05518nam 2200685Ia 450 991013958820332120170809165432.01-283-28286-097866132828661-118-14378-71-118-14375-21-118-14376-0(CKB)2550000000054432(EBL)693744(OCoLC)757511646(SSID)ssj0000538198(PQKBManifestationID)11335194(PQKBTitleCode)TC0000538198(PQKBWorkID)10557410(PQKB)10782690(MiAaPQ)EBC693744(EXLCZ)99255000000005443220110517d2011 uy 0engur|n|---|||||txtccrJet single-time Lagrange geometry and its applications[electronic resource] /Vladimir Balan, Mircea NeaguHoboken, N.J. John Wiley & Sonsc20111 online resource (212 p.)Description based upon print version of record.1-118-12755-2 Includes bibliographical references and index.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 Γ-linear connections; 2.2 Local torsion and curvature d-tensors2.3 Local Ricci identities and nonmetrical deflection d-tensors3 Local Bianchi identities in the relativistic time-dependent Lagrange geometry; 3.1 The adapted components of h-normal Γ-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 electromagnetism4.4.1 The jet single-time electromagnetic field4.4.2 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 εDL1n; 5.2 Geometrical Maxwell equations on εDL1n; 5.3 Geometrical Einstein equations on εDL1n; 6 Jet local single-time Finsler-Lagrange geometry for the rheonomic Berwald-Moór metric of order three6.1 Preliminary notations and formulas6.2 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-curvatures7.4 Geometrical gravitational theory produced by the rheonomic Berwald-Moór metric of order four7.5 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 four8 The jet local single-time Finsler-Lagrange geometry induced by the rheonomic Chernov metric of order fourDevelops the theory of jet single-time Lagrange geometry and presents modern-day applications Jet Single-Time Lagrange Geometry and Its Applications guides readers through the advantages of jet single-time Lagrange geometry for geometrical modeling. With comprehensive chapters that outline topics ranging in complexity from basic to advanced, the book explores current and emerging applications across a broad range of fields, including mathematics, theoretical and atmospheric physics, economics, and theoretical biology. The authors begin by presenting basic theoretical Geometry, DifferentialLagrange equationsField theory (Physics)Electronic books.Geometry, Differential.Lagrange equations.Field theory (Physics)530.14/3530.143MAT012000bisacshBalan Vladimir1958-947039Neagu Mircea1973-947040MiAaPQMiAaPQMiAaPQBOOK9910139588203321Jet single-time Lagrange geometry and its applications2139708UNINA