Some Aspects Of Differential Geometry
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On Some Aspects Of Oscillation Theory And Geometry
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Author : Bruno Bianchini
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-23
On Some Aspects Of Oscillation Theory And Geometry written by Bruno Bianchini 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 2013-08-23 with Mathematics categories.
The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.
Some Aspects Of Differential Geometry
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Author : A. Fialkow
language : en
Publisher:
Release Date : 1934
Some Aspects Of Differential Geometry written by A. Fialkow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1934 with Geometry, Differential categories.
Synthetic Geometry Of Manifolds
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Author : Anders Kock
language : en
Publisher: Cambridge University Press
Release Date : 2010
Synthetic Geometry Of Manifolds written by Anders Kock 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 2010 with Mathematics categories.
This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighborhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.
Differential Geometric Foundations Of Non Equilibrium Thermodynamics
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Author : Marcus Hildebrandt
language : en
Publisher: BoD – Books on Demand
Release Date : 2025-02-27
Differential Geometric Foundations Of Non Equilibrium Thermodynamics written by Marcus Hildebrandt and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-27 with Science categories.
While all field theories are nowadays available in a modern, differential geometric, coordinate free formulation on manifolds this has been so far only rudimentary accomplished in general non-equilibrium thermodynamics. In this work it is shown how a fitting geometric structure can be derived for arbitrary compact (discrete Schottky Systems) thermodynamic systems, such as stars and black holes, using only a few thermodynamic principles. This leads to deep geometric insights. Some central results are the following: while in the theory of relativity the energy-momentum tensor determines the geometry of the space, in non-equilibrium thermodynamics, the 1-form of the entropy production rate is responsible for the emergence of a well-known geometric structure: the contact geometry. Relaxation processes remain in the fibers in which they start and end on an attractor manifold, that can be identified with the classical equilibrium subspace of thermostatics. One then proves, that outside this attractor manifold there are no reversible process directions. As a consequence of this, the 2nd Law of thermodynamics lives mainly on the fibers of the state manifold, the so called vertical geometric structure, while the 1st Law of thermodynamics is formulated on the horizontal components of the state manifold. The internal energy provides a physical gauge for each fiber. The 1st and 2nd Law of thermodynamics are coupled via the representation of the entropy flux 1-form that can be represented in the dual basis of exchange 1-forms such as the heat 1-form. This fact can be used to provide a "coordinate free" ("invariant") definition of non-equilibrium temperature. Finally, it is shown that probably the most general geometric structure to model non-equilibrium thermodynamics of compact (discrete Schottky systems) systems is given by a composite fibred cocontact phase manifold that includes time as an explicit dimension.
Particles And Fields Proceedings Of The Ixth Jorge Andre Swieca Summer School
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Author : Joao Carlos Alves Barata
language : en
Publisher: World Scientific
Release Date : 1998-05-08
Particles And Fields Proceedings Of The Ixth Jorge Andre Swieca Summer School written by Joao Carlos Alves Barata and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-08 with categories.
This book contains the proceedings of the IXth Jorge André Swieca Summer School — Particles and Fields — held at Campos do Jordao in February 1997.It surveys some of the most interesting research topics in theoretical physics, like duality theory, quantum field theory in curved space-time, supersymmetry and the standard model, differential geometry and its applications in physics and cosmic ray physics.
Canadian Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1993-06
Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06 with categories.
Raoul Bott Collected Papers
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Author : Loring W. Tu
language : en
Publisher: Birkhäuser
Release Date : 2018-03-26
Raoul Bott Collected Papers written by Loring W. Tu and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-26 with Mathematics categories.
This book is the fifth and final volume of Raoul Bott’s Collected Papers. It collects all of Bott’s published articles since 1991 as well as some articles published earlier but missing in the earlier volumes. The volume also contains interviews with Raoul Bott, several of his previously unpublished speeches, commentaries by his collaborators such as Alberto Cattaneo and Jonathan Weitsman on their joint articles with Bott, Michael Atiyah’s obituary of Raoul Bott, Loring Tu’s authorized biography of Raoul Bott, and reminiscences of Raoul Bott by his friends, students, colleagues, and collaborators, among them Stephen Smale, David Mumford, Arthur Jaffe, Shing-Tung Yau, and Loring Tu. The mathematical articles, many inspired by physics, encompass stable vector bundles, knot and manifold invariants, equivariant cohomology, and loop spaces. The nonmathematical contributions give a sense of Bott’s approach to mathematics, style, personality, zest for life, and humanity. In one of the articles, from the vantage point of his later years, Raoul Bott gives a tour-de-force historical account of one of his greatest achievements, the Bott periodicity theorem. A large number of the articles originally appeared in hard-to-find conference proceedings or journals. This volume makes them all easily accessible. It also features a collection of photographs giving a panoramic view of Raoul Bott's life and his interaction with other mathematicians.
Dynamical Systems Vii
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Author : V.I. Arnol'd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-14
Dynamical Systems Vii written by V.I. Arnol'd 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 2013-12-14 with Mathematics categories.
A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.
Mathematical Aspects Of Chemical And Biochemical Problems And Quantum Chemistry
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Author : Donald S. Cohen
language : en
Publisher: American Mathematical Soc.
Release Date : 1974
Mathematical Aspects Of Chemical And Biochemical Problems And Quantum Chemistry written by Donald S. Cohen 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 1974 with Mathematics categories.
Handbook Of Global Analysis
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Author : Demeter Krupka
language : en
Publisher: Elsevier
Release Date : 2011-08-11
Handbook Of Global Analysis written by Demeter Krupka and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.
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