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[Alfa Beta Gamma Delta] - Compact spaces / Akos Csaszar
| [Alfa Beta Gamma Delta] - Compact spaces / Akos Csaszar |
| Autore | Csaszar, Akos |
| Pubbl/distr/stampa | Torino : Ist. Geometria Univ. Torino, 1979 |
| Descrizione fisica | 152 p. ; 25 cm. |
| Disciplina | 514.32 |
| Collana | Quaderni dei Gruppi di ricerca matematica del Consiglio Nazionale delle Ricerche |
| Soggetto topico |
Compact spaces
Special constructions of spaces |
| Classificazione | AMS 54D80 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000651329707536 |
Csaszar, Akos
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| Torino : Ist. Geometria Univ. Torino, 1979 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Connettificazione di spazi topologici. Tesi di laurea / laureando Leonardo Bulso ; relat. C. Guido
| Connettificazione di spazi topologici. Tesi di laurea / laureando Leonardo Bulso ; relat. C. Guido |
| Autore | Bulso, Leonardo |
| Pubbl/distr/stampa | Lecce : Università degli studi. Facoltà di Scienze. Corso di laurea in Matematica, a.a. 1988-89 |
| Disciplina | 514.322 |
| Altri autori (Persone) | Guido, Cosimo |
| Soggetto topico |
Compact spaces
Connected spaces Extension Maps |
| Classificazione |
AMS 54C
AMS 54C20 AMS 54D05 AMS 54D10 AMS 54D15 AMS 54D18 (1985) AMS 54D30 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | ita |
| Record Nr. | UNISALENTO-991000783029707536 |
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Bulso, Leonardo
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| Lecce : Università degli studi. Facoltà di Scienze. Corso di laurea in Matematica, a.a. 1988-89 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Ergodic theory on compact spaces / Manfred Denker, Christian Grillenberg, Karl Sigmund
| Ergodic theory on compact spaces / Manfred Denker, Christian Grillenberg, Karl Sigmund |
| Autore | Denker, Manfred |
| Pubbl/distr/stampa | Berlin : Springer-Verlag, 1976 |
| Descrizione fisica | iv, 360 p. ; 24 cm |
| Disciplina | 515.42 |
| Altri autori (Persone) |
Grillenberger, Christian
Sigmund, Karlauthor |
| Collana | Lecture notes in mathematics, 0075-8434 ; 527 |
| Soggetto topico |
Compact spaces
Ergodic theory Metric spaces Topological dynamics |
| ISBN | 3540077979 |
| Classificazione |
AMS 28D
AMS 54H20 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000869199707536 |
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Denker, Manfred
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| Berlin : Springer-Verlag, 1976 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Medial-skeletal linking structures for multi-region configurations / / James Damon, Ellen Gasparovic
| Medial-skeletal linking structures for multi-region configurations / / James Damon, Ellen Gasparovic |
| Autore | Damon James <1945-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2017 |
| Descrizione fisica | 1 online resource (180 pages) |
| Disciplina | 516.36 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Geometry, Differential
Generalized spaces Compact spaces Configurations |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-4210-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910480875703321 |
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Damon James <1945->
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| Providence, Rhode Island : , : American Mathematical Society, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Medial-skeletal linking structures for multi-region configurations / / James Damon, Ellen Gasparovic
| Medial-skeletal linking structures for multi-region configurations / / James Damon, Ellen Gasparovic |
| Autore | Damon James <1945-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2017 |
| Descrizione fisica | 1 online resource (180 pages) |
| Disciplina | 516.36 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Geometry, Differential
Generalized spaces Compact spaces Configurations |
| ISBN | 1-4704-4210-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Multi-Region Configurations in R[superscript n+1] -- Skeletal Linking Structures for Multi-Region Configurations in R[superscript n+1] -- Blum Medial Linking Structure for a Generic Multi-Region Configuration -- Retracting the Full Blum Medial Structure to a Skeletal Linking Structure -- Questions Involving Positional Geometry of a Multi-Region Configuration -- Shape Operators and Radial Flow for a Skeletal Structure -- Linking Flow and Curvature Conditions -- Properties of Regions Defined Using the Linking Flow -- Global Geometry via Medial and Skeletal Linking Integrals -- Positional Geometric Properties of Multi-Region Configurations -- Multi-Distance and Height-Distance Functions and Partial Multi-Jet Spaces -- Generic Blum Linking Properties via Transversality Theorems -- Generic Properties of Blum Linking Structures -- Concluding Generic Properties of Blum Linking Structures -- Reductions of the Proofs of the Transversality Theorems -- Families of Perturbations and their Infinitesimal Properties -- Completing the Proofs of the Transversality Theorems -- Appendix A: List of Frequently Used Notation -- Bibliography. |
| Altri titoli varianti | Medial, skeletal linking structures for multi-region configurations |
| Record Nr. | UNINA-9910795440603321 |
|
Damon James <1945->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Medial-skeletal linking structures for multi-region configurations / / James Damon, Ellen Gasparovic
| Medial-skeletal linking structures for multi-region configurations / / James Damon, Ellen Gasparovic |
| Autore | Damon James <1945-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2017 |
| Descrizione fisica | 1 online resource (180 pages) |
| Disciplina | 516.36 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Geometry, Differential
Generalized spaces Compact spaces Configurations |
| ISBN | 1-4704-4210-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Multi-Region Configurations in R[superscript n+1] -- Skeletal Linking Structures for Multi-Region Configurations in R[superscript n+1] -- Blum Medial Linking Structure for a Generic Multi-Region Configuration -- Retracting the Full Blum Medial Structure to a Skeletal Linking Structure -- Questions Involving Positional Geometry of a Multi-Region Configuration -- Shape Operators and Radial Flow for a Skeletal Structure -- Linking Flow and Curvature Conditions -- Properties of Regions Defined Using the Linking Flow -- Global Geometry via Medial and Skeletal Linking Integrals -- Positional Geometric Properties of Multi-Region Configurations -- Multi-Distance and Height-Distance Functions and Partial Multi-Jet Spaces -- Generic Blum Linking Properties via Transversality Theorems -- Generic Properties of Blum Linking Structures -- Concluding Generic Properties of Blum Linking Structures -- Reductions of the Proofs of the Transversality Theorems -- Families of Perturbations and their Infinitesimal Properties -- Completing the Proofs of the Transversality Theorems -- Appendix A: List of Frequently Used Notation -- Bibliography. |
| Altri titoli varianti | Medial, skeletal linking structures for multi-region configurations |
| Record Nr. | UNINA-9910809888103321 |
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Damon James <1945->
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| Providence, Rhode Island : , : American Mathematical Society, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Nonlinear waves and solitons on contours and closed surfaces / / Andrei Ludu
| Nonlinear waves and solitons on contours and closed surfaces / / Andrei Ludu |
| Autore | Ludu Andrei |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (583 pages) |
| Disciplina | 514.32 |
| Collana | Springer Series in Synergetics |
| Soggetto topico | Compact spaces |
| ISBN |
9783031146411
9783031146404 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- Symbols -- 1 Introduction -- 1.1 Intuitive Introduction to Nonlinear Waves and Solitons -- 1.2 Integrability -- 1.3 Algebraic and Geometric Approaches -- 1.4 A List of Useful Derivatives in Finite Dimensional Spaces -- References -- Part I Mathematical Prerequisites -- 2 Topology and Algebra -- 2.1 What Is Topology -- 2.1.1 Topological Spaces and Separation -- 2.1.2 Compactness and Weierstrass-Stone Theorem -- 2.1.3 Connectedness and Homotopy -- 2.1.4 Separability and Metric Spaces -- 2.2 Elements of Homology -- 2.3 Group Action -- References -- 3 Vector Fields, Differential Forms, and Derivatives -- 3.1 Manifolds and Maps -- 3.2 Differential and Vector Fields -- 3.3 Existence and Uniqueness Theorems: Differential Equation Approach -- 3.4 Existence and Uniqueness Theorems: Flow Box Approach -- 3.5 Compact Supported Vector Fields -- 3.6 Differential Forms and the Lie Derivative -- 3.7 Differential Systems, Integrability and Invariants -- 3.8 Poincaré Lemma -- 3.9 Fiber Bundles and Covariant Derivative -- 3.9.1 Principal Bundle and Frames -- 3.9.2 Connection Form and Covariant Derivative -- 3.10 Tensor Analysis -- 3.11 The Mixed Covariant Derivative -- 3.12 Curvilinear Orthogonal Coordinates -- 3.13 Special Two-Dimensional Nonlinear Orthogonal Coordinates -- 3.14 Problems -- References -- 4 The Importance of the Boundary -- 4.1 The Power of Compact Boundaries: Representation Formulas -- 4.1.1 Representation Formula for n=1: Taylor Series -- 4.1.2 Representation Formula for n=2: Cauchy Formula -- 4.1.3 Representation Formula for n=3: Green Formula -- 4.1.4 Representation Formula in General: Stokes Theorem -- 4.2 Comments and Examples -- References -- Part II Curves and Surfaces -- 5 Geometry of Curves.
5.1 Elements of Differential Geometry of Curves -- 5.2 Closed Curves -- 5.3 Curves Lying on a Surface -- 5.4 Problems -- References -- 6 Geometry of Surfaces -- 6.1 Elements of Differential Geometry of Surfaces -- 6.2 Covariant Derivative and Connections -- 6.3 Geometry of Parameterized Surfaces Embedded in mathbbR3 -- 6.3.1 Christoffel Symbols and Covariant Differentiation for Hybrid Tensors -- 6.4 Compact Surfaces -- 6.5 Surface Differential Operators -- 6.5.1 Surface Gradient -- 6.5.2 Surface Divergence -- 6.5.3 Surface Laplacian -- 6.5.4 Surface Curl -- 6.5.5 Integral Relations for Surface Differential Operators -- 6.5.6 Applications -- 6.6 Problems -- References -- 7 Motion of Curves and Solitons -- 7.1 Kinematics of Two-Dimensional Curves -- 7.2 Mapping Two-Dimensional Curve Motion into Nonlinear Integrable Systems -- 7.3 The Time Evolution of Length and Area -- 7.4 Cartan Theory of Three-Dimensional Curve Motion -- 7.5 Kinematics of Three-Dimensional Curves -- 7.6 Mapping Three-Dimensional Curve Motion into Nonlinear Integrable Systems -- 7.7 Problems -- References -- 8 Theory of Motion of Surfaces -- 8.1 Differential Geometry of Surface Motion -- 8.2 Coordinates and Velocities on a Fluid Surface -- 8.3 Kinematics of Moving Surfaces -- 8.4 Dynamics of Moving Surfaces -- 8.5 Boundary Conditions for Moving Fluid Interfaces -- 8.6 Dynamics of the Fluid Interfaces -- 8.7 Problems -- References -- Part III Solitons and Nonlinear Waves on Closed Curves and Surfaces -- 9 Kinematics of Fluids -- 9.1 Lagrangian Verses Eulerian Frames -- 9.1.1 Introduction -- 9.1.2 Geometrical Picture for Lagrangian Verses Eulerian -- 9.2 Fluid Fiber Bundle -- 9.2.1 Introduction -- 9.2.2 Motivation for a Geometrical Approach -- 9.2.3 The Fiber Bundle -- 9.2.4 Fixed Fluid Container -- 9.2.5 Free Surface Fiber Bundle. 9.2.6 How Does the Time Derivative of Tensors Transform from Euler to Lagrange Frame? -- 9.3 Path Lines, Stream Lines, and Particle Contours -- 9.4 Eulerian-Lagrangian Description for Moving Curves -- 9.5 The Free Surface -- 9.6 Equation of Continuity -- 9.6.1 Introduction -- 9.6.2 Solutions of the Continuity Equation on Compact Intervals -- 9.7 Problems -- References -- 10 Hydrodynamics -- 10.1 Momentum Conservation: Euler and Navier-Stokes Equations -- 10.2 Boundary Conditions -- 10.3 Circulation Theorem -- 10.4 Surface Tension -- 10.4.1 Physical Problem -- 10.4.2 Minimal Surfaces -- 10.4.3 Application -- 10.4.4 Isothermal Parametrization -- 10.4.5 Topological Properties of Minimal Surfaces -- 10.4.6 General Condition for Minimal Surfaces -- 10.4.7 Surface Tension for Almost Isothermal Parametrization -- 10.5 Special Fluids -- 10.6 Representation Theorems in Fluid Dynamics -- 10.6.1 Helmholtz Decomposition Theorem in mathbbR3 -- 10.6.2 Decomposition Formula for Transversal Isotropic Vector Fields -- 10.6.3 Solenoidal-Toroidal Decomposition Formulas -- 10.7 Problems -- References -- 11 Nonlinear Surface Waves in One Dimension -- 11.1 KdV Equation Deduction for Shallow Waters -- 11.2 Smooth Transitions Between Periodic and Aperiodic Solutions -- 11.3 Modified KdV Equation and Generalizations -- 11.4 Hydrodynamic Equations Involving Higher-Order Nonlinearities -- 11.4.1 A Compact Version for KdV -- 11.4.2 Small Amplitude Approximation -- 11.4.3 Dispersion Relations -- 11.4.4 The Full Equation -- 11.4.5 Reduction of GKdV to Other Equations and Solutions -- 11.4.6 The Finite Difference Form -- 11.5 Boussinesq Equations on a Circle -- References -- 12 Nonlinear Surface Waves in Two Dimensions -- 12.1 Geometry of Two-Dimensional Flow -- 12.2 Two-Dimensional Nonlinear Equations -- 12.3 Two-Dimensional Fluid Systems with Moving Boundary. 12.4 Oscillations in Two-Dimensional Liquid Drops -- 12.5 Contours Described by Quartic Closed Curves -- 12.6 Nonlinear Waves in Rotating Leidenfrost Drops -- References -- 13 Dynamics of Two-Dimensional Fluid in Bounded Domain via Conformal Variables (A. Chernyavsky and S. Dyachenko) -- 13.1 Introduction -- 13.2 Mechanics of Droplet and the Conformal Map -- 13.2.1 The Hamiltonian, Momentum and Angular Momentum -- 13.2.2 The Center of Mass -- 13.3 The Complex Equations of Motion -- 13.3.1 Kinematic Equation -- 13.3.2 Dynamic Condition -- 13.4 Traveling Waves Around a Disk -- 13.5 Linear Waves -- 13.6 Numerical Simulation -- 13.7 Series Solution -- 13.8 Nonlinear Waves -- 13.9 Conclusion -- References -- 14 Nonlinear Surface Waves in Three Dimensions -- 14.1 Oscillations of Inviscid Drops: The Linear Model -- 14.1.1 Drop Immersed in Another Fluid -- 14.1.2 Drop with Rigid Core -- 14.1.3 Moving Core -- 14.1.4 Drop Volume -- 14.2 Oscillations of Viscous Drops: The Linear Model -- 14.2.1 Model 1 -- 14.3 Nonlinear Three-Dimensional Oscillations of Axisymmetric Drops -- 14.3.1 Nonlinear Resonances in Drop Oscillation -- 14.4 Other Nonlinear Effects in Drop Oscillations -- 14.5 Solitons on the Surface of Liquid Drops -- 14.6 Problems -- References -- 15 Other Special Nonlinear Compact Systems -- 15.1 Solitons on Interfaces of Layered Fluid Droplet (Written by A. S. Carstea) -- 15.2 Nonlinear Compact Shapes and Collective Motion -- 15.3 The Hamiltonian Structure for Free Boundary Problems on Compact Surfaces -- References -- Part IV Physical Nonlinear Systems at Different Scales -- 16 Filaments, Chains, and Solitons -- 16.1 Vortex Filaments -- 16.1.1 Gas Dynamics Filament Model and Solitons -- 16.1.2 Special Solutions -- 16.1.3 Integration of Serret-Frenet Equations for Filaments -- 16.1.4 The Riccati Form of the Serret-Frenet Equations. 16.2 Soliton Solutions on the Vortex Filament -- 16.2.1 Constant Torsion Vortex Filaments -- 16.2.2 Vortex Filaments and the Nonlinear Schrödinger Equation -- 16.3 Closed Curves Solitons -- 16.4 Nonlinear Dynamics of Stiff Chains -- 16.5 Problems -- References -- 17 Solitons on the Boundaries of Microscopic Systems -- 17.1 Solitons as Elementary Particles -- 17.2 Quantization of Solitons on a Closed Contour and Instantons -- 17.3 Clusters as Solitary Waves on the Nuclear Surface -- 17.4 Nonlinear Schrödinger Equation Solitons on Quantum … -- 17.5 Solitons and Quasimolecular Structure -- 17.6 Soliton Model for Heavy Emitted Nuclear Clusters -- 17.7 Quintic Nonlinear Schrödinger Equation for Nuclear Cluster Decay -- 17.8 Contour Solitons in the Quantum Hall Liquid -- References -- 18 Nonlinear Contour Dynamics in Macroscopic Systems -- 18.1 Plasma Vortex -- 18.1.1 Effective Surface Tension in Magnetohydrodynamics and Plasma Systems -- 18.1.2 Trajectories in Magnetic Field Configurations -- 18.1.3 Magnetic Surfaces in Static Equilibrium -- 18.2 Elastic Spheres -- 18.3 Curvature Dependent Nonlinear Diffusion on Closed Surfaces -- 18.4 Nonlinear Evolution of Oscillation Modes in Neutron Stars -- References -- 19 Mathematical Appendix -- 19.1 Differentiable Manifolds -- 19.2 Riccati Equation -- 19.3 Special Functions -- 19.4 One-Soliton Solutions for the KdV, MKdV, and Their Combination -- 19.5 Scaling and Nonlinear Dispersion Relations1 -- References -- Index. |
| Record Nr. | UNISA-996499864303316 |
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Ludu Andrei
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||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Nonlinear waves and solitons on contours and closed surfaces / / Andrei Ludu
| Nonlinear waves and solitons on contours and closed surfaces / / Andrei Ludu |
| Autore | Ludu Andrei |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (583 pages) |
| Disciplina | 514.32 |
| Collana | Springer Series in Synergetics |
| Soggetto topico | Compact spaces |
| ISBN |
9783031146411
9783031146404 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- Symbols -- 1 Introduction -- 1.1 Intuitive Introduction to Nonlinear Waves and Solitons -- 1.2 Integrability -- 1.3 Algebraic and Geometric Approaches -- 1.4 A List of Useful Derivatives in Finite Dimensional Spaces -- References -- Part I Mathematical Prerequisites -- 2 Topology and Algebra -- 2.1 What Is Topology -- 2.1.1 Topological Spaces and Separation -- 2.1.2 Compactness and Weierstrass-Stone Theorem -- 2.1.3 Connectedness and Homotopy -- 2.1.4 Separability and Metric Spaces -- 2.2 Elements of Homology -- 2.3 Group Action -- References -- 3 Vector Fields, Differential Forms, and Derivatives -- 3.1 Manifolds and Maps -- 3.2 Differential and Vector Fields -- 3.3 Existence and Uniqueness Theorems: Differential Equation Approach -- 3.4 Existence and Uniqueness Theorems: Flow Box Approach -- 3.5 Compact Supported Vector Fields -- 3.6 Differential Forms and the Lie Derivative -- 3.7 Differential Systems, Integrability and Invariants -- 3.8 Poincaré Lemma -- 3.9 Fiber Bundles and Covariant Derivative -- 3.9.1 Principal Bundle and Frames -- 3.9.2 Connection Form and Covariant Derivative -- 3.10 Tensor Analysis -- 3.11 The Mixed Covariant Derivative -- 3.12 Curvilinear Orthogonal Coordinates -- 3.13 Special Two-Dimensional Nonlinear Orthogonal Coordinates -- 3.14 Problems -- References -- 4 The Importance of the Boundary -- 4.1 The Power of Compact Boundaries: Representation Formulas -- 4.1.1 Representation Formula for n=1: Taylor Series -- 4.1.2 Representation Formula for n=2: Cauchy Formula -- 4.1.3 Representation Formula for n=3: Green Formula -- 4.1.4 Representation Formula in General: Stokes Theorem -- 4.2 Comments and Examples -- References -- Part II Curves and Surfaces -- 5 Geometry of Curves.
5.1 Elements of Differential Geometry of Curves -- 5.2 Closed Curves -- 5.3 Curves Lying on a Surface -- 5.4 Problems -- References -- 6 Geometry of Surfaces -- 6.1 Elements of Differential Geometry of Surfaces -- 6.2 Covariant Derivative and Connections -- 6.3 Geometry of Parameterized Surfaces Embedded in mathbbR3 -- 6.3.1 Christoffel Symbols and Covariant Differentiation for Hybrid Tensors -- 6.4 Compact Surfaces -- 6.5 Surface Differential Operators -- 6.5.1 Surface Gradient -- 6.5.2 Surface Divergence -- 6.5.3 Surface Laplacian -- 6.5.4 Surface Curl -- 6.5.5 Integral Relations for Surface Differential Operators -- 6.5.6 Applications -- 6.6 Problems -- References -- 7 Motion of Curves and Solitons -- 7.1 Kinematics of Two-Dimensional Curves -- 7.2 Mapping Two-Dimensional Curve Motion into Nonlinear Integrable Systems -- 7.3 The Time Evolution of Length and Area -- 7.4 Cartan Theory of Three-Dimensional Curve Motion -- 7.5 Kinematics of Three-Dimensional Curves -- 7.6 Mapping Three-Dimensional Curve Motion into Nonlinear Integrable Systems -- 7.7 Problems -- References -- 8 Theory of Motion of Surfaces -- 8.1 Differential Geometry of Surface Motion -- 8.2 Coordinates and Velocities on a Fluid Surface -- 8.3 Kinematics of Moving Surfaces -- 8.4 Dynamics of Moving Surfaces -- 8.5 Boundary Conditions for Moving Fluid Interfaces -- 8.6 Dynamics of the Fluid Interfaces -- 8.7 Problems -- References -- Part III Solitons and Nonlinear Waves on Closed Curves and Surfaces -- 9 Kinematics of Fluids -- 9.1 Lagrangian Verses Eulerian Frames -- 9.1.1 Introduction -- 9.1.2 Geometrical Picture for Lagrangian Verses Eulerian -- 9.2 Fluid Fiber Bundle -- 9.2.1 Introduction -- 9.2.2 Motivation for a Geometrical Approach -- 9.2.3 The Fiber Bundle -- 9.2.4 Fixed Fluid Container -- 9.2.5 Free Surface Fiber Bundle. 9.2.6 How Does the Time Derivative of Tensors Transform from Euler to Lagrange Frame? -- 9.3 Path Lines, Stream Lines, and Particle Contours -- 9.4 Eulerian-Lagrangian Description for Moving Curves -- 9.5 The Free Surface -- 9.6 Equation of Continuity -- 9.6.1 Introduction -- 9.6.2 Solutions of the Continuity Equation on Compact Intervals -- 9.7 Problems -- References -- 10 Hydrodynamics -- 10.1 Momentum Conservation: Euler and Navier-Stokes Equations -- 10.2 Boundary Conditions -- 10.3 Circulation Theorem -- 10.4 Surface Tension -- 10.4.1 Physical Problem -- 10.4.2 Minimal Surfaces -- 10.4.3 Application -- 10.4.4 Isothermal Parametrization -- 10.4.5 Topological Properties of Minimal Surfaces -- 10.4.6 General Condition for Minimal Surfaces -- 10.4.7 Surface Tension for Almost Isothermal Parametrization -- 10.5 Special Fluids -- 10.6 Representation Theorems in Fluid Dynamics -- 10.6.1 Helmholtz Decomposition Theorem in mathbbR3 -- 10.6.2 Decomposition Formula for Transversal Isotropic Vector Fields -- 10.6.3 Solenoidal-Toroidal Decomposition Formulas -- 10.7 Problems -- References -- 11 Nonlinear Surface Waves in One Dimension -- 11.1 KdV Equation Deduction for Shallow Waters -- 11.2 Smooth Transitions Between Periodic and Aperiodic Solutions -- 11.3 Modified KdV Equation and Generalizations -- 11.4 Hydrodynamic Equations Involving Higher-Order Nonlinearities -- 11.4.1 A Compact Version for KdV -- 11.4.2 Small Amplitude Approximation -- 11.4.3 Dispersion Relations -- 11.4.4 The Full Equation -- 11.4.5 Reduction of GKdV to Other Equations and Solutions -- 11.4.6 The Finite Difference Form -- 11.5 Boussinesq Equations on a Circle -- References -- 12 Nonlinear Surface Waves in Two Dimensions -- 12.1 Geometry of Two-Dimensional Flow -- 12.2 Two-Dimensional Nonlinear Equations -- 12.3 Two-Dimensional Fluid Systems with Moving Boundary. 12.4 Oscillations in Two-Dimensional Liquid Drops -- 12.5 Contours Described by Quartic Closed Curves -- 12.6 Nonlinear Waves in Rotating Leidenfrost Drops -- References -- 13 Dynamics of Two-Dimensional Fluid in Bounded Domain via Conformal Variables (A. Chernyavsky and S. Dyachenko) -- 13.1 Introduction -- 13.2 Mechanics of Droplet and the Conformal Map -- 13.2.1 The Hamiltonian, Momentum and Angular Momentum -- 13.2.2 The Center of Mass -- 13.3 The Complex Equations of Motion -- 13.3.1 Kinematic Equation -- 13.3.2 Dynamic Condition -- 13.4 Traveling Waves Around a Disk -- 13.5 Linear Waves -- 13.6 Numerical Simulation -- 13.7 Series Solution -- 13.8 Nonlinear Waves -- 13.9 Conclusion -- References -- 14 Nonlinear Surface Waves in Three Dimensions -- 14.1 Oscillations of Inviscid Drops: The Linear Model -- 14.1.1 Drop Immersed in Another Fluid -- 14.1.2 Drop with Rigid Core -- 14.1.3 Moving Core -- 14.1.4 Drop Volume -- 14.2 Oscillations of Viscous Drops: The Linear Model -- 14.2.1 Model 1 -- 14.3 Nonlinear Three-Dimensional Oscillations of Axisymmetric Drops -- 14.3.1 Nonlinear Resonances in Drop Oscillation -- 14.4 Other Nonlinear Effects in Drop Oscillations -- 14.5 Solitons on the Surface of Liquid Drops -- 14.6 Problems -- References -- 15 Other Special Nonlinear Compact Systems -- 15.1 Solitons on Interfaces of Layered Fluid Droplet (Written by A. S. Carstea) -- 15.2 Nonlinear Compact Shapes and Collective Motion -- 15.3 The Hamiltonian Structure for Free Boundary Problems on Compact Surfaces -- References -- Part IV Physical Nonlinear Systems at Different Scales -- 16 Filaments, Chains, and Solitons -- 16.1 Vortex Filaments -- 16.1.1 Gas Dynamics Filament Model and Solitons -- 16.1.2 Special Solutions -- 16.1.3 Integration of Serret-Frenet Equations for Filaments -- 16.1.4 The Riccati Form of the Serret-Frenet Equations. 16.2 Soliton Solutions on the Vortex Filament -- 16.2.1 Constant Torsion Vortex Filaments -- 16.2.2 Vortex Filaments and the Nonlinear Schrödinger Equation -- 16.3 Closed Curves Solitons -- 16.4 Nonlinear Dynamics of Stiff Chains -- 16.5 Problems -- References -- 17 Solitons on the Boundaries of Microscopic Systems -- 17.1 Solitons as Elementary Particles -- 17.2 Quantization of Solitons on a Closed Contour and Instantons -- 17.3 Clusters as Solitary Waves on the Nuclear Surface -- 17.4 Nonlinear Schrödinger Equation Solitons on Quantum … -- 17.5 Solitons and Quasimolecular Structure -- 17.6 Soliton Model for Heavy Emitted Nuclear Clusters -- 17.7 Quintic Nonlinear Schrödinger Equation for Nuclear Cluster Decay -- 17.8 Contour Solitons in the Quantum Hall Liquid -- References -- 18 Nonlinear Contour Dynamics in Macroscopic Systems -- 18.1 Plasma Vortex -- 18.1.1 Effective Surface Tension in Magnetohydrodynamics and Plasma Systems -- 18.1.2 Trajectories in Magnetic Field Configurations -- 18.1.3 Magnetic Surfaces in Static Equilibrium -- 18.2 Elastic Spheres -- 18.3 Curvature Dependent Nonlinear Diffusion on Closed Surfaces -- 18.4 Nonlinear Evolution of Oscillation Modes in Neutron Stars -- References -- 19 Mathematical Appendix -- 19.1 Differentiable Manifolds -- 19.2 Riccati Equation -- 19.3 Special Functions -- 19.4 One-Soliton Solutions for the KdV, MKdV, and Their Combination -- 19.5 Scaling and Nonlinear Dispersion Relations1 -- References -- Index. |
| Record Nr. | UNINA-9910624313903321 |
|
Ludu Andrei
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Pseudodifferential analysis on conformally compact spaces / / [Robert Lauter]
| Pseudodifferential analysis on conformally compact spaces / / [Robert Lauter] |
| Autore | Lauter Robert <1967-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2003] |
| Descrizione fisica | 1 online resource (114 p.) |
| Disciplina |
510 s
515/.7242 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Pseudodifferential operators
Compact spaces Manifolds (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0375-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Acknowledgments:""; ""Part 1. Predholm theory for 0-pseudodifferential operators""; ""Chapter 1. Review on basic objects of 0-geometry""; ""1.1. The 0-structure algebra""; ""1.2. The extended 0-blow up""; ""1.3. Relation to the 0-double space X[sup(2)][sub(0)]""; ""1.4. The extended 0-triple space X[sup(3)][sub(0,e)]""; ""1.5. 0-densities""; ""Chapter 2. The small 0-calculus and the 0-calculus with bounds""; ""2.1. The Schwartz kernel theorem revisited""; ""2.2. The small 0-calculus""; ""2.3. Basic properties of the small 0-calculus""
""2.4. The 0-calculus with bounds""""2.5. Basic properties of the 0-calculus with bounds""; ""2.6. The indicial function""; ""2.7. General bundles""; ""Chapter 3. The b-c-calculus on an interval""; ""3.1. The b-c-structure algebra""; ""3.2. The b-c-double space""; ""3.3. b-c-densities""; ""3.4. The b-c calculus with bounds""; ""3.5. Basic properties of the b-c-calculus""; ""3.6. Fredholm theory for the b-c-calculus""; ""3.7. Invariance of the b-c-calculus under the R[sub(+)]-action""; ""3.8. C*-algebras of b-c-operators""; ""3.9. General bundles""; ""Chapter 4. The reduced normal operator"" ""4.1. Definition of the reduced normal operator""""4.2. Coordinate invariance of the reduced normal operator""; ""4.3. Scale invariance of the reduced normal operator""; ""4.4. Characterization of the reduced normal operator""; ""4.5. Basic properties of the reduced normal operator""; ""4.6. The case of 0-differential operators""; ""4.7. General bundles""; ""Chapter 5. Weighted 0-Sobolev spaces""; ""5.1. Boundedness of 0-operators of order 0 on L[sup(2)]-spaces""; ""5.2. Weighted 0-Sobolev spaces""; ""5.3. General bundles""; ""Chapter 6. Fredholm theory for 0-pseudodifferential operators"" ""6.1. Symbol reproducing families""""6.2. Characterization of Fredholm operators in Î?[sup(0)][sub(0)](X; [sup(0)]Ω[sup(1/2)])""; ""6.3. Characterization of Fredholm operators inÎ?[sup(m,k)][sub(0)](X; [sup(0)]Ω[sup(1/2)])""; ""6.4. General bundles""; ""Part 2. Algebras of 0-pseudodifferential operators of order 0""; ""Chapter 7. C*-algebras of 0-pseudodifferential operators""; ""7.1. Solvable C*-algebras""; ""7.2. The reduced normal operator on S*â??X""; ""7.3. Extension of the symbolic structure""; ""7.4. The C*-algebra generated by the reduced normal operator"" ""7.5. The C*-algebra B[sup((a))][sub(0)](X,[sup(0)]Ω[sup(1/2)])""""7.6. The spectrum of the C*-algebra B[sup((a))][sub(0)](X,[sup(0)]Ω[sup(1/2)])""; ""Chapter 8. Î?*-algebras of 0-pseudodifferential operators""; ""8.1. Submultiplicative Î?*-algebras""; ""8.2. Î?*-completions of b-c-and 0-calculus""; ""Appendix A. Spaces of conormal functions""; ""Bibliography""; ""Notations""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""V""; ""W"" |
| Record Nr. | UNINA-9910478893403321 |
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Lauter Robert <1967->
|
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| Providence, Rhode Island : , : American Mathematical Society, , [2003] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Pseudodifferential analysis on conformally compact spaces / / [Robert Lauter]
| Pseudodifferential analysis on conformally compact spaces / / [Robert Lauter] |
| Autore | Lauter Robert <1967-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2003] |
| Descrizione fisica | 1 online resource (114 p.) |
| Disciplina |
510 s
515/.7242 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Pseudodifferential operators
Compact spaces Manifolds (Mathematics) |
| ISBN | 1-4704-0375-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Acknowledgments:""; ""Part 1. Predholm theory for 0-pseudodifferential operators""; ""Chapter 1. Review on basic objects of 0-geometry""; ""1.1. The 0-structure algebra""; ""1.2. The extended 0-blow up""; ""1.3. Relation to the 0-double space X[sup(2)][sub(0)]""; ""1.4. The extended 0-triple space X[sup(3)][sub(0,e)]""; ""1.5. 0-densities""; ""Chapter 2. The small 0-calculus and the 0-calculus with bounds""; ""2.1. The Schwartz kernel theorem revisited""; ""2.2. The small 0-calculus""; ""2.3. Basic properties of the small 0-calculus""
""2.4. The 0-calculus with bounds""""2.5. Basic properties of the 0-calculus with bounds""; ""2.6. The indicial function""; ""2.7. General bundles""; ""Chapter 3. The b-c-calculus on an interval""; ""3.1. The b-c-structure algebra""; ""3.2. The b-c-double space""; ""3.3. b-c-densities""; ""3.4. The b-c calculus with bounds""; ""3.5. Basic properties of the b-c-calculus""; ""3.6. Fredholm theory for the b-c-calculus""; ""3.7. Invariance of the b-c-calculus under the R[sub(+)]-action""; ""3.8. C*-algebras of b-c-operators""; ""3.9. General bundles""; ""Chapter 4. The reduced normal operator"" ""4.1. Definition of the reduced normal operator""""4.2. Coordinate invariance of the reduced normal operator""; ""4.3. Scale invariance of the reduced normal operator""; ""4.4. Characterization of the reduced normal operator""; ""4.5. Basic properties of the reduced normal operator""; ""4.6. The case of 0-differential operators""; ""4.7. General bundles""; ""Chapter 5. Weighted 0-Sobolev spaces""; ""5.1. Boundedness of 0-operators of order 0 on L[sup(2)]-spaces""; ""5.2. Weighted 0-Sobolev spaces""; ""5.3. General bundles""; ""Chapter 6. Fredholm theory for 0-pseudodifferential operators"" ""6.1. Symbol reproducing families""""6.2. Characterization of Fredholm operators in Î?[sup(0)][sub(0)](X; [sup(0)]Ω[sup(1/2)])""; ""6.3. Characterization of Fredholm operators inÎ?[sup(m,k)][sub(0)](X; [sup(0)]Ω[sup(1/2)])""; ""6.4. General bundles""; ""Part 2. Algebras of 0-pseudodifferential operators of order 0""; ""Chapter 7. C*-algebras of 0-pseudodifferential operators""; ""7.1. Solvable C*-algebras""; ""7.2. The reduced normal operator on S*â??X""; ""7.3. Extension of the symbolic structure""; ""7.4. The C*-algebra generated by the reduced normal operator"" ""7.5. The C*-algebra B[sup((a))][sub(0)](X,[sup(0)]Ω[sup(1/2)])""""7.6. The spectrum of the C*-algebra B[sup((a))][sub(0)](X,[sup(0)]Ω[sup(1/2)])""; ""Chapter 8. Î?*-algebras of 0-pseudodifferential operators""; ""8.1. Submultiplicative Î?*-algebras""; ""8.2. Î?*-completions of b-c-and 0-calculus""; ""Appendix A. Spaces of conormal functions""; ""Bibliography""; ""Notations""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""V""; ""W"" |
| Record Nr. | UNINA-9910788849603321 |
|
Lauter Robert <1967->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2003] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
