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The Resource Mathematics of Climate Modeling, by Valentin P. Dymnikov, Aleksander N. Filatov, (electronic resource)
Mathematics of Climate Modeling, by Valentin P. Dymnikov, Aleksander N. Filatov, (electronic resource)
Resource Information
The item Mathematics of Climate Modeling, by Valentin P. Dymnikov, Aleksander N. Filatov, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Mathematics of Climate Modeling, by Valentin P. Dymnikov, Aleksander N. Filatov, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 The present monograph is dedicated to a new branch of the theory of climate, which is titled by the authors, "Mathematical Theory of Climate. " The foundation of this branch is the investigation of climate models by the methods of the qUalitative theory of differential equa tions. In the Russian edition the book was named "Fundamentals of the Mathematical Theory of Climate. " Respecting the recommenda tions of Wayne Yuhasz (we are truly grateful to him for this advice), we named the English edition of the book "Mathematics of Climate Modelling. " This title appears to be more appropriate, since the con structive results of the theory are at present preliminary and have not been fully tested with experiments in climate modelling. This branch of science is yet developing and its practical results will be obtained only in the near future. Nevertheless, we want to keep the terminology which we have used in the introduction to the Russian edition of the book, since the authors hope that this term will be accepted by the scientific community for identification of a given branch of climate theory. On preparing the English edition, new ideas were established con necting some significant new research results obtained by the author. We are deeply grateful to G. Marchuk for continual encourage ment of this scientific enterprise and fruitful discussions, to our young colleagues A. Gorelov, E. Kazantsev, A. Gritsun, and A
 Language

 eng
 eng
 Edition
 1st ed. 1997.
 Extent
 1 online resource (XVI, 264 p.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 1. Dynamical Systems. Attractors, Invariant Measures
 1.1 Metric Spaces. Compactness
 1.2 Dynamical Systems. Main Properties
 1.3 Invariant Sets
 1.4 Classification of Motions
 1.5 Recurrence of Domains
 1.6 Measure. KrylovBogolyubov Theorem
 1.7 Dynamical Systems with Invariant Measure
 1.8 Nonlinear Dissipative Systems
 1.9 Inertial Manifolds of Dissipative Systems
 2. NonAutonomous Dissipative Systems, their Attractor and Averaging
 2.1 Introduction
 2.2 Processes and their Attractors. Kernel of Processes, Section of Kernel
 2.3 Families of Processes and their Attractors
 2.4 Family of Processes and Semigroups
 2.5 Averaging of Nonlinear Dissipative Systems. Closeness between Attractors of Original and Averaged Systems
 2.6 On Closeness of Solutions of Original and Averaged Nonlinear Dissipative Systems on Infinite Time Interval
 3. Analysis of Barotropic Model
 3.1. Existence of Global Attractor
 3.2 Estimate of Dimension of Attractor
 3.3 Statistical Solutions and Invariant Measures on Attractor
 3.4 Estimate of Attractor Dimension with Respect to Orography
 3.5 Galerkin Approximations
 3.6 Existence of Inertial Manifold
 4. Discretization of Systems Possessing Attractor
 4.1 Discretization of Systems Possessing Inertial Manifolds
 4.2 TimeSpace Discretization of Systems Possessing Attractor
 4.3 Globally Stable Difference Schemes for Barotropic Vorticity Equation
 5. Numerical Study of Structure of Attractor Generated by Barotropic Equations on Sphere
 5.1 Equations and Parameters of Model. Methods of Solving of Stationary and Nonstationary Problems
 5.2 Statistical Stationary Solution and Stationary Points
 5.3 Lyapunov Exponents and Attractor Dimension
 5.4 Analysis of Analytical Estimates of Attractor Dimension of Barotropic Atmospheric Equations
 6. TwoLayer Baroclinic Model
 6.1 TwoLayer Baroclinic Model
 6.2 Estimate of Attractor Dimension
 6.3 Numerical Investigation of Attractor. Characteristics of TwoLayer Baroclinic Model
 7. Investigation of Structure of Climate Attractors by Observed Data Series
 7.1. Correlation Dimension of Attractor
 7.2. Calculation of Lyapunov Exponents
 7.3 Statistically Independent Degrees of Freedom and Attractor Dimension
 8. Regimes of Atmosphere Circulation
 8.1 Definition of Atmosphere Circulation Regimes
 8.2 Dynamical Theory of TwoRegime Barotropic Circulation
 8.3. Statistical Theory of TwoRegime Barotropic Circulation
 8.4 SRegimes of Atmosphere Circulation
 9. Solvability of Ocean and Atmosphere Models
 9.1 Introduction
 9.2 Solvability of Ocean and Atmosphere Models in Bounded Domains
 9.3 Solvability of Ocean and Atmosphere Models on Sphere in pSystem of Coordinates
 Isbn
 9781461241485
 Label
 Mathematics of Climate Modeling
 Title
 Mathematics of Climate Modeling
 Statement of responsibility
 by Valentin P. Dymnikov, Aleksander N. Filatov
 Language

 eng
 eng
 Summary
 The present monograph is dedicated to a new branch of the theory of climate, which is titled by the authors, "Mathematical Theory of Climate. " The foundation of this branch is the investigation of climate models by the methods of the qUalitative theory of differential equa tions. In the Russian edition the book was named "Fundamentals of the Mathematical Theory of Climate. " Respecting the recommenda tions of Wayne Yuhasz (we are truly grateful to him for this advice), we named the English edition of the book "Mathematics of Climate Modelling. " This title appears to be more appropriate, since the con structive results of the theory are at present preliminary and have not been fully tested with experiments in climate modelling. This branch of science is yet developing and its practical results will be obtained only in the near future. Nevertheless, we want to keep the terminology which we have used in the introduction to the Russian edition of the book, since the authors hope that this term will be accepted by the scientific community for identification of a given branch of climate theory. On preparing the English edition, new ideas were established con necting some significant new research results obtained by the author. We are deeply grateful to G. Marchuk for continual encourage ment of this scientific enterprise and fruitful discussions, to our young colleagues A. Gorelov, E. Kazantsev, A. Gritsun, and A
 http://library.link/vocab/creatorName
 Dymnikov, Valentin P
 Dewey number
 519
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 P_kMutp8IZg
 wQE8UcfmkxA
 Image bit depth
 0
 Language note
 English
 LC call number
 T5757.97
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Filatov, Aleksander N.
 Series statement
 Modeling and Simulation in Science, Engineering and Technology,
 http://library.link/vocab/subjectName

 Mathematics
 Applications of Mathematics
 Atmospheric Sciences
 Label
 Mathematics of Climate Modeling, by Valentin P. Dymnikov, Aleksander N. Filatov, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 1. Dynamical Systems. Attractors, Invariant Measures  1.1 Metric Spaces. Compactness  1.2 Dynamical Systems. Main Properties  1.3 Invariant Sets  1.4 Classification of Motions  1.5 Recurrence of Domains  1.6 Measure. KrylovBogolyubov Theorem  1.7 Dynamical Systems with Invariant Measure  1.8 Nonlinear Dissipative Systems  1.9 Inertial Manifolds of Dissipative Systems  2. NonAutonomous Dissipative Systems, their Attractor and Averaging  2.1 Introduction  2.2 Processes and their Attractors. Kernel of Processes, Section of Kernel  2.3 Families of Processes and their Attractors  2.4 Family of Processes and Semigroups  2.5 Averaging of Nonlinear Dissipative Systems. Closeness between Attractors of Original and Averaged Systems  2.6 On Closeness of Solutions of Original and Averaged Nonlinear Dissipative Systems on Infinite Time Interval  3. Analysis of Barotropic Model  3.1. Existence of Global Attractor  3.2 Estimate of Dimension of Attractor  3.3 Statistical Solutions and Invariant Measures on Attractor  3.4 Estimate of Attractor Dimension with Respect to Orography  3.5 Galerkin Approximations  3.6 Existence of Inertial Manifold  4. Discretization of Systems Possessing Attractor  4.1 Discretization of Systems Possessing Inertial Manifolds  4.2 TimeSpace Discretization of Systems Possessing Attractor  4.3 Globally Stable Difference Schemes for Barotropic Vorticity Equation  5. Numerical Study of Structure of Attractor Generated by Barotropic Equations on Sphere  5.1 Equations and Parameters of Model. Methods of Solving of Stationary and Nonstationary Problems  5.2 Statistical Stationary Solution and Stationary Points  5.3 Lyapunov Exponents and Attractor Dimension  5.4 Analysis of Analytical Estimates of Attractor Dimension of Barotropic Atmospheric Equations  6. TwoLayer Baroclinic Model  6.1 TwoLayer Baroclinic Model  6.2 Estimate of Attractor Dimension  6.3 Numerical Investigation of Attractor. Characteristics of TwoLayer Baroclinic Model  7. Investigation of Structure of Climate Attractors by Observed Data Series  7.1. Correlation Dimension of Attractor  7.2. Calculation of Lyapunov Exponents  7.3 Statistically Independent Degrees of Freedom and Attractor Dimension  8. Regimes of Atmosphere Circulation  8.1 Definition of Atmosphere Circulation Regimes  8.2 Dynamical Theory of TwoRegime Barotropic Circulation  8.3. Statistical Theory of TwoRegime Barotropic Circulation  8.4 SRegimes of Atmosphere Circulation  9. Solvability of Ocean and Atmosphere Models  9.1 Introduction  9.2 Solvability of Ocean and Atmosphere Models in Bounded Domains  9.3 Solvability of Ocean and Atmosphere Models on Sphere in pSystem of Coordinates
 Dimensions
 unknown
 Edition
 1st ed. 1997.
 Extent
 1 online resource (XVI, 264 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461241485
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461241485
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000090724
 (SSID)ssj0001297596
 (PQKBManifestationID)11779956
 (PQKBTitleCode)TC0001297596
 (PQKBWorkID)11229659
 (PQKB)11004136
 (DEHe213)9781461241485
 (MiAaPQ)EBC3075276
 (EXLCZ)993400000000090724
 Label
 Mathematics of Climate Modeling, by Valentin P. Dymnikov, Aleksander N. Filatov, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 1. Dynamical Systems. Attractors, Invariant Measures  1.1 Metric Spaces. Compactness  1.2 Dynamical Systems. Main Properties  1.3 Invariant Sets  1.4 Classification of Motions  1.5 Recurrence of Domains  1.6 Measure. KrylovBogolyubov Theorem  1.7 Dynamical Systems with Invariant Measure  1.8 Nonlinear Dissipative Systems  1.9 Inertial Manifolds of Dissipative Systems  2. NonAutonomous Dissipative Systems, their Attractor and Averaging  2.1 Introduction  2.2 Processes and their Attractors. Kernel of Processes, Section of Kernel  2.3 Families of Processes and their Attractors  2.4 Family of Processes and Semigroups  2.5 Averaging of Nonlinear Dissipative Systems. Closeness between Attractors of Original and Averaged Systems  2.6 On Closeness of Solutions of Original and Averaged Nonlinear Dissipative Systems on Infinite Time Interval  3. Analysis of Barotropic Model  3.1. Existence of Global Attractor  3.2 Estimate of Dimension of Attractor  3.3 Statistical Solutions and Invariant Measures on Attractor  3.4 Estimate of Attractor Dimension with Respect to Orography  3.5 Galerkin Approximations  3.6 Existence of Inertial Manifold  4. Discretization of Systems Possessing Attractor  4.1 Discretization of Systems Possessing Inertial Manifolds  4.2 TimeSpace Discretization of Systems Possessing Attractor  4.3 Globally Stable Difference Schemes for Barotropic Vorticity Equation  5. Numerical Study of Structure of Attractor Generated by Barotropic Equations on Sphere  5.1 Equations and Parameters of Model. Methods of Solving of Stationary and Nonstationary Problems  5.2 Statistical Stationary Solution and Stationary Points  5.3 Lyapunov Exponents and Attractor Dimension  5.4 Analysis of Analytical Estimates of Attractor Dimension of Barotropic Atmospheric Equations  6. TwoLayer Baroclinic Model  6.1 TwoLayer Baroclinic Model  6.2 Estimate of Attractor Dimension  6.3 Numerical Investigation of Attractor. Characteristics of TwoLayer Baroclinic Model  7. Investigation of Structure of Climate Attractors by Observed Data Series  7.1. Correlation Dimension of Attractor  7.2. Calculation of Lyapunov Exponents  7.3 Statistically Independent Degrees of Freedom and Attractor Dimension  8. Regimes of Atmosphere Circulation  8.1 Definition of Atmosphere Circulation Regimes  8.2 Dynamical Theory of TwoRegime Barotropic Circulation  8.3. Statistical Theory of TwoRegime Barotropic Circulation  8.4 SRegimes of Atmosphere Circulation  9. Solvability of Ocean and Atmosphere Models  9.1 Introduction  9.2 Solvability of Ocean and Atmosphere Models in Bounded Domains  9.3 Solvability of Ocean and Atmosphere Models on Sphere in pSystem of Coordinates
 Dimensions
 unknown
 Edition
 1st ed. 1997.
 Extent
 1 online resource (XVI, 264 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461241485
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461241485
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000090724
 (SSID)ssj0001297596
 (PQKBManifestationID)11779956
 (PQKBTitleCode)TC0001297596
 (PQKBWorkID)11229659
 (PQKB)11004136
 (DEHe213)9781461241485
 (MiAaPQ)EBC3075276
 (EXLCZ)993400000000090724
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/MathematicsofClimateModelingbyValentinP./VQKo_CxjiAY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/MathematicsofClimateModelingbyValentinP./VQKo_CxjiAY/">Mathematics of Climate Modeling, by Valentin P. Dymnikov, Aleksander N. Filatov, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>