We present several results on the inverse problem and equivalent contact Lagrangian systems. These problems naturally lead to consider smooth transformations on the z variable (i.e., reparametrizations of the action). We ...

It is well-known that the primal quadratic growth condition of the classical augmented Lagrangian around a local minimizer can be obtained under the second-order sufficient optimality condition. In this paper, we show that ...

It is well-known that the primal quadratic growth condition of the classical augmented Lagrangian around a local minimizer can be obtained under the second-order sufficient optimality condition. In this paper, we show that ...

We study the global centre symmetry set (GCS) of a smooth closed submanifold 'M POT.M'⊂'R POT.N', n≤2m . The GCS includes both the centre symmetry set defined by Janeczko (Geometria Dedicata 60:9–16, 1996) and the Wigner ...

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field ...

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field ...

In this work the inverse problem of the variational calculus for systems of differential equations of any order is analyzed. It is shown that, if a Lagrangian exists for a given regular system of differential equations, ...