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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…mehr

Produktbeschreibung
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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  • Produktdetails
  • Verlag: John Wiley & Sons
  • Seitenzahl: 216
  • Erscheinungstermin: 23.11.2011
  • Englisch
  • ISBN-13: 9781118143766
  • Artikelnr.: 37339406
Autorenporträt
VLADIMIR BALAN, PhD, is Professor in the Department ofMathematics and Informatics at the University Politehnica ofBucharest, Romania. He has published extensively in his areas ofresearch interest, which include harmonic maps, variationalproblems in fiber bundles, and generalized gauge theory and itsapplications in mechanics and mathematical physics. MIRCEA NEAGU, PhD, is Assistant Professor in theDepartment of Algebra, Geometry, and Differential Equations at theTransilvania University of Bra¿¿ov, Romania. He is theauthor of more than thirty-five journal articles on jetRiemann-Lagrange geometry and its applications.
Inhaltsangabe
Preface. Part I. The Jet Single
Time Lagrange Geometry 1. Jet geometrical objects depending on a relativistic time 3 1.1 d
Tensors on the 1
jet space J1(R, M) 4 1.2 Relativistic time
dependent semisprays. Harmonic curves 6 1.3 Jet nonlinear connection. Adapted bases 11 1.4 Relativistic time
dependent and jet nonlinear connections 16 2. Deflection d
tensor identities in the relativistic time
dependent Lagrange geometry 19 2.1 The adapted components of jet Gamma
linear connections 19 2.2 Local torsion and curvature d
tensors 24 2.3 Local Ricci identities and nonmetrical deflection d
tensors 30 3. Local Bianchi identities in the relativistic time
dependent Lagrange geometry 33 3.1 The adapted components of h
normal Gamma
linear connections 33 3.2 Deflection d
tensor identities and local Bianchi identities for d
connections of Cartan type 37 4. The jet Riemann
Lagrange geometry of the relativistic time
dependent Lagrange spaces 43 4.1 Relativistic time
dependent Lagrange spaces 44 4.2 The canonical nonlinear connection 45 4.3 The Cartan canonical metrical linear connection 48 4.4 Relativistic time
dependent Lagrangian electromagnetism 50 4.5 Jet relativistic time
dependent Lagrangian gravitational theory 51 5. The jet single
time electrodynamics 57 5.1 Riemann
Lagrange geometry on the jet single
time Lagrange space of electrodynamics EDLn/1 58 5.2 Geometrical Maxwell equations of EDLn/1 61 5.3 Geometrical Einstein equations on EDLn/1 62 6. Jet local single
time Finsler
Lagrange geometry for the rheonomic Berwald
Moór metric of order three 65 6.1 Preliminary notations and formulas 66 6.2 The rheonomic Berwald
Moór metric of order three 67 6.3 Cartan canonical linear connection. D
Torsions and d
curvatures 69 6.4 Geometrical field theories produced by the rheonomic Berwald
Moór metric of order three 72 7. Jet local single
time Finsler
Lagrange approach for the rheonomic Berwald
Moór metric of order four 77 7.1 Preliminary notations and formulas 78 7.2 The rheonomic Berwald
Moór metric of order four 79 7.3 Cartan canonical linear connection. D
Torsions and d
curvatures 81 7.4 Geometrical gravitational theory produced by the rheonomic Berwald
Moór metric of order four 84 7.5 Some physical remarks and comments 87 7.6 Geometric dynamics of plasma in jet spaces with rheonomic Berwald
Moór metric of order four 89 8. The jet local single
time Finsler
Lagrange geometry induced by the rheonomic Chernov metric of order four 99 8.1 Preliminary notations and formulas 100 8.2 The rheonomic Chernov metric of order four 101 8.3 Cartan canonical linear connection. d
torsions and d
curvatures 103 8.4 Applications of the rheonomic Chernov metric of order four 105 9. Jet Finslerian geometry of the conformal Minkowski metric 109 9.1 Introduction 109 9.2 The canonical nonlinear connection of the model 111 9.3 Cartan canonical linear connection, d
torsions and d
curvatures 103 9.4 Geometrical field model produced by the jet conformal Minkowski metric 115 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 121 10.1 Historical aspects 121 10.2 Solutions of ODEs systems of order one as harmonic curves on 1
jet spaces. Canonical nonlinear connections 123 10.3 from first order ODEs systems and Riemannian metrics to geometrical objects on 1
jet spaces 127 10.4 Geometrical objects produced on 1
jet spaces by first order ODEs systems and pairs of Euclidian metrics. Jet Yang
Mills energy 129 11. Jet single
time Lagrange geometry applied to the Lorenz atmospheric ODEs system 141 11.1 Jet Riemann
Lagrange geometry produced by the Lorenz simplified model of Rossby gravity wave interaction 135 11.2 Yang
Mills energetic hypersurfaces of constant level produced by the Lorenz atmospheric ODEs system 138 12. Jet single
time Lagrange geometry applied to evolution ODEs systems from Economy 141 12.1 Jet Riemann
Lagrange geometry for Kaldor nonlinear cyclical model in business 141 12.2 Jet Riemann
Lagrange geometry for Tobin
Benhabib
Miyao economic evolution model 144 13. Some evolution equations from Theoretical Biology and their single
time Lagrange geometrization on 1
jet spaces 147 13.1 Jet Riemann
Lagrange geometry for a cancer cell population model in biology 148 13.2 The jet Riemann
Lagrange geometry of the infection by human immunodeficiency virus (HIV
1) evolution model 151 13.3 From calcium oscillations ODEs systems to jet Yang
Mills energies 154 14. Jet geometrical objects produced by linear ODEs systems and higher order ODEs 169 14.1 Jet Riemann
Lagrange geometry produced by a non
homogenous linear ODEs system or order one 169 14.2 Jet Riemann
Lagrange geometry produced by a higher order ODE 172 14.3 Riemann
Lagrange geometry produced by a non
homogenous linear ODE of higher order 175 15. Jet single
time geometrical extension of the KCC
invariants 179 References 185 Index 191