The Resource Fundamentals of Finslerian Diffusion with Applications, by P.L. Antonelli, T.J. Zastawniak, (electronic resource)

Fundamentals of Finslerian Diffusion with Applications, by P.L. Antonelli, T.J. Zastawniak, (electronic resource)

Label
Fundamentals of Finslerian Diffusion with Applications
Title
Fundamentals of Finslerian Diffusion with Applications
Statement of responsibility
by P.L. Antonelli, T.J. Zastawniak
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
The erratic motion of pollen grains and other tiny particles suspended in liquid is known as Brownian motion, after its discoverer, Robert Brown, a botanist who worked in 1828, in London. He turned over the problem of why this motion occurred to physicists who were investigating kinetic theory and thermodynamics; at a time when the existence of molecules had yet to be established. In 1900, Henri Poincare lectured on this topic to the 1900 International Congress of Physicists, in Paris [Wic95]. At this time, Louis Bachelier, a thesis student of Poincare, made a monumental breakthrough with his Theory of Stock Market Fluctuations, which is still studied today, [Co064]. Norbert Wiener (1923), who was first to formulate a rigorous concept of the Brownian path, is most often cited by mathematicians as the father of the subject, while physicists will cite A. Einstein (1905) and M. Smoluchowski. Both considered Markov diffusions and realized that Brownian behaviour nd could be formulated in terms of parabolic 2 order linear p. d. e. 'so Further­ more, from this perspective, the covariance of changes in position could be allowed to depend on the position itself, according to the invariant form of the diffusion introduced by Kolmogorov in 1937, [KoI37]. Thus, any time­ homogeneous Markov diffusion could be written in terms of the Laplacian, intrinsically given by the symbol (covariance) of the p. d. e. , plus a drift vec­ tor. The theory was further advanced in 1949, when K
Member of
http://library.link/vocab/creatorName
Antonelli, P.L
Dewey number
576.8
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • KwJ_GdxxIi4
  • GQ5ikXNpWvI
Image bit depth
0
Language note
English
LC call number
QH359-425
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Zastawniak, T.J.
Series statement
Fundamental Theories of Physics,
Series volume
101
http://library.link/vocab/subjectName
  • Evolution (Biology)
  • Global differential geometry
  • Distribution (Probability theory
  • Global analysis
  • Evolutionary Biology
  • Differential Geometry
  • Probability Theory and Stochastic Processes
  • Global Analysis and Analysis on Manifolds
Label
Fundamentals of Finslerian Diffusion with Applications, by P.L. Antonelli, T.J. Zastawniak, (electronic resource)
Instantiates
Publication
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 Finsler Spaces -- 1.1 The Tangent and Cotangent Bundle -- 1.2 Fiber Bundles -- 1.3 Frame Bundles and Linear Connections -- 1.4 Tensor Fields -- 1.5 Linear Connections -- 1.6 Torsion and Curvature of a Linear Connection -- 1.7 Parallelism -- 1.8 The Levi-Cività Connection on a Riemannian Manifold -- 1.9 Geodesics, Stability and the Orthonormal Frame Bundle -- 1.10 Finsler Space and Metric -- 1.11 Finsler Tensor Fields -- 1.12 Nonlinear Connections -- 1.13 Affine Connections on the Finsler Bundle -- 1.14 Finsler Connections -- 1.15 Torsions and Curvatures of a Finsler Connection -- 1.16 Metrical Finsler Connections. The Cartan Connection -- 2 Introduction to Stochastic Calculus on Manifolds -- 2.1 Preliminaries -- 2.2 Itô’s Stochastic Integral -- 2.3 Ito Processes. Itô Formula -- 2.4 Stratonovich Integrals -- 2.5 Stochastic Differential Equations on Manifolds -- 3 Stochastic Development on Finsler Spaces -- 3.1 Riemannian Stochastic Development -- 3.2 Rolling Finsler Manifolds Along Smooth Curves and Diffusions -- 3.3 Finslerian Stochastic Development -- 3.4 Radial Behaviour -- 4 Volterra-Hamilton Systems of Finsler -- 4.1 Berwald Connections and Berwald Spaces -- 4.2 Volterra-Hamilton Systems and Ecology -- 4.3 Wagnerian Geometry and Volterra-Hamilton Systems -- 4.4 Random Perturbations of Finslerian Volterra-Hamilton Systems -- 4.5 Random Perturbations of Riemannian Volterra-Hamilton Systems -- 4.6 Noise in Conformally Minkowski Systems -- 4.7 Canalization of Growth and Development with Noise -- 4.8 Noisy Systems in Chemical Ecology and Epidemiology -- 4.9 Riemannian Nonlinear Filtering -- 4.10 Conformai Signals and Geometry of Filters -- 4.11 Riemannian Filtering of Starfish Predation -- 5 Finslerian Diffusion and Curvature -- 5.1 Cartan’s Lemma in Berwald Spaces -- 5.2 Quadratic Dispersion -- 5.3 Finslerian Development and Curvature -- 5.4 Finsleriam Filtering and Quadratic Dispersion -- 5.5 Entropy Production and Quadratic Dispersion -- 6 Diffusion on the Tangent and Indicatrix Bundles -- 6.1 Slit Tangent Bundle as Riemannian Manifold -- 6.2 hv-Development as Riemannian Development with Drift -- 6.3 Indicatrized Finslerian Stochastic Development -- 6.4 Indicatrized hv-Development Viewed as Riemannian -- A Diffusion and Laplacian on the Base Space -- A.1 Finslerian Isotropic Transport Process -- A.2 Central Limit Theorem -- A.3 Laplacian, Harmonic Forms and Hodge Decomposition -- B Two-Dimensional Constant Berwald Spaces -- B.1 Berwald’s Famous Theorem -- B.2 Standard Coordinate Representation
Dimensions
unknown
Edition
1st ed. 1999.
Extent
1 online resource (VII, 205 p.)
File format
multiple file formats
Form of item
online
Isbn
9789401148245
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-94-011-4824-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000123268
  • (SSID)ssj0001242950
  • (PQKBManifestationID)11825595
  • (PQKBTitleCode)TC0001242950
  • (PQKBWorkID)11268614
  • (PQKB)10670767
  • (DE-He213)978-94-011-4824-5
  • (MiAaPQ)EBC3105476
  • (EXLCZ)993400000000123268
Label
Fundamentals of Finslerian Diffusion with Applications, by P.L. Antonelli, T.J. Zastawniak, (electronic resource)
Publication
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 Finsler Spaces -- 1.1 The Tangent and Cotangent Bundle -- 1.2 Fiber Bundles -- 1.3 Frame Bundles and Linear Connections -- 1.4 Tensor Fields -- 1.5 Linear Connections -- 1.6 Torsion and Curvature of a Linear Connection -- 1.7 Parallelism -- 1.8 The Levi-Cività Connection on a Riemannian Manifold -- 1.9 Geodesics, Stability and the Orthonormal Frame Bundle -- 1.10 Finsler Space and Metric -- 1.11 Finsler Tensor Fields -- 1.12 Nonlinear Connections -- 1.13 Affine Connections on the Finsler Bundle -- 1.14 Finsler Connections -- 1.15 Torsions and Curvatures of a Finsler Connection -- 1.16 Metrical Finsler Connections. The Cartan Connection -- 2 Introduction to Stochastic Calculus on Manifolds -- 2.1 Preliminaries -- 2.2 Itô’s Stochastic Integral -- 2.3 Ito Processes. Itô Formula -- 2.4 Stratonovich Integrals -- 2.5 Stochastic Differential Equations on Manifolds -- 3 Stochastic Development on Finsler Spaces -- 3.1 Riemannian Stochastic Development -- 3.2 Rolling Finsler Manifolds Along Smooth Curves and Diffusions -- 3.3 Finslerian Stochastic Development -- 3.4 Radial Behaviour -- 4 Volterra-Hamilton Systems of Finsler -- 4.1 Berwald Connections and Berwald Spaces -- 4.2 Volterra-Hamilton Systems and Ecology -- 4.3 Wagnerian Geometry and Volterra-Hamilton Systems -- 4.4 Random Perturbations of Finslerian Volterra-Hamilton Systems -- 4.5 Random Perturbations of Riemannian Volterra-Hamilton Systems -- 4.6 Noise in Conformally Minkowski Systems -- 4.7 Canalization of Growth and Development with Noise -- 4.8 Noisy Systems in Chemical Ecology and Epidemiology -- 4.9 Riemannian Nonlinear Filtering -- 4.10 Conformai Signals and Geometry of Filters -- 4.11 Riemannian Filtering of Starfish Predation -- 5 Finslerian Diffusion and Curvature -- 5.1 Cartan’s Lemma in Berwald Spaces -- 5.2 Quadratic Dispersion -- 5.3 Finslerian Development and Curvature -- 5.4 Finsleriam Filtering and Quadratic Dispersion -- 5.5 Entropy Production and Quadratic Dispersion -- 6 Diffusion on the Tangent and Indicatrix Bundles -- 6.1 Slit Tangent Bundle as Riemannian Manifold -- 6.2 hv-Development as Riemannian Development with Drift -- 6.3 Indicatrized Finslerian Stochastic Development -- 6.4 Indicatrized hv-Development Viewed as Riemannian -- A Diffusion and Laplacian on the Base Space -- A.1 Finslerian Isotropic Transport Process -- A.2 Central Limit Theorem -- A.3 Laplacian, Harmonic Forms and Hodge Decomposition -- B Two-Dimensional Constant Berwald Spaces -- B.1 Berwald’s Famous Theorem -- B.2 Standard Coordinate Representation
Dimensions
unknown
Edition
1st ed. 1999.
Extent
1 online resource (VII, 205 p.)
File format
multiple file formats
Form of item
online
Isbn
9789401148245
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-94-011-4824-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000123268
  • (SSID)ssj0001242950
  • (PQKBManifestationID)11825595
  • (PQKBTitleCode)TC0001242950
  • (PQKBWorkID)11268614
  • (PQKB)10670767
  • (DE-He213)978-94-011-4824-5
  • (MiAaPQ)EBC3105476
  • (EXLCZ)993400000000123268

Library Locations

  • Architecture LibraryBorrow it
    Gould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US
    35.205706 -97.445050
  • Bizzell Memorial LibraryBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Boorstin CollectionBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Chinese Literature Translation ArchiveBorrow it
    401 W. Brooks St., RM 414, Norman, OK, 73019, US
    35.207487 -97.447906
  • Engineering LibraryBorrow it
    Felgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US
    35.205706 -97.445050
  • Fine Arts LibraryBorrow it
    Catlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US
    35.210371 -97.448244
  • Harry W. Bass Business History CollectionBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • History of Science CollectionsBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • John and Mary Nichols Rare Books and Special CollectionsBorrow it
    401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • Library Service CenterBorrow it
    2601 Technology Place, Norman, OK, 73019, US
    35.185561 -97.398361
  • Price College Digital LibraryBorrow it
    Adams Hall 102 307 West Brooks St., Norman, OK, 73019, US
    35.210371 -97.448244
  • Western History CollectionsBorrow it
    Monnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US
    35.209584 -97.445414
Processing Feedback ...