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000890535 020__ $$a9783030170318$$q(electronic book)
000890535 020__ $$a3030170314$$q(electronic book)
000890535 020__ $$z9783030170301
000890535 035__ $$aSP(OCoLC)on1101966666
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000890535 24500 $$aNonlinear PDEs, their geometry, and applications :$$bproceedings of the Wisła 18 Summer School /$$ceditors, Radosław A. Kycia, Maria Ułan and Eivind Schneider.
000890535 264_1 $$aCham :$$bBirkhäuser,$$c[2019]
000890535 264_4 $$c©2019
000890535 300__ $$a1 online resource.
000890535 336__ $$atext$$btxt$$2rdacontent
000890535 337__ $$acomputer$$bc$$2rdamedia
000890535 338__ $$aonline resource$$bcr$$2rdacarrier
000890535 4901_ $$aTutorials, schools, and workshops in the mathematical sciences
000890535 504__ $$aIncludes bibliographical references and index.
000890535 5050_ $$aIntro; Foreword; Preface; Acknowledgements; Contents; Contributors; Acronyms; Part I Lectures; 1 Contact Geometry, Measurement, and Thermodynamics; 1.1 Preface; 1.2 A Crash Course in Probability Theory; 1.2.1 Measure Spaces and Measurable Maps; 1.2.2 Operations Over Measures, Measure Spaces, and Measurable Maps; 1.2.3 The Lebesgue Integral; 1.2.4 The Radon-Nikodym Theorem; 1.2.5 The Fubini Theorem; 1.2.6 Random Vectors; 1.2.7 Conditional Expectation; 1.2.8 Dependency, Coherence Conditions, and Tensor Product of Random Vectors; 1.3 Measurement of Random Vectors
000890535 5058_ $$a1.3.1 Entropy and the Shannon Formula1.3.2 Gain of Information; 1.3.3 Principle of Minimal Information Gain; 1.3.4 The Gaussian Distribution; 1.3.5 Central Moments; 1.3.6 Change of Information Gain; 1.3.7 Constraints and Constitutive Relations; 1.3.8 Application to Classical Mechanics and Classical Field Theory; 1.4 Thermodynamics; 1.4.1 Laws of Thermodynamics; 1.4.2 Thermodynamics and Measurement; 1.4.3 Gases; 1.4.4 Thermodynamic Processes and Contact Transformations; References; 2 Lectures on Geometry of Monge-Ampère Equations with Maple; 2.1 Introduction
000890535 5058_ $$a2.2 Lecture 1. Introduction to Contact Geometry2.2.1 Bundle of 1-Jets; 2.2.2 Contact Transformations; 2.3 Lecture 2. Geometrical Approach to Monge-Ampère Equations; 2.3.1 Non-linear Second-Order Differential Operators; 2.3.2 Multivalued Solutions of Monge-Ampère Equations; 2.3.3 Effective Forms; 2.4 Lecture 3. Contact Transformations of Monge-Ampère Equations; 2.5 Lecture 4. Geometrical Structures; 2.5.1 Pfaffians; 2.5.2 Fields of Endomorphisms; 2.5.3 Characteristic Distributions; 2.5.4 Symplectic Monge-Ampère Equations; 2.5.5 Splitting of Tangent Spaces
000890535 5058_ $$a2.6 Lecture 5. Tensor Invariants of Monge-Ampère Equations2.6.1 Decomposition of de Rham Complex; 2.6.2 Tensor Invariants; 2.6.3 The Laplace Forms; 2.6.4 Contact Linearization of the Monge-Ampère Equations; References; 3 Geometry of Monge-Ampère Structures; 3.1 About These Lectures; 3.2 Lecture One: What Is It All About?; 3.2.1 Basic Geometric Structures; 3.2.2 Kähler, Special and Other Related Structures; 3.2.3 Holomorphic Symplectic Structures; 3.2.4 Lagrangian, Special Lagrangian and Complex Lagrangian Submanifolds; 3.2.5 Hyperkähler Manifolds; 3.2.6 Generalised Complex Structure
000890535 5058_ $$a3.2.7 Notes and Further Reading3.3 Lecture Two: Recursion (Nijenuijs) Operators and Some Related Algebraic Constructions; 3.3.1 Recursion Operators and Its Properties; 3.3.2 Triples of Symplectic Forms; 3.3.3 Notes and Further Reading; 3.4 Lecture Three: Symplectic Monge-Ampère Operators and Equations; 3.4.1 Monge-Ampère Equations; 3.4.2 Geometry of Differential Forms; 3.4.3 Notes and Further Reading; 3.5 Lecture Four: Monge-Ampère Structures; 3.5.1 General Properties; 3.5.2 (4m+2)-Dimensional MA Geometry
000890535 506__ $$aAccess limited to authorized users.
000890535 588__ $$aOnline resource ; title from PDF title page (viewed May 22, 2019).
000890535 650_0 $$aDifferential equations, Partial$$vCongresses.
000890535 650_0 $$aDifferential equations, Nonlinear$$vCongresses.
000890535 655_7 $$aConference papers and proceedings.
000890535 7001_ $$aKycia, Radosław A.,$$eeditor.
000890535 7001_ $$aUłan, Maria,$$eeditor.
000890535 7001_ $$aSchneider, Eivind,$$eeditor.
000890535 830_0 $$aTutorials, schools, and workshops in the mathematical sciences.
000890535 852__ $$bebk
000890535 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-17031-8$$zOnline Access$$91397441.1
000890535 909CO $$ooai:library.usi.edu:890535$$pGLOBAL_SET
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