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Some aspects of the homogeneous formalism in field theory and gauge invariance

Marcella Palese, Ekkehart Winterroth (2006)

Archivum Mathematicum

We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended configuration bundle. This new approach can be interpreted as a suitable generalization to Field Theory of the homogeneous formalism for Hamiltonian Mechanics. As an example of application, we obtain the expression of a formal energy for a parametrized version of the Hilbert–Einstein...

Some concepts of regularity for parametric multiple-integral problems in the calculus of variations

M. Crampin, D. J. Saunders (2009)

Czechoslovak Mathematical Journal

We show that asserting the regularity (in the sense of Rund) of a first-order parametric multiple-integral variational problem is equivalent to asserting that the differential of the projection of its Hilbert-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter ( m + 1 ) -form are holonomic.

Some results about dissipativity of Kolmogorov operators

Giuseppe Da Prato, Luciano Tubaro (2001)

Czechoslovak Mathematical Journal

Given a Hilbert space H with a Borel probability measure ν , we prove the m -dissipativity in L 1 ( H , ν ) of a Kolmogorov operator K that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.

Some results in Lagrangian mechanics

Emanuele Fiorani (2005)

Bollettino dell'Unione Matematica Italiana

We associate to a dynamic equation ξ three different connections and then we consider the meaning of the vanishing of their curvatures. Some peculiarities of the case of autonomous dynamic equation polynomial in the velocities q ˙ are pointed out. Finally, using the so-called Helmholtz conditions, we investigate a particular example.

Special motions of robot-manipulators

Adolf Karger (1994)

Applications of Mathematics

There exist many examples of closed kinematical chains which have a freedom of motion, but there are very few systematical results in this direction. This paper is devoted to the systematical treatment of 4-parametric closed kinematical chains and we show that the so called Bennet’s mechanism is essentially the only 4-parametric closed kinematical chain which has the freedom of motion. According to [3] this question is connected with the problem of existence of asymptotic geodesic lines on robot-manipulators...

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