities describing N a subset of the Euclidean space (E ,), endowed with its standard scalar product. Let us state precisely what we mean by a geometric quantity. Consider a subset N S of points of the N-dimensional Euclidean space E , endowed with its standard N scalar product. LetG be the group of rigid motions of E . We say that a 0 quantity Q(S) associated toS is geometric with respect toG if the corresponding 0 quantity Q[g(S)] associated to g(S) equals Q(S), for all g?G . For instance, the 0 diameter ofS and the area of the convex hull ofS are quantities geometric with respect toG . But the distance from the origin O to the closest point ofS is not, 0 since it is not invariant under translations ofS. It is important to point out that the property of being geometric depends on the chosen group. For instance, ifG is the 1 N group of projective transformations of E , then the property ofS being a circle is geometric forG but not forG , while the property of being a conic or a straight 0 1 line is geometric for bothG andG . This point of view may be generalized to any 0 1 subsetS of any vector space E endowed with a groupG acting on it.
Introduction To Hamiltonian Dynamical Systems And The N Body Problem
DOWNLOAD
Author : Kenneth Meyer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Introduction To Hamiltonian Dynamical Systems And The N Body Problem written by Kenneth Meyer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
The theory of Hamiltonian systems is a vast subject which can be studied from many different viewpoints. This book develops the basic theory of Hamiltonian differential equations from a dynamical systems point of view. That is, the solutions of the differential equations are thought of as curves in a phase space and it is the geometry of these curves that is the important object of study. The analytic underpinnings of the subject are developed in detail. The last chapter on twist maps has a more geometric flavor. It was written by Glen R. Hall. The main example developed in the text is the classical N-body problem, i.e., the Hamiltonian system of differential equations which describe the motion of N point masses moving under the influence of their mutual gravitational attraction. Many of the general concepts are applied to this example. But this is not a book about the N-body problem for its own sake. The N-body problem is a subject in its own right which would require a sizable volume of its own. Very few of the special results which only apply to the N-body problem are given.
Vorticity Statistical Mechanics And Monte Carlo Simulation
DOWNLOAD
Author : Chjan Lim
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-28
Vorticity Statistical Mechanics And Monte Carlo Simulation written by Chjan Lim and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-28 with Mathematics categories.
This book is drawn from across many active fields of mathematics and physics. It has connections to atmospheric dynamics, spherical codes, graph theory, constrained optimization problems, Markov Chains, and Monte Carlo methods. It addresses how to access interesting, original, and publishable research in statistical modeling of large-scale flows and several related fields. The authors explicitly reach around the major branches of mathematics and physics, showing how the use of a few straightforward approaches can create a cornucopia of intriguing questions and the tools to answer them.
The Calculus Of Variations In The Large
DOWNLOAD
Author : Marston Morse
language : en
Publisher: American Mathematical Soc.
Release Date : 1934-12-31
The Calculus Of Variations In The Large written by Marston Morse and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1934-12-31 with Mathematics categories.
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.