Jet Single-Time Lagrange Geometry and Its Applications

Name: Jet Single-Time Lagrange Geometry and Its Applications
Brand: Wiley
Price: 97.99 EUR
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Vladimir Balan Mircea Neagu(Autor*in)

Wiley (Verlag)

Erschienen am 23. November 2011

224 Seiten

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Beschreibung

Develops the theory of jet single-time Lagrange geometry andpresents modern-day applications
Jet Single-Time Lagrange Geometry and Its Applicationsguides readers through the advantages of jet single-time Lagrangegeometry for geometrical modeling. With comprehensive chapters thatoutline topics ranging in complexity from basic to advanced, thebook explores current and emerging applications across a broadrange of fields, including mathematics, theoretical and atmosphericphysics, economics, and theoretical biology.
The authors begin by presenting basic theoretical concepts thatserve as the foundation for understanding how and why the discussedtheory works. Subusequent chapters compare the geometrical andphysical aspects of jet relativistic time-dependent Lagrangegeometry to the classical time-dependent Lagrange geometry. Acollection of jet geometrical objects are also examined such asd-tensors, relativistic time-dependent semisprays, harmonic curves,and nonlinear connections. Numerous applications, including thegravitational theory developed by both the Berwald-Moór metricand the Chernov metric, are also presented.
Throughout the book, the authors offer numerous examples thatillustrate how the theory is put into practice, and they alsopresent numerous applications in which the solutions of first-orderordinary differential equation systems are regarded as harmoniccurves on 1-jet spaces. In addition, numerous opportunities areprovided for readers to gain skill in applying jet single-timeLagrange geometry to solve a wide range of problems.
Extensively classroom-tested to ensure an accessiblepresentation, Jet Single-Time Lagrange Geometry and ItsApplications is an excellent book for courses on differentialgeometry, relativity theory, and mathematical models at thegraduate level. The book also serves as an excellent reference forresearchers, professionals, and academics in physics, biology,mathematics, and economics who would like to learn more aboutmodel-providing geometric structures.

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Inhalt

Intro
Jet Single-Time Lagrange Geometry and Its Applications
CONTENTS
Preface
PART I THE JET SINGLE-TIME LAGRANGE GEOMETRY
1 Jet geometrical objects depending on a relativistic time
1.1 d-tensors on the 1-jet space J1 (R, M)
1.2 Relativistic time-dependent semisprays. Harmonic curves
1.3 Jet nonlinear connections. Adapted bases
1.4 Relativistic time-dependent semisprays and jet nonlinear connections
2 Deflection d-tensor identities in the relativistic time-dependent Lagrange geometry
2.1 The adapted components of jet G-linear connections
2.2 Local torsion and curvature d-tensors
2.3 Local Ricci identities and nonmetrical deflection d-tensors
3 Local Bianchi identities in the relativistic time-dependent Lagrange geometry
3.1 The adapted components of h-normal G-linear connections
3.2 Deflection d-tensor identities and local Bianchi identities for d-connections of Cartan type
4 The jet Riemann-Lagrange geometry of the relativistic time-dependent Lagrange spaces
4.1 Relativistic time-dependent Lagrange spaces
4.2 The canonical nonlinear connection
4.3 The Cartan canonical metrical linear connection
4.4 Relativistic time-dependent Lagrangian electromagnetism
4.4.1 The jet single-time electromagnetic field
4.4.2 Geometrical Maxwell equations
4.5 Jet relativistic time-dependent Lagrangian gravitational theory
4.5.1 The jet single-time gravitational field
4.5.2 Geometrical Einstein equations and conservation laws
5 The jet single-time electrodynamics
5.1 Riemann-Lagrange geometry on the jet single-time Lagrange space of electrodynamics eDL1n
5.2 Geometrical Maxwell equations on eDL1n
5.3 Geometrical Einstein equations on eDL1n
6 Jet local single-time Finsler-Lagrange geometry for the rheonomic Berwald-Moór metric of order three
6.1 Preliminary notations and formulas
6.2 The rheonomic Berwald-Moór metric of order three
6.3 Cartan canonical linear connection, d-torsions and d-curvatures
6.4 Geometrical field theories produced by the rheonomic Berwald-Moór metric of order three
6.4.1 Geometrical gravitational theory
6.4.2 Geometrical electromagnetic theory
7 Jet local single-time Finsler-Lagrange approach for the rheonomic Berwald-Moór metric of order four
7.1 Preliminary notations and formulas
7.2 The rheonomic Berwald-Moór metric of order four
7.3 Cartan canonical linear connection, d-torsions and d-curvatures
7.4 Geometrical gravitational theory produced by the rheonomic Berwald-Moór metric of order four
7.5 Some physical remarks and comments
7.5.1 On gravitational theory
7.5.2 On electromagnetic theory
7.6 Geometric dynamics of plasma in jet spaces with rheonomic Berwald-Moór metric of order four
7.6.1 Introduction
7.6.2 Generalized Lagrange geometrical approach of the non-isotropic plasma on 1-jet spaces
7.6.3 The non-isotropic plasma as a medium geometrized by the jet rheonomic Berwald-Moór metric of order four
8 The jet local single-time Finsler-Lagrange geometry induced by the rheonomic Chernov metric of order four
8.1 Preliminary notations and formulas
8.2 The rheonomic Chernov metric of order four
8.3 Cartan canonical linear connection, d-torsions and d-curvatures
8.4 Applications of the rheonomic Chernov metric of order four
8.4.1 Geometrical gravitational theory
8.4.2 Geometrical electromagnetic theory
9 Jet Finslerian geometry of the conformal Minkowski metric
9.1 Introduction
9.2 The canonical nonlinear connection of the model
9.3 Cartan canonical linear connection, d-torsions and d-curvatures
9.4 Geometrical field model produced by the jet conformal Minkowski metric
9.4.1 Gravitational-like geometrical model
9.4.2 Related electromagnetic model considerations
PART II APPLICATIONS OF THE JET SINGLE-TIME LAGRANGE GEOMETRY
10 Geometrical objects produced by a nonlinear ODEs system of first-order and a pair of Riemannian metrics
10.1 Historical aspects
10.2 Solutions of ODEs systems of order one as harmonic curves on 1-jet spaces. Canonical nonlinear connections
10.3 From first-order ODEs systems and Riemannian metrics to geometrical objects on 1-jet spaces
10.4 Geometrical objects produced on 1-jet spaces by first-order ODEs systems and pairs of Euclidian metrics. Jet Yang-Mills energy
11 Jet single-time Lagrange geometry applied to the Lorenz atmospheric ODEs system
11.1 Jet Riemann-Lagrange geometry produced by the Lorenz simplified model of Rossby gravity wave interaction
11.2 Yang-Mills energetic hypersurfaces of constant level produced by the Lorenz atmospheric ODEs system
12 Jet single-time Lagrange geometry applied to evolution ODEs systems from Economy
12.1 Jet Riemann-Lagrange geometry for Kaldor nonlinear cyclical model in business
12.2 Jet Riemann-Lagrange geometry for Tobin-Benhabib-Miyao economic evolution model
13 Some evolution equations from Theoretical Biology and their single-time Lagrange geometrization on 1-jet spaces
13.1 Jet Riemann-Lagrange geometry for a cancer cell population model in biology
13.2 The jet Riemann-Lagrange geometry of the infection by human immunodeficiency virus (HIV-1) evolution model
13.3 From calcium oscillations ODEs systems to jet Yang-Mills energies
13.3.1 Intracellular calcium oscillations induced by selfmodulation of the inositol 1,4,5-triphosphate signal
13.3.2 Calcium oscillations in a model involving endoplasmic reticulum, mitochondria, and cytosolic proteins
13.3.3 Yang-Mills energetic surfaces of constant level. Theoretical biological interpretations
14 Jet geometrical objects produced by linear ODEs systems and higher-order ODEs
14.1 Jet Riemann-Lagrange geometry produced by a non-homogenous linear ODEs system of order one
14.2 Jet Riemann-Lagrange geometry produced by a higher-order ODE
14.3 Riemann-Lagrange geometry produced by a non-homogenous linear ODE of higher-order
15 Jet single-time geometrical extension of the KCC-invariants
References
Index

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