The multi-field generalisation of the Bateman equation arises from considerations of the continuation of String and Brane equations to the case where the base space is of higher dimension than the target space. The complex extension of this equation possesses a remarkably large invariance group, and admits a very simple implicit form for its general solution, in addition to the special case of ...

The spin degrees of freedom for the relativistic particle are described by either Lorentz group variables (classically) or Grassmann variables (pseudo-classically). The relationship between those two descriptions are given. In doing that, appropriate constraints are constructed to put into the lagrangian. Especially a natural relation of Lorentz group variables and Grassmann variables is obtain...

We present a general relativistic version of the self-gravitating fluid model for the dark sector of the Universe (darkon fluid) introduced in Stichel and Zakrzewski (Phys Rev D 80:083513, 2009) and extended and reviewed in Stichel and Zakrzewski (Entropy 15:559, 2013). This model contains no free parameters in its Lagrangian. The resulting energy-momentum tensor is dustlike with a nontrivial e...

We consider construction of some Lagrangians which contain the Riemann zeta function. The starting point in their construction is p-adic string theory. These Lagrangians describe some nonlocal and nonpolynomial scalar field models, where nonlocality is controlled by the operator valued Riemann zeta function. The main motivation for this research is intention to find an effective Lagrangian for ...

We examine the ADM reformulation of the 5-D KK model: the dimensional reduction is provided to commute with the ADM splitting and we show how the time component of the gauge vector is given by combination of the Lagrangian multipliers for the 5D gravitational field. We consider 5D particles motion and after dimensional reduction the definition of charge is recovered within electrodynamic coupli...

We study Manin triples for a reductive Lie algebra, g. First, we generalize results of E. Karolinsky, on the classification of Lagrangian subalgebras (cf. KAROLINSKY E., A Classification of Poisson homogeneous spaces of a compact Poisson Lie group, Dokl. Ak. Nauk, 359 (1998), 13-15). Then we show that, if g is non commutative, one can attach , to each Manin triple in g , another one for a stric...

We present a linearization strategy for mixed 0-1 quadratic programs that produces small formulations with tight relaxations. It combines constructs from a classical method of Glover and a more recent reformulation-linearization technique (RLT). By using binary identities to rewrite the objective, a variant of the first method results in a concise formulation with the level-1 RLT strength. This...

This paper studies the stability and bifurcations of the relative equilibria of the double spherical pendulum, which has the circle as its symmetry group. This example as well as others with nonabelian symmetry groups, such as the rigid body, illustrate some useful general theory about Lagrangian reduction. In particular, we establish a satisfactory global theory of Lagrangian reduction that is...

This paper addresses the issue of Lagrangian transport in the Stratospheric Polar Vortex (SPV). The first part of the paper analyzes SPV data from the ECMWF using the technique of Lagrangian Descriptors (LDs, developed over the years by some of the authors of this paper and their collaborators) for a specific time period in September 2002. A three-mode kinematic model which possesses the gross ...