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Search Results: 1 - 10 of 711 matches for " Mircea Neagu "
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The geometry of autonomous metrical multi-time Lagrange space of electrodynamics
Mircea Neagu
International Journal of Mathematics and Mathematical Sciences , 2002, DOI: 10.1155/s0161171202011018
Abstract: The aim of this paper is to create a large geometrical background for the study of important branch of physics: electrodynamics, bosonic strings theory, magneto-hydrodynamics, and so forth. The geometrical construction is realized on the 1-jet fibre bundle J1(T,M) and is produced by a given quadratic multi-time Lagrangian function L. The Riemann-Lagrange geometry of the space EDMLpn=(J1(T,M),L), in the sense of d-connections, torsion and curvature d-tensors, allows the construction of a natural generalized multi-time field theory on EDMLPn, in the sense of generalized Maxwell and Einstein equations.
Ricci and Bianchi identities for -normal -linear connections on
Mircea Neagu
International Journal of Mathematics and Mathematical Sciences , 2003, DOI: 10.1155/s0161171203012419
Abstract: The aim of this paper is to describe the local Ricci and Bianchi identities of an h-normal Γ-linear connection on the first-order jet fibre bundle J1(T,M). We present the physical and geometrical motives that determined our study and introduce the h-normal Γ-linear connections on J1(T,M), emphasizing their particular local features. We describe the expressions of the local components of torsion and curvature d-tensors produced by an h-normal Γ-linear connection ∇Γ, and analyze the local Ricci identities induced by ∇Γ, together with their derived local deflection d-tensors identities. Finally, we expose the local expressions of Bianchi identities which geometrically connect the local torsion and curvature d-tensors of connection ∇Γ.
Jet Geometrical Objects Produced by Linear ODEs Systems and Superior Order ODEs
Mircea Neagu
Mathematics , 2007,
Abstract: The aim of this paper is to construct a Riemann-Lagrange geometry on 1-jet spaces, in the sense of d-connections, d-torsions, d-curvatures, electromagnetic d-field and geometric electromagnetic Yang-Mills energy, starting from a given linear ODEs system or a given superior order ODE. The case of a non-homogenous linear ODE of superior order is disscused.
Geometrical Objects on the First Order Jet Space $J^1(T,R^5)$ Produced by the Lorenz Atmospheric DEs System
Mircea Neagu
Mathematics , 2007,
Abstract: The aim of this paper is to construct natural geometrical objects on the 1-jet space J^1(T,R^5), where $T/subset R$, like a non-linear connection, a generalized Cartan connection, together with its d-torsions and d-curvatures, a jet electromagnetic d-field and a jet Yang-Mills energy, starting from the given Lorenz atmospheric DEs system and the pair of Euclidian metrics $/Delta = (1,/delta_{ij})$ on $T/times R^5$.
Jet Riemann-Lagrange Geometry Applied to Evolution DEs Systems from Economy
Mircea Neagu
Mathematics , 2007,
Abstract: The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems modelling economic phenomena, like the Kaldor model of the bussines cycle or the Tobin-Benhabib-Miyao model regarding the role of money on economic growth.
Jet Geometrical Objects Depending on a Relativistic Time
Mircea Neagu
Mathematics , 2008, DOI: 10.2478/v10157-010-0029-1
Abstract: In this paper we study a collection of jet geometrical concepts, we refer to d-tensors, relativistic time dependent semisprays, harmonic curves and nonlinear connections on the 1-jet space J1(R;M), necessary to the construction of a Miron's-like geometrization for Lagrangians depending on a relativistic time. The geometrical relations between these jet geometrical objects are exposed.
Local Bianchi Identities in the Relativistic Non-Autonomous Lagrange Geometry
Mircea Neagu
Mathematics , 2009,
Abstract: The aim of this paper is to describe the local Bianchi identities for an $h$-normal $\Gamma$-linear connection of Cartan type $\nabla\Gamma$ on the first-order jet space $J^1(R,M)$. In this direction, we present the local expressions of the adapted components of the torsion and curvature d-tensors produced by $\nabla\Gamma$ and we give the general local expressions of Bianchi identities which connect these d-torsions and d-curvatures.
Jet Berwald-Riemann-Lagrange Geometrization for Affine Maps between Finsler Manifolds
Mircea Neagu
Mathematics , 2008,
Abstract: In this paper we introduce a natural definition for the affine maps between two Finsler manifolds $(M, F)$ and $(N,\tilde F)$ and we give some geometrical properties of these affine maps. Starting from the equations of the affine maps, we construct a natural Berwald-Riemann-Lagrange geometry on the 1-jet space $J^1(TM;N)$, in the sense of a Berwald nonlinear connection $\Gamma^b_jet$, a Berwald $\Gamma^b_jet$-linear d-connection $B\Gamma^b_jet$, together with its d-torsions and d-curvatures, which geometrically characterizes the initial affine maps between Finsler manifolds.
The Geometry of Relativistic Rheonomic Lagrange Spaces
Mircea Neagu
Mathematics , 2000,
Abstract: The paper contains a geometrization of a time dependent Lagrangian function defined on the 1-jet space J^1(R,M) which identifies with R\times TM. The reader is invited to compare this geometrization with that developped by Miron and Anastasiei.
The Geometry of Autonomous Metrical Multi-Time Lagrange Space of Electrodynamics
Mircea Neagu
Mathematics , 2000,
Abstract: The paper contains a geometrization of the autonomous multi-time Lagrangian function of electrodynamics. We point out that this multi-time Lagrangian function comes from electrodynamics and the theory of bosonic strings.
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