Search

In this paper we study the local adapted components of the N-linear connections on the dual 1-jet space J^{1∗}(R,M), together with its local adapted torsion and curvature d-tensors.

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 electromagnetic Yang-Mills energies, starting from some given nonlinear evolution ODEs systems modelling biologic phenomena like the cancer cell population model or the infection by human immunodeficiency virus-type 1 (HIV-1) model., Comment: 14 pages

In this paper we present the distinguished (d-) Riemannian geometry (in the sense of nonlinear connection, Cartan canonical linear connection, together with its d-torsions and d-curvatures) for a possible Lagrangian inspired by optics in non-uniform media. The corresponding equations of motion are also exposed, and some particular solutions are given. For instance, we obtain as geodesic trajectories some circular helices (depending on an angular velocity \omega), certain circles situated in some planes (ones are parallel with xOy, and other ones are orthogonal on xOy), or some straight lines which are parallel with the axis Oz. All these geometrical geodesics are very specific because they are completely determined by the non-constant index of refraction n(x)., Comment: 19 pages

In this paper we construct some natural geometrical objects on the 1-jet space J^1(R,R^3), like a nonlinear connection, a Cartan linear connection (together with its d-torsions and d-curvatures), a jet "electromagnetic" d-field and its geometric "electromagnetic" Yang-Mills energy, starting from a given dynamical system governing the three-dimensional motion of the knee in the mathematical model introduced by Grood and Suntay. The corresponding Yang-Mills energetic surfaces of constant level (produced by this knee dynamical system) are studied., 15 pages

The paper develops the Finsler-like geometry on the 1-jet space for the jet conformal Minkowski (JCM) metric, which naturally extends the Minkowski metric in the Chernov-Pavlov framework. To this aim there are determined the nonlinear connection, distinguished (d-) Cartan linear connection, d-torsions and d-curvatures. The field geometrical gravitational and electromagnetic d-models based on the JCM metric are discussed.

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.

The aim of this paper is to study the local components of the relativistic time dependent d-linear connections, d-torsions, d-curvatures and deflection d-tensors with respect to an adapted basis on the 1-jet space $J^{1}(R,M)$. The Ricci identities, together with their corresponding identities of deflection d-tensors, are also given.

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., Comment: 19 pages; The author thanks the referee of Analele Stiintifice ale Universitatii "Al.I.Cuza" din Iasi. Matematica for its remarks and useful suggestions

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., 10 pages

Langmuir-Blodgett films (LB-films) consist from few LB-monolayers which are high structured nanomaterials that are very promising materials for applications. We use a geometrical approach to describe structurization into LB-monolayers. Consequently, we develop on the 1-jet space J 1 ([0,∞),R 2 ) the single-time Lagrange geometry (in the sense of distinguished (d-) connection, d-torsions and an abstract anisotropic electromagnetic-like d-field) for the Lagrangian governing the 2D-motion of a particle of monolayer. One assumed that an expansion near singular points for the constructed geometrical Lagrangian theory describe phase transitions to LB-monolayer. Trajectories of particles in a field of the electrocapillarity forces of monolayer have been calculated in a resonant approximation utilizing some Jacobi equations. A jet geometrical Yang-Mills energy is introduced and some computer graphic simulations are exposed.